Abstract: Climate change suggests long periods without rainfall will occur in the future quite often. Previous approach on dependence crop-yields from size of rain confirms the existence of a statistically significant relation. We built a model describing the amount of precipitation and taking into account periods of drought, using a mixture of gamma distribution and one point-distribution. Parameter estimators were constructed from rainfall data using the method of maximum likelihood. Long series of days or decades of drought allow to determine the probabilities of adverse developments in agriculture as the basis for forecasting crop yields in the future (years 2030, 2050). Forecasted yields can be used for assessment of productivity and profitability of some selected crops in Kujavian-Pomeranian region. Assumptions and parameters of large-scale spatial economic models will be applied to build up relevant solutions. Calculated with this approach output could be useful to expect decrease in agricultural output in the region. It will enable to shape effective agricultural policy to know how to balance food supply and demand through appropriate managing with stored food raw material and/or import/export policies. Used precipitation-yields dependencies method let verify earlier used methodology through comparison of obtained solutions concerning forecasted yields and closed to it uncertainty analysis.This work was co-financed by NCBiR, Contract no. FACCE JPI/04/2012 – P100 PARTNER

Abstract: The size of arable crop yields depends on many weather factors, such as precipitation and air temperature during the vegetation period. When studying the relation between yields and precipitation, not only the total amount of precipitation, but also the occurrence of long periods without precipitation must be taken into account. The paper [Bojar et al., 2014] demonstrated that barley yield significantly statistically depends on the length of the series of days without precipitation. This paper attempts to analyse the statistical data on daily precipitation totals recorded during the January – December periods in the years 1971 – 2013 at the weather station of the University of Science and Technology in Bydgoszcz, Faculty of Agriculture and Biotechnology, in the Research Centre located in an agricultural area in the Mochle township, situated 17 kilometres from Bydgoszcz. The primary statistical operation in the study is an attempt to estimate the Markov chain order. To this end, two criteria of chain order determination are applied: BIC (Bayesian information criterion, Schwarz 1978) and AIC (Akaike information criterion, Akaike 1974). Both are based on the log-likelihood functions for transition probability of the Markov chain constructed on certain data series. Statistical analysis of precipitation totals data leads to the conclusion that both AIC and BIC indicate the 2nd order for the studied Markov chain. The proposed method of estimating the variability of precipitation occurrence in the future will be utilised to improve region-related bio-physical and economical models, and to assess the risk of extreme events in the context of growing climate hazards. It will serve as basis for a search in agriculture for solutions mitigating those hazards.