The Askervein Hill Project: Mean wind variations at fixed heights above ground

This is one of a series of papers on the Askervein Hill Project. It presents results on the variations in mean wind speed at fixed heights (z) above the ground from linear arrays of anemometer posts and towers. Most of the data are for z = 10 m but some are for z = 3 m. Selected and directionally grouped data from the 55 Mean Flow runs are presented together with mean flow data from Askervein '83 Turbulence runs. Comparisons are made between the data and guideline estimates of fractional speed-up ratio at hilltop locations and between the data and MS3DJH/3 model predictions along the tower lines. There is good agreement in most cases.     

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.     

A dynamical analysis of the drag conditions at the sea surface

When applied to a sea surface, shortcomings are noted for the ordinary classification of drag conditions at rigid underlying surfaces according to the Reynolds roughness number Re _s . It is shown that in the case of mobile underlying surfaces, it would be more natural to use the dynamical classification of drag conditions according to the order of magnitude of the ratio ( = /) of the momentum flux toward the waves ( _w) to the viscous momentum flux through the surface ( _w). The relevant estimates of for the main stages of development of the wind waves indicate that the observed values of the drag coefficient of the sea surface correspond to the case of underdeveloped roughness.     

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.     

MCC and gull flight behavior

Wintertime observations of mesoscale cellular convection (MCC) over the East China Sea have resulted in criteria that have a remarkable similarity to those reported by Woodcock (1975) in the study of thermals and gull flight behavior. It has been determined that the surface wind speed (V) and the air-sea temperature difference (T) prescribe unique and compatible conditons for both the occurrence of MCC and soaring by sea gulls. Specifically, the onset of MCC when V is between 5 and 9 m s^–1 is inversely proportional to T in the range 5 to 7 °C. Elsewhere, the onset of MCC occurs under conditions of direct proportionality between V and T. Necessary conditions for the occurrence of MCC due to heating from below are T 5 °C and V 5 m s^–1. The boundaries of the convective regime for MCC are discussed and interpreted in accordance with the regime for sea-gull soaring and similarity concepts.     

Markov-chain simulation of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerian velocity variance

The Langevin equation is used to derive the Markov equation for the vertical velocity of a fluid particle moving in turbulent flow. It is shown that if the Eulerian velocity variance _wE is not constant with height, there is an associated vertical pressure gradient which appears as a force-like term in the Markov equation. The correct form of the Markov equation is: w(t + t) = aw(t) + b _wE + (1 – a)T _L ( _wE ²)/z, where w(t) is the vertical velocity at time t, a random number from a Gaussian distribution with zero mean and unit variance, T _L the Lagrangian integral time scale for vertical velocity, a = exp(–t/T _L), and b = (1 – a ²)^1/2. This equation can be used for inhomogeneous turbulence in which the mean wind speed, _wE and T _L vary with height. A two-dimensional numerical simulation shows that when this equation is used, an initially uniform distribution of tracer remains uniform.     

Major wet interval in white mountains medieval warm period evidenced inδ 13C of bristlecone pine tree rings

A long ¹³C chronology was developed from bristlecone pine (Pinus longaeva) at the Methuselah Walk site in the White Mountains of California. The chronology represents cellulose from five-year ring groups pooled from multiple radii of multiple trees. The most dramatic isotopic event in the chronology appears from A.D. 1080–1129, when ¹³C values are depressed to levels ~ 2 below the mean for the period A.D. 925–1654. This isotopic excursion appears to represent a real event and is not an artifact of sampling circumstances; in fact, a similar excursion occurs in a previously-reported, independent ¹³C chronology from bristlecone pine. By carbon isotope fractionation models, the shift to low ¹³C values is consistent with abundant soil moisture, permitting leaf stomata to remain open, and allowing ready access of CO₂ from which carbon fixation may discriminate more effectively against¹³C in favor of¹²C. According to this model, the¹³C-depleted 50-yr isotopic excursion represents the wettest period in the White Mountains in the past 1000 yr, during which isotope-reconstructed July Palmer Drought Severity Indices averaged ~ +2.2.     

