Impacts of a new bare-soil evaporation formulation on site, regional, and global surface energy and water budgets in CLM4

Abstract

[1] We describe the implementation of a new bare-soil evaporation formulation in the Community Land Model-version 4 (CLM4). This new formulation comprises two components: (1) a full-range (desiccated to fully saturated) soil water retention curve (SWRC) parameterization that extends the classical Clapp-Hornberger parameterization and (2) a mechanistically based formulation of soil resistance that considers the effects of water vapor diffusion and liquid mass flow. Predictions by the new SWRC parameterization matched measured soil matric pressure data across a wide soil moisture range for six very different soils. We assessed the revised bare-soil evaporation formulation with two types of global simulations, one with prescribed satellite plant phenology and the other with bare-soil conditions. Compared with the default CLM4 soil evaporation formulation, the revised model leads to (1) slightly lower (−0.2 ∼ 0 mm d⁻¹ averaged annually) bare-soil evaporation in moderately wet regions; (2) slightly higher (0 ∼ 0.2 mm d⁻¹ averaged annually) bare-soil evaporation in semiarid regions; (3) small changes in global surface energy and water balances across all temporal scales for both vegetated and nonvegetated simulations; and (4) a small reduction (−0.2 ∼ 0 mm d⁻¹ averaged annually) in the current overestimation of evapotranspiration in densely vegetated regions such as the Amazon basin. However, contrary to expectation and consistent with the default CLM4, the simulated bare-soil evapotranspiration remains higher than that of the vegetated soil in the same grid cells. We conclude that further studies are needed to identify the processes that lead to the overestimation of bare-soil evaporation in CLM4.

Key Points

• a new mechanistically based soil resistance formulation is proposed
• Water vapor transport dominates the latent heat flux in dry regions
• The beta factor approach compares equally well for modeling soil evaporation.

1. Introduction

[2] Soil evaporation is one of the few pathways through which the land surface returns precipitated water to the atmosphere, and is therefore a critical component of global water and energy cycling. For global climate modeling, any bias in estimated soil evaporation will propagate through the climate system and consequently degrade the quality of the simulation. Therefore, implementing an accurate bare-soil evaporation formulation has been a critical task in designing reliable climate models [e.g., Sellers et al., 1996; Lawrence et al., 2012].

[3] The community land model (CLM; version 4 used in this study) has been an important tool in our understanding of how land surface processes impact the climate system. CLM has been used to study various topics, including: land use change impacts on climate [Lawrence et al., 2012], permafrost degradation with warming [Lawrence et al., 2012], global CH₄ emissions under a changing climate [Riley et al., 2011], impacts of regional-scale land fluxes on the remote atmosphere [Subin et al., 2012; Murphy et al., 2012; Bonfils et al., 2012], and others (a more complete list can be found at http://www.cesm.ucar.edu/models/cesm1.0/clm/clm_bibliography.htm).

[4] Currently, CLM4 (and CLM4.5 to be released Summer 2013) uses the β-factor approach proposed by Lee and Pielke [1992] to compute the actual bare-soil evaporation from the potential bare-soil evaporation, with the former determined by the atmospheric demand (consequently, β-factor is just the soil evaporation efficiency that defines the ratio between the actual and potential evaporation). Although the β-factor approach has been considered an improvement compared to the empirical formulations used in earlier CLM versions [Lawrence et al., 2011] and has been used by many other land models (see the review by Tang and Riley [2013]), its lack of transient atmospheric control was shown to bias the estimated bare-soil evaporation for a range of atmospheric and soil moisture conditions [Komatsu, 2003; Tang and Riley, 2013]. Specifically, the β-factor approach overestimates bare-soil evaporation when soil is wet, and underestimates bare-soil evaporation when soil is dry. Tang and Riley [2013] also showed that a group of other empirical soil resistance formulations (including the formulation by Sellers et al. [1992] that was used in CLM3.5) are very likely error convolved, because even a small measurement uncertainty (e.g., 5% was used in Tang and Riley [2013]) can substantially bias the derived empirical formulations. In that paper, we also proposed a new soil resistance formulation that requires no empirical parameters other than soil hydraulic properties, which are available in all land models. Because this new formulation successfully explained when and why the existing empirical soil resistance formulations and the β-factor approach are likely biased, we believe its implementation could improve bare-soil evaporation simulations in land models, such as CLM4.

