Inverse Analysis of the Effect of Soil Vertical Heterogeneity on Land Surface andSubsurface Processes* Kun Yang1, Toshio Koike1, Baisheng Ye2(1: University of Tokyo, 2: Chinese Academy of Science)
River
Lab.,
Dept.
of
Civil
Engineering,
University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan.
*
e-mail: yangk@hydra.t.u-tokyo.ac.jp
Abstract
Surface soil moisture and temperature have been widely addressed in land surface processes modeling and satellite remotesensing, because they play a key role in land surface energy and water budget. However, it is rather difficult for most of land
surface models to reproduce the surface soil state in areas with high soil vertical heterogeneity, because these models use asingle parameter-set to characterize soil hydraulic and thermal processes. This study develops a single-source land surface
model to parameterize this heterogeneity. Its soil parameters are inversely estimated by minimizing a cost function that is
objectively determined by the discrepancy between observed and model-predicted values of soil moisture and temperature.
The approach is then used to investigate how the soil vertical heterogeneity affects subsurface processes and thus controls
soil surface state and surface energy budget. By a synthetic numerical experiment and a Tibet field experiment, we indicatethat (1) vertical heterogeneous soils cannot be effectively approximated by vertically homogenous soils in a land surface
model no matter how the soil parameters are adjusted; (2) soil vertical heterogeneity obviously affects soil subsurface
processes, and plays a very important role in controlling surface soil wetness and surface energy partition; (3) in particular,
the existence of dense vegetation roots in topsoils may significantly reduce thermal conductivity, increase soil water
potential, and enhance surface evaporation. We therefore conclude that it is indispensable to take the soil vertical
heterogeneity into account in land surface models, although most of them still assume vertically uniform soil parameters.
Keyword: Inverse approach, soil parameter estimation, soil vertical heterogeneity, surface energy partition

1. Introduction

2. A Single-Source Land Surface Model

Rn

Top
Mid

d1

H

G0
d2

ra

ra
rs

P
lE

Soil structures are not only horizontally heterogeneous
but also often vertically heterogeneous. The top layer of asoil can have a soil texture and amount of organic mattersdifferent from the deep layer. In this study, we intend toevaluate the effects of soil vertical heterogeneity in land
surface processes, which can play an important role insome regions but have not been widely addressed in land
surface models (LSMs). For this purpose, this study
develops a LSM that can take soil vertical heterogeneity
into consideration. Because some parameters are highlyvariable or sensitively change the input-state-output
response, we use an inverse approach to estimate soil
parameters in this LSM, so that the model can reproduce
the observed soil state. While many early studies (Gupta etal., 1999; Bastidas, 1999) only use near-surface soil
moisture and ground temperature, this study uses detailed
measurements of soil moisture and temperature at several
soil depths to estimate soil parameters and investigate soil
vertical heterogeneity. The inverse approach consists ofthree main steps, comprised of (1) a land surface model topredict soil moisture and temperature profiles and surface
fluxes, (2) a cost function to express the discrepancy
between observed and model-predicted values of soil
moisture and temperature (Section 3), and (3) an efficient
scheme to search the global minimum of the cost function(Section 4). Then, the inverse approach is used toinvestigate the effect of soil vertical heterogeneity on soil
wet ness, ground temperature, and surface energy partition(Section 5). Finally, we summarize the results (Section 6)

U a , Ta , qa

Roff
q0

G ↓

q ↓

G ↓

q ↓

z1
z2

Deep
zn-1
zn

Gb

qb

Fig. 1 Schematic of the single-source land surface model
Yang et al. (2004) suggested that single-source concept
is applicable to bare soil surfaces or sparsely and shortly
vegetated surfaces. The single-source model used in thisstudy is simplified from a dual-source model (Sellers et al.,1996). The single-source model structure is shown in Fig. 1.
It has three distinct features: (1) flux parameterizations forbare soils or shortly vegetated surfaces are improved basedon the GAME-Tibet experiments (Yang et al., 2002); (2)soil subsurface water and heat flows are simulated by amulti-layer scheme; and (3) soil vertical heterogeneity isparameterized. The model consists of a bulk
parameterization of surface turbulent fluxes, Richards’ Law
to calculate the soil water flow, and thermal diffusion
equation to calculate the soil heat flow. Verticallyheterogeneous soil column is approximated by two uniform
domains (top soil domain, bottom soil domain) and atransitional domain between the two. Each domain consistsof a number of layers, thinner in the top domain (~1 cm)
and thicker in the bottom domain (~10 cm). The number ofcomputational layers is adjustable.

3. Inverse model
Input data of the inverse model include forcing data todrive the LSM, and soil moisture and temperature profiles
for calibrations. There are many parameters in the LSM.
Surface albedo can be derived from measured downward
and upward short-wave radiations; aerodynamic roughness
length z0 can be derived from wind profiles; the surface
emissivity is specified as 0.97; the soil bulk density

ρ d ismeasurable by experiments; hydraulic conductivity isroughly estimated by an empirical formula. Therefore, we
select the parameters in Table 1 for optimization.
Table 1 Optimized parameters of the land surface model.
Parameter
SymbolUnit
Soil porosityθm 3 m −3sHydraulic parameters
Thermal parameters
Boundary of transitional
domain

ψs
b
λm
kT
d1
d2

m
—

W m -1 K −1—mmminimum, this study adopts the Shuffled Complex
Evolution method developed at The University of Arizona(SCE-UA) (Duan et al., 1992).

