Peter R. Oke

A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters

The use of perturbed observations in the traditional ensemble Kalman filter (EnKF) results in a suboptimal filter behaviour, particularly for small ensembles. In this work, we propose a simple modification to the traditional EnKF that results in matching the analysed error covariance given by Kalman filter in cases when the correction is small; without perturbed observations. The proposed filter is based on the recognition that in the case of small corrections to the forecast the traditional EnKF without perturbed observations reduces the forecast error covariance by an amount that is nearly twice as large as that is needed to match Kalman filter. The analysis scheme works as follows: update the ensemble mean and the ensemble anomalies separately; update the mean using the standard analysis equation; update the anomalies with the same equation but half the Kalman gain. The proposed filter is shown to be a linear approximation to the ensemble square root filter (ESRF). Because of its deterministic character and its similarity to the traditional EnKF we call it the ‘deterministic EnKF’, or the DEnKF. A number of numerical experiments to compare the performance of the DEnKF with both the EnKF and an ESRF using three small models are conducted. We show that the DEnKF performs almost as well as the ESRF and is a significant improvement over the EnKF. Therefore, the DEnKF combines the numerical effectiveness, simplicity and versatility of the EnKF with the performance of the ESRFs. Importantly, the DEnKF readily permits the use of the traditional Schur product-based localization schemes.

Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters

Abstract This paper considers implications of different forms of the ensemble transformation in the ensemble square root filters (ESRFs) for the performance of ESRF-based data assimilation systems. It highlights the importance of using mean-preserving solutions for the ensemble transform matrix (ETM). The paper shows that an arbitrary mean-preserving ETM can be represented as a product of the symmetric solution and an orthonormal mean-preserving matrix. The paper also introduces a new flavor of ESRF, referred to as ESRF with mean-preserving random rotations. To investigate the performance of different solutions for the ETM in ESRFs, experiments with two small models are conducted. In these experiments, the performances of two mean-preserving solutions, two non-mean-preserving solutions, and a traditional ensemble Kalman filter with perturbed observations are compared. The experiments show a significantly better performance of the mean-preserving solutions for the ETM in ESRFs compared to non-mean-preservi...

An Ensemble Ocean Data Assimilation System for Seasonal Prediction

Abstract A new ensemble ocean data assimilation system, developed for the Predictive Ocean Atmosphere Model for Australia (POAMA), is described. The new system is called PEODAS, the POAMA Ensemble Ocean Data Assimilation System. PEODAS is an approximate form of an ensemble Kalman filter system. For a given assimilation cycle, a central forecast is integrated, along with a small ensemble of forecasts that are forced with perturbed surface fluxes. The small ensemble is augmented with multiple small ensembles from previous assimilation cycles, yielding a larger ensemble that consists of perturbed forecasts from the last month. This larger ensemble is used to represent the system’s time-dependent background error covariance. At each assimilation cycle, a central analysis is computed utilizing the ensemble-based covariance. Each of the perturbed ensemble members are nudged toward the central analysis to control the ensemble spread and mean. The ensemble-based covariances generated by PEODAS potentially yield d...

An avenue of eddies: Quantifying the biophysical properties of mesoscale eddies in the Tasman Sea

[1] The Tasman Sea is unique - characterised by a strong seasonal western boundary current that breaks down into a complicated field of mesoscale eddies almost immediately after separating from the coast. Through a 16-year analysis of Tasman Sea eddies, we identify a region along the southeast Australian coast which we name ‘Eddy Avenue’ where eddies have higher sea level anomalies, faster rotation and greater sea surface temperature and chlorophyll a anomalies. The density of cyclonic and anticyclonic eddies within Eddy Avenue is 23% and 16% higher respectively than the broader Tasman Sea. We find that Eddy Avenue cyclonic and anticyclonic eddies have more strongly differentiated biological properties than those of the broader TasmanSea, as a result of larger anticyclonic eddies formed from Coral Sea water depressing chl. a concentrations, and for coastal cyclonic eddies due to the entrainment of nutrient-rich shelf waters. Cyclonic eddies within Eddy Avenue have almost double the chlorophyll a (0.35 mg m 3 ) of anticyclonic eddies (0.18 mg m 3 ). The average chlorophyll a concentration for cyclonic eddies is 16% higher in Eddy Avenue and 28% lower for anticyclonic eddies when compared to the Tasman Sea. With a strengthening East Australian Current, the propagation of these eddies will have significant implications for heat transport and the entrainment and connectivity of plankton and larval fish populations. Citation: Everett, J. D., M. E. Baird, P. R. Oke, and I. M. Suthers (2012), An avenue of eddies: Quantifying the biophysical properties of mesoscale eddies in the Tasman Sea, Geophys. Res. Lett., 39, L16608, doi:10.1029/ 2012GL053091.

