Validation of the Regional Wave Model

Validation of the regional wave model

Validation of the regional wave model

The wave hindcast model was driven by wind fields from a numerical weather prediction (NWP) model, because model data are the only datasets with complete coverage in space and time. It was found that the wind speed of the used NWP model is generally underestimated. Driving the wave model with this biased wind speed will result in an underestimation of the wave height. In some extend it is possible to correct for these errors afterwards but it is preferable to drive the wave model with a un-biased wind speed. Therefore the wind speed was first calibrated against satellite observations. Then, calibration of the wave model against altimeter measurements will remove the (possibly) remaining systematic errors of the wave model.

Method

Validation results of the regional wave model are based on satellite altimeter observations from Jan1992 until December2004.

The regional model is compared with the significant wave height and wind speed obtained from the ERS1, ERS2 GFO, Jason and Topex /Poseidon satellite altimeters and scatterometers.

The model results are grouped into 6 geographical regions:

¨  Mediterranean

¨  Black Sea

¨  Red Sea

¨  Aegean Sea

¨  Caspian Sea

¨  Arabian Gulf

The locations of the validated grid points are given in Figure 1.

Figure 1 Locations of the validation grid points.

The error is defined as the difference (satellite minus model) between the calibrated (Validation report offshore climate) satellite observations (wind speed and significant wave height) and the model results. The quality of the model data is expressed in terms of:

¨  Mean: Mean value of the altimeter observations.

¨  StDev: Standard deviation of error.

¨  Rrms: Relative root mean square of error.

¨  Corr: Correlation coefficient.

¨  Intercept,slope Interception and slope from a Linear regression fit.

The statistical parameters and calibration methods are defined in the ‘Validation offshore climate’ report but instead of buoy measurements one should read model data. The statistical wind and wave parameters were computed after applying the calibration corrections. The calibration constants are the results of least square fits of co-located data pairs at each grid point. Calibration constants using altimeter and scatterometer wind speeds were computed separately and then merged together using mutual weights depending on location and data density. Finally the calibration constants were spatially smoothed. For the significant wave height (Hs) the square of Hs was used. Therefore a least square fit on calibrated Hs values does not necessary result in a zero interception and a slope of one (y=x).

The statistics of the significant wave height and wind speed are collected in the tables below. Scatter plots are given in next sections.

Location / Statistical parameter
After calibration / calibration constants
grid ID / Region / (lat,lon)
[deg] / N / Mean [m] / Corr / StDev [m] / Rrms [%] / intercpt
[m2] / slope
105777 / Mediterranean / (43.0,4.0) / 1008 / 1.15 / 0.88 / 0.39 / 31 / -0.09 / 0.77
102775 / (36.0,-3.0) / 180 / 1.18 / 0.89 / 0.39 / 30 / -0.18 / 0.85
103723 / (38.0,5.5) / 153 / 1.46 / 0.94 / 0.37 / 22 / -0.18 / 0.99
104191 / (39.0,14.5) / 52 / 0.96 / 0.89 / 0.39 / 32 / -0.29 / 1.11
105569 / (42.5,16.0) / 674 / 0.85 / 0.83 / 0.35 / 35 / -0.22 / 0.95
101836 / (33.3,34.5) / 611 / 0.94 / 0.91 / 0.31 / 26 / -0.14 / 1.18
102555 / (35.3,12.5) / 610 / 1.11 / 0.91 / 0.32 / 24 / -0.15 / 1.03
106022 / Black Sea / (43.5,31.5) / 340 / 1.07 / 0.89 / 0.37 / 28 / -0.09 / 1.07
106054 / (43.5,39.5) / 233 / 0.83 / 0.79 / 0.40 / 45 / -0.40 / 1.05
100725 / Red Sea / (25.5,35.5) / 124 / 1.12 / 0.82 / 0.38 / 31 / -0.21 / 1.05
100229 / (16.5,40.5) / 188 / 0.81 / 0.66 / 0.38 / 42 / -0.15 / 1.22
103999 / Aegean Sea / (38.5,24.5) / 613 / 1.00 / 0.84 / 0.39 / 40 / -0.27 / 0.88
104017 / Caspian Sea / (38.5,51.5) / 24 / 1.04 / 0.75 / 0.68 / 49 / -0.12 / 1.17
100837 / Arabian Gulf / (27.0,52.0) / 119 / 0.86 / 0.78 / 0.42 / 44 / -0.29 / 0.95

Table 1 Error statistics of regional model significant wave height based on altimeter data.

Location / Statistical parameter
After calibration / calibration constants
grid ID / Region / (lat,lon)
[deg] / N / Mean [m/s] / Corr / StDev [m/s] / Rrms [%] / intercpt
[m/s] / slope
105777 / Mediterranean / (43.0,4.0) / 426 / 8.2 / 0.87 / 2.32 / 28 / 0.07 / 0.89
102775 / (36.0,-3.0) / 611 / 5.9 / 0.88 / 1.74 / 25 / 1.39 / 0.80
103723 / (38.0,5.5) / 915 / 5.8 / 0.88 / 1.46 / 23 / 0.13 / 0.92
104191 / (39.0,14.5) / 637 / 4.8 / 0.88 / 1.47 / 26 / 0.55 / 0.87
105569 / (42.5,16.0) / 312 / 5.1 / 0.78 / 1.89 / 33 / -0.31 / 0.92
101836 / (33.3,34.5) / 939 / 4.8 / 0.81 / 1.60 / 31 / 0.36 / 0.83
102555 / (35.3,12.5) / 896 / 6.5 / 0.90 / 1.45 / 20 / 0.0 / 0.95
106022 / Black Sea / (43.5,31.5) / 1099 / 5.9 / 0.88 / 1.46 / 22 / 0.48 / 0.91
106054 / (43.5,39.5) / 70 / 5.1 / 0.65 / 2.56 / 46 / 0.01 / 0.84
100725 / Red Sea / (25.5,35.5) / 840 / 5.8 / 0.83 / 1.72 / 26 / 0.21 / 0.86
100229 / (16.5,40.5) / 1226 / 4.5 / 0.71 / 1.78 / 35 / -0.21 / 1.04
103999 / Aegean Sea / (38.5,24.5) / 89 / 7.6 / 0.77 / 2.34 / 39 / 0.04 / 0.86
104017 / Caspian Sea / (38.5,51.5) / 1577 / 4.8 / 0.78 / 1.75 / 32 / 0.33 / 0.88
100837 / Arabian Gulf / (27.0,52.0) / 928 / 5.3 / 0.83 / 1.86 / 30 / 0.67 / 0.84

