Tracer Advection Schemes Research Articles

Quantitative analysis of numerically induced mixing in a coastal model application

In recent years, various attempts have been made to estimate the amount of numerical mixing in numerical ocean models due to discretisation errors of advection schemes. In this study, a high-resolution coastal model using the ocean circulationmodel GETM is applied to the Western Baltic Sea, which is characterised by energetic and episodic inflows of dense bottom waters originating from the Kattegat. The model is equipped with an easy-to-implement diagnostic method for obtaining the numerical mixing which has recently been suggested. In this diagnostic method, the physical mixing is defined as the mean tracer variance decay rate due to turbulent mixing. The numerical mixing due to discretisation errors of tracer advection schemes is defined as the decay rate between the advected square of the tracer variance and the square of the advected tracer, which can be directly compared to the physical variance decay. The source and location of numerical mixing is further investigated by comparing different advection schemes and analysing the amount of numerical mixing in each spatial dimension during the advection time step. The results show that, for the setup used, the numerically and physically induced mixing have the same orders of magnitude but with different vertical and horizontal distributions. As the main mechanism for high numerical mixing, vertical advection of tracers with strong vertical gradients has been identified. The main reason for high numerical mixing is due to bottom-following coordinates when density gradients, especially for regions of steep slopes, are advected normal to isobaths. With the bottom-following coordinates used here, the horizontal gradients are reproduced by a spurious sawtooth-type profile where strong advection through, but not along, the vertical coordinate levels occurs. Additionally, the well known relation between strong tracer gradients and high velocities on the one and high numerical mixing on the other hand is approved quantitatively within this work.

Consistency problem with tracer advection in the Atmospheric Model GAMIL

The radon transport test, which is a widely used test case for atmospheric transport models, is carried out to evaluate the tracer advection schemes in the Grid-Point Atmospheric Model of IAP-LASG (GAMIL). Two of the three available schemes in the model are found to be associated with significant biases in the polar regions and in the upper part of the atmosphere, which implies potentially large errors in the simulation of ozone-like tracers. Theoretical analyses show that inconsistency exists between the advection schemes and the discrete continuity equation in the dynamical core of GAMIL and consequently leads to spurious sources and sinks in the tracer transport equation. The impact of this type of inconsistency is demonstrated by idealized tests and identified as the cause of the aforementioned biases. Other potential effects of this inconsistency are also discussed. Results of this study provide some hints for choosing suitable advection schemes in the GAMIL model. At least for the polar-region-concentrated atmospheric components and the closely correlated chemical species, the Flux-Form Semi-Lagrangian advection scheme produces more reasonable simulations of the large-scale transport processes without significantly increasing the computational expense.

Comparative quantification of physically and numerically induced mixing in ocean models

A diagnostic method for calculating physical and numerical mixing of tracers in ocean models is presented. The physical mixing is defined as the turbulent mean tracer variance decay rate. The numerical mixing due to discretisation errors of tracer advection schemes is shown to be the decay rate between the advected square of the tracer variance and the square of the advected tracer and can be easily implemented into any ocean model. The applicability of the method is demonstrated for four test cases: (i) a one-dimensional linear advection equation with periodic boundary conditions, (ii) a two-dimensional flat-bottom lock exchange test case without mixing, (iii) a two-dimensional marginal sea overflow study with mixing and entrainment and (iv) the DOME test case with a dense bottom current propagating down a broad linear slope. The method has a number of advantages over previously introduced estimates for numerical mixing.

A comparison of the transport of long-lived atmospheric trace gas species from two advection schemes incorporated into an atmospheric general circulation model

Two tracer advection schemes have been compared using an atmospheric chemical transport model based on the U.K. Met Office’s Unified Model (UM). Two experiments were carried out. The first used an inert calibration tracer (SF6) whilst the second experiment modelled two methane (CH4) carbon isotopic species. In both experiments, tracer emissions were prescribed at the Earth’s surface. Results from both experiments suggest that the global distribution of long lived trace species in the troposphere is not strongly dependent on the choice of the advection scheme. This is attributed to the fact that turbulent boundary layer mixing and vertical transport by convection, in addition to advection play a role in determining the large-scale tracer distribution in the troposphere. For the SF6 experiment, results from the UM were comparable to results from other transport models using the same experimental protocol. The UM’s default, total variation diminishing (TVD) advection scheme produced low values of marine boundary layer mixing ratios compared with other models and measurements. This was attributed to the TVD scheme being too diffusive resulting in unrealistically fast vertical transport. Comparisons between measured and modelled CH4 profiles in the stratosphere clearly shows that the vertical transport in the TVD scheme is too fast.