A Modeling Study of the Three-Dimensional Continental Shelf Circulation off Oregon. Part I: Model–Data Comparisons

Sixty-day simulations of the subinertial continental shelf circulation off Oregon are performed for a hindcast study of summer 1999. Model results are compared with in situ currents, high-frequency radar‐derived surface currents, and hydrographic measurements obtained from an array of moored instruments and field surveys. The correlations between observed and modeled alongshore currents and temperatures in water depths of 50 m are in excess of 0.8. A study designed to test the model’s sensitivity to different initial stratification, surface forcing, domain size, and river forcing demonstrates that surface heating is important, and that the model results are sensitive to initial stratification. An objective criterion for assessing the skill of a model simulation relative to a control simulation is outlined, providing an objective means for identifying the best model simulation. The model‐data comparisons demonstrate that temperature fluctuations off Newport are primarily in response to surface heating and that subsurface density fluctuations are controlled by the wind-forced circulation through salinity. Experiments with river forcing indicate that, in the vicinity of Newport, the Columbia River plume is typically greater than 15 km from the coast and is confined to the top few meters of the water column. Additionally, the model‐data comparisons suggest that the strongest upwelling occurs to the north of Newport where the continental shelf is relatively narrow and uniform in the alongshore direction. Part II of this study investigates the modeled three-dimensional circulation and dynamical balances. A numerical modeling study of the coastal ocean circulation off Oregon during the 1999 upwelling season is presented. The model results are compared with in situ velocity, temperature and salinity measurements, and high-frequency (HF) radar‐derived surface currents obtained during summer 1999 as a part of the Oregon State University (OSU) National Oceanographic Partnership Program (NOPP) project. The aims of this study are to assess the performance of the model, to identify the dominant physical processes, and to assess the model’s sensitivity to variations in initial stratification, surface forcing, model domain size, and river forcing. Processes that are of particular interest in this study include the response to wind forcing and the generation of the northward flow that is commonly observed off Newport (44.658N) over the

Evaluation of a near-global eddy-resolving ocean model

Abstract. Analysis of the variability of the last 18 yr (1993–2012) of a 32 yr run of a new near-global, eddy-resolving ocean general circulation model coupled with biogeochemistry is presented. Comparisons between modelled and observed mean sea level (MSL), mixed layer depth (MLD), sea level anomaly (SLA), sea surface temperature (SST), and {\chla} indicate that the model variability is realistic. We find some systematic errors in the modelled MLD, with the model generally deeper than observations, which results in errors in the {\chla}, owing to the strong biophysical coupling. We evaluate several other metrics in the model, including the zonally averaged seasonal cycle of SST, meridional overturning, volume transports through key straits and passages, zonally averaged temperature and salinity, and El Nino-related SST indices. We find that the modelled seasonal cycle in SST is 0.5–1.5 °C weaker than observed; volume transports of the Antarctic Circumpolar Current, the East Australian Current, and Indonesian Throughflow are in good agreement with observational estimates; and the correlation between the modelled and observed NINO SST indices exceeds 0.91. Most aspects of the model circulation are realistic. We conclude that the model output is suitable for broader analysis to better understand upper ocean dynamics and ocean variability at mid- and low latitudes. The new model is intended to underpin a future version of Australias operational short-range ocean forecasting system.

