Selection of Abstracts

On the vertically averaged balance equation of atmospheric trace constituents

Gerhard Kramm, Ralph Dlugi, and Nicole Mölders

Meteorol. Atmos. Phys. (online published July 1, 2003, DOI: 10.1007/s00703-003-0015-1)

The vertically averaged balance equation of atmospheric trace constituents that customarily serves as a basis for one- and two-layer (box) models of the atmospheric boundary layer and the whole troposphere is derived and discussed. It is shown that this kind of balance equation is accompanied by several prominent short-comings so that the capability of such models to predict real situations of photochemical smog formation and depletion is strongly limited. Three of these short-comings are theoretically elucidated, namely (1) the vertically averaged source and sink terms owing to chemical reactions, (2) the parameterisation of the dry deposition and exhalation fluxes at the earth's surface that serve as lower boundary conditions, and (3) the parameterisation of the upper boundary conditions. Even though the consumption of computing time is much smaller than those of sophisticated Eulerian air pollution models like ADOM, DRAIS, EURAD, RADM, and TADAP, we have to conclude from our theoretical results that one- and two-layer (box) models should not be considered as a true alternative to such air pollution models.
We also suggest that the influence of these short-comings on the predicted results has to be estimated and evaluated in a reliable manner before vertically averaged balance equations of atmospheric trace constituents are introduced into general circulation models to investigate the influence of air pollution on climate change on the basis of long-term simulations.

On the dispersion of trace species in the atmospheric boundary layer: A re-formulation of the governing equations for the turbulent flow of the compressible atmosphere

Gerhard Kramm and Franz X. Meixner

Tellus 52A, 500-522 (2000)

Since especially the parameterisation of the vertical dispersion of trace species in the atmospheric boundary layer has controversially been discussed in the literature, the first-order balance equations for matter, momentum, and various energy forms were re-formulated with Hesselberg's density-weighted averaging calculus to point out that this problem arises from averaging the macroscopic balance equations of matter, momentum and various energy forms in the sense of Reynolds, rather than from the parameterisation of the vertical dispersion by first-order closure principles, as this discussion seems to reflect. Results of the SANA field experiment "Eisdorf" presented here substantiate that in the case of chemically reactive trace constituents segregation effects owing to turbulence cannot generally be neglected as usually performed in Eulerian air pollution models. Modelling such segregation effects, however, requires, at least, second-order-closure principles. Therefore, the second-order balance equations for second moments like the eddy flux densities of matter and momentum as well as covariances of scalar quantities were also re-formulated by considering Hesselberg's averaging procedure. This re-formulated set of governing first-order and second-order balance equations may be considered as most exact because the degree of simplification is reduced to a minimum. To distinguish between the Boussinesq approximated equation set for the turbulent atmospheric flow, denoted as Boussinesq fluid, and our re-formulated one, the turbulent flow of the compressible atmosphere for which the re-formulated governing balance equations are valid may be denoted as Hesselberg fluid. It is argued that averaging in the sense of Hesselberg reduces the risk to misinterpret turbulent atmospheric processes to a minimum. As exemplary shown on the basis of the balance equations for dry air, water vapour, and trace species, the so-called Webb correction will become insignificant if Hesselberg's averaging calculus is considered. Based on the results obtained from the "Eisdorf" experiment and from sensitivity studies with a Seinfeld-type kinetic mechanism for photochemical smog, it is argued that an evaluation and improvement of Eulerian air pollution models requires directly measured second-order moments. Since the number of fast-response physico-chemical analysers for chemically reactive trace constituents is strongly limited, such fast-response sensors have to be (further) developed to set-up a true platform for model evaluation that implies not only a comparison of calculated and observed distributions of first moments (necessary condition), but also a comparison of the calculated and observed distributions of second moments (sufficient condition).

