Prediction of surface potential temperature over complex terrain

Based on a statistical approach, the surface potential temperature at seven observing stations in complex terrain has been examined. It is shown that the surface potential temperature depends primarily on the rate of change of slope wind and on the geostrophic-level potential temperature.     

A new concept for high resolution temperature analysis over complex terrain

Summary The analysis of high resolution temperature data over complex topography is often problematic due to the specific influence of orography and thus, requires a special methodology. The new concept of Low Level Temperature (LLT) is defined, and can be obtained when potential temperature observations are reduced to the height of the so-called Minimum Topography, a special low level topography that accentuates basins and valleys but smoothes out single summits and scarped slopes. The Vienna Enhanced Resolution Analysis (VERA) is used to produce a comprehensive set of LLT analyses over the Alpine region by evaluating three-hourly synoptic ECMWF data for the period 1980–2001. LLT fields are then evaluated climatologically in order to gain two-dimensional representations and single grid point time series. Mean LLT fields for different months and times of the day provide highly resolved spatial and temporal information on temperature fields over basins and valleys i.e., the main settlement areas in mountainous terrain.     

Numerical study of wind energy characteristics over heterogeneous terrain — Central Israel case study

A numerical mesoscale meteorological model has been applied over the heterogeneous terrain of central Israel in order to study wind energy characteristics of three typical synoptic situations. The supportive nature of this method for observationally oriented wind energy studies has been emphasized. Mesoscale forcing effects on the availability of wind energy and on the exponent, p, in the vertical wind power law are evaluated.     

LLM – a nonhydrostatic model applied to high-resolving simulations of turbulent fluxes over heterogeneous terrain

Summary ?At the Deutscher Wetterdienst (DWD) an internal project named LITFASS was running to determine the representative turbulent fluxes of heat and momentum over heterogeneous land surfaces by observation and simulation. The project took advantage of the infrastructure of the Research Division at the DWD, where model research capacity is combined with the measurements made at and around the Meteorological Observatory Lindenberg. The paper describes the simulation component of the LITFASS-project. It consists of a high-resolving model, derived from the new operational non-hydrostatic, compressible Lokal-Modell (LM), which is denoted LLM (LITFASS-Lokal-Modell). The integration area covers the lower atmosphere in the vertical up to 3000 m with 39 model layers. The horizontal size of the integration area with 145 × 145 grid points (horizontal mesh width Δs = 96.5 m) corresponds to a typical grid box of a meso-scale model. The LLM has to operate under real meteorological conditions. Therefore, the LLM is driven by time-dependent measured vertical profiles of wind, temperature and humidity and surface-based measurements (of radiation, precipitation, soil properties) supported by satellite information. The profiles are available for a great variety of weather situations occurring during the simulation period (1–20 June 1998). First model results from extended 24 hour-integrations against different kinds of measurements are discussed. They reveal the LLM to become a promising validation instrument, from which a systematic, sustainable validation system can be established beyond LITFASS for improving parameterization schemes in the NWP models of the DWD. Received July 18, 2001; revised March 15, 2002; accepted May 30, 2002     

Wind profiles,momentum fluxes and roughness lengths at Cabauw revisited

We describe the results of an experiment focusing on wind speed and momentum fluxes in the atmospheric boundary layer up to 200 m. The measurements were conducted in 1996 at the Cabauw site in the Netherlands. Momentum fluxes are measured using the K-Gill Propeller Vane. Estimates of the roughness length are derived using various techniques from the wind speed and flux measurements, and the observed differences are explained by considering the source area of the meteorological parameters. A clear rough-to-smooth transition is found in the wind speed profiles at Cabauw. The internal boundary layer reaches the lowest k-vane (20 m) only in the south-west direction where the obstacle-free fetch is about 2 km. The internal boundary layer is also reflected in the roughness lengths derived from the wind speed profiles. The lower part of the profile (< 40 m) is not in equilibrium and no reliable roughness analysis can be given. The upper part of the profile can be linked to a large-scale roughness length. Roughness lengths derived from the horizontal wind speed variance and gustiness have large footprints and therefore represent a large-scale average roughness. The drag coefficient is more locally determined but still represents a large-scale roughness length when it is measured above the local internal boundary layer. The roughness length at inhomogeneous sites can therefore be determined best from drag coefficient measurements just above the local internal boundary layers directly, or indirectly from horizontal wind speed variance or gustiness. In addition, the momentum and heat fluxes along the tower are analysed and these show significant variation with height related to stability and possibly surface heterogeneity. It appears that the dimensionless wind speed gradients scale well with local fluxes for the variety of conditions considered, including the unstable cases.     

