A Field Study of Radiation Fog BY W. T. ROACH,? R. J. ADAMS,? AND P. GOLDSMITH? J. A. GARLAND$ Received 3rd January 1973 A survey of the history of theoretical and practical studies of the basic physics of fog formation in the atmosphere is followed by an account of some preliminary results of field investigations into fog. 1. INTRODUCTION A supersaturated atmosphere in which fog droplets may grow may be produced by cooling or by mixing of two damp (but not necessarily saturated) masses of air at different temperatures (due allowance being made for any consequential release of latent heat by condensation). However unlike the situation in many industrial processes involving fogs and smokes the conditions under which these processes may occur are uncontrolled and highly variable.Stewart 1v has said “. . . the inter- actions between the different processes lead to such complexities that there has been little success in calculating the important features of the final state on a foggy night from observable initial conditions ”. This situation has changed little in recent years. A deeper understanding of the physical processes of fog formation maintenance and dissipation is a necessary condition for assessing future prospects of improving methods of fog modification and forecasting. This paper consists of a brief summary of past investigations followed by an account of some preliminary results of the current Meteorological Office field investigations of radiation fog. 2. PAST INVESTIGATIONS (a) Taylor made a study of radiation fogs at Kew and noted that clear skies light winds and high relative humidities were conducive to fog formation but that fog actually occurred on about half the occasions when it was expected.He observed the cooling and drying-out of the atmosphere near the ground on a clear night and realized that the initial formation of fog appeared to depend upon a balance between these two processes. As he put it ‘‘ . . .if the dryness caused by the deposition of dew on the ground diffuses upwards at a greater rate than the coldness is conducted up- wards fog is less likely to form than if reverse conditions hold ”. He attributed the “conduction ” to turbulent diffusion and also suggested that “ . . .it is possible that the cooling due to radiation from the fog particles after a fog has started may have the effect of making it thicker ”.He discounted the effect of radiation before fog formation a view we now know to be wrong. However he laid the foundations for our understanding of the formation of radiation fog. (b) The next practical studies were made by Stewart who realized the need to measure simultaneously as many as possible of the parameters likely to be significant t Meteorological Office Bracknell Berks $ Atomic Energy Research Establishment Hanvell 209 FIELD STUDY OF RADIATION FOG in fog formation. From his observations he drew the following main conclusions. (i) Direct cooling of the lowest km of atmosphere by radiation and by convection (turbulent diffusion) were comparable.(ii) The surface deposition of water was comparable to that lost from the air by cooling. (iii) The lowest layers of atmosphere often reached and remained at saturation for up to a few hours before fog actually formed. Before saturation was reached however large fluctuations in relative humidity (not reflected in temperature observations) were usually observed. (iv) Once fog formed it usually did so within a few minutes. Subsequently its depth tended to increase in steps. Stewart also developed Taylor’s suggestion that fog droplets could produce their own contribution to radiative cooling. (c) Many investigations of the atmosphere near the ground have been made in conditions favourable for fog formation but with other objectives in view. Monteith noted that the rate of dew deposition decreased abruptly when the wind speed dropped below about 0.5 ms-’ at 2m above ground.The implication is that turbulent diffusion virtually ceased thus removing the primary mechanism for dew deposition. He also noted that “ saturation (within the grass cover below about 1 cm) was always followed by the formation of fog ”. This appears to conflict with Stewart’s observa- tion (iii) above and may reflect some significance of the state of the ground in fog formation. Rider and Robinson noted that “the change of temperature in the lowest layers of air is normally the small resultant of much larger tendencies due to changes in radiative and convective fluxes acting in opposite directions ”. They also noted a quasi-periodic oscillation of period of about 10min in temperature in the lowest 0.5 m on some radiation nights once at about the time of fog formation.In summary the occurrence