Examination of ‘global atmospheric temperature monitoring with satellite microwave measurements’: 2. Analysis of satellite data

Using Microwave Sounding Unit (MSU) channel 2 (Ch. 2, 53.74 GHz) data, Spencer and Christy (1992a) determined that the earth exhibits no temperature trend in the period 1979–90, while other authors find a temperature increase of roughly 0.1 K. Based on a theoretical analysis Prabhakara et al. (1995) showed that the information about the global atmospheric temperature deduced from MSU Ch. 2 observations has a small contamination, T ₂, as a result of the attenuation due to hydrometeors in the atmosphere. A method is developed in this study, that utilizes coincident measurements made by MSU in Ch. 1 (50.3 GHz), to estimate this T ₂ over the global oceans. The magnitude of T ₂ is found to be about 1 K over significant parts of the tropical oceanic rain belts and about 0.25 K over minor portions of the mid-latitude oceanic storm tracks. Due to events such as El Niôo, there is variability from year to year in the rain areas and rain intensity leading to significant change in the patterns of T ₂. The patterns of T ₂ derived for March 82 and March 83 reveal such a change. When averaged over the global oceans, from 50° N to 50° S, T ₂ has a value of 0.25 and 0.29 K for March 1982 and 1983, respectively. Due to these reasons the interannual temperature change derived by Spencer and Christy from MSU Ch. 2 will contain a residual hydrometeor effect. Thus in evaluating decadal trend of the global mean temperature of the order of 0.1 K from MSU Ch. 2 data one has to take into account completely the contamination due to hydrometeors.     

Stable Isotope Ratios: Hurricane Olivia

The oxygen and hydrogen isotopic compositions of rains from HurricaneOlivia (1994) in the eastern Pacific were measured. The rains werecollected on 24 and 25 September during airplane flights conducted at anelevation of 3 km. Hurricane Olivia peaked in intensity to a category-4storm between the two dates. Isotope ratios of rains from HurricaneOlivia were markedly lower ( ¹⁸O = –13.9to –28.8) than that of rain collected from a thunderstormat an elevation of 2.3 km outside the influence of Olivia (¹⁸O = –3.8). A distinct decrease in isotoperatios from the first day to the next ( ¹⁸O =–18.4 to –21.9) in Hurricane Olivia wasattributed to decreased updraft velocities and outflow aloft. Thisshifted the isotopic water mass balance so that fewer hydrometeors werelifted and more ice descended to flight level. A decrease in the averagedeuterium excess from the first day to the next (d = 15.5 to 7.1)was attributed to an increase in the relative humidity of the watervapor `source' area. We hypothesize that the `source' region for therain was in the boundary layer near the storm center and that becausethe hurricane was at peak intensity prior to the second day the relative humidity was higher.     

A note on the analogy between momentum transfer across a rough solid surface and the air-sea interface

The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re _s =h _s u _*/, whereh _s is the effective roughness height, -viscosity,u _*-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the sea roughness cannot be explained only on the basis of the classification of aerodynamic conditions of the sea surface proposed by Kitaigorodskii and Volkov (1965) and Kitaigorodskii (1968) even though the latter approach gains some support from recent experimental studies (see for example Geernaertet al. 1986). In this paper, an attempt is made to explain some of the recently observed features of the variability of surface roughness (Toba and Ebuchi, 1991; Donelanet al., 1993). The fluctuating regime of the sea surface roughness is also described. It is shown that the contribution from the dissipation subrange to the variability of the sea surface can be very important and by itself can explain Charnock's (1955) regime.     

On the inner-layer scale height of boundary-layer flow over low hills

Jackson and Hunt's (1975) equation for the depth of the inner layer of flows over low hills does not depend on any closure assumption as contrarily supposed in literature. This equation contains a constant which can arbitrarily be specified. It is suggested that this inner-layer constant should be determined from experimental data. A preliminary check with some data from the Askervein experiment suggests that Jackson and Hunt's equation fits these data almost as well as Jensen's equation provided that fitted inner-layer constants are used.     

