Cosmic rays and the electric field of thunderclouds: Evidence for acceleration of particles (runaway electrons)

We present the data on correlations of the intensity of the soft component of cosmic rays with the local electric field of the near-earth atmosphere during thunderstorm periods at the Baksan Valley (North Caucasus, 1700 m a.s.l.). The large-area array for studying the extensive air showers of cosmic rays is used as a particle detector. An electric field meter of the ‘electric mill’ type (rain-protected) is mounted on the roof of the building in the center of this array. The data were obtained in the summer seasons of 2000–2002. We observe strong enhancements of the soft component intensity before some lightning strokes. At the same time, the analysis of the regression curve ‘intensity versus field’ discovers a bump at the field sign that is opposite to the field sign corresponding to acceleration of electrons. It is interpreted as a signature of runaway electrons from the region of the strong field (with opposite sign) overhead.     

On the radiation characteristics of Antarctic Sea Ice

Abstract

Radiative measurements were carried out continuously during a cruise from Australia to Antarctica during austral summer 1995/96. Both shortwave and longwave radiative fluxes were measured. Some of the results are:

• The incoming solar radiation had a mean value of 217 W m^–2; this was a relatively weak value due to the large amount of fractional cloud cover observed. The sun was, for a large part of the trip, above the horizon for 24 hours a day.

• The reflectivity varied widely, not only as a function of sea‐ice concentration, but also as a function of ice type.

• Snow covered pack ice gave the highest albedo values (<70%), while flooded sea ice and thin ice reflected much less (<30%).

• For each sea‐ice type, short term observations showed a good relationship between albedo and ice concentration.

• The albedo increased with decreasing solar elevation.

• The net longwave radiation was negative (mean –27 W m–2); this small absolute value is due to a high amount of fractional cloud cover. There was a weak diurnal variation with a maximum loss (–33 W m^–2) in the early afternoon.

• On the average, the net radiation was positive for 17 hours, and negative for 7 hours a day. However, the duration of a positive balance depended strongly on the surface albedo.

• For the observed albedo values, modelling results showed that the net radiation was always positive when averaged over a day. The magnitude, however, depended strongly on the surface albedo, varying by more than the factor of three.

     

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

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

A Semi-Analytical Approach for Parametrization of the Obukhov Stability Parameter in the Unstable Atmospheric Surface Layer

A semi-analytical scheme is proposed to parametrize the Obukhov stability parameter \(\zeta \) (= \(z/L\) ; \(z\) is the height above the ground and \(L\) is the Obukhov length) in terms of the bulk Richardson number ( \(R_{iB}\) ) in unstable conditions within the framework of Monin–Obukhov similarity (MOS) theory. The scheme involves, (i) a solution of a cubic equation in \(\zeta \) whose coefficients depend on the gradient Richardson number ( \(R_{i}\) ), and (ii) a relationship between \(R_{i}\) and \(R_{iB}\) . The proposed scheme is applicable for a wide range (i) \(-5\le R_{iB}\le 0\) , (ii) \(0\le \hbox {ln}(z_{0}/z_{h})\le 29.0\) , and (iii) \(10\le z/z_{0}\le 10^{5}\) and performs relatively better than all other schemes in terms of accuracy in computation of surface-layer transfer coefficients. The absolute errors in computing the transfer coefficients do not exceed 7 %. The analysis presented here is found to be valid for different \(\gamma _{m}\) and \(\gamma _{h}\) appearing in the expressions of the similarity functions \(\varphi _{m}\) and \(\varphi _{h}\) (representing non-dimensional wind and temperature profiles), so long as the ratio of \(\gamma _{m}\) to \(\gamma _{h} \ge 1\) . The improved scheme can be easily employed in atmospheric modelling for a comprehensive range of \(R_{iB}\) and a variety of surfaces.     

