A Pragmatic Slope-Adjusted Curve Number Model to Reduce Uncertainty in Predicting Flood Runoff from Steep Watersheds
Abstract
:1. Introduction
1.1. The CN Model Framework
1.2. Effect of Slope on CN and Runoff Estimation
2. Materials and Methods
2.1. Study Area Description and Climate
2.2. Data Collection and Interpretation
2.3. Slope-Adjusted Curve Number Considerations and Development
2.4. Steps of Slope-Adjusted CN Parameter Optimization
- Data pertaining to 39 watersheds in which 1779 rainstorms events occurred provided the known values of the rainstorm events, P; the observed runoff, Qo; and the optimized CNs for each watershed. The least squares nonlinear orthogonal distance regression objective function in Origin Pro 9.6 software produced the optimized CN values from the following equation.
- To optimize parameter b in Equation (9), the CNs obtained for the 39 watersheds from Equation (10) were divided into two sets, those of 31 watersheds (1402 rainstorm–runoff events) for calibration and those of 8 watersheds (377 rainstorm-runoff events) for validation. For calibration, the optimized CNs in step 1 were set as the target values challenging the right side of Equation (9) using the nonlinear regression least squares Levenberg–Marquardt algorithm in SPSS v.25 software. To take into account the individual watersheds’ effects on parameter b optimization, the leave-one-out (LOOV) technique was adopted. The average of 31 calibrations repetitions was the value of b = 7.125. This led to recasting the proposed CNIIα as
3. Statistical Analysis for Model Performance Evaluation
4. Results and Discussion
4.1. Models’ Analysis Based on Descriptive Statistics
4.2. Model Performance Evaluation in Watersheds Used for Calibration
4.3. Models’ Performance Evaluation in Watersheds Used for Validation
4.4. Overall Performance of Models and Comparison Based on 1:1 Plot
5. Conclusions and Practical Implications
Author Contributions
Funding
Conflicts of Interest
References
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Parameters | |||
---|---|---|---|
Model Identity | λ | CN (CNIIα) | Model Expression |
M1 | 0.20 | *NEH-4 Tables | Equations (1) and (2) |
M2 | 0.05 | NEH-4 Tables | Equations (1)–(3) |
M3 | 0.20 | Sharpley and Williams [17] | Equations (1), (2) and (5) |
M4 | 0.20 | Huang et al. [19] | Equations (1), (2) and (7) |
M5 | 0.20 | Ajmal et al. [10] | Equations (1), (2) and (8) |
M6 | 0.20 | Proposed | Equations (1), (2) and (12) |
M7 | 0.05 | Proposed | Equations (1)–(3) and (12) |
M8 | 0.01 | Proposed | Equations (1), (2) and (12) |
Performance Rating | NSE [44] | NSE [45] | PB (%) |
---|---|---|---|
Very good | 0.75 < NSE ≤ 1.00 | 0.90 < NSE ≤ 1.00 | −10 < PB < +10 |
Good | 0.65 < NSE ≤ 0.75 | 0.80 ≤ NSE ≤ 0.90 | ±10 ≤ PB < ±15 |
Satisfactory | 0.50 < NSE ≤ 0.65 | 0.65 ≤ NSE < 0.80 | ±15 ≤ PB < ±25 |
Unsatisfactory | NSE ≤ 0.50 | NSE ≤ 0.65 | PB ≥ ±25 |
