Estimating turbulent fluxes through assimilation of geostationary ...

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, D09109, doi:10.1029/2010JD015150, 2011

Estimating turbulent fluxes through assimilation of geostationary operational environmental satellites data using ensemble Kalman filter Tongren Xu,1,2 Shunlin Liang,2 and Shaomin Liu1 Received 6 October 2010; revised 11 February 2011; accepted 15 February 2011; published 12 May 2011.

[1] In this study, a data assimilation scheme is developed on the basis of the ensemble Kalman filter algorithm and the common land model (CoLM); soil moisture and model parameters are simultaneously optimized to improve the estimates of turbulent fluxes. Land surface temperature (LST) is retrieved from geostationary operational environmental satellites (GOES) data, validated, and then assimilated into the model. The data assimilation results are validated at six observation sites in the United States that include grassland, cropland, and forestland cover types. Data assimilation results indicate that in addition to improvements in the prediction of turbulent fluxes, model uncertainties are also reduced as a result of the assimilation of GOES LST retrieval data. The average reductions in root mean square error (RMSE) values are 47.5 and 31.1 W m−2. The effects of simultaneous optimization of soil moisture and model parameters are compared with those resulting from separate optimization; simultaneous optimization is found to yield smaller RMSE values. Further, in this study, the effects of Moderate Resolution Imaging Spectroradiometer (MODIS) and GOES temporal resolution data on data assimilation results are studied. The assimilation results indicate that the average RMSE values for GOES temporal resolution data are smaller than that for MODIS temporal resolution data. During the assimilation time period, the soil moisture obtained from assimilation closely agrees with the observed values, and the four vegetation parameters show distinct seasonal variations. However, the lack of sufficient information makes it difficult to estimate the true value of these variables and parameters. Citation: Xu, T., S. Liang, and S. Liu (2011), Estimating turbulent fluxes through assimilation of geostationary operational environmental satellites data using ensemble Kalman filter, J. Geophys. Res., 116, D09109, doi:10.1029/2010JD015150.

1. Introduction [2] Energy and water exchanges are among the most important processes in land‐atmosphere interactions. Furthermore, accurate estimations of turbulent fluxes are critical for climate change research, planning, and management of water resources. Turbulent fluxes result from the splitting of the available net radiation energy at the land surface; these fluxes depend on the soil moisture content, soil temperature, soil physical properties, land cover, and biological and chemical parameters associated with particular vegetation types. The past two decades have seen the development of land surface models that can combine all the above mentioned factors in a mathematical framework to estimate turbulent fluxes on a continuous spatial and temporal scale [Dickinson et al., 1986; Sellers et al., 1996; Dai et al., 2003].

1 State Key Laboratory of Remote Sensing Science, School of Geography, Beijing Normal University, Beijing, China. 2 Department of Geography, University of Maryland, College Park, Maryland, USA.

Copyright 2011 by the American Geophysical Union. 0148‐0227/11/2010JD015150

[3] However, turbulent fluxes derived from land surface models are strongly impacted by uncertainties within the model parameters, the model structures, and forcing data. This fact adversely affects the development and application of such models. Ground measurements can parameterize models at the point scale, but accurate parameterizations become difficult when modeling at a large scale, because ground‐ based measurements cannot provide a monitoring network sufficient for global coverage. Satellites can be used to acquire land surface information at the regional scale, and thus, they provide new opportunities for monitoring turbulent fluxes [Bastiaanssen et al., 1998; Su, 2002; Liu et al., 2007]. However, remote sensing data are often contaminated because of the presence of clouds, and it becomes difficult to monitor turbulent fluxes on a continuous temporal scale. [4] In light of these issues, it is desirable to combine land surface models and remote sensing observations to accurately monitor turbulent fluxes on a continuous spatial and temporal scale. When satellite observations are available, they can be incorporated by models to update model state variables and parameters. Data assimilation is such a technique that can be used to correct model predictions [Liang, 2004; Liang and Qin, 2008]. In this technique, the observed numbers of a

D09109

1 of 16

D09109

XU ET AL.: TURBULENT FLUXES BY DATA ASSIMILATION

particular variable with known uncertainty are used to adjust predicted model state variables such as soil moisture [Margulis et al., 2002], soil temperature [Huang et al., 2008], and other related quantities such as turbulent fluxes [Albergel et al., 2010; Xu et al., 2011], during the time of observation. [5] Kalman [1960] developed an optimal recursive data processing technique for linear dynamic systems called the Kalman filter (KF). Jazwinski [1970] proposed the extended Kalman filter (EKF) for nonlinear systems, which is based on first‐order linearization; however, the EKF could result in large errors because of the strong nonlinearities of the model. Entekhabi et al. [1994] applied KF and EKF to retrieve the soil moisture and soil temperature profiles. The ensemble Kalman filter (EnKF) is a variation of KF, and it was proposed by Evensen [1994] to overcome the linearization problem of the EKF. Reichle et al. [2002] used EnKF to assimilate L band microwave brightness temperature observations into a hydrological model. Xu et al. [2011] assimilated the MODIS land surface temperature (LST) products into a land surface model with the EnKF. [6] It is well known that the land surface temperature is a crucial variable in determining land‐atmosphere interactions. The land surface temperature determines the splitting of incoming radiant energy into sensible and latent heat fluxes. Biases in land surface temperature may result in biases in sensible and latent heat fluxes. To overcome this problem, current research is focused on assimilating remote sensing land‐surface temperatures. Remote sensing‐based radiometric temperature measurements have been assimilated into land surface models to improve predictions of soil temperature profiles [Kumar and Kaleita, 2003; Huang et al., 2008]. Further, remote sensing‐based surface temperature has been assimilated into a water balance model to improve predictions of root‐zone soil moisture [Crow et al., 2008]. Variational techniques have also been coupled with relatively simple models to obtain surface energy balance components by assimilating surface temperature observations [Boni et al., 2001; Caparrini et al., 2004]. Xu et al. [2011] improved predictions of water and heat fluxes by assimilating MODIS LST products into common land model (CoLM) [Dai et al., 2003]. Besides the assimilation of surface temperatures directly into models, land surface temperatures can also be used to calculate turbulent fluxes using remote sensing models such as the surface energy balance algorithm for land (SEBAL). Schuurmans et al. [2003] improved the spatial distributions of latent heat flux in areas of high elevations by assimilating latent heat flux from SEBAL. Pipunic et al. [2008] tested the potential of assimilating sensible and latent heat fluxes derived from remote sensing data into a land surface model. [7] As described above, most data assimilation experiments aim to correct soil moisture and soil temperature profiles, and hence, they may indirectly correct turbulent fluxes predictions. However, achieving correct soil moisture or soil temperature estimates may not guarantee improved predictions of turbulent fluxes because model uncertainties are also caused by inaccurate model parameters and forcing data. Yang et al. [2007a] developed the first prototype to optimize both model parameters and state variables using an autocalibration data assimilation system. Qin et al. [2009]

