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Regression Models for Predictions of Water Levels in the Shallow Waters of the Gulf of Mexico Kelly Torres Texas A&M University - Corpus Christi Introduction • Outline – Background – Overview – Water Level Predictions – Future Direction – Conclusion 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) 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 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 Background • Multivariate statistical predictions using linear regression produce more accurate results than harmonic analysis alone Linear Regression Prediction (Red) vs. Actual Data (Black) 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 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 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 Water Level Predictions • Error – Error is defined as the predicted value p minus the observed value r: ei = pi - ri • Series Mean (SM) – The mean value of a time series of y: – y = (1/N) yi • Root Mean Square Error (RMSE) – Calculated as: RMSE = Sqrt ((1/N) ei2) Water Level Predictions • Standard Deviation (SD) – Calculated as: – SD = Sqrt ((1/(N-1)) (ei - 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 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 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 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 Comments or Questions?