Analysis of Factors Influencing the Lake Area on the Tibetan Plateau Using an Eigenvector Spatial Filtering Based Spatially Varying Coefficient Model
Abstract
:1. Introduction
2. Data and Methods
2.1. Study Area and Datasets
2.2. Methodology
2.2.1. Yearly Lake Area Extraction
2.2.2. Extraction and Processing of Influencing Factors
2.2.3. Construction of ESF-based Spatially Varying Coefficient Structure
- (1)
- The first step is to construct the spatial weight matrix based on the spatial relationships of each small watershed delineated in the HydroSHEDS dataset. If two watersheds share one or more boundary point, the corresponding value in the spatial weight matrix is 1; if not, the value is 0. The spatial weight matrix was constructed using the spdep package in R language.
- (2)
- Centralize the spatial weight matrix using the following method [55]:
- (3)
- Extract eigenvectors and perform preliminary screening. The spatial weight matrix is eigen-decomposed using linear variation, the eigenvalues and eigenvectors are calculated using the “spmoran” package in R language, and the eigenvectors are initially filtered using a threshold of 0.25 [56]; thus, the filtered eigenvectors correspond to eigenvalues equal to or greater than one-fourth of the largest eigenvalue.
- (4)
- Select the appropriate eigenvectors to be used in the model. ESF-SVC regression uses a set of eigenvectors as new variables. The model introduces two new parameters α, [21], and the eigenvectors that contribute more to the regression are selected by the method of great likelihood estimation from the centralized spatial weight matrix C in the previous step and added to the model as independent variables [55]. However, the introduction of the two new parameters leads to increased complexity of the ESF-SVC model.
- (5)
- Construct the ESF-SVC model. The ESF-SVC model is built on the basis of the ESF model. In the ESF model, the eigenvectors are added to the model as follows:
2.2.4. Variable Selection and Model Validation
3. Results
3.1. Pre-Analysis of Lake Area and Variables
3.2. Variable Selection
3.3. Model Accuracy Assessment
3.4. ESF-SVC Model Coefficients
4. Discussion
4.1. Analysis of Influencing Factors
4.2. Limitations and Future Enhancement
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Variable | Resolution | Products | Source |
---|---|---|---|
Surface reflectance | 500 m | MOD09A1 | https://search.earthdata.nasa.gov (accessed on 18 December 2020) |
DEM | 90 m | SRTM DEM | https://srtm.csi.cgiar.org/ (accessed on 4 November 2020) |
EVAP | 0.1° | Monthly mean evapotranspiration data set of the Tibet Plateau | https://data.tpdc.ac.cn/ (accessed on 29 September 2021) |
PREC | 1000 m | 1-km monthly precipitation dataset for China | https://data.tpdc.ac.cn/ |
SME | 0.25° | GLDAS_NOAH025_M | https://ldas.gsfc.nasa.gov/gldas/ (accessed on 14 September 2020) |
