Possibility of Using Selected Rainfall-Runoff Models for Determining the Design Hydrograph in Mountainous Catchments: A Case Study in Poland
Abstract
:1. Introduction
2. Materials and Methods
2.1. Research Area Characteristic
2.2. Hydrometeorological Data Verification
- n—number of elements in the time series.
- Var*(S)—corrected variance;
- n—the real number of observation;
- —effective number of observations calculated as:
- k—next group with repeating elements;
- ρk—value of the next significant autocorrelation coefficient.
2.3. Calculation of Maximum Annual Rainfall and Flows with Specific Occurrence Frequency
- xp—quantile of the theoretical log-normal distribution;
- ε—lower string limit;
- erf(2(1 − p) − 1)—Gauss error function.
2.4. Determination of the Design Hydrograph
- to—wave fall time (h);
- ts—wave rise time (h);
- Pe—excess rainfall (mm);
- P—total rainfall (mm);
- S—maximum potential catchment retention (mm).
- TL—delay time (h);
- Ct—factor related to catchment retention (-);
- L—maximum distance along the watercourse from the outlet cross-section to the drainage divide (km);
- Lc—distance along the main watercourse from the outlet cross-section to the centroid of the catchment (km).
- Qp—peak flow of the unit hydrograph (m3·s−1·mm);
- Cp—empirical coefficient resulting from the simplification of the hydrograph to triangular shape (-);
- A—catchment area (km2).
- qp—peak flow of the unit hydrograph (m3·s−1·mm);
- c—conversion factor (c = 0.208) (-);
- Tp—flood rise time, (h), calculated as:
- D—duration of excess rainfall (h);
- TLAG—lag time in the SCS-UH method, (h), calculated as:
- L—maximum length of the runoff path (km);
- CN—Curve Number value (-);
- I—average catchment slope (%).
- q0—infiltration indicator;
- tp—ponding time;
- Ks—saturated hydraulic conductivity;
- I—cumulative infiltration;
- Δθ—change in soil-water content between the initial value and the field saturated soil-water content;
- ΔH—difference between the pressure head at the soil surface and the matric pressure head at the moving wetting front.
- Lc, Lh—hillslope and channel flow paths, functions of DEM cell x, respectively;
- Vc, Vh—runoff velocity for hillslope cells and flow channel cells.
- A—catchment area (km2);
- T—duration of rainfall (h);
- Pn(t)—excess rainfall determined by the CN4GA method (mm/h).
2.5. Assessment of Quality of Analysed Hydrological Models
- Qm,max—maximum flow with a certain frequency of occurrence, calculated using rainfall-runoff models (m3·s−1);
- Qs,max—maximum flow with a specified frequency of occurrence, calculated using the log-normal distribution on observed data (m3·s−1).
3. Results
3.1. Hydrometeorological Data Verification
3.2. Determination of Rainfall and Peak Flows at a Specific Occurrence Frequency
3.3. Determination of Design Hydrographs Employing the Selected Rainfall-Runoff Models
3.4. Evaluation of the Quality of Analysed Hydrological Models
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Characteristic | Zc | pc | Varc | n/n * | Z | p | Var |
---|---|---|---|---|---|---|---|
Pmax | 1.582 | 0.114 | 7721.554 | 0.846 | 1.455 | 0.146 | 9129.333 |
Qmax | 1.143 | 0.253 | 9766.667 | 1.000 | 1.143 | 0.253 | 9766.667 |
Return Period | Tc (h) | CN | P (mm) | Pnet (mm) |
---|---|---|---|---|
500 | 4 | 68.1 | 95.8 | 24.7 |
100 | 76.6 | 14.6 | ||
10 | 50.2 | 4.1 |
Characteristic | Snyder | NRCS-UH | EBA4SUB | ||||||
---|---|---|---|---|---|---|---|---|---|
500 | 100 | 10 | 500 | 100 | 10 | 500 | 100 | 10 | |
Qmax [m3·s−1] | 122.909 | 74.191 | 21.975 | 113.235 * | 68.424 * | 20.329 * | 212.531 | 125.602 | 35.779 |
135.483 ** | 82.059 ** | 24.529 ** | |||||||
V [mln m3] | 2.291 | 1.377 | 0.403 | 2.291 | 1.377 | 0.403 | 2.078 | 1.226 | 0.346 |
t [h] | 15.250 | 15.250 | 15.000 | 21.750 * | 21.750 * | 21.500 * | 6.800 | 6.800 | 6.500 |
16.000 ** | 15.750 ** | 15.500 ** | |||||||
α [–] | 2.100 | 1.952 | 1.905 | 3.150 * | 3.000 * | 2.950 * | 1.545 | 1.545 | 1.500 |
2.095 ** | 2.095 ** | 2.150 ** |
Model | MAPE [%] | ||
---|---|---|---|
500 | 100 | 10 | |
Snyder | 22.0 | 26.9 | 50.5 |
NRCS-UH (PRF 484) | 28.2 | 32.6 | 54.2 |
NRCS-UH (PRF 600) | 14.1 | 19.1 | 44.7 |
EBA4SUB | −34.8 | −23.8 | 19.4 |
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Młyński, D.; Wałęga, A.; Książek, L.; Florek, J.; Petroselli, A. Possibility of Using Selected Rainfall-Runoff Models for Determining the Design Hydrograph in Mountainous Catchments: A Case Study in Poland. Water 2020, 12, 1450. https://doi.org/10.3390/w12051450
Młyński D, Wałęga A, Książek L, Florek J, Petroselli A. Possibility of Using Selected Rainfall-Runoff Models for Determining the Design Hydrograph in Mountainous Catchments: A Case Study in Poland. Water. 2020; 12(5):1450. https://doi.org/10.3390/w12051450
Chicago/Turabian StyleMłyński, Dariusz, Andrzej Wałęga, Leszek Książek, Jacek Florek, and Andrea Petroselli. 2020. "Possibility of Using Selected Rainfall-Runoff Models for Determining the Design Hydrograph in Mountainous Catchments: A Case Study in Poland" Water 12, no. 5: 1450. https://doi.org/10.3390/w12051450