a. Behavior of the latent and sensible heat flux

Since the incoming radiation was not altered in the sensitivity experiments discussed here, the increase in air temperature must lead to changes in the latent or sensible heat. This is achieved by an adjustment of surface temperature. Figure 1 shows the differences in the annual mean effective temperatures, T_s (the combined mean surface radiative temperature of the canopy and the ground) between Plus2 and Control (i.e., T⁺²_s − T^C_s), and that between Minus2 and Control (i.e., T⁻²_s − T^C_s) for all 23 PILPS schemes. It can be seen that annual mean effective surface temperature increases or decreases by about 1 K when air temperature increases or decreases by 2 K. BUCKET shows the largest annual mean increase (1.68 K) and the U.K. Meteorological Office (UKMO) the smallest (0.73 K) in Plus2 while SPONSOR showing the largest annual mean decrease (1.55 K) and the Goddard Institute of Space Sciences (GISS), ISBA the smallest (0.83 K) in Minus2. It should be noted that the change of the surface temperature with the increase or decrease of air temperature is the key mechanism that causes the change in the other quantities analyzed here (Qu et al. 1996).

Generally, most of the schemes exhibit similar, but opposite, behavior in Plus2 and Minus2. Figure 2 shows the difference of latent heat flux L and sensible heat flux H (W m⁻²) between Plus2 (Minus2) and Control for all 23 land-surface schemes. Compared to the control experiment, latent heat flux increases by about 6 W m⁻² in Plus2, with BUCKET showing the lowest increase (2.1 W m⁻²) and CAPS the highest (9.6 W m⁻²), and decreases by about 11 W m⁻² in Minus2, with UGAMP2 showing the lowest decrease (5.6 W m⁻²) and VIC-3L the highest (17.0 W m⁻²) (Fig. 2a). SPONSOR is the only scheme that produces a small decrease of latent heat flux in Plus2. A possible reason for this behavior will be discussed in section 3b(3). Sensible heat flux decreases by about 12 W m⁻² in Plus2, with CAPS showing the largest decrease (16.2 W m⁻²) and SPONSOR the lowest (4.7 W m⁻²), and increases about 16 W m⁻² in Minus2, with VIC-3L showing the highest increase (23.7 W m⁻²) and SWAP the lowest (9.9 W m⁻²) (Fig. 2b). It should be noted here that for Plus2 the annual means of sensible and latent heat fluxes have ranges across the schemes of 31 and 23 W m⁻², respectively, and for Minus2 of 24 and 28 W m⁻², respectively. These ranges are of a similar magnitude as those for the control experiment, which is significantly larger than the uncertainties of the measurements (Chen et al. 1997). After Beljaars and Bosveld (1997), the observational errors of the Cabauw dataset are within ±5 W m⁻² for sensible heat flux and ±10 W m⁻² for surface net radiation and latent heat flux.

Figure 3 shows the differences of L and H between Plus2 and Minus2. It can be seen that |H⁺² − H⁻²| is larger than |L⁺² − L⁻²| for all schemes; that is, sensible heat flux is more sensitive to the prescribed change of air temperature than latent heat flux. This is because of the linear relationship between H and T_s, which changes with the change of air temperature [Eq. (3)]. It can also be seen that if L of a certain scheme is sensitive to the change of air temperature, H is also sensitive.

The interesting result with regard to the behavior of latent heat flux is that the increases or decreases of latent heat flux in Plus2 and Minus2 are not linear with respect to the prescribed equal and opposite changes in air temperature (+2 K and −2 K). Figure 4 illustrates this nonlinearity. For clarity, 6 out of 23 schemes are shown, representative of median (UKMO, CLASS, SSIB, CSIRO9, ECHAM) and extreme (BUCKET) performance in the control experiment (cf. Chen et al. 1997). For latent heat flux, the nonlinear relation to the change of air temperature is evident.

