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.     

A numerical world ocean general circulation model

This paper describes a numerical model of the world ocean based on the fully primitive equations. A “Standard” ocean state is introduced into the equations of the model and the perturbed thermodynamic variables are used in the modle’s calculations. Both a free upper surface and a bottom topography are included in the model and a sigma coordinate is used to normalize the model’s vertical component. The model has four unevenly-spaced layers and 4 × 5 horizontal resolution based on C-grid system. The finite-difference scheme of the model is designed to conserve the gross available energy in order to avoid fictitious energy generation or decay.The model has been tested in response to the annual mean surface wind stress, sea level air pressure and sea level air temperature as a preliminary step to its further improvement and its coupling with a global atmospheric general circulation model. Some of results, including currents, temperature and sea surface elevation simulated by the model are presented.     

A unified theory of orographic influences upon cyclogenesis

Summary Cyclogenesis is known to take place frequently near the principal mountain complexes of the earth. However, a coherent and comprehensive theory of orographic cyclogenesis has never been offered in the literature. We propose here a unified theory of cyclogenesis in the presence of orography of various configurations, based on the generalization of a theoretical model concerning the interaction of baroclinic waves with local orography. This model has recently proved to be successful in accounting for some basic properties of Alpinecyclogenesis (Speranza et al. 1985). We consider, in particular, cyclogenesis in proximity of the Rocky Mountains (both to the west of the ridge, in the Gulf of Alaska, and to the east of it, over North America) and in proximity of the Himalaya-Tibetan Plateau.With regard to cyclogenesis over the Gulf of Alaska, results of numerical experiments, performed with the ECMWF model in order to isolate the orographic effects in realistic conditions, are also presented and compared with the theoretical results.

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Eine vereinheitlichte Theorie orographischer einflüsse auf die zyklogenese

Zusammenfassung Zyklogenese findet bekanntlich häufig in der Nähe der Hauptgebirgskomplexe der Erde statt. Dennoch wurde bis jetzt in der Literatur noch keine einheitliche und umfassende. Theorie orographischer Zyklogenese angeboten. Wir schlagen hier eine vereinheitlichte Theorie der Zyklogenese bei Vorhandensein einer Orographie mit unterschiedlichen Konfigurationen vor. Die Theorie basiert auf der Verallgemeinerung eines theoretischen Models über die Wechselwirkung von baroklinen Wellen mit der lokalen Orographie. Dieses Modell hat sich kürzlich bei der Erklärung einiger grundlegender Eigenschaften alpiner Zyklogenese als erfolgreich erwiesen (Speranza et al. 1985).Wir betrachten im besonderen die Zyklogenese in der Nähe der Rocky Mountains (sowohl westlich der Kette im Golf von Alaska als auch östlich davon über Nordamerika) und in der Nähe des Himalaya-Tibet-Plateaus.Hinsichtlich der Zyklogenese über dem Golf von Alaska werden auch Ergebnisse von numerischen Experimenten, die mit dem ECMWF-Modell durchgeführt wurden, um die orographischen Effekte unter realistischen Bedingungen zu isolieren, präsentiert und mit den theoretischen Ergebnissen verglichen.

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With 11 Figures     

Elements of the theory of wavelike formation of cohesive mudflows in erosion areas

Presented are the dependences that allow judging as a rough approximation about the process of accumulation of the cohesive mud mass in mudflow areas till the complete formation of a mudflow in the erosion inset of the main riverbed of a mudflow type.     

Dimethylsulphide production in the subantarctic southern ocean under enhanced greenhouse conditions

Dimethylsulphide (DMS) is an important sulphur‐containing trace gas produced by enzymatic cleavage of its precursor compound, dimethylsulphoniopropionate (DMSP), which is released by marine phytoplankton in the upper ocean. After ventilation to the atmosphere, DMS is oxidised to form sulphate aerosols which in the unpolluted marine atmosphere are a major source of cloud condensation nuclei (CCN). Because the micro‐physical properties of clouds relevant to climate change are sensitive to CCN concentration in air, it has been postulated that marine sulphur emissions may play a rôle in climate regulation. The Subantarctic Southern Ocean (41–53°S) is relatively free of anthropogenic sulphur emissions, thus sulphate aerosols will be mainly derived from the biogenic source of DMS, making it an ideal region in which to evaluate the DMS‐climate regulation hypothesis. We have extended a previous modelling analysis of the DMS cycle in this region by employing a coupled general circulation model (CGCM) which has been run in transient mode to provide a more realistic climate scenario. The CGCM output provided meteorological data under the IPCC/IS92a radiative forcing scenario. A DMS production model has been forced with the CGCM climate data to simulate the trend in the sea‐to‐air DMS flux for the period 1960 to 2080, corresponding to equivalent CO₂ tripling relative to pre‐industrial levels. The results confirm a minor but non‐negligible increase in DMS flux in this region, in the range +1% to +6% predicted over the period simulated. Uncertainty analysis of the DMS model predictions have confirmed the positive sign for the change in DMS flux, that is a negative DMS feedback on warming.     

