The dynamics of moist frontogenesis in a semi‐geostrophic model

Abstract

The effects of condensational heating on the semi‐geostrophic dynamics of frontogenesis are studied using a two‐dimensional deformation model. The model includes water vapour and allows the formation of stratiform clouds. Analysis and numerical results show that heating due to stratiform clouds has the effect of reducing stability to slantwise convection, as found in previous studies (Thorpe and Emanuel, 1985). In addition, heating‐induced potential vorticity and temperature anomalies play a very important role in the frontal circulation. The ageostrophic flow induced by these anomalies tends to reinforce the effect of heating and increases the strength of frontal cloud. The model is also able to produce the low‐level jet maximum ahead of a cold front at an elevated level, in agreement with observations, owing to the explicit condensation scheme used in the model.     

Some properties and comparative performance of the semi‐Lagrangian method of Robert in the solution of the advection‐diffusion equation

Abstract

A numerical method for solving the advection‐diffusion equation, based on the semi‐Lagrangian algorithm of Robert (1981, 1982) is described, analysed and evaluated in comparison with other methods through a series of test problems. It is found that this method is generally better than other semi‐Lagrangian methods, and is a viable alternative to existing methods for LRTAP and other meteorological modelling because of its flexibility in application, its computational stability and its accuracy.     

Integration of a semi‐implicit model with time‐dependent boundary conditions

A semi‐implicit barotropic primitive equations model is integrated over a limited area with time dependent boundary conditions using the standard mesh and a finer mesh. Following a theorem by Charney, a minimum number of variables are specified as boundary conditions for the limited area integrations in order to avoid mathematical over‐specification. The comparison of coarse mesh limited area forecasts with the corresponding forecasts made over a much larger domain demonstrates that the essential features, namely the Rossby type perturbations, are handled almost perfectly. The fine mesh forecasts over the same limited area are also very good. Finally, the effect of specifying inaccurate boundary conditions, in the form of twelve‐hour forecasts, is briefly illustrated.     

Sea‐ice dynamics and CO2 sensitivity in a global climate model

Abstract

Present‐day results and CO₂ sensitivity are described for two versions of a global climate model (genesis) with and without sea‐ice dynamics. Sea‐ice dynamics is modelled using the cavitating‐fluid method of Flato and Hibler (1990, 1992). The atmospheric general circulation model originated from the NCAR Community Climate Model version 1, but is heavily modified to include new treatments of clouds, penetrative convection, planetary boundary‐layer mixing, solar radiation, the diurnal cycle and the semi‐Lagrangian transport of water vapour. The surface models include an explicit model of vegetation (similar to BATS and SiB), multilayer models of soil, snow and sea ice, and a slab ocean mixed layer.

When sea‐ice dynamics is turned off, the CO₂‐induced warming increases drastically around ～60–80°S in winter and spring. This is due to the much greater (and unrealistic) compactness of the Antarctic ice cover without dynamics, which is reduced considerably when CO₂ is doubled and exposes more open ocean to the atmosphere. With dynamics, the winter ice is already quite dispersed for 1 × CO₂ so that its compactness does not decrease as much when CO₂ is doubled.     

Short‐term forecasting with a multi‐level spectral primitive equation model part I ‐ model formulation

A global baroclinic primitive equation model using the spectral technique has been constructed for short‐ and medium‐range numerical weather prediction. The spectral technique, which is a special case of the Galerkin method, employs spherical harmonic basis functions in the evaluation of all horizontal derivatives. The use of a transform technique allows all the horizontal operations to be performed efficiently and allows physical processes to be evaluated in real space. The model employs a semi‐implicit algorithm for time integration and finite differencing in the vertical. Physical processes include orography, moist convection, large scale precipitation and boundary layer processes.     

Graupel growth and trajectories in a shallow cb cloud determined by a forced 1‐D model

Abstract

A kinematic model is applied to graupel growth. The vertical velocity and ther‐modynamic field data are taken from the forced 1‐D time‐dependent model of Cb cloud developed by Curie and Jane (1988). The graupel embryo pocket was released at the height of the — 10°C isotherm. The influence of the forced lifting on further graupel growth and its trajectory is analysed by sensitivity experiments based on the amplitude of the forced lifting, and initial graupel radius, density and cloud droplet concentration for the forced lifting initiation time derived from the model and the forced lifting duration time that agreed with observations. In particular, the sensitivity analysis was carried out for the forced lifting initiation and duration times.

