# Impacts of Channel Network Type on the Unit Hydrograph

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{8}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hillslope Travel Time Distribution

#### 2.2. Channel Travel Time Distribution

#### 2.3. Total Travel Time Distribution

#### 2.4. Application

^{2}. The parallel and rectangular basins are the smallest with average areas of 217 km

^{2}and 254 km

^{2}, respectively. The DEM resolution depends on the DEM source. It is coarsest (on average 76.4 m) for pinnate basins in Ukraine and Moldova, for which the Shuttle Radar Topography Mission (SRTM) provided data at a resolution of 3 arc seconds. The other network types have an average resolution of 27 m. The channel threshold area (which also determines ${A}_{h\mathrm{max}}$) is largest for pinnate basins (on average 688,560 m

^{2}) and smallest for dendritic and parallel basins (on average 53,720 m

^{2}and 76,850 m

^{2}, respectively).

## 3. Results

#### 3.1. Distributions of A_{sh} and A_{sc}

#### 3.2. IUHs

#### 3.3. Hydrographs

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An example channel network from the (

**a**) dendritic, (

**b**) pinnate, (

**c**) trellis, (

**d**) parallel, and (

**e**) rectangular types. Black dots indicate the basin outlets.

**Figure 2.**Kolmogorov‒Smirnov (K‒S) statistics for the four best fitting distributions for (

**a**) ${A}_{sh}$ and (

**b**) ${A}_{sc}$. DEN denotes dendritic, PAR denotes parallel, PIN denotes pinnate, REC denotes rectangular, and TRE denotes trellis.

**Figure 3.**Histograms and fitted Johnson SB distributions for ${A}_{sh}$ (

**a–e**) and ${A}_{sc}$ (

**f**–

**j**) for an example basin of each type. The basins are the same as those in Figure 1.

**Figure 4.**Parameters (

**a**) ${\delta}_{h}$, (

**b**) ${\gamma}_{h}$, (

**c**) ${\xi}_{h}$, and (

**d**) ${\lambda}_{h}$ of the Johnson SB distribution for ${A}_{sh}$ plotted against the maximum hillslope area ${A}_{h\mathrm{max}}$. The symbols show the calibrated parameter values for each basin. The horizontal lines in (

**a**–

**c**) show the average parameter value for each network type. The lines in (

**d**) show power functions fitted to the ${\lambda}_{h}$ values for each network type.

**Figure 5.**Parameters (

**a**) ${\delta}_{c}$, (

**b**) ${\gamma}_{c}$, (

**c**) ${\xi}_{c}$, and (

**d**) ${\lambda}_{c}$ of the Johnson SB distribution for ${A}_{sc}$ plotted against the maximum upstream area ${A}_{\mathrm{max}}$. The symbols show the calibrated parameter values for each basin. The horizontal lines in (

**b**–

**c**) show the average parameter value for each network type. The lines in (

**d**) show power functions fitted to the ${\lambda}_{c}$ values for each network type.

**Figure 6.**Kolmogorov‒Smirnov (K‒S) statistics for the Johnson SB distribution for (

**a**) ${A}_{sh}$ and (

**b**) ${A}_{sc}$ when the distribution parameters are estimated separately for each network (Method 1), based on network type (Method 2), and neglecting network type (Method 3).

**Figure 7.**Instantaneous unit hydrographs (IUHs) estimated by the four methods described in the legend for an example basin of the (

**a**) dendritic, (

**b**) parallel, (

**c**) pinnate, (

**d**) rectangular, and (

**e**) trellis types. The basins are the same as those in Figure 1.

**Figure 8.**Performance metrics when the instantaneous unit hydrographs are estimated by either including or neglecting the network type as indicated in the legend. Column heights indicate the average performance and black bars indicate the range of performance for each case.

**Figure 9.**(

**a**) Rainfall intensity for a 6-h SCS Type II storm and the resulting specific discharge hydrographs for an example basin of the (

**b**) dendritic, (

**c**) pinnate, (

**d**) trellis, (

**e**) parallel, and (

**f**) rectangular types when the IUH is determined using the four methods described in the legend. The basins are the same as those in Figure 1.

**Table 1.**Basin areas and channel threshold areas for the 50 analyzed basins. The thresholds are identified between the colluvial and bedrock channel segments in the slope‒area plots.

