# Effects of the Digital Elevation Model and Hydrological Processing Algorithms on the Geomorphological Parameterization

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Study Site

^{2}, as illustrated in Figure 1. The geographic coordinates of the centroid are approximately 22°39′17″ N and 102°39′57″ W, datum WGS84. It is a rural watershed with a population minor to 500 inhabitants distributed in two towns; no sewage is discharged into the streams and there are practically no reservoirs over the streams or appreciable depressions. Regarding the use and soil covering, 62.4% of the surface is natural pasture, 18.6% is dedicated to annual seasonal agriculture, 9.3% is crasicaule scrub, 4.2% is for annual agricultural watering, 3.6% is secondary shrub vegetation, 0.43% is urban construction, and less than 0.03% is pine forest. The predominant soil type is phaeozem, with 61.8% of the surface, followed by kastañozem with 32.5%, and 3.7% leptosol [48]. The climate is semi-arid, with rains in the summer, mainly from June to September [49]. The average maximum and minimum temperatures are 29 °C and −2.8 °C, respectively, with a mean precipitation of 428 mm per year; the values were obtained by the weather station installed in the watershed and were cross-match referenced with data from [50]. The study area features four rain gauges and two hydrometric stations (Figure 1). It is assumed that the watershed is possibly one of the groundwater recharge sites of the “Benito Juarez” aquifer, one of the most important aquifers in the region, hence the interest of study.

#### 2.2. Data Set Used

#### 2.3. Geomorphological Parameterization

#### 2.3.1. Preprocessing

#### Filling Depressions

#### 2.3.2. Hydrological Processing

#### Flow Directions

#### Flow Accumulation

#### Determination of Drainage Network and Watershed Delimitation

#### Geomorphological Parameters Quantification

## 3. Results and Discussions

#### 3.1. Comparative of Fill DEMs

#### 3.2. DEM Comparison Flow Direction

#### 3.3. Geomorphometric Parameterization

^{2}to 103.524 km

^{2}and the average area of the watershed was 101.544 km

^{2}. According to the classification of Faustino and Jimenez [92], the watershed is classified as a micro-basin. The area value provided by the MFD algorithm over the fill DEM of W/L reaches 1.9% more than the average area—it was the most scattered. There is a greater difference in the estimated areas over a coarse resolution. On the other side, the average perimeter was 74.514 km, with a maximum variation of 19.351 km, representing approximately 26% of the difference. The perimeter directly affects the shape parameters that define the form of the watershed and provide an idea of the behavior of the runoff.

_{c}) was 20.665 km, with a maximum variation of 1.445 km (approximately 7%). The average slope of the main channel (S

_{c}) resulted in 1.21%, with a maximum difference of 0.167%. The values of L

_{c}and S

_{c}affect the concentration time Tc, generating a maximum variation between the scenarios of 0.398 h (24 min). This significant difference may disturb the peak flood time estimated, and thereby the safety of the areas adjacent to the main channel. In general, the shape parameters show minimum variations, the value compactness coefficient (K

_{c}>1.54) indicates a lobular watershed [91], and the circulatory ratio value (R

_{c}ranging from 0.24 to 0.26) implies low relief and an almost impermeable surface [1,78]. Nevertheless, the low value in the elongation ratio (R

_{e}) indicates that the watershed is on an undulating or steep relief [79], discordant with the slope analysis and R

_{c}; the contradiction is probably due to the high sinuosity of the mean channel. The shape parameters imply almost symmetrical hydrograms at the watershed outlet. Regarding drainage parameters, no significant variations were found between the variables, except in drainage density (D

_{d}), concentration time (Tc) and texture ratio (T). Based on the drainage parameters obtained, the watershed presents a rapid response to runoff.

