Journal of Hydrology 436–437 (2012) 1–12

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Calibrating a soil–vegetation–atmosphere transfer model with remote sensing estimates of surface temperature and soil surface moisture in a semi arid environment Marc E. Ridler a,⇑, Inge Sandholt a, Michael Butts b, Sara Lerer b, Eric Mougin c, Franck Timouk c, Laurent Kergoat c, Henrik Madsen b a

Geography and Geology, University of Copenhagen, Øster Voldgade 10, 1350 København K, Denmark DHI, Agern Allé 5, DK-2970 Hørsholm, Denmark c GET (umr 5563, CNRS/IRD/UPS), 16 Av. E. Belin, 31400 Toulouse, France b

a r t i c l e

i n f o

Article history: Received 5 May 2011 Received in revised form 16 December 2011 Accepted 22 January 2012 Available online 13 March 2012 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Cheif, with the assistance of Aiguo Dai, Associate Editor Keywords: Soil vegetation atmosphere transfer SVAT Multi-objective calibration Sensitivity Remote sensing Land surface temperature

s u m m a r y A series of numerical experiments has been designed to investigate how effective satellite estimates of radiometric surface temperatures and soil surface moisture are for calibrating a Soil–Vegetation–Atmosphere Transfer (SVAT) model. Multi–objective calibration based on error minimization of temperature and soil moisture model outputs is performed in a semi–arid environment. Model accuracy when calibrated using in situ versus satellite objectives is explored in detail. Observational meteorological datasets from the African Monsoon Multidisciplinary Analysis (AMMA) were used to force a column model during a growing season in Mali. Fourier Amplitude Sensitivity Test (FAST) revealed the most sensitive parameters to model outputs. Parameters found sensitive were subsequently optimized in a series of model calibrations to reveal trade-offs between model objectives. Our main findings are (1) the SVAT model performs well in the semi–arid environment, but underestimates peak growing season evapotranspiration and overestimates soil moisture, (2) most of the parameters important for flux estimates can be constrained using surface temperature and soil surface moisture with the three exceptions: root depth, the extinction coefficient and unstressed stomatal resistance, (3) flux simulations are improved when the model is calibrated using in situ surface temperature and soil surface moisture versus satellite estimates. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Environmental disciplines such as meteorology, climatology, agronomy and hydrology often require accurate monitoring of land surface water and energy fluxes. To this end, Soil–Vegetation– Atmosphere Transfer (SVAT) models have been designed to simulate the interaction between plant canopy processes and the environment. SVAT models are forced with standard meteorological data, but must first be parameterized to reflect the given land surface type. Although SVAT models are flexible enough to simulate environments as diverse as forests, shrub land or savannah, the challenge remains to accurately parameterize soil and vegetation characteristics. Proper land surface parameterization is crucial as it can induce small uncertainties at global scale but substantial uncertainties at the regional and seasonal scale (Fischer et al., 2010). This study focuses on model parameterization in the Sahel region of Africa. Being in a transition zone between the dry Sahara ⇑ Corresponding author. Tel.: +45 29704229. E-mail address: [email protected] (M.E. Ridler). 0022-1694/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2012.01.047

Desert and the tropical rain forest to the south, the Sahel has a very sensitive climate. This sharp climatic gradient impacts the atmospheric dynamics and water resources at different spatial and temporal scales. In order to better understand Sahelian climate, two major international projects have been designed. The first being the Hydrology–Atmosphere Pilot Experiment in the Sahel (HAPEX) between 1990 and 1992 (Goutorbe et al., 1994). More recently, the African Monsoon Multidisciplinary Analyses (AMMA) (Redelsperger et al., 2006), further investigated land—and atmosphere feedbacks during the monsoon. On a local scale (10 km), land surface feedback mechanism have a profound influence on the hydrological cycle (Taylor and Lebel, 1998) resulting in patterns of rainfall persistence. Improving land–atmosphere coupled models is a crucial step forward to capturing the dynamics of Sahelian monsoons to better predict its variability. Multi-objective calibration is a robust procedure to realize the overall optimal model parameters. The underlying principle is the recognition that a single parameter set is unlikely to optimize all model outputs (Gupta et al., 1999). For instance, calibration of a land surface model predictions against observations of the single

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several soil layers in the vertical direction which are characterized by the van Genuchten formulation (van Genuchten, 1980). Richards equation describes the relationship between hydraulic head, moisture content and hydraulic conductivity. The MIKE SHE land–surface–atmosphere component (Graham and Butts, 2006) used in this study, is based on the two–source approach first described by Shuttleworth and Wallace (SW) (Shuttleworth and Wallace, 1985). The revised land surface model (SW-ET) is coupled to MIKE-SHE (Overgaard, 2005). This method uses by analogy an electrical resistance system, where fluxes of heat and water are driven by gradients in humidity and temperature. The magnitudes of the fluxes being controlled by resistances are in turn related to the land–surface–vegetation parameters and atmospheric variables. Fig. 1 illustrates the system of resistances used for calculation of Latent Heat (LE), Sensible Heat (H) and Ground Heat (G) fluxes. For each time step the model calculates the energy balance by solving a system of equations with five temperatures and five humidities, using air temperature, relative humidity, wind speed, and global radiation as major climate input variables. Both soil and leaf temperatures are determined, from which the effective radiometric surface temperature, Ts is derived. In the MIKE SHE SVAT model, the effective radiometric temperature is scaled between Tl,eff and Ts,eff (effective leaf and soil surface temperatures, respectively) according to the actual leaf area index (LAI) and the extinction coefficient (Kext) accounting for the radiation interception by the canopy. The model has been tested both at the plot scale and at the field scale and in two different regions by Overgaard (Overgaard, 2005); at the FIFE test site on the American grass land, and in an agricultural area of Denmark. Also in Denmark, the Skjern River Basin of 2500 km2 was modeled to compare the efficacy of using conventional stream flow and groundwater head observations as opposed to distributed satellite based surface temperature retrievals as the calibration variable (Stisen et al., 2011). In the semi arid region of Andarax River basin in south-east Spain, Andersen (Andersen, 2008) implemented the MIKE SHE SVAT code to improve the spatial and temporal distribution of the output results. The SVAT was also tested in the Sahel as part of the AMMA Land Surface Model Intercomparison Project (ALMIP) (Boone et al., 2009). In this study, 17 surface variables and soil parameters were considered for sensitivity analysis and the ten most sensitive ones were used for calibration (see Table 1). The model was forced using 30 min

