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Accuracy of Point and Line Measures of Boundary Layer Cloud Amount. Berg, Larry K. 2011

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640 VOLUME 41J O U R N A L O F A P P L I E D M E T E O R O L O G Y q 2002 American Meteorological Society Accuracy of Point and Line Measures of Boundary Layer Cloud Amount LARRY K. BERG AND ROLAND B. STULL Atmospheric 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) ABSTRACT Many 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 averaging times commonly used with surface instruments. A set of empirical equations is found to provide an estimate of the errors associated with averaging time and earth cover. These relationships can be used to design observation strategies (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-looking pyranometer and earth cover observed by airborne scientists in a research aircraft. In general, the agreement between these two methods is good. 1. Introduction and motivation One of the oldest, and perhaps most common, meth- ods of observing cloud cover is to use a human observer stationed on the ground. In this case, the observer re- ports the fraction of sky dome that is covered with clouds. As an alternative, cloud cover can be reported in terms of the fraction of the earth’s surface that is covered by clouds. This value can be measured with a downward-looking satellite. It also can be measured as a cloud field is blown over a vertically looking, nar- rowbeam sensor on the ground or as a sensor on an aircraft is flown over or under a cloud field. These two measures of cloud amount are usually not the same, because both the cloud base and cloud sides block parts of the sky dome, so that sky cover is greater than earth cover (Appleman 1962; Hoyt 1977). Both Malick et al. (1979) and Henderson-Sellers and McGuffie (1990) have developed empirical relationships that couple these two kinds of observations. These different definitions of cloud cover may be useful for different applications. The sky cover is useful for radiation budget measurements in which presence of cloud sides contributes to both the short- and long- wave radiation received at a point on the surface. Earth cover of fair-weather cumuli is a pertinent parameter for coupling boundary layer processes to the amount of Corresponding author address: Larry K. Berg, Dept. of Earth and Ocean Sciences, The University of British Columbia, 6339 Stores Rd., Vancouver, BC V6T 1Z4, Canada. E-mail: lkberg@eos.ubc.ca cloud cover and for determining the transfer of pollut- ants out of the convective boundary layer. Many researchers, as well as the Automated Surface Observing System (ASOS) used by the National Weath- er Service and Federal Aviation Administration, use a ceilometer, 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 et al. (2000) are recent examples]. For these instruments a cloud is detected when the sensor’s emitted light is scattered off clouds and returned to a detector on the surface. Earth cover is the fraction of measurement in- tervals, over some arbitrary averaging time, in which clouds are detected. A typical averaging time is 0.5 h. Other methods are passive, detecting a cloud when sunlight reaching a pyranometer on the ground or on an aircraft is interrupted by cloud shadow (Ek and Mahrt 1991). When the sun is not directly overhead, errors arise because the silhouette of the cloud blocking the sunlight includes the vertical depth of the cloud, not just the horizontal cross-sectional area. Many observers have used vertically pointing sen- sors, but little has been mentioned of the accuracy of these measurements. Aviolat et al. (1998) are an ex- ception. They indicate that ceilometers are not a good tool to estimate cloud cover because they are point mea- surements. The sampling error associated with a point measurement can be large, particularly during periods with low wind speeds, when few clouds move over the sensor. To improve the accuracy of these measurements, a longer averaging time can be used; however, nonsta- JUNE 2002 641B E R G A N D S T U L L tionarity of the cloud field could become an important factor. Feijt and van Lammeren (1996) improved their cloud-cover measurements by combining ceilometer measurements 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 time or distance. For airborne sensors, this could be the length of time it takes to fly one flight leg. For sensors on the ground, this corresponds to the length of atmo- sphere advected over the sensor. Inspired by the work of Poellot and Cox (1977), who looked at the averaging time needed to measure accurate shortwave fluxes, and Santoso and Stull (1999), who designed optimal flight patterns to sample boundary layer turbulence, we con- ducted tests in which a virtual aircraft is ‘‘flown’’ under a simulated cloud field. An empirical set of equations is found for the virtual data that relates the measurement errors 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 Boundary Layer Experiment 1996 (BLX96; Stull et al. 1997; Berg et al. 1997). 