Averaging Intervals For Spectral Analysis Of Nonstationary Turbulence

We formulate a method for determining the smallest time interval Tover which a turbulence time series can be averaged to decompose it intoinstantaneous mean and random components. From the random part the method defines the optimal interval (or averaging window) AW over which this part should be averaged to obtain the instantaneous spectrum. Both T and AW vary randomly with time and depend on physical properties of the turbulence. T also depends on the accuracy of the measurements and is thus independent of AW. Interesting features of the method are its real-time capability and the non-equality between AW and T.     

Reactions of alkoxy radicals under atmospheric conditions: The relative importance of decomposition versus reaction with O2

The reactions of alkoxy radicals determine to a large extent the products formed during the atmospheric degradations of emitted organic compounds. Experimental data concerning the decompositions, 1,5-H shift isomerizations and reactions with O₂ of several classes of alkoxy radicals are inconsistent with literature estimations of their absolute or relative rate constants. An alternative, although empirical, method for assessing the relative importance under atmospheric conditions of the reactions of alkoxy radicals with O₂ versus decomposition was derived. This estimation method utilizes the differences in the heats of reaction, (H)=(H_{decomposition}–H_{O 2 reaction}), between these two reactions pathways. For (H)[22–0.5(H_{O 2 reaction})], alkoxy radical decomposition dominates over the reaction with O₂ at room temperature and atmospheric pressure of air, while for (H)[25-0.5(H_{O 2 reaction})], the O₂ reaction dominates over decomposition (where the units of H are in kcal mol^–1). The utility and shortcomings of this approach are discussed. It is concluded that further studies concerning the reactions of alkoxy radicals are needed.     

Three-dimensional modeling of synthetic cold fronts interacting with northern Alpine foehn

Summary The effect of the Alpine orography on prototype cold fronts approaching from the west is investigated by three-dimensional numerical model simulations. The numerical experiments cover a range of parameter constellations which govern the prefrontal environment of the front. Especially, the appearance and intensity of prefrontal northern Alpine foehn varies from case to case.The behaviour of a cold front north of the Alps depends much on the prefrontal condition it encounters. It is found that prefrontal foehn can either accelerate or retard the approaching front.An important feature is the pressure depression along the northern Alpine rim that results from the southerly foehn flow. In cases where this depression compensates the eastward directed pressure gradient associated with the largescale flow, the front tends to accelerate and the foehn breaks down as soon as the front passes. In contrast, the foehn prevents the front from a rapid eastward propagation if it is connected with a strong southerly wind component.No-foehn experiments are performed for comparison, where either the mountains are removed, or the static stability is set to neutral. Also shown are effects of different crossfrontal temperature contrasts.List of Symbols c _F propagation speed of a front - x, y horizontal grid spacing (cartesian system) - , horizontal grid spacing (geographic system) - t time step - z vertical grid spacing (cartesian system) - cross-frontal potential temperature difference - _i potential temperature step at an inversion - E turbulent kinetic energy - f Coriolis parameter - FGP frontogenesis parameter (see section 2.2) - g gravity acceleration (g=9.81 m s^–2) - vertical gradient of potential temperature - h terrain elevation (above MSL) - h _i height of an inversion (h _i =1000 m MSL) - H height of model lid (H=9000 m MSL) - K _M exchange coefficient of momentum - K _H exchange coefficient of heat and moisture - longitude - N Brunt-Väisäla-frequency - p pressure - Exner function (=T/) - latitude - q _v specific humidity - R _d gas constant of dry air (R _d =287.06 J kg^–1 K^–1) - density of dry air - t time - T temperature - potential temperature - TFP thermal front parameter (see section 2.2) - u, v, w cartesian wind components - u _g ,v _g geostrophic wind components - horizontal wind vector - x, y, z cartesian coordinates Abbreviations GND (above) ground level - MSL (above) mean sea level - UTC universal time coordinated With 20 Figures     

Numerical integration errors in calculated tropospheric photodissociation rate coefficients

