Disaggregation of screen-level variables in a numerical weather prediction model with an explicit simulation of subgrid-scale land-surface heterogeneity

The earth’s surface is characterized by small-scale heterogeneity attributable to variability in land cover, soil characteristics and orography. In atmospheric models, this small-scale variability can be partially accounted for by the so-called mosaic approach, i.e., by computing the land-surface processes on a grid with an explicit higher horizontal resolution than the atmosphere. The mosaic approach does, however, not account for the subgrid-scale variability in the screen-level atmospheric parameters, part of which might be related to land-surface heterogeneity itself. In this study, simulations with the numerical weather prediction model COSMO are shown, employing the mosaic approach together with a spatial disaggregation of the atmospheric forcing by the screen-level variables to the subgrid-scale. The atmospheric model is run with a 2.8?km horizontal grid resolution while the land surface processes are computed on a 400-m horizontal grid. The disaggregation of the driving atmospheric variables at screen-level is achieved by a three-step statistical downscaling with rules learnt from high-resolution fully coupled COSMO simulations, where both, atmosphere and surface, were simulated on a 400-m grid. The steps encompass spline interpolation of the grid scale variables, conditional regression based on the high-resolution runs, and an optional stochastic noise generator which restores the variability of the downscaled variables. Simulations for a number of case studies have been carried out, with or without mosaic surface representation and with or without atmospheric disaggregation, and evaluated with respect to the surface state variables and the turbulent surface exchange fluxes of sensible and latent heat. The results are compared with the high-resolution fully coupled COSMO simulations. The results clearly demonstrate the high importance of accounting for subgrid-scale surface heterogeneity. It is shown that the atmospheric disaggregation leads to clear additional improvements in the structures of the two-dimensional surface state variable fields, but to only marginally impacts on the simulation of the turbulent surface exchange fluxes. A detailed analysis of these results identifies strongly correlated errors in atmospheric and surface variables in the mosaic approach as the main reason for the latter. The effects of these errors largely cancel out in the flux parameterization, and thus explain the comparably good results for the fluxes in the mosaic approach without atmospheric disaggregation despite inferior performance for the surface state variables themselves. Inserting noise in the disaggregation scheme leads to a deterioration of the results.     

Latent heat fluxes simulated with a non-hydrostatic weather forecast model using actual surface properties from measurements and remote sensing

In this study the influence of land-surface parameters on latent heat fluxes simulated with the numerical weather prediction model Lokalmodell (LM) of the German Meteorological Service is investigated. The area of interest is the LITFASS area during the LITFASS-2003 campaign. Based on simulations with varying soil and vegetation properties, we confirm that simulated latent heat fluxes strongly depend on soil moisture and leaf area index. Both parameters are difficult to obtain from in situ measurements with sufficient spatial resolution over heterogeneous land surfaces. Therefore, a procedure is proposed to determine area average values of soil moisture from time domain reflectometer measurements performed at a limited number of sites. The area averages cover the 7 × 7 km² grid cells of the LM around Lindenberg (south-east of Berlin). Furthermore, satellite inferred plant parameters from NOAA–AVHRR are used to initialise model runs; the derived vegetation parameters show notable differences with those in the standard input of LM. The latent heat fluxes from the LM are compared with the aggregated eddy-covariance-measurements, and while the operational LM shows a strong overestimation of latent heat fluxes, it is demonstrated that the application of land-surface parameters derived from measurements can significantly reduce the deviation between the simulated and measured latent heat fluxes.     

下垫面非均匀性的模拟

用美国大气科学中心ＧＥＮＥＳＩＳ模式中的陆面过程方案,我们在一个全球大气模式网格尺度范围内,研究了来自非均匀下垫面的水汽,能量等通量。基于３种不同的模拟下垫面非均匀性的方法,即马赛克法、混合法以及显式次网格法,我们设计了４种不同的试验。模拟结果表明,３种方法计算出的结果有很大的不同：地面吸收的太阳辐射差异达４％;感热通量达１２％;潜热通量达６６％;土壤水分可达３０％。这一结果说明有必要用实测数据来检验不同的模拟下垫面非均匀性的方法以及用区域气候模式来模拟下垫面的非均匀性。     

