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  • View in gallery

    Impact of moisture stress on transpiration as the soil dries out from saturation in the off-line soil moisture model. Simulations are shown for surface root fractions of 10% (○), 30% (□), 50% (⋄), 70% (▵), and 90% (▿).

  • View in gallery

    Time evolution of soil moisture saturation fractions in the off-line soil moisture model. Saturation fractions for the surface layer (○: θ1/θ0) and the rest of the root zone (□: θ2/θ0) are shown for simulations with surface root fractions of (a) 10%, (b) 50%, and (c) 90%.

  • View in gallery

    Sensitivity of the seasonal transpiration Etr cycle to extreme values (10% and 90%) of surface root fraction. Shading is used to indicate the differences between the two simulations: light shading indicates higher transpiration with a surface root fraction of 10% and dark shading indicates the reverse sensitivity. Results are shown for (a) TRF S/D, (b) TRF rs(θ), (c) GRA S/D, (d) GRA rs(θ), (e) CAB S/D, (f) CAB rs(θ), (g) HAP S/D, and (h) HAP rs(θ).

  • View in gallery

    As in Fig. 3b but also showing transpiration Etr for surface root fractions of 30% (•), 50% (▪), and 70% (⋄). The thick-dashed line indicates where the bulk depth-weighted method deviates from the 10% case.

  • View in gallery

    Seasonal cycles of soil moisture saturation fraction for the two root-zone soil layers (θ1/θ0 and θ2/θ0) in the TRF S/D experiment. Results for surface root fractions of (a) 10% and (b) 90% are shown. The thick solid lines indicate the surface saturation fractions (θ1/θ0) and the thick-dashed lines represent the saturation fractions in the rest of the root zone (θ2/θ0). The thin horizontal dashed lines show the saturation fraction at the permanent wilting point (θwp).

  • View in gallery

    Fig. A1. Schematic representation of liquid and frozen hydrology in BASE, showing the three soil layers, the foliage mass store, and the snowpack. The light-shaded boxes indicate liquid moisture stores (the upper store being for the foliage). The dark-shaded boxes are for frozen soil moisture. Arrows are used to indicate mass fluxes. The flux labels are explained in the text. The unlabeled fluxes are for melting and freezing of soil moisture.

  • View in gallery

    Fig. A2. Schematic showing the physical arrangement of evaporation fluxes in BASE. Arrows are used to indicates evaporation fluxes. The flux labels are explained in the text.

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The Impact of Root Weighting on the Response of Transpiration to Moisture Stress in Land Surface Schemes

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  • 1 School of Earth Sciences, Macquarie University, Sydney, Australia
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Abstract

Land surface schemes (LSSs) for large-scale climate models use a variety of different methods to represent the influence of soil moisture on transpiration. One area in which they differ is in the treatment of vertical soil moisture distribution. While some schemes use root weighting to integrate moisture stress throughout the root zone, others use only the bulk root-zone soil moisture. The sensitivity of transpiration to surface root fraction is examined in a simple off-line soil moisture model and a complex Deardorff-type LSS. The seasonal cycle of transpiration is found to be quite sensitive to surface root fraction, with transpiration becoming progressively more susceptible to moisture stress as the surface root fraction is increased. Varying the surface (10 cm) root fraction between 10% and 90% produces local transpiration difference of up to 80 W m−2 and relative annual transpiration differences of up to 28%. The sensitivity of root-weighted methods to surface root fraction is found to be partly dependent on other aspects of the parameterization. Thus, differences between the treatment of vertical root distribution in LSSs have a considerable impact on simulated transpiration. These results have implications for LSSs and for the large-scale climate models in which they are employed.

Corresponding author address: Carl E. Desborough, School of Earth Sciences, Macquarie University, North Ryde, 2109, Australia.

Email: cdesboro@penman.es.mq.edu.au

Abstract

Land surface schemes (LSSs) for large-scale climate models use a variety of different methods to represent the influence of soil moisture on transpiration. One area in which they differ is in the treatment of vertical soil moisture distribution. While some schemes use root weighting to integrate moisture stress throughout the root zone, others use only the bulk root-zone soil moisture. The sensitivity of transpiration to surface root fraction is examined in a simple off-line soil moisture model and a complex Deardorff-type LSS. The seasonal cycle of transpiration is found to be quite sensitive to surface root fraction, with transpiration becoming progressively more susceptible to moisture stress as the surface root fraction is increased. Varying the surface (10 cm) root fraction between 10% and 90% produces local transpiration difference of up to 80 W m−2 and relative annual transpiration differences of up to 28%. The sensitivity of root-weighted methods to surface root fraction is found to be partly dependent on other aspects of the parameterization. Thus, differences between the treatment of vertical root distribution in LSSs have a considerable impact on simulated transpiration. These results have implications for LSSs and for the large-scale climate models in which they are employed.