5. Case studies
The inverse approach described above is used to calibrate
the land surface model to two different data sets. The firstis a numerically generated data set (hereafter identicaltwin). The second is a real data set collected at the
GAME-Tibet Anduo site. Both cases are used to clarify (1)how soil vertical heterogeneity can affect surface soil stateand energy partition, and (2) whether verticallyheterogeneous soils can be approximated by uniform soils
with adjustable parameters. In addition, we show thecapacity of the inverse approach in estimating parametersby the identical twin study, and address effects ofvegetation roots on soil properties by the Tibet case study.
5.1 Identical twin
5.1.1 Data set. We assume that the total soil depth is 1.6
m and that this total depth is represented by three soil
layers with thickness values of 0.10, 0.15, 1.35 meters (inother words, d1 = 0.1 m , d 2 = 0.25 m ). We also assume thatthe topsoil is a typical clay loam with a higher porosity andwater potential and the bottom soil is a typical sandy loamwith a lower porosity and water potential. The ground is abare soil surface, which is wetted by two-day continuous
precipitation every 10 days in the first month, and dried inother days. A diurnally varying wind speed, temperature,radiations, and a constant specific humidity are used todrive the model. The model is then integrated 60 days
(hereafter forward run). Soil moistures at five depths andsoil temperatures at nine depths are recorded hourly. These
data are used as input data in the inverse estimation.

In this study, we simultaneously estimate soil hydraulicand thermal parameters. To establish a single-criterion for a
multi-objective calibration, it is crucial to select weightnumbers to maintain a trade-off between different
measures in the cost function. In this study, we use thefollowing objective function:(1)
F = RMSET / RMSET ,min + RMSEθ / RMSEθ ,minwhere RMSET and RMSEθ represent the root mean squareerrors of soil temperature and soil water content,
respectively. RMSET,min and RMSEθ,min are their minimum
values.
The optimization includes two steps: step I, minimize
RMSET to obtain RMSET,min, and minimize RMSEθ toobtain RMSEθ,min; step II, minimize the multi-objectivefunction Eq. (1) using the same data set and the same LSM
as model operator.

4. Optimization Algorithm
Optimizing parameters is a tough task in inverse
problems of soil parameters because cost functions usually
have multi-parameters and are highly nonlinear,non-derivable and even discontinuous. The parameter
space usually contains multiple minima. To find the global

Fig. 2 Optimized soil properties of the heterogeneous caseand homogeneous case of the identical twin study.

5.1.2 Parameter estimation and optimized output. We
carry out two calibrations: one considers the heterogeneityand uses different parameter-sets to characterize top andbottom soils (hereafter heterogeneous case); the other uses
a single uniform parameter-set to characterize theheterogeneous soil (hereafter homogenous case). For
comparisons, results of the two cases are summarized inFig. 2 - Fig. 4. Fig. 2 shows the estimated soil hydraulicand thermal properties; Fig. 3 and Fig. 4 present the
scatter-plots showing the comparisons of simulated soil
surface variable and energy partition between the “truth”
run and the optimized run. The heterogeneous casereasonably optimizes soil hydraulic functions and thermal
properties, while the homogenous case does not (Fig. 2).
The heterogeneous case also output correct groundtemperature, soil water content, sensible heat fluxes, andlatent heat fluxes (Fig. 3) while the homogenous case doesnot (Fig. 4).

Fig. 3 Comparison of surface variables between the "true"
and the optimized values for the heterogeneous case of theidentical twin study

locates at the central Tibetan Plateau. This site is coveredby sparse and short grasses in the summer, but vegetationroots share a large volume of the surface soil layer in allseasons and the bulk density of the soil is therefore much
lower than the deeper soil. Intensive observations werecarried out during May-Sepetember 1998, including
30-minute-recorded forcing data, hourly-recorded soil
temperature and moisture profiles. Moreover, there are two
sets of observed energy partitions measured by theeddy-correlation technique and by the Bowen ratio method.
Note that the so-called eddy-correlation measured latent
heat fluxes were derived from surface energy budget
equation given eddy-correlation measured sensible heat
fluxes (the latent heat fluxes were actually measured by theeddy-correlation, but the measurements are not trustable
due to a sensor problem, see Yang et al. (2004) for moredetails). Additionally, five soil samples were tested toanalyze soil properties
5.2.2 Parameter estimation and optimized output.
Similar to the identical twin study, we have aheterogeneous case and a homogeneous case. In theestimations, the aerodynamic roughness length is a key
parameter in determining energy partition, and its value isderived by Yang et al. (2003) using wind and temperature
profiles. The results are summarized in Fig. 5 - Fig. 7. Fig.
5 shows the hydraulic and thermal functions. Fig. 6 - 7
present the scatter-plots of energy partition between thesimulation and the observation. The most impressive resultin Fig. 5 is that the top domain and the deep domain havecompletely different properties, indicating that theexistence of dense vegetation roots within the topsoil
significantly changes its properties. Particularly, the topsoil
has a high porosity, low thermal conductivity, and high soil
water potential. It also outputs reasonable surface soil
moisture and ground temperature (not shown), and energy
partition (Fig. 6), while the homogeneous gives lower
surface wetness, higher ground temperature (not shown),
lower latent heat fluxes, and higher sensible heat fluxes(Fig. 7).

