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  • View in gallery

    The study region used in the present work, outlined in thick black lines (24°–40°N, 35°–10°W). The thin black lines denote the grid boxes used to ensure even sampling throughout the domain. Climatologies of MODIS low-level cloud cover (CFLIQ) and ECMWF 10-m wind speed are shown for the dates used in this study (JJA 2000–06).

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    Histogram of MODIS low-level CF. The y axis denotes the fraction of all points that fall into each bin, and the dashed lines delineate terciles (SC, MC, and LC) in CF.

  • View in gallery

    Composite trajectories for the LC (thin black lines), MC (medium-width dark gray lines), and SC (thick light gray lines) terciles of MODIS low-level CF. Error bars denote the 95% confidence limits obtained using the bootstrap method described in the text. The full 500-m trajectories are shown, whereas only the endpoints are shown for the 2000-m trajectories. The circle at the center of the plot denotes the average starting position (t = 0) for both forward and back trajectories. Land areas are shaded in gray.

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    Composite trajectories for overlap-corrected MODIS low-level CF (CFLIQ) and CERES all-sky TOA net shortwave flux (FSW; W m−2).

  • View in gallery

    Composite trajectories showing different measures of cloud water path. All variables are displayed in units of g m−2. Displayed are (top)–(bottom) MODIS in-cloud LWP, MODIS all-sky LWP, and SSM/I all-sky LWP from the F15 satellite.

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    Composite trajectories showing LTS (defined as θ700θSFC; K), SST (K), and 700-hPa temperature (T700; K) and moisture (q700; g kg−1), all obtained from ECMWF analyses. Note that variations from one time to the next reflect large-scale trends as well as the diurnal cycle.

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    Composite trajectories showing the rate of SST change (ΔSST × 10−5 K s−1), 10-m wind speed (m s−1), surface sensible heat flux (FSH; W m−2), and surface latent heat flux (FLH; W m−2), all obtained from ECMWF analyses. Note that, in contrast with other analysis variables, ECMWF surface fluxes are only updated at 12-hourly intervals.

  • View in gallery

    Composite trajectories showing QuikSCAT and ECMWF surface divergence DIVQSCT and DIVECMWF (×10−6 s−1) and ECMWF 700-hPa pressure vertical velocity ω700 (Pa s−1).

  • View in gallery

    Composite trajectories showing MODIS retrievals of TTOP (K) and derived cloud-top height [ZTOP, which is defined as (SST − TTOP)/6.5; km], boundary layer lapse rate (ΓBL = ΓADB − ΓBL; K km−1), and deviation of the lapse rate from adiabatic (ΔΓ; K km−1).

  • View in gallery

    Lagged correlations between low-level CF (CFLIQ) at the time of observation (0 h) for the following variables: LTS, SST, specific humidity at 700 hPa (q700), SST advection (ΔSST), surface latent and sensible heat fluxes (FLH and FSH), 700-hPa pressure vertical velocity (ω700), and QuikSCAT and ECMWF surface divergence (DIVQSCT and DIVECMWF). Consistent with the focus of this study lag correlations are computed in the Lagrangian sense: following the trajectory. Confidence limits (95%) are estimated using a Fisher transformation and accounting for the degrees of freedom.

  • View in gallery

    Schematic diagram summarizing the differences between the SC and LC cases.

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Assessing the Impact of Meteorological History on Subtropical Cloud Fraction

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  • 1 University of Washington, Seattle, Washington
  • 2 Scripps Institution of Oceanography, La Jolla, California
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Abstract

This study presents findings from the application of a new Lagrangian method used to evaluate the meteorological sensitivities of subtropical clouds in the northeast Atlantic. Parcel back trajectories are used to account for the influence of previous meteorological conditions on cloud properties, whereas forward trajectories highlight the continued evolution of cloud state. Satellite retrievals from Moderate Resolution Imaging Spectroradiometer (MODIS), Clouds and the Earth’s Radiant Energy System (CERES), Quick Scatterometer (QuikSCAT), and Special Sensor Microwave Imager (SSM/I) provide measurements of cloud properties as well as atmospheric state. These are complemented by meteorological fields from the ECMWF operational analysis model. Observations are composited by cloud fraction, and mean trajectories are used to evaluate differences between each composite.

Systematic differences in meteorological conditions are found to extend through the full 144-h trajectories, confirming the need to account for cloud history in assessing impacts on cloud properties. Most striking among these is the observation that strong synoptic-scale divergence is associated with reduced cloud fraction 0–12 h later. Consistent with prior work, the authors find that cloud cover variations correlate best with variations in lower-tropospheric stability (LTS) and SST that are 36 h upwind. In addition, the authors find that free-tropospheric humidity, along-trajectory SST gradient, and surface fluxes all correlate best at lags ranging from 0 to 12 h. Overall, cloud cover appears to be most strongly impacted by variations in surface divergence over short time scales (<12 h) and by factors influencing boundary layer stratification over longer time scales (12–48 h).

Notably, in the early part of the trajectories several of the above associations are reversed. In particular, when trajectories computed for small cloud fraction scenes are traced back 72 h, they are found to originate in conditions of weaker surface divergence and stronger surface fluxes relative to those computed for large cloud fraction scenes. Coupled with a drier boundary layer and warmer SSTs, this suggests that a decoupling of the boundary layer precedes cloud dissipation. The authors develop an approximation for the stratification of the boundary layer and find further evidence that stratification plays a role in differentiating between developing and dissipating clouds.

Corresponding author address: Joel R. Norris, Scripps Institution of Oceanography, 9500 Gilman Dr., MC 0224, La Jolla, CA 92093-0224. Email: jnorris@ucsd.edu

Abstract

This study presents findings from the application of a new Lagrangian method used to evaluate the meteorological sensitivities of subtropical clouds in the northeast Atlantic. Parcel back trajectories are used to account for the influence of previous meteorological conditions on cloud properties, whereas forward trajectories highlight the continued evolution of cloud state. Satellite retrievals from Moderate Resolution Imaging Spectroradiometer (MODIS), Clouds and the Earth’s Radiant Energy System (CERES), Quick Scatterometer (QuikSCAT), and Special Sensor Microwave Imager (SSM/I) provide measurements of cloud properties as well as atmospheric state. These are complemented by meteorological fields from the ECMWF operational analysis model. Observations are composited by cloud fraction, and mean trajectories are used to evaluate differences between each composite.