A Modeling Study of the Three-Dimensional Continental Shelf Circulation off Oregon. Part II: Dynamical Analysis

Abstract Sixty-day simulations of the subinertial continental shelf circulation off Oregon are performed for a hindcast study of summer 1999. In Part I, the model results are shown to compare favorably with in situ currents and hydrographic measurements obtained from an array of moored instruments and field surveys and high-frequency radar–derived surface currents. In this paper, the modeled three-dimensional, time-varying circulation and dynamical balances are analyzed, providing a detailed synoptic description of the continental shelf circulation off Oregon for summer 1999. The circulation is clearly wind driven and strongly influenced by alongshore variations in shelf topography. In the region of the coast where the alongshore topographic variations are small the upwelling circulation is consistent with standard conceptual models for two-dimensional across-shore circulation. In the regions where the alongshore topographic variations are greater, the upwelling circulation is highly three-dimensional. Ov...

Representation Error of Oceanic Observations for Data Assimilation

Abstract A simple approach to the estimation of representation error (RE) of sea level (η), temperature (T), and salinity (S) observations for ocean data assimilation is described. It is assumed that the main source of RE is due to unresolved processes and scales in the model. Therefore, RE is calculated as a function of model resolution. The methods described here exploit the availability of mapped sea level anomalies (mSLAs) and along-track sea level anomalies (atSLAs). The mSLA fields or atSLA observations are regarded as the true ocean state. Here, they are averaged according to the resolution of the model grid, and the averaged field is taken as a representation of the true state on the given grid. The difference between the original data and the averaged field is then regarded as the RE for η. Subsequently, the RE is projected for η over depth using a standard technique, giving an estimate of the RE for T and S. Examples of RE estimates for an intermediate- and high-resolution global grid are presen...

Decadal changes in the South Pacific western boundary current system revealed in observations and ocean state estimates

Observations and ocean state estimates are used to investigate the nature and mechanism of decadal variability in the East Australian Current (EAC) system and South Pacific subtropical gyre. A 62 year record on the Tasmanian continental shelf shows decadal variations of temperature and salinity, as well as a long-term trend, which has been related to wind-driven variations in the poleward extension of the EAC. Repeat expendable bathythermograph lines spanning the last 15 years suggest that low-frequency variations in the transport of the EAC extension and Tasman Front are anticorrelated, but the time series are too short to draw firm conclusions. Here we use two ocean state estimates spanning the past 50 years to diagnose the physical mechanisms and spatial structure of the decadal variability of the South Pacific subtropical gyre. The observations and state estimates paint a consistent picture of the decadal variability of the gyre and EAC system. Strengthening of the basin-wide wind stress curl drives a southward expansion of the subtropical gyre. As the gyre shifts south, the EAC extension pathway is favored at the expense of the Tasman Front, resulting in the observed anticorrelation of the these two major currents. The results suggest that the subtropical gyre and western boundary current respond to decadal variability in basin-scale wind stress curl, consistent with Island Rule dynamics; that strong decadal variability of the South Pacific gyre complicates efforts to infer trends from short-term records; and that wind stress curl changes over the South Pacific basin drive changes in the EAC system that are likely to have implications for marine ecosystems and regional climate.

Objective Array Design: Application to the Tropical Indian Ocean

Abstract A simple, versatile, computationally efficient ensemble-based method for objectively designing an observation array is described. The method seeks to compute the observation array that minimizes the analysis error variance, according to Kalman filter theory. While most elements of the method have been described elsewhere, this paper attempts to present a simple, yet comprehensive, recipe for array design based on an ensemble of anomalies that represents the background error covariance. The versatility of the method is demonstrated through a series of applications to the tropical Indian Ocean (TIO). The first application uses model-generated fields of high-pass-filtered mixed layer depth to design an array to monitor intraseasonal variability. The second uses gridded observations of sea level anomaly to design an array to monitor intraseasonal-to-interannual variability. For both applications, the objectively designed arrays are compared to an array that will soon be implemented under the auspices...