The crucial point here is that for most schemes the nonlinear relationship between latent heat flux and air temperature is shown by the increase of latent heat flux in Plus2 being much smaller than the decrease of latent heat flux in Minus2 (Fig. 2a). If we define

View Expanded

this result can also be described as

r_L(5)

In the following sections, the theoretical aspects of the relationship between L_s and air temperature will be illustrated through an investigation of the formulation of L_s [Eq. (2)], and then we try to explain the behavior of latent heat flux in the Plus2 and Minus2 Cabauw experiments.

b. Theoretical aspects of the relationship between L_s and air temperature

Equation (2) shows clearly that there is a nonlinear relation between surface temperature and L_s induced by the nonlinearity between surface temperature and saturation specific humidity. A numerical evaluation of Eq. (2) will be used here to illustrate the response of L_s to the change of air temperature. Fixing all variables in Eq. (2) except T_s and λ (λ changes with T_s) and assuming ρ = 1.292 (kg m⁻³), U = 5.0 (m s⁻¹), C_E = 0.00597 (appendix of Chen et al. 1997), q_a = 0.005 (kg kg⁻¹), we allow T_s to increase or decrease 1 K because Fig. 1 shows that annual mean effective surface temperature increases or decreases by about 1 K when air temperature increases or decreases by 2 K. These changes in T_s are imposed upon a base surface temperature that varies from −10° to 30°C to match the annual range of air temperature in Cabauw (Beljaars and Bosveld 1997). In this numerical test, we use the symbol L⁺¹_s to represent L_s for T_s increased by 1 K, L⁻¹_s to represent L_s for T_s decreased by 1 K, and L^C_s for control.

Figure 5 shows the difference (absolute values) between L⁺¹_s and L^C_s and the difference between L⁻¹_s and L^C_s under different base surface temperature. If the two lines in Fig. 5 coincided, L_s would have a linear dependence on surface temperature. However, Fig. 5 shows that only when the base surface temperature is below about −5°C are the differences between |L⁺¹_s − L^C_s| and |L⁻¹_s − L^C_s| so small that the dependence of L_s on T_s is quasi linear. This is not the case for the most of the year in Cabauw: all monthly mean air temperatures in Cabauw are higher than 0°C (Beljaars and Bosveld 1997; Chen et al. 1997).

The interesting point here is that the nonlinear change of L_s with regard to the linear change of temperature is shown in a way that the amount of increase of L_s for +1 K T_s is larger than the amount of decrease of L_s for −1 K T_s, that is, |L⁺¹_s − L^C_s| > |L⁻¹_s − L^C_s|. However, in the Cabauw sensitivity experiments |L⁺² − L^C| is much smaller than |L⁻² − L^C| (i.e., r_L < 1). This implies that the nonlinear behavior of L in the Cabauw sensitivity experiments cannot be attributed to the nonlinear relationship between T_s and q∗ in the formulation of L_s [Eq. (2)] used by the PILPS schemes. As mentioned in section 2a, however, in the Cabauw sensitivity experiments, a so-called β_g formulation is generally involved in the parameterization of L (Shao et al. 1994; Mahfouf and Noilhan 1991; Kondo et al. 1990). The effect of β_g on the relationship between L and T_s has not been considered in the numerical test above. Also not considered in the numerical test above is the effects of the changes in drag coefficient induced by the change of the stratification due to the imposed change of air temperature by ±2 K. These will be reviewed in the next sections.

a. The β adjustment

As mentioned in section 2a, latent heat flux is commonly parameterized by using Eq. (1) in PILPS schemes. Most of the schemes determine L_s by using the aerodynamic method [Eq. (2)], while a few schemes (Table 1) use the Penman–Monteith formulation. We first consider the effect of β_g on the latent heat flux in these sensitivity experiments and, for clarity, assume drag coefficient C_E does not change in the sensitivity experiments.

After Beljaars and Bosveld (1997), the vegetation cover at Cabauw is close to 100% all year round. Even in winter, after mowing or after a dry spell, it is unusual to see any bare soil. Based on these observations, σ_f > 0.92 throughout the year was used in the Cabauw experiment (appendix of Chen et al. 1997). Therefore, (1 − σ_f)L_soil in Eq. (7) can be ignored. Hence,

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and

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In this case, we can see that the original scaling parameters in bare soil moisture parameterization, α and β, are not present in β_g formulation [Eq. (12)], and because of the consideration of the bulk stomatal resistance for transpiration, β_g is not only a function of soil moisture stress as is the case for estimation of bare soil evaporation, but it is also a function of aerodynamic resistance (drag coefficient) and other stresses, including the photosynthetically active radiation stress, vapor pressure deficit stress, and air temperature stress, which affect r_s. Therefore, we use β_g in Eq. (6) to distinguish between the generalized β_g and β or α used for parameterization of bare soil evaporation, which is often simply a function of soil moisture.

