A review of data assimilation of crop growth simulation based on remote sensing information

JIANG Zhiwei 1. Key Laboratory of Agri-informatics

Ministry of Agriculture 2. Institute of Agricultural Resources and Regional Planning

Chinese Academy of Agricultural Sciences Beijing, China

E-mail: zhiweijt@163.com

LIU Jia 1. Key Laboratory of Agri-informatics

Ministry of Agriculture 2. Institute of Agricultural Resources and Regional Planning

Chinese Academy of Agricultural Sciences Beijing, China

E-mail: liujia06@caas.cn

CHEN Zhongxin 1. Key Laboratory of Agri-informatics

Ministry of Agriculture 2. Institute of Agricultural Resources and Regional Planning

Chinese Academy of Agricultural Sciences Beijing, China

E-mail: chenzhongxin@caas.cn

SUN Liang 1. Key Laboratory of Agri-informatics

Ministry of Agriculture 2. Institute of Agricultural Resources and Regional Planning

Chinese Academy of Agricultural Sciences Beijing, China

E-mail: sunliang@caas.cn

Abstract—It is of great strategic importance of agricultural sustainable development for obtaining in timely the agricultural information, such as crop growing and yield. Data assimilation of remote sensing based on crop growth simulation becomes an effective means of monitoring regional agriculture information, which provides significant advantages in terms of economic cost, effectiveness, precision and suitability on regional scales. Data assimilation based crop growth process models can be defined as the methodology of improving process and precision of simulation which integrates simulated forecast with multi-source observation in the framework of dynamic models. According to mathematic principles of integrating model forecast with observation, three approaches of assimilating remote sensing information into crop models are concluded in this review, such as forcing, calibration and updating. Some critical issues and trends in the operation system of remote sensing data assimilation based on crop models on regional or global scales has been discussed, such as remotely sensed observation, uncertainty in assimilating process, data assimilation schemes. It is the significant and valuable research work for data assimilation of crop growth simulation based on remote sensing information. This review is a great of reference and summary for improving agricultural monitoring operation based on data assimilation technology.

Keywords- Data assimilation; Crop growth model; Remote sensing; Forcing method; Calibration method; Updating method

I. INTRODUCTION It is an important strategic significance to obtain crop yield

on regional scale timely and accurately for the sustainable development of agriculture and national food security[1-3]. In past years, the main approaches to obtain change information of regional crop yield include field statistic survey, agricultural and meteorological forecasting. Those approaches usually have obvious flaws in economic cost, timeliness, accuracy and suitability on regional scale. In recent years, some new earth observation technologies and land surface process simulation methods have been developed rapidly. These advance technologies give the urge to improve agricultural production monitoring and forecasting. There, therefore, appears to be a new potential research fields on how to integrate those technical advantages, such as crop growth model, remote sensing, to improve precision and efficiency of exiting agricultural monitoring system.

There have two means to describe crop growth processing, that is, simulation and observation. Crop models simulate crop growth under different environmental and management conditions, taking various limiting factors (e.g., soil, weather, water, nitrogen) into account in a dynamic way[4]. The process of crop growth simulation is continuously evolved in space and time. Thus, simulation models are good tools for understanding crop growing and predicting yield. However, poorer precision of simulation will be given when crop model is used on regional scale because of difficulties of obtaining regional input of model. The spatio-temporal uncertainties of regional parameters including weather, soil, field management, crop cultivar, and so on, lead to the error on regional crop model simulation results. In order to calibrate the regional simulation

This work was funded by National Natural Sciences Fund of China (41371396), “948” project of Ministry of Agriculture (2011-G6).

errors, the extensive spatial observation from remote sensing on the actual growth status of the crop throughout the growing season is an ideal choice[5]. Remote sensing has a significant advantage in spatial continuous observation, but it just instantaneously record pixel value, and is not good enough to describe spatio-temporal information of regional crop growing. In addition, the inversion of crop state variables from remote sensing signals is a complex process which involves images preprocessing, retrieval algorithm choice. Therefore, it is necessary to develop a new technology to integrate the advantages of crop growing simulation and remote sensing spatial observation over large area scales.

Several ways of integrating remote sensing data with crop models have been explored. Data assimilation technology is very feasible approach to address the issues confronted in traditional crop yield estimation on regional scale. According to mathematic principles, there are three approaches of assimilating remote sensing information into crop models, that is, forcing, calibration and update. These methods have their advantages and suitability. In past years, there are several researches on remote sensing data assimilation based on crop models. Some valuable results have been come out, including developing new algorithms, designing new schemes and regional application. At the same time, some new issues in data assimilation researches need to be addressed, such as how to improve the algorithms for the precision and efficiency of data assimilation results, deal with the uncertainties in the process of assimilating remote sensing information into crop models.

