E − ε − 〈θ 2〉 turbulence closure model for an atmospheric boundary layer including the urban canopy

A modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is presented. The model is based on tensor-invariant parameterizations for the pressure–strain and pressure–temperature correlations that are more complete than the parameterizations used in the Mellor–Yamada model of level 3.0. The turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence. The turbulent transport of heat and momentum fluxes is assumed to be negligibly small in this approximation. The three-parameter $E - \varepsilon - {\left\langle {\theta ^{2} } \right\rangle }$ model of thermally stratified turbulence is employed to obtain closed-form algebraic expressions for the fluxes. A computational test of a 24-h ABL evolution is implemented for an idealized two-dimensional region. Comparison of the computed results with the available observational data and other numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized ABL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city. The results of the computational test for the new model indicate that the motion of air in the urban canopy layer is strongly influenced by mechanical factors (buildings) and thermal stratification.     

Atmospheric back radiation in the tropical pacific: Intercomparison of in-situ measurements, simulations and satellite retrievals

Summary The back radiation has been measured with an Eppley pyrgeometer on board the R/V Vickers in the tropical Pacific Ocean during the field campaigns COARE (Coupled Ocean Atmosphere Response Experiment) and CEPEX (Central Equatorial Pacific Experiment) in February and March 1993, respectively. As part of these compaigns radiosondes have been launched from the Vickers several times per day and cloud cover was observed frequently. The radiosonde and cloud observations are used together with a radiative transfer model to calculate the back radiation for a subsequent intercomparison with the pyrgeometer measurements. Another means of comparison is derived from space-borne SSM/I (Special Sensor Microwave/Imager) measurements. The mean difference between pyrgeometer measurements and simulated downwelling irradiance at the sea surface is less than 2 W/m², at a mean of 425 W/m² in the warm pool, with a standard deviation of 8 W/m². The comparison of satellite measurements with pyrgeometer readings shows a mean difference of-3 W/m² and a standard deviation of 14 W/m². The mean difference between satellite-derived back radiation and simulated one is 3 W/m² with a standard deviation of 14 W/m². Comparisons with results obtained from bulk formulae applied to surface meteorological observations show a good performance of the bulk parameterisations in the cloud-free case but a general overestimation of the back radiation in cloudy situations.With 5 Figures     

Evaluation of the Weather Research and Forecasting Mesoscale Model for GABLS3: Impact of Boundary-Layer Schemes,Boundary Conditions and Spin-Up

We evaluated the performance of the three-dimensional Weather Research and Forecasting (WRF) mesoscale model, specifically the performance of the planetary boundary-layer (PBL) parametrizations. For this purpose, Cabauw tower observations were used, with the study extending beyond the third GEWEX Atmospheric Boundary-Layer Study (GABLS3) one-dimensional model intercomparison. The WRF model (version 3.4.1) contains 12 different PBL parametrizations, most of which have been only partially evaluated. The GABLS3 case offers a clear opportunity to evaluate model performance, focusing on time series of near-surface weather variables, radiation and surface flux budgets, vertical structure and the nighttime inertial oscillation. The model results revealed substantial differences between the PBL schemes. Generally, non-local schemes tend to produce higher temperatures and higher wind speeds than local schemes, in particular, for nighttime. The WRF model underestimates the 2-m temperature during daytime (about \(2\) K) and substantially underestimates it at night (about \(4\) K), in contrast to the previous studies where modelled 2-m temperature was overestimated. Considering the 10-m wind speed, during the night turbulent kinetic energy based schemes tend to produce lower wind speeds than other schemes. In all simulations the sensible and latent heat fluxes were well reproduced. For the net radiation and the soil heat flux we found good agreement with daytime observations but underestimations at night. Concerning the vertical profiles, the selected non-local PBL schemes underestimate the PBL depth and the low-level jet altitude at night by about 50 m, although with the correct wind speed. The latter contradicts most previous studies and can be attributed to the revised stability function in the Yonsei University PBL scheme. The local, turbulent kinetic energy based PBL schemes estimated the low-level jet altitude and strength more accurately. Compared to the observations, all model simulations show a similar structure for the potential temperature, with a consistent cold bias ( \(\approx \) 2 K) in the upper PBL. In addition to the sensitivity to the PBL schemes, we studied the sensitivity to technical features such as horizontal resolution and domain size. We found a substantial difference in the model performance for a range of 12, 18 and 24 h spin-up times, longer spin-up time decreased the modelled wind speed bias, but it strengthened the negative temperature bias. The sensitivity of the model to the vertical resolution of the input and boundary conditions on the model performance is confirmed, and its influence appeared most significant for the non-local PBL parametrizations.     

