Integration of remote sensing evapotranspiration (ET) model and hydrologic model for mapping daily ET time series at river basin scale

Evapotranspiration (ET), one of the most important hydrological processes, including soil evaporation and vegetation transpiration, is the key link between the land surface energy and water balances (WBs) (Norman et al. 2003; Anderson et al. 2007; Galleguillos et al. 2011; Long & Singh 2013). Currently, the regional ET in a river basin is normally estimated by the following three methods: empirical formulae, hydrological process models, and remote sensing ET models (RSTMs), each of which is insufficient to obtain precise and continuous regional ET. The associated empirical formulae mainly include the WB method, water heat coupling equations, and the complementary relationship method. The first two ET methods are suitable for calculating regional ET values over long time scales within closed basins, but with low precision (Wilson et al. 2001; Cammalleri et al. 2010; Wang & Dickinson 2012). The complementary relationship between actual and potential ET is not steady, and is tightly related to weather conditions (Szilagyi & Jozsa 2008), thus the relationship explaining the evaporation paradox is also unsteady (Liu et al. 2006). Therefore, regional ET estimates based on the relationship between actual and potential ET also contain uncertainties.

Hydrological models are good tools for simulating and analyzing the existence, movement, and distribution of water in a particular basin (Werth et al. 2009). Usually, the river basin is divided into a number of hydrological response units for hydrological process simulation. As the simulation error is cumulative in the simulation process, the ETs simulated by the hydrological models have low precision (Rakovec et al. 2012). Furthermore, poor representation of the dynamic underlying surface changes and the observation errors in the model input data lead to additional uncertainties in hydrological models (Immerzeel & Droogers 2008). Although hydrological models could be optimized based on the runoff observation, the optimization only refers to the WB mechanism, not the surface energy balance. The efficient optimization of ET processes simulation is affected by the lack of reliable observed ET.

The RSTMs can estimate the surface ET with sufficient accuracy, and have become important tools for estimating regional ET (Mauser & Schädlich 1998; Bastiaanssen et al. 2005; Kalma et al. 2008; Mercado et al. 2009). The applicability of RSTMs based on the surface energy balance is restricted by the lack of high-frequency and high-resolution thermal data (Baroncini et al. 2008). Therefore, continuous ET processes are difficult to monitor when using RSTMs alone (Cammalleri & Ciraolo 2012).

For practical applications, effective estimates of time-continuous daily, monthly, and yearly ET processes at the river basin scale are especially important for water resource management, climate change studies, and agricultural planning (Peters-Lidard et al. 2011). The RSTMs have the advantages of producing regional ETs with high spatial resolution and accuracy, but with poor temporal resolution, while hydrological models are the most effective means of obtaining time-continuous ETs. Thus, a new method could be developed to take advantage of the complementary properties of RSTMs and hydrological models, allowing both high precision and time-continuous ET estimates.

Currently, relatively few studies have considered such a combination (Pipunic et al. 2008). Irmak & Kamble (2009) used the 18 daily ETs from the SEBAL (surface energy balance algorithm for land) remote sensing model as observations to optimize the parameters of the SWAP (soil, water, atmosphere and plant) model based on the genetic algorithm, and improved the accuracy of the ET process simulation. However, the number of ET observation values was very small, and the optimization did not consider the observed outlet runoff; therefore, there were limited improvements in the results, and uncertainties remained in the SWAP simulation. Additionally, remote sensing ET is essentially simulated data, not actual data, so it is not suitable to be used as observations to optimize the hydrological simulation directly. The method will bring new uncertainties. Han et al. (2012) used data assimilation (DA) technology to combine remote sensing ETs and hydrological model-based ETs, while Parada & Liang (2008) demonstrated that the DA-based results have an optimal probability. Therefore, the DA-based ETs are better suited and more reliable for constructing the objective functions, when optimizing the hydrological models, than remotely sensed ETs.

This study aims to propose an integrated ET simulation approach integrating the advantages of the remote sensing and the hydrological model, by improving the hydrological model optimization. The optimization is not only based on the runoff observation, but also on a new probability optimal ET series which is produced by a DA scheme combining sparse remote estimates and continuous modeling of regional ET. The daily ETs in the Shahe River basin, Beijing, for typical days between 1999 and 2007, are estimated by a two-layer RSTM proposed by Zhang et al. (2007), using Landsat TM/ETM + data. The daily ETs in the Shahe River basin, Beijing, were also simulated by a chosen hydrological model, a distributed time-variant gain hydrology model (DTVGM) proposed by Xia et al. (2005). DTVGM has a small computational cost and has been applied successfully in the Haihe River basin, Huaihe River basin, and other areas in China (Li et al. 2010). A widely used DA algorithm, the ensemble Kalman filter (EnKF), is used to assimilate the regional ET series from the RSTM and DTVGM. The DTVGM is optimized by dual objective functions composed of the assimilated ETs and observed outlet discharge, and the optimized DTVGM is used to produce continuous daily ETs with higher precision. The rest of the paper is structured as follows. The next section describes the basic framework along with the data, models, and methods used. This is followed by a section presenting the simulated results and analysis. The paper closes with a discussion and conclusions.