ea elw

raa rac

ec

T rcs e d l

rac

Tc

d

ras d

esw

Ts

ras

Tsw

G

Model and data MIKE SHE is a fully distributed and physically based hydrological model (Abbott et al., 1986a,b; Graham and Butts, 2006) solving the major hydrological processes in each grid cell in the domain. For each time step the model simulates land–surface fluxes, overland flow and infiltration. The unsaturated zone is represented by

Ta raa

w l

Tl

rg 2. Model description

H

Rn

LE

evapotranspiration (ET) output does not accurately constrain other predictions, such as surface temperature or soil moisture (Gupta et al., 1999). Multi-objective calibration is thus a more holistic approach towards model optimization. The success of this scheme hinges on the choice of prognostic variables which in turn depend on model physics, resolution (time and space) as well as data uncertainty. Thermal infrared, and by extension surface temperature (Ts), is an excellent candidate for model optimization. Physically, it depends on both energy and water exchange which are linked to evapotranspiration. Evapotranspiration is in turn driven by water content in the soil and other key variables. Using thermal infrared data to parameterize land surface models has been previously studied (Olioso et al., 1999; Demarty et al., 2004; Crow et al., 2003; Renzullo et al., 2008) also taking into account diurnal surface temperature cycling features (Coudert et al., 2008). However, the interpretation of surface temperature to soil moisture values remains tenuous. Direct use of soil water content estimates during calibration is a promising approach to constrain SVAT model simulations (McCabe et al., 2005) when no fluxes measurements are present. Opportunely, both radiometric surface temperature and soil surface water content, can be estimated from space. A better understanding of land–atmosphere interactions in an area as large as the Sahel requires the use of remote sensing data. Although regional evapotranspiration can be estimated from satellite images by applying a range of methods (Sandholt and Andersen, 1993; Norman et al., 2003; Nishida et al., 2003; Boegh et al., 2002), they are limited to snapshots during clear sky conditions. For this reason, SVAT models are advantageous since they are capable of providing continuous monitoring of water and energy balances (Olioso et al., 1999). However, the challenge with SVAT models is they need meteorological input data with high temporal resolution. Thanks to the Spinning Enhanced Visible and Infra Red Imagers (SEVIRIs) on board the Meteosat Second Generation (MSG) geostationary satellites, radiometric surface temperature is estimated every 15 min using a split window technique. Air temperature, a key input for the SVAT model, can in turn be estimated from MSG surface temperatures (Stisen et al., 2007; Nieto et al., 2010), rendering possible a distributed model setup. Before a SVAT model can run in a distributed environment, a scheme is needed to optimize the land surface parameters using just satellite data. The purpose of this study is to investigate how effective satellite estimates of radiometric surface temperatures and soil surface moisture are for calibration. In this paper, multiobjective calibration based on the optimization of temperature and soil moisture characteristics is performed on a SVAT model. A column SVAT model is driven using in situ meteorological forcing data provided by AMMA during a growing season in Mali. First, sensitivity analysis is performed on the 17 SVAT parameters using the Fourier Amplitude Sensitivity Test (FAST) and the extendedFAST. In this way, the 10 most significant parameters to flux, soil moisture and surface temperature simulations, were selected. The trade-off between various model objectives was explored by incrementing model output weights, thus tracing a Pareto curve. The performance of model outputs when calibrated using in situ versus satellite objectives is explored in detail.

esd Fig. 1. Schematic representation of the MIKE SHE SVAT model structure (Overgaard, 2005). The squared box represents a leaf, the gray lines water on the soil and leaf surfaces, the lines interrupted by zigzags represent transport of latent heat, LE, (left-hand side) and sensible heat, H, (right-hand side) where zigzags illustrate resistances, r. T and e are temperature and humidities at the wet and dry surfaces (w and d, respectively) represented as nodes. Subscripts are l: leaf surface; s: soil surface; c: mean canopy level; a: air mass. Rn is net radiation and G is soil heat flux.

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Table 1 Model parameters and values used for sensitivity analysis. Parameters denoted with a star [⁄] were found to be significant during the sensitivity analysis and were hence those used for calibration. Range

Initial

Unit

Source

0.01–0.06

0.04

(m)

0.20–1.30 60.0–130

0.4 80.0

(m) (s m1)

Kabat et al. (1997), Boegh et al. (1999), Frison et al. (1998), Saux-Picart et al. (2009), Coudert et al. (2008), and Lhomme et al. (1997) Timouk et al. (2009) Lhomme and Monteny (2000), Braud (1998), Kahan et al. (2006), Goutorbe et al. (1997), Lauwaet et al. (2009), and Cayrol et al. (2000)

Root depth (Root) Extinction coefficient (Kext) Soil surface roughness (z0s) Interception coefficient (Cint) Root distribution coefficient (Aroot)

200–800 0.55–0.75 0.01–0.06 0.03–0.08 0.25–1.0

400 0.65 0.03 0.05 1.0

(mm) (–) (m) (mm) (–)

⁄

Soil parameters Saturated moisture content (hs)

0.275–0.45

0.36

(m3 m3)

