Circulation in the Arctic Ocean: Results from a high-resolution coupled ice-sea nested Global-FVCOM and Arctic-FVCOM system
Introduction
The circulation in the Arctic Ocean is poorly observed and our present knowledge is based mainly on models (Proshutinsky et al., 2001, Steele et al., 2001, Holloway et al., 2007) that can give insights into the science. The pictures that have emerged from different models are often not consistent and differ substantially in terms of particulars, most notably over the cyclonic flow over steep topographic slopes and the water transport through narrow straits and water passages. Topostrophy, which is defined as (where f is the Coriolis parameter, the unit vector for the vertical axis, the model velocity and D the total depth), was recommended as an indicator to assess the capability of a model to resolve the slope cyclonic flow in the Arctic during the Arctic Ocean Model Intercomparison Project (AOMIP) (Holloway, 2008). Velocity measurements suggested that the Arctic Ocean was characterized by a large positive, significantly time-varying , while the values produced by most of the Arctic Ocean models were too small in either amplitude or time variability (Holloway and Wang, 2009). Differences in subgrid parameterization were believed to be one cause for the inconsistencies between the model results, since the horizontal resolution in these models were too coarse to resolve steep slope topography (Holloway, 2008). The so-called “Neptune effect”, which was specified by a diffusion-based forcing in the form of (where AH is the horizontal eddy diffusivity, , and L is an eddy length parameter), was recommended to be implemented into the momentum equations for the purpose of improving the representation of the mean flow resulting from eddy-topography interaction (Eby and Holloway, 1994, Holloway and Wang, 2009). In this type of Neptune model, the Neptune flow was depth-independent and can vary with time if the surface elevation is considered in D. A Neptune model did show its capability of improving the simulation of cyclonic slope currents (Holloway and Wang, 2009), which illustrates our views on the importance of subgrid parameterization in the Arctic Ocean under conditions with the present limits in model resolution and computational resources.
The complex geometry of the Arctic coastlines, steep bottom bathymetry along continental slopes and ridges, numerous islands and narrow straits (Fig. 1) has challenged ocean modelling in this basin-scale ocean (Chen et al., 2009). The Arctic Basin is stratified, with a cross-shelf scale defined by an internal Rossby deformation radius of ∼6–10 km over the shelf and within narrow straits (Münchow et al., 2007). The Arctic Basin is characterized by an along-slope cyclonic flow with its cross-shelf scale constrained by the width of the steepest slope which is on the order of ∼10 km. Over a distance of 10 km over the slope, the water depth could abruptly vary about 1000 m or larger. Driven by astronomical tides, atmospheric forcing at the sea surface, and freshwater discharges from rivers, the spatial structure of the circulation in the Arctic Ocean is highly geometrically-controlled, which requires a state-of-the art model with its horizontal and vertical resolutions capable of resolving complex coastlines, steep continental slopes and strong upper ocean stratification. To satisfy this requirement, the model resolution over the slope and Canadian Archipelago should be of the order of 1/4 of the internal Rossby deformation radius and steepest slope width, which is of the order of ∼ 2–3 km.
It is clear that subgrid parameterization depends on model resolution. The Neptune model was developed on an assumption that the model resolution was not sufficient to resolve the slope geometry. As long as the basin-scale circulation was considered, the eddy-topographic interaction should become well resolved as model resolution increased to a level at which the cross-isobath slope of the continental shelf could be realistically represented. Under this condition, the Neptune approach should become unnecessary. Increasing resolution in a model, however, is not a trivial task since it always sacrifices computational efficiency and/or is constrained by computational resources. The surface area of the Arctic Ocean is about 9.0 × 106 km2. If a structured-grid model with horizontal resolutions of ∼1–3 km is used, a total of ∼1.0–3.0 × 106 grid cells are required to cover this region. If one uses the quadrilateral grid cells, the total grid cells could be up to ∼9 × 106. It is not practical to run such a model for multi-year simulation with limited computational resources.
