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fraction obtained at the 5 km scale is approximately 47%. By dividing the cloud top pressures into high (<440 hPa), mid (440-680 hPa), and low (>680hPa) levels, the overcast cloud fractions calculated for the high, mid, and low pressure levels are about 24%, 9%, and 29%, respectively. Since MODIS operational products made the single-layer assumption, the corresponding high, mid, and low overcast cloud amounts are about 24%, 6%, and 17%, which show fewer mid clouds and much fewer low clouds. The simulated ISCCP retrievals have about 15% in high, 15% in mid, and 17% in low for the corresponding dataset, which shows much fewer high and low clouds but much more mid clouds in comparisons with the Chang and Li method. The ISCCP operational products have been used for comparisons with GCM results and the ISCCP shows substantially more mid-cloud amounts than the GCMs (Webb et al., 2001; Zhang et al., 2005). The exceptional ISCCP mid-cloud amounts may result from misidentifications of semitransparent upper-level clouds that appeared warmer in the satellite 11 ¡m images and lower in altitude (Webb et al., 2001; Chang and Li, 2005a).

In a recent assessment of GCMs by the State University of New York at Stony Brook and the DOE ARM Cloud Parameterization and Modeling Working Group, Zhang et al. (2005) compared the high, mid, and low cloud climatologies generated by ten popular GCMs (NCAR, GFDL, GISS, GSFC, UKMO, etc.) along with two satellite products from the ISCCP and the Cloud and Earth's Radiant Energy System (CERES) program. The CERES cloud algorithm uses the 11 ¡m approach like the ISCCP to determine cloud top altitude, but it differs from the ISCCP in that it uses four instead of two channels to retrieve cloud phase, optical depth, particle size, and temperatures (Minnis et al., 1995; Minnis et al, 1998). Also different is that CERES products are based on the pixel radiance data from MODIS.

While large discrepancies exist among the GCMs, all GCMs produce less mid clouds but more high clouds than both the ISCCP and CERES. They show that GCMs generally produce more high-cloud amounts and less mid cloud amounts than the ISCCP and CERES. The results are consistent with those found in the MODIS and analysis by Chang and Li (2005b). The GISS (NASA Goddard Institute for Space Study) model produced the least high-cloud amount (<15%) while the GFDL (Geophysical Fluid Dynamics Laboratory) model produced the greatest (>35%). The GISS and GFDL were the two greatest in producing mid-level clouds, whereas all other models had significantly less mid clouds (<10%). As for low clouds, the GISS also had the greatest low-cloud amount and was closest to the ISCCP and CERES, whereas other models had much less low-cloud amounts. Nonetheless, all GCMs showed that their low-cloud amounts were two to three times larger than their mid-cloud amounts. Chang and Li (2005b) suggest that more than 30% of the low-level clouds were obscured by high-level clouds, and thus the low-level cloud amounts from satellite operational products like the ISCCP and MODIS were underestimated due to the single-layer assumption.

3.4. Cloud optical depth feedback

Cloud optical depth feedback is another major uncertainty in climate studies (Stephens, 2005). Tselioudis et al. (1992) and Tselioudis and Rossow (1994) used the ISCCP cloud data and reported a negative cloud optical depth (t ) and temperature (T) relationship. As such, they suggest a positive cloud optical feedback to climate warming. Concerns with the ISCCP-derived results are associated with the frequently observed partly cloudy pixels in nature (Wielicki and Parker, 1992; Chang and Coakley, 1993). The partly cloudy pixels can cause negative biases in t retrievals due to broken clouds (Harshvardhan et al., 2004; Coakley et al., 2005; Chang and Coakley, 2007). Whether cloud optical depth would increase or decrease in response to climate warming is still an open question. A negative t-T relationship implies that clouds would become thinner as climate warms. Thinner clouds would allow more solar radiation to enter and warm the climate system, leading to a positive feedback. Based on their studies with the GISS GCM simulations, Tselioudis et al. (1998) and Yao and Del Genio (1999) also show that low-level clouds exert an overall positive cloud optical depth feedback.

On the contrary, early arguments on the cloud optical depth feedback were related to the variation of cloud liquid water content (LWC) with temperature. For example, Somerville and Remer (1984) suggested that cloud optical depth would increase with temperature, if all other cloud variables remain constant. Their suggestion is based on aircraft in situ measurements made over the former Soviet Union (Feigelson, 1978), where the measured cloud LWC data showed an increase rate of dln(LWC)/dT = +0.04 to +0.05 for T between -25°C and +5°C. The observed rate of increase for dln(LWC)/dT is supported by Betts and Harshvardhan (1987) based on the moist adiabatic calculations. Although the rate of increase is calculated to be slightly smaller at +0.02 to +0.03, Betts and Harshvardhan (1987) also suggested that cloud optical depth will increase with climate warming.

To examine effects of partly cloudy pixels in the ISCCP cloud retrievals, Chang and Coakley (2007) explore the differences in cloud properties between overcast and partly cloudy pixels for low-level, single-layer cloud systems using the AVHRR data obtained between 55° S and 55° N

over the Pacific in March 1989. For single-layer systems, they separate overcast pixels from partly cloudy pixels through the use of the spatial coherence method (Coakley and Bretherton, 1982). Chang and Coakley (2007) also follow the ISCCP cloud detection method by applying the visible-IR threshold technique to the AVHRR data to simulate the ISCCP-like cloudy pixels that include both overcast and partly cloudy pixels. They compare the mean properties derived from the overcast pixels and threshold cloudy pixels for the Pacific region and show that the threshold cloudy pixels had substantially smaller 50%) cloud optical depths and larger 3°C) cloud top temperatures than the overcast pixels.

Having found the differences between overcast and threshold cloudy pixels, Chang and Coakley (2007) reexamine the t-T relationships through the use of the overcast pixels and threshold cloudy pixels. Despite the differences, correlations for the overcast and threshold cloudy pixels show similar negative t-T relationships and their corresponding values of d ln T/dT derived for the midlatitudes and subtropical regions agree in magnitude with those derived using the ISCCP data as reported by Tselioudis et al. (1992). Chang and Coakley (2007) suggest that the cloud thickness thinning is the main reason why similar negative t-T relationships were found in both overcast and threshold cloudy pixels.

Chang and Coakley (2007) further examine the variable effects of cloud liquid water content (L), droplet effective radius (re), cloud layer temperature (Tc), and cloud geometrical thickness (D) based on the fundamental relationship between t, re and cloud liquid water path (LWP) given by (Hansen and Travis, 1974)

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