[5] Implementing the new soil-resistance formulation by Tang and Riley [2013] requires a soil water retention curve (SWRC) parameterization capable of characterizing soil matric potential from saturated to desiccated (i.e., zero water content) conditions. Tang and Riley [2013] used the full-range SWRC parameterization proposed by Silva and Grifoll [2007] (“SG parameterization” henceforth), which states that the full-range SWRC can be represented with three connected regions: (i) wet region, where capillary effects control water movement; (ii) the medium to low soil water content region, where a cubic relationship relates water content to the logarithm of the soil matric pressure; and (iii) the hyperdry region, where water films are built up by condensed water molecules through molecular adsorption to the soil mineral surfaces and the moisture content can be related to the relative humidity by the BET isotherm [Brunauer et al., 1938], and consequently to the soil matric pressure with the Kelvin's equation [Skinner and Sambles, 1972]. Although the SG parameterization reproduced the experimental water retention curves for seven widely studied soils [Silva and Grifoll, 2007], numerical difficulties arose when we implemented it in CLM4. Specifically, we found that its fundamental assumption in region (ii) (i.e., that the relationship between soil water content and the logarithm of soil matric pressure can be represented by a cubic polynomial) often led to unphysical results. That is, we found cases with , indicating that the soil matric pressure P (Pa) increased in magnitude (more negative) as the soil water content θ (m³ m⁻³) increased. This unphysical condition can be explained by examining the derivative of ln(–P) with respect to θ in region (ii):

(1)

where as defined in Silva and Grifoll [2007],

(2)

[6] The coefficients a, b, c, and d are obtained by solving the equation 7 in Silva and Grifoll [2007] with proper configuration of the matching points. At the edge of region (ii), it should hold to ensure first-order continuity (equations (7b) and (7d) in Silva and Grifoll [2007]), leading to a solution for the critical soil water content (θ_c)

(3)

that must be outside the region spanned by θ_w1 (m³ m⁻³) and θ_w2 (m³ m⁻³), which are the water contents that connect the region (i) at P₁ (Pa) and region (iii) at P₂ (Pa). Mathematically, the restriction put on θ_c is equivalent to requiring that θ_w1 and θ_w2be on the same branch (either both on the left or on the right; see Figure 1 for an example) of the parabolic function defined by the right hand side of equation 1. However, when equations 1 and 2 were implemented in CLM4, the prior parameters (variables other than a, b, c, and d as specified in equation 7 in Silva and Grifoll [2007]) did not always lead to solutions of a, b, c, and d that ensured the critical soil water content θ_c met this restriction. Therefore, we contend that a new full range SWRC parameterization that not only shares the merits of the approach by Silva and Grifoll [2007], but also is appropriate under a wider range of soil conditions, needs to be developed for application with large-scale land models, such as CLM4.

Figure 1

A schematic diagram for the relationship between θ_c, θ_w1, and θ_w2(see discussions about equations 1-3 in the introduction, only one example is shown here). When θ_w1 = θ_w1,1, the restriction on θ_cis violated, such that a physically consistent SG parameterization is infeasible, whereas when θ_w1 = θ_w1,2, a physically consistent SG parameterization is feasible. Therefore, to make the SG parameterization feasible, θ_w1 and θ_w2 must be on the same branch of the parabolic function as defined in equation 1.

[7] In this study, we developed a new full range SWRC parameterization by extending the classical Clapp-Hornberger [Clapp and Hornberger, 1978] (CH henceforth) parameterization. Combined with the new soil resistance formulation proposed in Tang and Riley [2013], we obtained a new formulation of bare-soil evaporation. We analyzed the effect of this new bare-soil evaporation formulation on the simulated regional and global surface energy and water budgets in CLM4. We also tested the hypothesis that our new formulation would reduce the simulated global bare-soil evaporation (as CLM4 uses the β-factor approach, which tends to overestimate soil evaporation as was shown in Tang and Riley [2013]) and change the surface energy budget.

[8] The remainder of the paper is organized as follows: section 2. describes the (a) methods we used to develop and test the SWRC parameterization, (b) metrics used to evaluate the new bare-soil evaporation formulation globally in CLM4, and (c) numerical experiments to test our hypothesis; section 3. presents results, analyses, and discussion; and section 4. summaries our findings.

2. Methods

2.1. A Mechanistically Based Formulation of Soil Resistance

[9] A detailed theoretical derivation of the mechanistically based soil resistance formulation was presented in Tang and Riley [2013]; we summarize here the important features of that formulation for this study. The new formulation was obtained by assuming instantaneous equilibrium between water vapor and liquid water throughout the soil column (Figure 2). However, this assumption is relaxed to apply only in the topsoil control volume (TSCV; which is of thickness 1.75 cm in CLM4) in the new model. Therefore, the soil evaporation resistance comprises two parts: (i) the resistance for the water vapor to diffuse into (or out of) the TSCV through the soil-air interface (r_a (s m⁻¹)) and (ii) the resistance for the water vapor (r_g (s m⁻¹)) and liquid water (r_w (s m⁻¹)) to be replenished with water from deep in the soil column.

