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Accuracy of Point and Line Measures of Boundary Layer Cloud Amount. Berg, Larry K.; Stull, Roland B. 2002-06-30

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640 VOLUME 41JOURNAL OF APPLIED METEOROLOGYq 2002 American Meteorological SocietyAccuracy of Point and Line Measures of Boundary Layer Cloud AmountLARRY K. BERG AND ROLAND B. STULLAtmospheric Science Programme, Department of Earth and Ocean Sciences, The University of British Columbia,Vancouver, British Columbia, Canada(Manuscript received 29 January 2001, in final form 5 November 2001)ABSTRACTMany authors have used upward-looking instruments, such as a laser ceilometer, to estimate the cover of fair-weather cumuli, but little has been mentioned as to the accuracy of these measurements. Results are presented,using a simulated cloud field and a virtual aircraft, that show that sampling errors can be very large for averagingtimes commonly used with surface instruments. A set of empirical equations is found to provide an estimate ofthe errors associated with averaging time and earth cover. These relationships can be used to design observationstrategies (averaging time or flight-leg length) that provide earth-cover estimates within desired error bounds.These results are used to guide a comparison between earth cover measured by an airborne upward-lookingpyranometer and earth cover observed by airborne scientists in a research aircraft. In general, the agreementbetween these two methods is good.1. Introduction and motivationOne of the oldest, and perhaps most common, meth-ods of observing cloud cover is to use a human observerstationed on the ground. In this case, the observer re-ports the fraction of sky dome that is covered withclouds. As an alternative, cloud cover can be reportedin terms of the fraction of the earth’s surface that iscovered by clouds. This value can be measured with adownward-looking satellite. It also can be measured asa cloud field is blown over a vertically looking, nar-rowbeam sensor on the ground or as a sensor on anaircraft is flown over or under a cloud field. These twomeasures of cloud amount are usually not the same,because both the cloud base and cloud sides block partsof the sky dome, so that sky cover is greater than earthcover (Appleman 1962; Hoyt 1977). Both Malick et al.(1979) and Henderson-Sellers and McGuffie (1990)have developed empirical relationships that couple thesetwo kinds of observations.These different definitions of cloud cover may beuseful for different applications. The sky cover is usefulfor radiation budget measurements in which presenceof cloud sides contributes to both the short- and long-wave radiation received at a point on the surface. Earthcover of fair-weather cumuli is a pertinent parameterfor coupling boundary layer processes to the amount ofCorresponding author address: Larry K. Berg, Dept. of Earth andOcean Sciences, The University of British Columbia, 6339 StoresRd., Vancouver, BC V6T 1Z4, Canada.E-mail: lkberg@eos.ubc.cacloud cover and for determining the transfer of pollut-ants out of the convective boundary layer.Many researchers, as well as the Automated SurfaceObserving System (ASOS) used by the National Weath-er Service and Federal Aviation Administration, use aceilometer, lidar, or other vertically looking active sen-sor to estimate earth cover [Bretherton et al. (1995),White et al. (1995), Fairall et al. (1997), ASOS Program(1998), Grimsdell and Angevine (1998), and Lazarus etal. (2000) are recent examples]. For these instrumentsa cloud is detected when the sensor’s emitted light isscattered off clouds and returned to a detector on thesurface. Earth cover is the fraction of measurement in-tervals, over some arbitrary averaging time, in whichclouds are detected. A typical averaging time is 0.5 h.Other methods are passive, detecting a cloud whensunlight reaching a pyranometer on the ground or onan aircraft is interrupted by cloud shadow (Ek and Mahrt1991). When the sun is not directly overhead, errorsarise because the silhouette of the cloud blocking thesunlight includes the vertical depth of the cloud, not justthe horizontal cross-sectional area.Many observers have used vertically pointing sen-sors, but little has been mentioned of the accuracy ofthese measurements. Aviolat et al. (1998) are an ex-ception. They indicate that ceilometers are not a goodtool to estimate cloud cover because they are point mea-surements. The sampling error associated with a pointmeasurement can be large, particularly during periodswith low wind speeds, when few clouds move over thesensor. To improve the accuracy of