Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

Introductory remarks

The very first numerical models which were developed more than 20 years ago were drastic simplifications of the real atmosphere and they were mostly restricted to describe adiabatic processes. For prediction of a day or two of the mid tropospheric flow these models often gave reasonable results but the result deteriorated quickly when the prediction was extended further in time. The prediction of the surface flow was unsatisfactory even for short predictions. It was evident that both the energy generating processes as well as the dissipative processes have to be included in numerical models in order to predict the weather patterns in the lower part of the atmosphere and to predict the atmosphere in general beyond a day or two. Present-day computers make it possible to attack the weather forecasting problem in a more comprehensive and complete way and substantial efforts have been made during the last decade in particular to incorporate the non-adiabatic processes in numerical prediction models. The physics of radiational transfer, condensation of moisture, turbulent transfer of heat, momentum and moisture and the dissipation of kinetic energy are the most important processes associated with the formation of energy sources and sinks in the atmosphere and these have to be incorporated in numerical prediction models extended over more than a few days. The mechanisms of these processes are mainly related to small scale disturbances in space and time or even molecular processes. It is therefore one of the basic characteristics of numerical models that these small scale disturbances cannot be included in an explicit way. The reason for this is the discretization of the model's atmosphere by a finite difference grid or the use of a Galerkin or spectral function representation. The second reason why we cannot explicitly introduce these processes into a numerical model is due to the fact that some physical processes necessary to describe them (such as the local buoyance) are a priori eliminated by the constraints of hydrostatic adjustment. Even if this physical constraint can be relaxed by making the models non-hydrostatic the scale problem is virtually impossible to solve and for the foreseeable future we have to try to incorporate the ensemble or gross effect of these physical processes on the large scale synoptic flow. The formulation of the ensemble effect in terms of grid-scale variables (the parameters of the large-scale flow) is called 'parameterization'. For short range prediction of the synoptic flow at middle and high latitudes, very simple parameterization has proven to be rather successful.

The angular momentum constraint on climate sensitivity and downward influence in the middle atmosphere

It is shown that under reasonable assumptions, conservation of angular momentum provides a strong constraint on gravity wave drag feedbacks to radiative perturbations in the middle atmosphere. In the time mean, radiatively induced temperature perturbations above a given altitude z cannot induce changes in zonal mean wind and temperature below z through feedbacks in gravity wave drag alone (assuming an unchanged gravity wave source spectrum). Thus, despite the many uncertainties in the parameterization of gravity wave drag, the role of gravity wave drag in middle-atmosphere climate perturbations may be much more limited than its role in climate itself. This constraint limits the possibilities for downward influence from the mesosphere. In order for a gravity wave drag parameterization to respect the momentum constraint and avoid spurious downward influence, any nonzero parameterized momentum flux at a model lid must be deposited within the model domain, and there must be no zonal mean sponge layer. Examples are provided of how violation of these conditions leads to spurious downward influence. For planetary waves, the momentum constraint does not prohibit downward influence, but it limits the mechanisms by which it can occur: in the time mean, downward influence from a radiative perturbation can only arise through changes in reflection and meridional propagation properties of planetary waves.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

Interactions between different convection modes can be investigated using an energy–cycle description under a framework of mass–flux parameterization. The present paper systematically investigates this system by taking a limit of two modes: shallow and deep convection. Shallow convection destabilizes itself as well as the other convective modes by moistening and cooling the environment, whereas deep convection stabilizes itself as well as the other modes by drying and warming the environment. As a result, shallow convection leads to a runaway growth process in its stand–alone mode, whereas deep convection simply damps out. Interaction between these two convective modes becomes a rich problem, even when it is limited to the case with no large–scale forcing, because of these opposing tendencies. Only if the two modes are coupled at a proper level can a self–sustaining system arise, exhibiting a periodic cycle. The present study establishes the conditions for self–sustaining periodic solutions. It carefully documents the behaviour of the two mode system in order to facilitate the interpretation of global model behaviours when this energy–cycle is implemented as a closure into a convection parameterization in future.

Input type and parameter resetting: is naturalistic input necessary?

