Accounting for and Predicting the Influence of Spatial Autocorrelation in Water Quality Modeling
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Areas
2.2. Dependent Variables
2.3. Delineation of Upstream Area
2.4. Independent Variables
2.5. Data Preprocessing
2.6. Testing for Spatial Autocorrelation (SAC)
2.7. Statistical Models
2.8. Model Comparison
3. Results
3.1. Changes in R2 Values
3.2. Changes in rSAC
3.3. Overall Changes between Non-Spatial OLS and Spatial Regression Models
3.4. Summary of Findings
4. Discussion
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Larger Maps of the Study Areas for Better Visualization of the Water Quality Stations
References
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Region | Coordinates | Land Cover | Biogeographic Region | Geology | Climate | Soil | Surficial Lithology |
---|---|---|---|---|---|---|---|
Arizona | 34°40′54″ N, 112°00′47″ W | Herbaceous, low-intensity urbanization, and evergreen forest | North American Warm Desert | Late and middle Pleistocene surficial deposits and Pliocene to middle Miocene deposits | Cold semi-arid (BSk) | Alfisols/Inceptisols | Non-Carbonate and Silicic Residual Material; Alluvium and Fine-textured Coastal Zone Sediment |
California | 38°00′00″ N, 119°21′33″ W | Evergreen Forest, Barren Land, and Shrubs | Mediterranean California | Mesozoic granitic rocks, unit 3 (Sierra Nevada, Death Valley area, Northern Mojave Desert, and Transverse Ranges) | Temperate Mediterranean (Csb) | Rock outcrop/Entisols | Silicic Residual Material |
Colorado | 37°56′58″ N, 107°56′10″ W | Predominantly Evergreen and Deciduous Forest | Rocky Mountain | Mancos Shale; Pre-ash-flow andesitic lavas, breccias, tuffs, and conglomerates; Morrison, Wanakah, and Entrada Fms | Warm-summer humid continental (Dfb) | Rock outcrop/Mollisols | Non-Carbonate and Silicic Residual Material |
Delaware | 39°43′36″ N, 75°40′07″ W | High-, medium-, and low- intensity urbanization with some deciduous forest and pasture | Gulf and Atlantic Coastal Plain | Wissahickon Schist | Humid Subtropical (Cfa) | Ultisols | Non-Carbonate and Silicic Residual Material; Alluvium and Fine-textured Coastal Zone Sediment |
Idaho | 47°31′01″ N, 116°04′27″ W | Evergreen forest, shrub, and some medium-intensity urbanization | Rocky Mountain | Siltite, argillite, dolostone, and quartzite; Middle Proterozoic Wallace Formation | Temperate Mediterranean (Csb)/Warm, dry-summer continental (Dsb) | Andisols | Non-Carbonate Residual Material |
Iowa | 41°37′38″ N, 91°29′31″ W | High and medium urbanization level with crops and pasture | Eastern Great Plains | Cedar Valley Limestone | Humid Continental (Dfa) | Mollisols | Glacial Till, Loamy; Glacial Outwash and Glacial Lake Sediment, Coarse-textured; Alluvium and Fine-textured Coastal Zone Sediment |
Kansas | 38°55′00″ N, 94°41′14″ W | Predominantly high-, medium-, and low- intensity urbanization | Eastern Great Plains | Limestone—Kansas City and Lansing Group | Humid Subtropical (Cfa) | Mollisols | Non-Carbonate Residual Material |
Kentucky | 37°25′01″ N, 82°49′04″ W | Predominantly Deciduous Forest | Central Interior and Appalachian | Middle part of Breathitt Group | Humid Subtropical (Cfa) | Inceptisols | Colluvial Sediment |
