## Abstract

Atmosphere–ocean general circulation models (AOGCMs) employ very different land surface schemes (LSSs) and, as a result, their predictions of land surface quantities are often difficult to compare. Some of the disagreement in quantities such as soil moisture is likely due to differences in the atmospheric component; however, previous intercomparison studies have determined that different LSSs can produce very different results even when supplied with identical atmospheric forcing.

A simple off-line LSS is presented that can reproduce the soil moisture simulations of various AOGCMs, based on their modeled temperature and precipitation. The scheme makes use of the well-established Thornthwaite method for estimating potential evapotranspiration combined with a variation of the Manabe “bucket” model. The model can be tuned to reproduce the control climate soil moisture of an AOGCM by adjusting the ease with which runoff and evapotranspiration continue as the moisture level in the bucket goes down. This produces a set of parameter values that provides a good fit to each of several AOGCM control climates. In addition, the parameter values can be set to imitate the LSS from one AOGCM while the model is forced with atmospheric data from another, thus providing an estimate of the magnitude of variation caused by the differences in land surface parameterization and by differences in atmospheric forcing. In general, the authors find that differences in LSSs account for about half of the difference in soil moisture as simulated by different AOGCMs, and the differences in atmospheric forcing account for the other half of the difference. However, the LSS can be more important than differences in atmospheric forcing in some regions (such as the United States) and less important in others (such as East Africa).

## 1. Introduction

The prediction of soil moisture in climate models and in operational forecasting follows two distinctly different paradigms. The paradigm used in climate models makes use of the surface energy balance. The more recent implementations of this approach distinguish between evaporation from wet leaves, from inside leaves (through the stomata), and from the bare ground surface. The driving force is taken as the difference between *saturation* vapor pressure at the surface temperature and the overlying atmospheric vapor pressure. This is undisputedly valid from wet leaf surfaces and seems to be reasonable from the interior of leaf pores, which presumably are covered in a film of water. Water in unsaturated soils is concentrated in some fraction of the pore space, thereby also forming a liquid surface to which the saturation vapor pressure applies. Because the saturation vapor pressure depends on temperature, this approach requires explicit computation of the surface temperature, which in turn requires modeling the surface energy balance. As the soil moisture content decreases, the remaining soil water is bound more tightly to the soil and the stomatal openings decrease, thereby decreasing the evaporation rate for bare soil and the transpiration rate from dry leaves for a given vapor pressure difference. This effect is represented in climate models in one of two ways: either by multiplying the driving force by a factor *β* ≤ 1.0, which decreases in some way with decreasing soil moisture content, or by increasing the soil and stomatal resistances in a resistance-based approach to modeling evapotranspiration. The evapotranspiration rate with *β* = 1 or, equivalently, with the surface (but not the aerodynamic) resistance equal to zero, is referred to as the potential evapotranspiration rate *E _{p}*. Atmosphere–ocean general circulation models (AOGCMs) with energy-balance-based land surface schemes (LSSs) have been extensively used to assess the impact of greenhouse gas–induced warming on future soil moisture levels.

The other paradigm is an operational approach, used in real-world settings such as real-time monitoring of soil moisture as part of a warning system for drought or in the preparation of climatological atlases of soil moisture and evaporation. The surface temperature is readily available from climate model simulations but cannot be readily measured (Milly 1992). Thus, the surface energy–balance approach—which depends on knowledge of surface temperature—cannot be used without surface temperature output from AOGCMs or other numerical models. Alternative approaches, not requiring knowledge of surface temperature, are required. One of these is the Penman–Monteith approach (Monteith 1965) in which evaporation is computed from atmospheric temperature and from the surface net radiation. Rotstayn et al. (2006) recently used this approach to good success with both observed data and an AOGCM. However, surface net radiation data are also not generally available (and certainly not on a continuous, real-time basis over broad regions), so even simpler approaches have been used. Foremost among these is the Thornthwaite (1948) method, which computes potential evapotranspiration in terms of temperature and solar declination.

As reviewed by Cornwell and Harvey (2007), the Thornthwaite method has been used for over 40 years in water-balance calculations. The Thornthwaite equation is typically used in computing the Palmer Drought Severity Index (PDSI) (Palmer 1965), and the U.S. Weather Bureau (NOAA), and the U.S. Department of Agriculture use the Thornthwaite method to produce weekly and monthly PDSI and Crop Moisture Index Maps for the United States (see Heim Jr. 2002). A number of investigators have used the Thornthwaite equation to assess the potential impact on soil moisture of future human-induced warming (e.g., Rind et al. 1990; Feddema and Mather 1992; Huang et al. 1996; Feddema 1999; Georgakakos and Smith 2001; Hagemann and Gates 2001; Fan and van den Dool 2004).

Given that AOGCMs with a surface energy–balance scheme have been used to project future soil moisture conditions and that the Thornthwaite method is used in operational settings under present conditions also for projecting future soil moisture changes, the question arises: Are these two approaches compatible? Can the Thornthwaite method, when combined with the AOGCM equations for the other components of the soil moisture balance and as part of a structurally similar soil moisture model, replicate the soil moisture variation simulated by the AOGCM for the present climate when AOGCM temperature and precipitation are used in place of observed temperature and precipitation? If the answer to this question is yes, can it also replicate the change in soil moisture as the climate warms?

