Optical Depth of Overcast Cloud across Canada: Estimates Based on Surface Pyranometer and Satellite Measurements

H. W. Barker Cloud Physics Research Division, Atmospheric Environment Service, Downsview, Ontario, Canada

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T. J. Curtis Department of Geography, McMaster University, Hamilton, Ontario, Canada

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E. Leontieva Geophysical Institute and Department of Physics, University of Alaska, Fairbanks, Alaska

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K. Stamnes Geophysical Institute and Department of Physics, University of Alaska, Fairbanks, Alaska

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Abstract

Overcast cloud optical depths τ are inferred from hourly, broadband surface pyranometer measurements of global irradiance for 21 Canadian stations. A radiative transfer model that treats the atmosphere as plane-parallel and horizontally homogeneous is used so inferred τ are effective values that should resemble those used by GCM radiation routines. Results are presented mostly for June, July, and August (JJA), thus minimizing the impact of surface albedo errors that arise from unreported sea–ice and ground snow. Measurement periods for several sites exceed 20 yr. Frequency distributions of τ for JJA can be described well by gamma distributions with mean values τ that tend to be largest (30–35) for southern continental sites and smallest (20–25) for continental subarctic sites. Corresponding standard deviations are generally near ∼1.4τ. Diurnal amplitudes of hourly mean τ (dayside) are negligible for most sites but exceed 5 for some. There is some evidence of weak, yet occasionally significant, increases in monthly mean τ from the late 1960s to early 1990s. Annual results for four coastal sites exhibit maximum monthly mean τ during autumn.

The International Satellite Cloud Climatology Project (ISCCP)-CX optical depths τsat (means of ∼10 km cloudy pixel values inside 1° × 1° cells centered roughly on pyranometers) are compared with collocated surface-inferred values τsrf (means of two hourly values that flank ISCCP snapshots). Data for JJA of 1989 at a continental and a maritime site are considered. For the majority of cases, 1.25 < τsrf/τsat < 2.25 echoes an independent study. Many occurrences of τsatτsrf have ISCCP IR temperatures >273 K so cloud phase is not an issue. Moreover, for most of these cases, variances for the 10-km pixel optical depths suggest weak horizontal variability of cloud. A full explanation of this systematic discrepancy is beyond the scope of this study.

* Additional affiliation: Department of Oceanic and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada.

Corresponding author address: Dr. Howard W. Barker, Atmospheric Environment Service, Cloud Physics Research Division (ARMP), 4905 Dufferin St., Downsview, ON M3H 5T4, Canada.

Email: howard.barker@ec.gc.ca

Abstract

Overcast cloud optical depths τ are inferred from hourly, broadband surface pyranometer measurements of global irradiance for 21 Canadian stations. A radiative transfer model that treats the atmosphere as plane-parallel and horizontally homogeneous is used so inferred τ are effective values that should resemble those used by GCM radiation routines. Results are presented mostly for June, July, and August (JJA), thus minimizing the impact of surface albedo errors that arise from unreported sea–ice and ground snow. Measurement periods for several sites exceed 20 yr. Frequency distributions of τ for JJA can be described well by gamma distributions with mean values τ that tend to be largest (30–35) for southern continental sites and smallest (20–25) for continental subarctic sites. Corresponding standard deviations are generally near ∼1.4τ. Diurnal amplitudes of hourly mean τ (dayside) are negligible for most sites but exceed 5 for some. There is some evidence of weak, yet occasionally significant, increases in monthly mean τ from the late 1960s to early 1990s. Annual results for four coastal sites exhibit maximum monthly mean τ during autumn.

The International Satellite Cloud Climatology Project (ISCCP)-CX optical depths τsat (means of ∼10 km cloudy pixel values inside 1° × 1° cells centered roughly on pyranometers) are compared with collocated surface-inferred values τsrf (means of two hourly values that flank ISCCP snapshots). Data for JJA of 1989 at a continental and a maritime site are considered. For the majority of cases, 1.25 < τsrf/τsat < 2.25 echoes an independent study. Many occurrences of τsatτsrf have ISCCP IR temperatures >273 K so cloud phase is not an issue. Moreover, for most of these cases, variances for the 10-km pixel optical depths suggest weak horizontal variability of cloud. A full explanation of this systematic discrepancy is beyond the scope of this study.

* Additional affiliation: Department of Oceanic and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada.

Corresponding author address: Dr. Howard W. Barker, Atmospheric Environment Service, Cloud Physics Research Division (ARMP), 4905 Dufferin St., Downsview, ON M3H 5T4, Canada.

Email: howard.barker@ec.gc.ca

1. Introduction

The solar radiation budget of Earth’s surface is an important governor of climate and is significantly determined by clouds (Li and Leighton 1993). Hence, as global climate models (GCMs) become more sophisticated, their demand for improved representation of cloud optical properties increases too. To achieve this, it is essential to have reliable measurements and inferences of variables governing radiative transfer for cloudy atmospheres. Next to cloud fraction, which has received much attention (see Wielicki and Parker 1992), cloud optical depth τ is the most important of these variables. Little is known, however, about the statistical nature of τ precisely because it fluctuates greatly across wide ranges of time and space scales (Cahalan et al. 1994; Barker et al. 1996). Moreover, the most readily available data for inferring information about τ are radiation fields emerging from clouds; but the interaction of radiation and τ is, generally, very complicated (e.g., Stephens 1988; Barker and Liu 1995; Marshak et al. 1995).

Existing information about τ comes largely from the International Satellite Cloud Climatology Project (ISCCP) (Rossow 1989; Rossow and Schiffer 1991). The ISCCP provides an invaluable global record for validating cloud and radiation transfer algorithms used in GCMs. It is important, however, to have an independent validation of ISCCP results. One possibility is to infer τ from collocated measurements of solar irradiance at Earth’s surface (Leontyeva and Stamnes 1994;Leontieva et al. 1994; Min and Harrison 1996). An advantage that surface-inferred τ have over satellite values is that transmitted radiation is less sensitive than reflected radiation to uncertainties in cloud droplet-size distribution (Rawlins and Foot 1990). This can be appreciated by recognizing that as effective radius of cloud droplets increases, their single-scattering albedo and asymmetry parameters decrease and increase, respectively. Both these work together to enhance cloud albedo but have opposing impacts on transmittance. The disadvantage for surface-inferred τ is that they are very local estimates. However, surface irradiance measurements often began long before the advent of suitable, routine satellite observations and so potentially represent the longest known records of τ.