2. Earth-cover observation methods a. Simulated observations There has been much debate in the literature about the nature of the spatial distributions of real cumuli. Some researchers have suggested that cumuli are clumped (Plank 1969; Randall and Huffman 1980; Jo- seph and Cahalan 1990; Sengupta et al. 1990). Other authors believed that fields of cumuli were regular (Bretherton 1987, 1988; Ramirez and Bras 1990). Some authors have assumed that cloud fields were randomly distributed (Ellingson 1982; Zuev et al. 1987). Others have found that smaller cumuli were clumped and the larger cumuli tended to a more regular or random dis- tribution (Weger et al. 1992; Zhu et al. 1992). Ramirez and Bras (1990), Weger et al. (1992), and Zhu et al. (1992) related observed or simulated nearest-neighbor distributions to theoretical nearest-neighbor distribu- tions for a random process, for many different cloud fields. They found that very different looking cloud fields, including random cloud fields, could produce similar nearest-neighbor distributions. A random cloud field was used in this simulation study. Vertically thin, horizontally circular clouds were randomly placed on a regular 0.1-km grid in a 710 km 3 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 showed that 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 lognormal distribution were chosen to be consistent with the ob- servations of Lopez (1977) and Plank (1969). For the results presented, the mean cloud radius was 0.5 km and the 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 located within the domain, but clouds could hang off the edge of the domain. This method might lead to inaccurate earth-cover estimates near the edge, because no clouds were allowed to hang onto the domain. To eliminate edge effects, the simulated aircraft ‘‘flew’’ horizontal legs within a subdomain of 690 km 3 72 km. Each parallel leg was 0.1 km apart laterally and ranged in length from 5 to 70 km. During each virtual flight, the fraction of the flight leg that was under simulated clouds was recorded to provide a line average. These results also correspond to a cloud field advecting over a ground- based sensor at a variety of wind speeds. A second experiment using the virtual aircraft was conducted to compare earth-cover estimates made along a single line through the cloud field to the earth cover estimated using a swath (area) average centered on the aircraft. This experiment corresponds more closely to the earth-cover measurements by an observer on an air- craft who can see cloud shadows covering the ground to the left and right of the aircraft track, in addition to the shadows immediately ahead. The width of the swath (3.5 km) was chosen to be similar to the area beneath the aircraft used to estimate earth cover during the field experiment described in the next section. b. Boundary Layer Experiment 1996 observations BLX96 was conducted from 15 July to 13 August 1996 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 the daytime convective boundary layer. At aircraft speeds of roughly 90 m s21, each leg took about 15 min to complete. All of the flight legs were flown between 1000 and 1500 LST, with most legs between 1100 and 1400 LST. Solar zenith angles f ranged between approxi- mately 158 and 368 and were less than 308 for 80% of the legs flown. BLX96 was designed to meet several different goals (Stull et al. 1997). One of these goals was to provide data for verification of boundary layer cumuli param- eterizations. Earth cover is a key variable for verification of parameterizations. Standard surface observations are unsatisfactory because they measure sky cover rather than earth cover and would be valid for only a fraction of the flight track. Observations of earth cover by an 642 VOLUME 41J O U R N A L O F A P P L I E D M E T E O R O L O G Y observer on the ground (either human or electronic) would be unreliable because only one or two clouds might be directly over the observer, leading to a large sampling 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, two alternative methods for measuring earth cover were used during 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 m22 was applied to the unfiltered pyranometer time series to determine when the aircraft passed through a cloud shadow (Ek and Mahrt 1991). The estimated earth cover was defined as the fraction of the whole leg that was within cloud shadows. The pyranometer-measured earth