Six months of CloudSat and CALIPSO observations have been divided into over 8 million cloud scenes and collocated with ECMWF wind analyses to identify an empirical relationship between cloud overlap and wind shear for use in atmospheric models. For vertically continuous cloudy layers, cloud decorrelates from maximum toward random overlap as the layer separation distance increases, and the authors demonstrate a systematic impact of wind shear on the resulting decorrelation length scale. As expected, cloud decorrelates over smaller distances as wind shear increases. A simple, empirical linear fit parameterization is suggested that is straightforward to add to existing radiation schemes, although it is shown that the parameters are quite sensitive to the processing details of the cloud mask data and also to the fitting method used. The wind shear–overlap dependency is implemented in the radiation scheme of the ECMWF Integrated Forecast System. It has a similar-magnitude impact on the radiative budget as that of switching from a fixed decorrelation length scale to the latitude-dependent length scale presently used in the operational model, altering the zonal-mean, top-of-atmosphere, equator-to-midlatitude gradient of shortwave radiation by approximately 2 W m−2.
The representation of the vertical overlap of the cloud cover present in each grid cell of climate and numerical weather forecast models is key for their radiative transfer calculations. Some early models adopted one of two contrasting approaches, considering clouds to be either maximally (MAX) overlapped or randomly (RAN) overlapped (Geleyn and Hollingsworth 1979; Morcrette and Fouquart 1986). Physical arguments soon lead to the suggestion to combine these to give the maximum–random (MAX-RAN) overlap scheme (Geleyn and Hollingsworth 1979). This assumes that clouds present in adjacent vertical levels belong to a single coherent cloud system and thus are maximally overlapped, in contrast to clouds separated by clear layers that are randomly correlated.
The issue of cloud overlap assumptions was revisited by Hogan and Illingworth (2000), who used retrieval data from the Chilbolton radar in the United Kingdom. While the data confirmed that clouds separated by clear layers appeared randomly correlated [later corroborated in the analysis of ARM site data by Mace and Benson-Troth (2002)], the analysis revealed that vertically continuous cloudy layers decorrelated in height and that the maximum overlap assumption could thus underestimate cloud fraction in deep cloud systems. Hogan and Illingworth (2000) calculated the exponential decorrelation length scale for continuous clouds to be 2 km. The substitution of the MAX overlap assumption with an exponential decorrelation length scale led Tompkins and Di Giuseppe (2007) to name this approach the EXP-RAN scheme.
Since the publication of Hogan and Illingworth (2000), a number of other studies using both ground-based observations have confirmed their findings. Willén et al. (2005) found a similar value to Hogan and Illingworth (2000) for a nearby ground station in Holland, while Mace and Benson-Troth (2002) reported a wide range of decorrelation length scales related to location and season, ranging from less than 1 km to greater than 8 km. Naud et al. (2008) also reported the impact of the dynamical situation and the season on the overlap statistics and decorrelation length scales, while confirming the validity of the EXP-RAN approach, and Oreopoulos and Norris (2011) also highlighted differences in cloud overlap between summer and winter seasons.
In addition to ground-based information, the 94-GHz Cloud Profiling Radar (CPR) of CloudSat, which flies in the A-Train constellation of satellites with equatorial crossing times of 0130 and 1330 local time and a return period of 16 days (Stephens et al. 2008), provides global observations of the vertical structure of clouds, particularly when combined with CALIPSO lidar data to improve detection of thin cirrus clouds. Using a different methodology that amalgamated both continuous and noncontinuous cloud layers, Barker (2008) used 2 months of cloud mask data derived from CloudSat–CALIPSO satellite measurements and found a decorrelation length scale that varied as a function of latitude, but with a mean global value of 2 km. Cloud overlap was also examined in the CloudSat–CALIPSO dataset by Mace et al. (2009), who confirmed the model of EXP-RAN and reported larger decorrelation length scales in the tropics, where vertical velocities are high and wind shear is weaker.