Figure 2

A schematic diagram shows the conceptual configuration of the soil evaporation problem, where the soil evaporation, F_a, (mm H₂O m⁻² s⁻¹) is a summary of water vapor transport, F_g, (mm H₂O m⁻² s⁻¹) and direct liquid water evaporation F_w (mm H₂O m⁻² s⁻¹). Relative symbols: z_a (m) is the atmospheric reference height, q_a (g water vapor g⁻¹ air) is the atmospheric specific humidity, q_g,s (g water vapor g⁻¹ air) is the specific humidity at the soil-atmosphere interface, θ_s (m³ m⁻³) is the volumetric water content at soil surface and r_a (s m⁻¹) is the atmospheric aerodynamic resistance. The soil resistance is determined as a function of both the liquid flow resistance r_w (s m⁻¹) and the vapor flow resistance r_g (s m⁻¹). See main text for details.

[10] The new soil resistance r_s(s m⁻¹) is represented as:

(4a)

(4b)

where K₁ (m s⁻¹) is the hydraulic conductivity; ψ₁ (m) is the soil matric potential; ε₁ (m³ air m⁻³ soil) is the air filled porosity; D_g (m² s⁻¹) is the water vapor diffusivity in soil; ρ_l (kg m⁻³) is the liquid water density; ρ_a(kg m⁻³) is the air density; q_g,1 (g water vapor g⁻¹ air) is the specific humidity in the topsoil; and (m) is thickness of the TSCV. All variables in equations 4a and 4b are defined for the TSCV.

[11] Equation 4a can be rewritten as

(5)

where r_w is resistance for liquid mass flow and r_g is the resistance for water vapor transport.

[12] Using equation 5, one then can partition the soil evaporation F_a (mm H₂O m⁻² s⁻¹) with

(6a)

as the fraction of soil evaporation contributed by water vapor transport F_g (mm H₂O m⁻² s⁻¹), and with

(6b)

as the fraction of soil evaporation contributed by direct liquid water evaporation F_w (mm H₂O m⁻² s⁻¹).

2.2. Extending the Clapp-Hornberg Parameterization to the Full Soil Water Range

[13] Implementing the new soil resistance formulation into a numerical model requires a full range soil water retention curve parameterization. Because the SG parameterization often fails to provide physically consistent results, we propose the following parameterization to solve the problem.

[14] Following Silva and Grifoll [2007], we assume that (i) for a wet soil where the capillary mechanism dominates, any classical SWRC scheme can be used and (ii) for a soil with medium to low water content, a semilogarithmic relationship holds:

(7)

where P₁ and P₂ are the soil matric pressure (Pa) at the matching points, whose corresponding soil water contents are θ_w1 and θ_w2. Finally, (iii) for the hyperdry region, the theory of BET isotherm applies, such that

(8a)

(8b)

where θ_wn (m³ m⁻³) and B (unitless) are the characteristic BET isotherm parameters, is the liquid molar volume of water, R (Pa m³ K⁻¹ mol⁻¹) is the universal gas constant, and T (K) is the temperature. Silva and Grifoll [2007] referred to θ_wn as the pseudovolumetric water content at monolayer capacity (the volume of water required to cover the adsorption surface completely as a monolayer) and obtained it through curve fitting with measured soil water-pressure relationships. In our new scheme, we treat θ_wn as an unknown to be determined. We note equation 8b is also known as Kelvin's equation [Skinner and Sambles, 1972], which can be used to relate soil water saturation to relative soil air humidity.

[15] Assuming first-order continuity at the matching points characterized by (θ_w1, P₁) and (θ_w2, P₂), we obtain the following set of equations:

(9a)

(9b)

(9c)

(9d)

[16] The solution for the four unknowns, a, b, θ_w1, and θ_w2 requires values of P₂ and x₂, which we take to be P₂ ≈ −162 MPa (at 20°C) and x₂ = 0.3, following Silva and Grifoll [2007]. The derivation of equation 9d is in Appendix Appendix A, and a is found by substitution of equation 9d into equation 9c:

(9)

[17] To solve for the remaining unknowns, classical SWRC schemes that parameterize the water-retention curve for a wet soil were used. We integrated the BET parameterization with three classical schemes: the BC scheme [Brooks and Corey, 1964] (BC-BET), VG scheme [van Genuchten, 1980] (VG-BET), and the CH scheme (CH-BET). We found only the CH-BET scheme always provided analytically tractable and physically consistent solutions. Iteration is needed for the BC-BET scheme (see Appendix Appendix B for details). The VG scheme is not extendable with our approach, i.e., no analytical solution is available, and even the iterative equation has no solution under many conditions.

