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  • View in gallery

    (top) Shaded relief elevation above sea level (m); (bottom) land use classification (based on USGS data) of the research region.

  • View in gallery

    (top) Spatial patterns of the LAI (calculated by the empirical formula of CLM on the basis of the lookup table and USGS land cover classification) and (bottom) spatial patterns of the LAI (based on MODIS image) at 1200 LT 20 Aug 2003 (Julian day 232).

  • View in gallery

    Number of days with available assimilated remotely sensed LST data (blue is ocean).

  • View in gallery

    Histogram of the errors in the study regions where MODIS LST data were available between the MODIS Aqua daytime observed LST and the CLM simulation before and after assimilation, respectively, in two different times. Both the results before and after assimilation were based on MODIS LAI data. (top left) Aqua day 230 at 1300 LT vs before assimilation. (top right) Aqua day 230 at 1300 LT vs after assimilation. (bottom left) Aqua day 232 at 1230 LT vs before assimilation. (bottom right) Aqua day 232 at 1230 LT vs after assimilation.

  • View in gallery

    Spatial patterns of the resulting ET estimate at 1200 LT 20 Aug 2003 (Julian day 232). (top) Before assimilation (based on LAI data calculated using the empirical formula); (middle) before assimilation (based on MODIS LAI data); and (bottom) after assimilation (based on MODIS LAI data).

  • View in gallery

    As in Fig. 5, but for the soil surface layer moisture.

  • View in gallery

    Time series of the resulting LST estimate from these CLM runs for the Yucheng site before and after assimilation compared with the MODIS observation. Both the results before and after assimilation were based on MODIS LAI data. Shown are MODIS Terra observations in daytime (red dots), MODIS Terra observations at night (green dots), MODIS Aqua observations in daytime (blue dots), and MODIS Aqua observations at night (purple dot).

  • View in gallery

    As in Fig. 7, but for sensible heat flux.

  • View in gallery

    As in Fig. 8, but for the evapotranspiration.

  • View in gallery

    Scatterplots of the daytime ET estimation for the Yucheng site before and after assimilation in days 230, 231, and 232 compared with the observation: (a) before assimilation and (b) after assimilation.

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Variational Estimation of Land–Atmosphere Heat Fluxes and Land Surface Parameters Using MODIS Remote Sensing Data

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  • 1 Institute of Urban Meteorology, China Meteorological Administration, Beijing, China
  • | 2 Department of Earth Sciences, National Natural Science Foundation of China, Beijing, China
  • | 3 Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing, China
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Abstract

A variational data assimilation algorithm for assimilating the land surface temperature (LST) into the Common Land Model (CLM) was implemented using the land surface energy balance equation as the adjoint physical constraint. In this data assimilation algorithm, the evaporative fractions of the soil and canopy were adjusted according to the remotely sensed surface temperature observations. This paper developed a very simple analytical algorithm to characterize the errors’ weighting matrices in the cost function. The leaf area index (LAI) retrieved from the Moderate Resolution Imaging Spectroradiometer (MODIS) was also assimilated into CLM using the direct insertion method. The analysis results from the CLM with the LST assimilation algorithm compare well with MODIS and field observations for the Yucheng site, especially in daytime. On the basis of the histogram of the error of the LST, it can be concluded that after assimilation, the LST was greatly improved in comparison with the MODIS observations, especially in daytime. These results indicate that this surface temperature assimilation method is efficient and effective, even when only one time observational LST data point is available for each day, especially in daytime. The regional spatial patterns of evapotranspiration and soil surface moisture were also compared before assimilation on the basis of LAI data calculated using the empirical formula, before assimilation on the basis of MODIS LAI data, and after assimilation on the basis of MODIS LAI data.