Here we demonstrate that the involvement of β_g formulation in the parameterization of latent heat flux and the change of β_g induced by the increase and decrease of air temperature in the sensitivity experiments is the reason that causes r_L < 1 for the schemes using the aerodynamic method. For simplicity, we assume that β_g is only a function of soil moisture and assess its effects on the latent heat flux in the sensitivity experiments.

Soil moisture for Plus2 is lower than that for the control experiment and that for Minus2, due to the increase of evaporation in Plus2 [see section 3b(3)]. This, therefore, leads to differences in β_g for Plus2 and Minus2. We include this adjustment in β_g in the numerical test discussed in section 2b by using values from the Cabauw sensitivity experiments. The goal is to see if the inconsistency mentioned above disappears. We assume

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(cf. Liang et al. 1994; Pan and Mahrt 1987; Robock et al. 1995), where W_g is soil water content, W_wilt is wilting point soil water content, and W_cr is the critical soil moisture above which evaporation is not affected by the moisture stress in the soil. Since for most schemes W_g is the root zone soil moisture and the depth of the root zone was prescribed as 1 m in Cabauw experiments, we consider W_g as the soil moisture for the top 1 m in the analysis. For the top 1-m soil layer, we assume here that W_cr is 75% of Manabe’s (1969) effective water capacity (150 mm) plus the unavailable water content at wilting, W_wilt (214 mm) (appendix of Chen et al. 1997). Using monthly values of W_g from BASE output, annual mean values of β_g are calculated. These are 0.52, 0.75, and 0.65 for Plus2 (β⁺²_g), Minus2 (β⁻²_g), and the control experiment (β^C_g), respectively. These values are used to adjust the L_s from the numerical test discussed in section 2b [Eq. (2)], that is, to calculate L_s × β_g:

View Expanded

Table 2 gives L⁺¹, L⁻¹, and L^C for an arbitrary base temperature, T_s = 283 K. It can be seen that, after adjusting L with β_g, the relation is shifted, that is, |L⁺¹ − L^C| is smaller than |L⁻¹ − L^C|. This is then consistent with the situation in Cabauw sensitivity experiments. It is clearly shown that β_g has a profound effect on the performance of L. This becomes still clearer if we replot Fig. 5 with L adjusted by β_g.

Figure 6 shows |L⁺¹ − L^C| and |L⁻¹ − L^C| at different base surface temperatures and for two different sets of β_g value. In Fig. 6a, the β_g values in Table 2 are used, that is, β⁺²_g = 0.52, β⁻²_g = 0.75, β^C_g = 0.65. It can be seen that |L⁺¹ − L^C| < |L⁻¹ − L^C| when the surface temperature is between about −3° and 10°C. If we artificially tune β_g (i.e., assume β⁺²_g = 0.46, β⁻²_g = 0.70, β^C_g = 0.54), but still keep β⁺²_g < β^C_g < β⁻²_g, that is, accepting that modeled soil moisture for Plus2 is lower than that for the control experiment and that for Minus2 is higher than the control experiment, it can be seen that |L⁺¹ − L^C| is generally less than |L⁻¹ − L^C|, except for a small range around a surface temperature of about 7°C but which itself depends on the value of β_g (Fig. 6b). The location of this temperature range, here 7°C, is arbitrary, depending on q_a chosen for the test. It happens here that q∗ at the points around 7°C is nearly equal to q_a.

The analysis above shows that the involvement of the β_g formulation in the parameterization of latent heat flux causes the nonlinearity of L with regard to the linear change of air temperature in the form that the increase of latent heat flux in Plus2 is much smaller than its decrease in Minus2, that is, r_L ≪ 1. Without the involvement of the β_g formulation, the nonlinearity is different, namely, the increase of latent heat flux in Plus2 is larger than its decrease in Minus2, as discussed in section 2b.

For the schemes using the Penman–Monteith formulation to determine the scaling evaporation, the situation is more complicated. The following analysis will show, however, that r_L < 1 is still attributable to the involvement of a β_g formulation even for those schemes using a Penman–Monteith formulation.