It has been argued that extended exposure to naturalistic input provides L2 learners with more of an opportunity to converge of target morphosyntactic competence as compared to classroom-only environments, given that the former provide more positive evidence of less salient linguistic properties than the latter (e.g., Isabelli 2004). Implicitly, the claim is that such exposure is needed to fully reset parameters. However, such a position conflicts with the notion of parameterization (cf. Rothman and Iverson 2007). In light of two types of competing generative theories of adult L2 acquisition – the No Impairment Hypothesis (e.g., Duffield and White 1999) and so-called Failed Features approaches (e.g., Beck 1998; Franceschina 2001; Hawkins and Chan 1997), we investigate the verifiability of such a claim. Thirty intermediate L2 Spanish learners were tested in regards to properties of the Null-Subject Parameter before and after study-abroad. The data suggest that (i) parameter resetting is possible and (ii) exposure to naturalistic input is not privileged.

Effects of spatial resolution in the simulation of daily and subdaily precipitation in the southwestern US

We evaluate the effects of spatial resolution on the ability of a regional climate model to reproduce observed extreme precipitation for a region in the Southwestern United States. A total of 73 National Climate Data Center observational sites spread throughout Arizona and New Mexico are compared with regional climate simulations at the spatial resolutions of 50 km and 10 km for a 31 year period from 1980 to 2010. We analyze mean, 3-hourly and 24-hourly extreme precipitation events using WRF regional model simulations driven by NCEP-2 reanalysis. The mean climatological spatial structure of precipitation in the Southwest is well represented by the 10 km resolution but missing in the coarse (50 km resolution) simulation. However, the fine grid has a larger positive bias in mean summer precipitation than the coarse-resolution grid. The large overestimation in the simulation is in part due to scale-dependent deficiencies in the Kain-Fritsch convective parameterization scheme that generate excessive precipitation and induce a slow eastward propagation of the moist convective summer systems in the high-resolution simulation. Despite this overestimation in the mean, the 10 km simulation captures individual extreme summer precipitation events better than the 50 km simulation. In winter, however, the two simulations appear to perform equally in simulating extremes.

Sea surface temperature estimation from the Geostationary Operational Environmental Satellite 12 (GOES-12)

This paper describes the techniques used to obtain sea surface temperature (SST) retrievals from the Geostationary Operational Environmental Satellite 12 (GOES-12) at the National Oceanic and Atmospheric Administration’s Office of Satellite Data Processing and Distribution. Previous SST retrieval techniques relying on channels at 11 and 12 μm are not applicable because GOES-12 lacks the latter channel. Cloud detection is performed using a Bayesian method exploiting fast-forward modeling of prior clear-sky radiances using numerical weather predictions. The basic retrieval algorithm used at nighttime is based on a linear combination of brightness temperatures at 3.9 and 11 μm. In comparison with traditional split window SSTs (using 11- and 12-μm channels), simulations show that this combination has maximum scatter when observing drier colder scenes, with a comparable overall performance. For daytime retrieval, the same algorithm is applied after estimating and removing the contribution to brightness temperature in the 3.9-μm channel from solar irradiance. The correction is based on radiative transfer simulations and comprises a parameterization for atmospheric scattering and a calculation of ocean surface reflected radiance. Potential use of the 13-μm channel for SST is shown in a simulation study: in conjunction with the 3.9-μm channel, it can reduce the retrieval error by 30%. Some validation results are shown while a companion paper by Maturi et al. shows a detailed analysis of the validation results for the operational algorithms described in this present article.

Modeling ocean primary production: sensitivity to spectral resolution of attenuation and absorption of light