In this review, the definition of data assimilation is firstly summarized according to several literatures. Secondly, three kinds of data assimilation approaches will be introduced. Thirdly, we summarized the research process of data assimilation used in agricultural field, as well as the issues confronted in regional application. Finally, the research trends of remote sensing data assimilation based on crop models will be concluded.

II. DEFINITION OF DATA ASSIMILATION In order to solve the issues on whether correct value of

atmosphere variables can be obtained using imperfective remote sensing data, data assimilation was firstly proposed and applied successfully into the numerical weather prediction systems[6], such as European Centre for Medium-Range Weather Forecasts[7], America Naval Research Laboratory Atmospheric Variational Data Assimilation System [8], Météo France[9], Meteorological Service of Canada [10], Japan Meteorological Agency[11]. Then, the data assimilation approaches was introduced into marine forecasting systems, such as Australia Ocean Model, Analysis and Prediction System[12], Forecast Ocean Assimilation Model[13], Hybrid Coordinate Ocean Model/Navy Coupled Ocean Data Assimilation[14], The Meteorological Research Institue (MRI) multivariate ocean Variational estimation[15], Mediterranean Forecast System[16], The National Marine Environment Forcast Centre of China[17]. In 1990s, data assimilation technologies were used to research land surface processing. Subsequently, regional land surface data assimilation systems were established all over the worlds, including The North American Land Data Assimilation System[18], The Global

Land Data Assimilation System[19], European Land Data Assimilation System[20], as well as Chinese Land Data Assimilation[21].

As mentioned above, data assimilation has been applied widely into several fields of earth system science. The data assimilation, therefore, was described as many implication and extension by different experts. For ocean or atmosphere sciences, data assimilation was defined as a kind of general method to estimate precisely the marine or weather state variables, integrating observation and oceanography dynamic models. For land surface process, data assimilation was considered as a new approach and important tool which incorporates multi-source in-situ and remote observation into simulation of dynamic process models so that a dataset with the same patio-temporal and physical consistency was generated. In effect, incorporating remote sensing information into dynamic ecological model has become the important content in recent regional earth system researches. As a vital component of land data assimilation system, agricultural ecosystem data assimilation was regarded similarly as four fundamental elements, (a) the dynamic models of crop growth which quantitatively describe the process of crop growing under the stress environment, such as water, nutrition; (b) observation of crop growth state, including the in-situ measured and inversion from remote sensing signals indirectly; (c) data assimilation algorithms which will couple the observation with the process of crop model simulation in order to correct the model parameters and improve the accuracy of simulation; (d) uncertainty from observation and model. To address the errors from multi-source observation and modeling process are the main contents in data assimilation algorithms.

Concluding the description of data assimilation in different research fields, we consider the definition of data assimilation as a process and methodology which incorporates multi-source observation with model forecast under the frame of dynamic simulation in order to improve the process and prediction of dynamic models. The key goal is to estimate correctly the biophysical states, forecast, derivative parameters, as well as quantitative analysis and assessment for the uncertainty of simulating process, using the multi-source data.

III. THE STRATEGIES OF DATA ASSIMILATION In past years a number of researches on data assimilation

approaches were carried out. According to the integrating modes between observation and simulation, three ways could be summarized in literatures, that is, forcing, calibration and updating.

Forcing: the ‘forcing’ strategy replaces the state variables or initial input parameters in dynamic model using directly the observed data which will be regard as the input of next evolved simulation (Figure 1). For this approach, the assumption is that the observed data were much accurate then the modeled. It is much easier to be carried out, but the data assimilation results are excessive reliance on the observed information whose errors will diffuse and transfer into the process of simulating. The uncertainties from models themselves are not also taken into account.

Calibration: A minimum difference between the observed and the simulated state variables will be computed though adjusting iteratively the initial conditions or critical parameters, which usually impact sensitively on the modeled process and output in dynamic agroecosystem models(Figure 2). The optimal combination of model parameters in the realistic ranges results in the best simulation output. In this strategy, all uncertainties of model output are attributed to input parameters or initial conditions. This approach, therefore, failed to take into account the errors in the process of simulation. The iteration for calibrated the sensitive and uncertain model parameters is usually time consuming.

