A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

DK-1D: a drift-kinetic simulation tool for modelling the shear Alfvén wave and its interaction with collisionless plasma

We present a highly accurate tool for the simulation of shear Alfven waves (SAW) in collisionless plasma. SAW are important in space plasma environments because for small perpendicular scale lengths they can support an electric field parallel to the ambient magnetic field. Electrons can be accelerated by the parallel electric field and these waves have been implicated as the source of vibrant auroral displays. However, the parallel electric field carried by SAW is small in comparison to the perpendicular electric field of the wave, making it difficult to measure directly in the laboratory, or by satellites in the near-Earth plasma environment. In this paper, we present a simulation code that provides a means to study in detail the SAW-particle interaction in both space and laboratory plasma. Using idealised, small-amplitude propagating waves with a single perpendicular wavenumber, the simulation code accurately reproduces the damping rates and parallel electric field amplitudes predicted by linear theory for varying temperatures and perpendicular scale lengths. We present a rigorous kinetic derivation of the parallel electric field strength for small-amplitude SAW and show that commonly-used inertial and kinetic approximations are valid except for where the ratio of thermal to Alfv\'{e}n speed is between 0.7 and 1.0. We also present nonlinear simulations of large-amplitude waves and show that in cases of strong damping, the damping rates and parallel electric field strength deviate from linear predictions when wave energies are greater than only a few percent of the plasma kinetic energy, a situation which is often observed in the magnetosphere. The drift-kinetic code provides reliable, testable predictions of the parallel electric field strength which can be investigated directly in the laboratory, and will help to bridge the gap between studies of SAW in man-made and naturally occuring plasma.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Characterization of energy flux partitioning in urban environments: links with surface seasonal properties

A better understanding of links between the properties of the urban environment and the exchange to the atmosphere is central to a wide range of applications. The numerous measurements of surface energy balance data in urban areas enable intercomparison of observed fluxes from distinct environments. This study analyzes a large database in two new ways. First, instead of normalizing fluxes using net all-wave radiation only the incoming radiative fluxes are used, to remove the surface attributes from the denominator. Second, because data are now available year-round, indices are developed to characterize the fraction of the surface (built; vegetation) actively engaged in energy exchanges. These account for shading patterns within city streets and seasonal changes in vegetation phenology; their impact on the partitioning of the incoming radiation is analyzed. Data from 19 sites in North America, Europe, Africa, and Asia (including 6-yr-long observation campaigns) are used to derive generalized surface–flux relations. The midday-period outgoing radiative fraction decreases with an increasing total active surface index, the stored energy fraction increases with an active built index, and the latent heat fraction increases with an active vegetated index. Parameterizations of these energy exchange ratios as a function of the surface indices [i.e., the Flux Ratio–Active Index Surface Exchange (FRAISE) scheme] are developed. These are used to define four urban zones that characterize energy partitioning on the basis of their active surface indices. An independent evaluation of FRAISE, using three additional sites from the Basel Urban Boundary Layer Experiment (BUBBLE), yields accurate predictions of the midday flux partitioning at each location.

The surface urban energy and water balance scheme (SUEWS): evaluation in Los Angeles and Vancouver

An urban energy and water balance model is presented which uses a small number of commonly measured meteorological variables and information about the surface cover. Rates of evaporation-interception for a single layer with multiple surface types (paved, buildings, coniferous trees and/or shrubs, deciduous trees and/or shrubs, irrigated grass, non-irrigated grass and water) are calculated. Below each surface type, except water, there is a single soil layer. At each time step the moisture state of each surface is calculated. Horizontal water movements at the surface and in the soil are incorporated. Particular attention is given to the surface conductance used to model evaporation and its parameters. The model is tested against direct flux measurements carried out over a number of years in Vancouver, Canada and Los Angeles, USA. At all measurement sites the model is able to simulate the net all-wave radiation and turbulent sensible and latent heat well (RMSE = 25–47 W m−2, 30–64 and 20–56 W m−2, respectively). The model reproduces the diurnal cycle of the turbulent fluxes but typically underestimates latent heat flux and overestimates sensible heat flux in the day time. The model tracks measured surface wetness and simulates the variations in soil moisture content. It is able to respond correctly to short-term events as well as annual changes. The largest uncertainty relates to the determination of surface conductance. The model has the potential be used for multiple applications; for example, to predict effects of regulation on urban water use, landscaping and planning scenarios, or to assess climate mitigation strategies.