It is shown that for large values of the forced lifting amplitudes, the residence time of the graupel within cloud and the final graupel radius may be significantly larger compared with those in the non‐forced case. The residence time in a cloud can also be significantly larger for the smallest amplitude, whereas the final radius is rather insensitive owing to oscillations around the melting level. For some cases the forced lifting causes recycling inside the updraft, contrary to the results of previous non‐forced numerical models. The recycling mechanism is sensitive to the forced lifting duration time and the time interval between the graupel pocket injection in cloud and the initiation of the forced lifting. Initially the observed recycling mechanism is a consequence of the periodic forced lifting mechanism, but then combines with recycling of the Pflaum type (1980).     

Winter‐time near‐surface currents in the strait of Juan de Fuca

Abstract

During November 1976 to February 1977 near‐surface wind, current and temperature measurements were made at three sites along the Strait of Juan de Fuca. Strong tidal currents and major intrusions of warmer, fresher offshore coastal water were superimposed upon the estuarine circulation of near‐surface seaward flow. The r.m.s. amplitudes of the diurnal and semidiurnal tidal currents were ～30 cms^‐1 and 30–47 cm s^‐1, respectively. The vector‐mean flow at 4 m‐depth was seaward and decreased in speed from 28 cm s^‐1 at 74 km from the entrance to 9 cm s^‐1 at 11 km from the entrance. On five occasions intrusions of 1–3 C warmer northeast Pacific coastal water occurred for durations of 1–10 days. The 25 cm s^‐1 up‐strait speed of the intrusive lens agreed to within 20% of the gravity current speed computed from Benjamin's (1968) hydraulic model. The near‐surface currents associated with the intrusions and the southerly coastal winds were significantly correlated, indicating that the intrusions were initiated when shoreward Ekman currents advected Pacific coastal water into the Strait. The reversals were not significantly coherent with the along‐strait sea surface slope measured along the north side of the Strait nor were they strongly related to local wind forcing.     

Onset of convection in a rotating semi‐infinite fluid: Theory and experiment

Abstract

We look at the development of the first plumes that emerge from a convectively unstable boundary layer by modelling the process as the instability of a fluid with a time‐dependent mean density field. The fluid is semi‐infinite, rotating, dissipative ‐ characterized by the ratio of its viscosity to thermal diffusivity (Prandtl number Pr = ν/κ) ‐ and initially homogeneous. A constant destabilizing heat flux is applied at the boundary and the stability of the evolving density field is investigated both mathematically and in laboratory experiments.

Using a “natural convective” scaling, we show that the behaviour of the non‐dimensional governing equations depends on Pr and the parameter γ = f(ν/B)^1/2, where f is the Coriolis parameter, and B is the applied buoyancy flux. For the ocean, γ ≈ 0.1, whilst for the atmosphere γ ≈ 0.01. In the absence of rotation, the behaviour of the differential equations is independent of B, depending only on Pr. The boundary‐layer Rayleigh number (Ra_bl) is also independent of B. We show that Ra_bl, evaluated at the onset of rapid vertical motion, depends on the form of the perturbation.

Due to the time‐dependence of the mean density field, analytic instability analysis is difficult, so we use a numerical technique. The governing equations are transformed to a stretched vertical coordinate and their stability investigated for a particular form of perturbation function. The model predictions are, for the ocean: instability time ～2–4 h, density difference ～0.002–0.013 kg m^‐3, boundary‐layer thickness ～50–75 m and horizontal scale ～200–300 m; and for the atmosphere: instability time ～10 min, temperature difference ～2.0–3.0°C, boundary‐layer thickness ～400–500 m and horizontal scale ～1.5–2.0 km.

Laboratory experiments are performed to compare with the numerical predictions. The time development of the mean field closely matches the assumed analytic form. Furthermore, the model predictions of the instability timescale agree well with the laboratory measurements. This supports the other predictions of the model, such as the lengthscales and buoyancy anomaly.     