GRAPES NOAH-LSM陆面模式水文过程的改进及试验研究

土壤含水量的计算影响着陆面过程的能量平衡和水量平衡,是陆面模式的核心计算要素之一。目前,GRAPES_Meso模式采用的NOAH-LSM(Noah-Land Surface Model)陆面模式既不能有效地表达径流产源面积的变动情况,也不能完整描述水文循环过程。本次试验针对以上问题对其进行了改进:(1)加入蓄水容量曲线,考虑网格内产流面积的变化及土壤含水量的不均匀性;(2)加入汇流模式,以考虑水平二维水分再分配,提高模式对径流和流量模拟能力。选取2008年8月至9月降水进行模拟试验,研究陆面水循环过程对近地面气象要素的影响。结果表明:改进后的模式模拟土壤湿度、2 m温度等近地面气象要素更接近观测值,并最终对降水量以及降水落区也产生了一定的影响。     

Relevance of soil moisture for seasonal climate predictions: a preliminary study

In the framework of the Global Soil Wetness Project (GSWP), the ISBA land-surface scheme of the ARPEGE atmospheric general circulation model has been forced with meteorological observations and analyses in order to produce a two-year (1987–1988) soil moisture climatology at a 1^°×1^° horizontal resolution. This climatology is model dependent, but it is the climatology that the ARPEGE model would produce if its precipitation and radiative fluxes were perfectly simulated. In the present study, ensembles of seasonal simulations (March to September) have been performed for 1987 and 1988, in which the total soil water content simulated by ARPEGE is relaxed towards the GSWP climatology. The results indicate that the relaxation has a positive impact on both the model's climatology and the simulated interannual variability, thereby confirming the utility of the GSWP soil moisture data for prescribing initial or boundary conditions in comprehensive climate and numerical weather prediction models. They also demonstrate the relevance of soil moisture for achieving realistic simulations of the Northern Hemisphere summer climate. In order to get closer to the framework of seasonal predictions, additional experiments have been performed in which GSWP is only used for initialising soil moisture at the beginning of the summer season (the relaxation towards GSWP is removed on 1st June). The results show a limited improvement of the interannual variability, compared to the simulations initialised from the ARPEGE climatology. However, some regional patterns of the precipitation differences between 1987 and 1988 are better captured, suggesting that seasonal predictions can benefit from a better initialisation of soil moisture.     

Simulating evapotranspiration in a semi-arid environment

Summary In this work, simulations with the mesoscale meteorological model FOOT3DK for a semi-arid research site in southern morocco are presented. The main aim of this study is to introduce two different ways to improve the soil moisture distribution towards a more realistic pattern. One of them resembles the availability of groundwater resources below the lower boundary of the soil part of the model, the other one resembles irrigation practices in the region. Additionally, we introduce a newly derived land use/land cover data set obtained from analysis of LANDSAT data and compare the simulation results to those obtained with the USGS GLCC data. To evaluate the results with the refinements in soil moisture and land use/land cover, we focus on evapotranspiration, as the quantity which is most tentative to the changes in soil moisture and is an important part of the local hydrological cycle. To evaluate the importance of sub-grid scale surface heterogeneity in soil moisture and land use/land cover, we present simulations with enhanced surface resolution. Simulation results are compared to point measurements at different sites in the research area for validation.The results show, that a deep groundwater table and irrigation of parts of the research area can be represented by the methods we used. Simulated transpiration is overestimated compared to measured values, but this is due to the maximum approach used in this work. Finer tuning of the artificial enhancement of soil moisture with the two methods presented here are expected to lead to realistic distributions of evapotranspiration and related quantities, therewith drastically enhancing simulation accuracy for this site. As uncertainties of soil moisture distribution and restricted representation of soil moisture dynamics in meteorological models is a common problem especially for arid and semi-arid sites, we expect our results to be useful for meteorological simulations in other arid or semi-arid areas as well.     

Heat and moisture budgets from airborne measurements and high-resolution model simulations

High-resolution simulations with a mesoscale model are performed to estimate heat and moisture budgets of a well-mixed boundary layer. The model budgets are validated against energy budgets obtained from airborne measurements over heterogeneous terrain in Western Germany. Time rate of change, vertical divergence, and horizontal advection for an atmospheric column of air are estimated. Results show that the time trend of specific humidity exhibits some deficiencies, while the potential temperature trend is matched accurately. Furthermore, the simulated turbulent surface fluxes of sensible and latent heat are comparable to the measured fluxes, leading to similar values of the vertical divergence. The analysis of different horizontal model resolutions exhibits improved surface fluxes with increased resolution, a fact attributed to a reduced aggregation effect. Scale-interaction effects could be identified: while time trends and advection are strongly influenced by mesoscale forcing, the turbulent surface fluxes are mainly controlled by microscale processes.     