Corresponding author address: Chunlei Meng, Institute of Urban Meteorology, CMA, No. 55 Beiwaxili, Haidian District, Beijing 100089, China. E-mail: clmeng@ium.cn

Abstract

A variational data assimilation algorithm for assimilating the land surface temperature (LST) into the Common Land Model (CLM) was implemented using the land surface energy balance equation as the adjoint physical constraint. In this data assimilation algorithm, the evaporative fractions of the soil and canopy were adjusted according to the remotely sensed surface temperature observations. This paper developed a very simple analytical algorithm to characterize the errors’ weighting matrices in the cost function. The leaf area index (LAI) retrieved from the Moderate Resolution Imaging Spectroradiometer (MODIS) was also assimilated into CLM using the direct insertion method. The analysis results from the CLM with the LST assimilation algorithm compare well with MODIS and field observations for the Yucheng site, especially in daytime. On the basis of the histogram of the error of the LST, it can be concluded that after assimilation, the LST was greatly improved in comparison with the MODIS observations, especially in daytime. These results indicate that this surface temperature assimilation method is efficient and effective, even when only one time observational LST data point is available for each day, especially in daytime. The regional spatial patterns of evapotranspiration and soil surface moisture were also compared before assimilation on the basis of LAI data calculated using the empirical formula, before assimilation on the basis of MODIS LAI data, and after assimilation on the basis of MODIS LAI data.

Corresponding author address: Chunlei Meng, Institute of Urban Meteorology, CMA, No. 55 Beiwaxili, Haidian District, Beijing 100089, China. E-mail: clmeng@ium.cn

1. Introduction

Evapotranspiration (ET) is a major component of the water and energy exchanges between the atmosphere and the land surface. Although in situ measurements and remote sensing can provide ET estimates for limited spatial locations and time periods, mathematical models are the most efficient approach for the continuous monitoring of ET dynamics. Because of the incomplete model physics and/or input data uncertainties, model estimates may contain significant errors, and merging model estimates with available observations becomes necessary (Meng et al. 2009).

Data assimilation provides a framework for merging observations and model estimates. By appropriately weighting the sources of errors, data assimilation produces a statistically optimal and dynamically consistent estimate of the evolving state of the system (Margulis and Entekhabi 2003). Various assimilation techniques such as the triangle retrieval method, interpolation, ensemble Kalman filters, and variational methods have been implemented and tested (Margulis et al. 2005; McLaughlin 2002; Sabater et al. 2007). Variational data assimilation algorithms can combine the advantages of in situ measurement, remote sensing, and model simulations, and these algorithms have been applied widely in recent years. Many studies have used variational data assimilation methods for assimilating land surface temperature (LST) and/or soil moisture data using the adjoint model to evaluate the cost function gradient, and various kinds of land data assimilation systems have been developed (Balsamo et al. 2007; Boussetta et al. 2008; Ronda and Bosveld 2009; Sabater et al. 2008; Tian et al. 2008). With respect to the adjoint assimilation method, in the nonlinear case, the minima of the cost functions are evaluated by deriving adjoint or tangent linear models, which is often very complicated, especially for 3D and 4D variational assimilation schemes. To simplify the adjoint assimilation method, some parameters were used in the simplified variational assimilation algorithm. These parameters, such as the evaporative fractions (EFs) and the sensible heat transfer coefficient are nearly constant during the entire day or during the assimilation window (Caparrini et al. 2003, 2004a). The simplified variational method circumvents the problem to derive adjoint or tangent linear models by using a numerical linear approximation of the observation operator (Reichle et al. 2001a,b; Caparrini et al. 2004b; Boussetta et al. 2008).

Most of the literature reviewed above has been applied to the variational assimilation approaches to relatively simple models and equations. The variational data assimilation algorithm was applied to a more complicated model, the Common Land Model (CLM) (Dai et al. 2003), for improving evapotranspiration and LST estimates in Meng et al. (2009). This paper describes a simple variational assimilation method similar to that of Meng et al. (2009), which only uses the energy balance model for the first soil layer and the canopy as the physical constraint. The EFs were used as the tuned factors to link the LST to the land–atmosphere heat flux. Differing from Meng et al. (2009), which only tested the variational approach using observational data in several single-point sites, this paper tested the variational approach at the regional scale using remote sensing and observational data. For regional-scale validation, the errors’ weighting matrices in the cost function are not the same in different regions. This paper developed a very simple analytical algorithm to characterize the errors’ weighting matrices in the cost function J, which is often defined as the inverse of the error covariance matrix. This paper used Moderate Resolution Imaging Spectroradiometer (MODIS) LST and leaf area index (LAI) data in northern China to validate the variational assimilation approach. MODIS Terra daytime LST data were assimilated into CLM using the variational assimilation method, which will be discussed at length below; MODIS LAI data were assimilated into CLM using the direct insertion method.

