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

On the predictability of regional oceanic jet stream: The impact of model errors at the inflow boundary

When a jet is simulated in a fine-resolution regional model with inflow and outflow boundaries, its dynamical behavior depends crucially on the specified inflow boundary condition (IBC). Our primary goals are (1) to explore the model\u27s ability to simulate the jet when the IBC is approximately known, (2) to examine the dynamical propagation and growth of the IBC errors in both space and time, and (3) to assess the relative usefulness of different types of data used to specify the IBC. This paper represents the results of an ensemble of 30 IBC-perturbed experiments derived from the Semi-Spectral Primitive Equation Model (SPEM). It is found that the system is very sensitive to the IBC perturbation, particularly in the velocity component. Evaluation of the evolution of both ensemble-mean error variance and anomaly correlation shows that the system\u27s predictability limits are reached at 64 days for the streamfunction (ψ) field, 43 days for the density (ρ) field at the surface, and 50 days for the ρ field at the thermocline level. The longer predictability in the ψ field is mainly due to the use of the rigid-lid approximation, which filters out small-scale and hence unpredictable barotropic waves. A much shorter local predictability for all fields occurs in the domain\u27s central area, where the jet is most unstable and where the richest dynamical activity is concentrated. We also analyze the ensemble mean fields and the ensemble distribution of the jet-axis positions from the 30 IBC-perturbed simulations. The major results are: (1) the ensemble mean field exhibits a better representation of the reference jet than a single simulation, because the averaging procedure smooths out small-scale fluctuations for which there is little simulation skill left; (2) the least number of realizations necessary to constitute a usable ensemble lies between 12 and 20; (3) the distribution of jet-axis positions is Gaussian within 60 days and then becomes non-Gaussian and excursive. In addition, the difference of jet axis positions between the ensemble mean and the reference is not statistically distinguishable until 30 days. However, it deviates with time and becomes statistically significant at 60 days. Additional experiments are performed to help clarify (1) the difference between the present and traditional predictability known as the sensitivity to initial conditions, (2) the relative impact of velocity and density perturbations on the jet simulation, and (3) the minimum strength of the IBC perturbation that cause the jet system to be unpredictable

Analysis of the North Atlantic climatologies using a combined OGCM/adjoint approach

An exact adjoint for the full-scale Bryan-Cox primitive equation model is applied to assimilate the North Atlantic climatologies. The inverse calculation aims at searching a steady state oceanic general circulation consistent with observations, by controlling the model input parameters (such as the initial states and the upper thermal and haline boundary conditions). Two climatological hydrographies (Levitus (1982) and Fukumori and Wunsch (1991)) are used for the assimilation. This enables the examination of the sensitivity of the assimilated results to data quality. In addition, the consistency between the climatological hydrography and fluxes is discussed by examining the fits between the optimally estimated surface fluxes and the fluxes calculated by Oberhuber (1988). The efforts made in the study are directed toward assessing the effectiveness of the combined OGCM/ adjoint approach in estimating the state of the ocean from climatologies and identifying the associated problems. The major findings of the study include: (1) The results show that the full OGCM dynamics substantially helps the model in better simulating the frontal structure of the Gulf Stream system and the large-scale features of the velocity field, thus demonstrating the advantage of the full OGCM and its exact adjoint. (2) The study finds that the optimized temperature field has a systematic error structure in the vertical—the upper ocean is cooler and the deep ocean is warmer compared to the climatology. Our analysis indicates that the cool surface layer is a correction imposed by the optimization to reduce large data misfits in the deep ocean due to the deep warming. This deep warming is an outcome of using the steady state assumption, the annual mean climatology and the relaxation boundary condition at the model northern boundary. The annual mean hydrography has a surface water warmer than the observed winter surface water, and a deep ocean whose properties are determined by the surface water at high latitudes. Due to the imposed model northern boundary condition, the modeled deep waters are formed through the artificial sinking of surface waters with annual-mean temperature in the relaxation zone. This process leads to a warm deep ocean and large model-data discrepancies in the vast deep layer. In order to reduce the misfits as required by the optimal procedure, the surface layer which is the source for the modeled deep water needs to be cooler. The strong and deep vertical mixing formed in the model provides the means for an effective cooling. The results further show that the surface cooling is stronger for the experiment assimilating the Fukumofi and Wunsch hydrography because this climatology has an even warmer surface water due to the use of the summer-dominated data source. (3) The experiments assimilating the Levitus hydrography illustrate two anomalous features, one is a strong zonally integrated upwelling in the midlatitude and the other a very noisy flux estimation. The analysis shows that both features are induced by the smeared representation of the Gulf Stream frontal structure in the Levitus hydrography, which indicates that data quality is one of the important factors in obtaining satisfactory results from the assimilation. (4) Although the requirements for a global minimum are only partially satisfied, the experiments show that, comparing with the Levitus hydrography, the Fukumori and Wunsch hydrography is dynamically more compatible with the Oberhuber climatological fluxes

