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Aug 25, 2014 - only uses the first-order terms of the Taylor series expansion of nonlinear functions; and .... to the system state via the observation operator H at time k. ...... Jones, G., P. Willett, R. C. Glen, A. R. Leach, and R. Taylor, R (1997), ...
PUBLICATIONS Water Resources Research RESEARCH ARTICLE 10.1002/2012WR013473 Key Points:  A new data assimilation system  MODIS LST  Poorly gauged catchments

Correspondence to: X. Fu, [email protected] Citation: Yu, Z., X. Fu, L. Luo, H. L€ u, Q. Ju, D. Liu, D. A. Kalin, D. Huang, C. Yang, and L. Zhao (2014), One-dimensional soil temperature simulation with Common Land Model by assimilating in situ observations and MODIS LST with the ensemble particle filter, Water Resour. Res., 50, 6950–6965, doi:10.1002/ 2012WR013473. Received 31 DEC 2012 Accepted 6 AUG 2014 Accepted article online 8 AUG 2014 Published online 25 AUG 2014

One-dimensional soil temperature simulation with Common Land Model by assimilating in situ observations and MODIS LST with the ensemble particle filter Zhongbo Yu1,2, Xiaolei Fu1, Lifeng Luo3,4, Haishen L€ u1, Qin Ju1, Di Liu1, Dresden A. Kalin5, Dui Huang1, Chuanguo Yang1, and Lili Zhao1 1

State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Hydrology and Water Resources, Hohai University, Nanjing, China, 2Department of Geoscience, University of Nevada Las Vegas, Las Vegas, Nevada, USA, 3Department of Geography, Michigan State University, East Lansing, Michigan, USA, 4Center for Global Change and Earth Observations, Michigan State University, East Lansing, Michigan, USA, 5College of Osteopathic Medicine Business Office, Michigan State University, East Lansing, Michigan, USA

Abstract Soil temperature plays an important role in hydrology, agriculture, and meteorology. In order to improve the accuracy of soil temperature simulation, a soil temperature data assimilation system was developed based on the Ensemble Particle Filter (EnPF) and the Common Land Model (CLM), and then applied in the Walnut Gulch Experimental Watershed (WGEW) in Arizona, United States. Surface soil temperature in situ observations and Moderate Resolution Imaging Spectroradiometer Land Surface Temperature (MODIS LST) data were assimilated into the system. In this study, four different assimilation experiments were conducted: (1) assimilating in situ observations of instantaneous surface soil temperature each hour, (2) assimilating in situ observations of instantaneous surface soil temperature once per day, (3) assimilating verified MODIS LST once per day, and (4) assimilating original MODIS LST once per day. These four experiments reflect a transition from high-quality and more frequent in situ observations to lower quality and less frequent remote sensing data in the data assimilation system. The results from these four experiments show that the assimilated results are better than the simulated results without assimilation at all layers except the bottom layer, while the superiority gradually diminishes as the quality and frequency of the observations decrease. This demonstrates that remote sensing data can be assimilated using the ensemble particle filter in poorly gauged catchments to obtain highly accurate soil variables (e.g., soil moisture, soil temperature). Meanwhile, the results also demonstrate that the ensemble particle filter is effective in assimilating soil temperature observations to improve simulations, but the performance of the data assimilation method is affected by the frequency of assimilation and the quality of the input data.

1. Introduction Soil temperature is as important as soil moisture in many fields. For instance, in solar energy applications, soil temperature is an important parameter in the passive heating and cooling of buildings and agricultural greenhouses [Mihalakakou, 2002]; in land surface processes, it can influence energy and water cycles of the land-atmosphere system [Huang et al., 2008]. In environmental modeling, surface soil temperature plays a crucial role, especially in normalizing microwave radiobrightness measurements in the inverse radiative transfer model for the soil moisture and vegetation optical depth retrieval [Owe and De Jeu, 2003]. When direct observations are unavailable, soil temperature can be simulated using a variety of models. Land surface models (e.g., Common Land Model [Dai et al., 2003; Oleson et al., 2004], Simple Biosphere Model [Sellers et al., 1996]) can derive soil temperature from the meteorological, local soil and vegetation information. However, due to the uncertainties in these information and the land surface model itself [Mihalakakou, 2002], the simulated soil temperature inevitably contains errors. As far as in situ observations are concerned, traditional measuring techniques rely on the point measurements of soil temperature, and it is impractical to obtain high-density observations in large areas. Thus, these in situ measurements frequently introduce large errors because of the high spatial variability of soil temperature [Owe and De Jeu, 2003]. Remote sensing technology, such as the Moderate Resolution Imaging

