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Persistence in North American Palmer Drought Severity Index Data Reconstructed from Tree Ring History

Congress: 2008
Author(s): G. Padmanabhan(1), S. L. Shrestha(1), R. G. Kavasseri(2)
G. Padmanabhan, Professor of Civil Engineering, Director of North Dakota Water Resources Research Institute, North Dakota State University, Fargo, ND 58105, USA Rajesh G. Kavasseri, Assistant Professor in Electrical Engineering, North Dakota State Univ

Keyword(s): Droughts, Palmer Drought Severity Index, Hurst coefficient, Detrended Fluctuation Analysis, Long term correlation, Persistence
Article: Poster:
AbstractVulnerability to droughts with devastating consequences has come under scrutiny time and again. Recent droughts in the North American Plains are no exceptions. Climate is the driving mechanism of droughts. Therefore, a better understanding of the past spatial and temporal variability of climate in terms of drought indicators is essential to develop better perspectives of long-term variations and correlative structure of the drought characteristics. Several techniques have been used in the past to analyze the temporal structure of climatologic and hydrologic time series data such as temperature, rainfall, sea surface temperature, and river flow. Use of power spectral analysis has remained popular since late 1950ís with the development of Blackman-Tukey method to systematize and standardize the power spectra computation. A host of other spectral analysis methods have been introduced subsequently. Though classical tools such as autocorrelation function and spectral analysis can provide preliminary indications for the presence of long range correlation, it may be difficult to use them unambiguously because of their stationarity assumption. However, other developments in time series analysis techniques have not been taken advantage of in investigating the long-term persistence and temporal scaling characteristics of drought time series. Techniques such as re-scaled range analysis (R/S) and detrended fluctuation analysis (DFA) can be used to test long memory. Re-scaled range analysis is sensitive to trends in the data and therefore, may give spurious results. Large-scale variability and a mixture of temporal scale effects can also render the R/S analysis unreliable. Recently the DFA and its extensions have been proposed as alternate techniques to determine possible long range correlations and temporal scaling properties in data sets obtained from diverse disciplines. For using these techniques we need data over long periods of time. The drought indicator we chose to analyze is the commonly used Palmer Drought Severity Index (PDSI). Direct records of PDSI for long periods are not available. However, tree ring widths have long been used as proxy for North American Droughts. A recently published North American Drought Atlas uses provides 286 annual tree-ring reconstructions of summer PDSI on a 2.5 degree by 2.5 degree grid network. The data length of the reconstructed PDSI varies from as short as about 300 years to as long as about 2000 years at some locations. Areas with longest reconstructed data are concentrated in a region bounded between 122.5 W to 102.0 W and from 42.5 N to 30.0 N, mainly in the states of California, Nevada, Utah, Colorado, and New Mexico in the United States of America. In this study fourteen of these reconstructed PDSI time series are analyzed for their temporal scaling properties and long-term persistence. All the data sets used in the study span over 2000 years. All of them yielded Hurst coefficients greater than 0.5 and values of scaling index close to or greater than 0.5 in the DFA analysis, indicating long term memory. The findings suggest that short memory models with longer lag terms may not be adequate to model droughts. Long memory models may be necessary.
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