Observing Entrainment Processes Using a Small Unmanned Aerial Vehicle: A Feasibility Study

Measurement flights with the meteorological mini aerial vehicle (M $^2$ AV) were performed in spring 2011 to assess the capability of an unmanned aerial vehicle (UAV) to measure the structure of the transition zone between the convective boundary layer and the stably stratified free atmosphere. The campaign took place at the Meteorological Observatory Lindenberg/Richard-Aßmann-Observatory of the German Meteorological Service. Besides the M $^2$ AV flights, observations were made from a 12-m and a 99-m tower, a sodar, two ceilometers, radiosondes, and a tethered balloon with sensor packages at six different levels. M $^2$ AV measurements were intentionally combined with remote sensing systems. The height range of the entrainment zone as well as its diurnal cycle were provided by the remote sensing instruments. The UAV provided the high-resolution in situ data of temperature and wind for the study of turbulent processes. It is shown that the M $^2$ AV is able to maintain constant altitude with very small deviations—a pre-requisite to study processes inside the often quite thin entrainment zone and that M $^2$ AV high-resolution wind and temperature measurements allow for very detailed studies of the fine structure of the atmosphere and thus for the identification of quite local and/or short-duration processes such as overshooting thermals or downward intrusions of warm air. Spatial series measured by the M $^2$ AV during horizontal flights show turbulent exchange of heat in short turbulent bursts at heights close to and within the entrainment zone. Scaled vertical profiles of vertical velocity, potential temperature variance, and sensible heat flux confirm the general shape found by previous measurements and numerical studies.     

Evolution of Stratocumulus Over Land: Comparison of Ground and Aircraft Observations with Numerical Weather Prediction Simulations

Forecasting of low cloud continues to challenge numerical weather prediction. With this in mind, surface and airborne observations were made over East Anglia, UK, during March 2011 to investigate stratus and stratocumulus advecting from the sea over land. Four surface sites were deployed at various distances inland aligned approximately along the flow. In situ data include cloud-droplet measurements from an aircraft operating off the coast and a tethered balloon 100 km inland. Comparisons of thermodynamic and cloud properties are made with Met Office operational model simulations at horizontal resolutions of 4 and 1.5 km. The clouds contained droplet concentrations up to 600 cm \(^{-3}\) within polluted outflow off Europe. These measurements were compared to three different model schemes for predicting droplet concentration: two of them perform well at low to moderate concentrations but asymptote to 375 cm \(^{-3}\) . Microwave radiometers at the ground sites retrieved liquid water paths that reduced with distance inland and were generally below 200 g m \(^{-2}\) . The modelled water path performs well upstream but more erratically far inland. Comparisons of thermodynamic profiles are made within both Lagrangian and Eulerian frameworks and show the model predicted changes in equivalent potential temperature generally within 1 K, with occasional errors of 2 K or more. The modelled cloud-top temperatures were in good agreement with the observations down to \(-\) 7  \(^{\circ }\) C, but the magnitude of the temperature inversion, although good at times, was too small by on average 1.6 K. The different simulations produced different cloud-top water contents due to a combination of resolution and scientific upgrades to the model, but they generally underestimate the amount of cloud water. Major changes, such as the mesoscale temporary cloud breaks on 2 March 2011 and the complete clearance on 4 March, were seemingly predicted by the model for the correct reasons.     