Corresponding author address: Carl E. Desborough, School of Earth Sciences, Macquarie University, North Ryde, 2109, Australia.

Email: cdesboro@penman.es.mq.edu.au

1. Introduction

Early general circulation models (GCMs) used simple parameterizations of the land surface to provide their lower boundary conditions. The first model of land surface hydrology to be included in a GCM was Budyko’s (1956) bucket model, which Manabe (1969) implemented in the Geophysical Fluid Dynamics Laboratory GCM. The work of Deardorff (1978) led to the creation of more complex land surface schemes (LSSs) such as the Biosphere–Atmosphere Transfer Scheme (BATS: Dickinson et al. 1986; Dickinson et al. 1993) and the Simple Biosphere (SiB: Sellers et al. 1986). Since then there has been a large number of land surface schemes of varying degrees of complexity (e.g., Noilhan and Planton 1989; Pitman et al. 1991; Xue et al. 1991; Ducoudre et al. 1993) designed for large-scale climate models.

Recent off-line intercomparisons of LSSs conducted as part of PILPS (Project for Intercomparison of Land Surface Schemes) have identified considerable variability among model simulations of evaporation. During the RICE (Regional Interactions of Climate and Ecosystems) and PILPS soil moisture workshop (Shao et al. 1995), 14 land surface schemes were run with prescribed atmospheric forcing from the HAPEX-MOBILHY grassland site (Goutorbe and Tarrieu 1991). With an annual precipitation of 856 mm, the annual evaporation simulated by the models ranged between 550 and 820 mm. Other PILPS intercomparisons using observed (Chen et al. 1997) and GCM-generated (Pitman et al. 1993) atmospheric forcing have found similarly large differences in simulated evaporation between schemes. Analyzing the results from the RICE and PILPS soil moisture workshop, Mahfouf et al. (1996) identified the parameterization of soil moisture supply for transpiration as a crucial source of the variability among model simulations. A wide range of methods have been used in LSSs to parameterize this process and these methods are reviewed in section 2. About half of the reviewed schemes use vertical root distribution to weight moisture stress for transpiration, with the remaining schemes using only the bulk root-zone soil moisture. In this paper, it is shown that the transpiration rate simulated by root-weighted methods can be very sensitive to surface root fraction. Obviously, this sensitivity will not be exhibited by methods in which moisture stress depends only upon the bulk root-zone soil moisture. Thus, an area of disagreement among LSSs is shown to have a considerable impact on simulated transpiration.

Milly and Dunne (1994) examined the sensitivity of a GCM’s simulated global climate to the availability of moisture for evaporation. This sensitivity was examined by varying the globally constant soil-moisture-holding capacity in the GCM’s “bucket” hydrology model (Manabe 1969). They found that global evaporation increased by about 70 mm yr−1 for each doubling of the storage capacity in the range from 10 to 600 mm. There were corresponding decreases in runoff and temperature. The evaporation changes also affected atmospheric hydrology (precipitation and water vapor transport), and, in turn, these changes affected the atmospheric circulation. In this paper, it is shown that the parameterization of vertical root distribution can also have a significant effect on simulated transpiration.

Two sets of experiments are carried out to illustrate the sensitivity of transpiration to root weighting and surface root fraction. In section 3, an off-line soil moisture model with prescribed stress-free transpiration is used to test the sensitivity of a simple moisture availability function to root weighting. In section 4, a full land surface scheme (BASE: best approximation of surface exchanges) with atmospheric forcing from PILPS is used to test this response under more realistic conditions. The results and their implications are discussed in section 5. A brief description of BASE’s hydrology parameterization is included in the appendix.

2. Modeling transpiration in land surface schemes for large-scale climate models

Transpiration Etr is the loss of water from plants in the form of vapor and about 95% of all water absorbed by plants is lost in this way (Kramer 1983). It occurs mainly through the stomata on a plant’s leaves and, by varying the size of its stomatal apertures, the plant is able to reduce the rate of moisture loss when dehydration threatens. A gradient of decreasing moisture potential from the soil–root interface to the leaf–air interface is required to sustain Etr. This pathway is often conceptualized in terms of an electrical analog where water (current) is driven across a series of resistances by moisture potential gradients (Gradmann 1928; van den Honert 1948).

