Evapotranspiration (ET) is the main process controlling the water cycle and energy transport between the atmosphere, hydrosphere, and biosphere (Priestley and Taylor, 1972), and is an important subject of research on global and regional water and energy budgets (Rosenberg, 1983; Kustas and Norman, 1996; Vinukollu et al., 2011). Remote sensing and hydrological modeling are two key approaches to estimate evapotranspiration (Liu et al., 2007). Hydrological modeling is prone to errors due to uncertainties in input and output information, the model structure, initial conditions and model parameters, which affect the accuracy of the simulation (Renard et al., 2010). Using remote sensing to estimate ET has obvious advantages in accuracy and spatial resolution (Li et al., 2009), but cannot provide temporally continuous values and thus cannot meet the requirements of hydrological models (Liang et al., 2013). One possible approach to overcome these drawbacks involves applying multiple means or multi-source data to estimate ET, which is becoming the choice method for obtaining a continuous time series of ET with high precision (Conradt et al., 2013).

Data assimilation, as an advantageous technique for combining multi-source data, has been at the frontier of research on land surface hydrology and the water cycle (Song et al., 2011; Tang and Li, 2014) and has provided a new way of obtaining a highly accurate continuous time series of regional ET values. Pan et al. (2008) and Qin et al. (2008) applied the data assimilation technique and hydrological modeling to assimilate observed data, and this process improved the efficiency of the ET simulation, however, the assimilation effect was seriously affected by ET not being a state variable. Xie and Zhang (2010) assimilated flow into the Soil and Water Assessment Tool (SWAT) hydrological model, which did not significantly improve the accuracy of ET. The application of data assimilation based on hydrological models has made some progress (Xu et al., 2014) when the assimilated objects are primarily state variables; data assimilation for non-state variables, such as ET, is still being attempted (Spies et al., 2014). The potential of data assimilation in hydrological models should be further investigated. Therefore, we need to carry out studies of ET data assimilation based on hydrological models, and overcome the bottleneck for the use of the non-state variable ET when constructing data assimilation relationships, so as to obtain a highly precise continuous time series of ET values at the regional scale.

In this paper, a comprehensive review of evapotranspiration data assimilation based on hydrological modeling is provided. The difficulties and bottlenecks of using ET, being a non-state variable, to construct data assimilation relationships are elaborated upon, with a discussion and analysis of the feasibility of assimilating ET into various hydrological models. Based on this, a new easy-to-operate ET assimilation scheme that includes a water circulation physical mechanism is proposed. The scheme was developed with an improved data assimilation system that uses a distributed time-variant gain model (DTVGM), and the ET-soil humidity nonlinear time response relationship of this model. This scheme may provide a reference for an accurate simulation of regional evapotranspiration.

Data assimilation techniques, while only gradually being applied to hydrological simulations, have nevertheless recently become a hot research topic in the water cycle field. Data assimilation methods and their application to land surface and hydrological modeling have made several achievements in various systems, including the North American/Global Land Data Assimilation System (NLDAS/GLDAS) and European Land Data Assimilation System (ELDAS), as well as the assimilation systems in China, Canada and South Korea (Li et al., 2007). However, current research is mainly focused on state variables, such as soil moisture, leaf area index, etc., and relatively little on the non-state variable ET. Moreover, there has been little research on the emerging field of applying data assimilation in hydrology simulations for small-scale watersheds, and the potential of such data assimilation has not been fully realized (Moradkhani, 2008), especially for ET data assimilation based on hydrological models (Chen et al., 2013).

The amount of research dedicated to ET data assimilation began to ten years ago. Several papers have described attempts to use data assimilation techniques combined with various other models to estimate regional ET. Schuurmans et al. (2003) used ET estimates derived from remote sensing and the Surface Energy Balance Algorithm for Land (SEBAL) to improve distributed hydrological model (SIMGRO) simulations using a constant gain Kalman filter data assimilation algorithm, which calculated the state variable soil moisture using an empirical method after updating the ET value. In this study, the model was interpolated with ET observations relying on the calibration of empirical parameters, and hence was not statistically optimal. Pipunic et al. (2008) developed a data assimilation scheme with the ensemble Kalman filter (EnKF) to estimate latent heat flux and sensible heat flux based on a one-dimensional land surface model (LSM), which improved the simulation accuracy. However, assumptions in the LSM model have limited the popularity of this method. Qin et al. (2008) applied the extended Kalman filter to assimilate remote-sensing-derived ET estimates into a distributed hydrological model for improving the predictions of spatial water distribution over a large river basin, but the assimilation effect could not provide feedback into the model since ET is a non-state variable. The hydrological series had not been optimized as a whole, and was just equivalent to an interpolation. Irmak and Kamble (2009) proposed an assimilation methodology for the soil, water, atmosphere, and plant (SWAP) simulation model with remote sensing data from the SEBAL using genetic algorithm (GA) data assimilation. For this, uncertainty in the SEBAL model, due to its one evaporation mechanism, reduced the reliability of the methodology; besides, the assimilation method was virtually the further optimization of SWAP through genetic algorithm, no calibration between parameters within the SWAP model. Xie and Zhang (2010) tested a data assimilation system using streamflow to assimilate SWAT; this assimilation improved estimates of runoff and soil moisture, but not of ET. Dumedah and Coulibaly (2013) assimilated streamflow into the distributed hydrologic model (SWAT) using in-situ soil moisture data, and demonstrated some improvement in accuracy. However, the ET results were not effectively improved since the errors generated from the simulation were not completely corrected. Lei et al. (2014) assimilated synthetic surface soil moisture data into the SWAT model to evaluate their impact on other hydrological variables via the ensemble Kalman smoother (EnKS). The results showed that the assimilation of surface soil moisture can moderately improve estimates of deep layer soil moisture, surface runoff and lateral flow, while ET was still underestimated. Trudel et al. (2014) applied an ensemble Kalman filter into the distributed physically based hydrological model CATHY (CATchment HYdrology) to assimilate streamflow observations at different locations, as well as soil moisture at two different depths (15 and 45 cm). Assimilation of streamflow observations systematically increased the simulated soil moisture values, but no improvement in the accuracy of the ET sequence.