Scalar Flux–Gradient Relationships Under Unstable Conditions over Water in Coastal Regions

The scalar flux–gradient relationships of temperature ( $\phi _{T}$ ? T ) and specific humidity ( $\phi _{q}$ ? q ) under unstable conditions are investigated using eddy-covariance measurements of air–sea turbulent fluxes and vertical profiles of temperature and specific humidity collected from a marine meteorological platform. The gradients of temperature and specific humidity are obtained from measurements at five heights above the sea surface using the log-square fitting method and the simpler first-order approximation method. The two methods yield similar results. The proposed flux–gradient relationships $\phi _{T}$ ? T and $\phi _{q}$ ? q covers a wide range of instability: the stability parameter $\zeta $ ζ ranges from $-$ ? 0.1 to $-$ ? 50. The functional form of the proposed flux–gradient relationships is an interpolation between the Businger–Dyer relation and the free convection relation, which includes the “ $-$ ? 1/2” and “ $-$ ? 1/3” scaling laws at two different stability regimes. The widely used COARE 3.0 algorithm, which is an interpolation between the integrals of the Businger–Dyer and the free convection relations, is also evaluated and compared. The analysis and comparisons show that both schemes generate reasonable values of $\phi _{q}$ ? q in the whole unstable regime. The COARE 3.0 algorithm, however, overestimates $\phi _{T}$ ? T values under very unstable conditions. The errors in the flux–gradient relationships induced by the random errors in the turbulence measurements are assessed. When the random errors are taken into account, the observations agree with predictions of various schemes fairly well, implying that the dominant transport mechanism is adequately captured by the Monin–Obukhov similarity theory. The study also shows that $\phi _{q}$ ? q is significantly ${>}\phi _{T}$ > ? T under unstable conditions and that the ratio $\phi _{q}/\phi _{T}$ ? q / ? T increases with $-\zeta $ ? ζ . The ratio of $\phi _{q}$ ? q to $\phi _{T}$ ? T and the ratio of turbulent transport efficiencies of heat and water vapour ( $R_{wT}/R_{wq}$ R wT / R wq ) suggest that heat is transported more efficiently than water vapour under unstable conditions.     

A Method for Monitoring the Heat Flux from an Urban District with a Single Infrared Remote Sensor

The proposed methodology relies on the modelling capabilities of the thermo-radiative model Solene to simulate the heat and radiation energy exchanges between an actual urban district and the atmosphere. It is based on the comparison of the simulated upward infrared and sensible heat flux diurnal cycles that may be measured by elevated sensors above the three-dimensional scene, as a function of sensor position: the heat flux is a function of an equivalent surface temperature given by the infrared sensor and an equivalent heat transfer coefficient deduced from Solene simulations with the actual geometry. The method is tested against measurements obtained in the city centre of Toulouse, France during an experimental campaign in 2004–2005. To improve the computation of the heat exchanges between air and building surfaces a new algorithm is first implemented, based on an empirical model of the wind distribution within street canyons. This improvement is assessed by a direct comparison of the simulated brightness surface temperatures of the Toulouse city centre to measurements obtained with an airborne infrared sensor. The optimization of the infrared remote sensor position is finally analyzed as a function of its height above the mean roof level: it allows evaluation of the heat flux from an urban district when the three different classes of surfaces (roofs, walls, grounds) have similar contributions to the infrared flux towards the sensor, and to the heat flux into the atmosphere.     

Multi-Scale Sensible Heat Fluxes in the Suburban Environment from Large-Aperture Scintillometry and Eddy Covariance

Sensible heat fluxes ( \(Q_{H}\) ) are determined using scintillometry and eddy covariance over a suburban area. Two large-aperture scintillometers provide spatially integrated fluxes across path lengths of 2.8 and 5.5 km over Swindon, UK. The shorter scintillometer path spans newly built residential areas and has an approximate source area of 2–4 \(\text {km}^{2}\) , whilst the long path extends from the rural outskirts to the town centre and has a source area of around 5–10 \(\text {km}^{2}\) . These large-scale heat fluxes are compared with local-scale eddy-covariance measurements. Clear seasonal trends are revealed by the long duration of this dataset and variability in monthly \(Q_{H}\) is related to the meteorological conditions. At shorter time scales the response of \(Q_{H}\) to solar radiation often gives rise to close agreement between the measurements, but during times of rapidly changing cloud cover spatial differences in the net radiation ( \(Q^{*}\) ) coincide with greater differences between heat fluxes. For clear days \(Q_{H}\) lags \(Q^{*}\) , thus the ratio of \(Q_{H}\) to \(Q^{*}\) increases throughout the day. In summer the observed energy partitioning is related to the vegetation fraction through use of a footprint model. The results demonstrate the value of scintillometry for integrating surface heterogeneity and offer improved understanding of the influence of anthropogenic materials on surface-atmosphere interactions.     