cover 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 under the flight tracks was divided by roads and fence lines into 800-m (0.5 mi) sections, allowing for more accurate estimates of earth cover. All of the manual estimates for a given flight leg were averaged together to give a leg average. The number of human observations logged dur- ing any given leg ranged from 1 to 10. Four different airborne scientists flew during BLX96. Although all four scientists trained together before the field program in an attempt to equalize their observations, there may be biases in earth-cover estimates. Young (1967) found that differences among observers working with the same satellite images were as large as 2 oktas for the range of earth covers he studied. Similar errors might be ex- pected for the observations made during BLX96. The airborne scientists also logged cloud thickness of the cumulus humilis clouds in three ways: 1) by estimating aspect ratio (cloud width to cloud height) visually, 2) by logging cloud-base and cloud-top altitudes during ascent/descent slant aircraft soundings, and 3) via post- flight inspection of footage from the forward-looking automatic airborne video camera. c. Effect of solar zenith angle on cloud shadows Using 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, part of the sunlight could be blocked by the cloud sides, causing the shadow projected onto the earth’s surface to be larger than the true earth cover. Taller clouds en- hance this effect because more sunlight is blocked. For shallow clouds and high sun, however, the earth-cover errors are minimal. During BLX96 most flight legs were flown during fair-weather, anticyclonic conditions with- in a few hours of solar noon. It was observed during BLX96 that most the cumuli were short, with an aspect ratio between 1 and 2. A simple analytical experiment can be used to esti- mate the error in measured earth cover due to different f and cloud aspect ratios. For this analysis, the down- welling radiation is assumed to be plane parallel. Clouds are assumed to have flat bottoms, a square base, and to be semicircular or semielliptical in cross section parallel to the sun’s rays (Fig. 1). Clouds are assumed to have a rectangular cross section in the dimension perpendic- ular to the sun’s rays. One important implication of this cloud geometry is that cloud shadow is rectangular. With these assumptions and a value of f, the amount that cloud shadows overestimate earth cover can be cal- culated analytically. Figure 1 shows an example in which the cloud shadow is some amount dA larger than the true earth cover A. The geometric location of cloud top is defined using 2 2x z 1 5 1, (1) 2 2x zc c where xc is one-half the cloud width and zc is the cloud thickness. The location on the cloud at which the sun’s ray 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 derivative of (1) with respect to x to find the slope of the tangent line at any point along the cloud’s top. Combining this result with (1) and f yields equations for the z location (ztan) and the x location (xtan) at which the sun’s ray is tangent to the cloud’s top: 21/2 2 2x tan (p /2 2 f)cz 5 z 1 1 , and (2)tan c 2[ ]zc 2 2 1/2x 5 x [(1 2 z /z )] . (3)tan c tan c As shown in Fig. 1, the triangle (ABC) formed by a vertical line through the tangent point, the cloud base, and the line representing the sun’s ray can be used to find the length dx added to the cloud shadow. This equa- tion can be written as dx 5 x 1 z tan(f) 2 x .tan tan c (4) Equations (3) and (4) show that the error is a function of the cloud thickness, cloud width, and f. As a check of the behavior of these equations we find that, as f approaches 0 in (2), tan2(p/2 2 f) approaches infinity and ztan approaches 0. Using (3), we find that xtan 5 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 4x y 1 2y dx. (5)c c c c c The total area is a function of cloud height, cloud di- ameter, and f. A fractional error can be defined as [(A 1 dA)/A], which, by using (5), can be rewritten as 1 1 JUNE 2002 643B E R G A N D S T U L L FIG. 1. Sketch showing cloud geometry used to estimate the earth-cover error associated with cloud thickness and solar zenith angle f. Heavy descending arrows represent the actual sun’s rays; the thin one represents a ray striking the edge of an infinitely thin cloud. The shaded semicircle aloft is a single boundary layer cumulus with height zc. The point xtan, ztan marks the tangent point of the sun’s ray. Shading below the cloud shows the true cloud width 2xc and the error dx associated with the solar zenith angle. dx/2xc. Combining this form of the fractional error with (2)–(4) yields an equation for the fractional error that is a function of only the aspect ratio of the cloud (R 5 2xc ) and f:21zc A 1 dA A 1 2 2 21 1/25 ^1 1 {1 2 [0.25R tan (p /2 2 f) 1 1] } 2 22 2 22 21/21 4R [tan (p /2 2 f) 1 4R ] tan(f)&. (6) From the observations of cloud diameters and cloud heights during BLX96 and from the solar zenith angle calculated from the time, latitude, and longitude of the flights, the error in earth cover associated with the cloud shadows can be calculated. For shallow clouds with an aspect ratio of 2, the fractional error is small, 1.11 for f 5 358 (Fig. 2). As the clouds grow deeper, the error increases; for clouds with an aspect ratio of 1, the frac- tional error is 1.36 for f 5 358 but is much smaller for smaller f. For taller clouds, the error would be even more substantial. Thus, for most of the BLX96 obser- vations the error is small, and the cloud-shadow method can be used to infer earth cover (appendix). 3. Simulated cloud-field results a. Results The ‘‘observed’’ mean earth cover, estimated by sam- pling along lines with the virtual aircraft, is very close to the true simulated earth cover based on the known areal coverage of the synthetic clouds (Fig. 3). These results are almost independent of the length of the sim- ulated flight leg, at least for legs as short as 5 km, or about 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 for all legs can be calculated to give an estimate of likely measurement errors. This leg-to-leg standard deviation decreases with increasing leg length (Fig. 4). The chang- 644 VOLUME 41J O U R N A L O F A P P L I E D M E T E O R O L O G Y FIG. 2. Solar zenith angle vs earth-cover fractional error for aspect ratios of 2 (no symbol), 1 (squares), and 0.5 (circles). The dashed line marks a fractional error of 1. FIG. 3. Mean line-sampled earth cover vs true simulated earth cover for 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 length for single-line averages (circles) and vs leg length for a swath average (triangles) for a case with a true simulated earth cover of 20% (dashed line). es are smaller for longer legs, however. The standard deviation 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 swath measurements. For this case of 20% true simulated earth cover, the swath estimates of earth cover range from 10% to 33% while the single-line average ranges from about 7% to 42%. The leg-to-leg standard deviation increases with earth cover for simulated true earth cover values less than about 20% (Fig. 6). For the 5-km-long leg, the standard deviation is larger than the simulated true earth cover for earth covers ranging from 0% to just under 20%. For simulated earth cover greater than 20%, the standard deviation is only a weak function of earth cover. The qualitative 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 affected by the number of legs with no earth cover. For example, given 5-km-long legs and 5% earth cover, over 80% of the legs flown had no earth cover, leading to a smaller standard 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 true earth cover gets larger, there are fewer legs with 0% earth cover, and the standard deviation increases until the effects of the bounding are removed. Similar effects are 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 mean wind over ground-based instruments. A hypothetical wind speed of 10 m s21 and an averaging time of 30 min (such as that used by ASOS) corresponds to an averaging length of about 20 km. For legs of this length, the maximum leg-to-leg standard deviation is about 10%, and, for earth covers smaller than about 8%, the standard deviation is larger than the observed earth cov- er (Fig. 6). To reduce the standard deviation to close to 5%, an averaging time of 90 min is needed. This time period is long; the nonstationarity of the cloud field could be important. Cases with organized cloud fields have been ignored in this study. The clouds are assumed to be randomly distributed. During periods of strong wind, roll vortices can form (Etling and Brown 1993; Weckwerth et al. 1997). In this case, the clouds would be organized in rows that are nearly parallel to the mean wind. A ground-based sensor might measure earth covers that are very small or very large, depending on the location JUNE 2002 645B E R G A N D S T U L L FIG. 5. Simulated line-sampled vs simulated swath-sampled earth cover for a case with a true earth cover of 20% (white X) and a leg length of 70 km. The solid line is the 1:1 line; the dashed lines are 610% from the 1:1 line. FIG. 6. Leg-to-leg std dev of sample earth cover vs true earth cover for flight legs of 5- (solid line with triangles), 20- (dot–dashed line with squares), and 70-km (dashed with circles) length. The thin solid diagonal line is the 1:1 line, and points above this diagonal line have errors greater than the mean coverage signal. of the sensor