⁄

0.025–0.045 1.1–1.8 1E05 to 1E04 1.5–2.5

0.035 1.4 6.2E5

(1 a1) (–) (m s1)

2

(–)

3.7–4.7

4.2

(–)

-

-

(m) (–) (m3 m3)

Vegetation and land surface parameters ⁄ Leaf width (LeafWidth) ⁄ ⁄

Vegetation height (VegHeight) Unstressed stomatal resistance (RSC)

⁄ ⁄

Van Genuchten a (a) Van Genuchten n (n) ⁄ Saturated hydraulic conductivity (Ks) ⁄

⁄

Capillary pressure at field capacity (pFfc) Capillary pressure at wilting point (pFwp) Green and Ampt suction (GA) Van Genuchten shape parameter (l) Residual moisture content (hr)

1.3 to -0.7 0.45–0.55 0.002–0.05

1 0.5 0.004

in situ measurements of air temperature, global radiation, wind speed and relative humidity as well as leaf area index (LAI) and albedo measurements. 2.1. Study region The measurement site, known as Agoufou, is located in Sahelian Mali at 15°200 4000 N and 1°280 4500 W. The site, characterized as open woody savannah with fixed dunes (Mougin et al., 2009), is homogeneous over several kilometers. The top 0–6 cm of the soil is 90% sand, 3.3% silt and 4.6% clay (Mougin et al., 2009). The dominant herbaceous species are: Cenchrus biflorus, Aristida mutabilis, Zornia glochidiata, Tragus berteronianus, and dominant woody species: Acacia raddiana, A. senegal, Balanites aegyptiaca, Combretum glutinosum, Leptadenia pyrotechnica (Mougin et al., 2009). The region experiences a single rainy season with most precipitation falling between late June and mid September and is followed by a long dry season of around 8 months. The annual mean precipitation is 370 mm (De Rosnay et al., 2009) (1920–2003). The rainy season transforms the landscape from arid and desert-like to a lush and green environment. When the rains subside, the plants and grasses again dry and wilt away. A complete rainy and vegetation growth season (from July 15th (DOY 196) to September 30th (DOY 273) 2007) was analyzed. Also, in order to capture the savannah’s temporal dynamics, the 2007 growing season was divided into three periods of equal duration: (1) vegetation growth (DOY 196–221), (2) vegetation peak (DOY 222–247), and (3) the drying period (DOY 248–273). To ensure model steady-state prior to analysis, the SVAT has a spin-up period of one month from June 15th to July 15th 2007. 2.2. Data 2.2.1. In situ The in situ data was provided by AMMA. The four components (incoming and outgoing short- and long-wave) of the radiation budget were measured with a CNR1 (Kipp and Zonen CNR1, Delft,

Cayrol et al. (2000), Boegh et al. (1999), and Zhou et al. (2006) Frison et al. (1998)

Coudert et al. (2008), Saux-Picart et al. (2009), Verhoef et al. (1996), Braud (1998), and Lauwaet et al. (2009) Coudert et al. (2008) and van Genuchten (1980) Braud (1998), Coudert et al. (2008), Saux-Picart et al. (2009), and Lauwaet et al. (2009)

van Genuchten (1980) Saux-Picart et al. (2009) and Coudert et al. (2008)

Holland). Sensible heat flux was measured with sonic anemometers (Solent R3) measuring the three vector components of the wind at 20 Hz. The eddy–covariance system (Campbell CR3000 and CSAT3–LiCor7500, Campbell Scientific Inc. Logan, UT, USA and Li–Cor Inc., Lincoln, NE, USA) allowed computation of latent heat fluxes. Soil heat flux was computed from soil temperature profiles using harmonic decomposition (Timouk et al., 2009). At a 30 min time scale over the four year period (2005–2007), the energy closure is:

H þ LE þ S ¼ 0:87ðRNET  GÞ þ 14:5 with ðr 2 ¼ 0:92; n ¼ 8062Þ ð1Þ See Timouk et al. (2009) for more details. Gaps in flux data are present notably in late July to early August. Also measured was: wind speed and direction (Vector A100R), land surface temperature (Everest 4000.4zl), air temperature and humidity (HMP 45C, Vaisala) and Precipitation (Delta T, RG1). Leaf area index (LAI) was monitored every 10 days during the growing season along a 1 km long ’vegetation’ transect according to Mougin et al. (2009). Time domain reflectometry sensors (CampbellCS616) (De Rosnay et al., 2009) measured soil moisture at several depths where 5 cm is the top most measured soil moisture (h05). 2.2.2. Satellite data Land surface temperature (Ts) was provided by LSA SAF, computed from the MSG Spinning enhanced Visible and Infrared Imager (SEVIRI). Estimates of Ts were retrieved every 15 min with a spatial resolution of 0.05°. A scatter plot of Ts derived from MSG versus in situ for the entire growing season are shown in Fig. 2 for the entire day. Little bias is observed with a strong coefficient of determination (r2 = 0.815). Due to cloud cover and atmospheric effects, 3698 observations were available out of a possible 7392. The Advanced Microwave Scanning Radiometer on the Earth (AMSR-E) observing system on the AQUA satellite is used for soil surface moisture estimates. The NSCID products Level 3 v06 provide a 25 km regular grid once a day. To ensure good accuracy of the product, only data of descending orbits are used, for which

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non-monotonic models. It uses a periodic sampling approach and a Fourier transformation to decompose the variance of a model output into partial variances contributed by different model parameters (McRae et al., 1982; Xu and Gertner, 2010). Ratios of partial variances to model output variance are used to measure the parameters’ importance in their contributions to uncertainty in the model output. Two sensitivity analyses using FAST and extended FAST (Saltelli et al., 1999) were done to measure (1) the ‘‘main effect’’ contribution of each input parameter individually to the variance of the output, and (2) the ‘‘total effect’’ that takes into account parameter interactions on model output. The 17 adjustable model parameters (see Table 1) were varied within a range based on literature and known land surface characteristics. 3400 simulations ensured that the parameter space was adequately represented as recommended by (McRae et al., 1982). As the purpose of the sensitivity test is to reveal the most important parameters for model optimization, only parameters responsible for at least 5% of the output variance for at least one of the outputs, are considered significant. 3.2. Sensitivity analysis results Fig. 2. Satellite (MSG) versus in situ observations of land surface temperature for the 2007 growing season.