these measurements,a longer averaging time can be used; however, nonsta-JUNE 2002 641BERG AND STULLtionarity of the cloud field could become an importantfactor. Feijt and van Lammeren (1996) improved theircloud-cover measurements by combining ceilometermeasurements with satellite observations.The purpose of this article is twofold. First, earth-cover errors associated with observations from an up-ward-looking sensor are compared with averaging timeor distance. For airborne sensors, this could be thelength of time it takes to fly one flight leg. For sensorson the ground, this corresponds to the length of atmo-sphere advected over the sensor. Inspired by the workof Poellot and Cox (1977), who looked at the averagingtime needed to measure accurate shortwave fluxes, andSantoso and Stull (1999), who designed optimal flightpatterns to sample boundary layer turbulence, we con-ducted tests in which a virtual aircraft is ‘‘flown’’ undera simulated cloud field. An empirical set of equationsis found for the virtual data that relates the measurementerrors to an arbitrary averaging length and earth cover.Second, these virtual results are used to interpret a com-parison of passive pyranometer measurements with hu-man estimates of earth cover made during BoundaryLayer Experiment 1996 (BLX96; Stull et al. 1997; Berget al. 1997).2. Earth-cover observation methodsa. Simulated observationsThere has been much debate in the literature aboutthe nature of the spatial distributions of real cumuli.Some researchers have suggested that cumuli areclumped (Plank 1969; Randall and Huffman 1980; Jo-seph and Cahalan 1990; Sengupta et al. 1990). Otherauthors believed that fields of cumuli were regular(Bretherton 1987, 1988; Ramirez and Bras 1990). Someauthors have assumed that cloud fields were randomlydistributed (Ellingson 1982; Zuev et al. 1987). Othershave found that smaller cumuli were clumped and thelarger cumuli tended to a more regular or random dis-tribution (Weger et al. 1992; Zhu et al. 1992). Ramirezand Bras (1990), Weger et al. (1992), and Zhu et al.(1992) related observed or simulated nearest-neighbordistributions to theoretical nearest-neighbor distribu-tions for a random process, for many different cloudfields. They found that very different looking cloudfields, including random cloud fields, could producesimilar nearest-neighbor distributions.A random cloud field was used in this simulationstudy. Vertically thin, horizontally circular clouds wererandomly placed on a regular 0.1-km grid in a 710 km3 82 km domain. The clouds were not allowed to over-lap, but cloud edges could touch. As judged using stan-dards proposed by Joseph and Cahalan (1990), this sim-ulated cloud field is very slightly regular. Tests showedthat cloud-cover statistics generated from slightly reg-ular or completely random cloud fields were indistin-guishable from each other.The cloud diameters were chosen to follow a log-normal distribution. The parameters for the lognormaldistribution were chosen to be consistent with the ob-servations of Lopez (1977) and Plank (1969). For theresults presented, the mean cloud radius was 0.5 km andthe standard deviation was 2.0 km.Earth-cover values were allowed to range from 5%to 40% for the tests, which corresponds to ‘‘few cumuli’’to ‘‘scattered.’’ All of the cloud centers were locatedwithin the domain, but clouds could hang off the edgeof the domain. This method might lead to inaccurateearth-cover estimates near the edge, because no cloudswere allowed to hang onto the domain. To eliminateedge effects, the simulated aircraft ‘‘flew’’ horizontallegs within a subdomain of 690 km 3 72 km. Eachparallel leg was 0.1 km apart laterally and ranged inlength from 5 to 70 km. During each virtual flight, thefraction of the flight leg that was under simulated cloudswas recorded to provide a line average. These resultsalso correspond to a cloud field advecting over a ground-based sensor at a variety of wind speeds.A second experiment using the virtual aircraft wasconducted to compare earth-cover estimates made alonga single line through the cloud field to the earth coverestimated using a swath (area) average centered on theaircraft. This experiment corresponds more closely tothe earth-cover measurements by an observer on an air-craft who can see cloud shadows covering the groundto the left and right of the aircraft track, in addition tothe shadows immediately ahead. The width of the swath(3.5 km) was chosen to be similar to the area beneaththe aircraft used to estimate earth cover during the fieldexperiment described in the next section.b. Boundary Layer Experiment 1996 observationsBLX96 was conducted