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Dingming Hu

Abstract

Aimed at a further understanding of the role of vertical diffusivity in determining the vertical structure of the thermocline circulation and meridional heat transport in ocean general circulation models (OGCMS), sensitivity of a box-basin isopycnal ocean model to vertical diffusivity is examined. In constant diffusivity experiments, the model e-folding depth for potential density is proportional to the ⅓ power of vertical diffusivity, which is in agreement with previous sensitivity studies with the GFDL OGCM. In the experiments with an N −1 type of stability-dependent vertical diffusivity, we found that the minimum diffusivity in the vertical is a relevant scale for the stability-dependent diffusivity in describing the sensitivity of the thermocline depth. With the choice of this vertical diffusivity Scale, the ⅓ power law for the constant diffusivity cast can be extended to the stability-dependent diffusivity case. Contrary to the previous sensitivity studies, meridional heat transport in the present model is rather insensitive to vertical diffusivity. It is shown that the low sensitivity is mainly due to the different reference temperature and surface anomaly damping rate used in the model's Newtonian cooling parameterization for the surface heat flux. Since sensitivity of the thermocline depth is rather OGCM independent and that of meridional heat transport is dependent on the way surface heat flux is parameterized, the author suggests that vertical diffusivity be tuned to obtain a realistic thermocline. In this regard. the stability-dependent vertical diffusivity is recommended.

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Dingming Hu

Abstract

The goal of this study is to fill the gap in equilibrium solutions of the global-scale water masses, meridional circulation, and heat transport with isopycnal ocean models. To this end, a global isopycnal ocean general circulation model is described and used in the present study. A distinguishing feature of the isopycnal model is that it is formulated in the same parameter space, boundary conditions, and model configurations except the vertical coordinates are those of the GFDL model used by Danabasoglu et al. with an isopycnal-depth diffusion parameterization of eddy-induced tracer transport. With the global isopycnal model, the author repeated Danabasoglu et al.’s coarse-resolution simulation for a direct comparison.

For the same parameter values (except lateral viscosity), the isopycnal model is able to produce a larger northward heat transport in the Northern Hemisphere, and a better latitudinal dependence of heat transport in the Southern Hemisphere, than the GFDL model. The model is also able to produce a reasonable amount of total meridional overturning mass transport, which is in good agreement with the observations in the North Atlantic Ocean. The most significant result obtained in this study is that the model-simulated climatological vertical profiles of the globally averaged potential temperature and salinity are both more realistic than those simulated by the GFDL model with the isopycnal-depth diffusion parameterization. The model-simulated vertical temperature profiles show a significant improvement on both the chronic warm bias of the thermocline with the horizontal/vertical mixing parameterization and the cool bias of the abyss with the isopycnal depth-diffusion parameterization in the GFDL model. The model-simulated vertical salinity profiles are also in reasonable agreement with the observations. In particular, the observed salinity minimum at the intermediate depth is well represented. On zonal average, the model thermocline structure is in better agreement with that observed than in Danabasoglu et al. Salinity tongues associated with the global-scale water masses are also well simulated by the model, except the North Pacific Deep Water. Influence of vertical resolution on the model water mass properties in the deep ocean is discussed. In the model, the transport of the upper Deacon cell is not changed by different zonal integrations of the meridional streamfunction nor by isopycnal-depth diffusion. This result differs from those of Doos and Webb, and Danabasoglu et al. The reasons for the difference are discussed.

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Dingming Hu

Abstract

This paper addresses the problem of how to numerically incorporate diapycnal mixing and advection processes into isopycnal ocean general circulation models. A general expression of diapycnal velocity is derived for the case in which density is a function of both potential temperature and salinity. The expression is independent of turbulence closure parameterizations and thus can be viewed as a generalized definition of diapycnal velocity. With this definition, it is simple to derive expressions of diapycnal velocity for different parameterizations of turbulent mixing in isopycnal ocean models. Numerical algorithms are developed to overcome difficulties associated with massless layers in computing diapycnal diffusive and advective scalar fluxes in isopycnic-coordinate ocean models. In the diapycnal diffusive flux computation, a mass-weighted averaging is used to prevent linear instability in the time integration. In diapycnal advective flux computation, it is shown that the diapycnal mass exchange associated with density coordinate restoration should be consistent with that caused by diapycnal velocity. This consistency is achieved in the developed algorithms. The algorithms are tested and verified in one-dimensional Dirichlet and Neumann boundary value problems. Furthermore, through a simulation of a realistic ocean profile diffusion process, the author shows that the algorithms not only have the ability to simulate vertical mixing processes in the real ocean but also have computational efficiency good enough for application to three-dimensional isopycnal ocean models.