Following Leontyeva and Stamnes (1994) and Leontieva et al. (1994), the main purpose of this paper is to investigate the nature of overcast cloud optical depths across Canada as inferred from surface pyranometer measurements. Hourly integrated broadband solar irradiances, reports of sky conditions, and a multilayer plane-parallel, homogeneous (PPH) radiative transfer model were used to solve for τ during overcast conditions, free of snow and ice, at 21 Canadian stations over periods of up to 30 yr. Also, surface-based estimates of τ are compared with concurrent values reported in the ISCCP-CX data archives. Thus, in using two very different, but nearly simultaneously measured radiation fields, this study attempts to corroborate ISCCP values of τ.

Section two discusses the model used to infer τ as well as the algorithm in which it is implemented. The third section describes sources of data and criteria for data selection. Section four presents pyranometer-inferred τ for the Canadian stations while section five compares them with collocated ISCCP values for two geographically diverse stations. A summary and conclusion are given in the last section.

2. Method of solution

The first part of this section describes the radiative transfer model used to create look-up tables of transmittance as a function of cosine of solar zenith angle μ0 and τ. The second part describes how the look-up tables were used.

a. Model

In this study, the solar spectrum (0.25–4 μm) was partitioned into 24 spectral bands as defined by Slingo (1989). The vertically inhomogeneous radiation model of Tsay et al. (1989) was used to compute transmittances for a PPH medium above a nonreflecting surface. This model is a four-stream version of Stamnes et al.’s (1988) DISORT algorithm. Within DISORT, band transmission functions for the jth spectral interval were parameterized using the exponential sum fitting of transmittances method (Wiscombe and Evans 1977). Equivalent gaseous absorber amounts were scaled empirically to account for temperature and pressure profiles. Broadband Rayleigh optical depths were accounted for using Slingo and Schrecker’s (1982) procedure.

Defining the effective radius of spherical cloud droplets (μm) as
i1520-0442-11-11-2980-e1
where n(r) is droplet-size distribution and r is radius, it can be shown that if Mie extinction efficiency is proportional to r, cloud optical depth for the jth spectral interval is
i1520-0442-11-11-2980-e2a
where aj and bj are coefficients (Slingo 1989) and L is liquid water path (g m−2). In addition, spectral values of single-scattering albedo ω and asymmetry parameter g for water clouds were parameterized, respectively, as
ωjcjdjreje
and
gjfjgjrhje
where the primed symbols are coefficients (Hu and Stamnes 1993). Throughout this study, re was assumed to be 10 μm to remain consistent with ISCCP (Han et al. 1994) and scattering was described by Henyey and Greenstein’s (1941) phase function. Neglect of ice and mixed-phase clouds may lead to only slight overestimates of τ. This is because gj for ice clouds are roughly equal to those for liquid clouds (Q. Fu 1997, personal communication) and because differences between ωj for ice and liquid clouds have relatively minor impacts on transmittance. Furthermore, overcast clouds were assumed to reside between 1 and 2 km above the surface.

The midlatitude summer atmosphere (McClatchey et al. 1972) with 33 layers up to 100 km was used. Leontyeva and Stamnes (1994) demonstrated that use of a fixed water vapor profile (saturated inside cloud) has a minor impact on inference of τ. Continental tropospheric aerosol optical properties were taken from MODTRAN (Berk et al. 1989): fixed profiles at spring–summer background conditions with an optical depth at 0.5 μm of 0.17. A background stratospheric aerosol was also included.

b. Look-up tables

Ideally, a radiation model would be inverted to solve for τ given a measured irradiance or transmittance T. Since the one used here cannot be inverted analytically, an alternate method must be used. To avoid time-consuming root-finding iterations of the model for each spectral interval and admissible observation, an approach developed by Stamnes (1982) was employed. Using this efficient computational algorithm, look-up tables of spectral transmittances Tj, one for each of the 24 bands at several values of μ0, were generated for PPH clouds above a nonreflecting surface. Spectral atmospheric spherical albedos αj for upwelling radiation were also computed. Tables for the spectral bands with gaseous absorption store the monochromatic transmittances corresponding to each ESFT term along with αj.

Leontyeva and Stamnes (1994) showed that use of a spectrally invariant surface albedo αs is not a problem for snow. Therefore, since αs for Canadian snow-free surfaces show much less spectral dependence than that of snow (Li and Garand 1994), αs was assumed to be constant across the spectrum. Then, tables of spectral atmospheric transmittance for a specific αs were calculated as
i1520-0442-11-11-2980-e3
Knowing the spectral distribution of solar irradiance at the top of the atmosphere, Tj(τj, μ0, αs) can be weighted and summed to produce a single two-dimensional table of broadband solar irradiance at the surface. Hence, the final table includes values of broadband transmittance for a given αs as a function of μ0 and τ; (which for simplicity are represented hereinafter by values corresponding to radiation between 0.57 and 0.64 μm to be consistent with ISCCP). The tables consist of values at 165 equal increments of μ0 and 52 unequal intervals of τ between 0 and 100.
For an admissible observation (see section 3b), μ0 is calculated and will generally fall between the kth and the (k + 1)th columns of a table; that is, μk < μ0 < μk+1. Therefore, a working vector of 52 broadband transmittances is created by linear interpolation with entries
i1520-0442-11-11-2980-e4
Then, 2M ordered pairs, {τ(i), T[τ(i), μ0, αs]}, are selected from this vector and used to form an Mth-order Padé approximant:
i1520-0442-11-11-2980-e5
To ensure accurate representation, M = 7 was used. Once the coefficients pm and qm are determined, T derived from a pyranometer measurement is used in (5) to solve for τ. This avoided rounding retrieved values of τ to the nearest value in the table.

3. Data

a. Geographical distribution and instrumentation

Surface solar irradiance measurements were obtained from the Digital Archive of Canadian Climatological Data maintained by Environment Canada. Stations selected for this study had to have coincidental sky-condition reports and radiation measurements, and the ability to be assigned a reliable and suitable value of αs. Only 21 out of a possible 54 radiation stations satisfied these constraints and Fig. 1 and Table 1 show and list their locations. It is evident from Fig. 1 that these stations are distributed fairly evenly across Canada.