Performance of a second‐order moments advection scheme in an Ocean General Circulation Model

The reliability of Ocean General Circulation Models (OGCMs) strongly depends on the quality of their tracer advection schemes. For the sake of simplicity and computing time, tracer advection schemes most commonly used in large‐scale OGCMs tend to be low‐order schemes, which suffer from spurious numerical diffusion and dispersion that result in distorted solutions. The application of high‐order schemes would reduce numerical errors, but at a considerable cost in terms of computing time. An alternative to the use of high‐order methods is the implementation of algorithms that take into account the sub‐grid distribution of tracers. One such method is the Second‐Order Moments (SOM) scheme of Prather (1986), which is more accurate than a fourth‐order scheme, but at the time consumption of a second‐order algorithm. This article presents results from coarse‐resolution, global‐ocean simulations with very low explicit diapycnal mixing, in which active and passive tracers were advected with the SOM method. We compare the performance of the method with that of more traditional schemes, namely, the FCT (flux corrected transport) and QUICKer (quadratic upstream interpolation for convective kinematics) schemes. In general, the use of the SOM method significantly improves tracer distributions and transports compared to FCT and QUICKer, thus leading to a better representation of ocean currents, notably boundary currents and frontal systems. While model simulations employing the FCT and QUICKer schemes recreate a global overturning circulation with strong upwelling occurring in low latitudes, the SOM simulations admit a circulation pattern closer to that known as the “reconfigured conveyor belt” (Toggweiler and Samuels, 1993), in which the bulk of the global ocean upwelling occurs in the Southern Ocean.

A Decomposition of the Atlantic Meridional Overturning Circulation into Physical Components Using Its Sensitivity to Vertical Diffusivity

Abstract The sensitivity of the Atlantic Ocean meridional overturning circulation to the vertical diffusion coefficient κ in the global coupled atmosphere–ocean–sea ice model CLIMBER-3α is investigated. An important feature of the three-dimensional ocean model is its low-diffusive tracer advection scheme. The strength Mmax of the Atlantic overturning is decomposed into three components: 1) the flow MS exported southward at 30°S, 2) the large-scale upward flow that balances vertical diffusion in the Atlantic, and 3) a wind-dependent upwelling flux Wbound along the Atlantic boundaries that is not due to vertical diffusion. The export of water at 30°S varies only weakly with κ, but is strongly correlated with the strength of the overflow over the Greenland–Scotland ridge. The location of deep convection is found to be mixing dependent such that a shift from the Nordic seas to the Irminger Sea is detected for high values of κ. The ratio R = MS/Mmax gives a measure of the interhemispheric overturning efficiency and is found to decrease linearly with κ. The diffusion-induced upwelling in the Atlantic is mostly due to the uniform background value of κ while parameterization of enhanced mixing over rough topography and in stratified areas gives only a weak contribution to the overturning strength. It increases linearly with κ. This is consistent with the classic 2/3 scaling law only when taking the linear variation of the density difference to κ into account. The value of Wbound is roughly constant with κ but depends linearly on the wind stress strength in the North Atlantic. The pycnocline depth is not sensitive to changes in κ in the model used herein, and the results suggest that it is primarily set by the forcing of the Southern Ocean winds. The scaling of the total overturning strength with κ depends on the combined sensitivity of each of the terms to κ. In the range of background diffusivity values in which no switch in deep convection sites is detected, Mmax scales linearly with the vertical diffusivity. It is argued that scalings have, in general, to be interpreted with care because of the generally very small range of κ but also because of possible shifts in important physical processes such as deep convection location.