Updating: According to the mathematic principles of errors analysis and agroecosystem dynamic rules, the state variables in modeling process will be updated whenever the observation are available, which makes comprehensively considerations on the various uncertainties from the observed, model parameters, modeling process(Figure 3). In recent years, ‘updating’ strategy has received increased attention for agro-ecologic and hydrologic modeling due to its versatility in combing models and observation. Some algorithms have been developed to carry out this strategy.

Figure 1. Forcing strategy for data assimilation

Figure 2. Calibration strategy for data assimilation

Figure 3. Updating strategy for data assimilation

A. Sequential data assimilation algorithms The typical sequential data assimilation algorithms, such as

Ensemble Kalman filter (EnKF), particle filter (PF), are based on the assumption that a better simulated state variable at day t will also improve the accuracy of the simulated state variable at succeeding days. They are the sophisticated methods which apply an ensemble or particle of model states to represent the error statistics of the model estimate. Sequential data assimilation methods apply ensemble or particle integrations to predict the error statistics forward in time, and they uses an analysis scheme which operates directly on the ensemble of model states when observations are assimilated. The sequential methods, especially EnKF, have proven to efficiently handle strongly nonlinear dynamics and large state spaces and are now used in realistic applications with primitive equation models for the ocean and atmosphere.

Sequential data assimilation algorithms usually proceed by analysis cycles. In each analysis cycle, observations of the current (and possibly past) state of a system are combined with the results from a numerical prediction model (the forecast) to produce an analysis, which is considered as ‘the best’ estimate of the current state of the system. This is called the analysis step. Essentially, the analysis step tries to balance the uncertainty in the data and in the forecast. The model is then advanced in time and its result becomes the forecast in the next analysis cycle.

B. Variational data assimilation algorithms The variational approach includes three-dimensional

variational data assimilation (3D-Var) and the four-dimensional variational data assimilation (4D-Var). Four dimension variational data assimilation algorithm (4D Var) is in some sense the theoretical counterpart of the extend Kalman filter within the family of control theoretically inspired methods. Incremental 4D Var represents a particular attempt at its operational implementation. This approach has been extensively used in data assimilation for meteorological models and shows promising results.

The 4D-Var searches for an optimal set of model parameters (e.g., optimal initial state of the model) which minimizes the discrepancies between the model forecast and time distributed observational data over the assimilation window. A practical implementation of the minimization process requires a fast and accurate evaluation of the gradient of a cost function which may be provided by adjoint modeling.

4D-Var minimizes the objective function J that measure the weighted sum of squares of distances Jb to the background state xb and Jo to the observations yo distributed over a time interval [t0, tn],

(1) B-1 is an a prior weight matrix, with B meant to approximate the error-covariance matrix of xb,and the minimization of (1) is done with respect to the initial state x(t0). The formulation (1) reflects the imposition of a strong constraint. Alternative formulations that only impose a weak constant and their connection to various smoothers derived from sequential-estimation results are given by a number of literatures. Efficient methods for performing the minimization of J require its partial derivatives with respect to the elements of x(t0).

IV. THE PROGRESS OF DATA ASSIMILATION IN AGROCULTURE

A. Calibration strategy of model parameters for data assimilation Calibration approach is most widely used in recent data

assimilation researches. Some researchers have obtained successfully good results. For instance, minimization between the modeled and the observed LAI, in Fang’s study[22], is computed through combining iteratively the initial input parameters which include planting date, plant population, width per row, fertilization volume, using the optimization algorithm POWELL. In some literatures, Shuffled Complex Evolution method developed at the University of Arizona was applied widely to calibrate the initial condition and parameters of crop growth models, such as WOFOST, ORYZA2000, DSSAT[23, 24]. A ‘best’ yield estimation of crop is often easy to be predicted using the global optimized algorithm SCE-UA to find out the ‘best’ combination of sensitive parameters which effect significantly the modeling process and simulated output. In Dente’s research, regional winter wheat LAI inverted from remote sensing images ASAR and MERIS was applied to correct model initial condition, the planting data, wilting point of soil layer and field moisture capacity. The acceptable yield of winter wheat on regional scale was estimated finally though assimilated LAI in critical development periods, especially jointing and filling stages, into CERES-Wheat model[25].

In fact, calibration strategy fails to consider the errors from observation and model itself. It, therefore, is important signification for accuracy of observation and ‘perfect’ of crop growth models.

