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The method was applied to a 655-km2 area surrounding Roundtop Mountain, Quebec, Canada, during a carefully selected sample period from the summer of 1993. Field measurements of fog water volume were used to estimate the cloud-base height and the rate of change of the LWC with height. Topographic data were used both as a forcing function in the wind flow model and as a means of defining the three-dimensional geometry for deposition calculations. The goal is the development of a simple model that can be used over large geographic areas.

DECEMBER 1996 WALMSLEY ET AL.A Method for Estimating the Hydrologic Input from Fog in Mountainous TerrainJOHN L. WALMSLEY AND ROBERT S. SCHEMENAUERAtmospheric Environment Service, Downsview, Ontario, Canada HOWARD A. BRIDGMANDepartment of Geography, University of Newcastle, Newcastle, New South Wales, Australia(Manuscript received 3 October 1995, in final form 10 May 1996)ABSTRACT A methodology for obtaining estimates of the spatial distribution of fog water volume collected by a treecanopy in complex terrain is described. The method includes assumptions about the shape and spacing of thetrees, their fog water collection efficiency, the fog frequency, and the vertical rate of change of the liquid watercontent (LWC) within ground-based clouds. The method was applied to a 655-km2 area surrounding Roundtop Mountain, Quebec, Canada, during acarefully selected sample period from the summer of 1993. Field measurements of fog water volume wereused to estimate the cloud-base height and the rate of change of the LWC with height. Topographic data wereused both as a forcing function in the wind flow model and as a means of defining the three-dimensionalgeometry for deposition calculations. The goal is the development of a simple model that can be used overlarge geographic areas. Results of the application are presented over various domains ranging from 2 to 164 km2 in size. Spatialvariations in the wind velocity field just above the canopy were found to be related to the main terrain features(summits, ridges, and valleys). The fog water deposition rate was specified as a linear function both of terrainheight above cloud base and of wind speed. Near the summit of Roundtop Mountain, variations in terrain heightwere more pronounced than those of treetop wind speeds. Spatial patterns of fog water deposition, therefore,strongly reflected the pattern of topographic contours, with some modifications being apparent due to spatialvariations in wind speed. Calculated deposition values ranged up to 0.69 mm h-~ and were found to be typicalof measured values in the literature.1. Introduction Mountaintops are frequently enveloped in fog as aresult of the advection of clouds over and around thehigher elevations. The fog is used by plant species inforests as a source of moisture and nutrients, and toassist in their growth and development. This is welldocumented, particularly for tropical forests (e.g., Kerfoot 1968). The fog droplets, however, can also containhighly concentrated solutions of various pollutants.This problem has been reviewed by McLaughlin(1985), Schemenauer (1986), Lovett and Kinsman(1990), Vong et al. (1991), and others. In 1985 the Chemistry of High Elevation Fog(CHEF) experiment began on two mountains in southern Quebec, Canada (Schemenauer 1986), out of concern that much of the wet deposition at higher elevations may come from fog water. The CHEF project was Corresponding author address: Dr. John L. Walmsley, Atmospheric Environment Service, 4905 Dufferin Street, Downsview, ONM3H 5T4, Canada.E-mail: jwalmsley @row.on.doe.calinked with the Mountain Cloud Chemistry Project(MCCP) in the Appalachian Mountains. Both projectswere designed to measure concentrations of inorganicions in fog and precipitation, as well as their relationship to meteorological conditions, and to assess theirimpact on high-elevation forests. Results from theMCCP have been published or used by several authors(e.g., Mohnen and Kadlecek 1989; DeFelice and Saxena 1991; Lin and Saxena 1991; Mueller et al. 1991).CHEF wet chemistry data were given in Schemenaueret al. (1995). These and other studies of fog and cloudwater chemistry, with samples from high-elevationsites or from aircraft, have consistently shown higherconcentrations of the major ions in fog water than inprecipitation. The primary reason for this is that themajor entry point for particulate and gaseous pollutantsis through cloud base. As cloud droplets rise in updraftregions of the cloud, they grow by condensation, whichdilutes the concentrations of major ions such as sulfate.There is normally, therefore, a vertical gradient in theconcentration of pollutants in cloud water, with higherconcentrations near cloud base. It is typically samplesfrom near cloud base that are collected as fog at mountain sites. In contrast, the precipitation that is sampledc 1996 American Meteorological Society2238 JOURNAL OF APPLIED METEOROLOGY -OLUME35at these sites reflects the integrated cloud chemistrydownward from the top of the cloud, since the raindrops, for example, have usually formed through a process beginning with an ice crystal at higher altitudesand followed by growth by sublimation, condensation,and coalescence during the particle's fall through thecloud. Bridgman et al. (1994, hereafter BWS94) presenteda topographic description of Roundtop Mountain inQuebec and the surrounding region (Fig2 1 ). The MSMicro/3 model (hereafter MS-Micro) used to ,obtainthe wind velocity fields has been described in Walmsley et al. (1986). The ultimate purpose is to provide anestimate of the spatial distribution of acidic ion deposition over Roundtop Mountain. In the present paper,we describe the next step toward that goal--the estimation of spatial variations in fog water volume. Schemenauer (1986) found that the summit (970 m) ofRoundtop and the adjacent ridge (845 m), where elevations are above mean sea level (MSL), were in cloudabout 44% and 38% of the time, respectively, duringthe year. Significant opportunities are, therefore, available for the collection of fog water. We present a sample calculation and compare it with field measurementstaken during the summer of 1993.2. Measurement program Three sites on or near Roundtop were fully instrumented to measure meteorological parameters and collect precipitation and fog water. Full details were presented in Schemenauer (1986) and Schemenauer et al.