The relation of meridional pressure gradients to North Atlantic deep water volume transport in an ocean general circulation model

We use a coarse resolution ocean general circulation model to study the relation between meridional pressure and density gradients in the Southern Ocean and North Atlantic and the Atlantic meridional overturning circulation. In several experiments, we artificially modify the meridional density gradients by applying different magnitudes of the Gent–McWilliams isopycnal eddy diffusion coefficients in the Southern Ocean and in the North Atlantic and investigate the response of the simulated Atlantic meridional overturning to such changes. The simulations are carried out close to the limit of no diapycnal mixing, with a very small explicit vertical diffusivity and a tracer advection scheme with very low implicit diffusivities. Our results reveal that changes in eddy diffusivities in the North Atlantic affect the maximum of the Atlantic meridional overturning, but not the outflow of North Atlantic Deep Water into the Southern Ocean. In contrast, changes in eddy diffusivities in the Southern Ocean affect both the South Atlantic outflow of North Atlantic Deep Water and the maximum of the Atlantic meridional overturning. Results from these experiments are used to investigate the relation between meridional pressure gradients and the components of the Atlantic meridional overturning. Pressure gradients and overturning are found to be linearly related. We show that, in our simulations, zonally averaged deep pressure gradients are very weak between 20°S and about 30°N and that between 30°N and 60°N the zonally averaged pressure grows approximately linearly with latitude. This pressure difference balances a westward geostrophic flow at 30–40°N that feeds the southbound deep Atlantic western boundary current. We extend our analysis to a large variety of experiments in which surface freshwater forcing, vertical mixing and winds are modified. In all experiments, the pycnocline depth, assumed to be the relevant vertical scale for the northward volume transport in the Atlantic, is found to be approximately constant, at least within the coarse vertical resolution of the model. The model behaviour hence cannot directly be related to conceptual models in which changes in the pycnocline depth determine the strength of Atlantic meridional flow, and seems conceptually closer to Stommel’s box model. In all our simulations, the Atlantic overturning seems to be mainly driven by Southern Ocean westerlies. However, the actual strength of the Atlantic meridional overturning is not determined solely by the Southern Ocean wind stress but as well by the density/pressure gradients created between the deep water formation regions in the North Atlantic and the inflow/outflow region in the South Atlantic.

The earth system model of intermediate complexity CLIMBER-3α. Part I: description and performance for present-day conditions

We herein present the CLIMBER-3a Earth System Model of Intermediate Complexity (EMIC), which has evolved from the CLIMBER-2 EMIC. The main difference with respect to CLIMBER-2 is its oce- anic component, which has been replaced by a state-of- the-art ocean model, which includes an ocean general circulation model (GCM), a biogeochemistry module, and a state-of-the-art sea-ice model. Thus, CLIMBER- 3a includes modules describing the atmosphere, land- surface scheme, terrestrial vegetation, ocean, sea ice, and ocean biogeochemistry. Owing to its relatively simple atmospheric component, it is approximately two orders of magnitude faster than coupled GCMs, allowing the performance of a much larger number of integrations and sensitivity studies as well as longer ones. At the same time its oceanic component confers on it a larger degree of realism compared to those EMICs which in- clude simpler oceanic components. The coupling does not include heat or freshwater flux corrections. The comparison against the climatologies shows that CLIMBER-3a satisfactorily describes the large-scale characteristics of the atmosphere, ocean and sea ice on seasonal timescales. As a result of the tracer advection scheme employed, the ocean component satisfactorily simulates the large-scale oceanic circulation with very little numerical and explicit vertical diffusion. The model is thus suited for the study of the large-scale climate and large-scale ocean dynamics. We herein describe its per- formance for present-day boundary conditions. In a companion paper (Part II), the sensitivity of the model to variations in the external forcing, as well as the role of certain model parameterisations and internal parame- ters, will be analysed.

