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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. D3, PAGES 2717-2728, FEBRUARY 28, 1992

A Land-Surface Hydrology Parameterization With Subgrid Variability for General Circulation Models

ERIC F. WOOD

Department of Civil Engineering, Princeton University, Princeton, New Jersey

DENNIS P. LETTENMAIER

Department of Civil Engineering, University of Washington, Seattle, Washington

VALERIE G. ZARTARIAN

Camp Dresser & McKee, Cambridge, Massachusetts

Most of the existing generation of general circulation models (GCMs) use so-called bucket algorithms to represent land-surface hydrology. Biosphere-atmosphere models that include the transfer of energy, mass, and momentum between the atmosphere and the land surface are a recent alternative to this highly simplified representation of the land surface in GCMs. These models require estimation of a large number of parameters for which parameter estimation methods and supporting data remain to be developed. We describe a more incremental approach to generalizing the bucket representation of land-surface hydrology based on a model that represents the variation in infiltration capacity within a GCM grid cell. The variable infiltration capacity (VIC) model requires estimation of three parameters: an infiltration parameter, an evaporation parameter, and a base flow recession coefficient. The VIC model was explored through direct comparisons with the Geophysical Fluid Dynamics Laboratory (GFDL) bucket model for the French Broad River, North Carolina, and via sensitivity analysis for the GFDL R30 grid cell which contains the French Broad River. Generally, the bucket model runoff had much greater variability than the historic streamflows for short time scales (e.g., 1 day); the VIC model was much more similar to the observed flows in this respect. The results also showed that the bucket model tended to have unrealistically high short-term variability. The sensitivity analysis showed that the base flow parameter exerted the greatest influence on both the mean and variability of most of the hydrologic variables, especially winter runoff, summer evaporation, and summer and winter soil moisture.

INTRODUCTION

The redistribution of solar energy over the globe is central to studies of climate and climate change. Water plays a fundamental role in this redistribution through the energy associated with evapotranspiration, the transport of atmospheric water vapor, and precipitation. Residence times for atmospheric water are of the order of a week, and for soil moisture from a week to months, as opposed to years to thousands of years for large inland water bodies (e.g., the Great Lakes) and the oceans. The rapid cycling of water in the atmosphere/land-surface, and the control on this cycling exerted by soil moisture, emphasize the importance of the hydrologic cycle to global energy fluxes.

Understanding the importance of the land-surface hydrology to climate has emerged as an important research area since the mid-1960s, when researchers at Geophysical Fluid Dynamics Laboratory (GFDL) incorporated a land hydrology component into their general circulation model (GCM) [see Manabe et al., 1965; Manabe, 1969]. During the past 20 years, a steady progression of research has shown the importance of the land hydrology on Earth's climate: the sensitivity of albedo to climate [Charney et al., 1977] and the influence of soil moisture anomalies [e.g., Walker and Rown-

Copyright 1992 by the American Geophysical Union.

Paper number 91JD01786. 0148-0227/92/91JD-01786505.00

tree, 1977; Shukla and Mintz, 1982; Rind, 1982; Rowntree and Bolton, 1983].

Among climate modelers, the term "parameterization" refers to functional relationships that describe the processes being modeled. The most prevalent parameterization for land hydrology is Budyko's "bucket" model used by Man- abe et al. [1965]. It is widely recognized that this parameterization highly simplifies the hydrologic processes of infiltration and evaporation; it does not explicitly consider vegetation, and it assumes that parameter values, like soil moisture capacity, are constant over the globe. Nonetheless, the development of more realistic parameterizations is diffi- cult, in part because of questions having to do with the relevant land-surface dynamics at the GCM grid scale (tens to hundreds of thousands of square kilometers) and in part due to problems of estimating parameters globally. For instance, while it is known that the 15-cm soil moisture capacity that is used by most of the current generation of GCMs must in fact be a spatially varying quantity, incorpo- ration of a more realistic representation will require proce- dures and data bases to estimate parameters of any alternative formulation for all the land surfaces of the globe. This daunting task has to date discouraged implementation of more realistic land-surface process representations in GCMs.

An awareness of the shortcomings of the bucket hydrology of the current generation of GCMs has led to several

2717

2718 WOOD ET AL.: LAND-SURFACE HYDROLOGY PARAMETERIZATION

recent studies of alternative land-surface parameterizations. These studies have sought to relax two of the major simpli- fications of Budyko's bucket: (1) soil moisture availability is based on field capacity and water budget accounting only, and (2) evaporation modeling does not explicitly incorporate physiological resistance from vegetation. Results of modeling studies from the late 1970s and early 1980s [e.g., Shukla and Mintz, 1982] showed that precipitation and temperature are sensitive to soil moisture anomalies. The inclusion of

vegetation in the land-surface hydrology representation of climate models has been motivated by questions about biosphere-climate interactions, such as the effects of ongoing deforestation in the tropics, and climate feedbacks due to long-term vegetation changes that might accompany climate change.