Sublayer-Stanton Numbers of Heat and Matter for Aerodynamically Smooth Surfaces: Basic Considerations and Evaluation

Gerhard Kramm, Ralph Dlugi, and Nicole Mölders

Meteorol. Atmos. Phys. 79, 173-194 (2002)

Sublayer-Stanton numbers, B_i, of heat and matter for the interfacial sublayer over aerodynamically smooth surfaces determined for forced convective conditions by elementary and numerical integration are reviewed and evaluated. The results are based on Roth's modified Heisenberg model for the spectral energy transfer in the equilibrium range under locally isotropic conditions and the approaches of Reichardt, Elser, Deissler, van Driest, Rannie, Sheppard, and Spalding for the normalised eddy diffusivity K_m/ν. The results substantiate that with the exception of Sheppard's approach all formulations are appropriate to provide sublayer-Stanton numbers with a sufficient degree of accuracy. From a theoretical point of view the K_m/ν-relationships of Roth, Reichardt, van Driest, and Spalding are to be preferred, when a turbulent Prandtl number Pr_t = 1 is presumed.
Since within the framework of mesoscale meteorological modelling numerical integration techniques would consume too much CPU-time because of the large number of near-wall grid points, a parameterisation formula for the sublayer-Stanton number is proposed and evaluated. Compared to the B_i^-1-results obtained by numerical integration, this kind of parameterisation leads to a relative error of less than 5 per cent for roughness Reynolds numbers ranging from 30 to 600.

Stability Functions for Momentum, Heat and Water Vapour and the Vertical Transport of TKE and Pressure Fluctuations Estimated from Measured Vertical Profiles of Wind Speed, Temperature and Humidity

Gerhard Kramm, Fritz Herbert, Karlheinz Bernhardt, Hans Müller, Peter Werle, Thomas Foken, and Sieghard H. Richter

Beitr. Phys. Atmosph. 69, 463-475 (1996).

Vertical wind speed, temperature and humidity profile data from three known atmospheric field campaigns are used to determine the surface layer similarity functions for the transport of momentum and heat as well as TKE (turbulent kinetic energy) and pressure fluctuations. The basic principles on which we carry out this determination are the simplified TKE-budget equation obeying Monin-Obukhov similarity laws and a one-and-a-half-order closure concept. Least squares techniques are utilised for the calculations. The numerical analysis provides all important internal and external surface layer parameters like the friction velocity, u_*, the temperature and humidity scales, Θ_*, and q_*, the roughness length, z₀, the zero-plane displacement, d, as well as the temperature and humidity values Θ_r and q_r at the height z_r = z₀ + d. With these data we can determine the individual γ-coefficients in the empirical Businger-Dyer and O'KEYPS relations. This is the main interest of this study. It is found that the computed empirical coefficients appreciably depends on the thermal stratification in the atmospheric surface layer. These estimates document that the γ's apparently vary so considerable within the stability regime that the usually adopted constant coefficients were not suitable in these cases. Moreover, one is led to the further important result that the parameters z₀ and d found here, considerably differ from those values obtained with the conventional γ-coefficients suggested in the literature.

On the Sublayer-Stanton Numbers of Heat and Matter for Different Types of Natural Surfaces

Gerhard Kramm, Thomas Foken, Nicole Mölders, Hans Müller, and Kyaw Tha Paw U

Beitr. Phys. Atmosph. 69, 417-430 (1996).

It is well established that the transfer of heat and matter across the interfacial sublayer in the immediate vicinity of any surface is strongly controlled and limited by molecular transfer properties, whereas the shear stress is destroyed at the surface by skin friction and by form drag. The sublayer-Stanton number, B_i, can be considered as a measure of the difference in the corresponding transfer of momentum and heat as well as matter to and from surfaces, no matter how irregular they may be. This quantity plays, therefore, an important role in modelling the exchange of heat and matter between the atmosphere and the vegetation-soil system and natural water systems, respectively, and, hence, in deriving surface fluxes of sensible and latent heat by remote sensing techniques. Usually, B_i is related to the ratio z₀/z_p, where z₀ is the roughness length for momentum, and z_p is that for heat and matter, respectively. It is argued that the derivation of this relationship is not straight-forward. Instead, more physically adequate relationships are presented. Sublayer-Stanton numbers of heat and matter for different types of surfaces are presented and discussed. The results are derived from the vertical profile data of wind speed, temperature, humidity and HNO₃ concentrations, collected during the GREIV I 1974 project and the experiment 'ecosystem wheat' of the EUROTRAC subproject BIATEX, and from model studies for aerodynamically smooth surfaces. The model results for aerodynamically smooth surfaces are based on Roth's (1972) modified Heisenberg model for the spectral energy transfer under locally isotropic conditions. These results are compared with those provided by Reichardt's (1951) approach for an effective diffusivity. The B_i^-1-values obtained from the field and the model studies are much larger values than those suggested by Garratt and Hicks (1973).

