1. Integration of Statistics and Harmonic Analysis to Predict Water Levels in Estuaries and Shallow Waters of the Gulf of Mexico Texas A&M University - Corpus Christi 6300 Ocean Dr. Corpus Christi, Texas 78412 USA Alexey L. Sadovski Patrick Michaud Carl Steidley Jessica Tishmack Kelly Torres Aimee Mostella

2. There are shallow estuaries and bays on the coast of the Gulf of Mexico Tide charts, based on harmonic analysis, are inaccurate for the Texas coast Weather is a predominant factor Tide Prediction on the Texas Coast

3. Project Goals Develop effective & reliable prediction tools Developed methods: –Harmonic analysis –Numerical methods based equations of hydrodynamics –Statistical models –Neural networks

4. Texas Coastal Ocean Observation Network TCOON water level station –Data collection computer –Communication components –Environmental sensors

6. Texas Coastal Ocean Observation Network Monitors water levels and other coastal parameters along the Texas coast

7. Tide Charts In general this is the first choice Astronomical forcing –Earth, Sun, Moon motions Limitations –Areas such as the Gulf of Mexico where the dominant forcing is meteorological in nature

8. Harmonic Analysis Standard method for tide predictions Represented by constituent cosine waves with known frequencies based on gravitational (periodic) forces Elevation of water is modeled as h(t) = H 0 +  H c f y,c cos(a c t + e y,c – k c ) h(t) = elevation of water at time t a c = frequency (speed) of constituent c f y,c e y,c = node factors/equilibrium arg-s H 0 = datum offset H c = amplitude of constituent c k c = phase offset for constituent c

9. Harmonic Prediction

10. Prediction vs. Observation It’s nice when it works…

11. Prediction vs. Observation …but it often doesn’t work in Texas

12. Water Levels Tides In Texas, meteorological factors have significant effect on water elevations

13. Statistical Models Multi-regression model Unreliable model ( R<0.5 ) Based on data provided by TCOON such as: –Water level, direction and speed of wind over previous 48 hours –Temperature –Salinity

14. Two Reliable Models –Both are linear multi-regression models –Both deal with combinations of previous water levels only –Difference in models Between 4 and 8 variables in one kind of model, which takes into account first and second differences of water levels All 12 to 48 variables in the other models, in which only previous water levels are used

15. Statistical Models

16. One possible future application –Occasional losses of data Regression models, using forward and backward regression, evaluate lost data as a linear combination of forward and backward predictions with weights proportional to the distances from the edges of the gap

17. Statistical Models Statistical characteristics of prediction errors (in meters) MeanMedianStd. Dev. Min. range Max. range Error 6hr0.01240.01210.310 -0.858 0.796 Error 12hr0.01290.01170.105 -0.421 0.442 Error 18hr0.01550.01080.313 -0.951 0.866 Error 24hr0.00920.00230.177 -0.580 0.622 Error 30hr0.01760.00620.297 -0.748 0.803 Error 36hr0.01400.01980.184 -0.653 0.641 Error 42hr0.0156- 0.00340.293 -0.746 0.828 Error 48hr0.02650.02890.193 -0.568 0.593

18. Factor Analysis Question: Why do models with only previous water levels work better than models with all data provided by TCOON stations? No more than 5 factors explain over 90% of variance for water levels

19. Factor Analysis –In off-shore deep waters, the first two or three components are periodical –In coastal shallow waters and estuaries the major or the first component is not periodical –Our conclusion is that the prime factor is “weather” –Linear regression models for different locations have different coefficients for the same variables –This difference may be explained by the geography where the data is collected

20. Bob Hall Pier (014)

22. Flower Garden (028)

24. Improved Predictions Model differences between the observed water levels and the harmonic predictions by using multiple regression (so-called marriage of harmonic and regression analysis) Build a model based on past observations; use that to make a model to predict differences in future observations

25. Statistical Models

26. Predicted Levels

29. Rockport (015) Training Set - March 2003 Prediction for 48 hours

32. Bob Hall Pier (014) Training Set - March 2003 Prediction for 24 hours

34. Evaluation Criteria Criteria for the evaluation of water level forecasts –Different criteria were developed mostly by the U.S. National Oceanic and Atmospheric Administration (NOAA) to address the different priorities of coastal users

35. Evaluation Criteria Average error will address the possible bias of a model The absolute error will give information on the overall accuracy of the model Standard deviation will give information on the variability of the forecasts

36. Evaluation Criteria Specialized criteria,e.g., positive and negative outlier frequencies, will be useful to characterize model performance for unusually high or low water level situations Some forecasting methodologies will be better suited for some criteria and worse for others, e.g., predictions based on harmonic analysis are very good when evaluated by the standard deviation criteria and not as good when using the absolute error criteria.

37. Acknowledgments The work presented in this paper is funded in part by the following federal and state agencies of the U.S. –National Aeronautic and Space Agency (NASA Grant #NCC5-517) –National Oceanic and Atmospheric Administration (NOAA) –Texas General Land Office –Coastal Management Program (CMP)