Systematic differences in meteorological conditions are found to extend through the full 144-h trajectories, confirming the need to account for cloud history in assessing impacts on cloud properties. Most striking among these is the observation that strong synoptic-scale divergence is associated with reduced cloud fraction 0–12 h later. Consistent with prior work, the authors find that cloud cover variations correlate best with variations in lower-tropospheric stability (LTS) and SST that are 36 h upwind. In addition, the authors find that free-tropospheric humidity, along-trajectory SST gradient, and surface fluxes all correlate best at lags ranging from 0 to 12 h. Overall, cloud cover appears to be most strongly impacted by variations in surface divergence over short time scales (<12 h) and by factors influencing boundary layer stratification over longer time scales (12–48 h).

Notably, in the early part of the trajectories several of the above associations are reversed. In particular, when trajectories computed for small cloud fraction scenes are traced back 72 h, they are found to originate in conditions of weaker surface divergence and stronger surface fluxes relative to those computed for large cloud fraction scenes. Coupled with a drier boundary layer and warmer SSTs, this suggests that a decoupling of the boundary layer precedes cloud dissipation. The authors develop an approximation for the stratification of the boundary layer and find further evidence that stratification plays a role in differentiating between developing and dissipating clouds.

Corresponding author address: Joel R. Norris, Scripps Institution of Oceanography, 9500 Gilman Dr., MC 0224, La Jolla, CA 92093-0224. Email: jnorris@ucsd.edu

1. Introduction

It is well established that stratocumulus clouds found over eastern ocean basins exert a strong cooling effect on the earth’s climate, primarily because of their weak greenhouse effect, extensive coverage, and high albedo relative to the ocean. As a result, small perturbations to these clouds have the potential to significantly impact the earth’s energy balance. An improved understanding of boundary layer cloud sensitivities is necessary to estimate the magnitude of aerosol-cloud effects, improve current model parameterizations, and properly assess the consequences of climate change.

Prior work indicates that the dynamical forcing of stratocumulus clouds occurs at scales larger than the mesoscale (Rozendaal and Rossow 2003; Lewis et al. 2004), meaning it is feasible to assess meteorological impacts on cloud properties using large-scale datasets. Norris and Iacobellis (2005) combined surface observations with meteorological reanalysis data to show that the dominant parameters associated with cloud properties are vertical velocity, advection, and sea surface temperature (SST). An earlier study by Klein et al. (1995) combined several decades of surface observations from the northeast Pacific with radiosonde data and large-scale observations. They showed that low-cloud amount correlates better with SST and upper air temperature 24–30 h upwind than with the local SST and upper air temperature. These results imply that stratocumulus clouds have “memory” or that the history of forcings is an important determinant of cloud state. This can be interpreted in terms of the time scale for boundary layer adjustment, as governed by surface fluxes, entrainment and subsidence rates, and temperature and humidity profiles of the free troposphere.

Accounting for previous meteorological impacts necessitates a Lagrangian perspective on cloud evolution. In addition to the study by Klein et al. (1995), several other investigations have evaluated stratocumulus dynamics from a Lagrangian perspective. During the Atlantic Stratocumulus Transition Experiment (ASTEX), a suite of airborne, ship-based, and balloon measurements were used to track the Lagrangian evolution of a boundary layer air mass, with the goal of investigating the transition from stratocumulus to trade cumulus (Albrecht et al. 1995). Observations made during ASTEX showed that synoptic variability in the northeast Atlantic cloud field is much greater than that observed off the California coast. Building on insights gained from ASTEX, Pincus et al. (1997) computed parcel trajectories using 1000-hPa winds to evaluate the downstream evolution of cloud fields in the northeastern Pacific. Their results were consistent with those of Klein et al. (1995) showing that cloud response is best correlated with stability at a lag of 16 h and suggesting that warming SSTs play a dual role by thickening clouds over shorter time scales and accelerating the transition to trade cumulus over longer time scales.

The above studies have provided invaluable information on the meteorological sensitivities of subtropical clouds. However, all three studies are limited in terms of spatial and temporal sampling. In the Klein et al. (1995) study, the analysis is centered on a unique ocean weather station and therefore cannot be extended to other geographic regions. Conversely, the in situ observations of ASTEX and the analysis of Pincus et al. (1997) cover a fairly broad geographic region but are severely limited in sample size. A new Lagrangian analysis method is needed that includes greater flexibility in spatial and temporal sampling, making it possible to obtain robust statistical estimates of cloud meteorological sensitivities while allowing greater flexibility to assess different cloud regimes.

The goal of the present work is to develop such a method. This paper presents work that builds on the preliminary work of Mauger and Norris (2007), in which global meteorological analyses are combined with three-dimensional trajectories to provide the basis for a Lagrangian evaluation of cloud sensitivities. Parcel back trajectories are used to identify the locations and movement of air within and above the boundary layer relative to the time of cloud measurements. Satellite observations and meteorological analysis fields are interpolated onto back-trajectory positions, permitting a Lagrangian perspective on cloud evolution. By focusing uniquely on global datasets, the new technique allows for broad geographic sampling and a dramatic increase in sample size. Specific improvements to the work of Mauger and Norris (2007) include greatly expanded temporal coverage, incorporation of new satellite measurements, and the addition of forward trajectories to accompany back-trajectory information.

