1. Introduction

Most land surface models (LSMs) used with atmospheric general circulation models (AGCMs) keep track of the moisture state of the soil with a prognostic (state) variable called “soil moisture” or “soil wetness,” typically defined at a number of vertical subsurface levels. Given the general dearth of in situ large-scale observations of soil moisture, this model-generated quantity is often made available to the scientific community as a data product. The National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis, for example, provides global “soil wetness” values on a T62 Gaussian grid (Kalnay et al. 1996), and the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) provides volumetric soil water in four soil layers on a roughly 1° spatial grid (Simmons and Gibson 2000). The Japanese 25-yr reanalysis (JRA-25) includes a dimensionless global data product called “soil wetness” (http://jra.kishou.go.jp/JRA-25/elements_en.html). The Global Land Data Assimilation System (GLDAS) provides real-time estimates of soil moisture fields derived from land model integrations of realistic atmospheric forcing (Rodell et al. 2004).

The scientific community, in turn, is filled with potential users of soil moisture data. Forecasts of weather and seasonal climate variations in particular can benefit from realistic initial states for the soil moisture variables used in the forecast system (Fennessey and Shukla 1999; Douville and Chauvin 2000; Koster et al. 2004). Models of ecosystem and carbon cycle processes (Yuste et al. 2007; Friend and Kiang 2005) require soil moisture estimates as inputs since soil moisture regulates both soil respiration and plant water stress, which affects stomatal conductance and carbon uptake. Agricultural (crop growth) models similarly rely on soil moisture estimates (Rosenzweig et al. 2002). Soil moisture estimates can benefit the modeling of dust generation (Fecan et al. 1999) and trace gas fluxes (Holtgrieve et al. 2006) from the earth’s surface. Groundwater resources can be estimated from Gravity Recovery and Climate Experiment (GRACE) satellite data, but only if independent near-surface soil moisture estimates are available to subtract from the total terrestrial water signal (Rodell et al. 2007). Beyond the immediate scientific community, potential users of soil moisture data include those interested in the pricing of agricultural futures and those monitoring agricultural drought (Narasimhan and Srinivasan 2005).

These are but a few of many potential users of soil moisture data. A question, then, naturally arises: are the reanalysis and LDAS-type soil moisture products being provided to users in a form appropriate to these applications? At first glance, one might think that they are. The products are generally given straightforward names (“soil moisture,” “soil water,” “soil wetness”) with seemingly unambiguous meanings and clear-cut units (e.g., percent volumetric water content). Uninitiated users might reasonably assume that, once model-specific treatments of such parameters as soil layer depth, soil texture, and porosity are accounted for, reanalysis-generated soil moisture products are ready to be used directly in their own specialized models.

This, however, is not the case, as indicated to varying degrees by a wealth of literature (e.g., Koster and Milly 1997; Chen et al. 1997; Entin et al. 1999; Schaake et al. 2004; Dirmeyer 2004). Simulated “soil moisture” does not have an unambiguous meaning. It is a strongly model-specific quantity, essentially an “index” of the moisture state, with a dynamic range defined by the specific evaporation and runoff formulations utilized by the given model (Koster and Milly 1997), in addition to model-specific soil parameters such as porosity, hydraulic conductivity, wilting point, and layer depth. Large differences are seen in the soil moisture products generated by different land models, even when the models are driven with precisely the same meteorological forcing (Dirmeyer et al. 2006). Given these differences, the direct transfer of one model’s soil moisture into another model is, in fact, inappropriate.

While this issue is generally well understood by the land surface modeling community, it is often overlooked or unappreciated by the scientific community at large, that is, by many potential users of the data. Over the years, the authors of this paper have come across numerous requests from across the community for soil moisture products, and they have seen numerous proposals for inappropriate uses of these data, uses that neglect the model dependencies discussed here. While we avoid here the naming of investigators and projects that have made this mistake, we assert that the problem is widespread enough to justify a highly focused study on the topic, one that will make clear the potential problems associated with transferring soil moisture contents between models and will point to a potential resolution of such problems: the proper statistical interpretation of model-generated soil moisture data.

