Published May 13, 2016

Review and Analysis

Core Ideas• A community effort is needed tomove soil modeling forward.
• Establishing an international soilmodeling consortium is key inthis respect.
• There is a need to better integrate
existing knowledge in soil models.
• Integration of data and models is a
key challenge in soil modeling.

*Corresponging author (h.vereecken@
fz-juelich.de). See end of paper for
author affiliations.
Vadose Zone J.
doi:10.2136/vzj2015.09.0131
Received 28 Sept. 2015.
Accepted 29 Mar. 2016.
Open accessVol. 15, Iss. 5, 2016

© Soil Science Society of America.
This is an open access article distributed
under the CC BY-NC-ND license(http://creativecommons.org/licenses/
by-nc-nd/4.0/).

Modeling Soil Processes:
Review, Key Challenges,
and New Perspectives

H. Vereecken,* A. Schnepf, J.W. Hopmans, M. Javaux,
D. Or, T. Roose, J. Vanderborght, M.H. Young, W. Amelung,
M. Aitkenhead, S.D. Allison, S. Assouline, P. Baveye, M. Berli,
N. Brüggemann, P. Finke, M. Flury, T. Gaiser, G. Govers,
T. Ghezzehei, P. Hallett, H.J. Hendricks Franssen, J. Heppell,
R. Horn, J.A. Huisman, D. Jacques, F. Jonard, S. Kollet, F. Lafolie,
K. Lamorski, D. Leitner, A. McBratney, B. Minasny, C. Montzka,
W. Nowak, Y. Pachepsky, J. Padarian, N. Romano, K. Roth,
Y. Rothfuss, E.C. Rowe, A. Schwen, J. Šimůnek, A. Tiktak,
J. Van Dam, S.E.A.T.M. van der Zee, H.J. Vogel, J.A. Vrugt,
T. Wöhling, and I.M. Young
The remarkable complexity of soil and its importance to a wide range of
ecosystem services presents major challenges to the modeling of soil processes. Although major progress in soil models has occurred in the last
decades, models of soil processes remain disjointed between disciplines or
ecosystem services, with considerable uncertainty remaining in the quality of predictions and several challenges that remain yet to be addressed.
First, there is a need to improve exchange of knowledge and experienceamong the different disciplines in soil science and to reach out to other
Earth science communities. Second, the community needs to develop a
new generation of soil models based on a systemic approach comprising
relevant physical, chemical, and biological processes to address criticalknowledge gaps in our understanding of soil processes and their interactions. Overcoming these challenges will facilitate exchanges between
soil modeling and climate, plant, and social science modeling communities. It will allow us to contribute to preserve and improve our assessmentof ecosystem services and advance our understanding of climate-change
feedback mechanisms, among others, thereby facilitating and strengthening communication among scientific disciplines and society. We review therole of modeling soil processes in quantifying key soil processes that shapeecosystem services, with a focus on provisioning and regulating services.
We then identify key challenges in modeling soil processes, including thesystematic incorporation of heterogeneity and uncertainty, the integrationof data and models, and strategies for effective integration of knowledge
on physical, chemical, and biological soil processes. We discuss how the soilmodeling community could best interface with modern modeling activities
in other disciplines, such as climate, ecology, and plant research, and how
to weave novel observation and measurement techniques into soil models.
We propose the establishment of an international soil modeling consortium
to coherently advance soil modeling activities and foster communication
with other Earth science disciplines. Such a consortium should promote soilmodeling platforms and data repository for model development, calibration and intercomparison essential for addressing contemporary challenges.
Abbreviations: AIC, Akaike information criterion; BE, Bayesian model evidence; BIC, Bayesian
information criterion; BMA, Bayesian model averaging; CLM, Community Land Model; DEM,
digital elevation model; EnKF, Ensemble Kalman Filter; ET, evapotranspiration; GHG, greenhousegases; GIS, geographic information system; GPS, global positioning system; IC, information criteria; ISMC, International Soil Modeling Consortium; KIC, Kashyap information criterion; LIDAR, Light
Detection and Ranging; MCMC, Markov chain Monte Carlo; MRI, magnetic resonance imaging; MW, microwave spectrum; MWIR, mid-wave infrared spectrum; NIR, near-infrared spectrum;
OTU, operational taxonomic units; pdf, probability density function; PSS, proximal soil sensing; PTF,
pedotransfer function; SAR, Synthetic Aperture Radar; SDA, sequential data assimilation; SVAT,
soil–vegetation–atmosphere transfer; SWIR, short-wave infrared spectrum; TE, treated effluents;
TIR, thermal infrared spectrum; UAV, unmanned air vehicles; mCT, microcomputed tomography;
VIS, visible spectrum; VSP, virtual soil platform.

Vadose Zone Journal | Advancing Critical Zone Science66A Brief History ofSoil Modeling

The quantitative description of physical, chemical, and biological interactions in soil at multiple scales and levels of refinement
has been a long-standing goal and key challenge in soil science.
The earliest numerical and analytical models in the field of soil
science date back to the last century and dealt mainly with thesimulation of water flow (e.g., Hanks and Bowers, 1962; Rubin
and Steinhardt, 1963; Whisler and Kulte, 1965; Bresler and Hanks,
1969; Van Keulen and Van Beek, 1971), heat flow (Wierenga and
De Wit, 1970), solute transport processes (Dutt and Tanji, 1962;
Lindstrom et al., 1967; Bear, 1972; Bresler, 1973; Gerke and van
Genuchten, 1993), soil organic carbon dynamics (Russell, 1964,
1975; Van Veen and Paul, 1981), and nutrient dynamics (Kirkham
and Bartholomew, 1955; Cole et al., 1978). These models consisted
mostly of analytical solutions of partial differential equations forwell-defined soils and porous media, numerical solutions of single
partial differential equations, or conceptual models that weresolved with analog or digital computers.
These first generation models that proliferated with the availabilityof the digital computer focused primarily on physical and chemical
processes without explicit consideration of biotic processesor accounting for the role of soil structural related processes.
One of the first models addressing the role of soil structurein the decomposition of organic matter by microorganisms
was developed by Van Veen and Paul (1981) and Van Veen etal. (1985) and reviewed in Van Veen and Kuikman (1990). An
early model that considered the role of soil structure on solutetransport and leaching was developed by Addiscott (1977). The
role of soil structure on soil physical processes, including waterflow and solute transport, was conceptualized and framed in amathematically consistent approach in the early 1990s by Gerkeand van Genuchten (1993). A first suite of soil ecosystem dynamics
models including detrital food webs was published in the early
1970s by Patten (1972) and McBrayer et al. (1977), and in the
1980s by Rosswall and Paustian (1984) and later de Ruiter et al.
(1993). These studies addressed the role of soil microbes and soil
fauna within the framework of food webs and nutrient dynamics.
Recently, soil ecosystem models have been developed that allow
modeling of soil biodiversity and its loss, as well as the role ofmicrobes and soil fauna in soil nutrient transfer processes (Huntand Wall, 2002).
Due to availability of novel measurement and analytical techniquessuch as X-ray tomography, soil neutron tomography, magnetic
resonance imaging, as well as molecular techniques that enable
quantification of molecular-driven soil biological processes andsoil microbial composition, data have now become available thatallow the development and validation of soil models that are able
to quantify physical, chemical, and biological processes at the levelof the pore scale and smaller. Combined with an increased understanding of the complex interactions of soil processes, the advent

VZJ | Advancing Critical Zone Science

of computers and progress in the development of analytical andimproved numerical algorithms, especially at the end of the 1980s,
have empowered the development of complex soil models integrating
physical, chemical, and biological processes from the pore scale to theglobal scale (Parton et al., 1998). Notwithstanding the considerable
progress from early modeling efforts, fundamental soil processes andtheir interactions remain lacking and deficient, such that it hampers
the prediction and quantification of key soil functions and services.
Moreover, the integration and quantification of available knowledge
on soil processes remain sketchy due to lack of coherence and limited communication among research communities and disciplines.
In this paper we review the state-of-the-art soil modeling as well as
Table 1. Contents.
A Brief History of Soil Modeling����������������������������������������������������������������������������������������������������2
The State-of-the-Art of Modeling Soil Processes ���������������������������������������������������������������������3
The Role of Soil Modeling in Quantifying Ecosystem Services ������������������������������������������3
Modeling Soil Supporting and Degrading Processes���������������������������������������������������������������5
Supporting Processes�������������������������������������������������������������������������������������������������������������������������5
Soil Formation���������������������������������������������������������������������������������������������������������������������������������5
Water Cycling���������������������������������������������������������������������������������������������������������������������������������5
Nutrient Cycling����������������������������������������������������������������������������������������������������������������������������7
Biological Activity�������������������������������������������������������������������������������������������������������������������������9
Soil Degrading Processes����������������������������������������������������������������������������������������������������������������10
Salinization and Alkalinization����������������������������������������������������������������������������������������������10
Erosion ��������������������������������������������������������������������������������������������������������������������������������������������11
Compaction���������������������������������������������������������������������������������������������������������������������������������� 12
Soil Modeling and Ecosystem Services ������������������������������������������������������������������������������������� 13
Regulating Services������������������������������������������������������������������������������������������������������������������������� 13
Climate Regulation��������������������������������������������������������������������������������������������������������������������� 13
Buffering and Filtering ��������������������������������������������������������������������������������������������������������������14
Recycling of Anthropogenic Waste����������������������������������������������������������������������������������������15
Provisioning Services�����������������������������������������������������������������������������������������������������������������������16
Biomass Production for Food, Fiber, and Energy ��������������������������������������������������������������16
Soil Physical Support�������������������������������������������������������������������������������������������������������������������17
Soil and Biologial Habitat����������������������������������������������������������������������������������������������������������18
Challenges in Dealing with Soil Heterogeneity and Uncertainty�������������������������������������19
Heterogeneity: Aggregate to Landscape, Microbe to Forest, Grains to Ecology����������19
Model Concepts��������������������������������������������������������������������������������������������������������������������������� 20
Exploring Heterogeneity ��������������������������������������������������������������������������������������������������������� 20
Formalisms for Considering Uncertainties Related To Model Choice����������������������������21
Does Local-Scale Model Complexity Matter for Predictions at Larger Scales?������������ 22
Numerical Approaches and Model Data Integration������������������������������������������������������������ 23
Numerical Approaches ������������������������������������������������������������������������������������������������������������������ 23
Novel Optimization Methods and Their Application to Soil Modeling������������������������ 24
Data Assimilation�����������������������������������������������������������������������������������������������������������������������������25
Bayesian Approach for Model–Data Integration ������������������������������������������������������������������ 26
Modern Sources of Spatial and Temporal Data for Soil Modeling ���������������������������������� 28
Informing Soil Models Using Remote Sensing ���������������������������������������������������������������������� 28
Model Forcings���������������������������������������������������������������������������������������������������������������������������� 28
Model Parameters������������������������������������������������������������������������������������������������������������������������ 28
State Variables������������������������������������������������������������������������������������������������������������������������������ 29
Fluxes���������������������������������������������������������������������������������������������������������������������������������������������� 29
Vegetation Canopy Properties Providing Information About Soil Status ��������������� 29
Proximal Soil Sensing, Geographical Databases of Soil Properties for Soil Process
Modeling ��������������������������������������������������������������������������������������������������������������������������������������� 29
Proximal Soil Sensing���������������������������������������������������������������������������������������������������������������� 29
Soil Databases�������������������������������������������������������������������������������������������������������������������������������31
Informing Soil Models Using Pedotransfer Functions����������������������������������������������������������31
Parameterizing Models with Nondestructive and High Resolution Water Stable
Isotope Data ����������������������������������������������������������������������������������������������������������������������������������33
Toward a Soil Modeling Platform ���������������������������������������������������������������������������������������������� 34
Virtual Soil Platform���������������������������������������������������������������������������������������������������������������������� 34
Model Coupling Approaches��������������������������������������������������������������������������������������������������������35
Benchmarks and Soil Model Intercomparisons ����������������������������������������������������������������������35
Linking Soil Modeling Platforms with Climate, Ecology, and Hydrology������������������� 36
Linking Soil Modeling Platforms with Crop and Biomass Production ������������������������� 37
Summary and Outlook ������������������������������������������������������������������������������������������������������������������ 39

p. 2 of 57

future challenges and perspectives. Table 1 shows the content andorganization of the paper refering to the specific sections.

soil and crop processes, generating new knowledge and opening
new perspectives for their mathematical description.

The State-of-the-Art of Modeling
Soil Processes

The Role of Soil Modeling in Quantifying
Ecosystem Services

Advanced soil models today use the Richards equation and theconvection–dispersion equation to describe water and solute
movement through soils, and often are able to account for preferential flow and transport (Šimůnek et al., 2003). Many of thesemodels include the simulation of heat flow and energy balance
approaches, providing information on soil temperature dynamics
and water vapor flow. Soil chemistry ranges from simple equilibrium or nonequilibrium sorption models to complex multi-species
models, such as that by Jacques et al. (2008). For contaminatedsoils, the typical single phase flow models have been extended toinclude multiphase flow phenomena to take into account complex
interactions between solid, liquid, gas, and contaminant phases.
Soil carbon dynamics are typically conceptualized by multi-compartment approaches, where each compartment is composed oforganic matter with similar chemical composition or degradability(Coleman et al., 1997; Bricklemyer et al., 2007). Nitrogen turnover is strongly related to carbon turnover, and both are often partof an overall model of C, N, and nutrient cycling in terrestrial
ecosystems (Priesack et al., 2008; Manzoni and Porporato, 2009;
Batlle-Aguilar et al., 2011). Compared to the above process descriptions, several process descriptions presented below are still in theirinfancy. At present, many soil models consider the soil to be a rigid
medium. Yet, we know that management practices and natural
events such as droughts and floods may drastically change soil’s
architecture and structure. The description of root water uptake ismostly based on simple approaches such as the model of Feddes etal. (1976). Only recently more complex approaches that explicitly
describe the three-dimensional soil root system have become available (Hopmans and Bristow, 2002; Schroder et al., 2008; Javaux
et al., 2013) and are not yet widespread. Improved descriptionsof root solute uptake include root hairs, root exudation, and rhizodeposition, which increases microbial activity (Kuzyakov andDomanski, 2000), or the role of arbuscular mycorrhizal fungi(Schnepf et al., 2008b; Leitner et al., 2010; Schnepf et al., 2012).
However, these improved descriptions are not yet sufficiently
incorporated into soil–crop models (Hinsinger et al., 2011). Thereis an overall lack of spatially explicit models that properly describe
soil C and nutrient dynamics at different spatial scales (Manzoni
and Porporato, 2009). Approaches to simulating temporal changesof soil structure, a major determinant of water movement, biological activity and root growth, and soil erosion, are relatively rare
and at an early stage of development (Leij et al., 2002; Stamati etal., 2013). There are few models of interactions between physicaland biological processes (Tartakovsky et al., 2009; Laudone et al.,2011). However, the impact of soil biodiversity on soil productivity, crop growth, and yield has hardly been included in current soil
simulation models. Recent advances in measurement technologies
have provided new insights about the role of soil biodiversity on

VZJ | Advancing Critical Zone ScienceWe capitalize on the framework of ecosystems services to analyze
challenges and offer perspectives on soil modeling. Soil plays aprominent role in regulating and provisioning ecosystem services,
as well as degrading and supporting processes, all linked to societal
and population issues and central to scientific underpinning of
how the planet functions (Adhikari and Hartemink, 2016). We
rely on the conceptual framework of Dominati et al. (2010) toframe soil modeling activities related to the description and prediction of soil processes and properties (Fig. 1). The Dominati
framework offers a holistic view of how soil processes and related
ecosystem services are impacted by external drivers (both naturaland anthropogenic) and affecting processes and soil natural capital. The various components and subcomponents, including basic
processes, natural capital of soils, and ecosystem services, can beharnessed to meet human needs. But, these can also be impacted bychanges in land use, agricultural practices, technological developments, climate change, and natural hazards. The natural capital ofsoils is defined as the stocks of mass and energy in the soil and theirorganization (entropy) (Robinson et al., 2009, 2014). It is related to
the notion of soil properties, some of which are considered inherent and others which can be modified through management. The
paper addresses a range of soil modeling activities that attempt

Fig. 1. Link between soil processes, soil natural capital and ecosystemservices from a soil modeling perspective (adapted after Dominati etal., 2010). The gray arrows indicate the controls exerted by the soil
processes on the supporting and degrading processes. The red arrows
show the control of supporting and degrading processes on inherent
soil processes, which in turn affect key soil processes. The green
arrow indicates the impact of the soil natural capital on regulating
and provisioning ecosystem services. The dots indicate that this list
is not exhaustive.

p. 3 of 57

to quantify and predict the soil supporting and degradation processes, as well as regulating and provisioning services. Supporting
processes refer to basic soil processes that enable soils to functionand ensure the formation and maintenance of natural capital.
These processes include soil formation and soil structure, nutrient
cycling and primary production, and soil biological activity, which
is closely related to biodiversity and the gene pool. Soil degrading
processes diminish the natural capital of soils and include erosion,
surface sealing, compaction, salinization, loss of nutrients, acidification, and loss of organic matter and biodiversity.
Regulating services provide means to humans to live in a stable,
healthy and resilient environment (Dominati et al., 2010). They
include climate regulation, water regulation, erosion control, buffering, and filtering. Climate regulation is defined as the capacityof the soil to control states and fluxes energy, water and matterthat impact climate. Water regulation comprises services of the soil
related to storage and retention of quantities of water. It impacts
soil hydrological processes, such as runoff, leaching, and groundwater recharge, and water management practices, such as irrigationand drainage. Soils have the capacity to store and release chemicals,
thereby controlling soil, water, crop, and air quality. Provisioning
services are related to products derived from ecosystems (e.g., food,
wood, fiber, fresh water, physical support, and genetic resources),in all of which soils play a key role. Underlying these processes
are basic biological, physical, and geochemical processes. Most soilmodeling research thus far has been focused on addressing thesebasic processes independently or coupled with a limited set of basic
processes. The goal of this review is to present the key roles of stateof-the-art soil modeling approaches. The key questions addressed
here are how soil modeling activities can better serve quantification of soil processes and related ecosystem services, and what areas
and key challenges need to be addressed to improve the applicability and usefulness of current soil models. We substantially expand
on the review paper by Jury et al. (2011), which mainly focusedon the status and challenges in soil physics research dealing withsoil physical methods and approaches to characterize soil water
properties, scaling and effective hydraulic properties, unstableflow and water repellency, effects of plants on transport processes,
characterizing soil microbial diversity, and the role of soil ecology
in providing ecosystem services.

at quantifying the supply side of ecosystem services, and several
models have been developed in this respect, such at the polyscale
scape model (Jackson et al., 2013), Invest (Nelson et al., 2009),
ARIES (Villa et al., 2014), and SolVES (Sherrouse et al., 2011).
However, testing and validating the accuracy and precision ofthese models and approaches are still open issues that need tobe addressed (Schägner et al., 2013). Ensemble calculations of
ecosystem services using different model approaches including
more complex mechanistic models to quantify specific ecosystem
functions may be valuable in quantifying uncertainty following
approaches similar to the ensemble calculations used in IPCC.
The proposed modeling and intercomparison platform presented
later in this paper may provide an excellent opportunity to perform these kinds of analyses. Using more complex models basedon a mechanistic representation of soil processes may serve as
benchmarks for selecting the simpler models in these ecosystemservice models. In addition, highly complex modeling approaches
have the potential to be simplified to be more easily embedded
in such models. One of the main reasons for using simplified
models vs. more complex models for the assessment and quantification of soil processes is the issue of data availability. Soil science
research has developed several approaches to address this data
scarcity issue, such as proximal soil sensing, pedotransfer functions, and remote sensing of the soil surface. These approaches
have not yet been applied in ecosystem services quantification.
Also, issues of spatial variability of key ecosystem properties, a
topic that has been at the core of soil science research, has been
identified in ecosystem services research as a topic warranting
more attention to better assess uncertainty (Schägner et al.,2013). In recent years, the spatial mapping of ecosystem services
has gained increasing importance, while in combination withgeographic information system (GIS) methods larger areas canbe quantified, and spatial patterns of ecosystem services can bebetter identified (e.g., Calzolari et al., 2016). In the mapping of
ecosystem services, such a GIS framework typically constitutes
the core engine of ecosystem service quantification, allowing thequantification not only of vertically driven and local scale processes but also laterally controlled processes, such as overland
flow, routing and erosion, and sediment transport (e.g., polyscapemodel). Also, there is a need to assess the quality and accuracyof the predictions and to validate them against real world data.

In the field of ecosystem services research, mechanistic descriptions of soil functions used to quantify ecosystem services are
rarely used. Typical approaches for quantification of ecosystemservices comprise the use of one-dimensional proxies based onland use or land cover, nonvalidated models based on likely
combinations of explanatory variables derived from expert
knowledge, validated equations that are calibrated on primaryand secondary data, representative data collected within the areaused to quantify ecosystem services, and implicit modeling of
the ecosystem service quantity within a monetary value transfer function (Schägner et al., 2013). All these approaches aim

The demand for ecosystem services is mainly determined bysocioeconomic characteristics and drivers, and its quantification
or valuation has mainly been addressed by economists. There areseveral approaches used in ecosystem services research to do thisvaluation, but this is outside the scope of this paper. We refer thereader to the work of Bateman et al. (2013), Schägner et al. (2013),
and Obst (2015), among others. Here we address soil mechanistic
models and their application to quantify ecosystem services. Figure
1 illustrates the link between soil processes, soil natural capital, andecosystem services from a soil modeling perspective (adapted from
Dominati et al., 2010).

VZJ | Advancing Critical Zone Sciencep. 4 of 57

Table 2 shows in an exemplary manner a number of published studies in which mechanistic soil models have been used to quantify
ecosystem services. A community-supported list of soil models canbe found in Aitkenhead (2016) and at https://soil-modeling.org/
models (accessed 26 Apr. 2016).
Both Fig. 1 and Table 2 are organized along the ecosystem services
provided by soil, and the entries in Table 2 refer to the ecosystemservices presented in the following two major sections, “Modeling
Soil Supporting and Degrading Processes” and “Soil Modeling andEcosystem Services.” Both sections are organized along these entries.

66Modeling Soil Supporting and

Degrading Processes

In this section, we will address the state of modeling soil processes
with respect to quantifying soil supporting and degrading
processes. They directly influence soil structure, architecture,and basic soil properties, thereby affecting the regulating andprovisioning services. As shown in Fig. 1, supporting processes
include the formation of soil, cycling of water and nutrients, andbiological activity. Degrading processes include salinization,
erosion, and compaction. At the end of the section we present
five key challenges to modeling soil supporting and degrading
processes (Table 3).

Supporting Processes
Soil Formation
Soil formation refers to the combination of physical, chemical,
biological, and anthropogenic processes acting on a soil parent
material over periods from years to millennia. Human activities,
often related to agricultural practices, strongly contribute toshort-term soil formation by causing aggregation, compaction,leaching, clay migration, salinization, and changes in the carbon
stock. Many specific modeling studies focus on leaching (Dannet al., 2006; Jabro et al., 2006), soil carbon change (Smith et al.,1997), soil acidification (Kros et al., 1999), compaction (Nawaz
et al., 2013), or other processes. However, few models treat soil
formation as a coevolution of a large number of soil parameters(Finke and Hutson, 2008) in an integrated approach, thus limiting
pedogenetic modeling progress (Opolot and Finke, 2015).
Soil formation is often associated with volumetric changes fromstrain (Brimhall and Dietrich, 1987) because of elastic andinelastic responses to pressure, decalcification, clay transport, andperturbations of different types, including tillage and bioturbation.
However, most models assume a constant soil volume, neglectingchanges in macroporosity and the dynamic impact of changing
water quality on soil hydraulic properties. Thus, most soil models
ignore soil structure dynamics and its relevance to the physicalisolation of soil components like soil organic carbon by aggregation

VZJ | Advancing Critical Zone Science(Six et al., 2002; Six and Paustian, 2014). This may seem insignificant for short-term studies, but changes in soil structure are key
processes at the time scales of decades and centuries associatedwith long-term soil formation. For example, short time scale processes of colloid transport are key in pedogenetic clay migration(illuviation) in soil profile development.
Volume strain also induces soil heterogeneity, as both aggregationand compaction affect macroporosity and may cause high spatial
variability in surface and subsurface flow and transport processes,
and in turn affect local rates of soil erosion and soil formation.
For example, preferential flow may cause persistent leaching
pathways at short (leaching hot spots; Koestel et al., 2013), andlong time scales (persistent leaching through ripening cracks andalbeluvic tongues; Sauer et al., 2009). Research questions remain
on development of soil heterogeneity with time, and the possible
self-enforcing or self-limiting mechanisms, as well as the relevant
spatial scales with appropriate upscaling and downscaling techniques (Bierkens and de Willigen, 2000). At pedogenetic timescales, boundary input values are uncertain, meaning that climate,vegetation, and historic human activities are highly uncertain as
well, and influence the degree to which soil models can be calibrated. The effect of such uncertainties must be determined toallow for accurate scenario-like quantification of ecosystem services under global change.