Multiple temporal scale variability during the twentieth century in global carbon dynamics simulated by a coupled climate–terrestrial carbon cycle model

A coupled climate–carbon cycle model composed of a process-based terrestrial carbon cycle model, Sim-CYCLE, and the CCSR/NIES/FRCGC atmospheric general circulation model was developed. We examined the multiple temporal scale functions of terrestrial ecosystem carbon dynamics induced by human activities and natural processes and evaluated their contribution to fluctuations in the global carbon budget during the twentieth century. Global annual net primary production (NPP) and heterotrophic respiration (HR) increased gradually by 6.7 and 4.7%, respectively, from the 1900s to the 1990s. The difference between NPP and HR was the net carbon uptake by natural ecosystems, which was 0.6 Pg C year^?1 in the 1980s, whereas the carbon emission induced by human land-use changes was 0.5 Pg C year^?1, largely offsetting the natural terrestrial carbon sequestration. Our results indicate that monthly to interannual variation in atmospheric CO₂ growth rate anomalies show 2- and 6-month time lags behind anomalies in temperature and the NiNO₃ index, respectively. The simulated anomaly amplitude in monthly net carbon flux from terrestrial ecosystems to the atmosphere was much larger than in the prescribed air-to-sea carbon flux. Fluctuations in the global atmospheric CO₂ time series were dominated by the activity of terrestrial vegetation. These results suggest that terrestrial ecosystems have acted as a net neutral reservoir for atmospheric CO₂ concentrations during the twentieth century on an interdecadal timescale, but as the dominant driver for atmospheric CO₂ fluctuations on a monthly to interannual timescale.     

Does the integration of the dynamic nitrogen cycle in a terrestrial biosphere model improve the long-term trend of the leaf area index?

The carbon cycle strongly interacts with the nitrogen cycle. Several observations show that the effects of global change on primary production and carbon storage in plant biomass and soils are partially controlled by N availability. Nevertheless, only a small number of terrestrial biosphere models represent explicitly the nitrogen cycle, despite its importance on the carbon cycle and on climate. These models are difficult to evaluate at large spatiotemporal scales because of the scarcity of data at the global scale over a long time period. In this study, we benchmark the capacity of the O–CN global terrestrial biosphere model to reproduce temporal changes in leaf area index (LAI) at the global scale observed by NOAA_AVHRR satellites over the period 1982–2002. Using a satellite LAI product based on the normalized difference vegetation index of global inventory monitoring and modelling studies dataset, we estimate the long-term trend of LAI and we compare it with the results from the terrestrial biosphere models, either with (O–CN) or without (O–C) a dynamic nitrogen cycle coupled to the carbon–water-energy cycles. In boreal and temperate regions, including a dynamic N cycle (O–CN) improved the fit between observed and modeled temporal changes in LAI. In contrast, in the tropics, simulated LAI from the model without the dynamic N cycle (O–C) better matched observed changes in LAI over time. Despite differential regional trends, the satellite estimate suggests an increase in the global average LAI during 1982–2002 by 0.0020 m² m^?2 y^?1. Both versions of the model substantially overestimated the rate of change in LAI over time (0.0065 m² m^?2 y^?1 for O–C and 0.0057 m² m^?2 y^?1 for O–CN), suggesting that some additional limitation mechanisms are missing in the model. We also estimated the relative importance of climate, CO₂ and N deposition as potential drivers of the temporal changes in LAI. We found that recent climate change better explained temporal changes in LAI when the dynamic N cycle was included in the model (higher ranked fit for O–CN vs. O–C). Using the O–C configuration to estimate the direct effect of climate on LAI, we quantified the importance of climate-N cycle feedbacks in explaining the LAI response. We found that the warming-induced release of N from soil organic matter decomposition explains 17.5 % of the global trend in LAI over time, however, reaching up to 40.9 % explained variance in the boreal zone, which is a more important contribution than increasing anthropogenic nitrogen deposition. Our analysis supports a strong connection between warming, N cycling, and vegetation productivity. These findings underscore the importance of including N cycling in global-scale models of vegetation response to environmental change.     