DAYT | 1000 m | TRIMS LST-TP | https://data.tpdc.ac.cn/ |
SMO | 0.25° | SMsmapTE | https://data.tpdc.ac.cn/ |
NDVI | 1000 m | MOD13A3 | https://search.earthdata.nasa.gov |
DAYT (Days) | EVAP (mm/Month) | SMO (cm3/cm3) | PREC (mm/Month) | SME (kg/m2) | VAREA (km2) | ELEV (masl) | |
---|---|---|---|---|---|---|---|
Mean | 189.70 | 36.12 | 0.11 | 129.30 | 14.71 | 818.71 | 951.75 |
Max | 276.25 | 67.10 | 0.20 | 400.06 | 90.81 | 22,669.03 | 3194.80 |
Min | 102.05 | 11.78 | 0.06 | 10.08 | 0.69 | 0.00 | 113.98 |
Std.dev | 32.11 | 13.28 | 0.02 | 96.49 | 10.24 | 1962.52 | 517.47 |
Skewness | 0.52 | 0.25 | 1.02 | 1.19 | 4.12 | 6.25 | 0.79 |
Kurtosis | −0.53 | −1.03 | 1.13 | 0.72 | 21.74 | 51.90 | 0.79 |
DAYT | EVAP | SMO | PREC | SME | VAREA | ELEV | |
---|---|---|---|---|---|---|---|
2000 | 0.145 ** | \ | 0.311 ** | 0.248 ** | 0.227 ** | 0.841 ** | 0.406 ** |
2001 | 0.169 ** | 0.278 ** | \ | 0.230 ** | 0.266 ** | 0.847 ** | 0.409 ** |
2002 | −0.003 | 0.298 ** | 0.273 ** | 0.259 ** | 0.251 ** | 0.845 ** | 0.410 ** |
2003 | 0.156 ** | 0.190 ** | 0.285 ** | 0.246 ** | 0.160 ** | 0.848 ** | 0.413 ** |
2004 | 0.137 ** | 0.218 ** | 0.293 ** | 0.247 ** | 0.238 ** | 0.847 ** | 0.411 ** |
2005 | 0.165 ** | 0.178 ** | 0.283 ** | 0.247 ** | 0.273 ** | 0.854 ** | 0.411 ** |
2006 | 0.124 * | 0.258 ** | 0.284 ** | 0.244 ** | 0.214 ** | 0.846 ** | 0.412 ** |
2007 | 0.136 ** | 0.201 ** | 0.283 ** | 0.250 ** | 0.123 * | 0.850 ** | 0.415 ** |
2008 | 0.147 ** | 0.180 ** | 0.289 ** | 0.252 ** | 0.286 ** | 0.837 ** | 0.418 ** |
2009 | 0.145 ** | 0.239 ** | 0.289 ** | 0.237 ** | 0.317 ** | 0.861 ** | 0.415 ** |
2010 | 0.076 | 0.183 ** | 0.290 ** | 0.270 ** | 0.169 ** | 0.864 ** | 0.417 ** |
2011 | 0.134 ** | 0.223 ** | 0.294 ** | 0.246 ** | 0.145 ** | 0.855 ** | 0.419 ** |
2012 | 0.084 | 0.135 ** | 0.312 ** | 0.250 ** | 0.282 ** | 0.863 ** | 0.420 ** |
2013 | 0.092 | 0.281 ** | 0.339 ** | 0.253 ** | 0.193 ** | 0.850 ** | 0.421 ** |
2014 | 0.136 ** | 0.283 ** | 0.333 ** | 0.268 ** | 0.141 ** | 0.842 ** | 0.421 ** |
2015 | 0.111 * | 0.272 ** | 0.370 ** | 0.241 ** | 0.168 ** | 0.868 ** | 0.422 ** |
DAYT | EVAP | SMO | PREC | SME | VAREA | ELEV | |
---|---|---|---|---|---|---|---|
2000 | 1.367 | \ | 2.798 | 3.197 | 1.168 | 1.391 | 1.352 |
2001 | 1.516 | 3.050 | \ | 2.728 | 1.776 | 1.386 | 1.441 |
2002 | \ | 2.145 | 2.846 | 3.393 | 1.369 | 1.362 | 1.408 |
2003 | 1.518 | 2.382 | 2.358 | 3.683 | 1.235 | 1.384 | 1.403 |
2004 | 1.444 | 2.360 | 2.581 | 4.100 | 1.280 | 1.401 | 1.389 |
2005 | 1.313 | 3.382 | 2.679 | 5.379 | 1.279 | 1.389 | 1.371 |
2006 | 1.328 | 2.600 | 2.214 | 3.923 | 1.140 | 1.381 | 1.495 |
2007 | 1.450 | 1.708 | 2.311 | 3.140 | 1.315 | 1.395 | 1.461 |
2008 | 1.432 | 1.739 | 2.475 | 2.867 | 1.224 | 1.387 | 1.465 |
2009 | 1.277 | 3.661 | 2.766 | 5.785 | 1.398 | 1.393 | 1.523 |
2010 | \ | 2.307 | 2.599 | 3.893 | 1.182 | 1.408 | 1.319 |
