Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method
<p>Framework of the resample processes of the bootstrap method.</p> "> Figure 2
<p>The flow chart of the uncertainty estimation using Bootstrap method.</p> "> Figure 3
<p>The distribution of hydrological and rainfall stations in (<b>a</b>) the upstream of the Qingjian River basin and (<b>b</b>) the Longxi River basin.</p> "> Figure 4
<p>Classification results of rainfall stations of three typical events in the upstream of the Qingjian River basin: (<b>a</b>) 2001, (<b>b</b>) 2002 and (<b>c</b>) 2006. Classification using clustering based on the total depths and correlation methods based on the processes of rainfall measurements are conducted.</p> "> Figure 5
<p>Calibrated runoff processes compared with observations of the three events in the upstream of the Qingjian River basin: (<b>a</b>) 2001, (<b>b</b>) 2002 and (<b>c</b>) 2006.</p> "> Figure 6
<p>Cumulative rainfall of each station in the 2002 rainfall event in the upstream of the Qingjian River basin.</p> "> Figure 7
<p>Uncertainty of the three rainfall-runoff events on different number of stations in the upstream of the Qingjian River basin: (<b>a</b>) Average basin rainfall, (<b>b</b>) Non-dimensional uncertainty of average basin rainfall, (<b>c</b>) Simulated runoff depth and (<b>d</b>) Non-dimensional uncertainty of simulated runoff depth. Note: every three boxes represent the results of 2001, 2002 and 2006 events from left to right.</p> "> Figure 8
<p>The non-dimensional uncertainty range of the average basin rainfall over the representative area of a single station.</p> "> Figure 9
<p>Performance of simulated runoffs of the three cases using different numbers of resampled stations in the upstream of the Qingjian River basin: (<b>a</b>,<b>c</b>,<b>e</b>) NSE; (<b>b</b>,<b>d</b>,<b>f</b>) the ratio of simulated runoff depth over measured.</p> "> Figure 10
<p>Estimation of the effect of rainfall station density on hydrological simulation events in the upstream of the Qingjian River basin: (<b>a</b>) 2001, (<b>b</b>) 2002 and (<b>c</b>) 2006. The solid lines are the fitting curve between the NSE of simulated runoff and the rainfall station density and the dot dash lines are the prediction if the <span class="html-italic">D<sub>S</sub></span> increase. And the dash lines are the predicted NSE values with the upper limit of 1.</p> ">
Abstract
:1. Introduction
2. Methodology
2.1. Bootstrap Method
2.2. Framework Methodology
2.3. Digital Yellow River Integrated Model
2.4. Calibration of the DYRIM
3. Application
3.1. Study Areas and the Rainfall Cases
3.2. Runoff Simulation
3.3. Uncertainty Quantization of Basin Rainfall and Simulated Runoff
4. Results and Discussion
4.1. Spatial Variation of Measured Rainfall
4.2. Uncertainty of Basin Rainfall
4.3. Areal Representation of Rainfall Stations
4.4. Uncertainty of Simulated Runoff
4.5. Effect of Rainfall Station Density on Hydrological Simulations
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
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Methods/Literatures | Strength/Weakness | Applicability |
---|---|---|
Data-driven and analytical methods [18,19,20] | Statistical/High computational demand | Identify the errors and uncertainties from rainfall measurements |
Control variables of rainfall input [15,21,22,23,24,25,26,27] | Operability/Poor extensibility for different study cases | Estimate the rainfall influence on simulated runoff |
Conditional simulation [28,29] | Demonstrate rainfall uncertainty on runoff and model structural | |
Model parameters analysis with rainfall uncertainty [31,32,33] | Quantify the uncertainty of rainfall with model parameters | |