Modeling the vertical penetration of photosynthetically active radiation (PAR) through the ocean, and its utilization by phytoplankton, is fundamental to simulating marine primary production. The variation of attenuation and absorption of light with wavelength suggests that photosynthesis should be modeled at high spectral resolution, but this is computationally expensive. To model primary production in global 3d models, a balance between computer time and accuracy is necessary. We investigate the effects of varying the spectral resolution of the underwater light field and the photosynthetic efficiency of phytoplankton (α∗), on primary production using a 1d coupled ecosystem ocean turbulence model. The model is applied at three sites in the Atlantic Ocean (CIS (∼60°N), PAP (∼50°N) and ESTOC (∼30°N)) to include the effect of different meteorological forcing and parameter sets. We also investigate three different methods for modeling α∗ – as a fixed constant, varying with both wavelength and chlorophyll concentration [Bricaud, A., Morel, A., Babin, M., Allali, K., Claustre, H., 1998. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters. Analysis and implications for bio-optical models. J. Geophys. Res. 103, 31033–31044], and using a non-spectral parameterization [Anderson, T.R., 1993. A spectrally averaged model of light penetration and photosynthesis. Limnol. Oceanogr. 38, 1403–1419]. After selecting the appropriate ecosystem parameters for each of the three sites we vary the spectral resolution of light and α∗ from 1 to 61 wavebands and study the results in conjunction with the three different α∗ estimation methods. The results show modeled estimates of ocean primary productivity are highly sensitive to the degree of spectral resolution and α∗. For accurate simulations of primary production and chlorophyll distribution we recommend a spectral resolution of at least six wavebands if α∗ is a function of wavelength and chlorophyll, and three wavebands if α∗ is a fixed value.

High resolution simulation of the variability of surface energy balance fluxes across central London with urban zones for energy partitioning

The parameterization of surface heat-flux variability in urban areas relies on adequate representation of surface characteristics. Given the horizontal resolutions (e.g. ≈0.1–1km) currently used in numerical weather prediction (NWP) models, properties of the urban surface (e.g. vegetated/built surfaces, street-canyon geometries) often have large spatial variability. Here, a new approach based on Urban Zones to characterize Energy partitioning (UZE) is tested within a NWP model (Weather Research and Forecasting model;WRF v3.2.1) for Greater London. The urban land-surface scheme is the Noah/Single-Layer Urban Canopy Model (SLUCM). Detailed surface information (horizontal resolution 1 km)in central London shows that the UZE offers better characterization of surface properties and their variability compared to default WRF-SLUCM input parameters. In situ observations of the surface energy fluxes and near-surface meteorological variables are used to select the radiation and turbulence parameterization schemes and to evaluate the land-surface scheme

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

Modelling of urban sensible heat flux at multiple spatial scales : a demonstration using airborne hyperspectral imagery of Shanghai and a temperature–emissivity separation approach

Urbanization related alterations to the surface energy balance impact urban warming (‘heat islands’), the growth of the boundary layer, and many other biophysical processes. Traditionally, in situ heat flux measures have been used to quantify such processes, but these typically represent only a small local-scale area within the heterogeneous urban environment. For this reason, remote sensing approaches are very attractive for elucidating more spatially representative information. Here we use hyperspectral imagery from a new airborne sensor, the Operative Modular Imaging Spectrometer (OMIS), along with a survey map and meteorological data, to derive the land cover information and surface parameters required to map spatial variations in turbulent sensible heat flux (QH). The results from two spatially-explicit flux retrieval methods which use contrasting approaches and, to a large degree, different input data are compared for a central urban area of Shanghai, China: (1) the Local-scale Urban Meteorological Parameterization Scheme (LUMPS) and (2) an Aerodynamic Resistance Method (ARM). Sensible heat fluxes are determined at the full 6 m spatial resolution of the OMIS sensor, and at lower resolutions via pixel aggregation and spatial averaging. At the 6 m spatial resolution, the sensible heat flux of rooftop dominated pixels exceeds that of roads, water and vegetated areas, with values peaking at ∼ 350 W m− 2, whilst the storage heat flux is greatest for road dominated pixels (peaking at around 420 W m− 2). We investigate the use of both OMIS-derived land surface temperatures made using a Temperature–Emissivity Separation (TES) approach, and land surface temperatures estimated from air temperature measures. Sensible heat flux differences from the two approaches over the entire 2 × 2 km study area are less than 30 W m− 2, suggesting that methods employing either strategy maybe practica1 when operated using low spatial resolution (e.g. 1 km) data. Due to the differing methodologies, direct comparisons between results obtained with the LUMPS and ARM methods are most sensibly made at reduced spatial scales. At 30 m spatial resolution, both approaches produce similar results, with the smallest difference being less than 15 W m− 2 in mean QH averaged over the entire study area. This is encouraging given the differing architecture and data requirements of the LUMPS and ARM methods. Furthermore, in terms of mean study QH, the results obtained by averaging the original 6 m spatial resolution LUMPS-derived QH values to 30 and 90 m spatial resolution are within ∼ 5 W m− 2 of those derived from averaging the original surface parameter maps prior to input into LUMPS, suggesting that that use of much lower spatial resolution spaceborne imagery data, for example from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is likely to be a practical solution for heat flux determination in urban areas.