Louisiana | 31°48′17″ N, 91°42′21″ W | Predominantly cultivated crops | Gulf and Atlantic Coastal Plain | Sub/supra-glacial sediment | Humid Subtropical (Cfa) | Vertisols | Alluvium and Fine-textured Coastal Zone Sediment |
Virginia | 38°55′51″ N, 77°18′25″ W | Deciduous Forest and developed open space | Central Interior and Appalachian | Schist | Humid Subtropical (Cfa) | Alfisols/Inceptisols | Non-Carbonate Residual Material |
Study Areas | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
State | LA | AZ | KS | VA | CA | CO | DE | ID | IA | KY |
Watershed | Bayou Louis/ Lake Louis | Cherry Creek | Indian Creek | Difficult River | Headwaters Tuolumne River | Upper San Miguel River | Clay, Mill, Bradywine Creek, and Cristina River | Lower South Fork Coeur d’Alene River | Iowa River | Beaver Creek |
Area (km2) | 288.58 | 586.26 | 193.8 | 150.84 | 553.66 | 763.71 | 352.24 | 308.49 | 193.96 | 407.07 |
Stations | 29 | 31 | 33 | 33 | 31 | 32 | 36 | 32 | 32 | 54 |
Water quality parameter (Moran’s I) | pH (0.13) | DO (−0.08) * | TN (0.013) | Tur (−0.28) * | Csu (−0.20) * | DO (0.39) | SC (−0.05) * | Pb (0.11) | DO (0.18) | Al (0.005) |
T (0.15) | pH (−0.07) * | SC (0.022) | TDS (−0.26) * | T (0.30) | SC (0.36) | T (−0.006) * | T (0.15) | pH (0.34) | Ba (0.06) | |
SC (0.20) | T (0.54) | DIN (0.07) | SC (0.06) | Mg (0.42) | pH (0.37) | Chla (0.02) | Zn (0.24) | NO3− (0.36) | Alk (0.11) | |
DO (0.28) | SC (0.59) | KjN (0.10) | Br (0.09) | K (0.46) | T (0.67) | TN (0.03) | pH (0.31) | T (0.49) | Na (0.14) | |
TDS (0.53) | TP (0.15) | Cl (0.12) | Ca (0.55) | Nin (0.05) | Cd (0.35) | PO43− (0.66) | Cl (0.23) | |||
T (0.20) | Mg (0.15) | Cl (0.58) | Alk (0.08) | As (0.47) | Cl (0.67) | K (0.26) | ||||
Tur 0.25) | Na (0.15) | Na (0.59) | TP (0.12) | SC (0.56) | Nin (0.29) | |||||
DO (0.44) | DO (0.16) | SiO2 (0.62) | DO (0.15) | TDS (0.32) | ||||||
pH (0.72) | Ca (0.17) | SO42− (0.65) | pH (0.16) | SO42− (0.38) | ||||||
SiO2 (0.19) | TDS (0.73) | Cl (0.23) | Fe (0.40) | |||||||
Fe (0.21) | Alk (0.80) | TOC (0.32) | KjN (0.43) | |||||||
K (0.25) | pH (0.82) | DOC (0.32) | Mg (0.47) | |||||||
CO2 (0.34) | Ca (0.55) | |||||||||
Mn (0.34) | Mn (0.58) | |||||||||
pH (0.39) | ||||||||||
Alk (0.40) | ||||||||||
TP (0.42) | ||||||||||
SO42− (0.45) | ||||||||||
F (0.54) | ||||||||||
T (0.69) |
Agency Source | Variable | Year/Data | PC Group | Derived Variable | Original Data |
---|---|---|---|---|---|
WQP | Dependent | 2011 to 2017—Water quality parameters | - | Physical water quality data | |
USGS | Independent | 2017—National Elevation dataset (10 m) | Topographic | Mean elevation | Elevation |
Elevation standard deviation | |||||
Mean slope | |||||
Slope standard deviation | |||||
USGS | Independent | 2011—National Land Cover dataset (30 m) | Land use | Agriculture | Pasture, cultivated crops |
Forest | Deciduous forest, evergreen forest, mixed forest | ||||
Urban | Low-, medium-, high-intensity urbanized areas, open space | ||||
Wetland | Woody wetland, emergent herbaceous wetland | ||||
USDA, NRCS | Independent | 2017—Hydrologic Soil Groups | Soil | A, B, C, D, A/D, B/D, C/D | Soil Survey Geographic (SSURGO) database |
California | Colorado | Delaware | Idaho | Iowa | Kentucky | Arizona | Kansas | Louisiana | Virginia | All States Combined | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Samples | 12 | 4 | 12 | 7 | 6 | 14 | 4 | 9 | 5 | 20 | 93 | ||