A variety of different methods have been used in the LSSs of large-scale climate models to parameterize the effect of moisture availability on Etr. Manabe (1969) modeled soil moisture with a single slow response bucket and total evaporation (including Etr) from the surface (E) as
i1520-0493-125-8-1920-e1
where ρ is the density of air, q*s is the saturated specific humidity of the surface, qa is the specific humidity of the air, ra is the aerodynamic resistance, and β parameterizes the effect of soil moisture on evaporation,
i1520-0493-125-8-1920-e2
where θs is the volumetric soil moisture content of the surface bucket, and θfc and θwp are, respectively, the values of θs at field capacity and permanent wilting point.
Plants exert some control over Etr by varying the size of the stomatal apertures on their leaves, and this stomatal resistance is nonzero even when the soil is wet. Manabe’s (1969) bucket model did not include an explicit treatment of stomatal control and evaporation proceeded at the potential rate from wet soil. Some four years earlier, Monteith (1965) had proposed the use of a bulk stomatal resistance rs to describe the net influence of a canopy’s stomata on Etr:
i1520-0493-125-8-1920-e3
Equation (3) is often used to simulate the total evaporation E from a vegetated surface, in which case rs is referred to as the “surface resistance.” This extension is only valid when Etr dominates the other components of E (see Shuttleworth and Wallace 1985). A number of different methods (Stewart 1983) have been used to parameterize the dependence of rs on environmental factors such as radiation intensity, vapor pressure deficit, temperature, carbon dioxide concentration, and moisture availability. The multiplicative approach of Jarvis (1976) is often used.
Drawing upon the work of Monteith and others, Deardorff (1978) proposed a more detailed treatment of the land surface, incorporating an explicit canopy layer. Instead of treating evaporation as a single flux from the surface to the atmosphere (Manabe 1969), Deardorff modeled it as the sum of three component fluxes,
EEtrEgEdw
where Eg and Edw are, respectively, soil evaporation and evaporation of intercepted water from the foliage dewstore. He divided the soil column into two layers, separating a thin (10 cm) rapid-response surface layer from the bulk of the root zone. While Etr could occur from anywhere in the root zone, Eg was restricted to the surface layer. An additional moisture reservoir was used to store water intercepted by the foliage. Deardorff followed Monteith’s example and added a bulk stomatal resistance rs to the aerodynamic evaporation equation [(Eq. 1)] to model Etr from the dry vegetated portion of the surface as
i1520-0493-125-8-1920-e5
where q*f is the saturated specific humidity at the leaf surface, qc is the specific humidity of the air in the canopy air space (CAS), and ra,f is the aerodynamic resistance between the foliage and the CAS.

A large number of LSSs have been developed from the framework proposed by Deardorff, and a variety of different methods have been used to parameterize the dependence of Etr on soil moisture [Table 1: the reference(s) used for each LSS are also listed in this table]. Following Deardorff’s example, most of the schemes (CAPS, CLASS, CSIRO9, ECMWF, ISBA, MOSAIC, SiB, SSiB, and VIC-2L) include a moisture stress term in their parameterization of rs [in this paper, such an approach will be referred to as an rs(θ) formulation]. BATS, BEST, BASE, LSX, and PLACE use the “supply and demand” philosophy: Etr is limited by either the unstressed atmospheric demand or the maximum rate at which water can be supplied to the leaves. Although more commonly used for modeling E or Eg (Desborough et al. 1996), the α (SECHIBA) and β (GISS and MIT) methods for modeling soil moisture stress have also been used to model Etr. In SiB2 and LSM, Etr is linked to photosynthesis following Farquhar et al. (1980), Collatz et al. (1991), and Ball (1988). Moisture stress is incorporated in these parameterizations through a simple dependence on root-zone moisture potential.

In addition to using different basic moisture availability formulations, LSSs also differ in their treatment of vertical soil moisture distribution. Many LSSs (Manabe’s bucket, CAPS, CLASS, ISBA, LSM, LSX, MOSAIC, SiB, SiB2, and SSiB) use only the bulk root-zone soil moisture to parameterize Etr supply, while others use vertical root distribution to integrate moisture stress throughout the root zone. A large number of functions have been proposed for this purpose (see reviews by Molz 1981; Campbell 1985; Feddes et al. 1988), but extensive “calibration” (Molz 1981) makes it difficult to assess their suitability for situations in which they have not been calibrated. This is a major drawback for large-scale applications. Additional uncertainty is associated with the specification of parameters such as surface root fraction. Nevertheless, root-weighing methods are used by BASE, BATS, BEST, CSIRO9, ECMWF, GISS, MIT, PLACE, and VIC-2L. Roots are usually distributed between root-zone soil layers according to the type of vegetation. In the ECMWF model, vertical root distribution is the same for all grid squares. In this paper, the sensitivity of simulated Etr to the treatment of vertical soil moisture distribution is investigated in both an off-line soil moisture model (section 3) and a full LSS (section 4).

