Introduction
Studies of longwave radiative transfer under cumulus cloud conditions reveal that the cloud fraction can be altered significantly by the shading and emission of energy by cloud sides. This has a direct impact on calculations of longwave radiative fluxes and cooling rates and ultimately influences the performance of atmospheric general circulation models (GCMs) and climate studies. In current climate models, however, the effects of broken cumulus clouds are often calculated as the cloud amount weighted average of clear and black-cloud overcast conditions (i.e., the black plate approximation) (Killen and Ellingson 1994). The effects of cloud geometry are neglected. To overcome the simplicity of the black plate approximation, several groups (Ellingson 1982; Harshvardhan and Weinman 1982; Naber and Weinman 1984; Killen and Ellingson 1994; Han and Ellingson 1999) have proposed an effective cloud fraction as a modification. The effective cloud fraction by definition is the flat plate absolute cloud fraction that generates the same flux for a given broken cloud field after taking into account the effects of particular geometric shapes, size, and spatial distributions of the clouds. This practical approach is intended to incorporate the essential physics with a simple modification to existing climate model radiation codes. However, the validity of these parameterizations has largely not been tested because of inadequate measurements of atmospheric radiative properties.
Recently, there have been comprehensive ground-based measurements at the Atmospheric Radiation Measurement Program (ARM) southern Great Plains (SGP) Cloud and Radiation Test Bed (CART) central facility that allow testing of the various cloud models. The simultaneous observations include downwelling longwave fluxes, spectral zenith longwave radiances, cloud base heights, water vapor and liquid water column burdens, the sky conditions, and vertical distributions of temperature, water vapor, and horizontal winds. These observations are used herein to estimate a set of comprehensive cloud variables that characterize cumulus clouds.
In this paper, the validity of selected parameterizations is tested by comparing effective cloud amounts derived from hemispheric flux observations with values predicted by the parameterizations using measured cloud quantities as input. Section 2 briefly describes parameterizations of the effective cloud fraction. Section 3 outlines the technique for determining single-layer cumulus cloud fields. Section 4 presents the detailed algorithms for extracting cloud variables from the ground-based measurements. Section 5 compares “observed” with model-calculated longwave cumulus cloud parameters. The last section offers several conclusions and points out directions for future studies.
Parameterizations of effective cloud fraction
Under cumulus cloud conditions, cloud sides will obscure part of the clear sky fraction and Eq. (1) no longer holds. A small disparity in cloud cover can significantly alter the gradient and/or magnitude of longwave radiative properties, which may in turn affect the cloud evolution and life span (Ellingson 1982; Guan et al. 1997; Han and Ellingson 1999). A practical approach to account for the effects of cumulus clouds in climate models is to adopt the effective cloud fraction Ne instead of N. Ne is the cloud fraction required to give the “correct” fluxes for the assumptions made concerning the clouds.
Unlike shortwave radiative transfer, longwave scattering effects are much smaller than the effects of bulk geometry even in the window region (8–12 μm) (Takara and Ellingson 1996) after clouds exceed about 300 m in depth. If one neglects scattering, Ne depends on the cloud base height zb, thickness h, aspect ratio β, cloud spatial and size distributions, and the vertical distributions of temperature and water vapor. Details concerning the dependence of models of Ne on these parameters are discussed by Ellingson (1982), Killen and Ellingson (1994), Han and Ellingson (1999), etc. For tests with observations, the following cloud models are selected: the Han–Ellingson cuboidal/cylinder model with exponential cloud size and spatial distributions (Han and Ellingson 1999), the Ellingson random cylinder model (Ellingson 1982; Han and Ellingson 1999), the Harshvardhan–Weinman regular cuboidal model (Harshvardhan and Weinman 1982), and the Naber–Weinman shifted periodic array cuboidal model (Naber and Weinman 1984).
Determination of single-layer cumulus cloud fields
To assure the quality of the validation of the cumulus cloud parameterizations, we focus on single-layer cumulus cloud fields and extract cloud variables from them. Using this approach, variations in other layer clouds and cloud overlapping are excluded.
