Assimilation of hyperspectral data into crop growth models: Precision farming application for maize in Catalonia

The goal is the development of a system based on hyperspectral remote sensing data which provides agricultural relevant information about the crop fields at a reasonable level of costs. The information will be offered to farmers or governmental institutions interested in the monitoring of the cultivation to improve the environmental conditions.

The paper is organized as follows: Chapter II describes the proposed method to derive agricultural relevant parameters from hyperspectral CASI data based on physical models. In Chapter III, the concept of data assimilation is explained in more detail. Chapter IV describes the measurement and flight campaigns, which took place at maize test sites in Catalonia. In chapter V, the results of calibration and validation of the proposed method and the crop growth models are described and discussed.

I. DERIVATION OF CROP PARAMETERS FROMHYPERSPECTRAL DATA

A.    Radiative transfer models
The radiative transfer plays an important role in modern remote sensing techniques, as optical remote sensing sensors measure the earth surface reflected solar irradiation. For this project, we choose the ACRM canopy spectral model (A two­layer Canopy Reflectance Model) [5] for the calculation of the radiative transfer within vegetation canopies. It is based on the homogeneous multispectral model MSRM [6] and the SAIL model, which models the diffuse radiative transfer. The ACRM model accounts for non-lambertian soil reflectance, specular reflection of direct sun rays on leaves, the hot spot effect, a two-parameter leaf angle distribution and the spectral effect of cultivation rows. For the spectral properties of leaves, we choose the PROSPECT model [4].

B.    Inverse problem
The derivation of crop parameters from hyperspectral remote sensing data can be regarded as an optimization problem, i.e. the goal is to search the set of crop and soil parameters, which are “best” suited to the observations. One possibility to solve this problem is to search the most probable set of parameters, which is the basis of the maximum likelihood methods. In our case, the goal is to find a set of unknown crop and soil parameters, for which the a posteriori probability of the parameters Vˆ with measured reflectances r* is maximal.

A basic problem is that the number of parameters describing the scene exceeds the number of the independent observations available. The reasons for this are the complexity of the vegetated earth surface and the influences on the measured reflectances. Therefore, it is impossible to find unique estimators only by relying on the measured reflectances, because the inverse function is ill-posed. A first step to solve this problem is to reduce the number of variable parameters, i.e. the input parameters of the physical models are divided in variable V and constant c.

C.   Introduction of a priori information
The introduction of a priori information is another possibility to solve this ill-posed problem. In general, there are several possibilities to introduce a priori information into the inversion process due to the variety of available “knowledge”:

To introduce this knowledge into the derivation process, we use a priori values V* and probabilities P_VV and apply penalties p to maintain the parameters within the definition range. The final cost function C, which has to be minimized, is described in equation (1). It contains the difference between observed r* and physically modeled reflectances r=f_ACRM(V,c), the stochastic model for the observations P_bb, the a priori information, and the penalties p (see [2]).

C = (r* – r)P_bb (r* – r)+ … (V – V*)P_VV (V – V*) + p ⁽¹⁾  

The stochastic model for the a priori information P_VV contains no covariances, and the variances are defined as a priori weights according to the definition range and the natural variability of each parameter. For example, the variance of the leaf area index (LAI) is defined as high as the whole definition range, because this parameter show high variability, whereas the specific leaf weight is supposed to remain constant within the fields and thus, the variance is defined as a fraction of the definition range. The a priori values themselves were set to in-situ measured values according to the specific hybrid or are set to standard values in case of parameters with high variability.

D.    Model fitting
Due to the complexity of the physical models, an analytical minimization of C is not possible. Thus, the model inversion is conducted numerically using common mathematical methods. The following numerical optimization methods are applied: Simplex algorithm (Simulated annealing) SA, Quasi-Newton QN, and Levenberg-Marquardt LM.

II. ASSIMILATION OF DERIVED PARAMETERS INTO CROP GROWTH MODELS

For precision farming purposes, crop growth models are necessary, as the information derived only from remote sensing data is not sufficient for the agronomists. Remote sensing techniques provide information about the plant’s present state, but not about the growth and development processes. Therefore, the assimilation of remote sensing data into crop growth models could improve the prediction of later crop development. Besides, the use of crop growth models over large areas is limited by our ability to provide them with required input parameters. It is impossible to obtain area wide plant and soil characteristics directly from in-situ observations. Thus, remote sensing data are acquired to provide information about crop processes over large areas.

We select two crop growth models for the data assimilation, the STICS model [1] and the ISBA model [6] supported by simple SVAT (Soil Vegetation Atmosphere Transfer) models. Figure 1 gives an overview about the proposed assimilation of hyperspectral remote sensing data into the applied crop growth models. Crop and soil parameters are derived from the CASI reflectances using radiative transfer models like the ACRM model. Part of the derived parameters act as interface parameters, which are used to correct the continuous crop growth simulation of the STICS and ISBA models at the image acquisition dates. For this, various techniques can be applied: forcing (continuous), sequential assimilation (non continuous), and variational assimilation (adjustment). We propose a sequential assimilation of the derived parameters to improve the prognosis of water and fertilization use as well as crop yield.

First, we calibrate the STICS and ISBA models using in-situ measurements (not in this paper) to fit the hybrid and cultivation practices, then we validate the results of these models with non stressed crops (v. chapter V). Further investigations will be conducted to test the proposed data assimilation concept.