Land-surface models in which the biosphere-atmosphere interactions are fully developed for calculating the transfer of energy, mass, and momentum between the atmosphere and the vegetated surface of the Earth have been developed by Dickinson et al. [1986] (called BATS, for biosphere- atmosphere transfer scheme), Sellers et al. [1986] (called SiB, for simple biosphere model), and Abramopoulos et al. [1988].

As described by Sellers et al. [1986], SiB consists of a two-layer vegetation canopy whose elements and roots are assumed to extend uniformly throughout the GCM grid. From the prescribed physical and physiological properties of the vegetation and soil, the model calculates (1) the reflec- tion, transmission, absorption, emission of direct and diffuse radiation in the visible, near-infrared, and thermal wave- length intervals, (2) the interception of rainfall and its evaporation from the leaf surfaces, (3) the infiltration, drainage, and storage of the residual rainfall in the soil, (4) the control of the photosynthetically active radiation and the soil moisture potential, inter alia, over the stomatal functioning and thereby over the return transfer of the soil moisture to the atmosphere through the root-stem-leaf system of the vegetation, and (5) the aerodynamic transfer of water vapor, sensible heat, and momentum from the vegetation and soil to a reference level within the atmospheric boundary layer. The model has seven prognostic physical-state variables: two temperatures (a canopy temperature and ground temperature), two interception water storages (one for the canopy and one for the ground cover), and three soil moisture storages, of which two are for the two classes of vegetation and one for the soil recharge lay;,l [Sellers et al., 1986].

The BATS representation of the land surface, while different than SiB, is of comparable complexity. The development of these models was motivated by recent advances in the understanding of small-scale plant physiology, microme- teorology, and hydrologic interactions that control biosphere-atmosphere interactions. For this reason, BATS and SiB, in particular, have a high level of vertical resolution and structure. In contrast, BATS and SiB assume horizontal homogeneity, and for this reason have often been referred to as "big leaf" models. The model by Abramopoulos et al. considers spatial subgrid variability through an area- weighted compositing scheme for the soil and vegetation parameters.

Both BATS and SiB have been incorporated into GCM simulations. Because of the complexity of the SiB and BATS land-surface representations, there have been two major limitations to these studies. First, attempts to calibrate such

detailed biosphere models have relied on small-scale mi- crometeorological studies [Sellers et al., 1989], and there are unresolved questions as to whether the use of point or small-scale parameters are valid at the GCM grid scale. Second, to date, GCM simulations using the biosphere models have been limited to short time horizons (of the order of one to several months), over which the initial land-surface conditions (e.g., soil moisture) may mask the performance of the land-surface representation.

Some attempts have been made to develop simpler land- surface models that still incorporate important features of the governing hydrological processes. One line of investiga- tion has explored land-surface representations that account for subgrid variability associated with terrain, soil, and vegetation inhomogeneities. Such investigations have been motivated by work such as that of Avissar and Pielke [1989], who showed, using a regional mesoscale model, that spatial heterogeneity in vegetation can have significant effects on temperature and precipitation. Entekhabi and Eagleson [ 1989], for instance, prescribed the subgrid spatial variability of soil moisture and storm precipitation statistically and then, given the assumed subgrid soil and precipitation vail- ability, derived expressions for the hydrologic fluxes. Their analysis facilitates exploration of major model sensitivities to soil characteristics and climatic forcing. It is, however, limited to the specific statistical distributions assumed for the subgrid variability of soil moisture and precipitation. Avissar [1990] suggests a land-surface model based on land- scape patchiness heterogeneity. The effects from such het- erogeneities can be significant, as shown by A vissar and Pielke [1989]. Famiglietti and Wood [ 1990] have developed a land-surface hydrology model in which the runoff response (hence, soil moisture) is controlled by variations in topography and soil properties, as characterized by the topography- soil index suggested by Beven and Kirkby [1979].

The issue of the appropriate level of complexity needed in the land-surface parameterization to represent spatial heter- ogeneities is still unresolved. This issue is critical, since the computational feasibility of any new scheme will be weighed against the simpler schemes at higher spatial resolution (for example, R60 spectral resolution). Recent comparisons between the GFDL R15 and R30 model runs showed that the

higher resolution improved the climate simulations even though the bucket model remained (S. Manabe, personal communication, 1990).