Roughness length for heat over an urban canopy

The roughness length for heat z_T was evaluated over an urban canopy, using the measured sensible heat flux and radiometric temperature. To overcome thermal heterogeneity in the urban area, the measured radiometric temperature was transformed into the equivalent temperature of an upward longwave radiation flux. The equivalent temperature was found to provide an effective parameterization of the radiometric temperature. The daytime average of the resulting ln(z_T/z₀) was 10, where z₀ is the aerodynamic roughness length. This result generally agrees with previous studies; however, the anthropogenic heat is a large uncertainty, which could cause an error at least 240% in z_T.     

Estimation of turbulent sensible heat and momentum fluxes over a heterogeneous urban area using a large aperture scintillometer

The accurate determination of surface-layer turbulent fluxes over urban areas is critical to understanding urban boundary layer (UBL) evolution. In this study, a remote-sensing technique using a large aperture scintillometer (LAS) was investigated to estimate surface-layer turbulent fluxes over a highly heterogeneous urban area. The LAS system, with an optical path length of 2.1 km, was deployed in an urban area characterized by a complicated land-use mix (residential houses, water body, bare ground, etc.). The turbulent sensible heat (Q H) and momentum fluxes (τ) were estimated from the scintillation measurements obtained from the LAS system during the cold season. Three-dimensional LAS footprint modeling was introduced to identify the source areas ("footprint") of the estimated turbulent fluxes. The analysis results showed that the LAS-derived turbulent fluxes for the highly heterogeneous urban area revealed reasonable temporal variation during daytime on clear days, in comparison to the land-surface process-resolving numerical modeling. A series of sensitivity tests indicated that the overall uncertainty in the LAS-derived daytime Q H was within 20%-30% in terms of the influence of input parameters and the non-dimensional similarity function for the temperature structure function parameter, while the estimation errors in τ were less sensitive to the factors of influence, except aerodynamic roughness length. The 3D LAS footprint modeling characterized the source areas of the LAS-derived turbulent fluxes in the heterogeneous urban area, revealing that the representative spatial scales of the LAS system deployed with the 2.1 km optical path distance ranged from 0.2 to 2 km2 (a "micro-α scale"), depending on local meteorological conditions.     

Wind profiles over complex terrain

A large set of routine wind profiles has been analyzed at three towers, located in various types of complex terrain in New England. After allowing for effects of roughness change, uphill flow and stability, roughness lengths have been estimated. In general, the profiles and roughness lengths could be explained by differences in terrain features and stability.     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Near Wall Flow over Urban-like Roughness

In this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s^-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry.The results haveconfirmed the strong three-dimensionalityof the turbulent flow inthe roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can,together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves.The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the `roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates.     

Boundary-layer pollutant concentrations over complex terrain

Given the incident profiles of wind velocity and pollutant concentration, we seek to determine the 3-dimensional concentration field of a pollutant upon a region with complex terrain. The analytic solution of the wind velocity in a 3-dimensional boundary-layer model by Walmsley et al. (1980) is utilized as a forcing function in the simplified concentration perturbation equation for a pollutant. The resulting solution applies to an isolated cosine-squared hill in a neutrally stratified boundary-layer flow with a surface type which absorbs the pollutant totally. The solution shows that the concentration perturbation field is organized in accordance with the wind field. In particular, the east-west cross-section is 180° out of phase with the velocity perturbation field. The vertical profiles of the concentration perturbations for selected grid points approach the value of the upper boundary condition very rapidly.     

