a. MODIS retrieval

Traditionally, cloud LWP is derived using retrievals of cloud optical depth, τ, and droplet effective radius, r_e, as given by

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where τ and r_e are defined by (Hansen and Travis 1974)

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Here, ρ_w is the density of liquid water, Q_e is the extinction efficiency and is equal to the constant 2, z is the altitude, r is the droplet radius, and n(r) is the droplet number distribution between r and dr. The LWP calculated by Eq. (1) assumes that r_e is vertically constant.

In this study, MODIS 1-km L1B data (version 4) are utilized to retrieve cloud properties. The cloud optical depth, τ, is retrieved from the MODIS 0.86-μm reflectance measurement for the clouds over ocean. The selection of the 0.86-μm channel reduces uncertainties of the cloud optical depth retrieval because ocean surface reflectances are small and less variable at the 0.86-μm channel (King et al. 2003). Three different cloud DER values, namely, r_e3.7, r_e2.1, and r_e1.6, are retrieved using a single NIR channel from each of the MODIS measurements at 3.7, 2.1, and 1.6 μm. Following the method of Chang and Li (2003), a linear DER vertical profile (DVP) defined by a cloud-top DER and a cloud-bottom DER is also retrieved using a combination of all three NIR channels. The cloud-top temperature is retrieved from the 11-μm brightness temperature measurement. Atmospheric effects are corrected using the temperature and humidity profiles obtained from the MODIS 07 (MOD07, version 4) atmospheric products (Menzel and Gumley 1998), which are mainly obtained from the National Centers for Environmental Prediction (NCEP) Global Data Assimilation System (Derber et al. 1991). The effects of thin cirrus contamination are eliminated using the cirrus detection reported in the MOD06 cirrus product (King et al. 2003).

The single NIR retrieval of r_e3.7 follows the iterative method of Chang et al. (2000) applied earlier to the AVHRR data, which is similar to the methods of Han et al. (1994) and Platnick and Valero (1995). In the method, the retrievals of cloud optical depth, DER, and top temperature are applied through an iterative procedure to determine the optimal retrievals. The retrievals of r_e2.1 and r_e1.6 in this study essentially follow the same method as the retrieval of r_e3.7, except that the 3.7-μm measurement contains both emission and reflection. The contribution of the 3.7-μm emission is calculated using radiative transfer modeling with cloud-top temperature retrieved from the 11-μm channel. Platnick and Valero (1995) provided a detailed discussion on the uncertainties of the retrieved cloud optical depth and DER. They showed that the accuracy of the optical depth retrieval is primarily affected by the visible-channel reflectance uncertainties and the accuracy of the DER retrieval is primarily affected by the NIR-channel reflectance uncertainties. A visible reflectance error of 5% causes a 10% error for typical cloud optical depths ∼5–20, but large changes in cloud optical depth can occur for small changes in the reflectance for thick clouds. An NIR reflectance error of 5% causes a similar magnitude of error in DER. However, large errors in both DER and optical depth can occur for thin clouds. The calibration errors for MODIS data are expected to be less than 2% (King et al. 1997). Some modeling errors may also result in uncertainties that are estimated to be on the order of 10% for the retrieval of DER and on the order of 15% for the retrieval of cloud optical depth (King et al. 1997; Rossow et al. 1989).

Figure 1 shows the frequency distribution of the overcast cloud optical depth retrieved from the 1-km MODIS 0.86-μm reflectance and Fig. 2 compares the frequency distributions of the three DERs (r_e3.7, r_e2.1, and r_e1.6) retrieved from each of the MODIS 3.7-, 2.1-, and 1.6-μm channels. The overcast clouds are defined over an AMSR-E footprint (∼13 km × 7 km) and only successful DER retrievals from all three NIR channels are included in Figs. 1 and 2. The mean cloud optical depth is 13.9 (±13.2) with a maximum occurrence at ∼8. The mean DER increases from r_e3.7 = 13.0 μm to r_e2.1 = 13.4 μm and to r_e1.6 = 13.8 μm. The spread (standard deviations, hereafter referred to as “std” in the figures and tables) of the distribution also increases from r_e3.7 to r_e2.1 and to r_e1.6. The RMS differences in the DER are 1.1 μm between r_e3.7 and r_e2.1, 1.2 μm between r_e2.1 and r_e1.6, and 2.2 μm between r_e3.7 and r_e1.6.

