Articles | Volume 16, issue 10
https://doi.org/10.5194/gmd-16-2777-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-2777-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A generalized spatial autoregressive neural network method for three-dimensional spatial interpolation
Junda Zhan
School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
Sensen Wu
School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
Zhejiang Provincial Key Laboratory of Geographic Information Science,
Hangzhou 310028, China
Jin Qi
School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
Zhejiang Provincial Key Laboratory of Geographic Information Science,
Hangzhou 310028, China
Jindi Zeng
School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
Mengjiao Qin
School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
Zhejiang Provincial Key Laboratory of Geographic Information Science,
Hangzhou 310028, China
Yuanyuan Wang
Ocean Academy, Zhejiang University, Zhoushan 316022, China
Zhejiang Provincial Key Laboratory of Geographic Information Science,
Hangzhou 310028, China
Zhenhong Du
CORRESPONDING AUTHOR
School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
Zhejiang Provincial Key Laboratory of Geographic Information Science,
Hangzhou 310028, China
Related authors
No articles found.
Enjiang Yue, Mengjiao Qin, Linshu Hu, Riel Bryan, Sensen Wu, and Zhenhong Du
Geosci. Model Dev., 18, 6275–6293, https://doi.org/10.5194/gmd-18-6275-2025, https://doi.org/10.5194/gmd-18-6275-2025, 2025
Short summary
Short summary
Laboratory earthquakes are an important means to understand natural earthquakes. While previous work focused on transient prediction, lacking future prediction capability, we propose a method and evaluate on data from laboratory experiments with different slip behaviours. It shows stable predictions in modelling slip moments, intervals, and predictions beyond trained horizons, especially for challenging slip scenarios, which is crucial for cyclic geophysical process such as seismicity.
Ziyu Yin, Jiale Ding, Yi Liu, Ruoxu Wang, Yige Wang, Yijun Chen, Jin Qi, Sensen Wu, and Zhenhong Du
Geosci. Model Dev., 17, 8455–8468, https://doi.org/10.5194/gmd-17-8455-2024, https://doi.org/10.5194/gmd-17-8455-2024, 2024
Short summary
Short summary
In geography, understanding how relationships between different factors change over time and space is crucial. This study implements two neural-network-based spatiotemporal regression models and an open-source Python package named Geographically Neural Network Weighted Regression to capture relationships between factors. This makes it a valuable tool for researchers in fields such as environmental science, urban planning, and public health.
Cited articles
Abd El-Hady, A. E.-N. M., Abdelaty, E. F., and Salama, A. E.: GIS-mapping of
soil available plant nutrients (potentiality, gradient, anisotropy), OJSS,
8, 315–329, https://doi.org/10.4236/ojss.2018.812023, 2018.
Adhikary, S. K., Muttil, N., and Yilmaz, A. G.: Cokriging for enhanced
spatial interpolation of rainfall in two Australian catchments, Hydrol.
Process., 31, 2143–2161, https://doi.org/10.1002/hyp.11163, 2017.
Allard, D., Senoussi, R., and Porcu, E.: Anisotropy models for spatial data,
Math. Geosci., 48, 305–328, https://doi.org/10.1007/s11004-015-9594-x, 2016.
Arowolo, A. O., Bhowmik, A. K., Qi, W., and Deng, X.: Comparison of spatial
interpolation techniques to generate high-resolution climate surfaces for
Nigeria, Int. J. Climatol, 37, 179–192, https://doi.org/10.1002/joc.4990,
2017.
Aumond, P., Can, A., Mallet, V., De Coensel, B., Ribeiro, C., Botteldooren,
D., and Lavandier, C.: Kriging-based spatial interpolation from measurements
for sound level mapping in urban areas, J. Acoust.
Soc. Am., 143, 2847–2857, https://doi.org/10.1121/1.5034799,
2018.
Babak, O. and Deutsch, C. V.: Statistical approach to inverse distance
interpolation, Stoch. Environ. Res. Risk. Assess., 23, 543–553,
https://doi.org/10.1007/s00477-008-0226-6, 2009.
