Markov chains to determine the probability of climate change for planting selection in the city of Caxias do Sul

ABSTRACT: The Markov stochastic chain model and the analytical hierarchy process (AHP) were used as tools to support decision-making for the best crop-planting choice in the city of Caxias do Sul, Brazil. Temperature and precipitation information were collected from the Meteorological Database for Teaching and Research of the National Institute of Meteorology of Brazil for the period 1997-2017. The stochastic model was applied to obtain the probability of transition between a range of variations for temperature and precipitation. In the second phase of the study, an algebraic model was developed, making it possible to link the probability of the Markov chain transition matrix to the AHP judgment matrix. In the third phase, the AHP was applied as a tool to determine the most beneficial crop that could be planted for the studied city, considering the evaluated criteria: temperature, precipitation, and soil pH. The alternatives for crop planting were carrots, tomatoes, apples, and grapes. These were chosen because they are the most-planted crops in the city of Caxias do Sul. The ranking of the benefit-force results of applying the model for spring was carrots (0.297), apples (0.259), grapes (0.228), and tomatoes (0.215); for summer: grapes (0.261), tomatoes (0.261), apples (0.238), and carrots (0.230); for autumn: carrots (0.316), grapes (0.243), tomatoes (0.228), and apples (0.213); and for winter: carrots (0.327), tomatoes (0.235), apples (0.222), and grapes (0.216). Thus, it was concluded that farmers would have a better chance of success if they planted carrots during the spring, autumn, and winter, and grapes during the summer.

摘要：本研究以马尔可夫随机链模型（Markov stochastic chain model）与层次分析法（Analytical Hierarchy Process，AHP）为决策工具，为巴西卡希亚斯杜苏尔市遴选最优作物种植方案提供支撑。研究收集了1997—2017年巴西国家气象学院教学研究气象数据库的气温与降水数据。通过构建随机模型，获取气温与降水的区间变化转移概率。研究第二阶段构建代数模型，实现马尔可夫链转移概率矩阵与AHP判断矩阵的关联耦合。第三阶段运用层次分析法，结合气温、降水、土壤pH三项评估准则，确定该市最优种植作物。备选种植作物为胡萝卜、番茄、苹果与葡萄，上述品类均为卡希亚斯杜苏尔市的主栽作物。本研究得出的各季节效益得分排序结果如下：春季为胡萝卜（0.297）、苹果（0.259）、葡萄（0.228）、番茄（0.215）；夏季为葡萄（0.261）、番茄（0.261）、苹果（0.238）、胡萝卜（0.230）；秋季为胡萝卜（0.316）、葡萄（0.243）、番茄（0.228）、苹果（0.213）；冬季为胡萝卜（0.327）、番茄（0.235）、苹果（0.222）、葡萄（0.216）。综上，该市农户若在春、秋、冬三季种植胡萝卜，夏季种植葡萄，可获得更高的种植成功率。