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Spectroradiometer (MODIS) thermal infrared (TIR) has the potential for providing more reliable estimation of spatially averaged surface soil temperature [Owe and De Jeu, 2003; Njoku and Li, 1999; Owe and Van de Griend, 2001], and surface temperature obtained via satellites can then be used to improve models and methods for evaluating the land-surface energy balance [Wan and Dozier, 1996; Diak and Whipple, 1993]. However, MODIS Land Surface Temperature (LST) also has shortcomings. It is instantaneous, so, it cannot capture the continuous variation of land surface temperature. The accuracy of the retrieval is also influenced by atmospheric conditions such as cloud cover and water vapor content. Additionally, because satellite sensors do not penetrate the soil surface, remote sensing of deep layer soil temperature is infeasible [Huang et al., 2008]. Given the shortcomings of the available data sources and the importance of accurate soil temperature inputs in determining the predictive capability of hydrological and climatic models, data assimilation is used in this study to improve the model results. Numerous data assimilation methods have been developed over the past several decades with varying levels of performance. For instance, the Kalman filter [Kalman, 1960] is limited by the assumed linear dynamic system with Gaussian distribution; the extended Kalman filter (EKF) [Anderson and Moore, 1979; Miller et al., 1999; L€ u et al., 2010a, 2010b, 2011; Han and Li, 2008; Kumar and Kaleita, 2003] only uses the first-order terms of the Taylor series expansion of nonlinear functions; and the ensemble Kalman filter (EnKF) [Burgers et al., 1998; Huang et al., 2008; Evensen, 1994; Houtekamer and Mitchell, 1998; Han and Li, 2008; Yu et al., 2012, 2014; Fu et al., 2014] is limited by the conventional distribution (e.g., Gaussian distribution). The particle filter (PF) is limited by the instantaneous posterior density function. A new method, the ensemble particle filter (EnPF), was introduced [Yu et al., 2012, 2014] and evaluated against EnKF and PF with the predictions of soil moisture [Yu et al., 2012] and soil temperature [Yu et al., 2014]. Both studies suggested that EnPF is the most accurate method. Thus EnPF is also used in this study. Before the experiments were conducted, the genetic algorithm (GA) [Deb et al., 2002; Bies et al., 2006; Jones et al., 1997; Arifovic, 1994] was used to optimize soil thermal conductivity to obtain more accurate soil moisture simulations. Both MODIS LST and in situ observations were collected at the Walnut Gulch Experiment Watershed (WGEW) in Arizona, United States. A short description of the study area and available observations are provided in section 2, followed by the experimental design in section 3. Sections 4 and 5 present results and discussion, respectively, while the findings for this study are summarized in section 6.

2. Study Area and Data The Walnut Gulch Experimental Watershed (WGEW), located in southeastern Arizona and covering an area of approximately t 149 km2, is a tributary of the San Pedro River [Keefer et al., 2008]. Precipitation has been measured in this area since August 1953. Other meteorological and soil hydrology records are available from 1990 to 2006. The average annual precipitation measured with six gauges during the period of 1956– 2005 is 312 mm, with approximately 60% falling during the summer monsoon season [Goodrich et al., 2008; Wang et al., 2011]. Meteorological measurements at three weather stations (LHMet, KENMet, and ShopMet) include air temperature (Ta), relative humidity (RH), wind speed (Ws), wind direction (Wd), barometric pressure (Bar), solar radiation (Sol), photosynthetically active radiation (PAR), and net radiation (Rnet). Soil hydrological properties measured at 3 weather stations, 5 trench sites, and 19 rain gauges include soil moisture (SM), soil temperature (ST), soil heat flux (SHF), and soil surface temperature (Tsur). Details about the database can be found in Keefer et al. [2008], and the data set can be obtained at http://www.tucson.ars.ag.gov/ dap. In this study, inputs in the model consist of the meteorological and soil hydrologic parameters Ta, Ws, Bar, Rnet, and SM, ST, SHF, Tsur; other required parameters and variables such as air temperature, leaf area index, wind speed, net radiation, and day length are also included. Soil hydrological variables are measured with a time interval of 20 min. Among the three sites, only LHMet and KENMet provided complete meteorological and soil hydrological variables and parameters, so they are selected for conducting the numerical experiments in this study (Figure 1). These two sites both have sandy loam soil but with different vegetation cover. The LHMet site is mainly covered by shrubs while the KENMet site is covered by grass. The slopes in LHMet and KENMet sites are 3–8% and 4–9%, respectively. LAI used in the model comes from the MODIS land products, and the description of MODIS land products can be found in Wang et al. [2011]. The MODIS land products also include MODIS land surface temperature

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(MODIS LST) that is assimilated in this study. The MODIS land products can be obtained from NASA Land Processes Distributed Active Archive Center (https://lpdaac.usgs.gov/ lpdaac/). Although there are many gaps in the MODIS LST at the two sites in 2004, but an unbroken period of daily observations about MODIS LST exists from Figure 1. The location of LHMet and KENMet sites at WGEW. 22 September to 21 October, 2004, so this period data were used to conduct the experiments to avoid the interpolation error in the model inputs. The data from 22 September (day 266) to 1 October (day 275), 2004 at WGEW were used to calibrate the model, and the data from 2 October (day 276) to 21 October (day 295) were used to conduct the assimilation experiments.