These are the questions that motivated the study presented here. Potential evapotranspiration, as given by the Thornthwaite method or any other method, is only one factor in the soil moisture balance. To answer the above questions, we need to apply the Thornthwaite method within an overall soil moisture model. Previous work has demonstrated that, on seasonal time scales, the variation of soil moisture is dominated by precipitation, its immediate partitioning into interception, infiltration, and runoff; whether subsurface runoff without saturated conditions is included; and the dependence of subsurface runoff on soil moisture content (Cornwell and Harvey 2007). The simplest soil moisture model is the “bucket model” of Manabe (1969), in which rainfall accumulates in the soil until the soil reaches its water-holding capacity, and only then does any additional rainfall occur as runoff. The evapotranspiration rate is given by the potential evapotranspiration (computed from the surface energy balance) multiplied by a factor that varies linearly with soil moisture between certain limits. We adopt a modified version of this model, called the Potential Evapotranspiration–Leaky Bucket (PELB, or “pebble”) model, in which subsurface runoff can occur out the bottom of the bucket even when it is not full, and the Thornthwaite potential evapotranspiration is used in place of one derived from the surface energy balance.

It must be emphasized here that the goal of this study is not to produce a “better” soil moisture simulation. Rather, the purpose of PELB is to reproduce the behavior of AOGCM–LSSs as a tool for experimentation and intercomparison; in essence, the goal is to model the models. For this reason, PELB is validated through comparison with AOGCM output rather than with land surface observations. Also, additional features that might otherwise improve the PELB representation of reality are omitted unless they are present in the AOGCM being replicated.

The parameters of the PELB model when applied to any given AOGCM are set to replicate the same parameters or the effective values of the parameters in the AOGCM. The AOGCM-adjusted PELB model is then driven with monthly temperature and precipitation from the AOGCM to assess its ability to replicate the AOGCM-simulated soil moisture.

The following sections describe the three AOGCMs used in this study, the PELB model, the method for tuning it to match each of the AOGCMs, and our results.

## 2. Models and data

Data for this study were acquired from the Intergovernmental Panel on Climate Change (IPCC) Data Distribution Centre (more information is available at http://ipcc-ddc.cru.uea.ac.uk/index.html). The center provides access to monthly mean temperature and precipitation data from several AOGCMs, three of which we have chosen to study here:

**CGCM1**—Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model, version 1, Canada (Flato et al. 2000);**HadCM2**—Second Hadley Centre Coupled Ocean–Atmosphere General Circulation Model, United Kingdom. (Johns et al. 1997); and**CCSR/NIES**—Center for Climate Research Studies and National Institute for Environmental Studies General Circulation Model, Japan (Emori et al. 1999).

The above acronyms will be used in the subsequent discussion.

The three AOGCMs here are relatively simple; all of them use a single layer for soil moisture storage, with no deeper layers. However, they differ in important respects as identified by Cornwell and Harvey (2007): the moisture capacity of the soil, the inclusion of stomatal resistance, and the dependence of evapotranspiration efficiency on soil wetness. The design of PELB discussed below must explicitly represent these differences.

## 3. The PELB model

Changes in the amount of soil moisture storage can be described by

where *w* is a measure of the equivalent depth of water in the soil column and *P*, *E*, and *R* are the rates of precipitation, evapotranspiration, and runoff/drainage, respectively. Precipitation is an output of the atmospheric component of an AOGCM, while evapotranspiration and runoff must be determined by the land surface scheme.

### a. Potential evapotranspiration in AOGCM–LSSs

In some AOGCMs, the evaporation rate is computed as

which has the form

where *ρ* is air density; *C _{D}* is a “drag” coefficient that depends on wind speed, atmospheric stability, and surface roughness;

*U*is the near-surface wind speed;

*q*

_{sat}(

*T*) is the saturation specific humidity at the surface temperature

_{s}*T*;

_{s}*q*is the air specific humidity; and

_{a}*β*—the evapotranspiration efficiency—is a factor equal to 1.0 when the availability of soil moisture does not restrict evaporation and less than 1.0 when soil water is limiting. Potential evapotranspiration

*E*is the evaporation rate with

_{p}*β*= 1. The surface saturation specific humidity is computed as

where *e*_{sat}(*T _{s}*) is the saturation vapor pressure evaluated at the surface temperature

*T*. Potential evapotranspiration is thus given by

_{s}Alternatively, evapotranspiration in AOGCMs can be computed in terms of the aerodynamic and surface resistances as

where *r _{s}* is the surface or stomatal resistance (governing vapor flow from inside the leaf, through the stomata to the surface of the leaf) and

*r*is the aerodynamic resistance (governing the flow of both heat and moisture from the surface of the leaf to the surrounding air). The surface resistance

_{a}*r*depends on the stomatal opening, which in turn depends on soil moisture. (In the most recent AOGCMs, in which the coupled moisture and carbon fluxes are computed,