In summary, a number of studies, using ground-based or satellite cloud observations have demonstrated that the EXP-RAN approach appears to be valid. They have reported a range of cloud decorrelation length scales for continuous cloudy columns and documented interlocation and interseasonal variations in this length scale. The variations have been attributed to changes in dynamics and stability: for example, whether cloud structures are dominated by convective conditions or the passage of mesoscale frontal systems (Naud et al. 2008), which are associated with different vertical velocities and wind shears. Higher-vertical-velocity cloud systems will decorrelate less for a given wind shear. Likewise, clouds containing small pristine ice crystals with low sedimentation rates will also decorrelate more for a given wind shear. In addition, Tompkins and Di Giuseppe (2015) shows that some of these differences can be attributed to the assumptions used to calculate the cloud overlap statistics themselves and that decorrelation length scales are underestimated when sampled at spatial scales that are smaller than the typical cloud system scale.
In this paper, we focus on the basic impact of wind shear on the decorrelation of cloud systems. Hogan and Illingworth (2003) documented the impact of shear on ice clouds using ground-based data in southern England, and Lin and Mapes (2004) studied how wind shear impacts cloud–radiation feedback in the western Pacific warm pool. Naud et al. (2008) also conditionally sampled cloud overlap as a function of weak and strong wind shear and found only a limited impact. In their recent analysis of 4 years of CloudSat and CALIPSO measurements, Li et al. (2015) concluded that a statistical parameterization for the impact of dynamics including wind shear on cloud overlap would be beneficial for numerical models. Here, we employ 6 months of CloudSat and CALIPSO data to study cloud overlap statistics in conjunction with collocated ECMWF wind analysis data and identify a simple empirical relationship between cloud overlap and wind shear that can be applied to atmospheric models. The new parameterization is then implemented in the ECMWF Integrated Forecasting System to assess its impact on radiative budget calculations.
CloudSat and CALIPSO data for the period of January–July 2008 are used (CSU 2013, 2014, 2015). All data are available at approximately 240-m vertical resolution (interpolated to a regular 250-m vertical grid) and 1.1-km horizontal resolution (Marchand et al. 2008). Three datasets are used and are summarized in Table 1. The first cloud mask dataset is created based only on CloudSat data. A layer is flagged as cloudy when the threshold is greater than 20 on the CloudSat cloud mask (Stein et al. 2011; Tompkins and Adebiyi 2012) (see Fig. 1b). This dataset is referred to as CloudSat (CS).
The thin cirrus that are not detected by the CloudSat radar (Mace et al. 2009) can be detected by combining CloudSat radar data with CALIPSO’s dual-wavelength lidar data. The CloudFraction product provides the fraction of lidar volumes in a radar volume identified as containing hydrometeors (Mace 2007; Mace et al. 2009; Mace and Zhang 2014). Following Barker (2008), a layer is flagged as cloudy either if it is identified as such by the CloudSat algorithm or if the lidar-identified cloud fraction exceeds 99%. This combined product is referred to as CloudSat–CALIPSO (CS–C).
A problem that has been frequently pointed out is that the CloudSat CPR detects precipitation, in addition to cloud droplets. The faster fall speeds imply that vertical correlations for rain will be higher than for cloud droplets, biasing cloud overlap statistics toward maximum overlap (Mace et al. 2009). However, filtering out rainfall from the CloudSat dataset is not straightforward. An algorithm was proposed by Barker (2008) in an attempt to remove precipitation below the melting level by setting cloud fraction to zero if cloud was detected in the lowest retrieval layers, which are likely to contain precipitation unless foggy conditions prevail. This simple approach would leave precipitation that is present above the melting layer (e.g., snow) and would remove cloud near the surface. Alternatively, CloudSat also provides level-3 products with profiles of precipitation liquid and ice water content (2C-RAIN-PROFILE) that are consistently derived from the CloudSat profiling radar reflectivity and a constraint on the path-integrated attenuation of the radar beam (L’Ecuyer and Stephens 2002; Lebsock and L’Ecuyer 2011). Here, these products are used to determine a precipitation mask, and only levels where no precipitable water is detected are flagged as cloudy (following Haynes and Stephens 2007; Haynes et al. 2009). This dataset is referred to as CloudSat–CALIPSO-norain (CS–C-nr).