To account for the vertical variation of r_e following the method of Chang and Li (2003), a linear r_e profile is retrieved using combined information from the multi-NIR channels at 3.7, 2.1, and 1.6 μm. Here, the linear r_e profile is defined as a function of height, z, by

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where z′ = (z − z_top)/(z_base − z_top) denotes the fractional cloud height with z′ = 0 for the cloud top and z′= 1 for the cloud base. Thus, the linear r_e profile is parameterized by r_e1 at z′ = 0 and r_e2 at z′ = 1 representing the cloud-top and cloud-base r_e, respectively. For retrievals of r_e1 and r_e2, an optimal solution set is determined by matching the MODIS measurements with radiative transfer calculations at all three NIR channels, that is, 3.7, 2.1, and 1.6 μm. In their theoretical study, Chang and Li (2002) have analyzed the potential biases associated with the assumption of a linear r_e profile and reflectance error. They showed that the linear DER retrieval works best for median-thick cloud optical depths ∼10–28 and the retrieval mean biases are on the order of 1 μm for cloud top and slightly larger for cloud base if the DER profile has a close-to-linear variation. However, if the DER variation is very nonlinear, large biases will occur, in particular for cloud-base DER. Also, when clouds have large optical depth (>28), the quality of DER profile estimation does not change much for cloud top, but gets much worse for cloud base because the signal from cloud base is weak for such thick clouds. In these cases, the retrieved r_e2 probably represents the middle portion of a thick cloud and does not represent for the cloud base. Over all, the uncertainties in r_e2 can be larger by 2–3 factors than the uncertainties in r_e1.

Figure 3 shows the frequency distributions of the retrieved r_e1 and r_e2 for the data shown in Fig. 2. While the mean and standard deviation of the r_e1 distribution are similar to those of the r_e3.7 distribution shown in Fig. 2, the mean and standard deviation of the r_e2 distribution are much larger than those of the r_e2.1, r_e1.6, and r_e1 distributions. Because of droplet absorption, the DER retrieved from a single NIR channel like r_e3.7 is more sensitive to the layer near the cloud top, which can cause biases in LWP calculations if r_e varies vertically. For a cloud with a decreasing DER profile (DDP) with height, that is, a smaller r_e toward the cloud top, the calculated LWP would be underestimated. On the contrary, for a cloud with an increasing DER profile (IDP), that is, a larger r_e toward the cloud top, the calculated LWP would be overestimated.

To show the effects of the different r_e on LWP estimations, different LWPs are calculated using r_e3.7, r_e2.1, and r_e1.6 with assumptions of a vertically constant r_e (hereafter referred to as LWP_3.7, LWP_2.1, and LWP_1.6) and using the linear r_e profile (hereafter referred to as LWPrep). Table 1 shows the comparisons of these LWPs. The RMS difference between LWPrep and LWP_3.7 is 0.031 mm, which is about 25% of the mean value. LWP_1.6 is the closest to LWPrep, but there is still an RMS difference of 0.017 mm. Therefore, the vertical variation of cloud DER has a considerable impact on the LWP estimation for the overcast warm cloud. As the above LWPs are derived from cloud optical depths and DER, the uncertainties in these LWP estimates are on the order of ∼20%. Han et al. (1995) found a similar magnitude of uncertainties of 20% in their cloud LWPs derived using AVHRR cloud optical depths and DERs when they are compared with LWP estimation from an in situ microwave radiometer.

