Improved Treatment of Surface Evapotranspiration in a Mesoscale Numerical Model Part I:Via the Installation of the Penman-Monteith Method

The Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model version 4 (PSU/NCAR MM4) system shows that the simplified bucket method pioneered by Manabe (1969) to parameterize surface evapotranspiration (ET) has an apparent tendency to overestimate surface ET during nighttime and daytime due to (1) the inappropriate as­ signment of a parameter called moisture availability (M) in the method, and (2) the use of the saturation mixing ratio at the skin temperature as the surface mixing ratio when the long-term observational data from the At­ mospheric Radiation Measurement (ARM) program are used for verifica­ tion. It is also noted that the degree of overestimating latent heat fluxes decreases with the forecasting time. This is the so-called 'spinup problem' that is common in many numerical models owing to the inadequate assign­ ment of the initial skin temperature and the associated saturation surface mixing ratio. A Penman-Monteith (PM) method of estimating potential ET is imple­ mented into the modeling system and is shown to lead to a more reasonable estimation (less overestimation) of ET. The degree of overestimating or underestimating latent heat flux by the PM method is mainly controlled by the se.tting of stomatal resistance given a fixed M. Less surface evaporative cooling, as implied by the PM method, leads to a warmer skin temperature and, consequently, a stronger estimation of daytime sensible heat flux by the model. Compared with the bucket method, the PM method leads to a lower moisture supply from the model's ground surface; thus, there is less probability of low-level cloud formation. A more reasonable estimation of net radiation at the ground surface is then proven to be associated with the use of the PM method. This method restricts the moisture supply from the ground surface and enables the model to make a prediction of the amount and tendency of the mixing ratio at the lowest model level (about 40 meters 1 Meteorological Satellite Center, Central Weather Bureau, Taipei, Taiwan, ROC 2 School of Meteorology, University of Oklahoma, Norman, Oklahoma, USA 481 482 TAO, Vol. 8, No. 4, December 1997 above ground level), which is in more agreement with the corresponding observations. (

surface ET during nighttime and daytime due to (1) the inappropriate as signment of a parameter called moisture availability (M) in the method, and (2) the use of the saturation mixing ratio at the skin temperature as the surface mixing ratio when the long-term observational data from the At mospheric Radiation Measurement (ARM) program are used for verifica tion. It is also noted that the degree of overestimating latent heat fluxes decreases with the forecasting time. This is the so-called 'spinup problem' that is common in many numerical models owing to the inadequate assign ment of the initial skin temperature and the associated saturation surface mixing ratio.
A Penman-Monteith (PM) method of estimating potential ET is imple mented into the modeling system and is shown to lead to a more reasonable estimation (less overestimation) of ET. The degree of overestimating or underestimating latent heat flux by the PM method is mainly controlled by the se.tting of stomatal resistance given a fixed M. Less surface evaporative cooling, as implied by the PM method, leads to a warmer skin temperature and, consequently, a stronger estimation of daytime sensible heat flux by the model. Compared with the bucket method, the PM method leads to a lower moisture supply from the model's ground surface; thus, there is less probability of low-level cloud formation. A more reasonable estimation of net radiation at the ground surface is then proven to be associated with the use of the PM method. This method restricts the moisture supply from the ground surface and enables the model to make a prediction of the amount and tendency of the mixing ratio at the lowest model level (about 40 meters above ground level), which is in more agreement with the corresponding observations.

