# Introducing a volume change function in process-based modelling of soil development due to land management: A proof of concept

Hamza Chaif, Saba Keyvanshokouhi, Peter Finke, Cédric Nouguier, Nicolas Moitrier, Nicolas Beudez, Sophie S. Cornu

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Hamza Chaif, Saba Keyvanshokouhi, Peter Finke, Cédric Nouguier, Nicolas Moitrier, et al.. Introducing a volume change function in process-based modelling of soil development due to land management: A proof of concept. Geoderma, 2025, 455, pp.117228. 10.1016/j.geoderma.2025.117228. hal-05101745

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# Introducing a volume change function in process-based modelling of soil development due to land management: A proof of concept

Article in Geoderma · February 2025

DOI: 10.1016/j.geoderma.2025.117228

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# Introducing a volume change function in process-based modelling of soil development due to land management: A proof of concept

Hamza Chaif<sup>a, *</sup>, Saba Keyvanshokouhi<sup>a,b</sup>, Peter Finke<sup>b</sup>, Cédric Nouguier<sup>c,D</sup>, Nicolas Moitrier<sup>c</sup>, Nicolas Beudez<sup>c,D</sup>, Sophie Cornu<sup>a</sup>

## ARTICLE INFO

Handling editor: Budiman Minasny

### Keywords:

- Soil modelling

- OC-VGEN model

- Pedotransfer function

- Global change

- Bulk density

- Soil organic carbon

## ABSTRACT

Most process-based models of soil development with explicit water transfer are based on an assumption of constant soil volume over time. Nevertheless, the consequences of this simplification on model outputs are not negligible when used on a several decades to a century time scale since, over such a time scale, soils experience strain due to multiple processes, which results in significant change in soil volume over depth and time. We propose in this paper a new approach to considering volume change in a process-based model of soil evolution over short to medium time scales (10 to 70 years). The model takes into account the feedbacks among processes responsible for soil evolution including soil organic carbon dynamics as well as transfer of water, heat and gas while considering the impacts of climate change as well as human activities on soil. To replace the constant volume hypothesis, we introduce in the model an estimation, by a pedotransfer function, of the bulk density that was then used to estimate soil volume in the model. The feasibility of this approach was demonstrated using a simple bulk density pedotransfer function based on soil organic carbon content for three long-term experiment sites with different scenarios of land use or tillage practices on Haplic Luvisols in the north of France. Both versions of the model (constant and changing volume) were tested. Soil dilation was predicted over the top soil (<15 cm) when the tillage practices were reduced. Conversion from agriculture to pasture induced an expansion of all layers of the soil profile. Hydraulic properties of the soil were also impacted by the volume change. Over longer time scales, other pedotransfer functions accounting for the impact of various pedological processes on bulk density should be implemented along with the inclusion of other processes responsible for volume change in order to accurately represent the retroactions between the soil volume and the processes affecting its development.

## 1. Introduction

Soils are experiencing severe changes due to anthropogenic factors (Richter & Markewitz, 2003) and climate change. Some of these changes may be reversible, while others are irreversible and occur on time scales from a few tens of years to a century (Cornu et al., 2012; Montagne et al., 2008; Robinson et al., 2016, 2019; Sombroek, 1990) making it urgent and necessary to project the development of soil properties over such time scales. Models of soil evolution are therefore necessary to assess the effects of global change on soil properties.

Soil formation (or pedogenesis) results from the combined actions of physical, chemical and biological processes on a parent material. These

actions are modulated depending on the soil forming factors, i.e. relief, organisms (including human activities), climate and time (Jenny, 1941) as they condition the expression of these processes (their hierarchy). As shown in several pedological studies (Jamagne & King, 2002; Lin, 2011), soil formation is a continuous phenomenon giving birth to a first poorly differentiated soil (e.g. Cambisol) that further evolves into a more differentiated soil (e.g. Luvisol when developed on loess material (Jamagne, 1978)). This further development in which the formation of the new soil is made at the expense of a former one is called hereafter soil evolution. Both soil formation (over thousands of years to millennia) and soil evolution (over tens to hundreds of years), sometimes referred to together with the wider term soil development (Finke, 2024), are the

<footnote><sup>a</sup> Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France</footnote>

<footnote><sup>b</sup> Ghent University, Department of Environment, Coupure links 653, 9000 Ghent, Belgium</footnote>

<footnote><sup>c</sup> EMMAH, Avignon Université, INRAE, 84000 Avignon, France</footnote>

<footnote>* Corresponding author at: UMR CEREGE, INRAE, Technopôle de l'Arbois Méditerranée BP 80 13545, Aix-En-Provence Cedex 04, France.
E-mail address: hamza.chaif@inrae.fr (H. Chaif).</footnote>
result of tens to thousands of years of the cumulative effects on the solid phases of soil functioning, consisting in short cycles (generally intra-annual) of water, gas and heat transfer and of the action of biota which, on the long term, produce effects which may be irreversible (Lin, 2011). Human activities over the past centuries are well documented with information on the types and timing of land use and management practices changes. They are responsible for soil evolution (Cornu et al., 2012; Cornu et al., 2022; Montagne et al., 2016) and their knowledge made the evolution of soil properties measurable over short time periods.

Multiple soil development models have been developed in the past decades with different levels of complexity (Hoosbeek & Bryant, 1992; Minasny et al., 2008; Samouëlian et al., 2012; Samouëlian & Cornu, 2008; Stockmann et al., 2011; Vereecken et al., 2016). Some focus only on the solid part of the soil (Cohen et al., 2010; Salvador-Blanes et al., 2007), while others include water, solutes and solids (WITCH model (Goddéris et al., 2006); SoilGen model (Finke & Hutson, 2008)). If the aim is to project the evolution of soil under global change, an explicit description of water flow as the motor of soil evolution is fundamental (Lin, 2011; Samouëlian & Cornu, 2008), as well as the interactions and feedback loops between the considered processes. On the whole, among all the available models, only a few attempted to couple major soil forming processes, while considering the role of water and solute transport, to simulate the feedback mechanisms among the soil properties (SoilGen (Finke & Hutson, 2008)). As shown by Keyvanshokouhi et al. (2016), 1D soil evolution models have a great potential to be used for projection purposes due to their wide coverage of processes and their sensitivity to environmental forcing factors.

