The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

Characterising errors in airborne laser altimetry data to extract soil roughness

Airborne laser altimetry has the potential to make frequent detailed observations that are important for many aspects of studying land surface processes. However, the uncertainties inherent in airborne laser altimetry data have rarely been well measured. Uncertainty is often specified as generally as 20cm in elevation, and 40cm planimetric. To better constrain these uncertainties, we present an analysis of several datasets acquired specifically to study the temporal consistency of laser altimetry data, and thus assess its operational value. The error budget has three main components, each with a time regime. For measurements acquired less than 50ms apart, elevations have a local standard deviation in height of 3.5cm, enabling the local measurement of surface roughness of the order of 5cm. Points acquired seconds apart acquire an additional random error due to Differential Geographic Positioning System (DGPS) fluctuation. Measurements made up to an hour apart show an elevation drift of 7cm over a half hour. Over months, this drift gives rise to a random elevation offset between swathes, with an average of 6.4cm. The RMS planimetric error in point location was derived as 37.4cm. We conclude by considering the consequences of these uncertainties on the principle application of laser altimetry in the UK, intertidal zone monitoring.

Improving flood models using LiDAR: progress and problems

Airborne scanning laser altimetry (LiDAR) is an important new data source for river flood modelling. LiDAR can give dense and accurate DTMs of floodplains for use as model bathymetry. Spatial resolutions of 0.5m or less are possible, with a height accuracy of 0.15m. LiDAR gives a Digital Surface Model (DSM), so vegetation removal software (e.g. TERRASCAN) must be used to obtain a DTM. An example used to illustrate the current state of the art will be the LiDAR data provided by the EA, which has been processed by their in-house software to convert the raw data to a ground DTM and separate vegetation height map. Their method distinguishes trees from buildings on the basis of object size. EA data products include the DTM with or without buildings removed, a vegetation height map, a DTM with bridges removed, etc. Most vegetation removal software ignores short vegetation less than say 1m high. We have attempted to extend vegetation height measurement to short vegetation using local height texture. Typically most of a floodplain may be covered in such vegetation. The idea is to assign friction coefficients depending on local vegetation height, so that friction is spatially varying. This obviates the need to calibrate a global floodplain friction coefficient. It’s not clear at present if the method is useful, but it’s worth testing further. The LiDAR DTM is usually determined by looking for local minima in the raw data, then interpolating between these to form a space-filling height surface. This is a low pass filtering operation, in which objects of high spatial frequency such as buildings, river embankments and walls may be incorrectly classed as vegetation. The problem is particularly acute in urban areas. A solution may be to apply pattern recognition techniques to LiDAR height data fused with other data types such as LiDAR intensity or multispectral CASI data. We are attempting to use digital map data (Mastermap structured topography data) to help to distinguish buildings from trees, and roads from areas of short vegetation. The problems involved in doing this will be discussed. A related problem of how best to merge historic river cross-section data with a LiDAR DTM will also be considered. LiDAR data may also be used to help generate a finite element mesh. In rural area we have decomposed a floodplain mesh according to taller vegetation features such as hedges and trees, so that e.g. hedge elements can be assigned higher friction coefficients than those in adjacent fields. We are attempting to extend this approach to urban area, so that the mesh is decomposed in the vicinity of buildings, roads, etc as well as trees and hedges. A dominant points algorithm is used to identify points of high curvature on a building or road, which act as initial nodes in the meshing process. A difficulty is that the resulting mesh may contain a very large number of nodes. However, the mesh generated may be useful to allow a high resolution FE model to act as a benchmark for a more practical lower resolution model. A further problem discussed will be how best to exploit data redundancy due to the high resolution of the LiDAR compared to that of a typical flood model. Problems occur if features have dimensions smaller than the model cell size e.g. for a 5m-wide embankment within a raster grid model with 15m cell size, the maximum height of the embankment locally could be assigned to each cell covering the embankment. But how could a 5m-wide ditch be represented? Again, this redundancy has been exploited to improve wetting/drying algorithms using the sub-grid-scale LiDAR heights within finite elements at the waterline.