3. Methodology In situ soil temperature observations are available every 20 min, and MODIS LST data are available at daily intervals. We conducted four experiments in this study for assimilating different observations with different frequencies: 1. Assimilating in situ observations of surface layer soil temperature hourly into the model; 2. Assimilating in situ observations of surface soil temperature once per day at the same time that MODIS LST is available; 3. Assimilating the MODIS LST corrected by the in situ surface soil temperature observation. This is basically the same as experiment 2, but replacing the in situ soil temperature observations with the bias-corrected MODIS LST; 4. Assimilating the original MODIS LST into the model once per day. These experiments are designed to show how the quality and frequency of soil temperature observations can affect the performance of a data assimilation scheme, as well as to demonstrate the usefulness of data assimilation under different situations. Figure 2 shows the flowchart of the data assimilation system. The Common Land Model (CLM) [Dai et al., 2003; Oleson et al., 2004] is used as the model operator, and the ensemble particle filter [Yu et al., 2012, 2014] is used to integrate the simulated results and update the state variables produced by the model operator. GA is used in this study to optimize the thermal conductivity during the model calibration. Details of the model operator, EnPF, and GA are given here. 3.1. Model Operator The model used in this study is version 3.0 of the CLM. The CLM was designed for coupling with atmospheric models and it can provide lower boundary conditions to atmospheric modeling, including surface albedos, upward longwave radiation, sensible heat flux, latent heat flux, water vapor flux, and zonal and meridional surface stresses. The CLM is a simplified treatment of surface processes but can reproduce important essential characteristics of land-atmosphere interactions for climate simulations and weather prediction at a minimal computational cost. Details of the CLM can be found in Oleson et al. [2004]. The CLM can have up to 10 layers in the soil column and up to five layers of snow depending on the snow depth [Oleson et al., 2004]. In this study, we discretized the soil column into five layers. The one-dimensional heat diffusion equation for soil temperature in the CLM is written as:

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c

@T @F 52 @t @z

(1)

where c is volumetric soil heat capacity (Jm23K21), T is soil temperature (K), t is time (h), F is heat flux (Wm22), and z is vertical depth (m). F can be described as: F52k

@T @z

(2)

where k is thermal conductivity (Wm21K21). Equation (1) is discretized for each soil layer [Oleson et al., 2004] by using the Crank-Nicholson method, which combines the explicit method with fluxes  n  evaluated at n Fi21 ; Fin and the implicit method with fluxes evaluated at n 1 1  n11 n11  Fi21 ; Fi , ci Dzi  n11 n   n n  Ti 2Ti 5a Fi 2Fi21 Dt   n11 1ð12aÞ Fin11 2Fi21

(3)

where a 5 0.5, and ci and Dzi are volumetric soil heat capacity (Jm23K21) and soil thickness (m) at the layer i, respectively. Dt is the time step (h). Tin is soil temperature (K) at layer i and time n. Fin is heat flux across layer i to layer i 1 1.   Ti 2Ti11 (4) Fi 52k½zh;i  zi11 2zi where k½zh;i  is thermal conductivity at the interface zh,i between layer i and layer i 1 1 and k½zh;i  is optimized using the genetic algorithm (GA) (Figure 3) which is described in section 3.3 to replace the calculation using Johansen’s method as reported in Farouki [1981]. Before solving the equations, appropriate initial and boundary conditions need to be specified. Initial soil temperature and top boundary (soil surface) are set as Tðz; t50Þ5TðzÞ at different layers and F5Rn;g 2Hg 2LEg , respectively, where F is the subsurface heat flux, Rn,g represents Figure 2. Flowchart of assimilating observations in situ and MODIS LST with the net radiation absorbed by the EnPF. ground surface, and Hg and LEg represent the sensible and latent heat fluxes, respectively. At the bottom of the soil column, heat flux Fi is assumed to be zero [Oleson et al., 2004; Dai et al., 2003]. 3.2. Ensemble Particle Filter (EnPF) In the data assimilation system, there are two functions: the nonlinear state function G, which maps the previous state Xk21 at time k 2 1 to state Xk at time k and the linear or nonlinear observation function H, which specifies the deterministic relationship between the system states and observations [Chen et al., 2005;

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Figure 3. Flowchart of the genetic algorithm.

Ferrante and Frigo, 2009; Yu et al., 2012; Han and Li, 2008; Oppenheim et al., 2008; Simandl and Straka, 2008; Zhao and Li, 2010; Kumar et al., 2008; Xie and Zhang, 2010]. These two functions can be expressed as follows: Xk 5GðXk21 ; Vk21 Þ

(5)

(6) Zk 5HðXk ; Uk Þ  k k k k k where Xk 5 T1 ; T2 ; T3 ; T4 ; T5 simu is the state vector (vector of simulated soil temperature) at time k; and Zk 5  k k k k k T1 ; T2 ; T3 ; T4 ; T5 obs is the measurement vector (vector of observed soil temperature) which is connected to the system state via the observation operator H at time k. Vk and Uk are independent and identically distributed noise for the state vector and measurement vector, respectively, at time k.