#### 3.4. Drainage Networks Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Workflow chart of geomorphological parameterization: (

**a**) flow diagram of the general methodology in GIS environments for geomorphological analysis; (

**b**) watershed assessment derived from the different delimitations; and (

**c**) assessment of drainage networks for each scenario.

**Figure 3.**Difference of cell elevation in pre-treated DEMs against fill DEMs: (

**a**) merged DEM–fill DEM J/D, (

**b**) merged DEM–fill DEM W/L, (

**c**) DEM 30 m–fill DEM J/D, and (

**d**) DEM 30 m–fill DEM W/L.

**Figure 5.**Accomplished delimitations by the D8, D∞, and MFD algorithms over the merged DEM, including part of the hydrography.

**Figure 6.**Comparison between the control points and nearest channels of each drainage network: (

**a**) distances of stream order 1, (

**b**) distances of stream order 2, (

**c**) distances of stream order 3, (

**d**) distances of stream order 4, and (

**e**) distances of stream order 5.

**Figure 9.**Drainage networks, control points, channels of stream order 3, and X-X’ axis over filled cells.

**Figure 10.**Drainage networks, control points, channels of stream order 4 and Y-Y’ axis over filled cells.

**Figure 14.**Allocation of elevations on DEMs and depression identification: (

**a**) planar view of a hypothetical channel; (

**b**) high-resolution DEM; and (

**c**) low-resolution DEM.

**Table 1.**System of methods and principles used for the computation of the geomorphometric parameters of basic and shape.

No. | Name | Equation | Reference |
---|---|---|---|

Basic parameters | |||

(1) | Area (A) | A = Watershed surface area (km^{2}) | [75] |

(2) | Perimeter (P) | P = Watershed perimeter (km) | [75] |

(3) | Main channel length (L_{c}) | L_{c} = Main flow channel length (km) | [75] |

(4) | Stream order (u) | u = Stream order (unitless) | [76] |

(5) | All number of flow channels (N_{u}) | N_{u} = Number of flow channels | [75] |

(6) | All channel lengths (L_{u}) | L_{u} = Length of all the flow channels in the watershed (km) | [75] |

(7) | Mean slope of the main channel (S_{c}) | ${S}_{c}=\left(\frac{{H}_{max}-{H}_{min}}{{L}_{c}}\right)100$ (%) | [75] |

Shape parameters | |||

(8) | Compactness coefficient (K_{c}) | ${K}_{c}=\frac{P}{2\sqrt{\pi A}}$ (unitless) | [77] |

(9) | Circularity ratio (R_{c}) | ${R}_{c}=\frac{4\pi A}{{P}^{2}}$ (unitless) | [78] |

(10) | Elongatio ratio (R_{e}) | ${R}_{e}=1.128\frac{\sqrt{A}}{L}$ (unitless) | [79] |

**Table 2.**System of methods and principles used for computation of geomorphometric parameters related to drainage.

No. | Name | Equation | Reference |
---|---|---|---|

Drainage parameters | |||

(11) | Stream frequency (F_{u}) | ${F}_{u}={N}_{u}/A$ (channels/km^{2}) | [80] |

(12) | Drainage density (D_{d}) | ${D}_{d}={L}_{u}/A$ (km/km^{2}) | [75] |

(13) | Overland flow length (Lof) | $Lof=1/2{D}_{d}$ (km) | [75] |

(14) | Constant channel maintenance (C) | $C=A/{L}_{u}=1/{D}_{d}$ (km) | [79] |

(15) | Concentration time (Tc) | $Tc=0.066{\left(\frac{{L}_{c}}{\sqrt{{S}_{c}}}\right)}^{0.77}$ (h) | [81] |

