Neural Network Forecasting of Neural Network Forecasting of Water Levels along the Texas Gulf Water Levels along the Texas Gulf

CoastCoast

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

Presentation OutlinePresentation 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

TidesTides

• 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?

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

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TCOON MeasurementsHarmonic Forecasts

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(c)

Tidal Charts Performance along Tidal Charts Performance along the Texas Coast (1997-2001)the Texas Coast (1997-2001)

BHP RMSE=0.12 CF=82.71

Sab. RMSE=0.16 CF=70.09

Port Isab. RMSE=0.10 CF=89.1

Coast Guard RMSE=0.12 CF=81.7

Pleasure Pier RMSE=0.16 CF=71.65Pier 21

RMSE=0.15 CF=74.37

Water Level Changes and TidesWater 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:

Differential atmospheric pressures

Wind Precipitations

Riverine inputs Evaporation

Changes in density Salinity Changes

Study Area: Corpus Christi EstuaryStudy Area: Corpus Christi Estuary

Bob Hall Pier

Packery Channel

Naval Air Station

AquariumIngleside

Port AransasNueces Bay

Corpus Christi Bay

Gulf of Mexico

Oso Bay

Port of Corpus Christi

TCOON Data Streams in the Corpus TCOON Data Streams in the Corpus Christi EstuaryChristi Estuary

Bob Hall Pier

Packery Channel

Naval Air Station

Aquarium InglesidePort Aransas

Nueces Bay

Corpus Christi Bay

Gulf of Mexico

Oso BayPort of Corpus Christi

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

• 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

Data Intensive ModelingData 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

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

Data Intensive ModelingData Intensive Modeling

Neural Network ModelingNeural 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

Neural Network FeaturesNeural Network Features

Non linear modeling capability

Generic modeling capability

Robustness to noisy data

Ability for dynamic learning

Requires availability of high density of data

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

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TCOON MeasurementsHarmonic Forecasts

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Neural Network Forecasting of Neural Network Forecasting of Water LevelsWater Levels

Philippe Tissot - 2000

H (t+i)

Output LayerHidden Layer

Wind Stress History

Water Level History

Barometric Pressure History

Wind Stress Forecast

Input Layer

Water Level Forecast

(a1,ixi)

b1

b2

(X1+b1)

b3

(X2+b2)

(X3+b3)

(a2,ixi)

(a3,ixi)

Activation FunctionsActivation Functions

xx

xx

ee

eey

2xey

xy

xey

1

1

radbas tansig

logsigpurelin

-3 -2 -1 0 1 2 3

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y = radbas(x)

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y = tansig(x)

-3 -2 -1 0 1 2 3

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y = logsig(x)

-3 -2 -1 0 1 2 3-3

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3y = purelin(x)

Training of a Neural NetworkTraining of a Neural Network

Philippe Tissot - 2000

Error SurfaceError Surface

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

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

Persistence ModelPersistence 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

Performance MeasurementsPerformance MeasurementsAverage 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.

Performance Analysis of the Performance Analysis of the Model for BHP and CCNASModel 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

BHP Performance AnalysisBHP Performance Analysis

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Forecasting Period

harmonic forecasts (blue/squares), Persistence model (green/diamonds), ANN model without wind forecasts (red dashed/triangles) and ANN model with wind forecasts

(red/circles)

CCNAS Performance AnalysisCCNAS Performance Analysis

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Forecasting Period

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)

Comparison of ANN & Harmonic Forecasts Comparison of ANN & Harmonic Forecasts for 24 Hour Forecasts (’97-’01)for 24 Hour Forecasts (’97-’01)

 BHP

Tide Tables

ANN Model

Average error (bias)

-2.7 2.9 cm

-0.4 1.7 cm

Average Absolute error

8.9 1.5 cm

6.0 0.6 cm

Normalized RMS error

0.29 0.05

0.20 0.02

POF (15 cm) 4.5% 1.9%

2.6% 1.3%

NOF (15 cm) 12.8%6.8%

3.8%2.6%

MDPO (15 cm)

