1. Introduction
The dynamic role of the land surface in the climate system is nowadays widely recognized. Fluxes of latent heat from the land surface into the atmosphere transport large amounts of energy and water and limit direct heating of the lower atmosphere. Their magnitude, however, strongly depends on the soil moisture content of the soil. Model studies have shown that without soil moisture interacting freely with the atmosphere, warm season precipitation and temperature variability over land are significantly reduced (e.g., Douville 2003; Koster et al. 2004; Seneviratne et al. 2006a). It is also known that there is a tight relation between soil moisture and screen-level temperature and humidity (Mahfouf 1991). In addition, there is a two-way coupling between the memory of the land surface and the strength of the coupling between the land surface and the atmosphere (Koster and Suarez 1996, 2001).
The correct simulation of land surface–atmosphere interactions requires the realistic representation of both soil moisture and evapotranspiration. Unfortunately, current land surface models (LSMs) depend on many uncertain parameters; as a result, they strongly differ on both soil moisture and evapotranspiration (e.g., Lohmann and Wood 2003; Teuling et al. 2006), with consequent divergence in land–atmosphere coupling strength (e.g., Koster et al. 2004) or persistence patterns (e.g., Seneviratne et al. 2006b).
The uncertainty in many LSM parameters combined with the high sensitivity of simulated states and fluxes to these parameters can cause spurious drifts in the soil moisture state. To address this issue in model-based soil moisture products, different land data assimilation systems have been developed to constrain simulated soil moisture to observations of screen-level temperature and humidity (e.g., Bouttier et al. 1993; Rhodin et al. 1999; Douville et al. 2000), surface soil moisture or surface emissivity (e.g., Heathman et al. 2003; Galantowicz et al. 1999; Reichle and Koster 2005), latent heat fluxes (e.g., van den Hurk et al. 1997; Schuurmans et al. 2003), or to a combination of these (e.g., Seuffert et al. 2003).
While data assimilation provides a pragmatic solution to momentarily improve soil moisture states, later biases are not prevented since most data assimilation approaches deal with model states rather than parameters (in contrast to calibration). In fact, many data assimilation techniques assume bias-free models as well as observations. In addition, some data assimilation schemes (especially in reanalysis data products) mostly aim at an improvement of the turbulent fluxes through the soil moisture increments. As a consequence, some soil moisture assimilation schemes may even lead to a deterioration of the soil moisture fields (e.g., Betts et al. 2003; Seneviratne et al. 2004). Calibration of soil parameters to effective rather than physical values improves soil moisture data, but observations at larger scales are scarce (Ines and Mohanty 2008). To effectively prevent, or even reduce, soil moisture biases, improvements in model parameterization are thus needed (Jacobs et al. 2008).
Soil parameters control the storage capacity and loss rates of the soil per unit depth; hence they affect the simulation of soil moisture and evapotranspiration in LSMs. The variability in soil parameters within different textural classes often exceeds the variability between the classes (Soet and Stricker 2003; Gutmann and Small 2006), likely resulting in large differences between LSMs that derive their parameters from different soil databases. Also, the exact magnitude of this effect is uncertain. Some studies report a high sensitivity of both soil moisture and evapotranspiration to soil characteristics, such as the water-holding capacity or other soil hydraulic properties (e.g., Soet et al. 2000; Seneviratne et al. 2006b), while others reported mainly an effect on soil moisture (Richter et al. 2004; Braun and Schädler 2005; Kato et al. 2007). The sensitivity of a LSM to its parameters also depends on the climate conditions (e.g., Pitman 1994; Bastidas et al. 1999; Soet et al. 2000; Liang and Guo 2003; Kahan et al. 2006). A general framework that can help to understand why these sensitivities to soil parameters differ between models and climates is currently lacking.
In this study, we investigate the potential, or isolated, effect of soil parameters (e.g., wilting point, porosity, saturated hydraulic conductivity) on soil moisture and the mean water budget components under stochastic forcing. Here, potential means that the soil parameters are isolated from their original model, and their effect is evaluated using a parsimonious framework of stochastic soil moisture models. Through this methodology, we only evaluate the effect of parameters from different LSMs, not the LSMs themselves. Also, model-dependent compensating effects as a result of parameter interactions (see, e.g., Liang and Guo 2003) are avoided. Finally, the results are obtained under statistical steady-state conditions. While sensitivity studies with full LSMs require specification of initial and transient forcing conditions (which are typically far from being steady state), the results obtained with our current approach are independent of both. Therefore, they are likely to be more general.