Characterising the background errors for the boundary-layer capping inversion

The one-dimensional variational assimilation of vertical temperature information in the presence of a boundary-layer capping inversion is studied. For an optimal analysis of the vertical temperature profile, an accurate representation of the background error covariances is essential. The background error covariances are highly flow-dependent due to the variability in the presence, structure and height of the boundary-layer capping inversion. Flow-dependent estimates of the background error covariances are shown by studying the spread in an ensemble of forecasts. A forecast of the temperature profile (used as a background state) may have a significant error in the position of the capping inversion with respect to observations. It is shown that the assimilation of observations may weaken the inversion structure in the analysis if only magnitude errors are accounted for as is the case for traditional data assimilation methods used for operational weather prediction. The positional error is treated explicitly here in a new data assimilation scheme to reduce positional error, in addition to the traditional framework to reduce magnitude error. The distribution of the positional error of the background inversion is estimated for use with the new scheme.

Population growth rate and carrying capacity for springtails Folsomia candida exposed to ivermectin

Forecasting the effects of stressors on the dynamics of natural populations requires assessment of the joint effects of a stressor and population density on the population response. The effects can be depicted as a contour map in which the population response, here assessed by Population growth rate, varies with stress and density in the same way that the height of land above sea level varies with latitude and longitude. We present the first complete map of this type using as our model Folsomia candida exposed to five different concentrations of the widespread anthelmintic veterinary medicine ivermectin in replicated microcosm experiments lasting 49 days. The concentrations of ivermectin in yeast were 0.0, 6.8 28.83 66.4 and 210.0 mg/L wet weight. Increasing density and chemical concentration both significantly reduced the population growth rate of Folsomia candida, in part through effects on food consumption and fecundity. The interaction between density and ivermectin concentration was "less-than-additive," implying that at high density populations were able to compensate for the effects of the chemical. This result demonstrates that regulatory protocols carried out at low density (as in most past experiments) may seriously overestimate effects in the field, where densities are locally high and populations are resource limited (e.g., in feces of livestock treated with ivermectin).

A spectral performance model for the High Resolution Dynamics Limb Sounder (6-18µm)

A spectral performance model, designed to simulate the system spectral throughput for each of the 21 channels in the HIRDLS radiometer, is described. This model uses the measured spectral characteristics of each of the components in the optical train, appropriately corrected for their optical environment, to determine the end-to-end spectral throughput profile for each channel. This profile is then combined with the predicted thermal emission from the atmosphere, arising from the height of interest, to establish an in-band (wanted) to out-of-band (unwanted) radiance ratio. The results from the use of the model demonstrate that the instrument level radiometric requirements for the instrument will be achieved. The optical arrangement and spectral design requirements for filtering in the HIRDLS instrument are described together with a presentation of the performance achieved for the complete set of manufactured filters. Compliance of the predicted passband throughput model to the spectral positioning requi rements of the instrument is also demonstrated.

The temperature response to stratospheric water vapour changes

This study uses an analytical model, based on the cooling-to-space approximation, and a fixed dynamical heating model to investigate the structure of the stratospheric cooling that occurs in response to a uniform increase in stratospheric water vapour (SWV). At all latitudes, the largest cooling occurs in the lower stratosphere and decreases in magnitude with height. The cooling is strongly enhanced in the Extratropics compared to the Tropics. This is markedly different to the case of an increase in CO2, which causes maximum cooling near the stratopause and a small warming in the tropical lower stratosphere. The qualitative differences in the structure of the cooling can be explained by the smaller opacity of water vapour bands in the stratosphere compared to CO2. The small opacity means that the magnitude of the initial heating rate perturbation only decreases by a factor of four between the upper and lower stratosphere for a SWV perturbation. Therefore, to balance the heating rate perturbation, the largest temperature change is required in the lower stratosphere. Increasing the background concentration of SWV causes the water vapour bands to become more opaque. For a SWV perturbation applied to a background SWV concentration ≥30 ppmv, the heating rate perturbation and temperature change structurally resemble those from an increase in CO2. In the Extratropics, the lower height of the tropopause is found to cause the enhancement in the cooling at those latitudes. By controlling the depth of atmosphere which adjusts to the SWV perturbation, the tropopause height affects the net exchange of radiation between the layers in the stratosphere as they cool. The latitudinal gradient in upwelling infrared radiation at the tropopause and variations in the background temperature are found to have only a minor effect on the structure of the stratospheric temperature response to a change in SWV.