Tropospheric photodissociation rate coefficients (J values) were calculated for NO₂, O₃, HNO₂, CH₂O, and CH₃CHO using high spectral resolution (0.1 mm wavelength increments), and compared to the J values obtained with numerically degraded resolution (=1, 2, 4, 6, 8, and 10 nm, and several commonly used nonuniform grids). Depending on the molecule, substantial errors can be introduced by the larger increments. Thus for =10 nm, errors are less than 1% for NO₂, less than 2% for HNO₂, +6.5% to -16% for CH₂O, -6.9% to +24% for CH₃CHO, and -24% to +110% for O₃. The errors for CH₂O arise from the fine structure of its absorption spectrum, and are prevalently negative (underestimate of J). The errors for O₃, and to a lesser extent for CH₃CHO, arise mainly from under-resolving the overlap of the molecular action spectrum and the tropospheric actinic flux in the wavelength region of stratospheric ozone attenuation. The sign of those errors depends on whether the actinic flux is averaged onto the grid before or after the radiative transfer calculation. In all cases studied, grids with 2 nm produced errors no larger than 5%.     

Standard deviation of vertical two-point longitudinal velocity differences in the atmospheric boundary layer

The standard deviation of vertical two-point longitudinal velocity fluctuation differences is analyzed experimentally with eleven sets of turbulence measurements obtained at the NASA 150-m ground-winds tower site at Cape Kennedy, Florida. It is concluded that /u _*0 is proportional to (fz/u _*0)^0.22, where the coefficient of proportionality is a function of fz/u _*0 and u _*0/fL ₀. The quantities f and L₀ denote the Coriolis parameter and the surface Monin-Obukhov stability length, respectively; u _*0 is the surface friction velocity; z is the vertical distance between the two points over which the velocity difference is calculated; and zz is the mean height of the mid-point of the interval z above natural grade. The results of the analysis are valid for 20<-u _*0/fL ₀<2000.     

Über die mittlere lineare sukzessive Differenz und ihre Anwendung auf die Untersuchung meteorologischer Beobachtungsreihen

Zusammenfassung Eine endliche Reihe (Sequenz) wird als eine der möglichen Permutationen ihrer Glieder aufgefaßt. Es wird gezeigt, daß die Summe der absoluten Differenzen der aufeinanderfolgenden Glieder gleich ist , wo die natürliche Zahlen sind und nur von der Rangordnung der Glieder der Reihe (von der Permutation) abhängen; die _j sind von der Reihenfolge unabhängig und werden durch die Dispersion der Reihenglieder bestimmt. Die _j und die _j werden separat untersucht; der Erwartungswert der erwähnten Differenzsumme wird abgeleitet. Verschiedene bereits bekannte und auch erstmalig hier vorgeschlagene Maßzahlen werden geprüft. An Reihen jährlicher Regenmengen wird die Rolle der _j und der _j und das Verhalten der besprochenen Maßzahlen veranschaulicht.

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Summary A series ofn members can be considered as one of the possible permutations of its members. It is shown that the sum of the linear successive differences is equal to the expression , where the _j are positive integers, dependent only upon the rank-order (the permutation) of the members, while the _j are independent of the order of the succession and are determined by the dispersion of the members of the series. The factors _j and _j are separately investigated; the expected value of the sum of the linear successive differences is established. Various related statistical measures, already in usage and new ones suggested here, are discussed. Series of yearly rainfall amounts are used to show the effects of the _j and _j and to discuss the behaviour of the various measures.

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Résumé Une série, constituée parn valeurs, est regardée comme une des possibles permutations de ces valeurs. L'auteur montre que la somme des différences absolues, qui se présentent entre les valeurs consécutives de la série, est égale à l'expression . Les _j sont des nombres entiers positifs et ne dépendent que de l'ordre des membres de la série, tandis que les _j, indépendants de l'ordre, sont déterminés par la dispersion des membres. Les facteurs _j et _j sont étudiés séparément; l'espérance mathématique de la somme mentionnée est dérivée. Des paramètres statistiques déjà connus ou proposés ici pour la première fois, sont discutés. Le rôle des _j et des _j et le comportement des divers paramètres sont montrés à l'aide de séries de totaux annuels de pluies.