[18] The CH scheme parameterizes the SWRC as

(11)

where ε (m³ m⁻³) is the soil porosity, P_b (Pa) is the bubbling pressure, and λ_CH is the CH shape parameter. We ignore the parabolic correction in the high soil water content region [Clapp and Hornberger, 1978], which is not relevant to the solution of equation 9a-9d.

[19] Substitution of equation 11 into equations 9a and 9b leads to,

(12a)

(12b)

[20] The derivation of equation 12a is in Appendix Appendix C.

[21] Substitution of equation 12b into equation 9d yields θ_w2, with leads to the solution of θ_wn from equation 8a-8b.

2.3. Evaluating the New Full Range SWRC Parameterization

[22] We used a data set of six very different soil types (Table 1) from Campbell and Shiozawa [1992] to evaluate our SWRC parameterization. The same data set has been used in other studies [e.g., Webb, 2000; Silva and Grifoll, 2007]. We compared model predictions with measured soil water content and soil matric pressure data. The comparisons were assessed with the root-mean square error (RMSE) for the logarithm of the soil matric pressure and the mean absolute biases for soil moisture. The RMSE is computed as

(13)

where is the magnitude of the soil matric pressure predicted by the new SWRC parameterization and is the magnitude of the measured soil matric pressure. The mean absolute bias is computed as

(14)

where θ_w,i is the soil water content predicted by the new SWRC parameterization and is the measured soil water content.

Table 1. Summary of the CH Soil Fitting Parameters

Soil	Ba	Pb (Pa)	λCH	εa
Palouseb	39.49	−4674	0.269	0.44
Palouse Bb	11.39	−5826	0.240	0.55
Walla Wallab	23.49	−4096	0.289	0.39
Salkumb	124.3	−10412	0.267	0.48
Royalb	68.00	−2267	0.334	0.35
L-Soilb	42.98	−233	0.226	0.18

• ^a The values of the B and soil porosity are adapted from the study by Silva and Grifoll [2007].
• ^b Campbell and Shiozawa [1992].

[23] As an additional evaluation in the dry soil range, we also applied the Kelvin's equation (equation 8b) to compare the relationship between water saturation and relative humidity computed from the different SWRC parameterizations with respect to that derived from measurement. Specifically, we computed the soil matric pressure P based on the soil water saturation, and then derived the relative humidity with equation 8b.

[24] For all comparisons, we used three different parameterizations: CH, CH-Webb (CH modified with Webb's approach [Webb, 2000]), and CH-BET (Figures 3-5). The Webb approach does not include the BET isotherm for the hyperdry region; it rather assumes that the zero soil water saturation occurs at a soil matric pressure of −10⁹ Pa, and uses the linear logarithmic relationship equation 7 for this region, with P₂ = −10⁹ Pa and P₁ determined by first order continuity condition. In evaluating the model predictions for the dry region, we also included the SG parameterization (Figures 4 and 5).

Figure 3

Predicted relationship between soil matric pressure and soil water saturation by different formulations of soil water retention curves, where CH is the default Clapp-Hornberger parameterization, CH-BET is an extension of CH parameterization based on BET theory and CH-Webb is an extension of CH parameterization based on Webb's approach. The two dash-dotted lines in different plots indicate the matching points where the SWRC is divided into three different regions as described in section 2.2..

Figure 4

Predicted relationship between soil water saturation and relative soil air humidity using different formulations of soil water retention curves. The dashed lines indicate the threshold relative humidity 0.3 at the matching point (P₂, θ_w2).

Figure 5

Predicted first derivative of soil matric pressure with respect to volumetric soil moisture by different formulations of soil water retention curves.

2.4. Evaluating the New Bare-Soil Evaporation Formulation

[25] We conducted two types of global simulations to analyze the effect of our new bare-soil evaporation formulation on the modeled water and energy budgets predicted by CLM4. The simulation protocol for the first type of simulations used the prescribed satellite phenology data and ran the model for 40 years to equilibrium and then for another 5 years to provide data for the analysis. A similar simulation protocol was used for the second type of simulations, except that all the vegetated area was replaced with bare soil. The second type of simulations is used to assess the potential overestimation in the bare-soil evaporation by the β-factor approach [Tang and Riley, 2013; P. Lawrence, personal communication, 2012]. Each type of simulation has one control simulation with the default CLM4 model structure and one perturbed simulation implemented with our new SWRC parameterization and the mechanistically based soil resistance formulation. All simulations are driven with meteorological data from Qian et al. [2006].