Non‐linear coupling between modes in a low‐dimensional model of ENSO

Abstract

An intermediate coupled model of the tropical Pacific ocean‐atmosphere system was reduced by projecting the non‐linear model onto a truncated basis set of its own empirical orthogonal functions (EOFs). For moderate coupling strengths, the simulated El Niño/Southern Oscillation (ENSO) variability consists of a dominant quasi‐quadrennial mode with a period of approximately four years and a smaller quasi‐biennial mode at a period of approximately two years. In the absence of a seasonal cycle, the leading two EOFs capture the dynamics of the leading interannual mode, with a further two EOFs being required to capture the secondary oscillation. The presence of seasonal forcing increases the EOF requirement by two, the leading pair of EOFs being dominated by the annual cycle. Normal mode analysis of the reduced models indicates that the quasi‐biennial mode manifests itself, even though it is linearly stable, by non‐linear coupling to the quasi‐quadrennial mode. The nonlinearity does not produce the quasi‐biennial signal unless the spatial degrees of freedom associated with the linear quasi‐biennial mode are present. Other linearly stable modes also couple non‐linearly to the leading interannual mode and to the seasonal cycle, but the quasi‐biennial mode is favoured over other, less‐damped linear modes because of its proximity to a multiple of the quasi‐quadrennial frequency.     

Short‐term forecasting with a multi‐level spectral primitive equation model part II ‐ Hemispheric prognoses and verification

The spectral global baroclinic primitive equation model described in Part I of this paper has been extensively tested. The model has been run daily from operational analyses for over a year. From this large sample of forecasts, verification statistics have been collected and compared with similar statistics collected from three competitive grid‐point models. The spectral model is also compared with the grid‐point models in a synoptic case study.

A second case study demonstrates the effect of horizontal resolution and physical effects on spectral model forecasts. The results of these experiments demonstrate that the spectral model is highly competitive with other models, in terms of both accuracy and computational efficiency. On 18 February 1976 the spectral model became the operational Canadian large‐scale forecast model.     

The role of the intra-daily SST variability in the Indian monsoon variability and monsoon-ENSO–IOD relationships in a global coupled model

The impact of diurnal SST coupling and vertical oceanic resolution on the simulation of the Indian Summer Monsoon (ISM) and its relationships with El Ni?o-Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) events are studied through the analysis of four integrations of a high resolution Coupled General Circulation Model (CGCM), but with different configurations. The only differences between the four integrations are the frequency of coupling between the ocean and atmosphere for the Sea Surface Temperature (SST) parameter (2 vs. 24?h coupling) and/or the vertical oceanic resolution (31 vs. 301 levels) in the CGCM. Although the summer mean tropical climate is reasonably well captured with all the configurations of the CGCM and is not significantly modified by changing the frequency of SST coupling from once to twelve per day, the ISM–ENSO teleconnections are rather poorly simulated in the two simulations in which SST is exchanged only once per day, independently of the vertical oceanic resolution used in the CGCM. Surprisingly, when 2?h SST coupling is implemented in the CGCM, the ISM–ENSO teleconnection is better simulated, particularly, the complex lead-lag relationships between the two phenomena, in which a weak ISM occurs during the developing phase of an El Ni?o event in the Pacific, are closely resembling the observed ones. Evidence is presented to show that these improvements are related to changes in the characteristics of the model’s El Ni?o which has a more realistic evolution in its developing and decaying phases, a stronger amplitude and a shift to lower frequencies when a 2-hourly SST coupling strategy is implemented without any significant changes in the basic state of the CGCM. As a consequence of these improvements in ENSO variability, the lead relationships between Indo-Pacific SSTs and ISM rainfall resemble the observed patterns more closely, the ISM–ENSO teleconnection is strengthened during boreal summer and ISM rainfall power spectrum is in better agreement with observations. On the other hand, the ISM–IOD teleconnection is sensitive to both SST coupling frequency and the vertical oceanic resolution, but increasing the vertical oceanic resolution is degrading the ISM–IOD teleconnection in the CGCM. These results highlight the need of a proper assessment of both temporal scale interactions and coupling strategies in order to improve current CGCMs. These results, which must be confirmed with other CGCMs, have also important implications for dynamical seasonal prediction systems or climate change projections of the monsoon.     

The near‐surface circulation and exchange in the newfoundland grand banks region

Abstract

Analysis of 39 satellite‐tracked drifter records from the Newfoundland Grand Banks region has allowed maps of the mean and variable flows to be drawn. The variable currents are particularly large relative to the mean for the shelf, Flemish Cap and in the Newfoundland Basin. The ratio of the mean to variable flow is largest along the path of the Labrador Current. Drifters that either have been released on or migrate onto the Grand Banks remain therefor an average of 71 d. A statistical study of the effect of wind on drifter motion has shown that winds can only account for about 10% of current variability. This result is examined with consideration given to data noise, aliasing and non‐stationary conditions. Some drifters that were deployed in the Labrador Current moved onto the shelf and vice versa. These observations have been used to estimate the rate of exchange between the Current and the Grand Banks. Using this exchange rate in a box model, it is calculated that, over the iceberg season, 30% of the bergs will be in the Avalon Channel, 20% on the Grand Banks and 50% in the Labrador Current, in good agreement with the observed distribution. An alternative model based solely on advection is considered as well. The exchange model is also applied to the salinity budget for the Labrador Current with some success.     