Results are presented using this latter dataset, CS–C-nr, as a baseline. The data processing has, nevertheless, been performed using all three retrieval datasets, and discrepancies in the final suggested parameterization are reported to provide an indication of the uncertainties associated with the retrieval assumptions. Table 1 summarizes the datasets employed and processing assumptions made.
The wind information is derived by locating the 25-km grid point of the ECMWF operational Integrated Forecast System (IFS) that contains each individual 1.1-km column in the CloudSat overpass (the nearest-neighbor method is used, and no spatial interpolation is applied). The vertical profile of zonal and meridional winds u and υ from the closest 6-hourly analysis time is projected onto the satellite overpass track and then averaged in the along-track direction for all columns in a CloudSat data segment (described below) to give , the scene-average, along-track horizontal wind. The wind shear between layers i and j is then simply defined as , where is the layer separation distance. Note that variations in wind between the two layers are neglected, and it is the meridional wind that contributes the most to the statistics, implying that cross-track shear associated with jets contributes little to the statistics.
b. Analysis method
Each CloudSat data file is divided into scene segments of horizontal length of 50 km. Previous analysis typically used averaging length scales on the order of 50–300 km to simulate the gridbox sizes presently used in global numerical weather predictions or regional climate models, and Hogan and Illingworth (2000) reported a significant sensitivity to this chosen sampling length scale. We apply a relatively short sampling scale to avoid averaging out wind shear features. Tompkins and Di Giuseppe (2015) address some of the reasons for the previous sensitivity of the decorrelation length to the sampling scale and suggest a simple filter of rejecting layers with cloud cover greater than 0.5 to reduce the scene-length dependency of the cloud overlap statistics, which is applied here.
Figure 1a shows the orbits of 3 days of observations (1–3 July 2008) and the associated along-track cloud profile (Fig. 1b). Individual cloud subscenes are shown in Figs. 1c(1) and 1c(2), along with the collocated wind profile. For each of the cloud scenes, the vertical overlap between any two layers with cloud cover Ci and Cj is analyzed if both Ci and Cj exceed 1%. Nonadjacent layers are considered to belong to a continuous cloud block if all layers found between are also classified as cloudy. The existence of any clear (cloud free) layers instead will classify the two layers as noncontinuous cloud. The observed total cloud cover is simply the projection of the two layers’ cloud mask . The joint Ci and Cj total cloud cover in the assumption of maximum overlap is , while in the assumption of random overlap, it is . As in Hogan and Illingworth (2000), the observed total cloud cover can be expressed as a linear combination of the cloud covers derived from the MAX and RAN overlap assumptions:
where α is the overlap parameter and can be written as
Two cloud layers that are maximally overlapped will have , while they will have if they are randomly overlapped. The overlap parameter could assume negative values in case of minimum overlap. We note the relatively short scene length of 50 km, combined with the CloudSat resolution of 1.1 km, implies that cloud fraction is resolved to the nearest 2%, approximately, meaning that α is poorly resolved as or (although the latter case is precluded by the cloud cover filter).
For each of the layer pairs, α has been calculated as a function of the interlayer separation distance . No information is retained on the height of the two layers; only their separation is considered. Thus, two cloud layers at the same separation distance but at different altitudes will populate the same statistic group. Once this dataset is created, it is subsequently conditionally sampled as a function of the wind shear, , between the two layers.
