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  • Warren, W. G., C. J. Hahn, J. London, R. M. Chervin, and R. L. Jenne, 1986: Global distribution of total cloud cover and cloud type amounts over land. NCAR Tech. Note TN-273+STR, 229 pp. [Available from Data Support Section, National Center for Atmospheric Research, Boulder, CO 80307.].

  • ——, ——, ——, ——, and ——, 1988: Global distribution of total cloud cover and cloud type amounts over oceans. NCAR Tech. Note TN-317+STR, 212 pp. [Available from Data Support Section, National Center for Atmospheric Research, Boulder, CO 80307.].

  • Weare, B. C., 1989: Uncertainties in estimates of surface heat fluxes derived from marine reports over the tropical and subtropical oceans. Tellus,41A, 357–370.

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  • View in gallery

    Average number of surface observation per month in each 2.5° × 2.5° grid for 1984–88. Letters A, B, C, D, and X indicate the locations at which the sensitivity analyses were carried out.

  • View in gallery

    Summary of sensitivity analysis. (top) Annual-mean cloud cover for the four locations A, B, C, and D. (a)–(d) sensitivity results for the four locations. Values are fractional differences between the reconstructed cloud amounts and the original observations (reconstructed estimate − original). The legend notes refer to experiments described in the text and outlined in Table 2.

  • View in gallery

    Fractional differences between the 1984–88 annual-mean total cloud cover reconstructed from the solution of Eq. (1) and the original observations (reconstructed estimate − original). (a) Hahn et al. and (b) ISCCP C2. Zero contours are heavier, solid contours; negative values are dashed; positive values are lighter solid.

  • View in gallery

    Differences between the 1984–88 annual-mean low cloud cover reconstructed from the solution of Eq. (1) and the original. (a) Hahn et al. low cloud as observed from below and (b) ISCCP C2 low cloud as observed from above. As in Fig. 3.

  • View in gallery

    Differences between the 1984–88 annual-mean ISCCP C2 cloud cover reconstructed from the solution of Eq. (1) and the original: (a) high cloud and (b) middle cloud.

  • View in gallery

    1984–88 annual means of the percent of estimated fraction of single-layer clouds (p1 + p5 + p7) vs the total cloud cover (1 − p8).

  • View in gallery

    Percent differences between 1984–88 annual-mean total cloud cover using (a) the random overlap approximation [Eq. (12)] minus the reconstructed total cloud cover (1 − p8) and (b) the mixed overlap approximation [Eq. (13)] minus the reconstructed zero contours are heavier, solid contours; negative values are dashed; positive values are lighter solid.

  • View in gallery

    Percentages of 1984–88 annual-mean cloud in the low ISCCP layer relative to the total cloud cover. (a) From the solution to Eq. (1) [(p3 + p4 + p6 + p7)/(1 − p8)] and (b) that from the LMDZ climate model.

  • View in gallery

    Percentages of 1984–88 annual-mean cloud in the high ISCCP layer relative to the total cloud cover. (a) From the solution to Eq. (1) [(p1 + p2 + p3 + p4)/(1 − p8)] and (b) that from the LMDZ climate model.

  • View in gallery

    Differences between the 1984−88 annual-mean cloud cover reconstructed from the solution of Eq. (1), using the additional Hahn et al. middle and high cloud estimates, and the original, (a) ISCCP high cloud amounts and (b) H high cloud amounts. As in Fig. 3.

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Combined Satellite- and Surface-Based Observations of Clouds

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  • 1 Department of Land, Air, and Water Resources, Atmospheric Science Program, University of California, Davis, Davis, California
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Abstract

A new method for combining satellite and surface-based cloud observations into a self-consistent three-dimensional field is presented. This method derives the probabilities of the cloud states, which are most consistent with all of the observations and assumptions concerning the nature and relative uncertainties of the observations. It is applied to a three-layer atmosphere using monthly satellite- and surface-based cloud observations. The reconstructions of the observed fields usually lead to modifications of the surface-observed low cloud amount of less than 0.008 fractional cloud cover. Over the ocean the satellite-view low cloud amounts are usually decreased by between 0.06 and 0.12 for most of the middle latitudes and southeastern tropical Pacific. Over land the adjustments in the satellite low cloud amounts are generally smaller. The method leads to increases in satellite high cover of between 0.03 and 0.09 over most regions, and increases in middle cloud cover of up to around 0.03 over the subtropical oceans. Comparisons between derived total cloud cover and that calculated with the commonly used random and mixed overlap assumptions suggest that the mixed assumption generally better fits the results. On the whole there is overall fairly good agreement between the percent low cloud relative to total cloud cover in the reconstructed observations and a global climate model, but the model has a far larger percentage of high clouds nearly everywhere, especially in the tropical convective regions and over the Indian subcontinent.