Advances in Air–Sea \hbox {CO}_2 Flux Measurement by Eddy Correlation

Eddy-correlation measurements of the oceanic \(\hbox {CO}_2\) flux are useful for the development and validation of air–sea gas exchange models and for analysis of the marine carbon cycle. Results from more than a decade of published work and from two recent field programs illustrate the principal interferences from water vapour and motion, demonstrating experimental approaches for improving measurement precision and accuracy. Water vapour cross-sensitivity is the greatest source of error for \(\hbox {CO}_2\) flux measurements using infrared gas analyzers, often leading to a ten-fold bias in the measured \(\hbox {CO}_2\) flux. Much of this error is not related to optical contamination, as previously supposed. While various correction schemes have been demonstrated, the use of an air dryer and closed-path analyzer is the most effective way to eliminate this interference. This approach also obviates density corrections described by Webb et al. (Q J R Meteorol 106:85–100, 1980). Signal lag and frequency response are a concern with closed-path systems, but periodic gas pulses at the inlet tip provide for precise determination of lag time and frequency attenuation. Flux attenuation corrections are shown to be \(<\) 5 % for a cavity ring-down analyzer (CRDS) and dryer with a 60-m inlet line. The estimated flux detection limit for the CRDS analyzer and dryer is a factor of ten better than for IRGAs sampling moist air. While ship-motion interference is apparent with all analyzers tested in this study, decorrelation or regression methods are effective in removing most of this bias from IRGA measurements and may also be applicable to the CRDS.     

辐射参数化的变化对模式中期和月预报的影响

在T106中期数值预报模式和T63气候模式中进行了两种辐射过程参数化的对比试验。目前在这两个模式中用作对照积分的辐射方案(OPE)是ECMWF的早期业务方案，而新的辐射方案(NEW)是ECMWF 1989年5月2日成为业务的版本。试验结果表明，OPE高估了短波水的吸收，导致太大的短波大气吸收和地表太小的向下短波辐射；OPE还低估了长波辐射冷却和大气顶的向外长波辐射(OLR)；NEW增加了地表有效辐射能量和对流层总的冷却，产生了较大的湍流热通量，对流活动加强，降水量明显增加；NEW还使平流层温度偏暖得到矫正。业务平行试验的统计检验表明，NEW对4～7天中期预报有较显著的改进。     

Large-Eddy Atmosphere–Land-Surface Modelling over Heterogeneous Surfaces: Model Development and Comparison with Measurements

A model is developed for the large-eddy simulation (LES) of heterogeneous atmosphere and land-surface processes. This couples a LES model with a land-surface scheme. New developments are made to the land-surface scheme to ensure the adequate representation of atmosphere–land-surface transfers on the large-eddy scale. These include, (1) a multi-layer canopy scheme; (2) a method for flux estimates consistent with the large-eddy subgrid closure; and (3) an appropriate soil-layer configuration. The model is then applied to a heterogeneous region with 60-m horizontal resolution and the results are compared with ground-based and airborne measurements. The simulated sensible and latent heat fluxes are found to agree well with the eddy-correlation measurements. Good agreement is also found in the modelled and observed net radiation, ground heat flux, soil temperature and moisture. Based on the model results, we study the patterns of the sensible and latent heat fluxes, how such patterns come into existence, and how large eddies propagate and destroy land-surface signals in the atmosphere. Near the surface, the flux and land-use patterns are found to be closely correlated. In the lower boundary layer, small eddies bearing land-surface signals organize and develop into larger eddies, which carry the signals to considerably higher levels. As a result, the instantaneous flux patterns appear to be unrelated to the land-use patterns, but on average, the correlation between them is significant and persistent up to about 650 m. For a given land-surface type, the scatter of the fluxes amounts to several hundred W $\text{ m }^{-2}$ , due to (1) large-eddy randomness; (2) rapid large-eddy and surface feedback; and (3) local advection related to surface heterogeneity.     

