Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

The integrated WRF/urban modelling system: development, evaluation, and applications to urban environmental problems

To bridge the gaps between traditional mesoscale modelling and microscale modelling, the National Center for Atmospheric Research, in collaboration with other agencies and research groups, has developed an integrated urban modelling system coupled to the weather research and forecasting (WRF) model as a community tool to address urban environmental issues. The core of this WRF/urban modelling system consists of the following: (1) three methods with different degrees of freedom to parameterize urban surface processes, ranging from a simple bulk parameterization to a sophisticated multi-layer urban canopy model with an indoor–outdoor exchange sub-model that directly interacts with the atmospheric boundary layer, (2) coupling to fine-scale computational fluid dynamic Reynolds-averaged Navier–Stokes and Large-Eddy simulation models for transport and dispersion (T&D) applications, (3) procedures to incorporate high-resolution urban land use, building morphology, and anthropogenic heating data using the National Urban Database and Access Portal Tool (NUDAPT), and (4) an urbanized high-resolution land data assimilation system. This paper provides an overview of this modelling system; addresses the daunting challenges of initializing the coupled WRF/urban model and of specifying the potentially vast number of parameters required to execute the WRF/urban model; explores the model sensitivity to these urban parameters; and evaluates the ability of WRF/urban to capture urban heat islands, complex boundary-layer structures aloft, and urban plume T&D for several major metropolitan regions. Recent applications of this modelling system illustrate its promising utility, as a regional climate-modelling tool, to investigate impacts of future urbanization on regional meteorological conditions and on air quality under future climate change scenarios. Copyright © 2010 Royal Meteorological Society

A simple model of convection with memory

There are at least three distinct time scales that are relevant for the evolution of atmospheric convection. These are the time scale of the forcing mechanism, the time scale governing the response to a steady forcing, and the time scale of the response to variations in the forcing. The last of these, tmem, is associated with convective life cycles, which provide an element of memory in the system. A highly simplified model of convection is introduced, which allows for investigation of the character of convection as a function of the three time scales. For short tmem, the convective response is strongly tied to the forcing as in conventional equilibrium parameterization. For long tmem, the convection responds only to the slowly evolving component of forcing, and any fluctuations in the forcing are essentially suppressed. At intermediate tmem, convection becomes less predictable: conventional equilibrium closure breaks down and current levels of convection modify the subsequent response.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part I: gravity wave forcing

Parameterization schemes for the drag due to atmospheric gravity waves are discussed and compared in the context of a simple one-dimensional model of the quasi-biennial oscillation (QBO). A number of fundamental issues are examined in detail, with the goal of providing a better understanding of the mechanism by which gravity wave drag can produce an equatorial zonal wind oscillation. The gravity wave–driven QBOs are compared with those obtained from a parameterization of equatorial planetary waves. In all gravity wave cases, it is seen that the inclusion of vertical diffusion is crucial for the descent of the shear zones and the development of the QBO. An important difference between the schemes for the two types of waves is that in the case of equatorial planetary waves, vertical diffusion is needed only at the lowest levels, while for the gravity wave drag schemes it must be included at all levels. The question of whether there is downward propagation of influence in the simulated QBOs is addressed. In the gravity wave drag schemes, the evolution of the wind at a given level depends on the wind above, as well as on the wind below. This is in contrast to the parameterization for the equatorial planetary waves in which there is downward propagation of phase only. The stability of a zero-wind initial state is examined, and it is determined that a small perturbation to such a state will amplify with time to the extent that a zonal wind oscillation is permitted.

Parameterization of contrails in the UK Met Office Climate Model

Persistent contrails are believed to currently have a relatively small but significant positive radiative forcing on climate. With air travel predicted to continue its rapid growth over the coming years, the contrail warming effect on climate is expected to increase. Nevertheless, there remains a high level of uncertainty in the current estimates of contrail radiative forcing. Contrail formation depends mostly on the aircraft flying in cold and moist enough air masses. Most studies to date have relied on simple parameterizations using averaged meteorological conditions. In this paper we take into account the short‐term variability in background cloudiness by developing an on‐line contrail parameterization for the UK Met Office climate model. With this parameterization, we estimate that for the air traffic of year 2002 the global mean annual linear contrail coverage was approximately 0.11%. Assuming a global mean contrail optical depth of 0.2 or smaller and assuming hexagonal ice crystals, the corresponding contrail radiative forcing was calculated to be less than 10 mW m−2 in all‐sky conditions. We find that the natural cloud masking effect on contrails may be significantly higher than previously believed. This new result is explained by the fact that contrails seem to preferentially form in cloudy conditions, which ameliorates their overall climate impact by approximately 40%.

