The dependent variable of Secchi Depth was explored for its correlation to the independent variable of Turbidity.

Transcription

1 November 4, 9 Mr. Trent Martin Watershed Protection Group Harris County Storm Water Quality Section 98 Northwest Freeway, Suite 35 Houston, Texas 779 RE: Statistical Analysis Dear Mr. Martin: Dannenbaum Engineering Corporation is pleased to submit this technical memo detailing the statistical analysis performed on several samples from the Brazos River Authority, Lavaca Navidad River Authority, Nueces River Authority, Sabine River Authority and the Trinity River Authority. The analysis was performed to investigate trends in the samples by correlation of defined independent variables. The dependent variable of Secchi Depth was explored for its correlation to the independent variable of Turbidity. Definitions Turbidity A measure of water clarity which describes how much the material suspended in water decreases the passage of light through the water. Secchi Depth The depth at which a Secchi disk is no longer visible from the surface of a body of water. Analysis Methodology The general methodology was to produce a graphical x-y comparison for the analyzed pair of variables. The dependent variable was plotted against the independent variable. Using one of several regression methods, the best curve-fit to the data was performed with an analytical relationship established with a corresponding correlation coefficient squared (r ) value. Then a Spearman statistical test for correlation was performed on the data to establish an r s statistic value indicative of a correlation between the two variables. The r s values obtained from the Spearman test were assessed based on established statistical rules that r s <.5 indicated a weak correlation while.5 r s. was indicative of a strong correlation. A negative r s statistic indicates an inverse correlation. C:\Documents and Settings\hsanders\Desktop\Research\Turbidity_SecchiDepth_Analysis.doc

2 Study Results In total, 695 samples were considered. Measurements taken both in the field and in a lab were considered. In some samples, the reported Secchi depths and turbidities were given as either greater than or less than a particular value instead of a specific depth or turbidity. One analysis was performed in which the value that the actual value was reported as being greater or less than was taken as the actual value. Another analysis was performed in which these indefinite values were discarded, analyzing only the 6793 definite values. In addition, each set of data reported by the respective river authorities was analyzed individually with indefinite values excluded to check for potential systemic error. The following analyses results were obtained: Turbidity Vs Secchi Depth With Indefinite Values Included The dependent Secchi Depth was plotted against the independent variable Turbidity. The plot is shown in Attachment a. The best regression fit was a power equation with r value of This indicated a strong relationship between turbidity and Secchi depth. The relationship obtained was y=.7786x -.54 where y is the Secchi depth in Meters and x is turbidity in NTU. A non-parametric test for correlation, Spearman s test, was performed to test for any correlation between the two variables. The results of the test can be seen in Attachment b. A negative r s correlation statistic of.84 was attained. This was an indication that within 95% confidence intervals there was a strong inverse correlation between instantaneous turbidity and Secchi depth. Turbidity Vs Secchi Depth With Indefinite Values Excluded The dependent Secchi Depth was plotted against the independent variable Turbidity. The plot is shown in Attachment a. The best regression fit was a power equation with r value of.69. This indicated a strong relationship between turbidity and Secchi depth. The relationship obtained was y=.973x where y is the Secchi depth in Meters and x is turbidity in NTU. A non-parametric test for correlation, Spearman s test, was performed to test for any correlation between the two variables. The results of the test can be seen in Attachment b. A negative r s correlation statistic of.84 was attained. This was an indication that within 95% confidence intervals there was a strong inverse correlation between instantaneous turbidity and Secchi depth. Individual River Authority Data Analysis For each set of samples given by the respective river authorities, the dependent Secchi Depth was plotted against the independent variable Turbidity, and the best fitting power equation r value C:\Documents and Settings\hsanders\Desktop\Research\Turbidity_SecchiDepth_Analysis.doc

3 was determined. The results of this analysis can be found in the appendix, and a summary of these values is given in Table. For each set of samples given by the respective river authorities, a non-parametric test for correlation, Spearman s test, was performed to test for any correlation between the two variables. The results of this analysis can be found in the appendix, and a summary of the resulting rs statistics is given in Table. Conclusion and Summary Data Source Table Power Equation r^ value rs Statistic n-value BRA LNRA NRA SRA TRA The results of the analysis show a strong, inverse relationship between the water properties of Turbidity and Secchi Depth. If you have any questions or need additional information, please do not hesitate to let us know. Sincerely yours, DANNENBAUM ENGINEERING CORPORATION Elizabeth Parent, P.E., CFM Project Manager C:\Documents and Settings\hsanders\Desktop\Research\Turbidity_SecchiDepth_Analysis.doc