We present such a study here. We begin in section 2 with two examples that illustrate clearly the potential danger of utilizing a reanalysis-based soil moisture product directly within another model. The discussion following section 2 has two purposes. First, in section 4, we highlight with a single, focused, global-scale study (outlined briefly in section 3) the degree to which soil moisture values produced by different land surface models do indeed differ, even when the models are driven with identical atmospheric forcing. Then, in sections 5 and 6, we show that the different soil moisture products, when properly interpreted, nevertheless are mutually consistent and thus do have intrinsic value. These results support the suggestion of Saleem and Salvucci (2002) that the true information content of soil moisture data lies not necessarily in their absolute magnitudes but in their time variability. In essence, we demonstrate here on the global scale that, if the nature of soil moisture in two models is well understood, a “mapping” could be derived that would allow the soil moisture variable from one model to be transformed and then used effectively in the second. We conclude in section 7 with some general remarks about model-generated soil moisture data and its applications.

2. Consequences of inappropriate transfer of soil moisture data

3. The Global Soil Wetness Project

Both of the examples above demonstrate the dangers associated with treating a reanalysis soil moisture as one would treat, say, a model or reanalysis air temperature—that is, as a quantity that is intrinsically comparable (in magnitude and range) to a true, observable geophysical quantity. With these examples in mind, we now turn our attention to a study performed with data from the second phase of the Global Soil Wetness Project (GSWP-2). GSWP-2 was a component of the modeling efforts of the Global Energy and Water Cycle Experiment (GEWEX), efforts focused on the large-scale performance and assessment of LSMs commonly used in weather and climate models and on the production of global datasets for use by the earth science community (Dirmeyer et al. 2006). In GSWP-2, a number of LSMs were run on a common, global 1° × 1° grid (excluding Antarctica), each driven by the same 10-yr time series of observations-based meteorology. The forcing time series were derived from a combination of gridded 3-hourly reanalysis output, 3-hourly satellite-derived surface radiation data, and monthly gridded observational data (Zhao and Dirmeyer 2003). The precipitation data, in particular, were forced to agree with observational datasets at the monthly time scale. The core period of 1986–95 covered by the offline simulations corresponds exactly to that of the International Satellite Land Surface Climatology Project (ISLSCP) Initiative II dataset (Hall et al. 2006).

As part of GSWP-2, each participating LSM produced a standard set of output grids at the same 1° resolution, data comprised of land surface state variables, fluxes, and other diagnostic quantities. Among these are several variables related to soil moisture, including the change in column-integrated water content, volumetric soil moisture in each model layer (layers vary amongst the models), and total column soil moisture. In this paper, we focus on the average soil moisture in the top meter of soil (nominally, the “root zone”), as computed from layer totals using an objective procedure (Guo et al. 2006). We normalize this quantity by dividing it by the total water holding capacity of the top meter (porosity times depth), yielding a dimensionless quantity known as the degree of saturation, which can vary from 0 to 1.

Note that until now in this paper, we have freely utilized the term “soil moisture” in deference to its widespread usage in the community, despite recognizing that it is a model-specific quantity with no direct observational analog. Even “degree of saturation” has a precise hydrologic meaning (e.g., Eagleson 1970), one inappropriate for such a model-specific variable. Thus, for greater precision in our discussion of the GSWP-2 analysis, we will hereafter refer to the computed degree of saturation for a GSWP-2 model as a root-zone “soil wetness index.” Always keep in mind, however, that, given its simple definition, all stated results regarding “soil wetness index” apply directly to model-generated “soil moisture” or “soil wetness” values, of the type provided as data products from reanalyses or LDAS systems.

Data from 7 of the 15 participating models are used hereafter in this study. These 7, which can be considered representative and which for simplicity are referred to in this paper as models A–G, were selected from the 15 based on the availability of water holding capacity data and an independence of historical development (i.e., data from different versions of the same model, though available through GSWP-2, were not considered, though experience tells us that even different versions of the same model can produce the types of differences illustrated below).

For a proper statistical analysis, the time series examined should be stationary; long-term trends need to be removed. Thus, prior to all analyses, the time series of soil wetness index produced by each model at each grid point were “detrended” by first fitting a line, through simple regression, through each time series, translating the line vertically downward to give it zero mean over the 10-yr period, and then subtracting this line from the time series. This detrending was, in fact, mostly performed to prevent spurious intermodel time series correlations in desert regions associated with incomplete spinup—if two models are continuously drying over the 10-yr period, the two raw (not detrended) time series will show a strong correlation that has little meaning. The detrending has no noticeable impact on our results outside of desert regions.

4. Examples of soil wetness index inconsistency

Figure 4 shows, for five representative sites, the 10-yr time series of daily averaged root-zone soil wetness index produced by the seven GSWP land models. Again, the wetness index can vary by definition from 0, for completely dry conditions, to 1, for completely saturated conditions.