2. Methodology

The variational assimilation approach assimilates the LST through the adjustment of the EFs because EFs do not vary much in daytime when there is no heavy precipitation (Crago and Brutsaert 1996). The corresponding cost function J is
e1
where , , and are the top-layer soil temperature, the sunlit canopy temperature, and the shaded canopy temperature, respectively. The first and second terms are the observational errors of the assimilation algorithm normalized by the measurement inverse error covariances and . The first term on the right-hand side of the equation represents the forecast error at the end of the observation period, while the second term is the same error over the whole period. The values and are the MODIS-retrieved and the CLM-simulated radiative temperatures, respectively. In the CLM, the land surface temperature can be parameterized as follows:
e2
where is the Stefan–Boltzmann constant and is the outgoing longwave radiation. The third, fourth, and fifth terms on the right-hand side of Eq. (1) represent the error in the EF estimates with respect to the “true,” yet unknown value. Here , , and are the weight of different terms, often defined as the inverse of the covariance matrix; , , and are the EFs of the bare soil, the ground surface under the canopy and the canopy, respectively. The EF of the bare soil is represented as
e3
the EF of the ground surface below the canopy is represented as
e4
and the EF of the canopy is represented as
e5
where , , and are evapotranspiration of the bare soil, the ground surface under the canopy, and the canopy, respectively, and , , and are sensible heat flux of the bare soil, the ground surface under the canopy, and the canopy, respectively. The sixth, seventh, and eighth terms on the right-hand side of Eq. (1) are the background errors of the assimilation algorithm, which are the adjoint physical constraints of the ground surface, the sunlit canopy, and the shaded canopy, respectively. The background errors are obtained by adjoining the state equation to the performance index with the time-dependent Lagrange multiplier vectors , , and . This constraint ensures that the estimates produced by the assimilation procedure satisfy the CLM within the range specified by the model. The value c is the soil’s volumetric heat capacity (J m−3 k−1); is the thermal conductivity (W m−1 K−1); is the thickness of the surface soil layer (m); is the temperature of the second-layer soil (K); and , , and are the net radiation of the soil surface, the sensible heat flux of the soil surface, and the latent heat flux of the soil surface (W m−2), respectively. The values and are the net radiation absorbed by the sunlit canopy and the shaded canopy (W m−2); and are the sensible heat flux from the sunlit canopy and the shaded canopy (W m−2); and and are the latent heat flux from the sunlit canopy and the shaded canopy (W m−2), respectively. The relationship of , , , , , and could be described as follows:
e6
e7
The relationship of , , , , , and could be described as follows:
e8
e9
Integrating the first variation of the cost function by parts and grouping the independent variations gives Euler–Lagrange equations, which need to be integrated in time both forward and backward (Castelli et al. 1999). These Euler–Lagrange equations are
e10
e11
e12
e13
e14
e15
e16

The detailed solutions of the cost function and the procedures of the LST assimilation algorithm are the same as those detailed in Meng et al. (2009).

An analytical method was developed to compute the weight of the cost function precisely and simply. All of the partial derivatives used in the assimilation method were analytically derived using a very simple method, and most of the key parameters could be found in the CLM. With respect to the assimilation algorithm used for regional applications, the inverse error covariances, namely , , , and , need to be reconsidered and can be defined as follows:
e17
e18
e19
e20
From Eqs. (14)(16), , , and can be derived as follows:
e21
e22
e23
where n is the iterative time. The partial derivatives in Eqs. (21)(23) can be derived as follows on the basis of the CLM:
e24
e25
e26
e27
where is the latent heat of evaporation for water, is the specific heat of dry air, is the air density, is the heat conductance for ground, and is the air temperature within canopy space.