Characteristics of the precipitation recycling ratio and its relationship with regional precipitation in China

A dynamic recycling model (DRM) with an analytical moisture trajectory tracking method, together with Japan Meteorological Agency 25-year reanalysis data, is used to study the regional precipitation recycling process across China, by calculating the regional recycling ratio (ρ _r ) at the daily time scale during 1979–2010. The distribution of ρ _r shows that, in western China, especially the Tibetan Plateau and its surrounding areas, precipitation is strongly dependent on the recycling process associated with regional evaporation. In Southeast China, however, the contribution from the recycling processes is much smaller due to the influence of the summer monsoon. A precipitation threshold value of about 4 mm/day is obtained from detailed analysis of both extreme and all-range ρ _r years. According to this threshold, China is classified into three types of sub-regions: low-precipitation sub-regions (mainly in the northwest), high-precipitation sub-regions (mainly in the south), and medium-precipitation sub-regions (mainly in the northeast). It is found that ρ _r correlates positively with precipitation, as well as convective precipitation (P _CP) and large-scale precipitation (P _LP) in the low-precipitation sub-regions. However, negative ρ _r ?～?P _LP correlations are found in the high-precipitation sub-regions and nonsignificant correlations exist in the medium-precipitation sub-regions. As P _CP is mainly locally generated due to mid-latitude mesoscale systems and the cumulus parameterization used in producing the reanalysis, the recycling ratio positively correlates to the ratio P _CP/P _LP in almost all sub-regions, particularly in the Tibetan Plateau and its surrounding areas. The correlation between radiation flux and ρ _r suggests more net radiation supports more evaporation and higher ρ _r , especially in the high-precipitation sub-regions. The influence of clouds on shortwave radiation is crucial, since evaporation is suppressed when the amount of cloudiness increases, especially in the high-precipitation sub-regions. Together with the consideration of soil moisture, it can be inferred that limited soil moisture inhibits evaporation in the low-precipitation sub-regions, while the energy or radiation is the dominant factor controlling evaporation in the high-precipitation sub-regions.     

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

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

Water-Channel Estimation of Eulerian and Lagrangian Time Scales of the Turbulence in Idealized Two-Dimensional Urban Canopies

Lagrangian and Eulerian statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the Eulerian \((T^{\mathrm{E}})\) and Lagrangian \((T^{\mathrm{L}})\) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width (W) to the height (H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the Eulerian time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the Lagrangian time scale, \(T_\mathrm{u}^\mathrm{L} \) and \(T_\mathrm{w}^\mathrm{L} \), follow Raupach’s linear law within the constant-flux layer. The same holds true for \(T_\mathrm{w}^\mathrm{L} \) in both the canopies analyzed \((AR= 1\) and \(AR= 2\)) and also for \(T_\mathrm{u}^\mathrm{L} \) when \(AR = 1\). In contrast, for \(AR = 2\), \(T_\mathrm{u}^\mathrm{L} \) follows Raupach’s law only above \(z=2H\). Below that level, \(T_\mathrm{u}^\mathrm{L} \) is nearly constant with height, showing at \(z=H\) a value approximately one order of magnitude greater than that found for \(AR = 1\). It is shown that the assumption usually adopted for flat terrain, that \(\beta =T^{\mathrm{L}}/T^{\mathrm{E}}\) is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, \(\gamma /i_\mathrm{u} \) fits well \(\beta _\mathrm{u} =T_\mathrm{u}^\mathrm{L} /T_\mathrm{u}^\mathrm{E} \) in both the configurations by choosing \(\gamma \) to be 0.35 (here, \(i_\mathrm{u} =\sigma _\mathrm{u} / \bar{u} \), where \(\bar{u} \) and \(\sigma _\mathrm{u} \) are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, \(\beta _\mathrm{w} =T_\mathrm{w}^\mathrm{L} /T_\mathrm{w}^\mathrm{E} \) follows approximately \(\gamma /i_\mathrm{w} =0.65/\left( {\sigma _\mathrm{w} /\bar{u} } \right) \) for \(z > 2H\), irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum \((K_\mathrm{{T}})\) and the Kolmogorov constant \((C_0)\). It is found that \(C_0\) depends appreciably on the velocity component both for the flat terrain and canopy flow, even though for the latter case it is insensitive to AR values. In all the three experimental configurations analyzed here, \(K_\mathrm{{T}}\) shows an overall linear growth with height in agreement with the linear trend predicted by Prandtl’s theory.     