Carbon dioxide and the δ18O record of late-Quaternary climatic change: a global model

A dynamical model for the late-Quaternary global variations of ¹⁸O, mean ocean surface tempeature , ice mass I, deep ocean temperature , and atmospheric carbon dioxide concentration , is constructed. This model consists of two diagnostic equations (for ¹⁸O and ), and three prognostic equations (for I, , and ) of a form studied extensively in previous articles. The carbon dioxide equation includes forcing by a representation of the Milankovitch earth-orbital radiation effects, and contains a basic instability that drives a free oscillation of period near 100,000 years. The system is constrained to conserve mass and energy, contain physically plausible feedbacks including a system time constant no greater than 10.000 years, and be robust (i. e., structurally stable in the presence of expected noise levels and uncertainties in values of coefficients). Within the limits of these constraints, coefficients are chosen such that (i) the solution gives a good fit to the observed SPECMAP ¹⁸O variations, and (ii) the ice mass variations are qualitatively similar to the ¹⁸O variations. The predicted long term variations of sea surface temperature and atmospheric carbon dioxide are in reasonably good agreement with the limited observational evidence available for these quantities, while the predicted variations of deep ocean temperature remain to be verified when paleoclimatic estimates of this quantity become available. The relative contributions of ice mass changes and surface water temperature changes to the variations of ¹⁸O at any time are given by the model.     

Reconstruction of the last deglaciation: deconvolved records of δ18O profiles,micropaleontological variations and accelerator mass spectrometric14C dating

Bioturbation acts as a low-pass filter in displacing and reducing the amplitudes of stratigraphic signals. This often leads to a loss of high-frequency events in the stratigraphic record. In addition, when considering an isotopic signal ¹⁸O,¹⁴C measured in stratigraphic carriers, such as foraminifera, bioturbation and carrier abundance changes can create artifacts which may be falsely interpreted as leads or lags in the paleoclimatic record.We presenthere a model in which bioturbationis treated as a time-invariant filter whose impulse response function (IRF) is like that of a first-order system. The method involves first deconvoluting the abundance curves of the carriers and then the isotopic signals using the restored carrier abundances. This analysis was initially used to artificially generate ideal curves, with the aim of qualitatively modelling the effects of bioturbation. Following this, deconvolved curves were obtained using data from the core CH73-139C using ¹⁸O, A. M. S. C-14 ages, and abundances of two planktonic foraminifera:G. bulloides andN. pachyderma left-coiling. A comparison of the data with the unmixed curves enables separation of the bioturbation artifacts and the construction of a common deglaciation curve based on the restored signals.Importantly, the model emphasizes some severe limitations of mathematical analysis of stratigraphic signals.     

One-dimensional checkerboards and blending heights

We analyze the checkerboard problem of many alternating surfaces with different properties, on scales up to (say) 3,000 m. Power-law representations of the vertical profiles of mean wind speed and eddy diffusivity lead to solutions in terms of Kelvin and trigonometric functions.These solutions are used to determine blending heights (_*), where deviations from the mean of concentration, or of vertical flux density, fall to some small fraction, , of their value at the surface. Values of _*are important for regional and larger-scale meteorological models. In smaller scale micrometeorological studies, they may serve also as the top levels of surface boundary layers.An important result for both theoretical and experimental contexts is that deviations of flux persist with elevation much more strongly than those of concentration, so that, in general, _* should be based on flux rather than concentration. Representative values of _*, for = 0.05, are of order 5 and 30 m for surface pattern wavelengths of 10² and 10³ m, respectively. Values of _* are robust to changes in adopted power-law indices, and are independent of wind speed. Surface roughness has a mild but calculable effect.     

On Modelling the One-Dimensional Atmospheric Boundary Layer

Several commonly used turbulence closure schemes forthe atmospheric boundarylayer (ABL) are applied to simulate neutral, nocturnal and diurnal cyclesituations in a one-dimensional ABL. Results obtained with the differentschemes, E-, E- and its modified versions, and twoversions ofthe q ² Level 2.5, are compared and discussed.     

