philippe tissot, patrick michaud, daniel cox**

Optimization and Performance of a Neural Network Model

Forecasting Water Levels for the Corpus Christi, Texas, Estuary

Philippe Tissot*, Patrick Michaud*, Daniel Cox**Philippe Tissot*, Patrick Michaud*, Daniel Cox**

*Texas A&M University-Corpus Christi, Corpus *Texas A&M University-Corpus Christi, Corpus Christi, TexasChristi, Texas

**Oregon State University, Corvallis, Oregon**Oregon State University, Corvallis, Oregon

Texas A&M University-Corpus Christi Division of Near Shore Research

Presentation Outline

Texas Coastal Ocean Observation Network Texas Coastal Ocean Observation Network (TCOON)(TCOON)

Tides and Water Levels in the Gulf of MexicoTides and Water Levels in the Gulf of Mexico Artificial Neural Network Forecasting of Water Artificial Neural Network Forecasting of Water

Levels and Application to the Corpus Christi Levels and Application to the Corpus Christi EstuaryEstuary

ANN Performance for Water Level ForecastingANN Performance for Water Level Forecasting ANN performance during a Tropical StormANN performance during a Tropical Storm Conclusions Conclusions


Texas Coastal Observation Network (TCOON)

Started 1988Started 1988 Over 50 stationsOver 50 stations Primary SponsorsPrimary Sponsors

General Land OfficeGeneral Land Office Water Devel. BoardWater Devel. Board US Corps of EngUS Corps of Eng Nat'l Ocean ServiceNat'l Ocean Service


Typical TCOON station

Wind anemometerWind anemometer Radio AntennaRadio Antenna Satellite TransmitterSatellite Transmitter Solar PanelsSolar Panels Data CollectorData Collector Water Level SensorWater Level Sensor Water Quality SensorWater Quality Sensor Current MeterCurrent Meter


TCOON Web Site


Tides and Water Levels

Tide: The periodic rise and fall of a body of Tide: The periodic rise and fall of a body of water resulting from gravitational water resulting from gravitational interactions between Sun, Moon, and Earth.interactions between Sun, Moon, and Earth.

Tide and Current GlossaryTide and Current Glossary, National Ocean Service, 2000, National Ocean Service, 2000

Water Levels: Astronomical + Meteorological Water Levels: Astronomical + Meteorological forcing + Other effectsforcing + Other effects


Study Site: CC Estuary

Bob Hall Pier

Packery Channel

Naval Air Station

AquariumIngleside

Port AransasNueces Bay

Corpus Christi Bay Gulf of

Mexico

Oso BayPort of Corpus Christi


Comparison of Tides and Water Levels

TCOON MeasurementsTide Tables

Corpus Christi Naval Air Station


Comparison of Tides, Water Levels, and Winds (squared)

Wa

ter

Le

ve

l (m

)

0 50 100 150 200 250 300 350 400-0.5

0

0.5

Wa

ter

An

om

aly

(m

)

0 50 100 150 200 250 300 350 400-500

0

500

N-S

Win

d S

qu

are

d

0 50 100 150 200 250 300 350 400-400

-200

0

200

E-W

Wid

Sq

ua

red

Julian Day,1997

0 50 100 150 200 250 300 350 400-0.5

0

0.5

1


Challenge

Develop a water level forecasting model Develop a water level forecasting model that captures the non linear relationship that captures the non linear relationship between wind forcing and future water level between wind forcing and future water level changeschanges

Take advantage of the large amount of real-Take advantage of the large amount of real-time data available through TCOONtime data available through TCOON

Artificial Neural Network Model?Artificial Neural Network Model?


ANN Features for Water Level Forecasts

Non linear modeling capabilityNon linear modeling capability

Generic modeling capabilityGeneric modeling capability

Robustness to noisy dataRobustness to noisy data

Ability for dynamic learningAbility for dynamic learning

Requires availability of high density of dataRequires availability of high density of data


ANN Model

H (t+i)

Output LayerHidden Layer

Observed Winds

Observed Water Levels

Observed Barometric Pressures

Forecasted Winds

Input Layer

Water Level Forecast

(a1,ixi)

b1

b2

(X1+b1)

b3

(X2+b2)

(X3+b3)

(a2,ixi)

(a3,ixi)


ANNs Characterisitics

ANN models developed within the Matlab ANN models developed within the Matlab (R13) and Matlab NN Toolbox environment(R13) and Matlab NN Toolbox environment

Simple ANNs are optimumSimple ANNs are optimum Use of ‘tansig’ and ‘purelin’ functionsUse of ‘tansig’ and ‘purelin’ functions Levenberg-Marquardt training algorithmLevenberg-Marquardt training algorithm ANN Trained over 1 year of hourly data ANN Trained over 1 year of hourly data