[26] By comparing model output between the control and new evaporation model simulations, we assessed the impact of our new formulation on the simulated water and energy budgets. Five metrics were used in this impact assessment: (i) change in soil evaporation efficiency; (ii) change in bare-soil evaporation; (iii) change in bare-soil sensible heat; (iv) change in the water return efficiency, defined as the ratio between evapotranspiration (ET) and precipitation (Prec) (we note that these are uncoupled simulations, so that ET does not impact Prec); and (v) change in the ground surface temperature. The first two metrics were assessed for the vegetation removal experiments, and the other three for the simulations driven with satellite plant phenology data. We also analyzed how important water vapor transport was in contributing to global bare-soil evaporation.

3. Results and Discussion

[27] We first describe the results of using our new SWRC parameterization to predict the soil water-pressure relationship. Then, we assess the effect of our new bare-soil evaporation formulation on the CLM4 predicted global water and energy budgets. Next, we describe an analysis of the fractions of soil evaporation contributed by water vapor transport and direct liquid water evaporation from the TSCV. Finally, we discuss why in some regions the bare-soil evaporation is higher than that of a colocated vegetated soil.

3.1. Evaluation of the New SWRC Parameterization

[28] From the comparison statistics (Table 2), we found the CH-BET parameterization outperformed the CH parameterization in all aspects. The CH-Webb approach produced equally good results compared to the CH-BET scheme, implying that only a small difference should be expected when these two parameterizations are implemented in the same numerical model. However, the CH-BET scheme is physically more realistic, as no finite soil matric pressure can be exerted in the absence of water [e.g., Baggio et al., 1997].

Table 2. Comparison of the Goodness of the SWRC Function Fita

Soil	RMSE			R^2			(m^3 m^−3)
	CH	CH-BET	CH-Webb	CH	CH-BET	CH-Webb	CH-BET	CH-Webb
Palouse	0.482	0.369	0.357	0.860	0.984	0.982	0.100	0.007
Palouse B	0.807	0.663	0.614	0.722	0.986	0.973	0.186	0.025
Walla Walla	0.520	0.442	0.418	0.816	0.982	0.975	0.106	0.008
Salkum	0.334	0.319	0.323	0.974	0.989	0.987	0.158	0.016
Royal	0.545	0.443	0.438	0.738	0.924	0.960	0.035	0.003
L-Soil	0.679	0.756	0.739	0.869	0.987	0.986	0.018	0.110

• ^a The RMSEs are computed for the log transformed soil matric pressure. The R²s are for the linear fitting of the model predicted soil matric pressure against the measurement. is defined as the mean absolute difference between the measured and modeled relative soil water content.

[29] Visually, it is difficult to tell which of the three different parameterization schemes best described the soil water-pressure relationship (Figure 3). However, when the soil water approaches the hyperdry region, the CH parameterization predicts the soil matric pressure increases at a faster rate than the other two schemes. Such a prediction induces some numerical difficulties in implementing the CH parameterization for very dry soils, and it often causes the Richard's equation numerical solution to fail. We successfully avoided this difficulty by implementing the CH-BET scheme in CLM4.

[30] We evaluated four parameterization schemes (the three compared in Table 2 and the SG) with Kelvin's equation (equation 8b and Figure 4). As expected, the predictions by the SG parameterization agreed best with the inferred (from the measured data and Kelvin's equation) relationships between soil air relative humidity and soil matric pressure. The CH-BET and the CH-Webb parameterization performed equally well and better than the CH parameterization; in particular for the hyperdry region (marked with relative humidity smaller than 30% following the criteria by Silva and Grifoll [2007]).

[31] When the first-order derivative was assessed with the three different parameterization schemes (CH-BET, CH-Webb, and SG) for the six soils being studied, the SG scheme predicted some wiggles (due to the cubic polynomial that the SG scheme uses for region (ii)) at low soil moisture content (Figure 5). In general, such wiggles are not an issue in computing the soil resistance (equation 4a-4b), but they do result in occasional numerical difficulties in our implementation of the SG parameterization in CLM4.

[32] Therefore, with the advantages it provided, we assert that the CH-BET scheme is a good choice for SWRC parameterization in large-scale land models such as CLM4.