     

Quantifying the Impact of Global Climate Change on Potential Natural Vegetation

Impacts of climate change on vegetation are often summarized in biome maps, representing the potential natural vegetation class for each cell of a grid under current and changed climate. The amount of change between two biome maps is usually measured by the fraction of cells that change class, or by the kappa statistic. Neither measure takes account of varying structural and floristic dissimilarity among biomes. An attribute-based measure of dissimilarity (V) between vegetation classes is therefore introduced. V is based on (a) the relative importance of different plant life forms (e.g. tree, grass) in each class, and (b) a series of attributes (e.g. evergreen-deciduous, tropical-nontropical) of each life form with a weight for each attribute. V is implemented here for the most used biome model, BIOME 1 (Prentice, I. C. et al., 1992). Multidimensional scaling of pairwise V values verifies that the suggested importance values and attribute weights lead to a reasonable pattern of dissimilarities among biomes. Dissimilarity between two maps (V) is obtained by area-weighted averaging of V over the model grid. Using V, present global biome distribution from climatology is compared with anomaly-based scenarios for a doubling of atmospheric CO2 concentration (2 × CO2), and for extreme glacial and interglacial conditions. All scenarios are obtained from equilibrium simulations with an atmospheric general circulation model coupled to a mixed-layer ocean model. The 2 × CO2 simulations are the widely used OSU and GFDL runs from the 1980's, representing models with low and high climate sensitivity, respectively. The palaeoclimate simulations were made with CCM1, with sensitivity similar to GFDL. V values for the comparisons of 2 × CO2 with present climate are similar to values for the comparisons of the last interglacial and mid-Holocene with present climate. However, the two simulated 2 × CO2 cases are much more like each other than they are to the simulated interglacial cases. The largest V values were between the last glacial maximum and all other cases, including the present. These examples illustrate the potential of V in comparing the impacts of different climate change scenarios, and the possibility of calibrating climate change impacts against a palaeoclimatic benchmark.     

Small-Scale Variability in the Coastal Atmospheric Boundary Layer

The influence of the main large-scale wind directions on thermally driven mesoscale circulations at the Baltic southwest coast, southeast of Sweden, is examined. The aim of the study is to highlight small-scale alterations in the coastal atmospheric boundary layer. A numerical three-dimensional mesoscale model is used in this study, which is focused on an overall behaviour of the coastal jets, drainage flows, sea breezes, and a low-level eddy-type flow in particular. It is shown that synoptic conditions, together with the moderate terrain of the southeast of Sweden (max. height h₀ 206 m), governs the coastal mesoscale dynamics triggered by the land-sea temperature difference T. The subtle nature of coastal low-level jets and sea breezes is revealed; their patterns are dictated by the interplay between synoptic airflow, coastline orientation, and T.The simulations show that coastal jets typically occur during nighttime and vary in height, intensity and position with respect to the coast; they interact with downslope flows and the background wind. For the assigned land surface temperature (varying ±8 K from the sea temperature) and the opposing constant geostrophic wind 8 m s^-1, the drainage flow is more robust to the opposing ambient flow than the sea breeze later on. Depending on the part of the coast under consideration, and the prevailing ambient wind, the sea breeze can be suppressed or enhanced, stationary at the coast or rapidly penetrating inland, locked up in phase with another dynamic system or almost independently self-evolving. A low-level eddy structure is analyzed. It is governed by tilting, divergence and horizontal advection terms. The horizontal extent of the coastal effects agrees roughly with the Rossby radius of deformation.     