Grid refinement techniques, such as nesting, conjoined grids and adaptive grids, could be employed to endow Arctic Ocean models with variable resolution capabilities, and to permit these models to better resolve multi-scale processes in global simulations. Either one-way or two-way nesting is a common approach used in both atmosphere and ocean models. The nesting approach needs to enforce mass and energy conservation at the seam where two different-size grids are connected. This approach is, however, fraught with problems. Even if one-way or two-way nesting is used, the structured-grid approach needs to treat mass and energy conservation at the nesting boundary that connects the two different-size grids. In a free-surface shallow-water ocean model, for example, the surface gravity waves are non-dispersive long-waves with phase speed . In the discrete form of the finite-difference equations, the model-simulated gravity wave becomes a dispersive wave with a phase speed depending on horizontal resolution (∼, where k and l are the x and y components of the wave number, and and are the x and y components of model grid resolution). Since the grid sizes of the two domains differ at the nesting boundary, the model-computed phase speeds for the same wavelength wave are not equal, so that a special treatment is required to disperse inconsistent-energy from the small domain in order to ensure mass and energy conservation at the nesting boundary. This treatment usually works for a short-term simulation but requires validation for the long-term simulations that are generally done in climate change studies. The unstructured-grid model has the same grid-dependent dispersive phase issue. In the grid generation, a rule of thumb is usually used to avoid a rapid change of the mesh size. For a two-domain nesting problem, however, the unstructured-grid model could link the two domains with common cells. This approach produces the same surface gravity features in the nesting grid zone, which ensures volume and mass conservation on the nesting boundary cells and make this type of model practical to resolve multi-scale processes in the ocean.
We, a joint research team at the University of Massachusetts-Dartmouth (UMASSD) and Woods Hole Oceanographic Institution (WHOI) have developed the unstructured-grid Finite Volume Community Ocean Model (FVCOM) (Chen et al., 2003). The unstructured-grid finite-volume algorithm used in FVCOM combines the advantage of finite-element methods for grid geometric flexibility and finite-difference methods for simple and efficient discrete computation (Chen et al., 2006a, Chen et al., 2006b, Chen et al., 2007). FVCOM solves the flux form of the governing equations in an arbitrary control volume constructed by unstructured triangles with second-order accurate discrete flux schemes. This numerical approach provides an accurate presentation of local mass, heat and salt conservation. FVCOM was originally designed for regional, coastal and estuarine problems with complex irregular geometry. Flexibility of the triangular grid allowed us to design the model grid to be consistent with physical scales; higher resolution over the steep bottom topography along continental margins and narrow water passages and coarser resolution in the interior, to accurately simulate slope fronts and currents in basin-scale applications.
We have used FVCOM to configure an Arctic Ocean model (hereafter referred to as AO-FVCOM). With various grid configurations, this unstructured-grid model provided us a tool to examine the influence of geometric fitting and model resolution on the simulation results of the circulation in the Arctic and water transport through Bering and Fram Straits as well as the Canadian Arctic Archipelago (CAA). There are many Arctic Ocean models that have provided various results for the Arctic circulation. To our knowledge, however, only a few analyses have been conducted to examine how model performance is affected by how well the geometric details are fitted over slopes and in complex coastal regions. It is clear that we need a higher resolution model for the Arctic. However, it is unclear what is the resolution required to resolve the slope currents and the spatial variation of the flow through narrow straits. Within the known circulation scale, how does a model perform as the model horizontal resolution changes? If one defines the grid resolution as the numerical scale, what level of unreality could occur in the model simulation when its numerical scale does not match with the physical scale? For the Arctic Ocean, these questions could be addressed by comparing the flow spatial structures, including the location and intensity of the flow over the slope in the Arctic and complex geometrically featured narrow straits and water passages through the CAA. They are also better addressed based on climatological conditions, which help us distinguish the spatial variability from the temporal variability.