Soil moisture prediction over the Australian continent

Summary This paper describes an attempt to model soil moisture over the Australian continent with an integrated system of dynamic models and a Geographic Information System (GIS) data base. A land surface scheme with improved treatment of soil hydrological processes is described. The non-linear relationships between soil hydraulic conductivity, matric potential and soil moisture are derived from the Broadbridge and White soil model. For a single location, the prediction of the scheme is in good agreement with the measurements of the Hydrological and Atmospheric Pilot Experiment (HAPEX). High resolution atmospheric and geographic data are used in soil moisture prediction over the Australian continent. The importance of reliable land surface parameters is emphasized and details are given for deriving the parameters from a GIS. Predicted soil moisture patterns over the Australian continent in summer, with a 50 km spatial resolution, are found to be closely related to the distribution of soil types, apart from isolated areas and times under the influence of precipitation. This is consistent with the notion that the Australian continent in summer is generally under water stress. In contrast, predicted soil temperatures are more closely related to radiation patterns and changes in atmospheric circulation. The simulation can provide details of soil moisture evolution both in space and time, that are very useful for studies of land use sustainability, such as plant growth modelling and soil erosion prediction.With 12 Figures     

The effect of mountainous topography on moisture exchange between the “surface” and the free atmosphere

Typical numerical weather and climate prediction models apply parameterizations to describe the subgrid-scale exchange of moisture, heat and momentum between the surface and the free atmosphere. To a large degree, the underlying assumptions are based on empirical knowledge obtained from measurements in the atmospheric boundary layer over flat and homogeneous topography. It is, however, still unclear what happens if the topography is complex and steep. Not only is the applicability of classical turbulence schemes questionable in principle over such terrain, but mountains additionally induce vertical fluxes on the meso-γ scale. Examples are thermally or mechanically driven valley winds, which are neither resolved nor parameterized by climate models but nevertheless contribute to vertical exchange. Attempts to quantify these processes and to evaluate their impact on climate simulations have so far been scarce. Here, results from a case study in the Riviera Valley in southern Switzerland are presented. In previous work, measurements from the MAP-Riviera field campaign have been used to evaluate and configure a high-resolution large-eddy simulation code (ARPS). This model is here applied with a horizontal grid spacing of 350 m to detect and quantify the relevant exchange processes between the valley atmosphere (i.e. the ground “surface” in a coarse model) and the free atmosphere aloft. As an example, vertical export of moisture is evaluated for three fair-weather summer days. The simulations show that moisture exchange with the free atmosphere is indeed no longer governed by turbulent motions alone. Other mechanisms become important, such as mass export due to topographic narrowing or the interaction of thermally driven cross-valley circulations. Under certain atmospheric conditions, these topographical-related mechanisms exceed the “classical” turbulent contributions a coarse model would see by several times. The study shows that conventional subgrid-scale parameterizations can indeed be far off from reality if applied over complex topography, and that large-eddy simulations could provide a helpful tool for their improvement.     

Boundary Conditions for Scalar (Co)Variances over Heterogeneous Surfaces

The problem of boundary conditions for the variances and covariances of scalar quantities (e.g., temperature and humidity) at the underlying surface is considered. If the surface is treated as horizontally homogeneous, Monin–Obukhov similarity suggests the Neumann boundary conditions that set the surface fluxes of scalar variances and covariances to zero. Over heterogeneous surfaces, these boundary conditions are not a viable choice since the spatial variability of various surface and soil characteristics, such as the ground fluxes of heat and moisture and the surface radiation balance, is not accounted for. Boundary conditions are developed that are consistent with the tile approach used to compute scalar (and momentum) fluxes over heterogeneous surfaces. To this end, the third-order transport terms (fluxes of variances) are examined analytically using a triple decomposition of fluctuating velocity and scalars into the grid-box mean, the fluctuation of tile-mean quantity about the grid-box mean, and the sub-tile fluctuation. The effect of the proposed boundary conditions on mixing in an archetypical stably-stratified boundary layer is illustrated with a single-column numerical experiment. The proposed boundary conditions should be applied in atmospheric models that utilize turbulence parametrization schemes with transport equations for scalar variances and covariances including the third-order turbulent transport (diffusion) terms.     

