1. Introduction
Observational estimates of cloud optical depth τ are sought for many reasons, most of which hinge on the important role played by τ in determining earth's radiation budget and climate (Mitchell et al. 1995). Though satellite estimates of τ can be used to help assess global climate models (Han et al. 1998), they are not perfect (Min and Harrison 1996; Barker et al. 1998; Li et al. 1999) and must be validated independently. Moreover, satellites often provide inadequate sampling for some studies, notably field experiments. The other obvious platforms from which suitable observations can be made are fixed surface sites and aircraft. Estimates of τ from surface-based radiometric measurements are spatially limited but can provide excellent temporal coverage, as well as help validate satellite estimates. Conventional surface-based methods for inferring τ use pyranometer data and a plane-parallel homogeneous radiative transfer model (e.g., Leontyeva and Stamnes 1994; Leontieva et al. 1994; Barker et al. 1998) and are known to work fairly well for overcast only. Barker and Marshak's (2001, referred to hereinafter as BM2001) method for inferring τ from surface data extends Marshak et al.'s (2000) normalized difference cloud index (NDCI) and uses time series of zenith radiances and fluxes measured at two wavelengths that have different local area-averaged surface albedos αs. While their method was shown to do well for nonovercast clouds, it requires, in addition to spectral αs, estimates of cloud-base altitude and cloud advection rate. Moreover, like all fixed surface sites, it is at the mercy of advection, inevitable anisotropic biases in cloud structure, and undersampling.
Far fewer attempts have been made to infer τ from aircraft observations than from the surface. For example, Gultepe et al. (2001) used in situ data to estimate mean droplet extinction coefficient β, which was then multiplied by mean cloud geometric thickness deduced by flying above and below cloud. Techniques such as these are, however, subject to much uncertainty and, like the conventional surface method, can be expected to yield just mean τ and work well for extensive planar clouds only.
The primary purpose of this paper is to present an aircraft-based method of inferring τ for planar and broken-cloud conditions that builds on BM2001's surface technique. The advantages that this method has over Barker and Marshak's is that it does not require information about surface albedo and it is less susceptible to poor sampling.
In the second section, the method for inferring τ from aircraft-mounted radiometers is presented. The third section presents data and modeling techniques used to test the proposed method. As this method is based in part on a Green's function formulation of radiative transfer, properties of relevant Green's function are presented in the fourth section. In the fifth section, the method is demonstrated and contrasted against its surface-based counterpart (BM2001). The sixth section addresses the issue of feasibility, and conclusions are drawn in the final section.
2. Model development
This section has two subsections, the first of which presents the theoretical foundation and assumptions behind the retrieval algorithm and parallels that in BM2001. The second discusses additional assumptions and outlines application of the algorithm.
a. Theory
b. Application
The third key assumption of the method presented here is that measurements of
3. Experimental setup
a. Radiative transfer calculations
A 3D Monte Carlo photon transport algorithm employing cyclic horizontal boundary conditions was used to compute
b. Cloud fields
It is likely that vertical homogeneity of clouds in Scene A complicates the retrieval process for many simulated flightpaths inside clouds. This is because at any level, more cloud is beneath the plane, masking the surface (see section 6), than would be the case for a cloud with β increasing with altitude (e.g., Stephens and Platt 1987).
The second field, Scene B, was simulated by a 2D, nonhydrostatic cloud-resolving model (Szyrmer and Zawadzki 1999) that employed Brenguier and Grabowski's (1993) microphysical scheme. Vertical and horizontal grid spacings are 25 m and the domain extends from the surface to 1.5 km and is 100 km long; the 2D nature facilitated an extra long transect. For each cell, β, ω0, and g were determined as a function of liquid water content and re using the 0.75–0.78-μm band in Slingo's (1989) parameterization. Figure 3 shows τ and re for each cell in an 11-km stretch near the center of the domain. While some cloudy cells are at altitudes as low as 400 m, the vast majority are above 1 km.