Biomass functions and expansion factors in young Norway spruce (Picea abies [L.] Karst) trees

Roots, stems, branches and needles of 160 Norway spruce trees younger than 10 years were sampled in seven forest stands in central Slovakia in order to establish their biomassfunctions (BFs) and biomassexpansionfactors (BEFs). We tested three models for each biomass pool based on the stem base diameter, tree height and the two parameters combined. BEF values decreased for all spruce components with increasing height and diameter, which was most evident in very young trees under 1 m in height. In older trees, the values of BEFs did tend to stabilise at the height of 3–4 m. We subsequently used the BEFs to calculate dry biomass of the stands based on average stem base diameter and tree height. Total stand biomass grew with increasing age of the stands from about 1.0 Mg ha−1 at 1.5 years to 44.3 Mg ha−1 at 9.5 years. The proportion of stem and branch biomass was found to increase with age, while that of needles was fairly constant and the proportion of root biomass did decrease as the stands grew older.

The relationship between the North American summer monsoon, the Rocky Mountains and the North Pacific subtropical anticyclone in HadAM3

In this study the relationship between the North American monsoon, the Californian sea surface temperature (SST) cold pool, the Rocky Mountains and the North Pacific subtropical anticyclone is investigated using the Hadley Centre's atmospheric climate model, HadAM3. In 1996 Hoskins hypothesized that heating in the North American monsoon might be important for the maintenance of the summertime North Pacific subtropical anticyclone, since the monsoon heating may induce descent to the north-west of the monsoon in the descending eastern flank of the subtropical anticyclone. This descent is further enhanced by radiative cooling and is associated with equatorward surface winds parallel to the western coast of North America. These equatorward winds induce oceanic upwelling of cold water and contribute to the formation of the Californian SST cold pool, which may feed back on the anticyclone by further suppressing convection and inducing descent. More recently, Rodwell and Hoskins also investigated the global summer monsoon–subtropical anticyclone relationship. They examined the role that mountains play in impeding the progress of the low-level mid-latitude westerlies, either deflecting the westerlies northwards where they ascend along the sloping mid-latitude isentropes or deflecting them southwards forcing them to descend along the isentropes. In particular, the introduction of the Rockies into a primitive-equation model adiabatically induces descent in the eastern descending flank of the North Pacific subtropical anticyclone. These hypothesized mechanisms have been investigated using HadAM3, focusing on the possible suppression of convection by the Californian SST cold pool, the response of the North Pacific subtropical anticyclone to the strength of the North American monsoon and the ‘blocking’ of the mid-latitude westerlies by the Rocky Mountains. The role of the Rockies is examined by integrating the model with modified orography for the Rocky Mountains. Changing the height of the Rockies alters the circulation in a way consistent with the mechanism outlined above. Higher Rocky mountains force the westerlies southwards, inducing descent in the eastern flank of the subtropical anticyclone as the air descends along the sloping isentropes. The relationship between the North American monsoon and the North Pacific subtropical anticyclone is investigated by suppressing the monsoon in HadAM3. The suppression of the monsoon is accomplished by increasing the surface albedo over Mexico, which induces anomalous ascent on the eastward flank of the subtropical anticyclone and anomalous polewards surface winds along the western coast of the North American continent, also providing support for the above hypothesis. The removal of the Californian SST cold pool, however, has a statistically insignificant effect on the model, suggesting that in this model the feedback of the SST cold pool on the eastern flank of the anticyclone is weak.

Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge

Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states.

Space weather driven changes in lower atmosphere phenomena

During a period of heliospheric disturbance in 2007-9 associated with a co-rotating interaction region (CIR), a characteristic periodic variation becomes apparent in neutron monitor data. This variation is phase locked to periodic heliospheric current sheet crossings. Phase-locked electrical variations are also seen in the terrestrial lower atmosphere in the southern UK, including an increase in the vertical conduction current density of fair weather atmospheric electricity during increases in the neutron monitor count rate and energetic proton count rates measured by spacecraft. At the same time as the conduction current increases, changes in the cloud microphysical properties lead to an increase in the detected height of the cloud base at Lerwick Observatory, Shetland, with associated changes in surface meteorological quantities. As electrification is expected at the base of layer clouds, which can influence droplet properties, these observations of phase-locked thermodynamic, cloud, atmospheric electricity and solar sector changes are not inconsistent with a heliospheric disturbance driving lower troposphere changes.