Bayesian framework [34] | Statistical/Need model assumption | Quantify model structural errors to investigate the influence of rainfall input |
Bootstrap method [35,36,37,38,39,40] | Straightforward, simplicity, high-accuracy/High computational demand | Quantitatively analyze the spatial uncertainty of rainfall in river basins at different scales |
Number | 1 | 2 | 3 |
---|---|---|---|
Duration | 2001.8.16 | 2002.7.3–7.7 | 2006.7.30–8.3 |
Basin average rainfall (mm) | 34.2 | 144.9 | 27.5 |
Measured runoff depth (mm) | 4.7 | 86.9 | 1.5 |
Runoff coefficient | 0.137 | 0.600 | 0.055 |
Simulated runoff depth (mm) | 7.0 | 40.1 | 0.5 |
Independently simulated runoff depth (mm) | 7.9 | 111.5 | 2.1 |
Measured peak discharge (m3/s) | 881 | 4670 | 76 |
Simulated peak discharge (m3/s) | 1172 | 2079 | 28 |
Independently simulated peak discharge (m3/s) | 686 | 4407 | 61 |
Measured peak time | 8/16 6:18 | 7/4 7:15 | 7/31 5:24 |
Simulated peak time | 8/16 5:36 | 7/4 7:18 | 7/31 4:24 |
Independently simulated peak time | 8/16 6:00 | 7/4 8:06 | 7/31 4:54 |
NSE of flow discharge | 0.48 | 0.43 | 0.05 |
Independently NSE of flow discharge | 0.61 | 0.81 | 0.80 |
Parameters | Topsoil Vertical Saturated Conductivity Kzus | Subsoil Vertical Saturated Conductivity Ku-ds | Topsoil Lateral Saturated Conductivity Khu | Subsoil Lateral Saturated Conductivity Khd | Topsoil Initial Moisture θu,0 | Subsoil Initial Moisture θd,0 |
---|---|---|---|---|---|---|
Value | 3.7 mm/h | 5.2 mm/h | 5.9 mm/h | 3.6 mm/h | 0.15 m3/m3 | 0.23 m3/m3 |
NO | Station Name | Percentage of Controlling Area (%) | Rainfall Records (mm) and Group ID of Each Station | |||||
---|---|---|---|---|---|---|---|---|
2001.8.16 | 2002.7.3–7.7 | 2006.7.30–8.3 | ||||||
1 | Zichang | 7.48 | 18.0 | 1a | 283.2 | 2a | 42.8 | 3a |
2 | Jingzeyan | 16.37 | 75.2 | 1b | 114.6 | 2b | 23.8 | 3a |
3 | Lijiafen | 11.17 | 55.4 | 1c | 137.6 | 2b | 24.8 | 3a |
4 | Sanshilipu | 15.19 | 36.0 | 1d | 130.0 | 2c | 30.4 | 3a |
5 | Anding | 12.31 | 19.5 | 1d | 172.8 | 2d | 15.4 | 3b |
6 | Zhangjiagou | 10.02 | 27.4 | 1a | 145.6 | 2b | 36.2 | 3c |
7 | Siwan | 12.79 | 19.8 | 1e | 114.6 | 2e | 22.4 | 3a |
8 | Xinzhuangke | 10.88 | 0.0 | 1f | 126.2 | 2b | 32.6 | 3d |
9 | Yujiawan | 0.13 | 21.6 | 1g | 106.2 | 2b | 46.4 | 3e |
10 | Hecaogou | 0.09 | 16.2 | 1h | 225.4 | 2f | 35.6 | 3a |
11 | Yangkelangwan | 3.57 | 31.8 | 1d | 145.8 | 2b | 27.4 | 3f |
Total | 100 | 8 groups | 6 groups | 6 groups |
Event Year | U’ | Number of Stations | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | ||
2001 | Rainfall | 0.20 | 0.41 | 0.63 | 0.86 | 0.96 | 1.22 | 1.52 | 1.77 | 2.15 | 2.20 |
Runoff | 0.60 | 0.97 | 1.50 | 1.61 | 1.75 | 2.24 | 2.26 | 2.58 | 3.85 | 3.96 | |
2002 | Rainfall | 0.13 | 0.20 | 0.25 | 0.32 | 0.41 | 0.45 | 0.53 | 0.73 | 0.98 | 1.22 |
Runoff | 0.60 | 0.97 | 1.50 | 1.61 | 1.75 | 2.24 | 2.26 | 2.58 | 3.85 | 3.96 | |
2006 | Rainfall | 0.13 | 0.22 | 0.26 | 0.35 | 0.45 | 0.56 | 0.63 | 0.78 | 0.98 | 1.13 |
Runoff | 0.53 | 1.35 | 1.41 | 1.78 | 1.70 | 2.51 | 2.58 | 3.67 | 7.61 | 7.22 |
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Zhang, A.; Shi, H.; Li, T.; Fu, X. Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method. Atmosphere 2018, 9, 71. https://doi.org/10.3390/atmos9020071
Zhang A, Shi H, Li T, Fu X. Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method. Atmosphere. 2018; 9(2):71. https://doi.org/10.3390/atmos9020071
Chicago/Turabian StyleZhang, Ang, Haiyun Shi, Tiejian Li, and Xudong Fu. 2018. "Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method" Atmosphere 9, no. 2: 71. https://doi.org/10.3390/atmos9020071