In this paper, we present a water balance model for the land-surface parameterization that represents spatial variations in the infiltration capacity within a GCM grid cell. This model is presented in the next section, and comparisons with the GFDL bucket parameterization are made for two basins. In addition to these basin studies, a comparison was made for the GCM grid cell (with an R30 resolution) which contains the basin in the mid-Appalachian region of the United States. In this comparison, the two parameterizations were driven by the precipitation and potential evapotranspiration obtained from the GFDL R30 model with the bucket land parameterization. Sensitivities of the variable infiltration capacity water balance model to parameters controlling the infiltration dynamics, base flow simulation, and the evapotranspiration/potential evapotranspiration (ET-PET) relationship are explored as well.

WOOD ET AL.' LAND-SURFACE HYDROLOGY PARAMETERIZATION 2719

VARIABLE INFILTRATION CAPACITY

WATER BALANCE MODEL

As an alternative to Budyko's bucket, we used a variable infiltration capacity (VIC) water balance model that has sometimes been referred to as the Nanjing model, after investigators at the Water Resources Institute, Nanjing, People' s Republic of China, who apparently first suggested it for catchment rainfall-runoff modeling. The original model was extended to include an evapotranspiration term, and this model has been used for long-term water supply forecasting [Institute of Hydrology, 1985; Chenlai, 1990] and as a preprocessor for flood forecasting algorithms [Pandolfi et al., 1983].

The model assumes that infiltration capacities, and therefore runoff generation and evapotranspiration, vary within an area due to variations in topography, soil, and vegetation. First, define the variation in infiltration capacity i over an area (grid cell or catchment) as

i = i m[1 - (1 - A) I/B] (1)

where A represents the fraction of a grid cell (or catchment) for which the infiltration capacity is less than i (thus 0 -< A -< 1), i m is the maximum infiltration capacity within the grid cell or catchment, and B is a shape parameter (see Figure 1). By infiltration capacity, we mean the maximum depth of water that can be stored in the soil column for the incremen-

tal area fraction of dA. Note that, in this formulation, infiltration capacity is a depth (volume per unit area), and thus the parameter B is a function of the time step. In Figure 1, As is that fraction of the grid whose infiltration capacities are filled (i.e., As of the catchment is saturated) when the soil moisture storage is the depth W0. During a precipitation event, the fraction As will generate direct runoff. The infiltration capacity i0 represents the maximum infiltration capacity for the saturated fraction. The initial soil moisture storage W0 is the areally integrated infiltration capacity from zero to i0 (i.e., the area to the right of the infiltration capacity curve from the horizontal intercept at i0 as shown in Figure 1). For a precipitation amount P occurring during the time period and with initial soil moisture storage of W0, the amount of the precipitation that infiltrates is the areally integrated infiltration capacity

io + P A (i) di o

The remainder,

i0 + P P- A(i) di o

is the amount contributing to direct runoff. These are shown as A W0 and Qd, respectively, in Figure 1. Essentially, direct runoff Qd is the amount of P that falls on the saturated fraction As where the infiltration capacities are less than i0 and have been filled. The maximum soil moisture storage over the area (expressed as a depth) is given, after the integration, by

im Wc = (2)

(1 +B)

im

.9 io + P

• i o

.c:_ o

i

0 As 1 Fraction of the gdd/catchment

Fig. 1. Schematic showing the runoff and infiltration relationships as a function of grid wetness and infiltration capacity.

The generated (direct) runoff from the "active" portion of the area is

Qa = P - Wc + Wo io + P -> im (3a)

Qa= P- Wc + Wo

+ Wc 1 (i0+P)] -• 1 + B io + P -< im (3b) im

In the infiltration-runoff equations, the ratio Wo/Wc represents initial catchment wetness, to which the ratio of actual to potential evaporation can be related. We have used a function similar to (1) to represent this relationship:

e [W•OcO]l/Be - 1- 1- (4) ep

Ripple et al. [1972] observed evaporation values similar to those predicted by (4) with B e - 0.6.

The moisture storage-runoff relationship can be considered analogous to a nonlinear reservoir. Based on observed behavior of large catchments during dry periods, a reasonable approximation is that soil moisture storage contributes to base flow as a linear reservoir:

Q= kbWo O-< kb-< 1 (5)

The water balance equations are implemented as follows. First, let the soil moisture at the end of the previous time step be represented by W•-. The base flow and evapotranspiration are computed based on this end-of-previous-period soil moisture, which is then updated according to

W0 + = W0- - Q•-e (6)

where e is computed from (4) and e p, the potential evapotranspiration rate, is a driving variable to the model and is computed elsewhere in the GCM. The total runoff during the time step is Q = Q• + Q•. The variable W• is used for W0 in (1)-(3) and W•- is used for W0 in (4)-(5).