Effect of Surface Heterogeneity on the Boundary-Layer Height: A Case Study at a Semi-Arid Forest

We investigate the effects of an isolated meso-\(\gamma \)-scale surface heterogeneity for roughness and albedo on the atmospheric boundary-layer (ABL) height, with a case study at a semi-arid forest surrounded by sparse shrubland (forest area: \(28~\text{ km }^2\), forest length in the main wind direction: 7 km). Doppler lidar and ceilometer measurements at this semi-arid forest show an increase in the ABL height over the forest compared with the shrubland on four out of eight days. The differences in the ABL height between shrubland and forest are explained for all days with a model that assumes a linear growth of the internal boundary layer of the forest through the convective ABL upwind of the forest followed by a square-root growth into the stable free atmosphere. For the environmental conditions that existed during our measurements, the increase in ABL height due to large sensible heat fluxes from the forest (\(600~\text {W~m}^{-2}\) in summer) is subdued by stable stratification in the free atmosphere above the ABL, or reduced by high wind speeds in the mixed layer.     

Measurement of ocean temperature and salinity via microwave radiometry

Sea-surface temperature with an accuracy of 1 °C and salinity with an accuracy of 1 were measured with a 1.43 and 2.65 GHz radiometer system after correcting for the influence of cosmic radiation, intervening atmosphere, sea-surface roughness, and antenna beamwidth. The radiometers are a third-generation system using null-balancing and feed-back noise injection. Flight measurements from aircraft over bay regions and coastal areas of the Atlantic resulted in contour maps with spatial resolution of 0.5 km.     

A method to calculate cloud-free long-wave irradiance at the surface based on radiative transfer modeling and temperature lapse rate estimates

We demonstrate a method to improve the performance of commonly used parameterizations to calculate the cloud-free down-welling long-wave radiation at the surface. The method uses a monthly climatology of the effective radiating temperature of the atmosphere instead of the instantaneous screen-level temperature. The climatology of the effective radiating temperature can be derived from pyrgeometer measurements and was incorporated into two commonly used schemes. We compared the calculated cloud-free down-welling long-wave irradiances to high-quality pyrgeometer measurements from four Swiss sites. The discrepancies between observations and modified schemes can be reduced by up to 35 %, resulting in a model uncertainty close to 5 W m^?2 which corresponds to the measurement uncertainty of pyrgeometers. Furthermore, we introduce a new long-wave model which is based on radiative transfer calculations in the 8–14- $\upmu $ m wavelength range. In the remaining long-wave spectrum, the radiation is calculated using the Planck function with the effective radiating temperature of the atmosphere. The performance of this new model is consistent with the modified parameterizations.     

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

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

Raindrop Size Distribution Parameters Retrieved from Guangzhou S-band Polarimetric Radar Observations

According to the statistical shape–slope (μ–Λ) relationship observed for the first time by several 2D-Video-Distrometers (2DVD) in southern China, a constrained gamma (C-G) model was proposed for the retrieval of rain drop size distributions (DSDs) from Guangzhou S-band polarimetric radar observations. Two typical precipitation processes were selected to verify the accuracy of the retrieval scheme. The μ–Λ relationship: Λ = 0.0241μ² + 0.867μ + 2.453 was obtained based on the 2DVD observation results from at Huizhou Longmen station, which is a very representative location in the area. Relying on the Guangzhou polarimetric radar measurements of radar reflectivity (Z_HH) and differential reflectivity (Z_DR), the gamma (Γ) size distribution parameters (N₀, μ, and Λ) can be retrieved by the C-G model retrieval scheme. The results show that the Guangzhou polarimetric radar retrievals of DSDs were close to the 2DVD observations at Guangzhou Maofengshan station. The rain rate, mass mean diameter, and normalized intercept parameter of radar retrievals were in good agreement with the 2DVD observations, and the relative errors were less than 10%. The overall accuracy of the retrieval scheme was high. The retrieval scheme has established the relationship between the polarimetric radar measurements and gamma size distribution parameters. It will be helpful to in-depth research and application of the dual-polarization radar data in microphysical precipitation processes analysis, as well as convection-resolved numerical model data assimilation and prediction effect evaluation.     