It is worth noting that algorithmic performance is likely to be enhanced by the 2D nature of the clouds in Scene B. Since the clouds are fairly planar, however, this is likely to be minor.
c. Surface albedo fields
Two fields of surface albedos were used, both of which were assumed to be Lambertian. The first field was homogeneous with albedos of 0.1 and 0.5 representing wavelengths ∼0.65 and ∼0.87 μm. This field was used for Scene B. The second was used with Scene A and is based on data collected near the Atmospheric Radiation Measurement (ARM) Program's Southern Great Plains (SGP) site in Oklahoma (Stokes and Schwartz 1994). Land types were obtained from the 28.5-m-resolution Landsat database collected during spring and summer and classified by the U.S. Department of Agriculture Hydrology Lab and archived at the Goddard Space Flight Center-Distributed Active Archive Center (GSFC-DAAC). Albedos corresponding to wavelengths 0.65 and 0.87 μm were assigned, based on spectral surface measurements made during March 2000 (see Table 2). Figure 4 shows a marked contrast between these albedos. This is because much of the domain was covered by very young, green vegetation (e.g., Kimes 1983; Kimes et al. 1986; Myneni and Asrar 1993; Lyapustin 1999). Domain-averaged albedos and standard deviations at these wavelengths are 0.090 ± 0.049 and 0.381 ± 0.091, respectively. The fact that the maps in Fig. 4 are only first-order estimates of conditions around the SGP central facility is irrelevant for the present application. Nevertheless, it is interesting to note that one- and two-point statistics of the fields shown in Fig. 4 can be captured extremely well by a 2D cascade model with spectral exponent −1 (see Marshak et al. 1995b for details).
4. Normalized Green's function
The purpose of this section is to provide an approximate, yet simple, means of using
As z decreases below ∼1.15 km, an increasing number of photons begin their trajectories beneath cloud base and so can experience long initial lateral jumps (before the first scattering event) that are beyond the realm of diffusion. By the time the injection level is at the surface (z = 0), long initial lateral jumps significantly boost 〈s2〉, and thus 〈s2〉/〈Δz2〉, thereby signifying a radical departure from the diffusion domain. BM2001 dealt with this anomalous diffusive aspect by simple geometric ray tracing from surface to cloud base. This is evident in Fig. 5a as well: at z = 0, the mode of
Monte Carlo–derived estimates of
5. Cloud optical depth retrievals
The simulations reported here used θ0 of 40° for Scene A and 30° and 60° for Scene B. For this idealized pilot study, the instruments were assumed to be perfect (Monte Carlo noise being the only source of error). For Scene A, the sun shone from the south (from direction ↑ in Figs. 2 and 4); other solar azimuth angles were tested and all yielded results similar to those presented. Retrievals were done along transects running parallel and perpendicular to the direction of incident photons (i.e., at solar azimuth angles of 0° ↕ 180° and 90° ↔ 270°). For Scene B, the sun shone from the left (see Fig. 3). Since re for Scene B were available, (16) and (18) were solved using g derived from re at r0 (Slingo 1989) when the aircraft was inside cloud. When the aircraft was out of cloud, they were solved using g = 0.85.
This section consists of two parts. The main point of the first part is to assess the performance of the aircraft-based method for fairly dense broken clouds and to demonstrate the simplicity of the aircraft-based method relative to its surface-based counterpart (BM2001). This is done using Scene A and the SGP surface. The second part documents the impact of using
a. Scene A: Inhomogeneous surface albedo
Figure 9 shows mean bias error (MBE) and root-mean-square error (rmse) for the surface method as a function of surface albedo averaging radius. It is obvious from the rmse values that very local 〈αλ〉 (i.e., even those measured atop a 30-m tower) are inappropriate. Root-mean-square errors are minimized for about a ∼1-km radius (≈〈zbase〉) and are only about 20% larger than those for the aircraft method at z = 1 km (see Table 3).
Figure 10 shows a sample of τ, τ′, and 〈α
Figure 11 shows normalized frequency distributions p(τ) for inherent τ and τ′ for both the aircraft method at 1-km altitude and the surface method using 〈αλ〉 averaged out to 1 km around measurement sites. Up to τ ≈ 40 both inferred distributions resemble the inherent one extremely well. Then, the aircraft distribution cuts out entirely at τ ≈ 53 while the surface distribution registers numerous values topped out at
To summarize, both the aircraft and surface methods perform very well, the edge going to the aircraft method on account of systematically lower rmse's and slightly more accurate estimates of 〈αcld〉.
b. Scene B: The impact of
Figure 12 shows profiles of 〈τ〉 and 〈τ′〉 and corresponding values of η at θ0 = 30° and 60° for Scene B. For both θ0, results are excellent for flights above 〈zbase〉 ≈ 1km, regardless of the form of
Figure 14 shows plots of τ′ (using
Figure 15 provides a closer look at the impact of
Notice that for the 0.5-km flight in Fig. 15 the Green's function improves initial estimates most near cloud edges. To understand why, consider Fig. 16, which shows τ and τ′ (inferred for a flight at 0.5 km) along with the 6-km stretch of Scene B and its corresponding upwelling fluxes at 0.87 μm. For the sections of flight path labelled 𝗔 and 𝗕, initial estimates of τ are too small and large, respectively. Refined estimates using
6. Feasibility
The purpose of this section is to give an impression of the feasibility of this method as it applies to aircraft-mounted radiometers. The concern is whether radiometers can be expected to resolve the differences in (18).