Modeling the atmospheric life cycle and radiative impact of mineral dust in the Hadley Centre climate model

A parameterization of mineral dust within the Hadley Centre atmospheric general circulation model (AGCM) is described, modeled dust distributions are compared with observations, and estimates of the radiative forcing due to the inclusion of dust in the model are obtained. The parameterization uses six particle size divisions in the range 0.3–30 μm radius, and all calculations are performed on each division independently, using the GCM's prognostic variables. The dust production scheme works within the GCM and includes dependencies on particle size distribution, soil moisture, vegetation, and friction velocity. Dust transport is carried out by the GCM's tracer advection scheme and includes vertical motion due to convection, gravitational settling, and turbulent mixing in the boundary layer. Wet and dry deposition processes are included within the GCM's precipitation schemes. Representative dust radiative parameters are incorporated into the GCM's two stream radiation code. Modeled monthly average near‐surface dust concentrations are compared with observations: good agreement is seen in most locations, though the dust scheme tends to produce too little dust from China and too much from Australia in the southern spring. Global annual mean direct forcing due to the inclusion of dust in the GCM is +0.07 W m−2 at the top of the atmosphere (TOA) and −0.82 W m−2 at the surface. The geographical distributions of annual mean forcings are very inhomogeneous, with peak values exceeding the global means by a factor of approximately 2 orders of magnitude.

Sensitivity of a Global Ocean General Circulation Model to Tracer Advection Schemes

Abstract Vertical diffusivity at the thermocline depths is now believed to be as small as 1 × 10−5 m2 s−1. In order to accomplish a reliable simulation of the World Ocean for the vertical diffusivity of 1 × 10−5 m2 s−1, two advective tracer transport schemes, the Uniformly Third-Order Polynominal Interpolation Algorithm (UTOPIA) of Leonard et al and the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) of Smolarkiewicz, are incorporated into an ocean general circulation model. Intercomparison is made among simulations using UTOPIA, MPDATA, and the centered differencing scheme. When UTOPIA or MPDATA is adopted, features at the thermocline depths are realistically simulated. Increase in computational cost is moderate. Circulations associated with Antarctic Bottom Water (AABW) in the Atlantic and Circumpolar Deep Water (CDW) in the Pacific are not reproduced at all for such small vertical diffusivity, although the circulation associated with North Atlantic Deep Water (NADW) has reason...

A consideration of tracer advection schemes in a primitive equation ocean model

We consider several tracer advection schemes in the context of a simple sector configuration of a Bryan‐Cox‐Semtner type ocean model. The schemes are centered‐in‐time centered‐in‐space, donor cell upwind differencing, flux corrected transport (FCT), QUICKEST and MPDATA. While we discuss the transport of temperature and salinity, and apply alternative schemes to this transport within our model, we concentrate primarily on a problem which involves passive tracer advection in which vertical gradients are high and concentrations asymptote to zero near the sea surface, as is the case in biogeochemical ocean modeling. We find that flux correction (available optionally with the MPDATA scheme, as well as the FCT scheme) is required in order to produce acceptable results on this challenging problem. A method of supercycling of passive tracers relative to dynamic variables, whereby the time step for passive tracers is larger that that used for the other prognostic variables of the model, is introduced in order to apply these more expensive flux limited schemes efficiently. We also present a general method for the second‐order accurate application of one‐dimensional forward‐in‐time advection schemes in three dimensions.

A New Tracer Advection Scheme for Bryan and Cox Type Ocean General Circulation Models

In regions with large tracer gradients and/or velocities the advection scheme that is used in many ocean models leads to significant under- and overshoot of the tracer values. In the case of the U.K. Fine Resolution Antarctic Model (FRAM), this lead to unphysical negative surface temperatures in some regions and overheating in others. In this paper, a new advection scheme is proposed and tested in the ocean model context using a limited-area model centered on a region where problems occurred in FRAM.

Breaking Rossby Waves in a Model Stratosphere Diagnosed by a Vortex-Following Coordinate System and a Technique for Advecting Material Contours

Abstract This paper presents results from a single-layer, shallow-water, 100-day model integration that reproduces many features of the wintertime stratosphere, particularly in the tropics, more realistically than earlier single-layer integrations. The advective transport of passive tracers by breaking Rossby waves is examined using a new polar-vortex-following coordinate system and a technique for advecting material contours, in which they are followed very accurately using the contour-dynamics algorithm of Dritschel. Unlike any Eulerian tracer advection scheme, the technique for advecting material contours has no numerical diffusion and can handle the ultrafinescale, exponentially shrinking tracer features characteristic of chaotic advective transport or “stirring,” which is conspicuous here in the stratospheric “surfzone.” The technique may become important as a benchmark for quantitative comparison with Eulerian tracer advection schemes, such as those used in general circulation models. Averages with ...