Ensemble particle filter (EnPF) was introduced by Yu et al. [2012, 2014] to combine the advantages of EnKF [Burgers et al., 1998; Huang et al., 2008; Evensen, 1994; Houtekamer and Mitchell, 1998; Kumar et al., 2008] and PF [Rawlings and Bakshi, 2006]. EnKF works well only when forecast errors conform to Gaussian distribution. For PF, the Sequential Importance Resampling (SIR) [Gordon et al., 1993] and Residual Resampling (RR) [Liu and Chen, 1998] are often used in the assimilation process as methods

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of avoiding the degeneracy of the sequential importance sampling (SIS) [Weerts and Serafy, 2006]. EnPF first uses PF to obtain the predicted results which can be considered to conform to Gaussian distribution, then uses PF to obtain the new particles weights and returns to EnKF. The details of EnPF are given below. 3.2.1. Prediction Step First, the particles Xki ði51;    ; NÞ with initial values Xk0 are generated according to the uniform distribution   U Xk0 2R; Xk0 1R , and the corresponding weights Wki are obtained using the following equation [Liu and Chen, 1998; Weerts and Serafy, 2006; Van Leeuwen, 2010]:   2 expð20:5=RÞ Zk 2H Xki Wki 5 XN (7)   i 2 expð20:5=RÞ Z 2H X k k i51   0 NWki 2fix NWki (8) Wki 5 XN N2 i51 li   where li 5fix NWki (fixðXÞ rounds the elements of X to the nearest integers toward zero), Zk is the measured value, and R is the measurement noise variance. The following equation is then used to obtain the predicted values X^ k : X^ k 5

N X

0

Wki Xki

(9)

i51

3.2.2. Update Step Next, we resample the particles after obtaining the predicted X^ k in the prediction step, and recalculate the 0 weights Wki according to equation (7) and (8). The updated values are then obtained with the following equations: Xk 5

N X

0

Wki Xki

(10)

i51

  Ek 5 Xk1 2Xk ;    ; XkN 2Xk Pk 5

1 Ek EkT N21

Kk 5Pk HT ðHPk HT 1RÞ21

where R is the measurement noise variance and Kk is Kalman gain. h i up Xk;i 5Xki 1Kk Zki 2H½Xk 

(11) (12) (13)

(14)

The following is the estimated value at time k: Xkup 5

N X

0

up Wki Xk;i

(15)

i51

up where Xk;i is the updated state vector ensemble, and Zki is the generated ensemble of measurements [Weerts and Serafy, 2006]. If the measurements are a nonlinear combination of state variables, the terms PHT and HPHT can be calculated using the following equations [Huang et al., 2008; Houtekamer and Mitchell, 2001]:

PHT 5 HPHT 5

N      T 1 X Xki 2Xk H Xki 2H Xk N21 i51

N         T 1 X H Xki 2H Xk H Xki 2H Xk N21 i51

(16)

(17)

where

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N   1X   H Xk 5 H Xki N i51

(18)

3.3. Genetic Algorithm Soil thermal conductivity k is one of the most important parameters that affect soil temperature simulations in the CLM. However, its value at each soil layer for different experimental sites is uncertain. To obtain the optimized soil thermal conductivity, the genetic algorithm is used to calibrate the model before conducting data assimilation experiments. The genetic algorithm inspired by Darwin’s evolution theory is a very general, robust optimized algorithm [Bies et al., 2006; Deb et al., 2002; Jones et al., 1997; Arifovic, 1994]. It was developed on the basis of the mathematics of evolution/natural selection and survival of the fittest. It starts with a set of solutions called population. Motivated by a hope that the new population will be better than the old one, solutions from one population are taken to form a new offspring. Those solutions are selected according to their fitness, i.e. the more suitable they are, the more chances they have to reproduce. The flowchart of GA is shown in Figure 3, and the details of GA can be found in http://www.obitko.com/tutorials/genetic-algorithms/index.php. 3.4. Evaluation Criterion To evaluate the performance of the data assimilation system in helping improve simulation accuracy and whether the assimilation of MODIS LST can be used to obtain soil temperature profiles at poorly gauged catchments, the root mean square error (RMSE) is used to measure the performance of the simulations. It can be calculated as follows: n  2 1X RMSE5 Xpred;i 2Xobs;i n i51

!1=2 (19)

where Xpred;i is the simulated soil temperature at time i, Xobs;i is the observed soil temperature at time i, and n is the total number of simulated periods.