The four model parameters are the soil moisture storage Wc, the parameter of the infiltration equation B, the parameter of the evapotranspiration equation B e, and the base flow parameter k•. The model represented by (1)-(6) can be interpreted within the statistical framework provided by the concept of a distribution of storage elements of various

2720 WOOD ET AL.' LAND-SURFACE HYDROLOGY PARAMETERIZATION

TABLE 1. Estimated Parameters for the Variable Infiltration

Model Applied to the French Broad River at Blantyre, North Carolina

Definition Parameter Case 1 Case 2

Moisture storage capacity, cm Wc 32.0 15 Infiltration capacity B 0.085 0.129 Evaporation rate B e 0.261 0.069 Base flow, day -• k o 0.032 0.095

Case 1, all parameters optimized' case 2, moisture storage capacity fixed at 15.0 cm.

capacities [Moore and Clarke, 1981]. Such an interpretation is useful when one considers the subgrid spatial variability at the GCM grid scale, and for this reason we refer to the model as a variable infiltration capacity water balance model.

BASIN STUDIES

The VIC water balance model was applied to the French Broad River at Blantyre (USGS gage 03-4430), a 767 km 2 catchment in western North Carolina, along with the GFDL bucket model. The period of record was from water year 1953-1964 and included daily stream discharge. Daily pan evaporation, and 6-hourly precipitation and temperature data, were available from a nearby meteorological station.

Two sets of parameters were used for the variable infiltration capacity model: one set used the 150-mm infiltration capacity that has been used in the GFDL model, with the remaining three parameters estimated by minimizing the sum of squared differences between the simulated and observed streamflow. The second parameter set estimated all four parameters using the same objective function. For the bucket model, the standard GFDL parameters [Delworth and Manabe, 1988] were used. The models were driven using observed daily precipitation and potential evapotranspiration. Output was generated at the daily time step and was also aggregated to 30-day periods.

For the fitting and validation of the VIC model, the data record was divided into two periods. The period used to estimate the model parameters was from October 1, 1957, to

November 8, 1962. The verification period was October 14, 1953, through July 9, 1957. For both the parameter estimation and validation periods, the first year of this record was used to initialize the soil moisture storage, and the remaining period was used in the performance function evaluation of the estimated parameters. Table 1 gives the estimated parameter values for the two estimation conditions: the first

with all four VIC model parameters estimated and the second with the soil moisture capacity Wc fixed at 150 mm. The VIC model, the bucket model, and the observed runoff are compared in the remainder of this section for the last 1000 days of the validation period.

Table 2 summarizes the model comparisons for the French Broad River. The most important observation is that, at the daily time scale, the standard deviation of the GFDL bucket model-simulated streamflow is 3.86 times the observed stan-

dard deviation. At the 30-day aggregation level, this extreme variability is reduced to 1.57 times the observed streamflow standard deviation. By comparison, the streamflows simulated using the VIC water balance model have a standard deviation of 1.55 times the observed value when the soil

moisture capacity is fixed at 15 cm, and 0.82 times the observed value when the soil moisture capacity is estimated. Reproduction of the variability of streamflow at the daily time step is an important consideration, since this is directly linked to soil wetness at the time scale comparable to the computational time step of the GCM. Figure 2 shows observed, simulated (VIC water balance model, all parameters estimated), and runoff simulated with the bucket model for the validation period October 14, 1954, to July 9, 1957. These plots clearly show the extreme variability of the bucket model runoff, which has characteristics more similar to daily precipitation than daily runoff. The runoff simulated using the VIC model compares well, at least qualitatively, with the observed runoff. There is a tendency for the VIC model to underestimate extreme flows somewhat. This underestima-

tion is nowhere near as great as the overestimation of extreme flows by the GFDL bucket model.

From Table 2, two other aspects of the relative performance of the models are apparent. First, the estimated parameters derived from the estimation period, when ap-

TABLE 2. Aggregation Statistics for the Models Using the French Broad River at Blantyre, North Carolina

Estimation Period Validation Period

Daily 30-Day Daily 30-Day

Observed streamflow 0.34 0.24 0.34 0.16 0.24 0.22 0.24 0.14 Statistical water balance model*

Simulated 0.34 0.39 0.34 0.22 0.26 0.34 0.26 0.20 Residual 0.006 0.25 0.006 0.14 -0.02 0.23 -0.02 0.14

Statistical water balance model? Simulated 0.34 0.20 0.34 0.17 0.26 0.18 0.26 0.15 Residual 0.00 0.15 0.00 0.09 -0.02 0.15 -0.02 0.09

GFDL bucket models Simulated .... 0.18 0.85 0.18 0.22 Residual .... 0.059 0.81 0.059 0.15

Here, /x is mean of the time series, in centimeters; cr is standard deviation of the time series, in centimeters. The estimation period is October 1, 1958 to November 8, 1962; the validation period is October 14, 1954 to July 9, 1959.

*Using 15 cm for the total basin/grid infiltration capacity. ?Fitting all model parameters. $Using standard GFDL parameters (including 15 cm bucket).