4 Secchi Depth in Meters Attachment a 5 5 Secchi Depth Power (Secchi Depth) 5 y =.7786x -.54 R² = Turbidity in NTU

5 TRANSPARENCY, SECCHI DISC (METERS) Test Correlation - Spearman Attachment b TURBIDITY, NEPHELOMETRIC TURBIDITY UNITS, N v TRANSPARENCY, SECCHI DISC (METERS). rs Performed by todd.ward Date 7 September 9 v. n 695 rs statistic % CI -.85 to -.83 (normal approximation) t statistic DF 693 -tailed p <. (t approximation, corrected for ties) 7 Scatter Plot TURBIDITY, NEPHELOMETRIC TURBIDITY UNITS, N Page of

6 Secchi Depth in Meters Attachment a 8 6 Secchi Depth Power (Secchi Depth) 4 y =.973x R² = Turbidity in NTU

7 Transperency, Meters Test Correlation - Spearman Attachment b Turbidity, NTU v Transperency, Meters. rs Performed by todd.ward Date October 9 v. n 6793 rs statistic % CI -.84 to -.83 (normal approximation) t statistic -5.8 DF 679 -tailed p <. (t approximation, corrected for ties) 7 Scatter Plot Turbidity, NTU Page of

8 Secchi Depth in Meters 9 BRA Data Secchi Depth Power (Secchi Depth) 3 y =.555x R² = Turbidity in NTU

9 78 (m) Test Correlation - Spearman BRA 879 (NTU) v 78 (m). rs Performed by todd.ward Date October 9 v. n 9 rs statistic % CI -.8 to -.77 (normal approximation) t statistic DF 7 -tailed p <. (t approximation, corrected for ties) 7 Scatter Plot (NTU) Page of

10 Secchi Depth in Meters.8 LNRA Data Secchi Depth Power (Secchi Depth).6.4 y =.584x R² = Turbidity in NTU

11 Secchi Depth Test Correlation - Spearman LNRA Turbidity v Secchi Depth. rs Performed by todd.ward Date October 9 v. n 83 rs statistic % CI -.69 to -.55 (normal approximation) t statistic -3.5 DF 8 -tailed p <. (t approximation, corrected for ties).8 Scatter Plot Turbidity Page of

12 Secchi Depth in Meters.5 NRA Data..5 Secchi Depth Power (Secchi Depth)..5. y =.66x -.53 R² = Turbidity in NTU

13 SECCHI DEPTH Test Correlation - Spearman NRA TURBIDITY v SECCHI DEPTH. rs Performed by todd.ward Date October 9 v. n 7 rs statistic % CI -.78 to -.63 (normal approximation) t statistic -3.3 DF 69 -tailed p <. (t approximation, corrected for ties) Scatter Plot TURBIDITY Page of

14 Secchi Depth in Meters 4 SRA Data Secchi Depth Power (Secchi Depth).5.5 y =.658x -.57 R² = Turbidity in NTU

15 SECCHI - METERS Test Correlation - Spearman SRA TURBIDTY - NTU v SECCHI - METERS. rs Performed by todd.ward Date October 9 v. n 898 (cases excluded: 7 due to missing values) rs statistic % CI -.9 to -.88 (normal approximation) t statistic DF 896 -tailed p <. (t approximation, corrected for ties) 4 Scatter Plot TURBIDTY - NTU Page of

16 Secchi Depth in Meters 8 TRA Data Secchi Depth Power (Secchi Depth) 3 y =.54x -.67 R² = Turbidity in NTU

17 TRANSPARENCY, SECCHI DISC (METERS) Test Correlation - Spearman TRA TURBIDITY,LAB NEPHELOMETRIC TURBIDITY UNITS, NTU v TRANSPARENCY, SECCHI DISC (METERS). r Performed by todd.ward Date October 9 v. n 594 rs statistic % CI -.85 to -.8 (normal approximation) t statistic DF 59 -tailed p <. (t approximation, corrected for ties) 3.5 Scatter Plot TURBIDITY,LAB NEPHELOMETRIC TURBIDITY UNITS, NTU Page of