Adjoint Assimilation Method Research Articles

A Study of Wind Stress Effects on the Vertical Eddy Viscosity Coefficient Using the Ekman Model with Data Assimilation

The vertical eddy viscosity coefficient (VEVC) is an important parameter used in ocean dynamics studies to describe the intensity of mixing in the vertical direction and the process of momentum transport. In this paper, an adjoint assimilation method was used to invert the VEVC, based on the Ekman model, with the measured wind field and current data. The main purpose was to study the effect of changes in the background wind field on VEVC, and thus investigate the role of wind stress in the inversion process. The results indicated that the inverse vertical eddy viscosity coefficient increased slightly at the surface layer, reaching its maximum at around 10–12 m, and then decreased monotonically with depth. The maximum VEVC value corresponds to different depths for different wind speed ranges. Additionally, wind steering could affect the VEVC inversion curve, causing it to deviate from the general trend. The kinetic energy ratio increased with depth, peaked at 18–20 m, and then rapidly decreased to nearly zero beyond 24 m. The impact of wind field strength and steering on VEVC was observed in the kinetic energy ratio curve, which confirms the speculative wind stress effect. This study revealed the characteristics and mechanisms of VEVC in coastal waters under different wind conditions, which could provide a reference for further research on physical oceanography.

Effects of including the adjoint sea ice rheology on estimating Arctic Ocean–sea ice state

Abstract. The adjoint assimilation method has been applied to coupled ocean and sea ice models for sensitivity studies and Arctic state estimations. However, the accuracy of the adjoint model is degraded by simplifications of the adjoint of the sea ice model, especially the adjoint sea ice rheologies. As part of ongoing developments in coupled ocean and sea ice estimation systems, we incorporate and approximate the adjoint of viscous-plastic sea ice dynamics (adjoint-VP) and compare it with the adjoint of free-drift sea ice dynamics (adjoint-FD) through assimilation experiments. Using the adjoint-VP results in a further cost reduction of 7.9 % in comparison to adjoint-FD, with noticeable improvements in the ocean temperature over the open water and the intermediate layers of the Arctic Ocean. Adjoint-VP adjusts the model input more efficiently than adjoint-FD does by involving different sea ice retreat processes. For instance, adjoint-FD melts the sea ice up to 1.0 m in the marginal seas from May to June by overadjusting air temperature (>8 ∘C); adjoint-VP reproduces the sea ice retreat with smaller adjustments to the atmospheric state within their prior uncertainty range. These developments of the adjoint model here lay the foundation for further improving Arctic Ocean and sea ice estimations by comprehensively adjusting the initial conditions, atmospheric forcings, and parameters of the model.

A Method Using the Huber Function for Inversion of Tidal Open Boundary Conditions of the M2 Constituent in the Bohai and Yellow Seas

Abstract The adjoint assimilation method has been widely used in various ocean models, and a series of technical schemes have been developed at the same time. Open boundary conditions (OBCs) in the two-dimensional (2D) tidal model of the M2 tidal constituent in the Bohai and the Yellow Seas (BYS) were inverted successfully using the adjoint assimilation methods in previous studies. However, the cost function in the adjoint assimilation method usually used the L2 norm in the past, which is difficult to maintain the robustness of the method when there are outliers. Meanwhile, using the L1 norm with strong robustness will shield the outliers’ information fully. Therefore, we propose a new scheme that replaces the L2 norm with the Huber function to improve the robustness of the adjoint assimilation method and absorb the data’s useful information to some extent. This scheme was verified in the ideal experiments in which magnitudes of the misfit vector were significantly reduced and the quality control (QC) process was simplified consequently. In the practical experiments, the introduction of the Huber function improved the accuracy of inversion in the inshore area using mixed data containing tide gauges and satellite altimetry. With this scheme, the root-mean-square errors (RMSEs) between the estimation and the observed values at tide gauge stations were reduced from ∼8 cm with the original scheme to ∼6 cm. Testing the new scheme in more complex models and how it might be affected remains a topic for future study. Significance Statement The adjoint assimilation method has been effectively applied in various ocean models. The cost function in the adjoint assimilation is usually in the form of the L2 norm, which presents poor robustness. By using the Huber function instead of the L2 norm as the cost function, we proposed a new scheme that can perfectly handle the potential outliers in data and noticeably improve the robustness of the adjoint assimilation method. The new method was applied to the inversion of tidal open boundary conditions of the M2 constituent in the Bohai and the Yellow Seas. Both the ideal and practical experiments verified the effectiveness of the developed scheme.