_{s}*r*also depends directly on the atmospheric CO

_{s}_{2}concentration or on the rate of photosynthesis as governed by soil moisture, temperature, atmospheric CO

_{2}, and the availability of photosynthetically active radiation.) Potential evapotranspiration can be defined as

*E*when

*r*= 0. Thus, Eq. (6) can be written in a form similar to Eq. (3):

_{s}### b. Potential evapotranspiration in the PELB model

The PELB model uses an empirical method developed by Thornthwaite (1948) for estimating monthly potential evapotranspiration from the land surface based on temperature. Thornthwaite based his method on the ratio of the current month’s temperature to an annual heat index:

where

and *E _{p}* is the potential evapotranspiration (cm month

^{−1}),

*T*is the mean screen level air temperature (°C),

_{a}*T*is the climatological monthly average air temperature,

_{M}*I*is an annual heat index, and

*h*is the ratio of sunlit hours (depending on month and latitude) compared to a month of 30 days with 12 h of sunlight each.

Some authors (e.g., Milly 1994b) have argued that Thornthwaite’s method systematically underestimates the potential evapotranspiration. Milly (1994a) and Georgakakos and Smith (2001) compensated for this by uniformly multiplying Thornthwaite’s *E _{p}* by a factor of 1.2; we do the same here.

### c. Actual evapotranspiration

Thornthwaite (1948) and Thornthwaite and Mather (1955, 59–117) also proposed a simple procedure for calculating the change in storage of soil moisture (see also Mather 1978). This procedure is very similar to the popular bucket model introduced by Manabe (1969) and subsequently applied by many researchers at local, regional, and global scales. Variations of the Manabe model were employed by the majority of AOGCMs until the early 1990s (Milly 1992) and are still not uncommon.

When the bucket in the Manabe model is full or nearly full, evapotranspiration occurs at the potential rate as described in section 3b. However, as the soil moisture storage decreases in months with a moisture deficit (i.e., months with potential evapotranspiration greater than rainfall), the actual evapotranspiration also decreases since there is insufficient water available at the surface. Manabe (1969) proposed that this decrease would be directly proportional to decreases in moisture storage below a critical point (*w*_{crit}), as described below:

where *w* is the equivalent depth of plant-available water in the soil column (cm), *w*_{FC} is the capacity, and *s* relates *w*_{crit} to *w*_{FC}. If the moisture level should fall below the wilting point (i.e., there is no water available to plants), *w* and therefore *β* will be zero.

Thornthwaite (1954) set *s* = 1, but Manabe (1969) suggested that the value should lie between 0.7 and 0.8. Nonlinear relationships between *E* and *E _{p}* have also been employed (e.g., Mintz and Walker 1993).

PELB currently uses a linear relationship between *β* and *w*, but the value of *s* can vary so as to match the value (or effective value) in a given AOGCM–LSS. The CGCM1 LSS uses a value of *s* dependent on the soil and vegetation types in each grid cell (McFarlane et al. 1992). The HadCM2 LSS uses a uniform value of 1/3 (Warrilow et al. 1986), while the CCSR/NIES LSS uses a Manabe formulation (Phillips 2006) with *s* equal to 0.75 [these very different (factor of 2) choices for *s*, an inconsistency that is not very well justified]. The PELB model with parameters adjusted to represent the LSS of a given AOGCM will be designated as PELB-*AOGCM_name*, where *AOGCM_name* is the name of the specific AOGCM to whose LSS PELB has been adjusted.

### d. Evapotranspiration and vegetation

Vegetation cover can influence the hydrologic cycle by affecting the ease of evapotranspiration. Precipitation that is intercepted by the canopy collects on the leaves and evaporates freely. When there is adequate moisture in the soil, the plant capillaries act to pump water from the roots to the leaves where it transpires through stomatal openings. When the available moisture is inadequate, the stomata shrink and the amount of transpiration is reduced as the plant attempts to conserve water.

Of the AOGCMs included in this study, the CGCM1 and HadCM2 LSSs use a soil moisture capacity that depends on the local vegetation type (Warrilow et al. 1986; McFarlane et al. 1992). In this scheme, plants with deeper roots can access a deeper column of soil. The CCSR/NIES LSS uses a uniform moisture capacity. The CCSR/NIES and HadCM2 LSSs also account for stomatal resistance by reducing the evapotranspiration efficiency *β* according to the specified stomatal resistance of the vegetation (Warrilow et al. 1986; Phillips 2006).

In both the HadCM2 and CCSR models, the total evapotranspiration *E* is the sum of the evaporation through canopy stomata in the vegetated fraction *f _{υ}* of the grid cell (having surface resistance

*r*equal to canopy resistance

_{s}*r*), evaporation from the fraction

_{sc}*f*of the vegetation that is wet with intercepted precipitation (

_{υw}*r*= 0), and evaporation from the soil in the nonvegetated fraction of the cell (

_{s}*r*=

_{s}*r*= 60 sm

_{ss}^{−1}, a constant soil surface resistance):

where

*ρ* is the air density, *q _{s}* and

*q*are the specific humidities near the surface and at the reference level, respectively,

_{a}*r*is the aerodynamic resistance to vapor transport, and

_{a}*r*is the surface resistance to evapotranspiration.