The stochastic models are of considerably lower complexity than the full LSMs. Nonetheless, their equations for the soil moisture dependency on evapotranspiration and drainage are the same, or at least very similar. Indeed, it has been shown that just by using the point-specific linearized dependencies of evapotranspiration and drainage to soil moisture, most of the gridpoint soil moisture variability in original LSMs can be reproduced (Koster and Milly 1997). While stochastic soil moisture models have mainly been used for theoretical analysis (e.g., Rodríguez-Iturbe and Porporato 2004), they have also been applied to describe soil moisture observations in regions with either strong or weak seasonality in forcing (e.g., Calanca 2004; Teuling et al. 2005; Miller et al. 2007; Teuling et al. 2007). The stochastic models are described in section 2.
Soil parameters are taken from three LSMs used within the European Land Data Assimilation System project (ELDAS). For more information on the ELDAS soil moisture, we refer to Jacobs et al. (2008) and van den Hurk et al. (2008). The ELDAS LSMs differ widely in their treatment of the parameters governing the soil water balance, and they are likely to be representative for the whole range of operational LSMs. The soil parameterizations of the ELDAS models are described in section 3. It should be noted that some LSM parameters are calibrated to optimize a particular model’s performance, and their conceptual rather than physical meaning would prohibit direct intercomparison. This is, however, not the case for soil parameters. Their values are often derived from observations and are assigned to LMSs as attributes of soil textural classes.
2. Stochastic soil moisture models
a. General outline
b. Evapotranspiration losses
c. Drainage losses
d. Infiltration and runoff
e. Steady-state distributions
f. Climate conditions
Here, we will consider three different climatic conditions for simplicity: “humid,” “arid,” and “transitional.” Evapotranspiration in the humid climate is limited by the supply of energy. Potential evapotranspiration rates are relatively moderate as a result of higher humidity, lower temperatures, and lower net radiation, and the average infiltration exceeds the potential (unstressed) evapotranspiration: 〈P〉 − 〈I〉 > ETmax. In contrast, evapotranspiration is limited by the availability of soil moisture in the arid climate. Here, potential evapotranspiration exceeds the average infiltration: ETmax > 〈P〉 − 〈I〉. In the transitional climate, the average infiltration is balanced by ETmax, so that ETmax ≈ 〈P〉 − 〈I〉. The average specific humidity gradient Δq is chosen such that ETmax equals 3, 4, and 5 mm day−1 for the humid, transitional, and arid climate, respectively. The forcing is listed in Table 1. Figure 2 shows forcing realizations for the humid and arid climates, along with the resulting soil moisture.
g. Parameter sensitivity
Since no easy expression exists for the mean and variance of Eq. (15), we evaluate the sensitivity of soil moisture to the different parameters by looking at the pdf directly. The rationale behind this is that if changing any parameter affects soil moisture, this will also affect p(θ). Or, alternatively, if p(θ) does not change in response to a parameter perturbation, soil moisture has no sensitivity to this parameter. We will investigate the sensitivity to equal (namely, 10%) parameter perturbations, so that the relative (or normalized) effect can be directly compared. One should note that the actual uncertainty range is parameter dependent and that a 10% range can be too optimistic, especially for parameters that are known to vary over orders of magnitude (such as ks). For most parameters, however, realistic confidence intervals are unknown.
h. ELDAS Soil parameters
1) TESSEL and HTESSEL
Tiled ECMWF Scheme for Surface Exchanges over Land has been developed at the European Centre for Medium Range Weather Forecasts (ECMWF). In the original version of TESSEL, only one soil type exists. The physical properties of this soil (Table 2) were chosen, such that the water-holding capacity of 1 m of soil is approximately 15 cm (see Viterbo and Beljaars 1995), corresponding to the water-holding capacity of the original Bucket model (Manabe 1969). Gravitational drainage from the lowest layer is calculated from Eq. (7). Evapotranspiration is reduced for θ < θf , so that there is no distinction between θc and θf . The recent version of TESSEL, HTESSEL, has improved hydrology and distinguishes between six different soil types, each with its own parameters. Here, (H)TESSEL refers to both models.
2) ISBA
3) TERRA
3. Results
a. Model sensitivity
First, we discuss the sensitivity of soil moisture and ET to the model parameters in the most complex Laio et al. (2001) model [Eq. (15)] using average parameters corresponding to a typical loamy soil (Table 2). Figure 4 shows the perturbation in p(θ) resulting from equal (10%) perturbations in all parameters (including forcing) for the three climates. The gray areas in the figure correspond to the outer envelope of pdfs resulting from the parameter perturbation—that is, the gray area contains all possible pdfs within the ±10% parameter range.