The model differences are substantial. The examples, in agreement with the earlier findings of Chen et al. (1997) and Entin et al. (1999), illustrate the wide variety of wetness index behavior inherent in different state-of-the-art land surface models, both in terms of mean climatology (models C and D can be drier than model A throughout the simulation period) and dynamic range (in the Sahel the range for model D is about 0.2, whereas that for model B is about 0.5). The figure shows clearly that the wetness index variable, and thus the “soil moisture” variable from which it was derived, in a given model is specific to that model. Naturally, it would behoove climate modelers to characterize fully the values of the variable produced by their land model prior to performing sensitivity studies involving that variable. In examining, for example, wet and dry soil impacts on weather or climate, the assigned “wet condition” or “dry condition” should be made sensibly, in the context of the model’s own dynamic range, as determined through analyses such as that behind Fig. 4. Setting the initial perturbations too large, outside this inherent range, could seriously reduce the usefulness of such a study.

More to the point, the intermodel wetness index differences in Fig. 4 illustrate the potential problems associated with the direct replacement of one model’s soil moisture with that from another. In the Amazon, for example, the wettest state for model F is about equal to the driest state for model B. As a result, regardless of how wet the soil should be (following, say, an extensive rainy period), model B would always be initialized very dry if it used model F’s soil moisture without modification. Intuitively, using model F’s products to initialize model B would significantly degrade the performance of model B, even if the model F product was part of a trusted atmospheric reanalysis or offline land analysis. Again, such considerations lie behind the degradation of skill seen in Figs. 1 and 2, for the OSU land model tends to produce drier soil moistures than the Noah land model under the same atmospheric forcing.

5. Underlying information content on temporal soil moisture variability

We emphasize again that an LSM’s soil moisture variable is best thought of as a model-specific index of wetness, a monotonic function of the true average soil moisture that it is trying to represent. Because different LSMs use, in effect, different monotonic functions, the “soil moistures” they produce have different climatological means and variability characteristics. Even so, the time variations of the different LSM products should be correlated; for example, regardless of the LSM used, an excessively rainy period should lead to a higher value for its soil moisture variable than a dry period. Of course, perfect correlations will never be achieved, if only because soil moisture, through the conservation equation, also depends in part on runoff and evaporation fluxes, and different LSMs use different formulations for these fluxes.

We characterize here the “level of agreement” between different soil moisture products using such temporal correlations. (Again, throughout this paper, we focus on the total moisture in the root zone; a supplemental analysis of total column soil moisture produced equivalent results.) At each GSWP-2 grid cell, we first compute the square of the correlation between the time series of wetness index produced by each independent pairing of LSMs. The daily (detrended) data are used for this calculation with the mean seasonal cycle removed. For seven LSMs, we obtain 21 r² values. We then compute the average of these 21 values and call this average our measure of LSM agreement.

The global distribution of the average r² values is shown in Fig. 5. The average r² is low in Eastern Hemisphere deserts and in high northern latitudes. Almost everywhere else, however, LSM agreement is high, with average r² values exceeding 0.5, often substantially. The average r² values indicate that, despite the known differences in soil wetness index products (e.g., Fig. 4), the LSM products indeed share a great deal of underlying information about the time variability of the wetness index. This shared information suggests that a mapping of soil wetness indices, and thus soil moistures, between models may be possible.

Schaake et al. (2004), using a somewhat different analysis approach over the continental United States, produced a similar result; they found that four different models driven with the same meteorological forcing tended to produce similar temporal variations in wet areas but not in dry areas. In effect, the present study affirms their result using a greater number of models and a larger (global) spatial domain.

The low correlations in the deserts are, in some ways, not surprising. Arguably, model agreement should be largest in regions with large variations in precipitation forcing—a larger precipitation variance suggests a larger variation in moisture storage that all of the models can more easily capture. The deserts, by definition, have low mean precipitation and a correspondingly low precipitation variance. In high northern latitudes, the differences may relate in part to differences in the parameterization of snow and frozen soil.

6. Mapping of soil wetness index, and thus soil moisture, between models

a. Scaling with the first two statistical moments

The key to any proper transferability of soil moisture states between LSMs lies in the recognition of and correction for the differences in the statistical moments of the LSMs’ soil moisture distributions. If the differences in the LSM-based soil wetness indices in Fig. 4 relate mostly to differences in their means and standard deviations, then all models would produce roughly the same time series of standard normal deviates w′:

View Expanded

where w_m is the mean wetness index for the given LSM at the point and time of year in question and σ_w is that LSM’s standard deviation of wetness index for that point and time of year. Dirmeyer et al. (2004), using (1), suggest an equation for transforming a wetness index value for model A into one that can be used in model B:

View Expanded

For example, using (2), a relatively dry state in model A would be mapped into a correspondingly dry state in model B.