Occurrences of single-layer cumuliform cloud fields at the Oklahoma ARM site were found by using observations from the whole sky imager (WSI), micropulse lidar (MPL), and laser ceilometer (LC) (see Table 1). A millimeter cloud radar or a volume-imaging lidar would have been more useful to our search. Unfortunately these observations were not available during the time period reported herein.
The observations most useful for determining the locations of cloud bases come from the LC. The LC, which is pointed directly upward and samples at a time interval of 30 s, is claimed to detect zcb over a range from 15 to 7800 m with a vertical resolution of 7.6 m. The LC data can help to distinguish if a cloud field has a stable cloud base. For a single-layer cloud field, we found that zcb fluctuates within about 5%. If zcb scatters widely, the cloud field tends to consist of multiple-layer clouds.
Additionally, observations from a WSI and an MPL are also used for the determination of single-layer cumulus cloud fields. The WSI has a field of view (FOV) of 170°, and its angular resolution is 0.333°. The so-called grayscale “cloud decision” images used in this study have 10-min intervals (Koehler and Shields 1990). In these images, each pixel represents a value, ranging from 0 to 255, and indicates the sky status, such as background (0, 201–255), clear sky (1–99), and cloud (100–200). The MPL, sampling data every minute, has a 300-m resolution and detects backscattering from altitudes approximately between 300 m and 20 km. The MPL is able to detect cirrus clouds effectively.
In our study, a cloud field is considered to be composed of single-layer cumulus clouds if the following conditions are met.
The grayscale values of the WSI clear- and cloudy-sky pixels are at least 20 away from the threshold (100). This lowers the possibility of the existence of cirrus clouds.
The MPL does not or rarely detects cirrus clouds.
The LC observations indicate that the change in zcb is below about 5% and values of zcb are below 4 km. In addition, in order to lower the possibility of including stratocumulus clouds, cases were only selected when there were more than three cloud-to–no-cloud signal changes within 10 min.
Extraction of single-layer cumulus cloud variables
The quantities necessary to test the validity of longwave radiative cumulus cloud parameterizations include: the cloud-base and -top heights, zcb and zct; a measure of nonisothermality λ; the cloud effective side length D, or radius R; the cloud aspect ratio β; the exponents of cloud spatial and size distributions, u and υ; the absolute cloud fraction N; and the effective cloud fraction Ne. Table 1 summarizes the cloud variables necessary for the parameterizations, their determining sources, and their relative accuracies. Detailed descriptions of these variables are contained in Han and Ellingson (1999).
Determination of cloud-base height
The value zcb is directly determined by the LC. Figure 1 shows a typical example of a time sequence of zcb under fair weather conditions. During the local time period between 1000 and 1600 UTC 11 July 1994, the base of boundary layer clouds evolved with the time, and the detected zcb fluctuated around the quadratic regression line with a standard deviation (
Determination of cloud-top height
Perhaps the best way to obtain zct would be to use a millimeter cloud radar or a volume imaging lidar. Satellite observations, such as infrared measurements of the Geostationary Operational Environmental Satellite (GOES), also can play a significant role. To overcome its absence in the cloud parameterization test, zct is determined from radiosonde measured temperature and relative humidity profiles, since radiosondes are routinely operated and the relative humidity (RH) profile contains a signal of the desired zct.
Theoretically, 100% RH, that is, water vapor saturation, is a necessary but not sufficient condition for cloud formation or for cloud presence. However, radiosondes reveal that this is often not the case, especially for the broken cloud conditions (see Slingo 1980, 1987).
Slingo (1980, 1987) pointed out that radiosonde samples only a single profile and does not necessarily represent the larger horizontal area. With broken cloud cover, the RH profile is dependent on whether the radiosonde ascends through clear or cloudy air. Based on a large number of radiosonde ascents during the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE), Slingo (1980) found that low clouds almost always occur with RH over 80%, and that the probability of middle-level cloud occurring increases with increasing RH but clear skies are more likely than cloudy skies for RH below 65%. In Slingo’s (1980 and 1987) studies, the RH is the relative humidity at zcb, and the low- and middle-level clouds are bounded by the levels of 950–850 mb, and 700–500 mb, respectively.
