Simplified method of determining refraction coefficients for sea waves

In order to find the effect of wave refraction in one particular locality P only, it is useful to construct wave rays from this point outward to sea and to determine their variation in azimuth from θ at P to θ′ in deep water. The change of energy flux density for waves coming from a direction θ′ in deep water is, as customary, expressed by the square of a ‘refraction coefficient,’ . For waves of a given period whose energy in deep water is uniformly distributed over a finite azimuthal interval from θ1′ to θ2′, the average square of the refraction coefficient is given (with restrictions) by where C' and C are the phase velocities of the waves in deep water and at P, respectively. Some practical hints are given. A derivation of the above formula is given in the appendix.