B. Updating strategy of state variables for data assimilation The approaches of updating strategy include sequential and

variational methods by which the simulation process of dynamic agroecosystem model can be adjusted sequentially or in global over the assimilation window. With the deep research and the progress of computation technology, the theory and technology of update data assimilation have been constantly improved and supported. Four-dimension variational, EnKF, PF are typical updating methods, which are widely applied into land data assimilation system on the large region. Same valuable researches of agricultural data assimilation based on crop growth model had also been performed. An updating strategy based on EnKF was designed by de Wit to correct the error of water balance in WOFOST using the soil water index map derived from microwave remotely sensed data[26]. The significant improvement of modeling process results in the better yield map of winter wheat and maize in Europe.

Compared EnKF, 4D Var is little used in remote sensing data assimilation of crop growth models because of complexity of tangential and adjoint mode of forecast model which are very difficult to obtained for high non-linear and discontinuity system. However, this issue seems to be addressed successfully using the 4D Var based on ensemble which combines the proper orthogonal or singular value decomposition technology with the principles of EnKF. These 4D Var approaches based on ensemble give an efficient and easy way to update the state variables rather than the way to compute the complicated adjiont mode.

C. Synchronous updating of model parameters and state variables for data assimilation The synchronous updating strategy of model parameters

and state variables for data assimilation based on dynamic agroecosystem models is a new scheme which not only takes account for the uncertainties on input parameters and initial conditions, but the uncertainties on model itself, the assimilated observation are also included so that a reasonable simulating process can be worked on, the model results of cause can also obtained. This kind of approach is widely studied in hydrology fields. A smoothed ensemble Kalman filter proposed by Chen can estimate the state and the unknown parameters in dynamic model. It is better for accessing and insight into the uncertainties on model input, output and parameters[27]. Jia et al. (2009) had set up the data assimilation system for soil water in which the optimization algorithm SCE-UA was used firstly to correct the optical depth and face roughness of vegetation, then EnKF was up to assimilate the microwave brightness temperature data into land surface soil moisture model CLM (Community Land Model) to estimate correctly the water in soil[28]. For data assimilation in agroecosystem, Monsivais-Huertero et al.(2010) established a root zoon soil moisture data assimilation system coupling LSP (Land Surface Process ) with crop growth model DSSAT based on EnKF. Author suggested that a much lower standard error and root mean square error of soil moisture simulated in root zoon can be obtained when model state variables and parameters[29]. Other researchers had also proposed the double EnKF strategy. In this strategy, the EnKF was used firstly to correct the model state variables, then it was used secondly to calibrate the parameters.

The results showed that the simulated precision of soil temperature was improved to a certain extent[30].

V. ISSUES AND TRENDS As the critical components of land data assimilation, the

study on remote sensing data assimilation of agroecosystem model is much later, especially establishment of operational system for monitoring crop growing and yield estimation on the regional or global scales. Some significant issues need to be studied deeply. The critical problems are as follow.

(1) For remote sensing data assimilation of crop growth models, the current remote sensing productions of crop parameters are unable to satisfy the needs of operational agriculture system. The accuracy of crop state estimated from remote sensing images is the critical element to effect on the assimilation results. The poor correction is usually conducted because of the state map of crop in development periods with coarse spatial resolution and low observed frequency. Pixel mixture, inversion method are also another reasons.

(2) The issues on uncertainties of data assimilation. Data assimilation is the process integrating multi-source information, which involves in regional drive data of crop model, such as weather, soil, field management, crop cultivar and so on. Those elements have large change and are difficult to be collected on regional scale. The regional interpolation of these elements inevitably leads to uncertainties which impact on the assimilation results. The sensitivity analysis, therefore, is necessary to control the critical elements. In addition, data assimilation strategy and dynamic model itself are another elements results in uncertainties. How to design a reasonable scheme of data assimilation will be the most important research contents in the future.

(3) At present, minimum algorithms and ensemble Kalman filter are widely applied in data assimilation on crop growth models on regional scale. The former fails to take the errors from the observed and system into account. The later may actually lead to non-convergence because of weak constraints of dynamic models. However, the strategies combining the EnKF and variational algorithms could cope with those issues[31]. Unfortunately, there is little research on data assimilation of crop growth models based on 4D Var. In recent, particle filter is also paid much more attention because of strong ability to deal with the problems on strongly nonlinear and none-Gaussian[32].

(4) There is little research for comparing between different data assimilation strategies, especially in term of accuracy and efficiency in operational application to monitor the crop growing and estimate yield on the large scales. Therefore, evaluations on different data assimilation strategies are the next research focuses.

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