INTRODUCTION
Surface evapotranspiration (ET), along with other surface heat budget terms, is one of the lower boundary conditions in numerical models, such as the Numerical Weather Prediction (NWP) models, mesoscale numerical models, General Circulation Models/ Global Climate Models (G CMs) and the sin gle column models. It affects the formation process of low-level clouds or even deep convection (Segal et al. 1995). Since the studies of Walker and Rowen tree (1977), Shukla and Mintz (1982), Yeh et al. (1984) and others, it has become more and more apparent that NWP models are sensitive to the parameterization of the surface exchange pro cesses at the atmosphere-land surface interface. The development of the daytime planetary boundary layer is stron gly dependent upon the parameterized surface sensible and latent heat fluxes. Convective precipitation over land is also sensitive to soil-moisture surface-evapora tion parameterization. In daily short-and medium-range forecast applications, an inappropri ate representation of the ET leads to errors in cloud predictions and land surface precipitation forecasts. Such forecasts can be gr eatly enhanced from a more realistic thermodynamic struc ture due to an improved estimation of the ET (Beljaars et al. 1996). Many NWP models-such as the one used in this study, the PSU/NCAR MM4,-utilize a simple bucket-type method pioneered by Manabe (1969) to parameterize the surface latent heat flux process. With this method, there is a bucket at each grid point, and the ET is reduced from a potential value by the ratio (or, the so-called 'moisture availability') of soil water in the bucket and a specified field capacity value. The potential ET is evaluated under the assumption that the soil is saturated at the model -calculated "skin" (ground surface) temperature. The bucket method tends to over estimate surface ET (Section 3). One scheme, however, based on the concepts proposed by Penman (1948) and Monteith (1965), can more reasonably parameterize the potential ET over land and is, therefore, implemented into the modeling system used in this research.
The principal interest of this research is to improve a numerical model's estimation of surface ET by using the long-term observational data set from the Southern Great Plains (SGP) Atmospheric Radiation Measurement (ARM) program site (Stokes and Schwartz, 1994) for verification. Given the correct radiative forcing at the surface, the land surface schemes are also largely responsible for the q uality of model-produced near surface weather parameters, such as near surface temperature and dewpoint as well as low-level cloudiness. Furthermore, the surface conditions need to be such that they provide ade q uate feedback mechanisms for the other physical processes in the atmosphere: low-level cloudiness influences the surface radia tive balance, and sensible heat and latent heat fluxes affect the boundary layer exchan ge pro cesses. Similarly the intensity of moist con vection is related to these near surface physical processes. A correct partitioning between sensible and latent heat fluxes is helpful in deter mining soil wetness which acts as one of the forcing mechanisms of low-fre q uency atmo-spheric variability (Milly and Dunne, 1994 ).
In the following sections, the proposed Penman-Monteith (PM) method of estimating the potential ET over land area is outlined. The manner by which it affects the estimation of surf ace ET in the mesoscale numerical model is demonstrated. In Section 2, the description and derivation of the PM method is introduced. The observational data set used in this research and the basic statistical (long-term) performance in estimating surface ET by the model is presented in Section 3. The results from the use of the PM method are discussed in Section 4. Finally, the summary and conclusions from this research are stated in Section 5. A variational algorithm of assimilating satellite retrievals to improve a model's estimation of surface fluxes will be shown at a later date in Part II of this research proj ect.

THE PENMAN-MONTEITH (PM) METHOD
Penman (1948) first put forth a formula to estimate potential ET, but that, the original formulation can now be further modified to include the effect of stomata! resistance for veg etation based on Monteith ( 1965). Following Mahrt and Ek ( 1984 ), and with potential ET defined as the ET that can be determined if the soil is completely wet under the same environ mental conditions (i.e., net radiative flux at the ground surface and ground heat flux are not altered), a formula is derived here to calculate (parameterize) the potential ET based on the concepts proposed by both Penman and Monteith. It is presented in the following.
When the soil is saturated, a skin temperature T; can be defined such that the surface energy balance equation can be written as: where R is the net radiation flux at the ground surface; H is the ground heat flux (heat flow • m into the substrate); H is the sensible heat flux; L is the latent heat of vaporization; E is the s v I P potential evapotranspiration; cr is the albedo; S is the solar constant, so ( 1a )S � is the net shortwave radiative flux; L w J. is the downward longwave radiative flux; E g is the emissivity of the ground surface; cr is the Stefan-Boltzmann constant; and E g cr T; 4 is then the outgoing longwave radiative flux from the ground surface.