Corresponding author address: Prof. Bryan C. Weare, Department of Land, Air, and Water Resources, Atmospheric Science Program, University of California, Davis, Davis, CA 95616.

Email: bcweare@ucdavis.edu

Abstract

A new method for combining satellite and surface-based cloud observations into a self-consistent three-dimensional field is presented. This method derives the probabilities of the cloud states, which are most consistent with all of the observations and assumptions concerning the nature and relative uncertainties of the observations. It is applied to a three-layer atmosphere using monthly satellite- and surface-based cloud observations. The reconstructions of the observed fields usually lead to modifications of the surface-observed low cloud amount of less than 0.008 fractional cloud cover. Over the ocean the satellite-view low cloud amounts are usually decreased by between 0.06 and 0.12 for most of the middle latitudes and southeastern tropical Pacific. Over land the adjustments in the satellite low cloud amounts are generally smaller. The method leads to increases in satellite high cover of between 0.03 and 0.09 over most regions, and increases in middle cloud cover of up to around 0.03 over the subtropical oceans. Comparisons between derived total cloud cover and that calculated with the commonly used random and mixed overlap assumptions suggest that the mixed assumption generally better fits the results. On the whole there is overall fairly good agreement between the percent low cloud relative to total cloud cover in the reconstructed observations and a global climate model, but the model has a far larger percentage of high clouds nearly everywhere, especially in the tropical convective regions and over the Indian subcontinent.

Corresponding author address: Prof. Bryan C. Weare, Department of Land, Air, and Water Resources, Atmospheric Science Program, University of California, Davis, Davis, CA 95616.

Email: bcweare@ucdavis.edu

1. Introduction

Clouds are a major contributor to our uncertainty concerning the nature of climate and climate change. The uncertainties concerning clouds are manifold. First, the basic processes that determine the properties of clouds, especially ice clouds, are not well understood. This is partially the result of the complexity of the processes involved and partially due to the difficulties of making the necessary detailed observations. Second, although large-scale observations of clouds have been made by surface observers for many decades and from satellites for over a decade, both datasets describe only limited aspects of natural cloud fields and have uncertainties that are difficult to fully quantify. Finally, the modeling of clouds in climate models is relatively primitive because their scales are typically very much smaller than that of the models and because the current global observations are often inadequate to allow quantitative assessment of current parameterizations.

Hughes (1984) and Liou (1992) briefly summarize the very limited available climatologies of three-dimensional cloud structure, which might be compared to model output. Perhaps the best known is that of Gordon et al. (1984), which qualitatively incorporates both satellite and surface observations. Although this summary has been utilized by climate modeling groups and others, very little confidence can be placed in even its qualitative descriptions. For instance it shows zonal averages in which large portions of the atmosphere from 700 to about 200 hPa have no cloud whatsoever.

Despite the many problems, useful satellite and surface-observer data, describing portions of the three-dimensional cloud structure, are available. These include the satellite observations of the amount of low, middle, and high cloud amounts from the International Satellite Cloud Climatology Project (ISCCP, C2; Rossow and Schiffer 1991) and the Nimbus-7 Cloud Analysis (N7; Stowe et al. 1988); and total and low cloud properties from surface observers derived by Warren et al. (1986, 1988) and Hahn et al. (1982, 1984, 1994, 1996).

However, these data are most useful for quantitative comparisons with models if they are transformed to correspond to the model cloud fractions or vice versa. This is because each of these observations is a summary of the cloud in a fixed height interval observable from a given prospective, either the top of the atmosphere or the surface. Thus, for instance, the low cloud fraction determined by a satellite radiometer will not be equivalent to the amount in the lowest layer of a model, nor to the simple sum of the amount over a range of layers. In general the observed low cloud fraction may only be compared to model cloud amounts after the latter have been summed over the appropriate layers of the atmosphere and account has been made for the possible obscuration of lower layers by higher ones. This is usually done in terms of an overlap assumption (Tian and Curry 1989). The two extreme assumptions are “no overlap,” in which no cloud is assumed to be above or below another cloud, and “full overlap,” in which clouds are assumed to be stacked vertically to the maximum extent possible. The most common overlap assumptions are“random overlap” in which clouds at various levels are assumed to be randomly distributed in the horizontal, and “mixed” in which convective clouds are assumed to be maximally and all other clouds randomly overlapped. However, any combination of overlap between the no and full overlap extremes is possible.