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Dingming Hu
and
Yi Chao

Abstract

In this study, a global isopycnal ocean model (GIM) is described and used for a simulation of variabilities of the global upper ocean during 1992–93. The GIM simulations are compared and validated with both the available observations and simulations with the Geophysical Fluid Dynamics Laboratory Modular Ocean Model (MOM). The observations include sea surface height from TOPEX/Poseidon (T/P), sea surface temperature (SST) from weekly National Centers for Environmental Prediction analysis, and vertical temperature profiles from gridded expandable bathythermographs (XBTs) data. The major differences between the GIM and MOM used in this study are the vertical coordinates, a Kraus–Turner mixed layer, and a tracer-transport velocity associated with an isopycnal-depth diffusion. Otherwise, the two models are formulated in the same parameter space, model configuration, and boundary conditions. The effects of these differences in model formulation on the model simulations are investigated.

Due to the difference in the orientation of interior flow and mixing, SST and the thermocline stratification in the eastern equatorial Pacific in GIM are more sensitive to the wind-driven upwelling than they are in MOM. In GIM there is no effective means to transfer heat between the upwelling cold water and the surrounding warm water since subsurface flow and mixing predominantly occur along isopycnic layers. As a result, the SST tends to be cold and the front tends to be sharp compared with the observations in the wind-driven upwelling region. The sharp front could potentially cause numerical instability in GIM. Thus, a large isopycnal-depth diffusivity has to be used to maintain the model stability since the isopycnal-depth diffusion is the most effective way to reduce the steep slope of isopycnals and the strength of the front associated with the cold upwelling in GIM. But the large isopycnal-depth diffusion results in excessive smoothing in the meridional isotherm doming in the equatorial and tropical thermocline. The trade-off between the numerical instability and the excessive isopycnal smoothing points to the necessity of improvement in the isopycnal-depth diffusion.

Sea level variabilities during 1992–93 simulated with both GIM and MOM are in good agreement with T/P observations. However, MOM poorly simulates the vertical distribution of the seasonal temperature anomalies in the upper ocean (the baroclinic component of the sea level variability) during 1992–93. Due to the lack of a realistic surface mixed layer, the MOM-simulated temperature profiles have a sharp subsurface gradient, which is not evident in both the GIM simulation and the XBT observation. As a result, the region below the subsurface gradient is almost insulated from the influence of the seasonal temperature variation. The Kraus–Turner mixed layer used in GIM helps to improve the model-simulated seasonal variations of the upper-ocean temperature and the background sea level variability. Implications of deficiencies in both GIM and MOM on the altimetric sea level data assimilation and transient tracer simulations are discussed.

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Rainer Bleck
,
Claes Rooth
,
Dingming Hu
, and
Linda T. Smith

Abstract

An isopycnic-coordinate oceanic circulation model formulated with the aim of simulating thermodynamically and mechanically driven flow in realistic basins is presented. Special emphasis is placed on the handling of diabatic surface processes and on thermocline ventilation. The model performance is illustrated by a 30-year spinup run with coarse horizontal resolution (2° mesh) in a domain with North Atlantic topography extending from 10° to 60°N latitude. The vertical structure encompasses 10 isopycnic layers in steps of 0.2 σ units, capped by a thermodynamically active mixed layer. From an initially isohaline state with isopycnals prescribed by zonally averaged climatology, the model is forced by seasonally varying wind stress, radiative and freshwater fluxes, and by a thermal relaxation process at the surface. After a mechanical spinup time of about 15 years, a quasi-stationary pattern of mean circulation and annual variability ensues, characterized by pronounced subtropical mode-water formation and a gradual growth in the salinity contrast between the subtropics and the subpolar region. The effect of the freshwater flux forcing on the ventilation of the thermocline is a key point of discussion. Finally, a low-viscosity experiment suggests that the thermohaline processes represented in the model are quite insensitive to dynamic noise development at the grid resolution limit.

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Rainer Bleck
,
Dingming Hu
,
Howard P. Hanson
, and
Eric B. Kraust

Abstract

The annual buildup and obliteration of the seasonal thermocline and the associated ventilation of the permanent thermocline in a wind- and thermally driven ocean basin are simulated numerically. The model developed for this purpose is a combination of a single-layer model of the oceanic mixed layer, based on a simple closure of the turbulence kinetic energy equation, and a three-dimensional isopycnic coordinate model of the stratified oceanic interior. The joint model, set in a rectangular ocean basin, is forced by annually varying wind stress and radiative plus turbulent heal fluxes approximating zonnaly averaged conditions over the North Atlantic. Special emphasis is placed on the description of the mixed-layer detrainment process, which requires distributing mixed-layer water of continuously variable density among constant-density interior layers. The truncation errors associated with this process are found to be numerically tolerable.

The quasi-Lagrangian character of the model's vertical coordinate permits easy tracking of water masses left behind during the annual retreat of the mixed layer to form the seasonal thermocline. Likewise, the subduction of ventilated water into the permanent thermocline by the horizontal gyre motion is explicitly simulated.

While a comparison of simulated mixed-layer characteristics with actual observations is problematic due to the idealized basin configuration, the model appears to be reasonably successful in duplicating the seasonal cycle of the zonally averaged conditions over the North Atlantic.

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