The data in this study mainly include satellite images, meteorological measurements, hydrological observations, and some geographic information system (GIS) data. Eighteen cloud-free Landsat images from 1999 to 2007 were chosen from the US Geological Survey (USGS) data center (http://glovis.usgs.gov/). Based on image registration, radiometric correction and some necessary preprocessing of the initial images, the vegetation cover, surface albedo, surface temperature, and some other necessary parameters were estimated following the methods of Liang (2000) and Qin et al. (2001).

Hydrological observation data, including runoff, rainfall, water levels, and reservoir management information, were collected from two precipitation stations and six hydrological stations distributed within the basin. Meteorological measurements, including solar radiation, air temperature, vapor pressure, and wind speed at the Beijing meteorological station were obtained from the Chinese Meteorological Administration.

In addition, GIS data including a digital elevation model (DEM) with spatial resolution of 30 m, a 1:10,000 land use map, 1:100,000 soil type map, and 1:250,000 drainage map of the study area were obtained from the Science Data Center of Resources and Environment, Chinese Academy of Sciences (CAS). All GIS data sets were converted into ESRI grid format with the same grid size and map projection. Table 1 shows the types of data used in the study.

In the DTVGM, there are nearly 50 parameters, and some parameters are not important for the output response of interest. Therefore, the eight important or sensitive parameters listed in Table 2 are selected and all the parameters are uniformly distributed in the ranges (Li et al. 2010; Song et al. 2012).

The EnKF is utilized here for the ET DA. The EnKF is a direct observer assimilation method, and overcomes the linearization issue through a Monte Carlo approach (Reichle 2008). An ensemble of parallel model runs is generated for the same time period with the EnKF, and because the EnKF combines both observation and simulation errors the results have the ‘optimal’ probability (Crow & Wood 2003). Thus, the EnKF is employed to assimilate the RSTM-based daily ETs and the DTVGM-based daily ETs for obtaining a high-quality daily ET distribution. The DA method can reduce the uncertainty of ET estimates, so as to produce a more reliable ET time series. Thus, the DTVGM can be further optimized based on the assimilated daily ETs. The DA process adopted in this study is summarized as follows.

The proposed DA method is key to the effectiveness of further optimization. Statistically, a larger number of ensemble members in the DA method results in an ensemble mean and covariance which is closer to reality. However, large numbers rapidly increase the computational cost. Thus, it is desirable to use the minimum number of ensemble members while still obtaining satisfactory estimates of the ensemble mean and covariance. We conducted an assimilation experiment to determine the minimum number of ensemble members for accurate ET simulation, so as to optimize the computing power available for the subsequent assimilation experiments.

Observations from the Xiaotangshan flux observation station and Miyun station are used to validate the accuracy of remote sensing ET retrievals. The Xiaotangshan flux observation station is located in the No.1 sub-basin of the Shahe River basin, and the Miyun station is located close to the Shahe River basin and has the same geographic characteristics as those of the Shahe River basin. The test site of the flux observation station is 1 km long from north to south, and 0.5 km east to west wide. This scale is suitable for the verification of the Landsat data retrieval. Three sets of LAS are placed on three 4-meter-high towers, respectively; the LAS optical path length is 900 to 1,500 meters. The instrument data of LAS with a large optical path can be used as the data source of a sub-basin ET interpolation calculation. Based on the LAS measurement, the regional ET in the Beijing area estimated by MODIS data was validated (Jia et al. 2010). The results demonstrated that the proposed validation method based on LAS observation data was feasible. The RMSE and MAPE of estimated monthly and daily ET were 13.75, 0.91 mm and 22.79%, 18.61%, respectively (Jia et al. 2010).