Surface Heterogeneity Effects on Regional-Scale Fluxes in the Stable Boundary Layer: Aerodynamic Roughness Length Transitions

The effects of abrupt streamwise transitions of the aerodynamic roughness length ( $z_\mathrm{o}$ z o ) on the stable atmospheric boundary layer are evaluated using a series of large-eddy simulations based on the first Global Energy and Water Cycle Experiment Atmospheric Boundary Layer intercomparison study (GABLS1). Four $z_\mathrm{o}$ z o values spanning three orders of magnitude are used to create all possible binary distributions with each arranged into patches of characteristic length scales equal to roughly one-half, one, and two times the equivalent homogeneous boundary-layer height. The impact of the heterogeneity on mean profiles of wind speed and temperature, on surface fluxes of heat and momentum, and on internal boundary-layer dynamics are considered. It is found that $z_\mathrm{o}$ z o transitions do not significantly alter the functional relationship between the average surface fluxes and the mean profiles of wind speed and potential temperature. Although this suggests that bulk similarity theory is applicable for modelling the stable boundary layer over $z_\mathrm{o}$ z o heterogeneity, effective surface parameters must still be specified. Existing models that solve for effective roughness lengths of momentum and heat are evaluated and compared to values derived from the simulation data. The existing models are unable to accurately reproduce both the values of the effective aerodynamic roughness lengths and their trends as functions of patch length scale and stability. A new model for the effective aerodynamic roughness length is developed to exploit the benefits of the other models tested. It accurately accounts for the effects of the heterogeneity and stratification on the blending height and effective aerodynamic roughness length. The new model provides improved average surface fluxes when used with bulk similarity.     

Derivation of Structure Parameters of Temperature and Humidity in the Convective Boundary Layer from Large-Eddy Simulations and Implications for the Interpretation of Scintillometer Observations

We derive the turbulent structure parameters of temperature $C_{T}^2$ and humidity $C_q^2$ from high-resolution large-eddy simulations (LES) of a homogeneously-heated convective boundary layer. Boundary conditions and model forcing were derived from measurements at Cabauw in The Netherlands. Three different methods to obtain the structure-parameters from LES are investigated. The shape of the vertical structure-parameter profiles from all three methods compare well with former experimental and LES results. Depending on the method, deviations in the magnitude up to a factor of two are found and traced back to the effects of discretization and numerical dissipation of the advection scheme. Furthermore, we validate the LES data with airborne and large-aperture scintillometer (LAS) measurements at Cabauw. Virtual path measurements are used to study the variability of $C_{T}^2$ in the mixed layer and surface layer and its implications for airborne and LAS measurements. A high variability of $C_{T}^2$ along a given horizontal path in the LES data is associated with plumes (high values) and downdrafts (low values). The path average of $C_{T}^2$ varies rapidly in time due to the limited path length. The LES results suggest that measured path averages require sufficient temporal averaging and an adequate ratio of path length to height above the ground for the LAS in order to approach the domain average of $C_{T}^2$ .     

