Xianqing Lv

Original article: Estimation of spatially varying open boundary conditions for a numerical internal tidal model with adjoint method

The adjoint data assimilation technique is applied to the estimation of the spatially varying open boundary conditions (OBCs) for a numerical internal tidal model. The spatial variation of the OBCs is realized by the so-called independent point scheme (IPS): a subset is chosen as the independent points from the full set of open boundary points and the OBCs are obtained through linear interpolation of the values at the independent points. A series of ideal experiments are carried out on a real topography to further test this assimilation model, and to numerically investigate some properties of the IPS. On the basis of the numerical results, it is shown that, in most cases, the use of the IPS can indeed effectively improve the precision of the estimation of the OBCs. Furthermore, if the independent points can be arranged reasonably the improvement may be remarkable. The IPS shows us a way to improve the estimation of the OBCs for this model.

Inverse Estimation of Open Boundary Conditions in the Bohai Sea

This paper presents an algorithm for the estimation of open boundary conditions (OBCs) which force tides in the interior region by an adjoint data assimilation approach. Assuming that OBCs are position dependent, OBCs can be approximated by linear interpolation among values at certain independent points (IPs). Twin experiments are performed to examine the sensitivity of the model to the IP distribution and interpolation radius. It is proved that the prescribed OBCs can be well recovered with appropriate number of IP and interpolation radius. In the Bohai Sea model domain with horizontal resolution of , the appropriate number of IP is 3 and the interpolation radius is 60′. In the practical experiment, the M2 constituent in the Bohai Sea is simulated by assimilating the T/P data and tidal gauge data. The mean absolute errors in amplitude and phase are 5.0 cm and 5.7°, respectively, and the cochart obtained shows the character of M2 constituent in the Bohai Sea.

Estimation of Open Boundary Conditions for an Internal Tidal Model with Adjoint Method: A Comparative Study on Optimization Methods

Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS) method and two gradient descent (GD) methods (the normal one with Wolfe’s line search and the simplified one) are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs) are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.

Optimization of Open Boundary Conditions in a 3D Internal Tidal Model with the Adjoint Method around Hawaii

Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs) in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients of internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs). In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP) strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, the internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.

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.

Inversion of Tidal Open Boundary Conditions of the M2 Constituent in the Bohai and Yellow Seas

AbstractOpen boundary conditions (OBCs) of the M2 tidal constituent in the Bohai and Yellow Seas (BYS) were inverted successfully through assimilation of TOPEX/Poseidon (T/P) altimeter data. An improved independent points (IPs) scheme was employed in the inversion. Under the assumption that the OBC was spatially varying, values at a set of IPs along the open boundary were inverted using the adjoint method and those at other points were calculated by the spline interpolation. The OBC inverted with the improved scheme was closer to reality in terms of smoothness than that inverted with the Cressman interpolation. The scheme was calibrated in twin experiments. Practical experiments showed that the misfits between simulated results and observations were smaller when the spline interpolation was used.

Application of Surface Spline Interpolation in Inversion of Bottom Friction Coefficients

AbstractA new method for the inversion of bottom friction coefficients (BFCs) in a two-dimensional tidal model is proposed in this study. In this method, the field of BFCs is constructed by interpolating values at independent points using a surface spline. The surface spline interpolation has an advantage: that the constructed surface is smoother than the surface constructed by the traditionally used linear interpolation, which has unrealistic extrema. The method is validated in twin experiments where the prescribed nonlinear distribution of BFCs are better inverted with the surface spline interpolation. In practical experiments, the BFCs are inverted and the M2 tide in the Bohai Sea is simulated by assimilating the TOPEX/Poseidon (T/P) data. The small errors between the simulation results and the observations, as well as the accurate cotidal charts, demonstrate the feasibility of the new method in practical application.

The Parameters Estimation for a PM2.5 Transport Model with the Adjoint Method

Based on the theory of inverse problem and data assimilation, the adjoint method is applied for the estimation of parameters including the initial condition (IC), the source and sink (SS) in a PM2.5 transport model. To reduce the ill-posedness of the inverse problem, an independent point scheme (IPS) is implemented during the estimation process. In twin experiments, both the prescribed IC and SS can be inverted successfully and better inversion results are obtained when the IPS is used than not, suggesting the feasibility and validity of the PM2.5 transport model as well as the IPS. In practical experiments, several inversion strategies are compared based on the simulation results of PM2.5 concentrations over China. It is found that IC and SS are better estimated with smaller difference between simulated results and observations, when IC and SS are inverted simultaneously than separately. And the simulated results can reproduce the temporal and spatial variation feature of the observed PM2.5 concentrations. On the basis of the numerical results, it is shown that the adjoint method and the IPS are the powerful way to improve the precision of the simulation of the PM2.5 concentrations.

A Study on Bottom Friction Coefficient in the Bohai, Yellow, and East China Sea

The adjoint tidal model based on the theory of inverse problem has been applied to investigate the effect of bottom friction coefficient (BFC) on the tidal simulation. Using different schemes of BFC containing the constant, different constant in different subdomain, depth-dependent form, and spatial distribution obtained from data assimilation, the M2 constituent in the Bohai, Yellow, and East China Sea (BYECS) is simulated by assimilating TOPEX/Poseidon altimeter data, respectively. The simulated result with spatially varying BFC obtained from data assimilation is better than others. Results and analysis of BFC in BYECS indicate that spatially varying BFC obtained from data assimilation is the best fitted one; meanwhile it could improve the accuracy in the simulation of M2 constituent. Through the analysis of the best fitted one, new empirical formulas of BFC in BYECS are developed with which the commendable simulated results of M2 constituent in BYECS are obtained.

A Modified Interpolation Method for Surface Total Nitrogen in the Bohai Sea

AbstractA modified Cressman interpolation method (MCIM) is presented for the routine monitoring data of total nitrogen (TN) in the Bohai Sea to reduce interpolation errors by decreasing the influence radius and introducing background value. In twin experiments, two prescribed distributions are successfully estimated by MCIM with lower interpolation errors than the traditional Cressman interpolation method (TCIM) and the kriging method. In practical experiments, cross validation is applied to evaluate the interpolation results for four quarters in 2009 and 2010. Practical experimental results show that the interpolation results obtained with MCIM are greatly improved and can describe the spatial distribution characteristics of TN in the Bohai Sea with lower mean absolute error than the kriging method.