Reliably determining low-cloud heights using a cloud-top temperature from satellite infrared imagery is often challenging because of difficulties in characterizing the local thermal structure of the lower troposphere with the necessary precision and accuracy. To improve low-cloud-top height estimates over water surfaces, various methods have employed lapse rates anchored to the sea surface temperature to replace the boundary layer temperature profiles that relate temperature to altitude. To further improve low-cloud-top height retrievals, collocated Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) data taken from July 2006 to June 2007 and from June 2009 to May 2010 (2 yr) for single-layer low clouds are used here with numerical weather model analyses to develop regional mean boundary apparent lapse rates. These parameters are designated as apparent lapse rates because they are defined using the cloud-top temperatures from satellite retrievals and surface skin temperatures; they do not represent true lapse rates. Separate day and night, seasonal mean lapse rates are determined for 10′-resolution snow-free land, water, and coastal regions, while zonally dependent lapse rates are developed for snow/ice-covered areas for use in the Clouds and the Earth’s Radiant Energy System (CERES) Edition 4 cloud property retrieval system (CCPRS-4). The derived apparent lapse rates over ice-free water range from 5 to 9 K km−1 with mean values of about 6.9 and 7.2 K km−1 during the day and night, respectively. Over land, the regional values vary from 3 to 8 K km−1, with day and night means of 5.5 and 6.2 K km−1, respectively. The zonal-mean apparent lapse rates over snow and ice surfaces generally decrease with increasing latitude, ranging from 4 to 8 K km−1. All of the CCPRS-4 lapse rates were used along with five other lapse rate techniques to retrieve cloud-top heights for 2 months of independent Aqua MODIS data. When compared with coincident CALIPSO data for October 2007, the mean cloud-top height differences between CCPRS-4 and CALIPSO during the daytime (nighttime) are 0.04 ± 0.61 km (0.10 ± 0.62 km) over ice-free water, −0.06 ± 0.85 km (−0.01 ± 0.83 km) over snow-free land, and 0.38 ± 0.95 km (0.03 ± 0.92 km) over snow-covered areas. The CCPRS-4 regional monthly means are generally unbiased and lack spatial error gradients seen in the comparisons for most of the other techniques. Over snow-free land, the regional monthly-mean errors range from −0.28 ± 0.74 km during daytime to 0.04 ± 0.78 km at night. The water regional monthly means are, on average, 0.04 ± 0.44 km less than the CALIPSO values during day and night. Greater errors are realized for snow-covered regions. Overall, the CCPRS-4 lapse rates yield the smallest RMS differences for all times of day over all areas both for individual retrievals and monthly means. These new regional apparent lapse rates, used in processing CERES Edition 4 data, should provide more accurate low-cloud-type heights than previously possible using satellite imager data.
Measuring cloud-top altitude from satellite imagers has long been a challenge for cloud remote sensing. Although other approaches are used (e.g., Rozanov and Kokhanovsky 2004), cloud-top height has often been inferred by first retrieving cloud-top temperature and then matching the temperature to an altitude in a vertical temperature profile from an upper-air sounding (e.g., Reynolds and Vonder Haar 1977), a satellite sounding (e.g., Rossow and Schiffer 1999), a numerical weather prediction (NWP) model analysis (Menzel et al. 2008), or a lapse rate anchored to the surface temperature (Minnis and Harrison 1984). One of the largest sources of error in cloud-height retrievals based on the cloud-top temperature is a strong inversion at the top of the boundary layer (BL) where stratus clouds often occur. The lowest temperature below the BL top can be missed in radiosonde profiles for such cases because the lag in the sensor’s thermal response dampens the extremes in the temperature profile (e.g., Mahesh et al. 1997). Even when the radiosonde captures the strength of the inversion accurately, it can easily be diminished when assimilated in an NWP analysis, especially when the model profiles are output at discrete pressure levels. Using either the radiosonde or NWP profiles to translate cloud-top temperature Tt to cloud-top height Zt for low-level clouds results in significant Zt overestimates where strong inversions cap the boundary layer (Garay et al. 2008; Holz et al. 2008). Furthermore, there may be a slight temperature difference between the droplets near cloud top and the ambient air (Painemal et al. 2013).
To address this issue for determining marine stratus cloud-top altitude, Minnis et al. (1992) anchored a lapse rate of 7.1 K km−1 to the sea surface temperature to characterize the temperature–height relationship. This same lapse rate was adopted by Minnis et al. (2011) to substitute for the NWP model profile below the 700-hPa level over all surfaces for the Clouds and the Earth’s Radiant Energy System (CERES) Edition 2 Cloud Property Retrieval System (CCPRS-2). The CCPRS retrieves a variety of cloud properties including Tt and Zt from Moderate Resolution Imaging Spectroradiometer (MODIS) radiances. While the CCPRS-2 lapse rate approach reduced biases in low-cloud Zt over many marine areas (Minnis et al. 2007), particularly over marine stratocumulus regimes (Garay et al. 2008), it became apparent that the single-value lapse rate is not optimal everywhere, particularly over land (e.g., Dong et al. 2008).
Wood and Bretherton (2004) determined that the lapse rate could be parameterized as a function of the BL height for marine stratus (MS) areas. But, for cloud remote sensing, the lapse rate needs to be known first to determine the BL height for clouds formed under the inversion base. Zuidema et al. (2009) bypassed the lapse rate and, using 156 ship soundings, developed a method for the southeast Pacific stratocumulus area that allows direct estimation of Zt, if Tt and the sea surface temperature are known. While that technique is promising, it has only been tested for one area and season, and requires further study.
