A K-Theory of Dispersion,Settling and Deposition in the Atmospheric Surface Layer

Dispersion estimates with a Gaussian plume model are often incorrect because of particle settling (β), deposition (γ) or the vertical gradient in diffusivity (K _v (z) = K ₀ + μz). These “non-Gaussian” effects, and the interaction between them, can be evaluated with a new Hankel/Fourier method. Due to the deepening of the plume downwind and reduced vertical concentration gradients, these effects become more important at greater distance from the source. They dominate when distance from the source exceeds L _β = K ₀ U/β ², L _γ  = K ₀ U/γ ² and L _μ = K ₀ U/μ ² respectively. In this case, the ratio β/μ plays a central role and when β/μ = 1/2 the effects of settling and K gradient exactly cancel. A general computational method and several specific closed form solutions are given, including a new dispersion relation for the case when all three non-Gaussian effects are strong. A more general result is that surface concentration scales as C(x) ~ γ ⁻² whenever deposition is strong. Categorization of dispersion problems using β/μ, L _γ and L _μ is proposed.     

Parameter sensitivity of a coupled atmosphere-ocean model

 The sensitivity of a coupled model to the oceanic vertical diffusion coefficient κ _v is examined. This is compared to the sensitivity of an ocean-only model forced by mixed boundary conditions (BC). The atmospheric component of the coupled model is a moist energy balance model. The ocean component is a 12-level geostrophic model, defined on a midlatitude β-plane. Atmosphere and ocean are coupled through the fluxes of heat and moisture at their interface. The coupled model contains a number of feedback processes which are not represented in the ocean-only model. This results in a temperature and salinity response to κ _v which is stronger in the coupled model than in the ocean-only model. On the other hand, there is a weaker response in oceanic processes such as meridional heat transport, deep-water formation at high latitudes, etc. Ocean-only sensitivity experiments were also performed with modified BCs, which parametrise the feedback processes included in the coupled model. These are the modified thermal BC of Rahmstorf and Willebrand and a modified freshwater BC proposed in the present study. Large-scale features of the response in oceanic surface fields are well represented with modified BCs. However, the sensitivity of the deep ocean temperature is only partly captured due to local differences in the surface response. The scaling behavior of the zonal overturning stream function was found to depend on the surface BCs. In contrast to this, the meridional overturning stream function basically scales with κ^0.5 _v in all sensitivity experiments. Differences in the heat transport response among the experiments are thus primarily related to differences in the temperature response. Received: 28 February 1997/Accepted: 12 September 1997     

Century-scale variability in a randomly forced,two-dimensional thermohaline ocean circulation model

The response of a two-dimensional thermohaline ocean circulation model to a random freshwater flux superimposed on the usual mixed boundary conditions for temperature and salinity is considered. It is shown that for a wide range of vertical and horizontal diffusivities and a box geometry that approximates the Atlantic Ocean, 200–300 yr period oscillations exist in the basic-state, interhemispheric meridional overturning circulation with deep convection in the north. These fluctuations can also be described in terms of propagating salinity anomalies which travel in the direction of the thermohaline flow. For large horizontal (K _h = 15 × 103 m²/s) and small vertical (K _v = 0.5 × 10^–4 m²/s) diffusivities, the random forcing also excites deca-millennial oscillations in the basic structure of the thermohaline circulation. In this case, the meridional circulation pattern slowly oscillates between three different stages: a large positive cell, with deep convection in the North Atlantic and upwelling in the south; a symmetric two-cell circulation, with deep convection in both polar regions and upwelling near the equator; and a large negative cell, with deep convection in the South Atlantic and upwelling in the north. Each state can persist for 0 (10 kyr).     