Although there is no direct observation for zct, the LC data and radiosondes can be used to reveal the relationship between zcb and the corresponding measured RH at that level under broken cloud conditions. Such a relationship can help to estimate zct. For this purpose, 27 broken cloud cases were sorted from the time period of interest.
Figure 2 shows the relationships between zcb detected by the LC and their corresponding RH/pressures from radiosondes. Figure 2 implies that the RH for the broken cloud presence tends to correlate with the cloud vertical position and that 70% RH at a pressure of 780 mb may still indicate the existence of clouds. In Slingo’s (1980, 1987) cloud prediction scheme, the threshold of RH decreases from 80% at zcb = 950 mb to 65% at zcb = 700 mb. In general, our relationship between zcb and RH matches Slingo’s results under broken cloud conditions.
Furthermore, RH profiles above zcb were investigated to find an appropriate threshold for zct. It is found that the largest rate of RH decrease occurs in the RH range of 65%–75%, and that after this large decrease, the RH tends to decrease slowly. It is believed that the threshold of 65% RH, used by Slingo (1980) to predict middle-level clouds, was a consequence of the conditions present during GATE and it may not always be suitable to judge zct at the CART site.
The relationship between zct and RH is assumed to follow the same pattern as that between zcb and RH. In other words, the threshold of RH decreases with a decrease in pressure. We further assume that the boundary of zct may be better signaled by a large rate of RH decrease. Therefore, zct is estimated as the altitude above zcb that has the largest rate of RH decrease in the RH range of 65%–75%. The distance between the level of 65% RH and the determined zct is used to estimate the uncertainty in zct. The standard deviation of this uncertainty is denoted as
It is noteworthy that, unlike the lower boundary of a single-layer cloud field, the upper boundary is likely to have larger fluctuations. Here, zct might be better considered as the average upper-cloud boundary.
Determination of the nonisothermality factor
The nonisothermality factor λ is a term used in the Ellingson (1982) and Han and Ellingson (1999) Ne parameterizations to account for the altitude varying emission of the cloud sides. It is defined as the ratio of the range of black fluxes from the cloud (bottom–top) to the black flux from the cloud base. The value of λ has two extreme cases: λ = 0 for an isothermal cloud and λ = 1 for an extremely tall cloud. Shown in Fig. 3 are calculations of λ based on the McClatchey midlatitude summer atmosphere (McClatchey et al. 1972). With zcb set at 500, 1000, 1500, and 2000 m, respectively, this figure demonstrates that λ is nearly a linear function of the cloud thickness (h = zct − zcb) no matter the location of zcb.
Determination of the average cloud effective side length/radius
In order to use observations at a single site, we assume that the cumulus cloud field is temporally and spatially invariant. This leads the time variability to be interpreted as spatial variations or a spatial pattern. In this study a time sequence of ceilometer and radiosonde observations was used to determine the average effective cloud side length D, or radius R.
For the estimation of D, we assume that during the time period of observations
clouds are not aligned, and they are distributed isotropically;
the wind speed U at zcb is constant; and
the cloud projection on the ground surface is a square.
On the other hand, if the cloud projection is assumed to be a circle, then the effective cloud radius R can also be estimated by the above equation except that the coefficient is 0.64 rather than 1.41.
An important factor influencing the estimation of D or R is the wind speed. If a cloud field does not move, that is, U = 0.0 m s−1, the above method will not work. In our selected cases, U ranges from 4.0 to 20.0 m s−1. Therefore, this is not a major problem.
As a practical matter, to reduce the possibility of overestimating or underestimating D or R, we need to set an appropriate time period of ceilometer observations. Figure 4 gives an example of 10- and 20-min R profiles based on observations between 1000 and 1600 LT, 11 July 1994. The upper and lower panels show that the retrieved R from these two different sampling periods tends to match well. Currently, we lack other valid measurements to assess the reliability of this approach for R. However, the relative accuracy of R may be evaluated by the quantity of [R(10 min) − R(20 min)]/R(10 min). The analysis of the data in this specific time period indicates that the majority of the relative accuracies of R are within 20%–30%.