relative to the cloud streets. Thus, the error could be much larger than the values suggested by this study. It is for just this reason that research flights in the real convective boundary layer are usually flown across the wind. The size distributions of clouds cannot be inferred from 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, the cloud size statistics approach the true distribution (not shown). b. Applications An equation, or a set of equations, that relates the error in the measured earth cover of fair-weather cumuli to the leg length and the earth cover can be found. Such an equation would be useful to scientists planning a field program or interpreting results from previous field work. Figure 4 shows an example of the leg-to-leg standard deviation measured with the virtual aircraft for a true simulated earth cover of 20%. Similar plots were made for a range of simulated earth covers; the general shape of the curves is the same, but there are large differences in the fit parameters. It may be simpler to relate the noise-to-signal ratio (NSR) to the leg length, where NSR is defined to be NSR 5 s /x ,x (7) where is the average and sx is the standard deviationx of any variable x. The NSR curves unfortunately also vary 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 NSR of the shortest leg flown, which is the maximum NSR 646 VOLUME 41J O U R N A L O F A P P L I E D M E T E O R O L O G Y FIG. 7. Human-observed, swath (area) average, earth-cover fraction for each of the four different scientists (different symbols) vs pyr- anometer-observed, line-sampled, earth-cover fraction for all BLX96 cloudy legs. The thin solid line is the 1:1 line; the thin dashed lines are 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/NSRMAX points, yielding an expression of the form NSR 5 2(0.0832 6 0.006) NSRMAX 2(0.44560.005)1 (2.22 6 0.01)l , (8) where l is the averaging length in kilometers. NSRMAX is a function of earth cover (not shown). Again, a power- law relationship was fit to the NSRMAX data, yielding NSR 5 2(1.03 6 0.07)MAX 2(0.46260.01)1 (0.994 6 0.06)a , (9)cloud where acloud is the earth-cover fraction. Equations (7), (8), and (9) can be combined to give an expression for the leg-to-leg standard deviation given some arbitrary leg length and earth cover: 20.462 20.445s 5 a (0.0856 2 0.0827a 2 2.29lcloud cloud cloud 20.462 20.4451 2.21a l ). (10)cloud For leg lengths greater than 15 km, (10) is accurate to within 8% of the standard deviation observed by the virtual 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 the virtual aircraft by about 35% [i.e., 15% predicted by (10) as compared with 11% measured with the virtual aircraft]. As an alternative, when planning a field program, one might be interested in the leg length required to estimate the earth cover to some desired accuracy. Equations (8) and (9) can be manipulated to give 22.25NSR l 5 1 0.0374 . (11) 20.4621 222.28 1 2.21acloud The average error in leg length predicted by (11) for all simulated earth covers, as compared with the simulated flight legs, is about 3%. The maximum error in leg length estimated using (11) in comparison with obser- vations using the virtual aircraft is 14%, which occurs for a simulated earth cover of 20% [i.e., 60.5 km pre- dicted by (11) as compared with 70 km measured with the virtual aircraft]. In a strict sense, (11) is circular; one must know the earth cover to determine the leg length that is needed to measure the earth cover. In practice, however, a range of applicable earth cover or some approximate value of the earth cover is often known from the climatic data of the field site, so that (11) can be used to estimate the leg lengths needed. For example, during BLX96 all of the flights were to take place during conditions with fair-weather cumuli cover of 0%–30% but not during conditions with more earth cover. So, (11) could be used with hypothetical earth covers ranging from near 0% to as large as 30% to estimate the maximum leg length that would be required to give good earth-cover estimates. How does the leg length required for accurate esti- mates of earth cover compare to the leg lengths needed for accurate measurements of turbulent statistics? Len- schow et al. (1994) found that, for a leg length of 20 km, the random error in the scalar fluxes is about 18%. For a leg length of 70 km, the error in the scalar fluxes drops 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 strict than that required for measurements of earth cover. Thus, choosing a leg length to give accurate turbulent statistics should meet the requirements needed for ac- curate measurement of fair-weather boundary layer earth cover. 