Note that 4 out of every 10 pixels in the along-track direction do not have correct radiance measurements at 1.6 μm for MODIS 1-km L1B data because of nonfunctional detectors at 1.6 μm. The average of measurements made by the nearest pixels is used here. This should not affect the results much because only overcast clouds are considered in this study, as explained in later sections.

b. AMSR-E retrieval

Cloud LWP has also been retrieved using satellite microwave remote sensing. In comparison with the visible/NIR retrievals, the microwave LWP estimation has a different physical basis, spatial resolution of field of view, and scanner viewing geometry. Several important algorithms, based on physical models, were developed for a variety of sensors, including the SSM/I (Lin and Rossow 1994; Weng and Grody 1994; Greenwald et al. 1995; Wentz 1997), the AMSU (Grody et al. 2001; Ferraro et al. 2005), and the AMSR-E (Ashcroft and Wentz 2000). Although a direct validation of such estimates has proven challenging (i.e., matching fine time/space upward-looking radiometer calculated LWP from small islands and ships with the large areal average LWP from the radiometer), most of these studies have concluded that the uncertainty of the passive microwave estimates are on the order of 0.02 mm under rain-free conditions. Further physical validation studies (Marchand et al. 2003; Ashcroft and Wentz 2000) indicate similar values. Wentz (1997) has analyzed the uncertainty of SSM/I LWP product. Atmospheric modeling error incurs uncertainty on order of 0.019 mm, radiometer noise incurs uncertainty on order of 0.007 mm, wind direction incurs uncertainty on order of 0.004 mm, and other sources incur uncertainty on order of 0.014 mm. The comparison with in situ measurements has shown that the total observed root-mean-square error of SSM/I LWP estimation is 0.025 mm.

Lin and Rossow (1994) compared the visible/NIR LWP derived from the International Satellite Cloud Climatology Project (ISCCP) cloud product with the SSM/I microwave LWP estimation. They found that the ISCCP LWP estimation is often larger than the SSM/I LWP estimation for tropical nonprecipitating clouds, but the difference is generally less than 10%. Greenwald and Christopher (2003) compared the LWP products derived from the Tropical Rainfall Measuring Mission (TRMM) Visible and Infrared Scanner (VIRS) with those derived from the TRMM Microwave Imager (TMI). They showed a clear-sky background bias in the TMI LWP estimation. After removal of the TMI background bias, a good agreement was found between the monthly mean LWPs from the two instruments. Ferraro et al. (2005) found that the LWP estimates from AMSU on NOAA satellites were somewhat smaller than ground-based in situ retrievals, which may be due to the extremely large AMSU footprint (∼50 km).

The AMSR-E microwave measurements have 12 channels and 6 frequencies ranging from 6.9 to 89.0 GHz. Horizontally and vertically polarized radiation is measured separately at each frequency. The AMSR-E ocean product (version 4) from Wentz’s algorithm is utilized in this study. The AMSR-E standard ocean algorithm (Ashcroft and Wentz 2000; Wentz 1997) retrieves sea surface temperature, surface wind speed, column water vapor, and LWP from the signals emitted by surface and atmospheric components at 6.9, 10.7, 18.7, and 36.5 GHz. The algorithm can retrieve LWP when there is no rainfall or if the rain rate is less than 2 mm h⁻¹. Although no direct validation results of the AMSR-E algorithm have been published in the open literature, the performance is generally accepted to be as good, if not better, than those documented by Wentz (1997) since it utilizes the same physical model and retrieval algorithm. However, the AMSR-E spatial resolution is better than SSM/I; thus the AMSR-E uncertainty may be slightly less that 0.025 mm.

