A comparison of assimilation results from the ensemble Kalman Filter and a reduced-rank extended Kalman Filter

International audienceThe goal of this study is to compare the performances of the ensemble Kalman filter and a reduced-rank extended Kalman filter when applied to different dynamic regimes. Data assimilation experiments are performed using an eddy-resolving quasi-geostrophic model of the wind-driven ocean circulation. By changing eddy viscosity, this model exhibits two qualitatively distinct behaviors: strongly chaotic for the low viscosity case and quasi-periodic for the high viscosity case. In the reduced-rank extended Kalman filter algorithm, the model is linearized with respect to the time-mean from a long model run without assimilation, a reduced state space is obtained from a small number (100 for the low viscosity case and 20 for the high viscosity case) of leading empirical orthogonal functions (EOFs) derived from the long model run without assimilation. Corrections to the forecasts are only made in the reduced state space at the analysis time, and it is assumed that a steady state filter exists so that a faster filter algorithm is obtained. The ensemble Kalman filter is based on estimating the state-dependent forecast error statistics using Monte Carlo methods. The ensemble Kalman filter is computationally more expensive than the reduced-rank extended Kalman filter.The results show that for strongly nonlinear case, chaotic regime, about 32 ensemble members are sufficient to accurately describe the non-stationary, inhomogeneous, and anisotropic structure of the forecast error covariance and the performance of the reduced-rank extended Kalman filter is very similar to simple optimal interpolation and the ensemble Kalman filter greatly outperforms the reduced-rank extended Kalman filter. For the high viscosity case, both the reduced-rank extended Kalman filter and the ensemble Kalman filter are able to significantly reduce the analysis error and their performances are similar. For the high viscosity case, the model has three preferred regimes, each with distinct energy levels. Therefore, the probability density of the system has a multi-modal distribution and the error of the ensemble mean for the ensemble Kalman filter using larger ensembles can be larger than with smaller ensembles

Modeling distinct vertical biogeochemical structure of the Black Sea: Dynamical coupling of the oxic, suboxic, and anoxic layers

A one-dimensional, vertically resolved, physical-biogeochemical model is used to provide a unified representation of the dynamically coupled oxic-suboxic-anoxic system for the interior Black Sea. The model relates the annual cycle of plankton production in the form of a series of successive phytoplankton, mesozooplankton, and higher consumer blooms to organic matter generation and to the remineralization-ammonification-nitrification-dentrification chain of the nitrogen cycle as well as to anaerobic sulfide oxidation in the suboxic-anoxic interface zone. The simulations indicate that oxygen consumption during remineralixation and nitrification, together with a lack of ventilation of subsurface waters due to the presence of strong stratification, are the two main factors limiting aerobic biogeochemical activity to the upper similar to 75 m of the water column, which approximately corresponds to the level of nitrate maximum. The position of the upper boundary and thus the thickness of the suboxic layer are controlled by upper layer biological processes. The quasi-permanent character of this layer and the stability of the suboxic-anoxic interface within the last several decades are maintained by a constant rate of nitrate supply from the nitrate maximum zone. Nitrate is consumed to, oxidize sinking particulate organic matter as well as hydrogen sulfide and ammonium transported upward from deeper levels

Climatic warming and accompanying changes in the ecological regime of the Black Sea during 1990s

