On the influence of frictional parameterization in wind-driven ocean circulation models

In a series of numerical experiments the wind-driven ocean circulation is studied in an idealized, rectangular model ocean, which is forced by steady zonal winds and damped by lateral and/or bottom friction. The problem as described by the barotropic vorticity equation is characterized by a Rossby number (R) and horizontal and/or vertical Ekman numbers (E_L, E_B) only.With free-slip conditions at the boundaries steady solutions for all chosen values of R are obtained, provided the diffusivity is sufficiently large. For both the forms of frictional parameterization a northern boundary current emerges with an eastward penetration scale depending on R. The recirculation pattern in the oceanically relevant ‘intermediate’ range of R is strongly affected by the type of friction. If lateral diffusion dominates bottom friction, a strong recirculating sub-gyre emerges in the northwestern corner of the basin. Its shape resembles the vertically integrated transport fields in recent eddy resolving model (EGCM) studies. The maximum transport is increased to values several times larger than the Sverdrup transport. The increase in transport is coupled with a development of closed contours of potential vorticity, enabling a nearly free inertial flow.This behaviour provides a sharp contrast to the bottom friction case (Veronis) where inertial recirculation only takes place with values of R so large that the eastward jet reaches the eastern boundary. It is shown that the linear friction law puts a strong constraint on the flow by preventing an intense recirculation in a small part of the basin.A reduction of the diffusivity (E_L) in the lateral friction case leads to quasi-steady solutions. The interaction with eddies becomes an integral part of the time mean energetics but does not influence the recirculation character of the flow.The main conclusion of the study is that the horizontal structure of the EGCM-transport fields can be explained in terms of a steady barotropic model where lateral friction represents the dominant dissipation mechanism.     

On the validity of layered models of ocean dynamics and thermodynamics with reduced vertical resolution

With the purpose of studying the upper part of the ocean, the shallow water equations (in a `reduced gravity' setting) have been extended in the last decades by allowing for horizontal and temporal variations of the buoyancy field ϑ, while keeping it as well as the velocity field u as depth-independent. In spite of the widespread use of this `slab' model, there has been neither a discussion on the range of validity of the system nor an explanation of points such as the existence of peculiar zero-frequency normal modes, the nature of the instability of a uniform u flow, and the lack of explicit vertical shear associated with horizontal density gradients. These questions are addressed here through the development of a subinertial model with more vertical resolution, i.e., one where the buoyancy ϑ varies linearly with depth. This model describes satisfactorily the problem of baroclinic instability with a free boundary, even for short perturbations and large interface slopes. An enhancement of the instability is found when the planetary β effect is compensated with the topographic one, due to the slope of the free boundary, allowing for a `resonance' of the equivalent barotropic and first baroclinic modes. Other low-frequency models, for which buoyancy stratification does not play a dynamical role, are invalid for short perturbations and have spurious terms in their energy-like integral of motion.     

On stochastic stability of regional ocean models to finite-amplitude perturbations of initial conditions

We consider error propagation near an unstable equilibrium state (classified as an unstable focus) for spatially uncorrelated and correlated finite-amplitude initial perturbations using short- (up to several weeks) and intermediate (up to 2 months) range forecast ensembles produced by a barotropic regional ocean model. An ensemble of initial perturbations is generated by the Latin Hypercube design strategy, and its optimal size is estimated through the Kullback–Liebler distance (the relative entropy). Although the ocean model is simple, the prediction error (PE) demonstrates non-trivial behavior similar to that existing in 3D ocean circulation models. In particular, in the limit of zero horizontal viscosity, the PE at first decays with time for all scales due to dissipation caused by non-linear bottom friction, and then grows faster than (quasi)-exponentially. Statistics of a prediction time scale (the irreversible predictability time (IPT)) quickly depart from Gaussian (the linear predictability regime) and becomes Weibullian (the non-linear predictability regime) as amplitude of initial perturbations grows. A transition from linear to non-linear predictability is clearly detected by the specific behavior of IPT variance. A new analytical formula for the model predictability horizon is introduced and applied to estimate the limit of predictability for the ocean model.     