Poleward of 60°N, the Eppley precision spectral pyranometer is used because of its small cosine response error. South of 60°, the less sophisticated CM6 Kipp pyranometer is generally in use (Hay and Won 1980). These pyranometers respond to radiation between wavelengths 0.25 and 2.9 μm. It is maintained generally that these instruments are accurate to within ±5% (Hay and Won 1980), though errors may be smaller for overcast conditions on account of the calibration technique used (L. J. B. McArthur 1997, personal communication). Hourly integrated values of global solar irradiance are archived in thousandths of M J m−2. These data are subsequently quality-control filtered with transmittances finally calculated based on knowledge of latitude, date, and time of day (Spencer 1971). Measurements begin and end on the hour in local apparent time (i.e., they are symmetric about solar noon).

b. Data selection

Hourly irradiance and sky conditions were screened to select admissible observations. The selection criteria were as follows:

  • μ0 ≥ 0.2: to avoid overly small signals.

  • Snow-free ground: each radiation datum is flagged indicating its integrity and whether the observer reported ground snow. Snow conditions were avoided because of the ambiguity of assigning a suitable effective broadband αs for use in (3)–(5). This is because with overcast above highly reflective surfaces, multiple reflections between surface and atmosphere easily make surface irradiance at a point dependent on αs from a region much larger than that seen from ∼2 m above the surface (Barker and Davies 1989). This is especially problematic near discontinuous surfaces such as mixed vegetation and shoreline areas. After examining sea–ice atlases (LeDrew et al. 1992), most Arctic and subarctic coastal stations were omitted due to proximity to semipermanent pack ice. Likewise, the majority of temperate latitude stations were examined for summer months only.

  • Persistent overcast: cloud fraction and opacity were estimated by surface observers and reported at the beginning of each radiation hour. In an attempt to avoid unreported broken cloud events that may have occurred between observations, hourly integrated radiation measurements were used only if the preceding and following hour intervals were bounded by reports of overcast. While this should reduce the possibility of using data corresponding to partly cloudy conditions, some less persistent yet truly overcast hours were probably omitted inadvertently.

4. Results: Canadian radiation network

This section has four parts in which the first examines summer distributions of τ for 21 stations. The second part presents diurnal variations of τ for several stations. The third part reports on annual variations of monthly mean τ for four sites, and the fourth part deals with long-term trends.

a. Summer frequency distributions of τ

Figure 2 shows frequency distributions of hourly τ for June, July, and August (over entire periods of measurement) for the 21 stations listed in Table 1. All of the distributions have strong positive skews (see also Leontyeva and Stamnes 1994; Leontieva et al. 1994) with modes generally between 10 and 20. These histograms resemble closely gamma distributions that can be expressed as
i1520-0442-11-11-2980-e6a
Depending on whether ν is determined by the method of moments (mom) or the maximum likelihood estimate (mle), it is defined as either
i1520-0442-11-11-2980-e6b
where σ is standard deviation of τ and
i1520-0442-11-11-2980-e6c
Figure 3 shows how well (6) fits some of the measured distributions; Port Hardy and Baker Lake are two of the better fits while Big Trout Lake and Nitchequon are two of the worst. Although νmom and νmle differ typically by less than ∼0.25 (see Table 1 for values of τ, νmom, and νmle), νmom tend to predict the positions of the modes best, which for pΓ(τ) are defined as (ν − 1)τ/ν, but the slopes of the tails are usually defined best when νmle are used. Moreover, there is a fairly well-defined linear correlation (r2 = 0.6) between the quantity Δν = νmomνmle and τ: the larger τ the larger Δν. This is because for sites with large τ, the histograms were actually best fit with a weighted sum of two gamma distributions: one with ν close to those reported in Table 1 and another with a smaller value of ν (≈1). Note that in Fig. 3, pΓ(τ) decrease too fast for τ ≳ 80; this was almost ubiquitous among the 21 histograms and especially those with large τ. Regardless of location, histograms for individual summer months resemble very closely those shown in Figs. 2 and 3. The similarity between most histograms in Fig. 2 is also evident from Table 1 where it can be shown [using (6b)] that σ are remarkably well contained between 1.2 and 1.6τ.

Neglecting the four oceanic coastal sites (see Fig. 2), Fig. 4 shows τ and σ as functions of latitude for the remaining 17 locations. There are clear tendencies for both τ (and modal τ) and σ to decrease poleward. With respect to τ, this is due to cooler and drier conditions with less available precipitable water, less convection, and, consequently, thinner clouds. The decrease in σ is clearly due to diminishing probability of thick cloud events that limit greatly the second moment of τ.

It should be made clear that the effective area of the cloud field that determines an hourly pyranometer measurement can usually be expected to exceed 100 km2. Thus, the distributions of τ shown here must be interpreted differently than those shown by Barker et al. (1996) for (60 km)2 regions of 28.5 m resolution τ. Moreover, because substantial variability in τ potentially exists within a pyranometer’s hourly field-of-view, hourly inferred τ are necessarily effective values (Cahalan et al. 1994) stemming from the assumption of homogeneity. For instance, if p*(τ) is the inherent distribution of τ within a pyranometer’s hourly field-of-view, the inferred value will often be
τηττ
where
i1520-0442-11-11-2980-e7b
As such, p* (τ), corresponding to the histograms shown in Figs. 2 and 3, are quite likely stretched to the right. The same holds for histograms of τ that are passed to PPH radiative transfer models in GCMs: τ acted on by them should differ from what the GCM predicts; particularly if suitable radiation and cloud water budgets exist (e.g., McFarlane et al. 1992).

The look-up tables were defined for τ ∈ [0,100], but the Padé approximants in (5) can be extrapolated, precariously, to yield retrieved τ > 100. While these values were not presented, it is interesting to note that they appeared to be valid for in several cases (especially those with many samples), the rate at which the distributions fell off for τ < 100 were preserved well for τ > 100.

b. Diurnal variation of τ

Diurnal variations in τ for four coastal and four continental stations were analyzed based on local apparent time (LAT). Mean values and standard deviations are presented for JJA for the entire recording period. Figures 5a and 5c show results grouped into 2-h periods beginning at 0800 and ending at 1700 LAT. Diurnal ranges of τ are quite small (<3) except for Port Hardy where it exceeds 10 and Norman Wells where it is ∼5. Port Hardy has distinctively lower values of τ in the morning and this is similar to Leontieva et al.’s (1994) finding for Bergen, Norway. Norman Wells, on the other hand, tends to have largest values in the morning. Figures 5b and 5d show that all eight sites have standard deviations of τ between 18 and 23 with little diurnal variation.

