Neural Network Forecasting of Water Levels along the Texas Gulf Coast

1. Neural Network Forecasting of Water Levels along the Texas Gulf Coast Philippe Tissot*, Daniel Cox**, Patrick Michaud* Zack Bowles*, Jeremy Stearns*, Alex Drikitis* * Conrad Blucher Institute, Texas A&M University-Corpus Christi * * Hinsdale Wave Research Laboratory, Oregon State University

2. Presentation Outline • Introduction: Tides & Water Level Forecasts • Application of ANN Modeling to Water Level Forecasts in the Corpus Christi Estuary • Test of the Model for Tropical Storms and Hurricanes • Conclusions

3. Tides • Definition: Tides are caused by the gravitational pull of the Sun and Moon on the waters of the Earth • Difference between tides and water levels • How well do the tide table work along the Gulf Coast?

4. Comparison of Tide Charts and Measured Water Levels (CCNAS 1998)

5. Tidal Charts Performance along the Texas Coast (1997-2001) Sab. RMSE=0.16 CF=70.09 Pleasure Pier RMSE=0.16 CF=71.65 Pier 21 RMSE=0.15 CF=74.37 BHP RMSE=0.12 CF=82.71 Coast Guard RMSE=0.12 CF=81.7 Port Isab. RMSE=0.10 CF=89.1

6. Water Level Changes and Tides • There is a large non tidal related component for water level changes on the Texas coast • Other factors influencing water level changes:

7. Study Area: Corpus Christi Estuary Port Aransas Nueces Bay Ingleside Aquarium Corpus Christi Bay Oso Bay Gulf of Mexico Naval Air Station Port of Corpus Christi Packery Channel Bob Hall Pier

8. TCOON Data Streams in the Corpus Christi Estuary • 6 TCOON Stations Measuring: • Water levels (6) • Wind speeds (4) • Wind directions (4) • 10 x 8760 hourly measurements per year • Barometric pressure • Air temperature • Water temperature Port Aransas Aquarium Ingleside Nueces Bay Corpus Christi Bay Gulf of Mexico Naval Air Station Packery Channel Oso Bay Port of Corpus Christi Bob Hall Pier

9. Problem: The tide charts do not work for most of the Texas coast • Opportunity: We have extensive time series of water level and weather measurements for most of the Texas coast

10. Data Intensive Modeling • Real time data availability is rapidly increasing • Cost of weather sensors and telecommunication equipment is steadily decreasing while performance is improving • How to use these new streams of data / can new modeling techniques be developed

11. Data Intensive Modeling • Classic models (large computer codes - finite elements based) need boundary conditions and forcing functions which are difficult to provide during storm events • Neural Network modeling can take advantage of high data density and does not require the explicit input of boundary conditions and forcing functions • The modeling is focused on forecasting water levels at specific locations

12. Neural Network Modeling • Started in the 60’s • Key innovation in the late 80’s: Backpropagation learning algorithms • Number of applications has grown rapidly in the 90’s especially financial applications • Growing number of publications presenting environmental applications

13. Neural Network Features • Non linear modeling capability • Generic modeling capability • Robustness to noisy data • Ability for dynamic learning • Requires availability of high density of data

14. Comparison of Tide Charts and Measured Water Levels (CCNAS 1998)

15. Neural Network Forecasting of Water Levels Water Level History  (X1+b1)  (a1,ixi) Wind Stress History  (X3+b3) b1  (a3,ixi) H (t+i) Wind Stress Forecast b3 Water Level Forecast  (a2,ixi)  (X2+b2) Barometric Pressure History b2 Input Layer Hidden Layer Output Layer Philippe Tissot - 2000

16. Activation Functions radbas tansig purelin logsig

17. Training of a Neural Network Philippe Tissot - 2000

18. Error Surface

19. CCNAS ANN 24-hour Forecasts for 1997 (ANN trained over 2001 Data Set)

20. CCNAS ANN 24-hour Forecasts for 1997 (ANN trained over 2001 Data Set)

21. Persistence Model • The water anomaly builds progressively especially for the embayment location • Persistent model: assume that the water anomaly at the time of forecasts will persist throughout the forecasting period • Compare the ANN results with the Persistence model

22. Performance Measurements Average error: Eavg = (1/N)  ei Absolute Average Error: Eavg = (1/N) ei Root Mean Square Error: Erms = ((1/N)  ei2)1/2 CF(X) – Central Frequency or percentage of the forecasts within +/- 15 cm of actual measurement POF(X) – Positive Outlier Frequency or percentage of the forecasts X cm or more above the actual measurement. NOF(X) – Negative Outlier Frequency or percentage of the forecasts X cm or more below the actual measurement. MDPO(X) – Maximum Duration of Positive Outlier. MDNO(X) – Maximum Duration of Negative Outlier.