(1995). Sites S and R (Fig. 2) and a valley site 10 kmto the west were equipped with Campbell Scientificmeteorological stations to measure wind speed, winddirection, precipitation, and other parameters. The datawere sampled at 5-s intervals and stored as 15-min avRS~'00 -.,-,%_.., ,..~.oo+~-~'~ /co~eOc~ '"~:5~ ~'00 Fro. 1. The Roundtop Mountain complex from an azimuthal direction of 225-. The contour interval is 50 m, and the grid resolutionis 100 m. The locations of the CHEF ridge and summit sites areindicated. The x and y coordinates are displacements (m) in the UTMgrid from the position 690 000 m'east, 4 994 000 m north in UTMzone 18. The vertical scale is MSL height. The source is BWS94,with improved digitization of topographic contours. Roundtop Mountain-6400 -3200 0 3200 64000 3200 3200 E >,, -3200 -3200 -6400 -6400 -i400 -3200 0 3200 6400 x (m) FIG. 2. Same as Fig. 1 except a contour map of MSL heights witha contour interval of 100 m. The CHEF summit (S) and ridge (R)sites, Mont Gagnon (G), and Mont Brock (B) are indicated.erages. Table 1 gives newly corrected locations andelevations of the three sites. Uncertainties in elevationare indicated. Locations are believed to be accurate to+20 m (i.e., _+0.6" latitude or _+0.9" longitude). Fog water was collected by a Canadian-built passivecollector (AES/ASRC--Atmospheric EnvironmentService/Atmospheric Sciences Research Center), essentially identical to that used in the MCCP. The collector was also used successfully in collecting fog waterfor chemical analysis in Chile (Schemenauer and Cereceda 1992a), Australia (Post et al. 1991), and othercountries. The instrument stands about 1 m high andcontains approximately 370 vertical Teflon fibers, 50cm long and 0.53 mm thick, spaced 3 mm apart. TheAES/ASRC collector surface is a vertically mountedcylinder of 48.5-cm height and 25.3-cm diameter, giving surface and cross-sectional areas of 0.386 and 0.123m:, respectively. Droplets carried to the instrument inthe airflow impact on the fibers, and fog water runsdown into a polyethylene collection bottle. Collectionrates depend on wind speed. The AES/ASRC closelysimulates fog water collection by coniferous trees(DeFelice and Saxena 1990; Joslin et al. 1990), with acollection efficiency of 0.82 to 0.87 when wind speedsare between 5.6 and 10.3 m s -~ (Lin and Saxena 1991 ).(In the present study, cross-sectional areas of both thecollector and the treetops were used for calculations.) A second fog water collector, a vertically mountedplane of 1 m x 1 m dimensions, the surface of whichis composed of a polypropylene mesh, was orientedtoward the west. The measured collection efficiencynear the center of the plane was found to be 66% (Schemenauer and Cereceda 1994), based on earlier workDECEMBER 1996 WALMSLEY ET AL. 2239by Schemenauer and Joe (1989), but this decreasedtoward the edges. Its overall collection efficiency wasestimated to be 50%. No correction was made for variations in collection efficiency with wind direction, assuch corrections were believed to be small for the casepresented here (i.e., wind direction 264-). At sites R and S, the instruments were placed justabove treetop height, with full exposure on all sides.When the wind at R was from the south-southeast, therewas some terrain sheltering from the summit. In thevalley, the meteorological instruments were placed ona 3-m pole in a roughly triangular-shaped forest clearing, the sides of which were approximately 160 m. Theanemometer location was about 50 m from the northwest corner of the clearing; sheltering effects were expected for winds from the sector 2000-3600-70-. Thiswill be discussed further in section 5a.3. Estimating fog water volume The results of a number of different studies haveestablished that fog water is deposited on the canopytop from stratiform clouds by several major pathways:mixing by turbulent eddies interacting with the treetops, sedimentation of droplets, and advectional impaction on surfaces [see Saxena et al. (1989) for areview]. Of these, impaction is most important, especially on the canopy top in a windy environment (>2m s -~ ). Note that Mueller et al. ( 1991 ) used the termadvective cloud water flux to mean the component ofwind normal to the terrain. They found this contributionto be small; we assume it is zero. In this paper, on theother hand, the term advectional impaction means theadvection of wind through the vertical surfaces of thetreetop cones. In maintaining that advectional imPaction is important, we are, in fact, in basic agreementwith Mueller et al. (1991). Any apparent discrepancyis due to a different definition of advection. The amount of fog water deposition is highly sitedependent, based on five factors: canopy structure, horizontal wind speed, the collection efficiency of the treetops, the liquid water content (LWC) of the fog, andthe variation of fog frequency with altitude. In this section, the assumptions needed to perform the calculations are discussed. Details appear in appendix A. For the Roundtop Mountain calculations, the fivefactors were handled as follows. ~ ~ ~ I0 1 2 3 4 Horizontol distonce FIG. 3. Vertical cross section of three model trees. Trees are cylindrical (diameter b) and topped by a cone (height h, angle qb). Heightof trees up to the base of the cones, shown here as 5 m, is arbitrary.See appendix A for details. 