Compilation of the Fourier Analysis Results

Compilation of the Fourier Analysis Results

The following is a compilation of the fourier analysis for all of the river segments analyzed. The sites are in downstream order, starting with Lake Austin.

Segment 1403

Lake Austin, Site #1403.0100

The descriptive statistics for the two data sets:

The statistics for the regression analysis of the two data sets:

The plot of the best fit lines for the two data sets:

Comparing the means of the two data sets as determined by the two types of analysis:

Method	LCRA (n=27) Mean ± Standard Error	CRWN (n=90) Mean ± Standard Error
Standard Statistics	8.53 ± 0.30 mg/l	8.05 ± 0.17 mg/l
Fourier Analysis (Intercept)	8.70 ± 0.19 mg/l	8.19 ± 0.14 mg/l

There is good agreement between the two methods as shown above. The mean values determined by standard statistics and fourier analysis are within the margins of error. The CRWN data is well distributed temporally with at least one measurement per month throughout the time period analyzed. The difference in the mean of the two data sets is about 0.5 mg/l with both types of analysis.

Segment 1434

Bastrop #1428.0600

The descriptive statistics for the two data sets:

The statistics for the regression analysis of the two data sets:

The plot of the best fit lines for the two data sets:

The plots of the best-fit lines for the two data sets show a phase shift with the maximum peaks differing by 14 days and the minimums by 40 days.

Comparing the means of the data sets determined by the two methods:

Method	LCRA (n=26) Mean ± Standard Error	CRWN (n=104) Mean ± Standard Error
Standard Statistics	8.96 ± 0.34 mg/l	9.35 ± 0.19 mg/l
Fourier Analysis (Intercept)	9.04 ± 0.21 mg/l	8.55 ± 0.29 mg/l

The means of the LCRA data sets as determined by the two methods are in good agreement, differing by only 0.08 mg/l. The means of the CRWN data are considerably different, though, differing by 0.80 mg/l. The mean of the CRWN data set calculated by the fourier method is the lower value. The CRWN data set lacks summer data.

Smithville #1403.0100

The descriptive statistics for the two data sets:

The statistics for the regression analysis of the two data sets:

The plot of the best fit lines for the two data sets:

Comparing the means of the two data sets as determined by the two types of analysis:

Method	LCRA (n=23) Mean ± Standard Error	CRWN (n=39) Mean ± Standard Error
Standard Statistics	8.59± 0.32 mg/l	7.73 ± 0.36 mg/l
Fourier Analysis (Intercept)	8.52 ± 0.20 mg/l	7.57 ± 0.89 mg/l

The mean values determined by the two methods for the data sets are very close. The means for the LCRA data differ by only 0.07 mg/l and the CRWN data by 0.16 mg/l. The means of the two data sets differ from one another by almost 1.1 mg/l with both methods.

Segment 1402

LaGrange, Site #1402.0400

The descriptive statistics for the two data sets:

The statistics for the regression analysis of the two data sets:

The plot of the best fit lines for the two data sets:

Comparing the means of the two data sets as determined by the two types of analysis

Method	LCRA (n=13) Mean ± Standard Error	CRWN (n=34) Mean ± Standard Error
Standard Statistics	8.38 ± 0.25 mg/l	9.44 ± 0.40 mg/l
Fourier Analysis (Intercept)	8.42 ± 0.17 mg/l	8.75 ± 0.49 mg/l

The difference between the means of the two data sets is much lower with the fourier analysis, 0.33 mg/l with the fourier and 1.06 with standard statistics.

Columbus, Site #1402.0250

The descriptive statistics for the two data sets:

The statistics for the regression analysis of the two data sets:

The plot of the best fit lines for the two data sets:

Comparing the mean values determined by the two methods:

Method		LCRA (n=26) Mean ± Standard Error		CRWN (n=63) Mean ± Standard Error
Standard Statistics	7.70 ± 0..21 mg/l		7.98 ± 0.23 mg/l
Fourier Analysis (Intercept)	7.75 ± 0.16 mg/l		7.56 ± 0.28 mg/l

The mean values of the two data sets as determined by the two types of analysis are in good agreement. The two means for each data set are within the error range. The mean for the CRWN data is considerably lower when calculated by the fourier series method. Again, this is probably due to the lack of summer data for CRWN data set.