2. Basic methodology

This paper will depart from the usual convention of looking at cloud vertical structure in terms of an “overlap assumption,” but will instead define a three-dimensional cloud system in terms of the probabilities of all possible cloudiness configurations (I. Mokhov 1996, personal communication). This concept is similar to that recently discussed by Stubenrauch et al. (1997). For instance, one can define all of the possible cloud configurations in a three-layer atmosphere by eight classes illustrated by Table 1. The full description of any three-layer atmosphere is given by the distribution of the probabilities pi, which may be normalized such that Σ pi = 1.

Using the above definition a set of probabilities p = (p1, p2, . . .) can be used to describe any “observation” such that
Apn
where n is any combination of surface and satellite observations, and A is a known matrix, which need not be square. This matrix A is a set of rules that relate the cloud configuration probabilities to the given set of observations. For instance the low cloud seen by a satellite is nls = p7, whereas low cloud seen by a ground-based observer is nlg = p3 + p4 + p6 + p7.
In principle, given a set of observations n, Eq. (1) may be solved for p. To do so, one can assume a first guess p0, then
Ap0n0
where in general nn0. One can then hypothesize an improved p′ such that
Apnn
Given x = p′ − p0, and the fact the system is linear, then
Axnn0
In general this equation is underconstrained. However, it can be “solved” given
  1. the requirement that the desired solution fit as well as possible the data, Σ (nj′ − nj)2/σ2j is a minimum, where the σj’s are the uncertainties in the observations, and

  2. the assumption that the desired xi’s are the smallest possible corrections, Σ x2i/e2i is a minimum, where the ei’s are the uncertainties in the pi’s.

Under these conditions the best choices for the xi’s are given by
xW−1eATAW−1eATWσ−1nn0
where T designates the transpose, and where We and Wσ are diagonal matrices of the squared uncertainties of the cloud state probabilities and observations, respectively (Menke 1984; Isemer et al. 1989).

In principle this methodology can be applied to an atmosphere with an arbitrary number of levels. Increasing the number of levels, however, increases the dimensions of the vectors in Eq. (5) by 2m, where m is the number of levels. Furthermore, if the number of independent observations does not increase proportionately, then Eq. (1) becomes increasingly underconstrained. In general it seems appropriate to approximately match the number of degrees of freedom with the number of data types.

3. Sensitivity analysis

One set of available approximately coincident observations to which to apply this method are the monthly surface-based estimates of total cloud and low cloud cover summarized by Hahn et al. (H; 1996) and the satellite-based estimates of low, middle, and high cloud amounts as seen from above developed by the ISCCP (Rossow and Schiffer 1991). The individual edited records of the surface observations were obtained from cdiac.esd.ornl.gov. These data include separate files for land and ocean observations for each month. Individual monthly means of total and low cloud amounts for January 1984 through December 1988 were calculated for each 2.5° × 2.5° grid for the globe from 70°S to 70°N.“Means” were calculated for each grid month in which there was at least one observation containing both total and low cloud data. Only grids with adequate illumination (see Hahn et al. 1995) were included to eliminate possible biases introduced by inadequate moonlight to observe the sky. For grids with both oceanic and land data only the land-based observations were retained, since they were usually much better sampled in time. Figure 1 shows the average number of observations in each grid. The mean number of observations for most ocean grids north of 20°N generally exceeds 10; the numbers for other oceanic points are often less than 6. Over land areas with data there are usually more than 100 observations per grid month, and many parts of Europe and Asia have more than 600 observations per grid month. However, the mountainous regions of Asia and North America lack any observations as do the interiors of Africa, Australia, and South America.

The ISCCP C2 cloud observations for the same months were obtained from the National Center for Atmospheric Research data archive. The ISCCP C2 dataset includes monthly means for all daylight hours of the day of low, middle, and high cloud amounts (calculated from the cloud amounts for seven ISCCP C2 cloud types: C2 VAR 32, 36, 40, 44, 48, 52, and 56) corresponding to clouds with tops having pressures greater than 680 hPa, between 680 and 440 hPa, and less than 440 hPA, respectively. These demarcations were chosen to approximately mimic the variations in top elevations of the morphological cloud types of the surface observations. However, since the surface observations of cloud height are relative to that of the station and those of ISCCP are for fixed pressure levels, care must be taken in interpreting the following results over mountainous regions. These data were interpolated to the same 2.5° × 2.5° grid as the surface observations using the algorithm provided by ISCCP.

Assuming that the monthly means of these satellite- and surface-based observations are generally describing the same cloud fields, they define an observations vector n, such that
i1520-0442-12-3-897-e6
Assuming that a satellite observation of high or middle cloud gives no information about the cloud layers directly below and that the surface observer estimate of low cloud gives very little information about the cloud layers directly above, then the A necessary to transform the probability distribution p to these observations is given by
i1520-0442-12-3-897-e7
It should be emphasized that the basic methodology does not absolutely require that all terms of A be 0 or 1. If the satellite or surface observations gave information about cloud structure beyond the first sensed layer, the terms could be composed of fractions.

