Kalman Filters in crop models: old experiences in new contexts

Abstract

Data assimilation has been widely used for improvement of crop models’ estimates, for example to incorporate the effects of external events or compensate calibration errors in large areas. The term describes multiple approaches for those who want to take advantage of satellite imagery to reduce uncertainty or improve accuracy of model estimates. Kalman Filters are among the most used methods for achieving these goals. But their use in new contexts, i.e., from open field to protected environments, requires untangling aspects of the pipeline that are often performed in many different ways without guidelines, such as which variables to assimilate or how to ascribe uncertainty to observations or model estimates. This study is then divided in two parts. In the first, we review details on how uncertainty is ascribed on crop model estimates and in observations for applications of the Kalman Filter and three variations of the method, i.e., the Extended, Unscented and Ensemble, as well as which state variables are often updated and the frequency with which assimilation may occur, as well as how these aspects are connected to each other. In the second part, we apply different approaches from the reviewed literature in a greenhouse tomato crop model. We use artificial data with controlled noise levels as well as artificial data generated by simulation using other tomato crop model. We assess the impacts of using different methods and different approaches for ascribing uncertainty in model estimates and in observations, by assimilating artificial observations of fruit and of mature fruit biomass. We note that covariances should not be fixed values, that there are trade-offs between ascribing model uncertainty to the state itself and to other elements of the process, that observation covariance may have been considered disproportionality higher when using some ensemble generation approaches in the EnKF, and that bias in model estimates may lead to worse outcomes even when observations are high-quality ones. While we discussed aspects that should be considered in a new environment, many of them are also important for field crops, and we concluded assimilation should follow an assessment of which variables could be useful for assimilation.