Evaluation of Two Energy Balance Closure Parametrizations

A general lack of energy balance closure indicates that tower-based eddy-covariance (EC) measurements underestimate turbulent heat fluxes, which calls for robust correction schemes. Two parametrization approaches that can be found in the literature were tested using data from the Canadian Twin Otter research aircraft and from tower-based measurements of the German Terrestrial Environmental Observatories (TERENO) programme. Our analysis shows that the approach of Huang et al. (Boundary-Layer Meteorol 127:273–292, 2008), based on large-eddy simulation, is not applicable to typical near-surface flux measurements because it was developed for heights above the surface layer and over homogeneous terrain. The biggest shortcoming of this parametrization is that the grid resolution of the model was too coarse so that the surface layer, where EC measurements are usually made, is not properly resolved. The empirical approach of Panin and Bernhofer (Izvestiya Atmos Oceanic Phys 44:701–716, 2008) considers landscape-level roughness heterogeneities that induce secondary circulations and at least gives a qualitative estimate of the energy balance closure. However, it does not consider any feature of landscape-scale heterogeneity other than surface roughness, such as surface temperature, surface moisture or topography. The failures of both approaches might indicate that the influence of mesoscale structures is not a sufficient explanation for the energy balance closure problem. However, our analysis of different wind-direction sectors shows that the upwind landscape-scale heterogeneity indeed influences the energy balance closure determined from tower flux data. We also analyzed the aircraft measurements with respect to the partitioning of the “missing energy” between sensible and latent heat fluxes and we could confirm the assumption of scalar similarity only for Bowen ratios $\approx $ 1.     

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. $\approx $ 0.1–1 km) 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 and choice of surface parameters. For radiative fluxes, improved performance (e.g. $>$ 25 W m $^{-2}$ root-mean-square error reduction for the net radiation) is attained with UZE parameters compared to the WRF v3.2.1 default for all three methods from the simplest to the most detailed. The UZE-based spatial fluxes reproduce a priori expectations of greater energy storage and less evaporation in the dense city centre compared to the residential surroundings. Problems in Noah/SLUCM partitioning of energy between the daytime turbulent fluxes are identified with the overestimation of the turbulent sensible heat and underestimation of the turbulent latent heat fluxes.     

Characterization of Oscillatory Motions in the Stable Atmosphere of a Deep Valley

In a valley sheltered from strong synoptic effects, the dynamics of the valley atmosphere at night is dominated by katabatic winds. In a stably stratified atmosphere, these winds undergo temporal oscillations, whose frequency is given by $N \sin {\alpha }$ N sin α for an infinitely long slope of constant slope angle $\alpha $ α , $N$ N being the buoyancy frequency. Such an unsteady flow in a stably stratified atmosphere may also generate internal gravity waves (IGWs). The numerical study by Chemel et al. (Meteorol Atmos Phys 203:187–194, 2009) showed that, in the stable atmosphere of a deep valley, the oscillatory motions associated with the IGWs generated by katabatic winds are distinct from those of the katabatic winds. The IGW frequency was found to be independent of $\alpha $ α and about $0.8N$ 0.8 N . Their study did not consider the effects of the background stratification and valley geometry on these results. The present work extends this study by investigating those effects for a wide range of stratifications and slope angles, through numerical simulations for a deep valley. The two oscillatory systems are reproduced in the simulations. The frequency of the oscillations of the katabatic winds is found to be equal to $N$ N times the sine of the maximum slope angle. Remarkably, the IGW frequency is found to also vary as $C_\mathrm{w}N$ C w N , with $C_\mathrm{w}$ C w in the range $0.7$ 0.7 – $0.95$ 0.95 . These values for $C_\mathrm{w}$ C w are similar to those reported for IGWs radiated by any turbulent field with no dominant frequency component. Results suggest that the IGW wavelength is controlled by the valley depth.     

Accuracy and sensitivity analysis for 54 models of computing hourly diffuse solar irradiation on clear sky

Fifty-four broadband models for computation of solar diffuse irradiation on horizontal surface were tested in Romania (South-Eastern Europe). The input data consist of surface meteorological data, column integrated data, and data derived from satellite measurements. The testing procedure is performed in 21 stages intended to provide information about the sensitivity of the models to various sets of input data. There is no model to be ranked “the best” for all sets of input data. However, some of the models performed better than others, in the sense that they were ranked among the best for most of the testing stages. The best models for solar diffuse radiation computation are, on equal footing, ASHRAE 2005 model (ASHRAE 2005) and King model (King and Buckius, Solar Energy 22:297–301, 1979). The second best model is MAC model (Davies, Bound Layer Meteor 9:33–52, 1975). Details about the performance of each model in the 21 testing stages are found in the Electronic Supplementary Material.     

