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Christian L. Keppenne
and
Michele M. Rienecker

Abstract

A multivariate ensemble Kalman filter (MvEnKF) implemented on a massively parallel computer architecture has been developed for the Poseidon ocean circulation model and tested with a Pacific basin model configuration. There are about 2 million prognostic state-vector variables. Parallelism for the data assimilation step is achieved by regionalization of the background-error covariances that are calculated from the phase–space distribution of the ensemble. Each processing element (PE) collects elements of a matrix measurement functional from nearby PEs. To avoid the introduction of spurious long-range covariances associated with finite ensemble sizes, the background-error covariances are given compact support by means of a Hadamard (element by element) product with a three-dimensional canonical correlation function.

The methodology and the MvEnKF implementation are discussed. To verify the proper functioning of the algorithms, results from an initial experiment with in situ temperature data are presented. Furthermore, it is shown that the regionalization of the background covariances has a negligible impact on the quality of the analyses.

Even though the parallel algorithm is very efficient for large numbers of observations, individual PE memory, rather than speed, dictates how large an ensemble can be used in practice on a platform with distributed memory.

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Victoria J. Coles
and
Michele M. Rienecker

Abstract

This study considers the advective transport in the thermocline between the subtropical and tropical Pacific using two different models: MICOM (fully isopycnal) and Poseidon (quasi-isopycnal). The annually averaged model climatologies are comparable to other model and observational results, with Poseidon showing relatively greater western boundary current exchange and MICOM having a more significant basin interior pathway. This difference is related to the different representations of the thermocline ridge associated with the ITCZ, and of the zonal current systems at 8°–10°N.

In both models, the interior exchange pathway is highly seasonal, with pulsed southward flow occurring during the fall and early winter as the thermocline thickens. This is the time period when the thermocline is shallowest in the central Pacific associated with the maximum North Equatorial Countercurrent transport and when the Ekman pumping associated with positive wind stress curl is shifted northward in the Tropics.

Idealized tracer fields show both the continuity and seasonality of the transport pathway between subtropics and the equator, with enhanced pumping of tracer into the equatorial Pacific at 140°W over a 6-month (fall/winter) period, followed by a quiescent (spring/summer) period. Both models suggest that not only is the interior flow across the potential vorticity maximum constrained to a relatively small zonal region but, also, that the shallow subtropical overturning cell is a localized process with significant zonal variation in intensity.

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Michael S. Dinniman
and
Michele M. Rienecker

Abstract

A primitive equation model [Geophysical Fluid Dynamics Laboratory’s (GFDL’s) MOM 2] with one degree horizontal resolution is used to simulate the seasonal cycle of frontogenesis in the subarctic frontal zone (SAFZ) and the subtropical frontal zone (STFZ) of the North Pacific Ocean. The SAFZ in the model contains deep (greater than 500 m in some places) regions with seasonally varying high gradients in temperature and salinity. The gradients generally weaken toward the east. The STFZ consists of a relatively shallow (less than 200 m in most places) region of high gradient in temperature that disappears in the summer/fall. The high gradient in salinity in the STFZ maintains its strength year round and extends across almost the entire basin. The model simulates the location and intensity of the frontal zones in good agreement with climatological observations: generally to within two degrees of latitude and usually at the same or slightly stronger intensity. The seasonal cycle of the frontal zones also matches observations well, although the subarctic front is stronger than observed in winter and spring.

The model balances are examined to identify the dominant frontogenetic processes. The seasonal cycle of temperature frontogenesis in the surface level of the model is governed by both the convergence of the wind-driven Ekman transport and differential heating/cooling. In the STFZ, the surface Ekman convergence is frontogenetic throughout the year as opposed to surface heating, which is frontogenetic during winter and strongly frontolytic during late spring and summer. The subarctic front at 40°N in the central Pacific (not the maximum wintertime gradient in the model, but its location in summer and the location where variability is in best agreement with the observations) undergoes frontogenesis during spring and summer due to surface Ekman convergence and differential horizontal shear. The frontolysis during winter is due to the joint influence of differential heat flux and vertical convection in opposition to frontogenetic Ekman convergence. The seasonal cycle of salinity frontogenesis in the surface level is governed by Ekman convergence, differential surface freshwater flux, and differential vertical convection (mixing). For salinity, the differential convection is primarily forced by Ekman convergence and differential cooling, thereby linking the salinity and temperature frontogenesis/frontolysis. Below the surface level, the seasonal frontogenesis/frontolysis is only significant in the western and central SAFZ where it is due primarily to differential mixing (mostly in winter and early spring) with contributions from convergence and shearing advection during fall and winter. The shearing advection in the model western SAFZ is likely a result of the Kuroshio overshooting its observed separation latitude. The model’s vertical mixing through convective adjustment is found to be very important in controlling much of the frontogenesis/frontolysis. Thus, the seasonal cycle of the surface frontal variability depends strongly on the subsurface structure.