D09109

and Tian et al. [2009] produced improved soil moisture profile estimates by simultaneously optimizing soil moisture and model parameters. In the present study, we have aimed to obtain improved predictions of turbulent fluxes along with simultaneous optimization of state variables and model parameters, which, thus far, has not been seriously considered by other researchers. In order to achieve this, the most important state variables and model parameters for turbulent fluxes must be determined. We considered the case of Xu et al. [2011], who improved turbulent fluxes by adjusting the soil temperatures and soil moisture levels independently; they proved that turbulent fluxes are more sensitive to soil moisture changes than soil temperature. In the present study, we first conducted a sensitivity test to determine which model parameters are more important for the prediction of turbulent fluxes; subsequently, a data assimilation scheme was constituted to simultaneously optimize soil moistures and the selected model parameters through assimilation of surface temperatures. Compared to soil moisture, surface temperature is not a memory variable, which varies rapidly on a diurnal scale. If the temporal resolution of remote sensing surface temperature data is not very high (e.g., MODIS land surface temperature), the modeling improvement by assimilating such information can be easily lost due to modeling errors. Therefore, it is difficult to assimilate low temporal resolution temperature information into a land surface model. Geostationary Operational Environmental Satellites (GOES) provide approximately half‐hourly temporal resolution Earth observation data; this provides a promising opportunity for improving model predictions using the data assimilation method. Land surface temperature (LST) retrieval data from GOES have been addressed previously by Sun and Pinker [2003] and Sun et al. [2004], and the accuracy is within 3 K. In this study, LST retrieval data from GOES have been assimilated into CoLM for the first time. Further, the data assimilation algorithm applied in this research is the ensemble Kalman filter (EnKF) method [Evensen, 1994]. The assimilation results are validated at six observation sites including different land cover types (grassland, cropland, and forestland) in the United States. [8] This paper is organized as follows. Section 2 introduces the assimilation method. Section 3 discusses the experiment and methodology, including the description of observation sites, GOES data and LST retrieval data validation, observation operator, model operator, parameter selection, and ensemble generation. Section 4 presents the results and discussions, including the impacts of ensemble size (section 4.1), assimilation of GOES LST data (section 4.2), the effect of simultaneously optimizing soil moisture and model parameters (section 4.3), the effects of MODIS and GOES temporal resolution data on the assimilation results (section 4.4), and the retrievals of soil moisture and model parameters (section 4.5). The conclusions are provided in section 5.

2. Assimilation Method [9] As is well known, the ensemble Kalman filter (EnKF) has been widely used in land data assimilation systems; it is also used in this work. In one step, EnKF simultaneously runs several times by adding numerous Gaussian‐distributed

2 of 16

D09109


noises to the state variables and parameters. Therefore, the state prediction error covariance can be calculated using the statistical method. Information on the state vector and its covariance structure derived from previous predictions and observations are used in the subsequent estimate. When new observations are available, the prediction of the dynamical model is compared, updated, and then weighted according to the prediction and measurement error covariance. A brief algorithm summary presented by Huang et al. [2008] and Xu et al. [2011] provides a review of the data assimilation techniques relating to surface temperature, land surface modeling, and remote sensing observations. [10] In this paper, the model operators are described as follows: Xkþ1 ¼ M ðXk ; kþ1 ; kþ1 Þ;

Xi;0 ¼ X0 þ ui ui N ð0; P0 Þ;

ð2Þ

where mi is the background error vector that conforms to the Gaussian distribution with zero mean and covariance matrix of P0. The state variables then proceed by adding i (i represents the ensemble member) number of random noises, which conform to Gaussian distribution, and the size of its standard deviation, explained later in section 3.4. It is expressed as the following equation: Xi;1f ¼ M Xi;0 ; 1 ; 1 þ wi wi N ð0; QÞ;

ð3Þ

f where X i,1 represents the forecasted state variables of the ith member at time 1; the superscript “f ” represents the forecasted state variables; wi is the model error vector, which conforms to Gaussian distribution with zero mean and covariance matrix Q; and Q represents the model error. [12] When observations are unavailable, the model state variables will proceed using the following equation:

f Xi;kþ1 ¼ M Xi;kf ; kþ1 ; kþ1 þ wi wi N ð0; QÞ;

ð4Þ

f f where Xi,k , Xi,k+1 represent the forecasted state variables of the ith member at times k and k + 1. [13] When observations are available, the observation operator will predict the surface temperature as given by the following equation:

Yi ¼ H Xi f þ vi vi N ð0; RÞ;

matrix R (R: the observation error). Each state variable is updated as follows:

Pf HT ¼

ð5Þ

where Yi is the surface temperature of ith member; H(·), the observation operator that relates model state variables to observations; and vi, the observation error that conforms to Gaussian distributions with zero mean and covariance

HP f H T ¼

Xia ¼ Xi f þ K Y o Yi ;

ð6Þ

1 K ¼ P f H T HP f H T þ R ;

ð7Þ

N 1 X f f T Xi f X Xi f X ; N 1 i¼1

ð8Þ

N h ih iT 1 X f f H Xi f H X Xi f X ; N 1 i¼1

ð9Þ

Pf ¼

ð1Þ

where Xk+1 and Xk represent model state variables at time k + 1 and k, respectively; M(·), model operator; ak+1, forcing data at time k + 1; and b k+1, model parameters at time k + 1. [11] At the beginning of the algorithm, the first‐guest value X0, model parameter b0, and background error covariance P0 are determined on the basis of prior knowledge. The initial state variables ensemble can be obtained by adding random noises to X0 as follows:

D09109

N h ih iT 1 X f f H Xi f H X H Xi f H X ; N 1 i¼1

ð10Þ

where Xia represents the analyzed state variables of the ith member; K, Kalman gain matrix; Y 0, observations; P f, the forecasted background error covariance matrix; HT, the transposed matrix of observation operator; N, the number of ensembles; X if, the mean value of forecasted state variables; and [ ]T, the transposed matrix. [14] After the state variables are updated, the analysis error (AE) can be obtained as follows: AE ¼

N T 1 X X a X a Xia X a ; N 1 i¼1 i

ð11Þ

where X a is the mean value of the analyzed state variables. [15] In this work, in order to obtain accurate turbulent fluxes predictions, the model state variables and parameters are updated simultaneously. In the framework of sequential filtering techniques, the state augmentation method [Chen et al., 2005] can be used to simultaneously update state variables and model parameters; it regards model parameters to be updated as part of the state variables. Xu et al. [2011] indicated that soil moisture is a crucial state variable for turbulent fluxes predictions in CoLM, and the model parameter selection is presented in section 3.4. Therefore, the state variables X in above equations include soil moisture and the selected model parameters. When GOES LST retrieval data are available, the soil moisture and model parameters are updated using equations (6)–(10).

3. Experiment Data and Methodology [16] In this study, a land data assimilation scheme is developed to improve the predictions of turbulent fluxes by simultaneously optimizing soil moisture and model parameters. In a complete land surface data assimilation scheme, the land surface model is the primary part, and it calculates the turbulent fluxes using state variables, model parameters, and forcing data. Hence, CoLM is used as the model operator in the developed land data assimilation scheme, and EnKF introduced in section 2 is used as the data assimilation method. Further, land surface temperature retrieval data from

3 of 16

D09109

Table 1. Summary of the Six Observation Sites Site Brooking Goodwin Bondville Mead Chestnut Missouri

D09109


Location (State) Latitude Longitude Land Cover Date (Year) South Dakota Mississippi Illinois Nebraska Tennessee Missouri

44.34 34.25 40.01 41.16 35.93 38.74

N N N N N N

96.83 89.97 88.29 96.47 84.33 92.20

W W W W W W

Grass land Grass land Crop land Crop land Forest Forest

2006 2006 2006 2006 2006 2006

GOES brightness temperatures are assimilated into CoLM. The data assimilation scheme is validated at six observation sites in the United States. 3.1. Site Description [17] Data assimilation experiments are conducted at six FLUXNET observation sites in the United States in 2006, and the information of the six observation sites is listed in detail in Table 1. FLUXNET is a global network of micrometeorological tower sites that use eddy covariance methods to measure the exchanges of carbon dioxide, water vapor, and energy between terrestrial ecosystems and the atmosphere. More than 500 tower sites located in about 30 regional networks across five continents are currently operating on a long‐term basis. The surfaces of the selected sites in this study are smooth and evenly covered with grassland (the Brookings and Goodwin sites), cropland (the Bondville and Mead sites), and forestland (the Chestnut and Missouri sites). Meteorological data— including wind speed, wind direction, air temperature, relative humidity, atmosphere pressure, precipitation, radiation, and turbulent fluxes—are measured by various instruments mounted on a tower. More details of these sites are given at www. fluxnet.ornl.gov/fluxnet/index.cfm. FLUXNET data have been validated carefully [Baldocchi et al., 2001], and then used to access and improve the performance of land surface models [Fisher et al., 2008; Williams et al., 2009]. [18] Turbulent fluxes data collected by the eddy covariance (EC) system are used as the validation data in this study. Although the EC system is accepted as one of the best methods to measure turbulent fluxes [Baldocchi et al., 2001], it has its limitations. As observed in most experiments [Wilson and Falgec, 2002; Mauder et al., 2006; Oncley et al., 2007], “energy imbalance” is the biggest problem when applying EC data. The energy balance ratio (EBR) is defined in order to assess the energy balance closure of an EC system as follows: EBR ¼ ðH þ LE Þ=ðRn GÞ;