Several case studies showed an insignificant difference between 10- and 20-min sampling. Careful case selection may achieve a relative accuracy at the level of about 20%. In our study, we used D or R from a 10-min sampling to represent the average cloud effective side length or radius, matching the time for the Ne extraction.
Determination of cloud aspect ratio
Since σR/R is approximately 20%–30%, σβ/β is also about 20%–30%.
Determination of cloud spatial and size distribution exponents
The Han and Ellingson (1999) Ne parameterization specifies cloud spatial and size distributions using power-law functions with adjustable exponents. Unfortunately, these exponents could not be specified with the measurements made at the ARM site during the time period of this study. The analyses of Landsat Multispectral Scanner imagery by Welch et al. (1988), Cahalan and Joseph (1989), Sengupta et al. (1990), Zhu et al. (1992), etc. indicate that the exponent υ of cloud size distribution does not have a single value. This value is affected by the cloud development features and by regional variations. Fortunately, Oklahoma was included in the investigation of cumulus scenes both by Sengupta et al. (1990) and Zhu et al. (1992). The image data were collected on 22 June 1979, which may represent the cloud fields during the time period in this study. Based on those analyses over Oklahoma, we calculated υ from the figures in their papers to be 2.0, and this number is chosen to represent the cloud fields at the SGP CART site.
The studies by Sengupta et al. (1990) and Zhu et al. (1992) do not include data necessary to obtain the exponent u of cloud spatial distribution needed in the Han–Ellingson models. To overcome this problem, we adopted a value from the works of Cahalan and Joseph (1989) and Lee (1988). Cahalan and Joseph (1989) analyzed Landsat marine stratocumulus cloud data and found that the large cloud spacings give values of u in the range of 2–3. Lee (1988) analyzed AVHRR (Advanced Very High Resolution Radiometer) observations of cumuliform clouds over oceans and derived a mean value of 2.43 for u. We selected 2.5 for the results shown here.
Due to a lack of data for u and υ at the ARM SGP CART site, the relative accuracies of u and υ are assumed to be 10%. This number will be used later to assess their influence on the validation.
Determination of absolute cloud fraction
Shown in Fig. 5 is an example illustrating the effect of the sampling period on N. In this figure, N is determined from two different averaging periods. We found that the N from these two periods generally follows the same tendency and agree well. Due to the lack of more accurate data from other sources, we define the relative accuracy for N as [N(10 min) − N(20 min)]/N(10 min) to evaluate the uncertainty in N. The analysis of the data in this specific time period indicates that the relative accuracy of N is poorer than that of R, because N in many cases is below 0.1. Any change in N leads to poor relative accuracy. A rapid change in cloud patterns also can cause poor relative accuracy. Keep in mind, however, that we use observations at a single station. The value N for a 10-min interval does not have to strictly approach N for a 20-min interval, because the cloud field patterns in these two time domains are not necessarily the same. In our analysis, we choose 10-min intervals to extract N and use 20%–30% as the relative accuracy of N. Cases associated with poor relative accuracy are not selected.
It is also noteworthy that the WSI contains information on the cloud fraction. However, because of the wide field of view of the WSI, this cloud fraction includes the cloud side coverage, especially from those clouds located at large zenith angles. Obviously, it is not N. Furthermore, the hourly recorded cloud fraction in the weather logs suffers poor time resolution and also includes cloud side contamination. Additionally, data from the microwave radiometer contain the columnar liquid water amount. The difficulty of setting an appropriate threshold for this amount to represent either sky or cloud makes its use impractical. The approach we outline here may be the best available for the state and arrangement of instruments during the period of interest. Nonetheless, future studies will have data from the millimeter cloud radar.
Determination of effective cloud fraction
The approach used here to extract Ne is based on hemispheric flux observations. Thus, determining Ne is simple in principle, but there are significant technical problems associated with determining homogeneous clear- and cloudy-sky fluxes, that is, Fc↓ and Fo↓. Furthermore, inappropriate treatment of instrument errors may result in the same magnitude of the effects of broken clouds relative to the plane plate clouds.