To our knowledge, with the exception of the recent soil-crop model described by Jarvis et al. (2024), all 1D soil evolution models that explicitly couple water flow to other soil processes are still based on the assumption of a constant soil volume over time. As mentioned by Vereecken et al. (2016), this assumption is reasonable for short term modelling but is no longer valid when considering a time scale of several tens of years or centuries. For instance, Keyvanshokouhi et al. (2016) showed that the SoilGen model failed to predict bulk density evolution because of the constant volume assumption. Indeed, soil development induces large changes in soil volume at different depths as evidenced by mass balance approaches (Brimhall et al., 1991; Brimhall & Dietrich, 1987; Chadwick et al., 1990). Multiple soil processes can be responsible for volume change, with varying intensities depending on the considered time scales. Loss of matter under solute or particulate form leads to volume collapse once a threshold is reached (Warrington et al., 2007). As an example, Brimhall & Dietrich, (1987) estimated a soil volume collapse of 60 % due to chemical weathering over periods up to 400,000 years. At shorter time scales, Montagne & Cornu, (2010) calculated a 5 % soil compaction along the drain line over 16 years of drainage. Soil dilation or compaction can also occur due to physical restructure by living organisms (bioturbation) or to the swelling of clayey soils after an increase of moisture (Meurer et al., 2020a; Raats and a. C., & Klute, A., 1968; Smiles, 2000; Smiles & Rosenthal, 1968). Brimhall & Dietrich, (1987) estimated a 70 % dilation in the organic matter rich layers over the course of podzol formation. Tonneijck et al. (2016) simulated a 300 to 400 % soil dilation over the course of 4800 years of volcanic soil formation. Human activities can also contribute to these volume changes with compaction by field traffic (van Ouwerkerk & Soane, 1994) or soil loosening by tillage or subsoiling (Evans et al., 1996; Gassel, 1982). Hamza & Anderson, (2005) measured a 15 to 39 % compaction due to field traffic in cropped lands. As a result, the volume of soil horizons and their associated bulk density, structure and hydraulic properties may strongly change over time.

Accounting for volume change in a 1D soil development model including solid/liquid transfer processes requires (i) a method to estimate volume change induced by compaction and dilation processes, by having independent calculations of both soil mass and volume within the model and (ii) that all the transfer equations recognize the new

coordinates of soil layers on which the state variables are being calculated. Difficulties arise due to the lack of knowledge of volume change induced by the different soil processes.

To overcome these limits, a first simple approach could consist in linking soil volume evolution to other soil processes using pedotransfer functions (PTF) as proposed by Tonneijck et al. (2016) in a model simulating the dynamics of organic carbon. PTFs simplify the complex and intertwined relationships between soil processes and volume dynamics to a statistical relationship between soil bulk density and one or multiple soil properties acting as proxies for the processes involved in volume change. In the case of the work by Tonneijck et al. (2016), the volume was evaluated by a pedotransfer function (PTF) based on soil organic carbon (SOC) content. Evidently, other relationships between soil volume and other soil properties reflecting different soil processes (chemical weathering, soil swelling, tillage, ...) could be introduced depending on the considered soil type and the environmental forcing factors responsible for its development (Tóth et al., 2015; Tranter et al., 2007).

In this paper, we propose a proof of concept of the possibility to consider volume change in 1D process-based soil evolution models considering explicit water transfer. To do so, a simple PTF developed to evaluate bulk density was integrated in the process-based soil evolution model OC-VGEN developed by Keyvanshokouhi et al. (2019). OC-VGEN considers the following soil processes: water, heat and gas transfer, soil organic carbon dynamics, plant development, tillage and bioturbation. The new version of the model, and the corresponding constant volume version, were used to simulate the evolution of soil properties on three well characterized long-term experiments (Jagercikova et al., 2017; Keyvanshokouhi et al., 2016, 2019) subject to reduced tillage (switch from conventional tillage to reduced tillage) for more than ten years or land use change (switch from cropping to pasture) for several decades. Projections (until 2100) under two contrasted climate change scenarios were also conducted.

## 2. Material and methods

### 2.1. Soil evolution model

OC-VGEN (Keyvanshokouhi et al., 2019) is a 1D, mechanistic process-based model developed within the Virtual Soil "VSoil" modelling software platform (EMMAH, 2013; Lafolie et al., 2014). It takes into account the factors of soil formation as initial or boundary conditions. Both OC-VGEN and VSoil are briefly presented below. For more information, the reader is referred to Keyvanshokouhi et al. (2019).

#### 2.1.1. The VSoil modelling platform

VSoil (EMMAH, 2013; Lafolie et al., 2014) is a modelling software platform that aims at developing numerical models describing the physical, chemical and biological processes of the soil in interaction with the climate, plants and anthropogenic activities. This platform is characterized by its modular structure that facilitates the development of complex models by assembling multiple modules via an easy-to-use Graphical User Interface (GUI). It also makes it easier to improve and modify an existing model by editing the numerical expression of the modules considered within it without changing the overall structure of the model. This modular structure has consequences on the functioning of the platform in which the biological, chemical and physical soil processes are considered (e.g. bioturbation, sorption, water transfer, ...). In fact, each process can be associated to several numerical expressions (modules) that can differ by their levels of complexity (from empirical to fully mechanistic). This allows building models with different levels of complexity depending on the processes considered and the information (knowledge/data) available. Finally, a chosen set of ordered processes, each associated to one numerical expression (module) is what is considered a model in the platform.
<figure><img src="image_7.png" /><figcaption>Fig. 1. Interactions between soil mass, soil volume, bulk density and the soil processes considered by the OC-VGEN model. Blue dashed lines represent interactions within the classical version of OC-VGEN while the green solid lines refer to new interactions introduced in the volume change version of OC-VGEN. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

### 2.1.2. The OC-VGEN model

As previously mentioned, OC-VGEN (Keyvanshokouhi et al., 2019) includes the following processes: water, heat and gas transfer, soil organic carbon dynamics, plant development, tillage and bioturbation (Fig. 1). The numerical representation (module) used in OC-VGEN for each of these processes is described below.