from 15 July to 13 August1996 over three different regions of Oklahoma and Kan-sas located within the Atmospheric Radiation Measure-ment Program Cloud and Radiation Test Bed region(Stokes and Schwartz 1994). The University of Wyo-ming King Air aircraft flew horizontal legs, each ap-proximately 70 km long, at a number of altitudes in thedaytime convective boundary layer. At aircraft speedsof roughly 90 m s21, each leg took about 15 min tocomplete. All of the flight legs were flown between 1000and 1500 LST, with most legs between 1100 and 1400LST. Solar zenith angles f ranged between approxi-mately 158 and 368 and were less than 308 for 80% ofthe legs flown.BLX96 was designed to meet several different goals(Stull et al. 1997). One of these goals was to providedata for verification of boundary layer cumuli param-eterizations. Earth cover is a key variable for verificationof parameterizations. Standard surface observations areunsatisfactory because they measure sky cover ratherthan earth cover and would be valid for only a fractionof the flight track. Observations of earth cover by an642 VOLUME 41JOURNAL OF APPLIED METEOROLOGYobserver on the ground (either human or electronic)would be unreliable because only one or two cloudsmight be directly over the observer, leading to a largesampling error. Satellite observations were not used be-cause many of the small boundary layer cumuli (cu-mulus humilis) during BLX96 were smaller than weath-er satellite resolutions.Because of the shortcomings of these methods, twoalternative methods for measuring earth cover were usedduring BLX96: radiometric and manual. The upward-looking Eppley Laboratory, Inc., Precision Spectral Pyr-anometer (Model PSP) on the aircraft showed large dif-ferences between measurements made inside and out-side cloud shadows. A threshold value of 575 W m22was applied to the unfiltered pyranometer time series todetermine when the aircraft passed through a cloudshadow (Ek and Mahrt 1991). The estimated earth coverwas defined as the fraction of the whole leg that waswithin cloud shadows. The pyranometer-measured earthcover was insensitive to the threshold chosen, for thresh-olds between 375 and 775 W m22.The airborne scientist on each flight also made esti-mates of earth cover based on the cloud shadows pro-jected on the ground. It was fortunate that the area underthe flight tracks was divided by roads and fence linesinto 800-m (0.5 mi) sections, allowing for more accurateestimates of earth cover. All of the manual estimates fora given flight leg were averaged together to give a legaverage. The number of human observations logged dur-ing any given leg ranged from 1 to 10. Four differentairborne scientists flew during BLX96. Although allfour scientists trained together before the field programin an attempt to equalize their observations, there maybe biases in earth-cover estimates. Young (1967) foundthat differences among observers working with the samesatellite images were as large as 2 oktas for the rangeof earth covers he studied. Similar errors might be ex-pected for the observations made during BLX96. Theairborne scientists also logged cloud thickness of thecumulus humilis clouds in three ways: 1) by estimatingaspect ratio (cloud width to cloud height) visually, 2)by logging cloud-base and cloud-top altitudes duringascent/descent slant aircraft soundings, and 3) via post-flight inspection of footage from the forward-lookingautomatic airborne video camera.c. Effect of solar zenith angle on cloud shadowsUsing cloud shadows projected on the earth to esti-mate earth cover is exact only for a f of 08 or, alter-natively, for infinitely thin clouds. As f increases, partof the sunlight could be blocked by the cloud sides,causing the shadow projected onto the earth’s surfaceto be larger than the true earth cover. Taller clouds en-hance this effect because more sunlight is blocked. Forshallow clouds and high sun, however, the earth-covererrors are minimal. During BLX96 most flight legs wereflown during fair-weather, anticyclonic conditions with-in a few hours of solar noon. It was observed duringBLX96 that most the cumuli were short, with an aspectratio between 1 and 2.A simple analytical experiment can be used to esti-mate the error in measured earth cover due to differentf and cloud aspect ratios. For this analysis, the down-welling radiation is assumed to be plane parallel. Cloudsare assumed to have flat bottoms, a square base, and tobe semicircular or semielliptical in cross section parallelto the sun’s rays (Fig. 1). Clouds are assumed to havea rectangular cross section in the dimension perpendic-ular to the sun’s