Transcript torres-king-feb01 - Texas A&M University Corpus Christi

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?