#### 2.1.2.1. SOC dynamics module.
The soil organic carbon (SOC) dynamics module was developed based on the RothC model (Coleman et al., 1997) with some adaptations based on Finke & Hutson, (2008). In this module, SOC is split between five different pools (decomposable plant material (DPM), resistant plant material (RPM), biomass (BIO), humus (HUM), and inert organic matter (IOM)). Each SOC pool decomposes over time following a classical first-order kinetics equation with half-lives that differ strongly among pools (from a month to over 50 years) except for IOM, which is considered stable in the model. Additionally, the decomposition rates are subject to rate modifiers that depend on moisture deficit, temperature, clay content and soil cover (Coleman et al., 1997). This module is computed daily and affects the SOC mass in each layer and therefore modifies the soil mass ($M_{soil} = M_{clay} + M_{silt} + M_{sand} + 1.72*M_{SOC}$).

#### 2.1.2.2. Water, heat, and gas transfer modules.
Water transfer is simulated using the Richards' equation. The soil hydraulic properties required to solve this equation are estimated yearly using the HYPRES pedotransfer function that takes into account soil texture, SOC stock and bulk density (Finke (2012), adapted from Wösten et al. (1999)). Upper boundary conditions for water flow consider surface infiltration and evaporation. When the soil infiltrability is exceeded, a zero-surface soil water potential condition is imposed. Additionally, the evaporative flux is a function of the soil cover via a factor that depends on the land use. In this study, the lower boundary condition accounts only for free drainage.

Heat and gas transfers are simulated using an advection-diffusion equation. The convective transport of heat is induced by water transfer and the soil heat capacity and conductivity are functions of the bulk density and porosity.

All these transfer equations are resolved on a variable timestep in the interval $[10^{-10}; 0.1]$ day and have no impact on the mass of soil solids in each layer.

#### 2.1.2.3. Plant modules.
The plant modules provide organic carbon to the soil and uptake water from it. They consist of three modules: a) plant organic carbon input to the soil; b) plant root depth distribution; and c) water uptake by roots.

The first consists of an input file indicating organic carbon input to the soil through Net Primary Production (NPP) and/or organic amendments. This module introduces SOC to the soil and therefore modifies its soil mass.

The plant root depth distribution is defined by a root density function, a rooting depth and the ratio of above and below-ground fresh organic input. OC-VGEN uses a constant exponential root depth distribution for permanent vegetation following Finke (2012). For crops, the root system is assumed to be growing within the year based on the pre-defined dates of planting, germination and root maturity according to an approach introduced by Davidson (1978).

Root water uptake is based on the LEACHC model (Hutson & Wagenet, 1995). The function used in this model optimizes the root water potential to satisfy the actual transpiration of the plant taking into account the fraction of active roots present, and water availability in each soil layer (Finke, 2024). For now, feedbacks between water uptake and carbon inputs to the soil are not considered. Root water uptake is calculated on the same timestep as the one used by the water flow module.

#### 2.1.2.4. Mass mixing modules.
The mixing processes considered in OC-VGEN are bioturbation and tillage. These two processes were implemented in the model based on Finke & Hutson (2008). Both processes are simulated by a simple mixing module in which a fraction of each soil layer within the mixed depth contributes a fraction of its soil mass to a mixing pool (vertical mixing). The mixing pool is then redistributed over the mixed layers according to the same mass fraction (horizontal mixing). Both these mixings have no impact on the soil mass in each layer and are computed on a yearly time step (Finke, 2012).

#### 2.1.2.5. Mass, volume and processes interactions.
In OC-VGEN, volume is originally considered as constant through time and is used to calculate the bulk density $\rho$ (kg m$^{-3}$) defined as:

$$ \rho(z, t) = \frac{M_{soil}(z, t)}{V_{soil}(z)} \qquad (1) $$
where $M_{soil}$ (kg) and $V_{soil}$ (m³) respectively stand for the soil mass and volume at a given time $t$ and a grid cell's depth $z$ ($z = 0$ corresponds to the soil surface). In a one-dimensional model like OC-VGEN, the soil surface is assumed to be equal to $1 \text{ m}^2$ and therefore the soil volume is equivalent to its thickness $\Delta z$ (m) ($V_{soil} = S * \Delta z = 1 \text{ m}^2 * \Delta z = \Delta z$). Soil mass $M_{soil}$ is defined as the sum of the mass of clay, silt, sand and SOC ($M_{soil} = M_{clay} + M_{silt} + M_{sand} + 1.72 * M_{SOC}$) and only varies due to SOC dynamics in the current state of development of the model.

Since $M_{soil}$ is simulated by the model, either $\rho$ or $\Delta z$ ($V_{soil}$) have to be estimated (Fig. 1). Classically, $\Delta z$ ($V_{soil}$) is considered as constant in time and $\rho$ is then calculated following Eq. 1 and used, for instance, in water and heat transfer processes to estimate the thermal and hydraulic properties and to convert calculated soil particle and SOC stocks into mass percentages. This results in feedback effects between the solid balance module and the water and heat transfer modules. In addition, the distribution of water and heat in the profile directly affects the decomposition of SOC and thus contributes to the SOC dynamics in the model.