Surface temperature in Equation (2.1) is written as T; to denote that it is a hypothetical temperature from the saturated state. In contrast, the actual surface energy balance is defined as follows: where M is the moisture availability factor ranging from 0.0 to 1.0. The last term of Equation (2.2) is obtained from Equation (2.la). The difference between the two skin temperatures, Tg T;, can be greater than 10°K when the soil is dry. In the original bucket method, this difference is ignored by using T to calculate E , which then brings about an inappropriate estimag p tion of latent heat flux. In E q uation (2 . la), the single unknown variable is therefore the skin temperature T;. Mahrt and Ek (1984) showed that Penman's potential ET formula can be derived by starting from E q uation (2. la) and ignoring the effect of skin temperature, T;, on the outgoing longwave radiative flux and the ground heat flux. Such elimination is precisely what was done by Penman (1948) . In the modeling system used in this research (the PSU/NCAR MM4), the sensible heat flux (H) and potential ET (E ) are parameterized as: Pa is air density for the lowest model level; K is the von Karman constant (0.4); u* is friction velocity; e; is potential temperature of saturated soil surface; e a is potential temperature of the lowest model level; z .
is the height of the lowest model level; z 0 is roughness length; \jf h is the nondimensional stability parameter based on the similarity theory; q sa t ( T;) is the satura tion mixing ratio at T;; qa is the mixing ratio at the lowest model level; K . is the molecular diffusivity; and Z 1 is the depth of the molecular layer. Using Taylor's expansion, in which T . is the temperature at the lowest model level. Also, given (2.5) (2.6) with E= 0.622, R = 287.04 Joule/(kg°K), and L v =latent heat of vaporization, Teten's formula (Bolton, 1980) can be used to estimate q . E can then be expressed as:    Monteith ( 1965) and others suggested that, in the presence of plants, the stomatal resistance (r) must be included. In this research, the stomata} resistance r, (as defined by the resistance under no water stress) is set at 90 sm-1 (following Monteith 1965, Pan 1990, Pan et al. 1996.
As such: It should be noted that the above derivation of the PM method is aimed at obtaining potential ET. As for the predicted surface temperature (T ), the MM4 uses a force-restore slab g model based on the surface energy equation developed by Blackadar (1976): where C is the thermal capacity of the slab per unit area (Jm-2K-1); the terms on the right hand (1) excludes the use of the hypothetical saturation mixing ratio at ground surface to estimate the moisture gradient between the ground surface and the lowest model level; (2) includes the effect of stomatal resistance; and (3) uses surface energy balance as a bound to estimate the potential ET in each model grid.
Based on the above-stated procedure to obtain the formulation of the PM method, the potential ET estimated by. the PM method is a function of Rnet ' Hm and Hs. Obvious, therefore, is that during the daytime, when Hm and H, are positive, from the surface energy balance point of view (Equations 2.1 and 2.2), the upper bound of potential ET should be the net radiation at the ground surface. In contrast, the potential ET estimated by the bucket method tends to be unbounded as is demonstrated in Section 4.2.

THE MESOSCALE MODEL PERFORMANCE
The PSU/NCAR MM4, as described by Anthes and Warner (1978) and Anthes et al. (1987), is the modeling system used in this research. It contains various moist convective parameterization schemes and relatively detailed boundary layer processes (Blackadar 1976, Deardorff 1972). During the model simulations, an explicit moisture scheme (i.e., the variabil-ity of water vapor, cloud water and rain water are predicted; Dudhia 1989), multiple model levels in the planetary boundary layer and the time dependent inflow/outflow lateral boundary conditions are used.
As explained in many classical papers (such as those by Blackadar 1976, Deardorff 1972) and Chen (1996), the surface ET is expressed as: where p is the air density; L v is the latent heat of vaporization; Kq is the turbulent diffusion coefficient of water vapor; and d q / d z is the moisture gradient close to the ground surface.
Surface ET from the land surface in the MM4 is parameterized by a bucket-type method, following the concept pioneered by Manabe ( 1969). The exact formulation for the calculation of latent heat flux used in the MM4 is based on the work by Carlson and Boland (1978) as shown in Equations 2.2 and 2.4. It is now demonstrated how greatly the model's estimation of surface ET is improved with the implementation of the PM method.