rays. One important implication of thiscloud geometry is that cloud shadow is rectangular.With these assumptions and a value of f, the amountthat cloud shadows overestimate earth cover can be cal-culated analytically. Figure 1 shows an example inwhich the cloud shadow is some amount dA larger thanthe true earth cover A. The geometric location of cloudtop is defined using22xz151, (1)22xzccwhere xcis one-half the cloud width and zcis the cloudthickness. The location on the cloud at which the sun’sray is tangent to the cloud determines how much ra-diation the cloud blocks and the size of the cloud shadow(A 1 dA). This point is found by taking the derivativeof (1) with respect to x to find the slope of the tangentline at any point along the cloud’s top. Combining thisresult with (1) and f yields equations for the z location(ztan) and the x location (xtan) at which the sun’s ray istangent to the cloud’s top:21/222x tan (p/2 2 f)cz 5 z 1 1 , and (2)tan c2[]zc2 2 1/2x 5 x [(1 2 z /z )] . (3)tan c tan cAs shown in Fig. 1, the triangle (ABC) formed by avertical line through the tangent point, the cloud base,and the line representing the sun’s ray can be used tofind the length dx added to the cloud shadow. This equa-tion can be written asdx 5 x 1 z tan(f) 2 x .tan tan c(4)Equations (3) and (4) show that the error is a functionof the cloud thickness, cloud width, and f. As a checkof the behavior of these equations we find that, as fapproaches 0 in (2), tan2(p/2 2 f) approaches infinityand ztanapproaches 0. Using (3), we find that xtan5 xc,and (4) predicts that the error approaches 0, as expected.The total area of the cloud shadow can be found using(4) and a cloud length of 2yc:A 1 dA 5 2y (2x 1 dx) 5 4xy 1 2y dx. (5)cc cc cThe total area is a function of cloud height, cloud di-ameter, and f. A fractional error can be defined as [(A1 dA)/A], which, by using (5), can be rewritten as 1 1JUNE 2002 643BERG AND STULLFIG. 1. Sketch showing cloud geometry used to estimate the earth-cover error associated withcloud thickness and solar zenith angle f. Heavy descending arrows represent the actual sun’srays; the thin one represents a ray striking the edge of an infinitely thin cloud. The shaded semicirclealoft is a single boundary layer cumulus with height zc. The point xtan, ztanmarks the tangent pointof the sun’s ray. Shading below the cloud shows the true cloud width 2xcand the error dx associatedwith the solar zenith angle.dx/2xc. Combining this form of the fractional error with(2)–(4) yields an equation for the fractional error thatis a function of only the aspect ratio of the cloud (R 52xc) and f:21zcA 1 dAA122 211/25^1 1 {1 2 [0.25R tan (p/2 2 f) 1 1] }2222 22 21/21 4R [tan (p/2 2 f) 1 4R ] tan(f)&. (6)From the observations of cloud diameters and cloudheights during BLX96 and from the solar zenith anglecalculated from the time, latitude, and longitude of theflights, the error in earth cover associated with the cloudshadows can be calculated. For shallow clouds with anaspect ratio of 2, the fractional error is small, 1.11 forf 5 358 (Fig. 2). As the clouds grow deeper, the errorincreases; for clouds with an aspect ratio of 1, the frac-tional error is 1.36 for f 5 358 but is much smaller forsmaller f. For taller clouds, the error would be evenmore substantial. Thus, for most of the BLX96 obser-vations the error is small, and the cloud-shadow methodcan be used to infer earth cover (appendix).3. Simulated cloud-field resultsa. ResultsThe ‘‘observed’’ mean earth cover, estimated by sam-pling along lines with the virtual aircraft, is very closeto the true simulated earth cover based on the knownareal coverage of the synthetic clouds (Fig. 3). Theseresults are almost independent of the length of the sim-ulated flight leg, at least for legs as short as 5 km, orabout 2–5 times the mean distance to the nearest neigh-bor, depending on the earth cover. There is a small bias,which increases as the leg length gets shorter (approx-imately 2% bias for the 5-km-long leg).The standard deviation of the mean earth cover forall legs can be calculated to give an estimate of likelymeasurement errors. This leg-to-leg standard deviationdecreases with increasing leg length (Fig. 4). The chang-644 VOLUME 41JOURNAL OF APPLIED METEOROLOGYFIG. 