ð12Þ

where H and LE are the sensible and latent heat fluxes, respectively; Rn, net radiation; and G, soil heat flux. Table 2 summarizes the EBR at six sites; the departure of EBR value from 1.0 indicates an energy imbalance. Table 2 demonstrates that energy imbalance is observed at the test sites. 3.2. Retrieving Land Surface Temperature From Geostationary Operational Environmental Satellites [19] In recent years, studies on global changes have required continuous, dependable, and high‐quality observations of the Earth. GOES have fulfilled this need by providing frequent radiometric observations over large portions of the western hemisphere. The instruments on board the satellites measure

the Earth’s emitted and reflected radiations from which ocean/ land surface/atmosphere temperature and radiation energy are derived. GOES carries two critical Earth observation instruments, an Imager and a Sounder, both of which simultaneously acquire high‐resolution visible and infrared data. The Imager and Sounder continuously transmit these data to ground terminals where the data are processed for rebroadcasts to primary weather services in the United States and around the world, including the global research community. [20] GOES data has been used in many areas; for example, land surface temperatures have been retrieved by using the GOES Imager instrument [Sun and Pinker, 2003; Sun et al., 2004]. The GOES Imager is a multichannel instrument designed to sense radiant and solar‐reflected energies from the sampled areas of the Earth. The multielement spectral channels simultaneously sweep east to west and west to east along a north‐to‐south path with a two‐axis mirror scan system. The GOES data used in this study were acquired by GOES‐12, which was launched into orbit (75°W, over equator) in 2001. The GOES Imager has five channels that are centered at 0.67, 3.9, 6.5, 11.0, and 13.0 mm. The 3.9, 11.0, and 13.0 mm channels are infrared windows with little water vapor absorption, and they have a nominal spatial resolution of 4 km × 4 km at the nadir. The infrared‐band data used in this study were taken by the GOES‐12 imager at 30 min intervals. [21] According to Sun et al. [2004], LST can be obtained in the following manner. During nighttime, LST can be obtained by Ts ðk Þ ¼ a0 ðk Þ þ a1 ðk ÞT11 þ a2 ðk ÞðT11 T3:9 Þ þ a3 ðk ÞðT11 T3:9 Þ2 þa4 ðk Þðsec 1Þ;

ð13Þ

while during daytime, the equation is Ts ðk Þ ¼ b0 ðk Þ þ b1 ðk ÞT11 þ b2 ðk ÞðT11 T3:9 Þ þ b3 ðk ÞðT11 T3:9 Þ2 þb4 ðk Þðsec 1Þ þ b5 ðk ÞT3:9 cos s ;

ð14Þ

where Ts is the LST retrieval from GOES; k, the surface type index, k = 1–14; a and b, the coefficients listed by Sun et al. [2004]; T3.9 and T11, the brightness temperatures of 3.9 and 11.0 mm channels, respectively; and and s, the satellite‐ viewing and solar zenith angles, respectively. [22] Ground‐measured surface temperatures are used to validate LST retrievals from GOES. On the basis of the thermal radiative transfer theory, the upward longwave radiation at land surfaces depends on the surface temperature, emissivity, and downward longwave radiation [Liang, 2004; Wang et al., 2008]. The ground‐measured surface temperatures can be obtained as follows: Ts ¼ f½Fu ð1 "ÞFd ="g0:25 ;

ð15Þ

Table 2. Energy Balance Ratio (EBR) of Eddy Covariance System at Six Sites, 2006

EBR

4 of 16

Brookings

Goodwin

Bondville

Mead

Chestnut

Missouri

0.92

0.78

0.96

0.80

0.75

0.81

D09109


D09109

Figure 1. Comparisons between the GOES LST retrieval data and ground‐measured surface temperatures (OBS) at six test sites. RMSE and R are root mean square error and correlation coefficient between GOES LST and ground‐measured surface temperatures, respectively. The dots represent the data points of assimilation results and ground measurements; the line in the dots represents the relationship between the data points. where Fu is surface outgoing longwave radiation (W m−2); Fd, surface incoming longwave radiation (W m−2); s, the Stefan‐Boltzmann constant (5.67 × 10−8 W m−2 K−4); ", the broadband emissivity (−), which is 0.987 for grasslands and croplands, and 0.993 for forests according to Wang et al. [2008].

[23] The GOES LST retrieval data are compared with ground‐measured surface temperatures (Figure 1). As shown in Figure 1, the GOES LST and ground‐measured surface temperatures follow the same trend: the correlation coefficients (R2) are 0.798, 0.759, 0.841, 0.771, 0.729, and 0.859 during the daytime, and they are 0.629, 0.738, 0.919,

5 of 16

D09109

D09109

XU ET AL.: TURBULENT FLUXES BY DATA ASSIMILATION Table 3. The Regression Equations and RMSE Values Between GOES LST Retrievals and Ground‐Measured Surface Temperatures in Different Land Cover Typesa Daytime

Grassland Cropland Forest

Nighttime

Regression Equation

RMSE(K)

Regression Equation

RMSE(K)

Y = 0.860X + 44.217 Y = 1.090X − 23.525 Y = 1.052X − 12.038

3.35 3.94 3.01

Y = 0.756X + 76.899 Y = 1.084X − 22.580 Y = 1.036X − 8.997

2.65 2.09 1.59

a

In these equations, X means the ground‐measured surface temperature and Y means GOES LST retrievals.

0.883, 0.899, and 0.928 during nighttime at the Brookings, Goodwin, Bondville, Mead, Chestnut, and Missouri sites. In addition, the LST derived from GOES data are higher than ground‐measured surface temperatures; this is particularly evident at the Brookings and Goodwin sites. The root mean square error (RMSE) values between GOES LST retrieval data and ground‐measured surface temperatures are approximately 1–6 K. [24] Many factors must have contributed to the deviations between GOES LST retrieval data and the ground‐measured surface temperatures. The terrain effect can affect the accuracy of GOES LST retrieval data at the test sites. The different temporal scales (GOES LST is an instantaneous value, whereas the ground‐measured temperature is the mean value of 30 min) and spatial scales (GOES LST is a mean value of approximately 4 km × 4 km, and ground‐measured temperature is a mean value of approximately hundreds of square meters determined by mount level of the instrument) can also cause deviations. [25] In order to assimilate GOES LST retrieval data into a land surface model at the regional scale, the observational operators is constructed according to different land cover types. On the basis of the linearity equations and RMSE between GOES LST retrieval data and ground‐measured surface temperatures in different land cover types, the observational operators and observational errors are constructed for daytime and nighttime, respectively; these are listed in Table 3. The linearity equation (Table 3) for grassland considers the data of the Brookings and Goodwin sites, that for cropland considers the data of the Bondville and Mead sites, and the equation for forest considers the data of the Chestnut and Missouri sites (the scatter diagrams are not shown). Therefore, the simulated GOES LST from the simulated surface temperature by CoLM can be obtained using the observation operators in different land cover types. The observational errors comprise GOES LST retrieval errors and representative errors. 3.3. Common Land Model 3.3.1. Model Description [26] CoLM is used as a model operator of the developed assimilation scheme. CoLM comprises physical, hydrological, and biological processes that can simulate soil temperature, soil moisture, turbulent fluxes, and other variables [Dai et al., 2001, 2003, 2004]. [27] In CoLM, turbulent fluxes are calculated by solving the soil‐vegetation‐atmosphere energy balance equation. In the case of a nonvegetated surface, the energy balance equation is as follows: Rn;g Hg LEg Gg ¼ 0;