On the Response of the Greenland Ice Sheet to Greenhouse Climate Change

Numerical computations are performed with the three-dimensional polythermal ice-sheet model SICOPOLIS in order to investigate the possible impact of a greenhouse-gas-induced climate change on the Greenland ice sheet. The assumed increase of the mean annual air temperature above the ice covers a range from T = 1°C to 12°C, and several parameterizations for the snowfall and the surface melting are considered. The simulated shrinking of the ice sheet is a smooth function of the temperature rise, indications for the existence of critical thresholds of the climate input are not found. Within 1000 model years, the ice-volume decrease is limited to 10% of the present volume for T 3°C, whereas the most extreme scenario, T = 12°C, leads to an almost entire disintegration, which corresponds to a sea-level equivalent of 7 m. The different snowfall and melting parameterizations yield an uncertainty range of up to 20% of the present ice volume after 1000 model years.     

Statistical properties of 49 years of rainfall rate events

Summary The paper presents a detailed investigation of magnitudes and properties pertaining to the large population of rainfall events recorded during 49 years at the Fabra Observatory in Barcelona. The study includes a statistical analysis of event durationT and rainfall quantityQ together with the statistical rainfall rate parameters: , ²(R) and maximum Rm within an event. The decorrelation time is also analysed. It is found thatQ, T, and can be well modelled by a lognormal distribution, but , ² and Rm are only so for a limited range of precipitation ratesR. The regression analysis between pairs of logarithms of the magnitudes investigated is generally good and a regression coefficient is often better than 0.9. Comparison with published work is also carried out. An attempt is made to discriminate between heavy and non-heavy rainfall rates, and the 50 mm/h threshold is used for the study. The twelve-monthly running average indicates that the rainfall amount has a small increasing trend over the fifty year period. However, this trend is reversed when considering heavy rains. Finally, the return period in years to exceeding a thresholdR within an event is also investigated and the distribution of the population of annual extremes is found to be Gumbel II.With 6 Figures     

Gas-Phase Ozone Oxidation of Monoterpenes: Gaseous and Particulate Products

Atmospheric oxidation of monoterpenes contributes to formation of tropospheric ozone and secondary organic aerosol, but their products are poorly characterized. In this work, we report a series of outdoor smog chamber experiments to investigate both gaseous and particulate products in the ozone oxidation of four monoterpenes: -pinene, -pinene, ³-carene, and sabinene. More than ten oxygenated products are detected and identified in each monoterpene/O₃ reaction by coupling derivatization techniques and GC/MS detection. A denuder/filter pack sampling system is used to separate and simultaneously collect gas and aerosol samples. The identified products, consisting of compounds containing carbonyl, hydroxyl, and carboxyl functional groups, are estimated to account for about 34–50%, 57%, 29–67%, and 24% of the reacted carbon mass for -pinene, sabinene, -pinene, and ³-carene, respectively. The identified individual products account for >83%, 100%, >90%, and 61% of the aerosol mass produced in the ozone reaction of -pinene, sabinene, -pinene, and ³-carene. The uncertainty in the yield data is estimated to be ±50%. Many of the products partition between gas and aerosol phases, and their gas-aerosol partitioning coefficients are determined and reported here. Reaction schemes are suggested to account for the products observed.     

The stably stratified internal boundary layer for steady and diurnally varying offshore flow

A two-dimensional numerical mesoscale model is used to investigate the internal structure and growth of the stably stratified internal boundary layer (IBL) beneath warm, continental air flowing over a cooler sea. Two situations are studied — steady-state and diurnally varying offshore flow. In the steady-state case, vertical profiles of mean quantities and eddy diffusion coefficients (K) within the IBL show small, but significant, changes with increasing distance from the coast. The top of the IBL is well defined, with large vertical gradients within the layer and a maximum in the coast-normal wind component near the top. Well away from the coast, turbulence, identified by non-zero K, decreases to insignificant levels near the top of the IBL; the IBL itself is characterised by a critical value of the layer-flux Richardson number equal to 0.18. The overall behaviour of the mean profiles is similar to that found in the horizontally homogeneous stable boundary layer over land.A simple physical model is used to relate the depth of the layer h to several relevant physical parameters viz., x, the distance from the coast and U, the large-scale wind (both normal to the coastline) and g/, being the temperature difference between continental mixed-layer air and sea surface, is the mean potential temperature and g is the acceleration due to gravity. Excellent agreement with the numerical results is found, with h = 0.014x ^1/2 U (g/)^–1/2.In the diurnally varying case, the mean profiles within the IBL show only small differences from the steady-state case, although diurnal variations, particularly in the wind maximum, are evident within a few hundred kilometres of the coast. A mesoscale circulation normal to the coast, and superimposed upon the mean offshore flow, develops seawards of the coastline with maximum vertical velocities about sunset, of depth about 2 km and horizontal scale 500 km. The circulation is related to the advection, and subsequent decay, of daytime convective turbulence over the sea.     