Of course, such a transformation ignores the fact that soil moisture, and thus wetness index, distributions are often skewed rather than Gaussian, particularly when mean soil moisture is at the drier or wetter end of the spectrum. The non-Gaussian properties could allow, for example, the generation through (2) of scaled soil wetness indices that fall below 0 or exceed 1, indices that would then have to be constrained after the fact to sensible values. In principle, we could address this and other problems associated with the underlying non-Gaussian distributions explicitly using a transformation method that involves more sophisticated statistical techniques, such as cumulative distribution function (CDF) matching (e.g., Wood et al. 2002). Given, however, the availability of only 10 years of data from GSWP-2, use of such techniques, while not impossible (see, e.g., the ergodic approach of Reichle and Koster 2004), is nevertheless difficult, and thus for convenience we focus in this paper on the use of the simpler (2). Our justification for going ahead with (2) despite its limitations is simple: both the non-Gaussian nature of soil moisture and, indeed, our inability to estimate w_m and σ_w accurately from only 10 truly independent data points for a given time of year will only hinder our ability to develop an effective mapping between models. Thus, any success in mapping that we obtain through (2) can be considered conservative. As will be seen, our mapping success using (2) despite being “underestimated” is, indeed, considerable.

7. Discussion

The agreement in the LSM soil wetness index products illustrated in Fig. 5 and the success of the mapping demonstrated in Figs. 6 and 7 echoes somewhat the findings of Dirmeyer et al. (2004). The present study serves as a more focused and controlled analysis of intermodel soil moisture differences since each of the (more abundant) LSMs examined here is forced with identical meteorological data—thus we isolate the impacts of the LSM differences themselves. We similarly affirm and expand on the results of Schaake et al. (2004) by examining a greater number of land models over the full global domain. We find that, while the wetness indices, and thus the soil moisture products, from different land surface models are essentially very different, they contain generally the same information regarding temporal soil moisture variability so that the products generated by one model can potentially be transformed into quantities relevant to another. The presence of similar temporal variability information in the face of distinctly different soil moisture values (in essence a consequence of similarity in the simulated time series of the infiltration, evaporation, and runoff fluxes that control the models’ soil moisture states) is a clear demonstration of the “model-specific index” nature of the soil moisture variable; it underlines the fact that an LSM-derived “soil moisture” is not (as its name implies) a physical quantity that can be directly validated with field measurements.

Is the ambiguity of a given model’s soil moisture product acceptable? Or does it imply that modelers, before using their models, need to improve them until simulated soil moisture values are indeed comparable to those of other models and to observations? Arguably, the ambiguity is largely unavoidable given current computational constraints on LSM resolution. The single soil moisture variable at a given vertical level in a land surface model must reflect more than the average soil moisture across, say, 100 km. It must also—somehow—implicitly reflect the spatial variability of soil moisture and the effects of this variability on the surface energy and water fluxes. Even if we could construct a fully reliable macroscale model that represents the effects of porosity, tortuosity, etc., within a local soil volume without resolving these features explicitly (a complex topic in itself to address), soil moisture heterogeneity at larger spatial scales—e.g., at the hillslope scale (tens to hundreds of meters), where water table dynamics may lead to wet conditions at the bottom of a hill and dry conditions near the top—leads to corresponding heterogeneity in evaporation and runoff production (e.g., Famiglietti and Wood 1991). Given such soil moisture heterogeneity, and owing to strong nonlinearities in the governing soil moisture–evaporation relationship that exists at a point, a modeler simply cannot represent the true average soil moisture in an AGCM gridcell area with a single number and use that single number in a locally derived (single site) relationship to obtain the true areally averaged evaporation rate. For realistic evaporation rates so critical to the proper operation of the atmospheric model, either the evaporation–soil moisture relationship must be modified away from the observed relationship at a point (not something land surface modelers claim to know how to do) or the soil moisture variable in the LSM must take on a nebulous meaning, a meaning distinct from “areally averaged soil moisture.”

Again, although its meaning may be nebulous, we emphasize that the true information content—and thus value—of a model soil moisture product lies not in its absolute magnitudes but in its time variations. The proper use of a simulated soil moisture product demands an understanding of this basic element of its character.