ð16Þ

where Rn,g is the net radiation absorbed by the ground surface (W m−2) and Hg, LEg, and Gg, the sensible heat flux, latent heat flux, and soil heat flux at the soil surface, respectively (W m−2). In the case of a vegetated surface, the energy balance equation of the canopy is as follows: Rn;c Hc LEc ¼ 0;

ð17Þ

where Rn,c is the net radiation absorbed by the canopy (W m−2), and Hc and LEc are the sensible heat flux and latent heat flux from the leaves, respectively (W m−2). [28] Turbulent fluxes from the land surface can be obtained using the following equations: H ¼ a cp ðs a Þ=rah ;

ð18Þ

LE ¼ a ðqs qa Þ=raw ;

ð19Þ

where H and LE are the sensible and latent heat fluxes from the land surface, respectively; ra, the density of atmospheric air (kg m−3); cp, the specific heat of air at constant pressure (1012 J kg−1 K−1); s and a, the air temperature at land surface and reference height, respectively (K); rah, the aerodynamic resistance for sensible heat (s m−1); qs and qa, the air specific humidity at land surface and reference height, respectively (kg kg−1); and raw, the aerodynamic resistance for water vapor (s m−1). In CoLM, the land surface temperature is parameterized in the same manner as in equation (15). 3.3.2. Model Input Data [29] The input data of CoLM include land surface type, soil and vegetation parameters, and forcing data. CoLM is designed to handle a variety of data sources, and it is necessary to perform data preprocessing to take advantage of the data sets in CoLM. Land cover types are based on the International Geosphere‐Biosphere Programme (IGBP) classification system. Soil texture is sourced from a database in accordance with the percentage of sand and clay. All the data sets are available at a spatial resolution of 30 s. Thus, the thermal and hydraulic properties of the soil, such as specific heat capacity and thermal conductivity of dry soil and porosity can be calculated [Dai et al., 2001]. CoLM contains both time‐invariant and time‐varying vegetation parameters. The former are constant values related to different vegetation types. Leaf area index is a key parameter of CoLM, which, in this study, was sourced from the MODIS LAI data. The input forcing data used in this study were taken from a continuous series of meteorological data at the six FLUXNET observation sites, typically measured within 30 or 60 min. The data includes wind speed, air temperature, relative humidity, air pressure, precipitation, incoming shortwave radiation, and incoming longwave radiation. The model is run with 30 or

6 of 16

D09109

D09109

XU ET AL.: TURBULENT FLUXES BY DATA ASSIMILATION Table 4. Some Soil and Vegetation Parameters in Common Land Model Serial Number

Parameter

Description

Unit

Range

1 2 3 4 5 6 7 8 9 10 11 12

sand clay z0m d alpha vmax25 hlti hhti gradm binter d50 beta

Sand percentage of soil Clay percentage of soil Surface roughness length Zero plane displacement Quantum efficiency at 25°C Maximum rate of carboxylation at 25°C 1/2 point of low temperature inhibition function 1/2 point of high temperature inhibition function conductance‐photosynthesis slope parameter conductance‐photosynthesis intercept coefficient of root profile coefficient of root profile

% % m m mmol mol−1 mmol m−2 s−1 K K ‐ ‐ ‐ ‐

5.0–90.0 5.0–58.0 0.05–3.50 0.33–23.33 0.04–0.08 30.0–100.0 278.0–288.0 303.0–313.0 4.0–9.0 0.01–0.04 9.0–47.0 −3.24–1.0

60 min time steps in the experiments according to the measured meteorological data. [30] The model state variables such as soil moisture, soil temperature, and canopy temperature require initialization. Ideally, CoLM is initialized using the ground measurements. However, the model state variables are not measured in some experiment sites. Therefore, atmospheric forcing data over an annual cycle are used to spin up the model to an equilibrium state, and variables at the equilibrium state are then taken as the initial values for a model simulation. 3.4. Parameter Selection and Ensemble Generation [31] To identify the sensitive parameters, the responses of the parameters to the predictions of turbulent fluxes are analyzed by the Gaussian error propagation (GEP) method. The GEP method has been used to calculate standard deviations of predicted variables that result from the standard deviations of the model parameters that the turbulent fluxes depends on [Meyer, 1975]. This method was originally applied in engineering and physics and has been introduced into ecological and meteorological fields [Beaudet et al., 2000; Mölders, 2005; Lo, 2005]. In these fields, it has been applied to determine the model uncertainties due to the standard deviations of the model parameters that the turbulent fluxes depend on. [32] The land surface model can provide distinct turbulent fluxes for different sets of model parameters. Thus, for each set of model parameters, along with their standard deviations, the GEP method can determine the standard deviations of the predicted turbulent fluxes. Therefore, the standard deviation of the predicted turbulent fluxes can be analyzed for a typical range of environmental conditions. [33] Let us consider turbulent fluxes 8 as an example. 8 is a function of one or more physical and biological parameters bi, which are the mean values obtained from field measurements. Since the errors in the model parameters bi are typically given by the standard deviation sbi, each calculated flux 8 will have an error of an amount s8. The standard deviations of the predicted turbulent fluxes can be calculated from these individual deviations, while the standard deviations sbi of the empirical parameters bi are given by [Meyer, 1975] vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n 2 uX @8 8 ¼ t 2i ; @ i i¼1

ð20Þ

where n represents the number of empirical parameters. The ratio of the standard deviation to the mean value is the relative error (RE); RE = (s8/8). The following equation describes the percentage standard deviations (PSD) of the individual parameter in entire standard deviations: PSD ¼

i8 8

100%;

ð21Þ

where si8 is the individual standard deviations of 8 because of the change in the ith parameter. [34] The model parameters (soil and vegetation parameters) used to calculate the turbulent fluxes in CoLM are listed in Table 4. The standard deviations of the model parameters are arbitrarily assumed to be 10% of the respective empirical parameter value [Mölders, 2005], and the Bondville site is selected as the experiment site for this sensitivity test. [35] According to the GEP analysis, the RE values for the surface temperature, sensible, and latent heat fluxes are 0.05%, 21.07%, and 5.81%, respectively. The PSD values of the CoLM parameters are shown in Figure 2. The six most sensitive parameters, which are directly related to the predictions of turbulent fluxes—sand, clay, z0m, alpha, vmax25, and gradm—are selected. Among the above six parameters, sand and clay describe the soil texture that can influence soil moisture, whereas the other parameters are related to the stomata resistance that can influence vegetation transpiration.

Figure 2. Percentage standard deviation (PSD) of model variables at Bondville site from Julian days 191 to 220, 2006. Ts, H, and LE refer to surface temperature and sensible and latent heat fluxes, respectively; the names and descriptions of the model parameters are listed in Table 4.

7 of 16

D09109

D09109


ranges from zero to porosity, and the variation of model parameters are listed in Table 4.

4. Results and Discussions [37] In this section, the data assimilation results are validated using field measurements of six experiment sites. In section 4.1, the impact of ensemble size is discussed. In section 4.2, the GOES LST retrievals are assimilated into CoLM using the EnKF technique. The RMSE values between the model outputs and observations are calculated to assess the performance of the developed assimilation scheme. Furthermore, AE is used to assess the uncertainty of the model: a smaller AE implies smaller uncertainties of the model and vice versa. The results of simultaneous optimization of soil moisture and model parameters are compared with those obtained from individual optimization in section 4.3. The effects of MODIS and GOES temporal resolutions on the assimilation results are discussed in section 4.4. The retrievals of soil moisture and model parameters are described in section 4.5.

Figure 3. Impacts of ensemble sizes on assimilation results at Brookings site from Julian days 171 to 200, 2006.