On the Relationship between the Roughness Length of a Scalar Quantity and the Corresponding Sublayer-Stanton number

Gerhard Kramm, Hans Müller, and Ralph Dlugi

Meteorol. Zeitschrift, N.F., 4, 209-212 (1995).

Considering Sheppard's effective diffusivity approach for the molecular-turbulent sublayer, the relationship between the roughness length of a scalar quantity, z_p, and the corresponding sublayer-Stanton number, B_i, is re-formulated. This re-formulation leads to B_i^-1 = κ^-1 ln (1 + z₀/z_p), where z₀ is the roughness length for momentum. Based on this equation, it is evident that (a) the relationship B_i^-1 = κ^-1 ln (z₀/z_p) commonly used is a doubtful approximation for the interfacial sublayer, and (b) the sublayer-Stanton number is positive-definite even if z_p ≥ z₀ > 0. This is in contrast to negative B_i^-1 values found in the literature. Moreover, it is shown that B_i^-1 derived with Sheppard's approach are much smaller than those provided by the more adequate Reichardt's approach.

A Re-Evaluation of the Webb-Correction Using Density-Weighted Averages

Gerhard Kramm, Ralph Dlugi, and Donald H. Lenschow

J. Hydrol. 166, 283-292 (1995).

Results from a re-evaluation of the flux correction suggested by Webb et al. (1980) are presented and discussed. This re-evaluation is based on the equation of continuity as well as the budget equations for dry air, water vapour and atmospheric trace species, where a density-weighted averaging procedure introduced by Hesselberg (1926) is used. This averaging procedure seems to be more appropriate than that of Reynolds, especially in the case of atmospheric trace species. Consequences derived from this flux correction referring to the exchange of atmospheric trace gases between the atmosphere and the ground (vegetation, soil, water) are pointed out.

Estimation of the Surface Layer Parameters from Wind Velocity, Temperature and Humidity Profiles by Least Squares Methods

Gerhard Kramm

Boundary-Layer Meteorol. 48, 315-327 (1989).

The estimation of the surface layer parameters u_* (friction velocity), Θ_* and q_* (temperature and humidity scales), Θ_r and q_r (temperature and humidity reference values), z₀ (roughness length) and d (zero-displacement) from vertical profiles of wind velocity, temperature and humidity by least squares methods is described. The estimation is based on the flux-gradient relationships and the constant flux assumption for the transfer of momentum, sensible heat and matter near the Earth,s surface. Test calculations were carried out with the vertical profile data from the GREIV I 1974 experiment and the Great Plains Turbulence Project.

Evaluation of Micrometeorological Methods for Determining the Evapotranspiration over Natural Surfaces

Gerhard Kramm, Ralph Dlugi, Franz X. Meixner, Hans Müller, and Peter Werle

In: Tetzlaff, G., Grünewald, U. (Edn.), 2. Tagung des Fachausschusses Hydrometeorologie, 15.-16. November 1999. Mitt. Meteorol. Inst., Univ. Leipzig 16, 37 - 56 pp. (1999).

In this contribution micrometeorological techniques like eddy covariance and variance methods are elucidated, where their accuracy is evaluated on the basis of various criteria like the stationary state criterion and the fetch requirement, which have to be fulfilled to deduce reliable results on evapotranspiration. Furthermore, a brief overview on micrometeorological modelling techniques is given.