## 2.2. The new volume change module

### 2.2.1. Principle of the approach

In this study, to move beyond the constant volume assumption, we estimate the bulk density $\rho_{new}$ on a yearly timestep by a pedotransfer function independent from Eq. 1 and then calculate $\Delta z_{new}$ based on Eq. 1, as follows:

$$ \Delta z_{new}(z, t) = \frac{M_{soil}(z, t)}{\rho_{new}(z, t)} \qquad (2) $$

Layers that grow beyond a thickness threshold (2 times the initial thickness in this work) are divided into two equally thick layers. The opposite situation with layers becoming too thin is not likely to occur over the studied time scales and is thus not considered.

Changing the soil layer thickness affects the coordinates of the layers on which the model solves the transfer equations (water, gas, heat). The newly calculated soil layer thicknesses are used to define a new grid in the OC-VGEN model. Then, each model output $X$ (e.g. water content, soil temperature, ...) that is impacted by the volume change is updated as follows:

$$ X_{new} \Delta z_{new} = X_{old} \Delta z_{old} \qquad (3) $$

### 2.2.2. Choice of the pedotransfer function

Different modelling approaches can be adopted when considering the evolution of soil volume through that of soil bulk density. One approach considers a physically-based estimation of bulk density by accounting for the dynamics of the volume of the different pore types present in the soil as well as variations of mineral and organic solid masses (Adams, 1973; Federer et al., 1993; Stewart et al., 1970). This approach is used today in some crop models (Jarvis et al., 2024; Meurer et al., 2020b). Another approach consists in establishing statistical relationships (i.e. pedotransfer functions) between the soil bulk density and other soil properties. However, for modelling purposes, the choice of the pedotransfer function (PTF) is crucial. In fact, the selected PTF should link the bulk density to model outputs that are susceptible to evolve under the simulated conditions. For instance, a PTF linking soil bulk density to sand or clay fractions cannot be used in a model that considers these properties constant. Multiple PTFs linking soil bulk density to various soil properties exist in the literature. Some link the soil bulk density to its mineral (sand, silt and clay) and organic composition (Tranter et al., 2007) and are therefore ideal for models that account for clay translocation and alteration of soils (Salvador-Blanes et al., 2007; Temme & Vanwalleghem, 2016; Vanwalleghem et al., 2013). Others link soil bulk density to SOC as a proxy for biological activity (Alexander, 1980) or to hydraulic properties (Tóth et al., 2015).

Since in the state of development of our model, only the SOC mass

<table><caption>**Table 1**

General description of the studied sites.</caption><thead><tr><th>Site</th><th>Mons</th></tr></thead><tbody><tr><td>Coordinates</td><td>49°52'01" N – 3°01'53" E</td></tr><tr><td>Elevation</td><td>88 m</td></tr><tr><td>Mean annual rainfall</td><td>680 mm</td></tr><tr><td>Mean annual temperature</td><td>11 °C</td></tr><tr><td>Vegetation</td><td>Wheat – corn – sugar beet when cropped; Pasture since 1939</td></tr><tr><td>Tillage depth history</td><td>Conventional tillage plot:<br>Reduced tillage: Pasture: last tillage in 1939<br>- 1939–1960: 20 cm;<br>- 1961–1990: 40 cm;<br>- 1991–2011: 25 cm.<br>- 1939–1960: 20 cm;<br>- 1961–1990: 40 cm;<br>- 1991–1999: 25 cm;<br>- 2000–2011: 10 cm.</td></tr><tr><td>Maximal distance between plots</td><td>2 km</td></tr><tr><td>Sampling date</td><td>March 2011</td></tr></tbody></table>

evolves over time, we chose to independently estimate the soil bulk density $\rho_{new}$, with a pedotransfer function (PTF) that can calculate $\rho_{new}$ based on SOC (Alexander, 1980):

$$ \rho_{new}(z, t) = \rho_{max} - a \sqrt{\%OC(z, t)} \qquad (4) $$

where %OC ($g_{soc}$ 100$g_{soil}^{-1}$) is the mass percentage of SOC, $\rho_{max}$ (kg m$^{-3}$) is the maximum soil bulk density, and $a$ (-) is an empirical coefficient. The estimation of $\rho_{max}$ and $a$ will be addressed in section 2.2.3. With this formulation, the bulk density profiles are, by default, a direct consequence of the simulated vertical distribution of SOC.

This PTF was selected because: (i) given the considered processes in this version of OC-VGEN and their numerical expression, SOC is the main model output that can be directly linked to volume change through a PTF, (ii) it was classically used in multiple previous studies to evaluate bulk density through SOC (Boschi et al., 2018; Kaur et al., 2002; Manrique & Jones, 1991; Tamminen & Starr, 1994; Yi et al., 2016), (iii) it was developed on a relatively large dataset (721 samples from cultivated and uncultivated soils), (iv) it is relatively simple which simplifies its implementation and calibration. In this PTF, SOC is in fact a proxy of the biological processes that modify the bulk density. Therefore, it does not reflect well changes in bulk density at depths where SOC content becomes more or less constant and bulk density changes are more related to weathering processes not reflected in SOC content changes (e.g., carbonate dissolution). For that reason, we limited the studied depth to the first 50 cm of the soil.

This PTF can be substituted by more complex PTFs, thanks to the modularity of the VSoil platform, when more processes will be integrated in the model and knowledge linking volume change to soil processes becomes available.

