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Ichiro Fukumori

Abstract

A new approach is advanced for approximating Kalman filtering and smoothing suitable for oceanic and atmospheric data assimilation. The method solves the larger estimation problem by partitioning it into a series of smaller calculations. Errors with small correlation distances are derived by regional approximations, and errors associated with independent processes are evaluated separately from one another. The overall uncertainty of the model state, as well as the Kalman filter and smoother, is approximated by the sum of the corresponding individual components. The resulting smaller dimensionality of each separate element renders application of Kalman filtering and smoothing to the larger problem much more practical than otherwise. In particular, the approximation makes high-resolution global eddy-resolving data assimilation computationally viable. The approach is described and its efficacy demonstrated using a simple one-dimensional shallow water model.

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Tong Lee and Ichiro Fukumori

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Interannual-to-decadal variations of tropical–subtropical mass exchange in the Pacific Ocean are investigated using a near-global ocean general circulation model along with satellite observations of sea level and wind and a data assimilation product. The analysis focuses on the variability of pycnocline transports through the western boundary and interior near 10°N and 10°S. In contrast to time-mean exchange, where boundary and interior pycnocline transports are both equatorward, the variations of boundary and interior pycnocline transports are found to be generally anticorrelated to each other. Moreover, the variation of the boundary pycnocline transport is smaller than that of the interior, again different from time-mean exchange, where the boundary transport at 10°N is substantially larger than that through the interior. Interannual variations of the boundary and interior transports are consistent with near-surface geostrophic flow inferred from sea level data. Interior pycnocline flow into the Tropics is weaker in the 1990s than that in the 1980s, in agreement with recent observations. However, approximately half of it is compensated by an opposite change in boundary flow at 10°N. The results indicate that the interior pathway is more important to interannual and decadal variability of tropical–subtropical exchange than the boundary pathway, despite a much larger time-mean transport of the western boundary current at 10°N. To a large extent, the counteracting tendency of the boundary and interior flow and the larger variation of the latter can be explained by the combined effect of variability in off-equatorial wind stress curl in the western Pacific and near-equatorial zonal wind stress. The former changes the strength of horizontal circulation and results in a variation of boundary pycnocline flow that is opposite in direction but comparable in magnitude to that of the interior pycnocline flow. The latter primarily affects the strength of the shallow meridional overturning circulation with net pycnocline flow (mostly in the interior) opposing the surface Ekman flow. The covariability of these two forcings leads to an enhancement of interior transport. The relative variability of boundary and interior pycnocline flow is insensitive to whether the Indonesian Throughflow is present or not.

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Dimitris Menemenlis, Ichiro Fukumori, and Tong Lee

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Observations and numerical simulations show that winds near Gibraltar Strait cause an Atlantic Ocean to Mediterranean Sea sea level difference of 20 cm peak to peak with a 3-cm standard deviation for periods of days to years. Theoretical arguments and numerical experiments establish that this wind-driven sea level difference is caused in part by storm surges due to alongshore winds near the North African coastline on the Atlantic side of Gibraltar. The fraction of the Moroccan coastal current offshore of the 284-m isobath is deflected across Gibraltar Strait, west of Camarinal Sill, resulting in a geostrophic surface pressure gradient that contributes to a sea level difference at the stationary limit. The sea level difference is also caused in part by the along-strait wind setup, with a contribution proportional to the along-strait wind stress and to the length of Gibraltar Strait and adjoining regions and inversely proportional to its depth. In the 20–360-day band, average transfer coefficients between the Atlantic–Alboran sea level difference and surface wind stress at 36°N, 6.5°W, estimated from barometrically corrected Ocean Topography Experiment (TOPEX)/Poseidon data and NCEP–NCAR reanalysis data, are 0.10 ± 0.04 m Pa−1 with 1 ± 5-day lag and 0.19 ± 0.08 m Pa−1 with 5 ± 4-day lag for the zonal and meridional wind stresses, respectively. This transfer function is consistent with equivalent estimates derived from a 1992–2003 high-resolution barotropic simulation forced by the NCEP–NCAR wind stress. The barotropic simulation explains 29% of the observed Atlantic–Alboran sea level difference in the 20–360-day band. In turn, the Alboran and Mediterranean mean sea level time series are highly correlated, ρ = 0.7 in the observations and ρ = 0.8 in the barotropic simulation, hence providing a pathway for winds near Gibraltar Strait to affect the mean sea level of the entire Mediterranean.

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Seung-Bum Kim, Ichiro Fukumori, and Tong Lee

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Entrainment is an important element of the mixed layer mass, heat, and temperature budgets. Conventional procedures to estimate entrainment heat advection often do not permit the closure of heat and temperature budgets because of inaccuracies in its formulation. In this study a rigorous approach to evaluate the effect of entrainment using the output of a general circulation model (GCM) that does not have an explicit prognostic mixed layer model is described. The integral elements of the evaluation are 1) the rigorous estimates of the temperature difference between mixed layer water and entrained water at each horizontal grid point, 2) the formulation of the temperature difference such that the budget closes over a volume greater than one horizontal grid point, and 3) the apparent warming of the mixed layer during the mixed layer shoaling to account for the weak vertical temperature gradient within the mixed layer.