2. Methods

a. Study region and dates

The analysis is focused on the subtropical northeast Atlantic. The northeast Atlantic is chosen because it is a transitional region and thus exhibits greater variability in cloud fraction (CF). The study region is larger than that of Mauger and Norris (2007), extending from 24° to 40°N and 35° to 10°W (Fig. 1). These bounds are chosen to include all regions influenced by subtropical clouds while avoiding the heavy dust region west of Africa and the predominance of extratropical cyclones to the north. The conclusions of this study are not sensitive to the exact location of the region considered. To maximize the statistical significance of the results, observations are obtained for June through August (JJA) during 2000–06.

b. Trajectory analysis

Parcel back trajectories are computed from European Centre for Medium-Range Weather Forecasts (ECMWF; ECMWF 2007) operational analyses using the Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT; Draxler and Rolph 2003). Trajectory calculations are started at the center of each 1° × 1° box and extend 72 h prior to and 72 h beyond the time that cloud properties are observed. Two trajectories are performed for each instance: one within and one above the boundary layer (500 and 2000 m). Satellite observations and meteorological analyses are interpolated onto trajectory positions to obtain estimates of cloud properties and meteorological conditions.

HYSPLIT computes three-dimensional parcel trajectories using a simple advection scheme and gridded meteorological fields as input. We use ECMWF analysis winds, temperature, heights, and surface pressure as input to HYSPLIT calculations. Stohl and Seibert (1998) show that trajectory calculations perform well in undisturbed conditions and that the majority of error arises in the presence of fronts, where winds and transport are poorly resolved. Focusing on stratocumulus clouds thus conveniently avoids the dominant sources of error. Although difficult to assess, studies attempting to quantify uncertainty in trajectories generally center on a position uncertainty of 20% of the distance traveled (Stohl et al. 1998). The mean displacement for the 72-h trajectories is 1000 km, which implies a position uncertainty of approximately 200 km at the trajectory endpoints. This uncertainty is one reason, in addition to our synoptic focus, that low-resolution satellite fields are chosen for the present analysis. Errors associated with trajectory position are also unlikely to be systematically biased and will thus be reduced by averaging numerous trajectories. An important caveat to the use of trajectories is that air parcels do not travel adiabatically along wind streamlines but instead mix with their environment. However, the present analysis is focused on the impact of large-scale meteorological forcings on clouds. Two different tests—comparisons of adjacent trajectories as well as estimates of the decorrelation distance—confirmed that meteorological variations occur at length scales large enough that mixing can be neglected.

All trajectories are initiated based on the overpass time of the Moderate Resolution Imaging Spectroradiometer (MODIS; described below) from which cloud properties are retrieved. The MODIS instrument flies aboard the polar-orbiting, sun-synchronous Terra satellite, the descending pass of which has an equatorial crossing time of 1030 local time (LT). Because of the inclination of the Terra orbit, overpass times in the study region range from approximately 1130 to 1300 UTC. For simplicity, we choose to approximate the overpass time by initiating all trajectories at 1200 UTC (hereafter referred to as the “time of observation”).

An advantage of the trajectory technique is that satellite observations need not be coincident to provide useful information: earlier or later observations can be associated by following the trajectories out to a given lag. As with MODIS, overpass times for all satellite observations are assigned to the 3-hourly bin that is most representative of overpass times for the study region and the satellite platform under consideration. Using the instantaneous trajectory position corresponding to the midpoint of each 3-hourly time interval, a simple linear spatial interpolation of the gridded data is employed to obtain estimates of cloud and meteorological properties for that time and position. Although there will be small variations in overpass times that are not resolved by the 3-hourly time intervals, these are not expected to vary systematically with meteorology.

c. Satellite data

Satellite data are obtained from four different instruments and are used to assess meteorological state as well as validate analysis fields. All of the satellite datasets are regridded from their native resolutions to match the MODIS 1° × 1° grid. A brief overview of each dataset is provided below; further details regarding data quality, potential sources of bias, and comparisons between independent measurements are discussed at length in Mauger (2008).

Cloud microphysical and macrophysical properties are obtained from MODIS as daily gridded averages (MOD08_D3, Collection 005) at a resolution of 1° × 1°. MODIS cloud-top temperature (TTOP) retrievals are made using the 11-μm brightness temperature. Although MODIS CF, effective radius RE, and liquid water path (LWP) retrievals are all differentiated by cloud phase, TTOP retrievals are not. In the present study, retrievals of CF, RE, and LWP are only taken for pixels identified as liquid phase clouds. Scenes containing high clouds are not excluded from the present analysis, because doing so could bias the results (e.g., by constraining the upper-level divergence). We use a random overlap assumption to account for low clouds that are masked by thick high clouds. Because high clouds are not common in the study region, this does not amount to a large correction. Tests employing both minimum and maximum overlap assumptions indicated a negligible sensitivity to the overlap assumption used.

Because MODIS cloud-top temperature retrievals are not differentiated by cloud phase, TTOP retrievals are biased cold when high clouds are present. Tests, performed by compositing TTOP against retrievals of high cloud cover, show that high clouds strongly impact the retrieved cloud-top temperature (Mauger 2008, Fig. III.2). As a result, TTOP observations are screened for high clouds. High clouds are screened by constraining Cloud_Fraction_Ice to be less than 1% and Cirrus_Fraction_SWIR to less than 25% (Platnick et al. 2003), which together provide a conservative test for high cloud contamination. The high threshold for Cirrus_Fraction_SWIR is chosen because, although useful because of its sensitivity to thin cirrus, the authors found evidence that the retrieval is biased high in the presence of bright, low-level clouds (Mauger 2008).

Because the high cloud screening could lead to a sample bias in TTOP-derived quantities, the “all sky” and “no ice” samples were compared for consistency. As expected given a constraint on high clouds, the no-ice samples featured a drier free troposphere and stronger surface divergence. These changes were accompanied by a reduction in latent heat flux, increases in stability, and a greater distinction in temperature advection between composites. Overall, however, the relationships present in the all-sky cases are all present in those that are filtered for high clouds. Although not completely interchangeable, our results indicate that the high cloud filtering does not strongly bias the composites of TTOP.

