Abstract

Lookup tables for estimating the cloud-top height and visible optical thickness of upper-tropospheric clouds by the infrared brightness temperature TB at 10.8 μm (T11) and its difference from TB at 12 μm (ΔT11–12) measured by a geostationary satellite are presented. These lookup tables were constructed by regressing the cloud radar measurements by the CloudSat satellite over the infrared measurements by the Japanese geostationary multifunctional transport satellite MTSAT-1R. Standard deviations of measurements around the estimates were also displayed as an indicator of the ambiguity in the estimates. For the upper-tropospheric clouds with T11 < 240 K, the standard deviations of the height estimations were less than 1 km. The dependences of the estimates of cloud-top height at each point in T11−ΔT11–12 space on latitude, season, satellite zenith angle, day–night, and land–sea differences were examined. It was shown that these dependences were considered uniform in the tropics except for the region with large satellite zenith angle. The presented lookup tables can provide hourly estimates of cloud-top height and optical thickness at a specified location and are fairly useful in comparing them with ground-based observations such as vertical profiles of humidity and/or wind.

1. Introduction

Cloud-top height is one of the crucial cloud parameters that provide information on the vertical structure of cloud water content. In field campaigns aiming mesoscale cloud systems, the cloud-top heights are needed to compare between the vertical profiles of ground-based measurements such as wind and humidity and those of cloud condensates (e.g., Nishi et al. 2007). Cloud-top heights are also required in studies that describe the temporal evolution of cloud parameters for long-lived cirrus clouds (e.g., Mace et al. 2006). For such purposes, measurements from a geostationary satellite that observes a wide area in a short time interval are useful to estimate the cloud-top height. Estimation by geostationary satellite measurements is quite useful to assess the behavior of cloud clusters with the scale of a few hundreds of kilometers that are numerically simulated with global cloud resolving model (e.g., Inoue et al. 2008).

Hamada et al. (2008; hereinafter referred to as H08) showed the lookup table for estimating the cloud-top height by the two brightness temperatures TB at infrared split-window wavelengths measured by the fifth Geostationary Meteorological Satellite (GMS-5). Their lookup table was constructed by regressing the cloud-top heights that were determined from shipborne cloud radar measurements in terms of two TB values. The presented lookup table, however, was limited to the nonrainy clouds, since ground-based cloud radar is inadequate to determine the cloud-top heights of rainy clouds because of heavy signal attenuation by precipitation particles (Lhermitte 1990). In addition, their analysis period and domain were insufficient to assess the dependencies of the season and geographical area on the estimated cloud-top height.

The CloudSat satellite (Stephens et al. 2002) launched on April 2006 carries a cloud radar and provides the information on the cloud-top height without concern for the existence of precipitation. However, the CloudSat swath is narrow (∼1.4 km) and observations are conducted only 2 times per day (0130 and 1330 local time). Therefore, for the purpose of monitoring a specific region or cloud system in a short time interval of ∼1 h, indirect methods that use the measurements by geostationary satellite are required to estimate the cloud parameters.

There have been several studies on the estimation of cloud parameters using a number of satellite measurements at near-infrared and/or infrared wavelengths, such as the CO2 slicing method (Menzel et al. 2008). Some of those have been applied to some geostationary satellites such as Meteosat Second Generation (Thies et al. 2008). Measurements by the Japanese geostationary Multifunctional Transport Satellite (MTSAT)-1R are important for examining the convective activities over the Maritime Continent that influence the climate on various temporal and spatial scales through pronounced cloud activities. However, MTSAT-1R unfortunately does not have the number of channels required to use these infrared multichannel methods. Estimation methods that use only infrared measurements and are applicable to MTSAT-1R are limited to such as the split-window method (Inoue 1985, 1987), which uses two measurements at infrared split-window wavelengths (∼11 and ∼12 μm), and the H2O-intercept method (Szejwach 1982), which uses two measurements at water vapor (∼6.8 μm) and infrared wavelengths (∼11 μm). In this study, we construct the lookup tables for estimating cloud-top height and visible optical thickness based on the split-window method, which is less affected by the variation of water vapor content in the atmosphere. It is also important to estimate the cloud microphysics such as the effective radius and phase of cloud. Although these characteristics could be inferred indirectly by, for example, estimating beta ratio (Inoue 1985; Heidinger and Pavolonis 2009), we chose the cloud-top height and visible optical thickness as the prior parameters since only two independent measurements are used in the split-window method.

The split-window method uses two brightness temperatures at infrared window wavelengths, 10.8 and 12 μm (hereinafter referred to as T11 and T12, respectively). There are two predominant advantages of using T11 and T12: to be applicable to almost all the recent geostationary satellites as well as MTSAT-1R and to be available during both daytime and nighttime. At split-window wavelengths, the radiative transfer equation for the ground surface and a single-layer “cloud” without geometrical thickness can be simplified as follows (hereinafter referred to as the simplistic model):

 
formula

where Iiobs, Iiin, and Iicld, are the radiance received by the ith channel of the satellite, the radiance entering the cloud base from the ground through the lower atmosphere, and the radiance emitted by the cloud that is assumed to be equal to the Planck blackbody radiance at the cloud temperature. Here τi is the optical thickness of the cloud at the ith channel. The extinction coefficients for water at 12 μm are larger than those at 10.8 μm in all of the solid, liquid, and gaseous states. Therefore, the difference between the two brightness temperatures, ΔT11–12 = T11T12, usually takes a positive value related to cloud parameters in the simplistic model, and the cloud temperature and optical thickness each can be described as the function of T11 and ΔT11–12 (e.g., Cooper et al. 2003). The corresponding cloud-top height is estimated by matching the cloud temperature to the vertical temperature profile of local atmospheric sounding or objective analysis. Based on these facts, a number of methods for the estimation of cloud-top height and optical thickness have been proposed (e.g., Katagiri and Nakajima 2004; Minnis et al. 1998). However, validation using observational data is not sufficient, mainly because of the difficulty in direct observation of nonrainy clouds such as cirrus.