Table 2 Error statistics of the model wind speed based on scatterometer data.

Location / Statistical parameter
After calibration / calibration constants
grid ID / Region / (lat,lon)
[deg] / N / Mean [m/s] / Corr / StDev [m/s] / Rrms [%] / intercpt
[m/s] / slope
105777 / Mediterranean / (43.0,4.0) / 1008 / 7.1 / 0.85 / 2.24 / 28 / 0.07 / 0.89
102775 / (36.0,-3.0) / 182 / 5.7 / 0.88 / 2.02 / 29 / 1.39 / 0.80
103723 / (38.0,5.5) / 153 / 5.8 / 0.87 / 1.68 / 25 / 0.13 / 0.92
104191 / (39.0,14.5) / 52 / 4.9 / 0.80 / 1.84 / 32 / 0.55 / 0.87
105569 / (42.5,16.0) / 674 / 5.1 / 0.79 / 1.94 / 33 / -0.31 / 0.92
101836 / (33.3,34.5) / 611 / 4.5 / 0.78 / 1.78 / 33 / 0.36 / 0.83
102555 / (35.3,12.5) / 610 / 6.1 / 0.88 / 1.63 / 24 / 0.0 / 0.95
106022 / Black Sea / (43.5,31.5) / 340 / 5.8 / 0.85 / 1.63 / 25 / 0.48 / 0.91
106054 / (43.5,39.5) / 233 / 4.3 / 0.68 / 2.28 / 46 / 0.01 / 0.84
100725 / Red Sea / (25.5,35.5) / 124 / 6.1 / 0.77 / 1.76 / 28 / 0.21 / 0.86
100229 / (16.5,40.5) / 188 / 4.1 / 0.70 / 1.89 / 43 / -0.21 / 1.04
103999 / Aegean Sea / (38.5,24.5) / 613 / 6.3 / 0.85 / 1.88 / 28 / 0.04 / 0.86
104017 / Caspian Sea / (38.5,51.5) / 24 / 4.4 / 0.68 / 2.66 / 46 / 0.33 / 0.88
100837 / Arabian Gulf / (27.0,52.0) / 119 / 4.5 / 0.74 / 2.47 / 43 / 0.67 / 0.84

Table 3 Error statistics of the model wind speed based on altimeter data.

1  Scatter plots of raw model and altimeter significant wave height

Least squares fits of the raw (not-calibrated) model significant wave height and the satellite altimeter wave height per region are given in the figures below.

Figure 2 Mediterranean.

Figure 3 Black Sea.

Figure 4 Red Sea.

Figure 5 Aegean Sea. Figure 6 Caspian Sea. Figure 7 Arabian Gulf.

2  Scatter plots of calibrated model and altimeter significant wave height

Least squares fits of calibrated model significant wave height and the satellite altimeter wave height per region are given in the figures below.

Figure 8 Mediterranean.

Figure 9 Black Sea.

Figure 10 Red Sea.

Figure 11 Aegean Sea. Figure 12 Caspian Sea. Figure 13 Arabian Gulf.

3  Scatter plots of raw model and scatterometer wind speed

Least squares fits of the raw (not-calibrated) NWP wind speed and the scatterometer wind speed are given in the figures below.

Figure 14 Mediterranean.

Figure 15 Black Sea.

Figure 16 Red Sea.

Figure 17 Aegean Sea. Figure 18 Caspian Sea. Figure 19 Arabian Gulf

4  Scatter plots of calibrated model and scatterometer wind speed

Least squares fits of the calibrated NWP wind speed and the scatterometer wind speed are given in the figures below.

Figure 20 Mediterranean.

Figure 21 Black Sea.

Figure 22 Red Sea.

Figure 23 Aegean Sea. Figure 24 Caspian Sea. Figure 25 Arabian Gulf

5  Scatter plots of raw model and altimeter wind speed

Least squares fits of the raw (not-calibrated) NWP wind speed and the altimeter wind speed are given in the figures below.

Figure 26 Mediterranean.

Figure 27 Black Sea.

Figure 28 Red Sea.

Figure 29 Aegean Sea. Figure 30 Caspian Sea. Figure 31 Arabian Gulf

6  Scatter plots of calibrated model and altimeter wind speed

Least squares fits of the calibrated NWP wind speed and the altimeter wind speed are given in the figures below.

Figure 32 Mediterranean.

Figure 33 Black Sea.

Figure 34 Red Sea.

Figure 35 Aegean Sea. Figure 36 Caspian Sea. Figure 37 Arabian Gulf

www.waveclimate.com

June 2006

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