1 ) Figure 3 depicts the assumptions about the treetop geometry. Each tree was assumed to be a verticalcylinder topped by a cone (~b ~ 60-, h = 1.5 m, Tv= 1.30 m2, Tn = 3.00 m2). (Refer to appendix A formore details.) The term canopy means the top of thecylinders, whereas canopy top means the treetop cones.The horizontal spacing between the tree centers was1.73 m (in reasonable agreement with visual observations), and the horizontal tree density was 3333 ha-~.In (AS) the ratio Tv/Tn is 0.433. 2) Spatial variations in wind speed and directioncaused by variations in terrain were calculated by MSMicro, as applied in BWS94. MS-Micro wind fieldswere assumed to apply at the treetop level--that is, 1.5m above the base of the treetop cones. The wind flowmodel assumes that the flow follows streamlines. It operates in a terrain-following coordinate system and pro~duces two components of horizontal wind velocity. Inthe present study, it was assumed that close to the forestcanopy the streamlines and, hence, the flow were par T^BI~E 1. Locations and elevations of CHEF summit and ridge sites on Roundtop Mountain and CHEF valley site near Sutton, Quebec (Schemenauer 1986, with modifications). Elevation Latitude Longitude UTM east UTM north Site (m MSL) (N) (W) (m) (m)Summit 970 - 2 45-04'52" 72-32'51" 693 025 4 994 625Ridge 845 _+ 5 45-05'17" 72-33'09" 692 625 4 995 400Valley 245 - 2 45004'32" 72040'33" 682 950 4 993 8252240 JOURNAL OF APPLallel to the canopy top. Similarly, Coe et al. (1991)assumed that trajectories of the fog water droplets followed the airflow streamlines. Mueller et al. (]L991)discussed the fact that streamlines are not always parallel to the surface. In the present case, however, at aheight of 1.5 m above the forest canopy, the flow wasunlikely to be very far from parallel. 3) The collection efficiency of the treetops was as sumed to be represented by the samples from the AES / ASRC fog water collector (]oslin et al. 1990). 4) The LWC of the fog could not be directly deter mined from collector sample amounts because of the variation in collector efficiency with wind speed and droplet size (Mueller and Imhoff 1989). The cloud LWC at different elevations was calculated from cloud base height observations and an assumption thai: LWC above cloud base was 38% of the value calculated for adiabatic ascent (Leaitch et al. 1986). When compared with the LWC of the fog, as given by Saxena et al. (1989), reasonable agreement was found. 5) In general, the variation of fog frequency with altitude was assumed to be a linear function of MSL height (Schemenauer 1986). For the particular 4-h case examined in the present study, however, the frequency was assumed to be 100% everywhere abo.ve cloud base. A possible sixth factor affecting deposition is droplet size. Coe et al. (1991) investigated the influence of droplet size on deposition velocity and concluded that, to a good approximation, the liquid water deposition velocity could be set to the momentum deposition ve locity. That is, the effect of droplet size could be ne glected. Gallagher et al. (1992), on the other hand, found that for moderate wind speeds the turbulent de position velocities were strong functions of droplet size. Nevertheless, since detailed droplet size measure ments for Roundtop Mountain were lacking, these ef fects were not considered in the present study. The cal culations presented here examine fog water deposition over an area of 164 km2. Ultimately, calculations of deposition over much larger areas are needed. In such calculations, field measurements of droplet sizes will not be available and an assumption that fog water de position on large scales is independent of droplet size will be necessary. The fog water flux, defined as the product of LWC and wind speed (Joslin et al. 1990), describes the fog water deposition on the canopy top. The fog water flux increased with height above cloud base, due to in creases in both LWC and wind speed.4. Selection of the example period To verify the methodology, an observation periodwas needed during which fog was present bat no precipitation occurred. Periods in which the winds werereasonably steady in both speed and direction, were preferred, in order to satisfy the requirements of theIED METEOROLOGYVOLUME 35steady-state MS-Micro model. Data collected during a3-day period, 15-17 July 1993 [Julian days (JD) 196198], contained candidate periods, which were examined in more detail. Figure 4 displays time series plotsof wind speed and direction at the CHEF ridge andvalley sites, together with the fog water collection rateand output from a fog detector at the ridge site. Periodswith fog and without precipitation are identified in Table 2, together with wind speed and direction statisticsfor those periods. The second period (JD 197) was rejected because fog was only continuous for about 1 h during the 4-h period. The first-period (JD 196) had very light wind speeds and unacceptable variations in wind directions at the valley site. During the third period (0430-1130 EST JD 198), valley winds were slightly stronger but variations in wind direction were high, due to a brief wind shift (Fig. 4b). This period was subdivided to obtain the fourth period (0730-1130 EST JD 198), which satisfied all the selection criteria--fog, no pre cipitation, and steady winds.5. Preparation of input dataa. Upwind wind speed and direction The MS-Micro model is initialized with a wind velocity at 10 m above uniform vegetation in flat terrain.In the present case, the CHEF valley site wind measurements were used, despite the fact that they presented certain problems. The valley site anemometerwas located at a height of 3 m within a forest clearing.Although the clearing was grass covered, suggesting aroughness length of 0.05-0.1 m, the "very rough" category of Wieringa (1992) best described the situation.Accordingly, a local roughness length of 0.5 m wasassumed. The surrounding forest was well representedby Wieringa's "closed" category, with a roughnesslength of 1 m. In addition, there were believed to besignificant sheltering effects from a 10-m-high peakedroof house located approximately 