The diurnal sea surface temperature variation (DSV) influences atmospheric convection and precipitation through air–sea interactions in the equatorial Pacific. Deep learning-based DSV forecasting has been less explored compared to traditional methods, presenting the potential for a substantial leap in forecast accuracy. In this study, a forecast model is developed for 24 h DSV in the equatorial Pacific using an improved coupled Transformer-CNN (CoTCN-DSV) by incorporating a new loss function including maximal and minimal values. The CoTCN-DSV forecasts diurnal variation in SST at the interval of 3 h based on 3 h SST from the WHOI dataset. The CoTCN-DSV captures DSV well with root mean square error (RMSE) of DSA below 0.03 °C/0.13 °C at 3 h/12 h lead times and maintains high forecast skill with the temporal correlation coefficient (R) of 0.78 at the lead times of 12 h in the equatorial Pacific. The CoTCN-DSV reduces RMSE for daily max/min SST by 10.9% and 12.8% due to replacing the new loss function, then significantly improving DSV forecast. There are systematic SST biases in the WHOI dataset and this leads to relatively large RMSEs when DSV forecasts trained using WHOI are evaluated against TAO observations. Replaced WHOI SST by TAO SST, the forecasted DSA RMSE by CoTCN-DSV is reduced by an average of 43%. This confirms that the CoTCN-DSV has good generalization ability and high-quality data are important to advance the forecast accuracy. These finding show that CoTCN-DSV has the potential to forecast extreme values for different scenarios.

The aim of this paper is to investigate homogenization of stationary Navier-Stokes equations with a Dirichlet boundary condition in domains with 3 kinds of typical holes. For space dimension $N$ =2 and 3, we utilize a unified approach for 3 kinds of tiny holes to accomplish the homogenization of stationary Navier-Stokes equations. The unified approach due to Lu [1] is mainly based on the uniform estimates with respect to ε for the generalized cell problem inspired by Tartar.