For flights at most altitudes with τ aloft exceeding 5, values of ΔI are typically between 10% and 30% and should be resolvable by most radiometers. When τ aloft are less than 5, ΔI are generally between 5% and 10%. Moreover, for θ0 = 60°, α
The other factor influencing ΔF and ΔI is Δα ≡ α
7. Summary and conclusions
The purpose of this paper was to introduce and assess a method for inferring cloud optical depth τ above some altitude z that uses data from radiometers mounted on an aircraft flying at z. This method was motivated by Marshak et al. (2000) and utilizes two similar wavelengths λ of radiation involved in multiple reflections between the atmosphere above z and the surface–atmosphere system below z. It is based on the assumptions that
average horizontal transport of upwelling diffuse radiation for real clouds can be approximated by 1D horizontal transport of upwelling isotropic radiation for homogeneous clouds [see Eq. (9)];
upwelling fluxes measured along an aircraft's trajectory
L L optical properties at both λ are similar for the atmosphere above the aircraft but differ for the surface–atmosphere system beneath the aircraft.
Some potential difficulties inherent in BM2001's surface-based technique are alleviated with an aircraft. Specifically, the surface method requires cloud-base fluxes based on time series of measured downwelling fluxes, which in turn, depend on estimates of cloud-base altitude, cloud advection rate, and local effective surface albedos. While their method works extremely well under ideal conditions, it is at the mercy of cloud advection and the potential for poor sampling and anisotropic biases associated with advecting cloud. An aircraft flying in the vicinity of cloud base, however, moves quickly relative to cloud advection and evolution and, with a down-facing pyranometer, can measure upwelling flux directly over any surface type. Moreover, cloud and aerosol present beneath the aircraft are, in principle, not problematic. The primary drawbacks to the aircraft method are cost and limited application. Performing the operation from the surface can be inexpensive and data collection can be continuous and long-term (e.g., necessary instruments are being installed presently at the ARM-SGP site; C. Pavloski 2001, personal communication). Obviously the aircraft method will be used only during relevant field experiments.
The aircraft method uses an approximate, normalized radiative Green's function to refine initial estimates of τ. It was shown that for inhomogeneous boundary layer clouds, an analytic, horizontally and azimuthally averaged Green's function usually improves results. In particular, for flights beneath cloud base, a simple ballistic account of upwelling photon trajectories between aircraft and cloud base appears to work well. For very broken, cumuliform clouds, a more sophisticated approach is needed to deal with side illumination and leakage. Nevertheless, it is expected that estimates of τ will often satisfy most needs.
This method will provide a constraint (time series of τ) for more elaborate synergetic inversion techniques that utilize several measurements; for example, use of τ together with cloud water path from microwave radiometer data and millimeter cloud radar reflectivities to estimate profiles of cloud droplet concentration and effective radius (cf. Boers et al. 1998). In closing, it is noted that studies are in progress that focus on aircraft (and surface) applications of the method documented here to situations involving multilayer cloud fields, tropospheric aerosols, and realistic instruments.
Acknowledgments
This study was supported by grants from the U.S. Department of Energy's ARM Program [DE-FG02-90ER61071 to The Pennsylvania State University (PSU), DE-A105-90ER61069 to NASA/GSFC, and DE-FG02-97ER2361 to the Canada Centre for Remote Sensing]. A. Marshak was also supported by NASA's EOS Project Science Office at GSFC (under Grant NAG5-6675) as part of the EOS Validation Program. We thank B. A. Wielicki (NASA/Langley) for making computer time available; E. E. Clothiaux, A. B. Davis, Y. Knyazikhin, C. F. Pavloski, and W. J. Wiscombe for helpful discussions; and W. Evans for the loan of the spectrometer.