Water Cycling
Water cycling in soils involves the infiltration of precipitation insoils and the subsequent release of this water to the atmosphere,
and groundwater and surface water systems by evapotranspiration(ET) and leaching, respectively. To characterize and predict
ecosystem services provided by soils, we must quantify theamount of rainfall, interception, soil infiltration, soil moistureredistribution and root water uptake. Among these processes,
rainfall is highly variable in space and time, difficult to measureand extremely difficult to predict (Villarini, 2009). In addition,
climate change will lead to an increase in its spatial-temporalvariability and intensity (e.g., strong convective rainfall events)
challenging the quantification of infiltration and overland flow
processes. For soil moisture redistribution, common soil water flow
models employ the Richards equation, which combines the Darcy
equation with the continuity equation; including a sink term forsoil water extraction by roots (see Eq. [1]).

¶q= Ñ×(KÑH )- S¶t[1]

where q is the volumetric water content (L3 L−3), t is the time (T),K is the unsaturated soil hydraulic conductivity tensor (L T−1), H
is the hydraulic head (L), and S is the sink term accounting for root
water uptake (L3 L−3 T−1). A description of these basic processes
and methods to solve this equation were provided by Aksoy andKavvas (2005), Feddes et al. (1988). Some of the frequently used
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Table 2. Examples of studies in which soil models have been used to quantify ecosystem services.
Ecosystem services and soil processes

Numerical package to model
this ecosystem service or soil process

References

SoilGen2

Finke (2012), Finke and Hutson (2008)

Soil-Landscape Model

McBratney et al. (2006)

Orthod Model

Hoosbeek and Bryant (1994)

mARM3D

Cohen et al. (2010)

MILESD

Vanwalleghem et al. (2013)

HYDRUS 1D

Karimov et al. (2014)

WaSim-ETH

Krause and Bronstert (2007)

Community Land Model (CLM)

Wu et al. (2014b)

SiSPAT-Isotope

Braud et al. (2005)

SWAP

van Dam et al. (2006)

HP1

Thaysen et al. (2014)

RothC

Dungait et al. (2012)

Century

Parton et al. (1993)

SWAP
DEMENT

Perego et al. (2012),
Bonfante et al. (2010)
Allison (2012, 2014)

Soil food web model

Holtkamp et al. (2011)

HYDRUS-2D

Ramos et al. (2012)

UNSATCHEM

Schoups et al. (2006)

SALTMED

Ragab (2002)

SODIC

van der Zee et al. (2014)

SWAP

Jiang et al. (2011)

KINEROSNedkov and Burkhard (2012)

WEPP

Savabi et al. (1995)

SIDASS

Simota et al. (2005)

STICS/COMPSOIL

Défossez et al. (2014)

SOCOMO

Van den Akker (2004)

SOILFLEX

Keller et al. (2007)

CLM4.5

Oleson et al. (2013)

SWAP

Pollacco and Mohanty (2012)

HP1

Leterme et al. (2014)

SWAP

Bonten et al. (2012)

DSCB Dynamic Soil Composition Balance

Moolenaar et al. (1997), Moolenaar and Beltrami (1998)

MACRO

Steffens et al. (2015)

PEARL

Tiktak et al. (2004)

APSIM

Robertson et al. (2002), Luo et al. (2005), Yang et al. (2014)

DSSAT
DAISY

Pequeno et al. (2014), Shi et al. (1997), Li et al. (2015),
Wajid et al. (2014)
Ghaley and Porter (2014)

ORCHIDEE-STICS

de Noblet-Ducoudré et al. (2004)

CLM

Oleson et al. (2013)

SWAP

Kroes and Supit (2011)

Volumetric Soil Model

Sheng et al. (2008)

Slope Stability Model

Arrouays et al. (2014)

BBA

Alonso et al. (1990)

RipRoot

Pollen-Bankhead and Simon (2009)

Self_org

Crawford et al. (2011)

Supporting processes
Soil formation

Water cycling

Nutrient cycling

Biological activity
Degrading processes
Salinization

ErosionCompaction

Regulating services
Climate regulation
Buffering and filtering
Recycling of wastes

Provisioning services
Biomass production for food, fiber and energy

Physical support

Soil and habitat

VZJ | Advancing Critical Zone Science

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Table 3. Key challenges to modeling soil supporting and degrading processes.
Key challenges s
Challenge 1

To quantify and predict the development of soil heterogeneity across a broad range of space and time scales. This includes soil structural dynamics
and preferential flow paths.

Challenge 2

To better integrate key biophysical processes including spatial consideration of organismal traits with ecological interactions at appropriate spatial
and temporal scales.

Challenge 3

To better link nutrient dynamics and availability in soils with hydrological and biogeochemical processes.

Challenge 4

To combine soil modeling tools with management tools to better assess degradative processes.

Challenge 5

To improve water, erosion and sediment routing modeling in complex landscapes.

model codes to solve this equation were described in more detail by,for example, Šimůnek et al. (2003), Šimůnek and Bradford (2008),
and van Dam et al. (2008). Model comparison studies have been
conducted by, for example, Bonfante et al. (2010) and Scanlon etal. (2002), but these efforts have been quite rare up to now. For
more details on numerical solutions used in these models, we referreaders to the “Numerical Approaches” section below.
The spatial and temporal dynamics of soil water flow are usuallyassumed to be controlled by the soil’s unsaturated hydraulic conductivity and hydraulic head gradients; in cultivated topsoils, bothvary rapidly in space and time. Soils with shallow groundwaterlevels may show a continuous alternation of percolation and capillary rise (Li et al., 2014). Soil heterogeneity is caused by both soil
deposition and formation, as well as by land use and soil management practices. Pore-scale models have been developed to generate
the change of soil hydraulic properties due to compaction, shearing and shrinkage (Alaoui et al., 2011). Soil heterogeneity may
cause preferential flow through macropores and flow instabilities(Šimůnek et al., 2003), which will reduce soil water residence timeand accelerated soil chemical transport. Also, hydrophobicity andwettability of soil surfaces may induce preferential flow processes
and nonhomogeneous movement of water in soils (Dekker andRitsema, 1994) (Ritsema et al., 1993). Despite being in use formore than a century, Richards equation–based models are still
not suitable for all soil types (particularly soils with high clay ororganic matter contents), and there is still not an adequate physical theory linking all types of flow (Beven and Germann, 2013).
Soil water and root zone processes are fundamental to the wellbeing of plants because they control the transport of nutrientsand assimilates from photosynthesis, facilitate numerous chemical reactions, and indirectly support the transport of hormones,
cell turgor, and cooling of leaves by transpiration due to root
water uptake (Ehlers and Goss, 2003). Soil water flow and vegetation development are therefore closely related. For example,
in periods with low leaf area index, rainfall interception androot water uptake are reduced, which may enhance runoff. Viceversa, soil moisture and oxygen availability have a large influenceon vegetation growth. Existing agrohydrological models typically focus on the soil’s physical processes and treat transpiration,

VZJ | Advancing Critical Zone Scienceroot water uptake, and crop development in a simplified way. In
contrast, common crop and agronomic models include detailed
CO2 assimilation and plant organ development modules, but lackrigorous description of soil root zone processes. To address theclose interactions between vegetation and soil, future models mustbetter integrate soil physical knowledge with agronomic and plant
physiological knowledge. Main challenges include the simulationof root development and soil water uptake, plant transpirationand vegetation growth in response to heterogeneous soil conditions. Crop root water extraction should account for root density,
soil hydraulic functions, root mucilage, soil water status, and thesuction of roots. Regarding crop transpiration, coupled crop–soilmodels should apply Penman–Monteith without the empiricalcrop factor (Shuttleworth, 2006). Typically, crop coefficients arebeing used to adapt the predicted reference ET for a well-watered
grass cover to the specific crop (Farahani et al., 2007). The stomatal resistance plays a key role in transpiration, and it is controlled
by solar radiation, air temperature, air humidity, CO2 concentration, and leaf water potential. In addition, leaf area index, plantheight, albedo, and nonuniform soil moisture distribution need tobe accounted for (Kool et al., 2014). A large number of initiatives
to integrate soil water flow and plant growth exist (Romano etal., 2011; van Lier et al., 2013; Wohling et al., 2013; Gayler et al.,2014). To better address the water cycle at a range of scales, there
is a need for more efficient integrated modeling tools, which will
be elaborated in the final major section, “Toward a Soil Modeling
Platform.” The models described in this section are based on theassumption that the soil is a rigid porous medium. Soil structuraldynamics will be discussed in the “Soil Formation” section andhave been addressed by, for example, Or et al. (2000), and Basu
and Kumar (2014).

Nutrient Cycling
The availability of plant nutrient elements often limits plant productivity in natural and agricultural ecosystems (Marschner andMarschner, 1995). Since primary production is strongly linked toprovisioning services and carbon sequestration and is often inversely
related to biodiversity, the cycling of nutrients is a supporting process that has strong effects on ecosystem services (e.g., see “Biomass
Production for Food, Fiber, and Energy” section). In natural systems,
nutrient inputs from weathering and deposition are generally veryp. 7 of 57

limited, and biomass and soil C stocks are governed by long-term
rates of influx and loss. In agriculture and production forestry, productivity is often boosted by fertilizer and manure additions, but
the cycling of nutrients remains important in determining nutrient
use efficiency, the maintenance of nutrient stocks, and groundwaterpollution. Management has major effects on nutrient cycling.
Nutrient transport in soil is intrinsically linked to water flow (see“Water Cycling” and “ Linking Soil Modeling Platforms with
Climate, Ecology, and Hydrology” sections). Most soils receive a
net throughput of water at least in certain seasons. This is important for preventing salinization, but it also means that plant
nutrients can easily be leached beyond the rooting zone, particularly during the early stages of crop growth (Rowe et al., 2001). The
main aim of predictive models of nutrient cycling is to quantify
the availability in time and space of nutrient elements in soil andto assess likely effects on plant growth and on nutrient loss fluxes,
which can affect water and air quality. Quantifying nutrient availability requires an understanding of the rates with which nutrient
elements enter, move within, and leave the soil and are mineralized
from organic materials (Havlin et al., 2013). Transport and leaching of nutrients and other dissolved substances in soils are typicallydescribed by the convection–dispersion equation (CDE):¶(qc +rs ) = Ñ×(qD eÑc - qc )- Sr¶t[2]

where q is the soil moisture content (L3 L−3), c is the concentrationof a substance in the liquid phase (M L−3), s is the concentrationof the component in the solid phase, De is the effective dispersion
tensor (L2 T−1), q is the Darcy flux of water (L T−1), which is typically obtained from solving the Richards equation (Eq. [1]), Sr isthe sink term for nutrient uptake by roots (M L−3 T−1). For linear
equilibrium sorption, the left term of Eq. [2] becomes:

matter mineralization via exudates, exo-enzymes and mycorrhizae.
Nutrient cycling models are increasingly taking these effects into
account (Taylor et al., 2011).
The mineralization and transformation of plant litter and soilorganic matter has mainly been modeled using schemas of conceptual pools that turn over at different rates; these were reviewed
recently by Manzoni and Porporato (2009) and Falloon and Smith(2010). For example, the Roth-C model (Coleman et al., 1997)
splits litter into “resistant” and “decomposable” material and soilorganic matter into “microbial,” “humified,” and “inert” material
and tracks transfers among these pools using first-order rate coefficients. The values of these coefficients are modified according totemperature, moisture, and soil cover. Similar schemas are used in
CENTURY (Parton et al., 1988), DAISY (Hansen et al., 1991),
and ECOSSE (Smith et al., 2010), among other models. Several
challenges exist with this approach. Most turnover is of recent
material, but the bulk of the organic matter in soil is relatively
old. Understanding how nutrients will be incorporated into andreleased from this large stock depends on quantifying transfers
into more inert pools, which are relatively small and difficult toobserve. Given several organic matter pools and unconstrained
rate coefficients, it is possible to reproduce a very wide range ofdecomposition trajectories, which limits the predictive ability ofthese models. Predictions of nutrient cycling rates are likely to be
improved by constraining models using actual measurements ofelement stocks and fluxes. The average age of soil organic carbon
obtained through 14C dating is a particularly useful measurement,
and is used in models such as N14C (Tipping et al., 2012) (Fig. 2)
to reduce the number of unconstrained parameters. An additional
way forward in flux quantification is stable isotope tracking;¶ éë(q+rK d )c ùû¶twhere Kd is the distribution coefficient (L3 M−1).
Nutrient cycling models must take into account the major fluxes ofnutrient elements into soil via litter, animal excreta, and manures
and fertilizers and already predict nutrient availability fairly well,particularly in response to mineral fertilizers (e.g., Archontoulis
et al., 2014). More difficult to predict are microbial-mediatedfluxes, such as organic nutrient mineralization rates that can beenormously variable. Predictions of mineralization rates of organic
materials have frequently been based on their composition in termsof element stoichiometry, on compounds that are relatively labileor recalcitrant, and/or compounds that directly inhibit enzyme
activity such as soluble phenolics. Plants also exert strong control
on the soil nutrient system, indirectly by determining nutrient andcarbon inputs in litter, but also directly by depleting solutes, andby accelerating removal of nutrients from minerals and organic

VZJ | Advancing Critical Zone ScienceFig. 2. Schematic diagram of N14C, showing carbon (black arrows)
and nitrogen (white arrows) stocks and flows in soil and vegetation.
Plants are considered to consist of two types of material, coarse or fine;soil organic matter is considered to consist of three pools with firstorder rate constants of 0.25 yr−1 (slow), 0.025 yr−1 (slow), or 0.0005
yr−1 (passive). From N14C (Tipping et al., 2012).

p. 8 of 57

see the “Parametrizing Models with Nondestructive and High
Resolution Water Stable Isotope Data” section.
As well as providing nutrient inputs in litter, plants influence
nutrient cycling by removing nutrient elements from the soil solution as they become available either in mineral form or as smallorganic molecules (Chapin et al., 1993). The efficiency of thisprocess means that observed nutrient concentrations in soil solution are often close to zero during active plant growth. A major
challenge in modeling nutrient availability is therefore determining the most appropriate measurement with which to compare
model predictions (Schimel and Bennett, 2004). Time-integrated
measurements, such as net mineralization (Rowe et al., 2011) or
sorption onto resins (Qian and Schoenau, 2002), are generally preferable. The prediction of nutrient availability in terms of a metricthat is measurable remains a key goal for soil nutrient modeling.

QUEFTS (Janssen et al., 1990). The most appropriate approach
to modeling nutrient interactions may vary with the ecosystem andwith data availability—a law-of-the-minimum approach (Liebig,1840) may be adequate for agricultural systems, whereas concurrent limitation may be a more appropriate concept for more natural
systems (Rastetter, 2011).
Examples of biogeochemical models at the larger scale are given
in “Linking Soil Modeling Platforms with Climate, Ecology, andHydrology.” In summary, the aspects of modeling nutrient cyclingthat currently offer the most scope for improvement are: interactions between litter composition and intrinsic soil properties indetermining mineralization rates, links between rapid turnover oforganic matter and the slower processes that determine soil development, links between nutrient availability and transport models,a focus on modeling aspects of nutrient availability that can bemeasured, direct effects of plants and mycorrhizae on mineralization, and interactions among nutrient elements.

Considerable progress has been made to resolve rhizosphericprocesses (see “Biomass Production for Food, Fiber, and Energy”
section), yet mechanistic modeling of the direct effects of plants
on nutrient release from organic matter and weatherable minerals through root exudation and enzyme production are currently
limited to a few models of nutrient cycling at the ecosystem scale.
Organic acids exuded by roots or microbes can increase nutrient
solubility via effects on the pH of microsites, and/or provide asource of labile C, which allows bacteria and fungi to mineralize more recalcitrant substrates. Accounting for root exudates isimportant because comparatively small exudate fluxes can havea disproportionate effect in increasing nutrient availability (Yinet al., 2014). Roots and mycorrhizae also produce enzymes that
directly solubilize nutrients. Production of such enzymes may belimited by N availability, sometimes leading to counterintuitive
responses, such as increasing plant tissue P content with increasing
N inputs (Rowe et al., 2008).

Soils are home to 25% of all living species on Earth (Turbé etal., 2010) and contain a vast amount of genetic diversity, mainly
derived from microbes but also plant roots (Torsvik et al., 1990;
Torsvik and Ovreas, 2002). Soil biological activity derived fromgenetic diversity is a critical supporting ecosystem service becauseof the diverse metabolic pathways encoded in microbial DNA(Daniel 2004; Ferrer et al., 2009; Chan et al., 2013). These pathways include antibiotic production and resistance as well as othermedically and industrially relevant natural products (Handelsman
et al., 1998). In both managed and unmanaged systems, soil biological activity and genetic diversity supports emergent ecosystemservices, including soil nutrient cycling, plant productivity, soil
formation, and carbon storage (van der Heijden et al., 2008; Singhet al., 2010).

Many studies of nutrient cycling have addressed only a single
element, most commonly N. Nitrogen is the nutrient element
required in largest quantities, but the cycling of N into and outof plants can be controlled by other elements. Productivity innatural systems may ultimately be limited by the availability ofelements essential for N fixation, such as P or Mo (van Groenigen
et al., 2006), and terrestrial ecosystems often develop toward a
multiply co-limited state (Harpole et al., 2011). Processes governing availability of nutrient elements, including micronutrients,
were well summarized by Marschner and Marschner (1995). Few
ecosystem-scale models take into account micronutrients, but
P has increasingly been included in such models, particularly
those addressing soil formation over multicentury or longer timescales (Taylor et al., 2011). As well as predicting the availability of
individual elements, it is important to consider how interactions
among nutrient availabilities can determine plant production. The
concept that nutrients are used more efficiently when other nutrients are in greater supply has been implemented in models such as

Despite the importance of soil biological activity, we currently
lack adequate tools to predict rates of biological processes in specific soil environments or link genetic diversity to soil ecosystem
functioning. Many empirical studies have begun to make this link
(Hawkes et al., 2005; Prosser and Nicol, 2008; Mackelprang etal., 2011), the large number of interacting biological and physicalprocesses pose a key challenge for modeling soil biological activity(Blagodatsky and Smith, 2012). Even at very small scales, many
thousands to millions of distinct genotypes (or operational taxonomic units, OTU) may inhabit a single gram of soil (Torsvik et al.,
1990; Curtis et al., 2002; Schloss and Handelsman, 2006; Or et al.,2007). Genetic diversity interacts with environmental heterogeneity in physical and chemical properties and states (Dion, 2008).
Heterogeneity occurs both in time and in space, thereby driving
changes in community structure and activity of soil organisms(Torsvik et al., 1996; Curtis and Sloan, 2005; Prosser et al., 2007).
For example, soil hydration status and pore-space characteristics
influence microbial motility, an important trait for expansion

VZJ | Advancing Critical Zone Science

Biological Activity

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and survival in highly patchy soil environments (Barton and Ford,
1997; Chang and Halverson, 2003; Or et al., 2007; Dechesne etal., 2010), especially in unsaturated soils with limited advective
transport (Ebrahimi and Or, 2014).
Progress in resolving soil ecological questions requires quantitative models that integrate key biophysical processes with ecologicalinteractions at appropriate spatial and temporal scales (Prosser etal., 2007). Still, such models are not yet well developed (ToddBrown et al., 2012). Most current models of soil functioning are
based on correlations between biological activity and ecosystem
functions. At scales from the soil pore (Hallett et al., 2013) tothe landscape (Attard et al., 2011; Eisenhauer et al., 2012) correlations between broad measurements of biodiversity or biologicalactivity (e.g., guilds, phyla, functional groups, nutrient cycling)and soil properties (e.g., nutrients, pH, texture, pore structure) areused to parameterize soil models (Hunt and Wall, 2002; Youngand Crawford, 2004; Cazelles et al., 2013). Some of these models
describe the trophic relationships between organisms, including
plants (Hunt and Wall, 2002). These food web models have suggested that the relationship between biodiversity and ecosystemprocesses is affected by land use (de Vries et al., 2013).
A new generation of models is accounting for diversity in soilorganismal traits at appropriate spatial and temporal scales (Longand Or, 2009; Allison, 2012; Crawford et al., 2011). Organisms
with favorable combinations of traits in a given environment will
proliferate and contribute to ecological functioning or to the formation of “hot spots,” such as within soil aggregates (Ebrahimi
and Or, 2015). There are several advantages to these trait-based
approaches. First, they do not require information about specificorganisms. Instead, genetic or other trait information can bederived from a range of sources and used to establish trait distributions for modeling. Trait values can be assigned to hypotheticalorganisms from these distributions at random to represent a wide
range of potential ecological strategies. The environmental conditions then determine which strategies are actually viable. Second,
the traits and their interrelationships can be derived from existing genomic and metagenomics data. These datasets include richinformation on functional gene frequencies and correlations(Berlemont and Martiny, 2013). Finally, trait-based models canbe run in different physiochemical contexts to mimic soil heterogeneity and make predictions of ecosystem services, such as thetotal amount of carbon storage or rates of nutrient cycling (see“Nutrient Cycling” section). Trait-based models have been applied
to predict enzyme activities, decomposition rates, and N cycling
in decomposing litter (Allison, 2012; Kaiser et al., 2014), as well as
the warming response of C use efficiency in soils (Allison, 2014).
In soil systems, significant progress can be made by implementing organismal traits in spatially explicit, individual-based models(Wang and Or, 2014). The question of what part of genetic diversity estimates is directly linked and shaped by present ecological

VZJ | Advancing Critical Zone Science

conditions and what fraction is shaped by population and interspecies interactions with time remains a central challenge for modern
microbial ecology (Curtis and Sloan, 2005; Martiny et al., 2006;
Prosser et al., 2007). Integrating these poorly understood processes
into soil models presents an even greater challenge.

Soil Degrading Processes

Salinization and Alkalinization

Salinization of soil and water resources is a chronic problem inmany arid regions where ET exceeds rainfall. The expansion ofirrigated agriculture with marginal water sources to meet thegrowing demand for food is likely to increase the range of soils
impacted by salinity. A confluence of conditions ranging fromthe projected hotter and drier climate patterns, to increasing salt
loads due to use of marginal water sources, saltwater intrusion
due to over exploitation of coastal aquifers; rapid withdrawal of
slowly replenishing inland aquifers (e.g., Ogallala Aquifer in theUSA), and mismanagement of rapidly expanding irrigation inarid regions are expected to confound this long standing problem(Assouline et al., 2015). Land degradation and loss of agricultural
productivity due to salinity and sodicity hazards are among theearliest anthropogenic ecological disasters responsible for thedemise of the civilizations of Mesopotamia and the Indus valley(Hillel, 1992; Van Schilfgaarde, 1994; Ghassemi et al., 1995).
Additionally, in some regions the buildup of calcium carbonate
modifies soil hydraulic properties through the formation of low
permeability carbonate enriched soil layers. Presently, about 20 to
50% of the irrigated land worldwide is salt-affected (Ghassemi etal., 1995; Flowers, 1999; Pitman and Lauchli, 2002; Tanji, 2002).
Salinity damage in agriculture is estimated at US $12 billion peryear, and it is expected to increase with persistent salinization ofwater resources (Ghassemi et al., 1995).
Crop response to the spatial and the temporal distributions of soil
water content and soil salinity is complex and not fully understood,
whereas it is often the combined effects of the osmotic and capillarycomponents of the soil solution that affects plant transpiration andcrop yield (Childs and Hanks, 1975; Bresler and Hoffman, 1986;
Bras and Seo, 1987; Bresler, 1987; van Genuchten, 1987; Hanson
et al., 2008; Russo et al., 2009; Duffner et al., 2014). Salinization
has been extensively modeled based on numerical models of waterand solute dynamics in agroecosystems, for example, based on the
SWMS and HYDRUS codes (Tuli and Jury, 2004; Mguidiche etal., 2015). However, one of the most urgent modeling challenges
is to improve quantitative description of the interactions between
soil water salinity and plant response. Much of the know-how inthe basis of salinity management (leaching, crop selection, water
quality mixing) is empirically based and derived from seasonal
averages, making it difficult to generalize and adapt to changing
climate and future water quality and more intensive agriculture(Assouline et al., 2015).

p. 10 of 57

The standard salinity management strategies often involve mixingof waters of different qualities, the selection of salt-tolerant crops,
avoidance of overly sensitive soils, and compensating for highsalinity water by increasing irrigation dosage above plant transpiration demand (Russo and Bakker, 1987; Shani and Dudley,
2001; Shani et al., 2007; Dudley et al., 2008; Russo et al., 2009).
The traditional approach, where the leaching fraction increases
with irrigation water salinity, introduces significant risks due toincreasing salt loads on groundwater resources that could reduce
available freshwater at the regional scale (Assouline and Shavit,
2004; Schoups et al., 2005; Shani et al., 2005). Proper assessmentof such environmental risks, and the sustainability of irrigatedagriculture in such systems hinges on the ability to model andpredict multi-season and regional hydrologic processes well beyond
the single field–single season irrigation decisions of the past.
A rapidly expanding alternative source for water irrigation inarid and semiarid regions is the application of treated effluents(TE) (Hamilton et al., 2007; Qadir et al., 2007; Pedrero et al.,2010), especially in agricultural regions near urban areas (Shuval
et al., 1986). Global estimates of effluent reuse indicate thatabout 20 million hectares of agricultural land are irrigated withTE (Jimenez and Asano, 2008). However, the increased relianceon TE for irrigation in arid regions is often practiced with little
consideration of long-term impact on soil, hydrology, and ecology of the irrigated area. The primary risks associated with TE
irrigation involve high concentrations of salts, especially sodium,and of organic compounds (Feigin et al., 1991; Balks et al., 1998;
Hamilton et al., 2007; Pedrero et al., 2010). Recent studies haveshown that long-term effects of TE irrigation resulted in a significant degradation of soil structure and hydraulic properties due
to increased exchangeable sodium percentage (Leij et al., 2004;
Lado et al., 2005; Assouline and Narkis, 2011, 2013; Levy et al.,2011). Evidence from other studies have shown other negative
effects related to chemical aspects (Xiong et al., 2001; Wallach
et al., 2005; Lado et al., 2012), as well as human health and other
ecological risks associated with introduction of pathogenic microorganisms, heavy metals, and toxic organic compounds into thesoil and crop (Toze, 2006; Pedrero et al., 2010; Scheierling et al.,2010; del Mar Alguacil et al., 2012). Hence, the sustainability of acoupled agro-urban hydrological cycle, where TE is used for irrigation hinges on proper management to mitigate adverse impacts oflong-term TE application to avoid potential collapse of soil ecological functions.
Soil salinity management is likely to remain a challenge in the foreseeable future, especially with the growing pressure of agriculturalintensification to feed the growing world population, changes inclimate patterns, and increased reliance on marginal water sources.
Meeting these challenges will require multidisciplinary approaches
that combine modeling tools with management strategies to ensuresustainable and safe use of irrigation water resources of variable
quality. We clearly need a new generation of quantitative models

VZJ | Advancing Critical Zone Sciencethat integrate key biophysical processes with ecological interactions at appropriate spatial and temporal scales.