Sublayer-Stanton numbers of heat and matter for aerodynamically smooth surfaces: basic considerations and evaluation

Summary 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 normalized eddy diffusivity K_m/v. The results substantiate that with the exception of Sheppard’s K_m/v-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/v-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 parameterization formula for the sublayer-Stanton number is proposed and evaluated. Compared to the B_i ⁻¹-results obtained by numerical integration, this kind of parameterization leads to a relative error of less than 5 percent for roughness Reynolds numbers, η_r, ranging from 30 to 600. Received January 2001 Revised November 5, 2001     

近海海面油类漂流扩散的研究和预测实践

根据珠江口气象站风速与潮汐站潮位资料，对1955－1998年12次El Nino过程的珠江口季风强度与海平面变化特点进行合成分析，结果表明，El Nino发生前一年冬季，珠江口冬季平均风速较常年值大0．4m/s,El Nino发生当年，月平均风速也普遍大于常年，而月平均海平面则普遍较常年偏低，其中10与11月份负距平为6cm左右。东亚地区的季风异常对珠江口海平面异常有着重大的影响。     

Three-dimensional modeling of synthetic cold fronts approaching the Alps

Summary A numerical model was used to study the behaviour of prototype cold fronts as they approach the Alps. Two fronts with different orientations relative to the Alpine range have been considered. One front approaches from west, a second one from northwest. The first front is connected with southwesterly large-scale air-flow producing pre-frontal foehn, whereas the second front is associated with westerly largescale flow leading to weak blocking north of the Alps.Model simulations with fully represented orography and parameterized water phase conversions have been compared with control runs where either the orography was cut off or the phase conversions were omitted. The results show a strong orographic influence in case of pre-frontal foehn which warms the pre-frontal air and increases the cross-frontal temperature contrast leading to an acceleration of the front along the northern Alpine rim. The latent heat effect was found to depend much on the position of precipitation relative to the surface front line. In case of pre-frontal foehn precipitation only falls behind the surface front line into the intruding cold air where it partly evaporates. In contrary, precipitation already appears ahead of the front in the case of blocking. Thus, the cooling effect of evaporating rain increases the cross-frontal temperature difference only in the first case causing an additional acceleration of the front.List of symbols C _pd specific heat capacity of dry air at constant pressure (C _pd =1004.71 J kg^–1 K^–1) - C _pv specific heat capacity of water vapour at constant pressure (C _pv =1845.96 J kg^–1 K^–1) - C _f propagation speed of a front - x, y horizontal grid spacing (cartesian system) - , horizontal grid spacing (geographic system) - t time step - E turbulent kinetic energy - f Coriolis parameter - g gravity acceleration (g=9.81 ms^–1) - h terrain elevation - H height of model lid (H=9000 m) - k Karman constant (k=0.4) - K _Mh horizontal exchange coefficient of momentum - K _Hh horizontal exchange coefficient of heat and moisture - K _Mz vertical exchange coefficient of momentum - K _Hz vertical exchange coefficient of heat and moisture - l mixing length - l _c specific condensation heat (l _c =2500.61 kJ kg^–1) - l _f specific freezing heat (l _f =333.56 kJ kg^–1) - l _s specific sublimation heat (l _s =2834.17 kJ kg^–1) - longitude - m ₁,m ₂,m ₃ metric coefficients - p pressure - Exner function - Pr Prandtl number - latitude - _M profile function - q _v specific humidity - q _c specific content of cloud droplets - q _i specific content of cloud ice particles - q _R specific content of rain drops - q _S specific content of snow - R _d gas constant of dry air (R _d =287.06 J kg^–1 K^–1) - R _v gas constant of water vapour (R _v =461.51 J kg^–1 K^–1) - r _E radius of earth (r _E =6371 km) - Ri _F flux Richardson number - density of dry air - t time - T temperature - _dia period of diastrophy - potential temperature - _v virtual potential temperature - _e equivalent potential temperature - U relative humidity - u, v, w cartesian wind components - u _F ,v _F front-normal and front-parallel wind components - x, y, z cartesian coordinates - w ^* transformed vertical wind component - W _R speed of falling rain - W _S speed of falling snow - z ^* transformed vertical coordinate Abbreviations GND (above) ground level - MSL (above) mean sea level With 12 Figures     

Measurement and investigation of chamber radical sources in the European Photoreactor (EUPHORE)