In the case of simplistic model-based estimation of the cloud-top height and optical thickness with two split-window TB measurements, the rest of the cloud parameters, such as cloud coverage and shape and size distribution of cloud ice, which are related to optical thickness, remain a priori parameters. It is essential to adequately determine such parameters for estimating the cloud-top height and optical thickness accurately, since the uncertainties in the cloud-top height and optical thickness expected from models that are based on the simplistic model are mainly caused by these a priori parameters (Stephens and Kummerow 2007). However, it is difficult to determine these parameters since they are highly variable in every cloud and hard to obtain by direct measurements over large areas and long periods. In this study, the observation-based lookup tables are constructed by statistical method where the 2-yr measurements by the cloud radar on board the CloudSat satellite are regressed over the split-window measurements by the geostationary satellite MTSAT-1R.

The paper is organized in the following manner. Section 2 describes the data used. The results are described in section 3. Discussions are presented in section 4, and conclusions are given in section 5.

2. Data

We used two TB measurements by channel 1 and 2 of MTSAT-1R. Spectral response function for each channel is centered on 10.8 and 12.0 μm in the infrared window region, respectively. The horizontal resolution of the original data is ∼4 km at the nadir (0°, 140°E). We used the hourly data gridded on 0.05° in both longitude and latitude. The brightness temperature resolution is ∼0.1 K at TB = 300 K, and it is slightly coarser at lower temperatures, ∼0.3 K at TB = 210 K. Hereinafter, the brightness temperatures at channel 1 and 2 are described as T11 and T12, respectively. We also defined the difference between T11 and T12 as ΔT11–12 = T11T12. Cloud-top height and visible optical thickness will be estimated as the function of T11 and ΔT11–12.

To determine the cloud types, cloud-top height, and visible optical thickness, 94-GHz cloud profiling radar (hereinafter referred to as cloud radar) measurements by the CloudSat satellite (Stephens et al. 2002), which was launched in April 2006, were used. Cloud radar has high sensitivity to the cloud particles, although the radar signal is heavily attenuated by the precipitation particles. Observations are made only just under the satellite with the footprint of 1.4 km × 2.5 km (cross- and along-track) and the vertical resolution of ∼240 m. Since CloudSat is sun-synchronous orbital satellite, the observation times are fixed at 0130 and 1330 local time. In this study, we used the data provided by Colorado State University (http://www.cloudsat.cira.colostate.edu/). Vertical profiles of radar reflectivity and cloud mask, and land–sea flag in 2B-GEOPROF data—cloud scenario data that include the information on cloud type and precipitation flag in 2B-CLDCLASS data—were used to estimate cloud type and cloud-top height. Optical depth data in 2B-TAU data were also used to estimate visible optical thickness. Note that the 2B-TAU optical depth data were retrieved using not only CloudSat radar measurements but also some auxiliary data from the constellation measurements by the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Aqua satellite and the global objective analysis by European Centre for Medium-Range Weather Forecasts (ECMWF; Polonsky et al. 2008).

We used a 2-yr CloudSat dataset from the beginning of July 2006 to the end of June 2008. The analysis domain was between 90°E and 170°W and between 45°S and 45°N. Within this analysis period and domain, we selected CloudSat measurements where the difference of the observation times between CloudSat and MTSAT-1R was within 60 s. If more than one CloudSat observation corresponded to an MTSAT-1R observation, temporal averaging was applied to CloudSat locations and observations. Corresponding values of T11 and ΔT11–12 measured by MTSAT-1R were obtained by linear spatial interpolation, using four grids encompassing the CloudSat location. We obtained 259 617 samples with paired CloudSat and MTSAT-1R measurements within this analysis period and domain.

Nine types of clouds (cirrus, altostratus, altocumulus, stratus, stratocumulus, cumulus, nimbostratus, deep convection, and no cloud) were stored in 2B-CLDCLASS cloud scenario data. This dataset also has four types of precipitation (liquid and solid precipitation, drizzle, and no precipitation). The cloud scenario was determined using horizontal and vertical distribution of cloud radar reflectivity (Sassen and Wang 2008; Wang and Sassen 2007). We classified the samples into the following four categories (hereinafter referred to as cloud types) by using these cloud scenario and precipitation flag data:

  • (i) rainy clouds (R type) are samples that have any cloud and at least five consecutive vertical bins with nondrizzling precipitation,

  • (ii) nonrainy high clouds (H-NR type) are samples that are not R type and have cirrus, altostratus, altocumulus, nimbostratus, and/or deep convection,

  • (iii) nonrainy low clouds (L-NR type) are samples that are not the above two types and have stratus, stratocumulus, and/or cumulus, and

  • (iv) clear sky (C type) are samples with no cloud.

There were 14 515, 79 361, 53 506, and 112 435 samples for R, H-NR, L-NR, and C type, respectively. In this study, R type was defined simply as whether the cloud precipitates, being different from H08 where it was defined as whether the precipitation reached the ground.

For each sample, cloud layers were defined by using the cloud mask value. The cloud layer was defined as the echo layer with at least three consecutive vertical bins (∼720 m) where cloud mask values were higher than 20 and the boundaries of the echo layer were at least two bins (∼480 m) away from those of neighboring echo layers. Hereinafter, the echo-top height and visible optical thickness of the uppermost echo layer are referred to as the cloud-top height and optical thickness, respectively.

We did not use the constellate lidar measurements from the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO; Winker et al. 2007) satellite, since the main subject of this study is the estimation of top height and visible optical thickness of mesoscale convective cloud systems, which consist of deep convective clouds surrounded by large nimbostratus and nonprecipitating dense cirriform cloud area (e.g., Houze et al. 1980). Because of the higher sensitivity to small cloud particles than cloud radar, lidar measurements are often used to determine the cloud-top height. The echo-top height of the lidar is expected to be more close to the “true” cloud-top height, which is determined to be the top boundary of cloud water content, than that of cloud radar. While the lidar can detect the thin cirrus clouds associated with anvils (Garrett et al. 2004), at the same time it also detects the optically thin clouds with smaller ice crystals (∼10 μm; e.g., McFarquhar et al. 2000; Iwasaki et al. 2004) that are not related with convective systems and exist in the tropical tropopause layer with large horizontal extent. In terms of estimating the cloud-top heights of the high clouds that originate from convective activity, such thin cirrus should be precluded. It is, however, difficult to completely determine whether these thin cirrus clouds are associated with convective systems. In addition, CALIPSO lidar measurements could be affected by signal noise effects in the daytime (Sassen et al. 2008).