(16) | Texture ratio (T) | T = N_{u}/P (channels/km) | [82] |

(17) | Drainage intensity (Di) | $Di={F}_{u}/{D}_{d}$ (unitless) | [83] |

(18) | Average extent of runoff (E) | $E=A/4{L}_{u}$ (km) | [84] |

(19) | Torrential coefficient (Ct) | $Ct={N}_{u1}/A$ (channels/km^{2}) | [85] |

Elevation Difference (m) | Cells Percentage (%) | |||
---|---|---|---|---|

Fill Merged DEM | Fill DEM 30 m | |||

J/D | W/L | J/D | W/L | |

<−2 | 0 | 0 | 0 | 9.8 |

−2 to 0 | 0 | 0 | 0 | 56.2 |

0 to 2 | 99.1 | 98.3 | 96.5 | 26.3 |

>2 | 0.9 | 1.7 | 3.5 | 7.7 |

Min. value (m) | 0.0 | 0.0 | 0.0 | −9.0 |

Max. value (m) | 19.0 | 19.4 | 29.4 | 27.2 |

Relief Type | Range Slope (%) | Watershed Area (%) | ||||
---|---|---|---|---|---|---|

Fill Merged DEM | Fill DEM 30 m | |||||

J/D | W/L | J/D | W/L | |||

Flat | 0–3 | 68.9 | 69.0 | 18.7 | 21.7 | |

Lightly flat | 3–7 | 1.0 | 1.0 | 41.8 | 44.3 | |

Lightly inclined | 7–12 | 0.0 | 0.1 | 28.9 | 26.1 | |

Strongly undulating | 12–25 | 20.6 | 20.7 | 10.2 | 7.7 | |

Strongly inclined | 25–50 | 8.7 | 8.4 | 0.4 | 0.2 | |

Steep | 50–75 | 0.7 | 0.7 | 0.0 | 0.0 | |

Very steep | >75 | 0.0 | 0.0 | 0.0 | 0.0 | |

Mean slope of the watershed | 7.20 | 7.08 | 6.59 | 6.04 |

Flow Direction | Cells Percentage (%) | ||||
---|---|---|---|---|---|

Merged DEM | DEM 30 m | Max Difference | |||

J/D | W/L | J/D | W/L | ||

E | 24.2 | 23.0 | 14.1 | 13.7 | 10.5 |

SE | 0.8 | 1.5 | 10.3 | 9.3 | 9.6 |

S | 23.3 | 23.2 | 14.5 | 15.1 | 8.8 |

SW | 0.6 | 1.1 | 8.8 | 9.0 | 8.3 |

W | 21.0 | 21.5 | 11.9 | 14.6 | 9.6 |

NW | 0.8 | 1.5 | 10.0 | 9.7 | 9.1 |

N | 28.3 | 26.6 | 18.9 | 18.3 | 9.9 |

NE | 0.9 | 1.6 | 11.5 | 10.3 | 10.6 |

DEM | Fill Algorithm | Routing Algorithm | Area (km^{2}) | Perimeter (km) |
---|---|---|---|---|

Merged DEM | J/D | D8 (W1) | 101.069 | 72.699 |

W/L | D8 | 100.767 | 71.946 | |

MFD | 102.820 | 89.133 | ||

D∞ (W2) | 100.914 | 72.531 | ||

DEM 30 m | J/D | D8 (W3) | 101.099 | 72.375 |

W/L | D8 | 100.381 | 70.385 | |

MFD | 103.524 | 77.261 | ||

D∞ (W4) | 101.776 | 69.782 | ||

Max difference | 3.144 | 19.351 |

Subclassification | Symbol | Units | Merged DEM | DEM 30 m | Max Difference | |||
---|---|---|---|---|---|---|---|---|

D8 (W1) | KRA (W2) | D8 (W3) | KRA (W4) | |||||

Basic parameters | L_{c} | km | 21.3802 | 21.1426 | 20.2043 | 19.9349 | 1.445 | |

S_{c} | % | 1.127 | 1.149 | 1.274 | 1.294 | 0.167 | ||

Shape parameters | K_{c} | unitless | 2.040 | 2.037 | 2.031 | 1.951 | 0.089 | |

R_{c} | unitless | 0.240 | 0.241 | 0.243 | 0.263 | 0.022 | ||

R_{e} | unitless | 0.530 | 0.536 | 0.561 | 0.571 | 0.040 | ||

Drainage parameters | F_{u} | channels/km^{2} | 3.136 | 3.221 | 2.948 | 2.928 | 0.293 | |