23. Performance Analysis of the Model for BHP and CCNAS • Five 1-year data sets: ‘97, ‘98, ’99, ’00, ‘01 including water level and wind measurements, tidal forecasts and wind hindcasts • Train the NN model using one data set e.g. ‘97 for each forecast target, e.g. 12 hours • Apply the NN model to the other four data sets, • Repeat the performance analysis for each training year and forecast target and compute the model performance and variability

24. BHP Performance Analysis harmonic forecasts (blue/squares), Persistence model (green/diamonds), ANN model without wind forecasts (red dashed/triangles) and ANN model with wind forecasts (red/circles)

25. CCNAS Performance Analysis Harmonic forecasts (blue/squares), Persistent model (green/diamonds), ANN model with only NAS data (red dashed/triangles) and ANN model with additional BHP data (red/circles)

26. CCNAS Tide Tables ANN Model BHP Tide Tables ANN Model Average error (bias) -2.6  2.4 -0.1  1.1 cm Average error (bias) Average Absolute error -2.7  2.9 cm 8.5  1.5 cm 4.5  0.4 cm -0.4  1.7 cm Average Absolute error Normalized RMS error 8.9  1.5 cm 0.40  0.05 0.21  0.01 6.0  0.6 cm POF (15 cm) Normalized RMS error 0.29  0.05 4.8%  1.1% 0.9%0.4% 0.20  0.02 NOF (15 cm POF (15 cm) 4.5%  1.9% 11.4%5.6% 1.3%1.4% 2.6%  1.3% NOF (15 cm) MDPO (15 cm) 12.8%6.8% 103  31 hrs 19  6 hrs 3.8%2.6% MDPO (15 cm) MDNO (15 cm) 205177 hrs 67  25 hrs 29  33 hrs 24  7 hrs MDNO (15 cm) 103  67 hrs 39  34 hrs Comparison of ANN & Harmonic Forecasts for 24 Hour Forecasts (’97-’01)

27.  Packery Channel Tide Tables Tide Tables ANN Model ANN Model Average error (bias) Average error (bias) -2.4  2.6 cm -2.6  2.2 cm -0.2  0.8 cm -0.2  1.3 cm Average Absolute error Average Absolute error 8.4  1.4 cm 7.6  1.6 cm 3.5  0.4 cm 5.2  0.5 cm Normalized RMS error Normalized RMS error 0.31  0.05 0.45  0.07 0.21  0.03 0.19  0.02 POF (15 cm) POF (15 cm) 4.6%1.8% 2.6%1.1% 0.4%  0.3% 1.8%  0.6% NOF (15 cm) NOF (15 cm) 11.1%5.9% 9.6%6.4% 1.0%  1.3% 2.2%  2.2% MDPO (15 cm) MDPO (15 cm) 74  21 hrs 77  41 hrs 14  10 hrs 23  7 hrs MDNO (15 cm) MDNO (15 cm) 123  81 hrs 201187 hrs 30  38 hrs 31  37 hrs Comparison of ANN & Harmonic Forecasts for 24 Hour Forecasts (’97-’01) Port Aransas

28. ETA-12 Forecast Locations

29. Comparison Eta-12 Wind Forecasts / TCOON Measurements - Bias

30. Model Assessment for non Storm Conditions • ANN models and Persistence model improve considerably on the harmonic forecasts during regular conditions and frontal passages • ANN and Persistence models are being implemented as part of TCOON

31. Tropical Storms and Hurricanes • Need for short to medium term water level forecasts during tropical storms and hurricanes • Tropical storms and hurricanes are relatively infrequent and have each their own characteristics. • ANN model performance?

32. Tropical Storm Frances - September 7-17, 1998 Frances Trajectory Landfall on Sept. 11

33. CCNAS ANN 12-hour Forecasts During 1998 Tropical Storm Frances (ANN trained over 2001 Data Set)

34. CCNAS ANN 24-hour Forecasts During 1998 Tropical Storm Frances (ANN trained over 2001 Data Set)

35. Storm Name Storm Type at Landfall Landfall Locations Landfall Date Lili H Vermillion Bay 10/03/2002 Isidore TS New Orleans 9/26/2002 Faye TS Palacios 9/7/2002 Bertha D Port Mansfield 8/9/2002 2002 Tropical Storms and Hurricanes

36. Isidore Landfall 9/26/2002, near New Orleans

37. Effect on Water Levels of 2002 Tropical Storms and Hurricanes Isidore Isidore Faye Faye Lili Lili Bertha Bertha NAS: up to ~ + 80 cm BHP: up to ~ + 80 cm Galveston Pleasure Pier: up to ~ + 110 cm Sabine: up to ~ + 80 cm

38. Comparison of Measured and Forecasted (12-Hour) Water levels during the 2002 Tropical Storms and Hurricanes at CCNAS Black - measurement Blue – Harmonic Green – Persistent Red - ANN

39. Conclusions • ANN models leads to significant improvements for the forecasting of water levels in general and especially during frontal passages • Computationally and financially inexpensive method • The quality of the wind forecasts will likely be the limiting factor for the accuracy of the water level forecasts • Implementing ANN model on a number of TCOON stations • The persistence model results are comparable to ANN forecasts for a number of cases and a great improvement over tide tables in all cases

40. Ongoing/Future Work • Implement the Persistence model for most TCOON stations with the necessary water level history. • Implement a real time transfer of NWS Eta-12 wind forecasts into TCOON and the ANN models • Implement the ANN model for selected stations (~ 10) important to coastal users • Study and document the performance of the models (Persistent/ANN) during the past TS and Hurricanes.

41. Questions?

42. Non-Linear Relationship Between Wind Forcing and Water Level Changes Group

43. Histogram (amount of errors vs. location of error)