Several authors have indicated the potential for retrieval biases in pixels that are only partially covered by cloud (Wielicki and Parker 1992; Matheson et al. 2006). Matheson et al. (2006) compare threshold cloud retrievals with cloud properties derived from a new method that accounts for the subpixel cloud fraction. Using Advanced Very High Resolution Radiometer (AVHRR) data at 4-km resolution, their analysis suggests that this bias is small relative to other factors that influence cloud forcing. Tests were performed by compositing TTOP and RE retrievals against low-level cloud fraction (Mauger 2008). These indicate that partial pixel contamination of TTOP retrievals is most pronounced for cloud cover less than about 30%. Variations in effective radius are less straightforward to interpret, though partial pixel biases appear to only impact retrievals for cloud cover less than 10%.

Data from the Clouds and the Earth’s Radiant Energy System (CERES) instrument, also aboard Terra, are used to obtain observations of the top-of-atmosphere (TOA) broadband shortwave flux. This study uses the swath-level single scanner footprint (SSF) product to obtain observations of scene albedo and top-of-atmosphere radiative flux. Both quantities are retrieved for all-sky conditions. Only over-ocean observations are included in the present study. Regions of sun glint and scenes with solar zenith angles greater than 70° are also excluded from the analysis. Finally, CERES pixels are rejected if the Angular Distribution Model (ADM), used to convert from directional radiances to hemispheric fluxes, is obtained from the CERES artificial neural network technique (Loukachine and Loeb 2003) instead of the standard empirical scene-based ADMs. This is done to maintain consistency between retrievals.

All-sky liquid water path and precipitable water are obtained from the Special Sensor Microwave Imager (SSM/I) deployed on board the F15 satellite. The retrieval products are obtained from Remote Sensing Systems, Inc., using the version 6 (V6) retrieval algorithm. Mauger (2008) performed a comparison between the SSM/I retrievals of LWP and those of MODIS. The agreement was found to be well within the estimated accuracy of 25 g m−2 for SSM/I retrievals (Wentz 1997). However, a small systematic bias was observed, in which SSM/I retrievals of LWP for thin clouds (LWP < 200 g m−2) were systematically larger than those of MODIS. Notably, the disagreement is primarily associated with the difference in overpass times between the two sensors.

Surface divergence is computed from Quick Scatterometer (QuikSCAT) 10-m wind retrievals (level 2B swath). In this study we use the level 2B Direction Interval Retrieval with Threshold Nudging (DIRTH) product from QuikSCAT. Because the level 2B grid is not orthogonal, we average the zonal and meridional wind components separately onto a regular grid before computing the divergence. Rain-flagged retrievals are excluded from the regridding. The analysis of Milliff et al. (2004) indicates that removal of rain-flagged data does not bias the wind observations for the region under consideration in this study.

Meteorological parameters are obtained from the ECMWF operational analyses. The data are obtained from the National Center for Atmospheric Research (NCAR), regridded from T106 spectral resolution with 21 vertical levels (NCAR 1990). ECMWF is chosen to provide meteorological fields based on its superior performance in simulating boundary layer development and evolution (Stevens et al. 2007). In contrast with the reanalysis, the ECMWF operational analysis has a finer spatial resolution and an improved atmospheric model, and assimilates newly available data. Similar advantages could be achieved by using ECMWF reanalysis (ERA)-Interim; however, data are currently not available prior to 2001.

QuikSCAT surface winds are assimilated into ECMWF. Recent studies indicate that the quality of the assimilation is high for divergence (McNoldy et al. 2004; Stevens et al. 2007). However, given the potential for model influence on ageostrophic motions and near-surface winds, QuikSCAT is included in the present study for comparison with ECMWF surface divergence.

d. Sample selection, composite averages, and confidence intervals

Low-level cloud fraction is chosen as the dependent variable in this study. Satellite retrievals of cloud fraction involve more straightforward calculations than water path, cloud albedo, or even shortwave cloud forcing. In addition, cloud cover is commonly used in sensitivity studies, and exerts the greatest influence on shortwave cloud forcing. Clear-sky (CF = 0) scenes are included in the analysis, because they represent a relevant part of the continuum in cloud cover.

We composite trajectories and their associated meteorological conditions for three terciles of cloud fraction. Samples are selected randomly from the upper, middle, and lower terciles of cloud fraction. Terciles are chosen for simplicity, though tests indicate that subdividing the data differently, such as into quartiles or into clear and overcast scenes, does not alter the conclusions of this study. Because cloud sensitivities may not vary linearly or even monotonically with cloud fraction, the middle tercile is included in the analysis.

Sample biases associated with geographic and seasonal variations in cloudiness could artificially bias the results. To eliminate this possibility, the study region is split into 19 grid boxes, each one being 4° latitude by 5° longitude (see Fig. 1). These dimensions are consistent with our estimate of the decorrelation scale, which is discussed below. The data are then sampled uniformly from each grid box for each month to maintain even spatial and temporal sampling.

Composite averages are computed from the roughly 10 000 trajectories (effective sample size is ∼2000; see below) that fall into each tercile. As a result, each cloud and meteorological variable has three trajectories that can be compared: one for each of the large, medium, and small cloud cover cases. Following this sample selection, the composite trajectories are referred to as large low-level cloud fraction (LC), medium low-level cloud fraction (MC), and small low-level cloud fraction (SC).

Confidence intervals (95%) in all composites are estimated using a bootstrap method. The bootstrap method works by sampling with replacement from the pool of trajectories in a particular composite. A mean is computed from the randomly selected sample of approximately 2000 trajectories. This process is repeated 1000 times, which permits an estimation of the probability distribution for the average of each sample, from which we obtain our 95% confidence limits.

Our procedure for calculating the ratio of effective sample size to nominal sample size was as follows: We obtained the decorrelation scale as twice the estimated e-folding scale for lagged autocorrelations, resulting in time and length scales of approximately 24 h and 500 km, respectively. Counting all observations within 24 h and 500 km of each other as a single independent sample, we found the effective sample size was only one-fifth of the nominal sample size. Thus, the bootstrap error calculation described above reduced the number of points included in each randomly selected composite by a factor of 5.