2. Solar zenith angle vs earth-cover fractional error for aspectratios of 2 (no symbol), 1 (squares), and 0.5 (circles). The dashedline marks a fractional error of 1.FIG. 3. Mean line-sampled earth cover vs true simulated earth coverfor legs of 5- (thick solid), 20- (dot–dashed), and 70-km (dashed)length. The thin solid line is the 1:1 line.FIG. 4. Leg-to-leg std dev of the observed earth cover vs leg lengthfor single-line averages (circles) and vs leg length for a swath average(triangles) for a case with a true simulated earth cover of 20% (dashedline).es are smaller for longer legs, however. The standarddeviation is smaller for the swath than for the single-line average. Figure 5 provides another, more explicit,look at the differences between the single-line and swathmeasurements. For this case of 20% true simulated earthcover, the swath estimates of earth cover range from10% to 33% while the single-line average ranges fromabout 7% to 42%.The leg-to-leg standard deviation increases with earthcover for simulated true earth cover values less thanabout 20% (Fig. 6). For the 5-km-long leg, the standarddeviation is larger than the simulated true earth coverfor earth covers ranging from 0% to just under 20%.For simulated earth cover greater than 20%, the standarddeviation is only a weak function of earth cover. Thequalitative shape of the standard deviation curve in Fig.6 can be explained by the bounded nature of earth cover,which can only range between 0% and 100%. The rel-atively small leg-to-leg standard deviation ‘‘measured’’by the virtual aircraft at smaller earth covers is affectedby the number of legs with no earth cover. For example,given 5-km-long legs and 5% earth cover, over 80% ofthe legs flown had no earth cover, leading to a smallerstandard deviation (although still larger than the ob-served earth cover) than would be expected if a distri-bution with negative earth covers was used. As the trueearth cover gets larger, there are fewer legs with 0%earth cover, and the standard deviation increases untilthe effects of the bounding are removed. Similar effectsare expected at larger earth covers, because the maxi-mum earth cover is also bounded.These results have important implications for ground-based instruments. Clouds are advected by the meanwind over ground-based instruments. A hypotheticalwind speed of 10 m s21and an averaging time of 30min (such as that used by ASOS) corresponds to anaveraging length of about 20 km. For legs of this length,the maximum leg-to-leg standard deviation is about10%, and, for earth covers smaller than about 8%, thestandard deviation is larger than the observed earth cov-er (Fig. 6). To reduce the standard deviation to close to5%, an averaging time of 90 min is needed. This timeperiod is long; the nonstationarity of the cloud fieldcould be important.Cases with organized cloud fields have been ignoredin this study. The clouds are assumed to be randomlydistributed. During periods of strong wind, roll vorticescan form (Etling and Brown 1993; Weckwerth et al.1997). In this case, the clouds would be organized inrows that are nearly parallel to the mean wind. Aground-based sensor might measure earth covers thatare very small or very large, depending on the locationJUNE 2002 645BERG AND STULLFIG. 5. Simulated line-sampled vs simulated swath-sampled earth cover for a case with a trueearth cover of 20% (white X) and a leg length of 70 km. The solid line is the 1:1 line; the dashedlines are 610% from the 1:1 line.FIG. 6. Leg-to-leg std dev of sample earth cover vs true earth coverfor flight legs of 5- (solid line with triangles), 20- (dot–dashed linewith squares), and 70-km (dashed with circles) length. The thin soliddiagonal line is the 1:1 line, and points above this diagonal line haveerrors greater than the mean coverage signal.of the sensor relative to the cloud streets. Thus, the errorcould be much larger than the values suggested by thisstudy. It is for just this reason that research flights inthe real convective boundary layer are usually flownacross the wind.The size distributions of clouds cannot be inferredfrom a single leg. There were many legs, even at 40%earth cover and for 70-km-long legs, for which the vir-tual aircraft intercepted only a small number of clouds.When all of the flight legs were combined, however, thecloud size statistics approach the true distribution (notshown).b. ApplicationsAn equation, or a set of equations, that relates theerror in the measured earth cover of fair-weather cumulito the leg length and the earth cover can be found. Suchan equation would be useful to scientists planning a fieldprogram or interpreting results from previous field work.Figure 4 shows an example of the leg-to-leg standarddeviation measured with the virtual aircraft for a truesimulated earth cover of 20%. Similar plots were madefor a range of simulated earth covers; the general shapeof the curves is the same, but there are large differencesin the fit parameters. It may be simpler to relate thenoise-to-signal ratio (NSR) to the leg length, where NSRis defined to beNSR 5 s /x,x(7)where is the average and sxis the standard deviationxof any variable x. The NSR curves unfortunately alsovary greatly with different amounts of earth cover. How-ever, the simulated observations collapse onto one ‘‘uni-versal’’ curve when the NSR is normalized by the NSRof the shortest leg flown, which is the maximum NSR646 VOLUME 41JOURNAL OF APPLIED METEOROLOGYFIG. 