On momentum flux and velocity spectra over waves

Data from a research tower in Lake Ontario are used to study the validity of Monin--Obukhov scaling in the marine atmospheric boundary layer under various wave conditions. It is found that over pure wind seas, the velocity spectra and cospectra follow established universal scaling laws. However, in the presence of swells outrunning weak winds, velocity spectra and cospectra no longer satisfy universal spectral shapes. Here, Monin–Obukhov similarity theory, and the classical logarithmic boundary layers, are no longer valid. It is further shown that, in the presence of such swells, the momentum flux can be significantly modified in comparison to pure wind sea values. The implications of these findings for bulk flux estimations and on the inertial dissipation method for calculating fluxes are discussed.     

Turbulent dispersion of pollutant over complex terrain

A two-dimensional turbulent diffusion equation is derived in a streamline coordinate system, defined for rotational flow over complex terrain and limited aloft by an elevated, impenetrable inversion. In the first instance, the steady-state equation is solved for an inner region of the boundary layer, in which the effect of curvature is negligible and, for simplicity, it is assumed that vorticity has a power-law dependence upon stream function. A variational method of solution is also discussed, in which vorticity may have a more general representation. A numerical calculation is performed for a special case of symmetrical flow over an isolated hill. The dependence of pollutant concentration upon the flow field, downwind distance and source is examined and the effect of wind acceleration in the neighbourhood of the top of the hill is discussed. It is pointed out that the diffusion model can be applied to any realistic flow field, provided that the streamlines are specified.     

Fractal dimension of rainbands over Hilly terrain

Summary The fractal geometry of nature has been discerned in a bewildering variety of places. Perhaps the most fundamental property is the existence of structure at almost every space or time scale. It is generally accepted today for convective cloud and rain areas to have fractal structure with dimensionD4/3 for many orders of magnitude in area.During the ALPEX-SOP the Vienna airport weather radar's echoes on a PPI display were evaluated within a range of 150 km. The results indeed confirm the general thesis, but sometimes exhibit considerable deviations both in space and in time from the expected fractal dimension. AsD ought to be determined by the physical processses (includinginteraction with orography) which shape clouds, we have split the data set according to different orographic regions (upstream side, ridge, lee-side), and weather process types (prefrontal, frontal, postfrontal; type of organization of precipitation). Hence follows a moderate reduction in fractal dimension on the upwind side, a substantial growth ofD on the lee-side, especially in situations with strong vertical shear of flow velocities, e.g. characteristic of narrow cold-frontal precipitation bands.There is evidence that the individual change in shape of clouds and precipitation patterns is related to mesoscale variability of physical parameters involved. Furthermore there might be a possibility to interpret this transitory modification from the rule during the flow over hills in terms of turbulence alternation in the boundary layer.

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Fraktale Dimension von Niederschlagsbändern über hügeligem Gelände