4. Observed BLX96 results The agreement between the airborne observer and the aircraft-mounted pyranometer during BLX96 is good but not perfect (Fig. 7). These observations have been corrected for the cloud-shadow error using (6). Most of the 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 airborne observer tended to estimate larger amounts of earth cov- er than was recorded by the pyranometer. A straight line can be fit to the observations. The errors in the pyranometer and the errors in the human observations must both be accounted for when fitting a straight line to the data (Press et al. 1992). The error in the aircraft pyranometer was assumed to follow (10) using a 70-km-long leg. The human errors were taken JUNE 2002 647B E R G A N D S T U L L to be similar to those suggested by Young (1967). Two factors should be considered when using Young’s error analysis. His data were for humans analyzing satellite photos rather than taking a quick look at a real cloud field, so the errors in BLX96 are likely to be larger than those found by Young. The smallest earth cover he used was about 3 oktas. This value is about the maximum earth cover observed during BLX96. Young found that the error in measured earth cover shrinks as the true earth cover increases. He argues that as the true earth cover shrinks, the error in measured earth cover shrinks as well. He suggests that for an earth cover of 0, there would be 0 error in the human observations. This as- sumption precludes using some of the BLX96 data in the prescribed fitting procedure because 0 error leads to a singularity in the calculations. With all human obser- vations of 0 earth cover removed, the calculated slope of the best-fit line is 0.9 6 0.13 and the intercept is 0.0004 6 0.0002. These fit parameters indicate that the two observed distributions are drawn from the same parent distribution. A second test, the Kolmogorov–Smirnov test, can be used to determine if the observed distributions came from the same parent distribution (Press et al. 1992). This test compares the cumulative distributions of two variables. The largest value of the difference between these two distributions is used as a test statistic and is compared with the Kolmogorov–Smirnov probability function 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 value was 0.24, so there is insufficient evidence to indicate that the distributions are different. While the statistical tests suggest that the parent dis- tributions are the same, there are a number of reasons for the scatter in the figure. Sampling errors are a likely explanation. The airborne observer looked at cloud shadows projected within a swath area on the ground under the aircraft. When averaged over the entire flight leg, this corresponds to a wide swath, approximately 3.5 km wide during BLX96, through the cloud field. The pyranometer 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 virtual aircraft can also provide insight into this question. Al- though constructed using only one true simulated earth cover of 20%, Fig. 5 is illuminating. Points for cases of different simulated earth cover could be added to the plot, but the qualitative results would be unchanged. Many of the differences between the swath-based and the line-sampled earth cover in Fig. 5 are similar in magnitude to the differences shown in Fig. 7. Hender- son-Sellers and McGuffie’s (1990) results are similar. They compared sky cover and earth cover measured from all-sky images and had much scatter. They found many cases in which there were not clouds directly above the sensor although some clouds were reported nearby, similar to the BLX96 results at small earth cover. Another factor that could contribute to the differences at smaller earth cover is the method used by the airborne observer to measure earth cover. During most of the flights with clouds, it was usual for earth cover to vary along any single 70-km leg as the aircraft flew through meso-g-scale regions that were relatively clearer or cloudier than others. For these situations, the observer only reported the earth cover at the start of each leg and again 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 are portions of the leg having no earth cover that might not be accurately reported. If some 0 values were missed, then the leg average would be too large. 