of radiation fog depends upon a fine balance between the drying and cooling of the atmosphere near the ground. The drying-out is caused by dew deposition which generates a water-vapour gradient down which turbulent diffusion drives a flux of water vapour. The cooling is caused by a combination of radiation and turbulent diffusion. The strength of the turbulent diffusion is con- trolled by the wind field which is always a fluctuating quantity. These however are essentially qualitative conclusions which do not tell us why fog forms when it does nor what its evolution and structure will be given initial meteorological and aerosol information nor does it give any precise quantitative information on heat and water budgets and the role of latent heat release in these.3. THE METEOROLOGICAL OFFICE PROJECT This investigation is a collaborative field project between the Cloud Physics and the Boundary Layer Research Departments of the Meteorological Office and the Aerosol Group of the Health Physics Department A.E.R.E. Harwell. The first exercise was carried out at Cardington Beds. late in 1971 when the following para- meters were measured. CLOUD PHYSICS DEPARTMENT METEOROLOGICAL OFFICE (i) Net radiative fluxes at 2 9 and 37 m above ground using Funk net flux radio- meters (F2, F,,F3,). (ii) Downward flux of radiation at 1 m using a Linke-Feussner (directional) radiometer (&).(iii) Fog top detector and thermistor (for temperature profile up to 300m) on 700ft3 balloon. (iv) Continuous record of temperature at surface and 2 m (To,Tz). (v) Continuous record of dew-point at 2 m. (vi) Spatial and size distribution of fog droplets using holography at 1 m. W. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 211 BOUNDARY LAYER RESEARCH UNIT METEOROLOGICAL OFFICE (vii) Wind speed measurements at 2 4 8 16m (Uz, U,,W,,UI6).(viii) Wind direction measurements at 16m. (ix) Soil flux measurements at depths of 6 and 15 cm. (x) Deposition of moisture at surface using a lysimeter (So). (xi) Tempera-ture measurements at 4 8 16 m at 2-min intervals (T4, T8,T16). (xii) Tethered balloon ascents at 6-h intervals giving temperature dew-point and wind speed to 1 km.HEALTH PHYSICS DEPARTMENT A.E.R.E. HARWELL (xiii) Visibility at Im (Vl) with a transmissometer and at 5m (Vs)with a nephelo-meter. (xiv) Liquid water content using an impinger. (xv) A cloud condensation nucleus counter. (xvi) A cascade impactor for drop size distribution. (xvii) Air chemistry sampling equipment. The meteorological instrumentation used to make these measurements is in general well established. Special arrangements had to be made to keep the polythene domes protecting the detector surfaces of the radiometers free from moisture. The construction and operation of the radiometers is described by Funk.6 The aerosol instrumentation included some relatively novel features particularly the use of holographic techniques for obtaining 3-dimensional " snapshots " of the spatial distribution and size of fog droplets (above about 5 pm radius) within a volume of about 500cm3.A description of this technique has been published by Pavitt Jackson Adams and Bartlett.7 Drop-size distributions down to about 1 pm were also obtained by impacting fog droplets on thin plastic foils coated with gelatin as described by Garland.8 The fog top detector consisted essentially of a hot-wire detector which evaporated fog droplets in an air-stream drawn over it by a pump. The resulting change of resistance in the detector element is converted to frequency change and transmitted to a ground receiver using standard electronic techniques.The instrument was mounted on a tethered balloon which was moved up and down through the fog top. The cloud condensation nucleus counter was developed at Harwell from a thermal diffusion cloud chamber and maintained supersaturations of up to I % in an airflow of 10 cm3 s-l. Droplets formed on cloud nuclei in the chamber scatter light from a narrow collimated beam to a photomultiplier and the resulting pulses are counted automatically by a specially designed electronic counter. The transmissometer consisted of a collimated receiver and projector separated by about 30 m. The integrating nephelometer consists essentially of a photomultiplier which detects the amount of light scattered in a small volume of the atmosphere illuminated by a flash lamp. The chemical sampling of the atmospheric aerosol was obtained by drawing air at about 0.3m3 min-l (but 0.01 m3min-l for gaseous sampling) through an area of a filter paper tape.The paper tape is moved forward once per hour. Further details of the samplers and analytical techniques are described in Eggleton and Atkins." 