Title: Patterns in All-India rainfall during 1813-2006

Abstract:

Analysis of All-India rainfall from 1813-2006 using time-series analysis techniques was used in this paper to understand the variability of rainfall across the country during the 194 year period. On average, the country as a whole receives about 1150.5 (mm) of rainfall. June was the month with the higest mean rainfall (174.7 mm), while December through March the rainfall was at its monthly lowest, with the lowest in December (13.3 mm). By year, the higest rainfall was observed in and the lowest rainfall was observed in (). Spectrum analysis showed significant cycles in the 194-year series, but these tend to be low frequencies.

Introduction:

The techniques used in time series analysis are commonly applied to data from the geophysical sciences. This paper analyzes annual and monthly All-India rainfall between 1813-2006. Source of data came from the India Institute of Tropical Meteorology. One note-worthy aspect of our dataset is that annual All-India rainfall follows a normal distribution, implying that yearly rainfall across the country may be modeled by a Gaussian process. However, monthly data for the entire 194-year period indicates that on a monthly level rainfall certainly fluctuates periodically and that there are seasonal lags present. Of particular interest in this paper is analyzing seasonal rainfall patterns across India, determining whether there is any long-range dependence in our dataset.

Method:

First, annual and monthly raw data are analyzed using appropriate (diagonostic) plots such as the autocorrelation and partial autocorrelation plots. These plots identify whether the dataset follows a moving average or autoregressive process, as well as determining seasonal lags in the data.
Spectral analysis is used to look for possible long-range dependence. Since we expect patterns to occur at least monthly, annual, and possibly of higher orders such as bi-annual and 4-years, low-pass filters are used to study the low frequency patterns in the monthly rainfall dataset.

Finally, we fit an ARIMA model to our monthly data and test the model against the 2328 monthly observations in the dataset. We use the ARIMA model to make forecasts for the next 120 months (or the next ten years).

Results:




(?) Possible monsoon cycles are irregular, but tend to be around for years on average.

Evaluations:

The main objective of this paper is to make as much meaningful inference from one particular dataset. Hence, as much time-series analysis techniques were performed on the appropriate dataset, especially on the monthly rainfall data collected between 1813-2006.

? Displaying estimates on the log scale tends to emphasize the harmonic components. There is a necessity for having some relatively systematic procedure for deciding whether peaks are significant.

Appendix:
All-India rainfall dataset
R codes

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Ein Deutsches Requiem, Opus 45

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