12-

10-

0-

ß 1) OBSERVED RUNOFF

I i • I t • I • ' I r f I ' • I

Jan July Jan July Jan July Months

12-

10-

2-

0

b) VIC MODEL

i • I I I , I I , I ' I i v i I

Jan July Jan July Jan July Months

12-

10-

o c

n- 6-

co 4- o

2-

O-

c) GFDL BUCKET

Jan I ' : I ' ' I • • I ' I I

July Jan July Jan July Months

Fig. 2. Comparison of observed streamflow with streamflow simulated by VIC model and GFDL bucket model for French Broad River at Blantyre, North Carolina, for period October 14, 1954 to July 9, 1957.

absence of between-storm flow in the bucket model contrib-

utes to the upward bias in the variability, which cannot be resolved by changing the bucket size.

GCM GRID CELL ANALYSIS

Five years of daily results from the GFDL R30 GCM for the continental United States were analyzed. The variables analyzed were precipitation, potential evapotranspiration, temperature, and runoff for the grid overlying the French Broad River. Initially, the GFDL precipitation and potential evapotranspiration for the GFDL R30 grid cell (centered at 37ø7.5'N, 82ø30'W) overlying the French Broad River basin were used to drive the VIC water balance model. The model

parameters were those estimated for the French Broad River during the basin study described in the previous section. As in the basin study, the first year was used to initialize soil moisture. The results shown here are based on the last 4

years of the simulation period. Figure 3 shows the corre- sponding 4-year time series of precipitation produced by the R30 GCM. Figure 4 compares the GFDL runoff to the VIC water balance model runoff. It is interesting to make this comparison along with Figure 2, since the VIC model runoff was found to be consistent with the observations for the

French Broad River, and the GFDL runoff characteristics were similar to those of the French Broad River simulated

using the GFDL bucket model with observed rainfall. One implication of these results is that the R30 GCM produces, for this grid, precipitation whose statistical characteristics are quite similar to those of the observed precipitation. This observation is being investigated in detail, and will be the subject of a future paper.

Figure 5 compares the evaporation inferred by the VIC water balance model to that from the R30 GCM; Figure 6 does the same for soil moisture. Two major comments are in order. First, the differences in evaporation are less between the models than for runoff, implying that the "natural" controls on evaporation may constrain the modeled values to be reasonable even for fairly simplistic evaporation func- tions. This is of particular importance, since, as shown in the following section, the PET values simulated by the GFDL GCM are clearly unreasonably high in the summer months; the same PET was used to drive both the GFDL and VIC

water balance models. The second major comment is that the soil wetness time series for the proposed model is far more dynamic than for the GFDL GCM model. For the

plied to the validation period, gave consistent performance statistics. This shows that the parameters are stable. Sec- ond, concerning the performance of the models compared to the observed data, the bucket model has a large downward bias in the estimated mean runoff. The bias is not apparent in the VIC model for the two estimation cases considered.

Even with the soil moisture capacity fixed at 15 cm, the VIC model seems to capture the daily runoff dynamics more realistically than the bucket model (see Figure 2).

The structure of the model has less influence on the

long-term (30-day) variability of streamflow, which is deter- mined more by the variability of the rainfall. The bias in the short-term runoff variability could be reduced somewhat by estimating, rather than fixing, the soil moisture capacity in the bucket model. However, as shown by Figure 2, the

10-

8-

o

0- ' I ' ' I ' ' I ' ' I ' ' ' ' I ' ' I ' ' I ' '

July Jan July Jan July Jan July Jan Months

Fig. 3. Precipitation time series from a 5-year GFDL R30 GCM simulation.


10-

8-

-' 4-

2-

O-

a) GFDL BUCKET

' I ' ' I ] ' I ' ] I ' ' I ' ' I [ ' I ' [ ] ' '


10-

8-

-, 4-

2-

O-

b) VIC MODEL

''"' i , ! i ! , i [ , i , • I , , i ! • i , , i ! ,


Fig. 4. Comparison of GFDL R30 runoff for southeastern U.S. grid cell from 5-year GCM simulation with runoff simulated by VIC model using GFDL PET and precipitation.

al., 1983]. Based on the river basin and grid cell comparisons described above, we made one change in the bucket models: we added a base flow component using the same formulation (5) and the same recession constant used in the VIC water balance model. In the GISS bucket, base flow was taken from the lower zone only.

From the 100-year simulations, we computed (1) the means of the daily values of the three hydrologic variables for each month, (2) the coetficient of variation of the daily values, and (3) the coetficient of variation of the 30-day means of each variable. The same statistics were computed for the input variables PET and precipitation. The initial, or base, values of the parameters were similar to those used for the French Broad River simulations, specifically, B = 1.3, B e = 0.5, k b = 0.01. For all models, the soil moisture capacity was fixed at the GFDL value of 15 cm. In the case of the GISS model, we maintained the same ratio of upper to lower zone soil moisture capacity used by Hansen et al. [1983], with the sum of the upper and lower zone storage scaled from the Hansen et al. value of 14.4--15 cm.