7. Human-observed, swath (area) average, earth-cover fractionfor each of the four different scientists (different symbols) vs pyr-anometer-observed, line-sampled, earth-cover fraction for all BLX96cloudy legs. The thin solid line is the 1:1 line; the thin dashed linesare 60.1 from the 1:1 line.(NSRMAX) observed at a given true simulated earth cov-er. A power-law relationship was fit to the NSR/NSRMAXpoints, yielding an expression of the formNSR52(0.0832 6 0.006)NSRMAX2(0.44560.005)1 (2.22 6 0.01)l , (8)where l is the averaging length in kilometers. NSRMAXis a function of earth cover (not shown). Again, a power-law relationship was fit to the NSRMAXdata, yieldingNSR 52(1.03 6 0.07)MAX2(0.46260.01)1 (0.994 6 0.06)a , (9)cloudwhere acloudis the earth-cover fraction. Equations (7),(8), and (9) can be combined to give an expression forthe leg-to-leg standard deviation given some arbitraryleg length and earth cover:20.462 20.445s 5 a (0.0856 2 0.0827a 2 2.29lcloud cloud cloud20.462 20.4451 2.21a l ). (10)cloudFor leg lengths greater than 15 km, (10) is accurate towithin 8% of the standard deviation observed by thevirtual aircraft flying under the simulated cloud field.For shorter flight legs, (10) is not as accurate. For ex-ample, given 5-km-long legs and 5% earth cover, (10)overestimates the standard deviation observed by thevirtual aircraft by about 35% [i.e., 15% predicted by(10) as compared with 11% measured with the virtualaircraft].As an alternative, when planning a field program, onemight be interested in the leg length required to estimatethe earth cover to some desired accuracy. Equations (8)and (9) can be manipulated to give22.25NSRl 510.0374 . (11)20.4621222.28 1 2.21acloudThe average error in leg length predicted by (11) for allsimulated earth covers, as compared with the simulatedflight legs, is about 3%. The maximum error in leglength estimated using (11) in comparison with obser-vations using the virtual aircraft is 14%, which occursfor a simulated earth cover of 20% [i.e., 60.5 km pre-dicted by (11) as compared with 70 km measured withthe virtual aircraft]. In a strict sense, (11) is circular;one must know the earth cover to determine the leglength that is needed to measure the earth cover. Inpractice, however, a range of applicable earth cover orsome approximate value of the earth cover is oftenknown from the climatic data of the field site, so that(11) can be used to estimate the leg lengths needed. Forexample, during BLX96 all of the flights were to takeplace during conditions with fair-weather cumuli coverof 0%–30% but not during conditions with more earthcover. So, (11) could be used with hypothetical earthcovers ranging from near 0% to as large as 30% toestimate the maximum leg length that would be requiredto give good earth-cover estimates.How does the leg length required for accurate esti-mates of earth cover compare to the leg lengths neededfor accurate measurements of turbulent statistics? Len-schow et al. (1994) found that, for a leg length of 20km, the random error in the scalar fluxes is about 18%.For a leg length of 70 km, the error in the scalar fluxesdrops to about 12%. From the Lenschow et al. work,the requirements for the accurate measurement of tur-bulent quantities in the boundary layer are more strictthan that required for measurements of earth cover.Thus, choosing a leg length to give accurate turbulentstatistics should meet the requirements needed for ac-curate measurement of fair-weather boundary layerearth cover.4. Observed BLX96 resultsThe agreement between the airborne observer and theaircraft-mounted pyranometer during BLX96 is goodbut not perfect (Fig. 7). These observations have beencorrected for the cloud-shadow error using (6). Most ofthe observations (90%) are within 610% of each other.There apparently is little bias among the different ob-servers. When the earth cover is small, the airborneobserver tended to estimate larger amounts of earth cov-er than was recorded by the pyranometer.A straight line can be fit to the observations. Theerrors in the pyranometer and the errors in the humanobservations must both be accounted for when fitting astraight line to the data (Press et al. 1992). The error inthe aircraft