Net radiation — soil heat flux relations as influenced by soil water content variations

Net radiation, soil heat flux, incoming and reflected solar radiation, and soil water content were measured during several clear day periods following approximate 10-cm applications of water to loam soils at Phoenix, Arizona, and at Sidney, Montana. The regression of soil heat flux on net radiation changed significantly as the soil dried, with the difference between them being a linear function of the volumetric soil water content of the uppermost 2 to 4 cm of soil. The net radiation-soil heat flux difference for soil in an air-dry state was only about one-half of what it was on the day after irrigation. Techniques discussed allow evaluation of what the net radiation-soil heat flux difference would be under conditions of no surface saturation deficit at any time of year from measurements of net solar radiation, soil water content, and air temperature, thereby improving the utility of many evaporation models. The data also indicate that water content measurements may be replaced by more easily measured soil albedo.     

Retrieving air humidity,global solar radiation,and reference evapotranspiration from daily temperatures: development and validation of new methods for Mexico. Part III: reference evapotranspiration

We evaluated two methods to estimate evapotranspiration (ETo) from minimal weather records (daily maximum and minimum temperatures) in Mexico: a modified reduced set FAO-Penman-Monteith method (Allen et al. 1998, Rome, Italy) and the Hargreaves and Samani (Appl Eng Agric 1(2): 96–99, 1985) method. In the reduced set method, the FAO-Penman-Monteith equation was applied with vapor pressure and radiation estimated from temperature data using two new models (see first and second articles in this series): mean temperature as the average of maximum and minimum temperature corrected for a constant bias and constant wind speed. The Hargreaves-Samani method combines two empirical relationships: one between diurnal temperature range ΔT and shortwave radiation Rs, and another one between average temperature and the ratio ETo/Rs: both relationships were evaluated and calibrated for Mexico. After performing a sensitivity analysis to evaluate the impact of different approximations on the estimation of Rs and ETo, several model combinations were tested to predict ETo from daily maximum and minimum temperature alone. The quality of fit of these models was evaluated on 786 weather stations covering most of the territory of Mexico. The best method was found to be a combination of the FAO-Penman-Monteith reduced set equation with the new radiation estimation and vapor pressure model. As an alternative, a recalibration of the Hargreaves-Samani equation is proposed.     

Peculiarities of diurnal variations of the vertical gradient of the atmosphere refraction index in Eastern Russia

In this paper, diurnal variations of the vertical gradient of the atmosphere refraction index in the lower 300-m layer are computed and analysed in detail for a vast territory of Eastern Siberia and Far East of Russia by using 10-year observation data obtained at 32 aerological stations. In particular, it was found out that diurnal variation of the gradient is more diverse in summer and less diverse in fall. In the most north-easterly regions, unlike other climate zones where maximum gradient changes occur in summer and in winter, the greatest diurnal fluctuations of g _n are observed in spring. In the studied region, amplitudes of diurnal variations of g _n are significant and quite comparable with those of inter-seasonal oscillations of g _n .     

Baroclinicy along some meridional cross sections through the atmosphere

In view of the importance of baroclinicy for the dynamics of the general circulation of the atmosphere, the intensity of solenoidal field alongHess' mean meridional cross sections through the atmosphere as well as the baroclinicy alongPalmén's individual meridional cross section through the atmosphere are computed, tabulated and illustrated.     

A review of the relevance of the ‘CLOUD’ results and other recent observations to the possible effect of cosmic rays on the terrestrial climate

The problem of the contribution of cosmic rays to climate change is a continuing one and one of importance. In principle, at least, the recent results from the CLOUD project at CERN provide information about the role of ionizing particles in ’sensitizing’ atmospheric aerosols which might, later, give rise to cloud droplets. Our analysis shows that, although important in cloud physics the results do not lead to the conclusion that cosmic rays affect atmospheric clouds significantly, at least if H₂SO₄ is the dominant source of aerosols in the atmosphere. An analysis of the very recent studies of stratospheric aerosol changes following a giant solar energetic particles event shows a similar negligible effect. Recent measurements of the cosmic ray intensity show that a former decrease with time has been reversed. Thus, even if cosmic rays enhanced cloud production, there would be a small global cooling, not warming.     