Fig. 4 Same as Figure 3, except for the homogeneous case
5.2 GAME-Tibet Anduo site
5.2.1 Description of site and data set. The GAME-Tibet
Anduo site (Lat. 32.241o N, Lon. 91.635o E, Elev. 4700m)

Fig. 5 Comparison of soil properties between optimization
cases and experiments for the Anduo site. Retention curvesin (b) were analyzed from five soil samples

Fig. 6 Comparison of sensible heat flux and latent heat flux
between the observations and the optimized values (fromthe inverse calibration) for the heterogeneous case of the
Anduo site for the optimizing period.

evaporation fluxes while reduce ground temperature andsensible heat fluxes. Therefore, the top domain, althoughshallow, is not only very important to sustain the plateau
ecological system, but also control water and energy
budget.
Moreover, we indicate that the subsurface and surface
processes in vertically heterogeneous soils cannot be
parameterized in the framework of a single uniform soil.
Therefore, it seems to be difficult for most of current LSMs
to account for the effects of the soil heterogeneity, since
they use a single parameter-set to characterize soil
properties. Fortunately, the Global Soil Data Task (2000) ismaking efforts to build a globally covered data set of soil
parameters, which can provide soil information of bothhorizontal heterogeneity and vertical heterogeneity.
Although there are still many uncertainties inside the data
set due to high variability of soil texture, it provides a
possibility to update current LSMs models by consideringsoil vertical heterogeneity.

References

Fig. 7 Same as Fig. 6, except for the homogeneous case

6. Conclusions
This work develops an inverse system to evaluate therole of soil vertical heterogeneity in controlling surface soil
wetness, ground temperature, and surface energy partition.
It consists of a single-source land surface model to predict
soil temperature and soil moisture, a cost function to
calculate the discrepancy between observed andmodel-predicted values of soil moisture and temperature,
and an efficient scheme SCE-UA to search the global
minimum of the cost function. The estimated parameters
can effectively characterize subsurface thermal andhydraulic processes.
We apply this system to a numerical synthetic data set
and a GAME-Tibet data set. Both suggest that soil vertical
heterogeneity plays a very important in determining
surface soil wetness, ground temperature, and thus surface
energy partition. Particularly, dense vegetation roots in the
Tibetan Plateau can significantly change the properties of
the topsoil, such as high porosity, high soil water potential,
and low thermal conductivity. The high soil water potential
may result in a wet soil surface, and thus enhance

Bastidas, L. A., H. V. Gupta, S. Sorroshian, W. J. Shuttleworth,and Z. L. Zhang, Sensitivity analyis of a land surface scheme
using multicriteria methods. J. Geophys. Res., 104 (D16),
19,481-19,490, 1999.
Duan, Q., S. Sorooshian, and V.K. Gupta, Effective and efficient
global optimization for conceptual rainfall-runoff models. Water
Resour. Res. 28, 1015-1031, 1992.
Global Soil Data Task, Global Soil Data Products CD-ROM(IGBP-DIS), CD-ROM, International Geosphere-Biosphere
Programme, Data and Information System, Potsdam, Germany.
Available from Oak Ridge National Laboratory Distributed
Active Archive Center, Oak Ridge, Tennessee, U.S.A.
[http://www.daac.ornl.gov], 2000.
Gupta, H. V., L. A. Bastidas, S. Sorroshian, W. J. Shuttleworth,and Z. L. Zhang, Parameter estimation of a land surface scheme
using multicriteria methods. J. Geophys. Res., 104 (D16),
19,491-19,503, 1999.
Sellers, P. J., D. A. Randall, G. J. Collatz, J. A. Berry, C. B. Field,
D. A. Dazlich, C. Zhang, G. D. Collelo, and L. Bounoua, A
revised land surface parameterization (SiB2) for atmospheric
GCMs, Part I: Model formulation. J. Climate, 9, 676-705, 1996.
Yang, K., T. Koike, H. Fujii, K. Tamagawa, and N. Hirose,
Improvement of surface flux parametrizations with aturbulence-related length. Q. J. R. Meteor. Soc, 128, 2073–2087,
2002.
Yang, K., T. Koike, and D. Yang, Surface flux parameterization in
the Tibetan Plateau. Boundary-Layer Meteorol., 106, 245-262,
2003.
Yang, K., T. Koike, H. Ishikawa, and Y. Mao, Analysis of the
Surface Energy Budget at a site of GAME/Tibet using aSingle-Source Model. J. Met. Soc. Jap., 82, 131-153,2004.