With regard to the present analysis, it is important to note the distinction between the Eulerian decorrelation time described above and the decorrelation time scale following a Lagrangian trajectory. As expected, our analysis indicates that the latter time scale is much longer than 24 h. Indeed, we estimate that, for low-level cloud cover, the Lagrangian decorrelation time scale is closer to 84 h.

3. Results

a. Cloud properties

Figure 2 shows a histogram of cloud fraction including data from all three terciles. As discussed above, low-level cloud fraction is defined using the MODIS retrieval of liquid water cloud fraction and correcting the retrieval for overlap by high cloud. The U-shaped distribution is a confirmation of the fact that the spatial autocorrelation scale is greater than the scale at which the observations are gridded. As a consequence, if one portion of the grid box is cloudy, it is very likely that the rest will be cloudy as well. The converse is true for clear-sky cases, and the result is that overcast (CF = 1) and clear-sky (CF = 0) scenes are much more likely to be present than any compromise between the two. A more interesting detail is the skewness of the distribution, which shows 2–3 times as many clear-sky as overcast days. This is consistent with observations made during the ASTEX campaign (Bretherton et al. 1995).

The dashed lines show the average delineation between the three terciles. As a result of the skewness, over 30% of the SC observations are clear-sky cases. However, as discussed later, the mean of these small cloud fraction observations represents the endpoint of a continuous decline in cloud fraction over the course of the 72-h back trajectory.

Figure 3 shows the mean position along each composite trajectory, including both the 72-h back trajectory and the 72-h forward trajectory for each. An indication of the speed along each composite trajectory is given by the position of the error bars, which are displayed at 3-hourly intervals. For clarity, only the 500-m trajectories are shown in full. Vertical shear is present in the trajectories: the 2000-m trajectories generally circulate along tighter anticyclonic paths than those at 500 m (the endpoints of the 2000 m trajectories are displayed in Fig. 3), showing warmer SSTs and weaker divergence at t = −72 h and cooler SSTs and stronger divergence at t = +72 h relative to those initiated at 500 m. However, the cloud and meteorological differences between composites are qualitatively similar for the 500- and 2000-m trajectories, such that focusing uniquely on those at 500 m does not impact the conclusions of this study.

All composite trajectories are seen to follow anticyclonic paths defined by the climatological high pressure region found over the eastern North Atlantic. There is no significant distinction between the forward trajectories, where winds are subject to significantly less synoptic and regional variability. In contrast, the SC back trajectories originate farther south and west than those for the LC cases. This difference in the trajectories is associated with a southwest shift in the Azores high for the SC composite.

Composite trajectories of low-level cloud fraction and CERES all-sky TOA net shortwave flux are shown in Fig. 4. The differences in low-level cloud fraction are greatest in the 48 h surrounding the time of observation (t = −24 to t = +24). Notably, the differences remain significant from the beginning of the trajectory, extending to 48 h beyond the time of observation, consistently showing greater cloud cover for the LC composite and less for the SC composite. Cloud cover is also seen to vary nonlinearly between the SC, MC, and LC composites, with the LC case showing a substantial jump in cloud fraction relative to the MC case. Associated with the changes in low-level cloud fraction, Fig. 4 shows the composite trajectories for all-sky TOA net shortwave flux from CERES (FSW). The flux values retrieved from CERES are representative of Terra overpass times, which occur shortly before noon local time (see section 2) and are thus much larger than the diurnally averaged fluxes. As expected, shortwave fluxes retrieved from CERES reflect the strong cooling effect of low-level clouds.

Because the interpretation of all-sky LWP can be somewhat ambiguous, Fig. 5 shows trajectories of MODIS in-cloud and all-sky LWP alongside all-sky LWP from SSM/I. As discussed above, SSM/I retrievals are consistently larger than those of MODIS for the range of water paths considered. The scale of this discrepancy increases as cloud cover decreases, suggesting that a partial pixel bias in the MODIS retrievals is responsible for the difference. Overall, the retrievals presented in Fig. 5 are consistent in associating increasing water paths with growing cloud decks and the converse for dissipating clouds.

b. Thermodynamic conditions

The Lagrangian analysis developed herein is motivated by the observation that cloud cover correlates best with upwind variations in the stability of the lower atmosphere (e.g., Klein et al. 1995; Mauger and Norris 2007). Lower-tropospheric stability (LTS) is defined here as the difference in potential temperature between 700 hPa and the surface (θ700θSFC). Figure 6 shows that the above observation is confirmed by the present study: the differences in LTS in the earlier parts of the trajectory are greater than at t = 0. Large cloud fraction cases are associated with a significantly more stable atmosphere, a condition that persists throughout the course of the 72 h prior to the time of observation. The greater stability, due to both a warmer free troposphere and cooler SSTs, is also accompanied by an increase in moisture above the boundary layer, as seen in the trajectories of specific humidity at 700 hPa (q700). It is worth noting that these trends are superposed on the diurnal cycle, which can be seen in this and subsequent plots that present results from 6-hourly ECMWF data.

Figure 7 shows the composite trajectories for the rate of sea surface temperature change (ΔSST), 10-m surface wind speed (W10m), and sensible (FSH) and latent (FLH) heat fluxes, all obtained from ECMWF analyses. Note that ECMWF surface fluxes, in contrast with other analysis variables, are only updated at 12-hourly intervals. The Lagrangian analog of SST advection is simply the along-trajectory rate of sea surface temperature change. This is equivalent to the conventional definition of temperature advection (−υ · T) applied to the trajectory path and is therefore hereafter referred to as SST advection. The plots in Fig. 7 are displayed in order of increasing model influence: Surface winds and temperatures are directly observed and are likely less influenced by the model than surface fluxes. Consequently, more confidence should be placed in the composite differences in SST advection and surface wind speed.