2011 | 1.407 | 2.370 | 2.612 | 4.101 | 1.325 | 1.428 | 1.544 |
2012 | \ | 1.641 | 2.991 | 3.458 | 1.171 | 1.414 | 1.414 |
2013 | \ | 2.134 | 2.120 | 3.001 | 1.149 | 1.381 | 1.446 |
2014 | 1.413 | 2.882 | 2.882 | 4.359 | 1.252 | 1.412 | 1.653 |
2015 | 1.282 | 1.891 | 1.949 | 2.333 | 1.396 | 1.440 | 1.622 |
Criteria | OLS | SEM | SLM | ESF | GWR | ESF-SVC |
---|---|---|---|---|---|---|
R2/Pseudo R2 (*) | 0.760 | 0.760 | 0.756 | 0.821 | 0.893 | 0.977 |
Adjust R2 | 0.756 | * | * | 0.813 | 0.880 | 0.976 |
RMSE | 105.631 | 104.499 | 103.452 | 91.165 | 70.233 | 31.912 |
AIC | 4892.236 | 4887.080 | 4878.113 | 4793.832 | 4573.523 | 4388.568 |
RMC | 0.093 | −0.009 | 0.067 | −0.061 | −0.037 | −0.083 |
RMC’s p-value | 0.020 | 0.587 | 0.012 | 0.836 | 0.800 | 0.980 |
DAYT | EVAP | SMO | PREC | SME | VAREA | ELEV | |
---|---|---|---|---|---|---|---|
2000 | −13.043 | \ | 13.715 | −0.599 | 27.435 | 83.037 | 20.665 |
2001 | −21.206 | −5.129 | \ | 17.189 | 19.997 | 92.865 | 20.933 |
2002 | \ | −4.091 | 6.745 | 7.994 | 18.513 | 70.368 | 25.275 |
2003 | −17.226 | 3.877 | 8.882 | 31.129 | 23.958 | 91.716 | 25.980 |
2004 | −27.322 | 3.436 | 7.688 | −1.694 | 49.162 | 97.793 | 21.582 |
2005 | −22.745 | −5.016 | 2.055 | 10.478 | 25.976 | 102.070 | 34.046 |
2006 | −9.397 | −4.500 | 9.784 | 12.378 | 37.994 | 105.679 | 30.591 |
2007 | −8.623 | −12.112 | 6.778 | 13.220 | 21.150 | 115.889 | 33.024 |
2008 | −8.790 | −15.598 | 4.563 | 22.838 | 21.656 | 94.174 | 32.156 |
2009 | −12.429 | −1.498 | 10.184 | 1.637 | 10.163 | 120.882 | 35.164 |
2010 | \ | 2.295 | 6.289 | 11.000 | 49.994 | 99.399 | 24.477 |
2011 | 2.103 | −3.512 | 19.913 | 0.017 | 22.417 | 123.165 | 32.207 |
2012 | \ | 5.790 | 14.622 | −5.420 | 26.959 | 114.631 | 25.676 |
2013 | \ | 4.558 | 18.209 | −5.134 | 24.344 | 121.842 | 28.033 |
2014 | −11.514 | −3.972 | 16.660 | 5.434 | 24.462 | 121.960 | 37.158 |
2015 | −16.758 | −3.500 | 9.375 | 5.218 | 20.407 | 120.320 | 29.268 |
16-year average | −13.913 | −2.598 | 10.364 | 7.855 | 26.537 | 104.737 | 28.515 |
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Xiong, Z.; Chen, Y.; Tan, H.; Cheng, Q.; Zhou, A. Analysis of Factors Influencing the Lake Area on the Tibetan Plateau Using an Eigenvector Spatial Filtering Based Spatially Varying Coefficient Model. Remote Sens. 2021, 13, 5146. https://doi.org/10.3390/rs13245146
Xiong Z, Chen Y, Tan H, Cheng Q, Zhou A. Analysis of Factors Influencing the Lake Area on the Tibetan Plateau Using an Eigenvector Spatial Filtering Based Spatially Varying Coefficient Model. Remote Sensing. 2021; 13(24):5146. https://doi.org/10.3390/rs13245146
Chicago/Turabian StyleXiong, Zhexin, Yumin Chen, Huangyuan Tan, Qishan Cheng, and Annan Zhou. 2021. "Analysis of Factors Influencing the Lake Area on the Tibetan Plateau Using an Eigenvector Spatial Filtering Based Spatially Varying Coefficient Model" Remote Sensing 13, no. 24: 5146. https://doi.org/10.3390/rs13245146