With the advent of the Afternoon Satellite Constellation (A-Train; Stephens et al. 2002), it has become possible to better quantify the global variation of the apparent BL lapse rates without soundings. Wu et al. (2008) and Sun-Mack et al. (2008) pioneered techniques to derive marine BL lapse rates using matched MODIS, Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO; see Winker et al. 2007), and surface temperature data. Wu et al. (2008) computed lapse rates for January 2007 over a region in the southeastern Pacific Ocean using Ts from Advanced Microwave Scanning Radiometer for Earth Observing System (EOS) (AMSR-E) retrievals of sea surface temperature, estimates of Tt from MODIS, and Zc from CALIPSO lidar returns. Sun-Mack et al. (2008) used a similar approach to determine the zonal variation of cloudy BL lapse rates for one month over land and water, but replaced the AMSR-E temperatures with surface temperatures from the Global Modeling and Assimilation Office (GMAO) Goddard Earth Observing System Model, version 4 (GEOS-4), documented by Bloom et al. (2005). Baum et al. (2012) incorporated sea surface temperatures from a different NWP model to develop monthly-mean zonal BL lapse rates for use in an updated cloud-height scheme for the MODIS Atmosphere Science Team Collection 6 algorithms. Because BL lapse rates vary zonally, meridionally, and diurnally, and strong inversions occur over land, Sun-Mack et al. (2010) developed a preliminary regional lapse rate model for CCPRS Edition 3 (Minnis et al. 2010), which is an alternative methodology used to analyze MODIS data. However, CCPRS Edition 3 was superseded by CCPRS Edition 4 (CCPRS-4) before it was ever implemented.
This paper describes the development and testing of the final global, regional lapse rate database that is being used in the CCPRS-4 cloud analyses. Two years of matched Aqua MODIS, CALIPSO, and CloudSat data are used to derive boundary layer monthly regional apparent lapse rates over ice-free water, snow-free land, and snow-covered surfaces for both daytime and nighttime. The parameters determined here are denoted as apparent lapse rates because they are based on satellite-derived cloud-top temperatures and surface skin (for water) or 24-h averaged air (for land) temperatures. They are determined solely for the purposes of determining cloud-top height and should not be confused with or used as actual boundary layer lapse rates, which are determined from the surface air and boundary layer top air temperatures. The data and method for deriving the monthly global BL apparent lapse rates are described in section 2. Section 3 presents the seasonal global lapse rates for ice-free water, snow-free land, and snow-covered surfaces, respectively, during daytime and nighttime. In section 4, the newly derived lapse rates are used to process 2 months of MODIS data with CCPRS-4 to calculate cloud-top heights, which are then compared with their collocated CALIPSO counterparts. Additional comparisons are performed using a variety of currently available methods for retrieving low clouds from thermal infrared data. The differences provide an estimate of the errors in the CERES–MODIS Edition 4 low-cloud heights. The conclusions are presented in section 5.
2. Data and methodology
The mean boundary layer lapse rate Γ is defined as
where Zs is the surface elevation and Ts is the surface temperature. In the standard definition of Γ, Ts is defined as the air temperature above the surface and Tt is the temperature of the air at the top of the cloud. In this study, the cloud-top temperature and surface temperature are defined differently, the computed value is the apparent lapse rate, denoted as Γa. Hereinafter, the apparent lapse rate will be referred to simply as the lapse rate. The term standard lapse rate will be used when referring to Γ computed according to the standard definition.
To compute the lapse rates, the collocated CALIPSO, CloudSat, CERES, and MODIS (CCCM) dataset developed by Kato et al. (2010) provides the values of Zt from CALIPSO and Tt from CCPRS. The CCPRS retrieves the effective radiating temperature Tc of the cloud (Minnis et al. 2011) using the infrared window channel (10.8 μm for MODIS channel 31). It accounts for the semitransparency of optically thin clouds using the visible optical depth retrieved using the visible channel during sunlit conditions or a three-channel simultaneous retrieval at night. For clouds having an optical depth exceeding 6, the temperature corresponds to a pathlength equivalent to an optical depth of ~1.1 (e.g., Minnis et al. 2008). Using the empirical formula for cloud thickness as a function of cloud optical depth for California MS (Minnis et al. 1992), this optical depth corresponds to a distance of ~54 m from the cloud top for a nadir view that decreases with increasing viewing zenith angle. Considering other sources of error in the data and the retrievals, this difference is assumed to be negligible and, in effect, the top temperature and effective temperature are equivalent for the clouds considered here. However, when the cloud optical depth is less than 6, a small correction is made, such that
where B is the Planck function evaluated at the effective wavelength of the infrared window channel (10.8 μm for MODIS channel 31) and B−1 is its inverse. This formula assumes that the radiating depth of the cloud is equivalent to an emissivity of 0.99 relative to the cloud-top temperature. The difference between Tc and Tt for these cases is roughly −0.5 K.
The value of Zt is determined from the CALIPSO lidar backscatter at a 30-m vertical resolution. Only clouds detected by both CALIPSO and CCPRS are considered here. Figure 1 is a schematic diagram of the matching process used for the CALIPSO, CloudSat, and Aqua MODIS data. For a MODIS pixel to be considered as cloudy in this study, two or more matched CALIPSO shots must be classified as confident clouds in the CALIPSO vertical feature mask (VFM).
The value of Ts is taken from the GMAO GEOS-5.03 6-hourly, 1°-resolution analyses (Rienecker et al. 2008). Over water surfaces, Ts is set equal to the sea surface temperature interpolated to the pixel location and observing time. The actual air temperature above the surface often differs from the sea surface temperature. Over land, Ts is equal to the running 24-h mean value of the surface air (2 m) temperature interpolated to the pixel in time and space. Thus, four values of the 6-hourly air temperatures are employed in the running average. Lapse rates are not computed for areas having Zs > 4 km. This 24-h mean is used over land to minimize large diurnal swings in the lapse rate or cloud-top heights due to possible errors in the model diurnal cycle phasing or to the absence or presence of clouds not diagnosed in the reanalysis. In summary, the apparent lapse rate calculation differs from the standard lapse rate in that the sea surface temperature is used instead of air temperature over water bodies, a 24-h mean instead of the instantaneous surface air temperature is used over land, and the cloud-top temperature may differ from the actual ambient air temperature at cloud top (Painemal et al. 2013).