3.2. Changes in Bare-Soil Evaporation

[33] We analyzed the difference in soil evaporation efficiency (i.e., the β-factor) predicted by our new soil evaporation formulation and that by the default CLM4 approach (Figure 6). For both methods, higher soil evaporation efficiencies occurred in wet regions and lower evaporation efficiencies in dry regions (Figures 6a and 6b; shown for the default CLM4 formulation). Soil evaporation efficiencies in the Northern Hemisphere (NH) summer half year (defined as the 5 year average over the months from June to November) are lower than their NH winter counterparts, due to the lower water content in summer. Snow cover in the winter half year also contributed to this contrast in winter and summer half-year evaporation efficiency, where CLM4 regarded the snow-covered soil as being water vapor saturated. Throughout the relatively wet regions, as expected, our new formulation predicted lower soil evaporation efficiency than the default CLM4 formulation, whereas it predicted higher soil evaporation efficiency in the low soil moisture content regions, such as the Sahara Desert and the Arctic (Figures 6c and 6d).

Figure 6

(a and b) Soil evaporation efficiency predicted by the default CLM4 formulation. (c and d) Percent difference in soil evaporation efficiency predicted by the new bare-soil evaporation formulation and the default CLM4 formulation.

[34] When differences (between the default and new model) in bare-soil evaporation were analyzed for the four seasons (Figure 7), the new formulation predicted lower soil evaporation in many places over the globe, particularly in the JJA period. Slightly higher soil evaporation was predicted by the new formulation in some regions depending on the time of the year; however, this signal is smaller than the reduction of soil evaporation, which resulted in a global reduction of soil evaporation. Globally, our new approach predicted lower soil evaporation, with 5 year average magnitudes of −0.08 ± 0.0008 mm m⁻² d⁻¹ (in the form of mean ± σ), −0.12 ± 0.003 mm m⁻² d⁻¹, −0.06 ± 0.005 mm m⁻² d⁻¹, and −0.06 ± 0.003 mm d⁻¹ for the spring (MAM), summer (JJA), fall (SON), and winter (DJF) seasons, respectively. Such a small soil evaporation change exerted a small yet statistically significant (p = 0.0011 with the two-sample Kolmogorov-Smirnov test) perturbation to the simulated global hydrological cycle, though strong reductions (annually, −0.8 ∼ −0.6 mm d⁻¹ smaller than that from the default CLM4 formulation) did exist in two or three grid cells (at the grid resolution 1.9° (lat) × 2.5° (lon)).

Figure 7

Simulated differences in bare-soil evaporation for vegetation removal experiments by subtracting the default CLM4 simulation from that with the revised bare-soil evaporation formulation.

[35] Corresponding to the reduction in bare-soil evaporation, we also found the new model predicted higher (statistically significant with p = 0.0011 using the two-sample Kolmogorov-Smirnov test) sensible heat fluxes (positive into the atmosphere) with 5 year average magnitudes of 2.82 ± 0.016, 3.85 ± 0.048, 2.39 ± 0.049, and 2.75 ± 0.048 W m⁻² for the four seasons, respectively. In about 7% of the grid cells, mostly in the tropical region (results not shown), the increase of sensible heat was as large as 6 ∼ 10 W m⁻² averaged annually.

3.3. Partitioning of Bare-Soil Evaporation

[36] We find that water vapor transport played a critical role in returning soil water to the atmosphere (Figure 8). The fraction of soil evaporation contributed by direct diffusive water vapor transport (f_g) varied temporally and regionally. In wet regions such as the northern high latitudes, soil evaporation is dominated by liquid water evaporation from the surface soil (f_g < 20%), whereas in arid regions, such as the Sahara Desert, soil evaporation is dominated by water vapor transport (f_g > 80%). The magnitude of f_g is greater in summer when the soil is dry and smaller in winter when the soil is wet (e.g., northern hemisphere midlatitude region). When averaged globally and over the 5 year period, direct water vapor transport contributed about 6.6 ± 0.003%, 10 ± 0.002%, 7.0 ± 0.007%, and 5.2 ± 0.005% to bare-soil evaporation in the spring, summer, fall, and winter seasons, respectively.

Figure 8

Contributions of direct water vapor diffusion to the bare-soil evaporation predicted by the new soil evaporation scheme.

3.4. Change in Global Water and Energy Budget

[37] The analysis of water return efficiency (or ET:Prec ratio) for different land cover types indicates that there are small changes to the global water cycle with the implementation of our new bare-soil evaporation formulation (Figure 9). Statistically significant changes (p < 10⁻⁸ with the two-sample Kolmogorov-Smirnov test) in the ET:Prec ratio occurred in bare soils (Figure 9a); whereas the changes in forests (Figure 9b) and grasslands (Figure 9c) were statistically insignificant, though the changes in forests was slightly greater than those in grasslands.

