Master of Science / Department of Statistics / Juan Du / Space and time are often vital components of research data sets. Accounting for and utilizing the space and time information in statistical models become beneficial when the response variable in question is proved to have a space and time dependence. This work focuses on the modeling and analysis of crop yield over space and time. Specifically, two different yield data sets were used. The first yield and environmental data set was collected across selected counties in Kansas from yield performance tests conducted for multiple years. The second yield data set was a survey data set collected by USDA across the US from 1900-2009. The objectives of our study were to investigate crop yield trends in space and time, quantify the variability in yield explained by genetics and space-time (environment) factors, and study how spatio-temporal information could be incorporated and also utilized in modeling and forecasting yield. Based on the format of these data sets, trend of irrigated and dryland crops was analyzed by employing time series statistical techniques. Some traditional linear regressions and smoothing techniques are first used to obtain the yield function. These models were then improved by incorporating time and space information either as explanatory variables or as auto- or cross- correlations adjusted in the residual covariance structures. In addition, a multivariate time series modeling approach was conducted to demonstrate how the space and time correlation information can be utilized to model and forecast yield and related variables. The conclusion from this research clearly emphasizes the importance of space and time components of data sets in research analysis. That is partly because they can often adjust (make up) for those underlying variables and factor effects that are not measured or not well understood.

Die Anzahl der unterernährten Menschen in der Welt steigt seit 2017 wieder an. Der Klimawandel wird den Druck auf die Landwirtschaft und die Ernährungssicherheit weiter erhöhen, insbesondere für kleinbäuerliche und von Subsistenzwirtschaft geprägte Agrarsysteme in den Tropen. Um die Widerstandsfähigkeit der Ernährungssysteme und die Ernährungssicherheit zu stärken, bedarf es eines Klimarisikomanagements und Klimaanpassung. Dies kann sowohl die Antizipation als auch die Reaktion auf die Auswirkungen der globalen Erwärmung ermöglichen. Eine zentrale Rolle spielen in dieser Hinsicht landwirtschaftliche Modelle. Sie können die Reaktionen von Pflanzen auf Veränderungen in den Klimabedingungen quantifizieren und damit Risiken identifizieren. Diese Dissertation demonstriert anhand dreier in Peru, in Tansania und in Burkina Faso durchgeführten Fallstudien, wie statistische Ertragsmodelle das Klimarisikomanagement und die Anpassung in der tropischen Landwirtschaft unterstützen können. Während die erste Studie zeigt, wie Klimaanpassungsbestrebungen unterstützt werden können, werden in Studie zwei und drei statistische Modelle genutzt, um Ertrags- und Produktionsvorhersagen zu erstellen. Die Ergebnisse können dazu beitragen, Frühwarnsysteme für Ernährungsunsicherheit zu unterstützen. In den drei Veröffentlichungen werden neue Ansätze statistischer Ertragsmodellierung auf verschiedenen räumlichen Ebenen vorgestellt. Ein besonderer Fokus liegt hierbei auf der Weiterentwicklung von bisherigen Ertragsvorhersagen, insbesondere in Bezug auf unabhängige Modellvalidierungen, eine stärkere Berücksichtigung von Wetterextremen und die Übertragbarkeit der Modelle auf andere Regionen. / The number of undernourished people in the world has been increasing since 2017. Climate change will further exacerbate pressure on agriculture and food security, particularly for smallholder and subsistence-based farming systems in the tropics. Anticipating and responding to global warming through climate risk management is needed to increase the resilience of food systems and food security. Crop models play an indispensable role in this regard. They allow quantifying crop responses to changes in climatic conditions and thus identify risks. This dissertation demonstrates how statistical crop modelling can inform climate risk management and adaptation in tropical agriculture in the case studies of Peru, Tanzania and Burkina Faso. While the first study shows how statistical crop models can support climate adaptation, studies two and three provide yield and production forecasts. The results can contribute to supporting early warning systems on food insecurity. The three publications present novel approaches of statistical yield modelling at different spatial scales. A particular focus is on further developing existing yield forecasts, especially with regard to independent rigorous model validations, improved consideration of weather extremes, and the transferability of the models to other regions.