Three important parameters must be prescribed: the distribution of the first guess probabilities p0, the matrix of the uncertainties of those probabilities We, and the matrix of the uncertainties in the observations Wσ. To explore the affect of various choices of these parameters on the results, data for a number of oceanic and continental locations were selected for detailed analyses. The locations of these observations are indicated in Fig. 1. These points represent a sampling of climatic regimes in which there were generally more than 10 surface-based observations in a month. This minimum of 10 observations is based upon Weare (1989), who suggests that this is the minimum number of observations in a month likely to result in a representative monthly mean.

Since it is difficult to estimate the magnitude of the terms of We from observations, in all the following calculations the values of We will be specified by assuming that the uncertainties in all of the probabilities are ±0.1. That is
i1520-0442-12-3-897-e8

The explored range for the choices for the values of Wσ and p0 is illustrated in Table 2. In the reference model it was assumed that all uncertainties of all of the observed variables are 0.2 in units of fractional cloud cover. This value is based upon previous estimates of the combined random and systematic uncertainties in the surface-derived observations (e.g., Hahn et al. 1995;Weare 1989) and those in the ISCCP observations (e.g., Liao et al. 1995a; Loeb and Coakley 1998). The reference uncertainties for the ISCCP C2 data are further justified by the fact that the difference between the annual-mean “adjusted” total cloud cover (C2 VAR 8) and the “unadjusted VIS–IR” cloud cover (sum C2 VAR 32, 36, 40, 44, 48, 52, and 56) is up to 0.1 over some land areas, and that the differences between the adjusted total cloud cover and the unadjusted IR-only cloud cover (sum C2 VAR 23, 26, and 29) is up to about 0.16. Also, in the reference model the initial probabilities of each of the cloud states 1–7 (see Table 1) are all set equal to the surface-based total cloud cover divided by seven, which corresponds to a minimum prior knowledge of the true cloud states.

Other specifications of Wσ were chosen to explore the effects of the likely range of uncertainties in the observations. Thus it was assumed that alternately the ISCCP uncertainties were twice or half the reference values, the H uncertainties were either twice or half, and finally that only the uncertainties in the ISCCP low cloud estimates were twice the reference values. The alternate specifications of p0 are described in Table 2. These were designed to explore the effects of different hypotheses concerning true states of the monthly cloud fields. It was assumed alternately that (a) the only nonzero p0’s are for cloud states having only a single layer, (b) the only nonzero values are for cloud states with only multiple layers, and (c) the first-guess cloud states correspond as much as possible to the surface-derived data. In this last case the hypothesized states having cloud in the lowest layer have equal probabilities, which sum to the observed H low amount, and all other states have equal probabilities, which sum to the difference between the H total and low cloud amounts. Thus
i1520-0442-12-3-897-e9

Figure 2 summarizes a subset of the results for the cases shown in Table 2 for representative ocean and land points designated as A–D on Fig. 1. At the A and C locations the H total and low amounts are much larger than the ISCCP values. In B the ISCCP total cloud amount is similar to that of H, but the ISCCP low cloud cover is much smaller than that of H, and at D the H and ISCCP total cloud amounts are nearly identical and the low cloud cover estimates are similar. Nearly all combinations of p0 and Wσ lead to adjustments (reconstructed minus original) that have the same sign for all variables. In addition the magnitudes of the adjustments are quite similar for all of the studied Wσ’s. However, important quantitative differences do exist for the different choices of p0. Assuming nonzero initial probabilities only for single-layer states results in relatively large decreases in H low cloud and relatively small changes in ISCCP high cloud, whereas assuming nonzero initial probabilities only for multilayer states or initial probabilities closely aligned with the H data, gives rise to quite small adjustments to the H low amounts and moderate adjustments in ISCCP low and high cloud amounts.

The analysis of Fig. 2 and the results (not shown) for the other points shown in Fig. 1 suggests that the qualitative results are quite insensitive to choices of Wσ, but that distinct quantitative differences do exist for different choices of po. Thus, special care is required in the specifications of po. Based upon the full array of sensitivity results and the fundamental assumption that adequately sampled surface-based observations may be considered “ground truth” for all but subvisual clouds, then the chosen p0 corresponds to that labeled H Total, Low. This choice was combined with the reference assumption for the observational uncertainties such that the final model are those of the upper-right corner of Table 2. This corresponds to the assumptions that all observational uncertainties are equal to 0.2, and that the first guess conforms to the surface-based observations as much as possible. Other plausible assumptions are certainly possible. However, the described analysis suggests that they will lead to results that are qualitatively similar to those to be discussed.