Figure 9

Histograms of water return efficiency (defined as ET divided by precipitation) simulated in the satellite phenology experiment for different vegetation covers. All trees are grouped into the category “forest,” and all grasses are grouped into the category “grass.” CLM4-new refers to the revised model with the new bare-soil evaporation formulation, and CLM4-Default refers to the standard CLM4 formulation.

[38] We found both slight warming and cooling of ground surface temperatures occurred at different places and times, in accordance with the decreasing and increasing soil evaporation (Figure 10). In the summer season, a stronger warming was identified than in the other three seasons. When averaged globally, the warming is smaller than 0.06 (±0.002) K for all four seasons and is statistically insignificant when averaged over the 5 year period. Therefore, as for the ET changes, our new bare-soil formulation exerted a small perturbation to the global surface energy budget as compared to the default CLM4 configuration.

Figure 10

Simulated differences in ground surface temperature for the satellite phenology experiment by subtracting CLM4 default simulations from that using the new bare-soil evaporation formulation.

[39] We also analyzed the differences in ET predictions when driven with satellite phenology data and with globally nonvegetated soils using both the default CLM4 approach and our revised model (Figure 11). We found higher ET for bare soil than for a colocated vegetated soil in many grid cells. Because the topsoil (i.e., the first numerical node of the discretized soil column) is not always wet and the vegetation generally has higher conductance than the soil for water exchange with the atmosphere in our numerical experiments, we believe the higher bare-soil ET is a positive bias. Others in the CLM4 community (e.g., P. Lawrence, personal communication, 2012) have also identified this bias and it could potentially mislead our interpretations of climate predictions when considering land use change [Lawrence et al., 2012]. Using our new bare-soil evaporation formulation slightly reduces this positive bias, however, the overestimation pattern remains, indicating further model revision is needed to resolve this model deficit.

Figure 11

Simulated differences in ET between that by the vegetation removal experiment and that by the satellite phenology experiment: (a) The default CLM4 formulation of bare-soil evaporation was used for the simulation. (b) The new bare-soil evaporation formulation was used for the simulation.

3.5. Possible Reasons for Overestimating the Evapotranspiration During the Vegetation-Removal Experiment

[40] In section 3.4., we found that removing vegetation resulted in higher surface ET in some (previously) densely vegetated areas, such as interior Amazon and East China (vegetation map not shown). We tested two hypotheses to explain these predictions: (1) the bare-soil ET overestimation is due to omission of the litter layer resistance with the removal of the vegetation and (2) the default 30 min time step is not fine enough to resolve the coupling between soil water dynamics and surface evaporation.

[41] Sakaguchi and Zeng [2009] introduced a litter layer to predict the soil resistance for vegetated soils (see their equations 13, (16), and (17)). This litter layer resistance was set to zero for bare soil in the simulations presented above. We added this litter layer to the bare soil (using an identical formulation as for the vegetated soil) and repeated the vegetation removal experiment. We found that including this litter layer resistance reduced bare-soil evaporation in some places during portions of the year (Figure 12). However, the reduction was small, and increases were found in some regions (e.g., Southern Africa). Globally, the mean reduction over the 5 year period was −0.01 mm d⁻¹. We performed another simulation by increasing the litter layer resistance by a factor of ten, and found that the bare-soil evaporation changed slightly and the problem with higher bare-soil ET compared to a colocated vegetated soil remained. Therefore, the litter layer is unlikely to be the cause of the CLM4 bare-soil ET bias.

Figure 12

Simulated effects of litter resistance on the bare-soil evaporation in the vegetation removal experiments. All plots show differences by subtracting the simulation without litter resistance from that with litter resistance. The new bare-soil evaporation formulation was used for all simulations.

[42] CLM4 calculates the surface energy budget by assuming that the topsoil control volume is vertically uncoupled from soil water in deeper layers. The soil water content is updated by imposing the soil evaporation computed from the surface energy budget subroutine as the top boundary condition to the Richard's equation. This numerical iteration is cycled every 30 min, raising the possibility that the coupling between surface evaporation and soil water in deeper layers is underestimated. We conducted simulations with seven model configurations for an Amazon gridcell and time steps of 30 min and 10 s (Figure 13; see figure caption for details on the model configuration). The results indicate that using smaller time steps only slightly changed the simulated ET, and that the higher bare-soil ET than a colocated vegetated surface remains. Therefore, we assert that time step size is not the cause that leads to overestimation of bare-soil ET.

