Performance of Artificial Neural Network Models for the Prediction of Water Levels

You will find in the tables below a comparison of the ANN performance with the Tide charts and a simple persistence model for 14 stations along the Texas coast. The performance is evaluated using a National Ocean Service standard, the Central Frequency of 15 cm for each model/location, i.e. the percentage of predictions that are within 15 cm of the measured water level. The models are evaluated based on a perfect prog approach for the wind predictions. While the performance of the NAM model was verified to be unbiased and of good quality for the stations below, the predictions are not perfect. Actual ANN water level predictions will be lower depending on the accuracy of the NAM wind predictions.

Bird Island

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 12hours (%) 18 hours (%) 24 hours (%) 36 hours (%) 48 hours (%)
ANN 99.97 99.95 99.97 99.9 99.6
Persistence Model 99.96 99.8 99.7 99.0 98.1
Tide Charts 84.3 84.3 78.5 84.3 84.3

Root Mean Square Error (cm)

Prediction 12 hours 18 hours 24 hours 36 hours 48 hours
ANN 1.8 2.1 3.5 4.2
Persistence Model 2.5 3.1 3.6 4.8 5.6
Tide Charts 11.1 11.1 12.0 11.1 11.1

Optimized by Dr. Philippe Tissot

Bob Hall Pier

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 48 hours (%)
ANN 99.5 98.6 97.3 96.3 94.8 91.0
Persistence Model 98.8 96.1 93.5 91.7 89.1 84.2
Tide Charts 81.3 81.3 81.3 81.3 81.3 81.3

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 48 hours
ANN 4.3 5.5 6.3 6.9 7.6 8.8
Persistence Model 5.1 7.0 8.1 8.9 9.8 11.6
Tide Charts 12.1 12.1 12.1 12.1 12.1 12.1

Optimized by Dr. Philippe Tissot & Sergey Reid

Eagle Point

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 99.25 97.00 94.54 93.12 90.94 89.52 88.22
Persistence Model 95.93 88.40 82.51 78.46 74.57 71.60 68.67
Tide Charts 70.35 70.37 70.38 70.37 70.34 70.29 70.26

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 4.6 6.5 7.8 8.5 9.2 9.6 10.0
Persistence Model 6.8 10.7 13.6 15.6 17.3 18.4 19.2
Tide Charts 16.1 16.1 16.1 16.1 16.1 16.2 16.2

Optimized by Samantha Quisenberry

USCG Freeport

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 98.47 96.19 93.87 92.59 90.84 89.67 88.18
Persistence Model 96.65 91.30 86.90 84.44 80.90 78.25 75.89
Tide Charts 76.21 76.22 76.22 76.16 76.10 76.07 76.05

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 5.5 7.2 8.3 8.8 9.4 9.8 10.2
Persistence Model 6.7 9.4 11.3 12.6 13.9 14.8 15.4
Tide Charts 14.0 14.0 14.0 14.0 14.0 14.0 14.0

Optimized by Sergey Reid

Galveston Pleasure Pier

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 96.89 94.55 92.02 90.94 89.3 88.56 87.23
Persistence Model 93.54 87.89 82.55 79.84 76.2 73.71 71.36
Tide Charts 70.86 70.87 70.86 70.81 70.8 70.76 70.76

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 6.6 7.9 9.0 9.4 9.9 10.2 10.5
Persistence Model 8.3 11.0 13.5 15.0 16.3 17.2 17.6
Tide Charts 15.6 15.6 15.6 15.6 15.6 15.6 15.6

Optimized by Sergey Reid

Ingleside

Model trained on 1 year of hourly data, 2004. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 99.9 99.8 99.4 98.6 97.7 96.5 94.6
Persistence Model 99.9 99.2 97.9 96.2 93.9 91.9 89.3
Tide Charts 80.9 80.9 80.9 80.9 80.9 80.9 80.9

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 2.5 3.8 4.8 5.7 6.4 7.1 7.9
Persistence Model 3.0 4.6 5.7 6.6 7.5 8.4 9.6
Tide Charts 11.9 11.9 11.9 11.9 11.9 11.9 11.9

Optimized by Angelica Villarreal

Manchester Houston

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 96.70 93.29 90.34 88.75 86.88 85.90 84.90
Persistence Model 89.13 79.95 73.94 71.09 64.95 61.45 59.76
Tide Charts 65.58 65.59 65.63 65.63 65.61 65.58 65.60

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 7.4 9.5 10.8 11.5 12.2 12.6 12.9
Persistence Model 10.6 15.1 18.3 20.4 22.7 24.2 25.2
Tide Charts 19.7 19.7 19.6 19.7 19.7 19.7 19.7