Long-term investigations on the water budget quantities predicted by the hydro-thermodynamic soil vegetation scheme (HTSVS) – Part II: Evaluation, sensitivity, and uncertainty

Summary ¶Various water budget elements (water supply to the atmosphere, ground water recharge, change in storage) are predicted by HTSVS for a period of 2050 days. The predicted water budget elements are evaluated by routine lysimeter data. The results show that land surface models need parameterizations for soil frost, snow effects and water uptake to catch the broad cycle of soil water budget elements. In principle, HTSVS is able to simulate the general characteristics of the seasonal changes in these water budget elements and their long-term accumulated sums. Compared to lysimeter data, there is a discrepancy in the predicted water supply to the atmosphere for summer and winter which may be attributed to the hardly observed plant physiological parameters like root depth, LAI, shielding factor, etc., the lack of measured downward long-wave radiation, and some simplifications made in the parameterizations of soil frost and snow effects. The fact that high resolution data for the evaluation of model results are missing and evaluation is made on the basis of the data from routine stations of a network is typical for the results of long-term studies on climate. Taking into account the coarse resolution of climate models, the coarse vertical resolution that is used in their LSMs, and the lack of suitable parameters needed, it seems that discrepancies in the order of magnitude found in this study are a general uncertainty in the results of land surface modeling on typical spatial and temporal scales of the climate system.Received October 8, 2001; revised February 15, 2002; accepted September 20, 2002 Published online: April 10, 2003     

Non-isothermal scavenging of highly soluble gaseous pollutants by rain in the atmosphere with non-uniform vertical concentration and temperature distributions

We suggest a non-isothermal one-dimensional model of precipitation scavenging of highly soluble gaseous pollutants in inhomogeneous atmosphere. When gradients of soluble trace gases’ concentrations and temperature in the atmosphere are small, scavenging of gaseous pollutants is governed by two linear wave equations that describe propagation of a scavenging and temperature waves in one direction. If wash-down front velocity is much larger than the velocity of the temperature front, scavenging is determined by propagating scavenging front in the atmosphere with inhomogeneous temperature distribution. We solved the derived equation by the method of characteristics and determined scavenging coefficient and the rates of precipitation scavenging for wet removal of sulfur dioxide using measured initial distributions of trace gases and temperature in the atmosphere. It is shown that in the case of exponential initial distribution of soluble trace gases and linear temperature distribution in the atmosphere, scavenging coefficient in the region between the ground and the position of a scavenging front is proportional to rainfall rate, solubility parameter in the under-cloud region, adjacent to a bottom of a cloud and to the growth constant in the formula for the initial profile of a soluble trace gas in the atmosphere. The derived formula yields the same value of scavenging coefficient for sulfur dioxide scavenging by rain as field estimates presented by McMahon and Denison (Atmos Environ 13:571–585, 1979). It is demonstrated that in the case when the altitude variation of temperature in the atmosphere is determined by the environmental lapse rate, scavenging coefficient increases with height in the region between the scavenging front and the ground. In the case when altitude temperature variation in the atmosphere is determined by temperature inversion, scavenging coefficient decreases with height in a region between the scavenging front and the ground. Theoretical predictions of the value of the scavenging coefficient for sulfur dioxide washout by rain and of the dependence of the magnitude of the scavenging coefficient on rain intensity are in good agreements with the atmospheric measurements of Martin (Atmos Environ 18:1955–1961, 1984).     

Investigation of the Stable Atmospheric Boundary Layer at Halley Antarctica

Boundary-layer measurements from the Brunt Ice Shelf, Antarctica are analyzed to determine flux–profile relationships. Dimensionless quantities are derived in the standard approach from estimates of wind shear, potential temperature gradient, Richardson number, eddy diffusivities for momentum and heat, Prandtl number, mixing length and turbulent kinetic energy. Nieuwstadt local scaling theory for the stable atmospheric boundary-layer appears to work well departing only slightly from expressions found in mid-latitudes. An $E$ E – $l_{\mathrm{m}}$ l m single-column model of the stable boundary layer is implemented based on local scaling arguments. Simulations based on the first GEWEX Atmospheric Boundary-Layer Study case study are validated against ensemble-averaged profiles for various stability classes. A stability-dependent function of the dimensionless turbulent kinetic energy allows a better fit to the ensemble profiles.