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Schematic illustration of components making up zenith radiance
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Schematic illustration of components making up zenith radiance
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Schematic illustration of components making up zenith radiance
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Optical depth inferred from Landsat imagery for a single layer, marine boundary layer cloud field. Horizontal grid spacing is 114 m and the domain is (11.4 km)2. In the Monte Carlo simulations, the sun shone in at θ0 = 40° from the bottom of the plot (i.e., from the south, as indicated). See Table 1 for scene information
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Optical depth inferred from Landsat imagery for a single layer, marine boundary layer cloud field. Horizontal grid spacing is 114 m and the domain is (11.4 km)2. In the Monte Carlo simulations, the sun shone in at θ0 = 40° from the bottom of the plot (i.e., from the south, as indicated). See Table 1 for scene information
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Optical depth inferred from Landsat imagery for a single layer, marine boundary layer cloud field. Horizontal grid spacing is 114 m and the domain is (11.4 km)2. In the Monte Carlo simulations, the sun shone in at θ0 = 40° from the bottom of the plot (i.e., from the south, as indicated). See Table 1 for scene information
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Profiles of optical depth and droplet effective radius in each cell for an 11-km stretch near the center of Scene B, which measures 100 km long and was simulated by a cloud-resolving model (Szyrmer and Zawadzki 1999). Horizontal and vertical grid spacings are 25 m. Some cloud did exist below 850 m (the lower limit of this plot) though not over this stretch. In the Monte Carlo simulation, the sun shone from the left, as indicated on the plots. See Table 1 for scene information
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Profiles of optical depth and droplet effective radius in each cell for an 11-km stretch near the center of Scene B, which measures 100 km long and was simulated by a cloud-resolving model (Szyrmer and Zawadzki 1999). Horizontal and vertical grid spacings are 25 m. Some cloud did exist below 850 m (the lower limit of this plot) though not over this stretch. In the Monte Carlo simulation, the sun shone from the left, as indicated on the plots. See Table 1 for scene information
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Profiles of optical depth and droplet effective radius in each cell for an 11-km stretch near the center of Scene B, which measures 100 km long and was simulated by a cloud-resolving model (Szyrmer and Zawadzki 1999). Horizontal and vertical grid spacings are 25 m. Some cloud did exist below 850 m (the lower limit of this plot) though not over this stretch. In the Monte Carlo simulation, the sun shone from the left, as indicated on the plots. See Table 1 for scene information
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Surface albedos used for experiments involving Scene A. These (11.4 km)2 fields are centered on the ARM-SGP central facility (36°36′18″N, 97°29′06″W) and were concocted from Landsat surface classification and measurements made at the surface during Mar 2000 (see Table 2)
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Surface albedos used for experiments involving Scene A. These (11.4 km)2 fields are centered on the ARM-SGP central facility (36°36′18″N, 97°29′06″W) and were concocted from Landsat surface classification and measurements made at the surface during Mar 2000 (see Table 2)
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Surface albedos used for experiments involving Scene A. These (11.4 km)2 fields are centered on the ARM-SGP central facility (36°36′18″N, 97°29′06″W) and were concocted from Landsat surface classification and measurements made at the surface during Mar 2000 (see Table 2)
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
(a) Points represent normalized frequency distributions of horizontal distance s between entry points of upwelling photons, at altitudes as listed, and downwelling exit points. These were generated by a Monte Carlo algorithm injecting horizontally uniform distributions of upwelling isotropic photons at a particular altitude in Scene B and thus represent horizontally averaged, normalized Green's functions
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
(a) Points represent normalized frequency distributions of horizontal distance s between entry points of upwelling photons, at altitudes as listed, and downwelling exit points. These were generated by a Monte Carlo algorithm injecting horizontally uniform distributions of upwelling isotropic photons at a particular altitude in Scene B and thus represent horizontally averaged, normalized Green's functions
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
