By J. N. Kapur, H. K. Kesavan (auth.), V. P. Singh, M. Fiorentino (eds.)
Since the landmark contributions of C. E. Shannon in 1948, and people of E. T. Jaynes a couple of decade later, purposes of the idea that of entropy and the main of utmost entropy have proliterated in technology and engineering. fresh years have witnessed a extensive variety of recent and intriguing advancements in hydrology and water assets utilizing the entropy suggestion. those have encompassed leading edge tools for hydrologic community layout, move of data, circulation forecasting, reliability overview for water distribution structures, parameter estimation, derivation of likelihood distributions, drainage-network research, sediment yield modeling and pollutant loading, bridge-scour research, development of speed profiles, comparative review of hydrologic versions, etc. a few of these tools carry nice promise for development of engineering perform, allowing rational possible choices to standard techniques. nonetheless, the thoughts of power and effort dissipation are being more and more utilized to a large spectrum of difficulties in environmental and water assets. either entropy and effort dissipation have their foundation in thermodynamics, and are comparable recommendations. but, some of the advancements utilizing entropy appear to be established solely on statistical interpretation and feature possible little actual content material. for instance, lots of the entropy-related advancements and functions in water assets were in response to the information-theoretic interpretation of entropy. We think if the ability of the entropy thought is to be absolutely discovered, then its actual foundation should be established.
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Extra info for Entropy and Energy Dissipation in Water Resources
Consisting of a number of sub-basins. We focus our attention on. say. the uppermost firstorder watershed. that has a certain amount or disorder. As we move down from this watershed to a second-order watershed that encompasses the first-order watershed. the disorder increases. This means the entropy increases. One may, somewhat presumptuously. postulate that on the average, the entropy increases with the watershed order in a river network. The concept of entropy or disorder can also be related to the concept of space-time scales of hydrologic processes.
1980a) MOM, modified MOM, MLE and modified MLE Comparable to MLE; and better than others. Wei bull Singh, Cruise and Ma (1989, 1990b) MOM, PWM, MLE and MOLS Comparable to MLE; and better than others Extreme-value type III Singh (1987); Singh and Rajagopal (1986) MOM and MLE Comparable to MLE; and better than MOM 44 V. P. SINGH AND M. FIORENTINO Table 3. Root mean square error (RMSE) and bias (BIAS) by MOM, MLE and POME methods for six selected rivers for log-Pearson type 3 distribution (after Singh and Singh, 1985b).
The histogram may have several peaks and may exhibit great disorder. If the time scale is increased to. say. one hour. the resulting histogram may have only one peak and will certainly display a higher degree of order and lower entropy. Ir the time scale is increased to the duration of the rainfall event, the resulting histogram will simply plot as a rectangular pulse. Clearly then, as the time scale increases the observed rainfall data exhibit greater order. and lower entropy. In general. the entropy of a hydrologic system decreases with increasing time scale or decreases with decreasing time-variability.
Entropy and Energy Dissipation in Water Resources by J. N. Kapur, H. K. Kesavan (auth.), V. P. Singh, M. Fiorentino (eds.)