The AMSR-E LWP product is compared with the LWPs derived from coincident MODIS measurements. Because of the highly variable emission of land surfaces, LWP estimations from passive satellite microwave observations are only applicable over oceans. The AMSR-E ocean product also provides rain flags, which are used to determine whether a cloud is raining or not. The rain flag is defined by an LWP threshold of 0.18 mm. This threshold is based on the comparison of SSM/I LWP retrievals with in situ rain observations (Wentz 1990; Wentz and Spencer 1998).

a. Effect of broken clouds

For each matched AMSR-E footprint, cloud fraction is determined based on the 1-km MODIS cloud mask by calculating the ratio of cloudy pixel number to total pixel number within the footprint. Figure 5 shows the impact of cloud fraction on the comparison between AMSR-E LWP_MW and MODIS LWP_2.1. In the figure, the correlation coefficients, R, and associated slopes, β, from linear regression are derived and plotted against the different partitioning of AMSR-E cloud fraction. It is seen that cloud fraction has a large impact on the correlation between AMSR-E LWP_MW and MODIS LWP_2.1. The two LWPs correlate well when the cloud fraction of AMSR-E footprint approaches 100%, but poorly when the cloud fraction is small.

It is a complex problem when broken clouds occur because the microwave LWP estimation may be significantly affected by the column water vapor amount, sea surface temperature, and surface wind speed. There is a background bias in microwave LWP estimations under clear-sky conditions (Lin and Rossow 1994; Greenwald and Christopher 2003). The background bias affects the accuracy of the AMSR-E LWP estimations for thin or broken clouds because the microwave signal from the cloud LWP is weak. To illustrate the clear-sky bias, Fig. 6 shows the frequency of occurrence of the AMSR-E LWP estimates when the MODIS indicates clear-sky conditions. As shown in the figure, the mean background bias is about 0.007 mm and the standard deviation of the bias is 0.017 mm for the single day’s worth of data obtained between 40°N and 40°S over oceans.

After removing all nonuniform broken clouds (AMSR-E footprint cloud fraction < 100%), the agreement between AMSR-E and MODIS overcast LWP retrievals improves substantially with a correlation coefficient R ∼ 0.90 and β ∼ 1.01. Note that in the following sections (3b–3d), we focus on overcast clouds (AMSR-E footprint cloud fraction = 100%), for which the potential of using the DER vertical variation for warm rain detection and the effects on the cloud LWP estimation due to variability in cloud optical depth and DER are further examined.

b. Effect of cloud optical depth

Since cloud LWP depends strongly on cloud optical depth, variability of cloud optical depth within the AMSR-E footprint also affects the outcome of the comparison between the AMSR-E and MODIS LWPs. The microwave signal from optically thin clouds can be affected by the clear-sky background bias. The bias is due to uncertainties in column water vapor and surface emission that dominate the microwave measurements. In analyzing all overcast AMSR-E footprints, the data are divided into four groups based on the ISCCP cloud-type classification: τ < 3.6, τ = 3.6–9.4, τ = 9.4–23, and τ > 23. Table 2 shows the comparison of LWP_2.1 with LWP_MW for clouds with various optical depths. The LWPs derived from the two instruments show poor agreement for clouds with optical depths less than 3.6. The comparisons show better agreement with increasing cloud optical depth. Optically thick clouds (τ > 23) are excluded in the following studies because MODIS retrievals of DER at cloud base have large uncertainties for these clouds (Chang and Li 2002).

