Skip to main content
SpringerLink
Log in

Sensitivity of Spatial Analysis Neural Network Training and Interpolation to Structural Parameters

  • Published:
Mathematical Geology Aims and scope Submit manuscript

Abstract

A Spatial Analysis Neural Network (SANN) algorithm was applied for the analysis of geospatial data, on the basis of nonparametric statistical analysis and the concepts of traditional Artificial Neural Networks. SANN consists of a number of layers in which the neurons or nodes between layers are interconnected successively in a feed-forward direction. The Gaussian Kernel Function layer has several nodes, and each node has a transfer or an activation function that only responds (or activates) when the input pattern falls within its receptive field, which is defined by its smoothing parameter or width. The activation widths are functions of the model structural parameters, including the number of the nearest neighbor points P and a control factor F. The estimation method is based on two operational modes, namely, a training-validation mode in which the model structure is constructed and validated, and an interpolation mode. In this paper we discuss the effect of varying F and P upon the accuracy of the estimation in a two-dimensional domain for different input field sizes, using spatial data of wheat crop yield from Eastern Colorado. Crop yield is estimated as a function of the two-dimensional Cartesian coordinates (easting and northing). The results of the research led to the conclusion that optimal values of F and P depend on the sample size, i.e., for small data sets F=1.5 and P=7 while for large data sets F=2.5 and P=9. In addition, the accuracy of the interpolated field varies with the sample size. As expected for small sample sizes, the interpolated field and its variability may be significantly underestimated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Ahmed, S., and De Marsily, G., 1987, Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity: Water Resourc. Res., v. 23, no. 9, p. 1717–1737.

    Google Scholar 

  • ASCE Task Committee on Geostatistical Techniques, 1990, Review of Geostatistics in Geohydrology: I. Basis Concepts, J. of Hydraulic Engineering, v. 116, no. 5, p. 612–632.

    Google Scholar 

  • Aziz, A. R. A., and Wong, K. F. V., 1992, Neural network approach to the determination of aquifer parameters: Ground Water, v. 30, no. 2, p. 164–166.

    Google Scholar 

  • Bedient, P. B., and Huber, W. C., 1992, Hydrology and flood plains analysis: Addison-Wesley, Reading, MA, 692 p.

    Google Scholar 

  • Bishop, C. M., 1995, Neural networks for pattern recognition: Clarendon Press, Oxford, 482 p.

    Google Scholar 

  • Bonafe, A., Galeati, G., and Sforna, M., 1994, Neural networks for daily mean flow forecasting: Hydr. Engr. Software V: ComputationalMechanics Publications, Southampton, UK, Vol. 1, p. 131–138.

    Google Scholar 

  • Creutin, J. D. and Obled, C., 1982, Objective analyses and mapping techniques for rainfall fields: An objective comparison, Water Resources Res., v. 18p. 413–431.

    Google Scholar 

  • Dawson, C.W., and Wilby, R., 1998, An artificial neural network approach to rainfall-runoffmodeling: Hydrol. Sci., v. 43, no. 1, p. 47–66.

    Google Scholar 

  • Fernando, D. A. K., and Jayawardena, A.W., 1998, Runoff forecasting using RBF networks with OLS algorithm: J. Hydrol. Eng. ASCE, v. 3, no. 3, p. 203–209.

    Article  Google Scholar 

  • French, M. N., Krajewski, W. F., and Cuykendal, R. R., 1992, Rainfall forecasting in space and time using a neural network: J. Hydrol., v. 137, p. 1–37.

    Article  Google Scholar 

  • Goovaerts, P., 2000, Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall: J. Hydrol., v. 228, p. 113–129.

    Article  Google Scholar 

  • Govindaraju, R. and Rao, A. R., 2000, Artificial neural networks in hydrology: Kluwer Academic, Dordrecht, 329 p.

    Google Scholar 

  • Hayken, S. S., 1994, Neural networks: A comprehensive foundation: MacMillan College, New York, 696 p.

    Google Scholar 

  • Hjelmfelt, A. T. and Wang, M., 1996, Predicting runoff using artificial neural networks: Surf. Water Hydrol., p. 233–244.

  • Hoeksema, R. J., Clapp, R. B., Thomas, A. L., Hunley, A. E., Farrow, N. D., and Dearstone, K. C., 1989, Cokriging model for estimation of water table elevation: Water Resour. Res., v. 25, no. 3, p. 429–438.

    Google Scholar 

  • Hsu, K., Gao, X., Sorooshian, S., and Gupta, H.V., 1997, Precipitation estimation from remotely sensed information using artificial neural networks: J. Appl. Meteorol., v. 36, no. 9, p. 1176–1190.

    Article  Google Scholar 

  • Hsu, K., Gupta, H. V., and Sorooshian, S., 1995, Artificial neural network modeling of the rainfall-runoff process: Water Resour. Res., v. 31, no. 10, p. 2517–2530.

    Article  Google Scholar 

  • Islam, S. and Kothari, R., 2000, Artificial neural networks in remote sensing of hydrologic processes: J. Hydrol. Eng. ASCE, v. 5, no. 2, p. 138–144.

    Article  Google Scholar 

  • Kuligowski, R. J., and Barros, A. P., 1998, Experiments in short-term precipitation forecasting using artificial neural networks: Mon. Weather Rev., v. 126, no. 2, p. 470–482.