It should be described in detail for the correspondence between the cloud-top height defined in this study and the “true” one determined as the boundary of cloud water content. Cloud mask values that determine the cloud-top heights of samples were determined by statistically processing the along-track vertical section of the returned power of cloud radar (Marchand et al. 2008). The obtained values correspond to the reliability of the detection of the spatially continuous hydrometeor field. The cloud mask values take from 0 to 40, and increasing values indicate reduced probability of false detection. In this study, the cloud radar echo with cloud mask value greater than 20 is considered as a significant hydrometeor echo. This threshold indicates the false detection rate of ∼5% for hydrometeors whose radar reflectivity is below the sensitivity limit (∼−30 dBZe). The cloud-top height that is defined as the echo-top height of cloud radar corresponds approximately to the height where the lidar optical depth accumulated from the top reaches from ∼0.15 to ∼0.25 (McGill et al. 2004). We examined the CloudSat and CALIPSO measurements for some cases and compared the differences between the echo-top heights of radar and lidar. The differences were found to be a few hundred meters but sometimes up to ∼1 km even for nimbostratus and deep convective clouds. Therefore, in strict terms, the estimates of cloud-top height in this study should be considered as the echo-top height measured by cloud radar rather than the true cloud-top height.

3. Methods and results

a. Distribution and occurrence rate of each cloud type in T11−ΔT11–12 space

The bivariate probability density function (PDF) in T11−ΔT11–12 space for each cloud type was computed and used to evaluate the estimated values of cloud-top height and optical thickness. As will be described in detail, the lookup table for estimating cloud-top height mainly depends on the latitude and satellite zenith angle of MTSAT-1R. We therefore show the results for the region between 120° and 160°E and between 15°S and 15°N (hereinafter referred to as the nadir region) to reduce the dependences of the latitude and satellite zenith angle. This longitudinal section corresponds to the satellite zenith angle of MTSAT-1R less than ∼30°. In the nadir region, there were 3000, 14 245, 4197, and 11 708 samples for R, H-NR, L-NR, and C type, respectively. The PDFs were computed by the nonparametric kernel smoothing method adopted in H08, using a one-dimensional Epanechnikov kernel in both the T11 and ΔT11–12 dimensions (Silverman 1986):

 
formula

where x and y correspond to T11 and ΔT11–12 coordinates; Xi and Yi are those of ith sample, respectively; and N is the number of samples of each cloud type. Smoothing parameters (hT11, hΔT11–12) for PDF computation were determined from the T11 and ΔT11–12 of samples by the maximum-likelihood cross-validation technique. The computed smoothing parameters were (2.86, 0.31 K), (1.39, 0.32 K), (1.15, 0.33 K), and (0.69, 0.24 K) for R, H-NR, L-NR, and C type, respectively.

Figures 1a–d show the distributions of samples and corresponding PDFs (as the common logarithm) in T11−ΔT11–12 space for R, H-NR, L-NR, and C types, respectively. As H08 pointed out, the distribution of the samples for H-NR type are broad in both the T11 and ΔT11–12 direction, while the distribution in ΔT11–12 direction for R type is narrower than H-NR type. The samples for both the L-NR and C types are concentrated in the high T11 region, and there are almost no samples in the region where T11 < 260 K.

Fig. 1.

Distributions of samples belonging to (a) R, (b) H-NR, (c) L-NR, and (d) C type defined by CloudSat radar observations. Abscissa and ordinate represent T11 and ΔT11–12, respectively (K). Colors show the cloud-top heights (km) of samples. Solid contours indicate the bivariate PDF (K−2) in T11 − ΔT11–12 space for each cloud-type sample. The PDF is shown as a common logarithm and the contour interval is 0.5 from −4.5. The percentage of samples of each cloud type is shown at the upper right of each figure.

Fig. 1.

Distributions of samples belonging to (a) R, (b) H-NR, (c) L-NR, and (d) C type defined by CloudSat radar observations. Abscissa and ordinate represent T11 and ΔT11–12, respectively (K). Colors show the cloud-top heights (km) of samples. Solid contours indicate the bivariate PDF (K−2) in T11 − ΔT11–12 space for each cloud-type sample. The PDF is shown as a common logarithm and the contour interval is 0.5 from −4.5. The percentage of samples of each cloud type is shown at the upper right of each figure.

Some of the H-NR-type samples can be found in the region with larger ΔT11–12 than H08. This is mainly because the interval between the central wavelengths in the split-window channels for MTSAT-1R is larger than that for GMS-5 used in H08. The value of ΔT11–12 at the extrema of the PDF for C type is not zero but positive. This is mainly because the absorption by the water vapor at 12 μm is stronger than that at 10.8 μm, resulting in T11 being higher than T12 because of absorption by the water vapor in the lower troposphere (Inoue 1985). Some of C-type samples can be found in the region with low T11 of ∼250 K. Visual inspection of the cloud radar measurements for all of C-type samples with T11 less than 250 K shows that there are scattered cirrus clouds near the sampled location (not shown). In such case, CloudSat may miss the clouds that exist partly in the field of view of MTSAT-1R because of the smaller footprint of CloudSat relative to MTSAT-1R.

There are many samples of R and H-NR type with negative ΔT11–12. The number of samples with negative ΔT11–12 increases in the region with lower T11. This fact indicates that there exist calibration errors in T11 and T12 measurements of MTSAT-1R and will be discussed in section 4a.