Figure 7 shows the simulation results for the daily means. The fight lower plot in Figure 7 shows the input rainfall and PET means. The extremely high values of PET (around 6 cm/d in June and July) are unreasonable by comparison with any observational data (e.g., pan evaporation) in the southeastern United States; maximum values less than 1 cm/d are more typical. The reason for the extremely high PET values is that in the GFDL model, PET is computed as the evaporation that would occur from a free surface at the calculated surface skin temperature. The computation of the

GFDL model, the soil wetness seems to have a very strong seasonal character in which it is either full (15 cm) or empty. The proposed model has more dynamic soil moisture values and a lower equilibrium soil wetness content. This should provide some motivation to revisit the analysis of Delworth and Manabe [1988], who evaluated the spectral characteristics of the GFDL soil wetness using the bucket formulation.

LONG-TERM COMPARISONS OF

LAND-SURFACE MODELS

Although the S-year simulations provided some insight into the relative performance of the GFDL and VIC water balance models, $ years is too short to provide good infor- mation about the long-term statistical behavior of the land surface by the two models. Ideally, this problem would be resolved by using much longer GCM simulations (of the order of 100 years). For this study, however, we were limited to the $ years of GCM results, so we extended the results using a resampling approach as follows. Given the 5-year record of GCM PET, precipitation, and surface air temperature, we synthesized a 100-year record by reselect- ing months at random from the S-year sequence. Because the principal driving variable (precipitation) has relatively low autocorrelation at the monthly time scale, this resampling should have minimal effect on the statistical characteristics

of the precipitation inputs. Using the 100-year synthesized sequences of precipitation, PET, and temperature, we then simulated runoff, evaporation, and soil moisture using the VIC water balance model, the GFDL bucket, and the two-layer bucket model used in the GISS GCM [Hansen et

10-

8-

0-

a) GFDL BUCKET

ß , i , , i ! , i , , i , , i , , i , , i , , i , ,


10-

8-

O-

b) VlC MODEl_

' I ' ' I ' ' I ' ' I ' ' I ' ' I ' ' I ' ' I ' '


Fig. 5. Comparison of GFDL R30 evaporation for southeastern U.S. grid cell from 5-year GCM simulation with evaporation simulated by VIC model using GFDL PET and precipitation.


25-

20-

•15-

•10-

5-

O-

a) GFDL BUCKET

' I ' • I ' • I ' • I ' • I s [ I " • I • • I ' '


25- b) VIC MODEL

20-

E

•15-

o i :•10-

5-

O-- , I [ ' I [ ' I ' ' I [ ' I ' ] I ' ' I ' ' I • '


Fig. 6. Comparison ofGFDL R30 soil moisture for southeastern U.S. grid cell from S-year GCM simulation with soil moisture simulated by VIC model using GFDL PET and precipitation.

surthce skin temperature is part of the GCM's atmospheric energy budget computation and is linked to the Bowen ratio at the land surface. Therefore, if soil moisture is low (as is the case in Figure 7 during the summer), the latent heat fraction, hence surface temperature, can become quite high in the model; PET computed at this temperature may greatly exceed typical observed values. As shown in the Figure 7 plots for soil moisture and evaporation, the extremely high summer PET dominates the land-surface model behavior, and is in fact more important that the differences between models (an obvious exception is the modest evaporation from the GISS model; the reason for this is that evaporation is assumed to occur only from the upper layer, which has a relatively low soil moisture capacity, and therefore severely limits evaporation regardless of the high PET). Recently, revisions have been made to some versions of the GFDL

model so that the PET computation is more physically reasonable; however, the results of model runs made with these revisions were not available for this study.

Because of the controlling effect of the high model PET on the performance of the land-surface models, we adopted an alternative approach. Rather than using the GFDL model PET, we instead computed PET using Hamon's formula [Hamon et al., 1954] at the latitude of the grid cell midpoint, using the GCM surface air temperature. Figures 8a-8c show the simulation results for the daily means, coefficients of variation (designated CV(1) for one day), and 30-day coefficients of variation, or CV(30). These results were derived using the same precipitation used in the Figure 7 results, but with Hamon, rather than GFDL, PET. Figure 8a shows that

z

o LL LL

o z

n' o

X ' VIC

/• GFDL x GISS

+_+-+-+ , * ,"+ , •. '+

x

,

ß VlC +Sx + GFDL /* / x GlSS . X

0 2 4 6 8 10 12 0 2 4 6 8 10 12

MONTH MONTH

z

uJ o .

ß VlC

GFDL

GISS

• •:•.•.•

z

iii +•+

+ ' [:lAINFALL .

.

