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.

Abstract: Nowadays, you can forecast that in twenty-first century a probability of drought risk occurrence, a one of the threatening a type of risk in agriculture, will reach a level between 66 and 90 per cent [IPCC 2001].The beginning of the twenty-first century is a time to seek new methods of risk management in agriculture. This is confirmed by the reports and surveys carried out in many research centres, as well as commissioned by public authorities [Xu et al. 2008]. Currently, you can observe the growing importance of the issue of risk in agriculture due to the worsening climate change, changes in the Common Agricultural Policy, the progressive liberalization of food trade on a global scale (less market intervention, increased price volatility and fluctuations in food supply and demand) and associated with those phenomena increase market risk [Jerzak 2008]. Demographic boom, growth in epidemics and diseases or changes in models of consumer behaviour as a result of today’s food trends healthy diet have an impact on food security. It is of interest to large research teams in Europe, just as the above risk factors affect the imbalance of global supply and demand for food in the long term. The Stern [Stern 2006] and report the Foundation for the Development of Polish Agriculture – FDPA) [Report FDPA 2008] and the communications of the European Commission show that in agriculture a lack of system solutions for the management of various risks and set of management instruments it is inadequate to the current situation of the sector.Analyzing historical data, one can conclude that in Poland more often we have to deal with losses caused by deficiency of precipitation than the excess [Mizak et al. 2013]. Droughts in Poland are most common when during the growing season flows very warm and dry air. In 2008, the area of arable land, determined in accordance with the applicable System Monitoring Agricultural Drought criterion of a 20 percent reduction in crop yields covered more than 8.1 million hectares, which accounted for 54% of arable land in Poland [Mizak et al. 2011]. Appropriate agricultural policy and trade policy should ensure sufficient food for the rapidly growing global population under mentioned above extreme natural events circumstances.Research centers in many EU countries and beyond should create appropriate models, tools and techniques in order to solve signaled above specific problems at farms, regions, countries and groups of countries in order to reduce the risks associated with food production [Bojar et al. 2012]. Such models were created as part of the research carried out in the Kujawy & Pomorze region where their results show the possibility of predicting the effects of climate change in the long term [Bojar et al., 2013, Zarski et al. 2014, Bojar at al., 2013].In particular, the series established the likelihood of a lack of rain in the forecast for the years 2030 and 2050 at a certain level and so the series 7, 8, 9 and 10 decades without rain likely to occur by 2030 amounts to 0.302, 0.109, 0.032 and 0.009, while for the year 2050 decades for a series of 7, 8, 9 and 10 respectively 0,543, 0,222, 0,070 and 0,019. It follows that, for a series of seven and eight decades without rain probability of such unfavorable phenomena is highest. Then established the relationship that the lack of rainfall will decrease yields of cereals in total, winter wheat, spring barley and potatoes. It results in the decline in land productivity in the years 2030 and 2050 will amount to cereals in total, winter wheat, spring barley and potatoes in the range of the maximum and minimum respectively 2.51 t/ha -3.67 t/ha, 3.10 t/ha- 4.10 t/ha, 1.63 t/ha – 3.33 t/ha and 15.30 t/ha- 21.00 t/ha [Bojar et al. 2013].The above-described conditions of risk of conducting agricultural activities indicate the need to develop methods of mitigating their negative effects.Mitigation of production and business risks in agriculture can be reached as follows:-        advancement models for defining dependencies between yields and whether in long-term to forecasts negative effects in farming productivity and profitability and this way minimize production and business risks,-        advancement of system of crop insurance,-        improvement of the infrastructure of small retention and simulation of the impact of various forms of cooperation of agricultural producers to increase the efficiency of their operations (joint purchasing of inputs, selling of agricultural products and/or use of machinery [Bojar 2008], work specialization versus production specialization [Bojar W., Drelichowski L., 1994.], common trainings, advertisements [Bojar, Kinder 2008, etc.]. Own preliminary research findings confirmed that approximately one third of the respondents jointly purchases and sales their products and forms of farmer cooperation with a joint market activities (transaction) in the Kujavian & Pomeranian region.For more detail and more precise explanation of dependency between yield and rainfalls some efforts will be focused on mathematical models describing agriculture and climate change problems that can be encountered in risk and safety analysis. We need to describe the uncertainties from incomplete knowledge, imperfect models or measurement errors.Because yields of crops depend strongly on rainfall there will be considered different models of rainfall. You will attempt of the generalization of model mixture the gamma distribution and a single point at zero distribution. This approach will be a continuation of the work that has been sent to print. To extend this application it could be performed calculations for the empirical data coming from the Kujavian & Pomeranian region for different crops.This work was co-financed by NCBiR, Contract no. FACCE JPI/04/2012 – P100 PARTNER No Label