3. Experiments with an off-line soil moisture model

a. Methodology

A simple generic three-layer soil moisture diffusion model is used to investigate the sensitivity of a simple root-weighted Etr supply parameterization to surface root fraction R1. The soil column is divided into three vertical layers: a thin (0.1 m) surface layer, the rest of the root zone (0.9 m), and a subroot layer (4 m). The evolution of soil moisture content θ is modeled with a three-layer vertical discretization of the Richards equation. The dependence of hydraulic conductivity KH and matric potential ϕ on θ is parameterized following Cosby et al. (1984). A linearly interpolated θ is used for KH. Free drainage occurs from the base of the third layer. Soil parameters for an average-textured soil are specified.

Manabe’s (1969) moisture availability function [β; (Eq. 2)] is integrated throughout the two-layer root zone by assuming that the influence on Etr of the soil moisture content in a particular layer is proportional to the fraction of roots contained in that layer. The root-weighted transpiration Eroottr is given by
i1520-0493-125-8-1920-e6a
where R1 is the fraction of roots contained in the first soil layer, θ1 and θ2 are the volumetric moisture contents (m−3 m−3) in the first and second soil layers, and Eroot1 and Eroot2 are their root-weighted transpiration extraction terms. The sensitivity of Eroottr to R1 is examined by performing simulations with surface root fractions of 10%, 30%, 50%, 70%, and 90%. The depth-weighted bulk transpiration rate Ebulktr is also calculated:
i1520-0493-125-8-1920-e7a
where d1 and d2 are, respectively, the depths of the first and second soil layers, and Ebulk1 and Ebulk2 are their depth-weighted transpiration extraction terms.

For each simulation, all soil moisture stores are initialized as saturated and a constant unstressed Etr rate of 4 mm day−1 is imposed. The soil dries out via Etr and liquid diffusion processes within the soil. There is no precipitation or soil evaporation.

b. Results

Figure 1 shows how Etr responds to moisture stress as the soil dries out from saturation for each value of R1. The timing and intensity of moisture stress is very sensitive to R1 and this sensitivity is exhibited across the whole range of R1 values. When only 10% of the roots are placed in the surface layer, Eroottr is identical to Ebulktr (not shown). As the surface root fraction is increased, the onset of moisture stress becomes progressively earlier and more intense. Thus, Etr is affected by whether or not root weighting is used to integrate soil moisture stress throughout the root zone and by the value of R1.

When R1 exceeds 10%, the root density in the surface layer is higher than in the rest of the root zone (i.e., R1/d1 > R2/d2), and, consequently, root-weighted extraction depletes θ1 more rapidly than θ2 (Fig. 2). Because Etr is more sensitive to the soil moisture content in the densely rooted surface layer than it is to the moisture content in the rest of the root zone, considerable moisture stress occurs when θ1 becomes depleted even though the root zone as a whole is still quite wet. Thus, an uneven root distribution leads to an uneven soil moisture distribution and their combination produces an earlier onset of moisture stress.

The scenario considered here was kept deliberately simple in order to isolate the response of transpiration to moisture stress and to test the sensitivity of that response to the treatment of vertical moisture distribution. In a more realistic scenario, the moisture gradient established between the two layers in the root zone would be affected by additional sinks and sources of water such as precipitation and evaporation from the soil surface. The evaporative demand would also vary diurnally and from day to day. In section 4, the sensitivity of evaporation to the parameterization of transpiration supply is tested in a full LSS with atmospheric forcing from both a GCM and observations. As well as providing a more realistic testing environment, this scenario allows for an assessment of the magnitude of the impacts on transpiration.

4. Sensitivity of BASE to surface root fraction in off-line tests with atmospheric forcing from PILPS

a. Methodology

The dependence of Etr on soil moisture is often parameterized with either an S/D (supply and demand) formulation or an rs(θ) formulation (section 2; Table 1). A procedure similar to that used in section 3 is used here to test the sensitivity of specific S/D and rs(θ) formulations to the treatment of vertical soil moisture distribution. The S/D formulation tested is that of Cogley et al. (1990) (see the appendix). The rs(θ) formulation uses the standard Manabe (1969) β function [(Eq. 2)] as a multiplier for rs, with Etr given by
i1520-0493-125-8-1920-e8
All other aspects of the model are identical (see the appendix). Root-weighted and bulk versions of each method are tested, and the sensitivity of the root-weighted methods to R1 is examined. While the basic procedure used here is the same as that used in section 3, the experimental environment is somewhat more complex. The simple soil moisture model used in section 3 is replaced by a full Deardorff-type LSS (BASE) and the constant unstressed Etr is replaced by more realistic atmospheric forcing from PILPS.