The CART pyrgeometer measurements report 1-min flux averages at a time interval of 1 min. This flux cannot be used directly for the extraction of Ne because it is not representative of a spatially extended cloud field. Equation (11) applies instantaneously to an area large compared to an individual cloud or averaged over a time period sufficient to measure the equivalent spatial coverage. In our case, the hemispheric flux observations are performed at a single site. We need to use the time domain to represent the space domain. For an average horizontal wind speed of 10 m s−1, a 10-min temporal interval may represent an equivalent length of 6000 m measured by the pyrgeometer. We found that a 10-min mean flux, F↓, determined from 1-min-averaged fluxes is best for the extraction of Ne, because it represents a relatively stable cloud pattern (Han 1996). The problem in estimating Ne from the pyrgeometer data then reverts to accurately determining Fc↓ and Fo↓.
We use the ground-based AERI observations to estimate Fc↓ and Fo↓, because the AERI has a high likelihood of obtaining a more correct representation of the clear- and cloudy-sky radiances—Ic↓ and Io↓. The AERI data are obtained at approximately 8-min intervals. For each interval, the mean and the standard deviation of the radiances are calculated from 10 instantaneous observations. The cases with a field of view completely covered by clear- or cloudy-sky have significantly smaller standard deviations than those with a field of view partially covered by cloudy sky. To determine Ic↓, the averaged standard deviation of clear-sky radiances, which is calculated using accumulated homogeneous clear-sky cases, serves as a reference. For a sequence of observations, the mean radiances with the standard deviations close to the reference value are considered as representatives of clear-sky radiances—Ic↓. Ic↓ is converted to Fc↓ using the same technique as that described by Ellingson and Wiscombe (1996). With the similar approach, Io↓ and Fo↓ can be determined.
According to Han (1996), the AERI and pyrgeometer observations were in very good agreement under both homogeneous clear- and cloudy-sky conditions during the time period of interest. There were only small steady biases (1–4 W m−2) between them, with the AERI-based fluxes greater than the nearly collocated pyrgeometer observations. The standard deviation of the biases arising from the conversion is less than about 1.5 W m−2. We infer that under broken cloud conditions, a clear-sky AERI radiance can be converted to a homogeneous clear-sky flux, a cloudy AERI radiance can be converted to a homogeneous cloudy flux, and both have a bias whose standard deviation is about 1.5 W m−2.
Occasionally, when the AERI observations did not observe either a clear- or a cloudy-sky scene, we determine Fc↓ or Fo↓ entirely based on the Ellingson radiation model using radiosonde data as input. Although a 3-h interval of radiosondes may not always provide an acceptable temporal resolution for the flux interpolation, model calculations can compensate for the absence of AERI observations. According to Han (1996), for the clear-sky cases, the flux from the Ellingson radiation model averages 1.8 W m−2 less than the pyrgeometer observation, while for cloudy-sky cases, it averages 2.8 W m−2 larger. For both clear- and cloudy-sky cases, the standard deviation between the Ellingson radiation model calculations and the pyrgeometer observations is about 2.5 W m−2.
After obtaining Fc↓ and Fo↓, either from the AERI observations or radiation model calculations, we calculate the 10-min-averaged Ne using the expression given by Eq. (11). For the extraction of Ne at a specific time, we use 11 pyrgeometer data points (5 immediately before and after the time, respectively) to calculate the average flux, labeled as Fpyrg. This Fpyrg is used to extract Ne. Additionally, we also assume that Fc↓ and Fo↓ do not change during each 10-min averaging period.
Realizing the existence of flux measurement errors and the fluctuation of pyrgeometer observations within each sampling period, we need to evaluate their influence on the estimation of Ne. An inspection of the right-hand side of Eq. (11) shows that both the numerator and the denominator are the difference of two quantities that are intercalibrated between the pyrgeometer and the AERI. Therefore, the absolute accuracy of the pyrgeometer data, that is, the systematic errors in the pyrgeometer data, should not influence Ne.