3. Data

a. MODIS data

The above variational data assimilation algorithm was tested using MODIS remote sensing data in northern China around the Bohai Sea and using in situ observational sensible heat flux and evapotranspiration data from the Yucheng site within the research region. The research region is located at 35°–40°N, 115°–120°E. The area has a relatively homogenous physiography and a low terrain (Fig. 1). Figure 1 also shows that the predominant land cover type of the area is cropland/pasture. The Pacific Ocean is located to the northeast and southeast of the research region; there are no observational data for the regions in the ocean.

Fig. 1.
Fig. 1.

(top) Shaded relief elevation above sea level (m); (bottom) land use classification (based on USGS data) of the research region.

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

The MODIS LAI–retrieved algorithm is based on the relationships between the normalized difference vegetation index (NDVI) and the LAI (Myneni et al. 2002), which has been validated widely (Tian et al. 2002a,b; Privette et al. 2002; Pisek and Chen 2007; Gitelson et al. 2007). While in the CLM, the LAI is calculated using an empirical formula, which can be expressed as follows:
e28
where is the leaf area index, and are the maximum and minimum LAI values that are associated with the land cover classification and can be calculated using the lookup table, and is the soil temperature of a certain layer (from this layer above the root fraction is more than 90%).

The spatial patterns of the LAI based on the CLM and a MODIS image taken at 1200 local time (LT) 20 August 2003 are plotted in Fig. 2. From Fig. 2, we can see that in the western and southern areas of the research region, the MODIS LAI was apparently lower than that calculated by the empirical formula of the CLM on the basis of the lookup table and U.S. Geological Survey (USGS) land cover classification.

Fig. 2.
Fig. 2.

(top) Spatial patterns of the LAI (calculated by the empirical formula of CLM on the basis of the lookup table and USGS land cover classification) and (bottom) spatial patterns of the LAI (based on MODIS image) at 1200 LT 20 Aug 2003 (Julian day 232).

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

The MODIS Terra/Aqua LST products (MOD11A1 and MYD11A1) are tile based, are gridded in the sinusoidal projection, and are produced daily at 1-km spatial resolution. The MODIS Terra daytime LST data were used to perform the assimilation algorithm. The Aqua daytime LST data were used to compare the results before and after assimilation.

The number of days with available remotely sensed LST data in the assimilation window (10 days) is plotted in Fig. 3. The assimilation was only performed for these days. From Fig. 3, we can see that there were no observational data available for the southwest and southeast areas of the research region, so the assimilation algorithm was not performed for these regions.

Fig. 3.
Fig. 3.

Number of days with available assimilated remotely sensed LST data (blue is ocean).

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

b. Observation data

The Yucheng station is located at 36.83°N, 116.57°E. It is an agricultural experiment station in which corn is planted during the summer and wheat is planted in the winter. Sensible heat flux and evapotranspiration data were measured at the station using the eddy correlation method.

c. Forcing data

The period of analysis was 10 days, from 11 to 21 August 2003 (Julian days 223 to 233). The meteorological data used by the model originated from the Global Land Data Assimilation System (GLDAS; Rodell et al. 2004) and can be downloaded from http://disc.gsfc.nasa.gov/hydrology/data-holdings. The time scale of the data was interpolated from 3 h to 30 min. Cubic spline function method was used to interpolate 2-m air temperature, 2-m relative humidity, 2-m air pressure, 10-m wind, downward shortwave radiation, and downward longwave radiation; stochastic method (Kundu and Bell 2003) was used to interpolate precipitation. The regional resolution of the data are 0.25° × 0.25°.

The method described in this paper uses a linear double regional interpolation method to merge the different spatial scales of the meteorological data and the MODIS data. That is, the MODIS LST and LAI data were scaled to the scale of the meteorological data.