Basin Name | Basin Area (km^{2}) | Channel Threshold Area (m^{2}) | Basin Name | Basin Area (km^{2}) | Channel Threshold Area (m^{2}) | |
---|---|---|---|---|---|---|

Dendritic | Bluestone, WV | 324 | 33,300 | Rockcastle, KY | 314 | 53,400 |

Buffalo, WV | 419 | 56,000 | Tenmile, PA | 512 | 95,500 | |

Captina, OH | 460 | 29,200 | Turkey, SC | 625 | 63,000 | |

Cedar, GA | 219 | 115,500 | Tygarts, KY | 291 | 79,100 | |

Little Saluda, SC | 565 | 102,900 | Wheeling, WV | 739 | 36,500 | |

Parallel | Albert, WY | 439 | 57,400 | Piceance 1, CO | 156 | 70,600 |

Black Sulphur, CO | 266 | 73,300 | Piceance 2, CO | 74 | 47,600 | |

Duck, CO | 142 | 80,300 | Sheep, WY | 487 | 215,100 | |

Greasewood, CO | 61 | 65,200 | Willow, UT | 350 | 55,400 | |

Mancos River, CO | 113 | 133,100 | Yellow, CO | 85 | 110,000 | |

Pinnate | Dniester 1, UKR | 2114 | 1,037,900 | Dniester 6, UKR | 761 | 1,045,100 |

Dniester 2, UKR | 1356 | 488,500 | Nistru 1, MDA | 697 | 639,400 | |

Dniester 3, UKR | 1005 | 707,800 | Nistru 2, MDA | 589 | 758,400 | |

Dniester 4, UKR | 1573 | 540,300 | Nistru 4, MDA | 723 | 614,600 | |

Dniester 5, UKR | 967 | 706,700 | Nistru 5, MDA | 350 | 983,800 | |

Rectangular | Boquet, NY | 241 | 108,500 | Salmon, NY | 495 | 146,200 |

Boreas, NY | 218 | 250,500 | Schroon, NY | 239 | 172,300 | |

Cold, NY | 218 | 104,300 | Summer, NY | 147 | 88,900 | |

Hudson, NY | 198 | 239,700 | Walker, NY | 133 | 198,400 | |

Saint Regis, NY | 344 | 124,600 | W. St. Regis, NY | 304 | 116,100 | |

Trellis | Aughwick, PA | 823 | 141,700 | Juniata, PA | 539 | 62,700 |

Cacapon, WV | 865 | 125,100 | Middle, PA | 219 | 166,300 | |

Chestuee, TN | 339 | 54,300 | Penns, PA | 480 | 956,900 | |

Evitts, MD | 240 | 168,600 | Peters, WV | 609 | 59,600 | |

Jackson, VA | 251 | 116,300 | Sleepy, WV | 294 | 51,500 |

**Table 2.**Distribution parameters that exhibit significant differences between the network types based on the analysis of variance (ANOVA) and analysis of covariance (ANCOVA) tests. For each pairing of network types, the top row reports parameters for ${A}_{sh}$, and the bottom row reports parameters for ${A}_{sc}$.

Network Type | Parallel | Pinnate | Rectangular | Trellis |
---|---|---|---|---|

Dendritic | ${\gamma}_{h}$ | ${\delta}_{h}$, ${\xi}_{h}$, ${\lambda}_{h\mathrm{coef}}$, ${\lambda}_{h\mathrm{exp}}$ | ${\delta}_{h}$, ${\gamma}_{h}$, ${\xi}_{h}$ | ${\delta}_{h}$, ${\gamma}_{h}$, ${\xi}_{h}$ |

${\xi}_{c}$ | ${\gamma}_{c}$, ${\xi}_{c}$, ${\lambda}_{c\mathrm{coef}}$ | ${\gamma}_{c}$, ${\xi}_{c}$, ${\lambda}_{c\mathrm{coef}}$ | ${\gamma}_{c}$, ${\xi}_{c}$ | |

Parallel | ${\xi}_{h}$ | ${\delta}_{h}$, ${\gamma}_{h}$, ${\xi}_{h}$ | ${\delta}_{h}$, ${\gamma}_{h}$, ${\xi}_{h}$, ${\lambda}_{h\mathrm{coef}}$, ${\lambda}_{h\mathrm{exp}}$ | |