Chen, D., Tian, Y., Yao, T., and Ou, T.: Satellite measurements reveal
strong anisotropy in spatial coherence of climate variations over the Tibet
Plateau, Sci. Rep., 6, 30304, https://doi.org/10.1038/srep30304, 2016.
Cheng, M., Wang, Y., Engel, B., Zhang, W., Peng, H., Chen, X., and Xia, H.:
Performance assessment of spatial interpolation of precipitation for
hydrological process simulation in the Three Gorges Basin, Water, 9, 838,
https://doi.org/10.3390/w9110838, 2017.
da Silva Júnior, J. C., Medeiros, V., Garrozi, C., Montenegro, A., and
Gonçalves, G. E.: Random forest techniques for spatial interpolation of
evapotranspiration data from Brazilian's Northeast, Comput.
Electron. Agr., 166, 105017,
https://doi.org/10.1016/j.compag.2019.105017, 2019.
Du, Z., Wang, Z., Wu, S., Zhang, F., and Liu, R.: Geographically neural
network weighted regression for the accurate estimation of spatial
non-stationarity, Int. J. Geogr. Inf. Sci.,
34, 1353–1377, https://doi.org/10.1080/13658816.2019.1707834, 2020.
Gao, B., Hu, M., Wang, J., Xu, C., Chen, Z., Fan, H., and Ding, H.: Spatial
interpolation of marine environment data using P-MSN, Int. J.
Geogr. Inf. Sci., 34, 577–603,
https://doi.org/10.1080/13658816.2019.1683183, 2020.
Greenberg, J. A., Rueda, C., Hestir, E. L., Santos, M. J., and Ustin, S. L.:
Least cost distance analysis for spatial interpolation, Comput.
Geosci., 37, 272–276, https://doi.org/10.1016/j.cageo.2010.05.012,
2011.
He, K., Zhang, X., Ren, S., and Sun, J.: Delving deep into rectifiers:
surpassing human-level performance on ImageNet classification, in: 2015 IEEE
International Conference on Computer Vision (ICCV), Santiago, Chile, 1026–1034,
https://doi.org/10.1109/ICCV.2015.123, 2015.
Hu, S., Cheng, Q., Wang, L., and Xu, D.: Modeling land price distribution
using multifractal IDW interpolation and fractal filtering method, Landscape
Urban Plan., 110, 25–35,
https://doi.org/10.1016/j.landurbplan.2012.09.008, 2013.
Ioffe, S. and Szegedy, C.: Batch normalization: accelerating deep network
training by reducing internal covariate shift, in: Proceedings of the 32nd
International Conference on International Conference on Machine Learning –
Volume 37, Lille, France, 448–456, https://doi.org/10.48550/arXiv.1502.03167, 2015.
Jian, Z. and Jin, H.: Ocean carbon cycle and tropical forcing of climate
evolution, Adv. Earth Sci., 23, 221–227,
https://doi.org/10.11867/j.issn.1001-8166.2008.03.0221, 2008.
Kanevski, M., Timonin, V., and Pozdnoukhov, A.: Automatic Decision-Oriented
Mapping of Pollution Data, in: Computational Science and Its Applications –
ICCSA 2008, edited by: Gervasi, O., Murgante, B., Laganà, A.,
Taniar, D., Mun, Y., and Gavrilova, M. L., Springer Berlin Heidelberg,
Berlin, Heidelberg, vol. 5072, 678–691, https://doi.org/10.1007/978-3-540-69839-5_50, 2008.
Krige, D. G.: A statistical approach to some basic mine valuation problems
on the Witwatersrand, Journal of the Chemical, Metallurgical and Mining
Society of South Africa, 53, 159–162, 1952.
Kumar, S., Lal, R., and Liu, D.: A geographically weighted regression
kriging approach for mapping soil organic carbon stock, Geoderma, 189–190,
627–634, https://doi.org/10.1016/j.geoderma.2012.05.022, 2012.
Li, C., Liu, Y., Wu, J., Wang, C., and Liu, X.: A contrastive study on the
spatial interpolation for precipitation data using back propagation learning
algorithm and support vector machine model – a case study of Gansu
Province, Grassland and Turf, 38, 12–19,
https://doi.org/10.13817/j.cnki.cyycp.2018.04.002, 2018.