_{s}The *E _{s}* appearing in the second and third terms of Eq. (13) is not the same as

*E*(because

_{p}*r*≠ 0), so the

_{s}*β*appearing in Eq. (13) is not the same

*β*as used in Eq. (3); we have designated it as

*β*. Here

_{s}*β*can be calculated from Eqs. (11) and (12) using a uniform value

_{s}*s*= 0.33 when matching PELB to the HadCM2 model and 0.75 for CCSR/NIES. Furthermore,

*r*(and hence

_{s}*E*) is independent of soil moisture (as expected for an

_{s}*E*-like quantity), all the dependence of evapotranspiration on soil moisture bring handled by the variation of

_{p}*β*with soil moisture. By requiring that

_{s}*β*in Eq. (3) be such that the evapotranspiration given by Eq. (3) is equal to that given by Eq. (13), it can be easily seen that

where, as previously noted, *β _{s}* is computed from Eqs. (11) and (12). There is a problem incorporating Eq. (15) into PELB in that

*f*and

_{υw}*r*are difficult to calculate using only temperature and precipitation as input. However, if we assume that over the course of the monthly time step

_{a}*f*is roughly equal to

_{υw}*w/w*

_{crit}and

*r*can be given a constant value, then Eq. (15) becomes dependent only on

_{a}*w*. Thus, we have derived a

*β*for the HadCM2 and CCSR/NIES models that varies only with

*w*, as in the original use of

*β*in Eqs. (11) and (12).

Assigning a constant value to *r _{a}* is a significant assumption in this derivation. The aerodynamic resistance can be determined by

where *u* is the wind speed, *k* is the von Kármán constant, *z _{r}* is the reference height, and

*z*

_{0}is the roughness length. Here

*r*is dependent on both the surface roughness, which varies with vegetation type but not (in these AOGCMs) with time, and also the surface wind speed, which can be quite variable) Assuming a constant

_{a}*r*requires assuming a constant wind speed; PELB therefore uses a typical value of 3 m s

_{a}^{−1}everywhere. Figure 1 shows the effect of varying this wind speed in Eqs. (15) and (16) on the value of

*β*for three representative vegetation types.

In Eq. (15) the value of *β* is always less than one, even when *β _{s}* = 1. This is in contrast to

*β*calculated using Eqs. (11) and (12), where the maximum value is 1.0. For the purpose of illustration, the maximum value of

*β*in Eq. (15) can be determined by

Figure 2 illustrates the relationship between *β* and *β _{s}* from Eq. (15). Table 1 shows the values of

*f*,

_{υ}*r*,

_{a}*r*, and

_{sc}*β*

_{max}for the nine vegetation types defined by Warrilow et al. (1986, based on data from Wilson and Henderson-Sellers 1985).

In summary, so as to fit PELB to the HadCM2 and CCSR/NIES LSSs, we had to develop an alternative formulation of *β* in terms of *w* [given by Eq. (15)], for use instead of Eqs. (11) and (12). With this formulation, *β* asymptotes to a maximum value of less than 1.0 even when *w* ≥ *w*_{crit}: *β _{s}* [used in Eq. (15) to compute

*β*] is computed using Eqs. (11) and (12) and thus varies linearly with

*w*up to

*w*

_{crit}. Then

*E*is computed from Eq. (3) using the Thornthwaite

*E*[Eqs. (8)–(10)] and

_{p}*β*from Eq. (15).

### e. Runoff—The leaky bucket

In Manabe’s model, a moisture surplus or deficit is calculated by subtracting evapotranspiration from precipitation after each time step. The bucket concept is that moisture surpluses and deficits are added to or subtracted from the existing soil moisture storage until the storage reaches the maximum plant-available moisture capacity, at which point any additional surplus overflows the bucket and is lost as runoff. Despite criticisms that bucket models systematically overestimate evapotranspiration (e.g., Bell et al. 2000; Henderson-Sellers et al. 2003), it has been shown that at monthly or larger time scales, bucket models can be just as capable as more complex schemes (Desborough 1999; Pitman et al. 2004). Robock et al. (1995) tested a bucket model versus the Simplified Simple Biosphere Model (SSiB), the more complex soil hydrology model of Xue et al. (1991), and found that the bucket model performed equally well when compared with observations.

This overflow quantity is often referred to as the Dunne runoff. Of less significance are the Hortonian runoff (when the rate of precipitation exceeds the maximum infiltration capacity of the soil) and the subsurface base flow or drainage. Some AOGCM–LSSs neglect these quantities while others use soil characteristics to calculate them in detail. To provide flexibility for additional runoff in our model, it was decided to use a leaky bucket where runoff can occur even when the soil is below capacity. This would also make some allowances for runoff that occurs at a shorter time scale than the monthly scale used by PELB. This additional runoff term is proportional to the moisture storage, as in

where *R* is the additional drainage and/or runoff (cm month^{−1}) and *γ* is a runoff parameter (month^{−1}).