Bistability of the thermohaline circulation identified through comprehensive 2-parameter sweeps of an efficient climate model

The effect of changes in zonal and meridional atmospheric moisture transports on Atlantic overturning is investigated. Zonal transports are considered in terms of net moisture export from the Atlantic sector. Meridional transports are related to the vigour of the global hydrological cycle. The equilibrium thermohaline circulation (THC) simulated with an efficient climate model is strongly dependent on two key parameters that control these transports: an anomaly in the specified Atlantic–Pacific moisture flux (F_a) and atmospheric moisture diffusivity (K_q). In a large ensemble of spinup experiments, the values of F_a and K_q are varied by small increments across wide ranges, to identify sharp transitions of equilibrium THC strength in a 2-parameter space (between Conveyor On and Off states). Final states from this ensemble of simulations are then used as the initial states for further such ensembles. Large differences in THC strength between ensembles, for identical combinations of F_a and K_q, reveal the co-existence of two stable THC states (Conveyor On and Off)—i.e. a bistable regime. In further sensitivity experiments, the model is forced with small, temporary freshwater perturbations to the mid-latitude North Atlantic, to establish the minimum perturbation necessary for irreversible THC collapse in this bistable regime. A threshold is identified in terms of the forcing duration required. The model THC, in a Conveyor On state, irreversibly collapses to a Conveyor Off state under additional freshwater forcing of just 0.1 Sv applied for around 100 years. The irreversible collapse is primarily due to a positive feedback associated with suppressed convection and reduced surface heat loss in the sinking region. Increased atmosphere-to-ocean freshwater flux, under a collapsed Conveyor, plays a secondary role.     

Modeling Modern and Late Pleistocene Glacio-Climatological Conditions in the North Chilean Andes (29–30 °)

An empirical-statistical climate-glacier model is used to reconstruct Late Pleistocene climate conditions in the south-central Andes of northern Chile (29–30° S). The model was tested using modern climate data and the results compare favorably with key glaciological features presentlyobserved in this area. Using several glaciers at 29° S as casestudies, the results suggest an increase in annual precipitation( P = 580 ± 150 mm, today 400 mm), and a reduction inannual mean temperature ( T = –5.7 ± 0.7 ° C).These data suggest full glacial LGM (Last Glacial Maximum) conditionsfor the maximum glacier advances at 29° S, a scenario that is asynchronous with the timing of maximum advances north of the Arid Diagonal (18–24° S) where late-glacial climate was moderately cold but very humid.The reconstructed case study glaciers at 29° S do not allow conclusions to be drawn about the seasonality of precipitation. However, comparison with regional paleodata suggests intensified westerly winter precipitation and a stable position for the northern boundary of the westerlies at 27° S. However, the meridional precipitation gradients were much steeper than today while the core area of the Arid Diagonal remained fixed between 25–27° S.     

Analytical solutions for the Ekman layer

The PBL equation that governs the transition from the constant-stress surface layer to the geostrophic wind in a neutrally stratified atmosphere for which the eddy viscosityK(z) is assumed to vary smoothly from the surface-layer value U _*z (0.4,U _*=friction velocity,z=elevation) to the geostrophic asymptoteK _GU _*d forzd is solved through an expansion in fd/U _*1 (f=Coriolis parameter). The resulting solution is separated into Ekman's constant-K solution an inner component that reduces to the classical logarithmic form forzd and isO() relative to the Ekman component forzd. The approximationKU _*d is supported by the solution of Nee and Kovasznay's phenomenological transport equation forK(z), which yieldsK–U _*d exp(–z/d), where is an empirical constant for which observation implies, 1. The parametersA andB in Kazanskii and Monin's similarity relation forG/U _* (G=geostrophic velocity) are determined as functions of . The predicted values ofG/U _* and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value ofB based on the assumption of asymptotically constantK is 4.5, while that based on the Nee-Kovasznay model is 5.1; these compare with the observed value of 4.7 for the Leipzig profile. A thermal wind correction, an asymptotic solution for arbitraryK(z) and 1, and an exact (unrestricted ) solution forK(z)=U _*d[1–exp(–z/d)] are developed in appendices.     