Zusammenfassung Für die fraktale Geometrie der Natur gibt es eine Fülle von Beispielen. Die vielleicht hervorstechendste Eigenheit ist dabei die Existenz von Strukturen von fast jeglicher räumlicher oder zeitlicher Größenordnung. Es gilt heute als gesichert, daß konvektive Wolken- und Niederschlagsfelder über viele Größenordnungen ihrer Flächenausdehnung fraktale Strukturen der DimensionD4/3 aufweisen.Wetterradarbeobachtungen am PPI-Display des Flughafens Wien-Schwechat, während der ALPEX-SOP innerhalb 150 km Radius durchgeführt, stützen erwartungsgemäß diese These. Allerdings treten gelegentlich Abweichungen von der erwarteten fraktalen Dimension sowohl in räumlicher als auch in zeitlicher Hinsicht auf. DaD durch physikalische Prozesse (einschließlich derWechselwirkung mit der Orographie) bestimmt wird, welche die Wolken formen, haben wir die Echo-Daten nach verschiedenen orographischen Regionen (Luv, Kammlage, Lee) und nach Typen des Wetterablaufes (präfrontal, frontal, postfrontal; Art der Niederschlagsanordnung) getrennt. Damit zeigt sich eine geringe Abnahme der fraktalen Dimension im Luv von Hügelketten sowie ein beträchtliches Anwachsen vonD über der LeeSeite. Dies ist besonders in Fällen mit starker vertikaler Geschwindigkeitsscherung zu erkennen, wie es z.B. für schmale Niederschlagsbänder an Kaltfronten typisch ist.Es gibt Hinweise, daß die individuellen Formveränderungen von Wolken und Niederschlagsfeldern mit der mesoskaligen Variabilität der eingreifenden physikalischen Parameter verknüpft sind. Weiters sollte es möglich sein, diese vorübergehende Modifizierung des allgemeinen Verhaltens beim Überströmen einer Hügellandschaft, durch gleichzeitig einhergehende Veränderungen der Turbulenz-Charakteristik innerhalb der atmosphärischen Grundschicht zu deuten.

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With 3 Figures     

On mountain wave drag over complex terrain

Summary Mountain wave drag is calculated for rotating, stratified, nonhydrostatic Boussinesq flow over a mountain ridge using linear theory for a variety of mountain profiles representing complex/irregular terrain. The inclusion of a sinusoidal corrugation to the familiar witch-of-Agnesi profile creates a stegosaurus profile. The associated drag is greatly enhanced for mesoscale mountains when the corrugation wave-number matches that for the dominant inertia-gravity wave contribution to the cross-mountain surface pressure gradient. Similarly, increasing the jaggedness (by decreasing the exponentb) increases the drag for mesoscale mountains whose topographic spectral intensity,M(k), has the form of a power law:M(k)=mk ^–b wherek is the zonal wavenumber.Spectral analysis of one-kilometer resolution topographic data for the Appalachian Mountains suggests that a power law profile withb=1.7 accurately represents the topographic spectral intensity and that it yields good estimates of the drag.The application of these results to the parameterization of mountain wave drag in general circulation models is discussed.With 7 Figures     

Physical modelling of flow and dispersion over complex terrain

Atmospheric motion and dispersion over topography characterized by irregular (or regular) hill-valley or mountain-valley distributions are strongly dependent upon three general sets of variables. These are variables that describe topographic geometry, synoptic-scale winds and surface-air temperature distributions. In addition, pollutant concentration distributions also depend upon location and physical characteristics of the pollutant source. Overall fluid-flow complexity and variability from site to site have stimulated the development and use of physical modelling for determination of flow and dispersion in many wind-engineering applications. Models with length scales as small as 1:12,000 have been placed in boundary-layer wind tunnels to study flows in which forced convection by synoptic winds is of primary significance. Flows driven primarily by forces arising from temperature differences (gravitational or free convection) have been investigated by small-scale physical models placed in an isolated space (gravitational convection chamber). Similarity criteria and facilities for both forced and gravitational-convection flow studies are discussed. Forced-convection modelling is illustrated by application to dispersion of air pollutants by unstable flow near a paper mill in the state of Maryland and by stable flow over Point Arguello, California. Gravitational-convection modelling is demonstrated by a study of drainage flow and pollutant transport from a proposed mining operation in the Rocky Mountains of Colorado. Other studies in which field data are available for comparison with model data are reviewed.     

Mesoscale modelling of wind energy over non-homogeneous terrain

The use of numerical mesoscale models for the evaluation of wind energy potential over non-homogeneous terrain is outlined, focusing on the following: (i) an overview of modelling investigations of relevance to wind energy; and (ii) a discussion of the optimal implementation of mesoscale models in wind energy studies.     