A global ocean biogeochemistry general circulation model and its simulations

An ocean biogeochemistry model was developed and incorporated into a global ocean general circulation model (LICOM) to form an ocean biogeochemistry general circulation model (OBGCM). The model was used to study the natural carbon cycle and the uptake and storage of anthropogenic CO2 in the ocean. A global export production of 12.5 Pg C yr-1 was obtained. The model estimated that in the pre-industrial era the global equatorial region within 15o of the equator released 0.97 Pg C yr-1 to the atmosphere, which was balanced by the gain of CO2 in other regions. The post-industrial air-sea CO2 flux indicated the oceanic uptake of CO2 emitted by human activities. An increase of 20－50 mol kg-1 for surface dissolved inorganic carbon (DIC) concentrations in the 1990s relative to pre-industrial times was obtained in the simulation, which was consistent with data-based estimates. The model generated a total anthropogenic carbon inventory of 105 Pg C as of 1994, which was within the range of estimates by other researchers. Various transports of both natural and anthropogenic DIC as well as labile dissolved organic carbon (LDOC) were estimated from the simulation. It was realized that the Southern Ocean and the high-latitude region of the North Pacific are important export regions where accumulative air-sea CO2 fluxes are larger than the DIC inventory, whereas the subtropical regions are acceptance regions. The interhemispheric transport of total natural carbon (DIC+LDOC) was found to be northward (0.11 Pg C yr-1), which was just balanced by the gain of carbon from the atmosphere in the Southern Hemisphere.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing layer analogy for the flow at a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

A numerical world ocean general circulation model: Part II. A baroclinic experiment

A new six-layer world ocean general circulation model based on the primitive system of equations is described in detail and its performance in the case of a homogeneous ocean is described. These test integrations show that the model is capable of reproducing the observed mean barotropic or vertically-integrated transport, as well as the seasonal variability of the major ocean gyres. The surface currents, however, are dominated by the Ekman transport, and such non-linear features as the western boundary currents and the equatorial countercurrents are poorly represented. The abyssal boundary countercurrents are also absent due to the lack of thermohaline forcing. The most conspicuous effect of the bottom topography on a homogeneous ocean is seen in the Southern ocean where the calculated Antarctic circumpolar transport through the Drake passage ( ≈ 10 Sv, with bathymetry included) greatly underestimates the observed transport (≈ 100 Sv).     

A Coupled General Circulation Model for the Tropical Pacific Ocean and Global Atmosphere

On the basis of Zeng’s theoretical design, a coupled general circulation model (CGCM) is developed with its characteristics different from other CGCMs such as the unified vertical coordinates and subtraction of the standard stratification for both atmosphere and ocean, available energy consideration, and so on. The oceanic component is a free surface tropical Pacific Ocean GCM between 30oN and 30oS with horizontal grid spacing of 1o in latitude and 2o in longitude, and with 14 vertical layers. The atmospheric component it a global GCM with low-resolution of 4o in latitude and 5o in longitude, and two layers or equal man in the vertical between the surface and 200 hPa. The atmospheric GCM includes comprehensive physical processes. The coupled model is subjected to seasonally-varying cycle. Several coupling experiments, ranging from straight forward coupling without flux correction to one with flux correction, and to so-called predictor-corrector monthly coupling (PCMC), are conducted to show the existence and final controlling of the climate drift in the coupled system. After removing the climate drift with the PCMC scheme, the coupled model is integrated for more than twenty years. The results show reasonable simulations of the annual mean and its seasonal cycle of the atmospheric and oceanic circulation. The model also produces the coherent interannual variations of the climate system, manifesting the observed El Ni?o / Southern Oscillation (ENSO).     

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.     

An event-by-event assessment of tropical intraseasonal perturbations for general circulation models