pyranometer was assumed to follow (10)using a 70-km-long leg. The human errors were takenJUNE 2002 647BERG AND STULLto be similar to those suggested by Young (1967). Twofactors should be considered when using Young’s erroranalysis. His data were for humans analyzing satellitephotos rather than taking a quick look at a real cloudfield, so the errors in BLX96 are likely to be larger thanthose found by Young. The smallest earth cover he usedwas about 3 oktas. This value is about the maximumearth cover observed during BLX96. Young found thatthe error in measured earth cover shrinks as the trueearth cover increases. He argues that as the true earthcover shrinks, the error in measured earth cover shrinksas well. He suggests that for an earth cover of 0, therewould be 0 error in the human observations. This as-sumption precludes using some of the BLX96 data inthe prescribed fitting procedure because 0 error leads toa singularity in the calculations. With all human obser-vations of 0 earth cover removed, the calculated slopeof the best-fit line is 0.9 6 0.13 and the intercept is0.0004 6 0.0002. These fit parameters indicate that thetwo observed distributions are drawn from the sameparent distribution.A second test, the Kolmogorov–Smirnov test, can beused to determine if the observed distributions camefrom the same parent distribution (Press et al. 1992).This test compares the cumulative distributions of twovariables. The largest value of the difference betweenthese two distributions is used as a test statistic and iscompared with the Kolmogorov–Smirnov probabilityfunction to determine the confidence of the estimate.For the BLX96 data, the largest difference in the cu-mulative distribution functions was 0.18 and the p valuewas 0.24, so there is insufficient evidence to indicatethat the distributions are different.While the statistical tests suggest that the parent dis-tributions are the same, there are a number of reasonsfor the scatter in the figure. Sampling errors are a likelyexplanation. The airborne observer looked at cloudshadows projected within a swath area on the groundunder the aircraft. When averaged over the entire flightleg, this corresponds to a wide swath, approximately 3.5km wide during BLX96, through the cloud field. Thepyranometer is a line estimate through the cloud field.The two methods are sampling different areas to esti-mate the earth cover. The experiment with the virtualaircraft can also provide insight into this question. Al-though constructed using only one true simulated earthcover of 20%, Fig. 5 is illuminating. Points for casesof different simulated earth cover could be added to theplot, but the qualitative results would be unchanged.Many of the differences between the swath-based andthe line-sampled earth cover in Fig. 5 are similar inmagnitude to the differences shown in Fig. 7. Hender-son-Sellers and McGuffie’s (1990) results are similar.They compared sky cover and earth cover measuredfrom all-sky images and had much scatter. They foundmany cases in which there were not clouds directlyabove the sensor although some clouds were reportednearby, similar to the BLX96 results at small earth cover.Another factor that could contribute to the differencesat smaller earth cover is the method used by the airborneobserver to measure earth cover. During most of theflights with clouds, it was usual for earth cover to varyalong any single 70-km leg as the aircraft flew throughmeso-g-scale regions that were relatively clearer orcloudier than others. For these situations, the observeronly reported the earth cover at the start of each leg andagain when they noticed a change during the flight. Also,at other times, the observer was busy with other duties.So, particularly when the earth cover is small, there areportions of the leg having no earth cover that might notbe accurately reported. If some 0 values were missed,then the leg average would be too large.5. ConclusionsThe primary goal of this work was to determine theaccuracy of earth-cover measurements by both ground-based and aircraft-mounted sensors for a range ofboundary layer earth covers. Two different comparisonswere made. First, sampled results for both line and swathaverages were compared with the prescribed cloud coverfrom a simulated cloud field. These results suggestedthat, for short flight legs or averaging times, the ob-served standard deviation was often larger than the meanearth cover. When longer flight legs or averaging timeswere used, the earth-cover measurements were within65% of the true cover for a wide range of earth cover.Using the virtual data, a set of empirical equationswas presented so that