The Penman–Monteith equation for the evaporation from wet surfaces can be written as

View Expanded

(cf. Mahrt and Ek 1984), where r_a is the aerodynamic resistance between the surface and the reference height;R_n is net radiation, G is ground heat flux that can be assumed proportional to R_n, that is, G = aR_n [for the ground with vegetation cover, a ranges between 2 to 20 or so percent (Thom 1975)]; and ∂e∗/∂T is the change of saturation vapor pressure with temperature. Assuming G = aR_n, we have

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and

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where e⁺²_∗ = e∗(T_a + 2), e⁻²_∗ = e∗(T_a − 2) and e^C_∗ = e∗(T_a). Since the net radiation is given by

R_nα_sR_sR_LR_L(18)

where R_s is shortwave solar radiation, α_s is surface albedo, R_L↓ is downward longwave radiation, and R_L↑ is upward longwave radiation. In the sensitivity experiments, R_s and R_L↓ are the same as those in the control experiment. In Plus2 and Minus2, α_s changes in the winter months due to the change in snow cover induced by 2 K increase or decrease of air temperature. However, this change is quite small (Qu et al. 1996), and on the annual average it can be neglected; that is, we assume that (1 − α_s)R_s in Plus2 and Minus2 is also same as that in the control experiment. Hence, we have

R⁺²_nR^C_nR^C_LR⁺²_L(19)

Since the emissivity of the surface was set to unity, we have

R⁺²_LσT⁺²_s⁴(20)

and

R^C_LσT^C_s⁴(21)

where σ is the Stefan–Boltzmann constant, and T^C_s and T⁺²_s are the surface temperatures in the control and sensitivity experiments, respectively. If we write (T⁺²_s − T^C_s) = ΔT⁺_s, Eq. (19) can be expressed as

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where negligible terms in (ΔT⁺_s)³ and (ΔT⁺_s)⁴ are omitted. The value ΔR_n can therefore be expressed as

R⁺²_nR^C_n−4σT³_sΔT⁺_s(23)

with an error given by 1.5ΔT⁺_s/T_s. For T_s = 298 K, the error is only 0.5% per degree temperature difference. Using Eq. (23), Eqs. (16) and (17) can be rewritten as

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and

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where ΔT⁺_s = T⁺²_s − T^C_s and ΔT⁻_s = T⁻²_s − T^C_s. In Eqs. (24) and (25), small changes of γ, ρ, c_p, and ∂e∗/∂T are neglected. Therefore, without the β_g adjustment, the ratio r_L,s = |(L⁺²_s − L^C_s)/(L⁻²_s − L^C_s)| is dependent on ΔT⁺_s, ΔT⁻_s, e⁺²_∗ − e^C_∗, and e⁻²_∗ − e^C_∗. As the signs of the first and second term of the right-hand side in Eqs. (24) and (25) are opposite, r_L,s could be smaller than 1. However, since |ΔT⁺_s| ≈ |ΔT⁻_s| (Fig. 1) and |e⁺²_∗ − e^C_∗| is always larger than |e⁻²_∗ − e^C_∗| because the function e∗(T) is convex, r_L,s is in fact larger than 1. Therefore, for the schemes using the Penman–Monteith formulation, r_L < 1 in the sensitivity experiments can still be also explained by the β_g adjustment as discussed above.

b. Influence of the stress factors on the change of β_g in the sensitivity experiments

From the discussions in section 3a, it can be seen that (i) the involvement of the β_g formulation in the parameterization of latent heat flux and (ii) the change of β_g induced by the change of air temperature is responsible for r_L < 1 both for the schemes using the aerodynamic method to determine the scaling evaporation, and for the schemes using Penman–Monteith. As β_g is a function of r_a and a series of stress factors, we will discuss in the following section which factors most strongly influence the change of β_g and therefore the change of latent heat flux in the sensitivity experiments.

1) The influence of air temperature on drag coefficient

As drag coefficient C_E (some models use alternatively aerodynamic resistance) for water vapor transfer, which is involved in β_g [Eq. (11)], depends on thermal stability, increasing or decreasing forcing air temperature also influences C_E. The following analysis shows that the changes in C_E induced by air temperature changes of ±2 K have a significant influence on monthly or annual latent heat flux for most of the schemes.