    Article  Google Scholar 

  • Kyriakidis, P. C. and Journel, A. G., 1999, Geostatistical space-time models: A review: Math. Geol., v. 31, no. 6, p. 651–684.

    Article  Google Scholar 

  • Luthi, S. M. and Bryant, I. D., 1997, Well-log correlation using a back-propagation neural network: Math. Geol., v. 29, no. 3, p. 413–425.

    Google Scholar 

  • Maier, H. R., and Dandy, G. C., 1996, The use of artificial neural networks for the prediction of water quality parameters: Water Resour. Res., v. 32, no. 4, p. 1013–1022.

    Article  Google Scholar 

  • Masters, T., 1994. Advanced algorithms for neural networks: A C++ source book: Wiley, New York p. 158–191.

    Google Scholar 

  • McCuen, R. H., 1998, Hydrologic analysis and design, 2nd Edition, Prentice Hall, New Jersey, 814 pp.

    Google Scholar 

  • Moody, J. E., and Darken, D. J., 1989, Fast learning in networks of locally-tuned processing units: Neural Comput., 1, p. 281–294.

    Google Scholar 

  • Musavi, M. T., Chan, K. H., Hummels, D. M., Kalantri, K., and Ahmed, W., 1992, A probabilistic model for evaluation of neural networks classifiers: Pattern Recognit., v. 25, no. 10, p. 1241–1251.

    Article  Google Scholar 

  • Olea, R. A., 1984, Sampling design optimization for spatial functions: Math. Geol., v. 16, no. 4, p. 369–392.

    Google Scholar 

  • Rizzo, D.M., and Dougherty, D. E., 1994, Characterization of aquifer properties using artificial neural networks: Neural kriging: Water Resour. Res., v. 30, no. 2, p. 483–497.

    Article  Google Scholar 

  • Saha, A., and Keeler, J. D., 1990, Algorithms for better representation and faster learning in radial basis function networks, inAdvances in Neural Information Processing Systems 2, Touretzky, D. S., et al., eds., Morgan Kaufmann, San Mantec, CA, v. 2, p. 482–489.

    Google Scholar 

  • Salas, J. D., Markus, M., and Tokar, A. S., 2000, Streamflow forecasting based on artificial neural networks, Chapter 4 inArtificial neural networks in hydrology, G. Rao and A. R. Rao, eds., Kluwer Academic Publishers, London, p. 23–51.

    Google Scholar 

  • Sanchez, L., Arroyo, V., Garcia, J., Koev, K. and Revilla, J., 1998, Use of neural networks in design of coastal sewage systems: J. Hydr. Eng. ASCE, v. 124, no. 5, p. 457–464.

    Article  Google Scholar 

  • Shin, H. S., and Salas, J. D., 2000, Spatial analysis of hydrologic and environmental data based on artificial neural networks, Chapter 13 inArtificial neural networks in hydrology, G. Rao and A. R. Rao, eds., Kluwer Academic Publishers, London, p. 259–286.

    Google Scholar 

  • Singer, D. A., and Kouda, R., 1996, Application of a feedforward neural network in the search for Kuroko deposits in the Hokuroku Distric, Japan: Math. Geol., v. 28, no. 8, p. 1017–1023.

    Google Scholar 

  • Smith, J., and Eli, R. N., 1995, Neural-network models of rainfall-runoff process: J. Water Resour. Plang. Mgmt. ASCE, v. 121, no. 6, p. 499–508.

    Article  Google Scholar 

  • Specht, D. F., 1991, A general regression neural network: IEEE Trans. Neural Netw., v. 2, no. 6, p. 568–576.

    Article  Google Scholar 

  • Tabios, G. Q., and Salas, J. D., 1985, A comparative analysis of techniques for spatial analysis interpolation of precipitation: Water Resour. Bull., v. 21, no. 3, p. 365–380.

    Google Scholar 

  • Tokar, A. S., and Johnson, P. A., 1999, Rainfall-runoff modeling using artificial neural networks: ASCE J. Hydrol. Engr., v. 4, no. 3, p. 232–239.

    Article  Google Scholar 

  • Tsoukalas, L. H., and Uhrig, R. E., 1997, Fuzzy and neural approaches in engineering: Wiley Interscience; New York, 587 p.

    Google Scholar 

  • Zimmerman, D., Pavlik, C., Ruggles, A., and Armstrong, M. P., 1999, An experimental comparison of ordinary and universal Kriging and inverse distance weighting: Math. Geol., v. 31, no. 4, p. 375–390.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Colorado State University, B208 Engr. Bldg., Fort Collins, Colorado, 80523, USA

    Ana Martinez & Jose D. Salas

  2. USDA-ARS, Great Plains Systems Research Unit, Fort Collins, Colorado, USA

    Timothy R. Green

Authors
  1. Ana Martinez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jose D. Salas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Timothy R. Green
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martinez, A., Salas, J.D. & Green, T.R. Sensitivity of Spatial Analysis Neural Network Training and Interpolation to Structural Parameters. Mathematical Geology 36, 721–742 (2004). https://doi.org/10.1023/B:MATG.0000039543.89653.57

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:MATG.0000039543.89653.57

Search

Navigation