Figure 6 shows morning and afternoon frequency histograms of τ for Sable Island, Port Hardy, Churchill, and Big Trout Lake. Morning and afternoon differences can be seen clearly for Port Hardy and to a lesser extent for Big Trout Lake, but for Sable Island and Churchill the stable mean and standard deviation values seen in Fig. 5 carry over to almost identical morning and afternoon distributions. Port Hardy has ∼62% of its overcast events during the morning. Most others, including the three shown in Fig. 6, have very similar numbers in the morning and afternoon.

c. Annual variations of monthly mean τ

Due to the data selection criteria, only temperate coastal stations have sufficiently many admissible observations to allow examination of annual variations in monthly mean optical depth τ. Figure 7 shows the annual march of τ for four coastal stations. Values of τ typically exceed corresponding median values by three to seven units of optical depth as expected for the skewed distributions seen in Figs. 2 and 3. There is a tendency for maximum values to occur between September and November. This is likely the result of large-scale movements of cool air masses over the still warm oceans: large vertical temperature gradients drive high moisture fluxes. The three west coast stations have minimums during spring while Sable Island’s minimum is during summer. Also shown are annual variations in the standard deviation of τ but they are much less pronounced than those for τ.

d. Long-term trends

Figure 8 illustrates some annual progressions of summer-mean optical depths τ for four stations with lengthy, well-populated records. Upon fitting least squares linear regression lines to the data, only the slope for Port Hardy was found to be significantly greater than zero.1 Prince George’s slope (not shown) was significantly less than zero but its record is quite sparse. The three other plots in Fig. 8, like all others, show no meaningful trends.

For the two most complete records, Port Hardy and Sable Island, values of monthly mean τ (for all months) were smoothed with a 13-month running mean in order to get a clearer picture of long-term trends in monthly τ. Figure 9 shows that overcast events in Port Hardy appear on average to be much thicker in the early part of the 1970s and at two distinct periods in the 1980s. Sable Island also showed an enhancement in τ during the early 1980s but this was followed by a substantial decrease from 1983 to 1985. Both regression lines in Fig. 9 have statistically significant positive slopes. Though it is difficult to emphasize this too much, it does suggest that mean overcast τ has increased by ∼2.5 over the past 30 yr. The trend at Port Hardy was dominated by increases during spring and summer while at Sable Island the trend was due largely to increases during fall.

5. Results: Concurrent ISCCP results

As a pilot study, values of hourly τ inferred for Big Trout Lake (continental boreal forest) and Sable Island (coastal) have been compared with ISCCP results. ISCCP optical depths τsat reported here are from the CX archive and are mean values of pixel optical depths inside 1° × 1° regions covering the stations (pixel sizes are ∼10 km and grid spacings are ∼30 km). The intercomparison was done for June, July, and August of 1989. Since τsat are three-hourly snapshots, corresponding surface-inferred values, denoted as τsrf, were determined by simply averaging the hourly values on either side of the ISCCP measurement. In addition, admissible data had to have >95% of the 10-km ISCCP pixels in the 1° × 1° region flagged as overcast. There were 63 satisfactory observations for Big Trout Lake and 127 for Sable Island.

It is important to stress the intrinsic differences between τsat and τsrf. The τsat presented here are mean values of all 10-km cloudy pixels inside the 1° × 1° cells. Thus, one could expect most often that τsat < τ* where τ* is inherent mean optical depth (Marshak et al. 1995). On the other hand, τsrf derive from two-hourly mean transmittances that could correspond to a swath across a cloud field of up to 20 km × 100 km. Given these differences in spatial scale, any single occurrence of τsatτsrf should be taken lightly: it is expected that τsat > τsrf if for no other reason than the fact that τsat derive from horizontal averaging scales that are often at least an order of magnitude smaller than those used to estimate τsrf.

Contrary to this expectation, Figs. 10a and 10b show that for both locations, the overwhelming tendency is τsat < τsrf and often τsatτsrf. In fact, on average, values of τsrf are ∼1.6 τsat (see Table 2).2 These disparities are in surprising agreement with Min and Harrision’s (1996) comparison of τ derived using surface-based microwave radiometer and pyranometer data with GOES-East satellite-derived values for the Southern Great Plains Atmospheric Radiation Measurement site. This may be significant as the ISCCP data used in this study came from an earlier version of GOES-East.

Some data were collected during rainfall events and this could have adverse effects on the pyranometers. These data tended to occur at large τsrf and this may signify either contaminated data or the fact that when it rains clouds tend to be thick. In the case of a localized thundershower above a pyranometer, surface irradiance would be attenuated much but when the locally high reflectance of the thunder cloud is averaged over a 1° × 1° satellite grid, its impact would be disproportionally less: the expectation being τsatτsrf. Figures 10c and 10d show, however, that for these cases, which tend to be in the lower right-center of the plots in Figs. 10a and 10b, the standard deviation of ISCCP pixel optical depths σsat are only modest when τsatτsrf suggesting weak variability and low likelihood of localized thundershower activity. The other possibility is that during rain, pyranometers yield anomalously small signals (that are interpreted by the algorithm as overly thick cloud). In the end, however, eliminating these data reduced the disparity between mean values of τsat and τsrf (see Table 2) by only ∼3.

Figures 10c and 10d show that for the few occurrences of τsat > τsrf (i.e., our initial expectation), the majority have large (and indeed the largest) σsat. This stands to reason as mean τ derived from several small-area samples (τsat) is influenced much by a few large τ but mean transmittance is influenced weakly by a few large τ (τsrf); unless the thickest regions are directly over the pyranometer.

Figures 10a and 10b symbolize observations by local apparent time of observation (highest sun at 1200 LAT). For Sable Island there is a clear tendency for τsat > τsrf at 1200 LAT (μ0 ≈ 0.9), while at other times τsatτsrf with few exceptions. Figure 11b shows that for Sable Island, τsat depends strongly on μ0. This could also be interpreted as a relative azimuth dependence too given the geostationarity of GOES-East (see Fig. 12). Figure 11a shows, as expected, no such dependence for τsrf. Figures 11c, 11d, and 12b show that the dependencies seen for τsat for Sable Island are not visible in the Big Trout Lake data: this is reflected in Fig. 10 as well, where τsat < τsrf with only a few exceptions at relatively low sun.

