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Jiang Zhu and Masafumi Kamachi

Abstract

It is found that some stable time-integration schemes for some nonlinear models do not guarantee stable integrations of the associated tangent linear models with the same time step size. These problems usually occur when the nonlinear models describe vertical diffusion processes and are numerically implemented by semi-implicit time-integration schemes that are unconditionally stable. The direct linearization procedure performed on such numerical schemes of nonlinear models can be interpreted as some conditionally stable numerical schemes of the underlying linearized equations.

Numerical experiments using a simple, illustrative model and a realistic ocean mixed layer model and their tangent linear models showed instabilities in the tangent linear models. Several methods are tried to reduce the nonphysical noise caused by the numerical instabilities. This study suggests that reducing time step size can give good results compared to some other methods that either are not accurate enough or change too much from the original nonlinear model.

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Norihisa Usui, Yosuke Fujii, Kei Sakamoto, and Masafumi Kamachi

Abstract

The authors have developed an assimilation system toward coastal data assimilation around Japan, which consists of a four-dimensional variational (4DVAR) assimilation scheme with an eddy-resolving model in the western North Pacific (MOVE-4DVAR-WNP) and a fine-resolution coastal model covering the western part of the Japanese coastal region around the Seto Inland Sea (MOVE-Seto). The 4DVAR scheme is developed as a natural extension of the 3DVAR scheme used in the Meteorological Research Institute Multivariate Ocean Variational Estimation (MOVE) system. An initialization scheme of incremental analysis update (IAU) is incorporated into MOVE-4DVAR-WNP to filter out high-frequency noises. During the backward integration of the adjoint model, it works as an incremental digital filtering. MOVE-Seto, which is nested within MOVE-4DVAR-WNP, also employs IAU to initialize the interior of the coastal model using MOVE-4DVAR-WNP analysis fields. The authors conducted an assimilation experiment using MOVE-4DVAR-WNP, and results were compared with an additional experiment using the 3DVAR scheme. The comparison reveals that MOVE-4DVAR-WNP improves mesoscale variability. In particular, short-term variability such as small-scale Kuroshio fluctuations is much enhanced. Using MOVE-Seto and MOVE-4DVAR-WNP, the authors also performed a case study focused on an unusual tide event that occurred at the south coast of Japan in September 2011. MOVE-Seto succeeds in reproducing a significant sea level rise associated with this event, indicating the effectiveness of the newly developed system for coastal sea level variability.

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Yosuke Fujii, Toshiyuki Nakaegawa, Satoshi Matsumoto, Tamaki Yasuda, Goro Yamanaka, and Masafumi Kamachi

Abstract

The authors developed a system for simulating climate variation by constraining the ocean component of a coupled atmosphere–ocean general circulation model (CGCM) through ocean data assimilation and conducted a climate simulation [Multivariate Ocean Variational Estimation System–Coupled Version Reanalysis (MOVE-C RA)]. The monthly variation of sea surface temperature (SST) is reasonably recovered in MOVE-C RA. Furthermore, MOVE-C RA has improved precipitation fields over the Atmospheric Model Intercomparison Project (AMIP) run (a simulation of the atmosphere model forced by observed daily SST) and the CGCM free simulation run. In particular, precipitation in the Philippine Sea in summer is improved over the AMIP run. This improvement is assumed to stem from the reproduction of the interaction between SST and precipitation, indicated by the lag of the precipitation change behind SST. Enhanced (suppressed) convection tends to induce an SST drop (rise) because of cloud cover and ocean mixing in the real world. A lack of this interaction in the AMIP run leads to overestimating the precipitation in the Bay of Bengal in summer. Because it is recovered in MOVE-C RA, the overestimate is suppressed. This intensifies the zonal Walker circulation and the monsoon trough, resulting in enhanced convection in the Philippine Sea. The spurious positive correlation between SST and precipitation around the Philippines in the AMIP run in summer is also removed in MOVE-C RA. These improvements demonstrate the effectiveness of simulating ocean interior processes with the ocean model and data assimilation for reproducing the climate variability.

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Nozomi Sugiura, Shuhei Masuda, Yosuke Fujii, Masafumi Kamachi, Yoichi Ishikawa, and Toshiyuki Awaji

Abstract

Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled by adjusting initial conditions to bring all stable modes closer to observations and by using a continuous guide to direct unstable modes toward a reference time series. This interpretation provides a consistent and effective procedure for solving problems of long-term state estimation. By applying this approach to an ocean general circulation model with a parameterized vertical diffusion procedure, it is demonstrated that tangent linear and adjoint models in this framework should have no unstable modes and hence be suitable for tracking persistent signals. This methodology is widely applicable to extend the assimilation period in 4D-Var.

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