Abstract
Inconsistent model prediction results were reported worldwide against SCS (now USDA) runoff model since its inception in 1954. Non parametric inferential statistics was used to reject two Null hypotheses and guided the numerical analysis optimization study to formulate a statistical significant new runoff prediction model. The technique performed regional hydrological conditions calibration to SCS base runoff model and improved runoff prediction by 27 % compared to the non-calibrated empirical model. A rainfall runoff difference model was created as a collective visual representation of runoff prediction error from the non-calibrated SCS empirical model under multiple rainfall depths and CN scenarios in Peninsula Malaysia. Statistical significant correction equations were formulated through swift data mining from the model to study the under and over-design worse case scenarios which are nearly impossible to quantify by solving the complex mathematical equation. Critical curve number concept was introduced in this study.
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Notes
- 1.
This study used DID HP11 dataset only. Same methodology was used to analyse DID HP27 dataset. Results were reported in a different article.
- 2.
Rearrange Eq. (1) and solve for S (P, Q, λ), the formula is: \( S_{\lambda } = \tfrac{{\left[ {P - \tfrac{{\left( {\lambda - 1} \right)Q}}{2\lambda }} \right] - \sqrt {PQ - P^{2} + \left[ {P - \tfrac{{\left( {\lambda - 1} \right)Q}}{2\lambda }} \right]^{2} } }}{\lambda } \). Different λ will yield different S values, denotes by S λ. Correlation between S λ and S 0.2 is required. S 0.2 is represented by S throughout this report.
- 3.
Results presented by Efron and Tibshirani (1993, chap. 19) suggest that basing bootstrap confidence intervals on 1,000 bootstrap samples generally provides accurate results, and using 2,000 bootstrap replications should be very safe.
- 4.
\( RSS = \sum\limits_{i = 1}^{n} {\left( {Q_{predicted} - Q_{observed} } \right)}^{2} \).
- 5.
\( E = 1 - \frac{RSS}{{\sum\limits_{i = 1}^{n} {\left( {B_{predicted} - B_{mean} } \right)^{2} } }} \).
- 6.
\( BIAS = \frac{{\sum\limits_{i = 1}^{n} {\left( {Q_{predicted} - Q_{observed} } \right)} }}{n} \).
- 7.
Refer to first author for the calibration results and correction equations for DID HP27 dataset. Closed form equation for the critical rainfall amount has been solved under this study.
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Acknowledgments
The author would like to thank Universiti Teknologi Malaysia, Centre for Environmental Sustainability and Water Security, Research Institute for Sustainable Environment of UTM, vote no. Q.J130000.2509.07H23 and R.J130000.3009.00M41 for its financial support in this study. This study was also supported by the Asian Core Program of the Japanese Society for the Promotion of Science (JSPS) and the Ministry of Higher Education (MOHE) Malaysia. The author would also like to acknowledge the guidance provided by Prof. Richard Hawkins (University of Arizona).
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Appendices
Appendix A: Numerical Table of Eq. (8)
Appendix B: Extracted Minimum and Maximum Runoff Predictions (Left Table). Hypothetical Runoff Amount on 1 Km2 Area (Right Table)
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Ling, L., Yusop, Z. (2015). The Collective Visual Representation of Rainfall-Runoff Difference Model. In: Badioze Zaman, H., et al. Advances in Visual Informatics. IVIC 2015. Lecture Notes in Computer Science(), vol 9429. Springer, Cham. https://doi.org/10.1007/978-3-319-25939-0_24
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