.

;.+ +.•-+'+ -+.•-;

0 2 4 6 8 10 12 0 2 4 6 8 10 12

MONTH MONTH

Fig. 7. Mean simulated runoff, soil moisture, and evaporation for three land-surface models using GFDL R30 GCM PET and rainfall for southeastern U.S. grid cell. Record length is 100 years, extended from 5-year GCM simulation by resampling.

2724 WOOD ET AL..' LAND-SURFACE HYDROLOGY PARAMETERIZATION

X ß VIC

GFDL

,• GISS

-U.S"

0 2 4 6 8 10 12

+-+ t + + /,+.+ ß * -...-.+.

x-x x ix *x. x+/x.X +/ /

ß v,o ß GFDL

GISS

0 2 4 6 8 10 12

MONTH MONTH

Z

LLI ß vlc :•

GFOL 0•3

x G•SS • O

/•½X • -J x.•.x,x :• '• t'•:•:x, x _z o I '

.

+ PET 0•3 <1: RAINFALL d iii

-*'*'+'+ n•-•: . ß

ß +", I-- - "+¾ ILl

+ø'•' C) Q..

0 2 4 6 8 10 12 0 2 4 6 8 10 12

MONTH MONTH

Fig. 8a. Mean simulated runoff, soil moisture, and evaporation for three land-surface models using GFDL R30 GCM rainfall and Hamon PET for southeastern U.S. grid cell. Record length is 100 years, extended from 5-year GCM simulation by resampling.

this gives much more reasonable values of summer PET, and results in a substantial increase in the mean summer soil moisture.

In Figure 8a, mean runoff for all of the models is quite similar except during the spring, when the GFDL model has much lower values. This occurs during the time when mean soil moisture begins to drop rapidly, and when the G FDL

model rarely produces direct runoff (spill) because the storage is rarely at capacity. Figure 8b, which reports the one-day coefficients of variation, shows that there are substantial differences between the models; perhaps surpris- ingly (given the results for the river basin comparisons), the GFDL model has lower variability than the other two models during the summer and fall months. This may in part be an

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Fig. 8b. Coefficient of variation of daily simulated runoff, soil moisture, and evaporation for three land-surface models using GFDL R30 GCM rainfall and Hamon PET for southeastern U.S. grid cell. Record length is 100 years, extended from 5-year GCM simulation by resampling.


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Fig. 8c. Coefficient of variation of 30-day average simulated runoff, soil moisture, and evaporation for three land-surface models using GFDL R30 GCM rainfall and Hamon PET for southeastern U.S. grid cell. Record length is 100 years, extended from 5-year GCM simulation by resampling.

artifact of the short length of the original GFDL model simulation; the CV(1) values were computed using the first day of each month only (as opposed to using all days in the month). Recall that there were only five different months in the period of analysis; although the resampling procedure extended this to 100 years, the inherent variability of the five original years is retained in the resampled record. The other obvious difference is the inclusion of a base flow parameter, which tends to reduce the variability. The soil moisture results are more revealing, especially during the summer months. Here, the VIC water balance model is clearly more dynamic than the other two, which is consistent with the basin modeling results. Comparison of the CV(1) and CV(30) values (Figures 8b and 8c) shows that the differences in runoff variability between the models is a short time scale phenomenon. At the 30-day scale, the CV(30) values are almost identical and are, in fact, not much different than the CV(30) values for precipitation. On the other hand, evaporation varies much more slowly, and the model differences in the CV(1)'s for soil moisture are much the same as for CV(30). In summary, the VIC water balance model is considerably more dynamic than the two modified bucket models.

We also conducted a sensitivity analyses (using Hamon PET) of the VIC water balance model to the parameters B, Be, and k b. Results for the mean runoff, soil moisture, and evaporation for January and July are shown in Figures 9a-9c. In the sensitivity analyses, B was allowed to vary from 0.01 to 10.0 (base value 0.30), k b from 0.001 to 0.10 (base 0.01), and B e from 0.1 to 1.0 (base 0.5). The sensitivity analysis shows that in general, winter runoff, summer and winter soil moisture, and summer ET are more sensitive to the base flow parameter k b than to either the infiltration or evaporation parameters B and B e, respectively. Summer runoff is most sensitive to the infiltration parameter B. Similar plots for the daily variability (not shown) indicate

that the daily runoff variability is sensitive to both B and kb, but not Be. Summer evaporation is relatively sensitive only to kb. Summer soil moisture variability is sensitive to kb and B e (but not B), but winter soil moisture variability is sensitive only to k•. The 30-day variability of runoff is relatively insensitive to all of the parameters (being controlled primarily by the rainfall statistics), but the 30-day variability of summer evaporation and summer and winter soil moisture are quite sensitive to k•. Summer soil moisture 30-day variability is sensitive to B e, but all other variables are relatively insensitive to Be.