30-40 m west of theanemometer and a 9-m-high forest about 50-60 maway in the southwest, west-southwest, and west sectors. The shelter-correction model of Taylor and Salmon (1993) was applied. The resulting correction facttors were clearly overestimates of what would be expected, even for the conditions at the CHEF valley site.The shelter-correction model is apparently not valid forobstacles in the very near field. For other wind directions (e.g., sectors east-northeast to south-southwest)with fetches of about 75-200 m, correction factors produced by the shelter-correction model ranged from 2.1to 1.2, respectively. A correction factor of 1.4 wouldseem to be a reasonable, though possibly conservative,estimate for winds in the period selected--that is, from264- (see Table 2). Accordingly, the following corrections were applied to the valley wind speed to provide appropriate inputDECEMBER 1996 WALMSLEY ET AL. 2241(o)01200 (c)~1.5~1.0 0.0 1200 (e)? 4.0~o 2.52.0~0.5 0.0 ~200 Ridge........ Volley JD 196 JO 197I ~ I - :M~ ~:': :~! i~ '*' ',':': ,',?;,,~i "l v.j b.; ' 19'20 ' '26'40 ' 5560 4080 Time (rain)JD 196No precip. - ~/.. b'., ' 1920 '26'40-- Plonor collector........ AES/ASRC - JD 197 ~o_p~ecip.3360 ' 40'80Time (rain)JD 196No preclp. - ~ ~ ~ :: it 19'20 26'40-- Plonor collector........ AES/ASRC JD 197 _. r?'~3go '40'80Time (rain)JD 198(b)560 300 -~ ~ 240 No precip. ~ j [-- --~l C , ~ ~ 120 I ,: ._c I ~ 602:'":" U' '"! '48b0' ' ~ ' 55200 i, ~1 , , ~1200 1920 2640JD 198NO preclp.4~00 5520(d)4000 5000~ 2000 10000 ,1200 26'40 JD 196 NO precip. I~ ~ I t I I I I I I: .A 1920-- Ridge........ Volley JD 197No precip.'3360' '40'80Time rain) JD 198No precip.4800 5520 JD 197o_ precip.' 33~60 4080Time (rain) JD 198 No precip. F -- ~ -Ii~I I , ~ , 48005520JD 198No precip.' 48'00' 55~0 ' FtG. 4. Time series plots spanning intervals when fog waspresent at the CHEF ridge site. Plots begin at 0000 EST 14July 1993. Solid vertical lines are drawn at midnight, andJulian days 196-198 (15-17 July) are labeled. Periods without precipitation are indicated. (a) Wind speed (m s-~) atCHEF ridge and valley sites. (b) Wind direction (degrees) atCHEF ridge and valley sites. (c) Fog water collection rate(L h-I) at CHEF ridge site from 1-m2 planar and AES/ASRCcollectors (Schemenauer and Cereceda 1994). (d) Fogwater detector output at CHEF ridge site; values greater than2800 indicate fog. (e) Estimated fog water deposition rate(L m-2 h-~), as derived from the data in Fig. 4c. The amountof water collected has been corrected for the cross-sectionalarea and the estimated collection efficiency of each collectorsurface.for MS-Micro. First, a shelter-correction factor of 1.4was applied to the observed 3-m wind of 2.3 m s-~,yielding 3.2 m s -~ as representative of wind in a largeforest clearing during the study period. Next, using the"guidelines" method of Walmsley et al. (1989), thecorrected valley wind speeds were adjusted from anassumed roughness length of 0.5 m in the clearing atthe measurement site to 1.0 m, a value more appropriate for the surrounding forest. This gave a speedof 2.4 m s -~ at 3 m above the forest canopy in thevicinity of the valley site. At the same time, the measurement height of 3 m was adjusted to the standard10-m height required for input to MS-Micro. Thisadjusted value was 4.2 m s-~. The upwind, uniformterrain wind direction was assumed to remain constant at 264-.2242JOURNAL OF APPLIED METEOROLOGY VOLUME35TABLE 2. Observations and statistics at CHEF ridge and valley sites during selected periods in July 1993.Julian dayParameter 196 197 198 198FD (min) 1590-1950 3090-3300 4590-5010 4590-5010NP (min) 1650-1950 2910-3450 4530-5130 4530-5130Period: (min) 1650-1950 3090-3300 4590-5010 4770-5010 (hhmm) 0330-0830 0330-0730 0430-1130 0730-1130RidgeWD (o) 289 _+ 10 271 + 14 292 _+ 11 297 +_ 4WS (m s-1) 3.5 + 0.3 4.2 +- 0.3 3.1 +_ 0.6 3.1 ___ 0.5ValleyWD (-) 243 _+ 46 239 +- 51 255 +_ 30 264 +- 8WS (ms-l) 1.1 + 0.5 0.8 + 0.3 1.8 + 0.6 2.3 +- 0.3FD--fog detected; hourly data ending at hh30; fog was not continuous throughout the period on JD 197.NP--no precipitation.min--minutes after 0000 EST 14 July 1993 (JD 195; see Fig. 4).hhmm--hours and minutes EST.WD--wind direction; circular mean and standard deviation (appendix B); quarter-hourly data ending at hh00, hhl5, hh30, and hh45.WS--wind speed; mean and standard deviation; quarter-hourly data ending at hh00, hhl5, hh30, and hh45.b. Liquid water content During the 4-h period selected for study, the volumeof water collected by the planar and AES/ASRC collectors is shown in Table 3. It was possible to estimatethe fog water volume deposition rate using these dataand the relation lO-3Vc D AcEAt' ( 1 )where D is the deposition rate (L m-2 h -~ ), Vc is thevolume collected (mL), Ac is the cross-sectional area(m2) of the collector, E is the collection efficiency, andAt is the sample period (h). The next step was to calculate the LWC and the adiabatic LWC (ALWC) from D w w-3.6V, wa-0.38, (2) TABLE 3. Calculations with 17 July 1993 (JD 198) data from fogcollectors at CHEF ridge site during the 4-h period 0730-1130 EST.Parameter PlanarCollectorAES/ASRCVolume collected (mL) 1624 -+ 2Cross-sectional area (m2) 1.000 -+ 1%Assumed collectionefficiency (%) 50 _+ 5Estimated deposition rate(L m-2 h-b) 0.81 _+ 0.09Wind speed (m s-1) 3.1 +__ 0.5Estimated LWC (gm-3) 0.07 +_ 0.02Estimated ratio LWC/ALWC 0.38 +-4- 0.18Estimated ALWC (g m-3) 0.19 +_ 0.14 440 _+_ 10.123 + 1% 85_+3 1.05 _+ 0.05 3.1 +_0.5 0.10 _+ 0.02 0.38 _+ 0.18 0.25 _+ 0.17where w and wa are, respectively, the LWC and ALWC(g m-3); Vis the wind speed (m s -2 ); and the constant3.6 has dimensions of ( s h - ~ ) ( L g - ~ ). In ( 2 ), the windwas assumed to be horizontal. Table 3 includes estimates of fog deposition, LWC, and ALWC obtainedfrom (1) and (2), together with estimated uncertainties. The ratio 0.38 reflects the fact that, due to entrainment, the LWC values found in small cumuli and stratocumuli in Canada are less than those