Figures 13b and 13d show τsat as a function of ISCCP infrared temperature Tir. Here it is seen that for Sable Island, the largest τsat (those at 1200) have Tir ≲ 250 K (less pronounced for Big Trout Lake). Thus, it is tempting to conclude that since significant fractions of ice must have been present in these cases, errors have been committed by both techniques in assuming a scattering phase function based on 10-μm liquid droplets. Use of an ice crystal phase function might bring τsat into better agreement with τsrf (that presumably are affected less by having assuming 10-μm liquid drops). This, however, does not explain why many observations with Tir > 273 K (little or no ice) have τsat < 10 ≪ τsrf. Figures 13a and 13c show that τsrf tend to decrease with increasing Tir: this is again reasonable for the shallower and thinner clouds become, the warmer their effective radiating temperature.

a. Discussion

While the data presented here were screened extensively to maintain control of the experiment, it is still very difficult, and beyond the scope of this study, to explain fully the systematic discrepancies between τsat and τsrf. The close quantitative agreement with Min and Harrison’s (1996) results should, however, be considered important.

There are several possibilities that might explain why τsat < τsrf. First, the digitization of satellite imagery may lead to systematic underestimations of τ when reflectances are near sensor saturation: getting to the next count could represent a large, and often missed, jump in τ. Also, if 10-km ISCCP pixels flagged as containing cloud were not overcast, as they were assumed to be, τsat would be underestimates. This, however, is unlikely to be the case here given the stringent screening that was imposed on the data in order to isolate truly overcast events.

A third issue involves the possibility of anomalous absorption of solar radiation by cloudy atmospheres (Stephens and Tsay 1990; Cess et al. 1995; Cess et al. 1996; Li et al. 1995; Barker and Li 1997). Consider the impacts an anomalous absorber might have on the inference of τ from surface and satellite measurements. Anomalous absorption would make cloud albedo and transmittance less than values predicted by radiative transfer models used to construct inversion algorithms. Values of τsat would, therefore, be too small (algorithm senses a thinner cloud) if the anomalous absorber influences the (usually) narrowband of a satellite sensor. Transmittance should be affected more than albedo as transmitted photons have longer pathlengths and more scattering events than do reflected photons. Therefore, τsrf will be too large. Thus, an anomalous absorber would tend to drive apart values of τ inferred from satellite and surface radiometric measurements such that τsat < τsrf. Such an absorber may be as commonplace as an unacknowledged aerosol or as exotic as absorption by polymers. For the sites examined here, the former is much more plausible than the latter (P. Chýlek 1997, personal communication).

6. Summary and conclusions

This study has two main parts. First, it produced frequency distributions and various time series of hourly and monthly mean overcast cloud optical depths τ for 21 sites across Canada. Values of τ were inferred from surface pyranometer data and the inverse of a plane-parallel, homogeneous solar radiative transfer model (Leonyeva and Stamnes 1994; Leontieva et al. 1994). As overcast conditions often contribute much to monthly mean cloud radiative forcings, results presented here may be useful to help diagnose GCMs (that also use PPH models and have horizontal grid spacings similar to the effective size of an hourly pyranometer measurement).

Frequency distributions for hourly τ during summer months are described extremely well for most stations by the gamma distribution. Mean and standard deviation of hourly τ during summer for continental stations exhibit strong negative correlations with latitude. Mean τ decrease from ∼35 at 50°N to ∼22 near the Arctic Circle. Diurnal and seasonal trends are seen in the data. Optical depth of overcast clouds tend to be slightly larger in the afternoon, likely due to convective cloud development. For coastal sites at least, fall has the thickest overcast clouds, probably a result of large-scale frontal migration and changing air–sea temperature gradients. A great degree of interannual variability was seen for all stations. Very few statistically significant long-term trends (>20 yr) were elucidated, but those deemed significant showed minor increases to monthly mean τ from the late 1960s to early 1990s.

The second main part compared collocated ISCCP-CX (GOES-East) optical depths with those inferred from surface pyranometers for a continental and a maritime site during the summer of 1989. There is general disagreement between the two datasets. Surface-inferred τ are typically ∼25% to ∼125% larger than the satellite values; even for cases in which cloud droplets are certainly liquid. Oddly enough, given the nature of the data and methods, ISCCP values were expected to be largest; this makes the magnitude of the disparities all the more unsettling. Moreover, it echoes an entirely independent study whose satellite values were also based on GOES-East data (Min and Harrison 1996). Several possible explanations for the differences were alluded to but a full explanation is beyond the scope of this study. Thus, it is recommended strongly that additional testing be carried out.

Acknowledgments

We thank W. R. Rossow and A. Walker (NASA-GISS) for supplying ISCCP data, and D. Brown (AES-Downsview) for supplying hourly surface radiation and meteorological data. We also thank J. A. Davies (McMaster University) for providing financial support for TJC during his master’s of science work, and Q. Min (SUNY-Albany) and Z. Li (CCRS) for helpful discussions.

REFERENCES

  • Barker, H. W., and J. A. Davies, 1989: Multiple reflections across a linear discontinuity in surface albedo. Int. J. Climatatol.,9, 203–214.

  • ——, and D. Liu, 1995: Inferring optical depth of broken clouds from Landsat data. J. Climate,8, 2620–2630.

  • ——, and Z. Li, 1997: Interpreting shortwave albedo-transmittance plots:True or apparent anomalous absorption. Geophys. Res. Lett.,24, 2023–2026.

  • ——, B. A. Wielicki, and L. Parker, 1996: A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part II: Validation using satellite data. J. Atmos. Sci.,53, 2304–2316.

  • Berk, A., L. S. Bernstein, and D. C. Robertson, 1989: MODTRAN: A moderate resolution model for LOWTRAN7, Geophysics Laboratory Rep. GL-TR-89-0122, 38 pp. [Available from Geophysics Laboratory, Hanscom AFB, MA 01731-5000.].

  • Cahalan, R. F., W. Ridgway, W. J. Wiscombe, T. L. Bell, and J. B. Snider, 1994: The albedo of fractal stratocumulus clouds. J. Atmos. Sci.,51, 2434–2455.

