USE OF FOURIER HARMONICS IN GROUND-WATER MODELING WITH APPLICATION TO PALEOHYDROLOGICAL SPRING DISCHARGE

Recharge is often problematic for input into mathematical ground water flow models simulating paleohydrologic conditions. Typically, paleo-precipitation data are either incomplete or non-existent for the temporal study period. However, surrogate values for ground-water recharge in paleohydrologic systems can be obtained through dendroclimatology, which provides precipitation estimates via tree-ring chronologies. A complication inherent in using tree-ring- derived surrogate recharge values is that precipitation over long periods of time is cyclic in nature. A technique is presented for analysis of cyclic dendroclimatic precipitation trends using Fourier harmonics as applied to paleohydrologic ground water modeling and simulated spring discharge. The temporal study period is from AD 600 to 1300 for the springs of the Sand Canyon and Yellow Jacket Pueblos in the Central Mesa Verde region of Colorado.

Numerical experiments on paleo-precipitation data with low-frequency filters were performed. As part of these experiments, regression statistics were calculated, and ANOVA values determined. The outputs of each of these numerical experiments were subjected to Fourier harmonic expansion through five cycles. Resultant F-values and t-statistics for the sine and cosine variable pairs were evaluated against appropriate F-critical and t-critical values for specific degrees of freedom. Additionally, the multiple-R regression statistic for each of the 25 numerical experiments performed was compared for strength of linear relationship.

Results indicate that the 6.25-year and 12.5-year paleo-precipitation harmonics are observed for both of the two springs analyzed. The 6.25-year cycle curves display more variability than the 12.5-year cycle curves. Also, in comparing Fourier expansions to modeled spring discharge rates, both the 6.25 and 12.5-year cycles accurately simulated the Sand Canyon and Yellow Jacket Pueblo spring discharge. This result suggests a direct correlation between climatic variability on a frequency comparable to the North American Monsoon with inferred recharge functions and simulated paleohydrologic system response. The Fourier harmonics technique adds validity and confidence for using surrogate recharge parameter values to derive paleohydrological model spring output.