### 2.2.3. Calibration of the PTF

The parameters $\rho_{max}$ and $a$ of the Alexander PTF (Eq. 4) were calibrated using the nonlinear least square method. For this purpose, the numerical R routine “nls” was used (R core Team, 2013). Measurements of soil organic carbon and bulk density obtained on Luvisols developed in loess were extracted from two databases: (i) the first campaign of the French soil monitoring network (RMQS) (Jolivet et al., 2006) and (ii) the SOLHYDRO database (Bruand et al., 2004). Only measurements above the 50 cm depth were considered and forest sites were excluded. A total of 106 soil layers with both bulk density and SOC measurements was extracted and used for the calibration.
<table><caption>**Table 2**
General layout of the simulation protocol.</caption><thead><tr><th>Simulation</th><th>Model</th><th>Land use</th><th>Tillage</th><th>Period</th></tr></thead><tbody><tr><td>1</td><td>OC-VGEN</td><td>Crop</td><td>Conventional tillage</td><td>1939–2011</td></tr><tr><td>2</td><td>OC-VGEN</td><td>Crop</td><td>Reduced tillage</td><td>1939–2011</td></tr><tr><td>3</td><td>OC-VGEN</td><td>Pasture</td><td>No tillage</td><td>1939–2011</td></tr><tr><td>4</td><td>OC-VGEN</td><td>Pasture</td><td>No tillage</td><td>2012–2100 (H2.6)</td></tr><tr><td>5</td><td>OC-VGEN</td><td>Pasture</td><td>No tillage</td><td>2012–2100 (H8.5)</td></tr><tr><td>6</td><td>OC-VGEN volume change</td><td>Crop</td><td>Conventional tillage</td><td>1939–2011</td></tr><tr><td>7</td><td>OC-VGEN volume change</td><td>Crop</td><td>Reduced tillage</td><td>1939–2011</td></tr><tr><td>8</td><td>OC-VGEN volume change</td><td>Pasture</td><td>No tillage</td><td>1939–2011</td></tr><tr><td>9</td><td>OC-VGEN volume change</td><td>Pasture</td><td>No tillage</td><td>2012–2100 (H2.6)</td></tr><tr><td>10</td><td>OC-VGEN volume change</td><td>Pasture</td><td>No tillage</td><td>2012–2100 (H8.5)</td></tr></tbody></table>

## 2.3. Evaluation dataset

### 2.3.1. Study sites

Three Haplic Luvisol (IUSS Working Group WRB, 2022) profiles developed on loess deposits in the Paris Basin at Mons were selected for this study (Table 1). They were already extensively characterized elsewhere (Jagercikova et al., 2014, 2015, 2017; Keyvanshokouhi, 2018; Keyvanshokouhi et al., 2016, 2019). Two profiles are part of the long-term experiment “Mons Essay system”. They are cropped and subject to different tillage practices (conventional and reduced). The third profile belongs to a farm located at a maximum of 2 km from the cropped plots and is used as pasture (Jagercikova et al., 2014). In each plot, soils were continuously sampled with varying increments of 2–10 cm depth. Collected samples were oven-dried at 40 °C and sieved to 2 mm. These samples were analyzed for their organic carbon content (NF ISO 10694

method). Soil bulk densities were also determined by the cylinder method for each horizon and by gamma-ray attenuation for surface horizons.

All the studied plots were cropped for at least the last 270 years as can be seen on Cassini, 1750. In 1939, i.e., 72 years before the sampling date (2011), one of the plots was converted to pasture (Mons-P hereafter) while the other two experienced differentiated tillage (conventional tillage and reduced tillage, called respectively Mons-CT and Mons-RT hereafter) over the last 11 years (Fig.A.1).

### 2.3.2. Model inputs

Forcing data consist in climate (annual precipitation, January and July temperatures, and annual evapotranspiration), NPP, land use and tillage history for the three considered plots. Organic carbon inputs to the soil are known for the last 11 simulated years (2001–2011) for the two-cropped plots and were estimated at 5 t ha⁻¹ yr⁻¹ from 1939 to 1970 and then at 4 t ha⁻¹ yr⁻¹ from 1970 to 2001 (Keyvanshokouhi et al., 2019). This decrease in organic carbon inputs to the soil was due to an increase of crop exportation and the introduction of chemical fertilizers following agriculture intensification in the 1970 s. For Mons-P, organic carbon inputs to the soil were estimated at 15 t ha⁻¹ yr⁻¹ based on the annual yields measured of another pasture on a similar soil type of this region of France (Corbeille et al., 2016). Climate input data were provided by METEO France for this site (SAFRAN grid; (Quintana-Seguí et al., 2008)) for the period extending from 1939 to 2011.

## 2.4. Models’ evaluation

### 2.4.1. Simulation protocol

To study the impact of volume change in simulations of the evolution of soil properties, we ran OC-VGEN with and without volume change on the three considered plots over the period 1939–2011 (Table 2). Before these simulations, a 300 years spin-up run was conducted to determine the initial conditions of the target simulations (mainly the distribution of carbon between the five pools of the SOC dynamics module, as well as

<figure><img src="image_8.png" /><figcaption>**Fig. 2.** Soil bulk density as a function of soil organic carbon concentration. RMQS (green squares) and SOLHYDRO (blue dots) data were used to calibrate the Alexander pedotransfer function (black line). The grey ribbon represents the standard error around the best fit provided by the “nls” algorithm. The best fitted values of parameters (ρ<sub>max</sub>; a) are reported on the plot. Mons data from the studied sites (red triangles) are also reported. They were not used for the calibration but serve for its validation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 3. Simulated and measured vertical profiles of bulk density for the three studied plots. The simulated profiles correspond to those obtained at the end of the simulation with volume change (solid lines, vch) and no volume change (dashed lines, no-vch). The shaded areas correspond to the upper and lower limits linked to the uncertainty range of the fitted Alexander PTF parameters. These limits were obtained by two simulations considering the following parameters [ρmax, a]: [1.679 + 0.035 g cm⁻³; 0.248 - 0.037] and [1.679 - 0.035 g cm⁻³; 0.248 + 0.037]. The origin of the vertical axis (depth) refers to the position of the soil surface at the start of the simulation. Measurements were positioned following the depth axis at the end of the simulation with volume change.</figcaption></figure>

the soil bulk density). This run was conducted without volume change on a plot profile subject to agriculture with conventional tillage. The forcing data for this spin-up run consisted in input fluxes and climate data of the 1939–1958 period repeated over the span of the 300 years run.

