Abstract
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.
Highlights
GONDIM et al (2017) predicted that if the burning of fossil fuels progresses at the current rate, without any changes in climate policy, there is at least a 66% probability that global temperatures will increase by at least 2.5 C by 2100 compared to pre-industrial levels (1850 to 1900)
This study evaluated the probabilities of possible climate changes, starting from an initial climatic state in the city of Caxias do Sul, Brazil, using the stochastic Markov chain model, and, based on this, indicated the best planting option per season for the city studied, using a multicriteria method
Markov chains Initially, the results of the temperature and precipitation transition matrices were analyzed, observing that there is a probability between 84% and 86% of a temperature increase
Summary
GONDIM et al (2017) predicted that if the burning of fossil fuels progresses at the current rate, without any changes in climate policy, there is at least a 66% probability that global temperatures will increase by at least 2.5 C by 2100 compared to pre-industrial levels (1850 to 1900). According to the Intergovernmental Panel on Climate Change (IPCC) (2014), a 1 °C rise in temperature may have a negative impact on the cultivation of rice, wheat, and corn in tropical areas. The Markov chain was first proposed in a 1906 article written by Russian mathematician Andrei Andreyevich Markov, in which he described the stochastic process and provided the probability information in a transition from one state to another (MARKOV, 1906). The probability distribution of the future state is based only on its current state, and is independent of previous events in the time series (YEH & HSU, 2019)
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