Modeling Texas Groundwater Constituents using a Multivariate Geostatistical Model
Fatima Anderson, M.S. Candidate, Department of Statistics, Colorado State University.
Friday, July 10, 2009
10:00 a.m., 223 Weber
Most of the water used by the State of Texas comes from groundwater sources. The TGPC monitors groundwater quality for the State. In this project we construct a multivariate geostatistical model for seven constituents found in groundwater: calcium, chloride, nitrate, sodium, magnesium, sulphate, and potassium.
We first perform an exploratory analysis to understand the behavior of the data. We find no significant temporal effect in the groundwater measurements, but do see spatial patterns. Further exploratory analysis shows that the data are intrinsically correlated. That is, the spatial effects and the between-constituent effects can be modeled separately.
Our model consists of a regression piece which allows the mean to be modeled as a linear function of latitude, longitude, altitude, water depth and aquifer effect. It also consists of a covariance structure which relates the different constituents and the spatial structure. The intrinsic correlation allows us to use a Kronecker form for the covariance matrix. We construct our model for the seven constituents at one thousand randomly selected locations. We then test our model by performing prediction at locations not used in the model fitting.
Estimates of iteratively re-weighted generalized least squares converged after four iterations. To show that our assumptions are reasonable and the choice of the model is appropriate we perform residual validation and universal kriging
Dr. Dan Cooley, Advisor
Dr. Myung-Hee Lee, Committee Member
Dr. Michael J. Ronayne, Outside Member