Each of the Etr supply methods is tested against four sets of off-line atmospheric forcing from phases 1, 2a, and 2b of PILPS. In this paper, the GCM forcing from the phase 1 grassland and tropical forest “sites” will be referred to as GRA and TRF, while CAB and HAP will be used to refer to the observed forcing from Cabauw (phase 2a) and HAPEX-MOBILHY (phase 2b). All four sets of atmospheric forcing contain 1 year of data at a 30-min time step and consist of precipitation, incident shortwave (solar) and longwave (thermal infrared) radiation, and near-surface values of air temperature, humidity, pressure, and wind speed. The experiments conducted here are consistent with the corresponding PILPS experiments in terms of both atmospheric forcing and specification of land surface properties. For a description of the PILPS sites and atmospheric forcing, the reader is referred to Pitman et al. (1993) for GRA and TRF, Chen et al. (1997) for CAB, and Shao et al. (1995) for HAP.

BASE, the LSS used in these experiments, is based on Deardorff’s (1978) framework and is similar in design and complexity to two other Deardorff-type schemes: BATS (Dickinson et al. 1993; Dickinson et al. 1986) and BEST (Cogley et al. 1990; Pitman and Desborough 1996; Pitman et al. 1991). It includes an explicit canopy layer with a CAS through which the foliage and ground exchange heat and moisture with each other and the atmosphere. The CAS-free portion of the ground interacts directly with the atmosphere but has the same temperature and moisture content as the rest of the ground. Precipitation falls uniformly across the grid square, and any rain that falls on the foliage may be intercepted and evaporated at the potential rate. Transpiration occurs from the dry portion of the foliage. The three-layer soil moisture diffusion model is similar to the model used in section 3 but also allows for frozen soil moisture, soil evaporation, and partial infiltration of water reaching the soil surface. A finite difference heat diffusion model with the same three layers as the soil moisture model handles the calculation of soil temperatures. BASE’s one-layer snowpack is characterized by its mass, density, and fractional extent. It interacts both thermally and hydraulically with the atmosphere and the ground. BASE’s representation of surface hydrology is outlined in the appendix.

For each experiment, BASE is run continuously against 1 year of forcing data until equilibrium is achieved. For these experiments, equilibrium is defined as being when the January average values of all fluxes are within 0.1 W m−2 of the fluxes from the previous year and the January average temperatures are within 0.01 K of their values in the previous year.

b. Results

Varying R1 between extreme values of 10% and 90% produces large localized Etr differences (ΔEtr = E10trE90tr) for all but one of the eight experiments (Fig. 3). The R90 case (R1 = 90%) is considerably more susceptible to moisture stress than the R10 case (R1 = 10%). The TRF site is the most sensitive to R1 with ΔEtr values of order 80 W m−2 over most of a 3-month period for both the S/D and rs(θ) formulations, CAB has a 20-day period of high sensitivity in which ΔEtr reaches 60 W m−2, HAP has differences of 53 W m−2 for S/D and 33 W m−2 for rs(θ), and ΔEtr for GRA is only 12 W m−2 for S/D and 3 W m−2 for rs(θ). The HAP site also has periods of reverse sensitivity in which Etr is higher for the R90 case than the R10 case. This reverse sensitivity is a reaction through soil wetness to earlier positive ΔEtr values.

Table 2 contains some simple annual statistics for the eight experiments. Annual ΔEtr values range from −4 mm yr−1 for HAP S/D to 178 mm yr−1 for TRF S/D. These differences are more meaningful when expressed as percentages of annual precipitation and average annual Etr. The precipitation fractions are of order 5% or less. The Etr fractions range between −4% and 28%. The rs(θ) formulation produces annual ΔEtr values that exceed 20% of the annual Etr for TRF, GRA, and HAP. The TRF S/D experiment also produces a ΔEtr of more than 20% of annual Etr. The HAP S/D experiment produces a negative ΔEtr due to the compensatory period and a lower equilibrium soil moisture content.