The occurrence rate for each cloud type in T11−ΔT11–12 space can be defined as the ratio of the corresponding PDF to the sum of PDFs for all cloud types (H08). Figures 2a and 2b show the computed occurrence rate for the H-NR and R types, respectively. The results are basically consistent with those of H08. Higher occurrence rates of H-NR type, over 70%, are found in the region with T11 between 220 and 270 K and large ΔT11–12. The occurrence rates for the H-NR type fall in the region with T11 > 270 K, mainly because of the higher number of the L-NR- or C-type samples (Figs. 1c,d). The occurrence rates for the R type (Fig. 2b) show higher values in regions with lower T11 and smaller ΔT11–12.

Fig. 2.

Occurrence rates of (a) H-NR- and (b) R-type samples in T11−ΔT11–12 space. The contour interval is 10%. Contours and shadings are omitted where the sum of PDFs for all cloud types shown in Fig. 1 is <10−4.2.

Fig. 2.

Occurrence rates of (a) H-NR- and (b) R-type samples in T11−ΔT11–12 space. The contour interval is 10%. Contours and shadings are omitted where the sum of PDFs for all cloud types shown in Fig. 1 is <10−4.2.

b. Estimation of cloud-top height

The successful launch of CloudSat makes it possible to determine the cloud-top height for rainy clouds as well as nonrainy clouds by the spaceborne cloud radar. By using CloudSat measurements, a lookup table for estimating cloud-top height by the split-window measurements from a geostationary satellite, which has been limited to nonrainy clouds if using ground-based radar measurements (H08), can be extended to where the rainy clouds exist in T11−ΔT11–12 space. We will here show the results for the nadir region. Cloud-top height was locally estimated by the nonparametric method adopted in H08, using the Nadaraya–Watson estimator (Scott 1992) with the same kernel as used in PDF computation:1

 
formula

where zi is the cloud-top height of ith sample and wi is the weight same as used in Eq. (2). The smoothing parameter for the cloud-top height estimation was computed from the cloud-top height, T11, and ΔT11–12 values of the samples, and determined to be (1.35, 0.32 K).

Figure 3 shows the results of the cloud-top height estimation. H08 pointed out that although only for the nonrainy high clouds, isopleths of the estimated cloud-top height tend to tilt rightward from the vertical in T11−ΔT11–12 space, and the estimates significantly depended on the ΔT11–12 values. These characteristics can also be found clearly in the region where the occurrence rates for the R-type samples show high value in the T11−ΔT11–12 space (Fig. 2b). The estimates of the cloud-top heights at the upper and lower boundary of the lookup table are 13.8 and 15.4 km at T11 of 220 K, and 11.5 and 14.2 km at T11 of 250 K, respectively. The increments of the estimates with increasing ΔT11–12 of 1 K are ∼270 m at T11 of 220 K, and ∼380 m at T11 of 250 K, resulting in the significant dependence of the cloud-top height on ΔT11–12. As shown later, the dependence of the estimates of the cloud-top height on ΔT11–12 is mainly due to the difference in optical thickness.

Fig. 3.

Estimates (color shading and thin solid contours) and standard deviations of samples (dashed contours) for cloud-top height (km) obtained by regression of the cloud-top heights of all samples over T11 and ΔT11–12. The contour intervals are 1 and 0.5 km for the estimates and standard deviations of samples, respectively. No contours or shadings are shown where the sum of PDFs for all cloud types in Fig. 1 is <10−4.2.

Fig. 3.

Estimates (color shading and thin solid contours) and standard deviations of samples (dashed contours) for cloud-top height (km) obtained by regression of the cloud-top heights of all samples over T11 and ΔT11–12. The contour intervals are 1 and 0.5 km for the estimates and standard deviations of samples, respectively. No contours or shadings are shown where the sum of PDFs for all cloud types in Fig. 1 is <10−4.2.

The standard deviations of samples (note: not the standard deviations of estimator), which show the dispersion of measurements by the cloud radar around the estimate, could be an index of the ambiguity of estimation. Note that the estimates have no bias in principle since these estimates are calculated locally by a weighted average of samples. The standard deviations of samples increase with increasing T11 in the region with T11 < 280 K. The standard deviations of samples are at most ∼1 km for the clouds with T11 < 240 K. In the region with T11 between 250 and 280 K, the standard deviations of samples rapidly increase with increasing both T11 and ΔT11–12 and take the maximal value around T11 of ∼275 K and ΔT11–12 of ∼5.5 K. This is mainly because of the mixture of C- and L-NR-type samples in this region. Figures 4a–c show the estimates and standard deviations of samples for cloud-top height at T11 of 220, 250, and 280 K, respectively, as well as the distribution of the samples used for the computation of the estimates shown in each figure. As far as the H-NR-type samples, the dispersion in the cloud-top height grows slightly larger with increasing T11. In the region with T11 > 250 K, the increasing number of C- and L-NR-type samples makes the standard deviation of samples larger in the region with higher T11. Around T11 of 280 K, the number of R- and H-NR-type samples with higher cloud top is nearly the same as that for the C and L-NR type, resulting in the significant underestimation of cloud-top height and the large standard deviation of samples.

Fig. 4.

The estimates (solid lines) and standard deviations of samples (±1 σ, dashed lines) at (a) T11 = 220 K, (b) T11 = 250 K, and (c) T11 = 280 K. The distribution of the cloud-top height of the samples that were used for the estimation (within 1.4 K from T11 shown in each figure) is also shown by dots in each figure.

Fig. 4.

The estimates (solid lines) and standard deviations of samples (±1 σ, dashed lines) at (a) T11 = 220 K, (b) T11 = 250 K, and (c) T11 = 280 K. The distribution of the cloud-top height of the samples that were used for the estimation (within 1.4 K from T11 shown in each figure) is also shown by dots in each figure.

The estimated cloud-top height is higher than the height where T11 equals the air temperature, even in the region with ΔT11–12 ≤ 0 K. This fact indicates that the upper boundary of cloud water content is considerably higher than the effective radiation temperature of cloud, even for the rainy clouds such as cumulonimbus and nimbostratus, and will be discussed in section 4b.