A value of Γa is calculated for each Aqua MODIS pixel having high confidence single-layer cloud detections from the CALIPSO VFM and liquid water cloud phase from the CCPRS. Furthermore, the highest cloud-top height within the MODIS pixel from either active sensor is required to be less than 4 km above Zs. To obtain a seasonal variation in Γa, 2 yr of CCCM data were used to derive global distributions of the lapse rates. The individual pixel data were seasonally grouped separately over land and water, day and night, using the four boreal seasons, winter [December, January, February (DJF)], spring [March, April, May (MAM)], summer [June, July, August (JJA)], and fall [September, October, November (SON)], for July 2006–June 2007 and June 2009–May 2010. All calculated lapse rates for a given season were first averaged in 5° × 5° and 20° × 20° grid boxes. Because of CALIPSO’s limited spatial coverage, the lapse rates are noisy, especially during daytime. Therefore, residual error maps were created. The residual error δ or standard error is defined as
where σ is the standard deviation of lapse rates in the 5° × 5° grid box and N is number of CALIPSO collocated MODIS pixels that contribute to the lapse rate calculations. After examining the global δ distributions, a residual error of 0.5 K km−1 was chosen as the threshold for the lapse rate cutoff. The lapse rates in a 5° × 5° region with residual error exceeding 0.5 K km−1 were removed and filled with the lapse rate value calculated in the 20° × 20° grid box that covers the 5° × 5° region. Over areas having no 5° × 5° lapse rate values, 20° × 20° lapse rate values were used. Finally, a nine-point smoothing technique, shown in Fig. 2, was applied to avoid discontinuities among the 5° grid boxes.
The CCPRS uses a 10′ International Geosphere–Biosphere Programme (IGBP; see Belward et al. 1999) surface type map for many of its input parameters (e.g., surface albedo and emissivity), so to fit that framework, the lapse rates are also determined for each IGBP 10′ box. To accomplish this goal, this technique first populates the lapse rate in a 5° × 5° region to each 10′ × 10′ grid box within the region. It then calculates IGBP means for each surface type and fills any 10′ grid box having no Γa value with the IGBP mean for that box’s surface type. The lapse rate values of the nine 5° × 5° grid boxes are then averaged to provide Γa for the center 10′ × 10′ grid box (Fig. 2). This nine-point system is shifted by 10′ in the longitude direction first, and then the latitude direction to obtain a lapse rate value for each 10′ grid box. Over boxes including coastlines, only the surrounding land boxes are used in the smoothing. Similarly, only water surface boxes are used for smoothing ocean and lake areas near coastlines. The results yield regional BL lapse rates at a 10′ resolution for ice-free water, snow-free land, and snow/ice-covered surfaces for each of the four seasons separated by day and night.
The lapse rates for snow–ice-covered surfaces appear to have a zonal gradient, but lapse rates over Greenland are quite different than those over Antarctica, and lapse rates over the Arctic Ocean are quite different from their marine counterparts around Antarctica. To reduce the noise, the 10′ lapse rates over snow-covered areas are averaged for each 1° latitude belt over water and land, respectively, to obtain zonal lapse rates for snow- and ice-covered regions.
Monthly-mean lapse rates were created for all surfaces by linear interpolation between the neighboring seasons. The CCPRS-4 lapse rate database includes forty-eight 10′ × 10′ lapse rate maps: four maps per month over snow–ice-free land and water, respectively, for day and night separately, and 48 latitude zonal lapse rates: four per month for snow-covered surfaces over water and land, respectively, and for day and night separately.
The CCPRS normally processes data within a 32 × 32 km tile (Minnis et al. 2011). If the tile contains coastal pixels, then the coastal lapse rates are calculated with water and land lapse rates in the tile by weighting the relative number of water and land pixels in the tile. Because the lapse rates are derived from Aqua, the lapse rates for Terra during daytime are assumed to be the lapse rate averages between Aqua daytime and nighttime. Terra nighttime lapse rates are assumed to be the same as the Aqua nighttime lapse rates. This simple approach was taken based on the diurnal cycle of the surface temperature and BL height over land, which is relatively flat at night and varies sinusoidally during the day (e.g., Liu and Liang 2010). From the data of Liu and Liang (2010), the BL height at the Terra 1030 LT overpass, on average, is approximately halfway between that at 0600 LT and that at 1330 LT. Over water, the diurnal cycle of BL height is more variable (e.g., Liu and Liang 2010), but the value at 1030 LT is generally between the 0600 and 1330 LT values. The actual diurnal variation of Γa is unknown and could be something different than what is assumed here. Assessing that assumption is beyond the scope of this study and left for future analysis. The actual day − night lapse rate differences over a given area are generally small, so errors resulting from this assumption are also likely to be minimal.
The CCPRS retrieves Zt from the retrieved Tt using a modified temperature profile interpolated from the GEOS-5 model output. To account for the inversion height uncertainties in the estimation of Zt, the temperature profile in the model is modified between certain pressure levels using the derived lapse rates. The pressures, P1 and P2, are functions of three surface types and three latitude zones. They have constant values for the tropics (−30° < latitude < 30°) and polar regions (latitude > 60° or latitude < −60°). For midlatitudes (30° < latitude < 60° or −60° < latitude < −30°), P1 and P2 vary according to the formulas below:
where latitude is given in degrees; B2 = 650, 665, and 680 hPa; and B1 = 750, 765, and 780 hPa over land, coast, and water, respectively. Table 1 lists pressure levels, P1 and P2, for each of the three latitude zones (tropics, midlatitudes, and polar region) over three different snow-free surfaces (land, coast, and water).
