Proportionality hypothesis, hydrology, water balance models, water balance


There are many different controlling factors on the partitioning of rainfall into runoff. However, the influence of each of these controls varies across different temporal scales. Consequently, numerous water balance models have been developed in the literature for application across various time scales. These models are usually developed for a particular time scale so that the controls with the greatest influence on rainfall partitioning are captured. For example, the SCS curve number method was developed to simulate direct runoff at the event scale; the "abcd" model was developed as a monthly water balance model; and the Budyko model was developed for long-term water balance. More recently, the proportionality hypothesis, which traces its origins from the SCS curve number method, has been identified as the commonality between these three hydrologic models, suggesting that this hypothesis may be the unifying principle of hydrologic models across various time scales. The objective of this thesis is to develop a conceptual hydrologic model structure for continuous simulations for multiple time scales. The developed model is applicable to daily, monthly, and annual time scales. Direct runoff is computed by a proportionality relationship in the SCS curve number method. In the "abcd" model, evapotranspiration and storage at the end of each time period are computed by a proportionality relationship, however evapotranspiration is computed based on an exponential relationship of storage and potential evapotranspiration while base flow is computed based on a linear reservoir model. In the Budyko model, runoff and evapotranspiration are computed by a proportionality relationship. The primary difference with the proposed model in this thesis in comparison with the other three water balance models is the application of the proportionality hypothesis to the partitioning of surface runoff and continuing abstraction as well as the partitioning of continuing evapotranspiration and subsurface flow. The proposed model structure is implemented in Matlab. The developed model includes six parameters, which are estimated for 71 case study catchments in the United States using a genetic algorithm. The model performances at the daily, monthly and annual time scales are evaluated during calibration and validation periods, and compared with the "abcd" model and a Budyko-type model developed for multiple time scales. Evaluation of the models shows that the proposed model performs better or comparable to the other models at all time scales.


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Graduation Date





Wang, Dingbao


Master of Science (M.S.)


College of Engineering and Computer Science


Civil, Environmental, and Construction Engineering

Degree Program

Civil Engineering; Water Resources Engineering Track








Release Date

May 2014

Length of Campus-only Access


Access Status

Masters Thesis (Open Access)


Dissertations, Academic -- Engineering and Computer Science; Engineering and Computer Science -- Dissertations, Academic