1) Validation sites

Twelve stratus scenes were selected from MODIS imagery over the Midwest to Southeast during the autumn and winter months of 2005/06 for validation of the cloud-base algorithm. The individual scenes were hand selected on the basis of 1) the absence of upper-level cloud contamination, 2) the relatively uniform cloud-top temperatures (T_ct varied less than 0.5 K over a 5 × 5 pixel array), and 3) the sites over major airports with available ceilometer data. A list of the sites and dates, along with results of the validation are given in Table 1.

2) Monteverde Cloud Forest Preserve

The time period for the MCFP portion of the investigation is 1–15 March 2003, and the study region is centered at the Monteverde Cloud Forest Preserve, Costa Rica (10.2917°N, 84.7833°W). This time period was chosen to coincide with the Land Use and Cloud Interaction Experiment, which took place in this region (Ray et al. 2006). The Monteverde cloud mist forest, situated at the crest of the Cordillera de Tilarán, rises to elevations in excess of 1800 m. The volcanic Cordillera Central extends to the southeast (Fig. 2), with peaks ranging from 2100 to 3400 m, while isolated volcanic peaks of 1400–1800 m are found to the northwest. The flow of trade winds over these mountains results in the formation of orographic cloud banks along the windward Caribbean slopes. Because the terrain is far more complex at the MCFP than at the U.S. sites, and because coincident cloud ceilometer data were readily available for the U.S. sites, it was deemed reasonable to validate the approaches first at sites with relatively flat terrain.

1) Constant liquid water content method

Hutchison (2002) applied this approach to MODIS imagery and found the expected accuracy of retrieved cloud thickness H to be on the order of 100 m. Cloud liquid water path (LWP) is the column integration of LWC:

View Expanded

where

View Expanded

If the water cloud layer is assumed to be vertically homogenous with a constant LWC, the cloud geometrical thickness can the be expressed as

View Expanded

Values of r_e and τ are provided by the MODIS standard products, but LWC must be estimated in this approach. Hutchison (2002) assumes LWC = 0.44 g m⁻³ for stratus over land (based on Liou 1992), but values of 0.24 and 0.09 g m⁻³ are suggested for oceanic stratus and stratocumulus, respectively, indicating that there is significant uncertainty in the value to be assumed. On the basis of fog measurements at Monteverde, a value of LWC = 0.25 g m⁻³ for orographic clouds over TMCFs appears to be a reasonable assumption (Fig. 3).

2) Empirical relationship method

This method is mentioned in the Algorithm Theoretical Basis Document (ATBD) regarding cloud optical property retrievals for the Clouds and the Earth’s Radiant Energy System (CERES) Science Team by Minnis et al. (1997). The cloud thickness H is computed using empirical formulas.

For clouds below 4 km, cloud thickness H (km) may be estimated as

View Expanded

For clouds below 0.02 km,

View Expanded

for other clouds,

View Expanded

At Monteverde, orographic cloud-top heights are lower than 4 km, so Eq. (5) is applied.

3) Adiabatic model method

Brenguier et al. (2000) proposed an approach to estimate cloud thickness based on the assumption of adiabatic evolution in a closed convective cloud system. Ideally, the water vapor mixing reaches saturation at cloud base. During convective ascending, the air temperature decreases and the adiabatic saturation mixing ratio decreases. The adiabatic liquid water content (LWC_ad) is defined as the difference between the saturation water vapor mixing ratio at cloud base and the saturation water vapor mixing ratio at cloud level h above cloud base. Therefore, LWC_ad increases with altitude h, and this relationship is nearly linear (Brenguier et al. 2000):

View Expanded

View Expanded

where C_w is the moist-adiabatic condensation coefficient. The value of C_w varies from 1 × 10⁻³ to 2.5 × 10⁻³ g m⁻⁴ (∼0°–40°; cloud-base temperature), and it is nearly constant over a small vertical range of about 1 km. Brenguier et al. (2000) also provided two actual measured values of C_w within clouds, with both values very close to 2.0 × 10⁻³ g m⁻⁴. This constant value of C_w is appropriate in regards to the Monteverde area because orographic clouds there are low-level warm water clouds. Setting Eq. (3) equal to Eq. (9), we obtain