5. Conclusions The primary goal of this work was to determine the accuracy of earth-cover measurements by both ground- based and aircraft-mounted sensors for a range of boundary layer earth covers. Two different comparisons were made. First, sampled results for both line and swath averages were compared with the prescribed cloud cover from a simulated cloud field. These results suggested that, for short flight legs or averaging times, the ob- served standard deviation was often larger than the mean earth cover. When longer flight legs or averaging times were used, the earth-cover measurements were within 65% of the true cover for a wide range of earth cover. Using the virtual data, a set of empirical equations was presented so that the appropriate leg length could be found for some arbitrary NSR and to find standard deviation of earth cover from leg length and true earth cover. The accuracy of earth cover inferred from ceil- ometer or other vertically pointed instruments depends on a number of factors, including wind speed. At high wind 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 shading of 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 error was small in comparison with typical observation and sampling errors of about 17% for 5-km-long legs and was about the same size as the observation and sampling errors for 70-km-long legs. Second, estimates of earth cover from an aircraft- mounted pyranometer were compared with estimates from an airborne observer. In general, there was good agreement between the airborne human observer and the pyranometer-measured earth cover from BLX96. Tests were conducted that suggest that the two observed distributions came from the same parent distribution. However, it also seems that the human observer tends to estimate a larger earth cover at small values of earth 648 VOLUME 41J O U R N A L O F A P P L I E D M E T E O R O L O G Y TABLE 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 zenith angle (8) Cloud-base height (m) Cloud-top height (m) Boundary layer cloud type 15 Jul 1 2 3 4 5 6 7 10.2 11.4 11.6 11.9 13.2 13.4 13.7 16.2 17.4 17.6 17.9 19.2 19.4 19.7 32.7 20.7 18.7 17.0 18.2 20.1 22.3 1552 1654 1675 1697 1872 1906 1939 1825 2343 2452 2565 2704 2731 2758 Cu humilis Cu humilis Cu mediocris/Cu humilis Cu mediocris/Cu humilis Cu humilis Cu humilis Cu humilis 16 Jul 1 2 3 4 5 6 7 10.8 11.9 12.2 12.4 13.7 13.9 14.1 16.8 17.9 18.2 18.4 19.7 19.9 20.1 26.2 15.5 14.5 14.1 21.2 23.7 26.1 973 1142 1177 1213 1195 1192 1188 1626 2039 2124 2213 1926 1870 1816 Cu humilis Cu humilis Cu humilis Cu humilis Cu humilis Cu humilis Cu humilis 23 Jul 1 2 3 4 5 11.8 12.9 14.1 14.3 14.6 17.8 18.9 20.1 20.3 20.6 19.1 17.0 26.1 28.9 31.9 804 802 1347 1467 1592 1197 1081 1576 1684 1798 Cu humilis Cu humilis Cu humilis Cu humilis Cu humilis 25 Jul 1 2 3 4 5 6 7 11.1 12.3 12.6 12.8 14.1 14.3 14.6 17.1 18.3 18.6 18.8 20.1 20.3 20.6 24.7 17.4 17.4 18.1 27.8 30.4 33.3 1733 2253 2364 2467 2441 2436 2430 1965 2588 2720 2844 2664 2629 2590 Cu humilis Cu humilis Cu humilis Cu humilis Cu humilis Cu humilis Cu humilis 27 Jul 1 2 3 4 5 6 7 11.0 12.2 12.5 12.7 13.9 14.2 14.5 17.0 18.2 18.5 18.7 19.9 20.2 20.5 26.6 17.8 17.3 17.4 25.3 28.0 31.0 551 768 818 866 944 962 979 696 932 986 1038 1126 1146 1166 Cu humilis Cu mediocris/Cu humilis Cu humilis Cu mediocris/Cu humilis Cu humilis Cu humilis Cu humilis 28 Jul 1 2 3 4 5 6 7 11.3 12.5 12.8 13.1 14.3 14.6 14.9 17.3 18.5 18.8 19.1 20.3 20.6 20.9 22.1 16.5 17.2 18.6 29.8 33.1 36.3 941 1164 1217 1266 1305 1314 1323 1556 1782 1836 1886 1600 1532 1468 Cu mediocris/Cu humilis Cu mediocris/Cu humilis Cu mediocris/Cu humilis Cu mediocris/Cu humilis Cu mediocris/Cu humilis Cu humilis Cu humilis cover. Two suggestions are made that might explain these 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 methodology for the airborne observer to measure earth cover. It is recommended that human estimates should be made at regular intervals during the flight and intercomparisons among the observers should be undertaken. This re- search also shows, however, that given the accuracy of the pyranometer-measured earth cover for long flight legs, human estimates might not be necessary. Acknowledgments. The lead author was funded by a University of British Columbia University Graduate Fellowship and by the Canadian Climate Research Net- work through grants from the National Science and En- gineering Research Council (NSERC), Meteorological Service of Canada (MSC), and the Canadian Foundation for Climate and Atmospheric Science. Additional sup- port was provided by the Geophysical Disaster Com- putational Fluid Dynamics Centre and grants from NSERC and Environment Canada. The BLX96 field program was funded by the U.S. National Science Foun- dation (NSF) under Grant ATM-9411467. E. Santoso and J. Hacker are thanked for their work as airborne scientists during BLX96. The staff and flight crew of the University of Wyoming King Air aircraft (sponsored by NSF) helped to make BLX96 a success. Suggestions provided by two anonymous reviewers greatly improved this article. APPENDIX BLX96 Cloud-Field Statistics Table A1 provides the descriptive material for all cloudy days during BLX96. JUNE 2002 649B E R G A N D S T U L L TABLE A1. 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