Although this is judged to be the most appropriate choice, there is a minor problem in applying it to all of the available data. The sample calculations were based upon grids with more than 10 surface-based observations in a month, but many grids, especially those south of 20°N, often have fewer than 10 observations. Weare (1992) shows that the uncertainties due to undersampling are relatively large when there are few samples, and that they are nearly linearly related to the square root of the number of observations. Following that analysis it is assumed that the squared uncertainties of the surface-based observations are given by
i1520-0442-12-3-897-e10
This corresponds to an uncertainty equal to that of the ISCCP data for 10 or more observations and nearly twice that of the ISCCP observation for grids with only two observations. In this case
i1520-0442-12-3-897-e11

4. Results

With n, A, We, p0, and Wσ specified by Eqs. (6), (7), (8), (9), and (11) (and the normalization condition), Eq. (5) is solved for x independently for each month at each 2.5° × 2.5° grid in which both surface and satellite data exist. This provides independent estimates at each grid point of the eight probabilities pi, which best fit the combined surface and satellite data. After these probabilities have been defined, any observation can then be reconstructed using Eq. (1). In addition, variables that are not directly observable, such as the cloud amount of clouds that exist only in a single layer, can also be calculated. Both the reconstructed observations and those additional variables are then the best estimates, which are consistent with the full set of observations and assumptions.

Figure 3 shows the differences between the 5-yr annual means of the directly observed total cloud amounts and those of the reconstructed estimates for the observations from both Hahn et al. and ISCCP C2 (highISCCP + midISCCP + lowISCCP). Consistent with our assumptions for the required solution of Eq. (1), all of the differences shown in Fig. 3 are much less than the uncertainties described by Wσ. In many parts of the subtropics and the highest latitudes the method decreases the H total cloud amount by between 0.01 and 0.02. It generally has a relatively small effect elsewhere except in the Indian Ocean where there are increases of about 0.02. The reconstructed ISCCP total cloud amount is adjusted relative to the original values by up to about 0.08. Positive adjustments in ISCCP total cloud cover are relatively large over the higher latitudes and the eastern tropical Atlantic and Pacific Oceans. Decreases are largest over the midlatitude oceans of both hemispheres and portions of the Indian Ocean. The latter may be due to slight positive biases in ISCCP cloud amounts at relatively large satellite view angles (see Rossow and Garder 1993; Loeb and Coakley 1998).

Figure 4 shows comparable plots for changes in the Hahn et al. and ISCCP C2 low cloud amounts. It must be borne in mind that these quantities are not equivalent since the first is the low cloud as directly observed from below and the second is the low cloud, which is not obscured by middle and high cloud layers. The reconstruction usually leads to very small adjustments of the Hahn et al. low cloud amount, usually by less than 0.008 equatorward of about 40° and by a somewhat larger amount at higher latitudes.

Over ocean the ISCCP low cloud amount are usually decreased by between 0.06 and 0.12 over most of the middle latitudes and southeastern tropical Pacific. Over land the adjustments in the ISCCP low cloud amounts are nearly always quite small. The suggested adjustment over ocean is generally consistent with the conclusion by Wielicki and Parker (1992). They state that due to sensor resolution the ISCCP algorithm overestimates the fraction of boundary layer clouds by about 0.05. Wielicki and Coakley (1981) show that this may result from pixels that are partly clouded with middle and high clouds, and that are improperly determined as low due to contamination of their emission temperatures by clear-sky radiation originating from the surface.

Figure 5 shows the percent differences between the directly observed and reconstructed ISCCP C2 high and middle cloud annual means. The method leads to increases in high cover of between 0.03 and 0.09 over much of the eastern and high-latitude ocean regions, and increases in middle cloud cover of around 0.03 over the subtropical oceans. Relatively large adjustments in both middle and high cloud are in the relatively clear subtropical high zones, where the satellite observations appear to be “missing” higher cloud “seen” in the surface observations. Overall, the high cloud adjustments agree with Jin et al. (1996), Liao et al. (1995a), and Minnis et al. (1993), who all suggest that ISCCP high cloud observations underestimate the “true” values by about a third. However, the earlier works do not readily explain the present result suggesting large numbers of missing high cloud in the subtropical high zones. The middle cloud changes are consistent with the hypothesis mentioned above that satellite cloud algorithms may interpret broken trade cumuli with tops at pressures less than 680 mb as low clouds. This may partially explain why these adjustments are largest over the subtropical highs, where trade cumuli are prevalent.