Erosion
Erosion can result from the action of wind, water, and tillage. In
semiarid zones, wind erosion is very significant and tillage erosion redistributes considerable amounts of soil at the field scale.
However, water erosion is globally the most important and willbe the focus of discussion here.
The intensification of agriculture and changes in rainfall patterns
with more intense rain events may increase rates of surface soil erosion. The damage is not limited to the removal of productive soil
top layer (Pimental and Sparks, 2000), but also affects surface water
quality downstream (stream and lake ecology, dam siltation, andenhanced pollution by agrochemicals and colloid facilitated transport). Soil erosion is strongly connected with drivers for climatechange, as the mobilization of large amounts of soil organic carbon
by soil transport may significantly contribute to atmospheric CO2
emissions (WMO, 2005). In addition, drier soil conditions associated with future climate extremes may limit rates of soil carbon
accumulation, thereby reducing soil aggregation and enhancing vulnerability to wind erosion. A host of soil conservation strategies forcombating land degradation due to soil erosion offer additional benefits such as enhanced soil water storage (Troeh et al., 1991; Pimental
and Sparks, 2000). Soil erosion leads to significant loss of agricultural land and reduction in agricultural productivity, as soil loss
diminishes soil water storage capacity, impacting crop growth andenhancing flood risk. Furthermore, soil erosion plays a significant
role in the biogeochemical cycles of C, N, P and Si as it redistributes
significant amounts of these elements over Earth’s surface (Van Oostet al., 2007; Quinton et al., 2010). (See also “Nutrient Cycling.”)
Several reviews on modeling soil erosion have been published in thepast, and the reader is referred to those papers for more information on the different concepts ranging from simple models such as
the Universal Soil Loss Equation (USLE), to more complex processbased models such as KINEROS (KINematic EROsion Simulation)and WEPP (Water Erosion Prediction Project) (Merritt et al., 2003;
Aksoy and Kavvas, 2005).
Soil erosion by water is a complex phenomenon resulting from soil
detachment by raindrop impacts and overland flow, and transport of particles by rain splash and by sheet and channel flow
(Ellison, 1944, 1945). Quantitative evaluation of erosion effects
at the different scales requires modeling capabilities to deal withthe complexity of the processes involved. In the different modeling approaches, the driving and resisting forces are conceptually
expressed by (i) flow erosivity (an indicator of the erosive potentialof rainfall and runoff) and (ii) soil erodibility (a measure of thesusceptibility of soil particles to detachment and transport by rainfall and runoff). Both are state variables that respond to variations
in local and regional conditions, making their evaluation the real
challenge of erosion modeling. The flow erosivity requires data on
p. 11 of 57

the timing and amount of runoff (Assouline et al., 2007). This isrequired for the nontrivial issue of modeling coupled infiltrationand overland flow (Furman, 2008; Chen et al., 2012; Langhans etal., 2013). Quantitative representation of the infiltration processitself requires multiscale information of soil hydraulic properties
and its spatial variations, soil surface conditions, topography, soil
profile initial conditions, and boundary conditions (Assouline,2013). The amount of sediment detached or transported either bydrop impact of flowing water will be determined by the soil “erodibility,” which is controlled by a range of both static and dynamic
soil properties, including soil texture and soil mechanical properties (Wischmeier, 1978; Watson and Laflen, 1986; Poesen and
Nearing, 1993; Bradford and Foster, 1996; Römkens et al., 2002;
Assouline and Ben-Hur, 2006)
Because of the multiscale nature of erosion, one can either focus on
the microscale and consider soil particle detachment by rain splash
and sediment transport using a process-based approach (Eckern,
1950; Rose, 1960; Lane, 1982; Diaz et al., 2008) or use an empirical macroscale approach (Pelletier, 2012). At the macroscale, themost commonly used quantitative expression of soil erosion continues to be the multiplication-of-factors type empirical equation,
as proposed by (Neal, 1938), where soil loss is a function of the
product of soil erodibility and rain erosivity (Wischmeier, 1978;
Meyer and Harmon, 1989; Kinnell and Wood, 1992; Kinnell,
1993; Zhang et al., 1998). Following this approach, soil erodibility
is considered an intrinsic soil property independent of rainfall andslope conditions (Lane et al., 1987). However, soil erodibility has
been found to be dependent on infiltration and runoff (Nearing
et al., 1990; Kinnell, 1993) and to change with time during therainfall event (West, 1988; Assouline and Ben-Hur, 2006). Soilerodibility also varies over the long term due to feedbacks between
erosion and soil properties (Govers et al., 2006). Another major
problem with current macroscale assessments is that the procedures used for upscaling are sometimes inadequate, which may leadto a significant overestimation of erosion rates (Cerdan et al., 2010;
Quinton et al., 2010).
Relatively little attention has been given to the modeling of soiltransport across the landscape, in connection with soil, nutrient,and carbon delivery to stream and open waters. Whereas spatiallydistributed sediment routing using transport and deposition laws
may offer better perspectives to understand sediment delivery, suchmodeling approaches have been relatively simple (Van Rompaey etal., 2001) and need further improvement to fully account for thecomplexity of real landscapes. Mitigating and controlling erosion
require advance modeling tools to evaluate the appropriateness andefficiency of alternative approaches and methods.

Compaction
Soil compaction caused by human activities that reduces soil porevolume has been recognized as a worldwide problem (Bridges, 1992;
Soane and van Ouwerkerk, 1995). Compaction affects soil fertility

VZJ | Advancing Critical Zone Science

by reducing water and airflow, which alters the soil’s biologicalactivity and redox potential, induces changes in Fe mobilization
and CH4 emission. These changes can turn soil into a source forenvironmental CH4 instead of a sink. Furthermore, the platy
structure caused by soil compaction reduces plant rootability.
Compaction also decreases water infiltration, which increases waterrunoff, soil erosion, and the likelihood of flooding and debris flow.
Efficient protection against unwanted soil compaction requires
knowledge of the mechanical processes and properties of structured,
unsaturated soils. Although compaction occurs naturally during soil
formation (see “Soil Formation”), the majority of soil compaction
studies assess the anthropogenic impacts that cause compaction,such as tillage, vehicle and animal traffic, or forest clear-cutting withheavy harvesting equipment. All soil deformation processes affectecosystem services and soil functions in the short term and some,such as those involving irreversible dewatering and compaction ofclay, in the long term as well.
Soil compaction models use empirical (simple cause–effectrelationships), semi-empirical (pedotransfer functions), andprocess-based approaches (Keller et al., 2013). Process-based
compaction modeling is generally a three-step approach. The firststep describes the load situation (e.g., pressure distribution at thesoil surface under the wheel or track of a vehicle). The second step
quantifies the change in the stress field within the soil due to theload applied to the soil surface. The third step uses constitutive
relationships to quantify soil deformation as a result of the change
in the soil stress field. These three steps are typically incorporated
into an analytical (Soehne, 1953; Soehne, 1958; Horn, 2003;
Van den Akker, 2004; Keller et al., 2007), or numerical model(Richards et al., 1997; Berli et al., 2003; Peth et al., 2006).
Recently, progress was made toward improving the characterizationof the pressure distribution at the soil surface (Gysi et al., 2001;
Keller, 2005; Lamandé et al., 2007), evaluating the different
stress transfer models within the soil (Défossez et al., 2014), anddetermining soil constitutive relationships (Horn, 2003; Keller
and Arvidsson, 2007; Berli et al., 2015). This progress allowed
for improved process-based compaction modeling that used acomprehensive framework to describe stress-deformation behavior
due to vehicle traffic. Although most compaction research is
being done at the bulk (centimeter) scale, recent advances innondestructive imaging (microcomputed tomography, mCT;
neutron tomography; and nuclear magnetic resonance imaging,
MRI) and numerical modeling with high-performance computing
have allowed for compaction research at the pore scale (Berliet al., 2006; Eggers et al., 2006; Berli et al., 2008; Peth et al.,2010). Additionally, more soil information has become available
because of georeferencing and global positioning systems (GPSs)
that allows for soil compaction modeling at the field scale using
pedotransfer functions. Horn and Fleige (2003) developed
pedotransfer functions to estimate compaction sensitivity based on
bulk density texture, organic matter content and soil structure asp. 12 of 57

well as moisture status. Horn and Fleige (2003) also addressed thechanges in physical soil functions that were related to soil surface
loads, for example, due to vehicle traffic (Duttmann et al., 2014).
Assouline (2006a,b) extended models for the soil water retention
and hydraulic conductivity curves to account for structuralchanges in soils resulting from changes in porosity, enabling theprediction of the hydraulic properties of compacted or tilled soils.
Despite the considerable progress in soil compaction modelingsince Soehne’s early work (Soehne, 1953, 1958), challenges
remain. For example, we have only a very limited quantitative
understanding of soil structure and dynamics and how they
influence the physical and mechanical processes and properties
of soil (Logsdon et al., 2013). Although the description of soil
stress-deformation behavior has largely improved, the impact ofsoil deformation on soil hydrological processes, soil chemistry,and soil biology is still not well understood. Another limitationis that classical soil mechanics were developed for mostly static
loads, whereas most soil compaction is caused by dynamic loads,
such as soil deformation under a rolling wheel. The differences
between compaction caused by static and dynamic loads werestudied only recently (Wiermann et al., 1999; Ghezzehei and Or,
2001). Finally, there is a huge gap in upscaling soil compaction
properties and processes measured in the laboratory to the field
scale, as well as understanding the effects of field-scale compaction
on hydrological and ecological processes in the landscape. For an
ecosystem-scale soil model, we suggest that a simplified semiempirical soil compaction modeling approach would likely be
the most effective to improve the quantification of soil ecosystemprocesses and identify the key challenges.

66Soil Modeling andEcosystem Services

In this section we will deal with the role of soil models in understanding, quantifying, and delivering ecosystem services. We focus
on two groups of ecosystem services as outlined in Fig. 1, that is,regulating and provisioning services. Regulating services include
climate regulation and recycling of wastes and buffering andfiltering capacity of soils; provisioning services include biomass
production for food, fiber, and energy, as well as soil as habitat andphysical support. We discuss the role of soil models to determine

the importance of the different soil properties, as affected by thedifferent soil processes, for the different ecosystem services. At
the end of this section, we formulate five key challenges on soilmodeling and ecosystem services (Table 4).

Regulating Services
Climate Regulation

Climate regulation may be assessed in terms of the time scales of its
regulatory function. For example, at hydrological short time scalessoil water storage affects various climate patterns (e.g., rainfall
events, droughts, heat waves) (IPCC, 2007), whereas for the longer
term, soil serves as a sink or source of greenhouse gases (GHG)
through levels of carbon sequestration (Smith et al., 2013). Soil
regulatory function could also be assessed through mechanistic
feedbacks related to its properties and hydro-ecological functioning, such as effects of soil on plant communities that affect climate,surface albedo, land use patterns, and more. The inextricable links
between soil and climate were highlighted in the section on soil
formation and have been quantified in various quantitative models
for soil formation. For purposes of this review, feedbacks fromsoil processes that modify climate processes constitute soil’s primary regulatory role. Soil water storage features prominently inthe definition of droughts (Alley 1984; Dai et al., 2004) and isconsidered an important factor in observed extreme heat waves(Jaeger and Seneviratne, 2011; Seneviratne et al., 2014). A recent
study (Trenberth et al., 2015) has argued that the omission of soil
processes (water content) in climate models seriously hampers theirability to explain the origins of a range of climate extremes ranging
from droughts to floods and heatwaves.
Soil properties control soil evaporation dynamics and transition
to stage 2 evaporation (Or et al., 2013), a short-term process withsignificant surface energy balance ramifications. On decadal tomillennial time scales, the most important aspect of soil climate
regulation is the soil’s role as a source or sink of carbon and other
GHG (Smith et al., 2013). This is linked to the amount and stability of estimated soil carbon stocks that vary with soil properties
and function (also with land use and climate). Changes in soil
surface temperature affect the fate of carbon stocks in arctic
regions and within a relatively short period, large tracts of land
may become significant sources of GHG at high rates, for example,
due to the rapid thawing of permafrost soils in northern latitudes(Schuur et al., 2015). On geologic time scales, rock weathering andformation of soils play a substantial role in supporting vegetation,

Table 4. Key challenges to soil modeling and ecosystem services.
Key challenges
Challenge 1

To include soil structural dynamics in the prediction of the soil’s buffering and filtering capacity.

Challenge 2

To link soil habitat and biodiversity modeling to soil function models.

Challenge 3

To model soil formation processes over long time scales.

Challenge 4

To upscale rhizosphere processes and soil–root interactions to the field scale.

Challenge 5

To integrate new understanding of structure dynamics, chemical and biological processes into operational biosphere models, such as those predicting
GHG emissions.

VZJ | Advancing Critical Zone Sciencep. 13 of 57

accumulating carbon, and thus regulation of planetary climate(e.g., Pagani et al., 2009; Maher and Chamberlain, 2014)
Soil management practices, such as tillage and land clearing (forests and grasslands), are among the main human activities thathave significantly increased CO2 emissions in the past centuries,
with much of the emissions mediated by soil microbial processes.
Additionally, the increase in fertilizer application to boost crop
production (part of what is known as the Green Revolution), hasresulted in significant releases of nitrous oxides to the atmosphere,
thereby reducing nutrient use efficiency and directly contributing
to global warming. Vinken et al. (2014) estimated that one-fourthof soil NOx emissions come directly from applied fertilizers. For
natural systems at the northern lower latitudes, it is expected thatsoil warming and melting of permafrost will result in positive feedbacks of unknown magnitudes (Schuur et al., 2015). In general,
wide ranging estimates of negative feedbacks are projected withrising temperatures that could decrease net primary production.
Hence, to understand the role of GHG emissions and to mitigate
their adverse impacts, the soil community must endeavor to study
the integrated soil system by linking physical, chemical and biological processes, and their variations with future climate patterns andintroduce state-of-the-art knowledge on soil processes in existingand operational terrestrial biosphere models (Fisher et al., 2014). In
particular, the assessment of the impact of management and land
use practices on GHG emissions requires models that are based ona fundamental understanding of these processes. However, there
are substantial deficits in presently used models both in terms ofappropriate parameterization and with respect to the underling
processes (see “Nutrient Cycling” and “Biological Activity” sections above). When considering regional soil carbon balances, onemust take account of changes caused by soil erosion and soil formation (longer time scales) that affecting the soil organic matter pooland the balance between its decomposition and sequestration (Lal,2014; Amundson et al., 2015).
Soil models for climate regulation are listed in Table 2. Advanced
soil modeling platforms offer a way forward that systematicallyuses available knowledge and considers and incorporates feedbacks(climate, soil biology, social aspects) to yield better understanding
and predictive capabilities of integrated soil systems (see “Toward a
Soil Modeling Platform” section). Integrated modeling approaches
informed by climate scenarios and feedback provide the necessary know-how for adapting agricultural and natural ecosystems
to changing temperatures and soil moisture regimes that affectplants and crop yields as well as soil ecological functioning andlong term sustainability. These aspects are further discussed in thesections “Linking Soil Modeling Platforms with Climate, Ecology,
and Hydrology” and “Linking Soil Modeling Platforms with Cropand Biomass Production.”

VZJ | Advancing Critical Zone Science

Buffering and Filtering
We may define the buffering capacity of soil as including processes that involve storage and transformation of chemicals,
including both anthropogenic and biogeogenic substances.
Soil buffering is crucial with regard to the filtering capacity ofsoil, that is, the soil’s capacity to temporarily retain chemicals
from emission to the atmosphere or groundwater. Addition andremoval of chemicals disturbs the state of a soil, affecting biota
as they require sufficiently stable conditions; however, such disturbances can be countered by biogeochemical processes. The
modeling goal is to quantify the extent and spatiotemporal variability of such buffering.
All soil related processes are connected with soil buffering andfiltering. Relevant physical processes concern the exchange of carrier fluids, such as water and gas with groundwater, surface water,
and atmosphere, as well as by physical filtration at phase interfaces,
whereas important biogeochemical processes are chemical ad- anddesorption, precipitation–dissolution, and transformation. In
addition, biological processes, like in the rhizosphere and biofilms
may play an important role in filtering and buffering and have notbeen explicitly considered in modeling until recently (Or et al.,2007; Schimel and Schaeffer, 2012). Soil clay minerals; Fe-, Al- andMn-hydroxides; organic matter; and carbonates play a major role insoil’s buffering and filtering capacity. Because soil organic matter isa major sorbent for many important chemicals, buffering is intensively linked with the major cycling of N, P, and C. Major inputs
of, for example, nitrogen to the soil system may affect the soil’s pH,
leading to acidification and changes in its buffering capacity (Guoet al., 2010; Tian and Niu, 2015). Connected with the unsaturated
soil zone is the capillary fringe at the groundwater table. Since
the capillary fringe is characterized by steep gradients in terms of
hydraulic state variables and chemical (e.g., redox potential) andbiological conditions, it involves both different processes and different rates of interactions with regard to buffering and filteringthan the vadose zone. Moreover, this biogeochemically importanttransition zone changes very dynamically with time and depth(Winter et al., 2015). Yet, our understanding of this important
zone between the vadose zone and the groundwater is still limited,
requiring more intensive research and an more improved incorporation of capillary fringe processes in soil models.
Significant advances have been made during the past decades inunderstanding, quantifying, and modeling of buffering and filtering processes. General mineral equilibria models have been
extended with validated ad- and desorption models for specificgroups of solutes, such as metals (Zhang et al., 2012; Duffner et al.,2014). Interaction between soil components is crucial for quantifying buffering and filtering; inorganic and organic components
might compete either for sorption sites or for forming aqueous
complexes increasing solubility or decreasing sorption. A numberof numerical tools have been developed during the last decadep. 14 of 57

accounting for these interactions, mainly based on principles ofthermodynamic equilibrium (Steefel et al., 2014). The genericnature of these tools allows for implementing complex conceptual models for fate and transport (Jacques et al., 2008; Leterme
et al., 2014; Thaysen et al., 2014), but these models generally lackkinetics, as well as the inclusion of physical nonequilibrium conditions. This includes nonequilibrium of water–air dynamics, asthese interfaces control interactions and access to sorption sites,
duration of interactions and local equilibrium assumption (LEA)
validity, and biological activity. Much of that dynamics is causedby soil heterogeneity, such as preferential and bypass flow. Manyadvances have been made in modeling soil heterogeneity both
explicitly by Bellin et al. (1993); Roth (1995), as well as implicitly
by Beven and Germann (2013).
Linking inorganic and organic biogeochemistry seems crucial forunderstanding the fate of many solutes. For example, some heavy
metals form strong complexes with dissolved organic matter, as
described in Fig. 3 for Hg (Leterme et al., 2014). Whereas modeling of inorganic chemical biogeochemistry often addresses specificcomponents (e.g., heavy metals) and equilibrium relationships,
models for biogeochemical N, P, K, and C typically emphasize
conversion rates such as for organic matter and nitrogen mineralization. For cases where the organic matter pool may change
significantly, with increasing occurrences of drought or water
logging with associated redox potential changes, links between
organic and inorganic interactions must be investigated. The
kinetics of abiotic soil chemical changes also requires attention(Werner Stumm 1995; Schroder et al., 2008). In addition to thekinetic behavior of soil chemical processes, soil biological processes
show similar rate-limited behavior, which is most likely controlled
by chemical and structural soil properties. In fact, whether certain
biological processes (as denitrification) occur at all, depends on
the presence of the necessary microbial populations. In addition,
bioavailability of contaminants for microorganisms affects theleaching behavior in essence (Beltman et al., 2008).
As soil models might be applied on long time scales for persistentcontaminant, buffering and filtering cannot be independent fromsoil formation structural dynamics (see “Soil Formation” above)as these determine flow paths and availability of reactive sites. In
summary, integrating physical aspects of nonuniform flow andsolute transport with chemical and biological processes will remaina prominent focus of soil-modeling research.

Recycling of Anthropogenic Waste
Many human activities produce waste that is often released to thesoil, such as chemotoxic and radioactive elements, toxic organic
compounds, and potentially harmful living organisms and viruses.
Waste inputs range from feedlots dung and farm animals, irrigation by wastewater nonpoint pollution by atmospheric deposition,
accidental spills to deliberate dumping of industrial byproducts
in highly engineered waste landfills. A specific pathway is soil

VZJ | Advancing Critical Zone ScienceFig. 3. Mercury cycle in soil systems. Oval shapes denote Hg sources,
rectangles are for Hg sinks and rounded rectangles are componentsthat can act as both sources and sinks.

amendment to reduce metal leaching or to control CO2 sequestration (Campbell et al., 2006; Abril et al., 2008; Thaysen et al.,2014). Supporting processes such as limiting water flow throughwaste zones, sorption of compounds, and biological degradation
help to regulate contaminant release to the biosphere by dilution,
dispersion, retardation, and decay (e.g., see “Water Cycling” or“Buffering and Filtering” sections). This ecosystem service aims
at quantifying the soil’s contribution to protect human health.
Related examples of available models are listed in Table 2.
Impacts of soil contamination, waste disposal, or site remediation are typically assessed with risk assessment (chemotoxic
compounds) or radiological impact (radioactive waste) models.
Although the safety or protection provided by a disposal system
is primarily focused on isolation and containment, quantificationof dilution and dispersion and bioaccumulation in soils systems ishighly relevant for impact calculations by biosphere models (Smithet al., 2014). Particularly within the framework of radiologicalimpact studies, time scales could be several tens of thousands tohundreds of thousands of years.
Generally, engineered covers are put in place in typical landfills
with hazardous materials. For near-surface disposal systems for
low-radioactive waste disposal, as well as for high-radioactive
wastes (Rosenberger, 2009), cement-based structures are buried
under an engineered layered system of natural materials (Flachet al., 2007). Although covers could have an isolation function,
protecting humans and other biota from the waste, their mainfunctions are related to provide a stable physical and chemical soil
environment for the waste and to limit water flow into the waste
zones. Stable chemical conditions are related to durability in physical terms (e.g., cracking, increase in permeability) and chemicalterms (sorption and solubility) affected by detrimental geochemical processes in the cement-based system (Glasser et al., 2008;
Wang et al., 2013). Geochemical degrading and leaching processes
are driven by soil pore water composition (Jacques et al., 2010) andthus different soil processes, such as weathering, microbiological,
p. 15 of 57

and chemical processes (e.g., oxidation of pyrite in clay barriers),
play a crucial role. The engineered barrier will also limit the waterflow through the waste zone. The properties of the engineered
barriers could be optimized to favor the evaporative capacity of thebarrier, that is, increasing water holding capacity of the top waterto promote ET or the divergence capacity by increasing lateral flow.
When contaminants are released into the soil, their transport andfate are governed by similar physical, chemical, and biological processes and pose similar modeling challenges as described for boththe buffering and filtering regulating services. The main variableof interest is the flux across environmental compartments, suchas the groundwater, biosphere, and atmosphere. A particular challenge is the development of a soil-like profile in the engineered
barrier that alters its relevant physical, hydrological, chemical, andbiological properties thereby altering their required performance.
For that purpose, long-terms field experiments of years to decades(Albright et al., 2004; Nyhan, 2005) must be combined with natural or archaeological analogs (e.g., burial tombs) to benchmark
conceptual and mathematical models. To deal with extremely
long time scales, models should be able to incorporate long-termchanges in climate, landforms, and other relevant boundary conditions. Integrated methodological approaches need to be developed
to verify such models beyond the time-scale of instrumental observations, for example, by including proxy variables serving as (paleo)
indicators of past hydrological conditions (e.g., vegetation, soil, or
historical archives; Zwertvaegher et al., 2013; Zlinszky and Timár,
2013). As in simulating soil formation, many input variables are
uncertain since they are in essence unknown for future conditions.
Nevertheless, soil waste modeling as described herein requires thesame kind of scenario-like quantification, as well as collaborations
with related modeling communities.