The Black Sea ecosystem is shown to experience abrupt shifts in its all trophic levels from primary producers to apex predators in 1995 - 1996. It arises as a manifestation of concurrent changes in its physical climate introduced by intensive warming of its surface waters as well as abrupt increases in the mean sea level and the net annual mean fresh water flux. The warming is evident in the annual-mean sea surface temperature (SST) data by a continuous rise at a rate of similar to 0.25 degreesC per year, following a strong cooling phase in 1991 - 1993. The most intense warming event with similar to2 degreesC increase in the SST took place during winters of the 1994 - 1996 period. It also coincides with 4 cm yr(-1) net sea level rise in the basin, and substantial change in the annual mean net fresh water flux from 150 km(3) yr(-1) in 1993 to 420 km(3) yr(-1) in 1997. The subsurface signature of warming is marked by a gradual depletion of the Cold Intermediate Layer ( characterized by T \u3c 8 °C) throughout the basin during the same period. Winters of the warming phase are characterized by weaker vertical turbulent mixing and upwelling velocity, stronger stratification and, subsequently, reduced upward nutrient supply from the nutricline. From 1996 onward, the major late winter-early spring peak of the classical annual phytoplankton biomass structure observed prior to mid- 90s was, therefore, either weakened or disappeared altogether depending on local meteorological and oceanographic conditions during each of these years. The effect of bottom-up limited unfavorable phytoplankton growth is reflected at higher trophic levels (e.g., mesozooplankton, gelatinous macrozooplankton, and pelagic fishes) in the form of their reduced stocks after 1995

The predictability of large-scale wind-driven flows

International audienceThe singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving examples of wind-driven, double-gyre circulations in different flow regimes are explored. By changing the Reynolds number in simple quasi-geostrophic models of the wind-driven circulation, steady, weakly aperiodic and chaotic states may be examined. The singular vectors of the steady state reveal some of the physical mechanisms responsible for optimally growing perturbations. In time-dependent cases, the dominant singular values show significant variability in time, indicating strong variations in the predictability of the flow. When the underlying flow is weakly aperiodic, the dominant singular values co-vary with integral measures of the large-scale flow, such as the basin-integrated upper ocean kinetic energy and the transport in the western boundary current extension. Furthermore, in a reduced gravity quasi-geostrophic model of a weakly aperiodic, double-gyre flow, the behaviour of the dominant singular values may be used to predict a change in the large-scale flow, a feature not shared by an analogous two-layer model. When the circulation is in a strongly aperiodic state, the dominant singular values no longer vary coherently with integral measures of the flow. Instead, they fluctuate in a very aperiodic fashion on mesoscale time scales. The dominant singular vectors then depend strongly on the arrangement of mesoscale features in the flow and the evolved forms of the associated singular vectors have relatively short spatial scales. These results have several implications. In weakly aperiodic, periodic, and stationary regimes, the mesoscale energy content is usually relatively low and the predictability of the wind-driven circulation is determined by the large-scale structure of the flow. In the more realistic, strongly chaotic regime, in which energetic mesoscale eddies are produced by the meandering of the separated western boundary current extension, the predictability of the flow locally tends to be a stronger function of the local mesoscale eddy structure than of the larger scale structure of the circulation. This has a broader implication for the effectiveness of different approaches to forecasting the ocean with models which sequentially assimilate new observations

Validation and application of an ensemble Kalman filter in the Selat Pauh of Singapore

The effectiveness of an ensemble Kalman filter (EnKF) is assessed in the Selat Pauh of Singapore using observing system simulation experiment. Perfect model experiments are first considered. The perfect model experiments examine the EnKF in reducing the initial perturbations with no further errors than those in the initial conditions. Current velocity at 15 observational sites from the true ocean is assimilated every hour into the false ocean. While EnKF reduces the initial velocity error during the first few hours, it fails after one tidal cycle (approximately 12 h) due to the rapid convergence of the ensemble members. Successively, errors are introduced in the surface wind forcing. A random perturbation ε [epsilon] is applied independently to each ensemble member to maintain the ensemble spread. The assimilation results showed that the success of EnKF depends critically on the presence of ε [epsilon], yet it is not sensitive to the magnitude of ε [epsilon], at least in the range of weak to moderate perturbations. Although all experiments were made with EnKF only, the results could be applicable in general to all other ensemble-based data assimilation methods.United States. Office of Naval ResearchSingapore. National Research FoundationSingapore-MIT Alliance for Research and Technology CenterSingapore-MIT Alliance. Center for Environmental Sensing and Monitorin

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