Numrical Study On The Spatially Varying Drag Coefficient In Simuation Of Strorem Surges Employing The Adjoint Method

Based on the simulation of storm surges resulting from Typhoons 7203 and 8509 in the Bohai Sea, Yellow Sea and East China Sea, water level data at tide stations are assimilated into a two-dimensional storm surge model, to study the spatially varying drag coefficient (DC) by employing the adjoint method. In this study, the DC at some grid points is uniformly selected as the independent DC, while the DCs at other grid points is obtained through linear interpolation of the independent DC. The DC at independent points is optimized by employing the adjoint assimilation method, and global optimization is achieved by optimizing the independent DC. To demonstrate the method's performance, three comparative experiments are carried out. In the first experiment, the DC is treated as a constant. In the second and third experiments, the DC is derived using an empirical formula. Comparing the experimental results, it is found that the simulation accuracy for both Typhoons 7203 and 8509 increases greatly when optimizing the independent DC. However, the number of independent points makes no great difference to the precision of simulation. Moreover, the DC inverted from Typhoons 7203 and 8509 differs in some sea areas because of the different typhoon tracks. However, the spatial distribution of the inverted DC, for both Typhoons 7203 and 8509, demonstrates a clear effect of the DC on the storm surge modeling near the coastal areas where the DC is highest or lowest. Besides, a series of random noises are applied to the wind field of the typhoon to study the effects of uncertainties in the wind field on the DC. By checking the change of simulated surge elevations and the inverted DC, we conclude that the inverted DC is affected by uncertainties in the wind field, but the effect is very small. The inverted DC is statistically analyzed and the results show that the DC is closely related to the local water depth and wind speed. Harmonic analysis of 10 years of TOPEX/Poseidon (T/P) along-track altimetry is performed to derive the semidiurnal and diurnal tides (M2,S2,N2,K2,K1,O1,P1 and Q1,) near Hawaii. The T/P solutions are evaluated through intercomparison for crossover points of the ascending and descending tracks and comparison with the data of tidal stations, which show that the T/P solutions in the study area are reliable. By using a suitable order polynomial to fit the T/P solutions along every track, the harmonic constants of any point on T/P tracks are acquired. A new fitting method, which is characterized by applying the harmonics from T/P tracks to produce directly empirical cotidal charts, is developed. Any point is selected in the study area. Based on the ratio of the distances between this point and its two nearest ascending (descending) tracks, a series of points on the descending (ascending) tracks that have the same ratio with this point between the two ascending (descending) tracks are obtained. By fitting the harmonics of these points with a suitable order polynomial, the harmonic constants of this point are acquired. The harmonic constants derived by this fitting method show good agreement with the data of tidal stations, the results of NAO.99b, TPXO7.2 and FES2004 models, which suggests that the fitting method is reasonable and the highly accurate cotidal chart could be directly acquired from T/P altimetry data by this fitting method.