[36] According to the EnKF algorithm, the error covariance matrix is calculated using the statistical method. Therefore, ensemble members for model state variables and parameters should be generated. In the EnKF algorithm, ensemble generation is an important step, and different perturbations can yield different assimilation results. Crow and Reichle [2008] have discussed this issue and proposed a series of adaptive filtering techniques. In this study, the ensemble members are generated using a relatively simple method; that is, the soil moisture and six selected parameters are disturbed by adding a series of Gaussian distributed noises. The standard deviation of the soil moisture ensemble members are set according to Xu et al. [2011], while the deviation of model parameter ensemble members are set to 10% of its default value, according to Mölders [2005]. At the point scale, it is assumed that the atmosphere forcing data are measured with a high accuracy as compared to model state variables and parameters; hence, the atmosphere forcing data is not disturbed. The variation of soil moisture

4.1. Impacts of Ensemble Size [38] As is well known, the size of ensembles is significant for the final assimilation results when the EnKF algorithm is applied. A small number of members can lead to instability and large sampling errors; however, this would reduce the computation burden. Conversely, the assimilation results must retain their stability, and the ensemble mean should be close to reality. The computational burden is acceptable when a large ensemble size is selected at the point scale, but it is unaffordable for applications at the global scale. Hence, an experiment must be conducted to determine the minimum number of ensemble members required to obtain optimal results from the application of EnKF to CoLM. For this purpose, a series of trials for turbulent fluxes estimations are performed with different ensemble sizes. [39] Assimilation procedures with GOES LST retrieval data are performed separately using five different ensemble sizes— 50, 100, 200, 500, and 1000 members—at the Brookings site. Figure 3 shows the results when five different ensemble sizes are used. The value corresponding to 0 ensembles refers to the model simulation results. As can be seen from the figure, the RMSE and AE values tend to become stable and have a minimum value when the ensemble size is larger than 100. Therefore, an ensemble size of 100 is selected to carry out the assimilation tests at all sites. 4.2. Assimilation of GOES LST Retrievals [40] The simulation and assimilation results are shown in Tables 5 and 6 and Figures 4, 5, and 6 at the test sites

Table 5. RMSE Values of Simulation and Assimilation Results Compared to Observationsa

Ts(K) H(W m−2) LE(W m−2) a

Sim/Ass

Brookings

Goodwin

Bondville

Mead

Chestnut

Missouri

Average

Sim Ass Sim Ass Sim Ass

3.7 2.2 69.4 37.1 143.7 86.4

4.7 2.5 48.7 29.3 64.6 55.7

4.9 2.3 91.2 30.4 82.7 37.1

4.9 2.7 91.0 49.6 88.5 43.6

5.1 4.0 129.0 43.0 94.2 80.6

3.7 3.3 83.7 38.5 71.9 55.4

4.5 2.8 85.5 38.0 90.9 59.8

Here Sim means model simulation results; Ass means data assimilation results.

8 of 16

D09109

D09109

XU ET AL.: TURBULENT FLUXES BY DATA ASSIMILATION Table 6. AE Values With and Without Data Assimilationa

Ts(K) H(W m−2) LE(W m−2) a

Non_ass/Ass

Brookings

Goodwin

Bondville

Mead

Chestnut

Missouri

Average

Non_ass Ass Non_ass Ass Non_ass Ass

1.9 0.7 41.3 16.1 71.1 27.9

1.6 1.1 33.2 28.4 59.4 44.4

0.5 0.3 10.8 7.5 15.8 9.8

0.8 0.4 15.9 9.7 32.8 15.4

0.6 0.1 28.6 4.3 35.1 5.0

0.5 0.2 23.2 6.7 28.7 7.7

1.0 0.5 25.5 12.1 40.5 18.4

Here Non_ass means results without data assimilation; Ass means results with data assimilation.

(continuously for approximately 30 days at every site). As is well known, turbulent fluxes data from an EC system are sometimes missing in the measurement process. Some bad data are also rejected in the processing procedure, such as data measured during a period of precipitation. Thus, it is difficult to obtain relatively continuous and concurrent turbulent fluxes observations for the six experiment sites considered in this study. Moreover, the GOES LST data are contaminated because of the presence of clouds over different experiment sites in some of the time periods. Therefore, the results cannot be validated using data of the same time period for the six sites. The data of Julian days from 151 to 180 is selected for the Brookings, Chestnut, and Missouri sites; from 171 to 200 for the Goodwin site; from 191 to 220 for the Bondville site; and from 181 to 210 for the Mead site. [41] Figures 4–6 show the simulation and assimilation results at the Goodwin (grassland), Bondville (cropland), and Chestnut (forestland) sites. From these figures, the model simulation can derive the diurnal variations of surface temperature and turbulent fluxes, but it usually overestimates the surface temperature and the sensible heat flux while underestimating the latent heat flux. These biases can be corrected through the assimilation of GOES LST retrieval data, and the resultant assimilation curves are found to be closer to the

observations than the model simulations. Further, Figure 6 shows that the assimilation results of the surface temperature are closer to the observations, while the latent heat flux is slightly overestimated at the Chestnut site. This phenomenon can be attributed to the incorrect simulation of aerodynamic resistance in CoLM [Yang et al., 2007b; Xu et al., 2011]; moreover, the EBR is 0.75 at this site, which implies that the turbulent fluxes are underestimated by the EC system. These results may looks more reasonable after the turbulent fluxes are corrected. [42] Table 5 summarizes the RMSE values of the simulation and the assimilation results compared with the observations at all sites. These results indicate that the estimates of surface temperature and turbulent fluxes are obviously improved with the EnKF techniques. Overall, the average reductions in the RMSE values of six sites are 47.5 and 31.1 W m−2 for sensible and latent heat fluxes, respectively. The most significant reductions in the RMSE values are 2.6 K, 86.0 W m−2, and 57.3 W m−2 for the surface temperature, sensible heat flux, and latent heat flux, respectively. [43] Table 6 summarizes the AE values with and without assimilation at six sites. For the nonassimilation case, forecast state variables are used to calculate AE using equation (11). Table 6 indicates that in addition to the improvements in the

Figure 4. Simulation and assimilation results at Goodwin site (grassland) from Julian days 171 to 200, 2006. 9 of 16

D09109


D09109

Figure 5. Simulation and assimilation results at Bondville site (cropland) from Julian days 191 to 220, 2006. model predictions, the model uncertainties can also be greatly reduced through the assimilation of GOES LST retrievals. Overall, the average reductions in AE values at six sites are 13.4 and 22.1 W m−2 for sensible and latent heat fluxes, respectively. The most significant reductions in the AE values are 1.2 K, 25.2 W m−2, and 43.2 W m−2 for the surface temperature, sensible heat flux, and latent heat flux, respectively.

