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 USA Alexey L. Sadovski Patrick Michaud Carl Steidley Jessica Tishmack Kelly Torres Aimee Mostella

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

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

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

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

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

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

Harmonic Prediction

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

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

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

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

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

Statistical Models

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

Statistical Models Statistical characteristics of prediction errors (in meters) MeanMedianStd. Dev. Min. range Max. range Error 6hr Error 12hr Error 18hr Error 24hr Error 30hr Error 36hr Error 42hr Error 48hr

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

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

Bob Hall Pier (014)

Flower Garden (028)

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

Statistical Models

Predicted Levels

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

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

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

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

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.

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)