The results shown in Fig. 3 are for the region in the tropics with a relatively small satellite zenith angle. The lookup table that is constructed by the method adopted in this study has a dependence on the latitude and the satellite zenith angle of geostationary satellite. Even if the effective radiation temperature of cloud does not change, its cloud-top height may differ because of the latitudinal variation of the vertical profile of air temperature. In the region with large satellite zenith angle, the optical path between the ground and satellite becomes longer than in the nadir region, and the measured values of T11 and T12 are reduced independently of cloud properties. These effects may cause a systematic bias in the estimated cloud-top height at each point in T11−ΔT11–12 space.

We at first examined the dependence of the latitude on the estimates of cloud-top height by estimating the cloud-top heights separately only with the samples in the latitudinal sections with a width of 10° between 120° and 160°E. Figure 5 shows the latitudinal variation of the estimates and standard deviations of samples for cloud-top heights between 45°S and 45°N. Within the nadir region (15°S–15°N), the variations of estimated cloud-top height with latitude are small relative to the standard deviation of samples. At the higher latitudes, the estimates lower rapidly with latitude.

Fig. 5.

Latitudinal variations of the estimates and standard deviations of samples for cloud-top height. Values are obtained by regressing the cloud-top heights of samples in 120°–160°E and the latitudinal section with a width of 10°. Estimated values at (a) T11 = 210 K, (b) T11 = 230 K, and (c) T11 = 250 K are shown. Open circles, squares, and triangles indicate the estimates at ΔT11–12 = 0, 2, and 4 K, respectively. Filled marks indicate the corresponding standard deviations of samples.

Fig. 5.

Latitudinal variations of the estimates and standard deviations of samples for cloud-top height. Values are obtained by regressing the cloud-top heights of samples in 120°–160°E and the latitudinal section with a width of 10°. Estimated values at (a) T11 = 210 K, (b) T11 = 230 K, and (c) T11 = 250 K are shown. Open circles, squares, and triangles indicate the estimates at ΔT11–12 = 0, 2, and 4 K, respectively. Filled marks indicate the corresponding standard deviations of samples.

At latitudes higher than 15°, the estimates of the cloud-top height show strong seasonal variation. Figure 6 shows the seasonal variation of estimates and standard deviations of samples for cloud-top height at the latitudinal sections; the same as is shown in Fig. 5. The estimates of cloud-top height become higher and lower in summer and winter, respectively, at latitudes higher than 15°. The amplitudes of seasonal variation become larger at higher latitudes.

Fig. 6.

Seasonal variations of the estimates and standard deviations of samples for cloud-top height. Values are obtained in the same latitudinal sections as shown in Fig. 5. Estimated values at (T11, ΔT11–12) of (a) (220, 0 K), (b) (230, 0 K), and (c) (240, 2 K) are shown. Open circles, squares, and triangles indicate the estimates for the whole year, boreal summer (May–September), and boreal winter (November–March), respectively. Filled marks indicate the corresponding standard deviations of samples.

Fig. 6.

Seasonal variations of the estimates and standard deviations of samples for cloud-top height. Values are obtained in the same latitudinal sections as shown in Fig. 5. Estimated values at (T11, ΔT11–12) of (a) (220, 0 K), (b) (230, 0 K), and (c) (240, 2 K) are shown. Open circles, squares, and triangles indicate the estimates for the whole year, boreal summer (May–September), and boreal winter (November–March), respectively. Filled marks indicate the corresponding standard deviations of samples.

Next, we examined the dependence of satellite zenith angle of MTSAT-1R by estimating separately in the regions with a width of 15° between 90°E and 170°W (Fig. 7). Since it has been shown that there is a latitudinal dependence in the estimates of cloud-top height, the latitudinal range was confined within 15°S–15°N. It is evident that the estimates of cloud-top height become lower with increasing satellite zenith angle. In the nadir region (satellite zenith angle <∼30°), the variation in the estimates with satellite zenith angle are small compared to the standard deviation of samples. Out of the nadir region, the difference between the estimates at the nadir and outer boundary of the MTSAT-1R viewing field becomes slightly greater with increasing T11 and is from ∼1 to ∼2.5 km.

Fig. 7.

Zenith-angle dependences on the estimates and standard deviations of samples for cloud-top height. Values are obtained by regressing the cloud-top heights of samples in the subarea with a width of 15° in the zenith angle of MTSAT-1R. Estimated values at (a) T11 = 210 K, (b) T11 = 230 K, and (c) T11 = 250 K are shown. Open circles, squares, and triangles indicate the estimates at ΔT11–12 = 0, 2, and 4 K, respectively. Filled marks indicate the corresponding standard deviations of samples.

Fig. 7.

Zenith-angle dependences on the estimates and standard deviations of samples for cloud-top height. Values are obtained by regressing the cloud-top heights of samples in the subarea with a width of 15° in the zenith angle of MTSAT-1R. Estimated values at (a) T11 = 210 K, (b) T11 = 230 K, and (c) T11 = 250 K are shown. Open circles, squares, and triangles indicate the estimates at ΔT11–12 = 0, 2, and 4 K, respectively. Filled marks indicate the corresponding standard deviations of samples.

In addition to the dependence of latitude and satellite zenith angle, the variations in some cloud properties, such as the shape and size distribution of cloud ice, can alter the radiance measured by the satellite, even if neither the cloud-top height nor optical thickness changes (Cooper et al. 2003). Such variations in cloud properties may be caused by a difference in the formation process of the clouds between land and sea (e.g., Liu et al. 2007) and daytime and nighttime (e.g., Sassen et al. 2008). We examined the land–sea contrast in the estimates of cloud-top height by estimating the cloud-top heights separately only with the samples in land or sea areas. Figure 8 shows the estimates of cloud-top height for the land area as the deviations from the estimates for the entire area shown in Fig. 3. The estimates for the sea area are almost equal to those for the entire area, since the number of samples in the sea area is ∼94% of all. At T11 less than ∼260 K, the deviations of estimates for the land area from the entire area become higher and lower in the region with lower and higher ΔT11–12, respectively. In this region, the deviations are at most ∼500 m and less than the half of the standard deviation of samples shown in Fig. 3.

