The common statistical parameters such as RMSE, CC, Bias, etc. are suitable to compare numerically modeled and field observed wave heights and wave periods. But due to the min/max range of wave directions which is 0 to 360 degree, they cannot represent a meaningful estimation on the model accuracy. Is there any statistical parameter such a polar nature parameter?
Hi Mostafa,
first of all, I will strongly recommend you to contact Saeed Moghimi [email protected]. He is an expert in waves modelling and measurments (and is Iranian as you). Well to compare wave measurements vs wave model, you can transform the wave direction in Unitarian vectors U (W-E) and V (N-S), so if you have a time series you can easily find the correlation between both data sets.
in that way as Oliver Way says, you can obtain more statistic parameters (e.g. bias, mean, std. dev., percentiles, etc.
by the way you should compare Tp and Hs to make a correct validation.
best regards
Adolfo Contreras
Dear Adolfo, Thanks for your reply. I will contact him. It is good to convert the wave direction to U and V components, but it's a bit hard for me to understand the physical meaning of it.
Dear George,
Many thanks for the interesting paper and toolbox. It was a straightforward answer to my question.
First of all you may want to make sure how the direction measurements you have are computed: for surface buoys, this is usually done from the 1st moments a1 and b1: a1(f)=sum of (E(ftheta) *cos(theta)*dtheta
b1(f)=sum of (E(ftheta) *sin(theta)*dtheta
th1m(f)=atan2(b1(f),a1(f))
That gives you a mean direction for each frequency. You can also define an overal direction for a frequency range fmin to fmax (be careful to use the same range in model and data when you compare them).
see chapter 3 in https://www.researchgate.net/publication/304990310_Ocean_Waves_in_Geosciences
Finally to get statistics, I usually go to complex numbers: Z = (cos theta, sin theta) and compute correlations and other things on these complex numbers.
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