An urban parameterization for a global climate model. Part I: Formulation and evaluation for two cities

Urbanization, the expansion of built-up areas, is an important yet less-studied aspect of land use/land cover change in climate science. To date, most global climate models used to evaluate effects of land use/land cover change on climate do not include an urban parameterization. Here, the authors describe the formulation and evaluation of a parameterization of urban areas that is incorporated into the Community Land Model, the land surface component of the Community Climate System Model. The model is designed to be simple enough to be compatible with structural and computational constraints of a land surface model coupled to a global climate model yet complex enough to explore physically based processes known to be important in determining urban climatology. The city representation is based upon the “urban canyon” concept, which consists of roofs, sunlit and shaded walls, and canyon floor. The canyon floor is divided into pervious (e.g., residential lawns, parks) and impervious (e.g., roads, parking lots, sidewalks) fractions. Trapping of longwave radiation by canyon surfaces and solar radiation absorption and reflection is determined by accounting for multiple reflections. Separate energy balances and surface temperatures are determined for each canyon facet. A one-dimensional heat conduction equation is solved numerically for a 10-layer column to determine conduction fluxes into and out of canyon surfaces. Model performance is evaluated against measured fluxes and temperatures from two urban sites. Results indicate the model does a reasonable job of simulating the energy balance of cities.

Local-scale urban meteorological parameterization scheme (LUMPS): longwave radiation parameterization and seasonality-related developments

Recent developments to the Local-scale Urban Meteorological Parameterization Scheme (LUMPS), a simple model able to simulate the urban energy balance, are presented. The major development is the coupling of LUMPS to the Net All-Wave Radiation Parameterization (NARP). Other enhancements include that the model now accounts for the changing availability of water at the surface, seasonal variations of active vegetation, and the anthropogenic heat flux, while maintaining the need for only commonly available meteorological observations and basic surface characteristics. The incoming component of the longwave radiation (L↓) in NARP is improved through a simple relation derived using cloud cover observations from a ceilometer collected in central London, England. The new L↓ formulation is evaluated with two independent multiyear datasets (Łódź, Poland, and Baltimore, Maryland) and compared with alternatives that include the original NARP and a simpler one using the National Climatic Data Center cloud observation database as input. The performance for the surface energy balance fluxes is assessed using a 2-yr dataset (Łódź). Results have an overall RMSE < 34 W m−2 for all surface energy balance fluxes over the 2-yr period when

A coupled cloud physics–radiation parameterization of the bulk optical properties of cirrus and its impact on the Met Office unified model global atmosphere 5.0 configuration

A new coupled cloud physics–radiation parameterization of the bulk optical properties of ice clouds is presented. The parameterization is consistent with assumptions in the cloud physics scheme regarding particle size distributions (PSDs) and mass–dimensional relationships. The parameterization is based on a weighted ice crystal habit mixture model, and its bulk optical properties are parameterized as simple functions of wavelength and ice water content (IWC). This approach directly couples IWC to the bulk optical properties, negating the need for diagnosed variables, such as the ice crystal effective dimension. The parameterization is implemented into the Met Office Unified Model Global Atmosphere 5.0 (GA5) configuration. The GA5 configuration is used to simulate the annual 20-yr shortwave (SW) and longwave (LW) fluxes at the top of the atmosphere (TOA), as well as the temperature structure of the atmosphere, under various microphysical assumptions. The coupled parameterization is directly compared against the current operational radiation parameterization, while maintaining the same cloud physics assumptions. In this experiment, the impacts of the two parameterizations on the SW and LW radiative effects at TOA are also investigated and compared against observations. The 20-yr simulations are compared against the latest observations of the atmospheric temperature and radiative fluxes at TOA. The comparisons demonstrate that the choice of PSD and the assumed ice crystal shape distribution are as important as each other. Moreover, the consistent radiation parameterization removes a long-standing tropical troposphere cold temperature bias but slightly warms the southern midlatitudes by about 0.5 K.