We extended the Mons-P simulation until the year 2100 in order to explore the effects of longer time-spans on volume change, and their consequences on soil properties. To do so, we considered the two climate changes based on the two IPCC scenarios RCP2.6 (emissions decreasing after 2020) and RCP8.5 (emissions continue to rise). The climate input data were simulated and bias corrected by the Earth System Model HadGEM. The NPP variations were estimated from an independent run of the land surface model ORCHIDEE (Krinner et al., 2005) forced by the same climate scenarios. In this study, we refer to these two additional scenarios as H2.6 and H8.5 respectively as already presented in Key-vanshokouhi et al. (2019).

### 2.4.2. Statistical analysis of models’ deviation

To quantify the effects of the volume change implementation on the model’s performance, we estimated the model-measurement discrepancy using the statistics of deviation proposed by Kobayashi & Salam, (2000).

The Mean Squared Deviation, MSD (Eq.5) was calculated as well as

its three components, i.e., the squared bias of simulation (SB – Eq.6), the squared difference between standard deviations of simulation and measurements (SDSD – Eq.7) and the lack of positive correlation weighted by the standard deviations (LSC – Eq.8).

$$MSD = \frac{1}{n} \sum_{i=1}^{n} (x_i - y_i)^2 \qquad (5)$$

$$SB = (\bar{x} - \bar{y})^2 \qquad (6)$$

$$SDSD = (SD_s - SD_m)^2 \qquad (7)$$

$$LCS = 2SD_sSD_m(1 - r) \qquad (8)$$

where n is the number of measurements, xᵢ and yᵢ are the simulated and measured values respectively, x⁻ and y⁻ are their corresponding arithmetic means, SDs is the standard deviation of simulations and SDm that of measurements, and finally r represents the correlation coefficient between the simulations and measurements, defined as:

$$r = \frac{\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{SD_m SD_s} \qquad (9)$$

The sum of the three components SB, SDSD and LCS equals the MSD by
<figure><img src="image_10.png" /><figcaption>**Fig. 4.** Simulated and measured vertical profiles of soil organic carbon mass concentrations for the three studied plots. The simulated profiles correspond to those obtained at the end of the simulation with volume change (solid lines) and no volume change (dashed lines). The shaded areas correspond to the upper and lower limits linked to the uncertainty range of the fitted Alexander PTF parameters. These limits were obtained by two simulations considering the following parameters [$\rho_{max}$, a]: [1.679 + 0.035 g cm$^{-3}$; 0.248 – 0.037] and [1.679 – 0.035 g cm$^{-3}$; 0.248 + 0.037]. The origin of the vertical axis (depth) refers to the position of the soil surface at the start of the simulation. Measurements were positioned following the depth axis at the end of the simulation with volume change.</figcaption></figure>

definition. The lower the value of MSD, the closer the simulation is to measurements. SB informs on the bias of the simulation from the measurements, SDSD on the difference in the magnitude of fluctuation between the simulation and measurements, whereas LCS quantifies the model's ability to reproduce the pattern of fluctuations across the measurements.

# 3. Results & discussion

## 3.1. Pedotransfer function calibration

Overall, the fitted curve ($[\rho_{max}, a] = [1.679 \text{ g cm}^{-3}; 0.248]$) reproduced reasonably well the distribution of the measured data with most of the points being within the uncertainty range of the fit (Fig. 2). The points that were outside the uncertainty ribbon —corresponding to the standard error of the fit— probably illustrate the effect of other soil processes, not taken into account by the Alexander PTF, on the soil bulk density. For instance, the points that were above the uncertainty ribbon were almost exclusively measured in the top soils (0–30 cm; 15/20 points) of cropped plots (18/20 points) with higher densities than predicted. This is probably due to soil compaction by agricultural field traffic that is not represented by the Alexander PTF since the bulk density values are higher under these conditions for the same SOC

content. Almost all the measured values for the Mons plots (validation points not used for the calibration) fall within the range of the calibrated curve suggesting that the considered PTF and its calibrated parameters are reasonably suited for our study site.

To quantify the implications of the uncertainty of the calibrated PTF parameters on the model performance, two additional simulations were conducted, for each plot, incorporating the standard errors of the fitted parameters $\rho_{max}$ and a (Fig. 2). More precisely, a first simulation was done using $[\rho_{max}, a] = [1.679 + 0.035 \text{ g cm}^{-3}; 0.248 - 0.037]$ as parameters of the PTF while the second simulation used $[\rho_{max}, a] = [1.679 - 0.035 \text{ g cm}^{-3}; 0.248 + 0.037]$. These two additional simulations provided the upper and lower bounds of all model outputs presented in this paper.

## 3.2. Bulk density depth distributions

For bulk densities of the cropped plots, both versions of the model predicted a similar depth distribution characterized by a constant bulk density in the tilled layer followed by an increase in the deeper layer (Fig. 3). We observe a systematic increase in simulated bulk densities with the soil volume change compared to the constant volume assumption. In Mons-CT, this increase induced an overestimation compared to the measured values especially in the top tilled layer. In
<figure><img src="image_11.png" /><figcaption>**Fig. 5.** Mean Squared Deviation (MSD) and its three components for the soil bulk density (g.cm⁻³): lack of correlation weighted by the standard deviation (LCS), the squared difference between standard deviations (SDSD), and the squared bias (SB). For the three studied plots, results of the versions of OC-VGEN with and without volume change are presented.</figcaption></figure>

Mons-RT, the volume change simulation showed bulk density increases at depths of around 15 cm and 40 cm (Hill & Cruse, 1985). These two depths reflect the tillage history of this plot since the first increase, at around 15 cm, could be linked to the reduction of tillage intensity and depth during the last 12 years of the simulation while the second increase, at around 40 cm, corresponds to the conventional tillage depth that was performed before the tillage reduction. This effect of the tillage reduction on bulk density was not simulated by the constant volume version, even though tillage reduction can have an impact on SOC depth distribution (Baker et al., 2007). This SOC change due to tillage represents a too small portion of the total soil mass to affect the bulk density when only mass change is considered (constant volume). In contrast, the systematic overestimation of the bulk density values by the model with volume change compared to measurements, even though the SOC distributions were well simulated by the model (Fig. 4), suggests that the Alexander PTF function does not fully describe the impact of tillage on bulk density but only its indirect consequences on SOC concentrations. In fact, the SOC proxy notably does not account for the mechanical decompaction effect of soil tillage near the surface. Therefore, introducing PTFs that link more explicitly bulk density to the related processes should improve the model's ability to simulate volume change. Other studies already developed such PTFs linking the soil bulk density to other properties like soil moisture and particle size distribution notably (Tóth et al., 2015; Tranter et al., 2007).

