# Estimation of Fractal Dimension of Suspended Sediments from Two Mexican Rivers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sampling Campaign

#### 2.2. Laboratory Analysis

#### 2.3. Fractal Dimension Calculation by the Box Counting Method (BC-Method)

_{r}vs. 1/r, where N

_{r}is the number of frames with at least a gray level that covers the image for each r value.

#### 2.4. Triangular Box Counting Method (TBC-Method)

_{r}.

#### 2.5. Models for Fractal Dimension Calculation

_{ep}) when calculating the permeable drag coefficient (C

_{Df}) and a is a constant (C

_{Df}= a/R

_{ep}

^{n}).

## 3. Results

## 4. Discussion

^{3}, which is similar to the one found in this study. Van der Lee [18] measured in situ floc size and settling velocity in the Dollard estuary, Holland using underwater video cameras-UVC. He found flocs size varying from 100 to 300 μm with densities varying from 1500 to 1100 kg/m

^{3}for a concentration of 350 mg/L. Using Kranenburg [2] equation, one can show that the floc densities of Grijava River sediment and the Usumacinta River sediments are in the range of floc densities found in the Dollard estuary. Xia et al. [19] measured floc sizes and settling velocities in the Pearl River estuary, China using LISST and found very small flocs (size under 96 μm).

^{−9})ρ

_{f}+ 7.32 × 10

^{−6}. This relationship gives the primary particle diameter for the Usumacinta River as 4.2 μm and for the Grijalva river as 4.1 μm. The former is very similar to the one used in this research for the Usumacinta River and the latter is almost half the one used for the Grijalva river. Many et al. [21] measured floc size and settling velocity in the Rhone estuary using LISST and found that primary particle diameters varied from 1 to 12 μm. Their analysis was able to show that the fractal dimension varied from 2.0 to 2.5, which agrees with the values found in this research.

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Location of Chichicastle #2 (Usumacinta) and Los Idolos # 1 (Grijalva) sampling stations. (

**a**) Overall location, (

**b**) los idolos cross section, (

**c**) Chichicastle cross section.

**Figure 4.**Division of frame image in two triangular frames with four patterns (

**a**) up triangular (

**b**) down triangular (

**c**) left triangular (

**d**) right triangular.

**Figure 8.**Time evolution of floc diameter in RAF experiments for the Grijalva river. Circles are experimental values and doted line the trend with time.

**Figure 9.**Best fit of the fractal dimension for the Usumacinta River with Garcia Aragon et al. [16] model at different flocculation times using TBC and BC methods; (

**a**) 30 min, (

**b**) 45 min, (

**c**) 60 min.

**Figure 10.**Best fit of the fractal dimension for the Grijalva River with Garcia Aragon et al. [16] model at different flocculation times using TBC and BC methods; (

**a**) 30 min, (

**b**) 45 min, (

**c**) 60 min.

**Figure 11.**Best fit of the fractal dimension for the Usumacinta River with Lau and Krishnappan [15] model at different flocculation times using TBC and BC methods; (

**a**) 30 min, (

**b**) 45 min, (

**c**) 60 min.

**Figure 12.**Best fit of the fractal dimension for the Grijalva River with Lau and Krishnappan [15] model at different flocculation times using TBC and BC methods; (

**a**) 30 min, (

**b**) 45 min, (

**c**) 60 min.

Hydraulic Parameters | Grijalva | Usumacinta |
---|---|---|

Flow rate (m^{3}/s) | 1420–1055 | 2085–1755 |

Top width (m) | 200–185 | No data |

Mean velocity (m/s) | 0.71–0.54 | 0.79–0.7 |

Maximum depth (m) | 13.2–12.2 | 9.9–9.1 |

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**MDPI and ACS Style**

Zepeda Mondragon, H.; Garcia Aragon, J.A.; Salinas Tapia, H.; Krishnappan, B.G.
Estimation of Fractal Dimension of Suspended Sediments from Two Mexican Rivers. *Water* **2022**, *14*, 2774.
https://doi.org/10.3390/w14182774

**AMA Style**

Zepeda Mondragon H, Garcia Aragon JA, Salinas Tapia H, Krishnappan BG.
Estimation of Fractal Dimension of Suspended Sediments from Two Mexican Rivers. *Water*. 2022; 14(18):2774.
https://doi.org/10.3390/w14182774

**Chicago/Turabian Style**

Zepeda Mondragon, Hilda, Juan Antonio Garcia Aragon, Humberto Salinas Tapia, and Bommanna G. Krishnappan.
2022. "Estimation of Fractal Dimension of Suspended Sediments from Two Mexican Rivers" *Water* 14, no. 18: 2774.
https://doi.org/10.3390/w14182774