4.3. Effects of Simultaneously Optimizing Soil Moisture and Model Parameters [44] Predictions of turbulent fluxes can be improved by optimizing soil moisture [Xu et al., 2011]. However, model uncertainties in turbulent fluxes are also caused by model parameters and forcing data. In this paper, errors in the forcing data are not considered, and soil moisture and model parameters are simultaneously optimized by assimilating GOES LST data. Hence, we discuss whether there is an

Figure 6. Simulation and assimilation results at Chestnut site (forest) from Julian days 151 to 180, 2006. 10 of 16

D09109

D09109


Figure 7. RMSE values of assimilation results by optimizing different variables: simulation, model output without assimilation; Ass_Joint, data assimilation results by the simultaneous optimization of soil moisture and model parameter; Ass_W, data assimilation results by only optimizing soil moisture; Ass_P, data assimilation results by only optimizing model parameters.

improvement in the prediction of the turbulent fluxes with simultaneous optimization of soil moisture and model parameters rather than separate optimization, and the results are presented in this section. [45] Figure 7 shows the RMSE values at six observation sites. In Figure 7, the average RMSE values of the assimilation results are smaller than the model simulation results, and the results from the optimization of model parameters have smaller RMSE values than soil moisture. It is obvious that the simultaneous optimization led to lower RMSE values than those obtained from others. This figure also indicates that soil moisture play a more important role than the model parameter in grasslands (Brookings and Goodwin sites), while the model parameters play a more important role than soil moisture in croplands (Bondville and Mead sites) and forestlands (Chestnut and Missouri sites). For land surfaces covered with dense vegetation, such as in cropland and for-

estland, the energy and water exchanges between canopy and atmosphere became the dominant processes. On the other hand, the roots of forest vegetation are distributed in deeper soil layers, where soil moisture is relatively stable compared to surface soil moisture. Therefore, the optimization of surface soil moisture is more efficient in grassland, while the optimization of model parameters, especially vegetation parameters, is more efficient in cropland and forestland. Table 7 summarizes the RMSE values of surface temperatures and turbulent fluxes at these experiment sites. 4.4. Effects of MODIS and GOES Temporal Resolution Data on Assimilation Results [46] As discussed above, the soil moisture and model parameters are simultaneously optimized by assimilating land surface temperatures. In theory, more the variables and parameters that have to be optimized, more the remote

Table 7. RMSE Values of Assimilation Results By Optimizing Soil Moisture and Model Parametersa

Ts(K) H(W m−2) LE(W m−2)

Ass_W/Ass_P

Brookings

Goodwin

Bondville

Mead

Chestnut

Missouri

Average

Ass_W Ass_P Ass_W Ass_P Ass_W Ass_P

2.2 3.2 38.9 57.1 91.0 132.6

3.4 2.8 31.4 31.2 51.5 54.5

4.8 2.4 89.0 31.7 80.2 38.9

4.8 3.1 85.3 59.4 79.5 44.7

4.2 4.3 61.8 48.8 63.3 67.6

3.4 3.4 63.6 40.2 57.3 54.9

3.8 3.2 61.7 44.7 70.5 65.5

a Here Ass_W means assimilation results by adjusting soil moisture only; Ass_P means assimilation results by adjusting model parameters only.

11 of 16

D09109

D09109

XU ET AL.: TURBULENT FLUXES BY DATA ASSIMILATION Table 8. RMSE Values of Assimilating MODIS and GOES Temporal Resolution Surface Temperatures

Ts(K) H(W m−2) LE(W m−2)

MODIS/GOES

Brookings

Goodwin

Bondville

Mead

Chestnut

Missouri

Average

MODIS GOES MODIS GOES MODIS GOES

2.1 1.4 34.4 16.7 93.8 65.9

3.4 2.8 34.4 32.4 51.3 52.8

2.3 2.3 25.2 31.4 40.6 37.9

2.5 2.4 37.4 35.8 47.1 47.9

4.1 3.9 47.9 42.8 75.8 84.8

3.2 3.2 37.1 37.6 57.9 57.3

2.9 2.7 36.1 32.8 61.1 57.7

sensing observations required. Thus, it is necessary to test the effects of MODIS and GOES temporal resolution data on the assimilation results. [47] As is well known, in addition to having different temporal resolutions, MODIS and GOES data have different spatial resolutions (1 km × 1 km for MODIS and 4 km × 4 km for GOES) as well as different accuracies. If MODIS and GOES LST data are assimilated into CoLM separately, it becomes difficult to identify whether the differences of the two assimilation results are a result of different temporal resolutions, spatial resolutions, or accuracies. Therefore, ground‐measured surface temperature data, with the same temporal resolutions as MODIS and GOES data, are assimilated into CoLM. [48] Tables 8 and 9 summarize the RMSE and AE values obtained by assimilating MODIS and GOES temporal resolution ground measurements at the six selected sites. From Tables 8 and 9, the average RMSE and AE values are seen to be smaller for assimilation of GOES than for the assimilation of MODIS temporal resolution data, and this conclusion is most evident at the Brookings site. Figure 8 shows the assimilation results at the Brookings site. From Figure 8, the results obtained from assimilating GOES temporal resolution data are clearly better than those obtained from assimilating MODIS temporal resolution data. The surface temperature and turbulent fluxes obtained from GOES are considerably closer to the 1:1 line than those obtained from MODIS. The RMSE values decreased from 2.1 to 1.4 K, from 34.4 to 16.7 Wm−2, and from 98.8 to 65.9 Wm−2, while R square increased from 0.958 to 0.968, from 0.515 to 0.818, and from 0.860 to 0.899 for surface temperature, sensible heat flux, and latent heat flux, respectively. 4.5. Retrievals of Soil Moisture and Model Parameters [49] In this study, the main object is to improve predictions of turbulent fluxes by assimilating GOES LST retrieval data. However, turbulent flux predictions from CoLM are determined by state variables and model parameters. Thus, soil moisture and model parameters are simultaneously estimated. The estimation of soil moisture is very important for research on climate change and management of water resources for agriculture. The vegetation parameters (z0m, alpha, vcmax25,

and gradm) play important roles in water and heat exchanges between the canopy and the atmosphere. However, these variables and parameters have high nonlinearity against remote sensing surface temperature, and it is difficult to retrieve the true values of soil moisture and model parameters simultaneously. [50] As is shown in Figure 7, soil moisture play an important role in the estimation of turbulent fluxes for grasslands, and model parameters play an important role for the estimation of cropland and forest. Thus, the variations in retrieved soil moisture at the Goodwin site (grassland) from Julian days 101 to 301 are shown in Figure 9. From Figure 9, the assimilation curve is closer to the observation curve for the 10 cm and 20 cm depths during most of the time period. The variations in the retrieved four vegetation parameters (z0m, alpha, vcmax25, and gradm) at the Bondville site (cropland) from Julian days 101 to 301 are shown in Figure 10. From Figure 10, it can be seen that the uncertainties of the parameters are within a reliable range, and they show seasonal variations. Along with the growth of vegetation from Julian days 180 to 260, z0m, vcmax25, and gradm increase to a high value, and alpha decreases to a low value. The seasonal changes of these four parameters lead to more latent heat flux and less sensible heat flux with the assimilation of GOES LST retrieval data (Figure 5). Since these parameters are not measured, the trend of seasonal change is physically reasonable. However, it is difficult to retrieve the true values of soil moisture and model parameters by using remote sensing surface temperature. Beven and Freer [2001] proposed that different initial model states can lead to similar end model states; this is known as equifinality. Thus, different combinations of soil moisture and model parameters can lead to similar turbulent fluxes predictions. The uncertainties in the retrieved parameters can be removed by assimilating observations that are closely related to them.

5. Conclusions [51] In this study, a data assimilation scheme was developed on the basis of the EnKF algorithm and CoLM to estimate turbulent fluxes by the simultaneous optimization of soil moisture and model parameters. GOES LST retrieval

Table 9. AE Values of Assimilating MODIS and GOES Temporal Resolution Surface Temperatures

Ts(K) −2

H(W m ) LE(W m−2)

MODIS/GOES

Brookings

Goodwin

Bondville

Mead

Chestnut

Missouri

Average

MODIS GOES MODIS GOES MODIS GOES

1.2 0.5 23.6 11.3 42.6 18.8

1.5 1.3 35.1 30.7 57.5 46.2

0.4 0.5 11.2 16.2 13.9 19.6

0.3 0.2 9.7 7.4 11.3 8.6

0.2 0.1 5.2 1.9 6.2 2.6

0.1 0.1 4.1 4.1 4.5 4.8

0.6 0.5 14.8 11.9 22.7 16.8

12 of 16

D09109


D09109

Figure 8. Comparisons between assimilation results of MODIS and GOES temporal resolution surface temperature at Brookings site from Julian days 171 to 200, 2006. OBS, ground measurements; MODIS Time and GOES Time, results with the assimilation of MODIS and GOES temporal resolution surface temperature. data were assimilated into this scheme, and the results were validated at six observation sites in the United States. [52] The average reductions in the RMSE values of six sites were 47.5 and 31.1 W m−2 for sensible and latent heat fluxes, respectively (Table 5). Besides the improvements in the model predictions, the model uncertainties (AE) were also considerably reduced. The average reductions in the AE values of six sites were 13.4 and 22.1 W m−2 for sensible and latent heat fluxes, respectively (Table 6). The effects of the simultaneous optimization were compared with inde-

pendent optimizations of soil moisture and model parameters, and simultaneous optimization results yielded the smallest RMSE values (Figure 7). Soil moisture was found to play a more important role than model parameters in grasslands than in cropland and forestland covers and vice versa. In order to explore the effects of MODIS and GOES temporal resolution data on the assimilation results, ground‐ measured surface temperatures were assimilated into CoLM with the same temporal resolution as MODIS and GOES data. The results indicated that the average RMSE and AE