Li, Z., Zhang, X., Zhu, R., Zhang, Z., and Weng, Z.: Integrating
data-to-data correlation into inverse distance weighting, Comput. Geosci., 24,
203–216, https://doi.org/10.1007/s10596-019-09913-9, 2020.
Liang, Q., Nittel, S., Whittier, J. C., and Bruin, S.: Real-time inverse
distance weighting interpolation for streaming sensor data, Trans.
GIS, 22, 1179–1204, https://doi.org/10.1111/tgis.12458, 2018.
Liu, Z., Wu, X., Xu, J., Li, H., Lu, S., Sun, C., and Cao, M.: China Argo
project: progress in China Argo ocean observations and data applications,
Acta Oceanol. Sin., 36, 1–11, https://doi.org/10.1007/s13131-017-1035-x,
2017.
Longley, P. A., Goodchild, M., Maguire, D. J., and Rhind, D. W. (Eds.):
Geographic information systems & science, 3rd Edn., Wiley, Hoboken, NJ,
539 pp., ISBN 978-0-470-72144-5, 2011.
Lu, G. Y. and Wong, D. W.: An adaptive inverse-distance weighting spatial
interpolation technique, Comput. Geosci., 34, 1044–1055,
https://doi.org/10.1016/j.cageo.2007.07.010, 2008.
Ma, X., Luan, S., Ding, C., Liu, H., and Wang, Y.: Spatial interpolation of
missing annual average daily traffic data using Copula-based model, IEEE
Intell. Transp. Sy., 11, 158–170,
https://doi.org/10.1109/MITS.2019.2919504, 2019.
Matheron, G.: Principles of geostatistics, Econ. Geol., 58, 1246–1266,
https://doi.org/10.2113/gsecongeo.58.8.1246, 1963.
Pan, S., Tian, S., Wang, X., Dai, L., Gao, C., and Tong, J.: Comparing
different spatial interpolation methods to predict the distribution of
fishes: a case study from Coilia nasus in the Changjiang River Estuary, Acta
Oceanol. Sin., 40, 1–14, https://doi.org/10.1007/s13131-021-1789-z,
2021.
Rigol, J. P., Jarvis, C. H., and Stuart, N.: Artificial neural networks as a
tool for spatial interpolation, Int. J. Geogr.
Inf. Sci., 15, 323–343,
https://doi.org/10.1080/13658810110038951, 2001.
Riser, S. C., Freeland, H. J., Roemmich, D., Wijffels, S., Troisi, A.,
Belbéoch, M., Gilbert, D., Xu, J., Pouliquen, S., Thresher, A., Le
Traon, P.-Y., Maze, G., Klein, B., Ravichandran, M., Grant, F., Poulain,
P.-M., Suga, T., Lim, B., Sterl, A., Sutton, P., Mork, K.-A.,
Vélez-Belchí, P. J., Ansorge, I., King, B., Turton, J., Baringer,
M., and Jayne, S. R.: Fifteen years of ocean observations with the global
Argo array, Nat. Clim. Change, 6, 145–153,
https://doi.org/10.1038/nclimate2872, 2016.
Samal, A. R., Sengupta, R. R., and Fifarek, R. H.: Modelling spatial
anisotropy of gold concentration data using GIS-based interpolated maps and
variogram analysis: Implications for structural control of mineralization, J.
Earth Syst. Sci., 120, 583–593, https://doi.org/10.1007/s12040-011-0091-4,
2011.
Sekulić, A., Kilibarda, M., Heuvelink, G. B. M., Nikolić, M., and
Bajat, B.: Random Forest Spatial Interpolation, Remote Sensing, 12, 1687,
https://doi.org/10.3390/rs12101687, 2020.
Shepard, D.: A two-dimensional interpolation function for irregularly-spaced
data, in: Proceedings of the 1968 23rd ACM national conference, the 1968
23rd ACM National Conference, New York, NY, US, 517–524,
https://doi.org/10.1145/800186.810616, 1968.
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., and
Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from
overfitting, J. Mach. Learn. Res., 15, 1929–1958,
https://dl.acm.org/doi/10.5555/2627435.2670313, 2014.
