Systematic analysis of retrospective crop yields time series based on their structure identification

Abstract

Agricultural production and crop production, as its basic branch, is characterized by a significant dependence on solar activity (the Shvabe cycle) and hydrometeorological conditions of a particular year, especially in areas of insufficient moisture, which are mainly characteristic of the regions of the Lower Volga region of Russia. For the planning and management of agricultural production, a reliable forecast of the yield of cultivated crops is important. Previously published results show that the empirical distribution of retrospective TS yields, including the example of grain crops, is statistically significantly different from the normal one. This justifies the use of more subtle research methods, such as singular value analysis (SSA). The algorithm of the SSA method includes several stages, the main of which is the singular decomposition of the trajectory matrix into the sum of elementary matrices, each of which is given by a set of eigenvalues. At the final stage, diagonal averaging is performed, according to which the elementary matrices within each set are summed. The singular decomposition of the data on the dynamics of the BP yield was carried out according to the data for 1950-2018 on the example of grain crops in arid conditions of the Volgograd region. For the practical implementation of the SSA method, a computer program in Python was developed, using specialized mathematical libraries. The program provided a singular decomposition of the trajectory matrix, diagonal averaging of the resulting matrices, as well as the restoration of the set of series, taking into account their contribution to the analyzed TS. The use of the SSA method allowed us to identify the main natural and economic cycles, including a cycle with a period of about 14 years, which plays a major role in the dynamics of the formation of grain yields. Pronounced cycles of a different duration, among those identified by the SSA method, have not been established. There is a strong negative autocorrelation of the levels of interannual variability of grain yield values, which is present on the graphs of many restored series.