As with LTS, the results are consistent with prior work associating advection over warmer water (cold advection) with increased incidence of low-level clouds (e.g., Klein et al. 1995). Significant differences in surface winds are seen from t = −72 through t = 24, with the LC case exhibiting the strongest winds and the SC winds being the weakest. Initially, the strongest cold advection is seen in the SC case, followed by the MC and LC cases, respectively. However, this association is quickly reversed, and from t = −48 onward the increase in SST is stronger in the MC and LC cases than in the SC case, so that the difference in SST between the three cases gradually decreases (see Fig. 6).

Both increased cold advection and stronger surface winds will promote increased surface fluxes. From t = −36 to t = 24, the stronger cold advection and stronger winds seen in the LC and MC cases result in stronger surface fluxes, despite cooler SSTs. Prior to t = −36, the cooler SSTs dominate and the SC case exhibits greater surface fluxes. The lack of distinction between the MC and LC fluxes probably results from the fact that higher wind speeds in the LC case are compensated by cooler SSTs.

c. Large-scale dynamics

Figure 8 displays the large-scale dynamic influences on cloud fraction. Both QuikSCAT retrievals and ECMWF surface divergence are shown to be inversely associated with cloud fraction. This is an interesting observation, because stratiform clouds are known to exist in regions that are climatologically defined by widespread subsidence. The present results suggest that these clouds actually exist in a delicate balance between excessively divergent and insufficiently divergent regimes. Pressure vertical velocity at 700 hPa (ω700; from ECMWF) is consistent with this result, showing a divergent regime overall but a decrease in cloud fraction with increasing divergence. Notably, as with surface fluxes, these fields too show a reversal in the relationship with cloud cover in the early part of the trajectory, showing that prior to t = −48 the LC cases are subject to greater divergence.

An important question is whether the above quantities constitute a valid proxy for the subsidence rate at cloud top. Estimates of the cloud-top subsidence rate, using both retrieved cloud-top height and a fixed inversion height, are consistent with the observed changes in surface divergence, showing weaker subsidence for the LC case at t = 0 but stronger subsidence at t = −72.

d. Boundary layer properties

A common challenge in remote sensing studies of boundary layer clouds is the estimation of quantities intrinsic to the boundary layer. These include the inversion height, boundary layer stability, and the strength of the inversion. By assuming a particular boundary layer lapse rate, MODIS retrievals of cloud-top temperature can be combined with retrievals of SST to obtain estimates of boundary layer height ZTOP. Conversely, by specifying an assumed inversion height, the same information can be used to estimate the boundary layer lapse rate ΓBL. Inspection of the results, shown in Fig. 9, provides a means of contrasting the potential veracity of the constant lapse rate assumption (used to estimate ZTOP) against the assumption of a constant boundary layer height (used to estimate ΓBL).

Before proceeding, it should be noted that although all variables derived from MODIS cloud-top temperature estimates are screened for high clouds, there is no straightforward correction for partial pixel error. It is thus likely that at least a part of the observed relationship results from the misattribution of partially filled MODIS pixels as cloudy. Calculations indicate that correcting for this bias results in a significantly reduced difference between composites, but does not alter the sign of the association with cloud cover. Nevertheless, it is likely that some bias exists, and that this bias impacts the observed relationship between estimates of cloud-top temperature and the composites of low-level cloud cover.

The trajectory of ZTOP indicates that the LC case has a shallower inversion early in the trajectory, which then becomes significantly deeper at the time of observation (t = 0), and remains larger than the MC and SC cases through to t = 72 h. The changes in ZTOP are consistent with the prediction that marine clouds maintain fairly constant entrainment rates (e.g., Schubert et al. 1979), showing a roughly inverse relationship between ZTOP and surface divergence. However, the scale of the changes in ZTOP is much larger than is typically observed in subtropical clouds, and changes in ZTOP appear to correlate better with changes in cloud cover (r = 0.43) than with changes in divergence (r = −0.16), suggesting that partial pixel biases are indeed influencing the measurements.

Turning to the estimate of a boundary layer lapse rate ΓBL, we can evaluate the assumption of a constant layer height. As above, the results are highly correlated with variations in cloud cover, associating decreased boundary layer stability with increases in cloud cover. This is consistent with the conception of a well-mixed layer for the LC case and a more stable SC boundary layer.

The degree of stratification in each case can be estimated by first calculating the adiabatic lapse rate ΓADB, which is approximated by assuming 100% cloud cover and using the all-sky liquid water path to estimate cloud thickness. Given the cloud thickness and the assumed inversion height, the mean boundary layer lapse rate is computed by partitioning the layer into cloud (moist adiabat) and subcloud (dry adiabat) layers. Because a well-mixed boundary layer is assumed in this calculation, the adiabatic lapse rate will always be greater than or equal to the actual lapse rate. The degree of decoupling, or stratification, is thus defined as the difference between the adiabatic and actual lapse rates (ΔΓ = ΓADB − ΓBL). There are two sources of error that could impact this calculation: partial pixel bias in TTOP (discussed above) and the overcast assumption used to estimate cloud thickness. The latter results in an underestimate of cloud thickness and, consequently, an overestimate of the boundary layer lapse rate. The magnitude of this error scales with cloud fraction but is always less than about 1°C km−1, far less than the differences observed in Fig. 9.

Shown in the bottom plot of Fig. 9, the composites of ΔΓ suggest that the differences in cloud cover are strongly associated with differences in boundary layer stratification. This implies a significant difference in the internal dynamics governing the boundary layers of the SC and LC cases. Interestingly, as with surface divergence, SST advection, and surface fluxes, the sign of the relationship is reversed in the early part of the trajectory, implying that the LC boundary layer is initially either more shallow or more stable than the SC case.

e. Lag correlations and nonlinearity in cloud response

The above results suggest an interesting pattern in the time dependence of different forcings in their association with cloud fraction. Figure 10 shows the lagged correlations between cloud fraction at t = 0 and a selection of the variables most strongly associated with changes in cloud cover. Consistent with the above analysis, lag correlations are computed in the Lagrangian sense: following the trajectory. Correlations are computed from the same sample of trajectories used throughout the present study. Confidence limits (95%) are estimated using a Fisher transformation and accounting for the degrees of freedom.