View Expanded

1) Cloud-top height

Two problems were encountered in utilizing the MODIS cloud-top pressure standard product. The first difficulty discovered is that the MODIS cloud-top pressure is reported at specific levels (see Platnick et al. 2003). We modified the publically available International MODIS/AIRS Processing Package (IMAPP) software (online at http://cimss.ssec.wisc.edu/~gumley/IMAPP) and modified it to output the actual computed values. A second, and much more substantial, problem then was discovered. The alternate technique used by the MODIS standard cloud-top pressure product (see section 4a) was found to yield contradictory results. Even though the alternate technique is employed to estimate cloud-top pressure that resides at levels > 700 hPa, it was found to yield cloud-top pressures < 700 hPa. A plausible reason for this contradiction is that the alternate technique determines the cloud-top pressure by determining the pressure level at which the atmospheric temperature profile has the same temperature value as the MODIS-derived cloud-top temperature. The alternate technique thus assumes a monotonic variation of temperature with height. However, in reality, the same temperature values can occur in a temperature profile at multiple pressure/height levels, especially when there are temperature inversions. Thus, multiple solutions are possible when using the alternate technique, and these can result in substantial errors. Indeed, over the United States, the cloud-base heights that are estimated using the cloud-top pressure that is retrieved using the standard MODIS cloud-top pressure algorithm were within the range of 2–4 km, in disagreement with ceilometer measurements, which placed cloud-base heights < 1 km (Table 1).

To determine if the existence of multiple solutions is indeed the reason for the substantial discrepancies between computed and observed cloud-base heights, thermodynamic profiles obtained from radiosonde measurements and NCEP FNL profiles at each site were examined. Examples of thermodynamic profiles associated with two of the cases considered in this study are shown in Fig. 4 where skew T–logp diagrams for two sites—(Fig. 4a) Birmingham on 29 December 2005 and (Fig. 4b) Nashville, Tennessee, on 9 October 2005—are given. From Table 1 the MODIS-derived cloud-top temperatures at these sites T_ct were found to be 272.2 K (−1°C) and 278.6 K (5.4°C), respectively. These were computed from MODIS channel 31 (11 μm) for a 5 km × 5 km array centered over the airports. Note that in Fig. 4a, following the 272-K (−1°C) isotherm in the skew T–logp diagram down until it intersects the temperature profile line, a value of approximately 720 hPa is produced, which is in agreement with the value that the MODIS algorithm returns. If the 272-K (−1°C) isotherm is extended farther down, it intersects with the temperature profile at approximately 860 hPa (determined from linear interpolation). Thus, for this case multiple solutions exist, and the second solution (860 hPa) is correct because the radiosonde sounding shows saturation just below this pressure level, indicating the presence of a cloud. Also note that the cloud-base height estimated using the first solution differs from the ceilometer observations by several hundred meters, while the estimate based on the second solutions differs only by about 150 m.

A new technique is proposed to avoid the ambiguity arising from the existence of multiple solutions. Because saturated conditions exist within a cloud, the dewpoint temperature within the cloud is the same at that of the temperature. Thus, it is proposed that the cloud-top pressure may be estimated as the pressure level at which the dewpoint temperature is equal to the cloud-top temperature that is estimated from the satellite data. Applying this new technique to the profile shown in Fig. 4a, we determine the pressure level at which the isotherm corresponding to the satellite-derived cloud-top temperature (272 K) intersects the dewpoint line. The cloud-top height Z_ct is determined as the geopotential height of this pressure level and is approximately 900 m. A radiosonde profile for another case day is shown in Fig. 4b, for which the intersection between the 278.6-K isotherm (MODIS standard cloud-top product algorithm) yields cloud-top pressure of about 700 hPa, while the new technique gives a value of about 840 hPa (1167 m).

Note that there is a disparity between the radiosonde (1200 UTC) and the satellite (∼1600 UTC) observation times. However, the cases considered in this study are relatively large-scale stratus cloud decks associated with synoptic-scale systems, and they undergo small changes over a 4-h time period; the errors associated with the time disparity are expected to be minimal.