4. Results 4.1. Model Calibration with GA The CLM model was calibrated to make sure that the accuracy satisfies the study requirements. In the process of calibration, the major parameter is soil thermal conductivity k½zh;i  at the interface zh,i between layer i and layer i 1 1. The documented k½zh;i  range from 0.19 to 1.12 Wm21K21 for sandy loam [Abu-Handeh and Reeder, 2000] was optimized through GA at the experimental sites LHMet and KENMet. It was assumed that k½zh;i  at different layers was independent. Based on the above assumption, k½zh;i  was optimized through GA to minimize the RMSE of soil temperature simulation, and the optimized results at the experimental sites LHMet and KENMet can be seen in Figure 4. The maximum number of generations (NG) was set at 50, and the population was set at 40. It can be seen that when NG 5 45, k½zh;i  was stable at every interface between layer i and layer i 1 1 for the two experimental sites. Here the optimal values of k½zh;i  were [1.1190, 1.1175, 0.8527, 1.1097] and [0.6023, 1.1190, 1.1199, 1.1199] at four interfaces between the five soil layers for LHMet and KENMet sites, respectively. The verified results are shown in Figure 5 for LHMet and KENMet sites. From Figure 5, it is not difficult to find that the simulated results without assimilation (hereafter only called simulated results) can reflect the soil temperature variation at the first four layers, but not at the fifth layer (100 cm). The simulated results changed linearly overall at the fifth layer. This is because the simulated results are mainly influenced by the soil heat flux, the content of soil moisture, the soil thermal conductivity, and the soil temperature at last layer (50 cm). However, the soil heat flux was assumed to be zero at the bottom boundary, the soil thermal conductivity was optimized with GA, the content of soil moisture was stable at such a deep layer, and the change of soil temperature at the last layer (50 cm) was not significant, so the change of simulated results seems linear. There may be other factors (e.g. ground water or deep water transpiration) that can affect the simulated results in deep soil layers, but their influences were ignored in this study.

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LHMet r1

1.15 1.1

Thermal conductivity (W/(m K))

1.05 1.15

LHMet r2

1.1 1.05 1 1

LHMet r3

0.8 0.6 0.4

LHMet r4

1.15 1.1 1.05 1

0

5

10

15

20

25

30

35

40

Number of generations 1.5

KENMet r1

1 0.5 1.15

Thermal conductivity (W/(m K))

1.1

KENMet r2

1.05 1 1.2

45

50

4.2. Constructing Observation Operators The observation operator specifies the deterministic relationship between the observation data and system state. So, based on the surface in situ observation data or MODIS LST and verified data in section 4.1, the linear observation operators were constructed (Table 1). The standard deviations are also shown in Table 1. Through the observation operator, the system error can be processed as the observation error. After their construction, the operators were used in the following four experiments.

KENMet r3

1

4.3. Assimilating Hourly In Situ Observations of Surface KENMet r4 Soil Temperature 1.1 1.05 The observed soil hydrology 1 0 5 10 15 20 25 30 35 40 45 50 data are measured at a time Number of generations interval of 20 min at WGEW. Here, the observed soil temFigure 4. The optimized thermal conductivity k½zh;i 5ri by using GA, and k½zh;i  is at the interface between layers i and i11 at LHMet and KENMet sites. peratures in the soil surface layer were assimilated hourly from 2 October (day 276) to 21 October (day 295), 2004. However, to facilitate validation of the simulated results, we compared only the last 10 day (from day 286 to day 295) simulated and assimilated results from this experiment and other three experiments, and used the 10 day results to verify the performance of the assimilation system. The ensemble size was set at 60 because the assimilated results tend to be stable when the ensemble size is greater than 50 [Moradkhani et al., 2005; Vrugt et al., 2006]. The soil temperature observation error (60.2 C) given by Keefer et al. [2008] was used to generate the ensemble particles. The assimilated results are shown in Figure 6 for LHMet and KENMet sites. 0.8

1.15

Figure 6 shows that the assimilated results are closer to the observed data than simulated results in the first four layers at the LHMet site (the upper panel in Figure 6). In the fifth layer (100 cm), the assimilated results were generally a poorer fit to the observed data. For the KENMet site, the similar results were obtained (the bottom panel in Figure 6). The RMSE values for soil temperature between the simulated results and assimilated results at different layers are summarized in Table 2 for the four different experiments at each of the two experimental sites. Table 2 shows that the RMSE values of assimilation were smaller than that of simulation in the first four layers of this experiment, but at both sites, assimilation showed a worse performance of assimilation in the fifth layer. 4.4. Assimilating Daily In Situ Observations of Surface Soil Temperature As the MODIS sensor passes over the watershed from around 10:30 a.m. to 11:00 a.m. every day, the in situ observations at 10:40 a.m. from 2 October (day 276) to 21 October (day 295), 2004 were assimilated into the assimilation system. The assimilated results of the last 10 day period are shown in Figure 7 for LHMet and KENMet sites. In this experiment, the assimilated results were better than the simulated results compared to the observed data in the first four layers at the LHMet site (the upper panel in Figure 7) of most time. In the second layer (5 cm), the assimilated results were worse than the simulated results when the soil temperature reached its

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Temperature (K) Temperature (K) Temperature (K) Temperature (K)

Temperature (K)

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Observation

LHMet(0cm)

Simulation

300

250 310

LHMet(5cm)

300 290 280

300

LHMet(15cm)

295 290

298

LHMet(50cm)

296 294

298

LHMet(100cm)

296 294 276

281

286

291

295

Temperature (K) Temperature (K) Temperature (K) Temperature (K)

Temperature (K)

Julian Day

320

KENMet(0cm)

Observation

300 280 260

320

KENMet(5cm)

300 280

300

KENMet(15cm)

295 290

300

KENMet(50cm)

295

Simulation

maximum value each day except the last 4 day period. However, the assimilated results were better than the simulated results as the soil temperature reached its minimum value each day. In the third and fourth layers, the assimilated results were better than the simulated results compared to the observed data, especially for the last 8 day period. In the fifth layer (100 cm), the performance of the assimilation method was negative. Similar results were obtained for the KENMet site (the bottom panel in Figure 7). The RMSE values in Table 2 show results similar to that of assimilating hourly in situ observations of surface soil temperature, but with different accuracy.