(a) Points represent normalized frequency distributions of horizontal distance s between entry points of upwelling photons, at altitudes as listed, and downwelling exit points. These were generated by a Monte Carlo algorithm injecting horizontally uniform distributions of upwelling isotropic photons at a particular altitude in Scene B and thus represent horizontally averaged, normalized Green's functions
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
This plot was constructed using 〈s2〉 as plotted in Fig. 5b, mean square distance between aircraft [referred to here as source (i.e., photon injection altitude)] and cloud top 〈Δz2〉, g = 0.85, and mean cloud optical depth 〈τ〉 above aircraft. A straight line of slope −1 corresponds to diffusion (Marshak et al. 1995a; Davis et al. 1997). The deviation from this line for altitudes less than ∼1.1 km indicates a break from diffusion
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
This plot was constructed using 〈s2〉 as plotted in Fig. 5b, mean square distance between aircraft [referred to here as source (i.e., photon injection altitude)] and cloud top 〈Δz2〉, g = 0.85, and mean cloud optical depth 〈τ〉 above aircraft. A straight line of slope −1 corresponds to diffusion (Marshak et al. 1995a; Davis et al. 1997). The deviation from this line for altitudes less than ∼1.1 km indicates a break from diffusion
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
This plot was constructed using 〈s2〉 as plotted in Fig. 5b, mean square distance between aircraft [referred to here as source (i.e., photon injection altitude)] and cloud top 〈Δz2〉, g = 0.85, and mean cloud optical depth 〈τ〉 above aircraft. A straight line of slope −1 corresponds to diffusion (Marshak et al. 1995a; Davis et al. 1997). The deviation from this line for altitudes less than ∼1.1 km indicates a break from diffusion
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
(Upper panel) Shows profiles of mean optical depth τ inherent to Scene A (see Fig. 2) and inferred by applying the method presented here to simulated radiances and fluxes that would have been measured by an aircraft flying at various altitudes and covering the entire domain. Values were inferred using normalized Green's functions defined by
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
(Upper panel) Shows profiles of mean optical depth τ inherent to Scene A (see Fig. 2) and inferred by applying the method presented here to simulated radiances and fluxes that would have been measured by an aircraft flying at various altitudes and covering the entire domain. Values were inferred using normalized Green's functions defined by
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
(Upper panel) Shows profiles of mean optical depth τ inherent to Scene A (see Fig. 2) and inferred by applying the method presented here to simulated radiances and fluxes that would have been measured by an aircraft flying at various altitudes and covering the entire domain. Values were inferred using normalized Green's functions defined by
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Scatterplots of inherent τ against τ′ inferred by an aircraft at altitudes of 1 and 0.5 km for Scene A using the SGP surface. Inferences are for use of Green's functions
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Scatterplots of inherent τ against τ′ inferred by an aircraft at altitudes of 1 and 0.5 km for Scene A using the SGP surface. Inferences are for use of Green's functions
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Scatterplots of inherent τ against τ′ inferred by an aircraft at altitudes of 1 and 0.5 km for Scene A using the SGP surface. Inferences are for use of Green's functions
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
MBE (upper) and rmse (lower) for τ retrieved by BM2001's surface-based method as a function of surface albedo averaging radius for Scene A using the SGP surface. Values at the extreme left correspond to use of point albedos in (27a) while those at the extreme right used albedos averaged over almost the entire domain. Results are shown for transects both ⊥ and ‖ to the direction of incident photons.
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
MBE (upper) and rmse (lower) for τ retrieved by BM2001's surface-based method as a function of surface albedo averaging radius for Scene A using the SGP surface. Values at the extreme left correspond to use of point albedos in (27a) while those at the extreme right used albedos averaged over almost the entire domain. Results are shown for transects both ⊥ and ‖ to the direction of incident photons.
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
MBE (upper) and rmse (lower) for τ retrieved by BM2001's surface-based method as a function of surface albedo averaging radius for Scene A using the SGP surface. Values at the extreme left correspond to use of point albedos in (27a) while those at the extreme right used albedos averaged over almost the entire domain. Results are shown for transects both ⊥ and ‖ to the direction of incident photons.