The estimated surf ace ET by the model is contrasted with the corresponding observations from the SGP ARM site. The measurement of surface ET and the associated observational error characteristics are discussed in Chen (1996). In addition, observational data, such as latent heat flux, sensible heat flux, net radiation flux at the ground surface, near surface air temperature, near surface moisture content and surface pressure, etc., taken from three obser vational stations in the SGP ARM site (i.e., E9 at 36.43°N, 98.28°W; E13 at 36.6°N, 97.48°W; and E15 at 37.13°N, 97.26°W, as shown in Figure 3.1) are averaged for January, April, July and October of 1995. These represent the mean state of the atmospheric surface layer and ground conditions in different seasons and are used for verification against model simulation results from the model grid that is closest to the 3 SGP ARM observation stations, which is located at 36.24°N and 97.64°W.
It may be considered remarkable that data from the 360 x 400 km domain of the SGP ARM site (centered at 36.73°N, 97.54°W) can readily reveal systematic errors in a complex numerical model. However, the accuracy of the forecast model over the dense US network, the representativeness of the SGP ARM surface data and the existence of a long time series to select weather regimes (such as sunny and non-rainy days in different seasons) make this kind of verification relatively straightforward. Often, errors at one or two grid points of the numeri cal model (closest to the SGP ARM site) are representative of continental-scale errors since they represent systematic errors in the model formulation. The variation in the MM4 is rela tively smooth over the region of Kansas and Oklahoma and if an adjacent grid point in the model was chosen, similar conclusions would be certainly reached about t h e model errors . It should be noted that several quantities used for verification against model results, such as ground surface (skin) temperature, temperature at about 40m above ground level (AGL) and mixing ratio at about 40m AGL (40m AGL is the model's lowest level in the atmosphere) are not directly observed at the SGP ARM site; on the contrary, they are derived from the two-level (one-and two-meter height) air temperatures and mixing ratios taken from the SGP ARM stations based on the atmospheric surface layer similarity theory (Paulson 1970, Nickerson and Smiley 1975, Benoit 1977). An iterative shooting scheme is designed to determine these quantities. The detailed procedures can be found in Chen (1996). A series of model runs using the Anthes/Kou (Anthes, 1977)   ( 1) There is a clear tendency for RMS errors to decrease with increased forecasting time in January, April, July and October 1995 except for the 49-72 hr forecast period in July. The - Vol. 8, No. 4, December 1997 GMT GMT >< 400 ::s c OJ 300 <!) ..<:: factor leading to an increase in the RMS error for the 49-72 hr forecast period in July is discussed in Section 4. The nighttime RMS errors are much smaller than daytime ones, but these differences decrease with increased forecasting time.
(2) There is also a definite tendency for percentage errors to decrease with increased forecast ing time. The mean percentage errors for nighttime are evidently greater than those for daytime.
(3) Together with the RMS error analysis, it appears that the model has a higher variability in the estimation of nighttime surface ET than that for daytime. Thus, it can be said that the model has a greater chance of capturing the trend of surface ET in daytime.
From the above discussion, it is clear that the model using the bucket method is better able to adequately estimate latent heat flux as the forecasting time is extended. Both the percentage and RMS errors decrease with increased forecasting time, which is due to the spinup effect resulting from the inadequate assignment of the initial skin temperature and accompanying moisture gradient at the model's ground surface. There is no routine surface observation on the skin temperature. The model is initialized with a skin temperature and the associated mois ture gradient at the ground surface which are both extrapolated from coarse conventional sound ing and surface observational data. Hence, in the beginning of simulation, the model cannot well determine the skin temperature and the associated saturation surface mixing ratio used to calculate potential ET (see Equations 2.2 and 2.4) in the bucket method. It is evident, there fore, that the model makes a very poor estimation of ET initially. As the forecasting time is extended, however, the model gradually adjusts its simulation of skin temperature and the associated moisture gradient at the ground surface in accordance with surface energy balance constraints. In other words, an improved calculation of ET is shown to result from the adjust ment of skin temperature and from a more reasonable (better) estimation of the associated moisture gradient between the ground surface and lowest model level, as the forecasting time is extended. In the simple bucket method used in the MM4, the latent heat flux from the land surface is parameterized using the bulk-aerodynarnical formula, as shown by Equations (2.2) and (2.4). In Equation (2.2), the factor Mi s defined as the ratio between the soil moisture content and (2) the use of the saturation mixing ratio at skin temperature as the surface mixing ratio.