2010; Smith et al., 2011), especially under limiting conditions. The
elements most often limiting to production are the macronutrients
N, P, and K, although growth may be limited by supply of any ofthe essential elements. Many soil processes are directly affected byplant activities, especially in the rhizosphere. Because of soil–root–
microbial interactions, the biophysical and chemical properties of
the rhizosphere are different from those of the bulk soil.
To meet the crop nutrient demand, nutrients must be transported
from the bulk soil into the rhizosphere toward the root surface(Marschner and Marschner, 1995). The most simple single root
uptake model considers soil nutrient transport by convection anddiffusion, desorption of nutrients from the soil solid phase, anduptake at the root surface, as by Michaelis–Menten kinetics (Darrah
et al., 2006). For nutrients of low mobility, uptake models include
root hairs, root exudation, and arbuscular mycorrhizal fungi ineither rhizosphere scale models (Schnepf et al., 2008a,b; Schnepf
et al., 2012) or in root system scale models (Tinker and Nye, 2000;
Roose et al., 2001; Schnepf et al., 2012). In addition, nutrient uptake
models have been coupled with water flow models (Somma et al.,
1998; Roose and Fowler, 2004). Rhizosphere modeling includes
root-induced changes in soil hydraulic properties through mucilage
exudation and related effects on water and solute dynamics in theroot zone as presented by Carminati and Vetterlein (2013). However,
the release of rhizodeposits by roots and associated microbial activity enhances soil organic matter decomposition (Kuzyakov andDomanski, 2000) and would require the inclusion of microbial andcarbon dynamics (Darrah, 1991).

Biomass Production for Food, Fiber,and Energy

Besides nutrients, plants also need water. The adequate description of water stress onset and water uptake distribution in soil is
crucial for predicting plant growth transpiration flux and crop
yield. Although we know water transpiration stream is driven byclimatic demand and controlled by plant and soil, questions remain
regarding the location and magnitude of controlling or regulating
mechanisms for plant water flow (Lobet et al., 2014).

By providing and storing nutrients and water, as well as serving as
mechanical support for plants, soil plays a central role in biomass
production. Soil also provides biochemical support for plant-essential symbionts. Optimizing crop and biofuel production relies ona thorough understanding of plant requirements, soil water andnutrient availability, and on plant uptake mechanisms. This can be
partly achieved via experimental work, but modeling is needed toinvestigate complex interactions and feedbacks between bulk soil,
rhizosphere, and plant systems under environmental constraints.
Examples of models addressing this ecosystem service are listed
in Table 2.

Bulk soil acts as a storage for water, and rhizosphere hydraulicproperties control the availability of water to plants (Couvreur etal., 2014). Root segment–scale models (called mesoscopic) havebeen developed that explicitly solve axisymmetric Richards equation around a given root segment (Philip, 1957; Gardner, 1960;
Raats, 2007) and allow one to estimate the soil hydraulic resistance.
Yet, soil compaction induced by root growth, shrinkage–swellingof roots and soil leading to gap formation between soil and root,and specific nonequilibrium processes induced by mucilage, forinstance, challenge these equations.

Plants change their bulk soil environment to maximize nutrient
and water availability, affecting nutrient and water cycling (see“Water Cycling” above). Interacting biological, chemical, and physical processes affect crop root uptake and production (Lynch, 2007;
Hinsinger et al., 2009; Richardson et al., 2009; Den Herder et al.,At the plant scale (called macroscopic scale) different approaches
exist to account for root water uptake. Typically a sink term is
included in the Richards equation, which includes soil resistance,
plant root distribution, climatic demand, and sometimes acompensation term (Javaux et al., 2013). The challenge is to find

Provisioning Services

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a mathematical expression for the root water uptake (or sink term)that best represents the key mechanisms embedded in a numerically
acceptable level of complexity for the application. The upscaling ofcomplex and dynamic rhizosphere processes can be assessed withthe help of mathematical modeling (Roose and Schnepf, 2008).
Different one-dimensional models have recently been proposed(de Jong van Lier et al., 2008; Jarvis, 2011). Couvreur et al. (2012)
developed a simple one-dimensional solution, considering complex
three-dimensional representations of root architecture. Siqueira
et al. (2008) suggested solving two one-dimensional Richards
equations to represent three-dimensional root water uptake. Novelroot growth models and tomography techniques have recently
allowed the development of three-dimensional models (Dunbabin
et al., 2013) that explicitly represent the root system architecture
an connect it to a sink term (see Fig. 4 with an example of a threedimensional simulation of root water uptake using the R-SWMS
model (Javaux et al., 2008).
At larger scale, the availability of many different models forroot water uptake translates into high uncertainty in predicting
transpiration. For land surface models, Wang and Dickinson(2012) showed that the ratio of transpiration to total ET ranged
from 0.25 to 0.64 for 10 widely accepted models, with an averageof 0.42. This uncertainty is due to the poor representation orvalidation of root water uptake modules, in particular under dry
conditions (Li et al., 2013; Canal et al., 2014) and in terms ofcompensation mechanisms (Tang et al., 2015).
An additional modeling challenge is to link soil–root zone
processes at the rhizosphere scale to the spatially variable landscapescale (Katul et al., 2012). Land surface or crop models typicallyhave a grid size between 100 and 100 km2 , in which plants uptake
is modeled in zero or one dimension for the sake of simplicity
and computational efficiency. In zero dimension, when spatially
explicit information is not available, the effects of soil properties
on nutrient and water uptake is treated simply by considering total
availability and access of soil water and nutrients in the soil. Moreadvanced crop models apply one-dimensional soil modeling, using
a simplified water balance and simple root depth models (Gerwitz
and Page, 1974) and thereby neglecting spatial variations in soil
water or nutrient content and uptake rates. However, in spatiallyvariable soil–root condition, the one-dimensional assumption does
not hold and may lead to erroneous results of ET and crop yield,
especially in soil-stressed conditions (Roose and Fowler, 2004).

Soil Physical Support
Most terrestrial ecosystems rely on soil for their physical supportand stability. The functional design of plant roots is optimized forsufficient anchorage to the ground (Coutts, 1983, 1986; Coutts
et al., 1999). Large trees and perennial shrubs especially have rootsystems that are intimately linked with the soil underneath, whichenables them to support the enormous weight of their own biomass
and external loads (such as animals and snow) as well as dynamic

VZJ | Advancing Critical Zone ScienceFig. 4. Relative water saturation in soil around a root system taking up
water simulated with R-SWMS.

stresses from wind, debris flow, and surface runoff (Stokes et al.,2014). Soils also bear the weight of all terrestrial animals and provide habitat to burrowing animals including rodents, birds, andinsects. At finer scales, soils provide physical support to microbialcommunities. The highly modified environment in the rhizosphere as well as biological soil crusts in many desert ecosystems
provide stable microstructure that serves as a habitat for microbialcommunities. In summary, physical support service provided bysoils is an essential ingredient for the health and sustainability ofterrestrial ecosystems. Soils also provide direct support services toengineered structures as well as human activities. In many places,soil—in the form of mud bricks and dirt roofs—literally serves asa physical shelter. Likewise, unpaved dirt roads and paths are vitalaccess routes and essential in management of natural resources.
A soil is able to provide the above stated services when its strengthis sufficient to support the stresses exerted on it, yet not too strong
to resist necessary deformations, such as for root growth andanimal burrowing. Therefore, a great deal of research related tosoil as a physical support system has been directed toward understanding distribution and propagation of stress and strain in soil,
as well as in quantifying the underlying rheological characteristics(including elasticity, plasticity, and viscosity) (Baumgarten et al.,2013; Hallett et al., 2013). The ability of heavy clay soils to provide
physical support may also be compromised when they swell andshrink on wetting and drying, respectively. In the United Statesalone, expansive soils cause billions of dollars of damage to civil
structures (Thomas et al., 2000). However, we need to include theaspect of rigidity in all our modeling approaches also because theshrink–swell processes alter the reference volume and may resultin a complete overestimation of, for example, flux processes (Hornp. 17 of 57

et al., 2014) Similarly, drainage of peatlands and soft organic soils
causes substantial consolidation that adversely impacts their physical support service (Schwarzel et al., 2002). The latter is further
exacerbated by progressive organic matter loss from drained soils(Dawson et al., 2010).
To gain a full perspective on the soil’s physical support services,
we need to have quantitative understanding of the following key
aspects of soil strength: (i) mechanisms of support in relation to
specific soil strength parameters, which includes mainly tensile
strength, compressive strength, and resistance to stress dependentshearing; (ii) properties that define shrink–swell potential of clays
and compressibility of peats; (iii) soil strength thresholds relevant
for the physical support functions; (iv) temporal dynamics of soil
strength and its relations with soil moisture and temperature; and(v) spatial variability of soil strength at multiple scales; and (vi)alteration in physical support through the growth or degradationof biological structures such as plant roots.
Fundamentally, the ability of soils to provide physical support
functions is a product of interplay between stabilizing and destabilizing processes. The key stabilizing processes include: soil
aggregation, which is mediated by a variety of physical, chemical,
and biological processes; cementation by mineral deposits; andstabilization by burrowing animals. Soil stabilization is continually countered by destabilizing processes, including shearing forces,
dynamic mechanical stresses, static loads, and slaking.
Theories and models of soil as a physical support system must
involve the following key elements: (i) basic theories and modeling capability concerning mechanical strength, stress, strain, andtheir distribution in soils, which are generally well understood formost soil conditions over wide scale ranges; (ii) reliable techniques
to quantifying stresses and strains, which are also well developed,
especially for stress propagation under traffic; (iii) combined
physical, chemical, and biological processes as the most influential
parameters to strengthen soil systems, including the dynamic stressstrength changes due to hydraulic processes also in mechanicaltheories; and (iv) quantitative understanding of particle-scale soil
strengthening and further extrapolation from the interparticle tothe meso- or macroscale.
The major open questions related to mechanistic understanding and modeling of physical support functions of soil include:(i) transient phenomena, including short-term elastic and elastoplastic responses, as well as transient coupled interactions between
mechanical, hydraulic, and biogeochemical processes; (ii) stabilizing and destabilizing processes; and (iii) stress-dependent changesof soil hydraulic, thermal, and gas diffusion processes.

Soil and Biological Habitat
Life in soil follows much the same pattern as human life on the surface of the planet. For life to persist, soil microbes require sufficient

VZJ | Advancing Critical Zone Science

accessible food resources, water, safe refuges from predators, andgaseous and hydraulic transport pathways through which they
move (if motile) and be active. In terms of the soil geometry to provide the physical living habitat, key soil attributes are its porosity
and its continuity and level of connectivity in space and time. Thus,
soil pore and hydraulic connectivity, specific surface area, and tortuosity become key determinants of all processes that impact onsoil life. The spatial distribution of porosity and nutrients determine distances between active microbes (and roots), whereas theconnected porosity determines the rate at which soil gases as CO2
and O2 can diffuse between microbial active sites. Therefore, thesoil water characteristic becomes one of the most important relationships in soil ecology (Assouline, 2013).
A traditional approach to understanding and modeling of the soil
habitat, driven by the need to capture field relevant and observable
metrics, has been coarse structural measures, together with somemeasure of “structure” through aggregate and pore size distribution and stability. The latter has driven the majority of researchin this area despite the fact that the level of aggregation is the relevant metric to capture and understand for most soils (Young etal., 2001). Many conceptual models on aggregates exist (Six et al.,2004), but are rarely put into actual mechanistic models. However,understanding the relevance of soil architecture within as it varies
over time is a difficult task due to the complexity of the processes athand and the significant spatial–temporal soil dynamics. In addition, what delineates soil from all other porous media is the myriadof life and its impact on the soil’s physical architecture (Young etal., 2001). Soil formation was discussed in the above section by that
name; the section “Biological Activity” addresses the incredible
diversity and abundance of microbes.
The challenge in relation to modeling habitat space is its linking
to the relevant functions. Biodiversity research in soils has failed
generally to account for the soil habitat that controls many of therelevant processes that generate soil biodiversity, the probabilityof movement of microbes and higher organisms, and the probability of gene transfer and the impact of pathogens on crop plants
Therefore, the inclusion of the soil habitat in biodiversity modeling(Young and Crawford, 2014) will ensure evaluations of the importance of soil geometry on soil biodiversity, including effects ofspatial isolation and population connectedness (Zhou et al., 2002).
Notwithstanding the difficult challenge of quantifying biological processes in any natural environment, modeling soil biologicalprocesses present specific challenges related to the complex andheterogeneous medium, limited observational capability into theopaque soil, and the wide range of scales where biological activity
matters. The issue of scale is particularly difficult, as modelers are
required to consider interactions taking place at the scale of microbial communities in pores (Young and Crawford, 2004; Or et al.,2007) all the way to root function affecting soil processes overlarge expanses of agricultural lands and forests (Dimitrov et al.,p. 18 of 57

2014). Description of dynamic changes in flow and transport andthe response of biological agents to the changes in aquatic habitats for microbes (Wang and Or, 2013) or the dynamic formationof microniches within soil aggregates that promote denitrification (e.g., Tiedje et al., 1983), require the balance between root
uptake and deep drainage and other soil physical and chemical
processes. Adding to the challenge is the soil opacity that hinders
direct observations and thus necessitating surrogate measures andmethods to obtain model parameters. Soil biological activity alterpore geometry characteristics, and related soil transport parameters. The changes and associated feedbacks may be gradual andslow (root growth) or occur overnight (earthworm burrows, ants,
and termites), thereby drastically modifying soil conditions

66Challenges in Dealing

with Soil Heterogeneity
and Uncertainty

Major challenges in soil modeling across all subdisciplines arise
from the fact that the soil environment is very heterogeneous, thatprocesses occur over a multitude of spatial and temporal scales,
and that one has to deal with uncertainties in both models anddata. It is the objective of this section to discuss these issues. In thefirst part, the effect of heterogeneity on the system’s functioningat various scales and how this is translated into model concepts
and model parameterizations is discussed. Heterogeneities andhierarchical structures may lead to different system behavior,requiring different model concepts to describe processes atdifferent scales and locations. The second part discusses how
appropriate model concepts and model parameters can beinferred from observations, bearing in mind that observations
may be uncertain, variable in space, and not representative for the
scale at which model predictions are made. Sophisticated model
concepts and parameterization procedures increase the precisionof model predictions at the location where measurements used toparameterize the model are obtained. However, local conditions
and predictions may not be representative, so the accuracy of
precise local predictions may be low for the conditions andthe region for which predictions are requested. The third partaddresses the issue of prediction precision and accuracy and its
consequences for model selection and parameterizations.

Heterogeneity: Aggregate toLandscape, Microbe to Forest, Grains
to Ecology
Most soil processes and related soil ecosystem functions dealt within this paper depend in one way or another on the architecture ofsoils, which determines the geometry and topology of the porespace inhabited by soil biota and through which water, gases, solutes, and particulate matter transit. The architecture of soils is
acknowledged as being heterogeneous at many different scales, all

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the way from the distribution of soils across the landscape down
to microscopic pore networks and the molecular structure of biogeochemical interfaces.
At large spatial scales (field to landscape scale), the distribution ofsoils is mainly determined by geology, topography, climate, andland use, whereas at smaller scales (pedon to pore scale) the continuous flow of energy promotes physical and biochemical structureformation. This produces characteristic soil architectures thattypically change vertically along the main direction of flow andtransport within soil profiles. Because of the nonlinearity of thedifferent interacting processes of structure formation and decay,these changes are often distinct, leading to heterogeneous structures and vertical organization of soils (e.g., layered soil profiles).
An immediate consequence of the heterogeneous structure of thesubsurface across spatial and temporal scales is that observed flow
rates of water, gases, and solutes or the dynamics of state variables,such as soil moisture, temperature, and biological activity, typicallydepend on the scale of observation. Thus, models of soil processes(e.g., flow and transport or matter turnover) need to account forthis heterogeneity, and we will discuss possible options and limitations in this section. A major challenge when one attempts tomodel physical, chemical, or biological processes in soils is the
opacity of soil materials that hampers the quantification of theirarchitecture.
An optimistic “fundamental approach” to represent a soil would
be to describe it at the pore scale with, for instance, the Stokes
equation describing the flux of water and air, the Young–Laplace
equation describing the vapor–liquid interfaces, multicomponent
transport equations with associated equilibrium relations at phaseboundaries, a slew of equations for the multitude of chemical interactions, and yet more complicated representations of the microbial
realm. For any reasonably sized soil volume, however, this is clearlyneither possible due to the lack of detailed information and limited
computing power, nor is it desirable because of the sheer flood of
mostly redundant information. Thus, it is one of the recent challenges to develop more theoretical approaches that deliver correct
representations of a given range of subscales and range of smallscale processes that reproduce the system’s behavior at a larger scalewith a desired level of accuracy (Daly and Roose, 2015).
The general approach to gain a representation at some larger(macroscopic) scale is to average the pertinent processes at thecorresponding smaller (microscopic) scale over an appropriate
domain. Necessary prerequisites for this approach to work are (i)that the macroscopic quantities are robust with respect to changes
in the averaging domain and (ii) that the microscopic quantities
are in thermodynamic equilibrium at the scale of the averaging domain. Given the wide temporal spectrum of forcings, forexample, through precipitation, such an averaging is restricted torather small domains. The issue is further exacerbated by nonlinear
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processes like soil water flow, transport of reactive solutes, freeze–
thaw cycles, or evaporation–condensation processes, which are
all capable of generating sharp fronts and intricate patterns. The
proper handling of such processes remains an open research question. Current engineering solutions typically involve the postulates
that (i) the large-scale mathematical formulations are of the same
form as those at small scales and (ii) so-called “effective parameterizations“ can be found, which complement the large-scale
formulations. An example is the consideration of nonequilibrium
phenomena by decoupling state variables through an additional
equation at the larger scale (Ross and Smettem, 2000). These
effective parameters are typically gained from inverting physicalnumerical models. However, there is no evidence that the postulates are valid. It appears that proceeding to larger scales—to a fieldor even to a larger catchment—demands numerical simulationsof the pertinent multiscale processes and quickly runs into supercomputer applications that include self-adaptive discretizations.
In the case of biological processes, such as microbial activity,
subsurface heterogeneity fosters the coexistence of biochemical
processes that cannot be captured or reproduced experimentallyin homogenized materials. This is true for the concurrence of aerobic and anaerobic processes, as well as for the turnover of organic
matter in general, which is promoted or hampered depending on
the relative spatial distribution of soil biota and substrate. Whileits importance is well recognized, it is still unclear how to represent this heterogeneity in modeling biological activity and organic
matter turnover.

Model Concepts
Homogenization is a possible approach in the case when thevarious scales of heterogeneity are clearly separable, so that
information from small scales can be transferred to larger scales
in a meaningful way. In this case, small-scale heterogeneities can beaveraged in time or space toward homogenized large-scale models
that account for all the essential ingredients from the small-scale
processes. Separable scales might rather be expected at small scales
when moving from soil pores to aggregates and up to soil horizons.
Here we can identify different levels of macroscopic homogeneity.
Examples for homogenization include derivation of the Darcy flow
and Richards equation (Daly and Roose, 2015), solute movementin the soil with dual porous structure (Zygalakis and Roose, 2012),
uptake of nutrients by root hairs (Leitner et al., 2010; Zygalakis etal., 2011), and effects of exudation by cluster roots and resulting
plant P uptake (Zygalakis and Roose, 2012).
If the scales of heterogeneity are interlaced and nested, which istypically the case at the pedon scale and beyond, modeling soil
processes needs to be adapted to the spatial or temporal scale
representing the relevant heterogeneity at this scale. The crucial
question is to determine what is “relevant.” The dissipative natureof most processes may help to address this question. In some cases,
perturbations at a given scale may smear out when the observation

VZJ | Advancing Critical Zone Sciencescale becomes much larger. This may not be true when the perturbations at the microscopic scale are associated with microbialactivity. However, this assumption applies, for example, for thetransport of solutes through the soil pore network that develops
towards a volume-averaged Fickian regime once the transport distance is much larger than the characteristic heterogeneities within
the flow field. Another example is the rapid drainage or filling of
single pores that translate into a smooth curve, known as the soil
water retention curve, at the larger scale. In both cases, the problem faced in reality is that heterogeneities at larger scales emerge
before the limit of a well-defined macroscopic behavior is reached.
A possible way to deal with this is to explicitly include the heterogeneity at the well-defined subscale, while heterogeneities at the
sub-subscale and smaller scales are described by effective parameterizations and averaging (Vogel and Roth, 2003). Examples,
where this concept is typically applied include (i) water dynamics
in soil profiles, where effective mean hydraulic properties are used
for soil horizons; (ii) water and gas exchange between the soil andthe atmosphere, where the lateral distribution of soil types is considered; and (iii) solute transport in groundwater, where only thecoarse structure of the conductivity field is explicitly considered,
while smaller scale heterogeneities are integrated into an effective
dispersivity length.
Concerning biochemical processes, the vast abundance of biodiversity in soils may allow for simplified representations at larger scales
since biological communities and their biological potential andactivity are controlled by the local site conditions and the metabolism of individual organisms in any specific part of the pore space
is not relevant. This might be true for highly productive soils inhumid regions. However, especially in water-scarce systems, thefeedback between soil biota, organic matter, and water dynamics
leads to complex patterns of system development (Jenerette et al.,2012) that are just starting to be explored.

Exploring Heterogeneity
Several recent technologies and conceptual tools provide novel
information on subsurface heterogeneity. Among these new methods are noninvasive three-dimensional methods, such as mCT,
chemical imaging, geophysics, and remote sensing with platforms
ranging from unmanned air vehicles (UAV) to satellites. Thesemethods differ widely in their capability, resolution, accuracy, andprecision (see "Modern Sources of Spatial and Temporal Data for
Soil Modeling"). Their most interesting aspects are the scales ofresolution and view. Some may be used in an undisturbed fieldsituation, while others are only applicable in carefully prepared lab
environments. Some capture the entire volume of interest, others
just its surface. Furthermore, the quantity of interest is often notobserved directly, but only indirectly via a proxy. This requires thedevelopment of appropriate transfer functions that are often justempirical relations that need data-intensive calibration procedures.

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The final challenge in representing the functional structure of
the subsurface irrespective of the target scale is the coherent integration of all the information on (i) the multiscale architecture(including the respective material properties); (ii) the process formulation for the chosen range of scales; (iii) the system’s coupling
to the environment, which is typically represented as an external
forcing but should also include the feedbacks to the atmosphere
and/or groundwater; and (iv) the available data, which often need
to be transferred into the chosen range of scales. In this context,
top-down approaches can be highly attractive to make use of themultitude of available information, which will certainly increase in
the near future, quantitatively as well as qualitatively. However, abottom-up approach rooted in fundamental basic science observations is required to complement the top-down approach because
ultimately the integration of the two, top-down and bottom-up
approaches, and their synergy will enable the synthesizing of newscientific knowledge about soil systems. A joint analysis toward a
consistent description of terrestrial systems may help an adequate
representation emerge.

Formalisms for Considering
Uncertainties Related to Model Choice
Uncertainties in soil models may arise on the conceptual level(model choice), on the parameter level (insufficient calibrationdata), through measurement errors, from stochasticity of system
forcing, and from scaling issues. Multimodel ensemble simulations,(e.g., Neuman, 2003; Clark et al., 2008; Wohling et al., 2008;
Gupta et al., 2012), such as Bayesian model averaging (BMA)
are a promising approach to quantify these uncertainties; BMA
reflects conceptual uncertainty through a weighted average ofmodel-wise ensembles. Each model ensemble represents parametricwithin-model uncertainty, restricted to the available data though
Bayesian updating (conditional simulation). The model weights
are given by the so-called Bayesian model evidence (BE), whichcorresponds to P(D) in Eq. [4]. The BE value expresses how gooda model (including its uncertain parameters before conditioning)matches the available data (including their possible measurement
errors), combined with a priori expert knowledge on model plausibility. Recently, Wöhling et al. (2015) demonstrated the advantagesof BMA approaches for soil modeling. Unfortunately, the BMA
approach is challenged by two issues. First, evaluating BE requires
Monte-Carlo techniques to evaluate the fitting quality (on averageover its uncertain parameters) of each model. This may becomecomputationally prohibitive for models with long run times andwith many uncertain parameters (requiring very large ensembles
in the BMA context). As an alternative, the so-called information criteria (IC), such as the Akaike (AIC), Bayesian (BIC), or
Kashyap (KIC) information criterion, are computationally much
more feasible approximations to BE. However, a recent study by
Schöniger et al. (2014) demonstrates that IC often provide very
inaccurate approximations to BE and thus can provide misleading results. Instead, the study reviews and benchmarks a list of

VZJ | Advancing Critical Zone Sciencealternative numerical schemes for more efficient computation of
BME that pose many additional future statistical and numericalresearch questions.
The second challenge in BMA is constructing a set of competingmodels to reflect conceptual uncertainty adequately (i.e., to test
different, plausible hypotheses of the soil–plant system behavior)and to ensure that a model sufficiently close to the “real” system isincluded. In many applications, however, building a model is timeconsuming and expensive, or only a single system conceptualizationis readily available. Even if a large set of plausible models exists, theentire set may, in hindsight, seem inadequate on comparison toextensive and accurate data sets.
Outside the BMA context, parameter-related uncertainty after
calibration can be quantified through classical Bayesian inference
and by Markov chain Monte Carlo (MCMC) simulation
techniques (e.g., Vrugt et al., 2009b; Wohling and Vrugt, 2011).
The use of MCMC is computationally more efficient than thebrute-force Monte Carlo sampling required to operate BMA. Still,
depending on the number of model parameters, the complexityof the problem and the data set size, MCMC can require up
to 10 6 or more model evaluations. If MCMC is not feasible,
uncertainty quantification is still possible when assuming that
all model parameters and measurement errors follow multiGaussian distributions (at least after transformation) and thatthe model equations can be linearized, and then using linear error
propagation (Moore and Doherty, 2005). However, soil–plantmodels are typically highly nonlinear, so that linearized techniquesmust be treated with extreme care.
Because soil models often involve many state variables (e.g., soil
moisture, matric head, transpiration, soil heat flux), the choiceof data types for the above analyses plays an exceptionally largerole. Different data types carry different information about theindividual compartments and their respective processes (Vereecken
et al., 2008). Therefore, the choice of data types has a large impact
on the resulting model predictions, model performance, or model
selection outcome, as shown by Wöhling et al. (2015). In suchsituations, multiobjective optimization (e.g., Marler and Arora,
2004; Reed et al., 2013) is a valuable tool to test how soil models
fit to different data types (Santra et al., 2009; Wohling et al., 2013)used multiobjective optimization as a diagnostic tool to detect
model structure errors and found large contrasts in the fitting
quality to individual or combined data types. They also showedthat an inadequate choice of calibration data sets may result in
unrealistic parameter estimates and poor predictive performance,
particularly for quantities that have not been included in model
calibration. Soil monitoring in the past has been largely restricted
to a limited set of standard observations (e.g., soil moisture), which
may or may not be decisive to inform the parameter inference ormodel selection process. Therefore, the worth of different and newp. 21 of 57

data types for the performance and robustness of predictive models
is an area of research that needs further attention.