This evaluation of entrainment heat advection is compared with the estimates by other commonly used ad hoc formulations by applying them in three regions: the north-central Pacific, the Kuroshio Extension, and the Niño-3 areas in the tropical Pacific. In all three areas the imbalance in the mixed layer temperature budget by the ad hoc estimates is significant, reaching a maximum of about 4 K yr−1.

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Seung-Bum Kim, Tong Lee, and Ichiro Fukumori

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Processes controlling the interannual variation of mixed layer temperature (MLT) averaged over the Niño-3 domain (5°N–5°S, 150°–90°W) are studied using an ocean data assimilation product that covers the period of 1993–2003. The overall balance is such that surface heat flux opposes the MLT change but horizontal advection and subsurface processes assist the change. Advective tendencies are estimated here as the temperature fluxes through the domain’s boundaries, with the boundary temperature referenced to the domain-averaged temperature to remove the dependence on temperature scale. This allows the authors to characterize external advective processes that warm or cool the water within the domain as a whole. The zonal advective tendency is caused primarily by large-scale advection of warm-pool water through the western boundary of the domain. The meridional advective tendency is contributed to mostly by Ekman current advecting large-scale temperature anomalies through the southern boundary of the domain. Unlike many previous studies, the subsurface processes that consist of vertical mixing and entrainment are explicitly evaluated. In particular, a rigorous method to estimate entrainment allows an exact budget closure. The vertical mixing across the mixed layer (ML) base has a contribution in phase with the MLT change. The entrainment tendency due to the temporal change in ML depth is negligible compared to other subsurface processes. The entrainment tendency by vertical advection across the ML base is dominated by large-scale changes in upwelling and the temperature of upwelling water. Tropical instability waves (TIWs) result in smaller-scale vertical advection that warms the domain during La Niña cooling events. However, such a warming tendency is overwhelmed by the cooling tendency associated with the large-scale upwelling by a factor of 2. In summary, all the balance terms are important in the MLT budget except the entrainment due to lateral induction and temporal variation in ML depth. All three advective tendencies are primarily caused by large-scale and low-frequency processes, and they assist the Niño-3 MLT change.

When the advective tendencies are evaluated by spatially averaging the conventional local advection of temperature, the apparent effects of currents with spatial scales smaller than the domain (such as TIWs) become very important as they redistribute heat within the Niño-3 domain. As a result, for example, the averaged zonal advective tendency counteracts rather than assists the Niño-3 MLT change. However, such internal redistribution of heat does not represent external processes that control the domain-averaged MLT.

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Tong Lee, Ichiro Fukumori, and Benyang Tang

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Local advection of temperature is the inner product of vector velocity and spatial gradient of temperature. This product is often integrated spatially to infer temperature advection over a region. However, the contribution along an individual direction can be dominated by internal processes that redistribute heat within the domain but do not control the heat content of the domain. A new formulation of temperature advection is introduced to elucidate external heat source and sink that control the spatially averaged temperature. It is expressed as the advection of interfacial temperature relative to the spatially averaged temperature of the domain by inflow normal to the interface. It gives a total advection of temperature that is identical to the spatial integration of local temperature advection, yet the contributions along individual directions depict external processes. The differences between the two formulations are illustrated by analyzing zonal advection of near-surface temperature in the eastern equatorial Pacific during the 1997–98 El Niño and the subsequent La Niña by an ocean general circulation model. The new formulation highlights the advection of warmer water at the western side of the Niño-3 region into (out of) the region to create part of the warming (cooling) tendency during El Niño (La Niña). In contrast, the traditional formulation is dominated by the effect of tropical instability waves within the region that redistribute heat internally. The difference between the two formulations suggests a need for caution in discerning mechanisms controlling heat content of a region. Spatial integration of local temperature advection does not explain external processes that control a domain's heat content. The conclusion applies not only to the advection of oceanic temperature, but also to that of any property in any medium.

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Ichiro Fukumori, Dimitris Menemenlis, and Tong Lee

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A new basin-wide oscillation of the Mediterranean Sea is identified and analyzed using sea level observations from the Ocean Topography Experiment (TOPEX)/Poseidon satellite altimeter and a numerical ocean circulation model. More than 50% of the large-scale, nontidal, and non-pressure-driven variance of sea level can be attributed to this oscillation, which is nearly uniform in phase and amplitude across the entire basin. The oscillation has periods ranging from 10 days to several years and has a magnitude as large as 10 cm. The model suggests that the fluctuations are driven by winds at the Strait of Gibraltar and its neighboring region, including the Alboran Sea and a part of the Atlantic Ocean immediately to the west of the strait. Winds in this region force a net mass flux through the Strait of Gibraltar to which the Mediterranean Sea adjusts almost uniformly across its entire basin with depth-independent pressure perturbations. The wind-driven response can be explained in part by wind setup; a near-stationary balance is established between the along-strait wind in this forcing region and the sea level difference between the Mediterranean Sea and the Atlantic Ocean. The amplitude of this basin-wide wind-driven sea level fluctuation is inversely proportional to the setup region’s depth but is insensitive to its width including that of Gibraltar Strait. The wind-driven fluctuation is coherent with atmospheric pressure over the basin and contributes to the apparent deviation of the Mediterranean Sea from an inverse barometer response.