The two moisture availability formulations exhibit different sensitivities to root distribution because the rs(θ) formulation becomes moisture stressed at a higher soil wetness than the S/D formulation. The impact of this increased sensitivity to moisture stress (Fig. 3) depends on the severity of the stress. For mild stress (GRA and CAB), the increased sensitivity leads to larger ΔEtr values through decreased R90 transpiration. In contrast, the moisture stress for TRF and HAP is severe enough to affect the R10 case as well, and consequently these sites have lower ΔEtr values for rs(θ) than S/D. For the HAP rs(θ) experiment, the smaller negative ΔEtr values produce a much higher annual ΔEtr than S/D despite the initial ΔEtr reduction. The differences between the sensitivities of the specific rs(θ) and S/D formulations examined here cannot be generalized to apply to all rs(θ) and S/D formulations. The differences simply indicate that different moisture availability formulations can have different sensitivities to root distribution.

Figure 4 shows that the sensitivity of Etr to root distribution for TRF S/D is not restricted to extreme values of R1, but occurs across the whole range of R1 values. The bulk depth-weighted S/D method resembles the 10% R1 case. Similar behavior was exhibited in the other seven experiments.

Figure 5 shows the annual soil moisture cycle for TRF S/D with R1 values of 10% and 90%. Comparing Figs. 3a and 5, it can be seen that the period of Etr sensitivity is initiated by surface moisture stress at the end of April. The response of Etr to this moisture stress depends on the root distribution. When the surface root density is very high compared to the rest of the root zone (R90), a large soil moisture gradient is established between the two layers. The surface roots are starved of water and Etr is partially moisture limited despite the relatively high moisture content of the root zone as a whole. The more uniform root density in the R10 case allows it to continue transpiring at a high rate. The sensitivity of Etr to R1 is reduced when the moisture stress becomes severe enough to also affect the root-zone wetness. The rate at which Etr responds to moisture stress is thus sensitive to R1. The other seven experiments produced similar relationships between Etr and soil moisture.

The results obtained with BASE and atmospheric forcing from PILPS are consistent with those from the simple scenario in section 3. The response of transpiration to moisture stress is very sensitive to whether it is parameterized in terms of bulk moisture content or with some form of root weighting. Root-weighted methods are very sensitive to surface root fraction, and this sensitivity is exhibited whenever the soil dries out enough to establish a significant moisture gradient between the two root-zone layers.

5. Summary and discussion

The transpiration simulated by LSSs is shown to be sensitive to the treatment of vertical root distribution. Tests in a simple off-line soil moisture model and a complex Deardorff-type LSS indicate that transpiration becomes progressively more susceptible to moisture stress as the surface (10 cm) root fraction is increased from 10% to 90%. This sensitivity is manifested principally at the seasonal timescale with transpiration difference of up to 80 W m−2, but it also has some impact at the annual timescale with relative transpiration differences of between −4% and 28%. Surface root fraction affects transpiration when surface soil moisture is depleted and the sensitivity can thus occur even when the bulk of the root zone is still wet.

Intermodel differences in the treatment of vertical root distribution are likely to have a significant effect on the transpiration simulated by LSSs. While root-weighted methods generally have high (60%–90%) surface root fractions, the effective surface root fraction for bulk methods is only about 10%. Thus, the differences between the 10% and 90% cases can be viewed as representing the differences between bulk and root-weighted methods based on the same moisture availability function. These differences imply that the same moisture availability functions cannot be appropriate for both methods. Interestingly, the functions used by both methods were originally developed for bulk formulations. The shape of bulk moisture availability functions is known only approximately, and the shape of root-weighted moisture availability functions is known even less well. Also, the sensitivity of transpiration to surface root fraction in root-weighted methods depends on other aspects of the parameterization and there is additional uncertainty associated with large-scale parameter specification. The current lack of understanding of how vertical root distribution affects transpiration at large spatial scales limits the usefulness of root-weighted methods. Simple bulk methods are more consistent with the current level of understanding and are thus to be preferred over root-weighted methods.

The sensitivity of simulated transpiration to vertical root distribution implies a need to improve our understanding of this dependence. Observational evidence is required to determine the actual sensitivity of transpiration to vertical root distribution and to develop an appropriate large-scale parameterization of that sensitivity. Such a parameterization would have to be based on meaningful parameters that could be specified with a reasonable degree of certainty across the modeled domain. Simple bulk methods should be replaced by more complex root-weighted methods if and when they can be shown to be appropriate.

By varying the globally constant water-holding capacity of the surface, Milly and Dunne (1994) showed that the global climate of a GCM is sensitive to changes in continental evaporation. A wide range of methods are used in LSSs to parameterize the availability of moisture for evaporation. This paper examines one aspect of that parameterization, the dependence of transpiration on vertical root distribution, and shows that intermodel differences in the treatment of that process can have a considerable impact on simulated transpiration. Combining these results with those of Milly and Dunne (1994) suggests that the treatment of vertical root distribution in LSSs is likely to have a considerable impact on other aspects of the simulated global climate as well.

