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Knopik, L., & Bojar, W. (2013). Mozliwosci zastosowania metody wielo – agentowej w analizie wybranych modeli (Possibilities of multiagent appliacation for analysis of selected models). In K. Rostek (Ed.), (pp. 199–208). Zarzadzanie wiedza w tworzeniu przewagi konkurencyjnej (Knowledge management in creating comparative advantage). Warsaw: Warsaw Technical University.
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Bojar, W., Żarski, J., Knopik, L., Kuśmierek-Tomaszewska, R., Sikora, M., & Dzieża, G. (2015). Markov chain as a model of daily total precipitation and a prediction of future natural events.. Braunschweig (Germany).
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.
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Bojar, W., Żarski, J., Knopik, L., Kuśmierek-Tomaszewska, R., Sikora, M., & Dzieża, G. (2015). Markov chain as a model of daily total precipitation and a prediction of future natural events.. Braunschweig (Germany).
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.
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Bojar, W., Żarski, J., Knopik, L., Kuśmierek-Tomaszewska, R., Sikora, M., & Dzieża, G. (2016). Markov Chain as a Model of Daily Total Precipitation and a Prediction of Future Natural Events.. Berlin (Germany).
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Bojar, W., Knopik, L., Żarski, J., & Kuśmierek-Tomaszewska, R. (2016). Integrated assessment of crop productivity based on the food supply forecasting. Agricultural Economics – Czech, 61(11), 502–510.
Abstract: Climate change scenarios suggest that long periods without rainfall will occur in the future often causing instability of the agricultural products market. The aim of our research was to build a model describing the amount of precipitation and droughts for forecasting crop yields in the future. In this study, we analysed a non-standard mixture of gamma and one point distributions as the model of rainfall. On the basis of the rainfall data, one can estimate parameters of the distribution. Parameter estimators were constructed using a method of maximum likelihood. The obtained rainfall data allow confirming the hypothesis of the adequacy of the proposed rainfall models. Long series of droughts allow one to determine the probabilities of adverse phenomena in agriculture. Based on the model, yields of barley in the years 2030 and 2050 were forecasted which can be used for the assessment of other crops productivity. The results obtained with this approach can be used to predict decreases in agricultural production caused by prospective rainfall shortages. This will enable decision makers to shape effective agricultural policies in order to learn how to balance the food supplies and demands through an appropriate management of stored raw food materials and import/export policies.
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