Does Local-Scale Model Complexity
Matter for Predictions at Larger Scales?
For local predictions, the processes and the parameters of theprocess model need to be described as precisely and accurately as
possible. Due to soil heterogeneity, information that is available
about local soil parameters or about state variables or fluxes thatare used to parameterize the model is very uncertain. This uncertainty is propagated into uncertainty about predictions, which may
therefore be imprecise. However, for several practical applications,
not the predictions at a certain given site and time, but the distribution of a certain variable in a specific region over a certain period
are required. For predictions of the percentile of the distribution
in a region the set of conditions in the region needs to be represented as precisely as possible. This implies that the model shouldbe able to represent the conditions in time and space that represent
the distribution of conditions for the area and time period thatis considered. The question arises therefore whether it is more
important to have spatial and temporal coverage of informationthat is required to run a simplified and locally less precise modelor whether it is better to use a more detailed and precise representation of the processes at a limited number of locations and time
periods. The problem of the second approach is that the relevanceof the predictions for the region and time period of interest cannot
be evaluated based on the lack of spatial and temporal coverage ofthe model parameters and boundary conditions. The distribution,
which is predicted based on a limited number of conditions orsituations, may therefore lack accuracy.
An illustrative example is the process of pesticide risk assessment
for pesticide registration (Leterme et al., 2007; Vanderborght
et al., 2011). The general principles and questions may also betransferred to other soil processes and predictions. The pesticide
fate parameters (sorption and degradation) often vary strongly
with location, but their variation cannot be predicted or derived
from other soil properties, so these parameters are often treatedas stochastic parameters. Figure 5 illustrates the effect of uncertainty of pesticide fate parameters on the predicted cumulative
distribution of leachate concentrations in a certain region. In
pesticide risk assessment, the question arises whether a prediction
with a detailed process model that requires detailed information

Fig. 5. Illustration of the effect of uncertainty of pesticide fate parameters on the predicted cumulative distribution of leachate concentrations in acertain region. Uncertainty about pesticide fate parameters may lead to large variations in predictions at a certain location (i.e., difference between mapsof predicted concentrations). Considering the distribution of concentrations in the whole region, uncertainty in pesticide fate parameters leads to awider distribution (blue solid curve) than in case fixed or deterministic parameters are considered (red dashed curve).

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about soil properties (including for instance a parameterizationof preferential flow and transport) and temporal information of
meteorological variables (rainfall data with high temporal resolution to capture rainfall intensities that trigger preferential flow)
is to be preferred over a prediction with a much simpler modelthat considers only yearly rainfall amounts and uses information about soil texture and organic matter. The problem withthe first approach is that an area-wide parameterization of adetailed model may not be possible due to a lack of data. For
instance, detailed soil and weather data may not be available
and the area-wide parameterization of preferential flow models
still poses a problem, although recent advances have been madein the development of pedotransfer functions (see “Informing
Soil Models Using Pedotransfer Functions” section) for thesetypes of models (Moeys et al., 2012; Tiktak et al., 2012). The
second problem is that computational resources may still be limiting to carry out simulations for millions of scenarios that are
required to represent the distribution of soil, vegetation (crop),
and weather conditions and to consider uncertainties or spatial
variability of stochastic parameters that cannot be mapped. A
workaround for this problem is to use meta-models that are
calibrated on a limited number of simulation runs that are performed using more detailed models (Tiktak et al., 2006; Stenemo
et al., 2007). Such meta-models are simple regression models thatmake a direct link between available input parameters and themodel output of interest. The structure of the regression model
can be based on analytical solutions of the process model that are
obtained for certain boundary and initial conditions. Since they
are much simpler, meta-models can easily be used to make predictions for a large number of scenarios and conditions. This allows
evaluation of the effect of stochastic parameters on the spatial
and temporal distribution of the prediction of interest, which
generally requires a large number of simulations. In general, stochastic parameters lead to wider distributions of predictions in acertain region for a certain time period (Heuvelink et al., 2010;
Vanderborght et al., 2011). In addition, the error in meta-model
predictions (lack of precision) could be treated similarly to theuncertainty due to stochasticity of the parameters. It is trivial
that uncertainty about the parameters or stochasticity and lackof precision of the model may lead to large uncertainties in thepredictions at a certain location. This prediction uncertainty canbe reduced by determining the specific parameters at that location using for instance inverse modeling. However, the accuracyof this parameterized model to make predictions at other locations, where parameters are unknown, is small. Although theprecision of predictions at a certain location might be low due
to stochasticity of parameters and lack of model precision, thedistribution of the predictions in a certain region is less affectedby parameter stochasticity and model uncertainty when there
is a large range of conditions and properties in the region andtime period.

66Numerical Approaches andModel Data Integration

Most of soil processes are strongly nonlinear and controlled
by time-variable boundary conditions requiring numerical
techniques to obtain solutions for states and f luxes. In thissection, we discuss the most commonly used numericalapproaches in modeling soil processes. Within model–dataintegration we use the terms forcing data and forcings for data
used to drive a model, such as most common meteorological input
including radiation, temperature, precipitation, air humidity, orwind velocity, among others. We discuss current approaches formodel–data integration in the framework of operational research,data assimilation, and Bayesian methods.

Numerical Approaches

Advances in measurement technology, computing technology,
and numerical techniques enable the development of models of
ever-increasing levels of sophistication. Such models, capable ofdescribing the inherent heterogeneity of soil environments, thetemporal and spatial variability of boundary conditions, and thenonlinearity of involved processes and various constitutive relationships are usually obtained using various numerical techniques.
The numerical solution of the Richards equation (Eq. [1]) has
always been highly challenging due to its dramatic nonlinearity. Early applications of numerical methods for solving variably
saturated flow problems generally used classical finite differences.
Integrated finite differences, finite volumes, and finite element
methods became increasingly popular in the 1970s and thereafter. While finite difference methods today are used in a majority
of one-dimensional models, finite volume methods and/or finite
element methods coupled with mass lumping of the mass balanceterm are usually used in two- and three-dimensional models. Finite
element and finite volume methods used with unstructured triangular and tetrahedral elements allow for a more precise descriptionof complex transport domains compared to finite differences. Most
popularly used vadose zone flow models (e.g., van Dam et al., 1997;Šimůnek et al., 2008) presently utilize the mixed formulation of
the Richards equation and the numerical scheme of Celia et al.
(1990), which possesses mass-conserving properties for both finite
element and finite difference spatial approximations. Other massconserving numerical approaches are also available (e.g., Rathfelder
and Abriola, 1994). To overcome problems of numerical stability
and convergence of the numerical solution, especially for problems
involving infiltration into initially dry soils, various primary variable switching techniques have been proposed (Forsyth et al., 1995;
Diersch and Perrochet, 1999; Krabbenhoft, 2007). Advances innumerical techniques allowing coarser spatial and temporal discretizations are urgently needed (Vogel and Ippisch, 2008).
The numerical solution of the convection–dispersion equation (Eq.
[2]) presents a different challenge, due to its simultaneous parabolic

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and hyperbolic character. Methods available to numerically solve
the convection–dispersion solute transport equation can be broadlyclassified into three groups: (i) Eulerian, (ii) Lagrangian (or methodof characteristics), and (iii) mixed Lagrangian–Eulerian methods. In
the Eulerian approach, well suited for parabolic equations, the transport equation is discretized by means of a usual finite difference or
finite element method using a fixed grid system. For the Lagrangian
approach, (e.g., methods of characteristics), well suited for hyperbolic
equations, the mesh moves along with the flow, or remains fixed in a
deforming coordinate system. A two-step procedure is followed for amixed Lagrangian–Eulerian approach. First, convective transport isconsidered using a Lagrangian approach in which Lagrangian concentrations are estimated from particle trajectories. Subsequently,
all other processes including sinks and sources are modeled with
an Eulerian approach using any finite element or finite difference
method, leading to the final concentrations.
For certain problems, such as convection-dominated transportor the transport of steep fronts, the Eulerian method can lead to
artificial oscillations (under or over shooting) or numerical dispersion due to truncation errors of the discretization (Neumann et al.,2011). Although these numerical oscillations can be minimizedby the use of upstream weighting, this can lead to considerable
numerical dispersion. Since in many applications the presenceof even minimal oscillations (such as negative concentrations inreactive transport models) can corrupt the solution, there exists
a large family of schemes that aim to suppress such oscillations.
These schemes, which use various types of flux/slope limiters, arecommonly referred to as total variation diminution schemes (e.g.,
Leonard, 1991), and they dramatically improve the solution nearsteep gradients and remove under- and overshoot problems by preserving local monotonicity.
A system of linear equations, resulting from discretization of
governing partial differential equations, is usually solved using
different types of iterative matrix solvers, such as the preconditioned conjugate gradient method (e.g., Herbst et al., 2008a), thegeneralized conjugate residual method Orthomin (e.g., Mendoza
et al., 1991), or algebraic multigrid methods like SAMG (Jonesand Woodward, 2001; Stuben, 2001).
Advances in computing technology allow development of codesthat significantly decrease the computational time by distributing complex large-scale problems over multiple processors working
in parallel (e.g., Vereecken et al., 1996; Hardelauf et al., 2007).
Standard parallelization approaches, such as MPI (message passing
interface; Balay et al. (2015) and OpenMP (open multiprocessing),
are currently being used to develop codes for both distributed andshared memory platforms, (e.g., Steefel et al., 2015). Parallelization
is especially valuable for reactive transport models, in which evaluation of various biogeochemical processes consumes substantiallymore computational time than evaluation of flow and transport
processes. The principal benefit of parallelization is that highly

VZJ | Advancing Critical Zone Sciencecomplex simulations can be performed in hours on a massively
parallel computer instead of weeks on a desktop computer. While
such models are readily available for computer systems runningLinux or Unix operating systems, they are not yet readily available for personal computers with the Windows operating systems.
Since most of the soil models are based on systems of partial differential equations, generic partial differential equation solvers
that were originally developed in computational fluid dynamics
are becoming more widely used in soil modeling. These tools offer
the advantage that the model development can be separated fromits numerical solution, at the same time providing highly efficient
numerical solvers for different classes of problems. Examples are
OpenFOAM (www.openfoam.org), Dune (www.dune-project.org/),and FlexPDE (www.pdesolutions.com) (accessed 27 Apr. 2016).

Novel Optimization Methods and Their
Application to Soil Modeling

Model predictions for flow and transport processes in the unsaturated zone are affected by systematic and random errors. This
concerns model input parameters like saturated hydraulic conductivity, model forcings like precipitation, model initial conditions
like soil moisture content or carbon pools, and boundary conditions like the functioning of drainagee. The model itself is also
affected by errors because some processes might be misrepresented
and other relevant processes not included in the model (e.g., preferential flow). In addition, model parameters are not necessarily
experimentally viable to measure, or perhaps data need to betransformed before it can be used within a model (inverse modeling). Temporal and spatial soil data can be expensive to collectand knowing how much data are useful for models can be hardto gauge, as discussed in “Does Local-Scale Model Complexity
Matter for Predictions at Larger Scales?” Upper and lower bounds
can be derived for parameters and models are used to find the best
estimate for those parameter values (fitting a given data set) via
the use of operational research. Operational research is a disciplinethat uses advanced analytical methods to help find a better solution for a problem (lower cost) or predict what may happen to
a commodity/resource in the future (forecasting). The advanced
analytical methods are generally in the form of algorithms which
are used to find the optimal solution of a problem. The main
properties of an algorithm include the run time, convergence, andfunction calls. These properties are different between algorithms,
with each algorithm having its own strengths and weaknesses forcertain types of problem. For a nontrivial problem, picking the“best” algorithm increases the chance of finding an optimal solution given desired constraints.
An optimization problem is generally of the form
minimizesubject toF( X 1 , X 2 ,¼, X n )g i ( X ) £ 0, i = 1,¼, nichi ( X ) = 0, i = 1,¼, nec[3]

p. 24 of 57

for an objective function F(X), with n parameters (X = [X1, X2 ,...
Xn]), nic inequality constraints g(X), and nec equality constraints
h(X). The type of variables used can either be integer, continuous,or mixed depending on the problem (Winston and Goldberg, 2004).
The mathematical models used to describe water or nutrient flow
or solute transport in soil and uptake into plant root systems can
produce complex parameter search spaces where numerical simulations often provide the best solution. When trying to validate suchmodels to experimental data, a set of parameters are often constrained to vary within specified upper and lower bound, ensuring
a realistic solution. This often leads to a nonlinear unconstrained
optimization problem that can be solved using a given algorithm.
Nonlinear unconstrained optimization methods can be split into
two categories, local and global optimization methods. Local optimization methods, or decent methods, can be categorized further
into zero-, first-, or second-order methods. Zero-order methods
do not use any derivatives of the objective function throughout
the optimization process, for example, simplex search (Nelder andMead, 1965), Hooke and Jeeves method (Al-Sultan and Al-Fawzan,1997), and a conjugate direction method (Powell, 1964). Firstorder methods take first-order derivatives of the objective function
throughout the optimization process, for example, gradientdescent (Guely and Siarry, 1993), quasi-Newton’s method (Dennis
and More, 1977), and a conjugate gradient method (Gilbert andNocedal, 1992). As it follows, second-order methods use secondorder derivatives throughout the optimization process, for example,
Newton’s method (Battiti, 1992), a trust-region method (Byrd etal., 1987), and Levenberg–Marquardt method (More, 2006). Firstorder derivatives give an indication of which direction to search in,
whereas second-order derivatives give an indication of how far to
search in a possible optimal direction. Local optimization methods,
however, converge to local optima and do not necessarily perform
well on the global scale, relying heavily on good initial starting
points. For complex search spaces, where there are many local optimal points, local search algorithms tend to perform worse thanglobal search algorithms due to converging early or being stuck at
one of the many local optimal points.
Global optimization methods can be split into two types, deterministic and stochastic. Deterministic methods involve no elementof randomness. Therefore, any change to the optimal solution
comes from different initial starting points or parameters set atthe beginning of the optimization process. Deterministic global
optimization algorithms include Lipschitz optimization ideas(Shubert, 1972), covering methods that iteratively tighten bounds
on the global solution (Hansen et al., 1991), and generalized
descent methods where local optima are penalized to encourage
global search (Cetin et al., 1993). Stochastic global algorithms
include clustering methods (Torn, 1977), random search methods
such as simulated annealing (Aarts and Korst, 1989) and genetic
algorithms (Horst et al., 2002), and methods based on stochastic

VZJ | Advancing Critical Zone Sciencemodels such as Bayesian methods (Mockus, 1989) and Kriging(Krige, 1952; Forrester et al., 2008), which, in addition, approximates the objective function.
There are many algorithms available for use in global optimization,and models can range from having cheap to expensive objectivefunctions, where the number of function calls from an algorithm
can become an issue. Expensive objective functions in combination with a large number of function calls make certain algorithms
unusable. A major concern with global optimization is the numberof variables used within a model, where the greater the number, thebigger the search space and less likely a good solution will be foundwithin a reasonable computational time. For problems with a large
number of variables, approximations models can be used that sacrifice accuracy for speed. Such approximations can take the formof simple regression models (a type of metamodel) and due to theirsimplistic nature, drastically decrease the run time of an algorithm.

Data Assimilation

Traditionally, model–data mismatch is handled in the soil modeling community by inverse modeling techniques. Inverse modelingtechniques adapt, for example, the uncertain soil hydraulic parameters so that observed and simulated time series of model states
coincide more closely. These inverse modeling techniques are typically based on the minimization of a two-part objective function,
which includes the weighted sum of squared deviations between
simulated and measured states and the weighted sum of squared
deviations between posterior and prior parameter values. Thisobjective function can be derived from Bayes theorem assuming
normal distributions for states, parameters, and observations. In
the last decade the focus has shifted toward calculating not justone, but multiple equally likely solutions for the inverse modelingproblem. The MCMC technique is a popular approach in thiscontext (Vrugt et al., 2003). It is a flexible approach that does
not require that states and/or parameters are normal distributed.
However, a disadvantage is that a large number of model evaluations is needed for the characterization of the posterior probability
density function (pdf), especially if many uncertain parameters
are considered and in case many measurement data are available.
Therefore, MCMC is often applied for the estimation of few
parameters only, for example the soil hydraulic parameters of a limited number of soil horizons. The MCMC methods have become
faster with multimethod adaptive evolutionary search approaches(Vrugt and Robinson, 2007; Vrugt et al., 2009a). Recent developments include multiple try sampling, snooker updates, andsampling from an archive of past states (Laloy and Vrugt, 2012).
It allows the estimation of hundreds of parameters with MCMC.
An interesting alternative that has emerged in the context of soilmodel–data fusion is sequential data assimilation (SDA). In thiscase, measurement data are not assimilated in a batch approach,but sequentially, stepping through time. Sequential data assimilation is based on the Markovian assumption, which would imply
p. 25 of 57

that the sequential incorporation of measurement data instead of
the batch approach does not significantly reduce the information
content of the data. A further simplifying assumption which canbe made in SDA for the updating step, is the normal distribution ofstates, parameters and data. The Markovian and normal assumptions give rise to the Ensemble Kalman Filter (EnKF) (Evensen,
1994; Burgers et al., 1998). EnKF needs much less CPU-timethan the McMC approach, although the full posterior pdf also isderived. The sequential nature of the approach is especially suitedfor real-time predictions of, for example, soil moisture evolution. In
addition, the framework is flexible for handling multiple sourcesof uncertainty. A further advantage is that time-dependent parameters can be estimated. The particle filter is another SDA methodand does not rely on the Gaussian assumption (Arulampalam etal., 2002). However, the approximation of the posterior pdf withthe particle filter requires a large number of model evaluations andis not as efficient as the EnKF (van Leeuwen, 2009).
Sequential data assimilation has been the method of choice formodel–data fusion in land surface modeling for more than a decade(e.g., Reichle et al., 2002) and more recently also for groundwatermodeling (Chen and Zhang, 2006). In land surface modeling, thisinvolves updating of soil moisture contents with remote sensing
information, (e.g., Dunne et al., 2007), or in situ measurements(e.g., De Lannoy et al., 2007), and updating of soil carbon pools inbiogeochemistry models, (e.g., Zhou et al., 2013). Soil parameters
are in general not updated in those applications. In the following,
we focus on parameter estimation with SDA for soil hydrological models, which is a less studied subject. Early applications of
SDA in soil hydrology are the one-dimensional synthetic experiments with the assimilation of soil moisture data by Montzka et al.
(2011) with the particle filter and Wu and Margulis (2011) with
EnKF. They updated both states and soil hydraulic parameters ofthe van Genuchten model. Montzka et al. (2013) estimated also
time-dependent variables of a radiative transfer model with theparticle filter and applied the filter on a site in Colorado, USA. Wu
and Margulis (2013) extended their framework for the assimilation of electrical conductivity data and applied the filter to data atsite in California, USA. Although these works showed promising
results, other one-dimensional studies pointed to the limitationsof EnKF. Erdal et al. (2014) pointed out that a wrong conceptual model of the vertical distribution of soil horizons affects soil
hydraulic parameter estimation, and they suggested the inclusionof an additional bias term to improve the filter performance. Erdal
et al. (2015) stressed that especially under dry conditions the pdf ofpressure is highly skewed and EnKF unstable. They showed that anormal score transformation (Zhou et al., 2011) strongly improved
filter performance. Song et al. (2014) estimated two-dimensional
spatially distributed saturated hydraulic conductivities of theunsaturated zone with an iterative variant of EnKF. However,their work made various simplifications, like perfect knowledgeof the other soil hydraulic parameters and a constant rainfall rate.
Integrated hydrological models also model flow in the unsaturated

VZJ | Advancing Critical Zone Sciencezone with the three-dimensional Richards equation. First efforts
are being made to estimate model parameters of integrated models
with SDA. Shi et al. (2014) estimated several soil hydraulic parameters of such an integrated model, assuming a spatial homogeneous
distribution. They used multivariate data assimilation with EnKF.
Pasetto et al. (2015) estimated three-dimensional spatially distributed saturated hydraulic conductivities for the unsaturated
zone using the integrated hydrological model CATHY (Paniconi
and Wood, 1993), assuming perfect knowledge on the other soil
hydraulic parameters. Kurtz et al. (2015) developed a data assimilation framework in combination with the integrated terrestrial
system model TSMP (Shrestha et al., 2014) and showed in a synthetic test the feasibility to estimate three-dimensional spatiallydistributed saturated hydraulic conductivities of the unsaturated
zone at a very high spatial resolution (both 2 ´ 10 7 unknown
parameters and states). Other data assimilation studies with integrated hydrological models excluded parameter updating in theunsaturated zone because of instabilities (Rasmussen et al., 2015).
In summary, SDA is of particular interest in soil modeling forreal-time applications with the need of forecasting, for example,
for real-time optimization of irrigation scheduling. Such applications require often only state updating. A second important areaof application in soil modeling is high-resolution characterizationof two- and three-dimensional distributed fields of soil hydraulicparameters. However, we are still facing many challenges. The
main obstacle is the joint estimation of distributed fields of saturated hydraulic conductivity, van Genuchten parameters a, n, andporosity. Even if enough conditioning information would be available, this is highly challenging given the strong nonlinearity andnon-Gaussianity of the problem. A further problem for real-world
applications is the lack of precise data. In addition, processes likepreferential flow might influence soil moisture redistribution
and are difficult to capture with the standard three-dimensional
Richards equation. We expect an increased use of SDA in thecontext of soil modeling and the use of variants of EnKF thatwork better for the described conditions. It is clear that a successful application requires some simplifications of the estimation
problem, but those should be less stringent than in many current
applications. Finally, SDA is also of interest for estimating timedependent soil and vegetation properties and provides information
helpful for improving monitoring designs.