It is essential to quantify the background reactivity of smog-chambers, since this might be the major limitation of experiments carried out at low pollutant concentrations typical of the polluted atmosphere. Detailed investigation of three chamber experiments at zero-NO _x in the European Photoreactor (EUPHORE) were carried out by means of rate-of-production analysis and two uncertainty analysis tools: local uncertainty analysis and Monte Carlo simulations with Latin hypercube sampling. The chemical mechanism employed was that for methane plus the inorganic subset of the Master Chemical Mechanism (MCMv3.1). Newly installed instruments in EUPHORE allowed the measurement of nitrous acid and formaldehyde at sub-ppb concentrations with high sensitivity. The presence of HONO and HCHO during the experiments could be explained only by processes taking place on the FEP Teflon walls. The HONO production rate can be described by the empirical equation W(HONO)_EUPHORE ^dry = a × j _{NO 2}× exp (− T ₀/T) in the low relative humidity region (RH < 2%, a = 7.3×10²¹ cm⁻³, T ₀ = 8945K), and by the equation W(HONO)_EUPHORE ^humid = W(HONO)_EUPHORE ^dry+ j _{NO 2}× b × RH ^q in the higher relative humidity region (2% < RH < 15%, b = 5.8×10⁸ cm⁻³ and q = 0.36, and RH is the relative humidity in percentages). For HCHO the expression W(HCHO)_EUPHORE = c × j _{NO 2}exp (− T′₀/T) is applicable (c = 3.1×10¹⁷ cm⁻³ and T′₀ = 5686 K). In the 0–15% relative humidity range OH production from HONO generated at the wall is about a factor of two higher than that from the photolysis of 100 ppb ozone. Effect of added NO₂ was found to be consistent with the dark HONO formation rate coefficient of MCMv3.1.     

A Study in Search of Interconnection between Surface Parameters and Surrounding Synoptic And Subsynoptic Features

The paper reveals that the variations in parameters like u*, the scaling velocity and θ*. The scaling tempera-ture during the various phases of monsoon might be linked with subsynoptic features. The rise in u* is mainly connected with the presence of lower tropospheric cyclonic vorticity over a subsynoptic scale of the site. However the variations in θ* is mainly linked with the various phases of monsoon and θ* shows a sharp rise in presence of low level convective cloud.Besides the correlation studies of u and u*, θv and θv* , θv-θv0 and θv* are undertaken. The correlation be?tween θv and θv* is poor. In other two cases correlations are good. Besides u/u* , has shown good coefficient of variation values within the ζ range.     

A numerical modeling study of the marine boundary layer over the Gulf Stream during cold air advection

A two-dimensional mesoscale model has been developed to simulate the air flow over the Gulf Stream area where typically large gradients in surface temperature exist in the winter. Numerical simulations show that the magnitude and the maximum height of the mesoscale circulation that develops downwind of the Gulf Stream depends on both the initial geostrophic wind and the large-scale moisture. As expected, a highly convective Planetary Boundary Layer (PBL) develops over this area and it was found that the Gulf Stream plays an important role in generating the strong upward heat fluxes causing a farther seaward penetration as cold air advection takes place. Numerical results agree well with the observed surface fluxes of momentum and heat and the mesoscale variation of vertical velocities obtained using Doppler Radars for a typical cold air outbreak. Precipitation pattern predicted by the numerical model is also in agreement with the observations during the Genesis of Atlantic Lows Experiment (GALE).List of Symbols u east-west velocity [m s^–1] - v north-south velocity [m s^–1] - vertical velocity in coordinate [m s^–1] - w vertical velocity inz coordinate [m s^–1] - gq potential temperature [K] - q moisture [kg kg^–1] - scaled pressure [J kg^–1 K^–1] - U _g the east-south component of geostrophic wind [m s^–1] - V _g the north-south component of geostrophic wind [m s^–1] - vertical coordinate following terrain - x east-west spatial coordinate [m] - y north-south spatial coordinate [m] - z vertical spatial coordinate [m] - t time coordinate [s] - g gravity [m² s^–1] - E terrain height [m] - H total height considered in the model [m] - q _s saturated moisture [kg kg^–1] - p pressure [mb] - p ₀₀ reference pressure [mb] - P precipitation [kg m^–2] - vertical lapse rate for potential temperature [K km^–1] - L latent heat of condensation [J kg^–1] - C _p specific heat at constant pressure [J kg^–1 K^–1] - R gas constant for dry air [J kg^–1 K^–1] - R _v gas constant for water vapor [J kg^–1 K^–1] - f Coriolis parameter (2 sin ) [s^–1] - angular velocity of the earth [s^–1] - latitude [^o] - K _H horizontal eddy exchange coefficient [m² s^–1] - t integration time interval [s] - x grid interval distance inx coordinate [m] - y grid interval distance iny coordinate [m] - adjustable coefficient inK _H - subgrid momentum flux [m² s^–2] - subgrid potential temperature flux [m K s^–1] - subgrid moisture flux [m kg kg^–1 s^–1] - u _* friction velocity [m s^–1] - _* subgrid flux temperature [K] - q _* subgrid flux moisture [kg kg^–1] - w _* subgrid convective velocity [m s^–1] - z ₀ surface roughness [m] - L Monin stability length [m] - _s surface potential temperature [K] - k von Karman's constant (0.4) - v air kinematic viscosity coefficient [m² s^–1] - K _M subgrid vertical eddy exchange coefficient for momentum [m² s^–1] - K subgrid vertical eddy exchange coefficient for heat [m² s^–1] - K _q subgrid vertical eddy exchange coefficient for moisture [m² s^–1] - z _i the height of PBL [m] - h _s the height of surface layer [m]     