A simple soil moisture scheme for regional climate simulations in the tropics

Summary A regional climate model (RCM) is described which incorporates an improved scheme for soil moisture availability (SMA) compared to an earlier version. The improvement introduces a sensitivity of SMA to soil type, vegetation cover and ground albedo, making the model more adaptable to divers regions. In addition, the interactive SMA depends on past precipitation, ground temperature and terrain relief. Six RCM simulations of the monthly mean climate over southern Africa are performed at 0.5° grid spacing. Improvements in the RCM climate simulations compared to control runs are attributed to the newer SMA scheme. Only a slight improvement in skill results from driving the RCM with observational analyses as opposed to GCM “predicted” lateral boundary conditions. The high spatial resolution of the RCM provides a distinct advantage in the simulated spatial distribution of precipitation compared with a global model run at an effective grid spacing of 2.8°. The mesoscale precipitation signal in the RCM simulations is more dominant during the rather dry December 1982 than during December 1988. The improved SMA scheme contributed to a realistic partition between latent and sensible heat fluxes at the ground-atmosphere boundary and consequently a realistic diurnal cycle of ground temperature. Simulated differences in the spatial distribution of rainfall between December 1982 and December 1988 are more realistic with the improved scheme. Received June 28, 2001 Revised August 27, 2001     

Effects of land-surface heterogeneity on numerical simulations of mesoscale atmospheric boundary layer processes

Landscape heterogeneity that causes surface flux variability plays a very important role in triggering mesoscale atmospheric circulations and convective weather processes. In most mesoscale numerical models, however, subgrid-scale heterogeneity is somewhat smoothed or not adequately accounted for, leading to artificial changes in heterogeneity patterns (e.g., patterns of land cover, land use, terrain, and soil types and soil moisture). At the domain-wide scale, the combination of losses in subgrid-scale heterogeneity from many adjacent grids may artificially produce larger-scale, more homogeneous landscapes. Therefore, increased grid spacing in models may result in increased losses in landscape heterogeneity. Using the Weather Research and Forecasting model in this paper, we design a number of experiments to examine the effects of such artificial changes in heterogeneity patterns on numerical simulations of surface flux exchanges, near-surface meteorological fields, atmospheric planetary boundary layer (PBL) processes, mesoscale circulations, and mesoscale fluxes. Our results indicate that the increased heterogeneity losses in the model lead to substantial, nonlinear changes in temporal evaluations and spatial patterns of PBL dynamic and thermodynamic processes. The decreased heterogeneity favor developments of more organized mesoscale circulations, leading to enhanced mesoscale fluxes and, in turn, the vertical transport of heat and moisture. This effect is more pronounced in the areas with greater surface heterogeneity. Since more homogeneous land-surface characteristics are created in regional models with greater surface grid scales, these artificial mesoscale fluxes may have significant impacts on simulations of larger-scale atmospheric processes.     

Simulation of surface energy fluxes using high-resolution non-hydrostatic simulations and comparisons with measurements for the LITFASS-2003 experiment

Land-surface heterogeneity effects on the subgrid scale of regional climate and numerical weather prediction models are of vital interest for the energy and mass exchange between the surface and the atmospheric boundary layer. High-resolution numerical model simulations can be used to quantify these effects, and are a tool used to obtain area-averaged surface fluxes over heterogeneous land surfaces. We present high-resolution model simulations for the LITFASS area near Berlin during the LITFASS-2003 experiment, which were carried out using the non-hydrostatic model FOOT3DK of the University of Köln with horizontal resolutions of 1 km and 250 m. The LITFASS-2003 experimental dataset is used for comparison. The screen level quantities show good quality for the simulated pressure, temperature, humidity and wind speed and direction. Averaged over the four week experimental period, simulated surface energy fluxes at land stations show a small bias for the turbulent heat fluxes and an underestimation of the net radiation caused by excessive cloudiness in the simulations. For eight selected days with low cloud amounts, the net radiation bias is close to zero, but the sensible heat flux shows a strong positive bias. Large differences are found for latent heat fluxes over a lake, which are partly due to local effects on the measurements, but an additional problem seems to be the overestimation of the turbulent exchange under stable conditions in the daytime internal boundary layer over the lake. In the area average over the LITFASS area of 20 ×  20 km², again a strong positive bias of 70 W m^?2 for the sensible heat is present. For the low soil moisture conditions during June 2003, the simulation of the turbulent heat fluxes is sensitive to variations in the soil type and its hydrological properties. Under these conditions, the supply of ground water to the lowest soil layer should be accounted for. Different area-averaging methods are tested. The experimental set-up of the LITFASS-2003 experiment is found to be well suited for the computation of area-averaged turbulent heat fluxes.     