Application of interpolation methodology with dynamical constraint to the suspended particulate matter in the Liaodong Bay

IntroductionSuspended Particulate Matter (SPM) influences the primary production and the distributions of pollutants in the ocean. Besides, the regulation mechanisms of SPM in the Liaodong Bay were complicated.MethodTo analyze the distributions and influencing factors of SPM, based on the adjoint assimilation method, an interpolation method with dynamical constraint was established in the Liaodong Bay.ResultIn two ideal experiments, the cost function, Mean Absolute Error (MAE) and Normalized Mean Error (NME) all had reduced by more than 90%, which proved the accuracy of the interpolation method. Based on conventional observations of SPM, the distributions of dynamically constrained, Kriging and radial basis function (RBF) interpolations in March, May, August and October of 2015 were obtained.DiscussionThe cross-validation was carried out to compare the dynamically constrained interpolation and the unconstrained interpolations. Among seven unconstrained interpolation methods, the averaged MAE of RBF interpolation was the lowest, which was 10.976 mg/L. The averaged MAE of dynamically constrained interpolation was 7.703 mg/L, reduced by 29.8% compared with the RBF interpolation. It was indicated that RBF interpolation was the most accurate among the seven unconstrained interpolations and dynamically constrained interpolation was more accurate than unconstrained interpolations at the observation stations. The distributions of dynamically constrained and RBF interpolations were compared with Korean Geostationary Ocean Color Imager (GOCI) satellite-derived distributions of SPM concentrations in the Liaodong Bay. Fully considering the influences of the hydrodynamic processes, the dynamically constrained interpolation provided distributions more consistent with the satellite-derived distributions. However, due to the lack of observations in some areas and ignoring the influences of currents, some high values of SPM concentration were not captured by the distributions of RBF interpolation. Moreover, in accordance with the results of dynamically constrained interpolation, it was found that the SPM concentrations in the bay were affected by the SPM discharge from the Liao River Basin.

Advancing parameter estimation with Characteristic Finite Difference Method (CFDM) for a marine ecosystem model by assimilating satellite observations: Spatial distributions

The ecosystem parameters are critical for precisely determining the marine ecological process and improving the simulations of the marine ecological model. In this study, based on the NPZD (nutrient, phytoplankton, zooplankton and detritus) model, the surface chlorophyll-a observations obtained from Sea-viewing Wide Field-of-view Sensor (SeaWiFS) data were assimilated to estimate spatially ecosystem parameters in the Bohai, Yellow, and East China Seas using an adjoint assimilation method with characteristic finite difference scheme. The experiments of the moving Gaussian hump indicated that the characteristic finite difference method (CFDM) can get rid of the limit of stability and permit using large time steps, which reduces long computation durations and large memory requirements. The model performance was significantly improved after data assimilation with CFDM using a large time step of 6 hours. Moreover, the distributions of parameters of the NPZD model in winter in the Bohai Sea, the Yellow Sea, and the East China Sea were simulated by our method. Overall, the developed method can efficiently optimize the ecosystem parameters and the results can be beneficial for determining reasonable parameters of the marine ecological model.

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

AbstractThe 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 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.

Numerical study on the spatially varying drag coefficient in simulation of storm surges employing the adjoint method

From 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 DC 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.

Data assimilation in a coupled physical-biological model for the Bohai Sea and the Northern Yellow Sea

One difficulty with coupled physical-biological ocean models is determining optimal values of poorly known model parameters. The variational adjoint assimilation method is a powerful tool for the automatic estimation of parameters. We used this method to incorporate remote-sensed chlorophyll-a data into a coupled physical-biological model developed for the Bohai Sea and the Northern Yellow Sea. A 3-D NPZD model of nutrients (N), phytoplankton (P), zooplankton (Z) and detritus (D) was coupled with a physical model, the Princeton Ocean Model. Sensitivity analysis was carried out to choose suitable control variables from the model parameters. Numerical twin experiments were then conducted to demonstrate whether the spatio-temporal resolutions of the observations were adequate for estimating values of the control variables. Finally, based on the success of the twin experiments, we included remote-sensed chlorophyll-a data in the NPZD model. With the adjoint assimilation of these chlorophyll-a data, the coupled model better describes spring and autumn phytoplankton blooms and the annual cycle of phytoplankton at the surface layer for the study area. The annual cycle of simulated surface nutrient concentrations also agreed well with field observations. The adjoint method greatly improves the modelling capability of coupled ocean models, helping us to better understand and model marine ecosystems.