Results of the sensitivity analysis are summarized in Fig. 4. The results show that of the initial 17 parameters, only 10 were significant to model estimates of flux, surface temperature and soil surface moisture. In general, little difference in relative sensitivity is noted between main and total effect, with the exception of the soil parameter pFfc. Taken by itself, pFfc has a negligible impact on G and h05. But through parameter interactions, pFfc becomes important for optimization. Of the soil parameters, the van Genuchten n which controls soil drying, has the greatest influence on Ts, h05, G and Rn. Also of significance is the saturated moisture content hs to h05 and the saturated hydraulic conductivity Ks as well as the capillary pressure at field capacity pFfc to the fluxes H and LE. As for land surface characteristics, the height of the vegetation is the most significant parameter, especially for Ts, Rn, H and G. 4. Multi-objective calibration 4.1. Multi-objective algorithm Calibration of the ten most sensitive SVAT parameters (parameters denoted by a ’⁄’ in Table 1) was performed using an automatic calibration procedure for optimization of multiple objective functions simultaneously (DHI, 2010; Madsen, 2000, 2003). The performance of the objective function is measured using RMSE

Fig. 3. Satellite (AMSR-E) versus in situ observations of soil surface moisture for the 2007 growing season.

the temperature gradient in the emitting layer are low. Scatter plot of AMSR-E soil moisture versus in situ h05 for the entire growing season is shown in Fig. 3. Consistent with previous studies in the region (Gruhier et al., 2010; Pellarin et al., 2009), AMSR-E overestimates soil moisture and seems unable to capture the low water content present in semi-arid sandy soil. 3. Sensitivity analysis 3.1. Fourier amplitude sensitivity test Fourier Amplitude Sensitivity Test (FAST) is one of the most popular uncertainty and sensitivity analysis techniques. It is computationally efficient and can be used for non linear and

 F i ðhÞ ¼

N 1P ½X obs;i  X sim;i ðhÞ2 N i¼1

12 ð2Þ

where Xobs,i and Xsim,i are the observed and simulated variable at time i, N is the number of time steps in the calibration period, and h is the parameter vector. When using multiple objectives, the calibration problem can be stated as follows:

MinfF 1 ðhÞ; F 2 ðhÞ; . . . ; F p ðhÞg; h 2 H

ð3Þ

where F(h), i = 1, 2, . . . , m are the different objective functions. The optimization problem is constrained in that h is restricted to the feasible parameter space H. The solution of Eq. (3) will not, in general, yield a single unique set of parameters but will consist of the so-called Pareto set of solutions, according to various trade-offs between the different objectives (Gupta et al., 1998; Madsen, 2000). Therefore, within the Pareto set, none of the solutions is better than the other in terms of all objective functions. A Pareto optimal

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5

Fig. 4. Sensitivity analysis results. The ten significant parameters are shown that account for at least 5 percent of model output variability. Top: Main effect measures parameters’ individual influence on model output whereas Bottom: Total effect takes into account parameter interactions.

solution can be found by optimizing an aggregate of the objective functions based on a weight put on each objective function:

F agg ðhÞ ¼

M P

wi g i ðF i ðhÞÞ

ð4Þ

i¼1

where M is the number of objective functions that are aggregated, wi, i = 1, 2, . . . , M are the weights, and gi(), i = 1, 2, . . . , M are the transformation functions assigned to each objective function. The transformation function is applied to compensate for differences in magnitudes of the different objective functions. The transformation functions are automatically estimated from the initial population so that all objective functions have about the same weight on the aggregated objective function near the optimum (DHI, 2010). To determine the Pareto front, several optimization runs using different values of wi are performed. The shuffled complex evolution (SCE) algorithm as implemented in the AUTOCAL software is applied (DHI, 2010). The SCE method combines different search strategies, including (i) competitive evolution, (ii) controlled random search, (iii) the simplex method, and (iv) complex shuffling. With the aim to quantify model performance and to determine objective function trade-offs, several objective functions were explored: in situ fluxes (G, H, LE and Rn) as well as both in situ observations and satellite estimates of Ts and h05. Optimization was performed on the ten most important parameters listed in Table 1 within the indicated range whereas all other parameters remained constant. A 2000 simulations were found sufficient to achieve model convergence for each weight combination. To compare calibration strategies, a benchmark model performance was determined by calibrating the SVAT using in situ data weighted at 100%, of the examined variable. To ensue stable model dynamics during calibration, the probability density function was found between simulated and observed Ts as well as MSG estimates and observed. See Fig. 5. As the bias and overall shape of both distribution functions are similar, no-preconditioning of the data was necessary for Ts. 4.2. Calibration results 4.2.1. Objective variable trade-offs Surface temperature is a key variable in SVAT models as it results from energy processes which is linked to water and

Fig. 5. Probability density of surface temperature Ts over the growing season. Dashed lines is the density of in situ minus simulated Ts with model calibration weight of 50% h05 and 50% Ts. Solid line is the probability density of in situ minus MSG estimates of Ts.

evapotranspiration. Soil moisture, another key variable, modulates surface temperature and controls the water available for the vegetation. Luckily, both these key variables (surface temperature and soil surface moisture) can be estimated from satellites and are excellent candidates for calibrating a distributed SVAT model. Furthermore, because these variables are physically linked to soil and vegetation properties, their quantification is justifiable. SVAT model response to these two variables (Ts and h05) was studied by using them as objective functions during calibration. The weights (wi) placed on the objective functions were varied by 10% increments, and for each case, optimal solutions were calculated from 2000 calibration runs. Thus a two dimensional pareto curve was found that relates the trade-off between Ts and h05.