The correlations provide a convenient means of identifying the lags at which each variable is most strongly associated with cloud fraction. Note that these lags are not indicative of a specific moment at which an influence is exerted but of the time scales over which the boundary layer responds to each forcing. A pattern is recognizable in several categories of forcing. LTS and SST are best correlated approximately 36 h upwind of cloud observations, consistent with the results of Klein et al. (1995). Similarly, latent and sensible heat fluxes are best correlated at lags exceeding 48 h, whereas SST advection is best correlated between 0 and 36 h upwind of cloud observations. Specific humidity at 700 hPa has a more varied response, showing a weak but fairly constant association with cloud cover throughout the 72-h back trajectories. Finally, variations in surface divergence are primarily associated with near-instantaneous changes in cloud properties. Overall, these results suggest a contrast between the thermodynamic and large-scale dynamic influences on cloud fraction, in which the time scales for boundary layer response to thermodynamic forcings is long compared to that of dynamic influences.

Finally, it is important to emphasize the motivation for the Lagrangian analysis used herein. If we take LTS as an example, the peak correlation along the Lagrangian trajectory occurs at t = −36 h and has a value of r = 0.36 (95% confidence limits: 0.34–0.38). An alternative would be to consider the Eulerian history: the changes in meteorological properties at the cloud’s t = 0 position. If we instead calculate the correlation with LTS following the Eulerian perspective, we find that it decreases substantially to r = 0.22 (0.19–0.24).

4. Discussion

We begin by summarizing the conditions near the time of observation (t = −12 to t = 12). By design, the LC cases exhibit significantly greater cloud cover. Accompanying the differences in cloud cover is a systematic increase in liquid water path and shortwave forcing relative to the MC and SC cases. Column water vapor (not shown) is also consistently larger for the LC composite. Combined with cooler SSTs, this suggests that the LC boundary layer is more humid.

We find that a greater stability of the lower atmosphere precedes the increase in cloud cover for the LC case. Given a well-mixed boundary layer, greater stability will result in a stronger capping inversion at layer top. This reduces entrainment and decreases the rate at which dry air from above the inversion is incorporated into the boundary layer, thus allowing the boundary layer to moisten and cloud cover to increase. As shown in Fig. 6, the LC case is also associated with a more humid free troposphere, which reduces the drying effect of the entrained air.

Surface fluxes also reflect the anticipated differences between dissipating and developing clouds. The LC composite is associated with stronger cold advection, increased surface wind speeds, and an increase in surface fluxes relative to the SC case. The differences are most pronounced from t = −36 onward and complement the above results regarding entrainment drying by implying a stronger supply of moisture from the surface to the cloud layer in the LC case.

Finally, we find that large, synoptic-scale changes in divergence are inversely associated with changes in cloud cover. Specifically, surface divergence and the associated cloud-top subsidence rate are weaker for the LC case, again promoting either increased growth or a decreased rate of dilution of the boundary layer.

The above results are summarized in the schematic shown in Fig. 11. Taken together, the evidence all points to a stronger coupling between the surface and cloud layers and suggests a slower rate of entrainment drying for the LC clouds. Our estimates of decoupling support this conclusion, suggesting that the SC boundary layer is significantly more stratified than in the other two cases.

Notably, there are several quantities whose relationships to cloud fraction change sign over the course of the trajectory. In particular, surface divergence is stronger for the LC case at −72 h, despite being significantly weaker than the other two cases at t = 0. This reversal is also seen in the composites of SST advection and surface fluxes, which show weaker surface exchanges for the LC case at t = −72. In addition to weaker surface fluxes, the LC boundary layer is either more shallow or less well mixed at t = −72.

The differences in surface fluxes and the potential for a deep SC boundary layer at t = −72 suggest that changes in surface fluxes may exert a long time-scale influence on cloud development. Several authors have noted an association between increased moisture fluxes and an increased stratification of the cloud and subcloud layers, which can eventually result in decoupling (e.g., Schubert et al. 1979; Bretherton and Wyant 1997). Throughout the course of the first 72 h, the SC composite is consistent with the two-stage model suggested by Wyant et al. (1997). The authors describe a first stage in which decoupling is driven by increased surface fluxes followed by a second stage in which continually increasing SSTs contribute to a transition to progressively more vigorous cumulus convection, which increasingly mixes across the inversion, causing the stratocumulus deck at the boundary layer top to dissipate. This is consistent with the fact that, prior to t = 0, the SC trajectory experiences SSTs that are substantially greater than those for the LC composite.

5. Summary and conclusions

We have presented a new method for assessing the Lagrangian impacts of meteorology on cloud evolution and applied the analysis to the subtropical cloud regime of the northeast Atlantic. The method used builds upon the Lagrangian trajectory method introduced by Mauger and Norris (2007), with the addition of new satellite observations of broadband fluxes, cloud water, and surface winds. We analyze cloud cover by compositing trajectories into terciles of low-level cloud fraction and evaluate the associated changes in meteorological and cloud properties along trajectories that extend both 72 h back as well as 72 h forward.

The Lagrangian analysis is used to identify the time lag at which each of the above quantities exerts the greatest influence on the evolution of boundary layer clouds. Increased atmospheric stability (LTS) and lower SSTs are found to associate with increases in cloud cover 24–48 h downwind. Increases in free-tropospheric humidity (q700) and stronger cold advection (ΔSST), for their part, are found to lead increases in cloud cover by 0–36 h. Finally, strong divergence favors reduced cloud fraction 0–12 h later. These quantities serve as proxies for the physical processes that govern boundary layer evolution.