Spectra of surface atmospheric quantities at ocean weathership P

Ten years of surface weather data from Ocean Weather Station P were subjected to spectral analysis. The wind speed and air pressure auto‐spectra reveal large variations at synoptic periods while the auto‐spectra of the sea temperature, air temperature and absolute humidity are dominated by the annual variations. The rotary auto‐spectrum of the wind features a broad peak of activity centered at a period of 3 days. In addition, the spectra of quantities representative of the wind stress and sensible and latent heat fluxes are discussed. Spectra of these surface weather quantities computed for each season show that the activity changes both with respect to the size and frequency of the variations during the course of a year. The cross‐spectra between selected pairs of quantities were also computed and are discussed.     

Simple general atmospheric circulation and climate models with memory

This article examines some general atmospheric circulation and climate models in the context of the notion of “memory”. Two kinds of memories are defined： statistical memory and deterministic memory. The former is defined through the autocorrelation characteristic of the process if it is random （chaotic）, while for the latter, a special memory function is introduced. Three of the numerous existing models are selected as examples. For each of the models, asymptotic （at t →∞） expressions are derived. In this way, the transients are filtered out and that which remains concerns the final behaviour of the models.     

Response Process of Oceanto AtmosphericForcing and Optimal Response Frequency in the CZ Ocean Model

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On the incompatibility of ocean and atmosphere models and the need for flux adjustments

The surface heat and freshwater fluxes from equilibrium ocean (OGCM) and atmospheric (AGCM) general circulation model climates are examined in order to determine the minimum flux adjustment required to prevent climate drift upon coupling. This is accomplished by integrating an OGCM with specified surface fluxes. It is shown that a dramatic climate drift of the coupled system is inevitable unless ocean meridional heat and freshwater (salt) transports are used as constraints for tuning the AGCM present-day climatology. It is further shown that the magnitude of the mismatch between OGCM and AGCM fluxes is not as important for climate drift as the difference in OGCM and implied AGCM meridional heat and freshwater (salt) transports. Hence a minimum flux adjustment is proposed, which is zonally-uniform in each basin and of small magnitude compared to present flux adjustments. This minimum flux adjustment acts only to correct the AGCM implied oceanic meridional transports of heat and freshwater (salt). A slight extension is also proposed to overcome the drift in the surface waters when the minimum flux adjustment is used. Finally, it is suggested that the flux adjustments which arise from current methods used to determine them are all very similar, leading to adjustment fields which are significantly larger than both AGCM and climatological fields over large regions.     

On the structure and variability of atmospheric circulation regimes in coupled climate models

In order to investigate whether climate models of different complexity have the potential to simulate natural atmospheric circulation regimes, 1000-year-long integrations with constant external forcing have been analysed. Significant non-Gaussian uni-, bi-, and trimodal probability density functions have been found in 100-year segments.     

The energy cycle in atmospheric models

The energy cycle characterizes basic aspects of the physical behaviour of the climate system. Terms in the energy cycle involve first and second order climate statistics (means, variances, covariances) and the intercomparison of energetic quantities offers physically motivated “second order” insight into model and system behaviour. The energy cycle components of 12 models participating in AMIP2 are calculated, intercompared and assessed against results based on NCEP and ERA reanalyses. In general, models simulate a modestly too vigorous energy cycle and the contributions to and reasons for this are investigated. The results suggest that excessive generation of zonal available potential energy is an important driver of the overactive energy cycle through “generation push” while excessive dissipation of eddy kinetic energy in models is implicated through “dissipation pull‘’. The study shows that “ensemble model” results are best or among the best in the comparison of energy cycle quantities with reanalysis-based values. Thus ensemble approaches are apparently “best” not only for the simulation of 1st order climate statistics as in Lambert and Boer (Clim Dyn 17:83–106, 2001) but also for the higher order climate quantities entering the energy cycle.     