  • Cess, R. D., and Coauthors, 1995: Absorption of solar radiation by clouds:Observations versus models. Science,267, 496–499.

  • ——, M. H. Zhang, Y. Zhou, X. Jing, and V. Dvortsov, 1996: Absorption of solar radiation by clouds: Interpretations of satellite, surface, and aircraft measurements. J. Geophys. Res.,101, 23 299–23 309.

  • Han, Q., W. Rossow, and A. Lacis, 1994: Near-global survey of effective droplet radii in liquid water clouds using ISCCP data. J. Climate,7, 465–497.

  • Hay, J. E., and T. K. Won, 1980: Proc. First Canadian Solar Radiation Data Workshop, Canadian Atmospheric Environment Service.

  • Henyey, L. C., and J. L. Greenstein, 1941: Diffuse radiation in the galaxy. Astrophys. J.,93, 70–83.

  • Hu, Y. X., and K. Stamnes, 1993: An accurate parameterization of the radiative properties of water clouds suitable for use in climate models. J. Climate,6, 728–742.

  • LeDrew, E., D. Barber, T. Agnew, and D. Dunlop, 1992: Canadian Sea Ice Atlas from Microwave Remotely Sensed Imagery: July 1987 to June 1990. Climatological Studies No. 44, Canadian Climate Program, 80 pp.

  • Leontieva, E., K. Stamnes, and J. A. Olseth, 1994: Cloud optical properties at Bergen (Norway) based on the analysis of long-term solar irradiance records. Theor. Appl. Climatol.,50, 73–82.

  • Leontyeva, E., and K. Stamnes, 1994: Estimations of cloud optical thickness from ground-based measurements of incoming solar radiation in the arctic. J. Climate,7, 566–578.

  • Li, Z., and H. G. Leighton, 1993: Global climatologies for solar radiation budgets at the surface and in the atmosphere from 5 years of ERBE data. J. Geophys. Res.,98, 4919–4930.

  • ——, and L. Garand, 1994: Estimation of surface albedo from space: A parameterization for global application. J. Geophys. Res.,99, 8335–8351.

  • ——, H. W. Barker, and L. Moreau, 1995: The variable effect of clouds on atmospheric absorption of solar radiation. Nature,376, 486–490.

  • Marshak, A. A. Davis, W. Wiscombe, and G. Titov, 1995: The verisimilitude of the independent pixel approximation used in cloud remote sensing. Remote Sens. Environ.,52, 71–78.

  • McClatchey, R. A., R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, 1972: Optical properties of the atmosphere. 3d ed. AFCLR-72-0497, 108 pp. [NTIS N7318412.].

  • McFarlane, N. A., G. J. Boer, J.-P. Blanchet, and M. Lazare, 1992: The Canadian Climate Centre second-generation general circulation model and its equilibrium climate. J. Climate,7, 1013–1044.

  • Min, Q., and L. C. Harrison, 1996: Cloud properties derived from surface MFRSR measurements and comparison with GOES results at the ARM SGP site. Geophys. Res. Lett.,23, 1641–1644.

  • Rawlins, F., and J. S. Foot, 1990: Remotely sensed measurements of stratocumulus properties during FIRE using the C130 aircraft multichannel radiometer. J. Atmos. Sci.,47, 2488–2503.

  • Rossow, W. B., 1989: Measuring cloud properties from space: A review. J. Climate,2, 201–213.

  • ——, and R. A. Schiffer, 1991: ISCCP cloud products. Bull. Amer Meteor. Soc.,72, 2–20.

  • Slingo, A., 1989: A GCM parameterization for the shortwave radiative properties of water clouds. J. Atmos. Sci.,46, 1419–1427.

  • ——, and H. M. Schrecker, 1982: On the shortwave radiative properties of stratiform water clouds. Quart. J. Roy. Meteor. Soc.,108, 407–426.

  • Spencer, J. W., 1971: Fourier series representation of the position of the sun. Search,2, 172.

  • Stamnes, K., 1982: Reflection and transmission by a vertically inhomogeneous planetary atmosphere. Planet. Space Sci.,30, 727–732.

  • ——, S.-C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt.,27, 2502–2509.

  • Stephens, G. L., 1988: Radiative transfer through arbitrarily shaped optical media. Part II: Group theory and simple closures. J. Atmos. Sci.,45, 1837–1848.

  • ——, and S.-C. Tsay, 1990: On the cloud absorption anomaly. Quart. J. Roy. Meteor. Soc.,116, 671–704.

  • Tsay, S.-C., K. Stamnes, and K. Jayaweera, 1989: Radiative energy budget in the cloudy and hazy Arctic. J. Atmos. Sci.,46, 1002–1018.

  • Wielicki, B. A., and L. Parker, 1992: The determination of cloud cover from satellite sensors: The effect of sensor spatial resolution. J. Geophys. Res.,97, 12 799–12 823.

  • Wiscombe, W. J., and J. W. Evans, 1977: Exponential-sum fitting of radiative transmisson functions. J. Comput. Phys.,24, 416–444.

Fig. 1.
Fig. 1.

Location of Canadian radiation/weather stations used in this study.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 2.
Fig. 2.

Normalized frequency histograms of effective, hourly, overcast cloud optical depths τ for 21 stations across Canada (see Table 1) inferred from surface pyranometer measurements made during June–August.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 3.
Fig. 3.

Heavy solid lines are as in Fig. 2. Broken lines are corresponding discrete gamma distributions (see Barker et al. 1996) based on the mean value of optical depth from the observations and ν in (6) derived from the method of moments (νmom in Table 1). Likewise, thin solid lines are maximum likelihood estimates of ν (νmle in Table 1). Viewing with linear-log axes emphasizes the goodness-of-fits in the tails.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 4.
Fig. 4.

(a) Mean cloud optical depth τ for JJA (from Table 1) as a function of latitude for all stations except the four coastal sites (see Fig. 2). Least squares linear regression line is also shown in which its coefficient of determination r2 is 0.82. (b) As in (a) except this is standard deviation σ of hourly optical depths (from Table 1). Value of r2 for the regression line is 0.80.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 5.
Fig. 5.

Mean hourly optical depths and corresponding standard deviations for June, July, and August as a function of local apparent time for four coastal sites, (a) and (b), and four continental sites, (c) and (d).