珠海凤凰山森林下垫面干季和湿季气象要素的对比分析与动量和感热交换系数的参数化研究

利用珠海凤凰山陆气相互作用观测塔站2014年11月至2016年5月的观测数据,对比分析了干湿季森林下垫面能量通量和气象要素的变化特征,分析了在不同稳定度下3个风向范围（315°～45°、45°～135°和135°～225°）的动量和感热交换系数随冠层表面风速的变化特征,并对动量和感热交换系数进行了参数化研究。结果表明:干季感热和潜热通量值相当,湿季潜热远大于感热。干季和湿季的夜晚都出现负感热现象,感热从大气向森林输送。相对湿度的变化幅度大,与该地气象状况密切相关,相对湿度的垂直梯度夜晚较大,白天较小。干季的气温垂直梯度比湿季的明显。风速在冬季变化平缓,夏季变化剧烈,低层风速随高度变化梯度明显,高层较紊乱。各高度风向差异不大。中性和近中性状态下,在风向为315°～45°、45°～135°和135°～225°时,动量交换系数C_dn分别为0.05、0.0055和0.022,感热交换系数C_hn分别为0.0055、0.003和0.004。在稳定和不稳定状态下,动量交换系数C_d、感热交换系数C_h随冠层表面风速v明显发生变化,稳定条件下,C_d、C_h随v的增大而增大;不稳定条件下,C_d、C_h随v的增大而减小。分不同风向对森林冠层C_d、C_h在稳定和不稳定条件下与v的关系进行了拟合,得到了参数化公式。     

Possibility of Solid Hydrometeor Growth Zone Identification Using Radar Spectrum Width

In this study, the correlation between simulated and measured radar velocity spectrum width(σ_v) is investigated. The results show that the dendrites growth zones(DGZs) and needles growth zones(NGZs) mostly contain dendrites(DN) and needles(NE), respectively.Clear σ_v zones(1.1 < σ_v(m s^–1) < 1.3 and 0.3 < σ_v(m s^–1) < 0.7 for the DGZ and NGZ, respectively) could be identified in the case studies(27 and 28 February 2016) n...     

Vertical velocity field in the convective boundary layer as observed with an acoustic Doppler sodar

The morning development of the daytime convective boundary layer (CBL) during fine weather has been observed with an acoustic Doppler sodar of the C.R.P.E. In particular, the vertical profile of the vertical velocity third-order statistic W* ³ has been obtained. This quantity is a maximum near 0.3z _I where z _I, is the height of the CBL. The histogram of vertical velocity in the CBL shows a relationship between W ³ and the convective velocity W _* and is useful for convective plume determination.     

A barotropic model of the Ekman planetary boundary layer based on the geostrophic momentum approximation

A model of a stationary planetary boundary layer is proposed based on the equation of motion with the advective term retained. The latter is modeled by means of the so-called geostrophic momentum approximation in two versions — original and modified. New expressions for the vertical velocity W at the top of the boundary layer are derived and analyzed. They underestimate W compared to the classical expression.     