67 25 hrs

24 7 hrs

MDNO (15 cm)

103 67 hrs

39 34 hrs

 CCNAS

Tide Tables

ANN Model

Average error (bias)

-2.6 2.4

-0.1 1.1 cm

Average Absolute error

8.5 1.5 cm

4.5 0.4 cm

Normalized RMS error

0.40 0.05

0.21 0.01

POF (15 cm) 4.8%

1.1%

0.9%0.4%

NOF (15 cm 11.4%5.6%

1.3%1.4%

MDPO (15 cm) 103 31 hrs

19 6 hrs

MDNO (15 cm) 205177 hrs

29 33 hrs

Comparison of ANN & Harmonic Forecasts Comparison of ANN & Harmonic Forecasts for 24 Hour Forecasts (’97-’01)for 24 Hour Forecasts (’97-’01)

 Packery Channel

Tide Tables

ANN Model

Average error (bias)

-2.6 2.2 cm

-0.2 0.8 cm

Average Absolute error

7.6 1.6 cm

3.5 0.4 cm

Normalized RMS error

0.45 0.07

0.21 0.03

POF (15 cm) 2.6%1.1%

0.4% 0.3%

NOF (15 cm) 9.6%6.4%

1.0% 1.3%

MDPO (15 cm) 77 41 hrs

14 10 hrs

MDNO (15 cm) 201187 hrs

30 38 hrs

 Tide

TablesANN

Model

Average error (bias)

-2.4 2.6 cm

-0.2 1.3 cm

Average Absolute error

8.4 1.4 cm

5.2 0.5 cm

Normalized RMS error

0.31 0.05

0.19 0.02

POF (15 cm) 4.6%1.8%

1.8% 0.6%

NOF (15 cm) 11.1%5.9%

2.2% 2.2%

MDPO (15 cm) 74 21 hrs

23 7 hrs

MDNO (15 cm) 123 81 hrs

31 37 hrs

Port Aransas

ETA-12 Forecast LocationsETA-12 Forecast Locations

Comparison Eta-12 Wind Forecasts / Comparison Eta-12 Wind Forecasts / TCOON Measurements - BiasTCOON Measurements - Bias

Model Assessment for non Storm Model Assessment for non Storm ConditionsConditions

• 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

Tropical Storms and HurricanesTropical 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?

Tropical Storm Frances - Tropical Storm Frances - September 7-17, 1998 September 7-17, 1998

Frances Trajectory

Landfall on Sept. 11

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CCNAS ANN 12-hour Forecasts During CCNAS ANN 12-hour Forecasts During 1998 Tropical Storm Frances (ANN 1998 Tropical Storm Frances (ANN

trained over 2001 Data Set)trained over 2001 Data Set)

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

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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 2002 Tropical Storms and HurricanesHurricanes

IsidoreIsidore

Landfall 9/26/2002, near New Orleans

Effect on Water Levels of 2002 Effect on Water Levels of 2002 Tropical Storms and HurricanesTropical Storms and Hurricanes

NAS: up to ~ + 80 cm BHP: up to ~ + 80 cm

Galveston Pleasure Pier: up to ~ + 110 cm Sabine: up to ~ + 80 cm

Bertha

FayeIsidore

LiliBertha

FayeIsidore

Lili

Comparison of Measured and Forecasted (12-Hour) Comparison of Measured and Forecasted (12-Hour) Water levels during the 2002 Tropical Storms and Water levels during the 2002 Tropical Storms and

Hurricanes at CCNASHurricanes at CCNAS

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Black - measurement

Blue – Harmonic

Green – Persistent

Red - ANN

ConclusionsConclusions• 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

Ongoing/Future WorkOngoing/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.

Questions?

Non-Linear Relationship Between Wind Non-Linear Relationship Between Wind Forcing and Water Level ChangesForcing and Water Level Changes

Group

(amount of errors vs. location of error)HistogramHistogram