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Fig. 6. Pareto curve derived from using soil moisture h05 and land surface temperature Ts as objective functions. The squares and circles are optimal solutions from 2000 calibration runs. The weights placed on h05 and Ts were varied by 10% increments. The optimal solutions at A and B are from weighing the objective function of h05 by 50% and Ts by 50%.

The results in Fig. 6 show that there is indeed a clear trade-off in objectives. For in situ objectives, when only Ts is used during calibration, the SVAT model is capable of estimating Ts to an accuracy of RMSE of 1.84 °C but leads to a poor estimate of h05 with RMSE of 0.163 m3/m3. Conversely, when only in situ h05 is used in the calibration, the SVAT model is capable of estimating h05 to an accuracy of RMSE of 0.013 m3/m3, but leads to poor estimates of Ts of RMSE of 3.70 °C. For overall model accuracy, a compromise solution with a 50% weight on each objective function (point A in Fig. 6) yields a RMSE of 0.025 m3/m3 and 2.01 °C for h05 and Ts respectivly. A similar relationship is noted when using satellite based objective functions. One obvious difference however is that the model simulates poorer estimates of both h05 and Ts regardless of the balance of weights. Soil moisture estimates were particularly erroneous as a result of AMSR-E bias overestimating actual soil water content (as seen in Fig. 3). Satellite calibrated estimates of surface temperature showed only about 0.2 °C more RMSE than in situ calibrated results. Again, a compromise solution can be obtained by equally weighing the two objectives (B in Fig. 6). 4.2.2. Model performance The time series plots in Fig. 7 show the SVAT model was capable of accurately simulating surface temperature and fluxes. The diurnal cycle of Ts was captured without time lags and with good overall estimates of night time and day time temperatures. Ts estimates held no significant bias, had low RMSE (around 2 °C) and high coefficient of determination (0.91). The sandy soil found in Mali can get extremely dry between rain events and during dry months, see Fig. 8. The soil moisture content measured at Agoufou dropped to under 0.02 (m3/m3) at 5 cm and 40 cm during the growing season. MIKE SHE solves a 1-D Richards equation based on the van Genuchten (van Genuchten, 1980) soil formulation. Despite appropriate parameters for sandy soils, the model was unable to simulate the absolute values of observed soil moistures at different depth profiles. The temporal dynamics are, however, very satisfactory. Simulation of water uptake and release followed very closely the observed values at various depths (not shown: 10, 30, 100, 120 cm), but again tended to overestimate actual water content. The effect initial soil moisture conditions had on growing season simulations was investigated by setting the entire unsaturated-zone water content to different values as shown in Fig. 10.

As the model has a spin-up period of a month prior to analysis, the soil moisture content converged over time, especially in the upper soil layers. During the growing season, the effect initial water content had on LE and H were negligible due to the soil’s sandy composition inability to retain water over time. Daytime evapotranspiration was systematically underestimated throughout the growing season, even when the model is calibrated using evapotranspiration observations (solid circles Fig. 7). The temporal dynamics of LE and H were accurate with timely daytime rises and nightly falls in flux estimates. G simulations systematically yielded too early a rise in the morning and underestimated ground flux in the daytime, a likely symptom of the model’s overestimation of soil water content. A key motive for SVAT model optimization is the simulation of growing season fluxes. Flux estimate errors of G, LE and H are shown in Fig. 9 using different calibration weights. Two important trends are discernible in the data. First, the slight ’U’ shape of most of the curves, shows that it is better to use both h05 and Ts during model calibration. But there is little difference in flux estimates between the weight combinations of 30/70–70/30 h05/Ts. Second, the RMSE between simulated and observed fluxes is always less when the SVAT model is calibrated using in situ versus satellite estimates of h05 and Ts. This last point gives credibility to the choice of h05 and Ts as physically important variables for model calibration. Model parameters optimized to reflect true soil moisture and surface temperature values also improve flux estimates. Scatter plots in Fig. 11 show the comparison between observed and modeled energy fluxes. Latent heat is systematically underestimated especially during peak vegetation conditions. Even when using latent heat is used as the objective function (Top Right in Fig. 11), the SVAT model does not simulate the high levels of evapotranspiration present during the daytime in Malian savannah. This suggests that despite optimal calibration to latent heat and in situ forcing data, the model is not capable of fully capturing the land surface processes. Net radiation estimates are however accurate with strong correlation between observation and simulation for all cases with r2 values above 0.90. Even when using latent heat as the objective function (Top Right in Fig. 11), the SVAT model does not simulate the high levels of evapotranspiration present during the daytime in Malian savannah. Net radiation estimates are accurate with strong correlation between observation and simulation for all cases with r2 values above 0.90. Data from the growing season was divided into three distinct periods representing (1) vegetation growth (DOY 196–221), (2) vegetation peak (DOY 222–247), and (3) the drying period (DOY 248–273). Model performance was calculated for each of these three periods and for the entire growing season as shown in Table 2. SVAT model estimates of LE and H are best in periods (1) and (3) but does not capture the high evapotranspiration rates during the peak vegetation season. Only a slight difference in accuracy of surface temperature and soil moisture estimates is observed during the three periods. A trend common to all three periods: H and LE estimates are best when in situ Ts and h05 data is used for calibration, but satellite data yielded optimal G. 4.2.3. Effect of AMSR-E soil moisture overestimation Table 2a and c shows flux estimates are best when in situ data is used to calibrate the SVAT model. To explore whether this trend is due to AMSR-E’s overestimation of soil moisture, the bias in the data was removed. The AMSR-E soil moisture estimates shown in Fig. 3 was reduced uniformly by 0.0470 m3/m3 to eliminate the bias with respect to in situ observations for the entire growing season. As expected, after SVAT model calibration with weights of 50Ts/50h05NO BIAS, estimates of soil moisture improve, resulting in the same RMSE accuracy of 0.020 m3/m3 as with in situ, see Table

