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| Titel |
Space-Time Modelling of Groundwater Level Using Spartan Covariance Function |
| VerfasserIn |
Emmanouil Varouchakis, Dionissios Hristopulos |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250090621
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| Publikation (Nr.) |
 EGU/EGU2014-4878.pdf |
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| Zusammenfassung |
| Geostatistical models often need to handle variables that change in space and in time, such as
the groundwater level of aquifers. A major advantage of space-time observations is that a
higher number of data supports parameter estimation and prediction. In a statistical context,
space-time data can be considered as realizations of random fields that are spatially extended
and evolve in time. The combination of spatial and temporal measurements in sparsely
monitored watersheds can provide very useful information by incorporating spatiotemporal
correlations. Spatiotemporal interpolation is usually performed by applying the
standard Kriging algorithms extended in a space-time framework. Spatiotemoral
covariance functions for groundwater level modelling, however, have not been widely
developed.
We present a new non-separable theoretical spatiotemporal variogram function which is
based on the Spartan covariance family and evaluate its performance in spatiotemporal
Kriging (STRK) interpolation. The original spatial expression (Hristopulos and Elogne 2007)
that has been successfully used for the spatial interpolation of groundwater level
(Varouchakis and Hristopulos 2013) is modified by defining the following space-time
normalized distance h = °h2r-+-α h2Ï, hr=r-
ξr, hÏ=Ï-
ξÏ; where r is the spatial lag vector,
Ï the temporal lag vector, ξr is the correlation length in position space (r) and Î¾Ï in time (Ï),
h the normalized space-time lag vector, h = |h| is its Euclidean norm of the normalized
space-time lag and α the coefficient that determines the relative weight of the time
lag.
The space-time experimental semivariogram is determined from the biannual
(wet and dry period) time series of groundwater level residuals (obtained from the
original series after trend removal) between the years 1981 and 2003 at ten sampling
stations located in the Mires hydrological basin in the island of Crete (Greece). After
the hydrological year 2002-2003 there is a significant groundwater level increase
during the wet period of 2003-2004 and a considerable drop during the dry period
of 2005-2006. Both periods are associated with significant annual changes in the
precipitation compared to the basin average, i.e., a 40% increase and 65% decrease,
respectively.
We use STRK to “predict” the groundwater level for the two selected hydrological
periods (wet period of 2003-2004 and dry period of 2005-2006) at each sampling station. The
predictions are validated using the respective measured values. The novel Spartan
spatiotemporal covariance function gives a mean absolute relative prediction error of 12%.
This is 45% lower than the respective value obtained with the commonly used product-sum
covariance function, and 31% lower than the respective value obtained with a non-separable
function based on the diffusion equation (Kolovos et al. 2010). The advantage of the Spartan
space-time covariance model is confirmed with statistical measures such as the root mean
square standardized error (RMSSE), the modified coefficient of model efficiency, E′ (Legates
and McCabe, 1999) and the modified Index of Agreement, IoA′(Janssen and Heuberger,
1995).
Hristopulos, D. T. and Elogne, S. N. 2007. Analytic properties and covariance functions
for a new class of generalized Gibbs random fields. IEEE Transactions on Information
Theory, 53, 4667-4467.
Janssen, P.H.M. and Heuberger P.S.C. 1995. Calibration of process-oriented models.
Ecological Modelling, 83, 55–66.
Kolovos, A., Christakos, G., Hristopulos, D. T. and Serre, M. L. 2004. Methods for
generating non-separable spatiotemporal covariance models with potential environmental
applications. Advances in Water Resources, 27 (8), 815-830.
Legates, D.R. and McCabe Jr., G.J. 1999. Evaluating the use of “goodness-of-fit”
measures in hydrologic and hydro climatic model validation. Water Resources Research, 35,
233–241.
Varouchakis, E. A. and Hristopulos, D. T. 2013. Improvement of groundwater level
prediction in sparsely gauged basins using physical laws and local geographic features as
auxiliary variables. Advances in Water Resources, 52, 34-49. |
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