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David Adamec
,
Michele M. Rienecker
, and
Jeffrey M. Yukovich

Abstract

The time-varying meridional Ekman heat transport for the World Ocean is calculated for the 30-year period 1960–1989 using wind stress and sea surface temperature data from the Comprehensive Ocean–Atmosphere Data Set The average monthly heat transports are dominated by poleward transport of heat in the tropical Pacific and Atlantic oceans. In the Indian Ocean, the strong monsoonal flow during summer is responsible for a large equatorward transport. If seasonal effects are removed, the tropical Pacific displays the most variance in Ekman heat transport and the Atlantic the least. Two sets of empirical orthogonal functions (EOFs) are computed to investigate the nonseasonal variability of the Ekman transport The first set, which uses the eigenvector decomposition of the covariance matrix, emphasizes covariability in the world's tropical oceans. The time series of the EOF amplitudes contain a clear signal that can be directly related to El Niño. The El Niño signal is manifest as an increase in the equatorward transport of heat in the western Pacific followed by an increase in the poleward transport of heat in the eastern Pacific. The second set of EOFs, which highlights spatial oscillations only, shows the influence of zonal bands of wind stress and the large-scale patterns of Ekman suction/pumping.

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Shu-Chih Yang
,
Eugenia Kalnay
,
Ming Cai
, and
Michele M. Rienecker

Abstract

The breeding method has been implemented in the NASA Global Modeling and Assimilation Office coupled general circulation model (CGCM) in its operational configuration in which ocean data assimilation is used to initialize the coupled forecasts. Bred vectors (BVs), designed to capture the dominant growing errors in the atmosphere–ocean coupled system, are applied as initial ensemble perturbations. The potential improvement for ensemble prediction is investigated by comparing BVs with the oceanic growing errors, estimated by the one-month forecast error from the nonperturbed forecast. Results show that one-month forecast errors and BVs from the NASA CGCM share very similar features: BVs are clearly related to forecast errors in both SST and equatorial subsurface temperature—in particular, when the BV growth rate is large. Both the forecast errors and the BVs in the subsurface are dominated by large-scale structures near the thermocline. Results suggest that the forecast errors are dominated by dynamically evolving structures related to the variations of the background anomalous state, and that their shapes can be captured by BVs, especially during the strong 1997/98 El Niño. Hindcast experiments starting from January 1997 with one pair of BVs achieve a significant improvement relative to the control (unperturbed) hindcast by capturing many important features of this event, including the westerly wind burst in early 1997.

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Anna Borovikov
,
Michele M. Rienecker
, and
Paul S. Schopf

Abstract

The surface heat budget in the equatorial Pacific Ocean was investigated through ocean model simulations, both the climatological cycle and the case of the 1994–95 warm event. The dominant processes governing the seasonal cycle of sea surface temperature (SST) vary significantly across the basin. In the western Pacific the annual cycle of SST is primarily in response to net surface heat flux. In the central basin the magnitude of the zonal advection term is comparable to that of the net surface heat flux. In the eastern basin the role of zonal advection is reduced and the vertical mixing and advection are more important. The model estimate of the vertical mixing contribution to the mixed layer heat budget compared well with estimates obtained by analysis of observations using the same diagnostic vertical mixing scheme. During 1994–95 the largest positive SST anomaly was observed in the midbasin and was related initially to reduced latent heat flux due to weak surface winds and later to anomalous zonal advection. In the eastern Pacific where winds were not significantly anomalous throughout 1994–95, only a moderate warm surface anomaly was detected. This is in contrast to strong El Niño events where the SST anomaly is largest in the eastern basin. Overall, the balances inferred from the model forced by Special Sensor Microwave/Imager winds are consistent with the balances derived using tropical atmosphere–ocean moorings data and Reynolds SST.

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Judith E. Ghirardelli
,
Michele M. Rienecker
, and
David Adamec

Abstract

Analyses of satellite-derived SSM/I winds and AVHRR sea surface temperatures are used to compute weekly estimates of global meridional ocean Ekman heat transport for the 4-year period 1987–1991. The heat transport is consistently poleward throughout the year over the Atlantic and much of the Pacific between 30°S and 30°N and equatorward at higher latitudes. The zonally integrated Ekman heat transport in the Pacific was weak and equatorward at 10°N in September 1989 and 1990, whereas in other years it is poleward throughout the year. In the Indian Ocean, equatorward heat transport was strongest in Northern Hemisphere summer 1990. The weekly time series provides better temporal resolution than previous studies that at best used monthly averages. The higher-frequency variations are explored through rotated empirical orthogonal functions (REOFs) of nonseasonal heat transport anomalies. The REOFs show large-scale coherence across the tropical and subtropical Pacific and Indian Oceans. The first REOF has a strong spectral peak at periods of 50–60 days and is dominated by the variability in the Southern Hemisphere Indian Ocean. The second REOF is dominated by the variance in the Northern Hemisphere Indian Ocean and western tropical North Pacific. The fist four REOFs, which explain 22.5% of the nonseasonal variance, have spectral peaks at periods consistent with the 30–60 day atmospheric Madden–Julian oscillation. These periods were not resolved in the monthly averaged data from COADS. Singular spectrum analysis has been used as a filter to show the long timescale variations. The early phase of the 1988–89 La Niña has a strong influence on the heat transport, indicating enhanced poleward heat transport in the eastern Indian Ocean, tropical North Pacific, and tropical and subtropical South Pacific and enhanced equatorward heat transport in the midlatitude North Pacific and western tropical Indian Ocean.