calculated foradiabatic ascent (Leaitch et al. 1986). This ratio, however, has a relatively large standard deviation, which isthe main source of uncertainty in the estimated LWCthat would be calculated from an adiabatic ascent.c. Vertical variation of liquid water content The ALWC computed from the planar collector volume (Table 3) was adopted for use at the ridge site(R). This was the more conservative of the two values,although the uncertainty (Table 3) suggests that thevalue calculated for the AES/ASRC collector couldequally well have been used. The elevation at R was Zr= 845 m MSL, and the mean pressure and temperatureduring the 4-h sample period were observed to be919.76 mb and 10.18-C, respectively. Integrating adiabatically downward from a value of wr = 0.19 g m'-3until zero LWC (i.e., wb = 0 g m-3) was obtained gavea cloud-base height of zb = 758 m MSL (i.e., 87 mbelow the ridge site). (Visual observations at 0800EST indicated that the cloud base near Roundtop wasat a height somewhere between 500 and 845 m MSL.)An estimate of the variation of LWC with height wasthen obtained from Wr- WbAwa - -- , Aw = 0.38Aw~, (3) Zr -- Z~DECEMBER 1996 WALMSLEY ET AL. 2243where Awa (gm-4) and Aw (gm-4) are the rates ofchange of ALWC and LWC, respectively. The factor0.38 is from Leaitch et al. (1986). From (3), a valueof Aw = 8.5 x 10-4 g m-4 was obtained. Togetherwith the cloud-base height z~,, this value was used in(A6) in appendix A to calculate the LWC at any elevation. In reality, cloud LWC does not increase with heightindefinitely. The low mountains of southern Quebec,however, have maximum elevations of about 1000 m.Their summits are usually covered in cloud whenevercloud bases are below the mountain tops. Cloud baseswere in the 500-700-m range, so it only required cloudthicknesses of 300-500 m to cover the mountain completely above cloud base. The vast majority of theclouds from which data were obtained were thickerthan 300-500 m.d. Probability of cloud Fog was present at the ridge site continuouslythroughout the sample period. Accordingly, it was assumed that a0 = 100% and a~ = 0% m-~ in (A10) inappendix A. This gave a value of Pc = 100% at allelevations. From (A6b), however, LWC was zero below cloud base, so fog water deposition calculated by(A.7)- (A.9) was restricted to elevations above cloudbase.e. Topographic data Topographic data were prepared as in BWS94 witha shift of the origin and some improvements to the original contour information, particularly near the CHEFridge and summit sites. [The caption in Fig. 1 ofBWS94 gave incorrect universal transverse Mercator(UTM) coordinates for the map origin. The actual position was at 690 050 m east, 4 993 600 m north, i.e.,50 m east and 400 m south of the origin in the presentpaper. ] Figures 1 and 2, therefore, exhibit some smalldifferences from the corresponding figures in BWS94.The coordinates (m) of the CHEF summit and ridgesites are (3025, 625) and (2625, 1400), respectively,relative to the origin of Figs. 1 and 2. The grid spacingis 100 m. Calculation of the topographic grid was performedin three stages. First, the 1:50 000 topographic map(31H/2 of the National Topographic System), with acontour interval of 50 ft (15.24 m), was scanned electronically and digitized with the help of PixelTrak software. The height of the maximum contour was 970 m,located at the Roundtop summit site (Table I ). Second,a master grid of 129 x 129 points was created on adomain defined by the limits of the digitized topographic contour information. Grid spacing of the master grid in this case was 130 x 141 m. The height interpolation procedure was estimated to be accuratewithin about __+5 m where the terrain was sloping. Elevafions of summits and ridges, however, tended to beunderestimated and those of valleys overesti~nated. Inthe master grid, for example, the largest elevation was961 m at the grid point nearest to the summit site-that is, 38 m to the west-southwest. The third stage inthe preparation of the topographic input was the creation of a grid of 256 x 256 points over the MS-Microdomain. This grid, the values of which were interpolated in the master grid, had a grid spacing of 100 m.The maximum elevation was 957 m at a location about10 m from the maximum in the master grid. Once againthe interpolation procedure reduced the summit height,this time to a level about 13 m below its true value(Table 1 ). Similarly, the elevation of the CHEF ridgesite was reduced to about 827 m--that is, about 18 mbelow its true value. These reductions were not expected to have a large effect on the MS-Micro windspeeds; decreases were estimated to be 0.1-0.2 m s-~(3%-6% in this case). Since Aw = 8.5 x 10-4 g m-4,the reduction in elevation also meant a decrease inLWC of 0.011 and 0.015 g m-z (i.e., 15% and 20% ofthe observed value of 0.0737 g m-3 in this case) at thesummit and ridge sites, respectively. These two effects(wind speed and LWC) combined could mean a decrease in computed fog water deposition of 18%-26%near the top of Roundtop Mountain, due to elevationreductions alone.f Mean height of calculations Fog water deposition was calculated for the meanheight z,~ of each of the four quadrant triangular planessurrounding each grid point (see appendix A). Anarea-weighted mean value of the deposition rate wasthen computed using (A4). Grid points adjacent to thesummit were in the approximate range 915-940 m.Hence, the value of z,~ was lower by perhaps 15-20 mthan the maximum elevation (957 m) in the topographic grid. This, in turn, caused an estimated decrease in LWC of about 0.014 g m-3 from a point valuecalculated at the summit. Therefore, the 100 m x 100m grid-square average value of the fog water depositionrate was calculated to be lower than a point value calculated at the summit by an estimated 17%. Similarreductions could be expected at the ridge site.6. Results Wind velocity results from MS-Micro at a height of1.5 m above the forest canopy are shown in Fig. 5 asa series of wind vectors. Calculations were performedon a 100-m grid, but only every fourth vector is plotted(i.e., at infervals of 400 m) to avoid overlap. The lengthof each arrow is proportional to the wind speed. Highest speeds were found on ridges and summits; lowestspeeds occurred in the valleys and hillside ravines.