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7

Fig. 7. Simulated and observed surface temperature (Ts) and flux (LE, H, and G) one day time plots for the three periods. Open circles are in situ measurements, solid lines are simulated output where the model is calibrated using an equal weighting of in situ Ts and h05 observations. dashed lines uses equal weighting of satellite Ts and h05 objectives. Solid circles is simulated output where in situ observations of the variable of interest is used as the objective function, thus representing the model benchmark performance.

2b. Interestingly, LE, H, and G flux estimates worsen with the elimination of soil moisture bias. In fact, the RMSE of LE jump from 72.40 to 80.00 w/m2, H from 58.97 to 72.15 w/m2 and G from 61.37 to 66.42 w/m2. Thus eliminating satellite soil moisture bias leads to poorer SVAT flux calibration possibly due to AMSR-E’s temporal resolution not capturing all the rain events. 4.2.4. Calibrated parameters Ten parameters (⁄ in Table 1) were selected for calibration based on a sensitivity analysis test (Fig. 4). When taken alone, neither Ts nor h05 provide enough information to fully parameterize a physically based SVAT model. But taken together (bottom of Fig. 4) most of the parameters sensitive to Ts and h05 are also sensitive to the fluxes, but with three notable exceptions. First, the root depth is defined as the maximum depth of active roots in the root zone. The roots remove water from the soil until the water content of the soil reaches a critical level. Once this level is reached, transpiration will decrease with decreasing water content until the wilting point is reached, where the amount of transpiration drops to zero. It is a parameter responsible for most of the variability in LE estimates, but is not a sensitive parameter to either of the two objective variables. In other words, using just Ts

and h05 to calibrate does not give much insight into the parameterization of the root depth. Second, the unstressed stomatal resistance (RSC) exerts a significant influence on LE, but again is not sensitive to either Ts or h05. An increasing stomatal resistance value leads to a decrease in humidity in the canopy and thus increases the humidity gradient between the soil and canopy level. The net result of this will be a reduction of the flux of sensible heat from the soil surface to the canopy, and hence more energy will be available for soil evaporation (Overgaard, 2005). Third, the extinction coefficient, Kext, depends on the angular distribution of foliage elements. Kext is not sensitive in itself to LE and H (main effect) but only through parameter interactions (total effect). This is because Kext affects in opposite directions evaporation and transpiration. Thus, in the context of calibrating and driving a SVAT model using only remote sensing data in a distributed environment, it is necessary to obtain estimates of root depth, RSC and Kext. Values of the ten calibrated parameters are shown in Fig. 12 for the entire growing season and for the three different periods. It is interesting that RSC and Kext calibrated to very different values when the objective function is based on in situ versus satellite

M.E. Ridler et al. / Journal of Hydrology 436–437 (2012) 1–12

3

Soil Moisture 5cm (m /m )

8

3

Soil Moisture 40cm (m3/m 3)

that altering those boundaries might improve model estimates. As previously mentioned, the root depth is not a parameter well constrained from Ts and h05 objectives. Consequently its value drifted over the three periods with a minimum during the peak growing season where one would expect it to reach its maximum value.

observations in situ satellite AMSR−E

0.25 0.2 0.15 0.1 0.05 0 190

200

210

220

230

240

250

260

270

280

0.15 0.1 0.05 0 190

200

210

220

230

240

250

260

270

280

DOY Fig. 8. Simulated and observed soil moisture at a depth of 5 and 40 cm. circles are in situ measurements, dashed lines are simulated output where the model is calibrated using an equal weighting of in situ Ts and h05 observations. solid lines are simulated output where the model is calibrated using an equal weighting of satellite Ts and h05 observations.

Fig. 9. Flux estimates of G, LE and H from using soil moisture h05 and land surface temperature Ts as objective functions. The weights placed on h05 and Ts were varied by 10% increments. The SVAT was calibrated using satellite derived objective functions (circles) and in situ (squares).

data. When constrained with satellite estimates of Ts and h05, RSC was overestimated and Kext underestimated. Both these parameters are significant to LE and H estimates which partially explains why the benchmark calibrated model produced better flux estimates. As well, the field capacity pFfc that relates the amount of water content held in the soil after excess water has drained away, was underestimated with satellite objectives. Temporal variation in soil parameters are noted over the three periods even though the soil characteristics should remain static. Ks was lowest during the vegetation growth (period 1) and conversely the value of a augmented during the drying (period 3). In terms of vegetation, only small changes in vegetation parameters are observable over the growing season. The leaf width, hs and the vegetation height both calibrated to the allowed parameter limits (0.01 m, 0.275 m3/m3 and 1.3 m, respectively) suggesting

