Assessment of Regression Models for Surface Water Quality Modeling via Remote Sensing of a Water Body in the Mexican Highlands
Abstract
:1. Introduction
WQP | Surface (km2) | Resolution (m) | Sample of Size | Bands of Normalization | R2 | Estimation Interval (mg/L) | Author |
---|---|---|---|---|---|---|---|
TSS | 12,000 | 30 m | 26 | 0.98 | 0–386 | [45] | |
30 m | 14 | 0.69 | 0–135 | [22] | |||
TN | 53 | 30 m | 18 | -------- | 0–36 | [3] | |
TP | 53 | 30 m | 18 | -------- | 0–26 | [3] | |
COD | 150 | 30 m | ------- | -------- | 0–19.3 | [19] |
2. Materials and Methods
2.1. Statistical Analysis for Model Development
2.2. Spatio-Temporal Distribution of Estimated WQPs
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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ID | X (W Longitude) | Y (N Latitude) | Season | Chemistry Parameters | Physics p. | ||
---|---|---|---|---|---|---|---|
TN (mg/L) | COD (mg/L) | TP (mg/L) | TSS (mg/L) | ||||
PL = 40–60 | PL = 60–75 | PL = 20–30 | PL = 12–75 | ||||
1 | −99.660564 | 19.451172 | Before the rain season 18th May | 33 | 173 | 99.76 | 92.5 |
2 | −99.658486 | 19.453087 | 11 | 127 | 46.27 | 151.5 | |
3 | −99.658131 | 19.455031 | 16 | 66 | 44.34 | 198 | |
4 | −99.650393 | 19.445229 | 9 | 93 | 34.25 | 48 | |
5 | −99.646237 | 19.436919 | 28 | 107 | 70.91 | 33 | |
6 | −99.642504 | 19.434917 | 20 | 98 | 67.34 | 55 | |
7 | −99.640462 | 19.431472 | 10 | 109 | 74.92 | 42 | |
8 | −99.662355 | 19.457317 | After the rain season 26th October | 7.2 | 67.5 | 33.16 | 35 |
9 | −99.657869 | 19.453669 | 6.3 | 64 | 34.46 | 34 | |
10 | −99.648234 | 19.445605 | 3.9 | 80 | 23.64 | 15.2 | |
11 | −99.644043 | 19.436555 | 4.4 | 21 | 30.76 | 11 | |
12 | −99.641932 | 19.435785 | 3.5 | 30 | 32.79 | 16 | |
13 | −99.639985 | 19.430514 | 2.8 | 26 | 30.39 | 17 | |
14 | −99.647021 | 19.437027 | 3.3 | 39.5 | 33.71 | 19 |
Statistical Test | WQP | Total Nitrogen (TN) | Chemistry Oxygen Demand (COD) | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Model Type | Exponential | Linear | Polynomial | Exponential | Linear | Polynomial | ||||||||||||||
Independent Variables | B1, B3 | B3, B6, (B3 + B7) | (B1/B3) | LN(B5), LN(B2/B3), LN(B7) | (B1/B6), (B7/B4), (B2/B1), (B2/B3) | (B3/B1), (B3/B5) | ||||||||||||||
Vcrit | V | Vcrit | V | Vcrit | V | Vcrit | V | Vcrit | V | Vcrit | V | |||||||||
Homoscedasticity | W-pvalue > Vcrit | 0.1 | 0.25 | 0.1 | 0.33 | 0.1 | 0.23 | 0.1 | 0.18 | 0.1 | 0.25 | 0.1 | 0.38 | |||||||
Square chi test | χ2 < Vcrit | 7.81 | 4.54 | 7.81 | 4.65 | 11.07 | 9.30 | 7.81 | 2.25 | 9.48 | 2.26 | 11.07 | 0.82 | |||||||
Atypical values | Vcalc ≤ Vcrit | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 0 | 2 | 1 | |||||||
Collinearity | VIF < Vcrit | 4 | 0.21 | 4 | 0.16 | 4 | 4.0 | 4 | 0.21 | 4 | 2.6 | 4 | 1.17 | |||||||
r ≤ Vcrit | 0.75 | 0.74 | 0.75 | 0.75 | 0.75 | 0.86 | 0.75 | 0.74 | 0.75 | 0.78 | 0.75 | 0.78 | ||||||||
Multicollinearity | F > Vcrit | 3.70 | 22.90 | 3.70 | 13.20 | 3.68 | 6.25 | 3.70 | 19.08 | 3.63 | 6.75 | 3.68 | 11.82 | |||||||
Normality | D < Vcrit | 0.22 | 0.12 | 0.22 | 0.17 | 0.17 | 0.22 | 0.22 | 0.19 | 0.22 | 0.08 | 0.22 | 0.16 | |||||||
Significance | Pvalue ≤ Vcrit | 0.05 | 0.19 | 0.05 | 0.05 | 0.05 | 0.06 | 0.05 | 0.00 | 0.05 | 0.09 | 0.05 | 0.79 | |||||||