(The peculiar behavior of the wind near the northeastern corner of this plot was attributed to very steep ter2244 JOURNAL OF APPLIED METEOROLOGY VOLUME35Wind Velocity1.5 m 6400 _~ 3200 --~ ._-> ' Ijpwlnd VeIocity~' o ~ >, h6 m/s :264- deg Height -3200 -6400 -6400 -3200 3200 640~x ' 900 700 500 / / 3OO 220022OO ' 2400 Wind Speed2400 2600 2800 3000 3200 5400 5600 1700 1500 1300 1100 900 700 500 300 2600 2800 3000 3200 3400 3600 x -n)(c) 1700 1500 1300~-~1100E >' 900 7OO22005O0300 22O0 Fogwater Deposition 2400 2600 2800 3000 3200 3400 3600 ~ I 1700 1300 1 lOO o% - 900 7o0 500, 2400 2600 2~00 3000 ~200 3~00 3~00 ~ (~) FIo. 7. Detailed results near the CHEF summit (S) and ridge(R) sites. Heavy line indicates crest of the ridge. Horizontalresolution is 100 m. (a) Topographic field as used by MSMicro. Contour interval is 20 m. (b) MS-Micro wind speedresults at 1.5 m above the forest canopy. Isotach interval is0.2 m s-~. (c) Fog water deposition rate. Isopleth interval is0.05 L m-2 h-l.deposition rate of 0.56 L m-2 h-' on a vertical treetopcross section (see section 3). The latter rate was somewhat lower than the measured value of 0.81 L m-2 h-~for the planar collector (Table 3). The reasons for thisdiscrepancy were explained in section 5e. In these calculations, the MS-Micro wind speed was very close tothe observed value at R, but the topographic elevationwas about 18 m too low and the mean height for calculations on the 100 m x 100 m grid square was afurther 6 m lower. This 24-m reduction in height fromthe true elevation at R implies a reduction in LWC of0.02 g m-z, or 29% of the observed value of 0.07g m-3. The fog water deposition was reduced by thesame percentage--that is, by 0.23 L m-2 h-~. Whensubtracted from the observed value of 0.81, this yieldedan estimate of 0.58 L m-2 h-~, which was very closeto the value of 0.56 L m-2 h -J mentioned above. It islikely, therefore, that the present estimates of fog waterdeposition rate were conservative near hilltops andridge crests. For similar reasons, the results could overestimate the true rates in valleys and ravines. The mostaccurate results were expected over sloping terrain,where the elevation errors were minimal and the areaweighted heights were expected to be similar to theheight at the grid points. Measured values of the fogcollection rates of trees expressed as the collection perunit area of vertical cross section are few, but Schemenauer and Cereceda (1992b) summarized seven re2246 JOURNAL OF APPLIED METEOROLOGY VOLUME35suits from four tree types. Their values ranged from 0.3to 2.9 L m-2 h-~, depending on tree type. The valuespresented here are at the lower end of this range. Reviews of deposition to forested upland areas (e.g.,Lovett and Kinsman 1990) have generally concludedthat the deposition of species such as SO~ is dominatedby cloud water. This does not necessarily mean thatmore water enters the forest from clouds than from precipitation. Relative water inputs are typically 10%100% of the water input from precipitation. Measuredand modeled cloud water deposition rates have beenfound to be a few tenths of a millimeter per hour (Lovett 1984) or slightly higher (e.g., Mueller et al. 1991).Deposition patterns produced by the model presentedhere, for the one case study, showed values rangingfrom a maximum of 0.69 mm h0~' (0.69 L m-:2 h-~)near S, to 0.24 mm h-~ at R, to zero below cloud base.These values were within the range measured inthroughfall studies by other authors and were similarto values produced by other models. From the fog water deposition, it was possJ, ble toestimate the total volume of water deposited in the areaduring the 4-h period simply by multiplying the valuein each grid square by its area (100 m x 100 m) andby the time period (4 h), and summing the results overall grid points. For this case, the volume of fog waterdeposited to the forest was estimated at 2065 m3. Sincethe horizontal Cross-sectional area of terrain covered bycloud was about 3.5 km2, the fog water volume wasequivalent to about 0.6 mm Of precipitation over thatsame area during the 4-h period.7. Conclusions The methodology for obtaining estimates of the spatial distribution of fog water volume collected by a treecanopy in complex terrain has been described. Themethod of applying topographic data tended, first, tounderestimate summit and ridge heights and, second,to produce a grid-square average height that was perhaps 20 m lower than point values on summits andridges. These two effects combined to yield a gridsquare average LWC that was invariably lower thanpoint values at the true heights of local terrain maxima.While the estimates of fog water volume are probablythe best that can be derived over sloping terrain, theywere conservative near summits and ridges--that is,the maxima were underestimates. Nevertheless, thepresent estimates of the volume of water captured fromfog water by the forest canopy are impressive (i.e.,about 2000 m3), despite the fact that the cloud basewas fairly high and only a small portion (3.5-km2 planarea) of the terrain was in cloud. This translates to theequivalent of about 0.6 mm of precipitation over theterrain covered by cloud in the 4-h case study. Data from the CHEF project in southern Quebecwere used to test the deposition model described here.It represents a major effort, however, to obtain chemical and meteorological measurements at a mountainsite. In extending this method to larger areas around theCHEF sites and then to large regions in southern Quebec, it will never be possible to obtain the detailed datafor each mountain needed to derive fog depositionmaps. (Nor, indeed, will it be possible to obtain precipitation amounts and chemistry at