Fig. 8.

Land–sea contrast of the estimates of cloud-top height. Shading and contours show the estimates of cloud-top height by using only the land and coastal samples as the deviation from those using all samples (Fig. 3). The contour interval is 0.5 km without 0, and contours for the value of ±0.2 km are added. No contours or shadings are shown where the sum of PDFs for all cloud types in Fig. 1 is <10−4.2. Estimates were smoothed 5 times with a 3-point running mean in both the T11 and ΔT11–12 directions for better visualization.

Fig. 8.

Land–sea contrast of the estimates of cloud-top height. Shading and contours show the estimates of cloud-top height by using only the land and coastal samples as the deviation from those using all samples (Fig. 3). The contour interval is 0.5 km without 0, and contours for the value of ±0.2 km are added. No contours or shadings are shown where the sum of PDFs for all cloud types in Fig. 1 is <10−4.2. Estimates were smoothed 5 times with a 3-point running mean in both the T11 and ΔT11–12 directions for better visualization.

We also examined the day–night contrast on the estimates for cloud-top height. Figure 9 shows the estimates of cloud-top height for nighttime as the deviations from the daily mean shown in Fig. 3. The result for daytime is almost the same as those for nighttime but opposite in sign (not shown). In almost all regions in the figure, the estimates for the nighttime are equal to or a little lower than those for the daily mean. The deviations from the daily mean are at most ∼500 m for the estimates of cloud-top height higher than 13 km in almost all regions and less than the half of the standard deviation of samples shown in Fig. 3.

Fig. 9.

As in Fig. 8, but for the daytime–nighttime contrast. Shading and contours show the estimates of cloud-top height by using only the nighttime samples as the deviation from those using all samples (Fig. 3).

Fig. 9.

As in Fig. 8, but for the daytime–nighttime contrast. Shading and contours show the estimates of cloud-top height by using only the nighttime samples as the deviation from those using all samples (Fig. 3).

In summary, in the tropics within the latitudes of 15°, the estimates of cloud-top height mainly depend on the zenith angle of geostationary satellite, and those variations with all the other effects examined above are small compared to the standard deviation of samples. Therefore, in the nadir region, where the satellite zenith angle is small, all the influences examined above can be considered uniform. Out of the nadir region, the estimates of cloud-top height mainly depend on the latitude, season, and zenith angle of the geostationary satellite. For out of the nadir region, the lookup table can also be constructed by dividing the analysis region into subregions, so as to minimize the dependences described above.

c. Estimation of visible optical thickness for nonrainy high cloud

In a similar manner to the cloud-top height, visible optical thickness can be estimated by regressing the visible optical thickness of samples in terms of T11 and ΔT11–12 measured by MTSAT-1R using Eq. (3), except that visible optical thicknesses of samples are used instead of cloud-top height. Here, we will show the results using only the H-NR-type samples, since the cloud radar signal is heavily attenuated by precipitation particles, and the 2B-TAU algorithm, which uses single visible and single infrared measurements by MODIS, may have less sensitivity for clouds with very large optical thickness. The smoothing parameter for the estimation was computed from the optical thickness, T11, and ΔT11–12 values of the samples, and determined to be (1.35, 0.31 K).

The results for the nadir region are shown in Fig. 10. The estimates of the optical thickness largely increase with decreasing T11 and ΔT11–12, except in the region with high T11 and small ΔT11–12. Isopleths for the estimates where the optical thickness are less than ∼10 tend to rise with decreasing T11, and this inclination becomes larger for the smaller estimates. This fact agrees with the theoretical result of the simplistic model. The standard deviations of samples are up to ∼70% relative to the estimates in the region where the occurrence rate for the H-NR type is higher than 80% (Fig. 2a), and they are rather larger than those retrieved by some methods that use the multichannel measurements including visible channels (e.g., Cooper et al. 2007).

Fig. 10.

Estimates (shading and thin solid contours) and standard deviations of samples (dashed contours) for visible optical thickness obtained by regressing the optical thicknesses of H-NR-type samples over T11 and ΔT11–12. The standard deviations of samples are shown as the ratio to the estimates, and the contour interval is 20%. No contours or shadings are shown where the PDF for H-NR type (Fig. 1a) is <10−4.2.

Fig. 10.

Estimates (shading and thin solid contours) and standard deviations of samples (dashed contours) for visible optical thickness obtained by regressing the optical thicknesses of H-NR-type samples over T11 and ΔT11–12. The standard deviations of samples are shown as the ratio to the estimates, and the contour interval is 20%. No contours or shadings are shown where the PDF for H-NR type (Fig. 1a) is <10−4.2.

It would be interesting to see the standard deviation of cloud-top height in terms of estimated optical thickness since it is a dominant modulator of the performance in radiative transfer model-based approach (e.g., Heidinger and Pavolonis 2009). Figure 11 shows a box plot for the standard deviations of cloud-top height in terms of optical thickness estimates using paired gridpoint values in T11−ΔT11–12 space (Figs. 3 and 10). It is clearly shown that the standard deviation of samples in cloud-top height depends little on optical thickness when optical thickness is more than ∼3.5. This value can be considered a thin-cloud threshold in terms of optical thickness beyond which our split-window method may somewhat break down.

Fig. 11.

A box plot (rectangles) for the standard deviations of cloud-top height (km) in terms of the estimates of visible optical thickness (unit arbitrary) using gridpoint values of lookup tables for nadir region (Figs. 3 and 10). Only the values whose optical thickness estimates are <20 are shown. In each box the bold solid line shows the median value and the height of box shows the interquartile distance. The numbers of samples were chosen to be equal among all bins. Distribution of the gridpoint values is also shown by cross marks.

Fig. 11.

