Weeki Wachee River System Recommended Minimum Flows and ...

similarly across the springsheds examined, then anthropogenic factors acting
disproportionately between one springshed and another should show up as departures
between plotted z-sores. Converting spring flows (or water well elevations) to z-scores
allows a direct comparison between spring flows of different springsheds or water
levels. In the absence of anthropogenic effects in the two watersheds, it might be
expected that the normalized historic flows should be correlated. For example, flows for
Weeki Wachee River, and Rainbow River were converted to z-scores using the mean
and standard deviations for the period 1935 to 1965. The data were then plotted for the
entire period of record with the assumption that the relationship between z-scores for
the standardization period (1935 to 1965 in this case) should be maintained for other
periods as long as other effects (e.g., anthropogenic withdrawals) did not vary among
the periods examined. Any deviation represents the anthropogenic affect relative to the
standardization period. To minimize reliance on a particular reference period, a number
of different standardization periods (1935-65, 1945-65, 1951-63 etc) were evaluated
and the strongest relationships were used (See Kelly et al. 2006 for examples). In
application, the mean difference in z-scores of the non-reference period is converted
back into flow by multiplying the difference by the standard deviation (in cfs) of the
reference period.
Using the z-score approach, the estimated anthropogenic loss (relative to Rainbow
River and 1951- 63 standardization period) is 11 cfs. A similar comparison with the
Sharpes Ferry water level resulted in an estimated loss of 16.3 cfs.
2.5.2 Wavelet Analysis
Wavelet transformation of times-series discharge data was undertaken to reduce the
short-term fluctuations for the period 1941 through 2004. The application is described in
more detail in a technical memorandum by Schultz (2007) which is included as
Appendix 2-1. The untransformed annual values and the wavelet filtered time series is
given in Figure 2-14. Using the smoothed data as input to a regression model, Schultz
analyzed the relationship to rainfall as a continuous variable and to the impact of
pumpage as a categorical variable using a regression of the form:
Smoothed Discharge = β o + β 1 * Rain + β 2 * Impact + ε
"Impact" was defined as insignificant (= 0) or significant (=1) and was assumed to
continue through time once the impact of withdrawals became significant.
The solution employed was to allow the regression model to determine the point at
which pumpage impacts became significant. The initial run (1941-2004) assumed that
all years were impacted. The second run assumed that years 1942 – 2004 were
impacted. The third run assumed that years 1943 – 2004 were impacted etc until the
point of impact was evaluated for all 64 starting points. F-test and r 2 results were
compared. Same year (Lag 0 ), prior year (Lag 1 ) and rainfall from two years ago (Lag 2 )
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Proposed Minimum Flows and Levels for Weeki Wachee River Page 30 of 164
Watershed Characteristics