more than a fewlow-elevation sites. Yet deposition maps are routinelyproduced from precipitation data.) Future use of this methodology is planned for lessideal circumstances, such as where precipitation maybe mixed with fog water or in periods when wind velocity is more variable, to estimate the deposition rateof acidic ions. It is also planned to incorporate a'simplerversion of the technique to produce composite monthlyestimates of the ion deposition rate on Roundtop Mountain. Finally, it is planned to use the experience with calculations on Roundtop to estimate deposition rates inother areas of southeastern Canada that regularly experience high-elevation fog but lack detailed physicaland chemical measurements. This will include the calculation of deposition rates over much larger uplandareas. As a step toward this goal, it is planned to eliminate one input parameter (the rate of change of theLWC with height) in favor of an upward integrationfrom a valley station to the height of each grid point. Acknowledgments. We thank Chuck Matthias for histhorough review of the manuscript and for help in deriving Eq. (A11 ). An anonymous referee provided several helpful comments and suggestions for improvements. John Walmsley was partially supported by theGovernment of Canada's Panel on Energy Researchand Development. During early stages of this work,Howard Bridgman was supported by a grant from theAtmospheric Environment Service. APPENDIX A Fog Water Deposition Calculations The purpose of this appendix is to describe thetails of calculating fog water deposition in mountainousterrain while accounting for slope, wind speed, andwind direction.a. Grid points, quadrants, and means Figure A1 is a sketch illustrating the three-dimensional geometry of the modeled deposition in complexterrain. The coordinates of grid point i are expressed as(xi, y~, z~ ). Here, i ~ 1 is the grid point of interest andi = 2 and 3 are two of the four adjacent grid points,chosen so that (x~, Yi, 0) are three points of a horizontalright-angled triangle. Together, the three points i = 1,2, and 3 represent one of four triangular planes associated with grid point i = 1. These four planes are located in the northeast, northwest, southwest, and southD~C~MSE~ 1996 WALMSLEY ET AL. 2247 F~G. A1. Sketch showing triangular plane, A123 in the northeastquadrant w.r.t, grid point. 1. The coordinates of the points definingthe plane are (x~, Yl, z0, where i = 1, 2, and 3. The horizontal projection of A123 is D, ABC. Grid spacing is ZZ, c = AB and Ay = AC.Vector V, which lies on A123, is the wind velocity at grid point 1.Vector Vu is the horizontal projection of V. Angle/3 is the inclinationof V from the horizontal. Angle 0 is the azimuthal direction of Vmeasured counterclockwise from the x axis to the vector Vu.east quadrants w.r.t, the grid point. Figure A 1 illustratesthe northeast quadrant. The area of each triangular plane (A123 in Fig. A1 )is expressed as I (al2 + a22 + a~)m, (A1)A=~whereal = Y2Z3 -- y2Z~ -- y~Z3 -- z2Y3 + z2y~ + ZlY3a2 = Z2x3 -- Z2Xl -- ZlX3 -- x2Z3 nt- x2~,l ~- XlZ.3 a3 = x2y3 - x2y~ -- xly3 -- y2x3 + y2xl + y~x3. (A2) The area of the corresponding horizontal projection(AABC in Fig. A1) is given by1An = ~ ]a31. (A3)For a given grid spacing, An is constant while A variesas the z coordinates change with each grid point andfor each quadrant. The relations (A1) and (A3) aregeneral expressions that may be simplified when thegrid spacings in the x and y directions are, respectively,Ax and Ay; for example, An = (l/2)AxAy. An area-weighted mean of variable q at a given gridpoint is computed by summation over the values of qin each of the four quadrant planes (i = 1, 2, 3, 4):~ qiAi(q) - -- (A4)EA~ The mean height Zm of a triangular plane is definedas 1Zm = ~ (Z~ + Z2 + Z3).(AS)b. Liquid water content The LWC at the base zb (m) of the stratiform cloudswas assumed to be Wb = 0 g m-3. Assuming a linearrate of increase Aw (gm-4) of LWC with height (Zm-- Zb) in the fog, then { wb+ AW(Zm-Zb), Zm-ZO (A6a) w(z~) = O, zm < z~ (A6b)is the LWC at height z~. The value of Aw was assumedto be 38% of the calculated rate of increase for adiabatic ascent (Leaitch et al. 1986).c. Fog water deposition It was assumed that deposition from fog occurs onthe canopy top, not at the ground surface. The averagefog water deposition rate (L m-2 h-~) for the period inquestion on a vertical treetop cross section in a givenquadrant is expressed as ca~ = 3.6wV cosfi, (A7)where V is the wind speed (m s-I) and fi is the inclination (radians, positive upward--see Fig. A1 ) of thewind speed to the horizontal. The constant 3.6 has dimensions of (s h-~)(L g-l). (Note that winds wereassumed to be parallel to the terrain.) Treetops were assumed to be conical, with a coneangle ~ and a height h. The diameter of the base is b= 2h tan(qb/2). The vertical cross-sectional area ofeach treetop is Tv = hb/2, and the horizontal crosssection is 7r(b/2)2, whereas the area occupied by eachtree (including spaces between trees) was assumed tobe Tn = be (i.e., the trees touched at a distance h downfrom the tops). Deposition was assumed to occur onthe vertical cross section of treetop cone that faced ~ewind. Therefore, if the deposition per unit ~ea on ave~ical surface is Cd~, then the deposition per unit ~eaof horizontal surface is C~h = c~ . ( A8 ) To calculate the deposition on ~e sloping quadrantplane (~123 in Fig. A1 ), the co~ection factor (An/A)was applied: ca = can , (A9)where Pc is the percentage of the time that the quadrantplane was in fog during the period of interest. Here, Pcwas assumed to be a linear function of MSL height,ZMSL:2248 JOURNAL OF APPLIED METEOROLOGY -OLUME35 Pc = ao + alZMSL, (A10)where a0 and a~ were determined from observations, Ifa~ = 0% m-~, then Pc is uniform with height. [In thepresent study, ao = 100% and a~ = 0% m-1. Depositionwas still zero below cloud base because of (Atb).] An area-weighted mean, (A4), was then applied tothe four quadrant results to obtain the