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Dimitris Menemenlis, Ichiro Fukumori, and Tong Lee

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Green's functions provide a simple yet effective method to test and to calibrate general circulation model (GCM) parameterizations, to study and to quantify model and data errors, to correct model biases and trends, and to blend estimates from different solutions and data products. The method is applied to an ocean GCM, resulting in substantial improvements of the solution relative to observations when compared to prior estimates: overall model bias and drift are reduced and there is a 10%–30% increase in explained variance. Within the context of this optimization, the following new estimates for commonly used ocean GCM parameters are obtained. Background vertical diffusivity is (15.1 ± 0.1) × 10−6 m2 s−2. Background vertical viscosity is (18 ± 3) × 10−6 m2 s−2. The critical bulk Richardson number, which sets boundary layer depth, is Ric = 0.354 ± 0.004. The threshold gradient Richardson number for shear instability vertical mixing is Ri0 = 0.699 ± 0.008. The estimated isopycnal diffusivity coefficient ranges from 550 to 1350 m2 s−2, with the largest values occurring at depth in regions of increased mesoscale eddy activity. Surprisingly, the estimated isopycnal diffusivity exhibits a 5%–35% decrease near the surface. Improved estimates of initial and boundary conditions are also obtained. The above estimates are the backbone of a quasi-operational, global-ocean circulation analysis system.

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Ichiro Fukumori, Tong Lee, Benny Cheng, and Dimitris Menemenlis

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The nature of subtropical–tropical water mass exchange in the Pacific Ocean is investigated, focusing on the origin, pathway, and destination of water occupying the surface layer of the eastern equatorial Pacific Ocean (Niño-3 region; 5°S–5°N, 150°–90°W). Simulated passive tracers and their adjoint are employed to explicitly follow the circulation of specific water masses accounting for advective and diffusive effects and their time variabilities. The evolution of the forward passive tracer and adjoint passive tracer can be identified as describing where the tracer-tagged water mass goes and from where it comes, respectively. Over 10 years on average, water mass of the Niño-3 region can be traced back to eastern subtropical thermocline waters of the Northern (27%) and Southern Hemispheres (39%). The Niño-3 water subsequently returns to these subtropical latitudes in the upper ocean. In contrast to the hypothesized “subtropical cell,” however, this circulation is an open circuit with water returning to the western regions of the two hemispheres (subtropical gyres) and to the Indian Ocean, instead of returning to its origins. The representative transit time scale from the subtropics to the Tropics is 10–15 yr. Temporal variability causes the tropical circulation inferred from a time-mean state to differ significantly from the average circulation. In particular, stirring due to nonseasonal, intra-annual variability significantly enhances the transport magnitude of the so-called interior pathways relative to that of the circuitous low-latitude western boundary pathways. Such short-circuit in the subtropical–tropical exchange may help better to explain tracer distributions, such as the observed midbasin tritium maximum in the equatorial Pacific Ocean. Significant differences in circulation pathways are also identified that are associated with El Niño and La Niña events. The strength of the subtropical–tropical water mass exchange is estimated to have weakened during the 1990s.

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Brady S. Ferster, Bulusu Subrahmanyam, Ichiro Fukumori, and Ebenezer S. Nyadjro

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The Southern Ocean (SO) is capable of transporting vast amounts of salt, heat, and nutrients, which allows it to influence and regulate global climate. The variability of depth- and density-integrated volume transports in the SO is studied using the Estimating the Circulation and Climate of the Ocean (ECCO), version 4, release 3 (1992–2015), ocean state estimate. The estimate has a net eastward transport of 150.6 ± 5.5, 162.6 ± 7.4, and 148.2 ± 5.4 Sv (1 Sv ≡ 106 m3 s−1) between the Atlantic–Indian, Indian–Pacific, and Pacific–Atlantic basins, respectively. The time-mean meridional volume transport across 30°S in the Atlantic is estimated to be −1.4 ± 0.6 Sv, −14.4 ± 3.5 Sv in the Indian basin, and 15.5 ± 4.1 Sv in the Pacific, where negative values are southward. Trends in net volume transport between the basins are statistically insignificant. Within the water column, however, the middle and lower branches of the meridional overturning circulation have trends of −0.289 and 0.248 Sv decade−1 in the Atlantic basin. The Indian and Pacific basins have decreasing trends in their lower overturning cells. These results indicate increased overturning circulation within the lower branch in the South Atlantic and decreased lower branch circulation within the Indian and Pacific basins and have implications on the thermohaline-driven circulation. Using ECCO, we estimate a southward potential temperature transport of −176.2° ± 197.2°C Sv and salinity transport of −1.71 ± 22.4 psu Sv into the SO and indicate potential temperature transport is increasing by −15.0° ± 13.2°C Sv decade−1.

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