2) Cloud-base height

Cloud thickness estimates were made using Eqs. (4), (5), and (10), and results are given in Table 1 as H₁, H₂, and H₃, respectively. For the Memphis, Tennessee, case on 3 February 2005, cloud thicknesses agreed to within 9 m for the three estimates. On the other hand, the Cincinnati, Ohio, case of 8 January 2005 and the Birmingham case of 9 October 2005 have particularly large discrepancies between the methods. Nevertheless, the three approaches usually produce cloud thickness estimates that agree to within about 100 m, with the H₁ being the largest in most cases. Table 1 also provides the mean effective drop radii r_e and mean optical thicknesses τ, along with their standard deviations (σ_r and σ_τ, respectively) derived from a 5 km × 5 km box centered over the airport sites. Note that the largest discrepancies in estimated cloud thickness between the three methods tend to occur for the combination of large values of r_e and τ. As pointed out by Hutchison (2002), optical thickness retrievals become increasingly sensitive to errors at large values of τ.

Using Eq. (1), cloud-base height Z_cb is computed for each method and then compared with the ceilometer measurements Z_a. Figures 5a–c show scatterplots of Z_cb versus Z_a for each of the three cases. The mean square errors are 171, 277, and 238 m, respectively, for the Z_cb1, Z_cb2, and Z_cb3 cloud-base height estimates. Note that the Cincinnati cases of 8 January 2005 and 3 January 2006 produce the largest errors, with large values of cloud optical thickness, τ = 50.7 and 46.5, respectively, and r_e = 11.8 μm and 9.6 μm, respectively. Although not evident in every case, errors in cloud-base height do tend to increase with increasing optical thickness, and especially for τ > 40.

Last, cloud thickness H′ was computed from cloud-top height Z_ct and measured cloud-base height Z_a, as shown in Table 1. Then, the liquid water content consistent with these values, LWC′, was computed using Eq. (4). Table 1 shows that values of LWC′ computed in this way vary from 0.2 to 0.65 g m⁻³. The value of 0.43 g m⁻³ suggested by Liou (1992) and used by Hutchison (2002) falls within this range, but obviously the use of liquid water content values with such variability may lead to significant variations in estimated cloud thicknesses.

Figure 5d shows a scatterplot of LWC′ versus τ. Values of LWC′ increase with increasing values of τ according to the following relationship:

View Expanded

However, the large scatter suggests that this relationship is only a rough guide to estimating liquid water contents of shallow stratus clouds. For the optical thicknesses shown in Table 1, Eq. (11) produces liquid water contents ranging from 0.34 to 0.51 g m⁻³, with mean value of 0.44 g m⁻³, which is precisely the value assumed by Hutchison (2002). Utilizing the derived values of liquid water content from Eq. (11) in Eq. (4), cloud-base heights again were computed and compared with the ceilometer measurements. Overall, the use of Eq. (11) does not produce significant improvements in cloud-base heights, and the mean square error is reduced insignificantly, from 171 to 152 m. We conclude that the assumed value of liquid water content of 0.44 g m⁻³ for low stratus clouds over land is adequate for cloud-base height retrievals. Plots of LWC′ versus r_e and r_e versus τ show no significant correlations (not shown).

3) NCEP FNL data

The above analysis for stratus clouds over the United States utilizes local radiosonde measurements to retrieve cloud-top heights. However, radiosonde datasets generally are not widely available globally, and especially not over remote locations where the TMCFs are found. Therefore, the above analysis is repeated using the atmospheric thermodynamic profiles obtained from the NCEP FNL 1° × 1° spatial resolution data.

The results are very encouraging. Differences in retrieved cloud-top heights using the radiosonde and FNL datasets are similar, and the mean square difference in cloud-top heights is 152 m. However, in eliminating the two Cincinnati cases, the mean square difference in cloud-top heights is reduced to only 62 m. Cloud-base heights again were computed for the three cloud thickness methods and compared with the ceilometer measurements, shown in Fig. 6. Mean square errors are 202, 265, and 231 m, respectively, for the Z_cb1, Z_cb2, and Z_cb3 cloud-base height estimates, as shown in Table 2. These values are very similar to those values obtained from the radiosonde measurements, as discussed above. Then, cloud thickness H′ was computed from cloud-top height Z_ct and measured cloud-base height Z_a. Last, the liquid water content consistent with these values, LWC′, was computed using Eq. (4). Table 2 shows that values of LWC′ computed in this way vary from 0.15 to 0.75 g m⁻³, with a mean value of 0.45 g m⁻³. These values are similar to those obtained using the radiosonde data. For the examined U.S. sites, the lower spatial resolution of the FNL dataset does not severely impact the cloud-base height retrievals, and we conclude that it can be used for retrieval of orographic cloud-base heights.