Figure 13

Comparison of simulated ET using different model setups for a grid located in the Amazon basin (longitude: 62.5°W, latitude: 2.84°S). All simulations were run to equilibrium for 30 years, then another 10 year simulation were output for the comparison. CLM4 Newlit refers to the simulation using the new soil evaporation formulation and the extra litter layer. CLM4 New-10s refers to the revised model run with a time step of 10 s. CLM4 Newlit-10s refers to run CLM4 Newlit with a time step of 10 s. (a) The 10 year mean annual cycle of ET. (b) The annual mean ET for the 10 year period.

[43] We therefore believe other model deficiencies are leading to the counterintuitive larger bare-soil evaporation compared to a colocated vegetated surface. These problems may include (1) improper formulation of the root water uptake profile, such that the plant transpiration responds incorrectly to soil water dynamics; (2) improper formulation of lateral water fluxes, such as subsurface drainage, which could modify the soil moisture profile incorrectly and lead to unexpected ET responses to land use change; and (3) exclusion of water redistribution through hydraulic lift by plant roots [e.g., Ryel et al., 2002]. Testing these hypotheses would require a suite of comprehensive measurements of ET and other water fluxes for a vegetated and bare soil that differs only by vegetation coverage. Then together with information on the aboveground and belowground plant physiological response to water cycle changes, a proper resolution of the ET overestimation problem could be achieved. Besides these three hypotheses, it is also possible that the conceptual model of the surface energy budget in CLM4 is flawed. To name two such flaws, for instance, CLM4 assumes the aerodynamic resistances for the transport of humidity and temperature are always identical, while some studies indicate they could be significantly different under many conditions [e.g., Li et al., 2012]; second, CLM4 assumes vegetation has no impact on soil physical properties, which contradicts many observations (e.g., root impacts on soil structure and channels [Rasse et al., 2000]). For these last two hypotheses, it would be interesting to see if other land models using similar conceptual hydrological models share the same counter-intuitive predictions.

4. Summary

[44] In this study, we implemented a new bare-soil evaporation formulation and analyzed its impact on the simulated water and energy budgets in CLM4. We found that the new mechanistically based formulation led to (i) lower bare-soil evaporation for moderately wet soils; (ii) slight changes in the ground surface temperature and surface water budgets; and (iii) higher evapotranspiration from a bare soil than that from a colocated vegetated soil surface in densely vegetated regions, such as the Amazon. Nevertheless, the more mechanistic treatment allows for other benefits, including a framework with which to accurately represent multiphase isotope and other tracer exchanges with the atmosphere. We conclude that the ET overestimation in CLM4 when the vegetation is removed is very likely caused by factors other than (i) an improper formulation of bare-soil resistance; (ii) a litter layer; or (iii) a coarse model time step. Further explorations are needed to pin down the causes for the bare-soil ET overestimation.

Acknowledgments

[56] This research was supported by the Director, Office of Science, Office of Biological and Environmental Research of the U.S. Department of Energy under Contract DE-AC02–05CH11231 as part of their Regional and Global Climate Modeling (RGCM) Program.

Appendix A: Derivation of Equation 9d

[45] Application of the BET isotherm (i.e., equation 8a) at the matching point (P₂, θ_w2) leads to

(A1)

[46] From the first order continuity at matching point (P₂, θ_w2), one has

(A2)

[47] Then by substitution of equation A1 into equation A2, one obtains equation 9d

Appendix B: Solution of the BC-BET Scheme

[48] The BC scheme parameterizes the SWRC as

(B1a)

(B1b)

where θ_r(m³ m⁻³) is the residual water content and λ_BC is the BC shape parameter.

[49] To solve for θ_w1, we define the variable transformation

(B2)

from which we obtain the iterative equation:

(B3a)

(B3b)

where n is the number of iterations.

[50] We note that s_n + ln s_n monotonically increases with s_n, and s_nhas its minimum value . Therefore, solution to equation B3a-B3b exists only when

(B4)

[51] With the solution of θ_w1 found from equations B2 and B3a-B3b, the remaining unknowns can be found similarly as described for the CH-BET scheme.

Appendix C: Derivation of Equation 12a

[52] Substitution of equation 12b into equation 9a leads to

(C1)

[53] Meanwhile, by evaluating the logarithm of equation 11 at the matching point (P₁, θ_w1), one has

(C2)

[54] Thence, substituting equation C1 into equation C2, one obtains

(C3)

[55] Now it is easy to verify that equation C3 is just the logarithm of equation 12a.