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Michele M. Rienecker
,
Christopher N. K. Mooers
, and
Allan R. Robinson

Abstract

The series of cruises off Northern California comprising OPTOMA11, during two months in summer 1984, were specifically designed as an ocean prediction experiment. In addition to a regional survey from Cape Mendocino to Monterey, six surveys were made of a (150 km)2 domain offshore of Pt. Arena/Pt. Arena/Pt. Reyes. During the initial phase (over about ten days) of OPTOMA11, an intense (speeds up to 50 cm s−1, relative to 450 m) jet/cyclone system propagated offshore at about 5 km day−1. The subsequent evolution (over about 40 days) of the streamfunction field was governed by the meandering of the jet and the associated changes in the intensity of the anticyclonic region to the north of the jet and the cyclonic region to the south. From quasi-geostrophic (QG) model hindcast experiments using the streamfunction data, wind stress curl was an important forcing mechanism in the later phase of the experiment. Forecast in a domain extending over the continental slope were in agreement with objective analyses (OA) in the upper water column when the local topographic slope was used in the model. Asynopticity in initialization data (in this case, data acquired over eight days) did not seriously degree forecasts, although forecasts which used synoptic estimates (via a time-dependent objective analysis) of initial and boundary data were more accurate. The repetition in sampling allowed estimation of a space-time covariance function which was used for statistical forecasts. Quasi-geostrophic dynamical forecasts, generated using statistically forecast boundary data, evolved consistent with the OA in the interior of the forecast domain (rms difference 56% after 16 days). Assimilation of truly synoptic data, in the interior of the forecast domain as well as on the boundaries, improved the forecast so that it gave a better estimate of the streamfunction field than the OA (rms difference from the best field estimate was 20% after 16 days). Energetics analyses, based on-best estimates of the streamfunction and vorticity fields obtained by dynamical interpolation, indicate that the cyclonic region to the south of the jet grew due to baroclinic instability. The inclusion of wind stress curl forcing was essential to the interpretation of the energetics.

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Anna Borovikov
,
Michele M. Rienecker
,
Christian L. Keppenne
, and
Gregory C. Johnson

Abstract

One of the most difficult aspects of ocean-state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model–observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross covariances between different model variables used. Here a comparison is made between a univariate optimal interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature profiles. In the UOI case only temperature is updated using a Gaussian covariance function. In the MvOI, salinity, zonal, and meridional velocities as well as temperature are updated using an empirically estimated multivariate covariance matrix.

Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimate of the forecast error statistics is made by Monte Carlo techniques from an ensemble of model forecasts. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross covariances between the fields of different physical variables constituting the model-state vector, at the same time incorporating the model’s dynamical and thermodynamical constraints as well as the effects of physical boundaries.

Only temperature observations from the Tropical Atmosphere–Ocean array have been assimilated in this study. To investigate the efficacy of the multivariate scheme, two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity, and temperature. For reference, a control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when the multivariate correction is used, as is evident from the analyses of the rms differences between these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating water masses with properties close to the observed, while the UOI fails to maintain the temperature and salinity structure.

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Christian L. Keppenne
,
Michele M. Rienecker
,
Jossy P. Jacob
, and
Robin Kovach

Abstract

In practical applications of the ensemble Kalman filter (EnKF) for ocean data assimilation, the computational burden and memory limitations usually require a trade-off between ensemble size and model resolution. This is certainly true for the NASA Global Modeling and Assimilation Office (GMAO) ocean EnKF used for ocean climate analyses. The importance of resolution for the adequate representation of the dominant current systems means that small ensembles, with their concomitant sampling biases, have to be used. Hence, strategies have been sought to address sampling problems and to improve the performance of the EnKF for a given ensemble size. Approaches assessed herein consist of spatiotemporal filtering of background-error covariances, improving the system-noise representation, imposing a steady-state error covariance model, and speeding up the analysis by performing the most expensive operation of the analysis on a coarser computational grid. A judicious combination of these approaches leads to significant performance improvements, especially with very small ensembles.

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