Estimates of effective surface roughness over complex terrain

Turbulence data collected in an area of three-dimensional complex terrain using instruments atteched to the tether cable of a captive balloon together with radiosonde ascents are presented. In addition, data collected using only radiosonde ascents in an area of two-dimensional complex terrain of large slope are also shown. Eddy correlation measurements of the turbulent momentum flux and wind velocity profiles are used to deduce the magnitude of the effective roughness from the drag coefficient and normalised velocity profiles. A relationship connecting the terrain characteristics and the roughness length is compared with the experimental data for both types of terrain plus previous experimental estimates of the roughness length over complex terrain. The formula taken from previous work by Grant and Mason (1990) is found to agree with the data when representing an area of order 100 km².     

Estimation of surface heat and momentum fluxes using the flux-variance method above uniform and non-uniform terrain

Eddy-correlation measurements above an uneven-aged forest, a uniform-irrigated bare soil field, and within a grass-covered forest clearing were used to investigate the usefulness of the fluxvariance method above uniform and non-uniform terrain. For this purpose, the Monin and Obukhov (1954) variance similarity functions were compared with direct measurements. Such comparisons were in close agreement for momentum and heat but not for water vapor. Deviations between measured and predicted similarity functions for water vapor were attributed to three factors: 1) the active role of temperature in surface-layer turbulence, 2) dissimilarity between sources and sinks of heat and water vapor at the ground surface, and 3) the non-uniformity in water vapor sources and sinks. It was demonstrated that the latter non-uniformity contributed to horizontal gradients that do not scale with the vertical flux. These three factors resulted in a turbulence regime that appeared more efficient in transporting heat than water vapor for the dynamic convective sublayer but not for the dynamic sublayer. The agreement between eddy-correlation measured and flux-variance predicted sensible heat flux was better than that for latent heat flux at all three sites. The flux-variance method systematically overestimated the latent heat flux when compared to eddy-correlation measurements. It was demonstrated that the non-uniformity in water vapor sources reduced the surface flux when compared to an equivalent uniform terrain subjected to identical shear stress, sensible heat flux, and atmospheric water vapor variance. Finally, the correlation between the temperature and water vapor fluctuations was related to the relative efficiency of surface-layer turbulence in removing heat and water vapor. These relations were used to assess critical assumptions in the derivation of the flux-variance formulation.     

Estimating minimum temperature and climatological freeze risk in hilly terrain

Differences between weather station and on-farm minimum temperatures in hilly terrain were related to general weather parameters, using stepwise multiple linear regression and correlation techniques. Opacity (cloud cover) and wind speed were the most significant parameters, explaining up to 79% of the variation in night-time temperature differences between base station and field sites 20–40 km away. Considering dew point depression, days since 0.25 cm rainfall, absolute minimum temperature, cloud base height, opacity as quadratic and an exponential relationship did not improve the regression estimates significantly. Standard error of estimates ranged from 0.8°C for sites on hilltops to 2.3°C for valley bottoms. In independent data tests using 19 cases, the average minimum temperature difference between the base station and a high risk site was estimated within 0.4°C of the measured value. Significance of the regression relationships increased proportionally with distance down the slopes. Base station-site minimum temperature differences on relatively clear calm nights averaged near 1°C on hilltops, 2° to 3°C midway down slopes and 5° to 6°C in the hollows.Regression equations developed from short-term temperature measurements at more than 50 sites were used to estimate daily site minimum temperatures for a 21-year period. Spring and fall freeze probabilities for critical temperatures of 32°, 30° and 28°F (0.0°, −1.1° and −2.2°C) were then calculated for each site using standard climatological techniques. Estimated average freeze dates in hollows were up to 34 days later in spring and 39 days earlier in fall than on hilltops. Average dates of spring and fall freeze occurrences were delayed and advanced respectively about 6 days for each degree (C) drop in critical temperature. In independent data tests the average spring and fall ground frost dates at the base station were estimated within 2 days of measured values, using similar techniques. Minimum temperatures measured by traverses on a clear, calm night were highly correlated with estimated frost dates (R = 0.99).