Finally, the reduction of α as a function of the separation distance is modeled by assuming an exponential decay (Fig. 3, described in more detail below) for each wind shear bin. The exponential function is chosen for the simplicity of being a single-parameter function and for coherence with previous studies. The exponential decorrelation length is thus derived from the best-fit function . We note that the fitting methodology varies in the literature, with the analysis of Shonk et al. (2010), in particular, applying the exponential fit only using the data from adjacent cloud layers. The drawback of this method is that attempting to derive an exponential decorrelation length scale that lies in the range of order 2–4 km, using points separated by 240 m (an order of magnitude smaller) will result in greater sensitivity to retrieval uncertainties, especially for cases of small cloud fraction. We therefore include a range of cloud separation distances when calculating the fit and calculate by least squares fitting an exponential curve to the contiguous cloud layer α values. Two methods are applied. In the first method, all layer separations are included, provided at least 100 observations have contributed to the bin’s statistics; this is referred to as fitall. In the second fitting method, a further restriction is applied that only layer separations up to 4 km are used; this is referred to as fit<4km.
c. Implementation into the ECMWF IFS radiation scheme
Tests are performed implementing the wind shear overlap parameterization derived in the paper into the shortwave and longwave radiation schemes of the latest cycle Cycle 41 Release 1 (CY41R1) of ECMWF IFS.
The IFS radiation calculations are based on the Rapid Radiative Transfer Model (RRTM) of Mlawer et al. (1997) and Mlawer and Clough (1997) for the longwave and shortwave. The model implements the Monte Carlo Independent Column Approximation (McICA) approach to handling overlap, whereby each g-point calculation of the radiation scheme is performed on a randomly sampled column, in which each layer is either cloud free or overcast (Pincus et al. 2003; Räisänen et al. 2005; Morcrette et al. 2008). The statistics of these subcolumns are such that, averaged over many subcolumns, the cloud fraction profile of the ECMWF grid column is obtained. Moreover, the total cloud cover of the columns corresponds to that of the imposed overlap scheme.
To generate the subcolumns, the algorithm of Räisänen et al. (2004) is employed. It is important to emphasize that this algorithm implements the overlap assumption of Bergman and Rasch (2002), which is a pure EXP scheme; that is, the same exponential decorrelation length scale is applied for both continuous and noncontinuous cloudy columns, as also suggested by Barker (2008). This scheme will thus show greater sensitivity to the choice of than the alternative EXP-RAN scheme of Hogan and Illingworth (2000), which instead assumes random overlap for layers separated by clear sky, but which is also (perhaps misleadingly) cited by Räisänen et al. (2004), when referring to the overlap assumption used in the sampling algorithm.1
The framework for testing the impact of the scheme is to integrate a lagged-start, 15-member ensemble of 24-h forecasts using start dates from 15 to 30 October 2009 at TL95 horizontal resolution and with 91 vertical levels. Short forecast integrations are used in order to prevent the cloud structures from diverging from their initial conditions; thus, cloud radiative impacts on the dynamics are largely precluded in these experiments.
The impact of the wind shear parameterization developed is benchmarked against three alternative schemes for setting , which are outlined in Table 2. In the first, is simply fixed to an arbitrarily chosen decorrelation length scale of 3 km, referred to as the “Fix” experiment. The second method is the default option of IFS cycle CY41R1, which uses a latitude-dependent function (“CY41R1” experiment). This scheme was a minor modification to the original latitude-dependent scheme of Shonk et al. (2010), which is also used as a benchmark (“Shonk” experiment). The wind shear schemes are implemented in the same way as the existing parameterizations for ; the scheme is applied to contiguous layers. As the wind shear parameterization derived later is linear, a minimum value of 0.5 km is applied to to prevent unphysical negative values in (rare) high–wind shear locations.
a. Wind shear impact on cloud decorrelation
The cloud vertical decorrelation as a function of wind shear and distance is similar for the three datasets. Statistics are presented for the CS–C-nr dataset algorithm as an example. In the case of noncontinuous cloud layers the assumption of random overlap is justified (Fig. 2a). The value of α is less than 0.15 and is not strongly sensitive to layer separation and wind shear. Vertical continuous clouds are maximally overlapped at small separation distances, which is unsurprising, since by definition as , because at zero separation one considers the overlap of a cloud with itself. The correlation reduces as layer separation distance increases (Fig. 2a). The different behavior of continuous and noncontinuous cloud layers thus confirms the ground-based studies of Hogan and Illingworth (2000).