average fog 'waterdeposition at the relevant grid point. In (A7), the angle ]~ (radians) was computed fromthe following algorithm: = f-(a~ cos0 + a2 sin0)a~~, tan~ [ w/2,a3 ~ 0,a3 ----- 0, (All)where a~, a2, and a3 are given in (A2), 0 = (270--/I~)(~r/180-), and - (degrees, meteorological convention) is the wind direction. Angle 0 is shown inFig. A1. APPENDIX B Circular Mean and Standard Deviation Mardia (1972) gives the formulas for computingmeans and standard deviations of directional data. Let~x, ~2 ..... On be a set of n directions, and let Pi be apoint on the circumference of the unit circle corresponding to the direction 0i. The center of gravity ofthe n points is (C, S), where ~=_1 ~cos-~, ~---1 ~sin0~. (B1) t/ i~ t/ i=~ The mean direction - is given as the solution of tan~ = ~-~. (B2)In Fortran code, this may be conveniently calculated as- = ATAN2(S, C), which returns an angle (rad) between -,r and +Tr. Multiplication by 180-/~c convertsthe angle to degrees. The addition of 360- to negativevalues changes the range to 00-360-. The resultant length of the unit vectors from theorigin of the unit circle to the points P~ is R = n,~,where/~, the mean resultant length, is given by /~ = (~2 + ~2)~/2 (B3) The circular variance is So = 1 -/~, (B4)the values of which lie in the range (0, 1 ). Finally, thecircular standard deviation is So = [-2 ln(1 - SO)ira, (B5)the values of which are in radians and lie in the range(0, ~). This measure is somewhat analogous to thesample standard deviation on the line.REFERENCESBridgman, H. A., J. L. Walmsley, and R. S. Schemenauer, 1994: Modelling the spatial variations of wind speed and direction on Roundtop Mountain, Quebec. Atmos.-Ocean, 32, 605-619.Coe, H, T. W. Choularton, D. J. Carruthers, M. W. Gallagher, and K. N. Bower, 1991: A model of occult deposition applicable to complex terrain. Quart. J. Roy. Meteor. Soc., 117, 803-823.DeFelice, T. P., and V. K. Saxena, 1990: Mechanisms for the operation of three cloudwater collectors: Comparison of mountaintop results. Atmos. Res., 25~ 277-292. , and , 1991: The characterization of extreme episodes of wet and dry deposition of pollutants on an above cloud-base forest during its growing season. J. Appl. Meteor., 30, 1548 1561.Gallagher, M. W., K. M. Beswick, and T. W. Choularton, 1992: Measurement and modelling of cloudwater deposition to a snow-covered forest canopy. Atmos. Environ., 26A, 2893 2903.Joslin, J. D., S. F. Mueller, and M. H. Wolfe, 1990: Tests of models of cloudwater deposition to forest canopies using ar tificial and living collectors. Atmos. Environ., 24A, 3007 3019.Kerfoot, O., 1968: Mist precipitation on vegetation. For. Abstr, 29, 8-20.Leaitch, W. R., J. W. Strapp, H. A. Wiebe, K. G. Anlauf, and G. A. Isaac, 1986: Chemical and microphysical studies of nonprecip itating summer cloud in Ontario, Canada. J. Geophys. Res., 91, 11 821-ll 831.Lin, N.-H., and V. K. Saxena, 1991: In-cloud scavenging and depo sition of sulfates and nitrates: Case studies and parameterization. Atmos. Environ., 25A, 2301-2320.Lovett, G. M., 1984: Rates and mechanisms of cloud water deposition to a subalpine balsam fir forest. Atmos. Environ., 18,361-371.--, and J. D. Kinsman, 1990: Atmospheric pollutant deposition to high-elevation ecosystems. Atmos. Environ:, 24A, 2767 2786.Mardia, K. V., 1972: Statistics of Directional Data. Academic Press, 357 pp.McLaughlin, S. B., 1985: Effects of air pollution on forests: A critical review. J. Air Poll. Cont. Assoc., 35, 512-534.Mohnen, V. A., and J. A. Kadlecek, 1989: Cloud chemistry research at Whiteface Mountain. Tellus, 41B, 79-91.Mueller, S. F., and R. E. Imhoff, 1989: Inferring cloud deposition to a forest canopy using a passive cloudwater collector. Geophys. Res. Lett., 16, 683-686.--, J. D. J. Joslin, and M. H. Wolfe, 1991: Estimating cloud water deposition to subalpine spruce-fir forests--II. Model testing. Atmos. Environ., 25A, 1105-1122.Post, D., H. A. Bridgman, and G. P. Ayers, 1991: Fog and rainwater composition in rural SE Australia. J. Atmos. Chem., 13, 83-95.Saxena, V. K., R. E. Stogner, A. H. Hendler, T. P. DeFelice,R. J.-Y. Yeh, and N.-H. Lin, 1989: Monitoring the chemicalclimate of the Mr. Mitchell State Park for evaluation of itsimpact on forest decline. Tellus, 41B, 92-109.Schemenauer, R. S., 1986: Acidic deposition to forests: The 1985 Chemistry of High Elevation Fog (CHEF) project. Atmos. Ocean, 24, 303-328.--, and P. Joe, 1989: The collection efficiency of a massive fog collector. Atmos. Res., 24, 53-69. , and P. Cereceda, 1992a: The quality of fog water collected for domestic and agricultural use in Chile. J. AppL Meteor., 31, 275-290.--, and , 1992b: The use of fog for groundwater recharge in arid regions. Proc. Int. Seminar on Groundwater and the En vironment in Arid and Semiarid Areas, Beiji}~g, China, Chinese Academy of Geological Sciences, 84-91. , and , 1994: A proposed standard fog collector for use in high-elevation regions. J. Appl. Meteor., 33, 1313-1322.DECEMBER 1996 WALMSLEY ET AL. 2249--, C. M. Banic, and N. Urquizo, 1995: High elevation fog and precipitation chemistry in southern Quebec, Canada. Atmos. En viron., 29, 2235-2252.Taylor, P. A., and J. R. Salmon, 1993: A model for correction of surface wind data for sheltering by upwind obstacles. J. Appl. Meteor., 32, 1683-1694.Vong, R. J., J. T. Sigmon, and S. F. Mueller, 1991: Cloud water deposition to Appalachian forests. Environ. Sc- Technol., 25, 1014-1021.Walmsley, J. L., P. A. Taylor, and T. Keith, 1986: A simple model of neutrally stratified boundary-layer flow over complex terrain with surface roughness modulations (MS3DJH/3R). Bound. Layer Meteor., 36, 157-186. , and J. R. Salmon, 1989: Simple guidelines for estimating wind speed variations due to-small-scale topographic features- An update. Climatol. Bull., 23(1), 3-14.Wieringa, J., 1992: Updating the Davenport roughness classification. J. Wind Engin. Indust. Aerodyn., 41, 357-368. 2b1af7f3a8

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