4. RESULTS One good case study was obtained on 7 Dee. 1971 and some account of this is given here as it illustrates the wealth of information which can be obtained from a project of this type and it has in our view served to bring some ofthe main problems into sharper focus. FIELD STUDY OF RADIATION FOG (a) THE RADIATION FOG OF 7 DEC. 1971 A sheet of stratocumulus cloud covered the observing site until 0330 GMT when a complete clearance of cloud occurred.Fog began to form soon after 0400 soon thickened and persisted until its rapid dispersal at 1030. Its depth never exceeded 40 m and for most of its duration was 15-25 m deep. Wind speeds within the fog were l.Ok0.5 m s-I until shortly before dispersal when there was a steady increase to 2-3 m s-l. The “ life ” of the fog appeared to consist of two major phases-an “ optically thin ” phase (phase I) followed by an “ optically thick ” phase (phase 11). The main phases can be subdivided into further identifiable phases. The transition between each phase usually lasted a few minutes. Table 1 gives a survey of the development of the fog. The ‘‘ optical thickness ” refers to the infra-red transmission properties of the fog in a vertical direction.TABLE 1.-HISTORYOFFOG DEVELOPMENT phase period remarks Ia 0400-0430 Layer of ground mist 1-2 m deep. Surface inversion begins to develop. I Ib 0430-0645 Visibility at 1 m fluctuates between 100 and 200 m until shortly before 0600 optically when it decreases to 50-100 m. Depth thin fog of fog fluctuates between 10 and 40 m. Surface inversion about 10 m deep by end of period. I1 a 0700-0845 Inversion lifts off ground and settles near 20 m taking the fog top with it. Sunrise at 0755. I1 b 0900-1000 Inversion and fog top lifted a further [ optically 5-10 m. thick fog I1 c 1000-1030 Dispersal phase. Gradual thinning followed by rapid dispersal. Freshening surface winds. (b) TEMPERATURE AND DEW-POINT Fig.la shows a temperature-time cross-section for the lowest 60 m of atmosphere based on 20-min means from (iii) (iv) and (xi) of the list of measurements. The vertical scale is linear in Jheight in order to offset undue cramping of isotherms near the ground. There are three main cooling events the first was associated with the sky clearance and onset of phase I; the second was associated with the transition from phase I to phase I1 when the surface inversion lifted off the ground; and the third was associated with the transition from phase IIa to phase 116. The major heating event occurred during the dispersal phase (IIc). There were also lesser but marked heating and cooling events during the fog period e.g. the heating in the lowest metre at the onset of phase 11.The atmosphere at 2 m became saturated at about 0400 and remained saturated during the rest of the period. Balloon measurements made at 0505 suggested that the atmosphere was saturated up to at least 100 m during this period. w. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 213 (C) WJND Fig. lb shows a wind speed-time cross-section for the 2-16m layer of atmosphere also based on 20-min means. The wind direction at 16m is also shown. There is a significant association between wind minima and cooling events. There is also some (b) 0400 0600 0800 1000 time (GMT) FIG.1.-(u) Temperature-time cross-section based upon 20 min means of To,T2 T4 Ts,T16and observations of temperature up to 60 m made at irregular intervals with a balloon-borne thermistor.The ordinate is linear in ,/height. Full lines are isotherms at intervals of 1°C. Dotted lines are approximate isopleths of local heating and cooling rates at intervals of 2"C/h. Observations of fog top height H maximum heating zone ; C maximum cooling zone. (b)Time cross-section of wind speed based upon 20-min means of wind speed at 2,4,8,16 m. The ordinate is linear in log (height). Full lines are isotachs at intervals of 0.2m s-I. Uniform separation of isotachs in the vertical indicate regions of log-linear wind profile. The dotted lines indicate the approximate field of gradient Richardson number between 2 and 16m. tendency for wind minima to be associated with wind veer. It follows that wind minima also occurred during the periods of fog development (transitions from phase I to 11 and IIa to IIb).The shape of the wind profile does not in general conform to a log-linear shape although there is (except for short periods) a general increase of wind with height. Wind speed averaged about 0.8 m s-l at 2 m increasing to 1.3 m s-l at 16 m. (d) TURBULENCE The wind and temperature structure of the atmosphere near the ground when averaged over about an hour is a function of and can therefore be used to give FIELD STUDY OF RADIATION FOG approximate information on the statistical properties of the turbulent