For Mons-P, volume change had a considerable impact on bulk density profiles (Fig. 3). The volume change assumption allowed a better description of the gradual increase of bulk density with depth, an increase that was in line with the measured values. In contrast, in the absence of volume change, bulk densities tended to remain constant for depths between 2.5 and 37 cm except in the first layer where bulk densities were significantly higher (of almost 0.39 g.cm⁻³ compared to volume change) probably due to an important accumulation of SOC

within this layer not compensated by a change in volume (Fig. 4). The difference between the two models tended to reduce with depth. It should be noted, however, that both measured and predicted values suffer from uncertainties ranging from around 0.23 g.cm⁻³ near the surface to 0.12 g.cm⁻³ at the bottom of the profile. These uncertainties have to be considered when comparing the simulations and measurements.

Quantitatively, the introduction of volume change significantly improved the bulk density simulations for two out of three considered plots (Fig. 5 & Table A.1). In Mons-P, the mean standard deviation (MSD) decrease was over 350 % after the introduction of volume change. For this plot, however, the decrease was mainly due to a reduction of the share of the lack of positive correlation weighted by the standard deviations (LCS) that dropped from 89 % to 66 %. This suggests that volume change allowed a significant improvement of the shape of the profile. In Mons-RT, the MSD decreased by around 300 % when volume change was considered. This decrease was mainly due to a reduction of the squared bias (SB) whose contribution dropped from 73 % to only 18 % suggesting that the improvement was mainly due to the average simulated bulk density of the profile tending towards the average measurement. In Mons-CT, volume change caused an increase of the MSD by around 280 %. This increase was mainly due to SB's contribution that changed from only 2 % to 75 % suggesting a significant deviation from the average measured bulk density. For all three plots, the share of the squared difference between standard deviations of simulation and measurements (SDSD) remained small and stable suggesting that the inclusion of volume change had little to no effect on the magnitude of fluctuations between the simulations and measurements.

### 3.3. Amplitude of soil volume change

The evolution of the soil layers' thicknesses evidenced a slight
<figure><img src="image_12.png" /><figcaption>Fig. 6. Evolution of grid cell thicknesses as a function of depth for the three studied plots in reference to those of the initial fixed grid. The simulated profiles correspond to those obtained at the end of the simulation (after 72 years). The shaded areas correspond to the upper and lower limits linked to the uncertainty range of the fitted Alexander PTF parameters. These limits were obtained by two simulations considering the following parameters [ρmax, a]: [1.679 + 0.035 g cm⁻³; 0.248 – 0.037] and [1.679 – 0.035 g cm⁻³; 0.248 + 0.037]. The origin of the vertical axis (depth) refers to the position of the soil surface at the start of the simulation.</figcaption></figure>

reduction of soil volume under conventional and reduced tillage and a significant expansion near the surface after conversion to pasture (Fig. 6). In Mons-CT and Mons-RT, the overall profile depths did not significantly change. However, conversion to pasture induced a significant expansion of the whole profile of around 3 cm. The magnitude of this expansion was maximum in the first layer (around 40 %) and quickly dropped to less than 10 % for all remaining layers. For all three plots, the numbers of soil layers remained the same since soil dilatation never exceeded double the initial thickness. Similarly, as expected, soil compaction was not substantial enough to trigger the need to merge two layers into one.

### 3.4. Impact of volume change on soil hydraulic properties

Volume change has consequences on hydraulic properties as it modifies the soil porosity. These consequences are partially reflected in the volume change version of OC-VGEN since the bulk density is used to update the water retention curve parameters through the HYPRES pedotransfer function (Fig. 1). In order to explore the amplitude of this effect, we calculated the Available Water Capacity (AWC), an intrinsic property of the soil that describes the amount of available soil water that could be extracted by the plant defined as follows:

$$AWC(z, t) = (W_{FC}(z, t) - W_{WP}(z, t)) * \Delta z(z, t) \quad (10)$$
<figure><img src="image_13.png" /><figcaption>**Fig. 7.** Simulated vertical profiles of the Available Water Capacity (AWC) for the three studied plots. The simulated profiles correspond to those obtained at the end of the simulation with constant volume (A) and volume change (B). The shaded areas correspond to the upper and lower limits linked to the uncertainty range of the fitted Alexander PTF parameters. These limits were obtained by two simulations considering the following parameters [$\rho_{max}$, a]: [1.679 + 0.035 g cm⁻³; 0.248 – 0.037] and [1.679 – 0.035 g cm⁻³; 0.248 + 0.037]. The origin of the vertical axis (depth) refers to the position of the soil surface at the start of the simulation.</figcaption></figure>

where $W_{FC}$ and $W_{WP}$ represent respectively the water content at field capacity and at wilting point at depth $z$ and time $t$. When constant volume was considered, both tillage reduction and conversion to pasture did not result in any significant change in the AWC compared to Mons-CT (Fig. 7A). When volume change was activated (Fig. 7B), the reduction of tillage still did not significantly change the AWC over the depth of the tillage reduction. However, a significant increase of the AWC was simulated after the conversion to pasture. It reached around 59 % at the very top layer and exponentially decreased to reach around 3 % at the bottom of the profile.

