The Application of the Modified Curve Number (Three Parameters Mishra-Singh) Model to Flood Estimation

Introduction
There are many models for flood prediction that are based on different conceptual bases. The standard SCS-CN method was developed in 1954 and it is documented in Section 4 of the National Engineering Handbook (NEH-4) published by Soil Conservation Service (now called the Natural Resources Conservation Service), U.S. Department of Agriculture in 1956. The document has been revised several times. It is one of the most popular methods for computing the volume of surface runoff for a given rainfall event from small agricultural, forest, and urban watersheds. The method is simple, easy to understand, and useful for ungauged watersheds. The method accounts for major runoff producing watershed characteristics, viz., soil type, land use/treatment, surface condition, and antecedent moisture condition.  Recent researches focus on the improvement of this model and improve its efficiency but it is necessary to evaluate the improved models for Iran's watersheds. The purpose of this study was the comparison of standard SCS-CN and developed three parameter Mishra-Singh models for flood hydrograph and peak estimation using data of five watersheds in Golestan Province.
Methodology
Study Area and Used Data
Five watersheds (including Galikesh, Tamer, Kechik, Vatana, and Nodeh) located in Golestan Province were considered to evaluate different models for flood hydrograph estimation. The characteristics of the selected watersheds are different. For Tamer, Galikesh, Kechik, Nodeh, and Vatana watersheds, the areas are equal to (1527, 401, 36, 790 and 11 km²), the parameters are (289, 139, 26, 208 and 20 km), the mean altitudes are (1131, 1358, 928, 1540 and 899 m), the mean slope of the watersheds are (19, 27, 19, 28 and 33%), the length of the main channels are (94, 58, 10, 66 and 8 km), and the number of rainfall-runoff events are (10, 13, 3, 9, and 4 cases).
Descriptions of Models
The standard curve number (SCS-CN) model was based on the following basic equations:









 
 





 


(1)




 
   


(2)




P is total rainfall, Q is excess rainfall, CN is curve number, Ia is initial abstraction, and S is maximum retention.
Using the concept of the degree of saturation (C=Sr), where C is the runoff coefficient (= )), Mishra and Singh (2002) and Mishra et al. (2006) modified the original SCS-CN model after the introduction of antecedent moisture Mas:

                               (3)
The relationships developed by Mishra et al. (2006) for Mare:                                        





(4)
 
(5)

 




P₅ is prior 5-day rainfall depth.
Three model accuracy criteria including root mean square error (RMSE), Nash-Sutcliff efficiency (NSE) and percentage error in peak (PEP) were applied to compare the results of models (Adib et al., 2010-2011).
Results
There were 39 rainfall-runoff events, of which 25 and 14 events were respectively selected for the calibration and validation steps. The parameters of investigated models for different events and watersheds and related model accuracy criteria were calculated. The root mean square error (RMSE) and Nash-Sutcliff efficiency (NSE) criteria can be used for the analysis of the flood hydrograph simulation while percentage error in peak (PEP) criteria is suitable for the analysis of the flood peak discharge simulation. In the Gallikesh watershed, for the developed three parameter Mishra-Singh and standard SCS-CN models, the RMSE criteria values were (16, 11.05, 2.8, and 10.63) and (17.94, 14 , 6.56 and 13.56), the values of NSE values were (-0.88, -84.44, -0.9 and -4.77) and (-1.37-, -1.38, -9.7, and -8.4), and the PEP values were (0.4, -1.4, 0.55, -0.3) and (0.24, -2.11, -1.39 and -0.62). For the Nodeh watershed in different events, the RMSE criteria values were (13.22, 23.57, 79.53 and 68.15) and (11.83, 22.74, 88.96 and 69.92), the NSE values were (-6.88, -2.7, -0.17 and -66) and (-5.31, -2.46, -0.46 and -69.5), and the values of PEP were (-1.19, -1.98, 0.83, -2.48) and (-1,-2.4, 0.99 and -2.57) for the developed three parameter Mishra-Singh and standard SCS-CN models were calculated. In the Tamer watershed for two models of developed three parameter Mishra-Singh and standard SCS-CN, the values of different criteria estimated as the RMSE criteria values were (13.04, 26.85, 5.9 and 19.26) and (12.04, 92.62, 5.26 and 48.81), the values of NSE criteria were (-0.92, -20.3, -4.9 and -0.14) and (-0.73, -252.5, -3.75 and -6.37), and the PEP criteria values were (0.52, -0.2, -0.8, and 0.62) and (0.62, -5.14, -0.74 and 1.09). In Vatana and Kechik watersheds for the developed three parameter Mishra-Singh model different criteria were calculated as the RMSE values (2.5) and (1.5), the NSE criteria values (0.51) and (-0.07), the PEP criteria values (0.45) and (-0.3). However, in these two watersheds for the SCS-CN standard model, the RMSE criteria values were (4.8) and (2.91), the NSE criteria values were (-0.82) and (-2.93) and the PEP criteria values were (0.95) and (0.6).
Discussion and Conclusion
The values of root mean square error (RMSE), Nash-Sutcliff efficiency (NSE) showed that the developed three parameter Mishra-Singh model improved the accuracy of the flood hydrograph estimation relative to the standard SCS-CN model for 71% of the studied events and the difference between two models for remaining 29% event was negligible. Also, the values of percentage error in peak (PEP) revealed that the three parameter Mishra-Singh model led to a decline equal to 78% in flood peak estimation in comparison with standard SCS-CN model application. In addition, the standard SCS-CN and the three parameter Mishra-Singh models were respectively 64% of and 57% of the studied cases. In this study, the accuracy of the standard SCS-CN andthedeveloped three parameter Mishra-Singh models compared the flood hydrograph and peak estimation considering data of five watersheds in Golestan Province. The investigation of the model accuracy criteria revealed that the developed model led to a considerable improvement of flood estimation in studied watersheds.