Evaluation of instability in the marine surface layer and its effect on wave height

In this study, using similarity laws and regression methods, numerical modeling of wave height estimations has been carried out for the data recorded by a station in the southern part of the Caspian Sea during the year 2008. Numerical simulations require powerful computers and their results may be accurate and reliable if proper physics is used. However, semi-empirical models can easily calculate wave heights but in practice are less accurate. In the latter methods, the surface temperature and instability effects have little impact on the effective wave height calculation. The nature of these methods is such that usually the effects of the instability of the surface layer are not considered in the calculation of wave heights. In experimental methods, the effects of variations of frictional velocity and the stability parameter are important factors which are considered as coefficients and directly applied in the equations. In this paper, the correlations between the wave height measurements and the friction velocity and the stability function are considered. These correlations are evaluated for exponential, logarithmic, polynomial and inverse polynomial functions. In order to calculate the friction velocity and the stability functions, a bulk aerodynamic model similar to the one used in Fairall et al. (2003) is used. It includes an iterative algorithm with an initial guess for the friction velocity and Monin–Obukhov length. The accuracies of the friction velocity and Monin–Obukhov length are then increased by iteration.
The wave height measurements are analyzed by multi-variable nonlinear regression on the outputs of the bulk model. This analysis shows that, for functions that have an acceptable correlation coefficient (exponential, logarithmic, polynomial and inverse polynomial functions), the stability function can reduce the wave height error. The following conclusions can then be made: a) In the semi-empirical models, the effect of stability function can be directly entered into the equation and the uncertainty in the coefficient can be reduced.
b) The stability function in the atmospheric surface layer has an important role in the air–sea interaction; hence its consideration can increase the accuracy of the wave height prediction.
Results show that compared to the warm months (stable cases), in the cold months (unstable cases) the stability function had smaller effects on wave height prediction. Results of the analyses are summarized as: a) In the cold months (October–December) in the port of Amir Abad, the conditions are more unstable, while in relatively warm months (July and August) there are more stable conditions.
b) The correlation coefficient between the friction velocity and the wave amplitude in the cold months is less than that for the warm months.
c) The correlation between the stability fiction and the wave height in the cold months is smaller than that in the warm months.
d) Regression error rates for the friction velocity in the cold months are higher than those for the warm months of the year.
Wave height calculation error in December (with a maximum error of linear regression with friction velocity) decreased down to ten percent by calculating the nonlinear regression with a mixture of the third-degree polynomial, inverse polynomial and logarithmic functions for the stability. This reduction in the wave height calculation error is simply due to the effect of stability function. The friction velocity seems to have little impact on the results of the regression method. Although the results are only for the data of the year 2008 recorded in the Amir Abad Port, but the results are not limited to a specific time and place and show the impact of stability function on wave height estimations. The main achievement of this paper is a reduction of error in wave height estimation that is achieved by taking into account the stability function. However, much higher reduction in the wave hight errors cannot be expected, because a large part of the waves characteristics are caused by wind effects at different times and places. Since the effect of the surrounding area of Amir Abad Port has not been considered in the present work, only a reduction of the calculated wave height error was possible.