Moisture availability (M) is regarded as the ratio of actual ET to its potential value. The concept of moisture availability was first suggested by Tanner and Pelton (1961) and later elaborated upon by Nappo (1975). This parameter basically expresses the efficiency of surface evaporation and is a fraction of the maximum possible evaporation for a saturated surface. M can be conceived as a measure of water saturation at ground surface. The use of the moisture availability concept is necessitated by the fact that the air layer in contact with the ground is not saturated except in those cases where the surface of the terrain is essentially saturated with water. The factor M is introduced to account for the reduction in the efficiency of evaporation due to the subsaturation of the ground surface. M probably approaches 1.0 over natural sur faces following a substantial rainfall, but for dry conditions or over artificial surfaces, such as concrete or developed urban areas, M may be quite low and basically independent of rainfall except for short periods following precipitation. For vegetation, M is related to the internal resistance (bulk stomata! diffusion resistance) discussed by Monteith (1975). Over vegetated terrain, M may also decrease with prolonged dryness and fall rather rapidly to low values after the wilting point is reached. Mis shown to be a complex function of soil type, canopy, vegeta tion, season and so on. (Taconet et al. 1986, Wetzel and Chang 1988, Gillies and Carlson 1995 In the bucket method, M is set to an empirical value as a function of land use and season, which on a daily basis tends to be far from reality. When the soil is wet, some stomatal res�s tance still remains in the plants which reduces ET from its potential value. When the soil is dry, ground surface temperature tends to be too high due to solar heating during the daytime, for example. Using it to determine the saturation surface mixing ratio, therefore, results in an overestimation of the potential value. In both situations, either wet or dry, the bucket method tends to overestimate ET, as illustrated in the above composite study of model runs. It is also shown in Section 4 that the MM4 tends to have a warmer lower atmosphere during nighttime, which would lead to stronger downward longwave radiation (greenhouse effect) during nighttime such that the model's nighttime skin temperature would tend to be warmer than the corresponding observation (see Figure 4.3, as one example). This causes the saturation mixing ratio at skin temperature during nighttime to be high -even higher than the mixing ratio at the lowest model level. Water molecules underground then have extra kinetic energy to get into the air; thus, there is always ET coming from the model's ground surface during nighttime though the observations show near zero ET (see Figure 3.3, for instance).

THE EFFECT OF PENMAN-MONTEITH METHOD
The Penman-Monteith (PM) method to calculate the potential ET over land area is imple mented into the MM4 in hope of improving the model's estimation of latent heat flux. Obser vational data taken from three observation stations in the SGP ARM site are averaged for January, April, July and October 1995 to serve as the mean state of atmospheric surface layer and ground conditions. Seventy-two-hour model simulations are executed �uring the same months. The hourly averages of the model output at a grid point that is closest to the 3 obser vation stations are compared to the corresponding observational data set. It should be noted that surface fluxes, temperature and moisture during the daytime are discussed more frequently than those during the nighttime in the following discussion since errors related to these surface fluxes during the daytime can penetrate over deep layers and therefore affect the synoptic pressure fields (Beljaars et al., 1996).

1 For1-24 hr Forecast Period
The bucket method has a tendency to overestimate latent heat flux (LHF) by 103%, 56%, 30% and 102% during the daytime in January, April, July and October, respectively, during the first 24-hr forecast period (Figure 3.3 and Table 3.1). However, the PM method effectively reduces the potential ET (PE) (by 17%, from 53 Wm-2 with the bucket method to 44 wm-2 with the PM method in January, for instance) by setting an upper bound to the PE. It causes the model to overestimate LHF by only 67%, 37%, 14% and 63% in January, April, July and October, respectively, during the daytime. The RMS errors for LHF are also decreased when the PM method is in use. For example, in July the RMS error for LHF is 65 Wm-2 with the bucket method but 29 Wm-2 with the PM method.