It should be noted that the whole simulation period was used as a single assimilation window in the variational LST data assimilation algorithm; in the whole simulation period, the EFs were adjusted during the iteration. The soil moisture and the LST were initialized by GLDAS. The initial soil temperature and soil moisture conditions of the assimilation and no assimilation were the same.

4. Results and discussion

A histogram of the errors (simulations minus observations) in the research region where MODIS LST data were available between the observed MODIS Aqua daytime LST values and the CLM simulation values before and after assimilation for two different time points are plotted in Fig. 4. Both the results before and after assimilation were based on MODIS LAI data. Since no regional LST observation data were available, in this paper, MODIS data were considered as the true data. We concluded that in daytime the LST simulation result was greatly improved after assimilation when compared with the MODIS Aqua data. Before assimilation, most of the LST errors were approximately 8–16 K (Figs. 4a,c), while after assimilation, the LST errors decreased to approximately 2–4 K (Figs. 4b,d). The reason for the improvement is most likely because, for the research region where remote sensing data are available, the EFs were increased to compensate for the differences between the simulated LST and the MODIS LST. The increased ET indicates that more heat is carried away from the surface, thereby causing the LST to decrease.

Fig. 4.
Fig. 4.

Histogram of the errors in the study regions where MODIS LST data were available between the MODIS Aqua daytime observed LST and the CLM simulation before and after assimilation, respectively, in two different times. Both the results before and after assimilation were based on MODIS LAI data. (top left) Aqua day 230 at 1300 LT vs before assimilation. (top right) Aqua day 230 at 1300 LT vs after assimilation. (bottom left) Aqua day 232 at 1230 LT vs before assimilation. (bottom right) Aqua day 232 at 1230 LT vs after assimilation.

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

The spatial patterns of the resulting ET (W m−2) estimates from these CLM runs before assimilation (based on LAI data calculated using the empirical formula), before assimilation (based on MODIS LAI data), and after assimilation (based on MODIS LAI data) at 1200 LT 20 August 2003 (Julian day 232) are plotted in Fig. 5. Before assimilation, the ETs in the western and southeastern regions based on the MODIS LAI data were lower when compared with the ETs based on LAI data calculated using the empirical formula because the LAI values retrieved from the MODIS image were smaller than those calculated using the empirical formula. After assimilation, the ETs at the center of the research region were higher because the EF increased after assimilation in these areas; at the southwest and southeast regions, the ETs remained nearly unchanged because no MODIS LST data were available.

Fig. 5.
Fig. 5.

Spatial patterns of the resulting ET estimate at 1200 LT 20 Aug 2003 (Julian day 232). (top) Before assimilation (based on LAI data calculated using the empirical formula); (middle) before assimilation (based on MODIS LAI data); and (bottom) after assimilation (based on MODIS LAI data).

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

The spatial patterns of the resulting soil surface layer moisture (kg m−2) estimated from these CLM runs before assimilation (based on LAI data calculated using the empirical formula), before assimilation (based on MODIS LAI data), and after assimilation (based on MODIS LAI data) at 1200 LT 20 August 2003 (Julian day 232) are plotted in Fig. 6. The depth of the soil surface layer is 7.1 mm. Before assimilation, in the southwestern and southeastern areas, the soil moisture estimations based on MODIS images were lower because of the decrease in the LAI. After assimilation, in the northern and central areas, the surface soil moistures were lower; in most of these regions, soil surface moisture was depleted, and soil moisture was reduced to zero to increase the soil evaporation and match the minimization of the error of the LST. Soil surface moisture also could be changed by the assimilation of LST. Therefore, to perfect the assimilation algorithm, soil moisture and LST values need to be assimilated simultaneously.

Fig. 6.
Fig. 6.

As in Fig. 5, but for the soil surface layer moisture.