Evaluation of Conditional Sampling Methods

Gerhard Kramm, Norbert Beier, Ralph Dlugi, and Hans Müller

Beitr. Phys. Atmosph. 72, 161-172 (1999).

In this paper the main differences between two different conditional sampling techniques namely the true conditional sampling (CS) method often called eddy accumulation method and the relaxed conditional sampling (RCS) method usually denoted as relaxed eddy accumulation method are described. It is shown that, in principle, the CS method should be able to provide true vertical eddy fluxes of trace species. Whereas the RCS method is based on a one-and-a-half-order closure scheme which has to be verified. The relative accuracy of the latter technique is estimated using Bowen-ratio similarity principles. It is found that the relative accuracy of RCS techniques is less satisfying compared to other micrometeorological methods like the conventional modified Bowen ratio method. Thus, RCS techniques should not be considered as an alternative to the CS method. It is argued that the latter method provides the only possibility to directly measure vertical eddy fluxes as long as fast-response physico-chemical analysers for eddy covariance (EC) measurements are unavailable.

Long-term numerical investigations on the water budget quantities predicted by the hydro-thermodynamic soil vegetation scheme (HTSVS) - part I: Description of the model and impact of long-wave radiation, roots, snow, and soil frost

Nicole Mölders, Ulrike Haferkorn, Jürgen Döring, and Gerhard Kramm

Meteorol. Atmos. Phys. (in press, 2002)

An earlier version of HTSVS was further developed to numerically investigate the long-term evolution of water budget elements (water supply to the atmosphere, ground water recharge, change in storage) in climate studies. In doing so, parameterizations of root effects, infiltration, soil frost, and snow insulation were included into HTSVS to predict these water budget elements for a period of 2050 days continuously covered by routine data of a lysimeter and a climate station. The results of simulations without and with inclusion of new parameterizations as well as various sensitivity studies indicate that the insulating effect of a snow-pack, soil water freezing as well as the Dufour- and Ludwig-Soret-effects play a notable role on the long-term water budget and soil temperature evolution. Including frost effects yields improved soil temperature predictions. Snow density and, hence, snow depth play a key role for the prediction of soil temperature, freezing and the water supply to the atmosphere, but hardly affect deep soil water fluxes like recharge in the long-term sum. The results also show that the kind of vertical root distribution can be important for predicting water budgets. Based on these results we conclude that land surface models considered for long-term integration purposes require parameterizations of soil frost, snow and water uptake by roots to appropriately catch the broad cycle of soil water budget elements.

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

Nicole Mölders, Ulrike Haferkorn, Jürgen Döring, and Gerhard Kramm

Meteorol. Atmos. Phys. (in press, 2002)

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 by roots 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 the 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.

Evaluation of Simulated Water Budget by Means of Measurements at Brandis Lysimeter Station

Nicole Mölders, Ulrike Haferkorn, Siegfried Knappe, Jürgen Döring, and Gerhard Kramm

In: Tetzlaff, G., Grünewald, U. (Edn.), 2. Tagung des Fachausschusses Hydrometeorologie, 15.-16. November 1999. Mitt. Meteorol. Inst., Univ. Leipzig 16, 67 - 83 pp. (1999).

Lysimeter- tensiometer-, and soil-temperature-data recorded at Brandis (51.32°N, 12.62°E, 133 m NN, about 50 km south-east of Leipzig) are used to evaluate a hydro-thermodynamic soil-vegetation-scheme (HTSVS) which has been further developed by including a parameterization of root effects. HTSVS is driven by meteorological datameasured at Brandis. Comparing simulated and observed yield of ground water, matric potential, soil temperature, and evapotranspiration shows that HTSVS well performs in spring and fall. Discrepancies occurring in winter may be attributed to the lack of a snow- and frost-parameterization. In summer, HTSVS provides better results when precipitation events are equally distributed in time than for strong precipitation events following long dry periods. Although the day to day differences with and without simulation of root effects hardly differ, accumulated recharge and evapotranspiration will meet slightly better the observed sums after 2049 days of integration if root effects are considered.