Bayesian Approach forModel–Data Integration
The usefulness and applicability of soil models for system characterization and science-based decision making depends in largepart on the parameterization that is used to characterize the soil
domain of interest. This includes (among others) the functional
form and assumed spatial variability of (i) the soil water retention and hydraulic conductivity curves; (ii) root distribution anduptake; (iii) biomass, nutrients, and biological activity; and (iv)
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preferential flow, as well as the assumed soil layering, and applied
lower and upper boundary conditions. In principle, in situ observation and experiments in the laboratory could help determine
an appropriate parameterization of the soil hydraulic parameters,presence of flow paths and layering, biologic activity, nutrient type,amount, and distribution and root characteristics. Yet, such data
often pertain to a relatively small soil volume, and the parameters
derived from this analysis cannot readily be used in soil models
that simulate water, ecological, biological, and biogeochemical
processes at much larger spatial scales. Because of the high nonlinearity of the soil hydraulic functions, their application acrossspatial scales is inherently problematic. Specifically, the averaging
of processes determined from discrete small-scale samples may not
be representative of the key processes of the larger spatial domain.
In addition, the dominant hydrologic flow processes may vary
between spatial scales, so that potentially different models need to
be used to describe water flow at the soil pedon, field, or watershedscale, as outlined in the “Heterogeneity: Aggregate to Landscape,Microbe to Forest, Grains to Ecology” section.
In recent years, Bayesian inference has found widespread application and use in the modeling of soil processes to reconcile systemmodels with data, including prediction in space (interpolation),prediction in time (forecasting), assimilation of observations anddeterministic/stochastic model output, and inference of the model
parameters. Bayes theorem states that the posterior probability,
P(H|D), of some hypothesis, H, is proportional to the product ofthe prior probability, P(H), of this hypothesis and the likelihood,
L(H|D), of the same hypothesis given the observations, D, orP( H | D) =P( H ) L( H | D)
P(D)

[4]

where the evidence, P(D), acts as a normalization constant of theposterior distribution, so that the posterior distribution integrates
to unity. The evidence (also called marginal likelihood) can beignored during inference of the parameters, but is of crucial importance in model selection. The hypothesis, H often constitutes somenumerical model, F(x), which summarizes, in algebraic and differential equations, state variables and fluxes, all our knowledgeof the system of interest, and the unknown parameter values, x are
generally subject to inference using the data D. Latent variables
can be used to specify explicitly errors in model inputs (boundary
conditions). For complex soil models the posterior distribution,
P(H|D) is often highly dimensional and analytically intractable,
and Monte Carlo simulation methods are required to approximate
the target (Vrugt et al., 2008, 2009a,b; Laloy and Vrugt, 2012).
The Bayesian approach provides a quantitative framework totreat explicitly all sources of uncertainty, including model input(boundary conditions), model parameter, calibration data, andmodel structural (epistemic) errors. This latter error summarizes the effects of (among others) incomplete knowledge of soil

VZJ | Advancing Critical Zone Science

processes and system heterogeneities. Practical experience suggeststhat model input and model structural errors are most difficult
to describe accurately. These two sources of error do not necessarily have any inherent probabilistic properties that can be easily
exploited in the construction of a likelihood (objective) function.
While we can assume an error model (stochastic or deterministic) for the model input (forcing data) errors, this will be purely
for the sake of mathematical convenience (Gupta et al., 1998).
Consequently, it is very difficult to decompose the residual error
between model simulations (predictions) and data into its constituent sources, particularly in cases common to complex systems
where the model is nonlinear and different sources of error interact
nonlinearly to produce the measured deviation (Vrugt et al., 2005;
Beven, 2006). One key challenge is therefore to improve our understanding of measurement data errors at different temporal andspatial scales. This would improve considerably Bayesian inferenceof soil models as prerequisite for advancing process understanding.
Another key challenge is to improve model calibration and evaluation methods so that they are powerful enough to diagnose, detect,and resolve model structural errors. This is key to improving ourprocess knowledge, and thus a prerequisite for scientific discovery
and learning.
In recent years, much progress has been made in the developmentof process-based model evaluation methods that much better
extract information from the available data (Gupta et al., 2008;
Vrugt and Sadegh, 2013). These methods have been developedin the surface hydrologic literature and recognize that the very
construction of the likelihood (objective) function, as a summary
variable of the (usually averaged) properties of the error residuals,
dilutes and mixes the available information into an index having
little remaining correspondence to specific behaviors of the system.
This inspired Vrugt and Sadegh (2013) to advocate a likelihoodfree diagnostics approach to model–data synthesis. This approach,also referred to as approximate Bayesian computation, uses summary metrics of the original data, rather than the data, D itself.
By designing each metric to be sensitive only to one componentof the model, any mismatch between the simulated and observed
summary metrics can be directly linked to a particular process inthe model. A step back to simpler boundary conditions and system
heterogeneities that allow an analytical solution or analysis of themodel may be a strategy to derive these summary metrics so that alarge step forward can be taken when analyzing numerical model
output with appropriate metrics. An alternative strategy could
be to analyze the model outputs using coherence spectra, wavelet
analyses, and other decomposition methods.
Thus, as community we face a large number of challenges. First,
there is the challenge of improving the description of measurement
data error and uncertainty at different spatial and temporal scales.
This would help us to much better constrain the model input data,and consequently help us understand whether a model is fit for a
purpose (input uncertainty explains model deviations from data)
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or whether structural improvements are warranted (deviation fromdata cannot be explained by errors in boundary conditions). Second
we are challenged to adapt the use of process-based model evaluation
procedures. These methods much better convey which components(equations) of the model are supported by experimental data, andwhich components should be refined. Finally, there is the challenge
of defining summary metrics of the model output that are sensitive only to one particular equation in the model. Of course, muchadditional work is also required on how to best represent soil heterogeneity in our numerical models, and how to incorporate andparameterize processes such as preferential flow. This is a prerequisite to improve our understanding of soil processes.

66Modern Sources of

Spatial and Temporal Data
for Soil Modeling

As soil models become increasingly complex and address spatial
scales larger than the field scale, the input requirements are becoming more and more demanding. In this section, we present existingand new measurement technologies that offer the possibility toprovide model input data to meet the before mentioned needs.
These include remote sensing technology, proximal data sensing
methods combined with geographical databases of soil properties,
pedotransfer functions to derive unknown model parameters fromeasily available soil properties and isotope technologies that allow
a better process identification and validation of water and matter
fluxes in soil models.

Informing Soil Models
Using Remote Sensing

In contrast to proximal sensing (see “Proximal Soil Sensing,Geographical Databases of Soil Properties for Soil Process
Modeling” section), remote sensing typically is the observation ofan object from a larger distance by using platforms such as towers,
aircraft, or satellites. Remote sensing appears to be an importantand promising milestone in soil science (Ben-Dor et al., 2009) andoffers possibilities for extending existing soil survey data sets also
used for larger scales and higher coverage (Mulder et al., 2011). For
the identification of field to regional scale spatial patterns in soil
characteristics, sensors in most cases operate in the visible (VIS,
400–750 nm), near-infrared (NIR, 750–1400 nm), short-wave
infrared (SWIR, 1400–3000 nm), mid-wave infrared (MWIR,
3000–6000 nm), thermal infrared (TIR, 6000–15000 nm), andmicrowave (MW, 1 mm–1 m) regions of the electromagnetic
spectrum. Whereas MW signals are able to penetrate a vegetation
cover, VIS–NIR–SWIR–MWIR sensors require bare soil or low
vegetation to record soil information. Several review papers withdifferent foci have been published on these topics (see, e.g., BenDor, 2002; Schmugge et al., 2002; Metternicht and Zinck, 2003;
Courault et al., 2005; Tang et al., 2009; Ge et al., 2011; Montzka
et al., 2012; Shi et al., 2012; Schimel et al., 2015).

VZJ | Advancing Critical Zone Science

Soil models can be informed by remote sensing in different ways.
For example, these can include providing information aboutmodel forcings, model parameters, state variables, and fluxes, aswell as by indirect methods using the plants as “sensors” of rootzone properties (Wilson, 2009). In the following, we discuss thesemain measurement applications separately, knowing that their roleof informing a soil model can change depending on the modelcharacteristics.

Model Forcings
Models can benefit from remotely sensed model-driving forces
when in situ measurements are not available or do not capture thespatial heterogeneity. Typically, soil models are driven by meteorological measurements, which are operationally recorded by remotesensing (Sheffield et al., 2006), such as for weather-forecast applications. One example is precipitation, measured by microwave
sensors on tower-based and spaceborne platforms. The Global
Precipitation Mission (GPM) is an international network of satellites that provide global observations of rain and snow, building on
its core satellite, Tropical Rainfall Measuring Mission (TRMM)(Huffman et al., 2007). Similarly, networks of local weather-radarsystems are combined to generate area-wide precipitation maps
in high spatial and temporal resolution (Krajewski et al., 2010).
Another system measures land-surface temperature, retrieved operationally by TIR sensors such as the Moderate Resolution Imaging
Spectroradiometer (MODIS) or the Spinning Enhanced Visible
and Infrared Imager (SEVIRI) via a generalized split-window technique (Tomlinson et al., 2011).

Model Parameters
Digital elevation models (DEMs) are among the first remotelysensed data sources to predict soil characteristics. By simple
landform attributes, such as elevation, slope, and aspect, in combination with geostatistical techniques, more information abouta catena such as topsoil gravel content, soil depth (Odeha et al.,1994), clay content (Greve et al., 2012), erosion (Lee and Liu,
2001; Vrieling, 2006), or even soil pH (Castrignano et al., 2011)
can be predicted. However, the acquisition of DEMs, typicallyby Light Detection and Ranging (LIDAR, Liu, 2008), Synthetic
Aperture Radar (SAR, e.g., Gruber et al., 2012), or stereoscopic
optical imagery (Fujisada et al., 2005) is not straightforward
because raw data can contain return signals from human-madeobjects or vegetation rather than bare-earth targets. Nonetheless,a large variety of high-accuracy DEMs are available from local
to global scale. Ground-based and near-ground based (e.g., UAVmounted) LIDAR and structure from motion techniques areproviding proximal tools for high resolution mapping of microtopography and vegetation.
Passive optical sensors operating from VIS to NIR bands typically are designed as multichannel detectors either with a few
broad bands (multispectral) or with more than one hundred
narrow bands (hyperspectral). A hyperspectral imaging system,p. 28 of 57

also known as an imaging spectrometer, is better able to represent the spectral response of a target soil surface and can provide
valuable information about soil properties; already a few examples
for operational application in agricultural management such as
precision agriculture exist (Ge et al., 2011). Specific absorption
features—?550 nm for iron oxide (Viscarra-Rossel and Behrens,2010) ?1730 nm for organic carbon (Ben-Dor et al., 1997), and?2206 nm for clay (Lagacherie et al., 2012)—correlate well within situ measurements of soil properties (Ben-Dor et al., 2009; Bayeret al., 2012; Babaeian et al., 2015).
Other studies do not directly provide a prediction of a soil property
but rather, valuable information via a spectral index. For example,
Galvao et al. (2008) used the absorption band depth values at 2210
nm (kaolinite) and 2260 nm (gibbsite) to develop a spectral-based
approach to describe the silica/aluminum ratio as a weatheringindex. Moreover, regression analyses, including multiple regression
analysis and partial least-squares regression, are the most popular
data-analysis techniques for relating soil properties to reflectancerecords (Ge et al., 2011; Gomez et al., 2012). Further soil properties
estimated by multi- and hyperspectral remote sensing are calcium
carbonate content (Lagacherie et al., 2008), salinity (MelendezPastor et al., 2010; Ghosh et al., 2012), and texture (Casa et al.,2013). The enhanced combination of soil spectral libraries (Brown,2007) and hyperspectral remote sensing may in the future lead to
improved maps of soil properties and may be able to monitor andautomate updates of changes in soil properties.
In some soil models, few of these observed properties can be useddirectly as parameters. Implementation in pedotransfer functions(PTFs) is an alternative approach to informing soil models by theseremote sensing–derived soil characteristics (see “Informing Soil
Models Using Pedotransfer Functions” section).

State Variables
Microwave sensors, such as radars (active) or radiometers (passive),are able to detect variables valid for upper soil layers, including
moisture (Njoku and Entekhabi, 1996; Kornelsen and Coulibaly,2013), roughness (Davidson et al., 1998; Panciera et al., 2009), andsalinity (Komarov et al., 2002). The challenge is to disentangle theimpacts of these variables on the MW signal, to retrieve the variables separately. Typically, salinity can be neglected for most soils,
but differentiating moisture from the altering roughness effects
is a remaining challenge (Shi et al., 1997; Verhoest et al., 2008).
One interesting approach to detect variables is the combination of
measurements obtained at different incidence angles (Srivastava etal., 2003) or different frequencies, that is, with different sensitivity to soil moisture and soil surface roughness. Use of time-lapse
MW observations and coupled-inversion or data-assimilation
techniques with hydrological soil models (see also “Numerical
Approaches and Model Data Integration”) also proved to be oneof the most potent venues for soil hydraulic property estimation

VZJ | Advancing Critical Zone Sciencefrom local to regional scales (Mohanty, 2013; Dimitrov et al., 2014;
Jonard et al., 2015). Other approaches make use of the spatiotemporal variability of surface soil moisture to indirectly estimate
hydraulic properties (van Genuchten, 1980), not only for the topsoil, but also for the root or vadose zone (Montzka et al., 2011;
Kumar et al., 2012).

FluxesEnergy-balance and mass-conservation rules should be consideredwhen informing soil models by remotely sensed flux measurements in the soil–plant–atmosphere continuum. Energy-balancecomponents, such as latent and sensible heat, or water-balancecomponents, such as actual ET, can be retrieved based on surface-characteristic parameters (e.g., leaf area index, land surface
temperature, surface albedo) obtained by a combination of VIS
to TIR data (see also “Informing Soil Models Using Remote
Sensing”) (Bastiaanssen et al., 1998; Mu et al., 2011).

Vegetation Canopy Properties Providing
Information About Soil Status
Spatial heterogeneity of subsurface properties, such as soil moisture,soil texture, and soil structure, as well as biochemical properties(e.g., organic carbon, nutrient status, pH) in combination with climatic conditions, are known to affect plant health (De Benedetto
et al., 2013). Inversely, indirect methods using the plants as “sensors” of root-zone properties (Wilson 2009) can therefore be used
to inform soil models. Rudolph et al. (2015) presented the link
between crop-status patterns in large-scale multispectral satellite
imagery with multi-receiver electromagnetic induction hydrogeophysical data. Moreover, Vereecken et al. (2012) analyzed thepotential of MW remote sensing to identify water stress–related
phenomena in vegetation canopies, which can be related to subsurface properties.
In general, several sensors and methods still make use of groundbased manual measurements using remotely sensed parameter
maps for regionalization and pattern recognition (e.g., Lagacherie
et al., 2012), but the number of solely air- and spaceborne applications for spatial and temporal soil property estimation is limited.
Instead of regression analyses to upscale from point to regional
scale, physical models describing radiative transfer processes need
to be developed. Future technical improvements and new sensor
developments will foster this field of research.

Proximal Soil Sensing, Geographical
Databases of Soil Properties for Soil
Process Modeling
Proximal Soil Sensing

Modeling soil processes at field, catchment, and larger extents
requires access to high resolution and spatially distributed information on soil properties. Proximal soil sensing (PSS) has thepotential to benefit soil process modeling by increasing the costeffectiveness and rapidity of soil characterization and monitoring.
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Proximal soil sensing is the acquisition of information about theobject or feature of interest using equipment either in direct physical contact with the in situ object or very close to it. “Very close”
means within a few meters, usually closer. In relation to soil, proximal sensing is both a very old and a relatively new discipline—oldin that the earliest soil scientists relied almost entirely on visualobservations of soils in the field, and new in that recent technologies have greatly expanded and improved our ability to acquire
information from the soil. Application of PSS will lead to easierprocess-model conceptualization, parametrization, initialization,and evaluation and will reduce the time and effort required in
the “transaction costs” that surround soil modeling. Examples of
PSS technology include portable X-ray fluorescence (Zhu et al.,2011), apparent electrical conductivity measurements using electrical resistivity tomography, (Samouëlian et al., 2005; Koestel etal., 2008), electromagnetic induction (Weller et al., 2007; Saeyet al., 2009; Rudolph et al., 2015), spectral-induced polarization(Slater et al., 2006), ground-penetrating radar (Huisman et al.,
2003; Lambot et al., 2010), and gamma-ray spectroscopy (Rossel
and McBratney, 1998; Rawlins et al., 2007) field NIR spectroscopy (Rossel and McBratney, 1998; Rodionov et al., 2014), andion-sensitive field-effect transistors (Lobsey et al., 2010).

a solution for soil moisture. Rodionov et al. (2014) expanded thesolution to handling moisture and soil surface roughness for thesensing of soil organic C. The use of spectral libraries derived fromdried ground samples to calibrate models that then use field-based
spectra is making good progress (Ge et al., 2014). Sampling andcalibration is another growth area for PSS; these are often considered separately, when in fact they are closely related. The samplingstrategy used in the field or laboratory strongly impacts data
availability for calibration purposes, and the calibration method
employed often places specific requirements on the quantity, variability, and type of data to be used. The interaction of sampling
and calibration has been studied in the iSOIL project (Nüsch et al.,2010) and in other research (Dematte et al., 2006; Brown, 2007;
Sankey et al., 2008).

Adamchuk and Rossel (2010) and Rossel et al. (2011) reviewed
PSS technologies and their applications. Recent developments insensor fusion examine the possibility of linking multiple sensors
with common calibration and data-analysis approaches (Kweon,
2012; Mahmood et al., 2012), which would allow researchers to
capture all of the data required to set up or validate a soil processmodel with one set of readings. A wide, constantly expanding
range of soil parameters can be estimated using PSS, including
particle-size fractions (Buchanan et al., 2012), soil moisture, root
density, and available water-holding capacity (Hedley et al., 2010),
clay content (Waiser et al., 2007), organic carbon (Viscarra Rossel
and McBratney, 2003; Stevens et al., 2013), organic carbon fractions like black carbon and particulate organic matter (Bornemannet al., 2008; Bornemann et al., 2010), and nutrients (Wu et al.,2014a). In addition to measurement of parameters, the evaluationof soil processes may also be amenable to PSS techniques (Dematteand Terra, 2014). Soil parameters estimated from proximal soil
sensors can be an input to a soil inference system, where properties
related to transfer of water, heat, gas, or solute can be estimated(McBratney et al., 2006). This procedure would have obvious benefits for soil process modeling because it would directly capture
detailed information about what is being modeled.

Proximal soil sensing techniques often produce big data that canrequire complex and customized analysis, whereas the priority interms of process modeling will be to increase data availability andeliminate much of the effort required in interpreting the sensor
data. Portable infrared instruments capture ultraspectral (i.e., data
across thousands of wavelengths), reducing the number of data
without losing useful information makes for more accessible analysis (Viscarra-Rossel and Behrens, 2010) or spectral response-based
PSS. In addition, methods of applying three-channel RGB data will
open up the possibility of using digital cameras and mobile phones
for PSS (Viscarra-Rossel et al., 2009; Aitkenhead et al., 2014).
Measurement of soil-horizon characteristics, including depth ofimpermeable layers, is also possible with digital imagery (Islam etal., 2014). Based on hyperspectral camera records it has also beenpossible to provide maps of elemental concentrations for C, N, Al, Fe,
and Mn for each mineral soil horizon. VIS-NIR spectroscopy also
allows differentiation of organic surface layers and the assessmentof their qualitative OM properties with a high spatial resolution(Steffens and Buddenbaum, 2013; Steffens et al., 2014). Digital soil
morphometrics (Hartemink and Minasny, 2014) is a subfield of PSS
in which the spatial variation of sensor reading within the profile isused to enhance information about the soil vertical dimension. In
addition to rapid and relatively inexpensive estimates of soil properties and processes, PSS can also rapidly provide information about
the short-scale spatial heterogeneity of soils, which is of particularuse in modeling soils (Kruger et al., 2013). Proximal soil sensing
can also play a gap-filling role in increasing the level of spatial detailavailable from existing monitoring networks (Ochsner et al., 2013;
Schirrmann et al., 2013), which will be important for soil processmodeling that incorporates spatial processes.

The integration of PSS within soil mapping, monitoring, andmodeling (SM3) is an active field closely linked to the European
Soil Thematic Strategy; notable examples of efforts in this area
are DIGISOIL (Grandjean et al., 2010) and iSOIL (Werban et al.,2010). Several challenges exist, including removal or accounting
for the effects of moisture and soil structure from sensor readings
obtained in the field. (Minasny et al., 2011), for example, provide

As shown above, a number of areas of development exist that will
improve the potential of PSS for soil process modeling. To realize
this potential, the following objectives must be achieved: (i) automated interpretation of sensor data, using standardized calibration
data sets and generally applicable calibration techniques, (ii) elimination of field- or sensor-specific effects on sensor data to allow
calibration from a wide range of available data and sensor types,

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(iii) multisensor or multiparameter readings to allow “snapshots”
of all soil parameters of interest across the whole profile, and (iv)development of methods to allow cheap, mass-produced sensor
devices (e.g., mobile-phone cameras) to be used in crowd-sourced
information acquisition
For each of the above objectives, significant progress has been madein recent years and will continue. In its current state, PSS can anddoes already benefit soil process modeling, and it is anticipatedthat future developments will increase the rapidity and ease withwhich data required for soil process model development, initialization, and validation can be acquired. The IUSS Working Groupon Proximal Soil Sensing (http://www.proximalsoilsensing.org/,
accessed 27 Apr. 2016) provides information and links to eventsand resources of relevance and is the forum in which developmentsin this area are discussed and disseminated.

Soil Databases
Soil information is the key to evaluating ecosystem services likewater regulation, water retention, nutrient regulation, waste treatment, and food production (de Groot et al., 2002). With the helpof computer-based geographic systems, many groups have generated geographical databases to organize and harmonize the hugeamount of soil information generated during the last century. Soil
databases enable the application of soil models at regional to global
extents. Many national agencies around the world have organized
their soil surveys in databases include SSURGO (Soil Survey Staff,
1995), with soil information mainly from the USA, the Australian
Soil Resource Information System (Johnston et al., 2003), theNational Soil Inventory of Scotland (Lilly et al., 2010), and theSoil-Geographic Database of Russia (Shoba et al., 2010).
Besides national databases, global efforts are underway to compile
databases from different countries or generate new soil information through the implementation of multinational projects. These
include the Soil and Terrain Database (SOTER; van Engelen andTing-Tiang, 1995), at 1:5000000 scale, containing digitized map
units and their attributes; the World Inventory of Soil Emission
Potentials, WISE, (Batjes, 2009), from 149 countries; theHarmonized World Soil Database (Nachtergaele et al., 2008) andthe Land Use and Cover Area Frame Survey from the European
Union (http://eusoils.jrc.ec.europa.eu/projects/Lucas/, accessed 27
Apr. 2016; (Toth et al., 2013). All these efforts manifest the need toorganize and distribute soil information within the soil scientificcommunity, and to make it available for interdisciplinary studies.
In 2006, the GlobalSoilMap, a global consortium that aims tocreate a digital map of the world’s key soil properties (Arrouays etal., 2014), was established. This global effort will provide accessto the best available map of soil properties across the globe at aresolution of 3 arc sec (?100 m) along with its 90% confidence ofprediction, in a consistent format at the depth ranges of 0 to 5, 5 to15, 15 to 30, 30 to 60, 60 to 100, and 100 to 200 cm. The methods

VZJ | Advancing Critical Zone Science

used for GlobalSoilMap consider the nature, availability, anddensity of existing soil data. For example, an initial approach to
mapping soil carbon in the United States is based on a 1:250,000
soil map from the USDA-NRCS, in which the soil polygons wereconverted to raster estimates of organic carbon content for thesix depth intervals of the GlobalSoilMap specifications (Odgers
et al., 2012). Thus far, the most comprehensive example of soil
property maps made according to GlobalSoilMap specifications
is the Australian Soil and Landscape Grid (http://www.clw.csiro.
au/aclep/soilandlandscapegrid/, accessed 27 Apr. 2016; Grundy
et al., 2015). Other examples include the mapping of soil texture
and organic carbon in Denmark (Adhikari et al., 2014). Anotherinitiative is the Soilgrids by ISRIC (http://soilgrids1km.isric.org/,
accessed 27 Apr. 2016), which used the GlobalSoilMap specification except that the spatial resolution is 1 km (Hengl et al., 2014).
The aforementioned databases in combination with pedotransfer
functions (see the following section) have been successfully used toevaluate the impact of agricultural expansion (Maeda et al., 2010),
global agricultural suitability (Zabel et al., 2014), nutrient stoichiometry under native vegetation groups (Bui and Henderson, 2013),
and soil erodibility estimates (Panagos et al., 2012). In addition,
global soil information should better inform global climate models(Wilson and Henderson-Sellers, 1985), hydrology models (Weiland
et al., 2010), and road planning (Laurance and Balmford, 2013).