A box plot (rectangles) for the standard deviations of cloud-top height (km) in terms of the estimates of visible optical thickness (unit arbitrary) using gridpoint values of lookup tables for nadir region (Figs. 3 and 10). Only the values whose optical thickness estimates are <20 are shown. In each box the bold solid line shows the median value and the height of box shows the interquartile distance. The numbers of samples were chosen to be equal among all bins. Distribution of the gridpoint values is also shown by cross marks.

d. Application

The lookup tables presented are particularly convenient in field campaigns aiming at mesoscale cloud systems. Since cloud-top height of precipitating cloud is hard to obtain directly from ground-based observations, hourly estimates of cloud-top height by geostationary satellites are very useful in comparing with other continuous ground-based observations such as vertical wind (e.g., Nishi et al. 2007), although vertical resolution of ground-based instruments is usually finer than the 1-km accuracy of cloud-top height estimated from geostationary satellite split-window measurements. Figures 12a,b show the horizontal distributions of T11 and ΔT11–12 observed by MTSAT-1R at 0540 UTC (∼1330 local time) 11 August 2006. The corresponding horizontal distributions of cloud-top height and visible optical thickness are estimated by using Figs. 3 and 10 and shown in Figs. 12c and 12d, respectively. These horizontal maps with wide area and relatively high temporal resolution are also quite useful in assessing the results by cloud-resolving numerical models, especially in the case of large mesoscale cloud systems with horizontal scale of a few hundred to thousand kilometers (e.g., Inoue et al. 2008).

Fig. 12.

Horizontal distributions of (a) T11 and (b) ΔT11–12 observed by MTSAT-1R at 0540 UTC 11 Aug 2006. The corresponding estimated values of (c) cloud-top height (km) and (d) visible optical thickness are shown by using Fig. 3. Thin solid lines denote the coastlines. Thick solid line indicates the part of CloudSat path for cross section in Fig. 13a.

Fig. 12.

Horizontal distributions of (a) T11 and (b) ΔT11–12 observed by MTSAT-1R at 0540 UTC 11 Aug 2006. The corresponding estimated values of (c) cloud-top height (km) and (d) visible optical thickness are shown by using Fig. 3. Thin solid lines denote the coastlines. Thick solid line indicates the part of CloudSat path for cross section in Fig. 13a.

Figure 13a shows the vertical section of CloudSat radar reflectivity along the path shown in Fig. 12. Corresponding values of T11 and ΔT11–12 measured by MTSAT-1R are shown in Fig. 13b. The cloud-top heights and standard deviations of samples are estimated by using Fig. 3 and superimposed on the radar reflectivity. For comparison, the heights where T11 equals air temperature are also plotted by interpolating the temperature and geopotential height of the 40-yr ECMWF Re-Analysis (ERA-40) data in space and time. For the geometrically and optically thick cloud observed north of ∼7.3°N, the estimates of cloud-top height fairly correspond with the echo-top heights of cloud radar for both the rainy and nonrainy clouds. It is important that there is no bias of underestimation that can be seen in the estimates only by T11, especially for the geometrically and optically thick clouds with relatively higher values of ΔT11–12. Between 8.6° and 9.5°N, the values of T11 monotonically increase from ∼205 to ∼240 K at lower latitudes, and the values of ΔT11–12 also increase from ∼0.5 to ∼3 K. These changes of T11 and ΔT11–12 correspond to the shift from lower-left to upper-right region in T11− ΔT11–12 space. As a result, the change of estimated cloud-top height is less than 2 km, which is much smaller than that inferred from the change in only T11 (∼4.2 km). Since both the values of T11 and ΔT11–12 are high in the south of 7.3°N, the visible optical thicknesses are dropped to ∼2.5 (Fig. 13c) and the standard deviation of samples for cloud-top height is very large.

Fig. 13.

Satellite observations along the CloudSat path shown in Fig. 12. (a) Shadings show the cloud radar reflectivity (dBZe) observed by CloudSat. Thick solid and dashed lines show the estimates and standard deviations of samples for cloud-top height by using the lookup table (Fig. 3), respectively. Thin solid lines show the heights where the value of T11 equals air temperature by using the mean vertical temperature profile of objective analysis ERA-40. (b) Solid and dashed lines show the values of ΔT11–12 and T11 observed by MTSAT-1R along the CloudSat path, respectively. The values are obtained by linear spatial interpolation using four grids encompassing the CloudSat location. (c) Solid and dashed lines show the values of estimated visible optical thickness where the occurrence rates of H-NR-type clouds are higher and lower than 45%, respectively.

Fig. 13.

Satellite observations along the CloudSat path shown in Fig. 12. (a) Shadings show the cloud radar reflectivity (dBZe) observed by CloudSat. Thick solid and dashed lines show the estimates and standard deviations of samples for cloud-top height by using the lookup table (Fig. 3), respectively. Thin solid lines show the heights where the value of T11 equals air temperature by using the mean vertical temperature profile of objective analysis ERA-40. (b) Solid and dashed lines show the values of ΔT11–12 and T11 observed by MTSAT-1R along the CloudSat path, respectively. The values are obtained by linear spatial interpolation using four grids encompassing the CloudSat location. (c) Solid and dashed lines show the values of estimated visible optical thickness where the occurrence rates of H-NR-type clouds are higher and lower than 45%, respectively.

4. Discussion

a. Negative values of ΔT11–12 measured by MTSAT-1R

The samples that are distributed in the region with negative ΔT11–12 (Fig. 1) partly indicate that calibration errors exist in the T11 and T12 measurements of MTSAT-1R. The samples with negative ΔT11–12 were broadly distributed in the T11 direction. In the region with lower T11, the number of samples with negative ΔT11–12 increased, and the samples tend to show negatively larger values.