### f. Calculating the surface water balance

The calculated values of both *E* and *R* depend on the current value of *w*. Because *w* changes over time and a relatively long time step (one month) is used, we have linearized the soil moisture storage equation. The soil moisture at the end of a time step of length Δ*t* is given by

where *w*_{0} is the moisture storage at the beginning of the time step and Δ*w* is computed from a linearization of Eq. (1), written in terms of Δ*w* rather than *w*:

This has the general form

where *β*_{0} is the value of *β* at the start of the time step.

Equation (21) can be solved analytically as

as long as Δ*w* does not become so large (and is positive) that *w*_{0} + Δ*w* exceeds *w*_{crit}. If that happens, we determine the Δ*t* at which this happens, then begin a new analytic integration over the remainder of the time step (starting from the updated *w*) with *a* and *b* modified as follows:

If Δ*t* grows large, Δ*w* approaches −*a*/*b* which, by Eq. (21), gives dΔ*w*/d*t* = 0. The time constant *b* reflects how strongly the rate of moisture loss responds to changing soil moisture conditions.

The key to successfully modeling the land surface water balance is partitioning moisture surpluses into evapotranspiration, runoff, and increased storage (Koster and Milly 1997). Of particular importance are the increasing resistances to evapotranspiration and to surface and subsurface runoff as the soil becomes dry (Desborough et al. 1996; Gedney et al. 2000). In PELB, these resistances are controlled by the parameters *s* and *γ*, which in turn determine both *a* and *b* through Eqs. (22) and (23).

### g. Soil moisture capacity

The field capacity of water in the soil can be divided into that which is available to plants and that which is tightly adsorbed to the soil pores and is thus inextricable (Dunne and Willmott 1996). The plant-available moisture-holding capacity is probably between one-half and two-thirds of the field capacity (Warrilow et al. 1986; Robock et al. 1995). The total plant-available moisture-holding capacity of a given area depends on the soil texture, the depth of soil, and the type and rooting depth of the vegetation.

Soil moisture capacity is a critical factor in calculating runoff and drainage (Mahfouf et al. 1996; Desborough 1999). An increase in the moisture capacity leads directly to an increase in the modeled annual mean evapotranspiration as more rainfall is retained and therefore available for evapotranspiration (Ducharne and Laval 2000). However, the various representations of moisture capacity used by different AOGCMs can make it difficult to compare results. Some AOGCMs with bucket LSSs use a geographically uniform value, but more recent schemes use a value that depends on local conditions at each grid cell (e.g., CGCM1) or even within the cell (e.g., Bonan 1996).

For this study, reasonable efforts were made to determine the plant-available moisture capacity used by each AOGCM, as outlined in their respective model descriptions. Manabe (1969) suggested a simplified field capacity of 15 cm everywhere but noted that this was a deliberate underestimation, apparently chosen to reflect the smaller (but unknown) plant-available capacity. Therefore, for the purposes of Eq. (12) we have used the plant-available capacity in place of the field capacity, a choice that is not without precedent (e.g., Mintz and Walker 1993; Feddema 1999).

### h. Snow cover

An additional complication of land surface modeling is the treatment of snow, snowmelt, and frozen soil. Precipitation that falls as snow accumulates on the land surface. When the snow cover melts, that water is rapidly released and made available to the soil. The problems lie in determining the timing of the snowmelt and partitioning it into infiltration and runoff components.

Many AOGCM–LSSs assume that, if the snow melts while the soil is still frozen, all of the water released is lost as runoff since ice in the soil seals off the soil matrix (Mitchell and Warrilow 1987; Robock et al. 1995). Pitman et al. (1999) have argued that this is not necessarily the case. Using the Best Approximation of Surface Exchanges (BASE) land surface model (Desborough and Pitman 1998), they compared simulations with and without the model’s scheme for frozen soil moisture, compared with observations from the Mackenzie Basin. They concluded that at the scale of an AOGCM, the presence of ice in the soil will not necessarily impede infiltration and may even enhance it.

For this study, the snow cover process must be heavily parameterized in PELB owing to the relatively long (monthly) time step and the absence of information about ice in the soil. It is assumed that precipitation falls as snow in any month in which the average temperature is below a critical threshold of 0°C. There is no runoff or other soil moisture change during winter months; additional precipitation is added to the snowpack. There is also no mechanism for estimating sublimation from the snowpack. The accumulated snowpack melts completely in the first subsequent month with an average temperature above 0°C. Snowmelt runs off only if the bucket is full. This approach is quite crude, but the timing of the spring soil moisture peak in the results seems reasonable.