The lapse rate is used to build a new temperature profile for pressures P larger than P1. For pressure levels between P1 and P2, the GEOS-5 temperature is retained if it is less than the temperature at the adjacent lower level. Otherwise, a new temperature is calculated based on linear interpolation between the GEOS-5 temperatures at P1 and P2. If the newly calculated temperature is still greater than that for the level below, then the lapse rate is used to compute the temperature at the inversion level. Thus, for P < P1, the modified sounding cannot be any warmer than the original sounding. For P < P2, the original GEOS-5 temperature profile is retained. This procedure is used because the exact location of the inversion, if it exists, is unknown, the cloud droplets may be colder than the air temperature, and it is desirable to use a realistic sounding for as much of the atmospheric column as possible. The value of Zt is set equal to the lowest height in the modified profile where the temperature T = Tt. If Tt is warmer than the greatest temperature in the profile, then Zt is set equal to the surface elevation plus 0.1 km.
Figure 3 shows an example of the GEOS-5 profile over the Indian Ocean before and after applying a modification based on a lapse rate given in [Fig. 6 for SON (Fig. 6 will be explained in detail in section 3)]. The lapse rate is used for P > P1 and linear interpolation between the new temperature at P1 and the GEOS-5 temperature at P2 was used to modify the temperatures between those levels. The actual lapse rate used for a given time and location will vary as the results show in later sections. In this instance, the lapse rate is used up to P = P1 even though its profile intersects the GEOS-5 temperatures at P > P1. If the intersection occurred for P < P2, then the GEOS-5 profile would have remained unmodified. The modified profile is not intended to be more realistic than the GEOS-5 profile, but rather is only to be used in assigning height to the cloud top from the retrieved effective temperature.
To further demonstrate how the technique assigns cloud heights, Fig. 4 shows temperature T and dewpoint Td profiles from analyses and modified lapse rates. For purposes of illustration only, the analyses are from the hourly Rapid Refresh (RAP; Zhu et al. 2013) NWP model and cloud-top temperatures were retrieved from Geostationary Operational Environmental Satellite (GOES) imagery using the same technique as CCPRS. Cloud-top heights Zt′ and Zt were retrieved using the RAP and modified profiles, respectively. The lapse rates were taken from the results given in the next section to aid the description of the methodology. The RAP and modified profiles off the Southern California coast (Fig. 4a) are dramatically different because of the presence of a strong inversion. The RAP temperature profile is quite similar to the average July profile along the California coast (Lin et al. 2009). This particular case coincides with a CALIPSO overpass that indicates the cloud-top height at ~300 m. In the RAP profile, the value of Tt = 290.9 K is found only above the inversion base at an altitude of 1.57 km. As discussed earlier, this type of Zt′ result is typical for all varieties of model analyses and balloon soundings (e.g., Garreaud et al. 2001) when clouds occur under strong inversions. Applying the lapse rate of 8.8 K km−1 yields a height of 0.11 km, which is too low, but much closer to the CALIPSO value.
For boundary layers lacking a strong inversion, presumably the apparent lapse rate is closer to the actual lapse rate in the part of the lower troposphere that is only marginally affected by surface heating. Over land, the surface temperature can swing dramatically over the course of the day, which would produce large diurnal oscillations in the lapse rate measured relative to the surface temperature. This can be seen in the profiles of Figs. 4b and 4c taken over a location south of Montgomery, Alabama, at night and 13 h later during the afternoon, respectively. At night, above the shallow surface-layer inversion near 0.35 km, the temperature drops at ~5.9 K km−1 up to 4 km, while the use of the surface temperature as Ts in Eq. (1) would yield 5.1 K km−1. By afternoon, the surface-layer inversion is long gone and the lapse rate between 4 km and the surface has increased to 7.5 K km−1 and the inferred temperature at any given height up to 4 km is overestimated relative to the actual profile. By averaging the surface temperature over 24 h, the diurnal swing is diminished and the apparent lapse rate more closely matches the actual lapse rate above the surface layer. Here, night and day apparent lapse rates from the CALIPSO–MODIS results in the next section are 6.1 and 5.8 K km−1, respectively. So, instead of being larger than the nighttime value, the daytime value of Γa is slightly smaller. In both instances, the value of Zt retrieved from the modified lapse rate is close to Zt′ from the RAP because the profiles above 1 km are nearly identical.
As seen in Fig. 4a and discussed above, NWP analyses do not reproduce cloud-top temperatures particularly well in the presence of strong inversions. Low stratiform cloudiness is not confined to the maritime subtropical highs. It often forms under inversions over midlatitude and polar land areas during colder months and can occur under surface-layer inversions in any location. Using the modified lapse rate can help determine the cloud height in those conditions, while still providing a reasonable lapse rate in inversion-free conditions. Of course, the boundary layer is not always so simple. Multiple inversions, frontal passages, and other phenomena affect both the surface and cloud temperatures, producing errors in the Zt retrieval that use of the simple lapse rate will be unable to avoid. The overall benefit of using modified instead of analysis profiles is explored in section 5.
To provide context for the lapse rates, the mean cloud-top heights from CALIPSO are plotted in Fig. 5 for the four seasons. Over ocean areas, an east-to-west gradient is common to all seasons except over the tropical convergence zones and the midlatitude storm tracks. The lowest clouds, on average, have Zt < 0.8 km. They mainly occur off the west coasts of North America and Africa, in the seas around Kamchatka during the summer, and over the Arabian Sea during spring. In addition to the convergence zones, the highest tops, Zt > 2.4 km, are evident off the tropical and subtropical east coasts of the continents during particular seasons. The mean low-cloud heights over the Arctic Ocean are mostly between 1.6 and 2.0 km. From a year of CloudSat and CALIPSO data, Kubar et al. (2011) found a relatively flat gradient in low-cloud Zt between Southern California and 10°S, 180°W during winter that steepened during the summer because of lower values near the coast. That seasonal change is also evident in Fig. 5 and, to some extent, in average BL heights from model reanalyses (von Engeln and Teixeira 2013). The mean low-cloud heights over the Arctic Ocean are mostly between 1.6 and 2.0 km. Over land, the clouds are much higher because of greater surface altitudes (e.g., southern Asia, western North America) and deeper convective development (e.g., Amazon basin, central Africa). The smallest average low-cloud heights occur over the eastern United States, eastern Europe, and northern Asia during winter and fall.