We detect and characterize each large-scale intraseasonal perturbation in observations (1979–2009) and in coupled general circulation models of Institut Pierre Simon Laplace (IPSL) and of Centre National de Recherches Météorologiques (CNRM). These ensembles of intraseasonal perturbations are used to assess the skill of the two models in an event-by-event approach. This assessment addresses: (1) the planetary-scale (i.e. the whole Indo-Pacific area) extent of wind and rainfall perturbations and the reproducibility of the perturbation patterns for a given season; (2) the size and amplitude of rainfall and wind anomalies at basin-scale (i.e. for a particular phase of the perturbation) and; (3) the evolution of the vertical structure of the perturbations (U, T and RH) for selected events. The planetary-scale extent of rainfall perturbations is generally too small for both models. This extent is also small for the wind perturbation in the IPSL model, but is correct, or even too large in boreal winter, for the CNRM model. The reproducibility of the planetary-scale patterns is exaggerated for wind perturbations in the CNRM model and is very poor for all parameters in the IPSL model. Over the Indian Ocean during boreal winter, rainfall and wind anomalies at basin-scale are too large for the CNRM model and too small for the IPSL model. The CNRM model gives a realistic baroclinic perturbations structure for wind, moisture and temperature, but with too large amplitude due in part to a zonally extended rainfall anomaly over the eastern Indian Ocean and the Maritime Continent. The IPSL model gives a realistic response for low-level wind only. Temperature and moisture perturbations are barotropic with a wrong warm anomaly at rainfall maximum and there is no gradual increase in low-level moisture prior to this rainfall maximum. These results suggest that this version of the IPSL model is unable to initiate the coupling between the convection and the dynamic necessary to develop the perturbation. It is difficult to say if this is due to, or is at the origin of the lack of basin-scale organization of the convection. We discuss the likely role of the convective schemes in the differences found between these two versions of the CNRM and IPSL models.     

A theory for polar amplification from a general circulation perspective

Records of the past climates show a wide range of values of the equator-to-pole temperature gradient, with an apparent universal relationship between the temperature gradient and the globalmean temperature: relative to a reference climate, if the global-mean temperature is higher (lower), the greatest warming (cooling) occurs at the polar regions. This phenomenon is known as polar amplification. Understanding this equator-to-pole temperature gradient is fundamental to climate and general circulation, yet there is no established theory from a perspective of the general circulation. Here, a general circulation-based theory for polar amplification is presented. Recognizing the fact that most of the available potential energy (APE) in the atmosphere is untapped, this theory invokes that La-Niña-like tropical heating can help tap APE and warm the Arctic by exciting poleward and upward propagating Rossby waves.     

A numerical world ocean general circulation model Part I. Basic design and barotropic experiment

A new six-layer world ocean general circulation model based on the primitive system of equations is described in detail and its performance in the case of a homogeneous ocean is described. These test integrations show that the model is capable of reproducing the observed mean barotropic or vertically-integrated transport, as well as the seasonal variability of the major ocean gyres. The surface currents, however, are dominated by the Ekman transport, and such non-linear features as the western boundary currents and the equatorial countercurrents are poorly represented. The abyssal boundary countercurrents are also absent due to the lack of thermohaline forcing. The most conspicuous effect of the bottom topography on a homogeneous ocean is seen in the Southern ocean where the calculated Antarctic circumpolar transport through the Drake passage ( ≈ 10 Sv, with bathymetry included) greatly underestimates the observed transport (≈ 100 Sv).     

Error evolution in the dynamics of an ocean general circulation model

The problem of error propagation is considered for spatially uncorrelated errors of the barotropic stream function in an oceanic general circulation model (OGCM). Such errors typically occur when altimetric data from satellites are assimilated into ocean models. It is shown that the error decays at first due to the dissipation of the smallest scales in the error field. The error then grows exponentially before it saturates at the value corresponding to the difference between independent realizations. A simple analytic formula for the error behavior is derived; it matches the numerical results documented for the present primitive-equation ocean model, and other models in the literature.     

Stability dependent parameterisations of vertical mixing in ocean general circulation models

Summary Parameterisations of mixing induced through shear instability, internal wave breaking, and double diffusion are investigated in simulations of ocean climate using a global ocean general circulation model (OGCM). Focus is placed on the sensitivity of the large scale circulation, water mass formation and transport of heat as measures of the model's ability to represent current climate. The model resolution is typical of OGCMs being coupled to atmospheric. GCMs in climate models and the parameterisations investigated are all computationally inexpensive enough to allow for integrations on long time scales. Under the assumption of constant vertical eddy coefficients (the control case), the model climatology displays acceptable values of North Atlantic Deep Water formation, Antarctic Circumpolar Current (ACC) transport, and Indonesian through-flow but an excessively deep and diffuse pycnocline structure with weak stratification in the deep ocean. It is found that various circulation and water mass properties are sensitive to the choice of parameterisation of vertical mixing and that determining a scheme which works satisfactorily over all regions (tropical, mid-latitude, and polar) of the domain is not straightforward. Parameterisations of internal wave breaking or upper ocean shear instability lead to some improvements in the model water mass formation. ACC and poleward heat transport when compared to the control case whereas parameterisations of double diffusive processes did not. Based on these and other results, various recommendations are made for mixing parameterisations in ocean climate models.With 8 Figures     

On the theory of a steady circulation in a baroclinic ocean

Some results are presented of numerical experiments associated with calculations of stationary fields of current velocity and temperature in the ocean. Results obtained by two different approaches to the theory of ocean circulation are compared: without regard for horizontal exchange under conditions of bottom sticking and with due regard for horizontal exchange in case of bottom slipping.