### i. PELB model summary

In summary, the LSS of each AOGCM is represented here by up to seven (potentially geographically varying) parameters: the field capacity (*w*_{FC}), the critical moisture fraction (*s*), the aerodynamic, canopy, and soil surface resistances to evapotranspiration (*r _{a}*,

*r*, and

_{sc}*r*), the vegetated fraction (

_{ss}*f*), and a linear subsurface runoff parameter (

_{υ}*γ*). Canopy interception is not explicitly treated, while snowfall and snowmelt are treated very crudely. The governing equation is linearized and integrated analytically one month at a time using AOGCM temperature and precipitation as inputs. We will see that the PELB model developed for each AOGCM does well in simulating the seasonal variation of soil moisture in that AOGCM. Having developed a PELB model for each AOGCM, we can then compare the impact of alternative PELB models with the same climate forcing, or different climate forcings with the same PELB model, on the simulated soil moisture.

## 4. Methods

### a. AOGCM output and parameters

For this study we have used monthly surface air temperature, precipitation, and soil moisture data obtained from control runs by each AOGCM, spanning the years 1900 through 2099. Output from a given AOGCM is labeled here according to its acronym (i.e., CGCM1, HadCM2, or CCSR/NIES), while versions of PELB that have been calibrated to match a particular AOGCM LSS will from here on be hyphenated (i.e., PELB-CGCM1, PELB-HadCM2, or PELB-CCSR), as noted above. So, for example, we will compare the CGCM1 soil moisture output with the output produced by using the CGCM1 precipitation and temperature to drive the PELB-CGCM1, PELB-HadCM2, and PELB-CCSR parameterizations.

Of the seven PELB parameters described above, five are specified according to geographical data according to the AOGCM–LSS model descriptions. With the exception of CCSR/NIES—which uses a uniform soil moisture capacity of 20 cm—the AOGCMs estimate soil moisture capacity based on datasets with higher resolution than the models themselves. Here, the moisture capacity for each of the other AOGCMs is calculated according to its methodology and then averaged, weighted by area, over the AOGCM grid. These are shown in Fig. 3; the contrast here is obvious, as PELB-CGCM1 uses a systematically higher capacity than PELB-CCSR, while PELB-HadCM2 generally uses a lower value than PELB-CCSR and has a lower *w*_{FC} than PELB-CGCM1 everywhere.

As noted above, the evapotranspiration factor *s* used by PELB-CGCM1 varies with the soil and vegetation types within each grid cell. This is shown in Fig. 3. For PELB-HadCM2 and PELB-CCSR the canopy and soil surface resistances (*r _{sc}* and

*r*) and the vegetated fraction

_{ss}*f*vary at each grid point according to Warrilow et al. (1986). The aerodynamic resistance

_{υ}*r*is approximated as described in section 3d and Fig. 1.

_{a}### b. Calibration and initialization

The runoff parameter *γ* is the seventh parameter and is the only one that was determined through a tuning procedure. It was calibrated to each AOGCM by determining a value at each grid point so as to minimize the root-mean-square error between the PELB and AOGCM *w* throughout the simulation, excluding time steps with freezing temperatures. The calibrated values of *γ* are shown in Fig. 4. The runoff parameter is thus being used to approximate structural differences in the AOGCM–LSS approach to runoff. For example, if the AOGCM–LSS is very conducive to soil moisture draining out to the groundwater, the value of *γ* will be high. However, other differences—such as AOGCM surface or aerodynamic resistances markedly different from the values used here—will also be lumped into this tuning process. Moreover, because *γ* has been selected based solely on model agreement and not on physical processes, care should be taken in relating the tuned value of *γ* to properties such as soil type and vegetation. Nevertheless, it is clear that high values of *γ* correspond directly to dry or arid regions in the AOGCMs. While it might be expected that deserts experience a significant amount of runoff during precipitation events, this is more likely due to insufficient evapotranspiration simulated by PELB in these regions. If this were the case, then owing to the dry conditions a large *γ* would be required in the calibration process to compensate for a small evapotranspiration deficiency.

The heat index in Eq. (10) was calculated at each grid point from the first 30 years of each model run and then applied to Eq. (8) throughout the simulation. As Thornthwaite’s method does not compute evapotranspiration at temperatures lower than 0°C, grid cells with *H* = 0 or from latitudes greater than 65° were excluded from the simulation along with cells that are entirely covered in water.

Experiments with PELB have shown that the memory of initial conditions persists less than 10 years at both dry and wet grid points. PELB was therefore spun up by initializing each point to zero and repeating the first year of forcing data 10 times before continuing with the simulation.

## 5. Results

A key difference among LSSs is the plant-available moisture capacity of the soil column (Cornwell and Harvey 2007). The “wetness” of the soil—that is, the ratio of moisture content to moisture capacity—is prominent in any calculation of the evapotranspiration efficiency *β* presented in Eq. (2). However, the differing moisture capacities can make this condition difficult to assess based on only the volumetric water content; the same amount of water that would cause the soil to be very moist in one LSS (with a relatively low capacity) could make it very dry in another. To make a comparison of the soil condition across LSSs (relevant to the propensity for soil moisture to evaporate in those models) we present the results in terms of the soil wetness, where “1” indicates that the soil is at capacity and “0” indicates that there is no plant-available moisture in the soil.

To analyze the effectiveness of PELB, we first look at the mean seasonal values across the grids to see how the soil moisture produced by PELB compares to the AOGCM–LSSs. We then compare the time series for individual points across the model combinations.