Sensitivity of an ecosystem model to hydrology and temperature

We tested the sensitivity of a dynamic ecosystem model (LPJ-GUESS) to the representation of soil moisture and soil temperature and to uncertainties in the prediction of precipitation and air temperature. We linked the ecosystem model with an advanced hydrological model (JULES) and used its soil moisture and soil temperature as input into the ecosystem model. We analysed these sensitivities along a latitudinal gradient in northern Russia. Differences in soil temperature and soil moisture had only little influence on the vegetation carbon fluxes, whereas the soil carbon fluxes were very sensitive to the JULES soil estimations. The sensitivity changed with latitude, showing stronger influence in the more northern grid cell. The sensitivity of modelled responses of both soil carbon fluxes and vegetation carbon fluxes to uncertainties in soil temperature were high, as both soil and vegetation carbon fluxes were strongly impacted. In contrast, uncertainties in the estimation of the amount of precipitation had little influence on the soil or vegetation carbon fluxes. The high sensitivity of soil respiration to soil temperature and moisture suggests that we should strive for a better understanding and representation of soil processes in ecosystem models to improve the reliability of predictions of future ecosystem changes.     

Comparison of two land surface schemes in week-long cloud-system-resolving simulations of warm season precipitation

This paper presents a case study of the impact of land surface treatment on warm season precipitation simulations at convection-permitting grid resolution. Two surface schemes are tested: Dudhia’s five-layer soil model (FLSM) and the Noah land-surface model (NLSM). The experimentation case involves a 1-week episode of active summertime convection over the central United States. The overall precipitation features, such as the diurnal regeneration of zonally propagating rainfall episodes and the spatial distribution of accumulative rainfall, are adequately replicated by the two parameterizations. In comparison, NLSM produces roughly 12% more and broader rainfall than FLSM. This differential rainfall amount is consistent with the differential surface moisture fluxes between the two schemes, whereas the precipitation feedback plays a negligible role. It is also found that FLSM generates comparatively stronger sensible heat transports from the land surface and thus a warmer temperature near the surface.     

Simulation of Pollutant Transport in Complex Terrain with a Numerical Weather Prediction–Particle Dispersion Model Combination

A new scaling approach, based on the convective velocity obtained from the sun-exposed eastern slopes and thus suited for steep and narrow Alpine valleys, is investigated with respect to pollutant dispersion. The capability of the new method is demonstrated with the operational emergency response system of MeteoSwiss, which consists of the COSMO (COnsortium for Small-scale MOdelling) numerical weather prediction model coupled with a Lagrangian particle dispersion model (LPDM). The new scaling approach is introduced to the interface between COSMO and LPDM, and is compared to results of a classical similarity theory approach and to the operational coupling type, which uses the turbulent kinetic energy (TKE) from the COSMO model directly. For the validation of the modelling system, the TRANSALP-89 tracer experiment is used, which was conducted in highly complex terrain in southern Switzerland. The ability of the COSMO model to simulate the valley wind system is assessed with several meteorological surface stations, and the dispersion simulation is evaluated with the measurements from 25 surface samplers. The sensitivity of the modelling system towards the soil moisture, horizontal grid resolution, and boundary-layer height determination is investigated, and it is shown that, if the flow field is correctly reproduced, the new scaling approach improves the tracer concentration simulation when compared to classical coupling methods.     