Lof | km | 0.870 | 0.887 | 0.820 | 0.795 | 0.092 | ||

C | km | 0.575 | 0.563 | 0.610 | 0.629 | 0.065 | ||

Dd | km/km^{2} | 1.740 | 1.775 | 1.639 | 1.591 | 0.184 | ||

Tc | h | 3.923 | 3.860 | 3.582 | 3.525 | 0.398 | ||

T | no. channels/km^{2} | 4.360 | 4.481 | 4.117 | 4.270 | 0.363 | ||

Di | unitless | 1.803 | 1.815 | 1.798 | 1.841 | 0.042 | ||

E | km | 0.144 | 0.141 | 0.153 | 0.157 | 0.016 | ||

Ct | unitless | 1.573 | 1.595 | | | 1.484 | 1.552 | 0.122 |

Order | Merged DEM | DEM 30 m | Mean | Max Difference | |||
---|---|---|---|---|---|---|---|

D8 | KRA | D8 | KRA | ||||

1 | No. Channels | 159 | 161 | 150 | 158 | 157 | 11 |

Length (km) | 84.8717 | 86.0173 | 82.2345 | 87.7623 | 85.2215 | 5.53 | |

2 | No. Channels | 78 | 80 | 74 | 59 | 72.8 | 21 |

Length (km) | 46.4873 | 48.2381 | 46.7814 | 34.4391 | 43.9865 | 13.8 | |

3 | No. Channels | 46 | 47 | 45 | 40 | 44.5 | 7 |

Length (km) | 25.4547 | 25.296 | 22.3186 | 21.7334 | 23.7007 | 3.72 | |

4 | No. Channels | 12 | 15 | 18 | 17 | 15.5 | 6 |

Length (km) | 7.3698 | 8.0719 | 7.9344 | 7.5575 | 7.7334 | 0.7 | |

5 | No. Channels | 22 | 22 | 11 | 24 | 19.8 | 13 |

Length (km) | 11.6603 | 11.4627 | 6.4404 | 10.3935 | 9.9892 | 5.22 | |

All Number of Flow Channels (N_{u}) | 317 | 325 | 298 | 298 | 309.5 | 27 | |

All Channel Lengths (L_{u}), in km | 175.8438 | 179.086 | 165.7092 | 161.8858 | 170.6312 | 17.2 |

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**MDPI and ACS Style**

Dávila-Hernández, S.; González-Trinidad, J.; Júnez-Ferreira, H.E.; Bautista-Capetillo, C.F.; Morales de Ávila, H.; Cázares Escareño, J.; Ortiz-Letechipia, J.; Robles Rovelo, C.O.; López-Baltazar, E.A.
Effects of the Digital Elevation Model and Hydrological Processing Algorithms on the Geomorphological Parameterization. *Water* **2022**, *14*, 2363.
https://doi.org/10.3390/w14152363

**AMA Style**

Dávila-Hernández S, González-Trinidad J, Júnez-Ferreira HE, Bautista-Capetillo CF, Morales de Ávila H, Cázares Escareño J, Ortiz-Letechipia J, Robles Rovelo CO, López-Baltazar EA.
Effects of the Digital Elevation Model and Hydrological Processing Algorithms on the Geomorphological Parameterization. *Water*. 2022; 14(15):2363.
https://doi.org/10.3390/w14152363

**Chicago/Turabian Style**

Dávila-Hernández, Sandra, Julián González-Trinidad, Hugo Enrique Júnez-Ferreira, Carlos Francisco Bautista-Capetillo, Heriberto Morales de Ávila, Juana Cázares Escareño, Jennifer Ortiz-Letechipia, Cruz Octavio Robles Rovelo, and Enrique A. López-Baltazar.
2022. "Effects of the Digital Elevation Model and Hydrological Processing Algorithms on the Geomorphological Parameterization" *Water* 14, no. 15: 2363.
https://doi.org/10.3390/w14152363