Figure 7a shows the diurnal variation of the bulk Richardson number [Ri = gz/T × (T_a − T_s)/U², T = (T_a + T_s)/2], calculated by using T_s from BATS for Plus2, Minus2, and the control experiment for the time from 10 to 13 September (see Chen et al. 1997 for details). It can be seen that the differences of the calculated Richardson number between Plus2 and control and also between Minus2 and control are quite small during the day but larger at night. This is due to the smaller difference between air temperature and surface temperature induced by strong dependence of surface temperature on absorbed solar radiation during the day. Using the calculated bulk Richardson number, the drag coefficient C_E can be estimated after Mahrt and Ek (1984) (Fig. 7b). From this estimation, C^C_E/C⁺²_E and C⁻²_E/C^C_E can be calculated, where C^C_E, C⁺²_E, and C⁻²_E are C_E for control, Plus2, and Minus2, respectively. The values of C^C_E/C⁺²_E and C⁻²_E/C^C_E have a quite large diurnal variation, but for most of the daytime both C^C_E/C⁺²_E and C⁻²_E/C^C_E are around 1.5. We therefore assume that C^C_E/C⁺²_E ≈ 1.5, that is, r⁺²_a/r^C_a ≈ 1.5, and C⁻²_E/C^C_E ≈ 1.5, that is, r^C_a/r⁻²_a ≈ 1.5 where r^C_a, r⁺²_a, and r⁻²_a are r_a for control, Plus2, and Minus2, respectively. The relative change of latent heat flux for Plus2 can then be estimated by using Eq. (11) and the relationr⁺²_a/r^C_a ≈ 1.5,

View Expanded

where ΔL⁺²/L is the relative change of latent heat flux induced by the change of drag coefficient due to the change of stratification when air temperature is increased by 2 K in Plus2. Here q⁺²_∗ and q^C_∗ are q∗ at T⁺²_s and T^C_s, respectively. Note that σ_f in Eq. (26) does not change between Plus2, Minus2, and control. Using a typical value of (q⁺²_∗ − q_a)/(q^C_∗ − q_a) = 1.3 for Cabauw in Eq. (26), we have

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Similarly, we have the relative change of latent heat flux for Minus2:

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Using a typical value of (q⁻²_∗ − q_a)/(q^C_∗ − q_a) = 0.8, we have

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We examine how the relative change of L in Plus2 differs from that in Minus2. In fact, r_L = (ΔL⁺²/L)/(ΔL⁻²/L), that is,

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Figure 8 shows r_L as a function of r_a and r_s after Eq. (30). It can be seen from Fig. 8 that r_L decreases with the increase of r_a and the decrease of r_s. This implies that for the schemes with explicit stomatal control, the involvement of bulk stomatal resistance r_s reduces the influence of the change of r_a on L. However, it can be seen from Eq. (30) that accounting only for the effects of temperature on q∗,

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Since the daily mean r_a in Cabauw is lower than 40 s m⁻¹ for most of the year, we assume r_a = 30 s m⁻¹. Because the observed midday average of r_s for Cabauw ranges from about 0–120 s m⁻¹ through the entire year (Beljaars and Bosveld 1997) and the mean value is about 60 s m⁻¹, we assume r_s = 60 s m⁻¹ here. Using these values in Eq. (30), we then have r_L = 1.1. This accounts for the change in q∗ and the change in r_a. The model average of r_L = 0.57, which can be considered as r_L accounting for change in q∗, r_a, and r_s. We can see from simple estimations above that the changes due to r_s appear to be only slightly larger than those due to r_a. This implies that drag coefficient effects in these sensitivity experiments have the same order of importance as the r_s effects, which will be discussed in the following sections.

It should be noted that for a cloudy day with lower net radiation, the differences of the calculated Richardson number between Plus2 and control and also between Minus2 and control could be quite large during the day, such as on 13 September. For Plus2, for example, C^C_E/C⁺²_E could be as large as 3. This may result in a higher relative change of latent heat flux being up to 50%. In this case, however, latent heat flux is also small (the daily mean L on 13 September is about 26 W m⁻², which is only about 60% of annual mean L) due to the smaller energy available for evaporation (for 13 September, daily mean R_n < 18 W m⁻²) and therefore makes only a small contribution to the monthly or annual latent heat flux.