(8750 forecasts)(8750 forecasts)


CCNAS ANN 24-hour Forecasts

0 50 100 150 200 250 300 350 400-0.5

0

0.5

1

Wat

er L

evel

s (m

)

Julian Day,1997

ANN trained over 2001 Data Set



75 80 85 90 95 100 105 110 115 120 125

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Wat

er L

evel

s (m

)

Julian Day,1997



Model Assessment

Based on five 1-year data sets: ‘97, ‘98, ’99, ’00, ‘01 Based on five 1-year data sets: ‘97, ‘98, ’99, ’00, ‘01 including observed water levels and winds, and tide including observed water levels and winds, and tide forecastsforecasts

Train the NN model using one data set e.g. ‘97 for Train the NN model using one data set e.g. ‘97 for each forecast target, e.g. 12 hourseach forecast target, e.g. 12 hours

Apply the NN model to the other four data sets, Apply the NN model to the other four data sets, Repeat the performance analysis for each training Repeat the performance analysis for each training

year and forecast target and compute the model year and forecast target and compute the model performance and variabilityperformance and variability


Performance Analysis(Coastal Station)

0.00

0.02

0.04

0.06

0.08

0.10

0 hr 6 hr 12 hr 18 hr 24 hr 30 hr 36 hr 42 hr 48 hr 54 hr

Forecasting Period

Ave

rage

Ab

solu

te F

orec

asti

ng

Err

or [

m]

Tides

Persistent Model

ANN model w/o Wind Forecasts

ANN model with Wind Forecasts


Performance Analysis(Estuary Station)

0.00

0.02

0.04

0.06

0.08

0.10

0 hr 6 hr 12 hr 18 hr 24 hr 30 hr 36 hr 42 hr 48 hr 54 hr

Forecasting Period

Ave

rage

Ab

solu

te F

orec

asti

ng

Err

or [

m]

Tides

Persistent Model

ANN model

ANN model (plus Coastal Obs.)


Performance Analysis(Estuary Station)

ANN inputs include Estuary and Coastal Measurements

82 %

84 %

86 %

88 %

90 %

92 %

94 %

96 %

98 %

100 %

102 %

0 10 20 30 40 50 60

Forecast Time [hrs]

Cen

tral

Fre

qu

ency

CF

(15

cm

)

ANN with Wind Forecasts

ANN without Wind Forecasts

Persistent Model

Tides

CF(15 cm) = 90%


Comparison of Tides and ANN forComparison of Tides and ANN for24- Hour Forecasts24- Hour Forecasts

BHP (Coastal) Tides ANN

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 Tides ANN


-2.6 2.4

-0.1 1.1 cm


8.5 1.5 cm

4.5 0.4 cm


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 Tides and ANN forComparison of Tides and ANN for24- Hour Forecasts24- Hour Forecasts

Packery Channel

Tides ANN


-2.6 2.2 cm

-0.2 0.8 cm


7.6 1.6 cm

3.5 0.4 cm


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%


14 10 hrs

MDNO (15 cm) 201187 hrs

30 38 hrs

Tides ANN


-2.4 2.6 cm

-0.2 1.3 cm


8.4 1.4 cm

5.2 0.5 cm


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%


23 7 hrs

MDNO (15 cm) 123 81 hrs

31 37 hrs

Port Aransas


Tropical Storm Frances - September 7-17, 1998

Frances Trajectory

Landfall on Sept. 11


230 235 240 245 250 255 260 265 270 2750

0.2

0.4

0.6

0.8

1

1.2

Wat

er L

evel

s (m

)

Julian Day,1998



CF(Tides) = 17 %CF(Persistent) = 94 %CF(NN w/o Forecasts) = 95%CF(NN with Forecasts) = 98 %



230 240 250 260 270 280

0

0.2

0.4

0.6

0.8

1

1.2

Wat

er L

evel

s (m

)

Julian Day,1998


CF(Tides) = 17 %CF(Persistent) = 92 %CF(NN w/o Forecasts) = 82%CF(NN with Forecasts) = 85 %


Conclusions

ANN models improve considerably on the tides ANN models improve considerably on the tides for regular conditions and frontal passagesfor regular conditions and frontal passages

Once trained computationally very efficient Once trained computationally very efficient Allow great modeling flexibilityAllow great modeling flexibility Accuracy and location of the Wind forecasts will Accuracy and location of the Wind forecasts will

determine model performance beyond 15 hoursdetermine model performance beyond 15 hours Promising for short term, up to 12 hours, water Promising for short term, up to 12 hours, water

level forecasts during stormslevel forecasts during storms


Questions?

philippe tissot*, patrick michaud*, daniel cox**

Documents

philippe tissot, patrick michaud, daniel cox**