The M2 Cotidal Chart in the Bohai, Yellow, and East China Seas from Dynamically Constrained Interpolation

The harmonic constants extracted from tidal gauge stations and satellite altimeter observations are usually sparsely distributed in the continental marginal seas, but they are precious data for addressing the main characteristics of different constituents. In this paper, a dynamically constrained interpolation methodology (DCIM) is developed and applied to interpolate the observed harmonic constants of the M2 constituent from satellite altimeter observations in the Bohai, Yellow, and East China Seas (BYECS) with those from tidal gauge stations for validation. In the DCIM, the tide model provides dynamical constraints to interpolate the observations, and the adjoint assimilation method provides iterative optimization for the interpolated results by adjusting key model parameters. In particular, a substantial quantity of enhanced “observations” generated from the interpolated results of the domain are further interpolated with the sparse observations in the subdomain. The final interpolated results for each subdomain, naturally blending the dynamical constraints from the dynamical model with statistical information from observations, can describe the main characteristics of the M2 constituent in the BYECS, the continental shelf sea of the East China Sea, and the Zhejiang–Fujian coastal area, respectively. The results indicate that the DCIM is feasible and effective to utilize the observations to obtain high-accuracy cotidal charts for regional ocean.

Application of Adjoint Data Assimilation Method to Atmospheric Aerosol Transport Problems

We propose combining the adjoint assimilation method with characteristic finite difference scheme (CFD) to solve the aerosol transport problems, which can predict the distribution of atmospheric aerosols efficiently by using large time steps. Firstly, the characteristic finite difference scheme (CFD) is tested to compute the Gaussian hump using large time step sizes and is compared with the first-order upwind scheme (US1) using small time steps; the US1 method gets E2 error of 0.2887 using Δt=1/450, while CFD method gets a much smaller E2 of 0.2280 using a much larger time step Δt=1/45. Then, the initial distribution of PM2.5 concentration is inverted by the adjoint assimilation method with CFD and US1. The adjoint assimilation method with CFD gets better accuracy than adjoint assimilation method with US1 while adjoint assimilation method with CFD costs much less computational time. Further, a real case of PM2.5 concentration distribution in China during the APEC 2014 is simulated by using adjoint assimilation method with CFD. The simulation results are in good agreement with the observed values. The adjoint assimilation method with CFD can solve large scale aerosol transport problem efficiently.

Estimation of Initial Field in the Bohai Sea with the Adjoint Method: A Comparative Study on Optimization Algorithms

The adjoint assimilation technique is used to invert the prescribed initial field in the Bohai Sea. Based on this technique, the practical performances of the limited-memory BFGS (L-BFGS) method, the Regularization method, and the Gradient Descent (GD) method are investigated computationally through a series experiments. Experimental results demonstrate that the prescribed initial field can be successfully estimated by these three methods. Inversion result with the Regularization method is better than that with the L-BFGS method, although errors of observations are higher. Though higher simulation errors than L-BFGS and Regularization method, the difference between the prescribed distribution and inversion result is the lowest, indicating that inversion result with the traditional GD method is the best.

Estimation of the Parameters in a Dynamical Marine Ecosystem Model Based on the Adjoint Assimilation

By utilizing spatial biological parameterizations, the adjoint variational method was applied to a 3D marine ecosystem model (NPZD-type) and its adjoint model which were built on global scale based on climatological environment and data. When the spatially varying Vm (maximum uptake rate of nutrient by phytoplankton) was estimated alone, we discussed how would the distribution schemes of spatial parameterization and influence radius affected the results. The reduced cost function (RCF), the mean absolute error (MAE) of phytoplankton in the surface layer, and the relative error (RE) of Vm between given and simulated values decreased obviously. The influence of time step was studied then and we found that the assimilation recovery would not be more successful with a smaller time step of 3 hours compared with 6 hours.

Estimation of Open Boundary Conditions Based on an Isopycnic-Coordinate Internal Tidal Model with Adjoint Assimilation Method

The isopycnic-coordinate internal tidal model with adjoint assimilation method is developed into a three-layer version. Two groups of ideal experiments are carried out in order to investigate the estimation of spatially varying open boundary conditions (OBCs). In group 1, different independent point schemes (IPSs) are used to invert 6 kinds of prescribed distributions of OBCs. Results show that, after assimilation, the cost functions and their gradient norms are reduced by about 2 orders of magnitude and by about 1 order of magnitude, respectively; the mean absolute errors (MAEs) in OBCs and the vector differences of horizontal current are reduced by 1 order of magnitude and by more than 23.53% compared with the values before assimilation, respectively. The results demonstrate that the three-layered model has a good ability in estimating the spatially varying OBCs; the use of IPSs can effectively improve the estimation precision; fewer independent points are feasible when the distribution is simpler, and appropriately more independent points are required when the distribution is more complex. In group 2, by using the optimal IPSs in group 1, the model is also able to successfully invert the OBCs on a real topography in the Luzon Strait area. The results are important to the study of the internal tide in the South China Sea.