field. For instance it should be possible to infer the magnitudes of the turbulent fluxes of heat water vapour and momentum. In the lowest 50-100m it is usually found (and assumed) that these fluxes are constant with height and would not therefore change the quantity of heat momentum and water vapour contained in a given layer.This is usually known as the " constant flux "layer. However in the case under discussion when light winds and very stable conditions are prevalent the turbulent field becomes very weak and may in fact become intermittent. The profiles of wind and temperature (particularly wind) become so irregular and variable that it is no longer possible to fit them to any existing model of low level turbulence. Direct observations of turbulent fluxes are difficult if not impossible to make and so the exchange coefficient can only be estimated from indirect methods. In fig. Ib isopleths of the gradient Richardson number is shown.Basically this represents the ratio of buoyancy forces (which inhibit vertical displacements of the atmosphere) and inertial forces (which tend to overturn the air through wind shear). When this number is less than about 4,turbulence will be generally prevalent; when it is greater than about unity turbulence has probably ceased throughout most of the volume and is confined to intermittent patches. Also over half the total wind change with height is confined below 2 m which is probably the depth of the " constant flux " layer on this occasion. The order of magnitude of the exchange coefficient can be obtained using scale analysis based on Fickian diffusion law e.g. AT/At = KAT/(Az)~ (4.1) where AT/At is a characteristic heating rate (with the radiative contribution removed) Az is the characteristic vertical dimension over which AT is observed to occur e.g.AT/Atx3°C h-l. A change of AT of 3°C is observed typically over a depth of 3-10 m which gives KNN m2 s-l. This gives a value on which to base numerical model- ling of the case. (e) FOG STRUCTURE Fig. 2a shows the approximate time variation of the visibility at heights of 1 m (solid line) and 5 m (dashed line) above the ground. This evidence taken together with the fog top and the radiation observations (Fig. la) suggest that in phase I the opacity of the fog decreased rapidly with height and the top was ill-defined and var- iable in height. In phase 11 the fog top became well-defined and identified with the radiation inversion.No obvious correlation between visibility and other meteoro- logical parameters has been found. The radiation observations show that radiative cooling (HR in fig. 3) was generally small in phase I but became large in phase 11. Hence the terms " optically thin " and " optically thick ". During the latter phase the fog top lay between the upper two radiometers and HRin this layer (the " upper layer ") remained high throughout the phase. In phase IIb the layer appeared to be in radiative equilibrium (HRx0) suggesting that the fog above this layer had become optically opaque thus shielding the lou7er layer from ftirther cooling. The drop-size distribution (fig. 2b) shows the development of a secondary peak in droplet sizes in the radius range 5-10 pm during phase 11 and is mainly responsible for the increase in liquid water concentration to about 0.2 g m-3 in this phase.Both the liquid water concentration and the optical extinction coefficient can be explained in terms of the observed droplet population. The number of cloud condensation nuclei (30-100 ~m-~) observed at 0.8 % supersaturation was of the same w. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 215 order as the total number of droplets in the large droplet peak. The infra-red extinction coefficient in a vertical direction could be approximately inferred from the radiation observations. In phase Ira this agreed roughly with that expected if the drop size distribution and liquid water concentration observed near ground level persisted throughout the depth of the fog.The holography results are summarized in fig. 4. The co-ordinates of each identifiable drop within a volume of 10cm3 was tabulated and for each drop the distance of its nearest neighbour was obtained and a histogram constructed. Two of the histograms shown are taken from the fog sampled a third from hill cloud on a mountain in Wales and the fourth represents the results of a Monte-Carlo-type \ I i-, ,I' j -nephelometer(5m.l loo 50 t I I I 0400 0600 0800 1000 time (GMT) FIG.2.44 Time plots of transmissometer(Vl)and nephelometer (Vs). Vlis taken from a contin- uous trace. Vs is taken from spot observations at variable intervals. (6)The histograms are drop- size distributions with the equivalent total liquid water content and time of observation written on each histogram.A 2 .................. ."a" t2 u 80 -2 --A -0400 0600 0800 1000 time (GMT) FIG.3.