We can speculate that, as the spatial resolution of land surface models improves and as modelers take better advantage of growing soil moisture databases for the continued improvement of hydrological parameterizations, the disconnect between modeled and observed soil moisture should decrease. Again, though, fine spatial scales of heterogeneity (tens of meters) help shape hydrological processes in nature, and our ability in the foreseeable future to resolve such scales explicitly in global simulations appears limited (though statistical approaches may provide a valid alternative strategy). Again, even with such highly resolved scales, the submillimeter scales of relevance to soil moisture transport within the soil matrix (i.e., the scale of soil pores) will not soon, if ever, be resolved—necessitating in any case a macroscopic representation of soil moisture.

The proper utilization of observations for development, calibration, and validation of models presents additional challenges. First and foremost, in situ soil moisture data have very limited availability, with many large regions of the world still unmonitored. Even where the in situ data exist, their interpretation is often difficult because the measurements are highly localized, and differences in soil properties can cause important differences in the mean and variance of soil moisture, even over small distances. Variations in forcing (e.g., convective precipitation) add another decorrelating factor on longer spatial scales, though this becomes less important as the time scale increases.

Interestingly, Saleem and Salvucci (2002) scaled each of a number of observational (in situ) soil moisture time series in Illinois with (1) and showed that the ostensibly different time series contain similar information, in direct analogy to our findings above. Saleem and Salvucci indeed suggest that scaling with (1) or with more complex statistical techniques could aid in model intercomparison. Our findings firmly support their suggestion, on a global scale.

The remote sensing of soil moisture via satellite holds particular promise to address the lack of in situ observations across the globe, but much work is still needed to address the proper use of these data for model improvement. In some existing cases, satellite methods seem to return their own forms of soil moisture indices rather than direct soil moisture estimates (Reichle et al. 2007). Also, satellite-based soil moisture data are limited to the top several centimeters (or less) of soil, whereas the soil moisture data of greatest relevance to many climatic applications spans a much larger depth, through at least the root zone of the native vegetation. We note, as an important aside, that satellite-based soil moisture data can indeed contribute to the estimation of root-zone soil moisture through the process of data assimilation (Reichle et al. 2007), essentially the mathematically optimal merging of satellite-based and land-model-based soil moisture estimates. For data assimilation to proceed with the current generation of land surface models, the model-dependent nature of simulated soil moisture must be recognized and accounted for prior to the data merging.

Finally, we note that, while the use of (1) does allow a mapping of the soil moisture variable between land models and while much more reliable approaches for mapping do exist (e.g., CDF matching) and should be used instead if adequate data are available, the use of any mapping comes with a cost—the modeler must generate and analyze a 10-yr (or preferably much longer) time series of soil moistures produced by both land models involved. Generating such time series is conceptually trivial, particularly given the availability of forcing data through GSWP-2, but the production and analysis of the time series may still, for various reasons (development of an offline driver, grid considerations, etc.), pose difficulties for generating a robust mapping algorithm. Model-specific vertical discretizations of the soil column may pose particular, though not insurmountable, difficulties for mapping.

This paper’s main result—that the representative cross section of LSM’s examined here contain largely the same information on the temporal variation of root-zone soil moisture so that the soil moisture produced by one land model can, if properly scaled, be utilized in another—may extend beyond such simple model-to-model mappings. Because an LSM’s soil moisture variable represents the time-integrated impacts of antecedent meteorological forcing on the hydrological state of the soil system, it has a potentially profound real-world application: unless all of the models examined here are wrong in precisely the same way, we can speculate from the agreement levels in Figs. 5, 6, and 7 that any of these models could, if forced with realistic meteorological data (and better yet, if also combined with satellite-based soil moisture information via data assimilation), provide a soil moisture product that, when suitably scaled, captures the time variation of real-world soil moisture. Indeed, the impact of any small model dependence that does exist—as represented by the degree to which the r² values in Fig. 5 are still less than 1 or as established through other techniques (e.g., Abramowitz and Gupta 2008)—can perhaps be mitigated by using some type of multimodel average. If the forcing data were provided in real time, the state of the soil could be estimated in real time. The model products could, if suitably scaled, serve to monitor the real world hydrological state. Perhaps, for example, they could be used to identify such events as the onset and demise of agricultural drought.

A note of caution about this, however, is appropriate here. It is possible that land surface models are, indeed, all “wrong in precisely the same way,” reducing their usefulness for such a real-world application. For example, they all lack, to some degree, sophisticated treatments of certain hydrological processes (e.g., baseflow, interflow), and most share similar simple representations of other hydrological processes (e.g., the use of Richard’s equation for subsaturated vertical flow). More research is needed into the question of how well land surface models in general capture real-world hydrological processes.