The above observations highlight a distinction between thermodynamic conditions (e.g., LTS, SST, etc.), which appear to influence cloud properties over longer time scales, and dynamical variables (e.g., divergence), which exert a near-instantaneous influence on cloud cover. Although many mixed layer simulations assume steady or slowly varying divergence, an important finding of the present work is that large synoptic-scale variations in divergence are commonplace. These dramatic changes in divergence are found to exert a dominant influence on cloud properties.

By estimating the degree of decoupling, we find evidence that the contrasting evolution of the large and small cloud cover cases is associated with a notable difference in the stability of the cloud layers. Although our estimate of decoupling is vulnerable to substantial measurement biases, the results are consistent with other factors influencing entrainment drying and the strength of surface fluxes. Nonetheless, the analysis could be significantly improved by the inclusion of coincident, independent measurements of boundary layer height. Such measurements are now possible from the operational Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) cloud height retrieval algorithm. The satellite was not in orbit during the dates used in the present analysis but could be used in future analyses.

The results presented above reveal the wealth of information that is available in the Lagrangian analysis developed herein. The present work represents a useful first step in the Lagrangian characterization of low-level cloud sensitivities. There are many respects in which the current work can be extended to provide additional information on cloud sensitivities, such as the inclusion of additional satellite measurements; investigation of other subtropical regimes (Sandu et al. 2010); or, as in ASTEX (Albrecht et al. 1995), to inform future field campaigns. The method can also be applied to model output, providing new, focused diagnostic information on model performance.

Acknowledgments

The authors thank the reviewers of this manuscript for their thoughtful comments and suggestions. This work was supported by NSF CAREER Award ATM02-38527. The HYSPLIT model was developed by the National Oceanic and Atmospheric Administrations (NOAA) Air Resources Laboratory (ARL). MODIS data were obtained from the Level 1 and Atmosphere Archive and Distributions System (LAADS) Web site, which is operated by the NASA Goddard Space Flight Center. CERES data were obtained from the Atmospheric Science Data Center at the NASA Langley Research Center. SSM/I data were obtained from Remote Sensing Systems, which is sponsored by the NASA Earth Science REASoN DISCOVER Project. The QuikSCAT level 2B data were obtained from the Physical Oceanography Distributed Active Archive Center (PODAAC) at the NASA Jet Propulsion Laboratory, Pasadena, California. ECMWF data were obtained from the CISL Data Support Section at the National Center for Atmospheric Research, Boulder, Colorado.

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Fig. 1.
Fig. 1.

The study region used in the present work, outlined in thick black lines (24°–40°N, 35°–10°W). The thin black lines denote the grid boxes used to ensure even sampling throughout the domain. Climatologies of MODIS low-level cloud cover (CFLIQ) and ECMWF 10-m wind speed are shown for the dates used in this study (JJA 2000–06).

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 2.
Fig. 2.

Histogram of MODIS low-level CF. The y axis denotes the fraction of all points that fall into each bin, and the dashed lines delineate terciles (SC, MC, and LC) in CF.

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 3.
Fig. 3.

Composite trajectories for the LC (thin black lines), MC (medium-width dark gray lines), and SC (thick light gray lines) terciles of MODIS low-level CF. Error bars denote the 95% confidence limits obtained using the bootstrap method described in the text. The full 500-m trajectories are shown, whereas only the endpoints are shown for the 2000-m trajectories. The circle at the center of the plot denotes the average starting position (t = 0) for both forward and back trajectories. Land areas are shaded in gray.

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 4.
Fig. 4.

Composite trajectories for overlap-corrected MODIS low-level CF (CFLIQ) and CERES all-sky TOA net shortwave flux (FSW; W m−2).

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 5.
Fig. 5.

Composite trajectories showing different measures of cloud water path. All variables are displayed in units of g m−2. Displayed are (top)–(bottom) MODIS in-cloud LWP, MODIS all-sky LWP, and SSM/I all-sky LWP from the F15 satellite.

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 6.
Fig. 6.

Composite trajectories showing LTS (defined as θ700θSFC; K), SST (K), and 700-hPa temperature (T700; K) and moisture (q700; g kg−1), all obtained from ECMWF analyses. Note that variations from one time to the next reflect large-scale trends as well as the diurnal cycle.

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 7.
Fig. 7.

Composite trajectories showing the rate of SST change (ΔSST × 10−5 K s−1), 10-m wind speed (m s−1), surface sensible heat flux (FSH; W m−2), and surface latent heat flux (FLH; W m−2), all obtained from ECMWF analyses. Note that, in contrast with other analysis variables, ECMWF surface fluxes are only updated at 12-hourly intervals.

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 8.
Fig. 8.

Composite trajectories showing QuikSCAT and ECMWF surface divergence DIVQSCT and DIVECMWF (×10−6 s−1) and ECMWF 700-hPa pressure vertical velocity ω700 (Pa s−1).

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 9.
Fig. 9.

Composite trajectories showing MODIS retrievals of TTOP (K) and derived cloud-top height [ZTOP, which is defined as (SST − TTOP)/6.5; km], boundary layer lapse rate (ΓBL = ΓADB − ΓBL; K km−1), and deviation of the lapse rate from adiabatic (ΔΓ; K km−1).

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 10.
Fig. 10.

Lagged correlations between low-level CF (CFLIQ) at the time of observation (0 h) for the following variables: LTS, SST, specific humidity at 700 hPa (q700), SST advection (ΔSST), surface latent and sensible heat fluxes (FLH and FSH), 700-hPa pressure vertical velocity (ω700), and QuikSCAT and ECMWF surface divergence (DIVQSCT and DIVECMWF). Consistent with the focus of this study lag correlations are computed in the Lagrangian sense: following the trajectory. Confidence limits (95%) are estimated using a Fisher transformation and accounting for the degrees of freedom.

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

Fig. 11.
Fig. 11.

Schematic diagram summarizing the differences between the SC and LC cases.

Citation: Journal of Climate 23, 11; 10.1175/2010JCLI3272.1

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