Rainfall statistics, stationarity, and climate change

Abstract

There is a growing research interest in the detection of changes in hydrologic and climatic time series. Stationarity can be assessed using the autocorrelation function, but this is not yet common practice in hydrology and climate. Here, we use a global land-based gridded annual precipitation (hereafter P) database (1940-2009) and find that the lag 1 autocorrelation coefficient is statistically significant at around 14% of the global land surface, implying nonstationary behavior (90% confidence). In contrast, around 76% of the global land surface shows little or no change, implying stationary behavior. We use these results to assess change in the observed P over the most recent decade of the database. We find that the changes for most (84%) grid boxes are within the plausible bounds of no significant change at the 90% CI. The results emphasize the importance of adequately accounting for natural variability when assessing change.

Keywords: precipitation; stationarity; variance.

Fig. 1.

Annual (1767–2010) $P$ time series at the Radcliffe Observatory, Oxford, United Kingdom. (A) $P$. (B) Autocorrelation of $P$ with 90% CI (dashed). Averages (solid) over (C) 30- and (D) 10-y time periods with 90% CI (dashed). Data are from ref. .

Fig. 2.

Estimate of the lag 1 autocorrelation of annual $P$ (1940–2009; GPCC). The four numbered time series are included for explanatory purposes. Significance ($\pm$0.197) is for the 90% confidence level.

Fig. 3.

Testing annual $P$ in the most recent decade for significant changes. The ordinate shows $\mathrm{\Delta }P$ (calculated as mean annual $P$ for 2000–2009 less that for 1940–2009) as a function of the variance of the annual time series (1940–2009) for the GPCC observations. Each cross denotes one grid box. The curves ($1{\sigma }_{\mathrm{\Delta }P}$, $2{\sigma }_{\mathrm{\Delta }P}$, $3{\sigma }_{\mathrm{\Delta }P}$, and $4{\sigma }_{\mathrm{\Delta }P}$) were estimated using Eq. 1.