<Emphasis>A</Emphasis> probability index for surface zonda wind occurrence at Mendoza city through vertical sounding principal components analysis

The aim of this work is to obtain an index for predicting the probability of occurrence of zonda event at surface level from sounding data at Mendoza city, Argentine. To accomplish this goal, surface zonda wind events were previously found with an objective classification method (OCM) only considering the surface station values. Once obtained the dates and the onset time of each event, the prior closest sounding for each event was taken to realize a principal component analysis (PCA) that is used to identify the leading patterns of the vertical structure of the atmosphere previously to a zonda wind event. These components were used to construct the index model. For the PCA an entry matrix of temperature (T) and dew point temperature (Td) anomalies for the standard levels between 850 and 300 hPa was build. The analysis yielded six significant components with a 94 % of the variance explained and the leading patterns of favorable weather conditions for the development of the phenomenon were obtained. A zonda/non-zonda indicator c can be estimated by a logistic multiple regressions depending on the PCA component loadings, determining a zonda probability index \( \widehat{c} \) calculable from T and Td profiles and it depends on the climatological features of the region. The index showed 74.7 % efficiency. The same analysis was performed by adding surface values of T and Td from Mendoza Aero station increasing the index efficiency to 87.8 %. The results revealed four significantly correlated PCs with a major improvement in differentiating zonda cases and a reducing of the uncertainty interval.     

Analysis of photosynthetically active radiation and applied parameterization model for estimating of PAR in the North China Plain

As photosynthetically active radiation (PAR) variability and PAR estimating methods play an important role in climate change and ecological process research, PAR variation trends and broadband global solar radiation (R _s ) ratios (PAR/R _s ) in the North China Plain (NCP) are examined using in situ PAR and R _s observed data for 2005 to 2011. The annual average PAR value found in the NCP is 22.9 mol m^?2 d^?1. The highest and lowest values were recorded at Changwu and Luancheng sites, respectively. The highest PAR/R _s value was found in Jiaozhouwan due to large water vapor volumes present in this area. PAR/R _s levels have increased in the NCP due to a decrease in fine aerosols and increase in water vapor concentration. From these analysis results, a parameterization model that can be applied to all sky conditions was checked. Empirical estimation model comparisons for obtaining PAR values indicate that model was least accurate when R _s was used independently. When the model included R _s, the clearness index (K _s) and the solar zenith angle, the model estimated PAR values with acceptable accuracy. A parameterization model was constructed by considering K _s and attenuation factors of PAR under clear weather conditions (ρ _clear). The improved parameterization model more accurately predicts values for local sites and for various observation sites.     

Radiation,evaporation and the maintenance of turbulence under stable conditions in the lower atmosphere

An expression is derived relating the critical flux Richardson number with the critical (gradient) Richardson number. In contrast to an earlier analysis by Townsend (1958), which is restricted to the atmosphere well outside the earth's boundary layer, the present treatment is intended specifically for turbulent flow in the lower atmosphere and it takes account of the effect of evaporation on the stability. The effect of radiation on the rate of destruction of the mean square of the temperature fluctuations is obtained by considering the radiative flux divergence in a stratified atmosphere and by using a simple functional relationship to represent empirical emissivity data.It was found that evaporation and radiation increase the critical Richardson number by a sensible amount depending on the atmospheric conditions, mainly temperature, humidity and the gradients. There is no definite critical Richardson number but rather a range between 0.25, below which turbulence is very likely, and somewhat higher than 0.5, above which turbulence is improbable. The value of the critical Richardson number can be expressed in terms of evaporation, radiation and the ratio ( _w /u _*) which also appears not to have a definite critical value. Evaporation and radiation cause the ratio ( _w /u ^*) to be larger than unity under neutral conditions. These results, based on the assumption of Reynolds' analogy,K ^H =K ^M , are consistent with the available experimental evidence.