We evaluated the influence of the calibration error in MTSAT-1R by using the statistics on the intercalibration between MTSAT-1R infrared measurements and high-spectral-resolution sounders on board operational polar-orbital satellites, for example, the Atmospheric Infrared Sounder on board Aqua. These statistics are reported monthly by the Meteorological Satellite Center of Japan Meteorological Agency (http://mscweb.kishou.go.jp/monitoring/calibration.htm). As a result, the biases in the ΔT11–12 measured by MTSAT-1R were found to increase with decreasing TB and to be up to ∼−1 K at T11 = 210 K. This bias has little impact on our observation-based estimates of cloud-top height and optical thickness, but it may cause a large estimation error in theoretical or numerical models, which convert observed radiances into physical and radiative parameters.

b. Cloud-top height estimates around ΔT11–12 = 0 K

If the effective radiation height is not equal to the upper boundary of cloud water content, ΔT11–12 typically takes positive value. However, the estimates of cloud-top height in the region with ΔT11–12 ≤ 0 K are considerably higher than the height where T11 equals air temperature. As will be described, since the clouds that consist of large cloud ice, such as cumulonimbus and nimbostratus, dominate in this region, the value of ΔT11–12 could tend to zero even in that case.

We calculated the mean vertical profile of air temperature over the analysis period and domain from the ERA-40 objective analysis to examine the difference from the estimates of cloud-top height in the region where ΔT11–12 ≤ 0 K in Fig. 3. It is found that the difference between the estimated cloud-top height and the height where the air temperature equals T11 is up to ∼2 km. For example, the estimates of cloud-top heights at T11 = 220 K and ΔT11–12 = 0 and −2 K are ∼14.4 and ∼13.8 km, respectively, while the mean air temperature of 220 K corresponds to ∼12.5 km. H08 has indicated such a discrepancy by using the split-window measurements of GMS-5 and shipborne cloud radar, although only for the nonrainy high clouds. Sherwood et al. (2004) also indicated that similar discrepancy in cloud-top heights exists even for deep convective clouds, by using the T11 measurements of the eighth Geostationary Operational Environmental Satellite (GOES-8; Menzel and Purdom 1994) and airborne lidar measurements.

The difference of extinction coefficients between 10.8 and 12 μm become largest for particles with a diameter of 10–20 μm, while they decrease considerably with the increasing diameter of cloud ice. Clouds that are close to the convective clouds in a cloud system consist of larger cloud ice particles (>100 μm in median volume diameter) than those around the edge of the anvil region (∼40 μm; e.g., Rickenbach et al. (2008)). Therefore, for clouds consisting of large ice particles such as cumulonimbus or nimbostratus, the difference between T11 and T12 measured by MTSAT-1R could be comparable to the accuracy of measurements.

Such a discrepancy between the cloud-top height and effective radiation height could also be caused if the air temperature decreases when the cloud exists. The temperature difference is ∼4 K in tropics, and can account for ∼22% of the ∼2 km (∼18 K) difference. Some substances that show extinction characteristics opposite to water at split-window wavelengths, such as sulfuric acid in volcanic ash clouds (Prata 1989) and nitric acid related to lightning activity (Chepfer et al. 2007), can cause the negative ΔT11–12, and the value of ΔT11–12 could be equal to or less than 0 in total. Further study will be needed to examine quantitative contributions of the factors listed above to the zero or negative value of ΔT11–12.

5. Conclusions

Lookup tables for estimating cloud-top height and visible optical thickness by the brightness temperature (TB) measurements of a geostationary satellite at two infrared split-window wavelengths were presented. These lookup tables were constructed by regressing the 94-GHz cloud radar measurements of the CloudSat satellite in terms of TB at 10.8 μm (T11) and its difference from TB at 12 μm (ΔT11–12 = T11T12) measured by geostationary satellite MTSAT-1R. These lookup tables by geostationary satellite measurements are useful for monitoring a particular cloud system or geographical location in a short time interval of ∼1 h.

Spaceborne radar measurements by CloudSat made it possible to construct the lookup table for cloud-top height for all clouds including rainy clouds whose top heights are difficult to determine by the ground-based measurements because of the heavy attenuation of its signal by precipitation particles (H08). This yields the lookup table for cloud-top height without concern for the existence of precipitation. The dispersions of measurements around the estimates were shown in the lookup table as an indicator of the ambiguity of estimation. The standard deviations of measurements were at most ∼1 km for the clouds with T11 < 240 K.

We examined the dependences of latitude, season, satellite zenith angle, day–night, and land–sea differences on the estimates of cloud-top height at each point in T11−ΔT11–12 space, and presented a lookup table for cloud-top height for the region where these influences were considered as being uniform. The dependences on latitude and season were negligible within 15°S–15°N, while they became the most significant factor affecting the estimates at higher latitudes. The dependences of the zenith angle of the geostationary satellite might also cause considerable bias in the region with a large zenith angle. The dependences on the land–sea and daytime–nighttime contrasts were found to be small compared to the standard deviation of measurements.

The lookup table for the visible optical thickness was also presented, although it was limited to the nonrainy high clouds. The distributions of estimates in T11−ΔT11–12 space were qualitatively consistent with those expected from a simplified theory, although the standard deviations of measurements were slightly large, up to ∼70%.

Since the CloudSat conducts cloud radar observations on a global scale, the method adopted in this study can easily be applied to other current geostationary satellites with split-window channels.

Acknowledgments

The authors are grateful to Dr. Hirohiko Ishikawa and Dr. Yuichiro Oku in Disaster Prevention Research Institute, Kyoto University, for their assistance in processing MTSAT-1R data. The authors thank Dr. Takehiko Satomura and Dr. Toshiro Inoue for helpful discussions. All figures were provided by the GFD-DENNOU Library. This work was supported by Grant-in-Aid for Scientific Research (19540460) of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan.

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Footnotes

Corresponding author address: Atsushi Hamada, Research Institute for Humanity and Nature, 457-4 Kamigamo-Motoyama, Kita, Kyoto 603-8047, Japan. Email: hamada@chikyu.ac.jp

1

For practical use, it is enough to use the lookup tables that are constructed by using a more simplified method where the estimate and standard deviation of samples at each point in T11−ΔT11–12 space are computed as the arithmetic mean and standard deviation of samples within a rectangular box with fixed size (i.e., the smoothing parameter) that is selected appropriately.