It can be seen in Fig. 4 that soil moisture is not equally sensitive to all parameters and that the sensitivity also depends on climate. Any perturbation in parameters that are associated with small water fluxes (θr, Ew, Δ) is hardly reflected in p(θ) (Figs. 4a, 4f, and 4i). As can be expected, soil parameters that regulate the soil moisture reduction on ET (θw,θc) have an effect on soil moisture in the arid and transitional climates but not in the humid climate, where ET is not limited by soil moisture. Similarly, soil parameters that control drainage (θf , θs, b, and ks) effect soil moisture in the humid and transitional climates but not in the arid climate. Because of the nonlinearity in drainage [Eq. (9)], a relative change in θf or θs has a larger effect on p(θ) than b or ks. Interestingly and somewhat counter intuitively, the sensitivity of volumetric soil moisture to a perturbation in the depth of the root zone drz is much smaller than for an equal perturbation in θs (Figs. 4e and 4j), since the effect of the former occurs through the water balance. However, actual variations in drz can be expected to be larger than ±10%, both within and between different models.
For the vegetation parameters that directly control ET (LAI,rs,min), the effect is rather independent of climate (Figs. 4k and 4l). Because of the additive nature of the canopy and aerodynamic resistance rc and ra, their individual effect on p(θ) is smaller than for LAI. Since ra ≪ rc, LAI and rs,min show higher sensitivities. Much larger effects are found in all climates for the parameters Δq, α, λ that are directly linked to atmospheric forcing (Figs. 4n–p). As mentioned earlier, not all parameters are equally uncertain in reality. Ideally, the sensitivity should be evaluated with realistic rather than equal perturbations. Figure 5 shows the effect of one of the most uncertain parameters, ks, with a 10% perturbation as compared to a more realistic 50%–200% scenario. In the latter case, the effect on p(θ) becomes comparable to a 10% uncertainty in θs (Fig. 4e).
With soil moisture being sensitive to certain parameters, this is not necessarily also true for 〈ET〉. Figure 6 shows the relative sensitivity σ [Eq. (22)] of 〈ET〉 to all parameters (again, including forcing). While some (soil) parameters have a profound effect on soil moisture, this effect is not reflected in ET. Only in the transitional climate is there a small relative sensitivity (order ±0.1) of 〈ET〉 to some soil parameters (θc,θs) compared to none for the humid and arid climates. This sensitivity dependence on the climate regime is as expected, since ET will be most significantly affected by soil moisture in the transitional climate (see also Koster et al. 2004). In the humid and transitional climates, 〈ET〉 is much more sensitive to (vegetation) parameters that directly determine ETmax (LAI, rs,min, Δq). In the arid climate, nearly all precipitation evaporates, resulting in a sensitivity of 1 to changes in α and λ. In the humid climate, 〈ET〉 becomes nearly insensitive to small changes in precipitation characteristics.
b. ELDAS soil parameters
Table 2 lists the soil parameters for different soil types in the ELDAS models. It should be noted that not all models include a distinction between the functional role of θr and θw, or between θc and θf . In TESSEL, for example, there is no mechanism that allows for drying below θw; hence, θw has the same function in the model as θr. Because of the small fluxes below θr, this distinction does not necessarily have a large effect on either θ or ET. Large differences in θw are found between the models. For coarse soils, θw in TERRA (0.042) is half of θw in ISBA (0.083). For very fine soils, the difference between TERRA and HTESSEL is even larger: 0.257 versus 0.335. Similar differences are found for θc and θs.
All models increase their relevant soil moisture contents from coarse to fine soils, though with different magnitude. For HTESSEL, the difference in θs between coarse and very fine soils is 0.211; for ISBA, this is only 0.076. Even larger differences are found in ks. For the same soil type, the models often differ over more than one order of magnitude. Similar to the previously discussed parameters, the range in ks between different soils in a single model also differs widely. In TERRA, this range is most extreme, with 4138 mm day−1 for sand and only 1 mm day−1 for clay. In ISBA, this range is much smaller, with 497 mm day−1 for sand and 37 mm day−1 for clay. This also illustrates the very large range of uncertainty that can be found for certain parameters (since the soil texture of a given model grid point will often lie between typical soil texture classes).