Since there is too much evaporative cooling associated with the bucket method, it follows that the surface temperature is too cold during the daytime. To illustrate, the mean skin tem perature in the model using the bucket method is 20% colder than the corresponding observa tion in January. The model with the PM method, on the other hand, generates less LHF, thereby producing a higher daytime skin temperature and subsequently a higher daytime sensible heat flux (SHF). In January and April, the bucket method is associated with a mean daytime skin temperature of 5.1 and 16.3°C, respectively (Figure 4.3 and Table 4.3). Whereas, the PM method is associated with a mean daytime skin temperature of 5.6 and 18.7°C, respectively. Observations, in fact, show a mean skin temperature of 6.3 and 20.0°C in January and April,  mean SHF of 108 wm-2• The main reason for this difference is that it is predicted that the temperature gradient between the model's ground surface and lowest model level is much smaller than the corresponding observation, such that not enough heat can be emitted from the model's ground surface into the air in October. The mean daytime temperature gradients are -0.3 and +0.2°C for the model with the bucket and PM methods, respectively. The correspond ing observations show a mean value of +4.4°C. The model's lowest model level is warmer when SHF is greater owing to the use of the PM method (Figure 4.2). In April, the PM method results in a mean daytime temperature at the lowest model level of 16.5°C. The bucket method is associated with a mean daytime temperature at the lowest model level of 14.9°C. The corre sponding observations reveal a mean value of 14.8°C in April. The PM method tends to generate less LHF than the bucket method which means there is less moisture supply from the ground surface. This naturally leads to a reduced chance of low level cloud formation. In this forecast period, there is a 26% possibility of low-level cloud formation in the model using the bucket method in January, but only a 16% possibility for low-level cloud formation in the model using the PM method during the same time period. This increases the possibility for incoming shortwave and longwave radiation to reach the model's ground surface during the daytime. Net radiation at the ground surface (R ) during  the daytime is then expected to be greater when the PM method is utilized. As shown in Figure  4.4 and Table 4.4, mean daytime R is adJ·usted from an underestimation of 3% (bucket method) net to an overestimation of 4% (PM method) in January. R is increased by 20% via the use of the net PM method in April. Both the PM and bucket methods contribute to an outstanding prediction of R in October. With either method, the daytime forecast error of R in the model is less net net than 6% in October. Less moisture is available at the ground surface when the PM method is in use which means that there is less moisture content in the model's lower atmosphere. The bucket method offers a better estimation of the mixing ratio at the lowest model level during the nighttime, while the PM method gives a more accurate estimation of the mixing ratio at the model's lowest level during the daytime in January (Figure 4.5a). The daily -nighttime plus daytime average mixing ratio at the model's lowest level are 4. 1 and 7 .5 g/kg for the model with the bucket method in January and April, respectively, but the same ratios are 3.8 and 6.5 g/kg for the model with the PM method. The corresponding observations show mean values of 3.9 and 6.7 g/kg in January and April, respectively. The rapid increase in the mixing ratio at the lowest model level shown by the bucket method during the daytime of April is obviously dampened by the use of the PM method (Figure 4.5b ). The model using the bucket method is skillful at predicting nighttime moisture content at 40m AGL, yet unable to predict the same trend for daytime in July (18.1 g/kg) (Figure 4.5c ). In contrast, the PM method is associated with a much better simulation of the mixing ratio at 40m AGL during the daytime in July (15.7 g/kg). The corresponding observations show a mean value of 15.0 g/kg in July. Again, the model's  forecast of mixing ratio at 40m AGL in October (Figure 4.5d) is evidently improved by the use of PM method (7 .2 g/kg). The bucket method leads to a moistening of the lowest model level atmosphere, which is very unrealistic (8.0 g/kg). The corresponding observations show a mean value of 6.5 g/kg in October.