Accuracy of the relaxed eddy-accumulation technique,evaluated using CO2 flux measurements

A system capable of measuring the fluxes of trace gases was developed. It is based on a simpler version of the eddy-accumulation technique (EA), known as the relaxed eddy-accumulation technique (REA). It accumulates air samples associated with updrafts and downdrafts at a constant flow rate in two containers for later analysis of the trace gas mean concentration. The flux integration is based on the durations of updraft and downdraft events, rather than on the vertical wind velocity (W) as is the case for EA and eddy-correlation (EC) techniques. The flux, calculated by the REA technique, is equal to the difference in the mean concentration of the trace gas of interest between the upward and downward moving eddies, multiplied by the standard deviation of the vertical wind velocity and an empirical coefficient. CO₂ fluxes measured for 162 half-hour periods over a soybean field by both EC and REA techniques showed excellent agreement (coefficient of determination,R ²=0.92). The slope (0.985) and the intercept (–0.042 mg m^–2 s^–1) were not significantly different from 1 and 0, respectively, at the 5% level; and the standard error of estimate was 0.074 mg m^–2 s^–1. It is also shown that the empirical coefficient can be calculated from either latent or sensible heat fluxes. A model describing the effect on this empirical coefficient of not sampling aroundW equal to zero is proposed.Centre for Land and Biological Resources Research Contribution No. 92-212.     

Prediction of the abiotic degradability of organic compounds in the troposphere

A statistically relevant correlation between the reaction rate coefficient, k _OH, for the OH radical reaction with 161 organic compounds in the gas phase at 300 K, and the corresponding vertical ionisation energies E _i,v, reveals two classes of compounds: aromatics where –log(k _OH/cm³s^-1)3/2E _i,v(eV)–2 and aliphatics where –log(k _OH/cm³s^-1)4/5E _i,v(eV)+3. The prediction of the rate coefficient, k _OH, for the reaction of OH with organic molecules from the above equations has a probability of about 90%. Assuming a global diurnal mean of the OH radical concentration of 5×10⁵ cm³, the upper limit of the tropospheric half-life of organic compounds and their persistence can be estimated.     

The Theoretical Model of Atmospheric Turbulence Spectrum in Surface Layer

It is shown that the slope of energy spectrum obtained from the velocity solution of Kdv-Burgers equation lies between -5/3 and -2 in the dilogarithmic coordinates paper. The spectrum is very close to one of Kolmogorov’s isotropic turbulence and Frisch’s intermittent turbulence in inertial region. In this paper, the Kdv-Burgers equation to describe atmospheric boundary layer turbulence is obtained. In the equation, the 1 / Re, corresponds to dissipative coefficient v, to dispersive coefficient β, then (v/ 2β)2 corresponds to .We prove that the wave number corresponding to maximum energy spectrum decreases with the decrease of stability (i.e., the increase of in eddy-containing region. And the spectrim amplitude decreases with the increase of (i.e., the decrease of stability). These results are consistent with actual turbulence spectrum of atmospheric surface layer from turbulence data.     

The response of a propeller anemometer to turbulent flow with the mean wind vector perpendicular to the axis of rotation

The system transfer function ¦H(v)¦² at frequencyv (units of Hz) for a vertical velocity propeller anemometer in a statistically stationary and horizontally homogeneous turbulent flow is determined from: (1) experimental estimates of propeller velocity spectra; and (2) estimates of Eulerian vertical velocity spectra based on the hypothesis that degradation of the input vertical velocity Fourier components occurs in the inertial subrange. The experimental estimates of ¦H(v)¦² were adequately summarized with the mathematical expression for the system transfer function of a first-order system with parameterT which has units of time and is analogous to the time constant of a horizontal velocity propeller anemometer. Dimensional analysis techniques and the Monin-Obukhov similarity hypothesis were used to construct a model for the system parameterT which yielded the result that _w /D ₁ ( _w /)^1/3, where _w , andD ₁ denote the standard deviation of the input vertical velocity fluctuations, the horizontal mean wind speed, and the diameter of the propeller, respectively. The system parameterT is interpreted in terms of the time required for the propeller velocity statistics to become asymptotically independent of time upon being released from rest in a statistically stationary turbulent flow.Currently on leave of absence from the Indian Institute of Technology, New Delhi, India.     