The North Atlantic current system : a scientific report, 19-20 April 1993, Woods Hole Oceanographic Institution, Woods Hole, MA 02543

Conference name: North Atlantic Current (NAC) System; 19-20 April 1993, Woods Hole Oceanographic Institution, Woods Hole, MAOn April 19-20, 1993 a two-day workshop was held at the Woods Hole Oceanographic Institution on "The North Atlantic Current (NAC) System". The workshop, which was sponsored by NSF/NOAA/ONR reflected a growing sense of excitement and interest in the oceanographic community in the NAC system and its role in the large scale circulation of the North Atlantic Ocean and Climate of the adjoining landmasses. The presence of the North Atlantic Current with its warm waters at such high latitudes, and its role in both the wind-driven and thermohaline circulations makes it unique amongst the Western Boundary Currents of the oceans. Being on the one hand part of the wind-driven circulation and on the other hand the upper branch of the "Global Conveyor Belt", the North Atlantic current is indeed an enigma, suggesting fundamental issues about the nature of the coupling between the two 'roles' of the current that will need to be addressed. But it was also clear from the workshop discussions that there remain considerable uncertainty about the basic structure of the NAC. A high level of interest in these questions was evident at the workshop. The lectures, presentations, and the discussion sessions where observational and modelling issues were debated, brought out many ideas for the development and focus of future research of the NAC and surrounding waters. This report is intended to provide not only a synopsis of the lectures, papers, and ideas that were discussed, but also a scientific statement from the workshop reflecting a growing consensus for initiating a coordinated research effort in the region.NSF/NOAA/ON

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

Assimilation of Altimeter Data into a Quasigeostrophic Model of the Gulf Stream System

The improvement in the climatological behavior of a numerical model as a consequence of the assimilation of surface data is investigated. The model used for this study is a quasigeostrophic (QG) model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height that have been obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations. Comparisons of the assimilation results with available in situ observations show a significant improvement in the degree of realism of the climatological model behavior, with respect to the model in which no data are assimilated. The remaining discrepancies in the model mean circulation seem to be mainly associated with deficiencies in the mean component of the surface data that are assimilated. On the other hand, the possibility of building into the model more realistic eddy characteristics through the assimilation of the surface eddy field proves very successful in driving components of the mean model circulation that are in relatively good agreement with the available observations. Comparisons with current meter time series during a time period partially overlapping the Geosat mission show that the model is able to 'correctly' extrapolate the instantaneous surface eddy signals to depths of approximately 1500 m. The correlation coefficient between current meter and model time series varies from values close to 0.7 in the top 1500 m to values as low as 0.1-0.2 in the deep ocean

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

Local feedback mechanisms of the shallow water region around the Maritime Continent