----· lllfl ll TAO, Vol. 8, No. 4, December 1997    tively. The corresponding observations show a mean value of 379 Wm·2• It should be stated that the daytime mean PE (358 Wm·2) estimated by the bucket method exceeds the mean daytime R n et in the model during the same period. This is a very unrealistic feature and is one of the major flaws of the bucket method. Neither the bucket nor the PM method can make a good estimation of daytime SHF in January. Both methods lead to an underestimation of day time SHF although the PM method does show some improvement (Figure 4. 7). The mean daytime SHF are estimated to be 8 and 13 wm·2 using the bucket and PM methods, respec tively, in January. The corresponding observations reveal a mean SHF of 44 Wm·2• It is sug gested that the main reason for this error is that the temperature gradient between the ground surface and lowest model level is in the opposite direction from the corresponding observa-, tion. The model with both the bucket and PM methods shows a mean daytime temperature gradient of -l.0°C in January. The observations reveal a mean temperature gradient of +2.5°C. When compared to the bucket method, the mean daytime SHF, in April, generated by the model is doubled (from 57 t� 119i Wm·2) and is very similar to the corresponding observation (134 wm -2) when the PM method is in effect. In October, the bucket method leads to a 47% overestimation of moisture content at the lowest model level (Figure 4.6). The PM method, in contrast, results in an overestimation of 17%, a significant degree of drying.
During the 49-72 hr forecast period, the bucket method has a tendency to overestimate LHF by 65%, 15% and 44% during the daytime in January, April and October, respectively, and to underestimate LHF by 10% in July (Figure 3.5 and Table 3.3). The PM method causes the model to overestimate LHF by only 51% and 27%, in January and October, respectively, but underestimate LHF by 10% and 11 % in April and July, respectively. For the bucket method used for July, it is found that the skin temperature and the associated saturation surface mixing ratio are too low (Figure 4.8), while the lower atmosphere is too moist (the mixing ratio at the lower atmosphere is too high, see Figure 4.9) during this forecast period, such that the corre sponding moisture gradient between the ground surface and lowest model level is 10-13 g/kg (or 50-60%) less than that from observation. This leads to a significant underestimation of the  potential ET by the bucket method, causing the ET to be reduced significantly in the model. In April and July, the PM method results in an underestimation of ET. The main reason is still that the stomatal resistance (90 sm·1) used in this study is too large for the growing season.

SUMMARY AND CONCLUSIONS
The bucket method demonstrates the expected overestimation of LHF emitted from the model's ground surface. The PM method to estimate the potential ET over land area is intro duced into the MM4 to solve this problem. Since the PM method sets an upper bound for the estimation of potential ET, the LHF estimated by the model is no longer too unreasonable. From the above discussion, six important facts are noted.  (1 ) For the first 24-hr forecast period, the model tends to severely overestimate LHF, especially in the cold season (January and October) due to the spinup effect resulting fro m the im proper assignment of the initial skin temperature. Both the percentage and RMS errors to estimate LHF by the model decrease with increased forecasting time in accordance with the constraint of surface energy balance.
(2) There is always ET coming fro m the model 's surface during the nighttime while observa tions show near -zero ET in the same time period. This is due to an inappropriate simu lation of the skin temperature as a result of the improper prediction of the lower atmospheric temperature.
(3) The bucket method tends to make an est imation of PE that is not within the bounds of  energy balance at ground surface during the daytime in July. This is one of the major draw backs of the bucket method.
(4) The PM method can effectively reduce the degree of the model's overestimation of LHF for the months of January, April, July and October. The improvement is most significant during the first 24-hr forecast period. The assignment of sto m ata! resistance, given a fixed mois ture availability, is crucial to whether the PM method overestimates or underestimates day time LHF in different seasons. It is proposed that in a future study by the authors a canopy soil model will be implemented into the numerical model to simulate the diurnal and sea sonal variability of stomata! resistance to account for different soil types (and their relative wetness), vegetation types (leaf area index, etc.), etc. This will enable the stomata! resis tance used in the model to realistically represent canopy transpiration, evaporation from wet canopy (dew, or precipitation intercepted by canopy), evaporation from ground soil and so on.
-·-····· qt.pm Fig. 4.9. Same as Figure 4.8 but for mixing ratio (g/kg) at the lowest model level in July 1995. (5) Less surface evap orative cooling as implied by the PM method leads to a better estimation of skin temperature and SHF by the model, especially during the daytime. The PM method is associated with a higher temperature at the lowest model level due to more available SHF.
( 6) The model using the PM method better estimates the net radiation at ground surf ace due to a reduced chance of low-level cl oud formation from a more reasonable moistu re supply from the ground surf ace by the use of the PM method.