-Observed heating rates averaged over upper (9-37 m) and lower (2-9 m) layers. -total heating rate HT ; --,radiative heating rate HR ; ..... non-radiative heating rate HN. FIELD STUDY OF RADIATION FOG numerical experiment which simulated the “nearest neighbour ” computation shown above except that the space co-ordinates of each droplet was chosen at random. The difference between the random experiments and the observations is large with discrepancies amounting to an order of magnitude for drop separation less than about 0.5 mm. In fact on one sample of 600 drops two droplet pairs separated by 50-100 pm was observed.The probability of this occurring at random appears to be of the -I I 0.2 0.4 0.2 distance /cm FIG.4.-Histograms of distance to nearest neighbour (a)radiation fog sample at 0500 GMT 609 drops ; (b)radiationfog sample at 0647 GMT 536 drops ; (c) hill cloud sample 639 drops ; (d)mean of 10 random samples of 609 drops each in volume identical to (a). This histogram is also super- imposed on (a)as a dashed line. order of 1 in lo9. The implications of this clustering of droplets for fog investigations in particular and cloud microphysics in general cannot at present be assessed. It seems possible however that this represents some aspects of the interaction of turbu-lence with droplet growth on scales at which dissipation of turbulent kinetic energy by viscosity becomes important.(f) CHEMICAL SAMPLING This was done at a site some 800 m from the main investigation site and was mostly out of fog. The results are summarized in fig. 5. The ion concentrations showed a more or less steady decrease during the period of the fog particularly the nitrate ion. This was followed by an abrupt increase in all concentrations following the dispersal of the fog. There was also a temporary increase at 0700 to 0800 just after the transi- tion to phase 11. The large chloride concentration so far inland suggests an industrial source. The anion-cation balance shows roughly 30 % excess anions throughout (except for 0600-0700) indicating the presence of moderate amounts of some cation other than ammonium.The sulphur dioxide concentration dropped prior to fog formation fluctuated about an ill-defined minimum during the fog period and increased again after fog dispersal. These changes probably reff ect changes in vertical mixing which appears to be a minimum during the fog period although it may also w. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 217 reflect the scavenging action of fog droplet deposition to some degree. No chemical analysis of fog water was undertaken on this exercise. (9)HEAT AND WATER BUDGET The net flux of radiation was measured at levels of 2 9 and 37 m. These levels defined two layers an upper and a lower layer. The measured radiative heating HR and observed total heating rate HT of these layers are shown in fig.3. The difference ... . .........-.... .. . ...... . .-. . . . . . ,. ......... All negative ions NH so;-0.3 c1-~ 0.1 -NO; I I I I (HR-HT) = HN,where HNmust be attributed to convergence of eddy heat flux or to latent heat release or to both. The principal feature of fig. 3 is the overall tendency for the radiative cooling to be greater than the observed cooling (HNpositive)-an observation also reported by Rider and Robinson. The cooling of the lowest 50 m or so of an initially-saturated atmosphere during the period of interest implies a removal of an amount of water vapour by condensation which can be directly estimated by using the Clausius-Clapeyron relationship and is compared with the lysimeter data in table 2 below.While the overall totals of condensed water are roughly in agreement the totals over shorter periods are not. The liquid water content of the fog accounts for only a few per cent of the total. The rate of water deposition on the surface is normally taken as a measure of the FIELD STUDY OF RADIATION FOG latent heat fluat the surface. This assumption cannot be made in fog as much of the water may be condensed as fog droplets (thus releasing its latent heat directly to the atmosphere) and then water is transferred to the ground by some mechanism other TABLE 2.