It should be pointed out that for the models without explicit stomatal control of transpiration and with no or small changes in predicted soil moisture for Plus2 and Minus2, the change in C_E may play a dominant role in resulting r_L < 1. Models SPONSOR and SWAP are examples of this situation. The transpiration in these two models is estimated by modifying potential evaporation through a β_T formulation that is a function of soil moisture only. Since the predicted soil moisture for Plus2, Minus2, and control is nearly the same and larger than W_cr [see section 3b(3)], β_T is nearly the same for Plus2, Minus2, and control. Therefore, r_L < 1 is mainly caused by decreases in C_E induced by the more unstable stratification in Plus2 in the calculation of the potential evaporation.

2) Influence of air temperature on bulk stomatal resistance

The surface resistance (bulk stomatal resistance) involved in β_g is usually represented in land-surface schemes as

View Expanded

(e.g., Noilhan and Planton 1989), where R_f, S_f, V_f, and M_f represent the dependence of r_s on solar radiation, air temperature, vapor pressure, and soil moisture, respectively; LAI is canopy leaf area index. The factor R_f measures the influence of the photosynthetically active radiation. As this does not change in Plus2 and Minus2, R_f also should not change.

The factor S_f introduces an air temperature dependence in the surface resistance. The parameterization of S_f is based on the fact that there is an optimal temperature for plant physiological processes that ranges from about 10° to 40°C. If the temperature is in this range, there is no (or small) temperature stress and S⁻¹_f is equal, or close, to 1. If the temperature is outside this range, it is likely to be a stress factor for the physiological processes of vegetation (here transpiration); hence S⁻¹_f will be larger than 1, that is, r_s will increase [Eq. (32)]. An example of S_f parameterization following Dickinson (1984) is given as follows:

View Expanded

Figure 9 gives the variation of S⁻¹_f as a function of air temperature for control (T_a = T_a), Plus2 (T_a = T_a + 2), and Minus2 (T_a = T_a − 2) after Eq. (33). For T_a = 285 K, for example, S_f for Plus2 decreases only about 10% compared to control, that is, r_s may decrease about 10%. In this case, the change of latent heat flux is less than 10% [cf. Eq. (11)]. It can be seen that the increase or decrease of air temperature by only 2 K has virtually no, or only a very small, effect on S⁻¹_f and therefore a small effect on r_s for most of the year in Cabauw, so that it can be ignored. Indeed, some PILPS land-surface schemes (e.g., SECHIBA, Ducoudre et al. 1993) neglect the influence of air temperature on r_s.

The factor V_f represents the effects of vapor pressure deficit of the atmosphere. Following Jarvis (1976), V_f can be expressed as

V_fgeT_ae_a(34)

where g is a species-dependent constant. We take g = 0.025 (Noilhan and Planton 1989). It can be seen from Eq. (34) that if air temperature increases vapor pressure deficit will also increase. Hence V⁻¹_f will increase. However, the increase of V⁻¹_f is quite small. Figure 10 shows the calculated daily mean values of the difference of the stress factor V⁻¹_f [Eq. (34)] between Plus2 and control and that between Minus2 and control. It can be seen that the differences of V⁻¹_f between Plus2 and control are within 0.1 for most of the year; that is, r_s may increase by 10% in Plus2 compared to control. In this case, the decrease of latent heat flux is less than 10%. On the other hand, the increase of air temperature will also make e∗(T_s) − e_a increase and this will counteract the stress effect of the increase of vapor pressure deficit. Therefore, the influence of increasing or decreasing air temperature on stress factor V_f can also be neglected for most situations.

Of particular importance is the factor M_f, which accounts for the effects of soil moisture stress on latent heat flux. Usually, M_f varies between 0 and 1 when soil moisture W_g varies between W_wilt and W_cr. In many schemes, M_f is a simple and explicit function of soil moisture. In some schemes (e.g., ISBA, CSIRO9, and VIC-3L), M_f takes the same form as Eq. (13). The change of predicted soil moisture in Plus2 and Minus2 leads to quite large change in M_f. For example, from the estimation given in section 3a, it can be seen that if M_f takes the form given in Eq. (13), the annual mean of M_f decreases from 0.65 for the control experiment to 0.52 for Plus2. That means an increase of r_s of about 25% for Plus2 compared to control, which will have a significant influence on latent heat flux. Thus, it can be seen that changes in the soil moisture in these sensitivity experiment induced (indirectly) by the increase or decrease of forcing air temperature plays an important role on the change of the scaling parameter β_g and therefore is one of the major factors affecting the behavior of the changes in latent heat flux.