On the influence of the parameterization of soil and vegetation processes upon the simulated water-cycle relevant quantities

Nicole Mölders and Gerhard Kramm

In: Fohrer, N., Döll, P. (Edn.), Modellierung des Wasser- und Stofftransports in großen Einzugsgebieten. Kassel University Press, 163-172 pp. (1999).

Two different soil-vegetation-schemes are compared with each other and evaluated against observational data. Sensitivity studies on parameters required by the schemes were carried out. The results substantiate that predicted evapotranspiration, local cloud and precipitation formation may be sensitive to the parameters and parameterizations of the soil and plant processes.

On the influence of bulk-parameterization schemes of cloud microphysics on the predicted water cycle relevant quantities - A case study

Nicole Mölders, Gerhard Kramm, Manfred Laube, Armin Raabe

Meteorol. Zeitschrift, N.F., 6, 21-32 (1997).

Two different bulk-parameterization schemes of cloud microphysics alternatively used in a meso-beta-scale meteorological model are compared to elucidate their influence on the predicted atmospheric water cycle. The different parameters (e.g., ice crystal types, density of ice) and parameterizations (e.g., terminal velocit y, riming, accretion) used by the schemes cause differences in the mixing ratios of the predicted water substances and in the release and consumption of heat resulting in appreciable differences in the vertical motion. The first scheme leads to a larger and more stratiform cloud coverage than the second one which provides broken cloud fields. Consequently, the latter scheme predicts a more shower-like precipitation with locally greater intensities while the first scheme provides a homogeneous precipitation horizontally larger extended with lower intensity. Moreover, the domain averaged maximal precipitation occurs in the afternoon for the second scheme and in the evening for the first scheme. Altogether, the differences in predicted cloud coverage, insolation, vertical motions, precipitati on and soil wetness caused by the different microphysical parameterizations applied, strongly affect the partitioning of energy between sensible and latent heat at the Earth's surface and hence, the amount of water locally re-provided to the atmosphere.

On the parameterization of ice microphysics in a mesoscale a weather forecast model

Nicole Mölders, Manfred Laube, and Gerhard Kramm

Atmos. Res. 38, 207-235 (1995).

Numerical experiments with a three-dimensional mesoscale weather forecast model are performed to investigate the influence of parameterized microphysics on predicted cloud structures and precipitation. Both the warm and the cold path of cloud and precipitation formation are taken into account. The parameterization of the warm path processes considers condensation, autoconversion, accretion, evaporation of both cloud water and rain water, and the sedimentation of rain. The parameterization of the cold path processes consists of water vapor deposition, sublimation, riming, melting, and also the sedimentation of ice crystals. Studies considering only the warm path processes showed that this scheme is overload when strong vertical motions and ice topped clouds are to be simulated. The inclusion of the cold path processes provides a more realistic description of the dynamics and microphysics of the troposphere, and leads to an improvement in the model performance. The results of sensitivity studies with and without riming show that the inclusion of riming leads only to slightly more adequate results. Further numerical experiments have been performed to investigate the sensitivity of the model to different parameters and processes. It is substantiated by all of these numerical studies that the relative humidity and water substance mixing ratio fields were only strongly altered by turning off the ice phase or the riming process. The results of the simulations are presented and discussed on the basis of the analysis and satellite data. Moreover, predicted precipitation rates over land are compared to observed data. Estimation of skill and uncertainty are determined for further model evaluation.

A SVAT Scheme for NO, NO₂, and O₃ - Model Description and Test Results

Gerhard Kramm, Norbert Beier, Thomas Foken, Hans Müller, Peter Schröder, and Wolfgang Seiler

Meteorol. Atmos. Phys. 61, 89-106 (1996).