Acknowledgments

The author thanks Dr. A. J. Pitman for his advice and support. The comments of two anonymous reviewers are acknowledged and appreciated. The efforts of those responsible for generating the PILPS datasets are also appreciated. The author thanks Chris Milly for his comments on an early draft of the paper. This work was performed with the support of an Australian Postgraduate Research Award.

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APPENDIX

Parameterization of Hydrology in Best Approximation of Surface Exchanges (BASE)

BASE’s representation of land surface hydrology is constructed around the three-layer soil moisture diffusion model used in section 3 and Deardorff’s (1978) canopy model. Figure A1 illustrates the physical arrangement of surface moisture stores in BASE and the fluxes of liquid and frozen water between them. There are four moisture stores each for liquid and frozen water: each of the three soil layers can store both liquid and frozen soil moisture, the foliage can store a small amount of intercepted rain, and snow can accumulate on the ground. Water enters the system from above as either rain (Pg + Pd) or snow (Pn). Rain is assumed to be distributed evenly across the land surface and the fraction that falls on the vegetated portion (Pd) may be intercepted. Every square meter of foliage can hold 0.1 mm of water (Dickinson et al. 1993), and any excess rain falls through to the ground. The flux of water at the top of the soil column consists of rain, canopy drip, and melted snow. The maximum infiltration rate is calculated following Eagleson (1970) and Cogley et al. (1990) and includes a simple saturation heterogeneity representation. Any water that is unable to infiltrate within a time step leaves the system as surface runoff.

Figure A2 shows the physical arrangement of evaporation fluxes in BASE. The CAS covers a fraction (fcas) of the surface and acts as a partial interface between the other components of the surface (foliage, ground, and snow) and the atmosphere. The CAS-free fractions of the ground and snow interact directly with the atmosphere. The total evaporation (E) from the land surface is an area-weighted average of the evaporation fluxes from the CAS (Eca) and the CAS-free fractions of the ground (Ega) and snow (Ena):
EEcaEgaEna
The foliage (Etr: transpiration, Edw: dewstore evaporation), ground (Egc), and snowpack (Enc) exchange moisture with each other and the atmosphere (Eca) according to the specific humidity (qc) in the CAS:
i1520-0493-125-8-1920-ea2
where Esuptr and Esupg are the maximum rates at which the soil can supply moisture for transpiration and soil evaporation, respectively (per square meter of active surface); fveg and fsno are the fractional extents of foliage and snow; fwet is the fraction of the foliage covered by water (following Dickinson 1993); qa is the specific humidity of the air above the CAS; q*f, q*g, and q*n are the saturated specific humidities of the foliage, ground, and snow; ra, ra,f, and ra,g are aerodynamic resistances above and within the CAS (following Cogley et al. 1990); r*s is the “wet” bulk stomatal resistance; ρ is the density of air; and “min” indicates that the smallest of the two following arguments is to be used. The system of CAS evaporative exchanges [Eqs. (A2)–(A7)] is combined with equations for sensible heat and radiation and solved using iterative numerical procedures (Newton’s method and bisection). Here, Ega and Ena are calculated independently of the CAS system:
i1520-0493-125-8-1920-ea8
In its standard mode, BASE uses the supply and demand transpiration parameterization of Cogley et al. (1990) in which the supply rate is given by
i1520-0493-125-8-1920-ea10
where S is a quadratic seasonality factor that goes from one at 25°C to zero at 0° and 50°C. The moisture availability function is calculated as a root-weighted average (Ri is the fraction of roots in layer i) and depends on the actual soil moisture potential (ϕi) and its value at the permanent wilting point (ϕwp). The maximum transpiration rate is set to 1.8 × 10−4 kg m−2 s−1. The supply function for ground evaporation also follows Cogley et al. (1990), but the supply and demand methodology is used explicitly rather than as a means to calculate an effective beta parameter.
The wet bulk stomatal resistance (r*s) is parameterized in terms of a vegetation-dependent minimum stomatal resistance and stress functions for radiation (fR), temperature (fT), and humidity (fH):
i1520-0493-125-8-1920-ea11
where rs,min and rs,max are the minimum and maximum values of r*s, KS is the incident solar radiation (W m−2), Tf and q*f are the temperature (K) and saturated specific humidity (kg kg−1) of the foliage, and qc is the specific humidity (kg kg−1) in the CAS. The stress functions are all constrained to lie between 0 and 1.
Snow hydrology in BASE is modeled following Cogley et al. (1990). Snow cannot be intercepted by the foliage and all snow falls through to the ground. As the snowpack increases in volume, it covers parts of the ground and foliage. These snowcover fractions depend on the mass and density of the snowpack and the height of the foliage. In contrast to Cogley et al. (1990), the snowpack in BASE is modeled as a single layer on top of the soil column with energy and mass balances calculated for its upper and lower boundaries. Its temperature may differ from that of the surface soil layer. The melting and freezing of soil moisture is also parameterized following Cogley et al. (1990), but because the temperature and soil moisture layers are identical in BASE, the geometric factors are not required and the ice production rate for a layer (Γi) is simply
i1520-0493-125-8-1920-ea12
where χi is an efficiency factor, Cv is the volumetric heat capacity (J m−3 K−1), Ti is the soil temperature (K), Lf is water’s latent heat of fusion (333 kJ kg−1), and Δt is the time step(s).
Fig. 1.
Fig. 1.

