Based on the Coupled Ocean-Atmospheric Response Experiment （COARE） bulk algorithm and the Naval Postgraduate School （NPS） model, a universal evaporation duct （UED） model that can flexibly accommodate the latest improvements in component （such as stability function, velocity roughness, and scalar roughness） schemes for different stratification and wind conditions, is proposed in this paper. With the UED model, the sensitivity of the model-derived evaporation duct height （EDH） to stability function （ψ）, ocean wave effect under moderate to high wind speeds, and scalar roughness length parameterization, is investigated, and relative contributions of these factors are compared. The results show that the stability function is a key factor influencing the simulated EDH values. Under unstable conditions, the EDH values from stability functions of Fairall et al. （1996） and Hu and Zhang （1992） are generally higher than those from others; while under stable conditions, unreasonably high EDHs can be avoided by use of the stability functions of Hu and Zhang （1992） and Grachev et al. （2007）. Under moderate to high wind speeds, the increase in velocity roughness length z0 due to consideration of the true ocean wave effect acts to reduce modeled EDH values; this trend is more pronounced under stable conditions. Although the scalar roughness length parameterization has a minor effect on the model-derived EDH, a positive correlation is found between the scalar roughness length z0q and the model-derived EDH.
This study aims to validate and improve the universal evaporation duct （UED） model through a further analysis of the stability function （ψ）. A large number of hydrometeorological observations obtained from a tower platform near Xisha Island of the South China Sea are employed, together with the latest variations inψ function. Applicability of different ψ functions for specific sea areas and stratification conditions is investigated based on three objective criteria. The results show that, under unstable conditions, ψfunction of Fairall et al. （1996） （i.e., Fairal196, similar for abbreviations of other function names） in general offers the best performance. However, strictly speaking, this holds true only for the stability （represented by bulk Richardson number RiB） range -2.6 ≤ RiB 〈 -0.1; when conditions become weakly unstable （-0.1 ≤ RiB 〈 --0.01）, Fairal196 offers the second best performance after Hu and Zhang （1992） （HYQ92）. Conversely, for near-neutral but slightly unstable conditions （-0.01≤ RiB 〈 0.0）, the effects of Edson04, Fairall03, Grachev00, and Fairal196 are similar, with Edson04 being the best function but offering only a weak advan- tage. Under stable conditions, HYQ92 is the optimal and offers a pronounced advantage, followed by the newly introduced SHEBA07 （by Grachev et al., 2007） function. Accordingly, the most favorable functions, i.e., Fairal196 and HYQ92, are incorporated into the UED model to obtain an improved version of the model. With the new functions, the mean root-mean-square （rms） errors of the modified refractivity （M）, 0-5-m M slope, 5-40-m M slope, and the rms errors of evaporation duct height （EDH） are reduced by 21.65%, 9.12%, 38.79%, and 59.06%, respectively, compared to the classical Naval Postgraduate School model.
Traditional variational data assimilation （VDA） with only one regularization parameter constraint cannot produce optimal error tuning for all observations. In this paper, a new data assimilation method of ＂four dimensional variational data assimilation （4D-Var） with multiple regularization parameters as a weak constraint （Tikh-4D-Var）＂ is proposed by imposing different reg- ularization parameters for different observations. Meanwhile, a new multiple regularization parameters selection method, which is suitable for actual high-dimensional data assimilation system, is proposed based on the posterior information of 4D-Var system. Compared with the traditional single regularization parameter selection method, computation of the proposed multiple regularization parameters selection method is smaller. Based on WRF3.3.1 4D-Vat data assimilation system, initiali- zation and simulation of typhoon Chaba （2010） with the new Tikh-4D-Var method are compared with its counterpart 4D-Var to demonstrate the effectiveness of the new method. Results show that the new Tikh-4D-Var method can accelerate the con vergence with less iterations. Moreover, compared with 4D-Var method, the typhoon track, intensity （including center surface pressure and maximum wind speed） and structure prediction are obviously improved with Tikh-4D-Var method for 72-h pre- diction. In addition, the accuracy of the observation error variances can be reflected by the multiple regularization parameters.