Linking urban water balance and energy balance models to analyse urban design options

Using a water balance modelling framework, this paper analyses the effects of urban design on the water balance, with a focus on evapotranspiration and storm water. First, two quite different urban water balance models are compared: Aquacycle which has been calibrated for a suburban catchment in Canberra, Australia, and the single-source urban evapotranspiration-interception scheme (SUES), an energy-based approach with a biophysically advanced representation of interception and evapotranspiration. A fair agreement between the two modelled estimates of evapotranspiration was significantly improved by allowing the vegetation cover (leaf area index, LAI) to vary seasonally, demonstrating the potential of SUES to quantify the links between water sensitive urban design and microclimates and the advantage of comparing the two modelling approaches. The comparison also revealed where improvements to SUES are needed, chiefly through improved estimates of vegetation cover dynamics as input to SUES, and more rigorous parameterization of the surface resistance equations using local-scale suburban flux measurements. Second, Aquacycle is used to identify the impact of an array of water sensitive urban design features on the water balance terms. This analysis confirms the potential to passively control urban microclimate by suburban design features that maximize evapotranspiration, such as vegetated roofs. The subsequent effects on daily maximum air temperatures are estimated using an atmospheric boundary layer budget. Potential energy savings of about 2% in summer cooling are estimated from this analysis. This is a clear ‘return on investment’ of using water to maintain urban greenspace, whether as parks distributed throughout an urban area or individual gardens or vegetated roofs.

Nocturnal cooling below a forest canopy: Model and evaluation

Nocturnal cooling of air within a forest canopy and the resulting temperature profile may drive local thermally driven motions, such as drainage flows, which are believed to impact measurements of ecosystem–atmosphere exchange. To model such flows, it is necessary to accurately predict the rate of cooling. Cooling occurs primarily due to radiative heat loss. However, much of the radiative loss occurs at the surface of canopy elements (leaves, branches, and boles of trees), while radiative divergence in the canopy air space is small due to high transmissivity of air. Furthermore, sensible heat exchange between the canopy elements and the air space is slow relative to radiative fluxes. Therefore, canopy elements initially cool much more quickly than the canopy air space after the switch from radiative gain during the day to radiative loss during the night. Thus in modeling air cooling within a canopy, it is not appropriate to neglect the storage change of heat in the canopy elements or even to assume equal rates of cooling of the canopy air and canopy elements. Here a simple parameterization of radiatively driven cooling of air within the canopy is presented, which accounts implicitly for radiative cooling of the canopy volume, heat storage in the canopy elements, and heat transfer between the canopy elements and the air. Simulations using this parameterization are compared to temperature data from the Morgan–Monroe State Forest (IN, USA) FLUXNET site. While the model does not perfectly reproduce the measured rates of cooling, particularly near the top of the canopy, the simulated cooling rates are of the correct order of magnitude.

Urban surface energy balance models: model characteristics and methodology for a comparison study

Many urban surface energy balance models now exist. These vary in complexity from simple schemes that represent the city as a concrete slab, to those which incorporate detailed representations of momentum and energy fluxes distributed within the atmospheric boundary layer. While many of these schemes have been evaluated against observations, with some models even compared with the same data sets, such evaluations have not been undertaken in a controlled manner to enable direct comparison. For other types of climate model, for instance the Project for Intercomparison of Land-Surface Parameterization Schemes (PILPS) experiments (Henderson-Sellers et al., 1993), such controlled comparisons have been shown to provide important insights into both the mechanics of the models and the physics of the real world. This paper describes the progress that has been made to date on a systematic and controlled comparison of urban surface schemes. The models to be considered, and their key attributes, are described, along with the methodology to be used for the evaluation.