13 of 16

D09109


D09109

Figure 9. Comparisons of soil moisture retrievals between simulation and assimilation at Goodwin site from Julian days 101 to 301, 2006. (a) Results in 10 cm depth. (b) Results in 20 cm depth. values obtained as a result of GOES assimilation were smaller than those obtained from the MODIS temporal resolution data; this conclusion is distinct for the Brookings site, while they are similar at other sites. Although GOES

observations have short revisit times, they are correlated in time. Since the model parameters are uncorrelated, using multisatellite data sets, such as land surface temperature, soil moisture, vegetation structure, and albedo (retrievals from

Figure 10. The averaged seasonal pattern of model parameters (a) z0m, (b) alpha, (c) vmax25, and (d)gradm at Bondville site from Julian days 101 to 301, 200. 14 of 16

D09109


MODIS, GOES, and SMOS), may overcome the defects of one data set. Meanwhile, upscaling and downscaling studies should be enhanced for multisatellite data at different spatial scales. Further, in this study, soil moisture and model parameters were estimated. The retrieved soil moisture was found to be closer to the observed value than that from simulation for most of the time period, and the uncertainties in the model parameters were within a relatively narrow range. The four vegetation parameters showed distinct seasonal variations. Because of insufficient information, it was difficult to retrieve the true value of these variables and parameters. [53] A few problems remain that need to be resolved to improve the estimation of turbulent fluxes by the assimilation of GOES LST retrieval data. First, although there are different spatial and temporal scales between GOES data and field measurements, there are still some large errors in the GOES LST retrieval data (Figure 1). Second, turbulent fluxes predictions are indirectly enhanced with the assimilation of land surface temperatures because the relationship between surface temperature and turbulent fluxes is also dependent on the model parameterization. Both LeMone et al. [2008] and Chen et al. [2010] indicated that because of an inappropriate parameterization of aerodynamic resistance, the land surface model tends to overestimate sensible heat flux and underestimate surface temperature in relatively dry conditions. Inappropriate parameterization could lead to suboptimal assimilation results, and the predicted turbulent fluxes might not be accurate even though the surface temperatures are well estimated. In order to resolve the above problems, first, land surface temperature retrieval theories and GOES LST retrieval algorithms must be improved. Second, studies on the parameterization scheme of land processes and calibrations of model parameters must be intensified. [54] In this study, the data assimilation system optimizes both model parameters and state variables at a short‐term scale. However, the model parameters (e.g., sand and clay) and state variables (e.g., soil moisture) vary at different time scales in the real world. Therefore, a time‐split (or a dual‐ pass) data assimilation framework optimizing model parameters and state variables at different time scales should be developed in the future. [55] Acknowledgments. This work was supported by NASA under grant NNX08AC53G, the National Natural Science Foundation of China (40971194 and 30911130504), and the Fundamental Research Funds for the Central Universities. The leading author is also funded by the Chinese Scholarship Program. We thank Xiufang Zhu and Xin Tao for processing some GOES data used in this paper.

References Albergel, C., J. C. Calvet, J. F. Mahfouf, C. Rudiger, A. L. Barbu, S. Lafont, J. L. Roujean, J. P. Walker, M. Crapean, and J. P. Wigneron (2010), Monitoring of water and carbon fluxes using a land data assimilation system: A case study for southwestern France, Hydrol. Earth Syst. Sci., 14, 1109–1124, doi:10.5194/hess-14-1109-2010. Baldocchi, D., E. Falge, L. H. Gu, and R. Olson (2001), FLUXNET: A new tool to study the temporal and spatial variability of ecosystem‐scale carbon dioxide, water vapor, and energy flux densities, Bull. Am. Meteorol. Soc., 82, 2415–2434, doi:10.1175/1520-0477(2001)0822.3. CO;2. Bastiaanssen, W. G. M., M. Menenti, R. A. Feddes, and A. A. M. Holtslag (1998), The surface energy balance algorithm for land (SEBAL): Part 1.

D09109

Formulation, J. Hydrol., 212–213, 198–212, doi:10.1016/S0022-1694 (98)00253-4. Beaudet, M., C. Messier, and D. W. Hilbert (2000), Leaf‐and plant‐level carbon gain in yellow birch, sugar maple, and beech seedlings from contrasting forest light environments, Can. J. For. Res., 30, 390–404, doi:10.1139/cjfr-30-3-390. Beven, K., and J. Freer (2001), Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, 11–29, doi:10.1016/S0022-1694(01)00421-8. Boni, G., D. Entekhabi, and F. Castelli (2001), Land data assimilation with satellite measurements for the estimation of surface energy balance components and surface control on evaporation, Water Resour. Res., 37, 1713–1722, doi:10.1029/2001WR900020. Caparrini, F., F. Castelli, and D. Entekhabi (2004), Estimation of surface turbulent fluxes through assimilation of radiometric surface temperature sequences, J. Hydrometeorol., 5, 145–159, doi:10.1175/1525-7541 (2004)0052.0.CO;2. Chen, T., J. Morris, and E. Martin (2005), Particle filters for state and parameter estimation in batch processes, J. Process Contr., 15, 665–673, doi:10.1016/j.jprocont.2005.01.001. Chen, Y., K. Yang, D. Zhou, J. Qin, and X. Guo (2010), Improving Noah land surface model in arid regions with an appropriate parameterization of the thermal roughness length, J. Hydrometeorol., 11, 995–1006, doi:10.1175/2010JHM1185.1. Crow, W. T., and R. H. Reichle (2008), Comparison of adaptive filtering techniques for land surface data assimilation, Water Resour. Res., 44, W08423, doi:10.1029/2008WR006883. Crow, W. T., W. P. Kustas, and J. H. Prueger (2008), Monitoring root‐zone soil moisture through the assimilation of a thermal remote sensing‐based soil moisture proxy into a water balance model, Remote Sens. Environ., 112, 1268–1281, doi:10.1016/j.rse.2006.11.033. Dai, Y. J., X. B. Zeng, and R. E. Dickinson (2001), Common Land Model (CLM): Technical documentation and user’s guide, 69 pp., Ga. Inst. of Technol., Atlanta. Dai, Y. J., et al. (2003), The common land model, Bull. Am. Meteorol. Soc., 84, 1013–1023, doi:10.1175/BAMS-84-8-1013. Dai, Y. J., R. E. Dickinson, and Y. P. Wang (2004), A two‐big‐leaf model for canopy temperature, photosynthesis, and stomatal conductance, J. Clim., 17, 2281–2299, doi:10.1175/1520-0442(2004)0172.0.CO;2. Dickinson, R. E., P. J. Kennedy, A. Henderson‐Sellers, and M. Wilson (1986), Biosphere‐Atmosphere Transfer Scheme (BATS) version 1E as coupled to the NCAR Community Climate Model, NCAR Tech. Rep. TN‐275+STR, 72 pp., NCAR, Boulder, Colo. Entekhabi, D., H. Nakamura, and E. Njoku (1994), Solving the inverse problem for soil moisture and temperature profiles by sequential assimilation of multifrequency remotely sensed observations, IEEE Trans. Geosci. Remote Sens., 32, 438–448, doi:10.1109/36.295058. Evensen, G. (1994), Sequential data assimilation with a nonlinear quasi‐ geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10,143–10,162, doi:10.1029/94JC00572. Fisher, J. B., K. P. Tu, and D. D. Baldocchi (2008), Global estimates of the land‐atmosphere water flux based on monthly AVHRR and ISLSCP‐II data, validated at 16 FLUXNET sites, Remote Sens. Environ., 112, 901–919, doi:10.1016/j.rse.2007.06.025. Huang, C. L., X. Li, and L. Lu (2008), Retrieving soil temperature profile by assimilating MODIS LST products with ensemble Kalman filter, Remote Sens. Environ., 112, 1320–1336, doi:10.1016/j.rse.2007.03.028. Jazwinski, A. H. (1970), Stochastic Processes and Filtering Theory, 376 pp., Elsevier, New York. Kalman, R. E. (1960), A new approach to linear filtering and prediction problems, J. Basic Eng., 82, 35–45. Kumar, P., and A. L. Kaleita (2003), Assimilation of near‐surface temperature using extended Kalman filter, Adv. Water Resour., 26, 79–93, doi:10.1016/S0309-1708(02)00098-2. LeMone, M., M. Tewari, F. Chen, J. Alfieri, and D. Niyogi (2008), Evaluation of the Noah land surface model using data from a fair‐weather IHOP_2002 day with heterogeneous surface fluxes, Mon. Weather Rev., 136, 4915–4941, doi:10.1175/2008MWR2354.1. Liang, S. (2004), Quantitative Remote Sensing of Land Surfaces, 534 pp., John Wiley, Hoboken, N. J. Liang, S., and J. Qin (2008), Data assimilation methods for land surface variable estimation, in Advances in Land Remote Sensing: System, Modeling, Inversion and applications, edited by S. Liang, pp. 319–339, Springer, New York. Liu, S. M., G. Hu, L. Lu, and D. F. Mao (2007), Estimation of regional evapotranspiration by TM/ETM+ data over heterogeneous surfaces, Photogramm. Eng. Remote Sens., 73, 1169–1178.