${\gamma}_{c}$ | ${\gamma}_{c}$ | - | ||

Pinnate | ${\delta}_{h}$, ${\gamma}_{h}$ | ${\delta}_{h}$, ${\gamma}_{h}$, ${\xi}_{h}$, ${\lambda}_{h\mathrm{coef}}$, ${\lambda}_{h\mathrm{exp}}$ | ||

${\gamma}_{c}$ | ${\gamma}_{c}$ | |||

Rectangular | ${\xi}_{h}$, ${\lambda}_{h\mathrm{coef}}$, ${\lambda}_{h\mathrm{exp}}$ | |||

- |

**Table 3.**Estimated parameters of the Johnson SB distribution for ${A}_{sh}$ (

**left**) and ${A}_{sc}$ (

**right**).

Type | ${\mathit{\delta}}_{\mathit{h}}$ | ${\mathit{\gamma}}_{\mathit{h}}$ | ${\mathit{\xi}}_{\mathit{h}}$ | ${\mathit{\lambda}}_{\mathit{h}\mathbf{coef}}$ | ${\mathit{\lambda}}_{\mathit{h}\mathbf{exp}}$ | ${\mathit{\delta}}_{\mathit{c}}$ | ${\mathit{\gamma}}_{\mathit{c}}$ | ${\mathit{\xi}}_{\mathit{c}}$ | ${\mathit{\lambda}}_{\mathit{c}\mathbf{coef}}$ | ${\mathit{\lambda}}_{\mathit{c}\mathbf{exp}}$ |
---|---|---|---|---|---|---|---|---|---|---|

Dendritic | 0.991 | 0.654 | −1.8 | 16 | 0.204 | - | −0.533 | −1339 | 398 | 0.579 |

Parallel | 1.036 | 0.881 | −3.9 | 76 | 0.081 | - | −0.288 | −556 | 1256 | 0.381 |

Pinnate | 1.069 | 0.711 | −13.7 | 15 | 0.255 | - | 0.352 | −479 | 4579 | 0.244 |

Rectangular | 1.300 | 1.300 | −14.0 | 258 | 0.006 | - | −0.011 | −341 | 5687 | 0.088 |

Trellis | 1.296 | 1.567 | −11.2 | 14 | 0.256 | - | −0.081 | −533 | 1203 | 0.414 |

All | 1.138 | 1.023 | −8.9 | 3 | 0.373 | 0.982 | −0.112 | −649 | 668 | 0.504 |

**Table 4.**Model parameters used in the development of the instantaneous unit hydrographs. Parameters that vary are determined from the digital elevation model for each basin.

Parameter | Value | Units |
---|---|---|

Channel roughness (${n}_{c}$) | 0.05 | s/m^{1/3} |

Hillslope roughness (${n}_{h}$) | 0.15 | s/m^{1/3} |

Grid cell area ($A$) | Varies | m^{2} |

Slope of hillslopes (${S}_{h}$) | Varies | m/m |

Slope‒area factor ($b$) | Varies | m^{−2θ} |

Slope‒area exponent ($\theta $) | Varies | - |

Channel width factor ($d$) | 0.02 | m^{1−2e} |

Channel width exponent ($e$) | 0.5 | - |

Fraction of area contributing ($r$) | 0.3 | m^{2}/m^{2} |

Runoff rate (${E}_{i}$) | 25.4 | mm/h |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Czyzyk, K.; Mirossi, D.; Abdoulhak, A.; Hassani, S.; Niemann, J.D.; Gironás, J. Impacts of Channel Network Type on the Unit Hydrograph. *Water* **2020**, *12*, 669.
https://doi.org/10.3390/w12030669

**AMA Style**

Czyzyk K, Mirossi D, Abdoulhak A, Hassani S, Niemann JD, Gironás J. Impacts of Channel Network Type on the Unit Hydrograph. *Water*. 2020; 12(3):669.
https://doi.org/10.3390/w12030669

**Chicago/Turabian Style**

Czyzyk, Kelsey, Dario Mirossi, Almoatasem Abdoulhak, Sediqa Hassani, Jeffrey D. Niemann, and Jorge Gironás. 2020. "Impacts of Channel Network Type on the Unit Hydrograph" *Water* 12, no. 3: 669.
https://doi.org/10.3390/w12030669