A soil/vegetation/atmosphere transfer (SVAT) scheme for determining the dry deposition and/or emission fluxes of NO, NO₂, and O₃ in the atmospheric surface layer over horizontally uniform terrain covered with fibrous canopy elements is presented and discussed. This transfer scheme is based on the micrometeorological ideas of the transfer of momentum, heat and matter near the Earth's surface, where chemical reactions between these trace gases are included. The fluxes are parameterized by first-order closure principles. The uptake processes by vegetation and soil are described in accord with Deardorff (1978). The SVAT scheme requires only routine data of wind speed, dry- and wet-bulb temperatures, short- and long-wave radiation, and the concentrations of O₃ and nitrogen species provided by stations of monitoring networks. First model results indicate that the dry deposition fluxes of NO, NO₂, and O₃ are not only influenced by meteorological and plant-physiological parameters, but also by chemical reactions between these trace species and by NO emission from the soil. Furthermore, a small displacement in the concentrations of NO, NO₂, and O₃ within in the range of the detection limits of the chemical sensors can produce large discrepancies in the flux estimates, which are manifested here by the shift from height-invariant fluxes substantiated by the photostationary state to strongly height-dependent fluxes caused by the departure from that state. Especially in the case of these nitrogen species the widely used 'big leaf' multiple resistance approach, which is based on the constant flux approximation, seems to be inappropriate for computing dry deposition fluxes and deposition velocities.

Determining the Dry Deposition of SO₂, O₃, NO, and NO₂ at the SANA Core Station Melpitz

Gerald Spindler, Nicole Mölders, Jörn Hansz, Norbert Beier, and Gerhard Kramm

Meteorol. Zeitschrift, N.F., 5, 205-220 (1996).

In 1992 the SANA core station was installed at Melpitz near Torgau providing, among other things, vertical profile data of the concentrations of SO₂, O₃, NO, and NO₂, wind speed, dry- and wet-bulb temperatures. Based on the data of July and October 1992, dry deposition fluxes were determined applying a one-dimensional diagnostic model of the atmospheric surface layer, where in the case of the triad NO-NO₂-O₃ the model calculations were carried out with and without chemical reactions to investigate the influence of the latter on dry deposition. The numerical results substantiate that the vertical profiles of fluxes and, hence, deposition velocities can strongly be affected by chemical reactions leading to larger absolute values of fluxes and deposition velocity. Furthermore, the calculated fluxes also depend slightly on vegetation activity, photochemically active radiation as well as on the turbulent mixing of the atmospheric surface layer.

On the Dry Deposition of Ozone and Reactive Nitrogen Species

Gerhard Kramm, Ralph Dlugi, Geoffrey J. Dollard, Thomas Foken, Nicole Mölders, Hans Müller, Wolfgang Seiler, and Herman Sievering

Atmos. Environ. 29 (21), 3209-3231 (1995)

Dry deposition of ozone and reactive nitrogen compounds, such as NO, NO₂, NO₃, N₂O₅, HNO₃, NH₃, and NH₄NO₃, is examined in the context of numerical methods. These methods are based on the generally accepted micrometeorological ideas of the transfer of momentum, sensible heat, and matter near the Earth's surface, where chemical reactions among these trace species are considered. The fluxes in the turbulent region of the atmospheric surface layer are parameterized by first-order closure principles. The uptake processes by vegetation and the soil are described by a Deardorff-type soil-vegetation-atmosphere transfer scheme. As in the case of HNO₃ and NH₃ the resistance of the system vegetation - soil against uptake of matter seems to be of minor importance, parameterization approaches for the more important transfer resistances of the interfacial sublayer adjacent to the surface are evaluated. The model results show that especially the dry deposition fluxes of reactive nitrogen compounds are not only influenced by micrometeorological and plant-physiological parameters, but also strongly affected by chemical reactions. In most cases, the fluxes of these trace constituents vary strongly with height and often show a change of direction. These flux results differ considerably from those derived with the constant flux approximation, sometimes of up to several hundred percent. Thus, in such cases the most widely used 'big leaf' multiple resistance approach which is based on the constant flux approximation seems to be inappropriate for deriving dry deposition fluxes and deposition velocities of reactive nitrogen compounds.

Wet Deposition

Fire Safety Research

For further information or reprints please contact kramm@gi.alaska.edu

Last update: November 12, 2003