Figures 6 and 7 show the seasonal mean snow-free lapse rate maps for daytime and nighttime, respectively. These figures reveal that nearly all ice-free water lapse rates are between 5 and 9 K km−1 with local variations. Areas lacking any samples are filled with the average lapse rate for the particular surface type. During the daytime, the larger lapse rates (Γa > 8 K km−1) over water are mainly found under subtropical high pressure systems where the lowest MS decks occur. Additionally, during DJF some pockets of Γa > 8 K km−1 are found east of North America (Fig. 7) and Asia (Fig. 6), and east of Australia (Fig. 7) during JJA and SON, presumably because of cold air flowing over relatively warm water. The smallest marine lapse rates, between 5 and 6 K km−1, are seen over the tropics with a seasonal variation marked by a northerly shift during JJA and a return southward during the winter. They generally coincide with higher cloud tops and are likely representative of nearly moist adiabatic profiles throughout the vertical column of the troposphere. During boreal summer, some of the smaller lapse rates occur off the east coasts of the northern continents. At night (Fig. 7), the maritime lapse rates increase in nearly all locations. The total area having Γa < 6 K km−1 shrinks, while Γa > 8 K km−1 becomes more common. Using a similar approach, Wu et al. (2008) found a mode lapse rate of ~8 K km−1 over the southeastern Pacific for January 2007 with a larger value at night than during the day. For that same region, the mean lapse rates are comparable to the earlier findings with means of 7.4 and 7.8 K km−1, during the day and night, respectively. The diurnal changes are seen more clearly in Fig. 8, which plots the mean night minus day differences. The magnitudes of the maritime night minus day differences are mostly less than 0.5 K km−1. A few areas of small nocturnal decreases in Γa are seen during winter over some of the subtropical marine stratus regimes and the Arabian Sea. These night minus day differences are discussed in section 5a.
Over land during the day (Fig. 6), the lapse rates are between 3 and 7 K km−1, smaller than their water counterparts. Overall, the lapse rates are smallest in the boreal winter during both day and night, and greatest during MAM and JJA. Similar to the marine areas, the lapse rates generally increase at night (Fig. 7), in some cases by more than 2 K km−1. The range shifts upward to between 4 and 8 K km−1. In some regions, such as central North America during winter, Γa drops from day to night, while increasing over other areas, such as southern Africa during DJF (Fig. 8). The greatest diurnal changes mostly occur over desert regions (Fig. 8). These seemingly large diurnal changes in the mean lapse rates are primarily due to the use of the 24-h mean surface temperature as illustrated using Fig. 4. The use of the near noon surface temperature would raise the lapse rates considerably during the day, while use of the true nighttime surface temperatures would slightly reduce the nocturnal lapse rates. The negative night-to-day changes in Γa (Fig. 8) over land are most extensive in mid- and high northern latitudes during the boreal winter and autumn when the atmosphere is more stably stratified. The change is negative in all seasons over northern North America. Otherwise, the night minus day Γa difference is mostly positive.
Mean seasonal lapse rates were computed from the 10′ regional data for each of the 19 modified IGBP surface types. Table 2 lists the IGBP types along with seasonal mean lapse rates and their spatial variations (sv, in the parentheses) during day and night. Results for a condensed set of land types, desert (IGBP = 7 and 16), grass (IGBP = 6, 8–14, and 18), and forest (IGBP = 1–5), are also provided. The ice-free mean daytime water (IGBP = 17) lapse rates range from 6.8 K km−1 during JJA up to 7.0 K km−1 during SON. At night, except for the minimum of 7.1 K km−1 during JJA, the lapse rates are similar in all seasons with a value of ~7.3 K km−1. Overall, the mean nocturnal Γa, 7.22 K km−1, is ~0.3 K km−1 greater than that during the day. The regional standard deviations, indicated as the spatial variation in Table 2, range from 0.4 to 0.7 K km−1.
The lapse rates over snow-free land surfaces are significantly smaller than their marine counterparts for both day and night (Table 2). During daytime, the mean IGBP Γa values over land surfaces generally vary by only 0.9–1 K km−1 among all of the surface types. At night, the means vary by as little as 0.5 K km−1 (summer) up to 0.9 K km−1 (autumn). The standard deviations about the regional means among all IGBP land types vary from 0.2 to 0.8 K km−1. The seasonal variations are also very similar among the different surface types with maximum values typically occurring during JJA or MAM. The smallest seasonal ranges (~0.3 K km−1) are found over evergreen broadleaf forests (IGBP = 2), while the greatest range (~1.9 K km−1) is seen over permanent wetlands (IGBP = 11). This large range may be an artifact of sampling as most of this surface type is found in high latitudes where chances of being snow free are small during winter. More typically, the seasonal range is ~0.8 K km−1. This is seen in the grouped averages for desert, grass, and forest, which have seasonal changes between 0.7 and 0.9 K km−1. On average, the nighttime lapse rates over land are 6.2 K km−1 compared to 5.5 K km−1 during the daytime. For coastal areas, both snow–ice-free land and water values, indicated as IGBP = 19_L and 19_O, respectively, are listed in Table 2 and available in the database. The 19_O values are greater than the typical land values, but less than the water values. The 19_L values are more similar to the average land values. As noted earlier, when the CCPRS is applied to a tile of imager data, the water and land pixels within the tile use the lapse rates computed for nearest water and land regions, respectively, and not the IGBP mean values.