Important to the modeling of soil moisture–limited ET is the moisture availability per unit depth between the wilting point θw and the critical moisture content θw. For convenience, this difference θc − θw is also listed in Table 2. Although within any model, the variability of the difference between soil types is limited and the differences between the models are very large. Whereas HTESSEL has differences in the range 0.196–0.250, the differences for ISBA are nearly 3 times smaller, 0.073–0.089. Next, the effect of the different parameters on soil moisture and the water balance components is investigated.
c. Effect of ELDAS soil parameters
Figure 7 shows the pdfs with ELDAS parameters calculated with Eq. (14) (ISBA parameters) and Eq. (15) (TERRA and HTESSEL parameters). The soil moisture distributions directly reflect the tendency of the soil parameters to increase with finer texture. Compared to our reference model, the ELDAS models all have a large difference θc − θw (see Table 2) in comparison to θf − θc. In combination with relatively rapid drainage above θf , this leads to a much smaller soil moisture variability (i.e., narrower pdfs) in the humid climate than in the arid climate.
The reference parameters also result in a rather wide pdf for the transitional climate when compared to the humid and arid climates (Fig. 4). For the HTESSEL and ISBA parameters, this behavior is almost absent. The small range over which soil moisture can vary in ISBA causes the pdfs for different climates to largely overlap. For TERRA and HTESSEL, the climate signal in the soil moisture pdfs is much stronger. Even for the same soil type, the soil moisture pdfs between the models sometimes hardly overlap, as is the case for HTESSEL and ISBA. This shows that soil parameters can be a major source of absolute bias when different soil moisture products are to be compared, which has also been identified in previous studies (e.g., Dirmeyer et al. 1999).
As shown before, effects on soil moisture do not necessarily translate into effects on water fluxes. Table 3 lists all average water fluxes that are affected by soil moisture and soil parameters (〈ET〉, 〈Q〉, 〈R〉) for the arid, transitional, and humid climates. The fluxes that are independent of soil moisture (〈P〉, 〈I〉) are listed in Table 1.
For TERRA and (H)TESSEL in the arid climate, 〈ET〉 approaches the average infiltration rate 〈P〉 − 〈I〉 = 1.90 mm day−1, and drainage losses are small. Because of the small dynamic range caused by the ISBA parameters, drainage losses are much larger (up to 10% of 〈ET〉 for sand). In the transitional climate, 〈ET〉 is highest for all models despite the smaller ETmax. The 〈ET〉 tends to be higher for finer soils, especially for peat/organic soil. The increased precipitation is accompanied by a general increase in 〈Q〉. There are, however, considerable intermodel differences. TERRA has a slightly higher 〈ET〉 than TESSEL, most likely due to the higher ET above θc. Again, the smaller dynamic range in ISBA leads to increased 〈Q〉 and thus reduced 〈ET〉 by 10%–20%. In the humid climate, 〈ET〉 approaches ETmax (3.0 mm day−1). In (H)TESSEL and ISBA, the more frequent soil moisture reduction on ET (below θf rather than θc) leads to smaller 〈ET〉 (5%–15%) and consequently larger 〈Q〉. Only for the cases with extremely low ks, 〈R〉 becomes significant at the cost of 〈Q〉. In the humid and transitional climates, model differences in 〈ET〉 are much larger than in the arid climate.
Next, we quantify the effect of the ELDAS parameters in the arid climate using Eqs. (19)–(21). Table 2 also lists the mean soil moisture 〈θ〉 for the arid climate. For all models, 〈θ〉 increases with finer soil texture, corresponding to the same tendency in the parameters θw and θc. For coarse soils, 〈θ〉 is very similar; however, the differences in θc − θw nonetheless result in completely different dynamics in terms of Var(θ) and Var(ET). For finer soils, both 〈θ〉 and θc − θw show large differences between the models, with differences in 〈θ〉 of up to 0.07. For loamy soils in HTESSEL and ISBA, 〈θ〉 is very similar; however, the large difference in θc − θw results in ISBA having a nearly 3 times larger Var(ET) and a corresponding Var(θ) 3 times smaller in comparison to HTESSEL. For clay soils, the difference in 〈θ〉 between the models can be as high as 0.09.
d. Model structure
TERRA differs from the other models not only by its reduction of 〈ET〉 below θc rather than θf (a parameter difference) but also by the variation of θc depending on ETmax [a model structure difference, Eq. (27)]. The question arises of how much the structural difference can add to the difference between the ELDAS parameters. Figure 8 shows Eq. (27). For low ETmax, the relative critical moisture content approaches 0.65, while for high ETmax it approaches 1 (or θf). Since in a humid climate ETmax is generally low and 〈ET〉 ≈ ETmax, a lowering of θc will only have a minor effect on 〈ET〉 and θ. In an arid climate with high ETmax, a higher θc will affect θ rather than 〈ET〉, since 〈ET〉 is mainly determined by the mean infiltration. In transitional climates, the sensitivity of 〈ET〉 to θc is highest (Fig. 6) and the effect on 〈ET〉 should be largest.
