| dc.description.abstract | Entropy spectral analysis is developed for monthly streamflow forecasting, which contains the use of configurational entropy and relative entropy. Multi-channel entropy spectral analysis is developed for long-term drought forecasting with climate indicators.
The configurational entropy spectral analysis (CESA) is developed with both spectral power and frequency as random variables. With spectral power as a random variable, the configurational entropy spectral analysis (CESAS) identical to the original Burg entropy spectral analysis (BESA) when the underlying process is Gaussian. Through examination using monthly streamflow from the Mississippi Watershed, CESAS and BESA yield the same results and two methods are considered equivalent or as one method. With frequency as a random variable, the configurational entropy spectral analysis (CESAF) is developed and tested using monthly streamflow data from 19 river basins covering a broad range of physiographic characteristics. Testing shows that CESAF captures streamflow seasonality and satisfactorily forecasts both high and low flows. When relative drainage area is considered for analyzing streamflow characteristics and spectral patterns, it is found that upstream streamflow is forecasted more accurately than downstream streamflow.
Minimum relative entropy spectral analysis (MRESA) is developed under two conditions: spectral power as a random variable (RESAS) and frequency as a random variable (RESAF). The exponential distribution was chosen as a prior probability in the RESAS theory, and in the RESAF theory, the prior is chosen from the periodicity of streamflow. Both MRESA theories were evaluated using monthly streamflow observed at
20 stations in the Mississippi River basin, where forecasted monthly streamflow shows
higher reliability in the Upper Mississippi than in the Lower Mississippi.
The proposed univariate entropy spectral analyses are generally recommended over the classical autoregressive (AR) process for higher reliability and longer forecasting lead time. By comparing two MRESA theories with the two maximum entropy spectral analyses (MESA) (BESA and CESA), it is found that MRESA provided higher resolution in spectral estimation and more reliable streamflow forecasting, especially for multi-peak flow conditions. The MRESA theory is more accurate in forecasting streamflow for both peak and low flow values with longer lead time than MESA. Besides, choosing frequency as a random variable shows advantages over choosing spectral power. Spectral density estimated by the RESAF or CESAF theory shows higher resolution than the RESAS or BESA theory, respectively, and streamflow forecasted by RESAF or CESAF is more reliable than that by RESAS or BESA, respectively.
Finally, multi-channel entropy spectral analysis (MCESA) is developed for bivariate or multi-variate time series forecasting. MCESA theory is verified by forecasting long-term standardized streamflow index with El Nino Southern Oscillation (ENSO) indicator. SSI was successfully forecasted using multi-channel spectral analysis with ENSO as an indicator. The monthly drought series is forecasted for lead times of 4-6 years by MCESA. | en |