Optimized by Cindy Valencia

Packery Channel

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 99.94 99.70 99.30 98.86 98.08 97.21 95.73
Persistence Model 99.91 98.55 98.66 97.47 96.25 95.05 93.30
Tide Charts 82.67 82.65 82.63 82.63 82.63 82.63 82.62

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 2.4 3.5 4.3 4.9 5.7 6.3 7.2
Persistence Model 2.6 3.8 4.8 5.5 6.3 7.0 7.8
Tide Charts 11.4 11.4 11.4 11.4 11.4 11.4 11.4

Optimized by Sergey Reid

Port Aransas

Model trained on 1 year of hourly data, 2004. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 36 hours (%) 48 hours (%)
ANN 99.6 99.0 97.9 97.3 95.0 93.2
Persistence Model 99.2 97.8 95.9 94.0 89.7 86.9
Tide Charts 81.5 81.5 81.5 81.5 81.6 81.6

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 36 hours 48 hours
ANN 4.0 5.1 5.9 6.4 7.6 8.3
Persistence Model 4.6 5.9 6.9 7.6 9.4 10.4
Tide Charts 11.7 11.7 11.7 11.7 11.7 11.7

Optimized by Angelica Villarreal

Port Arthur

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 98.58 95.76 93.01 91.41 88.96 89.54 88.23
Persistence Model 96.56 91.45 86.13 82.72 78.83 76.23 73.82
Tide Charts 66.64 66.64 66.64 66.61 66.56 66.51 66.49

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 7.0 8.4 9.1 9.9
Persistence Model 6.5 9.2 11.4 12.9 14.3 15.2 15.6
Tide Charts 15.9 15.9 15.9 15.9 15.9 15.9 15.9

Optimized by Sergey Reid

Port Isabel

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 99.93 99.61 99.05 98.49 97.63 96.86 95.26
Persistence Model 99.7 98.37 96.67 95.45 93.71 92.09 90.32
Tide Charts 85.97 87.01 87.01 87.01 87.00 87.0 86.97

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 4.4 5.1 5.7 6.2 6.7 7.5
Persistence Model 4.0 5.7 6.6 7.1 7.9 8.5 9.3
Tide Charts 10.7 10.4 10.4 10.4 10.4 10.4 10.4

Optimized by Angelica Villarreal & Sergey Reid

Rockport

Model trained on 1 year of hourly data, 1998. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 99.88 99.84 99.74 99.31 98.31 97.10 94.86
Persistence Model 99.81 99.38 98.01 96.38 94.21 92.03 88.89
Tide Charts 80.00 80.00 80.00 80.00 80.00 80.01 80.00

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 1.9 3.0 3.7 4.6 5.5 6.3 7.4
Persistence Model 2.7 4.2 5.4 6.5 7.5 8.3 9.5
Tide Charts 12.0 12.0 12.0 12.0 12.0 12.0 12.0

Optimized by Sergey Reid

Sabine Pass

Model trained on 1 year of hourly data, 2004. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 97.5 96.0 94.0 92.9 91.7 90.9 89.6
Persistence Model 94.1 91.0 85.5 83.5 79.4 77.1 75.3
Tide Charts 70.4 70.4 70.3 70.3 70.2 70.2 70.2

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 6.1 7.1 8.1 8.5 9.0 9.0 9.6
Persistence Model 8.0 9.7 1.2 1.3 1.5 1.5 1.6
Tide Charts 15.0 15.0 15.0 15.0 15.0 15.0 15.0

Optimized by Sergey Reid

Texas State Aquarium

Model trained on 1 year of hourly data, 2004. The performance is computed based on 4 years of hourly data (2000-2003).

Central Frequency (% within 15 cm)

Prediction 6 hours (%) 12hours (%) 18 hours (%) 24 hours (%) 30 hours (%) 36 hours (%) 48 hours (%)
ANN 99.9 99.8 99.4 98.9 98.0 97.0 95.2
Persistence Model 99.8 98.9 97.7 96.0 93.8 91.5 88.8
Tide Charts 80.4 80.4 80.4 80.5 80.5 80.5 80.5

Root Mean Square Error (cm)

Prediction 6 hours 12 hours 18 hours 24 hours 30 hours 36 hours 48 hours
ANN 2.8 3.7 4.6 5.3 6.1 6.8 7.6
Persistence Model 3.5 5.0 6.0 6.7 7.7 8.6 9.7
Tide Charts 12.0 12.0 12.0 12.0 12.0 12.0 12.0

Optimized by Sergey Reid