Multiple-edge noise barriers

A numerical model using boundary element techniques is discussed which enables the insertion loss for various noise barriers of complex profile and surface cover to be calculated. The model is applied to single-foundation noise barriers to which additional side-panels are added to create fork-like profiles. Spectra of insertion loss and mean insertion loss results over a range of receiver positions for a broadband source are presented. It is concluded that ‘multiple-edged’ barriers show a significant increase in acoustic-efficiency over a simple vertical screen. Adding lightweight side-panels would be a relatively inexpensive measure, and one which could be applied to barriers already in existence. This type of barrier would also allow the height of the construction to be kept to a minimum.

Sponge layer feedbacks in middle-atmosphere models

Middle-atmosphere models commonly employ a sponge layer in the upper portion of their domain. It is shown that the relaxational nature of the sponge allows it to couple to the dynamics at lower levels in an artificial manner. In particular, the long-term zonally symmetric response to an imposed extratropical local force or diabatic heating is shown to induce a drag force in the sponge that modifies the response expected from the “downward control” arguments of Haynes et al. [1991]. In the case of an imposed local force the sponge acts to divert a fraction of the mean meridional mass flux upward, which for realistic parameter values is approximately equal to exp(−Δz/H), where Δz is the distance between the forcing region and the sponge layer and H is the density scale height. This sponge-induced upper cell causes temperature changes that, just below the sponge layer, are of comparable magnitude to those just below the forcing region. In the case of an imposed local diabatic heating, the sponge induces a meridional circulation extending through the entire depth of the atmosphere. This circulation causes temperature changes that, just below the sponge layer, are of opposite sign and comparable in magnitude to those at the heating region. In both cases, the sponge-induced temperature changes are essentially independent of the height of the imposed force or diabatic heating, provided the latter is located outside the sponge, but decrease exponentially as one moves down from the sponge. Thus the effect of the sponge can be made arbitrarily small at a given altitude by placing the sponge sufficiently high; e.g., its effect on temperatures two scale heights below is roughly at the 10% level, provided the imposed force or diabatic heating is located outside the sponge. When, however, an imposed force is applied within the sponge layer (a highly plausible situation for parameterized mesospheric gravity-wave drag), its effect is almost entirely nullified by the sponge-layer feedback and its expected impact on temperatures below largely fails to materialize. Simulations using a middle-atmosphere general circulation model are described, which demonstrate that this sponge-layer feedback can be a significant effect in parameter regimes of physical interest. Zonally symmetric (two dimensional) middle-atmosphere models commonly employ a Rayleigh drag throughout the model domain. It is shown that the long-term zonally symmetric response to an imposed extratropical local force or diabatic heating, in this case, is noticeably modified from that expected from downward control, even for a very weak drag coefficient

Wind pressure on a single building immersed in a low-jet wind profile

This paper for the first time discuss the wind pressure distribution on the building surface immersed in wind profile of low-level jet rather than a logarithmic boundary-layer profile. Two types of building models are considered, low-rise and high-rise building, relative to the low-level jet height. CFD simulation is carried out. The simulation results show that the wind pressure distribution immersed in a low-jet wine profile is very different from the typical uniform and boundary-layer flow. For the low-rise building, the stagnation point is located at the upper level of windward façade for the low-level jet wind case, and the separation zone above the roof top is not as obvious as the uniform case. For the high-rise building model, the height of stagnation point is almost as high as the low-level jet height.

The bottomside mid-latitude ionospheric trough

The measured power losses and Doppler shifts of h.f. radio waves propagated over a long, west-east, sub-auroral path are found to exhibit features which cannot be explained by simple predictions and models. Both theory and the limited available data indicate that a bottomside F2-layer depletion should be present below the topside mid-latitude trough. Introducing this into the models (using the mean statistical positions of the trough deduced from Alouette I and II soundings) is shown to explain many of these features. From the Doppler shifts and a simple ray-tracing model the height of the depleted F2-peak inside the trough is deduced to be greater than its value outside the trough by an amount of the order of only 30–80 km.