The seasonal distributions of regional mean lapse rates computed over ice- and snow-covered surfaces are presented in Figs. 9 and 10 for day and night, respectively. During the colder months in each hemisphere, Γa, in the mean, is often less than 5 K km−1. The smallest values are seen over eastern Siberia and over western Antarctica. The greatest values tend to occur over the most equatorward snow-covered surfaces. Overall, the patterns are highly variable. To reduce the regional noise, zonally averaged lapse rates were calculated; the results are plotted in Figs. 11 and 12 for water and land surface, respectively. The zonal-mean 2006–07 and 2009–10 lapse rates (K km−1) over ice-covered water are plotted for the 4 seasons: winter (black solid circles), spring (green solid circles), summer (red solid circles), and fall (yellow solid circles). The two graphs on the left and the pair on the right are from daytime and nighttime, respectively. The top and bottom pairs of plots are for the Northern and Southern Hemispheres, respectively. During nighttime (right), Γa decreases in the poleward direction in each hemisphere for both ice- (Fig. 11) and snow-covered (Fig. 12) regions presumably because the atmosphere becomes more isothermal during the polar night. The smallest lapse rates generally occur during the respective winter hemisphere, although some exceptions are evident. For example, the JJA values over the Northern Hemisphere ocean (Fig. 11, top right) are slightly less than the DJF values at 80°N. During daytime, the zonal gradients are generally weak, except for Antarctica during MAM.
The apparent lapse rates computed here were designed for use with sea surface skin and 24-h mean land surface air temperatures from the GEOS-5 model analyses. So, caution should be used when applying them. Any differences between those same values from other sources and GEOS-5 will introduce some errors into a given retrieval. Evaluation of the errors in retrieved heights using other weather analysis air temperatures is beyond the scope of this paper. Because Tt is defined differently for clouds with optical depths greater than or less than 6, Γa probably corresponds, on average, to a temperature between Tc and Tt for most areas since clouds with a full range of optical depths were included in the analyses. For optically thin clouds, Tt is roughly 0.5 K less than Tc, which corresponds to ~70 and 100 m for Γa = 7.0 and 5.0 K km−1, respectively. Thus, the use of two cloud-top definitions introduces an uncertainty from approximately ±35 to ±50 m on top of the ±15 m CALIPSO cloud-top height uncertainty. Errors in the retrieved values of Tt and in Ts will translate to additional uncertainty in the retrievals. The day-to-day variability in the lapse rates is also not captured in the mean values, so it will increase the uncertainties in a given retrieval. Finally, in addition to being quite different from conventional lapse rates, the values given here are only for BLs capped by a single-layer cloud as well as can be determined from CALIPSO. The BL temperature structure can be different for clear or multilayered cloud conditions, or for clouds beneath the low cloud observed by CALIPSO. However, the CCPRS-4 uses the same BL lapse rates regardless of the actual vertical structure.
a. Relationships between apparent and conventional lapse rates
Because of the differences between the conventional and apparent lapse rate definitions, it is not possible to directly compare the results with the standard lapse rates. However, it is important to understand how these results compare to other relevant lapse rate studies. Dong et al. (2008) found that an apparent lapse rate of ~5.1 K km−1 would be optimal for estimating low-stratus-cloud heights over the Atmospheric Radiation Measurement Program Central Facility in north-central Oklahoma. This value is considerably smaller than the 7.1 K km−1 value used for CCPRS-2. The mean found here for that location is 5.0 K km−1, indicating that CCPRS-4 should yield a more accurate low-cloud height at that location.
Over the southeastern Pacific, Zuidema et al. (2009; hereafter, Z09), in their Eq. (2) determined from October radiosonde profiles, found that the standard mean BL lapse rate could be parameterized as a function of cloud-top height,
where Zt is given in kilometers. For areas with Zt = 0.8 km, Eq. (7) yields a lapse rate of 7.6 K km−1, while for Zt = 1.6 km, Γα = 7.2 K km−1. In Fig. 6 (SON) and Fig. 7 (SON), the values of Γα vary from ~9 K km−1 near the Chilean coast to a value of ~8 K km−1 near the edges of the domain used by Z09. The magnitude of the differences between the current results and those from Eq. (7) can be explained to some extent by the corrections applied to the data by Z09. Despite the differences in magnitude, the dependence of Γ on Zt in Eq. (7) appears to be similar to that found here. The lowest and highest low clouds over ocean are found primarily in the MS regions and the tropics, respectively (Fig. 5). The smallest lapse rates over ocean are found in the tropics and the greatest in the MS areas. It is clear that over the southeastern Pacific, Zt increases with distance from the South American coast during both day and night (Fig. 5). In both Figs. 6 and 7, Γa decreases with distance from the coast as Zt rises. The parameterization of Wood and Bretherton (2004), based on the apparent lapse rate, also indicates that Γa is negatively correlated with Zt for marine stratus and trade cumulus.
The differences between the standard and apparent lapse rates are primarily due to the discrepancies between the respective surface temperatures used and between the retrieved cloud-top temperatures and the ambient air temperature at cloud top. Z09 reconciled the differences by adding a constant value to the retrieved cloud-top temperatures to bring them into agreement with the mean ambient air temperature at cloud top over the southeastern Pacific. Furthermore, they added a 0.5°C correction to the sea surface temperature to bring it in alignment with the typical air temperature above the surface. Whether those corrections are applicable around the globe has not yet been demonstrated. Painemal et al. (2013) have suggested that the air − cloud temperature difference is due to cooling of the droplets relative to the air as a result of evaporation and radiative emission. While it has not yet been definitively demonstrated that those processes are responsible for the temperature differences, they suggest that the air-minus-cloud temperature difference would vary with the amount of mixing and entrainment and inversion strength at cloud top and the atmospheric humidity above cloud top. Since those quantities vary around the globe, the cloud − air temperature correction would likely be different in locations beyond the southeastern Pacific. However, the cloud-top radiative cooling for all clouds increases at night because it is no longer offset by the absorption of solar radiation. These factors together could be responsible for the general increase in the apparent lapse rates at night.
