Data Assimilation in Groundwater Quality Models Using Kriging. Part I
Dataverwerking in grondwaterkwaliteitsmodellen met behulp van Kriging. Deel I
Zhang XF, van Eijkeren JCH, Heemink AW
RIVM Rapport 959101008
As part of a research program directed towards the development of data assimiliation procedures for environmental models, in this report kriging techniques to integrate models and monitoring networks are studied. Simulated data are obtained from a random concentration field Z(x,t) which is generated as a sum of a deterministic component mu (x,t) giving the main trend of Z (x,t) and a stochastic component e (x) giving the natural variation of Z (x,t) around mu (x,t) with zero mean, constant variance and high spatial correlation. The deterministic part mu (x,t) with known mu (x,0) is formed as a superposition of a constant background concentration field and a rotating cone interpreted as the representation of a local pollution. To integrate models and data simple kriging and universal kriging techniques are implemented and compared. In each experiment the number of observations N is varied, as well as the spatial observation pattern which may be regular or irregular. Every case is subdivided into the situations that the spatial correlation structure, i.e. the semivariogram, is known or not. The method for fitting a semivariogram model is also investigated. In particular, some drawbacks existing in a popularly used cost criterion of weighted least squares method for fitting a semivariogram model are pointed out, and a new cost criterion is proposed. The simulation study illustrates the advantages of the proposed new cost criterion. Further, for a specified underlying realization of a stochastic process, different semivariogram models are employed for kriging. Since the real concentration is known in all these cases, the data assimilation methods are quantitatively compared with the real concentration field. In the next research phases emphasis will be on the elaboration of data assimilation procedures, the testing of their applicability in practice under various conditions, and if necessary and feasible the incorporation of more physics-based information into procedures.