A 1-D atmospheric energy balance model developed for ocean modelling

Summary We present a simple, deterministic energy balance model. The model is designed to represent the atmospheric component of the coupled atmosphere-ocean system. It is a one dimensional, global model with time and space resolutions of one year and 10° of latitude respectively. The model predicts the surface air temperature and estimates the surface freshwater flux diagnostically. The coupling between the atmospheric model and an ocean model is accomplished by heat and freshwater fluxes at their interface. The heat flux is calculated according to the difference in the surface air temperature and ocean surface temperature, while the freshwater flux is estimated from the latent heat transport in the atmosphere by a diagnostic equation. Two parameterizations for the latent heat transport are proposed, which distinguishes the two versions of the model.Before proceeding with interactive runs, we study the behaviour of the model in a decoupled mode. Some experiments with initial conditions altered and external forcings changed ar carried out to investigate the sensitivity and stability of the model. In particular, the influence of the ice-albedo feedback on model solutions is examined. The results of these experiments may be helpful both in understanding the characteristics of the model and in interpreting results when the model is coupled to an OGCM.With 9 Figures     

Coupling an ocean wave model to an atmospheric general circulation model

A coupled model, consisting of an ocean wave model and an atmospheric general circulation model (AGCM), is integrated under permanent July conditions. The wave model is forced by the AGCM wind stress, whereas the wind waves modify the AGCM surface fluxes of momentum, sensible and latent heat. We investigate the following aspects of the coupled model: how realistic are the wave fields, how strong is the coupling, and how sensitive is the atmospheric circulation to the spatially and temporally varying wave field. The wave climatology of the coupled model compares favorably with observational data. The interaction between the two models is largest (although weak) in the storm track in the Southern Hemisphere. Young windsea, which is associated with enhanced surface fluxes is generated mostly in the equatorward frontal area of an individual cyclone. However, the enhancement of the surface fluxes is too small to significantly modify the climatological mean atmospheric circulation.This paper was presented at the Second International Conference on Modelling of Global Climate Variability, held in Hamburg 7–11 September 1992 under the auspices of the Max Planck Institute for Meteorology. Guest Editor for these papers is L. Dümenil     

The buffer capability of the ocean to increasing atmospheric CO2

The CO2-seawaler system and the method for calculating the partial pressure of CO2 (pCO3) in seawater are stu-died. The buffer capability of the ocean to increasing atmospheric CO2, is expressed in terms of the differential buffer factor and buffer index. Dissolutions of aragonite and calcite have a significant influence on the differential buffer factor. The trend of change in the buffer factor is obtained by a box model.     

A framework for evaluating air quality models

This paper describes a framework to evaluate air quality model predictions against observations. We propose the following relationship between observations and predictions from an adequate model% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% WaaSbaaSqaaiaaicdaaeqaamXvP5wqonvsaeHbfv3ySLgzaGqbaOGa% e8hkaGIaamiEamaaBaaaleaacaaIXaaabeaakiaacYcacaWG4bWaaS% baaSqaaiaaikdaaeqaaOGae8xkaKIaeyypa0Jabm4qayaajaWaaSba% aSqaaiaadchaaeqaaOGae8hkaGIaamiEamaaBaaaleaacaaIXaaabe% aakiab-LcaPiab-TcaRiabew7aLjab-HcaOiaadIhadaWgaaWcbaGa% aGOmaaqabaGccqWFPaqkaaa!4F93!\[\hat C_0 (x_1 ,x_2 ) = \hat C_p (x_1 ) + \varepsilon (x_2 )\],where x ₁ refers to the inputs used in the model prediction C _p(x ₁), and x ₂denotes unknown variables which affect the observed concentration C ₀. The hats associated with C _pand C ₀denote transformations to convert the residual to a white noise sequence which is normally distributed. In this paper we assume % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% GaeyyyIORaciiBaiaac6gacaWGdbaaaa!3B39!\[\hat C \equiv \ln C\].The standard deviation of determines the expected deviation between model prediction and observation. The purpose of model improvement is to make this deviation as small as possible.The formalism we have proposed is applied to the evaluation of two models developed by this author. We show how careful analysis of residuals can lead to improvements in the model. We have also estimated for each of the models.In the last part of the part of the paper we show how the statistics of can be used to interpret model predictions.     