15 of 16

D09109


Lo, E. (2005), Gaussian error propagation applied to ecological data: Post‐ ice‐storm‐downed woody biomass, Ecol. Monogr., 75, 451–466, doi:10.1890/05-0030. Margulis, S. A., D. McLaughlin, D. Entekhabi, and S. Dunne (2002), Land data assimilation and estimation of soil moisture using measurements from the Southern Great Plains 1997 Field Experiment, Water Resour. Res., 38(12), 1299, doi:10.1029/2001WR001114. Mauder, M., C. Liebethal, M. Göckede, J. P. Leps, F. Beyrich, and T. Foken (2006), Processing and quality control of flux data during LITFASS‐2003, Boundary Layer Meteorol., 121, 67–88, doi:10.1007/s10546-006-9094-0. Meyer, S. L. (1975), Data Analysis for Scientists and Engineers, 513 pp., John Wiley, Hoboken, N. J. Mölders, N. (2005), Plant and soil parameter caused uncertainty of predicted surface fluxes, Mon. Weather Rev., 133, 3498–3516, doi:10.1175/ MWR3046.1. Oncley, S. P., T. Token, R. Vogt, W. Kohsiek, H. A. R. De Bruin, C. Bernhofer, C. Andreas, and E. V. Gorsel (2007), The energy balance experiment EBEX‐ 2000. Part I: Overview and energy balance, Boundary Layer Meteorol., 123, 1–28, doi:10.1007/s10546-007-9161-1. Pipunic, R. C., J. P. Walker, and A. Western (2008), Assimilation of remotely sensed data for improved latent and sensible heat flux prediction: A comparative synthetic study, Remote Sens. Environ., 112, 1295–1305, doi:10.1016/j.rse.2007.02.038. Qin, J., S. Liang, K. Yang, T. Koike, R. Liu, and I. Kaihotsu (2009), Simultaneous estimation of both soil moisture and model parameters using particle filtering method through the assimilation of microwave signal, J. Geophys. Res., 114, D15103, doi:10.1029/2008JD011358. Reichle, H. R., D. B. Mclaughlin, and D. Entekhabi (2002), Hydrologic data assimilation with the ensemble Kalman filter, Mon. Weather Rev., 130, 103–114, doi:10.1175/1520-0493(2002)1302.0. CO;2. Schuurmans, J. M., P. A. Troch, A. A. Veldhuizen, W. G. M. Bastiaanssen, and M. F. P. Bierkens (2003), Assimilation of remotely sensed latent heat flux in a distributed hydrological model, Adv. Water Resour., 26, 151–159, doi:10.1016/S0309-1708(02)00089-1. Sellers, P. J., D. A. Randall, G. J. Collatz, C. B. Field, D. A. Dazlich, C. Zhang, G. D. Collelo, and L. Bounoua (1996), A revised land surface parameterization (SiB2) for atmosphere GCMs, part I: Model formulation, J. Clim., 9, 676–705, doi:10.1175/1520-0442(1996)009 2.0.CO;2.

D09109

Su, Z. (2002), The surface energy balance system (SEBS) for estimation of turbulent heat fluxes, Hydrol. Earth Syst. Sci., 6, 85–100, doi:10.5194/ hess-6-85-2002. Sun, D., and R. T. Pinker (2003), Estimation of land surface temperature from a Geostationary Operational Environmental Satellite (GOES‐8), J. Geophys. Res., 108(D11), 4326, doi:10.1029/2002JD002422. Sun, D., R. T. Pinker, and J. B. Rasara (2004), Land surface temperature estimation from the next generation of Geostationary Operationary Environmental Satellites: GOES M‐Q, J. Appl. Meteorol., 43, 363–372, doi:10.1175/1520-0450(2004)0432.0.CO;2. Tian, X., Z. Xie, A. Dai, C. Shi, B. Jia, F. Chen, and K. Yang (2009), A dual‐pass variational data assimilation framework for estimating soil moisture profiles from AMSR‐E microwave brightness temperature, J. Geophys. Res., 114, D16102, doi:10.1029/2008JD011600. Wang, W. H., S. L. Liang, and M. Tilden (2008), Validating MODIS land surface temperature products using long‐term nighttime ground measurements, Remote Sens. Environ., 112, 623–635, doi:10.1016/j.rse.2007.05.024. Williams, M., A. D. Richardson, and M. Reichstein (2009), Improving land surface models with FLUXNET data, Biogeosciences, 6, 1341–1359, doi:10.5194/bg-6-1341-2009. Wilson, K. A. G., and E. Falgec (2002), Energy balance closure at FLUXNET sites, Agric. For. Meteorol., 113, 223–243, doi:10.1016/S0168-1923(02) 00109-0. Xu, T. R., S. M. Liu, S. Liang, and J. Qin (2011), Improving predictions of water and heat fluxes by assimilating MODIS land surface temperature products into Common Land Model, J. Hydrometeorol., 12, 227–244, doi:10.1175/2010JHM1300.1. Yang, K., et al. (2007a), Initial CEOP‐based review of the prediction skill of operational general circulation models and land surface models, J. Meteorol. Soc. Jpn., 85A, 99–116, doi:10.2151/jmsj.85A.99. Yang, K., W. Takahiro, and K. Toshio (2007b), An auto‐calibration system to assimilate AMSR‐E data into a land surface model for estimating soil moisture and surface energy budge, J. Meteorol. Soc. Jpn., 85A, 229–242, doi:10.2151/jmsj.85A.229. S. Liang, Department of Geography, University of Maryland, College Park, MD 20742, USA. S. Liu and T. Xu, State Key Laboratory of Remote Sensing Science, School of Geography, Beijing Normal University, 19 Xinjiekouwai Street, Beijing 100875, China. ([email protected])

16 of 16