In this paper, we attempt to assess the performance of AO-FVCOM under climatologically averaged conditions. The model-data comparison was made with an aim at evaluating the capability of AO-FVCOM to resolve the spatial variation of the multi-scale circulation patterns in the Arctic and CAA and to provide a statistically meaningful error analysis. Particular attention was paid to requisite resolutions to resolve the cyclonic flow over steep slopes that are characterized by a large positive, time-varying topostrophy. Running the AO-FVCOM with various horizontal resolutions, we also examined the dynamics involving grid refinement with support from previous theoretical studies.
Remaining sections of this paper are organized as follows. In Section 2, the AO-FVCOM and the design of the numerical experiments are described. In Section 3, results of model simulation under climatological forcing conditions are presented and compared with observations. In Section 4, the impacts of grid resolution on the slope currents and topostrophy are discussed and an empirical orthogonal analysis (EOF) is conducted to characterize the key features of the cyclonic flow over the Arctic slope. In Section 5, the conclusions are summarized.
Section snippets
AO-FVCOM/Global-FVCOM and design of numerical experiments
The AO-FVCOM was developed under the spherical coordinate framework of FVCOM. FVCOM is a prognostic, unstructured-grid, Finite-Volume, free-surface, 3-D primitive equation Community Ocean Model (Chen et al., 2003, Chen et al., 2006a, Chen et al., 2006b, Chen et al., 2007, Chen et al., 2013). The equations are cast in a generalized terrain-following coordinate system with spatially variable vertical distribution (Chen et al., 2013). In the horizontal, the equations are discretized using
Model-data comparisons
In region I – the Bering Sea-Bering Strait-the Alaska coast, AO-FVCOM captured the spatial distribution of subtidal currents (Fig. 5). The model showed that the Pacific Ocean water flowed around St. Lawrence Island and entered Bering Strait. The inflow of Bering Strait produced a northward current over the Chukchi Shelf and then separated into three branches: (1) a coastal current along the Alaska coast towards Barrow Canyon, (2) a northwestward current towards Herald Canyon, and (3) a
Impacts of grid resolution on the slope currents
The Arctic Ocean is characterized by the slope cyclonic flow and the key to capture this flow relies on whether or not a model can resolve the steep bottom slope topography. In the Arctic Basin, where the cross-isobath scale of topography change over the slope is the same as the internal Rossby deformation scale, the failure to resolve slope topography can be equivalent to misrepresenting the dynamical scale of the motion and thus lead to an unrealistic flow pattern. A clear example can be seen
Summary
Built on the success in developing a high-resolution, unstructured-grid global-regional nested ice-current coupled FVCOM system for the Arctic Ocean, we have examined the impact of model resolution and geometrical fitting on the basin-coastal scale circulation and the volume and salt fluxes entering and flowing out of the Arctic region. Without the need to invoke the Neptune theory, AO-FVCOM was capable of resolving multi-scale circulations in the Arctic, including cyclonic slope flow, inflow
Acknowledgments
This work was supported by US National Science Foundation (NSF) Grants OCE-1203393 for the UMASSD team and PLR-1203643 for the WHOI team. The Global-FVCOM/AO-FVCOM system was developed with infrastructure support by the Sino-US Joint Innovative Center for Polar Ocean Research (SU-JICPOR), International Center for Marine Studies, Shanghai Ocean University. G. Gao was supported by the National Natural Science Foundation of China under Grant number 41276197, the Shanghai Pujiang Program under
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2021, Advances in Climate Change ResearchCitation Excerpt :AO-FVCOM is driven by the atmospheric forcings including surface wind stress, sea level pressure, net heat flux at the surface plus shortwave irradiance in the water column and precipitation minus evaporation. Besides, the driving forcings also include astronomical tidal forcing with eight constituents (M2, S2, N2, K2, K1, P1, O1, and Q1) and river discharge (Chen et al., 2016; Zhang et al., 2016a, 2016b). Atmospheric forcing was taken from version 2 datasets for Common Ocean-ice Reference Experiments (CORE-v2) over the period 1978–2009 (Large and Yeager, 2009) and National Centers for Environmental Prediction and the National Center for Atmospheric Research (NCEP/NCAR) reanalysis datasets over the period 2010–2016 (Kalnay et al., 1996).