Using laboratory and field measurements to constrain a single habit shortwave optical parameterization for cirrus

A single habit parameterization for the shortwave optical properties of cirrus is presented. The parameterization utilizes a hollow particle geometry, with stepped internal cavities as identified in laboratory and field studies. This particular habit was chosen as both experimental and theoretical results show that the particle exhibits lower asymmetry parameters when compared to solid crystals of the same aspect ratio. The aspect ratio of the particle was varied as a function of maximum dimension, D, in order to adhere to the same physical relationships assumed in the microphysical scheme in a configuration of the Met Office atmosphere-only global model, concerning particle mass, size and effective density. Single scattering properties were then computed using T-Matrix, Ray Tracing with Diffraction on Facets (RTDF) and Ray Tracing (RT) for small, medium, and large size parameters respectively. The scattering properties were integrated over 28 particle size distributions as used in the microphysical scheme. The fits were then parameterized as simple functions of Ice Water Content (IWC) for 6 shortwave bands. The parameterization was implemented into the GA6 configuration of the Met Office Unified Model along with the current operational long-wave parameterization. The GA6 configuration is used to simulate the annual twenty-year short-wave (SW) fluxes at top-of-atmosphere (TOA) and also the temperature and humidity structure of the atmosphere. The parameterization presented here is compared against the current operational model and a more recent habit mixture model.

A simple, intuitive camera calibration tool for natural images

The paper reports an interactive tool for calibrating a camera, suitable for use in outdoor scenes. The motivation for the tool was the need to obtain an approximate calibration for images taken with no explicit calibration data. Such images are frequently presented to research laboratories, especially in surveillance applications, with a request to demonstrate algorithms. The method decomposes the calibration parameters into intuitively simple components, and relies on the operator interactively adjusting the parameter settings to achieve a visually acceptable agreement between a rectilinear calibration model and his own perception of the scene. Using the tool, we have been able to calibrate images of unknown scenes, taken with unknown cameras, in a matter of minutes. The standard of calibration has proved to be sufficient for model-based pose recovery and tracking of vehicles.

A stochastic parameterization for deep convection based on equilibrium statistics

A stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models. Theoretical arguments and the results of cloud-resolving models, are discussed in order to motivate the form of the scheme. In the deterministic limit, it tends to a spectrum of entraining/detraining plumes and is similar to other current parameterizations. The stochastic variability describes the local fluctuations about a large-scale equilibrium state. Plumes are drawn at random from a probability distribution function (pdf) that defines the chance of finding a plume of given cloud-base mass flux within each model grid box. The normalization of the pdf is given by the ensemble-mean mass flux, and this is computed with a CAPE closure method. The characteristics of each plume produced are determined using an adaptation of the plume model from the Kain-Fritsch parameterization. Initial tests in the single column version of the Unified Model verify that the scheme is effective in producing the desired distributions of convective variability without adversely affecting the mean state.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

An interpretation of baroclinic initial value problems: results for simple basic states with nonzero interior PV gradients

In the Eady model, where the meridional potential vorticity (PV) gradient is zero, perturbation energy growth can be partitioned cleanly into three mechanisms: (i) shear instability, (ii) resonance, and (iii) the Orr mechanism. Shear instability involves two-way interaction between Rossby edge waves on the ground and lid, resonance occurs as interior PV anomalies excite the edge waves, and the Orr mechanism involves only interior PV anomalies. These mechanisms have distinct implications for the structural and temporal linear evolution of perturbations. Here, a new framework is developed in which the same mechanisms can be distinguished for growth on basic states with nonzero interior PV gradients. It is further shown that the evolution from quite general initial conditions can be accurately described (peak error in perturbation total energy typically less than 10%) by a reduced system that involves only three Rossby wave components. Two of these are counterpropagating Rossby waves—that is, generalizations of the Rossby edge waves when the interior PV gradient is nonzero—whereas the other component depends on the structure of the initial condition and its PV is advected passively with the shear flow. In the cases considered, the three-component model outperforms approximate solutions based on truncating a modal or singular vector basis.