EVALUATING THE EFFICIENCY OF SPATIAL GEOSTATISTICAL METHODS FOR IDENTIFYING THE SPATIAL PATTERNS OF PRECIPITATION: A CASE STUDY OF NAMAK LAKE WATERSHED

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BAYAT BARDIA; ZAHRAIE BANAFSHEH; TAGHAVI FARAHNAZ; NASSERI MOHSEN

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Journal: IRANIAN JOURNAL OF GEOPHYSICS Year:2011 | Volume:5 | Issue:4 Page(s): 89-110

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Title

EVALUATING THE EFFICIENCY OF SPATIAL GEOSTATISTICAL METHODS FOR IDENTIFYING THE SPATIAL PATTERNS OF PRECIPITATION: A CASE STUDY OF NAMAK LAKE WATERSHED

Author(s)

BAYAT BARDIA | ZAHRAIE BANAFSHEH | TAGHAVI FARAHNAZ | NASSERI MOHSEN | Issue Writer Certificate

Keywords

BAYESIAN MAXIMUM ENTROPYQ2

KRIGINGQ2

COKRIGINGQ2

ANNUAL MEAN PRECIPITATIONQ2

GEOSTATISTICQ2

Abstract

Measurement and estimation of natural variables in space and time domains involve considerable uncertainties. Precipitation is an important hydrologic variable with a significant spatial uncertainty. Different methods have been developed to estimate areal average values of precipitation, such as Thiessen, Inverse Distance Weighting, Adaptive Inverse Distance Weighting, and KRIGING. Although these methods are simple, they suffer from lack of incorporating spatial dependencies and uncertainties of the available data.The purpose of the current research is to investigate the uncertainties of spatial precipitation over NamakLake watershed in central Iran. For this purpose, both classical and modern spatial exploration analysis methods including Ordinary KRIGING (OK) - BAYESIAN MAXIMUM ENTROPY (BME) (for univariate cases) and BME-Cokriging (for multivariate cases) methods have been used.BME is a method of spatial and spatiotemporal GEOSTATISTICs which can rigorously and efficiently incorporate uncertain features of available data. BME is the method which can provide maps with lower uncertainties and more reliable measurements with the contribution of strong mathematical computations and combination with different knowledge bases and uncertainty sources. Generally, BME processing consists of three stages: (1) The prior stage, which uses general knowledge including statistical moments (mean, variogram, and covariance) and scientific or experimental laws or theories, (2) the meta stage, which takes site-specific knowledge including hard and soft data. Hard data are measured values which are considered accurate with low error and high uncertainty and soft data are data with high error and low uncertainty can have different shapes such as interval and probabilistic, and (3) the posterior stage, which is the integration of the prior and meta stages and aims to maximize posterior probability distribution function (PDF). In this stage, the prior PDF is updated with specific data. The prior and posterior PDFs are related based on Bayes’ theorem. Based on our purpose of estimation, different conditions such as mean and mode (known as BMEmean and BMEmode) of the posterior PDF can be obtained. The BMEmean minimizes the mean square error, and the BMEmode is the most probable realization.Kriging is one of the optimum classical GEOSTATISTICal methods which can estimate unsampled stations with the contribution of sampled measurements. KRIGING is a special case of BME. Under some assumptions (considering mean and covariance as general knowledge and hard/ soft data as site-specific knowledge), kriged and BME predictions become the same. KRIGING is used in this study as a base for comparison.One hundred and five rain gauge stations are located in and around the study area, out of which 44 have full records of observations for the period of 1977 through 2008. The records of these stations are considered as the hard dataset. The remaining stations have some missing data and therefore observations in these stations are classified as the soft dataset.The stages of spatial modeling in this paper are as follows: (1) The primary processing of raw data, which includes investigating statistical missing data; the hard and soft data are distinguished in this stage. (2) The determination of variograms; the primary fitting of experimental variograms was done using GS+software based on the maximum correlation coefficient and then these parameters are optimized by the Iterated Non-linear Weighted Least Squares (INWLS) method for univariate cases and Iterated Least Squares (ILS) method for multivariate cases. (3) The application of the optimum theoretical variograms obtained through the KRIGING, COKRIGING and BME methods, and, finally, (4) the estimation of precipitation.The cross validation technique was used to evaluate the results of these two methods. The results of this study have shown that BME estimates were less biased and more accurate than those of the classical OK.

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APA: Copy

BAYAT, BARDIA, ZAHRAIE, BANAFSHEH, TAGHAVI, FARAHNAZ, & NASSERI, MOHSEN. (2011). EVALUATING THE EFFICIENCY OF SPATIAL GEOSTATISTICAL METHODS FOR IDENTIFYING THE SPATIAL PATTERNS OF PRECIPITATION: A CASE STUDY OF NAMAK LAKE WATERSHED. IRANIAN JOURNAL OF GEOPHYSICS, 5(4), 89-110. SID. https://sid.ir/paper/133748/en

Vancouver: Copy

BAYAT BARDIA, ZAHRAIE BANAFSHEH, TAGHAVI FARAHNAZ, NASSERI MOHSEN. EVALUATING THE EFFICIENCY OF SPATIAL GEOSTATISTICAL METHODS FOR IDENTIFYING THE SPATIAL PATTERNS OF PRECIPITATION: A CASE STUDY OF NAMAK LAKE WATERSHED. IRANIAN JOURNAL OF GEOPHYSICS[Internet]. 2011;5(4):89-110. Available from: https://sid.ir/paper/133748/en

IEEE: Copy

BARDIA BAYAT, BANAFSHEH ZAHRAIE, FARAHNAZ TAGHAVI, and MOHSEN NASSERI, “EVALUATING THE EFFICIENCY OF SPATIAL GEOSTATISTICAL METHODS FOR IDENTIFYING THE SPATIAL PATTERNS OF PRECIPITATION: A CASE STUDY OF NAMAK LAKE WATERSHED,” IRANIAN JOURNAL OF GEOPHYSICS, vol. 5, no. 4, pp. 89–110, 2011, [Online]. Available: https://sid.ir/paper/133748/en

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