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

A time series of the resulting LST estimates from these CLM runs for the Yucheng site before and after assimilation compared with the MODIS observations are plotted in Fig. 7. Both the results before and after assimilation were based on MODIS LAI data. We can draw almost the same conclusion as discussed for Fig. 4. The LST was greatly improved after the assimilation for daytime values compared with MODIS Aqua data but not at night when compared with MODIS Terra and Aqua data. The LST was decreased after assimilation in daytime, even if the LAI based on the MODIS data was decreased compared with that based on the empirical formula. Because the EF was increased in daytime after assimilation, the evapotranspiration was increased too, so the LST in daytime was decreased.

Fig. 7.
Fig. 7.

Time series of the resulting LST estimate from these CLM runs for the Yucheng site before and after assimilation compared with the MODIS observation. Both the results before and after assimilation were based on MODIS LAI data. Shown are MODIS Terra observations in daytime (red dots), MODIS Terra observations at night (green dots), MODIS Aqua observations in daytime (blue dots), and MODIS Aqua observations at night (purple dot).

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

The time series of the resulting sensible heat flux and the ET estimate from these CLM runs for the Yucheng site before and after assimilation compared with the observations are plotted in Figs. 8 and 9. Both the results before and after assimilation were based on MODIS LAI data. Figures 8 and 9 show that for days when the observation LST data were available, namely days 230, 231, and 232, the simulated sensible heat flux and ET values were improved for time points in daytime when compared with the observations. For days when the observational LST data were available in daytime, the ETs were increased at most hours after assimilation, even if the LAI based on MODIS data was decreased compared with that based on the empirical formula. For days when the observational LST data were available at night, the ETs were decreased at most hours after assimilation because EF was assumed as constant during a whole day, and ET was negative at night. For days when the observational LST data were unavailable, the simulated sensible heat flux values were nearly the same as those simulated before assimilation because, in this case, only the initial conditions could be changed for the simulation after assimilation, and LST remained nearly the same. For days when the observational LST data were unavailable in daytime, the simulated ET values decreased after assimilation compared with the ET values based on the empirical formula because the LAI values based on the MODIS image decreased. Figure 10 shows the scatterplots of the ET estimates in daytime for the Yucheng site before and after assimilation for days 230, 231, and 232 compared with the observation. The mean error (ME), the root-mean-square error (RMSE), and the correlation coefficients (R) are listed in Table 1. In daytime, the MEs and RMSEs were reduced from 97.0 to 59.6 W m−2 and from 121.4 to 73.6 W m−2, respectively; the correlation coefficients increased by approximately 0.19 compared with those without assimilation. This again demonstrates the improvement resulting from the LST data assimilation algorithm developed in this study for daytime values.

Fig. 8.
Fig. 8.

As in Fig. 7, but for sensible heat flux.

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for the evapotranspiration.

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

Fig. 10.
Fig. 10.

Scatterplots of the daytime ET estimation for the Yucheng site before and after assimilation in days 230, 231, and 232 compared with the observation: (a) before assimilation and (b) after assimilation.

Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-028.1

Table 1.

The ME, RMSE, and R of the daytime ET estimation before and after assimilation in days 230, 231, and 232 compared with the observation.

Table 1.

5. Conclusions

In this study, we applied the variational data assimilation method of the LST to the CLM to improve the estimation of land–atmosphere heat fluxes and land surface parameters. On the basis of land surface temperature data assimilation tests for some typical single sites (Meng et al. 2009), we validated the variational data assimilation method within a region in northern China that includes the Yucheng agricultural site. We also developed a very simple analytical algorithm to characterize the inverse error covariance in the cost function J. The LAI retrieved from MODIS was also assimilated in the CLM.