290

4.5. Assimilating the Verified MODIS LST The data used in this 294 276 281 286 291 295 experiment were also Julian Day from 2 October (day Figure 5. The verified results with the optimized soil thermal conductivity at LHMet and KENMet sites 276) to 21 October from day 276 (2 October) to 295 (21 October), 2004. (day 295), 2004 at WGEW. Before conducting the assimilation process, the MODIS LST was corrected. The in situ observations are point measurements and the model is one-dimensional while MODIS LST is the averaged value over 1 km 31 km area. 298

KENMet(100cm)

296

Table 1. The Observation Operators and Standard Deviations Between the Observations and Verified Results at LHMet and KENMet Sites for Four Casesa LHMet

Obs_hourly Obs_daily MODIS_Obs MODIS

KENMet

Observation Operator

Std (K)

Observation Operator

Std (K)

y51.16x-45.91 y51.98x-277.88 y52.32x-374.71 y52.85x-531.56

4.59 2.78 3.34 4.59

y50.92x125.50 y50.71x190.13 y50.95x130.62 y50.91x144.29

4.28 2.62 3.41 4.22

a The observation operators and standard deviations between the observations and verified results at LHMet and KENMet sites for four cases: Obs_hourly, Obs_daily, MODIS_obs, and MODIS mean assimilating the surface observation in situ hourly, surface observation in situ daily (consistent with the time of obtainning MODIS LST), corrected MODIS LST by the surface observation in situ daily, and original MODIS LST into the assimilation system, respectively. x, y are the simulated and observed data, respectively.

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Temperature (K)

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Temperature (K)Temperature (K) Temperature (K) Temperature (K)

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Range

LHMet(0cm)

Observation

Simulation

Assimilation

320 300 280 260

LHMet(5cm)

300 290 280 300

LHMet(15cm)

295

290 298

LHMet(50cm)

296 294 292 298

LHMet(100cm)

296 294 286

288

290

292

294

295

Temperature (K)Temperature (K) Temperature (K) Temperature (K) Temperature (K)

Julian Day 320

KENMet(0cm)

Range

Observation

Simulation

Assimilation

300 280 260 300

KENMet(5cm)

295 290 285 298

KENMet(15cm)

296 294 292 290 298

KENMet(50cm)

296 294 292 298

KENMet(100cm)

296 294 286

288

290

292

294

295

Julian Day

Figure 6. The results of assimilating the surface observation in situ hourly into the assimilation system at LHMet and KENMet sites from day 286 (12 October) to 295 (21 October), 2004. Range produced using the ensemble maximum assimilation result and minimum assimilation result.

Due to the disparity in scales, MODIS LST is likely to suffer systematic bias as compared to the in situ observations. In this experiment, MODIS LST was bias-corrected based on in situ observations and then assimilated into the assimilation system. The in situ observations at 10:40 a.m. were selected again to compare with daily MODIS LST data from 10:30 a.m. to 11:00 a.m. As shown in Figure 8, the MODIS LST was higher than the in situ observations every day. This is because the vegetation covering the soil leads to lower in situ observations in the daytime compared to MODIS LST which is influenced by vegetation, cloud, terrain

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Table 2. The Soil Temperature (K) RMSE of Simulation and Assimilation at LHMet (Upper) and KENMet (Bottom) Sites for the Last 10 Day Period Assimilation Site

Deep (cm)

Simulation

Obs_hourly

Obs_daily

MODIS_obs

MODIS

0 5 15 50 100 0 5 15 50 100

3.26 1.93 1.28 0.50 0.16 1.88 1.38 0.75 0.37 0.22

2.01 1.00 0.62 0.33 0.45 1.38 0.84 0.43 0.27 0.34

3.16 1.52 0.75 0.24 0.22 1.80 1.01 0.68 0.28 0.59

3.17 1.55 0.79 0.23 0.21 1.83 1.03 0.72 0.29 0.53

3.18 1.57 0.81 0.26 0.17 1.84 1.04 0.74 0.29 0.55

LHMet

Temperature (K) Temperature (K) Temperature (K) Temperature (K) Temperature (K)

KENMet

320

Range

LHMet(0cm)

Observation

Simulation

Assimilation

300 280 260 300

LHMet(5cm)

295 290 285 298

LHMet(15cm) 296 294 292 290 297

LHMet(50cm)

296 295 294 297

LHMet(100cm)

296 295 286

288

290

292

294

295

Temperature (K) Temperature (K) Temperature (K) Temperature (K) Temperature (K)

Julian Day

320

Range

KENMet(0cm)

Observation

Simulation

Assimilation

300 280 260 300

KENMet(5cm)

295 290 285 298

KENMet(15cm)

296 294 292 290 296

KENMet(50cm)

294 292 298

KENMet(100cm)

296 294 286

288

290

292

294

295

Julian Day

Figure 7. The results of assimilating the surface observation in situ daily (consistent with the time of obtainning MODIS LST) into the assimilation system at LHMet and KENMet sites from day 286 (12 October) to 295 (21 October), 2004.