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 6.
Fig. 6.

As in Fig. 2 except these are normalized histograms for hourly values of τ before (AM) and after (PM) 1200 LAT. The values N, τ, and νmom are number of observations, mean optical depth, and ν in (6) determined by the method of moments.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 7.
Fig. 7.

Annual march of monthly mean optical depths τ and corresponding standard deviations σ (based on hourly values) for four coastal sites. Only these sites had sufficiently many observations for each month to make meaningful annual plots.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 8.
Fig. 8.

Mean optical depth for the entire JJA period as a function of year for four stations with large numbers of samples.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 9.
Fig. 9.

Thin lines are mean-monthly optical depth for all months as a function of time. Heavy lines are the results of smoothing with a 13-month running mean in order to suppress much high frequency noise. Least squares linear regression lines are also shown and their slopes are listed on the plots.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 10.
Fig. 10.

(a) and (b) Scatterplots of optical depth inferred from surface pyranometer measurements (τsrf) and collocated values reported by ISCCP-CX (τsat) for JJA 1989. Data are differentiated according to average LAT over the pyranometer integration period (identical to the times that the GOES-East satellite images were made). Surface-inferred values derive from mean transmittances measured over two continuous hours; ISCCP values are mean values of all ∼10-km pixel values flagged as overcast inside 1° × 1° cells centered over the pyranometers. (c) and (d) Standard deviation of ISCCP pixel optical depths as a function of difference between grid-mean ISCCP and surface-inferred optical depths.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 11.
Fig. 11.

Surface-inferred and ISCCP values of optical depth shown in Fig. 10 as functions of cosine of solar zenith angle μ0.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 12.
Fig. 12.

Differences between grid-mean ISCCP and surface-inferred optical depths as a function of relative azimuth angle between GOES-East satellite and the sun.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Fig. 13.
Fig. 13.

(a) Surface-inferred optical depths for Sable Island as a function of infrared temperature as reported by ISCCP (mean value of ∼10-km pixel values flagged as cloudy). (b) As in (a) except this is for ISCCP optical depths. (c) and (d) As in (a) and (b) except these are for Big Trout Lake.

Citation: Journal of Climate 11, 11; 10.1175/1520-0442(1998)011<2980:ODOOCA>2.0.CO;2

Table 1.

Name and location of 21 Canadian radiation/meteorological stations used in this study. The period of observation (month/year) is indicated. The value N is the number of hourly values of overcast cloud optical depth for each station’s entire record for June, July, and August (JJA); τ is mean hourly cloud optical depth for JJA, and νmom and νmle are corresponding gamma distribution parameters [see Eq. (6)] deduced by the method of moments (mom) and maximum likelihood estimate (mle).

Table 1.
Table 2.

Mean τ and standard deviation σ of optical depths inferred from surface pyranometers (this study) and collocated ISCCP-CX data for overcast conditions during summer 1989. The value νmom is the parameter used in (6) as determined by the method of moments.

Table 2.

1

The statistical significance of nonzero slopes for least squares linear regression lines were assessed using a two-tailed Student’s t-test at the 95% confidence level.

2

Differences between τsat and τsrf are so clear that formal statistical analyses are redundant.

Save
  • Barker, H. W., and J. A. Davies, 1989: Multiple reflections across a linear discontinuity in surface albedo. Int. J. Climatatol.,9, 203–214.

  • ——, and D. Liu, 1995: Inferring optical depth of broken clouds from Landsat data. J. Climate,8, 2620–2630.

  • ——, and Z. Li, 1997: Interpreting shortwave albedo-transmittance plots:True or apparent anomalous absorption. Geophys. Res. Lett.,24, 2023–2026.

  • ——, B. A. Wielicki, and L. Parker, 1996: A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part II: Validation using satellite data. J. Atmos. Sci.,53, 2304–2316.

  • Berk, A., L. S. Bernstein, and D. C. Robertson, 1989: MODTRAN: A moderate resolution model for LOWTRAN7, Geophysics Laboratory Rep. GL-TR-89-0122, 38 pp. [Available from Geophysics Laboratory, Hanscom AFB, MA 01731-5000.].

  • Cahalan, R. F., W. Ridgway, W. J. Wiscombe, T. L. Bell, and J. B. Snider, 1994: The albedo of fractal stratocumulus clouds. J. Atmos. Sci.,51, 2434–2455.

  • Cess, R. D., and Coauthors, 1995: Absorption of solar radiation by clouds:Observations versus models. Science,267, 496–499.

  • ——, M. H. Zhang, Y. Zhou, X. Jing, and V. Dvortsov, 1996: Absorption of solar radiation by clouds: Interpretations of satellite, surface, and aircraft measurements. J. Geophys. Res.,101, 23 299–23 309.

  • Han, Q., W. Rossow, and A. Lacis, 1994: Near-global survey of effective droplet radii in liquid water clouds using ISCCP data. J. Climate,7, 465–497.

  • Hay, J. E., and T. K. Won, 1980: Proc. First Canadian Solar Radiation Data Workshop, Canadian Atmospheric Environment Service.

  • Henyey, L. C., and J. L. Greenstein, 1941: Diffuse radiation in the galaxy. Astrophys. J.,93, 70–83.

  • Hu, Y. X., and K. Stamnes, 1993: An accurate parameterization of the radiative properties of water clouds suitable for use in climate models. J. Climate,6, 728–742.

  • LeDrew, E., D. Barber, T. Agnew, and D. Dunlop, 1992: Canadian Sea Ice Atlas from Microwave Remotely Sensed Imagery: July 1987 to June 1990. Climatological Studies No. 44, Canadian Climate Program, 80 pp.

  • Leontieva, E., K. Stamnes, and J. A. Olseth, 1994: Cloud optical properties at Bergen (Norway) based on the analysis of long-term solar irradiance records. Theor. Appl. Climatol.,50, 73–82.

  • Leontyeva, E., and K. Stamnes, 1994: Estimations of cloud optical thickness from ground-based measurements of incoming solar radiation in the arctic. J. Climate,7, 566–578.

  • Li, Z., and H. G. Leighton, 1993: Global climatologies for solar radiation budgets at the surface and in the atmosphere from 5 years of ERBE data. J. Geophys. Res.,98, 4919–4930.

  • ——, and L. Garand, 1994: Estimation of surface albedo from space: A parameterization for global application. J. Geophys. Res.,99, 8335–8351.