These studies have been useful for estimating evapotranspiration, but bottlenecks remain, and an ET assimilation system based on a hydrological model has not yet been established in practice. Effectively combining and integrating observations and simulations is necessary. That is, by using “true values” and minimizing errors to constrain model simulations, and by effectively merging information obtained from different sources with different spatial and temporal resolutions, higher resolution as well as spatially and temporally continuous data can then be obtained, which can yield a multi-scale representation of the water and energy cycle (Li et al., 2007).

Hydrological modeling now pays more attention to the simulation of the generalized water cycle variables than previous, especially ET (Immerzeel and Droogers, 2008). A hydrological model that takes the water cycle system of a closed drainage basin as its study object can continuously simulate ET for every hydrologic unit (or space grid), and the temporal and spatial resolutions are flexible (Xu and Cheng, 2010). Moreover, it is physically based and easily applicable. If we can find a suitable hydrological model as the dynamic model of assimilation, continuous regional ET estimates may be achieved by assimilating this hydrological model. Methods used to estimate ET differ in different hydrological models, so constructing an ET assimilation system based on hydrological modeling is premised on taking full account of the relationship between ET (diagnostic variable) and other state variables, and then analyzing the feasibility of assimilating ET.

There are two groups of ET estimation methods in hydrological models: gathering methods and converting methods (Zhao et al., 2013). In both methods, ET is correlated with soil moisture, which is a state variable. Physically based hydrological models usually use gathering methods such as VIC and SHE to estimate ET; others commonly apply the converting methods, for which there are different ways to estimate potential ET and different soil moisture extraction functions. These functions are constructed based on soil moisture, and describe the relationship between ET and the state variables. A comparison of the feasibilities of the different hydrological models for ET assimilation is shown in Table 1.

ET, a non-state variable, is calculated for most of the hydrological models by using soil moisture. In addition to taking this state variable as an observation to influence the simulation of ET, data assimilation for hydrological modeling based on ET observations can be carried out in two ways. First, the observation operator AW=H (ET) associating soil moisture and ET can be constructed, which converts the observed ET into a state variable, so as to realize the direct assimilation. This approach can be used for various types of hydrological models, but requires extensive calculations. Moreover, rank-deficient problem may appear because the correlation between soil moisture and ET is not clear when calculating the covariance matrix. Second, we can construct a unit matrix operator ET = H (ET), assimilating the “observed” and simulated ET, and then calculate the state variable after updating ET. This method is easy to compute and rank-deficient problem does not appear. But it requires explicit relationships to be made between ET and state variables in the model, which is mainly applied to the model based on converting methods. Besides, the derivation of state variables is also worthy of attention. For example, in SWAT, soil moisture (which as mentioned above is a state variable) is the combined result of the entire duration of the simulation, so a sequential assimilation system of ET based on SWAT is difficult to construct. In other hydrological models based on converting methods, soil moisture evolves over time and can provide feedback of ET assimilation results, so we can first assimilate evapotranspiration, and then adjust soil moisture to calibrate the hydrological model. But it is hard to construct the sequential assimilation system without explicit relationships between ET and state variables. In addition, it is most convenient to directly assimilate simulated ET with observed ET under the conditions of few observations, since the assimilation efficiency is high when using a unit matrix.

To apply the assimilation procedures described above into hydrological models and determine ET levels with high precision, we should consider the requirements of the assimilation algorithm itself for hydrological models: first, the simulation variables must be state variables that can describe the time-domain behavior of a dynamic system; second, the simulation variable must evolve over time. In addition, ET is a prognostic variable to construct a data assimilation system, so we need to construct the time response relationship between ET and state variables by assimilating feedback and then optimizing the simulation, so as to obtain accurate estimates of ET. Thus, the key to construct an ET assimilation system is to select the hydrological model that meets the requirements of the assimilation algorithm, which means developing the time response relationship between ET and the state variable being used. By effectively transforming ET into a state variable, the hydrological model was modified by the assimilation conditions, and could be combined with sequential assimilation to establish a feasible ET data assimilation system.