Soil moisture: a residual problem underlying AGCMs

This paper critically reviews and intercompares land surface schemes (LSSs) as used in atmospheric general circulation models (AGCMs) to simulate soil moisture and its response to a warmer climate, and potential evapotranspiration approaches as used in operational soil moisture monitoring and in predicting the response of soil moisture to a warmer climate. AGCM predictions of overall soil moisture change are in broad agreement but disagree sharply in some regions. Intercomparison projects have sought to evaluate the LSSs used by AGCMs for both accuracy and consistency. These studies have found that different LSSs can produce very different simulations even when supplied with identical atmospheric forcing. As well, LSSs that produce similar surface results from present-day or control climates often diverge when forced with climatic change data. Furthermore, no single LSS has been identified that produces an adequate simulation of all of temperature, moisture, evapotranspiration and runoff. AGCM LSSs must resolve the surface energy balance (SEB) in order to compute realistic heat fluxes between with the atmospheric model. LSSs have been used with AGCMs in both on-line (fully coupled) and off-line modes. In off-line climatic change experiments, AGCM predictions of atmospheric temperature and precipitation have been used, along with model downward radiative fluxes at the surface, to drive their own uncoupled LSS. However, there are simple non-energy-balance methods for estimating evapotranspiration that have been traditionally used in agricultural and meteorological applications. These schemes compute a potential evapotranspiration (PE) based on temperature and/or net radiation inputs, with the PE modified based on the availability of soil moisture. Operational PE approaches have also been used with AGCM data in off-line climate change experiments. The advantages of this approach are that it is simpler and requires less information, although (like the off-line SEB approach) it leaves out the simulation of feedbacks between the surface and the atmosphere.Although the SEB approach is essential for LSSs that must be coupled to AGCMs, this does not necessarily make it superior to an off-line operational PE LSS when it comes to quantities such as soil moisture. The quality of current observational data is insufficient to demonstrate that either approach is better than the other. Both approaches should continue to be used and intercompared when predicting the impacts of climatic change on soil moisture.     

Parametrization of Heterogeneous Snowmelt

Summary Melting snow is often patchy, and advection of heat from warm patches of snow-free ground can accelerate the melting. For large-scale atmospheric modelling applications, snowmelt rates and fluxes of heat and moisture over surfaces with snow cover distributed on scales too small to be resolved by the model grid have to be parametrized. In this paper, a boundary-layer model is used to model advection over surfaces with short vegetation and varying fractions of snow cover. Boundary-layer model results are used to assess the performance of a tile model, which calculates separate fluxes for snow-covered and snow-free fractions of the surface given area-average temperatures, humidities and windspeeds at a reference height in the atmosphere. It is found that the tile model can give good results, but its performance depends strongly on the choice of reference height. Received August 21, 1997 Revised February 23, 1998     

应用风云气象卫星及融合降水资料改进地表参数模拟

气象卫星资料不仅对天气、气候研究非常重要, 对于地表参数模拟和预报也具有重要意义。本文首次将全国自动站观测、卫星降水估计和地面观测融合降水资料(CMORPH)以及风云二号D星(FY-2D)积雪覆盖率数据应用到了高分辨率陆面资料同化系统(u-HRLDAS)。融合降水资料用于驱动u-HRLDAS, 同时用于计算雪水当量;积雪覆盖率资料作为u-HRLDAS强迫变量。区域模拟结果表明, 积雪覆盖率对于地表反照率、地表温度以及地气交换通量模拟有极其重要的影响。密云站土壤湿度模拟结果表明, 融合降水资料准确度优于全球陆面资料同化系统(GLDAS)再分析资料。小汤山站单点验证结果表明, 应用融合降水资料及卫星积雪覆盖率资料可以改进地表温度及地气交换通量的模拟。     

A Variational Method for Estimating Near-Surface Soil Moisture and Surface Heat Fluxes

A variational data assimilation method is proposed to estimate the near-surface soil moisture and surface sensible and latent heat fluxes.The method merges the five parts into a cost function,i.e.,the differences of wind,potential temperature,anti specific humidity gradient between observations and those computed by the profile method,the difference of latent heat fluxes calculated using the ECMWF land surface evaporation scheme and the profile method,and a weak constraint for surface energy balance.By using an optimal algorithm,the best solutions are found.The method is tested with the data collected at Feixi Station (31.41°N,117.08°E) supported by the China Heavy Rain Experiment and Study (HeRES) during 7-30 June 2001.The results show that estimated near-surface soil moistures can quickly respond to rainfall,and their temporal variation is consistent with that of measurements of average soil moisture over 15-cm top depth with a maximum error less than 0.03 m~3 m~(-3).The surface heat fluxes calculated by this method are consistent with those by the Bowen ratio method,but at the same time it can overcome the instability problem occurring in the Bowen ratio method when the latter is about-1.Meanwhile,the variational method is more accurate than the profile method in terms of satisfying the surface energy balance.The sensitivity tests also show that the variational method is the most stable one among the three methods.