Here, by assuming the error to be random, the variances of the 10-min averages of the pyrgeometer observations (11 data points) and the 8-min averages of the AERI observations (10 data points) are estimated as the average of the individual variances divided by the square root of the number of observations. As an example, with both σFc↓ and σFo↓ set as 1.5 W m−2, Fig. 6 shows the effect of σFpyrg↓ on σNe. In the figure, σFpyrg↓ is directly calculated from 10-min pyrgeometer sampling, and Fc↓ and Fo↓ are determined by the AERI observations. This figure demonstrates that σFpyrg↓ is an important quantity influencing σNe. It is difficult to improve
Tests of selected cumulus cloud parameterizations
Overall, 436 single-layer cumulus cloud cases were collected from the observations at the ARM SGP CART central facility site during the time period of May–July 1994. Figure 7 illustrates the distribution of these cases. The majority of them have β in the range of 0.25–1.00 and N varying from 0.1 to 0.5. The relationship between the retrieved Ne and the retrieved N indicates that the effect of cumulus cloud bulk geometry really makes Ne significantly different from the flat-plate cloud cover.
To test the validity of various cloud parameterizations, we calculated the effective cloud fraction, Ne(calc), using the Han–Ellingson cuboidal/cylinder models (Han and Ellingson 1999), the Ellingson random cylinder model (Ellingson 1982), the Harshvardhan–Weinman regular cuboidal model (Harshvardhan and Weinman 1982), and the Naber–Weinman shifted-periodic array cuboidal model (Naber and Weinman 1984). The Ne calculations are based on the observed cloud variables. We computed the differences between Ne(calc) and Ne(retr) and plotted them against the retrieved N with β grouped into different ranges.
To account for the uncertainties associated with cloud variables, we conducted a sensitivity study to evaluate the impact of variations in each cloud variable on the validation by drawing box charts. In each box chart, the bottom of the vertical line marks the 5th percentile. The bottom of the box marks the 25th percentile, the median line marks the 50th percentile, the top of the box marks the 75th percentile, and the top of the vertical line marks the 95th percentile. Also included are the box charts of the standard deviation of retrieved effective cloud fractions and the relative accuracy of each tested cloud model. In the discussion, the model relative accuracy is defined as the ratio of the absolute difference of [Ne(calc) − Ne(retr)] to Ne(retr).
We conducted the same tests for each selected cloud model. Figure 8 provides an example of the various tests for the Han–Ellingson cuboidal model. As shown in Fig. 8a, differences of [Ne(calc) − Ne(retr)] tend to scatter around 0 and be independent of N(retr). Figure 8b indicates that ±10% changes in the nonisothermality factor λ and the exponent of cloud spatial distribution u generally do not have an important impact on the calculations of the Han–Ellingson cuboidal model, but uncertainties in cloud aspect ratio β, absolute cloud fraction N, and exponent of cloud size distribution υ significantly influence the model results. The scatter along the axis of [Ne(calc) − Ne(retr)] is likely caused by the uncertainties in coefficients (β, N, υ), by the uncertainty in the pyrgeometer observations, or by the inadequacy of the cloud models. Among the three cloud variables, the uncertainty in N affects Ne(calc) the greatest, whereas the uncertainties in β and υ influence Ne(calc) with nearly the same magnitudes. It is possible that our 10-min extraction methods for β and N generate random uncertainties.
For the data collected, the Han–Ellingson cuboidal model agrees well with the observations within the test range. The mean and standard deviation of [Ne(calc) − Ne(retr)] are 0.006, about 1.5% in the mean Ne(retr), and 0.018, close to σNe(retr), respectively. Additionally, the mean and standard deviation of the model relative accuracies are 3.9% and 3.8%, respectively, while the 75th and 95th percentiles of the model relative accuracy are 5.5% and 12.0%, respectively.
Table 2 gives a summary of the tests of each cloud model. The results indicate that, except for the Han–Ellingson cylinder model, the other models achieve a mean relative accuracy of about 4%. Furthermore, their relative accuracies at the 75th and 95th percentiles are about 5.5% and 12%, respectively. The Han–Ellingson cylinder model shares the characteristics of the Han–Ellingson cuboidal model in all aspects except that it predicts a slightly larger Ne. Compared with the Han–Ellingson cuboidal/cylinder model, the Ellingson random cylinder model, Harshvardhan–Weinman regular cuboidal model, and Naber–Weinman shifted-periodic array cuboidal model require fewer cloud variables to calculate Ne because they include fewer cloud features.