b. Assessment of overall height errors and comparison with other techniques
One way to determine if those constant corrections apply universally and to determine how accurately cloud-top heights can be determined using lapse rates from any source is to compare the resulting cloud-top heights with those determined by CALIPSO. For those purposes, snow-free CCCM MODIS data from October 2007 and January 2009—months not used to construct the Γa database—are analyzed using six different lapse rates and compared with the corresponding CALIPSO cloud-top altitudes. Except for the parameterization by Z09 and the GEOS-5 soundings, cloud-top heights are estimated from MODIS data using the CCPRS-4 algorithms, which employ the following formula:
where Γa is the BL lapse rate for the particular location. The values of Γa were supplied by the regional lapse rates for CCPRS-4, the zonal lapse rates from Sun-Mack et al. (2008) are denoted as CERES_zonal, CCPRS-2 has a constant value of 7.1 K km−1, and the MODIS Collection 6 zonal lapse rates (Baum et al. 2012) are denoted as MODIS-6. For the MODIS-6 retrievals, Tt and Ts were replaced by the observed and modeled clear-sky 10.8-μm brightness temperatures, respectively. The MODIS-6 values of Γa are generally smaller than those used here because the above-cloud humidity tends to diminish the differences between the observed cloudy and modeled clear temperatures relative to (Ts − Tt). The parameterization of Z09,
is used to estimate cloud-top heights directly from the retrieved cloud-top and sea surface temperatures. Cloud-top height was also found directly from the GEOS-5 soundings by determining the lowest altitude where Tt could be found in the temperature profile. Linear interpolation between the GEOS-5 soundings was used to construct the profile at the time of the CALIPSO overpass. Because they were designed for retrievals over water, no results are shown for the Z09 parameterization and MODIS-6 over land.
1) Differences at the pixel level
The instantaneous pixel differences between the MODIS and CALIPSO retrievals for October 2007 are summarized in the histograms plotted for daytime snow-free scenes in Fig. 13 and for snow-covered scenes in Fig. 14. The summing interval for the histograms is 0.20 km centered on zero. Table 3 provides the pixel means and standard deviations of the differences (SDD) for both October 2007 and January 2009. In Fig. 13, the CCPRS-4 (black) and CERES_zonal (gold) have very similar distributions over water during the day, with peaks near 0.1 km. The CCPRS-2 peak (red) is near 0.3 km over water and about −0.2 km over land. Over water, the GEOS-5 distribution is skewed in the positive direction from a mode value of roughly −0.3 km. Over land, the differences are more normally distributed with a maximum at ~0.2 km. A single mode near −0.1 km is seen for the Z09 cloud-top heights over water, while the MODIS-6 heights are peaked near 0.3 km. The MODIS-6 distributions over water are much like those presented by Baum et al. (2012), while the GEOS-5 differences are close to those given by Baum et al. (2012) for the MODIS Collection 5 differences with CALIPSO. Similar results are seen at night (not shown) for all of the methods, although some of the peaks shift, particularly those for Z09 and the CERES_zonal approaches.
Over water, the mean differences (Table 3) are all within ±0.11 km for CCPRS-4. Other methods yielding values in that range include Z09 at night and CCPRS-2 during daytime for both months, MODIS-6 during January daytime, and CERES_zonal for 2 of the 4 time combinations for snow-free scenes. For a given time period, the CCPRS-4 yields the smallest SDDs (~0.65 km) followed by Z09 and CCPRS-2 (~0.68 km), CERES_zonal (~0.71 km), and MODIS-6 (~0.81 km). The largest biases (>0.20 km) and SDDs (0.89–0.98 km) all result from the use of the GEOS-5 profiles. The largest SDDs, ~0.65 km, are found for the GEOS-5 and MODIS-6 cases. Overall, the CCPRS-4 and GEOS-5 methods yield the smallest and greatest RMS differences, respectively.
Considering snow-free land areas only, the greatest absolute mean differences are found for CCPRS-2 (−0.47 km), which also produces the smallest SDDs (0.85 km). CCPRS-4 yields the smallest differences (−0.04 km) and slightly larger SDDs (~0.88 km). The GEOS-5 gives mean differences exceeding 0.20 km and an average SDD of ~1.09. In between the CCPRS-4 and GEOS-5 results are the average mean and SDD of the CERES_zonal lapse rate technique. Again, the CCPRS-4 and GEOS-5 methods yield the smallest and largest RMS differences, respectively.
Over snow surfaces (Fig. 14), the CERES_zonal differences are peaked at large positive values both day and night with a skew toward negative values. Although the GEOS-5 results are similarly skewed at night, they are more normally distributed during the daytime. Both CCPRS values are normally distributed with peaks at ~0.1 km during the day. At night, the CCPRS-4 curve shifts to a mode near 0.0 km (Fig. 14b). In general, these distributions are similar in width to their land snow-free counterparts, as confirmed by the relative magnitudes of the biases and SDDs in Table 3. Although the CCPRS-4 approach reduced the snow-scene biases relative to those for either the CERES zonal or CCPRS-2, the average differences are still large with an average magnitude of 0.17 km, but yield a mean of 0.02 km for Zt when both periods are considered. A mean bias of nearly zero is obtained using the GEOS-5, but it is the result of a 0.22 km overestimate at night balanced by a 0.15 km underestimate during the day. Except for daytime results during January when the GEOS-5 value is the least, the smallest RMS differences are found using the CCPRS-4 approach over snow surfaces.