Informing Soil Models Using
Pedotransfer Functions

Pedotransfer functions, empirical relationships between parameters of soil models, and more easily obtainable data on soil
properties have become indispensable in modeling soil processes.
As alternative methods to direct measurements, they bridge thedata we have and data we need by using soil survey and monitoringdata to estimate parameters of soil models. Pedotransfer functions
are extensively used in soil models addressing the most pressing
environmental issues, such as carbon sequestration and gas emission, climate change and extreme events like floods and droughts,
and soil ecological services and sustainability (e.g., Decharme etal., 2011; Piedallu et al., 2011; Wiesmeier et al., 2012). Currently,
PTFs are mostly applied to estimating the soil water retention
curve and soil hydraulic conductivity curve (Vereecken et al.,2010), solute transport parameters (Koestel et al., 2012), erosion
and overland transport (Guber et al., 2014), and adsorption isotherms (Kodesova et al., 2011). However, the pedotransfer concept
can be applied to any soil attribute. In particular, as the interest
in modeling biogeochemical processes increases, development of
PTFs for parameters of those processes will become essential. The
process of PTF development is outlined in Fig. 6.
Because the equations to express PTF relationships are essentiallyunknown, a trend has emerged to employ machine-learning methodology (e.g., artificial neural networks, support vector machines,
decision trees), which in theory is flexible enough to simulate highlyp. 31 of 57

nonlinear dependences hidden in analyzed data. This methodology,
however, comes with the penalty of a large number of coefficientsthat are difficult to estimate reliably. Applying a preliminary classification to PTF inputs and PTF development for each of the resulting
groups holds the promise of providing simple, transparent, and morereliable pedotransfer equations. The existence of PTFs reflects theoutcome of some soil processes; thus, using models of those processes
to generate PTFs, or at least physics-based functional forms for PTFs,
is an expected research avenue.
Pedotransfer functions are evaluated by their accuracy (i.e., errors
with the development data set), their reliability (i.e., errors withdata that have not been used in the PTF development), and theirutility (i.e., errors of soil model where PTF-predicted parameters
are used). Depending on the sensitivity of the soil model to PTFestimated parameters, various levels of PTF accuracy and/or
reliability may be acceptable in terms of the PTF utility (Chirico
et al., 2010). The multiplicity of models (i.e., presence of several
models producing the same output variables) is a typical featurein the PTF research field. However, PTF intercomparisons arelagging behind PTF development, aggravated by the fact that coefficients of PTF based on machine-learning methods are usually
not reported. There is a pressing need to develop and implement
protocols for PTF utility evaluation and intercomparison.
Estimating the variability of soil model parameters becomesincreasingly important as newer modeling technologies (e.g., data
assimilation, ensemble modeling, and model abstraction) become
progressively more popular (Guber et al., 2006; Pan et al., 2012).
The variability of PTFs rely on the spatiotemporal dynamics ofsoil variables, which open new sources of PTF inputs stemmingfrom technology advances, such as monitoring networks, remoteand proximal sensing, and omics (e.g., Tranter et al., 2008; Janaand Mohanty, 2011).
Burgeoning PTF development has so far not filled several persisting regional knowledge gaps. Remarkably little effort so far has
been put into PTF development for saline soils, calcareous andgypsiferous soils, peat soils, paddy soils, soils with well-expressedshrink–swell behavior, and soils affected by freeze–thaw cycles.
The challenge is to correct this situation in the near future. Soils
from tropical regions are quite often considered as a pseudo-entity
for which a single PTF can be applied (Minasny and Hartemink,2011). This assumption will no longer be valid as more regional
data are accumulated and analyzed. Other advances in regional
PTFs will be possible because of the presence of large databaseson region-specific useful PTF inputs such as moisture equivalent(Ottoni et al., 2014), laser diffractometry data (Lamorski et al.,2014), or soil specific surface (Khlosi et al., 2013).
Most transport models in soils—whether water, solutes, gas, orheat—involve parameters that are scale dependent. Recently, theneed to match the scale of computational grid cells and scale of the

VZJ | Advancing Critical Zone ScienceFig. 6. Process of the pedotransfer function development. SWRC,
soil water retention curve; PSD, particle-size distribution; BD,bulk density; OC, organic carbon content; CEC, cation-exchange
capacity; ANN, artificial neural network; SVM, support vector
machines; kNN, k-nearest neighbor.

flux parameter PTF estimation was shown (Pachepsky et al., 2014).
Knowledge about scale effect on parameters is rapidly expandingfor overland flow and transport (Delmas et al., 2012). Including
scale dependencies in PTFs is the grand challenge in improving
PTF usability.
Another scale-related challenge is PTF development for coarsescale soil modeling, such as for land-use change or climate models.
Soil parameters in these models cannot be measured, and theefficiency of PTFs can be evaluated only in terms of their utility(Gutmann and Small, 2007; Shen et al., 2014). There is an urgent
need to determine combinations of pedotransfers and upscaling
procedures that can lead to the derivation of suitable coarse-scalesoil model parameters. Also, the coarse spatial scale often assumes
a coarse temporal support, which requires an understanding of
how to include in PTFs other environmental variables, such as
weather and management attributes.
Temporal and spatial aspects of PTF development and applications
have not received proper attention (Romano, 2004). Because PTF
input variables demonstrate dependencies of spatial location andtime, an effort will be made to determine whether PTF-estimatedparameters have the same spatial and temporal correlations asmeasured ones, and whether regionalization and upscaling of PTFestimated and measured soil parameters produce similar results.
More efficient use of topography as an essential spatial covariate
is also expected.
Pedotransfer functions are empirical relationships, and their accuracy outside the database used for PTF development is essentiallyunknown. Therefore, they should never be considered as an ultimate source of parameters in soil modeling. Rather, they strive toprovide a balance between accuracy and availability. The primaryp. 32 of 57

role of PTFs is to assist in modeling for screening and comparative purposes, establish ranges and/or probability distributions ofmodel parameters, and create realistic synthetic soil data sets andscenarios. Further exploration is needed before using PTFs as asource of hypotheses on and insights into relationships between
soil processes and soil composition as well as between soil structureand soil functioning. Developing and improving PTFs will remain
the mainstream way of packaging data and knowledge for applications of soil modeling.

Parameterizing Models with
Nondestructive and High Resolution
Water Stable Isotope Data
Physically based numerical soil–vegetation–atmosphere transfer
models (SVAT) gather state-of-the-art knowledge on processes
involved in the transfer of heat and water within the soil profile, on
soil–plant relations (root water uptake and/or hydraulic redistribution), and on soil and plant–atmosphere interactions (radiativetransfers and exchange of fluxes of momentum, heat and water
vapor, i.e., ET). They are complex models that require careful calibration of their many parameters, which can be done by feedingthem with high resolution input data, such as the temporal development of soil water isotopologue profiles.
For decades now, stable isotopologues of water (1H2H16O and1H 18O) have been used in identifying and quantifying sources2

and sinks as well as partitioning processes of terrestrial water, andhence are an invaluable source of information for improving soilhydrological and SVAT models. Mass differences of these heavy
isotopologues relative to the most abundant water molecule(1H216O) lead to thermodynamic and kinetic isotopic effects, causing detectable differences in the isotopic composition (d 2H andd18O) of water in different compartments, such as groundwater,
surface water, soil and plant water, and atmospheric water vapor.
These differences have been used to study groundwater recharge,
atmospheric moisture circulation, water-balance closure of lakes,
and reconstruction of root water uptake profiles, as well as for ET
partitioning from the plot to the global scale, (e.g., Craig, 1961;
Moreira et al., 1997; Yakir and Sternberg, 2000; Gibson, 2002;
Williams et al., 2004; Nippert et al., 2010; Rothfuss et al., 2010;
Wang et al., 2010; Jasechko et al., 2013).
The first analytical description of water isotopologue profiles for
an isothermal and saturated soil at steady state was proposed byZimmermann et al. (1967), which was later extended to nonsaturated profiles under non-steady state and nonisothermal conditions(Allison et al., 1983; Barnes and Allison, 1983; Barnes and Allison,
1984; Barnes and Walker, 1989). These analytical formulations
link the shape of the water isotopologue profiles to soil evaporation
flux and regime and to the soil physical properties associated withboth diffusive and convective water transport (such as tortuosity
length and dispersivity). In soils between rain events, the combined

VZJ | Advancing Critical Zone Science

action of convective capillary rise of water depleted in the heavy
stable isotopologues with back-diffusion of water enriched in
the heavy stable isotopologues from the evaporation site (i.e., soil
surface or evaporation front) downward leads to the formationof (typically exponential) soil water stable isotopologue profiles.
More recently, the movement of 1H2H16O and 1H218O was implemented in various SVAT models, including TOUGHREACT,SiSPAT-Isotope, Soil–Litter–Iso, and HYDRUS 1D (Singleton etal., 2004; Braud et al., 2005; Haverd and Cuntz, 2010; Rothfuss etal., 2012; Sutanto et al., 2012). In addition to the mass conservation
equation for water, these models solve an equivalent conservation
equation for the water isotopologues 1H2H16O and 1H218O andneed isotopic initial and boundary conditions. Fluxes of water isotopologues are considered throughout the entire soil profile, that is, inboth vapor and liquid phases, and not only in the vapor phase abovea so-called evaporation front (the minimal depth where nonequilibrium gas exchange occurs in the soil (defined as the minimal depth
where nonequilibrium gas exchange occurs in the soil, Rothfuss
et al., 2015), or only in the liquid phase below it. In addition, andcontrary to, for example, the study of Barnes and Walker (1989),
these numerical models do not make use of a similarity variable,
proportional to depth and (time)−1/2 , and do not require particularboundary conditions for the computation of 1H2H16O and 1H218O
profiles. In addition to thermodynamic (equilibrium) isotope effects,
which are only temperature dependent, kinetic isotope effects during
soil evaporation greatly affect the stable isotopic composition of soil
water and evaporation and can be highly variable (Braud et al., 2009).
Thus, a better understanding of the implications of these kinetic
effects in addition to the well-characterized equilibrium effects andtheir implementation in SVAT models are required for improving
the use of 1H2H16O and 1H218O as tracers of soil water processes.
An important challenge is to provide those models with high-resolution isotope data, both in space and time. Moreover, parallel to fieldstudies, effort should be made to design specific experiments undercontrolled conditions, allowing underlying hypotheses of the abovementioned isotope-enabled SVAT models to be tested. Using isotope
data obtained from these controlled experiments will improve thecharacterization of evaporation processes within the soil profile andameliorate the parametrization of the respective isotope modules.
Soil water d 2H and d18O typically have been measured by destructive sampling, followed by cryogenic soil water extraction (e.g.,
Araguás-Araguás et al., 1995) and offline analysis with isotoperatio mass spectrometers. Although this time-consuming andlabor-intensive procedure provides high-quality data, it has only
poor temporal and spatial resolution. As a consequence, measurements of the isotopic composition of evaporation, inferred fromthat of soil water at the evaporative site in the soil, are still sparse,
but crucial to constraining transpiration over ET ratios, (e.g.,
Dubbert et al., 2013; Hu et al., 2014). Another challenge is therefore to develop new methodologies toward monitoring soil waterd2H and d18O online with high resolution and in a nondestructive
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manner. The first successful attempt was made using microporous polypropylene tubing combined with laser-based infrared
spectrometers (Rothfuss et al., 2013, 2015; Volkmann and Weiler,2014). These methodologies have also been applied to both laboratory and field experiments and compared with traditional methods(e.g., cryogenic distillation) for determining soil-water d 2H andd18O signatures (Gaj et al., 2015; Gangi et al., 2015). Anotherexciting challenge of the coming years is to determine plant-root
water-uptake profiles via online and nondestructive determinationof soil water d 2H and d18O profiles using microporous tubing or
membrane-based setups. These high resolution nondestructive
isotope data will drastically improve the basis for constraining
the above-mentioned SVATs through, for example, inverse modeling and within the framework of specific (controlled conditions)experiments.

6T
6 oward a Soil

Modeling Platform

Since the advent of computer technologies in the 1980s, we haveseen an unprecedented development of mathematical models thatare able to simulate soil processes at an ever-increasing complexity
and at scales ranging from the pore to continents. Many of these
efforts have been undertaken by specific soil science disciplines orcommunities focusing on specific processes and scales, leading toa diverse landscape of soil models. In this section we will discuss
recent developments that aim to better integrate and improveexchange of knowledge, such as the establishment of a virtual
soil modeling platform, the development of technologies tocouple models, the establishment of benchmark initiatives, andsoil modeling intercomparison studies. Finally, the soil modelingcommunity should reach out to other communities that explicitly
deal with soil either as an environmental compartment controlling
key ecological, climatic and hydrological processes or as thesubstrate for producing crops and biomass. A recent initiative,
the International Soil Modeling Consortium (ISMC; https://soil-modeling.org/, accessed 27 Apr. 2016), has been established
as a community effort to address the current challenges of soilmodeling.

Virtual Soil Platform

In the environmental and soil science communities, the need forcoupling models and the associated knowledge has only emerged
recently. The development of a coupling tool or modeling platform is mainly driven by the necessity to create models thatconsider multiple processes and that take into account feedbacks
between these processes. Soil models often focus on specific processes, compartments, and scales, and they are often developed forspecific applications. The development of a modeling platform
may constitute an efficient and rapid way, not only to address
emerging challenges, such as predicting soil functions and soil
evolution under global change, but also to share our vision on soil

VZJ | Advancing Critical Zone Sciencefunctioning at different scales and to strengthen collaboration
among soil scientists, soil modelers, and the Earth-system researchcommunity. Such a modeling platform goes beyond the coupling
tools that have already been proposed, including OMS3 (Davidet al., 2013), CSDMS framework (Peckham et al., 2013), and theOpen MI project developed within the framework of the European
Community (http://www.openmi.org/, accessed 25 Apr. 2016).We
should expect a modeling platform that is more ambitious than the
coupling of existing numerical codes and one that shares underlying principles and knowledge. We need to develop complex models
that enable us with tools that bring responses to current issues
on soil functioning and soil evolution within the framework ofglobal change. We also need to share in a common framework our
visions of soil functioning at various scales—to both strengthen
our collaborations and to make them visible to other communities
working on environmental issues.
We therefore propose to develop a virtual soil platform (VSP) thatserves as a hub for sharing soil process knowledge, modules (i.e.,
numerical tools and algorithms simulating a process), and models(i.e., a logical combination of several modules) and that addresses
the issues discussed above. Virtual soil platform should enablesoil scientists not familiar with model development to develop
numerical representations of soil processes or to build their own
models. To make this possible, VSP should enable an easy exchangeof processes, variables, modules, and models between users. The
VSP should provide access to tools enabling sensitivity studies,parameter estimation, stochastic analysis and ensemble runs,
data assimilation, visualization of simulation results, and modelcomparison and benchmarking (recall section “Does Local-Scale
Model Complexity Matter for Predictions at Larger Scales?”).
In addition, VSP should be linked to soil databases providing
information on soil properties, spatial variability (see “Novel
Optimization Methods and Their Application to Soil Modeling”),
boundary conditions, validation data sets, and so on. The purpose
is to offer a common tool facilitating not only the exchange ofknowledge, the reuse of recognized modules and models and thedevelopment of new ones, and the access to various peripheral tools,
but also the exchanges between users.
At present, the VSoil platform (Lafolie et al., 2015) is being
developed (http://www6.inra.fr/vsoil, accessed 27 Apr. 2016). It
addresses the issues listed above and may serve as a starting point
toward the future development of the ISMC. More precisely,
VSoil offers a means of dealing with processes, not just with codes
representing these processes. Processes are clearly defined. Thismeans that all the entities (i.e., states, parameters, constants andfluxes) that describe processes and all the output Vsoil produces arelisted and visible to anyone using the framework, without having
to access the codes of the modules. The processes and entity lists
are open, as new items will be progressively added. VSoil clearly
differentiates between process knowledge, the various mathematical representations of soil processes, and their numerical
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implementation, thus favoring the use of the framework by those
not familiar with modeling. By using sets of processes and variables,
VSoil automatically ensures that the connections between processes and modules are checked for compatibility when assembled
for constructing a model. Having a set of uniquely defined entities (i.e., definition and units) on which models can draw is alsoessential, given that a reasonable objective is to couple the platform
with databases for model comparison, data assimilation, variables
forcing, or parameter estimation. In addition, a well-defined set ofvariables is fundamental when collaboration between people fromvarious fields of expertise (physics, biology, chemistry, and so on)
is sought. We view this as a goal for tools dedicated to the development of complex soil functioning models. Thus, we suggest thateffort be focused on the sharing of knowledge in addition to allthat can be accomplished in sharing and coupling numerical tools.
VSoil eliminates all the portability (compilation, version, and soon) problems that arise when exchanging computational tools. In
addition, given that the platform manipulates processes and variables, and that modules are linked to a process, all information
about a module or model is readily visible and not hidden somewhere in the code. In particular, the lists of exchanged variables are
explicitly displayed, as well as the list of parameters for a module.
Using a platform based on processes and modules also eases collaboration between coworkers since agreement on concepts andvariables can first be reached. Numerical code development can be
performed after this stage; this phase can be split into several tasks
that can be realized simultaneously in different places if needed,without worrying about compatibility or portability. Hence, working within a common framework would intensify communications
and exchanges, speed up model development, promote the reuseof well-recognized tools, and offer visibility to models developedby the soil science community.

2008b) where the CO2 production rate required by SOILCO2
is computed by the RothC model. Another example is the coupling of the dynamic root architectural model RootBox with themodel for water flow in soil and root system, R-SWMS (Leitneret al., 2014). Here, RootBox computes the geometry of the growing root system used by R-SWMS. The disadvantage is that it isrelatively inefficient compared to other approaches.
A minimally intrusive coupling approach attaches independent
models to a central coupler such as OASIS (https://verc.enes.org/
oasis, accessed 27 Apr. 2016) or MCT (http://www.mcs.anl.gov/
research/projects/mct/, accessed 27 Apr. 2016). Here, each model
must include a piece of software that enables communication withthe central coupler; thus, a slight change to the code is necessary.
The coupler establishes the global communication and memory
space; it exchanges data in memory instead of time-consuming
I/O procedures. A further advantage of this approach is that it
facilitates the running of models not only individually but also
while in ensemble (for data assimilation) or Monte Carlo mode (foruncertainty analysis), as well as the coupling of further computational tools, such as inversion algorithms for parameter estimation.
Examples of this approach are more commonly found in the Earthsystem community (Warner, 2008).

Benchmarks and Soil
Model Intercomparisons

In complex systems, such as soils, mathematical models generally
describe several distinct but simultaneously occurring processes.
The full mathematical model can often be split into several distinct
modules; a solution of the full model is achieved by operator splitting techniques. Or, in a bottom-up view, several models describing
distinct processes can be coupled together to characterize a more
complex system. In this way, additional processes can be integrated
as new modules if required for a specific scientific problem. Thisapproach also allows an exchange of modules, which enables theuser to analyze the impact of different modeling approaches.

Model verification, benchmarking, and intercomparisons are activities that are intrinsically linked with the development of complex
mathematical models simulating various processes in soils. Becauseof the inherent heterogeneity of soil environments, the temporaland spatial variability of boundary conditions, and the nonlinearity processes and various constitutive functions, general solutionsof the governing mathematical equations are usually achieved
using numerical approximations. Given the diversity of processes
and numerical approaches, scientists and model developers mustverify and test their models or demonstrate their models wereindependently verified and tested. Verification of a code should
ensure that the equations constituting the mathematical model
are correctly encoded and solved. Verification of a code consistsof showing that the results generated by the model for simpler
problems are consistent with available analytical solutions or are
the same as, or similar to, results generated with other numericalcodes (model intercomparisons). The latter procedure is also called
benchmarking.

Coupling methods include (i) light coupling that is based onshared input/output files, (ii) external approaches with a central coupler, or (iii) full coupling, using integrated classes orsubroutines. The advantage of the light-coupling approach isthat models are independent executables and only need to sharethe same format for the input/output files. One example of thisapproach is the coupling of SOILCO2 and RothC (Herbst et al.,Available analytical solutions are often limited to idealized transport domains, homogeneous and isotropic media, and uniform
initial and constant boundary conditions. The very reason fordeveloping numerical models is to go beyond the range of available
analytical solutions (i.e., to allow irregular transport domains, heterogeneous and anisotropic media, variable boundary conditions,and nonlinear processes). Verification in such conditions is often

Model Coupling Approaches

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accomplished using model intercomparisons that use approximate
tests for internal consistency and accuracy, such as mass conservation, global mass-balance errors, and sensitivity to changes in meshsize and time steps.
In the literature, many model intercomparison studies have beenreported for subsurface flow and transport models. For example,
Scanlon et al. (2002) compared water-balance simulation resultsfrom seven different codes (HELP, HYDRUS-1D, SHAW,
SoilCover, SWIM, UNSAT-H, and VS2DTI) using 3-yr waterbalance monitoring data from nonvegetated engineered covers(3-m deep) in warm (Texas) and cold (Idaho) desert regions.
Vanderborght et al. (2005) developed and used a set of analyticalbenchmarks (of differing complexity) to test numerical models(HYDRUS-1D, MACRO, MARTHE, SWAP, and WAVE) of
flow and transport in soils. Oster et al. (2012) compared the simulated crop yields grown under production practices and transientconditions (involving pressure head and osmotic stresses) in thewestern San Joaquin Valley of California, using the ENVIROGRO, HYDRUS-1D, SALTMED, SWAP, and UNSATCHEM
models. Finally, intercomparisons of results obtained by PEARL,PELMO, PRZM, and MACRO models for nine (MACRO only
for one) FOCUS scenarios/sites, which collectively represent agriculture (and different climate regions) in the EU, for the purposesof a Tier 1 EU-level assessment of the leaching potential of active
substances were performed by the FOCUS group (FOCUS, 2000).
Similar efforts are being performed in related environmental fields.
For example, Hanson et al. (2004) evaluated 13 models varying
in their spatial, mechanistic, and temporal complexity for theirability to capture intra- and interannual components of the waterand carbon cycle for an upland, oak-dominated forest of eastern
Tennessee. A set of well-described benchmark problems that can beused to demonstrate model conformance with norms establishedby the subsurface science and engineering community has recently
been developed for complex reactive transport numerical models(CrunchFlow, HP1, MIN3P, PFlotran, and TOUGHREACT)(e.g., Rosenzweig et al., 2013; Steefel et al., 2015; Xie et al., 2015).
Rosenzweig et al. (2013) described the Agricultural Model
Intercomparison and Improvement Project (AgMIP), which is amajor international effort linking the climate, crop, and economic
modeling communities with cutting-edge information technology to produce improved crop and economic models and thenext generation of climate-impact projections for the agricultural
sector. Finally, the World Climate Research Program (WCRP)
Working Group on Coupled Modeling (http://www.wcrp-climate.
org/wgcm/projects.shtml, accessed 27 Apr. 2016) catalogs a large
number of Model Intercomparison Projects (MIPs) related to various climate-related models.
Similar model intercomparison studies will undoubtedly continue
as advances in measurement technology, computing technology,
and numerical techniques enable the development of models of

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ever-increasing levels of sophistication that cannot be readily
verified using analytical solutions such as those developed and/or suggested by Vanderborght et al. (2005).The soil-modelingcommunity should thus expand on this work by establishinga benchmark and validation platform with standardized andhigh-quality data sets that would use common data formats,protocols, and ontologies and that would be readily available tomodel developers for further model testing and intercomparisons.
Ontologies refer to a standardized vocabulary enabling a common
understanding of the exact meaning of different terms (e.g.,parameters, variables) used in a science community. Examples canbe found in biology (http://www.plantontology.org/, accessed
27 Apr. 2016) or agriculture (http://aims.fao.org/vest-registry,
accessed 27 Apr. 2016). The database could include not only
experimental data sets, but also input and output files of mostcommonly used soil models applied to these data sets.

Linking Soil Modeling Platforms with
Climate, Ecology, and Hydrology
It is clear that soil plays a vital and pivotal role in environmental
responses to climate change and variability, in ecological vigor
and hydrologic extremes, and in the outcomes of models used tounderstand the strength and direction of these connections. Manyof these models focus on the supporting processes of soils, particularly related to water cycling (stocks and fluxes of water into/from the soil profile) and nutrient (C, N, P) cycling, which areclosely linked to provisioning services. The models also simulate
regulating services, described by Dominati (2013) as flood mitigation, filtering of wastewater, and so on. Predictive and hindcast
models used across scientific disciplines can provide substantial
insights into ecosystem processes and services, as well as into theintricate connection among the different pools of natural resources
provided by soil.
As described by Sellers et al. (1997), land–atmosphere models have
evolved into sophisticated soil–vegetation–atmosphere systems
that provide large-scale transfer of water vapor and carbon. Many
aspects of these climate circulation models connect to surface processes and the uppermost soil horizons of land. These processes
involve understanding soil hydrology, impacts on the soil’s energybalance, and ecological response to climate and climate variability, all of which impact soil properties, formation, and processes
that influence soil formation and degradation. This knowledge
base is being implemented, although slowly and at variable spatial
and temporal scales, into numerical codes that simulate biosphericprocesses.
We see the effective incorporation of these provisioning and regulating processes into scale-appropriate models as a significant
challenge, and one that could expand soil modeling applications to other scientific disciplines. For example, Ochsner et al.
(2013) discussed the connection of soil water storage and content
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to ecological function, biogeochemistry, and ecological model
platforms. This vital link between soil and ecosystem services isparameterized by lumping many soil processes into compartments
in which reactions occur. The CENTURY/DAYCENT model(Parton et al., 1998) focuses on carbon and nutrient dynamics,
and biosphere models like SiB (Sellers et al., 1986) and BATS
(Dickinson et al., 1986) simulate SVAT. These and other models
are now being widely used by the ecological and biogeochemicalcommunities, even though they generally do not use physically
based governing equations or constitutive relations when incorporating soil processes; the soil modeling community can makehighly relevant contributions in this regard. For example, recently
Ren et al. (2008) explicitly accounted for vegetation canopy andphysiological control of ET and soil water budgets, improving
water budget estimates deeper into the soil profile rather thanmatching soil response for the upper (15-cm) soil layer only.
Hydrologic models have for some time generally included soil
property parameters, though to varying degrees of sophistication. Regulating water exchange and movement are critical for
accurately predicting soil (and deeper) recharge, surface-runoff
timing and severity, and the ET component of hydrologic models
that ultimately connect to climate or atmospheric codes. Onedimensional approaches (e.g., HYDRUS-1D; Šimůnek et al.,2008) are used extensively in the agricultural and environmental fields. These often solve the Richards equation under variably
saturated conditions, using common forms of soil water retention
and hydraulic conductivity curves. But ,these approaches are lesscommonly used in landscape-scale approaches for water routing
like SWAT (Arnold and Fohrer, 2005; Chen et al., 2011) or HSPF
(e.g., Donigian et al., 1995; Bicknell et al., 1997), which rely on
a “bucket model” approach and the concept of field capacity andgravitational downward flow. There remains a divide between
physically based models at small spatial and temporal scales andlumped parameter models for landscape-type applications. This
divide exists because of computational limitations (i.e., lack ofsufficient memory or high-performance computer resources) or
theoretical limitations. In the latter case, soil physicists do notdeem pore-scale approaches scalable to landscape and regional
scales. Bridging this divide and using manageable soil properties
and governing equations across scales is a significant challenge thatneeds to be overcome for hydrologic models to be useful for decision makers.
Increasingly, integrated modeling platforms are collaboratively
developed, with model advancements occurring through specificmodules that spread scientific expertise across disciplinary boundaries. An excellent example is the Community Earth System Model(CESM), maintained by the National Center for AtmosphericResearch (NCAR). Among the principle modules of this global
model is the Community Land Model (CLM), the purpose ofwhich is to improve understanding of natural and human impacts
on vegetation and climate at the regional or global scales. The

VZJ | Advancing Critical Zone Science

CLM includes surface heterogeneities and consists of submodels
that represent the hydrologic cycle, biogeochemical cycling, andecosystem dynamics (Lawrence et al., 2011), many of which fit
neatly into the framework of Dominati (2013) that connects soil
capital to ecosystem processes and services. The CLM is well suited
to study the role of land processes in weather and climate change,and efforts are being devoted to improve the representation of therole of subsurface processes. For example, the mechanistic ParFlow
model was recently coupled to the CLM (Kollet and Maxwell,2008; Maxwell, 2013) for regional-scale applications, with theability to simulate complex topographies, geology, and subsurface
heterogeneities of the coupled vadose zone–groundwater system.
A challenge for the modeling community would be to incorporate nutrient cycling, erosion, and other supporting–degrading
processes at spatial and temporal scales that can facilitate thetracking of ecosystem services through time by changing land use
and climate.
For the future, a persistent question is how to effectively incorporate soil properties, taken at the point scale, into larger-scale (i.e.,
landscape, watershed) models that simulate ecological, biochemical,
and climatological (supporting) processes. The SoilML standard
for soil data transfer and storage (Montanarella et al., 2010) may
help in this process. Moreover, whereas advanced soil modelingplatforms increasingly integrate physical, chemical, and biologicalprocesses that couple climate with hydrology and geochemistry,
much of the biological components remain relatively underdeveloped. In part, much of the microbiological system remains a blackbox in many soil based models, especially as related to microbial
kinetics and effects of the dynamics of soil environmental changes(water, temperature, nutrients) on microbial processes. Althoughmuch experimental work is being done to understand soil fauna(e.g., fungi, worms) and how they alter the soil environment, weare unaware of soil modeling work that incorporates soil fauna
impacts on the soil–climate system. Finally, because the main purpose of the IPCC and Millennium Development Goals (MDG)
is to provide science for policy, and given the ongoing interest inincorporating ecosystem services into sustainable land management decisions, soil modeling platforms need to be designed tomore effectively integrate soil modeling output into policy decisions at the regional and global scales.