Summary and conclusions
Several different parameterizations of finite-size cloud effects for longwave radiation calculations have been proposed, but until now, their validity has not been tested with observed data. However, ground-based measurements at the ARM SGP CART central facility site allow one to estimate the variables characterizing cumulus clouds. With an empirically determined optimum sampling period of 10 min, these measurements were used to extract the effective cloud fraction, absolute cloud fraction, and many other cloud variables.
The tests indicate that the Han–Ellingson cylinder model tends to overestimate slightly the effective cloud fraction, while the other four models agree well with the observations. The tests also show that within the test range, cloud horizontal distributions do not significantly influence cloud mutual shading and the effective cloud fraction. The model assumptions for cloud spatial distributions include exponential, random, regular, and a shifted-periodic array, but these models all predict the effective cloud fraction very well. This occurs because most of our observations occur at small cloud amount, and cloud mutual shading is not important for these conditions. There are few cases with absolute cloud amount greater than 0.5, a range where different treatments of the horizontal distribution of cumulus clouds lead to a large disparity among various cumulus cloud parameterizations (Han and Ellingson 1999).
The current tests do not lead to a conclusion as to the best choice of models. There are few cases in the range of greatest sensitivity with large cloud aspect ratio and absolute amount. Nevertheless, this is the first validation of the form of the dependence of Ne on bulk cloud parameters using independently measured data at the surface.
This study points the direction for many future studies. The ongoing ARM Tropical Western Pacific (TWP) and North Slope of Alaska (NSA) sites will provide observations of cumulus cloud fields over those regions. These observations will feature a large diversity of cumulus clouds, including fair weather cumulus clouds, marine stratocumulus clouds, and also clouds with large aspect ratios. The sensitivity of various cloud parameterizations to a variety of cloud configurations, which the SGP CART site may seldom experience, can be further tested.
Moreover, observations from radar wind profilers may lead to a better speed determination of cloud movement, and observations from a vertically pointing cloud radar and/or volume-image lidar at the SGP site will allow more accurate definition of many cloud parameters, such as cloud thickness, amount, single-layer conditions, and so on. Extensions of the tests described herein with the new data should lead to an optimization of current cloud parameterizations and ultimately a better parameterization of longwave radiative transfer in climate models.
Acknowledgments
This paper was sponsored in part by the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) program under Grants DEFG05-90ER61075 and DEFG05-90ER60971.
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An example of cloud-base heights detected by a laser ceilometer.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
The relationship between cloud-base heights and their corresponding observed relative humidities.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
Relationships between the nonisothermality factor and cloud thicknesses with cloud bases at different altitudes.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
Comparisons of retrieved average cloud effective radii between two different sampling periods: (a) distributions of 10- and 20-min retrieved radii, and (b) a histogram of the differences between 10- and 20-min retrieved radii.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
Comparisons of retrieved absolute cloud fractions between two different sampling periods:(a) distributions of 10- and 20-min retrieved absolute cloud fractions, and (b) a histogram of the differences between 10- and 20-min retrieved absolute cloud fractions.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
The influence of uncertainty in pyrgeometer observations on the estimation of effective cloud fractions: (a) distributions of effective cloud fractions, standard deviations of effective cloud fractions and uncertainties in pyrgeometer observations, and relative accuracies of effective cloud fractions, and (b) a histogram of the accuracies of effective cloud fractions.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
The distribution of the differences between the retrieved effective and absolute cloud fractions. The vertical bars show ±one standard deviation of the uncertainty in the retrieved effective cloud fractions. The curves are the results from the Han–Ellingson cuboidal model.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
Tests of the Han–Ellingson cuboidal model with one parameter changed at each time: (a) distributions of the differences between the calculated and retrieved effective cloud fractions, and (b) box plots showing the sensitivity of the model to each cloud parameter, the standard deviation of retrieved effective cloud fractions, and the relative accuracies of the model.
Citation: Journal of Applied Meteorology 39, 7; 10.1175/1520-0450(2000)039<1147:AETFTT>2.0.CO;2
Cloud variables and their sources.
Summary of cloud model tests.