The least squares exponential curves fitted using all data points of separations up to 4 km are given in Fig. 3. Comparing the curves to the original data in Fig. 2a, it is noted that the exponential curve appears a poor fit to the full range of separation distances, particularly in the cases of stronger wind shears. The exponential curve overestimates the wind shear effect at small layer separations and underestimates it at large separation distances. This implies that the value obtained for will be sensitive to the conditions of the fitting method employed. The stronger–wind shear cases occur orders of magnitude less frequently than weak–wind shear categories, indicating that sampling may be an issue (Figs. 2b,c). On the other hand, the fact that the variability in α is so limited for levels separated by small distances may be because the IFS analysis data are unlikely to resolve the differences in winds well at these small scales, given the data’s coarser temporal and spatial resolution. This is why both fitting methods use a range of separation distances and is also the motivation to use two fitting approaches to crudely assess fitting uncertainty.
The decorrelation length scales are given in Table 3 as a function of cloud dataset, wind shear strength, and exponential fitting method. The broad range of decorrelation values spans those previously reported in the literature (e.g., Mace and Benson-Troth 2002; Naud et al. 2008; Kato et al. 2010; Oreopoulos and Norris 2011; Oreopoulos et al. 2012), although no values are found under 2.5 km greater than the values reported in Hogan and Illingworth (2000) and Barker (2008). The first thing to note from Table 3 is that there is considerable uncertainty in the derived values of , resulting from both the choice of dataset used for the analysis and the fitting method itself. For example, using the first fitting method, the length scale reduces from 5.1 to 4.3 km if the CS–C-nr dataset is used that attempts to filter out precipitation, which is an uncertainty of 15%. A similar uncertainty is also apparent resulting from the fitting method employed.
The table also shows a clear systematic impact of wind shear on the decorrelation length scale, with cloud decorrelating over smaller distances as wind shear increases. Again, the details of this relationship are sensitive to the fitting method employed, and it is clear from Fig. 2 that, had only adjacent layers been employed to derive the fit, limited sensitivity to wind shear would have been reported. Even with very weak shear, it is noted that cloud decorrelation occurs, likely because of a variety of causes. First, the calculation of wind shear only accounts for the difference in wind between the two cloud layers, ignoring changes in wind between these layers and the impact of cross-track wind shear. Second, the analysis of winds is subject to uncertainties and also, to a large extent, represents the large-scale geostrophic flow, unless nearby sonde data are available (e.g., Tompkins et al. 2005). In addition, the 6-hourly temporal resolution of the analysis means that the wind profile may be up to 3 h out of synchronization with the CloudSat overpass.
The values of only approach the 2 km reported by Hogan and Illingworth (2000) at strong wind shears. The study site of Hogan and Illingworth (2000) was in the midlatitudes, where wind shears are stronger and cloud decorrelation is expected to be higher (Shonk et al. 2010). It is also emphasized that the sensitivity to wind shear is likely to be underestimated here because of the inability of the model analyses to resolve wind fluctuations on small spatial and temporal scales and the fact that the influence of cross-track wind shear values is neglected, which would include more extreme values associated with jet structures in the tropics and midlatitudes.
Using the best-fit exponential decay length scale as a function of wind shear, , an empirical parameterization of can be derived (Fig. 4). A simple linear regression is suggested as
where γ and are the fitting parameters and are reported in Table 4 for all three datasets and both fitting methods. The relationship is derived by performing a linear fit to the wind shear composite decorrelation length-scale values. The value of represents the extrapolation of to exactly zero wind shear. As the wind shear increases vertically, continuous cloud layers decorrelate more rapidly, with decorrelation length scales down to values on the order of 2 km.
b. Impact on ECMWF Integrated Forecasting System
The two wind shear–related schemes are evaluated to assess their impact relative to the implementation of latitude-dependent parameterizations for . The zonally averaged decorrelation length scale as a function of pressure or model level is given in Fig. 5. Figure 5 shows that has higher values in the tropics, as expected because of the lower wind shear values there, with the exception of the upper troposphere, as a result of the tropical easterly jet. Decorrelation of low-level clouds in the boundary layer is also much higher. Zonal averaging masks the high variability in decorrelation length scale that can reach values as low as the minimum imposed value of 0.5 km in high–wind shear locations.