The energy of near‐surface internal waves in the strait of Georgia

An estimate of the energy content of near‐surface internal waves in the Strait of Georgia is obtained from a combination of aerial photographs and in‐situ measurements. The role of these waves in the tidal energy budget and in the mixing processes in the Strait is discussed.     

Grid‐size dependency of the meridional heat transport in a numerical model of an ocean

Abstract

The meridional heat transport across a latitude circle in a model ocean is calculated by using a general circulation model with a coarse grid, a medium grid and a fine grid capable of resolving the mesoscale eddies in order to show to what extent this transport depends on grid size. Although the grid size strikingly affects the current velocities, it has almost no effect upon the meridional heat transport.     

Application of a coupled ice‐ocean model to the Labrador Sea

Abstract

The steady, coupled ice‐ocean circulation model of Willmott and Mysak (1989) for a meridional channel is applied to the Labrador Sea for the winter season. The model consists of a thermodynamic reduced‐gravity ocean combined with a variable thickness ice cover that is in thermal equilibrium. Upon specifying the forcing fields of surface air temperature, wind stress and water temperature along the open southern boundary, the winter climatological ice‐edge position, ice thickness, ocean circulation and temperature fields are determined in the channel domain. The sensitivity of the results to the various model parameters is examined. In particular, the optimum heat exchange coefficients for the interfaces of air‐water, ice‐water and air‐ice are found.

The model ice‐edge position compares favourably with the 50% winter climatological ice concentration isoline obtained from an analysis of 32 years (1953–84) of sea‐ice concentration data. The simulations of the ocean temperature and ice thickness are also quite realistic according to the observed records available. The model is also applied to two specific winters (1981 and 1983) during which anomalous sea‐ice and weather conditions prevailed in the Labrador Sea.     

On tidal resonance in the global ocean and the back‐effect of coastal tides upon open‐ocean tides

Abstract

The resonance of semi‐diurnal tidal elevations is investigated with a forward numerical forced damped global tide model and an analytical model of forced‐damped tides in a deep ocean basin coupled to a shelf. The analytical model contains the classical half‐wavelength and quarter‐wavelength resonances in the deep ocean and shelf, respectively, as well as a forcing‐scale dependence which depends on the ratio of the phase speed of open‐ocean gravity waves to that of the astronomical forcing. In the analytical model, when the deep ocean and shelf resonate separately at the same frequency, the resonance in the coupled system shifts to frequencies slightly higher and lower than the original frequency, such that a ‘double bump’ is seen in plots of elevation amplitude versus frequency. The addition of a shelf to a resonant open ocean tends to reduce open‐ocean tides, especially when the shelf is also near resonance. The magnitude of this ‘back‐effect’ is controlled by shelf friction. A weakly damped resonant shelf has a larger back‐effect on the open‐ocean tide than does a strongly damped shelf. Numerical simulations largely bear out the analytical model predictions, at least qualitatively. Idealized simulations show that continents enhance tides by enabling the half‐wavelength resonance. Simulations with realistic geometry and topography but varying longitudinal structure in the astronomical forcing display an influence of the forcing scale on tidal amplitudes somewhat similar to that seen in the analytical model. A frequency sweep in the semi‐diurnal band in experiments with realistic geometry and topography reveals weakly resonant peaks in the amplitudes of several shelf regions and in the globally averaged open‐ocean amplitudes. Finally, the back‐effect of the shelf upon the open ocean is seen in simulations in which locations of resonant coastal tides are blocked out and open‐ocean tidal elevations are significantly altered (increased, generally) as a result.     

A global available potential energy‐kinetic energy budget in terms of the two‐dimensional wavenumber for the FGGE year

Abstract

A global vertically integrated available potential energy‐kinetic energy budget in terms of the two‐dimensional wavenumber is formulated using spherical harmonics. Results of the budget equations applied to the four mid‐season months of the FGGE year are given.