Investigating monthly precipitation variability using a multiscale approach based on ensemble empirical mode decomposition

In environmental and hydrological studies, the issue of variability in precipitation is of great importance, particularly for regions situated in arid and semiarid environments, such as Iran. Since precipitation is extremely complex spatial–temporal process, a time–space framework for rain gauges classification based on rate of information (entropy) can be very useful. The multi-temporal randomness in precipitation time series can be measured by an entropy-based approach. Therefore, an ensemble empirical mode decomposition (EEMD)-based multiscale entropy (EME) approach was implemented to measure and evaluate monthly variability in precipitation and spatially discriminate rain gauges across Iran. Monthly precipitation data spanning 612 months (1960–2010), drawn from rain gauges at 31 stations across Iran, served to verify the proposed model. Given the existence of noise in the time series, a wavelet de-noising approach was applied to remove the corruption of the time series which can influence EME values. An EEMD approach served to decompose the precipitation time series into an intrinsic mode function (IMF), with different periods and specifications, along with residual components. An entropy concept based on the IMFs’ energy and residual sub-series served in calculating the multiscale components’ dispersion. The entropy values of IMFs 1–9 and residual components showed different patterns across rain gauge sites, where IMF 8, IMF 9 and the residual components showed the greatest level of entropy, while IMF 1 showed the greatest variation in entropy among all components. The spatial distribution of EME values showed a downward trend from north to south. A k-means clustering approach based on EME values served to specify the location of rain gauges. On a statistical basis (Davies–Bouldin Index = 0.29, Dunn Index = 3.22 and Silhouette Coefficient Index = 0.64), a clustering number of 5 led to a more precise discrimination of EME-based homogenous areas than did other clustering numbers. An evaluation of the relationships between EME values and latitude/longitude, showed an inverse relationship between EME and longitude and a direct relationship between EME and latitude, though neither was significant.