Minimum relative entropy theory for streamflow forecasting with frequency as a random variable

Abstract

This paper develops a minimum relative entropy theory with frequency as a random variable, called MREF henceforth, for streamflow forecasting. The MREF theory consists of three main components: (1) determination of spectral density (2) determination of parameters by cepstrum analysis, and (3) extension of autocorrelation function. MREF is robust at determining the main periodicity, and provides higher resolution spectral density. The theory is evaluated using monthly streamflow observed at 20 stations in the Mississippi River basin, where forecasted monthly streamflows show the coefficient of determination (r 2 ) of 0.876, which is slightly higher in the Upper Mississippi (r 2 = 0.932) than in the Lower Mississippi (r 2 = 0.806).Comparison of different priors shows that the prior with the background spectral density with a peak at 1/12 frequency provides satisfactory accuracy, and can be used to forecast monthly streamflow with limited information. Four different entropy theories are compared, and it is found that the minimum relative entropy theory has an advantage over maximum entropy (ME) for both spectral estimation and streamflow forecasting, if additional information as a prior is given. Besides, MREF is found to be more convenient to estimate parameters with cepstrum analysis than minimum relative entropy with spectral power as random variable (MRES), and less information is needed to assume the prior. In general, the reliability of monthly streamflow forecasting from the highest to the lowest is for MREF, MRES, configuration entropy (CE), Burg entropy (BE), and then autoregressive method (AR), respectively.

Entropy-Based Investigation on the Precipitation Variability over the Hexi Corridor in China

“…The entropy theory presented by Shannon in the late 1940s [6] and the principle of maximum entropy presented by Jaynes in the late 1950s [7,8] have been applied in various research fields. Among them, there are many valuable hydrological applications of entropy theory (e.g., [9][10][11][12][13][14][15][16][17][18][19][20][21]). The aspects we want to address in this study include: (1) the detection of the spatial region and temporal year for high disorder features; (2) the identification of a monthly time series, which dominates the seasonal precipitation in Hexi corridor, and the identification of a seasonal time series, which dominates the annual precipitation in the corridor; (3) the correlations between drought-induced crop reduction and precipitation variability.…”

“…The AE value is in the range of 0 and log 2 (12) [1], in which the precipitation occurs only one out of twelve months and the annual precipitation amount is evenly distributed for twelve month respectively.…”

Application of Entropy Spectral Method for Streamflow Forecasting in Northwest China

“…Fortunately, entropy spectral analysis can extract significant information from streamflow process and forecast monthly streamflow accurately coupled with the time series analysis method. Actually, the spectral method has been successfully used by some researchers for monthly streamflow forecasting with different types of entropy including Burg entropy [3], configuration entropy [1,2], and minimum relative entropy [4,5].…”

“…The RESA spectra have higher resolution and are more accurate in detecting peak location than other methods for spectral computation [16]. The RESA method has been used for monthly streamflow forecasting [4,5,16] and has smaller errors than the other two entropy spectral methods.…”

Entropy-Based Parameter Estimation for the Four-Parameter Exponential Gamma Distribution

“…Among the above parameter estimation methods, entropy, which is a measure of uncertainty of random variables, has attracted much attention and has been used for a variety of applications in hydrology [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. For example, an entropy-based derivation of daily rainfall probability distribution [24], the Burrr XII-Singh-Maddala (BSM) distribution function derived from the maximum entropy principle using the Boltzmann-Shannon entropy with some constraints [25].…”