Final results of the CONDORS convective diffusion experiment

TheConvectiveDiffusionObserved byRemoteSensors (CONDORS) field experiment conducted at the Boulder Atmospheric Observatory used innovative techniques to obtain three-dimensional mappings of plume concentration fields, /Q, of oil fog detected by lidar and chaff detected by Doppler radar. It included extensive meteorological measurements and, in 1983, tracer gases measured at a single sampling arc. Final results from ten hours of elevated and surface release data are summarized here. Many intercomparisons were made. Oil fog /Q measured 40m above the arc are mostly in good agreement withSF ₆ values, except in a few instances with large spacial inhomogeneities over short distances. After a correction scheme was applied to compensate for the effect of its settling speed, chaff dy/Q agreed well with those of oil except in two cases of oil fog hot spots. Mass or frequency distribution vs. azimuth or elevation angle comparisons were made for chaff, oil, and wind, with mostly good agreements. Spacial standard deviations, _y and _z, of chaff and oil agree overall and are consistent at short range with velocity standard deviations _vand _w 0.6w^* (the convective scale velocity), as measured atz>100m. Surface release _y is enhanced up to 60% at smallx, consistent with the Prairie Grass measurements and with larger _v and reduced wind speed measured near the surface. Decreased _y at small dimensionless average times is also noted. Finally, convectively scaled dy, C _y, were plotted versus dimensionlessx andz for oil, chaff, and corrected chaff for each 30–60 min period. Aggregated CONDORSC _y fields compare well with laboratory tank and LES numerical simulations; surface-released oil fog compares expecially well with the tank experiments. However, large deviations from the norm occurred in individual averaging periods; these deviations correlated strongly with anomalies in measured distributions.On assignment to the US Environmental Protection Agency, Atmospheric Research and Exposure Assessment Laboratory, RTP, NC.     

The prediction of dust erosion by wind: An interactive model

We have devised a partial differential equation for the prediction of dust concentration in a thin layer near the ground. In this equation, erosion (detachment), transport, deposition and source are parameterised in terms of known quantities. The interaction between a wind prediction model in the boundary layer and this equation affects the evolution of the dust concentration at the top of the surface layer. Numerical integrations are carried out for various values of source strength, ambient wind and particle size. Comparison with available data shows that the results appear very reasonable and that the model should be subjected to further development and testing.Notation (x, y, z, t) space co-ordinates and time (cm,t) - u, v components of horizontal wind speed (cm s^–1) - u _g, v_g components of the geostrophic wind (cm s^–1) - V=(u²+v²)^1/2 (cm s^–1) - (û v)= 1/(h – k) _k ^h(u, v)dz(cm s^–1) - V _* friction velocity (cm s^–1) - z ₀ roughness length (cm) - k ₁ von Karman constant =0.4 - V _d deposition velocity (cm s^–1) - V _g gravitational settling velocity (cm s^–1) - h height of inversion (cm) - k height of surface layer (cm) - potential temperature (°K) - _gr potential temperature at ground (°K) - _K potential temperature at top of surface layer (°K) - P pressure (mb) - P ₀ sfc pressure (mb) - C _p/C_v - (t)= /z lapse rate of potential temperature (°K cm^–1) - A(z) variation of wind with height in transition layer - B(z) variation of wind with height in transition layer - Cd drag coefficient - C _HO transfer coefficient for sensible heat - C dust concentration (g m^–3) - C _K dust concentration at top of surface layer (g m^–3) - D(z) variation with height of dust concentration - u, v, w turbulent fluctuations of the three velocity components (cm s^–1) - A ₁ constant coefficient of proportionality for heat flux =0.2 - Ri Richardson number - g gravitational acceleration =980 cm s^–2 - Re Reynolds number = - D _s thickness of laminar sub-layer (cm) - v molecular kinematic viscosity of air - coefficient of proportionality in source term - dummy variable - t time step (sec) - n time index in numerical equations On sabbatical leave at University of Aberdeen, Department of Engineering, September 1989–February 1990.