In summary the combined surface–satellite dataset suggests that the atmosphere has fewer low clouds and more middle and high clouds than is indicated by the ISCCP C2 observations. Why are these shifts taking place? In the simplest sense the method is forcing the ISCCP C2 and Hahn et al. measurements of total cloud cover to agree given the specified constraints. For instance, if the ISCCP total cloud amount were less than that of Hahn, the agreement could be brought about by a combination of rearranging the overlap of the cloud layers to expose more low and middle clouds from above and adding cloud fraction to one or more layers. In general this agreement is not brought about solely by a rearrangement of cloud layers, but also by actual adjustments in the amounts in these layers. Such adjustments are appropriate if their magnitudes are smaller than the assumed uncertainties in the data, which they are in nearly all of the analyzed cases.

One of the strengths of this methodology is that it enables one to estimate useful cloud parameters, which are not directly observable. One such variable is the fraction of the monthly mean cloudiness, which has only one cloud layer, that is p1 + p5 + p7, versus the total cloud cover. Figure 6 illustrates the annual means for this quantity. As expected the regions of least overlap are in the subtropics, where stratus and shallow cumulus tend to dominate. This is in agreement with the work of Wang and Rossow (1995), who indicate that there are fewer multilayer clouds at their two subtropical eastern Pacific stations than at any of the other 30 stations they investigated.

Another useful example involves a comparison of the reconstructed total cloud cover given by 1 − p8 and the total cloud amount Tran using the classical random overlap assumption described by
i1520-0442-12-3-897-e12
where I is the total number of cloud layers (3), i = 1 at the top, and by definition F1 = f1. Figure 7a illustrates the percent differences in total cloud amount assuming random overlap and the reconstructed total cloud amount. At nearly all points the total cloud amount calculated using the random overlap assumption exceeds the reconstructed total cloud amount. The largest differences, more than 12% of the mean, are over the land areas and regions of the equatorial oceans. These results suggest that in many regions low, middle, and high clouds tend to overlie each other more often than is assumed using the random overlap assumption. This overestimate is smallest for the subtropical high zones in which little or no deep convection exists and in the higher-latitude regions of oceanic stratus.
The most commonly used overlap assumption in climate models is mixed overlap, such that full overlap is assumed for convective clouds and random overlap is assumed for large-scale clouds. Using the current results one estimate of the total cloud cover using the mixed overlap assumption is
TmixTranp3
where Tran is the total cloud cover computed using the random overlap assumption as in Eq. (12) excluding clouds in class 3, the deep cloud category. The distribution of p3 clouds (not shown) is similar to the sum of the surface-observed “cumulonimbus with and without anvils” illustrated in Norris (1998, Figs. 3 and 4). Figure 7b shows annual means of the percent differences between Tmix and the reconstructed total cloud cover. Overall, there is better agreement with the observed total cloud amount for the mixed than for the random overlap assumption. Relatively large differences remain over many land areas and large portions of the equatorial oceans, where the mixed cloud assumption gives too many clouds. In the North Atlantic region, where Tian and Curry (1989) suggest that a mixed overlap assumption is appropriate, there is fairly good agreement between the mixed model and the reconstructed amounts. These results suggest that the mixed model may be more applicable than the random overlap model over most regions of the world.

The results of this observational analysis can be directly compared with cloudiness developed in a global climate model. The cloudiness for the three ISCCP levels in the most recent version of the climate model of the Laboratory for Dynamic Meteorology (Li 1996), labeled LMDZ, will be used as an example. To emphasize differences in the vertical structure of the cloudiness, the comparisons are made for the ratio of the cloudiness in a given layer relative to the total cloudiness. Figure 8 illustrates the annual mean of this ratio for low cloud in the observational estimates and the model. In general the results show that the model underestimates the relative percent low cloud over higher latitudes oceans and the subtropical high zones by about 5%–10%. Several areas of larger disagreements do exist, however. These include the far eastern Atlantic and Pacific Oceans, where the model has up to about 35% less low cloud fraction. This is probably due to the lack of an explicit stratus formation mechanism in the LMDZ. The model also has a smaller percent of low clouds for the Indian subcontinent, and a larger percentage over eastern North America and Europe. The causes for these latter differences are unclear. Nevertheless, they may have sizable consequences on the realism of the model surface energy budgets.

Figure 9 shows the ratios of the high cloudiness relative to total cloud for the observational estimates and the model. It should be noted that the sum of the low, middle, and high cloud in both the model and observations may exceed the total cloud cover that incorporates overlap. Overall the level of agreement between the observations and model is somewhat poorer than for the low cloud amounts. In general the model has a larger relative percentage of high clouds nearly everywhere, especially in the tropical convective regions and over the Indian subcontinent. This is despite the fact that the current estimates of high cloud amounts are generally greater than in the original ISCCP C2 analyses. Over these convective zones the differences may be due to the fact that the model is developing a relatively large, perhaps excessive, number of thin high clouds, which are not observed by either the satellite or surface-based detection.