the appropriate leg length couldbe found for some arbitrary NSR and to find standarddeviation of earth cover from leg length and true earthcover. The accuracy of earth cover inferred from ceil-ometer or other vertically pointed instruments dependson a number of factors, including wind speed. At highwind speeds, these measurements might be suspect be-cause of horizontal roll vortices; at lower wind speeds,the measurements are suspect because of random sam-pling errors.For shallow boundary layer cumuli (i.e., cumulus hu-milis) and high sun angle it was shown that the shadingof the ground by the vertical portion of the cloud sil-houette caused errors of about 5%. For true earth cov-erage between 5% and 30%, this vertical silhouette errorwas small in comparison with typical observation andsampling errors of about 17% for 5-km-long legs andwas about the same size as the observation and samplingerrors for 70-km-long legs.Second, estimates of earth cover from an aircraft-mounted pyranometer were compared with estimatesfrom an airborne observer. In general, there was goodagreement between the airborne human observer andthe pyranometer-measured earth cover from BLX96.Tests were conducted that suggest that the two observeddistributions came from the same parent distribution.However, it also seems that the human observer tendsto estimate a larger earth cover at small values of earth648 VOLUME 41JOURNAL OF APPLIED METEOROLOGYTABLE A1. Date, time, solar zenith angle, cloud-base height, cloud-top height, and boundary layer cloud type [either Cumulus (Cu)humilis or Cu mediocris] of all BLX96 cloudy days.Date Leg Time (LST) Time (UTC)Solar zenithangle (8)Cloud-baseheight (m)Cloud-topheight (m)Boundary layercloud type15 Jul 123456710.211.411.611.913.213.413.716.217.417.617.919.219.419.732.720.718.717. humilisCu humilisCu mediocris/Cu humilisCu mediocris/Cu humilisCu humilisCu humilisCu humilis16 Jul 123456710.811.912.212.413.713.914.116.817.918.218.419.719.920.126.215.514.514.121.223.726.19731142117712131195119211881626203921242213192618701816Cu humilisCu humilisCu humilisCu humilisCu humilisCu humilisCu humilis23 Jul 1234511.812.914.114.314.617.818.920.120.320.619. humilisCu humilisCu humilisCu humilisCu humilis25 Jul 123456711.112.312.612.814.114.314.617.118.318.618.820.120.320.624.717.417.418.127.830.433.317332253236424672441243624301965258827202844266426292590Cu humilisCu humilisCu humilisCu humilisCu humilisCu humilisCu humilis27 Jul 123456711.012.212.512.713.914.214.517.018.218.518.719.920.220.526.617.817.317.425.328.031.05517688188669449629796969329861038112611461166Cu humilisCu mediocris/Cu humilisCu humilisCu mediocris/Cu humilisCu humilisCu humilisCu humilis28 Jul 123456711.312.512.813.114.314.614.917.318.518.819.120.320.620.922.116.517.218.629.833.136.39411164121712661305131413231556178218361886160015321468Cu mediocris/Cu humilisCu mediocris/Cu humilisCu mediocris/Cu humilisCu mediocris/Cu humilisCu mediocris/Cu humilisCu humilisCu humiliscover. Two suggestions are made that might explainthese differences: 1) different sampling techniques be-tween the human and pyranometer and 2) improper re-cording of 0% earth cover.Field work should include a structured methodologyfor the airborne observer to measure earth cover. It isrecommended that human estimates should be made atregular intervals during the flight and intercomparisonsamong the observers should be undertaken. This re-search also shows, however, that given the accuracy ofthe pyranometer-measured earth cover for long flightlegs, human estimates might not be necessary.Acknowledgments. The lead author was funded by aUniversity of British Columbia University GraduateFellowship and by the Canadian Climate Research Net-work through grants from the National Science and En-gineering Research Council (NSERC), MeteorologicalService of Canada (MSC), and the Canadian Foundationfor Climate and Atmospheric Science. Additional sup-port was provided by the Geophysical Disaster Com-putational Fluid Dynamics Centre and grants fromNSERC and Environment Canada. The BLX96 fieldprogram was funded by the U.S. National Science Foun-dation (NSF) under Grant ATM-9411467. E. Santosoand J. Hacker are thanked for their work as airbornescientists during BLX96. The staff and flight crew ofthe University of Wyoming King Air aircraft (sponsoredby NSF) helped to make BLX96 a success. Suggestionsprovided by two anonymous reviewers greatly improvedthis article.APPENDIXBLX96 Cloud-Field StatisticsTable A1 provides the descriptive material for allcloudy days during BLX96.JUNE 2002 649BERG AND STULLTABLE A1. 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