Linking Soil Modeling Platforms with
Crop and Biomass Production
Biomass production as an ecosystem service (“Biomass Production
for Food, Fiber, and Energy” section) is strongly dependent on soil
and crop interactions. Crop growth and development, as well as
yield formation, are complex processes with dominant anthropogenic influence. Besides the genetic characteristics of crop species
and crop cultivars, atmospheric conditions, soil properties and soil
processes, crop growth depends on the intensity of crop and soil
management. In general, in intensive high-input cropping systems
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under irrigation, the farmer is able to optimize management ina way that the growth of a specific crop is only constrained byradiation and air temperature (potential production conditions).
However, in terms of area, irrigated cropping systems have a low
share in the global cropland, and rainfed systems are predominant,where, depending on climate and soil water retention curve, soil
water is a major constraint. Therefore, among existing dynamic
crop models, the majority considers the soils’ function in storing
infiltrated water and supplying it to the crop. However, the level ofdetail of the representation of this important soil function and its
interaction with crop roots and crop water demand is highly variable. Most crop models use a one-dimensional conceptual approachsuch as a bucket type approach to characterize the dynamics of soil
water storage, either in a one layer or in a multilayered soil (DSSAT,
Jones et al., 2003; APSIM, Keating et al., 2003; MONICA,
Nendel et al., 2011). Physically based approaches to simulate soil
water fluxes integrated into dynamic crop models are rather scarce(DAISY, Abrahamsen and Hansen 2000). The SIMPLACE platform offers three different one-dimensional approaches to simulate
soil water dynamics, which can be combined with two different
approaches of root development and three different crop water
uptake mechanisms (Gaiser et al., 2013). Depending on the availability of input data, prevailing water management practices, andthe climatic conditions where the model is to be applied, simple ormore complex combinations can be selected by the user.
To be suitable for cropping systems with reduced management
intensity, crop models must consider additional soil processes thatare related to crop nutrient supply and in particular to nitrogen.
However, due to the fact that soil nitrogen dynamics including
mineralization and immobilization, leaching, nitrification, denitrification, volatilization, and crop uptake are extremely complex,
different approaches with varying levels of detail have been implemented or coupled with crop growth processes. In cropping systems
where application rates of mineral nitrogen fertilizers are on theorder of potential crop demand, only the uptake of the appliedmineral N may be considered to cover the actual or daily crop N
demand in the simulations. In organic agriculture or in low-input
systems, such as in small-holder subsistence farms in developing
countries, soil nitrogen routines must consider the nitrogen mineralization and immobilization processes linked to soil organic
matter. Usually, the more complex soil nitrogen routines in existing crop models consider different soil nitrogen pools (linked tosoil carbon pools), and their respective decomposition and mineralization rates are calculated taking into account environmental
variables like soil moisture, soil temperature, or soil clay content(CENTURY, Parton et al., 1992; CANDY, Franko et al., 1995;
DAISY, Abrahamsen and Hansen, 2000; SIMPLACE, Gaiser etal., 2013). Crop nitrogen uptake is then driven by the amount ofsoil mineral N over the rooted zone, crop nitrogen demand, andin some cases the density and N uptake capacity of the roots in therespective soil layers. Nitrogen leaching, as an important process inhumid climates, is usually also considered in these more complex

VZJ | Advancing Critical Zone Sciencesoil nitrogen subroutines, whereas other soil related processes likenitrification, denitrification, or ammonium fixation and volatilization are implemented in only a few models (e.g., DNDC, Kraus etal., 2015; and CropSyst, Stöckle et al. (2014).
Besides nitrogen as one of the major crop nutrients, there are only
a few crop models that consider phosphorus as a limiting factor
with (CropSyst, APSIM, DSSAT, SIMPLACE, EPIC; Williams
and Izaurralde, 2005) or without (WOFOST, van Ittersum et al.,
2003; Lintul5, Lefelaar, 2012) taking into account the dynamics of adsorption or fixation of inorganic P onto the soil matrix
or the transformation of organic soil P. Among other major crop
nutrients like K, Mg, Ca, or S, only K is taken into account by four
dynamic crop models either with (EPIC Version EPICSEAR; De
Barros et al., 2004) or without (WOFOST, Lintul5, SIMPLACE)
associated transformation and adsorption processes in the soil. To
our knowledge modeling of the availability of micronutrients inthe soil or their uptake by the crop is still a gap when coupling soil
processes with crop and biomass production, although micronutrient deficiency is a well-known obstacle to advance intensificationand increase yields on highly weathered soils in Africa, Asia, andSouth America (Voortman et al., 2003).
Modeling soil conditions that are adverse to crop growth (e.g., salt
toxicity, water logging, soil compaction, aluminum, and iron toxicity) and quantification of their impacts on crop roots and crop
growth are another bottleneck when coupling soil processes withcrop and biomass production. The crop models EPIC and STICS
use different relationships between either soil strength (Williams
and Izaurralde, 2005) or soil bulk density (Brisson et al., 2003) androot elongation rate to describe the effect of soil compaction on
root growth and, subsequently, water and nutrient uptake. In addition, the EPIC model estimates the effect of aluminum toxicity on
root growth by relating Al saturation in the soil to a crop specificmaximum Al saturation threshold (USDA, 1990). In a more recent
Windows-based version of EPIC, the effect of increased soil electrical conductivity as a measure of high salt concentrations in the soilon crop growth had been incorporated (Gerik et al., 2013). Water
logging can also be an important growth limitation to crops and inparticular to roots. The processes leading to water logging, that is,permanent saturation of the root zone with water, can be manifold
and involve reduced percolation of rainwater, occurrence of surface
water flooding, and groundwater rise. One the one hand, modeling of water logging therefore requires detailed parametrization ofsoil hydraulic conductivity curve and reliable estimation of one-,two-, and three-dimensional soil water fluxes, including landscapescale hydrological processes in the case of groundwater influence offlooding from adjacent surface water streams. On the other hand,modeling the crop-specific, physiological response of the rootsystem and its interaction with the shoot is neither fully understood nor adequately implemented in crop models. A first attempt
to cover some of the challenges was made recently by Stöckle etal. (2014) through coupling a landscape-scale hydrological model
p. 38 of 57

with CropSyst (CropSyst-Microbasin). In summary, there aremany interfaces between soil processes, the crop roots, and theirinteraction with the shoot that ultimately determine crop yield andbiomass production, all of which require further investigations at
the plot, field, and landscape level and subsequent implementation
into coupled soil–plant modeling platforms to simulate biomass
production under a wide range of climate, soil, and management
conditions.
Regarding the technical implementation of crop simulation
models, besides a wide range of one package crop simulation
models, there are several crop-simulation environments relying on
a modular structure to describe crop-growth processes at the field
scale. These environments all consider aboveground and belowground processes, but with different degrees of detail (Keating etal., 2003; Donatelli et al., 2010). Examples for developments inGermany are SIMPLACE (http://www.simplace.net, accessed
26 Apr. 2016; Gaiser et al., 2013), _ENREF_170, Expert-N(https://soil-modeling.org/models/model-descriptions/expert-n),
MONICA (Nendel et al., 2011), and HUME (Kage and Stuetzel,
1999; Ratjen, 2012). At the global scale, the DSSAT (http://dssat.
net/, accessed 26 Apr. 2016) platform is quite wide-spread for onedimensional applications from field to region. As an example forthree-dimensional applications, the OpenAlea (Cokelaer et al.,2010) open-source project should be mentioned.

66Summary and Outlook

Since the early attempts in systematic modeling of soil processes
that emerged with advances in analog and digital computers in
the midst of the 20th century, there has been great progress acrossa broad range of space and time scales (pores to catchments andseconds to decades). Yet, our current understanding of the complexity of soil processes and ability to observe these processes at
ever-increasing resolution point to significant gaps in representing
this critical compartment of biosphere. The growing importanceof soil in a host of topics and its central role in a range of ecosystem services, climate, food security, and other global terrestrial
processes make quantification and modeling of soil processes anurgent challenge for the soil science and neighboring communities.
We focused on identifying various key challenges in modeling soil

processes that are directly related to the hierarchical and complex
organization of soils and soil systems and the functioning of soils
in providing ecosystem services to society. Many of these challenges have been addressed in the individual sections, and here we
identify four overarching grand challenges, summarized in Table 5,that we think will dominate in the field of soil processes modeling.
The first challenge is that of sharing knowledge across disciplines.
It comprises the need to exchange knowledge about soil processesmodeling across the different soil disciplines, and among other
Earth, ecology, and plant sciences. Typically, many available soilmodels have been developed within different communities anddisciplines addressing specific research questions covering a broad
range of scales and often serving different purposes. Integrating
our knowledge of soil process modeling in climate models, crop
growth models, and ecological models may enhance our understanding of the complex interactions between the different
compartments and their feedback mechanisms. The development
and establishment of a community modeling platform could facilitate the exchange of knowledge on modeling soil processes, provide
techniques and approaches to efficiently couple soil processes, anddevelop integrated models and benchmarks to test existing andnewly developed models. The platform could also serve as a linkwith other disciplines listed above. A better interaction of thesoil science community with other Earth science disciplines may
enhance our understanding of soil processes in the landscape by,for example, coupling state-of-the-art approaches to soil infiltration with overland flow modeling, particle detachment, transportand deposition modeling across a heterogeneous landscape or bycoupling of soil physical and chemical processes and soil biology
to better understand and quantify supporting and degrading
processes and key ecosystem services. The soil supporting anddegrading processes and ecosystem services described here aredetermined by the combined effect of a multitude of individual
processes. We are convinced that improved modeling of soil processes will also lead to a better quantification and prediction of
ecosystem services. The development of more complex soil models
and soil modeling platforms, together with the availability of novel
experimental techniques, will also allow us to design new experimental setups based on soil model simulations, which will thenenable the retrieval of soil properties that are difficult to measure.

Table 5. Overarching challenges to modeling soil processes.
Overarching challenges
Challenge 1

To effectively exchange soil processes modeling and knowledge across different soil disciplines, and with Earth, ecology, and plant sciences.

Challenge 2

To build platforms for integrating soil processes from pore and local scales into field and ultimately global-scale land surface models, crop models,climate models, and terrestrial models of biogeochemical processes.

Challenge 3

To improve quantification and mechanistic representation of soil biological processes at scales ranging from microbial cells at pores or on root surfaces
to the emergence of vegetation patterns over extensive landscapes.

Challenge 4

To develop a framework that allows to differentiate soils based on their functioning properties and include land use and/or tracking changes of
supporting–degrading processes toward building spatial maps that quantifying ecosystem services and may contribute to improve the valuation of
ecosystem services.

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p. 39 of 57

The second overarching challenge for soil modeling is the integration of pore- and local-scale soil process modeling into field-scale
to global-scale land surface models, crop models, climate models,
and terrestrial models of biogeochemical processes. These complex
codes address issues such as parameterization of root water uptake
processes, biotic processes, and upscaling of hydraulic properties,
chemical and biological properties, and others. Effective integration will require the development of upscaling methods andapproaches to derive effective parameters and equations that allow
us to include pore- and local-scale process understanding, so we
can describe processes at the field scale and beyond. Upscaling soil
processes beyond the field scale will require us to embed and couple
soils and soil process modeling into a landscape setting. This willentail a larger focus on nonlocal processes that are controlled
by lateral water, energy, and matter fluxes. Lateral groundwaterflow plays an important role in linking these processes because it
influences, in part, the water table depth and its important consequences for soil water contents and water fluxes. Lateral fluxes
in the atmosphere also play an important role for determining theupper boundary of the soil system. Besides lateral water and energy
fluxes, lateral fluxes of soil material also become important when
considering soil building processes over longer time scales. These
processes need to be coupled with predominantly vertical fluxesof dissolved substances.
The third challenge embraces the monumental task of quantitativedescription of soil biotic processes at scales ranging from microbialactivity at pores or on root surfaces to the emergence of vegetation
patterns over extensive landscapes. At the core of this challenge
is the representation of highly adaptive and dynamic biologicalprocesses that respond in new and surprising ways to changes inclimate, land use, and management practices and their upscaling
to represent fluxes and changes in soil properties at agronomic
or climatic relevant scales. The rapid advances in remote observational methods and molecular genetic capabilities necessitate
advanced modeling frameworks for effective integration of new
observations with process understanding. Especially the upscalingof soil biotic processes may benefit from novel measurement techniques that enable to quantify and visualize microbial processes atthe pore-scale level and at the interfaces of water and soil matrix.
An important component of this is the need to agree on a framework of describing the soil microbial community in a manner thatallows its functional dynamics and interaction with soil physical,
chemical, and biological components to be described for modelingpurposes, without oversimplification or loss of meaning.
Finally, we need to address the question of how to value ecosystemservices using soil properties and processes in the proposed integrated modeling approach. We have used an ecosystem’s framework
to identify the role and importance of soil modeling in characterizing and quantifying ecosystem services and we have identified
specific challenges for improving soil process modeling. Froma soil modeling perspective, we may want to challenge our soils

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community to work with ecologists, sociologists, and economists
to develop such a framework that allows differentiation of soils
based on their functioning properties and includes land use and/or
tracking changes of supporting–degrading processes toward building spatial maps that quantify ecosystem services. This would behighly significant as the soil community’s contribution to local andregional policy and decision making and toward providing sustainable options for future land use and land use changes.
To meet these challenges, an international community effort isrequired, similar to initiatives in systems biology, hydrology, andclimate and crop research. We are therefore establishing an international soil modeling consortium (https://soil-modeling.org/,
accessed 26 Apr. 2016) with the following aims:
ʶʶ establishing formal structures for guiding and building community-wide capabilities (repository, conferences, journal
sections, liaisons with societies) to bring together experts insoil process modeling within all major soil disciplines;ʶʶ addressing major scientific gaps in describing key processes andtheir long-term impacts with respect to the different functions
and ecosystem services provided by soil;
ʶʶ intercomparing soil model performance based on standardized
and harmonized data set;ʶʶ providing adaptive and peer-reviewed protocols for modelcomponents, benchmarking and testing, input information,
ontologies, and data formats;ʶʶ integrating soil modeling expertise and state of the art knowledge on soil processes in climate, land surface, ecological, crop,and contaminant models;ʶʶ linking process models with new observations, measurements,
and data- evaluation technologies for mapping and characterizing soil properties across scales;ʶʶ developing partnerships with similar modeling endeavors,
industry, and funding agencies.
The consortium will bring together modelers and experimental soil
scientists at the forefront of new technologies and approaches tocharacterize soils. By addressing these aims, the consortium will
improve the role of soil modeling as a knowledge dissemination
instrument in addressing key global issues, and we will stimulate
the development of translational research activities.

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AUTHOR AFFILIATIONS: H. Vereecken, Agrosphere Inst., IBG-3, Inst. of
Bio-geosciences, Forschungszentrum Jülich GmbH, Jülich, Germany
and Centre for High-Performance Scientific Computing in Terrestrial
Systems, HPSC TerrSys, Geoverbund ABC/J, Forschungszentrum Jülich
GmbH, Germany; A. Schnepf, Agrosphere Inst., IBG-3, Inst. of Biogeosciences, Forschungszentrum Jülich GmbH, Jülich, Germany;
J.W. Hopmans, Dep. of Land, Air, and Water Resources, College ofAgricultural and Environmental Sciences, Univ. of California, Davis, CA
95616; M. Javaux, Earth and Life Inst., Environmental Sciences, Université
catholique de Louvain, Croix du Sud, 2, L7.05.02, 1348 Louvain-la-Neuve,
Belgium; D. Or, Soil and Terrestrial Environmental Physics, ETH-Zürich,
Universitätstrasse 16, CHN F 29.1.8092, Zürich; T. Roose, Bioengineering
Sciences Research Group, Faculty of Engineering and Environment,
Univ. of Southampton, University Road, Southampton SO17 1BJ, UK;
J. Vanderborght, Agrosphere Inst., IBG-3, Inst. of Bio-geosciences,
Forschungszentrum Jülich GmbH, Jülich, Germany and Centre for HighPerformance Scientific Computing in Terrestrial Systems, HPSC TerrSys,
Geoverbund ABC/J, Forschungszentrum Jülich GmbH, Germany; M.H.
Young, Bureau of Economic Geology, Jackson School of Geosciences,
Univ. of Texas at Austin; W. Amelung, Agrosphere Inst., IBG-3, Inst. of Biogeosciences, Forschungszentrum Jülich GmbH, Jülich, Germany andUniv. of Bonn, INRES- Inst. of Crop Science and Resource Conservation,
Soil Science and Soil Ecology, Nußallee 13, 53115 Bonn, Germany; M.
Aitkenhead, The James Hutton Inst., Craigiebuckler, Aberdeen AB15
8QH, UK; Allison S.D., Ecology & Evolutionary Biology School of Biological
Sciences, Univ. of California, Irvine; S. Assouline, Dep. of Environmental
Physics and Irrigation Inst. of Soils, Water and Environment Sciences
A.R.O- Volcani Center PO Box 6, Bet Dagan 50250, Israel; P. Baveye,
Unité EcoSys, AgroParisTech-INRA, Université Paris-Saclay, Avenue
Lucien Brétignières, Thiverval-Grignon F-78850, France; M. Berli, Div. of
Hydrologic Sciences, Desert Research Institute, 755 E. Flamingo Road,
Las Vegas, NV 89119; N. Brüggemann, Agrosphere Inst., IBG-3, Inst. of
Bio-geosciences, Forschungszentrum Jülich GmbH, Jülich, Germany;
P. Finke, Dep. of Geology and Soil Science, Ghent Univ., Krijgslaan
281 WE13, B9000 Ghent, Belgium; M. Flury, Soil Physics/Vadose Zone
Hydrology, Dep. of Crop and Soil Sciences, Washington State Univ., 2606
W Pioneer, Puyallup, WA 98371-4922; T. Gaiser, Univ. of Bonn Inst. of Crop
Science and Resource Conservation, Katzenburgweg 5, 53115 Bonn,
Germany; G. Govers, Dep. of Earth and Environmental Sciences, Div. of
Geography, KU Leuven, Celestijnenlaan 200E, 3001 Leuven, Belgium; T.
Ghezzehei, Life and Environmental Science School of Natural Science,
5200 North Lake Road, Merced, CA 95343; P. Hallett, Inst. of Biologicaland Environmental Sciences, Univ. of Aberdeen, Aberdeen, AB24
3UU, UK; H.J. Hendricks Franssen, Agrosphere Inst., IBG-3, Inst. of Biogeosciences, Forschungszentrum Jülich GmbH, Jülich, Germany and

VZJ | Advancing Critical Zone ScienceCentre for High-Performance Scientific Computing in Terrestrial Systems,
HPSC TerrSys, Geoverbund ABC/J, Forschungszentrum Jülich GmbH,Germany; J. Heppell, Bioengineering Sciences Research Group, Facultyof Engineering and Environment, Univ. of Southampton, University Road,
Southampton SO17 1BJ, UK; R. Horn, Inst. for Plant Nutrition and Soil
Science, Hermann Rodewaldstr. 2, 24118 Kiel, Germany; J.A. Huisman,
Agrosphere Inst., IBG-3, Inst. of Bio-geosciences, Forschungszentrum
Jülich GmbH, Jülich, Germany and Centre for High-Performance
Scientific Computing in Terrestrial Systems, HPSC TerrSys, Geoverbund
ABC/J, Forschungszentrum Jülich GmbH, Germany; D. Jacques, Inst.
for Environment, Health and Safety, Belgian Nuclear Research Centre(SCK-CEN), Mol, Belgium; F. Jonard, Agrosphere Inst., IBG-3, Inst. of Biogeosciences, Forschungszentrum Jülich GmbH, Jülich, Germany; S. Kollet,
Agrosphere Inst., IBG-3, Inst. of Bio-geosciences, Forschungszentrum
Jülich GmbH, Jülich, Germany and Centre for High-Performance
Scientific Computing in Terrestrial Systems, HPSC TerrSys, Geoverbund
ABC/J, Forschungszentrum Jülich GmbH, Germany; F. Lafolie, INRA,
UMR1114 EMMAH, F- 84914 Avignon Cedex 9, France; K. Lamorski, Inst. of
Agrophysics, Polish Academy of Sciences, Doświadczalna Str. 4, 20-290
Lublin, Poland; D. Leitner, Univ. of Vienna, Computational Science Center,
Oskar Morgenstern-Platz 1, 1090 Vienna, Austria; A. McBratney, Dep. ofEnvironmental Sciences, The Univ. of Sydney, NSW 2006, Australia; B.
Minasny, Dep. of Environmental Sciences, The Univ. of Sydney, NSW 2006,
Australia; C. Montzka, Agrosphere Inst., IBG-3, Inst. of Bio-geosciences,
Forschungszentrum Jülich GmbH, Jülich, Germany; W. Nowak,
Universität Stuttgart, Institut für Wasser- und Umweltsystemmodellierung(IWS), Lehrstuhl für Stochastische Simulation und Sicherheitsforschung fürHydrosysteme; Y. Pachepsky, Environmental Microbial and Food Safety
Laboratory, USDA ARS Beltsville Agricultural Research Center, Beltsville,
MD 20705, USA; J. Padarian, Dep. of Environmental Sciences, The Univ.
of Sydney, NSW 2006, Australia; N. Romano, Univ. of Naples Federico II,
Dep. of Agronomy, AFBE Division, Via Universita’ n. 100, 80055 Portici,
Napoli, Italy; K. Roth, Inst. of Environmental Physics, Im Neuenheimer
Feld 229, 69120 Heidelberg, Germany; Y. Rothfuss, Agrosphere Inst., IBG3, Inst. of Bio-geosciences, Forschungszentrum Jülich GmbH, Jülich,
Germany; E.C. Rowe, Centre for Ecology and Hydrology, Environment
Centre Wales, Deiniol Road, Bangor, LL57 2UW, UK; A. Schwen, Institut
für Hydraulik und landeskulturelle Wasserwirtschaft, Nußdorfer Lände 11,1190 Wien; J. Šimůnek, Dep. of Environmental Sciences, Univ. of California
Riverside, Riverside, CA, 92521; A. Tiktak, PBL Netherlands Environmental
Assessment Agency, Leeuwenhoeklaan 9, 3721 MA, PO Box 303, 3720
AH, Bilthoven, the Netherlands; J. Van Dam, WU Environmental Sciences,
Soil Physics and Land Management, PO Box 47, 6700AA Wageningen,the Netherlands; S.E.A.T.M. van der Zee, WU Environmental Sciences,
Soil Physics and Land Management, PO Box 47, 6700AA Wageningen,
The Netherlands and School of Chemistry, Monash Univ., Melbourne
VIC 3800, Australia; H.J. Vogel, Dep. Soil Physics, UFZ, Theodor-LieserStraße 4, 06120 Halle (Saale), Germany; J.A. Vrugt, Dep. of Civil andEnvironmental Engineering and Dep. of Earth System Science, Univ. of
California, Irvine, CA and Inst. for Biodiversity and Ecosystem dynamics,
Univ. of Amsterdam, the Netherlands; T. Wöhling, Technische Universität
Wöhling Dresden, Dep. of Hydrology, 01069 Dresden, Germany andWater & Earth System Science (WESS) Competence Cluster, Univ. of
Tübingen, Inst. for Geoscience, 72076 Tübingen, Germany and Lincoln
Agritech Ltd., Ruakura Research Centre, Hamilton 3240, New Zealand;
I.M. Young, School of Environmental & Rural Science, Univ. of New
England, Australia.

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