I | 0.56 | 0.45 | 0.13 | 0.31 | 0.45 | 0.30 | 0.31 | 0.22 | 0.26 | 0.29 | 0.32 | ||
OLS | R2 | 0.28 | 0.31 | 0.27 | 0.25 | 0.44 | 0.23 | 0.34 | 0.23 | 0.15 | 0.37 | 0.29 | |
rSAC | 0.39 | 0.21 | 0.09 | 0.19 | 0.12 | 0.19 | 0.19 | 0.26 | 0.16 | 0.17 | 0.21 | ||
After spatial regression | Improvement in R2 | lag-ols | 0.26 | 0.16 | 0.03 | 0.09 | 0.05 | 0.09 | 0.13 | 0.11 | 0.09 | 0.03 | 0.10 |
error-ols | 0.29 | 0.18 | 0.04 | 0.09 | 0.04 | 0.08 | 0.15 | 0.17 | 0.10 | 0.07 | 0.12 | ||
Reduction in rSAC | ols-lag | 0.37 | 0.13 | 0.05 | 0.09 | 0.02 | 0.15 | 0.13 | 0.14 | 0.11 | 0.04 | 0.12 | |
ols-error | 0.40 | 0.13 | 0.07 | 0.12 | 0.07 | 0.16 | 0.17 | 0.21 | 0.12 | 0.14 | 0.17 | ||
Linear regression models for the Change in R2 vs. I | Model fit Spatial Lag | R2 | 0.55 | 0.12 | 0.07 | 0.85 | 0.68 | 0.61 | 0.51 | 0.91 | 0.94 | 0.46 | 0.58 |
βo | 0.00 | 0.07 | 0.01 | −0.09 | −0.07 | −0.04 | −0.04 | −0.07 | −0.09 | −0.05 | −0.15 | ||
β1 | 0.46 | 0.19 | 0.11 | 0.58 | 0.26 | 0.44 | 0.55 | 0.86 | 0.70 | 0.30 | 0.74 | ||
p-value | <0.001 * | 0.10 * | 0.60 | 0.10 * | 0.53 | 0.08 * | 0.39 | 0.09 * | 0.38 | 0.28 | <0.001 * | ||
Model fit Spatial Error | R2 | 0.40 | 0.03 | 0.00 | 0.77 | 0.64 | 0.55 | 0.42 | 0.77 | 0.93 | 0.29 | 0.36 | |
βo | 0.07 | 0.11 | 0.03 | −0.13 | −0.04 | −0.04 | −0.02 | −0.01 | −0.10 | −0.04 | −0.04 | ||
β1 | 0.39 | 0.15 | 0.02 | 0.68 | 0.19 | 0.40 | 0.56 | 0.83 | 0.75 | 0.40 | 0.60 | ||
p-value | <0.001 * | 0.06 * | 0.52 | 0.15 | 0.62 | 0.10 * | 0.33 | 0.02 * | 0.39 | 0.06 * | <0.001 * | ||
Linear regression models for the Change in rSAC vs. I | Model fit Spatial Lag | R2 | 0.33 | 0.56 | 0.58 | 0.66 | 0.42 | 0.60 | 0.67 | 0.67 | 0.80 | 0.03 | 0.31 |
βo | 0.14 | −0.32 | 0.01 | −0.21 | −0.10 | −0.03 | −0.07 | −0.03 | 0.00 | −0.01 | −0.05 | ||
β1 | 0.41 | 1.01 | 0.36 | 0.98 | 0.27 | 0.57 | 0.66 | 0.80 | 0.42 | 0.17 | 0.18 | ||
p-value | <0.001 * | 0.18 | 0.01 * | 0.20 | 0.71 | <0.001 * | 0.34 | 0.08 * | 0.09 * | 0.32 | <0.001 * | ||
Model fit Spatial Error | R2 | 0.32 | 0.87 | 0.42 | 0.84 | 0.28 | 0.45 | 0.77 | 0.60 | 0.74 | 0.17 | 0.39 | |
βo | 0.22 | −0.26 | 0.02 | −0.15 | −0.03 | 0.01 | −0.05 | 0.05 | 0.00 | 0.05 | −0.03 | ||
β1 | 0.32 | 0.88 | 0.33 | 0.87 | 0.22 | 0.51 | 0.70 | 0.71 | 0.46 | 0.30 | 0.17 | ||
p-value | <0.001 * | 0.17 | 0.00 * | 0.11 | 0.15 | <0.001 * | 0.25 | 0.02 * | 0.08 * | <0.001 * | <0.001 * |
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Miralha, L.; Kim, D. Accounting for and Predicting the Influence of Spatial Autocorrelation in Water Quality Modeling. ISPRS Int. J. Geo-Inf. 2018, 7, 64. https://doi.org/10.3390/ijgi7020064
Miralha L, Kim D. Accounting for and Predicting the Influence of Spatial Autocorrelation in Water Quality Modeling. ISPRS International Journal of Geo-Information. 2018; 7(2):64. https://doi.org/10.3390/ijgi7020064
Chicago/Turabian StyleMiralha, Lorrayne, and Daehyun Kim. 2018. "Accounting for and Predicting the Influence of Spatial Autocorrelation in Water Quality Modeling" ISPRS International Journal of Geo-Information 7, no. 2: 64. https://doi.org/10.3390/ijgi7020064
APA StyleMiralha, L., & Kim, D. (2018). Accounting for and Predicting the Influence of Spatial Autocorrelation in Water Quality Modeling. ISPRS International Journal of Geo-Information, 7(2), 64. https://doi.org/10.3390/ijgi7020064