5. Discussion This study ascertained which SVAT model parameters are sensitive in a semi arid environment, and the effect of calibrating those parameters using only soil moisture and radiometric surface temperature. Of particular focus was the efficacy of using satellite estimates versus in situ observations of soil moisture and temperature for calibration. Our main findings are (1) the SVAT model performs well in the semi arid environment, but underestimates peak growing season evapotranspiration and overestimates soil moisture, (2) most of the parameters important for flux estimates can be constrained using Ts and h05 with the three exceptions: root depth, Kext and RSC, (3) flux estimates are improved when the model is calibrated using in situ surface temperature and soil surface moisture. The SVAT model was capable of simulating the heat fluxes and surface temperature for this semi arid savannah landscape. Ts and Rn estimates were particularly close to observations throughout the growing season. The extremely dry soil of the Malian Sahel was difficult to reproduce, a limitation shared with other models in this environment (Saux-Picart et al., 2009). LE and H flux showed excellent temporal dynamics even though evapotranspiration was underestimated. The pattern of all the flux scatter plots are markedly similar to those from a previous SVAT model study by Saux-Picart et al. (2009) in Niger. They modified the SEtHyS model specifically for savannah landscapes by adding a tree layer to the two-source model and then used surface fluxes as optimization variables. Despite added model complexity and a greater number of calibrated parameters, peak evapotranspiration was as well systematically underestimated and soil moisture overestimated during the growing season. Net radiation, however, was simulated with greater accuracy with correlations above 0.98 during the calibration period. Analysis of the sensitivity of model parameters, during the entire growing season, allows overall and specific parameter sensitivities to surface temperature, soil moisture and energy fluxes to be determined. The results clearly show that some parameters are relatively insensitive to all of these model outputs. This is the case for z0s, Cint, Aroot, pFwp, GA, l and hr whose range in values contribute less than 5% to output variance. Consequently, a default value or a literature based value is used for these parameters. Some parameters are very sensitive to some outputs and not others. The van Genuchten n is the most significant parameter for h05 and G, but has relatively little effect on sensible and latent heat. The parameter defines the soil’s hydraulic conductivity as well as water retention, which in turn relates to ground heat transfer. In this experiment, the feasible range of n (1.1–1.8) is larger than in other calibration studies (1.168–1.331) (Coudert et al., 2008) due to a lack of experimental data of van Genuchten parameters in the Sahel. Vegetation height, is the most significant parameter for Ts and H, but has little to no effect on soil moisture or evapotranspiration. It is semi-empirical in nature as it characterizes an average height between the dominant woody and herbaceous vegetation. In the dry season, much of the annual grass expires only to grow again when the first rains fall. The height of the vegetation therefore changes in time, a phenomenon not observed during the three calibration periods in this experiment (Fig. 12) where the maximum allowed value of vegetation height (1.3 m) was acquired for the entire growing season.

M.E. Ridler et al. / Journal of Hydrology 436–437 (2012) 1–12

9

Soil Moisture at 40 cm under different initial conditions (m3/m3) 0.16 Simulated SM (Intial SM of 0.05) Simulated SM (Intial SM of 0.005) In Situ

0.14 0.12 0.1

Spin Up ( June 15 − July 15 )

0.08 0.06 0.04 0.02 Jul

Aug

Sep

2007 Fig. 10. Soil moisture at 40 cm where soil moisture in the entire 7.7 m unsaturated zone is initialized at 0.05 and 0.005 m3/m3.

Fig. 11. Scatter plots comparing simulated with observed fluxes (W/m2) for the entire growing season. Different objective functions were used during calibration: Left in situ soil moisture and land surface temperature with equal weighting (50/50), Center satellite estimates of soil moisture and land surface temperature again with equal weighting (50/50) and Right in situ flux observations, representing the model benchmark performance. The coefficient of determination and RMSE are shown for each simulation set.

A challenge to using only h05 and Ts as objectives in model calibration, is that some parameters are insensitive to these two variables but play a significant role in flux estimation. In particular,

root depth, RSC and Kext require further experimental investigation in the Sahel. The depth of the grass roots varies over the growing season and is a function of plant type as well as an average of grass

10

M.E. Ridler et al. / Journal of Hydrology 436–437 (2012) 1–12

Table 2 Statistics comparing simulated output versus observations. The SVAT was calibrated four different ways (a–d). (a) Equally weighing satellite MSG Ts and AMSR-E h05, (b) equally weighing satellite MSG Ts and AMSR-E h05 where the known AMSR-E bias is removed, (c) equally weighing in situ Ts and h05, and (d) using in situ observations of the examined variable for benchmark model performance. The calibration was performed for the whole growing season All and for different time periods 1, 2, 3. Note that r2 is unitless. a Satellite Ts and h05

b Satellite Ts and h05 (no bias)

c in situ Ts and h05

d in situ Itself

RMSE

r2

RMSE

r2

RMSE

r2

RMSE

r2

LE (W/m2)

All 1 2 3

72.40 61.37 90.32 56.05

0.799 0.547 0.828 0.831

80.00 62.05 89.50 50.51

0.809 0.509 0.836 0.868

53.93 60.32 63.93 48.69

0.845 0.501 0.864 0.870

43.21 47.98 49.11 39.78

0.867 0.655 0.862 0.884

H (W/m2)

All 1 2 3

58.97 51.03 77.76 41.67

0.719 0.813 0.750 0.756

72.15 52.77 87.65 37.80

0.724 0.793 0.770 0.804

50.35 50.94 64.32 38.96

0.767 0.788 0.790 0.812

37.92 38.59 38.49 41.78

0.789 0.857 0.735 0.803

G (W/m2)

All 1 2 3

61.37 67.93 54.84 56.72

0.735 0.764 0.767 0.739

66.42 71.04 63.60 60.41

0.726 0.761 0.749 0.718

67.62 71.07 63.38 63.49

0.735 0.763 0.747 0.712

52.37 54.23 47.26 51.38

0.773 0.794 0.796 0.764

Rn (W/m2)

All 1 2 3

60.01 64.31 58.98 59.84

0.916 0.882 0.922 0.919

59.52 64.07 57.99 59.63

0.916 0.882 0.923 0.919

60.06 64.09 59.77 59.31

0.918 0.883 0.925 0.922

58.26 62.73 56.00 58.53

0.917 0.879 0.922 0.923

Ts (°K)