The focus of this study is the local-scale air-sea feedback mechanisms over the shallow shelf water region (water depth <200 m) of the Maritime Continent (MC). MC was selected as a pilot study site for its extensive shallow water coverage, geographic complexity, and importance in the global climate system. To identify the local-scale air-sea feedback processes, we ran numerical experiments with perturbed surface layer water temperature using a coupled ocean-atmosphere model and an uncoupled ocean model. By examining the responses of the coupled and uncoupled models to the water temperature perturbation, we identify that, at a local-scale, a negative feedback process through the coupled dynamics that tends to restore the SST from its perturbation could dominate the shallow water region of the MC at a short time scale of several days. The energy budget shows that 38% of initial perturbation-induced heat energy was adjusted through the air-sea feedback mechanisms within 2 weeks, of which 58% is directly transferred into the atmosphere by the adjustment of latent heat flux due to the evaporative cooling mechanism. The increased inputs of heat and moisture into the lower atmosphere then modifies its thermal structure and increases the formation of low-level clouds, which act as a shield preventing incoming solar radiation from reaching the sea surface, accounts for 38% of the total adjustment of surface heat fluxes, serving as the second mechanism for the negative feedback process. The adjustment of sensible heat flux and net longwave radiation play a secondary role. The response of the coupled system to the SST perturbation suggests a response time scale of the coupled feedback process of about 3–5 days. The two-way air-sea feedback tightly links the surface heat fluxes, clouds and SST, and can play an important role in regulating the short-term variability of the SST over the shallow shelf water regions

Coupled Ocean-Atmosphere Modeling Over the Maritime Continent: A Review

The Maritime Continent (MC) plays a vitally important role in the Earth\u27s climate system from both oceanic and atmospheric perspectives. While the critical role of ocean-atmosphere coupled dynamics over the MC has long been recognized, development of two-way coupled regional climate models for this region is still in its early stages. In this work, the authors review recent progress in two-way coupled ocean-atmosphere regional climate modeling. Development of coupled models and their applications in the MC are summarized. Model performances are discussed with a focus on regional oceanic and atmospheric characteristics. Through a critical review of modeling advances and limitations in simulating sea surface temperature, precipitation, and oceanic throughflows, the authors identify deficiencies of current models and discuss possible reasons. The review shows that model biases mainly stem from unresolved physical processes, inadequate model representations of the coupled system, and uncertainties in model configurations. The study reveals large-scale coupled modes of variability, local air-sea interactions, atmospheric dynamics, and oceanic processes play various roles in the observed modeling biases. Lastly, the authors offer suggestions on emerging opportunities for improving regional coupled modeling over the MC

Modeling the response of top-down control exerted by gelatinous carnivores on the Black Sea pelagic food web

Recent changes in structure and functioning of the interior Black Sea ecosystem are studied by a series of simulations using a one-dimensional, vertically resolved, coupled physical-biochemical model. The simulations are intended to provide a better understanding of how the pelagic food web structure responds to increasing grazing pressure by gelatinous carnivores (medusae Aurelia aurita and ctenophore Mnemiopsis leidyi) during the past 2 decades. The model is first shown to represent typical eutrophic ecosystem conditions of the late 1970s and early 1980s. This simulation reproduces reasonably well the observed planktonic food web structure at a particular location of the Black Sea for which a year-long data set is available from 1978. Additional simulations are performed to explore the role of the Mnemiopsis-dominated ecosystem in the late 1980s. They are also validated by extended observations from specific years. The results indicate that the population outbreaks of the gelatinous species, either Aurelia or Mnemiopsis, reduce mesozooplankton grazing and lead to increased phytoplankton blooms as observed throughout the 1980s and 1990s in the Black Sea. The peaks of phytoplankton, mesozooplankton, Noctiluca, and gelatinous predator biomass distributions march sequentially as a result of prey-predator interactions. The late winter diatom bloom and a subsequent increase in mesozooplankton stocks are robust features common to all simulations. The autotrophs and heterotrophs, however, have different responses during the rest of the year, depending on the nature of grazing pressure exerted by the gelatinous predators. In the presence of Mnemiopsis, phytoplankton have additional distinct and pronounced bloom episodes during the spring and summer seasons. These events appear with a 2 month time shift in the ecosystem prior to introduction of Mnemiopsis