Other authors also reported an improved water storage in response to changes of bulk density when soil disturbances are reduced (Kargas et al., 2012, 2016; Lampurlanés & Cantero-Martínez, 2003; Xu & Mermoud, 2001). Additionally, larger available water capacities under pasture in comparison to cropped lands were measured in other studies (Horel et al., 2015; Kodešová et al., 2011) and interpreted as resulting from a more stable soil structure, higher porosity and fraction of the large capillary pores under pasture.

### 3.5. Impact of volume change on soil properties' evolution under climate change

Results of the projections over the 2012–2100 period (Table 2) have shown that the volume change version of OC-VGEN predicted less

carbon storage than the constant volume version no matter the climate change scenario (Fig. 8A). In fact, the two versions of the model progressively diverged after 2011. By 2100, the divergence reached 6 % and 2 % for H2.6 and H8.5 respectively. The constant volume hypothesis could therefore lead to an overestimation of the effects of climate change scenarios on the soil carbon storage. The continuous increase of soil carbon stock by 2100 led to a significant increase of soil volume similar for the two climate change scenarios (almost 5 cm) with notably an expansion by almost 76 % of the first soil layer (Fig. 8C & Fig.A.2).

To further explore the effects of volume change on the soil properties, we calculated the variations of the profile AWC for the studied period (1939–2100) with and without volume change (Fig. 8B). When constant volume was considered, both climate change scenarios yielded the same evolution of the AWC for the whole period. It was characterized by a slow increase that reached a maximum of 2.2 % in 2040 after which it slowly decreased to 1.5 % by 2100. The volume change model, however, predicted a continuous and more significant increase of the AWC throughout the simulated period that reached by 2100 around 14 % for both H2.6 and H8.5. It should be noted, however, that the range of uncertainty around the estimation of ΔAWC was quite high (around 6 %). This range even dwarfed the variations due to the selected climate change scenarios (around 1 %) meaning that, when considering volume change for predicting the evolution of soil properties, the choice of the pedotransfer function can be more crucial than the considered climate
<figure><img src="image_14.png" /><figcaption>**Fig. 8.** Temporal evolution of the total soil carbon stock (A), the total Available water Capacity (B) and the total profile depth (C) simulated under the two climate change scenarios H2.6 (blue) and H8.5 (red) for Mons-P. Simulations were conducted with (solid line) and without (dashed line) volume change. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

change scenario. Therefore, development of precise and reliable pedo-transfer functions that can account for more volume changing processes such as soil compaction (e.g. Kay & VandenBygaart, 2002), and weathering would be of great interest to further develop this model (Tóth et al., 2015; Tranter et al., 2007). This would also necessitate the introduction of other soil processes such as chemical weathering and clay translocation. Depending on the introduced soil processes, special attention should be given to the proxy variables for volume change

involved in the selected pedotransfer functions. The volume change update frequency should also be compatible with the time scales on which the introduced soil processes operate (weekly for wetting/drying cycles and pluriannual for chemical weathering processes for instance). In fine, these new introductions should allow better simulation of soil volume evolution over different time scales and improve the modelling of the development of deep soil horizons in particular.
<figure><img src="image_15.png" /><figcaption>Fig. 8. (continued).</figcaption></figure>

## 4. Conclusion

This study demonstrates the feasibility of considering soil volume change in a mechanistic model of soil evolution simulating explicitly water transfer on a short to medium time scale (10 to 170 years). One approach is to use a bulk density pedotransfer function to estimate soil volume change in soil. It allowed modelling the evolution of soil volume under different scenarios of land use and tillage practices. Simulations of changes in soil volume following tillage reduction or conversion to pasture performed with the new model are in agreement with both observations and measurements in the studied sites and trends reported by other authors in the literature. The proposed modelling approach seems thus realistic at least for the considered site. Testing the proposed model on more soil types, land uses or soil managements would provide a better evaluation of the range and limits of applicability of the modelling approach.

Removing the constant volume assumption increased the sensitivity of the model to changes of land use and tillage practices. The feedback mechanisms between soil bulk density and soil hydraulic properties, allowed to reflect the observed effects of volume change on soil water dynamics. The addition of volume change did not significantly modify the SOC simulations relative to data in this study for the period 1939–2011. However, accounting for volume change when extending the pasture simulation to an additional 89 years produced a notable effect on simulated soil carbon stocks following conversion of arable land to pasture.

The use of the chosen pedotransfer function allowed us to represent volume changes induced by SOC dynamics as a proxy for the impact of the biological activity on bulk density in soil. This PTF does not account for all processes responsible for volume change, notably compaction due to field traffic among others. Thus, development of improved pedotransfer functions that can provide more precise estimation of soil bulk density and that can explicitly account for other processes responsible for volume change like chemical weathering, tillage, soil translocation, solute transport or shrinking/swelling of clays would be of great interest to further improve this model. The VSoil modelling platform, on which OC-VGEN was developed, facilitates these improvements thanks to its modularity and flexibility.

## CRediT authorship contribution statement

**Hamza Chaif:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Saba Keyvanshokouhi:** Writing – review & editing, Writing – original draft, Software, Methodology, Data curation, Conceptualization. **Peter Finke:** Writing – review & editing, Supervision, Software, Methodology, Conceptualization. **Cédric Nouguier:** Writing – review & editing, Software. **Nicolas Beudez:** Writing – review & editing, Software. **Sophie Cornu:** Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

Part of this research was conducted in the framework of the Agriped project (ANR-10-BLANC-605) supported by the French National Research Agency (ANR). S. Keyvanshokouhi received a PhD grant from the French National Institute for Agricultural, Food and Environment (INRAE) and the French agency for environment and energy (ADEME). The authors are grateful to F. Lafolie for his contribution to the model development, to INRAE Mons-En-Chaussée and ARVALIS for providing access to their long-term experimental site and the associated data, to B. Davis for supplying reconstructed temperature and precipitation time series and to METEO FRANCE for providing climatic data from the SAFRAN grid for the studied sites.
# Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.geoderma.2025.117228.

## Data availability

Data will be made available on request.

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