The boundaries of the sub-basins are often different to the boundaries of the grids in satellite data. In this study, the pixel-to-pixel RSTM simulation is based on the 30 × 30 m² grid mode, whereas the DTVGM is based on the sub-basin mode. The RSTM-based daily ETs are aggregated into 28 sub-basins to maintain spatial consistency between the hydrological simulation and the remote sensing retrievals. Then, the EnKF-based DA is used to improve the accuracy of RSTM-based ETs and DTVGM-based ETs. The comparisons between RSTM-based ETs, DTVGM-based Ets, and DA-based ETs are shown in Table 3. The average MAPE between DTVGM-based ETs and RSTM-based ETs is approximately 12.3%, while the average MAPE between DA-based ETs and RSTM-based ETs is 4.5%. This shows that the DA-based ETs are closer to the RSTM-based ET values than the DTVGM-based values.

The observed data from the Xiaotangshan station are chosen to validate the ET simulation by further optimization. The sub-basin that contains this station is flat with relatively homogeneous geographical characteristics, and the ET values at each pixel within this sub-basin are considered as equivalent to each other, so each observed ET value could be compared to the average ET value for sub-basin No.1. There are observed latent heat flux data available at Xiaotangshan station for 10 days during 2002–2007. The corresponding 10 daily ETs of the No.1 sub-basin simulated by DTVGM following Scenarios 1 and 2 are shown in Table 4, revealing that the simulated ETs from the DTVGM, optimized only with the objective function NSE, have a large error compared with the observed ETs. After further optimization based on NSE and RMSE_ET, the daily ET simulation of DTVGM is significantly improved, and the MAPE between the DTVGM-based ETs and LAS-based ETs is reduced by 5.84%.

In this study, the uncertainty in the DA process has been minimized as much as possible by determining the optimal ensemble size (100 members), observation error, and model error in the DA experiment. This is a key step in improving the optimization of the DTVGM on the basis of a DA-based ET series, when adopting an integrated approach that achieves a compromise between the DTVGM and RSTM in a DA scheme combining sparse remote sensing estimates and continuous modeling of daily ETs. The EnKF DA algorithm plays an important role and ensures the DA-based ETs used for validation are reliable. The DA-based ETs are used to further optimize the DTVGM when combined with the observed outlet discharge, so as to obtain accurate continuous daily ETs.

The proposed integrated approach provides a new method for minimizing the model uncertainties using DA-based daily ETs. The new methodology performs well in producing a continuous simulation of daily ETs, and will provide a practical solution for accurate, continuous estimates of ETs at basin and daily scales. The case study of the Shahe River basin indicates that the new method can more accurately simulate regional ET continuously. The MAPE between the DTVGM-based ETs (optimized only following Scenario 1 in Figure 2) and observed ETs at Xiaotangshan station is 13.8%, but the MAPE is reduced to 6.4% after further optimization based on DA-based ETs. The hydrological model with the further optimization in this paper can estimate ET with high accuracy and continuous time series for improving researches such as water resource management, climate change studies, agricultural planning, and so on. The new optimized ET model not only follows the surface energy balance but also meets the regional WB, and has a more perfect water thermal coupling mechanism. The study will further enrich the content of ET estimation disciplines and provide a scientific basis for better understanding of the laws of regional water cycles.

Although the ET simulation accuracy is improved by the further optimization, there are some limitations. First, the verification of ET is still a relatively difficult problem due to a lack of measurement conditions in some areas. Thus there is no spatially distributed ET data to verify the accuracy of the ET simulation by remote sensing and hydrological modeling. Additionally, the accuracy of this integrated method is closely related to the number of remotely sensed observations, which are usually temporally sparse due to the lack of high-frequency and high-resolution thermal data. We only obtained 18 high-quality TM/ETM + images during 1999–2007 from the USGS website, thus the simulation efficiency could still be improved further. Future work will focus on the construction of remote sensing observation data over a longer time series so as to further optimize the method.

In addition, the fitting effect of runoff simulation and observation is good in most years except 2003. The performance of the less effective simulation in 2003 shows that the observed discharge of rivers in the flood season (June to September) is smaller, which is inconsistent with rainfall–runoff relationship in the natural state. Under the condition of underlying surface change, the hydrological model produces the same runoff process caused by the same rainfall process generally. It is shown in Figure 9 that the precipitation is lower than usual in the spring and summer of 2003 when the crop water requirement is the largest of the year. It can be inferred that the water storage measure is used to reduce the annual drought and achieve the supply and demand balance of agricultural water. This indicates the distributed hydrological model also needs to take into account the impact of human activities more comprehensively, especially the human activities that are more obvious in the basin.

This work was partially supported by the National Key Basic Research Program of China (973 Program) (Grant No. 2015CB452701), the National Natural Science Foundation of China (41271003, 41401042), Anhui Provincial Natural Science Foundation (1508085QD69) and China Postdoctoral Science Foundation (2014M550823). The authors are grateful to the reviewers for the help and thought-provoking comments.