-ESTIMATES OF CONDENSED WATER condensed watcrlg m-2 paid (approx.) cooling lysirneter oQoeo630 50 20 06304730 20 10 0730-0830 small 25 0830-1OOO 5 10 - - 75 65 than dew deposition-particularly in the period after 0730.The observed deposition velocity (defined here as the rate of deposition of water/liquid water concentration at 1 m) is about 2 cm s-l. Gravitational settling can only account for 0.5-1 cm s-* of this. (h) QUA SI -PER I0 D I C 0sCI LLA TI0N S Another unexpected result was the observation of intermittent periods of marked oscillations of 10-12 min period in several of the meteorological parameters measured notably wind speed surface temperature and downward radiation intensity (from directional radiometer). Similar oscillations appeared occasionally in temperature at high levels apparently when these levels were lying in the radiation inversion. The traces of these elements are shown in fig.6. A possible interpretation of these fluctuations gives some account of the observed phase relationships. The oscillations are attributed to gravity wave propagation and the phenomenon can be regarded as a demonstration of the varying balance between radiation and turbulence-the latter being controlled by the wind speed oscillations while the former is influenced by a sympathetic oscillation of the fog depth. DISCUSSION The principal results requiring explanation are (i) the observed radiative cooling was in general greater than the observed total cooling in the lowest 40 m of atmos- phere. (ii) Lulls in wind were accompanied by maxima in cooling while major lulls coincided with periods of significant fog onset and development. (iii) The water condensed on cooling appears to have been mainly deposited on the ground.The water content of the fog was always a small fraction of the total water condensed out. (iv) The presence of quasi-periodic oscillations. (v) The clustering of droplets in space. Some of these features have been reported by earlier workers. They all point to the fundamental role played by turbulence and show that the lack of a satisfactory account of the water budget remains a central problem for on this rests an account of the heat budget and the role that microphysics plays in fog development. The probIem may be examined by considering the conventional one-dimensional equations for the heat and water budget. These are Heat w. T. ROACH R. J. ADAMS J.A. GARLAND P. GOLDSMITH 219 Water vapour Liquid water = +-)+c, a aw at aZ az (5.3) Where t = time z = vertical co-ordinate T = temperature p = air density c = specific heat at constant pressure F = net flux of radiation K = exchange coefficient (assumed the same for heat water vapour and momentum) L = latent heat of vapor-ization of water C = rate of condensation per unit mass of air x = humidity mixing ratio 11’ time (GMT) FIG.6.-Time plots for selected periods of the following parameters To,Tz,T4,Ts,T16, FLFbased on spot readings at 1-min intervals. U,,U4,Us,U169 D16 based on 2-min runs of wind. Eqn (3.1) represents local rare or cnange or temperature aue to raaiative neating turbulent diffusion and condensation. Eqn (5.2) and (5.3) represent local changes in the gaseous and liquid phases of water due to turbulent diffusion and condensation.Gravitational settling is ignored. First one may try and establish a condition whereby the atmosphere is maintained exactly at saturation with no liquid water present and then to study deviations from this. We do this by assuming the condensation term to be zero and eqn (5.3) also FIELD STUDY OF RADIATION FOG becomes identically zero. In this case x( = x, the saturation mixing ratio) is a function of T only through the Clausius-Clapeyron relationship hence axslat = xaT/at; ax,/az = xaT/az (5.4) where X = dx,/dT. Substituting eqn (5.4) into (5.2) and combining with (5.1) leads to where represents radiative heating rate. Eqn (5.5) can only be balanced when 9is positive since the terms on the right-hand side are essentially positive.But ,%? is observed to be negative; physically this means that because the mixing ratio has been taken as a monotonic function of temperature an eddy flux convergence of sensible heat is incompatible with an eddy flux divergence of water vapour. Thus the condensation and latent heat terms have to be re-introduced and condensation rates of the order of 1 g m-3 h-l are needed to balance the equations for typical values of the relevant parameters. Since the liquid water content of the fog is never greater than about 0.2 g IT^-^ this implies that the " life " of an individual droplet is of around 10 min before arriving at the surface. While the surface inversion is on the ground this balance can reasonably be accomplished by dew deposition but in phase 11 this seems to be no longer possible since the mechanism for dew deposition is removed.Further cooling should there- fore condense water directly into the atmosphere and produce a very dense fog. There is some indirect evidence that this occurred at the top of the fog in phase 1Ib as discussed in §3(e). This still leaves unexplained the increased rate of water deposition on the surface during phase 11. Some ideas may be worth investigating. (i) During this phase 11 surface moisture was in the form of frost. Above the surface the atmosphere satur- ated with respect to water would be supersaturated with respect to ice so that it is possible that a gradient of water vapour in the lowest metre may have been induced which was sufficient to maintain the observed deposition rate in the form of frost.