Water-Soluble dicarboxylic acids, ketoacids and dicarbonyls in the atmospheric aerosols over the southern ocean and western pacific ocean

Water-soluble dicarboxylic acids (DCAs), ketoacids, and α-dicarbonyls in the marine aerosol samples collected over the Southern Ocean and western Pacific Ocean were determined. Oxalic acid was the most abundant species, followed by malonic acid and then succinic acid. It is suggested that aerosol concentrations of the organics over the Southern Ocean in this work represent their global background levels. Over the Southern Ocean, total concentrations of DCAs ranged from 2.9 to 7.2 ng m⁻³ (average: 4.5 ng m⁻³), ketoacids from 0.14 to 0.40 ng m⁻³ (av.: 0.28 ng m⁻³), and dicarbonyls from 0.06 to 0.29 ng m⁻³ (av.: 0.11 ng m⁻³). Over the western Pacific, total concentrations of DCAs ranged from 1.7 to 170 ng m⁻³ (av.: 60 ng m⁻³), ketoacids from 0.08 to 5.3 ng m⁻³ (av.: 1.8 ng m⁻³), and dicarbonyls from 0.03 to 4.6 ng m⁻³ (av.: 0.95 ng m⁻³). DCAs over the western Pacific have constituted a large fraction of organic aerosols with a mean DCAs-C/TC (total carbon) of 7.0% (range: 0.59–14%). Such a high value was in contrast to the low DCAs-C/TC (av.: 1.8%; range: 0.89–4.0%) for the Southern Ocean aerosols. Based on the relative abundances and latitudinal distributions of these organics, we propose that long-range atmospheric transport is more important over the western Pacific Ocean, in contrast, in situ photochemical production is more significant over the Southern Ocean although absolute concentrations of the organics are much lower.     

Acoustic thermometry data compared with two ocean models: the importance of Rossby waves and ENSO in modifying the ocean interior

An interpretation is made of interannual changes in acoustic travel time between Oahu and seven receivers at distances of 3000–4000 km. Measurements were made in late 1983, and over two 5-month intervals between 1987 and 1989. Previous publications demonstrated that these changes stem from variations in temperature. Two hydrodynamic ocean models are used to identify plausible oceanic features that could cause these variations. They are from the Naval Research Laboratory and the Florida State University at (1/8)° and (1/6)° resolution, respectively, and are forced with different interannual wind sets for more than a decade. Modelled El Niño's and La Niña's generate poleward travelling Kelvin waves on the eastern boundary of the Pacific. These excite Rossby waves that propagate westward at mid-latitudes. Rossby waves are the dominant model features which affect the modelled acoustic travel times, and hence section-averaged temperatures in the eastern North Pacific. These waves yield travel times whose standard deviations and rates of changes are similar to the measurements. In the observations, some sections separated by less than 500 km exhibit trends in heat content with opposite signs. Similar variability can be explained with modelled Rossby waves. Model wavelengths less than 500 km, eddies, and seasonal cycles induced by seasonal winds yield travel times that are two orders of magnitude too small to account for the data.     

The deep water stratification of ocean general circulation models

Abstract

A central problem in climate and ocean modelling is the accurate simulation of the climatological state of the oceanic density field. A constant vertical diffusivity for heat and salt is frequently employed in ocean general circulation models (OGCMs) and it is usually assigned a value designed to optimize the depth of the pycnocline. One undesired consequence of this choice is a poor representation of the deep water, which is usually insufficiently stratified. In contrast to the uniform diffusivity of many models, some observational studies suggest that the vertical diffusivity is not constant but increases with depth, possibly in inverse proportion to the local buoyancy frequency. Numerical experiments with an OGCM are presented that demonstrate that allowing the vertical diffusivity to increase below the pycnocline substantially increases the stratification of the abyssal water mass of these models without significantly affecting the pycnocline depth, and hence may lead to a better representation of the vertical density structure.