### a. Climatological means

Figures 5 –7 compare AOGCM soil moisture storage with PELB simulations driven by the temperature and precipitation of that AOGCM. The figures are averaged over the AOGCM period 2070–99 of the control run for two seasons: June–August (JJA) and December–February (DJF). In all cases, the main geographical features of an AOGCM and its tuned version of PELB are very similar, although PELB does seem to be slightly drier at high latitudes. This is easily seen in Fig. 8a–c, which shows the difference in soil wetness between each AOGCM and its corresponding version of PELB. Some of this dryness is due to excessive evapotranspiration at these latitudes in PELB, while some may stem from problems in PELB’s treatment of snow.

The similarity through time of each version of PELB to its matching AOGCM can be analyzed by looking at the correlation coefficients. These are shown for all grid points in Fig. 9. The coefficient at grid points with significant snow cover is noticeably smaller; the correlation in these regions is likely very poor in winter. Overall, however, the correlation at middle and low latitudes is satisfactory.

To validate our assertion that PELB behavior is close to that of the AGOCM–LSSs, it is important to consider the partitioning between evapotranspiration and runoff (Cornwell and Harvey 2007). Figures 8d–f compare the JJA evapotranspiration of the same period, as simulated by each AOGCM and by the corresponding version of PELB. While the PELB evapotranspiration is too large at the highest latitudes and a little low in the tropics, overall the differences are small.

Table 2 shows the spatially averaged 2070–99 JJA forcing (temperature and precipitation) over continental areas in each AOGCM. The temperatures simulated by CGCM1 and HadCM2 are quite similar, but CGCM1 simulates more precipitation over land, which may also contribute to greater soil wetness in CGCM1.

Table 3 gives a measure of the accuracy of each version of PELB with respect to its corresponding AOGCM. In all three cases, the mean difference in JJA soil moisture fractions is quite small. The difference in means is statistically significant at the 99% confidence level at less then 50% of the grid points.

Figures 5 –7 also illustrate the effects of using the PELB parameters (i.e., *γ* and soil moisture capacity) for one AOGCM and the driving temperature and precipitation output of another. In some areas (e.g., Africa) the driving factors are dominant, while in other areas (e.g., North America) the land surface parameters appear to be more important. PELB-HadCM2 (which corresponds to the driest AOGCM) tends to be drier than the other two formulations, even when soil moisture is expressed as a fraction of capacity (which is also lower for PELB-HadCM2, as shown in Fig. 3).

Table 4 shows the mean soil moisture fractions of the AOGCM and PELB simulations. The first column contains the results produced by the AOGCMs themselves: it can be seen that the HadCM2 AOGCM simulates a markedly smaller mean soil moisture fraction than the other two AOGCMs. The PELB model corresponding to the AOGCM used as forcing gives the best match to the soil moisture simulated by that AOGCM (e.g., PELB-CGCM1 gives the best match to CGCM1 output). Consider next the table cell in the second row of the third column: this is the combination of HadCM2 forcing and PELB-HadCM2, which is fairly close to the AOGCM mean for HadCM2. Moving up or down from this cell represents a change in the forcing data, while moving left or right means keeping the same forcing but changing the LSS. It can be seen that changing to PELB-CGCM1 (moving left) has roughly the same effect as changing the source of forcing data to CGCM1 (moving up). This seems to imply that the difference between the CGCM1 and HadCM2 LSSs is responsible for roughly half of the disagreement between the two AOGCMs in the first column—but possibly even more, because, in absolute terms, the soil moisture capacity used by CGCM1 and PELB-CGCM1 is much larger than that used by HadCM2 and PELB-HadCM2.

The importance of the LSS is even more evident when comparing HadCM2 with CCSR/NIES. The difference moving down from HadCM2 to CCSR/NIES forcing in Table 4 is fairly small; in comparison, the difference moving right from the PELB-HadCM2 to the PELB-CCSR land surface formulation is several times as large.

The difference in land surface parameters can be either more important or less important than the difference in atmospheric forcing, depending on the grid point. Koster et al. (2004) performed a multiple AOGCM experiment with prescribed soil moisture time series so as to identify regions where the land–atmosphere coupling was most intense (i.e., where the influence of the prescribed soil moisture was the strongest). They concluded that this was typically in transition zones between wet and dry climates. In Tables 5 and 6, we repeat our analysis using only grid points from one of the regions identified by Koster et al. in the central United States. In this region, changing the source of the atmospheric forcing has relatively little effect on soil moisture compared to changing versions of PELB. In contrast, Tables 7 and 8 restrict the analysis to sub-Saharan East Africa, where the coupling is not as strong as in the Koster study. Here, changing the source of the atmospheric forcing is more important than changing the LSS parameterization, an importance enhanced by the significant disagreement in precipitation among the three AOGCMs in this region.

### b. Individual points

Figure 10 shows AOGCM precipitation and compares the corresponding AOGCM and PELB evapotranspiration and soil moisture storage for individual grid points over a 10-yr span. One wet (Amazon) point and one dry (southwestern United States) point were chosen as representatives. There are obvious differences between the AOGCMs, due in part to different grid sizes that represent slightly different geographical areas and in part to some combination of differences in the atmospheric forcing of soil moisture and in the LSSs used by the different models.

