Evaluation of irrigation requirement for the design of an irrigation system using a probabilistic approach for the estimation of evapotranspiration and rainfall

ABSTRACT Reference evapotranspiration (ET0) and rainfall are basic variables for estimating the net irrigation depth (NID). The objective of this study was to estimate the NID for designing irrigation systems in Piracicaba, SP, Brazil, using ET0 and rainfall probability distributions. A 30-year ET0 and rainfall dataset (1990-2019) was obtained from the ESALQ/USP weather station. The water balance between ET0 and rainfall indicated July, August, and September as months of higher water deficit. Based on the first-order Markov chain, August presented the highest water deficit. Rainfall and ET0 were estimated on 19 probability levels, and four probability distributions such as normal, log-normal, beta, and mixed gamma were evaluated. The analysis of historical August series using accumulated values in periods of five, ten, or 15 days is recommended for sizing irrigation designs in Piracicaba, SP, Brazil. The log-normal and mixed gamma probability distributions presented the best fit for ET0 and rainfall data, respectively. To reach a crop coefficient Kc = 1 in Piracicaba, SP, Brazil in August, the irrigation system should be designed for an NID of 4.1 mm day-1. The use of mean monthly rainfall and ET0 values for designing irrigation systems underestimates the NID by a mean of 26.6% compared to estimates made at a probability of 75% at five-, ten-, and 15-day intervals because the mean rainfall values occurred with exceedance probabilities of < 36%, and mean ET0 values occurred with non-exceedance probabilities of < 56%.

摘要：参考作物蒸散量（Reference evapotranspiration, ET0）与降雨量是估算净灌溉水深（Net Irrigation Depth, NID）的基础变量。本研究旨在借助参考作物蒸散量与降雨量概率分布，为巴西圣保罗州皮拉西卡巴市的灌溉系统设计估算净灌溉水深。研究获取了1990-2019年共30年的参考作物蒸散量与降雨量数据集，数据来源于ESALQ/USP气象站。通过参考作物蒸散量与降雨量的水平衡分析，确定7月、8月及9月为水分亏缺较高的月份；基于一阶马尔可夫链（first-order Markov chain）分析，8月的水分亏缺程度最高。

研究在19个概率水平上对降雨量与参考作物蒸散量进行估算，并评估了正态分布、对数正态分布、贝塔分布及混合伽马分布共4种概率分布的适配性。针对巴西圣保罗州皮拉西卡巴市的灌溉系统设计，研究建议采用5日、10日或15日周期的累积值对8月历史序列开展分析。其中，对数正态分布与混合伽马分布分别对参考作物蒸散量与降雨量数据的拟合效果最优。

若要在巴西圣保罗州皮拉西卡巴市的8月实现作物系数（crop coefficient, Kc）=1的目标，灌溉系统的设计净灌溉水深应达到4.1毫米/日。相较于以5日、10日及15日为间隔、概率75%时的估算结果，仅使用月均降雨量与月均参考作物蒸散量进行灌溉系统设计，会使净灌溉水深平均低估26.6%——这是因为月均降雨量的超越概率低于36%，而月均参考作物蒸散量的未超越概率低于56%。