2) Regional differences
The pixel difference statistics provide a measure of how accurately Zt can be retrieved for any given observation but do not reveal if there is a geographical dependence of the accuracy. For weather and climate applications, it is desirable to know if the uncertainties in the retrievals are randomly distributed around the globe. Figures 15 and 16 plot the mean regional cloud-top height differences, MODIS minus CALIPSO, for day and night, respectively, using the six different methodologies described above for October 2007. The CCPRS-4 analyses (Figs. 15a and 16a) yield differences that are generally between −0.2 and 0.2 km and appear somewhat randomly distributed. Over land, the scatter in the differences appears to be larger. At night, there are fewer data points, apparently because of the typical nocturnal low-cloud minimum over land convective areas. The GEOS-5 differences (Figs. 15b and 16b) generally exceed 0.8 km at all times of day over the MS domains with a mixture of over- and underestimates of Zt over other marine areas and land regions. Over MS regimes, the CCPRS-2 constant lapse rate tends to overestimate Zt by 0.0–0.4 km with better agreement over much of the remaining ocean areas. Over land, CCPRS-2 (Figs. 15c and 16c) yields values that are frequently too low by 0.8 km or more during the day and by smaller amounts at night. The CERES zonal lapse rates (Figs. 15d and 16d) produce significant gradients in the differences over the MS domains with the greatest overestimates near the coast and only slight underestimates in the trade cumulus areas. The parameterization of Z09 yields small (less than 0.2 km) underestimates of Zt over the MS regions (Figs. 15e and 16e) that increase in the trade cumulus areas, particularly during the day. The MODIS-6 differences (Figs. 15f and 16f) mostly range between 0.2 and 0.8 km over the MS regions and are closer to 0.0 km over the North and South Pacific. Large underestimates (<−0.8 km) are evident in many of the trade cumulus regions. The differences are similarly distributed during January 2009 (not shown).
The regional differences for October 2007 and January 2009 are summarized in Table 4. Over water, the regional mean differences (Table 4) are within ±0.15 km for most of the methods, except for GEOS-5 during October, the CERES zonal during January, and Z09 daytime for both months. The water-surface regional SDDs are less than 0.50 km for CCPRS-4, CCPRS-2, and Z09 for both months, while they are less than 0.50 km only during January 2009 for the CERES zonal data. The largest SDDs, ~0.65 km, are found for the GEOS-5 and MODIS-6 cases. As seen in Figs. 15e and 16e, the Z09 approach works well over MS areas but tends to underestimate Zt substantially in less stable regimes. Thus, its results are characterized by relatively small SDDs and significant regional negative biases. This regional change suggests that the air − sea temperature differences and possibly the air minus cloud temperature differences used in the Z09 parameterization change from the stable MS regimes to the less stable trade cumulus areas. Additionally, since the clouds tend to be smaller, there may be effects of partially filled pixels on the retrieved temperatures that could impact the application of the parameterization in trade cumulus areas. The MODIS-6 zonal lapse rate methods tends to have relatively small biases on a global average basis but larger SDDs because of relatively large positive regional biases over MS regions balanced by comparable negative biases over other areas (Figs. 15f and 16f). Similar behavior is seen in the October results for the CERES zonal statistics, but not for the January results. Zonal lapse rates capture the mean zonal and global differences well but cannot resolve the changes in the lapse rates from MS regions to warmer boundary layers. Similarly, the CCPRS-2 constant lapse rate yields both relatively small biases and SDDs but at the expense of regional biases, as seen in Figs. 15c and 16c. However, the regional biases are noticeably smaller than either of those for GEOS-5 and the two zonal lapse rates. As seen for the mean pixel differences, the CCPRS-4 produces the smallest RMS regional differences.
Seasonally averaged, regional apparent lapse rates were developed using 2 years of combined CALIPSO cloud-top heights, GEOS-5 water surface skin and 24-h averaged land air surface temperatures, and liquid water cloud-top temperatures retrieved using the CCPRS-4 algorithm applied to collocated A-Train Aqua–MODIS L1 data. A database of monthly averaged apparent lapse rates was created by interpolation between the seasons. This database includes monthly regional lapse rate maps on a 10′ grid over the snow–ice-free water, coast, and land areas, as well as monthly-mean zonal lapse rates over snow-covered surfaces, for both daytime and nighttime. This lapse rate database is used in the CCPRS-4 to determine low-cloud heights from cloud-top temperatures. These apparent lapse rates differ from standard lapse rates because the temperatures that define them are different.
The apparent lapse rates are greatest over marine stratus regions, decreasing westward from the coasts as found in previous studies. Over water areas in general, the locations of the smallest lapse rates vary seasonally but tend to occur off the east coasts of the continents during the warm season and in tropical convergence zones. The lapse rates shift systematically to slightly greater values from day to night. As defined, the apparent lapse rates over land are typically smaller than their water counterparts with the greatest values during the warm seasons. Over ice- and snow-covered areas, the zonal-mean apparent lapse rates tend to decrease toward the poles.
It is clear that use of the regional lapse rates reduces the errors in the low-cloud-top heights inferred from cloud-top temperature retrievals compared to any currently available technique. While the other methods can, in some cases, provide instantaneous errors comparable to those determined using the regional lapse rates, they cannot capture the regional variability and thus introduce artificial gradients into the cloud-height field. The use of the regional lapse rate approach minimizes the introduction of such gradients but cannot, like all of the techniques, eliminate the temporal variations in the boundary layer lapse rates that would be necessary to reduce the instantaneous errors beyond the 0.65 and 0.88 km found here for water and land, respectively. Additionally, the errors determined here from the CALIPSO comparisons only considered 2 months of independent data and only for single-layer cloud systems. While there is no reason to expect the errors to differ much from those reported here, the regional lapse rate method does not account for any systematic or interannual long-term changes in the apparent lapse rates. Thus, data using other years and months should be examined to determine if the current findings are robust in the long term. A more complete error assessment should also consider inclusion of all cloud types. Because that is a complex issue involving multilayered clouds, it must be the focus of future research.
Thanks are given to the three anonymous reviewers for their helpful comments. This research was supported by the NASA CERES Project. The CCCM data were obtained at http://ceres.larc.nasa.gov/compare_products-ed2.php. The GOES and Rapid Refresh analyses were acquired at the NASA Langley Satellite Imagery and Cloud Products Page: http://cloudsgate2.larc.nasa.gov/index.html.