The dynamic structure of climate is governed by changes in precipitation and temperature and can be studied by time series analysis of these factors. This paper describes investigation of time series and seasonal analysis of the monthly mean minimum and maximum temperatures and the precipitation for the Bhagirathi river basin situated in the state of Uttarakhand, India. The data used is from the year 1901–2000 (100 years). The seasonal ARIMA (SARIMA) model was used and forecasting was done for next 20 years (2001–2020). The auto-regressive (p) integrated (d) moving average (q) (ARIMA) model is based on Box Jenkins approach which forecasts the future trends by making the data stationary and removing the seasonality. It was found that the most appropriate model for time series analysis of precipitation data was SARIMA(0,1,1) (0,1,1)₁₂ (with constant) and of temperature data was SARIMA(0,1,0) (0,1,1)₁₂ (with constant). The model prediction results show that the forecast data fits well with the trend in the data. However, over-predictions are found in extreme rainfall events and temperature results. The information of pattern and trends can assist as a prediction tool for development of better water management practices in the area.

中文翻译：

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使用季节性ARIMA方法对气候变量进行时间序列分析

气候的动态结构受降水和温度变化的控制，可以通过对这些因素的时间序列分析进行研究。本文介绍了印度北阿坎德邦州Bhagirathi流域的月平均最低和最高温度以及降水的时间序列调查和季节性分析。使用的数据来自1901–2000年（100年）。使用了季节性ARIMA（SARIMA）模型，并对接下来的20年（2001–2020年）进行了预测。自回归（p）积分（d）移动平均值（q（ARIMA）模型基于Box Jenkins方法，该方法通过使数据稳定并消除季节性因素来预测未来趋势。发现用于降水数据时间序列分析的最合适模型是SARIMA（0,1,1）（0,1,1）₁₂（常数），温度数据是SARIMA（0,1,0）（ 0,1,1）₁₂（常数）。模型预测结果表明，预测数据与数据趋势吻合良好。但是，在极端降雨事件和温度结果中发现了过度预测。模式和趋势的信息可以作为预测工具，帮助开发该地区更好的水管理实践。