Sun, M., Liu, S., and Liu, J.: IDW interpolation algorithm considering
spatial anisotropy, Computer Engineering and Design, 41, 983–987,
https://doi.org/10.16208/j.issn1000-7024.2020.04.014, 2020.
Szczepańska, A., Gościewski, D., and Gerus-Gościewska, M.: A
GRID-based spatial interpolation method as a tool supporting real estate
market analyses, IJGI, 9, 39, https://doi.org/10.3390/ijgi9010039, 2020.
Tamura, S. and Tateishi, M.: Capabilities of a four-layered feedforward
neural network: four layers versus three, IEEE T. Neural Networ., 8,
251–255, https://doi.org/10.1109/72.557662, 1997.
Tang, M., Wu, X., Agrawal, P., Pongpaichet, S., and Jain, R.: Integration of
diverse data sources for spatial PM2.5 data interpolation, IEEE T.
Multimedia, 19, 408–417, https://doi.org/10.1109/TMM.2016.2613639, 2017.
Tao, H., Liao, X., Zhao, D., Gong, X., and Cassidy, D. P.: Delineation of
soil contaminant plumes at a co-contaminated site using BP neural networks
and geostatistics, Geoderma, 354, 113878,
https://doi.org/10.1016/j.geoderma.2019.07.036, 2019.
Tobler, W. R.: A computer movie simulating urban growth in the Detroit
region, Econ. Geogr., 46, 234–240, https://doi.org/10.2307/143141,
1970.
Wang, D., Chen, Y., and Zhan, W.: A geometric model to simulate thermal
anisotropy over a sparse urban surface (GUTA-sparse), Remote Sens.
Environ., 209, 263–274, https://doi.org/10.1016/j.rse.2018.02.051, 2018.
Wang, Q.: The fast three-dimentional kriging interpolation method based on Delaunay, ME thesis, University of Electronic Science and Technology of China, China, 71 pp., 2015.
Watson, D. F. and Philip, G. M.: A refinement of inverse distance weighted
interpolation, Geoprocessing, 2, 315–327,
https://doi.org/10.1016/S0735-1097(97)00186-1, 1985.
Wu, S., Du, Z., Wang, Y., Lin, T., Zhang, F., and Liu, R.: Modeling
spatially anisotropic nonstationary processes in coastal environments based
on a directional geographically neural network weighted regression, Sci.
Total Environ., 709, 136097,
https://doi.org/10.1016/j.scitotenv.2019.136097, 2020.
Zeng, J., Zhang, F., Wu, S., Du, Z., and Liu, R.: Spatial interpolation
based on spatial auto-regressive neural network, Journal of Zhejiang
University (Science Edition), 47, 572–581,
https://doi.org/10.3785/j.issn.1008-9497.2020.05.009, 2020.
Zhan, J. and Wu, S.: GSARNN Code and Data, figshare [data set], https://doi.org/10.6084/m9.figshare.18739571.v1, 2023.
Zhang, X., Liu, G., Wang, H., and Li, X.: Application of a Hybrid
Interpolation Method Based on Support Vector Machine in the Precipitation
Spatial Interpolation of Basins, Water, 9, 760,
https://doi.org/10.3390/w9100760, 2017.
Zhang, Y., Hidalgo, J., and Parker, D.: Impact of variability and anisotropy
in the correlation decay distance for precipitation spatial interpolation in
China, Clim. Res., 74, 81–93, https://doi.org/10.3354/cr01486, 2017.
Zhang, Y., Feng, M., Zhang, W., Wang, H., and Wang, P.: A Gaussian process
regression-based sea surface temperature interpolation algorithm, J. Ocean.
Limnol., 39, 1211–1221, https://doi.org/10.1007/s00343-020-0062-1, 2021.
Short summary
We develop a generalized spatial autoregressive neural network model used for three-dimensional spatial interpolation. Taking the different changing trend of geographic elements along various directions into consideration, the model defines spatial distance in a generalized way and integrates it into the process of spatial interpolation with the theories of spatial autoregression and neural network. Compared with traditional methods, the model achieves better performance and is more adaptable.
We develop a generalized spatial autoregressive neural network model used for three-dimensional...