1. Regression Models for Predictions of Water Levels in the Shallow Waters of the Gulf of Mexico Kelly Torres Texas A&M University - Corpus Christi

2. Introduction Outline –Background –Overview –Water Level Predictions –Future Direction –Conclusion

3. Background Due to meteorological factors, harmonic analysis does not provide reliable predictions for the Texas Gulf Coast Harmonic Analysis Prediction (Red) vs. Actual Data (Black)

4. Background Water level forecasts are vital to the success of industry Reliable forecasts would aid in hurricane preparedness We are striving to find better forecasting methods

5. Background The Texas Coastal Ocean Observation Network (TCOON) accumulates meteorological data for over 50 stations in the coastal waters of the Gulf Coast Map of CBI Stations

6. Background Multivariate statistical predictions using linear regression produce more accurate results than harmonic analysis alone Linear Regression Prediction (Red) vs. Actual Data (Black)

7. Overview Real time data is furnished by TCOON through a web- based tool to predict water levels The idea is to predict water levels for the next two hours by using a multi-regression model

8. Overview Two hour predictions are based solely on the levels of water during the previous 48 hours We assume here that information about weather is hidden

9. Water Level Predictions National Ocean Service (NOS) Skill Assessment Statistics Criteria for the evaluation of water level forecasts  Error, Series Mean, Root Mean Square Error  Standard Deviation, Central Frequency  Positive/Negative Outlier Frequency  Maximum Duration of Positive/Negative Outlier

10. Water Level Predictions Error –Error is defined as the predicted value p minus the observed value r: e i = p i - r i Series Mean (SM) –The mean value of a time series of y: –y = (1/N)  y i Root Mean Square Error (RMSE) –Calculated as: RMSE = Sqrt ((1/N)  e i 2 )

11. Water Level Predictions Standard Deviation (SD) –Calculated as: –SD = Sqrt ((1/(N-1))  (e i - mean error) 2 ) Central Frequency (CF) –Fraction of errors that lie within the limits of + X Positive/Negative Outlier Frequency (POF/NOF) –Fraction of errors that are greater/less than + X

12. Water Level Predictions Maximum Duration of Positive/Negative Outliers (MDPO/MDNO) –A positive/negative outlier event is two or more consecutive occurrences of an error greater/less than + X –MDPO/MDNO is the length (number of consecutive occurrences) of the longest event

13. Water Level Predictions Web-based Predictions Predictions can be made for any user specified time using linear regression Coefficients are found based on date range Use coefficients in linear regression equation to predict water level values

17. Future Direction To obtain better forecasting results than what statistics alone could provide, we fused the multivariate statistical model with harmonic analysis Implement backward and forward linear regression to fill gaps in water level data Document research

18. Comments or Questions?