All 1 2 3

2.157 2.413 2.192 1.695

0.918 0.920 0.897 0.955

2.210 2.500 2.230 1.701

0.914 0.909 0.899 0.956

2.084 2.359 1.987 1.784

0.912 0.910 0.882 0.952

1.850 1.840 1.780 1.594

0.931 0.940 0.905 0.961

h05 (m3/m3)

All 1 2 3

0.045 0.048 0.042 0.047

0.702 0.680 0.407 0.880

0.020 0.025 0.018 0.018

0.739 0.745 0.470 0.881

0.020 0.024 0.022 0.011

0.660 0.701 0.324 0.890

0.013 0.013 0.015 0.010

0.741 0.731 0.449 0.856

Fig. 12. Parameter values after calibration using equal weighting (50/50) of h05 and Ts. Top soil and Bottom land surface and vegetation parameters. The objective functions from squares (in situ) and crosses (satellite) were used to find the optimal parameter values for 1, 2, 3 the three growing periods and All the entire growing season. The two dashed lines is the allowed parameter range.

and tree roots, thus making it a difficult parameter to quantify. RSC and Kext values are important for flux estimates but again are difficult to measure experimentally. Taken together, surface temperature and soil surface moisture are objective variables that effectively tune model parameters towards better flux estimates as seen in Fig. 9. The Pareto optimal solutions of h05 and Ts in Fig. 6, shows a large variability of optimal model parameter sets all of which equally good model calibrations considering the two objective. Selecting a single solution can vary

according to the specific model application being considered. In this experiment, a balanced aggregated objective function is used for a holistically optimal model that encompasses the significant model components. An equal objective weighting on h05 and Ts ensured the best aggregated result of those two variables, but as well produced the best flux estimates. Multi-objective calibration must, by design, quantify the goodness of fit between model predictions and observations. For time series observations, the most common goodness of fit criteria is

M.E. Ridler et al. / Journal of Hydrology 436–437 (2012) 1–12

the root mean squared error and is extensively used in calibration experiments. By minimizing the root mean squared error in this experiment, it implicitly minimizes the bias as well as the variance of the errors. Other statistics might have proved beneficial, such as R2, bias or slope in error minimization. For instance in the ground flux scatter plot in Fig. 11, although the RMSE is less for in situ than satellite objectives, the resulting scatter plot has tilted. A combination of goodness of fit statistics might optimize land surface calibrations. Furthermore, the evaluation set in this study was not separated from the training set. The effect of which could be further investigated to assess how the calibration of a particular growing season relates to model performance in a different year. 6. Conclusion This study highlights the merits of using satellite estimates of both land surface temperature and soil surface moisture for SVAT calibration. Overall, the SVAT model performs well in semi arid environments, but underestimates peak growing season evapotranspiration. Sensitivity analysis highlighted the importance of constraining 10 of the 17 vegetation and soil parameters for optimal surface temperature, soil moisture and flux estimates. Although best overall calibration was achieved when using in situ objective function data, an equal weighting of satellite estimates of surface temperature and soil surface moisture also produced good results. However, three relatively sensitive parameters were not constrained with this approach: root depth, Kext and RSC. Acknowledgements This work contributes to the AMMA project. Based on a French initiative, AMMA was built by an international scientific group and is currently funded by a large number of agencies, especially from France, UK, US and Africa. It has been the beneficiary of a major financial contribution from the European Community’s Sixth Framework Research Program. Funding was provided by DHI Water and The Danish Research Council. Thanks to Monica Garcia and Simon Stisen for their input. References Abbott, M., Bathurst, J., Cunge, J., O’connell, P., Rasmussen, J., 1986a. An introduction to the European hydrological System – systeme hydrologique Europeen. Journal of Hydrology 87, 45–59. Abbott, M., Bathurst, J., Cunge, J., O’connell, P., Rasmussen, J., 1986b. Introduction to the European hydrological system – systeme hydrologique Europeen,’ SHE’, 2: structure of a physically-based, distributed modelling system. Journal of Hydrology 87, 61–77. Andersen, F., 2008. Hydrological modeling in a semi-arid area using remote sensing data. PhD Thesis, Department of Geography and Geology, University of Copenhagen, Denmark. Boegh, E., Soegaard, H., Hanan, N., Kabat, P., Lesch, L., 1999. A remote sensing study of the NDVI-Ts relationship and the transpiration from sparse vegetation in the Sahel based on high-resolution satellite data. Remote Sensing of Environment 69, 224–240. Boegh, E., Soegaard, H., Thomsen, A., 2002. Evaluating evapotranspiration rates and surface conditions using Landsat TM to estimate atmospheric resistance and surface resistance. Remote Sensing of Environment 79, 329–343. Boone, A., Rosnay, P., Balsamo, G., Beljaars, A., Chopin, F., Decharme, B., Delire, C., Ducharne, A., Gascoin, S., Grippa, M., et al., 2009. The AMMA land surface model Intercomparison Project (ALMIP). Bulletin of the American Meteorological Society 90, 1865–1880. Braud, I., 1998. Spatial variability of surface properties and estimation of surface fluxes of a savannah. Agricultural and Forest Meteorology 89, 15–44. Cayrol, P., Kergoat, L., Moulin, S., Dedieu, G., Chehbouni, A., 2000. Calibrating a coupled SVAT/vegetation growth model with remotely sensed reflectance and surface temperature. A case study for the HAPEX-Sahel grassland sites. Journal of Applied Meteorology 39, 2452–2472. Coudert, B., Ottlé, C., Briottet, X., 2008. Monitoring land surface processes with thermal infrared data: calibration of SVAT parameters based on the optimisation of diurnal surface temperature cycling features. Remote Sensing of Environment 112, 872–887.

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