Impact of moisture stress on transpiration as the soil dries out from saturation in the off-line soil moisture model. Simulations are shown for surface root fractions of 10% (○), 30% (□), 50% (⋄), 70% (▵), and 90% (▿).

Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1920:TIORWO>2.0.CO;2

Fig. 2.
Fig. 2.

Time evolution of soil moisture saturation fractions in the off-line soil moisture model. Saturation fractions for the surface layer (○: θ1/θ0) and the rest of the root zone (□: θ2/θ0) are shown for simulations with surface root fractions of (a) 10%, (b) 50%, and (c) 90%.

Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1920:TIORWO>2.0.CO;2

Fig. 3.
Fig. 3.

Sensitivity of the seasonal transpiration Etr cycle to extreme values (10% and 90%) of surface root fraction. Shading is used to indicate the differences between the two simulations: light shading indicates higher transpiration with a surface root fraction of 10% and dark shading indicates the reverse sensitivity. Results are shown for (a) TRF S/D, (b) TRF rs(θ), (c) GRA S/D, (d) GRA rs(θ), (e) CAB S/D, (f) CAB rs(θ), (g) HAP S/D, and (h) HAP rs(θ).

Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1920:TIORWO>2.0.CO;2

Fig. 4.
Fig. 4.

As in Fig. 3b but also showing transpiration Etr for surface root fractions of 30% (•), 50% (▪), and 70% (⋄). The thick-dashed line indicates where the bulk depth-weighted method deviates from the 10% case.

Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1920:TIORWO>2.0.CO;2

Fig. 5.
Fig. 5.

Seasonal cycles of soil moisture saturation fraction for the two root-zone soil layers (θ1/θ0 and θ2/θ0) in the TRF S/D experiment. Results for surface root fractions of (a) 10% and (b) 90% are shown. The thick solid lines indicate the surface saturation fractions (θ1/θ0) and the thick-dashed lines represent the saturation fractions in the rest of the root zone (θ2/θ0). The thin horizontal dashed lines show the saturation fraction at the permanent wilting point (θwp).

Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1920:TIORWO>2.0.CO;2

i1520-0493-125-8-1920-fa1

Fig. A1. Schematic representation of liquid and frozen hydrology in BASE, showing the three soil layers, the foliage mass store, and the snowpack. The light-shaded boxes indicate liquid moisture stores (the upper store being for the foliage). The dark-shaded boxes are for frozen soil moisture. Arrows are used to indicate mass fluxes. The flux labels are explained in the text. The unlabeled fluxes are for melting and freezing of soil moisture.

Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1920:TIORWO>2.0.CO;2

i1520-0493-125-8-1920-fa2

Fig. A2. Schematic showing the physical arrangement of evaporation fluxes in BASE. Arrows are used to indicates evaporation fluxes. The flux labels are explained in the text.

Citation: Monthly Weather Review 125, 8; 10.1175/1520-0493(1997)125<1920:TIORWO>2.0.CO;2

Table 1.

Summary of methods used by land surface schemes to parameterize the influence of moisture stress on transpiration. There are five basic formulations: rs(θ)—bulk stomatal resistance is subject to moisture stress; S/D—supply and demand; α, β, and PS—linked to photosynthesis. The reference used for each scheme is also shown.

Table 1.
Table 2.

Annual transpiration statistics for BASE experiments. Here, ΔEtr is the decrease in transpiration (mm yr−1) between runs with surface root fractions of 10% and 90%. The second and third columns express these differences as percentages of annual precipitation P and transpiration Etr.

Table 2.
Save