Part of the difference between ISBA and (H)TESSEL and TERRA parameters originates from the difference in drainage, that is, Eq. (8) versus Eq. (9). The “effective” saturated hydraulic conductivity C3 was derived under the requirement of the same e-folding time for free drainage from saturation (Mahfouf and Noilhan 1996). However, under normal wet conditions, the corresponding soil moisture level θ* is almost never reached (Fig. 9). The poor match between the linear and nonlinear drainage does not imply the former to be an incorrect model. With a proper choice of effective parameters, a reasonable fit can be obtained with the nonlinear drainage. Figure 9 also shows the “best fit” pdf obtained by minimizing the RMSE between the pdfs with linear and nonlinear drainage. This leads to a further reduction of ks to only 20% of its original (physical) value and to an increase in θf by 0.03.
4. Discussion and conclusions
In this paper, we analyzed soil parameters of three land surface models used within the ELDAS project, and we evaluated their potential effect on soil moisture and different water balance components. First, it was shown that soil moisture in LSMs is much more sensitive to soil parameters than evapotranspiration. The difference between the LSM soil parameters, however, was so large that evapotranspiration was also affected, resulting in differences of more than 10% in evapotranspiration as a result of soil parameters alone. We should note that it is most directly the effect of soil parameters on land fluxes (rather than absolute soil moisture content) that is relevant for coupled models. That models can have highly varying absolute soil moisture values does not necessarily mean that soil moisture dynamics and its effect on evapotranspiration is affected (see also Dirmeyer et al. 1999).
The available moisture content per unit depth and thus the range of soil moisture (which is, as mentioned, more important for the models’ behavior than for the absolute soil moisture bounds) differed between the models by up to a factor of 2. The ISBA parameters resulted in a smaller soil moisture range and less evapotranspiration for all soil types in comparison to (H)TESSEL and TERRA. The different behavior of the ISBA parameters can partly be explained by the different drainage parameterization. The linear force–restore drainage formulation in ISBA, when not used in combination with the proper effective field capacity and saturated hydraulic conductivity, results in a much more efficient drainage in comparison to the nonlinear formulation in (H)TESSEL and TERRA. In conclusion, the different soil parameters used in the investigated LSMs can lead to significant volumetric soil moisture biases of up to 0.10 and can cause differences in evapotranspiration of up to 10%.
The parsimonious (i.e., low dimensional) analytical models of the soil water balance are an easy tool used to investigate sensitivities of soil moisture and water fluxes to primary parameters without using full LSMs with more complex parameter interactions. Despite the simplicity of our model, the results are in line with previous studies on full LSMs. Large sensitivity of soil moisture to soil parameters was also reported by Braun and Schädler (2005). In an intermodel comparison, Koster and Milly (1997) found that ISBA was among the models with the lowest average evapotranspiration, consistent with the low water availability per unit depth discussed here. The dependency of parameter sensitivity to climate conditions that was reported in several studies (e.g., Bastidas et al. 1999; Soet et al. 2000; Kahan et al. 2006) is also well reproduced in the current study. More specifically, our results also agree on the higher sensitivity of evapotranspiration to vegetation parameters in comparison to soil parameters under dry conditions (Kahan et al. 2006). Kato et al. (2007) studied the sensitivity of different parameters of three LSMs used within the Global Land Data Assimilation System (GLDAS) project and also found that evapotranspiration was more sensitive to land cover, while soil moisture was more sensitive to soil characteristics. This is consistent with our Figs. 4 and 6.
