Mathematical and Statistical Applications in Life Sciences and Engineering by Avishek Adhikari Mahima Ranjan Adhikari & Yogendra Prasad Chaubey

Author:Avishek Adhikari, Mahima Ranjan Adhikari & Yogendra Prasad Chaubey
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

In Fig. 7.3, we have the plot of the Palmer Drought Severity Index (PDSI) for Campinas ranging from January 01, 1970 to May 01, 2011. From this plot, we also observe that the period tanging from the 300th month (01/01/1995) to 350th month (12/31/1998) has an atypical drought period, a result similar to the one obtained using the SPI-1 index (see Fig. 7.1).

The Standardized Precipitation Index (SPI) has many advantages when compared to the Palmer Drought Severity Index (PDSI) as pointed out by many climatologists since it quantifies the precipitation deficit for different timescales. These timescales reflect the impact of drought on the availability of the different water resources. Soil moisture conditions respond to precipitation anomalies on a relatively short scale; groundwater, streamflow, and reservoir storage reflect the longer term precipitation anomalies. In this way, many climatologists are using the SPI index in place of the PDSI index, although the statistical modeling approach based on time series SVM presented here could be easily extended to the PDSI index.

Other structures of SVM could also be considered to analyze SPI measures, for example, considering autoregressive model AR(L) structures with L larger than 1 to get better fit of the model for the data. The use of a Bayesian approach with MCMC (Markov Chain Monte Carlo) methods and existing freely available software like OpenBugs or JAGS could simplify the computational task to get the posterior summaries of interest. The choice of a better model could be made using some existing Bayesian discrimination criteria as the Deviance Information Criterion (DIC) criterion [22].

Using this family of SVMs we could possibly relate the time periods with atypical drought to some covariates (for example, the sea temperature in equatorial Pacific Ocean like El Niño by unusually warm temperatures or La Niña by unusually cool temperatures) which could be affecting the climate of the world, or even other causes showing atypical extremely wet or extremely dry periods.

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