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Top two panels show inherent τ, τ′ inferred using BM2001's surface method, as well as surface albedos at 0.87 μm used by the surface method. This is a N–S transect about 25% of the way across Scene A (see Fig. 2). Uppermost panel used point surface albedo values while the middle panel used values averaged within 1 km of measurement sites. Lower panel shows inherent τ and τ′ inferred with the aircraft method for a plane flying at 1 km. The Green's function was represented by
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Top two panels show inherent τ, τ′ inferred using BM2001's surface method, as well as surface albedos at 0.87 μm used by the surface method. This is a N–S transect about 25% of the way across Scene A (see Fig. 2). Uppermost panel used point surface albedo values while the middle panel used values averaged within 1 km of measurement sites. Lower panel shows inherent τ and τ′ inferred with the aircraft method for a plane flying at 1 km. The Green's function was represented by
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Top two panels show inherent τ, τ′ inferred using BM2001's surface method, as well as surface albedos at 0.87 μm used by the surface method. This is a N–S transect about 25% of the way across Scene A (see Fig. 2). Uppermost panel used point surface albedo values while the middle panel used values averaged within 1 km of measurement sites. Lower panel shows inherent τ and τ′ inferred with the aircraft method for a plane flying at 1 km. The Green's function was represented by
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Frequency distributions of inherent τ for Scene A and τ′ inferred by both the aircraft method for a plane at 1 km (using
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Frequency distributions of inherent τ for Scene A and τ′ inferred by both the aircraft method for a plane at 1 km (using
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Frequency distributions of inherent τ for Scene A and τ′ inferred by both the aircraft method for a plane at 1 km (using
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
As in Fig. 7 except these are for Scene B. Inferred values of 〈τ〉 (upper panels) and η (lower panels) are for two sun angles θ0 as listed. Plots on the left are for
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
As in Fig. 7 except these are for Scene B. Inferred values of 〈τ〉 (upper panels) and η (lower panels) are for two sun angles θ0 as listed. Plots on the left are for
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
As in Fig. 7 except these are for Scene B. Inferred values of 〈τ〉 (upper panels) and η (lower panels) are for two sun angles θ0 as listed. Plots on the left are for
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
As in Fig. 9 except these are for Scene B and for aircrafts flying at 1 and 0.5 km in which τ were inferred assuming either
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
As in Fig. 9 except these are for Scene B and for aircrafts flying at 1 and 0.5 km in which τ were inferred assuming either
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
As in Fig. 9 except these are for Scene B and for aircrafts flying at 1 and 0.5 km in which τ were inferred assuming either
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Scatterplots of inferred τ against inherent τ for Scene B for an aircraft at various altitudes (as indicated on the plots). Also indicated on the plots are mean cloud optical depth above aircraft 〈τ〉, MBE, and rmse. Values of τ′ were inferred using
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Scatterplots of inferred τ against inherent τ for Scene B for an aircraft at various altitudes (as indicated on the plots). Also indicated on the plots are mean cloud optical depth above aircraft 〈τ〉, MBE, and rmse. Values of τ′ were inferred using
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Scatterplots of inferred τ against inherent τ for Scene B for an aircraft at various altitudes (as indicated on the plots). Also indicated on the plots are mean cloud optical depth above aircraft 〈τ〉, MBE, and rmse. Values of τ′ were inferred using
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
A 20-km transect from Scene B showing inherent τ and τ′ estimated by the aircraft method using both
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
A 20-km transect from Scene B showing inherent τ and τ′ estimated by the aircraft method using both
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
A 20-km transect from Scene B showing inherent τ and τ′ estimated by the aircraft method using both
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Upper panel shows inherent and inferred τ for the first 6 km of the 11-km stretch of cloud in Scene B as shown in Fig. 3. Inferred values are for both
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Upper panel shows inherent and inferred τ for the first 6 km of the 11-km stretch of cloud in Scene B as shown in Fig. 3. Inferred values are for both
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Upper panel shows inherent and inferred τ for the first 6 km of the 11-km stretch of cloud in Scene B as shown in Fig. 3. Inferred values are for both
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Profiles of mean percentage differences between upwelling spectral fluxes
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Profiles of mean percentage differences between upwelling spectral fluxes
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Profiles of mean percentage differences between upwelling spectral fluxes
Citation: Journal of the Atmospheric Sciences 59, 13; 10.1175/1520-0469(2002)059<2093:IOCODF>2.0.CO;2
Properties of the cloud fields shown in Figs. 2 and 3: Ac is vertically projected cloud fraction; 〈τ〉 and τmax are mean and maximum cloud optical depths; η = e〈ln τ〉/〈τ〉, which provides a measure of horizontal variability (Cahalan et al. 1994). Minimum cloud optical depth was 0.01. Here, 〈ztop〉 and 〈zbase〉 are mean cloud-top and cloud-base altitudes, and Δz is cloud geometric thickness (km)
Spectral surface albedos used to create albedo maps for the (11.4 km)2 area around the ARM-SGP central facility (see Fig. 4). Here, f is fractional area occupied by a Landsat surface type. When albedos are weighed by their respective f and summed, domain-average values at 0.65 and 0.87 μm are 0.090 and 0.381, respectively. Albedo data were collected during Mar 2000 with the portable S2000/PC2000 spectrometer (Ocean Optics Inc.). The spectrometer was equipped with a cosine-corrected fiber optic flux sensor
Inherent mean optical depth 〈τ〉 and variance-related parameter η [see (26)] for clouds in Scene A. Also listed are corresponding values inferred by an aircraft at 1 km (or cloud base) using
As in Table 3 except these values are for Scene B with values inferred by an aircraft at two altitudes and by the surface method of BM2001. Inherent values are in parentheses as they depend on aircraft altitude