Calibration Watersheds (1402 Rainstorm–Runoff Events) | ||||||
---|---|---|---|---|---|---|
Parameter/Model | Mean | Minimum | First Quartile (Q1) | Median | Third Quartile (Q3) | Maximum |
P | 80.96 | 12.10 | 39.92 | 59.09 | 98.27 | 519.68 |
Qo | 38.60 | 0.17 | 8.23 | 19.61 | 49.04 | 348.46 |
M1 | 25.57 | 0.00 | 1.49 | 6.13 | 27.03 | 415.63 |
M2 | 23.56 | 0.00 | 1.14 | 7.26 | 25.79 | 383.27 |
M3 | 28.79 | 0.00 | 1.30 | 7.95 | 32.94 | 436.28 |
M4 | 26.06 | 0.00 | 1.52 | 6.31 | 28.33 | 419.65 |
M5 | 30.06 | 0.00 | 1.35 | 8.83 | 35.39 | 443.28 |
M6 | 30.26 | 0.00 | 1.23 | 9.38 | 35.34 | 445.73 |
M7 | 28.98 | 0.00 | 2.54 | 10.77 | 34.57 | 417.11 |
M8 | 39.67 | 0.53 | 7.93 | 20.13 | 49.30 | 458.55 |
Validation Watersheds (377 Rainstorm–Runoff Events) | ||||||
P | 75.22 | 20.52 | 40.97 | 57.05 | 86.95 | 376.86 |
Qo | 35.03 | 0.24 | 8.30 | 19.10 | 43.20 | 364.38 |
M1 | 22.04 | 0.00 | 1.48 | 6.35 | 20.35 | 294.27 |
M2 | 19.85 | 0.00 | 0.85 | 5.55 | 19.93 | 265.59 |
M3 | 24.75 | 0.00 | 1.52 | 6.27 | 25.99 | 309.31 |
M4 | 22.49 | 0.00 | 1.39 | 6.63 | 21.48 | 296.26 |
M5 | 26.48 | 0.00 | 2.03 | 7.87 | 30.12 | 309.72 |
M6 | 26.07 | 0.00 | 1.71 | 6.66 | 29.04 | 314.48 |
M7 | 24.98 | 0.00 | 2.10 | 9.43 | 26.71 | 293.91 |
M8 | 34.77 | 0.87 | 7.70 | 17.91 | 40.12 | 325.07 |
M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | |
---|---|---|---|---|---|---|---|---|
Performance Criteria | NSE [44] | |||||||
0.75 < NSE ≤ 1.00 | 14 | 15 | 14 | 14 | 14 | 14 | 20 | 30 |
0.65 < NSE ≤ 0.75 | 3 | 10 | 7 | 3 | 10 | 12 | 13 | 6 |
0.50 < NSE ≤ 0.65 | 10 | 9 | 13 | 13 | 11 | 9 | 4 | 2 |
NSE ≤ 0.50 | 12 | 5 | 5 | 9 | 4 | 4 | 2 | 1 |
NSE [45] | ||||||||
0.90 < NSE ≤ 1.00 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 5 |
0.80 ≤ NSE ≤ 0.90 | 6 | 12 | 12 | 8 | 11 | 11 | 11 | 20 |
0.65 ≤ NSE < 0.80 | 10 | 12 | 8 | 8 | 11 | 13 | 19 | 11 |
NSE ≤ 0.65 | 22 | 14 | 18 | 22 | 15 | 13 | 6 | 3 |
PB (%) | ||||||||
−10 < PB < +10 | 1 | 1 | 5 | 1 | 5 | 6 | 6 | 19 |
±10 ≤ PB < ±15 | 0 | 0 | 3 | 0 | 6 | 5 | 8 | 9 |
±15 ≤ PB < ±25 | 10 | 11 | 12 | 10 | 13 | 12 | 12 | 7 |
PB ≥ ±25 | 28 | 27 | 19 | 28 | 15 | 16 | 13 | 4 |
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Ajmal, M.; Waseem, M.; Kim, D.; Kim, T.-W. A Pragmatic Slope-Adjusted Curve Number Model to Reduce Uncertainty in Predicting Flood Runoff from Steep Watersheds. Water 2020, 12, 1469. https://doi.org/10.3390/w12051469
Ajmal M, Waseem M, Kim D, Kim T-W. A Pragmatic Slope-Adjusted Curve Number Model to Reduce Uncertainty in Predicting Flood Runoff from Steep Watersheds. Water. 2020; 12(5):1469. https://doi.org/10.3390/w12051469
Chicago/Turabian StyleAjmal, Muhammad, Muhammad Waseem, Dongwook Kim, and Tae-Woong Kim. 2020. "A Pragmatic Slope-Adjusted Curve Number Model to Reduce Uncertainty in Predicting Flood Runoff from Steep Watersheds" Water 12, no. 5: 1469. https://doi.org/10.3390/w12051469