While the stochastic soil moisture models can be seen as “generalized” land surface models for the water balance per unit depth, they obviously have their limitations. First, they lack interaction with the atmosphere. In coupled models, the effect of this interaction can be significant (Pitman 1994). Although coupling with the atmosphere will likely result in different sensitivities, high sensitivities to stomatal resistance and leaf area index (among other factors) were also reported by Pitman (1994) for a coupled experiment. Second, the fact that these models treat the unsaturated zone as a single layer makes them incapable of simulating processes, such as infiltration and vertical redistribution that take place on fine temporal scales and require fine vertical and horizontal discretization. For soils with low saturated hydraulic conductivity in arid climates, where infiltration excess runoff is not compensated by saturation excess runoff, the effect on the water balance might be significant. The stochastic soil models used here also lack seasonality in forcing. Since seasonality is an inherent property of most climates, the results should, therefore, be interpreted in a probabilistic manner. For short simulations, the role and sensitivity of parameters might depend more on the initial soil moisture state than on climate. Finally, any LSM grid cell will contain a mixture of different soil types. Different LSMs might determine the representative soil type for the grid cell differently, leading to additional intermodel differences not considered here.
Acknowledgments
We thank Martin Lange for providing documentation of the TERRA model. This research was supported by the Wageningen Institute for Environment and Climate Research (WIMEK), the research program Climate Change of Wageningen University and Research Center, the project Development of a European Land Data Assimilation System to predict floods and droughts (ELDAS, Project EVG1-CT-2001-00050), and ETH Zurich. A. J. T. acknowledges financial support from the Netherlands Organisation for Scientific Research (NWO) through a Rubicon grant.
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Definition of variables. (a) Loss function and associated variables for the (bottom x axis) regular and the (top x axis) dimensionless notation and for linear [Eq. (8), dash–dotted line) and nonlinear [Eq. (9), solid line] drainage. (b) Stochastic precipitation process. Here, the canopy storage Δ acts as a threshold for the rainfall, effectively reducing the mean storm arrival rate λ but not the mean storm depth α [Eq. (13)]. Note that in general, ks is several orders of magnitude larger than ETmax.
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
Illustration of the (top) marked Poisson rainfall process (P) and (bottom) resulting traces of soil moisture (θ) for the (a) arid and (b) humid climates. Note that in the arid climate, soil moisture losses generally occur at a lower rate.
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
Steady-state soil moisture distributions p(θ) for the arid climate. Thick line is the shifted gamma distribution. Dash–dotted line is the Laio et al. (2001) model. Both have the same parameter values.
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
(a)–(p) Sensitivity of the steady-state soil moisture distribution p(θ) to its parameters for arid (gray and in the background and left curves), transitional (light gray and the middle curves), and humid (white and in the front and right curves) climates. The filled areas correspond to the outer envelope, which contains all pdfs resulting from perturbing each parameter in a ±10% interval. Reference parameters were taken as θr = 0.08, θw = 0.11, θc = 0.22, θf = 0.29, θs = 0.47, Ew = 0.2 mm day−1, b = 6, ks = 400 mm day−1, Δ = 0.5 mm, drz = 600 mm, LAI = 3, rs,min = 150 s m−1, and ra = 10 s m−1. Here, Δq was inverted from ETmax. Values for ETmax, α, and λ depend on climate (Table 1).
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
Sensitivity of the steady-state soil moisture distribution p(θ) for ks for arid, transitional, and humid climates using the depiction scheme of Fig. 4: (a) ±10% ks range; (b) Half to double (50%–200%) ks range. Reference parameters are as in Fig. 4.
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
The relative sensitivity σ [Eq. (22)] of average evapotranspiration 〈ET〉 to model parameters, as in Fig. 4, for the arid, transitional, and humid climates. A sensitivity of 1 means that any relative change in the parameter results in an equal relative change in 〈ET〉. Reference parameters are as in Fig. 4.
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
Steady-state soil moisture distributions p(θ) with ELDAS parameters for (a)–(k) selected soil types and for arid (dash–dotted), transitional (solid), and humid (dashed) climates. Common parameters: Ew = 0.2 mm day−1, Δ = 0.5 mm, and drz = 600 mm. For convenience, the same x axis is chosen for similar soil types.
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
Dependence of the critical moisture content θc on ETmax in TERRA [Eq. (27)].
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
The effect of drainage parameterization on the soil moisture distribution p(θ): 1 indicates linear drainage with the same ks as nonlinear drainage; 2 is the effective ks using the approach of Mahfouf and Noilhan (1996); and 3 indicates the closest correspondence between the pdfs for linear and nonlinear drainage when also θf is varied. Inset shows the corresponding minimum in the RMSE between the two pdfs.
Citation: Journal of Hydrometeorology 10, 3; 10.1175/2008JHM1033.1
Climate characteristics for the typical arid, transitional, and humid climates used in this study.
Soil parameters of the three LSMs used within the ELDAS project, and the mean soil moisture <θ> for the arid climate. Columns are merged when there is no functional difference between two parameters.