To construct the data assimilation system based on evapotranspiration (ET), which is a non-state variable, we need to choose the hydrological model with a time response relationship between ET and the state variable, as the model operator of the assimilation system (Table 1). Based on the nonlinear theory of rain-derived flooding, and considering the preceding precipitation, Xia et al. put forward the distributed time-variant gain model (DTVGM) for watershed hydrological simulation (Xia et al., 1997; Xia, 2002; Xia et al., 2004). The model established the time response relationship between ET and soil moisture, and could be used to construct the data assimilation system based on ET. This section of the paper will use the DTVGM as an example to elaborate the new ET assimilation scheme.

In this paper, a new scheme to estimate evapotranspiration on a regional scale has been proposed. However, since the applications of this scheme are still at the experimental stage (Yin et al., 2014), more tests of these applications should be carried out at the regional level to validate the scheme. Research in ET data assimilation is still in the exploratory stage, and there are many bottlenecks that need to be overcome in this work, in contrast to assimilation research of other variables (e.g., land surface temperature, soil temperature, etc.). The biggest challenge in the assimilation of regional ET, a non-state variable in hydrological models, is how to improve the ET mechanism in the models as well as establish a rational isomorphic relationship of ET assimilation. Moreover, it is necessary to carry out further research on several aspects of this work, including on the accuracy of observational models, the stability of model operators, the capacity of data assimilation, the validation of regional ET processes, the optimization of the data assimilation method, the mechanism of the ET process and so on.

Accuracy of observational models. At present, most observational models adopt remote sensing (RS) ET models, which involve a number of parameters that describe the physical characteristics of the land surface. Due to external factors such as clouds, the atmosphere, the solar angle and observation angle, the accuracy of remote sensing data is limited to some extent. Besides, the cumulative effect of errors from retrieval of land surface parameters also affects the accuracy of observational models (Zhang et al., 2012). Therefore, it would be important to further explore the relationships between land surface physical characteristics and remote sensing information, so that we can reveal the basic laws underlying these relationships, and then realize cooperative retrieval of input data for the ET model using multi-source remote sensing information. This would improve the accuracy and spatio-temporal continuity of land surface parameters, so as to improve the accuracy of ET estimation at the regional scale.

Stability of model operators. The stability of model operators in data assimilation system, usually hydrological models, is of vital importance for obtaining accurate ET simulation results. Hydrological models synthetically consider the interactions between precipitation- runoff and landform, physiognomy, climate, and human activities. Since these models provide reliable mechanistic explanations for the hydrological cycle and use many parameters, uncertainties in these models have a great effect on ET simulation. Due to the high spatio-temporal heterogeneity of land surface variables, it is difficult to avoid large deviations between the hydrological model simulation and the observed data. Development of more mature, simple and effective model operators is necessary to achieve a reliable assimilation system. Therefore, further research is needed on the optimization and improvement of the hydrological model, as well as research on assessing the universality of the model. The convergence, rate of convergence and stability of the assimilation algorithm should also be comprehensively assessed.

Capacity of data assimilation. The capacity of data assimilation is closely related to the input frequency of “observations,” which means that an increase in the number of observed samples leads to better assimilation of ET, which promotes the influence of hydrological model calibration. When high-quality remote sensing data are lacking, it can be helpful to consider other sources of data, such as obtaining an observation field via spatial interpolation based on highly accurate flux data from regionally representative observational stations, moving/ fixed-point observations by radar remote sensing techniques, or calculation of energy flux by eliminating cloud interference for remote sensing data with large cloud coverage. These approaches will be the focus of future research.

Validation of the regional ET process. Direct comparison between assimilated ET and observed ET is the most efficient validation approach. Of these approaches, large-aperture scintillometry (LAS) is the most effective at a regional level, but a large-scale use of this method is often impeded by the high price of the equipment. The validation of actual ET still depends on the simulation data from a third party; thus, research focusing on finding an effective means of validating ET at the regional level is being carried out.

Development of data assimilation techniques. To further improve estimation of ET using hydrological models, it can be helpful in future research to use data fusion methods, such as the wavelet transform, to extract contact information between the grids of observational products and fuse them into the assimilation. Meanwhile, to enhance the accuracy of the estimation of hydrological variables and at the same time ensure high calculation efficiency, a more appropriate assimilation mechanism should be established. Research should be focused on the following: development of techniques to combine multiple and complementary remote sensing sources for hydrologic modeling (Xu et al., 2014); joint assimilation of multi-scale, multi-sensor products; and development of new techniques such as integration of new potential sensor products with hydrological models.