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that impeding radiation emissions into the air. Here, MODIS LST was corrected to the point scale using a simple linear regression. The correlation (R) between MODIS LST and surface soil temperature was 0.76 and 0.84 for LHMet and KENMet sites, respectively, and the standard deviation (std) of the difference between the MODIS LST and surface soil temperature was 3.34 K for LHMet and 2.60 K for KENMet. MODIS LST was assimilated after the bias correction, and it was assimilated once per day. This experiment is very similar to the previous experiment which assimilates in situ observations of surface soil temperature once per day. In fact, they were constructed to show how the source and quality of the observations can affect the performance of the data assimilation scheme. The last 10 day results of assimilating the verified MODIS LST are shown in Figure 9, which indeed suggests that the

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Figure 8. Comparison between MODIS LST and surface soil temperature measured in situ at LHMet and KENMet sites from day 276 (2 October) to 295 (21 October), 2004.

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results were comparable because the MODIS LST data are bias-corrected. Comparison of the results in Figures 6, 7 and 9 reveals that the assimilated results are significantly better in Figure 6 than that in Figures 7 and 9, which can be verified in Table 2. However, it is not easy to determine whether the performance of assimilating daily in situ observations of surface soil temperature (Figure 7) was better than that of assimilating the verified MODIS LST (Figure 9). Table 2 also shows that the difference between the two experiments was not significant, but the performance of assimilating daily surface in situ observations of surface soil temperature was better than that of assimilating the verified MODIS LST overall.

4.6. Assimilating the Original MODIS LST In the final experiment, the original MODIS LST without any correction was assimilated into the data assimilation system from 2 October (day 276) to 21 October (day 295), 2004. The assimilated results of the last 10 day period are shown in Figure 10 for LHMet and KENMet sites. Comparing the results of this experiment to those of assimilating daily in situ observations of surface soil temperature and assimilating the verified MODIS LST, it is not easy to find a significant difference among Figures 7, 9, and10, but the values of RMSE in Table 2 infer that the assimilated results of this experiment were generally worse than those of the other experiments. Nevertheless, it is clear that the performance of assimilation was better than that of simulation in these experiments in the first several layers at both sites.

5. Discussion According to the results displayed in Table 2, the performance of EnPF was significantly more efficient from the second layer to the fourth layer at both sites in all four experiments. As the conditions of data assimilation were relaxed from assimilating in situ observations of surface soil temperature hourly to daily, to assimilating the verified MODIS LST, to assimilating the original MODIS LST, it can be seen that assimilated results became worse in all but the fourth layer at the LHMet site, which became better. In the first layer at both sites, only the assimilated results were significantly better than the simulated results with assimilating hourly in situ observations of surface soil temperature. In the other three experiments, the EnPF can improve the simulated accuracy, but not significantly. One possible reason is that simulation of soil temperature at this layer is complicated by variations in land cover, soil characteristics, wind speed, and so on. Thus, assimilating the soil temperature observations once per day may not improve the simulated accuracy significantly at the surface soil layer. In the fifth layer, the assimilated results were always worse than the simulated results at both sites. This can be explained by the fact that we only assimilated the surface observations and MODIS LST, and verified the

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Temperature (K)Temperature (K) Temperature (K) Temperature (K) Temperature (K)

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Range

LHMet(0cm)

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Observation

Simulation

Assimilation

300 280 260 300

LHMet(5cm)

295 290 285 298 296

LHMet(15cm)

294 292 290 297

LHMet(50cm) 296 295 294 297

LHMet(100cm)

296 295 286

288

290

292

294

Temperature (K) Temperature (K) Temperature (K) Temperature (K) Temperature (K)

Julian Day

320

KENMet(0cm)

Range

Observation

Simulation

300 280 260 300

KENMet(5cm)

295 290 285 298

KENMet(15cm)

296 294 292 290 296

KENMet(50cm)

Assimilation

295

performance of EnPF at other layers, and the assimilated results at this layer were influenced by that in the fourth layer (50 cm). However, the assimilated results underestimated or overestimated the soil temperature compared to the simulated results at sites LHMet and KENMet, respectively, at the 50 cm depth, but the simulated results performed well compared to the observations after optimization in the fifth layer and the amplitude of observed soil temperature was no more than 1 K, so that the assimilated results were overall worse than the simulated results based on the model principle and data assimilation method in the fifth layer.