Statistical Test | WQP | Total Phosphorus (TP) | Total Suspended Solids (TSS) | |||||||||||||||||
Model Type | Exponential | Linear | Polynomial | Exponential | Linear | Polynomial | ||||||||||||||
Independent Variables | LN(B5), LN(B6) | (B5/B4), (B5/B6) | (B5/B2), (B5/B2) | LN(B4), LN(B3+B5), LN(B5+B7), LN(B2/B3), LN(B2/B4) | (B7/B4), (B7/B5) | (B3/B5), B3 | ||||||||||||||
Vcrit | V | Vcrit | V | Vcrit | V | Vcrit | V | Vcrit | V | Vcrit | V | |||||||||
Homoscedasticity | W-pvalue > Vcrit | 0.1 | 0.18 | 0.1 | 0.64 | 0.1 | 0.10 | 0.1 | 0.11 | 0.1 | 0.11 | 0.1 | 0.12 | |||||||
Square chi test | χ2 < Vcrit | 5.99 | 4.87 | 5.99 | 2.62 | 11.07 | 5.61 | 11.07 | 5.93 | 3.32 | 5.99 | 11.07 | 1.90 | |||||||
Atypical values | Vcalc ≤ Vcrit | 2 | 1 | 2 | 0 | 2 | 1 | 2 | 1 | 2 | 0 | 2 | 1 | |||||||
Collinearity | FIV < Vcrit | 4 | 2.63 | 4 | 6.31 | 4 | 2.88 | 4 | 4.1 | 4 | 1.28 | 4 | 1.38 | |||||||
r ≤ Vcrit | 0.75 | 0.78 | 0.75 | 0.9 | 0.75 | 0.80 | 0.75 | 0.87 | 0.75 | 0.46 | 0.75 | 0.52 | ||||||||
Multicollinearity | F > Vcrit | 3.98 | 18.65 | 3.98 | 24.3 | 3.68 | 25.63 | 3.68 | 30.60 | 3.98 | 11.28 | 3.68 | 136.12 | |||||||
Normality | D < Vcrit | 0.22 | 0.16 | 0.23 | 0.22 | 0.22 | 0.12 | 0.22 | 0.15 | 0.22 | 0.20 | 0.22 | 0.15 | |||||||
Significance | Pvalue ≤ Vcrit | 0.05 | 0.00 | 0.05 | 0.003 | 0.05 | 0.00 | 0.05 | 0.04 | 0.05 | 0.07 | 0.05 | 0.09 |
WQP | Type | Regression Model | RMSE | ||
---|---|---|---|---|---|
TN (mg/L) | Exp. | 5 | 3.82 | 0.79 | |
Linear | 7 | 4.24 | 0.73 | ||
Pol. | 14 | 31.13 | 0.68 | ||
COD (mg/L) | Exp. | 6 | 16.1 | 0.80 | |
Linear | 5 | 21.4 | 0.62 | ||
Pol. | 9 | 15.35 | 0.84 | ||
TP (mg/L) | Exp. | 8 | 10.25 | 0.74 | |
Linear | 5 | 9.63 | 0.79 | ||
Pol. | 5 | 5.49 | 0.92 | ||
TSS (mg/L) | Exp. | 5 | 14.37 | 0.90 | |
Linear | 5 | 43.9 | 0.61 | ||
Pol. | 6 | 7.19 | 0.98 |
WQP | Mean in Samples (mg/L) | Standard Deviation (mg/L) | Confidence Interval for Difference in Means (mg/L) | Author | |||
---|---|---|---|---|---|---|---|
A.M. | C.M. | A.M. | C.M. | ||||
TSS | 11.06 | 15.74 | 22.79 | 8.81 | −9.51 | 0.57 | [45] |
TN | 23.71 | 26.99 | 1.36 | 0.94 | −3.62 | −2.94 | [3] |
TP | 33.21 | 36.14 | 8.15 | 5.32 | −4.92 | −0.92 | [3] |
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Cruz-Retana, A.; Becerril-Piña, R.; Fonseca, C.R.; Gómez-Albores, M.A.; Gaytán-Aguilar, S.; Hernández-Téllez, M.; Mastachi-Loza, C.A. Assessment of Regression Models for Surface Water Quality Modeling via Remote Sensing of a Water Body in the Mexican Highlands. Water 2023, 15, 3828. https://doi.org/10.3390/w15213828
Cruz-Retana A, Becerril-Piña R, Fonseca CR, Gómez-Albores MA, Gaytán-Aguilar S, Hernández-Téllez M, Mastachi-Loza CA. Assessment of Regression Models for Surface Water Quality Modeling via Remote Sensing of a Water Body in the Mexican Highlands. Water. 2023; 15(21):3828. https://doi.org/10.3390/w15213828
Chicago/Turabian StyleCruz-Retana, Alejandro, Rocio Becerril-Piña, Carlos Roberto Fonseca, Miguel A. Gómez-Albores, Sandra Gaytán-Aguilar, Marivel Hernández-Téllez, and Carlos Alberto Mastachi-Loza. 2023. "Assessment of Regression Models for Surface Water Quality Modeling via Remote Sensing of a Water Body in the Mexican Highlands" Water 15, no. 21: 3828. https://doi.org/10.3390/w15213828