1) Automated approach

The question now becomes how one may take these facts into account when retrieving cloud-base heights with optimum results in an automated approach. We propose the following method. First, a cloud mask identifies all cloud pixels over the target region. Then, cloud optical thickness, cloud drop size, and cloud-top temperature are retrieved for each pixel. From the distribution of drop sizes, eliminate both the largest 10% and the smallest 10% of the drops (the smaller drop sizes most likely are found in regions of cloud dissipation near the edges). Of the remaining cloud pixels, select those that have cloud optical thicknesses in the range of 10 < τ < 25. This will provide those cloud pixels that have the maximum sensitivity for cloud thickness retrievals (and, thereby, cloud-base heights). Then, mean cloud-top temperature is computed from the remaining cloud pixels, and cloud-top height is derived using the FNL database by matching cloud-top temperature with cloud dewpoint temperature.

This new algorithm was tested first by applying it to the eight Monteverde scenes discussed above. However, all cloud pixels in the Monteverde region were examined, and then those pixels satisfying the criteria for r_e and τ were retained. Results are shown in Table 4. Note that values of r_e are almost unchanged, but that values of cloud optical thickness τ are significantly smaller in many cases, and especially on 1 and 10 March 2003. New cloud-top temperatures are computed from this reduced set of pixels; these values vary by 0.5° to about 1°C from those shown in Table 3, resulting in changes in cloud-top height Z_ct of up to 100 m. Once again the three methods were applied to derive cloud-base heights, with comparisons with photographically determined values.

Standard deviations (σ, in meters) for the three cases and for the 8 days are shown in Table 5. Note that the largest standard deviations consistently occur for the constant liquid water content approach. The empirical relationship and adiabatic model approaches produce similar standard deviation values, ranging from about 125 m on 4 March to as low as about 25 m on 10 March. The cloud-base-height-retrieved values were relatively random, and they showed no discernable spatial changes in surface across the cloud, in particular there was a lack of slope in cloud-base height. However, the cloud-base height might vary spatially across the extent of the cloud, and the limited number of pixels that satisfied our retrieval criteria may have been too few to detect such behavior.

Note that the constant liquid water content approach is sensitive to cloud optical thickness, whereas the other two approaches have the square root of τ dependence. Because cloud optical thickness varies substantially over the cloud range, the empirical relationship and adiabatic model approaches may be better suited to automated retrievals. Furthermore, the constant liquid water content approach requires an assumed value of liquid water. While the value of 0.25 g m⁻³ produced reasonable results for Monteverde, there is no guarantee that similar conditions will hold globally, or even for other seasons. Figure 3 shows that there can be significant variation in liquid water content within the orographic clouds, at least near the ground. With the very limited dataset evaluated in this study, it would be premature to suggest that any one approach is superior to the others.

While not shown in the results, independent computations of r_e were made for the 1.6-, 2.2-, and 3.7-μm channels, as discussed in section 3b. The retrieved values were nearly constant with height over the upper 80 m or so, suggesting that liquid water content in the upper orographic cloud is relatively constant.

Caution must be exercised when applying this method to global retrievals. While there are some observed adiabatic clouds (e.g., Albrecht et al. 1990), the majority are nonadiabatic (e.g., Pruppacher and Klett 1997, Fig. 2–22). If adiabatic water content is assumed according to cloud-base temperature, and in reality the clouds are nonadiabatic, then Eq. (10) would lead to an overestimation of cloud thickness. There are two possible approaches to mend this deficiency—one approach is to adopt fixed-adiabatic cloud water contents when in situ measurements are available for validation, as has been done in this study; the other possible approach is to use typical quoted values of 60% of the adiabatic water content determined by cloud-base temperature for reducing the errors (e.g., Betts and Albrecht 1987; Boers et al. 2000). Last, note that the value of C_w assumed in Eq. (10) is based upon values used by Brenguier et al. (2000) over the North Atlantic. The agreement in the present case may be fortuitous.