Because the EF is nearly invariant in daytime if no heavy precipitation has occurred, the variational assimilation method used in this paper can improve the simulation of the LST on the regional scale and for the Yucheng site, especially in daytime, when only one remote sensing LST data time point for each day is available. For days when the observational LST data were available in daytime, the LST simulation result was greatly improved after assimilation when compared with the MODIS Aqua data. After using the MODIS LAI data, the ETs based on the MODIS LAI data in the western and southeastern regions were lower when compared with the ETs based on LAI data calculated using the empirical formula. After assimilation, the ETs at the center of the research region were higher because the EF increased after assimilation in these areas. After assimilation, in the northern and central areas, the surface soil moistures were lower; in most of these regions, soil surface moisture was depleted, and soil moisture was reduced to zero to increase the soil evaporation and match the minimization of the error of the LST. The observed sensible heat flux and the ET also matched the simulated values well after the assimilation for the Yucheng site.

The variational assimilation algorithm this paper developed is relatively simple, so it also has some disadvantages. EF is often not constant during precipitation and at night, so at these circumstances, the results after assimilation are usually not very good. Because of the cloud cover of the MODIS images, the assimilation time is only 10 days, which is relatively short. To validate the popularity of the assimilation algorithm, other observational data should also be used in the assimilation algorithm.

In the near future, a variational data assimilation algorithm for assimilating LST and soil moisture data simultaneously will be implemented to improve the accuracy of the simulation at night. The processes that drive nighttime LST will also be considered in the future; at night, the level of evapotranspiration is much lower than in daytime. Other important land surface parameters, such as the emissivity and albedo, which can be retrieved by remote sensing, should be assimilated into the CLM as well.

Acknowledgments

We express our gratitude to Dr. Youjun Dou for his unselfish help. The NASA website provided the meteorology data for validating the assimilation algorithm. This work was supported by the National Natural Science Foundation of China under Grant 41005056 and the Key Projects in the National Science and Technology Pillar Program during the 11th Five-Year Plan period under Grant 2008BAC37B04.

APPENDIX

Notation List

 Lagrange multiplier of the adjoint physical constraints of the ground surface

 Lagrange multiplier of the adjoint physical constraints of the sunlit canopy

 Lagrange multiplier of the adjoint physical constraints of the shaded canopy

 Air density

 Stefan–Boltzmann constant

 Thickness of the surface soil layer (m)

c Soil volumetric heat capacity (J m−3 K−1)

 Canopy gap fraction

 Heat conductance for the ground

 Specific heat of the dry air

n Iterative times

 Thermal conductivity (W m−1 K−1)

 Weight of the forecast error at the end of the observing period

 Weight of the forecast error over the whole period

 Weight of the forecast error of the evaporative fraction of the bare soil

 Weight of the forecast error of the evaporative fraction of the ground surface under the canopy

 Weight of the forecast error of the evaporative fraction of the canopy

 Soil evaporation (mm)

 Evaporative fraction of the bare soil

 Evaporative fraction of the ground surface under the canopy

 Evaporative fraction of the canopy

 Sensible heat flux from the shaded canopy (W m−2)

 Sensible heat flux from the sunlit canopy (W m−2)

 Sensible heat flux from the soil surface (W m−2)

 Sensible heat flux of the bare soil

 Sensible heat flux of the ground surface under the canopy

 Sensible heat flux of the canopy

L Latent heat of evaporation for water

 Outgoing longwave radiation (W m−2)

 Leaf area index

 Maximum leaf area index

 Minimum leaf area index

 Latent heat flux from the shaded canopy (W m−2)

 Latent heat flux from the sunlit canopy (W m−2)

 Latent heat flux from the soil surface (W m−2)

 Latent heat flux of the bare soil

 Latent heat flux of the ground surface under the canopy

 Latent heat flux of the canopy

 Net radiation absorbed by the shaded canopy (W m−2)

 Net radiation absorbed by the sunlit canopy (W m−2)

 Net radiation absorbed by the soil surface (W m−2)

 Second-layer soil temperature (K)

 Air temperature within canopy space (K)

 Top-layer soil temperature (K)

 Shaded canopy temperature (K)

 Sunlit canopy temperature (K)

 MODIS-retrieved radiative temperature (K)

 Radiative temperature simulated by CLM (K)

 Soil temperature of a certain layer, from this layer above the root fraction is more than 90%

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