294

We found that the simulated results were KENMet(100cm) 297 improved more signifi296 cantly by assimilating 295 surface in situ observa286 288 290 292 294 295 Julian Day tions hourly rather than daily in the first four Figure 9. The results of assimilating the verified MODIS LST using the surface observation in situ daily layers, but not for the into the assimilation system at LHMet and KENMet sites from day 286 (12 October to 295 (21 October), 2004. fourth layer at the LHMet site. The difference between the two experiments is the frequency of assimilation that means the higher frequency of assimilation will provide more accurate results. As experiments progressed from assimilating daily surface in situ observations to assimilating corrected MODIS LST, the assimilated results performed worse, but were not degraded significantly as long as the quality of the assimilation inputs remained high. The assimilated results became worse significantly from assimilating daily surface in situ observations to assimilating MODIS LST without any processing, but assimilating uncorrected MODIS LST can still improve the simulation accuracy. From these three experiments, it can be inferred that the quality of the input data of the data assimilation will influence the performance of the ensemble particle filter. 292

Comparison of the results between LHMet and KENMet sites shows similar change trends (i.e., from better to worse) of the performance of assimilation with relaxing assimilation conditions in the first three layers of the two sites. However, at the fourth layer, the performance of assimilation became better from assimilating surface in situ observations hourly to daily at the LHMet site, but not at the KENMet site. This means that the lower frequency of assimilation may provide more accurate results at the bottom layer, at which the amplitude of soil temperature fluctuations is small. Possible reasons are that the soil thermal conductivity was optimized but not calculated using the Johansen’s method as reported in Farouki [1981] to obtain the minimized RMSE of soil temperature simulation and the assumption of the soil thermal conductivity is

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Temperature (K) Temperature (K) Temperature (K) Temperature (K) Temperature (K)

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Range

LHMet(0cm)

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Observation

Simulation

independent, so that the change trends of the performance of assimilation with relaxing assimilation conditions may be different at the bottom layer with a small amplitude of soil temperature at different sites.

Assimilation

300 280 260 300

LHMet(5cm)

295 290 285 298

LHMet(15cm)

296 294 292 290 297

LHMet(50cm) 296 295 294 297

LHMet(100cm)

296 295 286

288

290

292

294

295

Temperature (K) Temperature (K) Temperature (K) Temperature (K) Temperature (K)

Julian Day 320

Range

KENMet(0cm)

Observation

Simulation

Assimilation

300 280 260 300

KENMet(5cm)

295 290 285 298

KENMet(15cm)

296 294 292 290 296

KENMet(50cm)

294 292 298

KENMet(100cm)

296 294 286

288

290

292

294

295

Julian Day

Figure 10. The results of assimilating the orginal MODIS LST into the assimilation system at LHMet and KENMet sites from day 286 (12 October) to 295 (21 October), 2004.

All four experiments demonstrate that the MODIS LST can be used for data assimilation directly to obtain highly accurate soil temperature, especially in the first several layers. It should be mentioned that there is one experiment, i.e., assimilating the verified MODIS LST, which has two functions: the first is to check the correlation between MODIS LST and surface soil temperature, and the second is to relax the assimilation conditions gradually. After this experiment, the MODIS LST will be evaluated to determine whether it can be assimilated into the assimilation system directly without in situ observations, which has been verified in the fourth experiment.

6. Summary An assimilation system based on the ensemble particle filter (EnPF) and the Common Land Model (CLM) was tested through four experiments at the Walnut Gulch Experimental Watershed (WGEW) in Arizona, United States. The experiment of assimilating hourly in situ observations of surface soil temperature into the assimilation system verified that the ensemble particle filter was an efficient method. At different layers (from the second layer to the fourth layer), the accuracy of simulation after assimilation showed a significant improvement, but the performance of EnPF was negative in the bottom layer. As the conditions of data assimilation were relaxed from assimilating hourly in situ observations of surface soil temperature to assimilating daily in situ observations of surface soil temperature, to assimilating verified MODIS LST, to assimilating original MODIS LST, the assimilated results became worse overall in the first four layers at both sites, but they were still better than the simulated results. At the bottom layer, the assimilated results were worse than the simulated results. The four experiments show that not only the frequency of assimilation influences the performance of the ensemble particle filter, but also the quality of the input data to the assimilation system can influence the performance of ensemble particle filter. Overall, it can be inferred from this study that remote sensing data

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can be used with the ensemble particle filter to obtain high accurate soil variables (e.g., soil moisture and soil temperature) in poorly gauged catchments.

Acknowledgments This study was supported by the National Basic Research Program of China (2010CB951101), the National Natural Science Foundation of China (Grant Nos. 41323001, 41101015, and 41101016), the program of Dual Innovative Talents Plan and Innovative Research Team in Jiangsu Province, the National Technology Support Program in the 12th Five-year Plan of China (2012BAK10B04), NASA (grant NNX13AI44G), the Fundamental Research Funds for the Central Universities, and Program sponsored for scientific innovation research of college graduate in Jiangsu province in 2013 (CXZZ13_0251).

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