5. Discussion

A new method for combining satellite and surface-based cloud observations into a self-consistent three-dimensional field has been presented. The method derives the probabilities of all possible cloud states, which are most consistent with all of the observations and the stated assumptions. Trials for selected regions show that the results are relatively insensitive to the assumed uncertainties in the observations, but somewhat more sensitive to the assumed first-guess probabilities.

The method was applied to a three-layer atmosphere using ISCCP C2 satellite-based and Hahn et al. (1996) surface-based cloud observations. The results indicate that that satellite derived estimates of low cloud cover may be moderate overestimates and that the middle and high cloud cover may be moderate underestimates of the state of the true atmosphere. Comparisons of the reconstructed total cloud cover with total cloud calculated with the commonly used random and mixed overlap assumptions shows somewhat better agreement with the mixed overlap assumption.

As a further test of the robustness of these results Eq. (5) was solved using a modified set of observations. This set included not only the Hahn et al. (1996) “direct” observations of total and low cloud amounts, but also their estimates of the middle and high cloud amounts seen by a surface observer. These latter quantities were inferred without utilizing an overlap assumption from the differences between total and low cloud cover using morphological cloud type information to assign a height category. Thus in this case nT in Eq. (6) was replaced by
i1520-0442-12-3-897-e14
and A in Eq. (7) was appropriately modified to define the set of rules relating the probabilities p with this set of observations. The uncertainties of the Hahn et al. middle and low cloud estimates, midH and highH, respectively, are prescribed by an equation similar to Eq. (10) with uncertainties of 0.3 for 10 or more surface observations. This larger uncertainty than used for the H total and low cloud is appropriate due to the fact that cloud type information is sometimes subject to more than one interpretation. Using Eq. (14) and the normalization condition there are now eight constraints to solve for the eight probability classes. This suggests that the problem is no longer underconstrained. However, this is not strictly true (Menke 1984) since probability classes 3 and 4 still cannot be differentiated with either the surface or satellite observations.

Overall, the results of this modified analysis are very similar to those illustrated in Figs. 3–5. In general the reconstructed ISCCP low cloud amounts are less than the original observations and the middle and high cloud amounts are greater. Figure 10a shows the mean results for these revised estimates of the ISCCP high cloud. There are many more missing grids in this figure than in Fig. 5a since surface observations with low cloud amount data often do not have useful cloud-type data. The differences between Figs. 5a and 10a are measures of the impact in the methodology of utilizing the additional cloud type information in the surface observations. From such a comparison it may be seen that the revised reconstructed values of ISCCP high cloud are very similar to the original reconstructions. The primary systematic difference is that the revised analysis leads to less than 0.005 greater ISCCP high cloud cover over much of the World Ocean.

The pattern of the differences of the reconstructed Hahn et al. high clouds from the original estimates (Fig. 10b) is negative nearly everywhere. Thus the differences are generally opposite in sign to those in ISCCP high cloud, but have magnitudes that are nearly everywhere much smaller than for the ISCCP data. However, one must keep in mind that the ISCCP and Hahn et al. high cloud amounts describe high clouds as seen from above and as seen from below, respectively. Thus, one would not expect the patterns in Figs. 10a and 10b to be simple scaled inverses of one another. In particular, the differences for the H high cloud are largest for the Northern Hemisphere landmasses, a feature not seen for the ISCCP data. This suggests that there may be a systematic difference between ISCCP high cloud retrievals over land and sea or a difference in how land observers assign one or more cloud types compared to how ship observers do so. Although the latter may in part be a consequence of the fact that cloud heights are estimated relative to that of the observing station, there is no clear indication that the pattern of the differences in Fig. 10b is related to differences in topography.

Although these initial results are encouraging, much work remains before they or similar results could be said to be distinct improvements over the “raw” observations. Only then might they be used to make statements concerning the “true” overlap of the real atmosphere, regularly “adjust” the direct observations, or to quantitatively validate climate model–derived cloudiness (e.g., Weare et al. 1995, 1996). Perhaps most importantly, the suggested biases in the satellites and surface-based observations must be further verified and understood. For instance, over the subtropical oceans are the increases in ISCCP high cloud suggested by the reconstructions due to systematic overestimates of cirrus by surface observers, underestimates by the satellite algorithm, or possibly the result of inappropriate initial probabilities p0 in the current method? In addition a near-global “operational” application of this method would require a statistical scheme to interpolate the adjustments into regions with no or very small numbers of surface-based observations.