Perhaps the most striking result of the sensitivity analysis is the importance of the base flow parameter kb by comparison with the infiltration and evaporation parameters. This is especially significant because the GFDL bucket contains no base flow term. It is also of interest that the evaporation parameter is relatively unimportant, suggesting that the PE-PET relationship used in the current GFDL model may not be a bad approximation (or at least that a different approximation would not make much difference). By contrast, summer evaporation statistics are affected by both the infiltration parameter B and the base flow constant k b.

All of the results of this section and the previous section must be interpreted in light of the limitations of the zero- dimensional modeling approach used, which does not account for feedbacks between soil moisture, evaporation, and precipitation. The best way to account for these feedbacks is to incorporate the VIC model directly in a GCM. Such an implementation is the subject of ongoing research. However, we believe that much can be learned about the performance of alternative land-surface representations from zero- dimensional experiments such as those performed here. For instance, we think it is highly likely that the importance of the base flow, or drainage, parameter will be confirmed in on-line GCM simulations.


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DISCUSSION AND CONCLUSIONS

This paper presents an alternative land-surface parameterization for GCMs that represents subgrid variability in infiltration capacity, a drainage term for interstorm runoff and a nonlinear evaporation term. The model was tested in simulation of runoff for a river basin, as well as in GCM grid study, and a sensitivity study.

In the basin study, the proposed variable infiltration capacity model and a zero-dimensional version of the GFDL bucket model were compared to observed streamflow. This study showed that the GFDL model produces runoff time series that are too variable at a daily time scale but provide quite reasonable runoff statistics for a 30-day aggregated time series. The implications are quite significant. Since the

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Fig. 9b. Sensitivity of mean daily runoff, soil moisture, and evaporation simulated by VIC water balance model to base flow parameter kt,. Simulation record lengths, inputs, and values of B and B e are the same as for Figures 8a-8c.


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Fig. 9c. Sensitivity of mean daily runoff, soil moisture, and evaporation simulated by VIC water balance model to evaporation parameter B e. Simulation record lengths, inputs, and values of B and kb are the same as for Figures 8a-8c.

GCMs have a computational time step of the order of 15 min, it is important that the water and latent heat fluxes have statistical characteristics at small time steps (of the order of a day), consistent with observations. While seasonal statistics are important for large atmospheric circulations, daily statistics are important for those processes that influence precipitation, runoff, and soil moisture.

The implications of the alternative land-surface parameterization were also evaluated at the GCM grid scale. For this study, precipitation and potential evaporation from a 5-year GCM simulation were used to drive the VIC water balance model. The southeastern GCM grid chosen for this analysis was the grid that contained one of the catchments used for the basin study. The runoff results were similar to those found in the basin study, showing that the results found in the basin study cannot be attributed to differences in the GCM-simulated precipitation. For soil moisture, the GFDL model produced a series that was more extreme, in that the soil moisture was either full (15 cm) or empty, while the soil moisture time series from the VIC model showed

much more dynamic behavior. It also appears that the equilibrium soil moisture for the proposed model is lower than that for the GFDL GCM, at least for the grid cell being studied. Further grid cell comparisons were made using a 100-year record of GCM precipitation and PET resampled from the 5 years of R30 simulation results. In these comparisons, the GFDL bucket model, as well as the GISS bucket model, were modified slightly to include a base flow term similar in form to that used in the VIC water balance model.

The inclusion of the base flow term in the bucket models

resulted in first and second moments that were quite similar to the VIC water balance model. Further sensitivity tests of the VIC water balance model using the 100-year resampled record showed that the first two moments of the hydrologic variables are generally more sensitive to the base flow

parameter than to either the infiltration or the evaporation parameter. In particular, while the base flow parameter strongly affected winter runoff, soil moisture, and summer evaporation, as well as the variability of summer runoff, soil moisture, and summer evaporation, the infiltration parameter strongly affected only summer runoff and summer runoff variability.

Given the differences between the runoff and soil moisture

time series from the GFDL land parameterization and the proposed parameterization, it would appear that the new parameterization could significantly influence the land clima- tology being predicted from GCMs. This issue is being researched by including the proposed model within the GFDL GCM.

Acknowledgments. The research presented herein was sup- ported in part by the U.S. Department of the Interior (USGS) through grant 14-08-0001-Gl138, by Pacific Northwest Laboratory under contract DE-AC06-76RLO 1830 with the U.S. Department of Energy, by the U.S. Environmental Protection Agency under Co- operative Agreement CR 816335-01-0, and by the Electric Power Research Institute under project 2938-03. This support is gratefully acknowledged. The assistance of John Stamm in performing some of the model simulations is also appreciated.

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(Received January 16, 1991; revised June 25, 1991; accepted July 2, 1991.)

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