A statistical-dynamical downscaling procedure for global climate simulations

Summary A statistical-dynamical downscaling procedure for global climate simulations is described. The procedure is based on the assumption that any regional climate is associated with a specific frequency distribution of classified large-scale weather situations. The frequency distributions are derived from multi-year episodes of low resolution global climate simulations. Highly resolved regional distributions of wind and temperature are calculated with a regional model for each class of large-scale weather situation. They are statistically evaluated by weighting them with the according climate-specific frequency. The procedure is exemplarily applied to the Alpine region for a global climate simulation of the present January climate.List of Symbols west-east mesh size in geographic coordinates south-north mesh size in geographic coordinates N number of large-scale weather classes n number of regional-scale event classes p pressure P probability Ø large-scale event regional-scale event q _v specific humidity potential temperature u west-east wind component v south-north wind componentAbbreviations AGL above ground level - LT local time - UTC universal time coordinated With 13 Figures     

Effect of finite sampling on atmospheric spectra

The effect of a finite averaging time on variances is well known, but its effect on power spectra is less clearly understood. We present numerical solutions for the spectral distortion arising from sampling over a finite time interval T and show that the commonly used filter function (1 – sinc²f T), valid for variances, is a reasonable approximation for power spectra only when T 10 _m , where f is the cyclic frequency, and _m is the dominant time scale of the process. Our results exhibit an increasingly steeper low-frequency roll-off as T decreases relative to _m , indicating that the measured spectrum is subject to a greater suppression of the lower frequencies (f > 1/T) than predicted by (1 – sinc²f T). This suppression is, in a sense, compensated by an overestimation of spectral estimates in the frequency range f 1/T.     

On the representation of frequency spectra in meteorology

The common representation of frequency spectra in meteorology and climatology is discussed. It is pointed out that this representation is misleading since spectral peaks and spectral gaps are obtained even when the spectrum density is monotonously decreasing in the whole frequency range. A plea is made for using the spectrum distribution function, F() which gives an unambiguous picture of the distribution of variance with frequency.     

Numerical modeling of the nocturnal urban boundary layer

A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate , and turbulence intensities u ² and w ² increase rapidly at the upwind edge of the urban area. The Reynolds stress uw displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux w had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.     

Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

E- turbulence model predictions of the neutralatmospheric boundary layer (NABL) are reinvestigated to determine thecause for turbulence overpredictions found in previous applications. Analytical solutions to the coupled E and equations for the case of steady balance between transport and dissipation terms, the dominant balance just below the NABL top, are derived. It is found that analytical turbulence profiles laminarizeat a finite height only for values of closure parameter ratio c ₂ /_e equal toor slightly greater than one, with laminarization as z for greater . The point = 2 is additionally foundthat where analytical turbulent length scale (l) profilesmade a transition from ones ofdecreasing ( < 2) to increasing ( > 2)values with height. Numerically predicted profiles near the NABL topare consistent with analytical findings. The height-increasingvalues of l predicted throughout the NABL with standard values ofclosure parameters thus appear a consequence of 2.5(> 2), implied by these values (c ₂ = 1.92, _{= 1.3}, _{e = 1}). Comparison of numericalpredictions with DNS data shows that turbulence overpredictions obtained with standard-valued parameters are rectifiedby resetting and _e to 1.1 and 1.6, respectively, giving, with c ₂ = 1.92, 1.3, and laminarization of the NABL's cappingtransport-dissipation region at a finite height.