(ii) Impaction of fog droplets on grass blades. Both these methods would quickly dry out the lowest few metres of atmosphere so that local replenishment is required. This may be provided by radiative cooling. It may be significant that the rate of deposition dropped sIowly after transition from phase IIa to phase IIb ; in phase IIa the radiative cooling was about 4"C/h but dropped to zero in phase 116. Thus it is not possible to state what determines the total liquid water content of the fog or why it develops when it does without considering the role of microphysics. The balance required to keep the atmosphere within 0.1 % of 100 % relative humidity corresponds to a temperature-dew point difference not exceeding about 0.02"C-a change which will take place in about 20 s with normally observed rates of heating or cooling in the lowest few metres of the atmosphere under these conditions.This balance seems to be too fine in view of the considerable fluctuations in wind and therefore of turbulent diffusion which take place and it seems likely that an already- present droplet population may exert the main control on the relative humidity by release or absorption of latent heat as required. W. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 221 (a) ROLE OF ADVECTION The approach both in designing the observational programme and in the discussion has been deliberately one-dimensional.However this is not to deny the existence of horizontal inhomogeneities which must be considered in relation to the scale on which the relevant processes operate. It is a common observation that radiation fog forms more or less simultaneously over an area of mesoscale dimensions (say up to 100 km) implying that the vertical structure of the atmosphere is the main factor in the development of fog. On the scale of hundreds of metres to km,on the other hand there are always considerable spatial fluctuations of fog structure for which variations in the nature and slope of the local terrain are at least partly responsible and will produce mesoscale circulations which are likely to control temporal fluctuations in parameters observed at a fixed point over time intervals of up to a few minutes.In the absence of two-dimensional measurements it becomes increasingly likely that observed changes are due to advection rather than development the shorter the period over which the change takes place. A useful time scale is defined by D/U,where D is the depth of the fog and U is the mean wind speed in the fog. (In this case-study this is about 30 s). Providing a change takes place over a time t$ D/U,then it is reasonable to ascribe it to development. 6. CONCLUSIONS The development of fog is roughly controlled by a balance between radiation which encourages fog and turbulence which appears to inhibit it while fine control is exerted by a balance between the humidity and the droplet population.Quantitative details of these balances must await further resolution of the details of the water balance. One result which may prove useful in assessing future prospects of local forecasting or modification of fog is that given a saturated atmosphere and radiative cooling rapid development of fog is likely to occur if the wind speed drops below about 0.5 m s-I at 2 m above ground. Any conclusions which are based on one case study must be tentative but these results do demonstrate the complexity of the competing and interacting physical processes which result in meteorological fogs. Field Projects of this type involve a large number of participants and we grate- fully acknowledge the support of all our colleagues. This paper is published by permission of the Director General of the Meteorological Office.K. H. Stewart Air Ministry Met. Res. Cttee (1955) paper 912 43 pp. K. H. Stewart Air Ministry Met. Res. Cttee (1957) paper 1074 26 pp. G. I. Taylor Quart. J. Roy. Met. SOC.,1917 43 241. J. L. Monteith Quart. J. Roy. Met. Soc. 1957 83 p. 322. N. E. Rider and G. D. Robinson Quart. J. Roy. Met. Soc. 1951 77 375. J. P. Funk Quart. J. Roy. Met. Soc. 1962 88 233. 'K. W. Pavitt M. C. Jackson R. J. Adams and J. T Bartlett J. Phys. E 1970 3 971. J. A. Garland Quart. J. Roy. Met. Soc. 1971 97 483. J. A. Garland and J. B. Rae J. Phys. E 1970 3 275. lo A. E. J. Eggleton and D. M. F. Atkins A.E.R.E. R 6983 (1972).