The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference （FD） scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.
The vertical structures of atmospheric temperature anomalies associated with El Nio are simulated with a spectrum atmospheric general circulation model developed by LASG/IAP （SAMIL）. Sensitivity of the model’s response to convection scheme is discussed. Two convection schemes, i.e., the revised Zhang and Macfarlane （RZM） and Tiedtke （TDK） convection schemes, are employed in two sets of AMIP-type （Atmospheric Model Intercomparison Project） SAMIL simulations, respectively. Despite some deficiencies in the upper troposphere, the canonical El Nio-related temperature anomalies characterized by a prevailing warming throughout the tropical troposphere are well reproduced in both simulations. The performance of the model in reproducing temperature anomalies in ＂atypical＂ El Nio events is sensitive to the convection scheme. When employing the RZM scheme, the warming center over the central-eastern tropical Pacific and the strong cooling in the western tropical Pacific at sea surface level are underestimated. The quadru-pole temperature anomalies in the middle and upper troposphere are also obscured. The result of employing the TDK scheme resembles the reanalysis and hence shows a better performance. The simulated largescale circulations associated with atypical El Nio events are also sensitive to the convection schemes. When employing the RZM scheme, SAMIL failed in capturing the classical Southern Oscillation pattern. In accordance with the unrealistic anomalous Walker circulation and the upper tropospheric zonal wind changes, the deficiencies of the precipitation simulation are also evident. These results demonstrate the importance of convection schemes in simulating the vertical structure of atmospheric temperature anomalies associated with El Nio and should serve as a useful reference for future improvement of SAMIL.
Data assimilation is a powerful tool to improve ocean forecasting by reducing uncertainties in forecast initial conditions.Recently,an ocean data assimilation system based on the ensemble optimal interpolation(EnOI) scheme and HYbrid Coordinate Ocean Model(HYCOM) for marginal seas around China was developed.This system can assimilate both satellite observations of sea surface temperature(SST) and along-track sea level anomaly(SLA) data.The purpose of this study was to evaluate the performance of the system.Two experiments were performed,which spanned a 3-year period from January 1,2004 to December 30,2006,with and without data assimilation.The data assimilation results were promising,with a positive impact on the modeled fields.The SST and SLA were clearly improved in terms of bias and root mean square error over the whole domain.In addition,the assimilations provided improvements in some regions to the surface field where mesoscale processes are not well simulated by the model.Comparisons with surface drifter trajectories showed that assimilated SST and SLA also better represent surface currents,with drifter trajectories fitting better to the contours of SLA field than that without assimilation.The forecasting capacity of this assimilation system was also evaluated through a case study of a birth-and-death process of an anticyclone eddy in the Northern South China Sea(NSCS),in which the anticyclone eddy was successfully hindcasted by the assimilation system.This study suggests the data assimilation system gives reasonable descriptions of the near-surface ocean state and can be applied to forecast mesoscale ocean processes in the marginal seas around China.
This paper describes a dynamical downscaling simulation over China using the nested model system,which consists of the modified Weather Research and Forecasting Model(WRF)nested with the NCAR Community Atmosphere Model(CAM).Results show that dynamical downscaling is of great value in improving the model simulation of regional climatic characteristics.WRF simulates regional detailed temperature features better than CAM.With the spatial correlation coefficient between the observation and the simulation increasing from 0.54 for CAM to 0.79 for WRF,the improvement in precipitation simulation is more perceptible with WRF.Furthermore,the WRF simulation corrects the spatial bias of the precipitation in the CAM simulation.
A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander （KLM） state using the conditional nonlinear optimal parameter perturbation （CNOP-P） method. Because of their relatively large uncertainties, three model parameters were considered： the interracial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 （SPG2） algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation （CNOP-I） method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.