The carbon isotopic ratio of atmospheric carbon dioxide at Tsukuba,Japan

To find out the secular and seasonal trends of the ¹³C value and CO₂ concentration in the surface air and the determination of the ¹³C in the atmospheric CO₂ collected at Tsukuba Science City was carried out during the period from July 1981 to October 1983. The monthly average of the ¹³C value of CO₂ in the surface air collected at 1400 LMT ranged from -7.52 to \s-8.45 with an average of -7.96±0.25 and the CO₂ concentration in the air varied from 334.5 l 1^-1 to 359 l 1^-1 with an average of 347.2±6.3 l 1^-1. The ¹³C value is high in summer and low in winter and is negatively correlated with the CO₂ concentration. In general, the relationship between the ¹³C and the CO₂ concentration is explainable by a simple mixing model of two different constant carbon isotopic species but the relationship does not always follow the model. The correlation between the ¹³C value and the CO₂ concentration is low during the plant growth season and high at other times. The observed negative deviation of the ¹³C value from the simple mixing model in the plant growth season is partly due to the isotopic fractionation process which takes place in the land biota.     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.     

Nitrogen compound emission from biomass burning in tropical African savanna FOS/DECAFE 1991 experiment (Lamto,Ivory Coast)

Gaseous nitrogen compounds (NO _x , NO _y , NH₃, N₂O) were measured at ground level in smoke plumes of prescribed savanna fires in Lamto, in the southern Ivory Coast, during the FOS/DECAFE experiment in January 1991. During the flaming phase, the linear regression between [NO _x ] and [CO₂] (differences in concentration between smoke plumes and atmosheric background) results volumic emission ratio [NO _x ]/[CO₂]=1.37×10^–3 with only slight differences between heading and backing fires. Nearly 90% of the nitrogen oxides are emitted as NO. Average emission ratios of other compounds are: 1.91, 0.047, and 0.145×10^–3 for NO _y , NH₃ and N₂O, respectively. The emission ratios obtained during this field experiment are compred with corresponding values measured during former experiments with the same plant species in combustion chambers. An accurate determination of both the biomass actually burned and of the plant nitrogen content, allows an assessment of emission fluxes of N-compounds from Guinean savanna burns. Preliminary results dealing with the influence of fire on biogenic emissions from soils are also reported.     

The impact of turbulence closure schemes on predictions of the Mixed Spectral Finite-Difference model for flow over topography

Impacts of different closure schemes in the Mixed Spectral Finite-Difference model (Beljaarset al., 1987) for neutrally stratified atmospheric surface-layer flow over complex terrain are studied. Six different closure schemes, (Z+z ₀), Mixing Length,E–(Z+z ₀),E–,E–– andq ² l are compared. Model results for flow over an infinite series of sinusoidal ridges are examined in the context of the inner and outer layers defined by Jackson and Hunt (1975). Results are compared with rapid distortion estimates of the changes in normal stresses. The effects of streamline curvature are also examined in a qualitative sense.     

The wind-induced shaping and migration of an isolated dune: A numerical experiment

Numerical experiments are carried out to simulate the development and migration of a barchan dune starting with a conical pile of sand. Such an experiment is done in three steps: (1) computation of the steady-state wind field over and around a barchan using the numerical meso-scale simulation model FITNAH, whereby the horizontal variation of the friction velocity is also calculated; (2) computation of the sand transport using the friction velocity in the transport formula by Lettau and Lettau (1978); (3) computation of the erosion and deposition rates as the divergence of the sand transport, where a special treatment is used for the slip-face of the barchan dune. Adding these rates to the height field leads to a different shape of the dune after a time step t _h . Then this procedure has to be repeated for the next time step t _h .The results are in good agreement with observations: the initial pile of sand develops wings (horns) and a slip-face between them. In addition, flow separation over the lee-side can be simulated. Finally, the tendency to form a barchan in equilibrium is considered.