Assessment of spatial structure of groundwater quality variables based on the entropy theory

Abstract. Fundamental to the spatial sampling design of a groundwater quality monitoring network is the spatial structure of groundwater quality variables. The entropy theory presents an alternative approach to describe this variability. A case study is presented which used groundwater quality observations (13 years; 1987-2000) from groundwater domestic wells in the Gaza Strip, Palestine. The analyses of the spatial structure used the following variables: Electrical Conductivity (EC), Total Dissolved Solids (TDS), Calcium (Ca), Magnesium (Mg), Sodium (Na), Potassium (K), Chloride (Cl), Nitrate (NO3), Sulphate (SO4), alkalinity and hardness. For all these variables the spatial structure is described by means of Transinformation as a function of distance between wells (Transinformation Model) and correlation also as a function of distance (Correlation Model). The parameters of the Transinformation Model analysed were: (1) the initial value of the Transinformation; (2) the rate of information decay; (3) the minimum constant value; and (4) the distance at which the Transinformation Model reaches its minimum value. Exponential decay curves were fitted to both models. The Transinformation Model was found to be superior to the Correlation Model in representing the spatial variability (structure). The parameters of the Transinformation Model were different for some variables and similar for others. That leads to a reduction of the variables to be monitored and consequently reduces the cost of monitoring. Keywords: transinformation, correlation, spatial structure, municipal wells, groundwater monitoring, entropy

[1]  F. J. Alonso,et al.  A state-space model approach to optimum spatial sampling design based on entropy , 1998, Environmental and Ecological Statistics.

[2]  S. Kullback,et al.  The Information in Contingency Tables , 1980 .

[3]  Vijay P. Singh,et al.  Characterizing the spatial variability of groundwater quality using the entropy theory: I. Synthetic data , 2004 .

[4]  Vijay P. Singh,et al.  Characterizing the spatial variability of groundwater quality using the entropy theory: II. Case study from Gaza Strip , 2004 .

[5]  Jan C. van der Lubbe,et al.  Information theory , 1997 .

[6]  T. Hall,et al.  Geostatistical schemes for groundwater sampling , 1988 .

[7]  Evangelos A. Yfantis,et al.  Efficiency of kriging estimation for square, triangular, and hexagonal grids , 1987 .

[8]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[9]  Ricardo A. Olea,et al.  Geostatistics for Engineers and Earth Scientists , 1999, Technometrics.

[10]  Tahir Husain,et al.  HYDROLOGIC UNCERTAINTY MEASURE AND NETWORK DESIGN1 , 1989 .

[11]  J. O. Sonuga.  Entropy principle applied to the rainfall-runoff process , 1976 .

[12]  W. J. Deutsch.  Groundwater Geochemistry: Fundamentals and Applications to Contamination , 1997 .

[13]  J. Zidek,et al.  An entropy-based analysis of data from selected NADP/NTN network sites for 1983–1986 , 1992 .

[14]  Ricardo A. Olea,et al.  Sampling design optimization for spatial functions , 1984 .

[15]  Nilgun Harmancioǧlu,et al.  Water Quality Monitoring Network Design , 1998 .

[16]  H. Loáiciga.  An optimization approach for groundwater quality monitoring network design , 1989 .

[17]  Vijay P. Singh,et al.  Application of Information Theory to Groundwater Quality Monitoring Networks , 2002 .

[18]  Michael J. Sale,et al.  Cokriging to assess regional stream quality in the Southern Blue Ridge Province , 1990 .

[19]  Hugo A. Loáiciga,et al.  An optimization method for monitoring network design in multilayered groundwater flow systems , 1993 .

[20]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[21]  G. Marsily.  Quantitative Hydrogeology: Groundwater Hydrology for Engineers , 1986 .

[22]  Vijay P. Singh,et al.  Evaluation of rainfall networks using entropy: II. Application , 1992 .