Energy exchange in a dense urban environment – part I: temporal variability of long-term observations in central London

Though anthropogenic impacts on boundary layer climates are expected to be large in dense urban areas, to date very few studies of energy flux observations are available. We report on 3.5 years of measurements gathered in central London, UK. Radiometer and eddy covariance observations at two adjacent sites, at different heights, were analysed at various temporal scales and with respect to meteorological conditions, such as cloud cover. Although the evaporative flux is generally small due to low moisture availability and a predominately impervious surface, the enhancement following rainfall usually lasts for 12–18 h. As both the latent and sensible heat fluxes are larger in the afternoon, they maintain a relatively consistent Bowen ratio throughout the middle of the day. Strong storage and anthropogenic heat fluxes sustain high and persistently positive sensible heat fluxes. At the monthly time scale, the urban surface often loses more energy by this turbulent heat flux than is gained from net all-wave radiation. Auxiliary anthropogenic heat flux information suggest human activities in the study area are sufficient to provide this energy.

Infrared and millimetre-wave scintillometry in the suburban environment – Part 1: Structure parameters

Scintillometry, a form of ground-based remote sensing, provides the capability to estimate surface heat fluxes over scales of a few hundred metres to kilometres. Measurements are spatial averages, making this technique particularly valuable over areas with moderate heterogeneity such as mixed agricultural or urban environments. In this study, we present the structure parameters of temperature and humidity, which can be related to the sensible and latent heat fluxes through similarity theory, for a suburban area in the UK. The fluxes are provided in the second paper of this two-part series. A millimetre-wave scintillometer was combined with an infrared scintillometer along a 5.5 km path over northern Swindon. The pairing of these two wavelengths offers sensitivity to both temperature and humidity fluctuations, and the correlation between wavelengths is also used to retrieve the path-averaged temperature–humidity correlation. Comparison is made with structure parameters calculated from an eddy covariance station located close to the centre of the scintillometer path. The performance of the measurement techniques under different conditions is discussed. Similar behaviour is seen between the two data sets at sub-daily timescales. For the two summer-to-winter periods presented here, similar evolution is displayed across the seasons. A higher vegetation fraction within the scintillometer source area is consistent with the lower Bowen ratio observed (midday Bowen ratio < 1) compared with more built-up areas around the eddy covariance station. The energy partitioning is further explored in the companion paper.

Infrared and millimetre-wave scintillometry in the suburban environment – Part 2: Large-area sensible and latent heat fluxes

A millimetre-wave scintillometer was paired with an infrared scintillometer, enabling estimation of large-area evapotranspiration across northern Swindon, a suburban area in the UK. Both sensible and latent heat fluxes can be obtained using this "two-wavelength" technique, as it is able to provide both temperature and humidity structure parameters, offering a major advantage over conventional single-wavelength scintillometry. The first paper of this two-part series presented the measurement theory and structure parameters. In this second paper, heat fluxes are obtained and analysed. These fluxes, estimated using two-wavelength scintillometry over an urban area, are the first of their kind. Source area modelling suggests the scintillometric fluxes are representative of 5–10 km2. For comparison, local-scale (0.05–0.5 km2) fluxes were measured by an eddy covariance station. Similar responses to seasonal changes are evident at the different scales but the energy partitioning varies between source areas. The response to moisture availability is explored using data from 2 consecutive years with contrasting rainfall patterns (2011–2012). This extensive data set offers insight into urban surface-atmosphere interactions and demonstrates the potential for two-wavelength scintillometry to deliver fluxes over mixed land cover, typically representative of an area 1–2 orders of magnitude greater than for eddy covariance measurements. Fluxes at this scale are extremely valuable for hydro-meteorological model evaluation and assessment of satellite data products

Seasonal surface urban energy balance and wintertime stability simulated using three land-surface models in the high-latitude city Helsinki

The performance of three urban land surface models, run in offline mode, with their default external parameters, is evaluated for two distinctly different sites in Helsinki: Torni and Kumpula. The former is a dense city centre site with 22% vegetation, while the latter is a suburban site with over 50% vegetation. At both locations the models are compared against sensible and latent heat fluxes measured using the eddy covariance technique, along with snow depth observations. The cold climate experienced by the city causes strong seasonal variations that include snow cover and stable atmospheric conditions. Most of the time the three models are able to account for the differences between the study areas as well as the seasonal and diurnal variability of the energy balance components. However, the performances are not systematic across the modelled components, season and surface type. The net all-wave radiation is well simulated, with the greatest uncertainties related to snowmelt timing, when the fraction of snow cover has a key role, particularly in determining the surface albedo. For the turbulent fluxes, more variation between the models is seen which can partly be explained by the different methods in their calculation and partly by surface parameter values. For the sensible heat flux, simulation of wintertime values was the main problem, which also leads to issues in predicting near-surface stabilities particularly at the dense city centre site. All models have the most difficulties in simulating latent heat flux. This study particularly emphasizes that improvements are needed in the parameterization of anthropogenic heat flux and thermal parameters in winter, snow cover in spring and evapotranspiration in order to improve the surface energy balance modelling in cold climate cities.