MODFLOW 2000 Head Uncertainty, a First-Order Second Moment Method

Ground Water
By: , and 



A computationally efficient method to estimate the variance and covariance in piezometric head results computed through MODFLOW 2000 using a first-order second moment (FOSM) approach is presented. This methodology employs a first-order Taylor series expansion to combine model sensitivity with uncertainty in geologic data. MODFLOW 2000 is used to calculate both the ground water head and the sensitivity of head to changes in input data. From a limited number of samples, geologic data are extrapolated and their associated uncertainties are computed through a conditional probability calculation. Combining the spatially related sensitivity and input uncertainty produces the variance-covariance matrix, the diagonal of which is used to yield the standard deviation in MODFLOW 2000 head. The variance in piezometric head can be used for calibrating the model, estimating confidence intervals, directing exploration, and evaluating the reliability of a design. A case study illustrates the approach, where aquifer transmissivity is the spatially related uncertain geologic input data. The FOSM methodology is shown to be applicable for calculating output uncertainty for (1) spatially related input and output data, and (2) multiple input parameters (transmissivity and recharge).

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title MODFLOW 2000 Head Uncertainty, a First-Order Second Moment Method
Series title Ground Water
DOI 10.1111/j.1745-6584.2003.tb02603.x
Volume 41
Issue 3
Year Published 2003
Language English
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Ground Water
First page 342
Last page 350
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