The impact of the spatially and temporally variable wind shear on the top of atmosphere fluxes also displays a latitude dependence (Fig. 6), with the weak wind shears in the tropics resulting in a high value of and reduced total cloud cover with respect to the use of a fixed decorrelation value of 3 km. As a result, the net shortwave (SW) radiation absorbed at the top of the atmosphere (TOA) is increased by approximately 2 W m−2 using the fitting method fitall. The sign of the impact is the opposite of the two latitude-dependent (and very similar) schemes of Shonk et al. (2010) and CY41R1, which impose values for similar to 3 km in the tropics, but that reduce at midlatitudes. The magnitude of the impact of the wind shear scheme in terms of equator-to-midlatitude differences is roughly similar in magnitude at 2 W m−2 for fitall. Instead, using fitting method fit<4km reduces the impact on the radiation budget, as expected from the weaker–wind shear dependency, by approximately 40%.
4. Discussion and conclusions
This study has analyzed 6 months of CloudSat and CALIPSO data and confirmed that, to a good approximation, clouds separated by clear-sky gaps are randomly overlapped, while continuous cloud layers are close to maximally overlapped at small separations but decorrelate with increasing layer separation distance.
Focusing on the continuous cloudy layers, this study used collocated ECMWF wind profile analyses to composite these cases as a function of wind shear and found that the decorrelation length scale reduced with increasing wind shear, as expected. The range of decorrelation values, when averaged over millions of combinations, is between 5 and 2 km, which is in overall agreement with the range of values reported in previous studies. A simple linear fit parameterization relating cloud decorrelation to wind shear is suggested that is straightforward to add to existing radiation schemes in atmospheric models using EXP or EXP-RAN schemes.
The new parameterization has been implemented in the ECMWF Integrated Forecasting System, which uses the EXP overlap assumption (i.e., it assumes a single fixed decorrelation length scale for both continuous and noncontinuous cloud layers), to assess its possible impact on the radiative budget calculations. The wind shear scheme is compared to the use of a fixed decorrelation length scale of 3 km and to two experiments that implement a latitudinal dependency of . Relative to using a simple fixed decorrelation length scale of 3 km, the impact of introducing the wind shear–dependent decorrelation length scale was found to be similar in magnitude to that of introducing the latitude-dependent scheme of Shonk et al. (2010).
We recall from the introduction that wind shear is just one factor that influences cloud overlap decorrelation in addition to the analysis method, cloud dynamics in terms of updraft speeds, and cloud ice microphysical properties that affect sedimentation rates (Heymsfield 1972). These latter dynamical and microphysical effects are implicitly incorporated into the empirical latitude-dependent schemes of Shonk et al. (2010) and CY41R1; it is thus emphasized that the comparison of decorrelation schemes performed in this work merely aims to gauge the impact of the wind shear–specific parameterization relative to the use of a spatially variable latitude-dependent scheme and not to suggest which of the schemes is superior. The next logical step would therefore be to use multivariate statistical methodologies based on generalized linear models (Nelder and Wedderburn 1972; Wolfinger and O’Connell 1993) to jointly derive the dynamical and spatial dependencies of the cloud decorrelation statistics.
Richard Forbes and Howard Barker are thanked for discussions and feedback on this work, and three reviewers’ comments were very helpful. The NASA CloudSat project is thanked for providing the dataset used in this work. This work is part of the ICTP activity funded by the FP-7 European projects QWeCI EC Grant Agreement 243964 and GEOWOW EC Grant Agreement 282915.