The evapotranspiration curves in Fig. 10 show two areas of concern. The first is that evapotranspiration simulated by PELB is too low at the U.S. grid point. This reinforces the idea that the calibrated values of *γ* shown in Fig. 4 are likely too high in dry regions. The second is that PELB frequently lags one month behind the AOGCM evapotranspiration, especially at the U.S. grid point. This is due to the slow response of PELB to precipitation inputs and is directly related to the use of a monthly time scale.

It is evident from Fig. 10 that the PELB simulations of soil moisture, while not perfect, do track the AOGCM simulations very closely. Table 9 shows the root-mean-square error between each version of PELB and the AOGCM that supplied the forcing data. The slightly larger error terms for the Amazon grid point reflect the larger variation at that location. Once again, the error between an AOGCM and the corresponding version of PELB demonstrates the closest or almost closest match.

Table 10 shows the standard deviations for the time series of soil moisture depicted in Fig. 10. In general, the PELB variability is close to that of the corresponding AOGCM, and PELB is not systematically more or less variable. Differences between PELB and the corresponding AOGCM are generally small compared to the differences between different AOGCMs. Also, use of different versions of PELB with the same forcing leads to quite marked differences in variability.

Care should be taken in interpreting Tables 9 and 10 since the locations of these points are slightly different for each AOGCM grid. It is therefore difficult to repeat our earlier analysis of Table 4 by looking up or down the columns. Looking across the rows does show that PELB-CGCM1 often has a lower variability (in terms of soil wetness) than the other formulations; this is probably due to the much higher moisture capacity.

Figure 11 displays the time series for the Amazon grid points using all of the PELB parameterizations (see Table 9) for each driving climate. Table 11 compares the PELB parameters at this grid point for the three models. PELB-CCSR uses very different values for *s* and *γ* compared to the other versions, leading to less evapotranspiration and more runoff, and the effect is particularly dramatic in Fig. 19a.

Figure 12 shows the seasonal cycle of a grid point in central Russia, near Kazakhstan, representing an area with a significant snowy season. While PELB appears to be too dry during the winter months—no doubt due to the extremely simple treatment of snow and ice—it is quite accurate from May through October.

## 6. Discussion

The Thornthwaite evapotranspiration approach has been widely used in operational moisture and drought forecasting and has also been used in predicting changes in soil moisture as the climate changes (Cornwell and Harvey 2007). In the latter case, monthly temperature and precipitation outputs from AOGCMs have been used as driving variables. It is thus highly relevant to examine the effectiveness of the Thornthwaite *E _{p}* method in replicating AOGCM soil moisture simulations. We have done this here with appropriate modifications of the

*β*parameter where required to fit the structure of the soil moisture scheme in specific AOGCMs. Our scheme does not include a vegetation canopy, so the interception of precipitation by the canopy is considered only to the extent that canopy wetness is correlated with soil wetness, as assumed in solving Eq. (15). Also, the treatment of snow used here is extremely crude and does not include sublimation losses during freezing months or the effects of frozen water in the soil on infiltration.

Nevertheless, the PELB LSS has successfully demonstrated the ability to reproduce the overall character of multiple AOGCM–LSSs. Dry and wet grid points are both matched quite well, although high-latitude locations are less satisfactory.

Parameter settings for one AOGCM can be driven by the climate of another, providing insight into the effects of AOGCM–LSS choices. There is still a deficiency here because in a coupled system the LSS provides feedbacks in the form of evapotranspiration and sensible heat, which influence future temperature and precipitation in the AOGCM. This is not important when the PELB model matches the AOGCM soil moisture, inasmuch as the AOGCM soil moisture includes feedbacks. However, when the two do not match, the difference in soil moisture would be modified by feedbacks that are new differences because the soil moisture is different (see Cornwell and Harvey 2007). It is not certain whether these feedbacks are negative or positive (Qu et al. 1998), but the approach taken here will at least demonstrate some tendencies.

Overall, changing the LSS appears to account for roughly half of the difference between AOGCM simulations. The influence of the LSS is more important in some regions (such as the United States) and less important in others (such as East Africa). The next step in this research is to investigate the effectiveness of PELB in replicating AOGCM soil moisture under changing climatic conditions. We expect that this will serve to strengthen our understanding of the effects of climatic change on soil moisture.

## Acknowledgments

Acknowledgments are due to the AOGCM modeling groups and the IPCC Data Distribution Centre for making their efforts available to the public, and particularly to Toru Nozawa and David Viner for their help with CCSR/NIES and HadCM2 data, respectively. The careful and insightful attention of two anonymous reviewers has also been much appreciated. This research was supported by NSERC (Canada) Grant 1413-02.

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## Footnotes

*Corresponding author address:* A. Cornwell, Dept. of Geography, University of Toronto, 100 St. George Street, Toronto, ON M5S 3G3, Canada. Email: cornwella@geog.utoronto.ca