Furthermore, it might be useful to include in such an analysis other surface- and satellite-based observations. The most obvious would be the substitution of the new ISCCP D2 data (Rossow et al. 1996), which is currently being processed. These new data have revised satellite radiometer calibrations, improved cirrus and low cloud detection, and improved algorithms for determining cloud height. In addition one should also consider analysis of other distinctly different global cloud data such as high cloud amounts from SAGE II (Wang et al. 1996). However, such a new dataset requires a careful consideration of the appropriate specification of the terms of A in Eq. (1), relating the probability vector with the observation vector. For instance, if the SAGE II instrument detects not only relatively thick high clouds detectable by a surface observer or the ISCCP algorithm, but also subvisual cirrus cloud, then it may be necessary to include in matrix A nonzero terms, which are proportional to the assumed emissivity of the SAGE II clouds. Also, it would be possible to apply the methodology to an atmosphere with more than three layers if two or more observational datasets were available providing descriptions for clouds in those layers. Finally, a modified methodology is possible, which would allow the use of both cloud amount and cloud optical depth or transparency information (Menke 1984) to simultaneously derived best estimates of both fields.

Acknowledgments

The initial phase of this work was performed while the author was a visitor at the Laboratory for Dynamical Meteorology in Paris. The author thanks the Ecole Normale Supérieure and the Centre National de la Reserche Scientifique for partial support. Additional support was provided by grants from the Climate Dynamics Division of the National Science Foundation and the Western Regional Center of the National Institute for Global Environmental Change.

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Fig. 1.
Fig. 1.

Average number of surface observation per month in each 2.5° × 2.5° grid for 1984–88. Letters A, B, C, D, and X indicate the locations at which the sensitivity analyses were carried out.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 2.
Fig. 2.

Summary of sensitivity analysis. (top) Annual-mean cloud cover for the four locations A, B, C, and D. (a)–(d) sensitivity results for the four locations. Values are fractional differences between the reconstructed cloud amounts and the original observations (reconstructed estimate − original). The legend notes refer to experiments described in the text and outlined in Table 2.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 3.
Fig. 3.

Fractional differences between the 1984–88 annual-mean total cloud cover reconstructed from the solution of Eq. (1) and the original observations (reconstructed estimate − original). (a) Hahn et al. and (b) ISCCP C2. Zero contours are heavier, solid contours; negative values are dashed; positive values are lighter solid.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 4.
Fig. 4.

Differences between the 1984–88 annual-mean low cloud cover reconstructed from the solution of Eq. (1) and the original. (a) Hahn et al. low cloud as observed from below and (b) ISCCP C2 low cloud as observed from above. As in Fig. 3.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 5.
Fig. 5.

Differences between the 1984–88 annual-mean ISCCP C2 cloud cover reconstructed from the solution of Eq. (1) and the original: (a) high cloud and (b) middle cloud.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 6.
Fig. 6.

1984–88 annual means of the percent of estimated fraction of single-layer clouds (p1 + p5 + p7) vs the total cloud cover (1 − p8).

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 7.
Fig. 7.

Percent differences between 1984–88 annual-mean total cloud cover using (a) the random overlap approximation [Eq. (12)] minus the reconstructed total cloud cover (1 − p8) and (b) the mixed overlap approximation [Eq. (13)] minus the reconstructed zero contours are heavier, solid contours; negative values are dashed; positive values are lighter solid.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 8.
Fig. 8.

Percentages of 1984–88 annual-mean cloud in the low ISCCP layer relative to the total cloud cover. (a) From the solution to Eq. (1) [(p3 + p4 + p6 + p7)/(1 − p8)] and (b) that from the LMDZ climate model.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 9.
Fig. 9.

Percentages of 1984–88 annual-mean cloud in the high ISCCP layer relative to the total cloud cover. (a) From the solution to Eq. (1) [(p1 + p2 + p3 + p4)/(1 − p8)] and (b) that from the LMDZ climate model.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Fig. 10.
Fig. 10.

Differences between the 1984−88 annual-mean cloud cover reconstructed from the solution of Eq. (1), using the additional Hahn et al. middle and high cloud estimates, and the original, (a) ISCCP high cloud amounts and (b) H high cloud amounts. As in Fig. 3.

Citation: Journal of Climate 12, 3; 10.1175/1520-0442(1999)012<0897:CSASBO>2.0.CO;2

Table 1.

Structure of each cloud probability class in a three-layer atmosphere; x’s indicate cloud exists in a layer.

Table 1.
Table 2.

Summary of the sensitivity analysis for the marked locations in Fig. 1. Names indicate the specific combinations; results are discussed in the text and illustrated in Fig. 2. Here x’s refer to other tested combinations.

Table 2.
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