The predictability of meteo-oceanographic events

Abstract

We have explored the predictability of storms in a small enclosed basin with a complicated surrounding orography. We have considered two exceptional storms in the far past and three mild events happened in recent years. A posteriori forecasts have been done up to 6 days before the events. The results have been compared versus measured data and the related analysis. Good predictability (10–15% error in surface wind speed and wave height) have been found up to day 4, mildly larger (<30%) up to day 6 before the event. In no case was a storm missed. This suggests that the effective predictability in more open basins may extend to even larger ranges.

Appendix A

Intercomparison of two vector fields

We want to intercompare two vector fields on the same grid, say b with respect to a (see Marsden 1987). We consider each vector as a complex number, i.e. a = [ax,ay] → (ax + i ay) = a exp(iΦ), with a the modulus and Φ the phase. If we have only one vector (i.e. one-grid point)

$$ {\text{b}}/{\text{a}} = {\text{ b}}/{\text{a exp}}\left[ {{\text{i }}\left( {{\Phi_{\text{b}}} - {\Phi_{\text{a}}}} \right)} \right] $$

provides the ratio of the moduli and the phase difference. The result of a point-by-point comparison of the two fields is another vector field. To summarise this result in a more compact way, we can proceed as follows. Obviously

$$ {\mathbf{b}}/{\mathbf{a}} = \left( {{\mathbf{b}}{ }{\mathbf{a}}*} \right)/\left( {{\mathbf{a}}{ }{\mathbf{a}}*} \right) $$

with a* the complex conjugate of a. We consider the quantity

$$ \Psi = \left( {\sum {i\,{a_{i}}*{b_{i}}} } \right)/\left( {\sum {i\,{a_{i}}*{a_{i}}} } \right) $$

Ψ can be considered as the regression coefficient of the b field with respect to a. If we consider also the expression

$$ {\sum_{\text{i}}}||{{\text{b}}_{\text{i}}} - \Psi {{\text{a}}_{\text{i}}}||{2} $$

this can be interpreted as a sort of minimum square quantity. Alternatively, Ψ is the quantity that minimises the distance between the two points [b _i ] and [Ψa _i ] in an n dimensional space (i = 1–n).

The complex number

$$ \Psi = \alpha + {\text{i}}\beta $$

provides the ‘average’ ratio and the ‘average’ phase difference between the two fields.