  • ——, H. W. Barker, and L. Moreau, 1995: The variable effect of clouds on atmospheric absorption of solar radiation. Nature,376, 486–490.

  • Marshak, A. A. Davis, W. Wiscombe, and G. Titov, 1995: The verisimilitude of the independent pixel approximation used in cloud remote sensing. Remote Sens. Environ.,52, 71–78.

  • McClatchey, R. A., R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, 1972: Optical properties of the atmosphere. 3d ed. AFCLR-72-0497, 108 pp. [NTIS N7318412.].

  • McFarlane, N. A., G. J. Boer, J.-P. Blanchet, and M. Lazare, 1992: The Canadian Climate Centre second-generation general circulation model and its equilibrium climate. J. Climate,7, 1013–1044.

  • Min, Q., and L. C. Harrison, 1996: Cloud properties derived from surface MFRSR measurements and comparison with GOES results at the ARM SGP site. Geophys. Res. Lett.,23, 1641–1644.

  • Rawlins, F., and J. S. Foot, 1990: Remotely sensed measurements of stratocumulus properties during FIRE using the C130 aircraft multichannel radiometer. J. Atmos. Sci.,47, 2488–2503.

  • Rossow, W. B., 1989: Measuring cloud properties from space: A review. J. Climate,2, 201–213.

  • ——, and R. A. Schiffer, 1991: ISCCP cloud products. Bull. Amer Meteor. Soc.,72, 2–20.

  • Slingo, A., 1989: A GCM parameterization for the shortwave radiative properties of water clouds. J. Atmos. Sci.,46, 1419–1427.

  • ——, and H. M. Schrecker, 1982: On the shortwave radiative properties of stratiform water clouds. Quart. J. Roy. Meteor. Soc.,108, 407–426.

  • Spencer, J. W., 1971: Fourier series representation of the position of the sun. Search,2, 172.

  • Stamnes, K., 1982: Reflection and transmission by a vertically inhomogeneous planetary atmosphere. Planet. Space Sci.,30, 727–732.

  • ——, S.-C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt.,27, 2502–2509.

  • Stephens, G. L., 1988: Radiative transfer through arbitrarily shaped optical media. Part II: Group theory and simple closures. J. Atmos. Sci.,45, 1837–1848.

  • ——, and S.-C. Tsay, 1990: On the cloud absorption anomaly. Quart. J. Roy. Meteor. Soc.,116, 671–704.

  • Tsay, S.-C., K. Stamnes, and K. Jayaweera, 1989: Radiative energy budget in the cloudy and hazy Arctic. J. Atmos. Sci.,46, 1002–1018.

  • Wielicki, B. A., and L. Parker, 1992: The determination of cloud cover from satellite sensors: The effect of sensor spatial resolution. J. Geophys. Res.,97, 12 799–12 823.

  • Wiscombe, W. J., and J. W. Evans, 1977: Exponential-sum fitting of radiative transmisson functions. J. Comput. Phys.,24, 416–444.

  • Fig. 1.

    Location of Canadian radiation/weather stations used in this study.

  • Fig. 2.

    Normalized frequency histograms of effective, hourly, overcast cloud optical depths τ for 21 stations across Canada (see Table 1) inferred from surface pyranometer measurements made during June–August.

  • Fig. 3.

    Heavy solid lines are as in Fig. 2. Broken lines are corresponding discrete gamma distributions (see Barker et al. 1996) based on the mean value of optical depth from the observations and ν in (6) derived from the method of moments (νmom in Table 1). Likewise, thin solid lines are maximum likelihood estimates of ν (νmle in Table 1). Viewing with linear-log axes emphasizes the goodness-of-fits in the tails.

  • Fig. 4.

    (a) Mean cloud optical depth τ for JJA (from Table 1) as a function of latitude for all stations except the four coastal sites (see Fig. 2). Least squares linear regression line is also shown in which its coefficient of determination r2 is 0.82. (b) As in (a) except this is standard deviation σ of hourly optical depths (from Table 1). Value of r2 for the regression line is 0.80.

  • Fig. 5.

    Mean hourly optical depths and corresponding standard deviations for June, July, and August as a function of local apparent time for four coastal sites, (a) and (b), and four continental sites, (c) and (d).

  • Fig. 6.

    As in Fig. 2 except these are normalized histograms for hourly values of τ before (AM) and after (PM) 1200 LAT. The values N, τ, and νmom are number of observations, mean optical depth, and ν in (6) determined by the method of moments.

  • Fig. 7.

    Annual march of monthly mean optical depths τ and corresponding standard deviations σ (based on hourly values) for four coastal sites. Only these sites had sufficiently many observations for each month to make meaningful annual plots.

  • Fig. 8.

    Mean optical depth for the entire JJA period as a function of year for four stations with large numbers of samples.

  • Fig. 9.

    Thin lines are mean-monthly optical depth for all months as a function of time. Heavy lines are the results of smoothing with a 13-month running mean in order to suppress much high frequency noise. Least squares linear regression lines are also shown and their slopes are listed on the plots.

  • Fig. 10.

    (a) and (b) Scatterplots of optical depth inferred from surface pyranometer measurements (τsrf) and collocated values reported by ISCCP-CX (τsat) for JJA 1989. Data are differentiated according to average LAT over the pyranometer integration period (identical to the times that the GOES-East satellite images were made). Surface-inferred values derive from mean transmittances measured over two continuous hours; ISCCP values are mean values of all ∼10-km pixel values flagged as overcast inside 1° × 1° cells centered over the pyranometers. (c) and (d) Standard deviation of ISCCP pixel optical depths as a function of difference between grid-mean ISCCP and surface-inferred optical depths.

  • Fig. 11.

    Surface-inferred and ISCCP values of optical depth shown in Fig. 10 as functions of cosine of solar zenith angle μ0.

  • Fig. 12.

    Differences between grid-mean ISCCP and surface-inferred optical depths as a function of relative azimuth angle between GOES-East satellite and the sun.

  • Fig. 13.

    (a) Surface-inferred optical depths for Sable Island as a function of infrared temperature as reported by ISCCP (mean value of ∼10-km pixel values flagged as cloudy). (b) As in (a) except this is for ISCCP optical depths. (c) and (d) As in (a) and (b) except these are for Big Trout Lake.

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