c. Effect of cloud DER vertical variation

Because of the effects of broken cloud and optical depth, overcast clouds with optical depths ranging between 3.6 and 23 are selected to investigate the impact of the DER vertical variation on LWP estimations and warm rain detection. The overcast cloud samples are mostly obtained in the eastern Pacific Ocean covered by extensive single-layer low-level clouds. Figure 7 is a scatterplot of MODIS LWP_2.1 as a function of AMSR-E LWP_MW, which includes all overcast AMSR-E footprints and cloud optical depths ranging between 3.6 and 23. Table 3 shows the comparisons of LWP_MW with LWP_3.7, LWP_2.1, LWP_1.6, and LWPrep. The different values of LWP_3.7, LWP_2.1, and LWP_1.6 show the effects of different retrievals of DER at the three NIR channels. As previously stated, the DER retrieved from a single NIR channel is biased toward the cloud top. Using a vertically constant DER, the LWP is overestimated for clouds with an IDP, and is underestimated for clouds with a DDP. Because the microwave LWP estimation measures the entire cloud layer, it is utilized to evaluate whether the DER profile improves the LWP estimation or not. From Table 3, LWPrep is better correlated with LWP_MW than with LWP_3.7, LWP_2.1, and LWP_1.6. The regression coefficients do not change much because the vertical variation of DER has an opposite impact on LWP estimates for IDP clouds and DDP clouds. To show this effect in detail, clouds over AMSR-E footprints are separated into three categories: clouds with a neutral DER profile (NDP), and IDP clouds and DDP clouds based on re1 and re2. For DDP clouds re2 is 10% larger than re1, and it is 10% less than re1 for IDP clouds. For neutral clouds, the vertical variation of DER is within 10%. Table 4 shows the comparison between MODIS LWP and AMSR-E LWP for IDP, DDP, and NDP clouds. Because the vertical variation of DER causes the largest bias in LWP_3.7, LWP_3.7 is used to illustrate how the DER profile improves LWP estimations. LWP_2.1 and LWP_1.6 show similar biases of smaller magnitude.

LWP_3.7 is 12.6% larger than LWP_MW for IDP clouds, 2.6% larger than LWP_MW for NDP clouds, and 11.2% less than LWP_MW for DDP clouds. Since the DER profile is the only criterion separating the data, it must be the primary cause for the differences. LWPrep, LWP_3.7, LWP_2.1, and LWP_1.6 are almost identical for NDP clouds because there are no vertical variations in the DER. The approximate 2.6% difference between MODIS LWP estimations and AMSR-E LWP estimations for NDP clouds is due to other uncertainty factors. So over the AMSR-E footprint, the bias caused by the vertical variation of DER in visible/NIR LWP estimations is about +10% (12.6%–2.6%) for IDP clouds and −13.8% (−11.2%–2.6%) for DDP clouds. LWPrep is 5.2% larger than LWP_MW for IDP clouds and 0.1% larger than LWP_MW for DDP clouds. Both differences are close to the 3% difference for NDP clouds. This means that the DER profile improves the LWP estimations and corrects the bias caused by the vertical variation of the DER. As previously stated, the uncertainties of LWP estimations are on the order of 0.025 mm or 20% for microwave methods and solar methods. The improvements made by DER profile are on a less magnitude as compared with uncertainties of the LWP estimation. Nevertheless, the improvements are systematic and physically sound, rather than a random noise. A magnitude of ±10% improvements in LWP estimation can be of significance in cloud water and radiation budget studies.

d. Implication for warm rain clouds

IR rain detection algorithms (Adler and Negri 1988; Arkin 1979) generally miss the presence of precipitation in warm clouds because these algorithms depend on the cloud-top temperature. Microwave techniques cannot detect warm rain over land since the techniques rely on ice scattering over land (McCollum and Ferraro 2003). Over oceans, warm rain can be estimated from satellite microwave brightness temperatures because the surface emission is low and less variable (Wilheit et al. 2003). Recently, Ba and Gruber (2001) utilized the DER retrieved from the 3.9-μm channels on GOES satellites to detect warm rain clouds. As previously discussed, the DER retrieved from a single NIR channel is more sensitive to cloud-top than cloud-base values. In Fig. 3, the DER at the cloud base shows a wider spectrum than the DER at the cloud top, which may be explained by the cloud development phase: growing or decaying. Cloud droplet size increases with height during the developing stage due to condensation growth. Once a collision process starts, larger droplets tend to fall to the lower levels of the cloud. Therefore, the DER at cloud base is small for developing clouds and large for drizzling clouds. So the DER at the cloud base is more correlated with rainfall than DER at the cloud top. There were some previous studies that utilized the vertical DER variation to differentiate precipitating/nonprecipitating clouds (Shao and Liu 2004; Matsui et al. 2004). These studies combined microwave observation and shortwave observation to infer the vertical variation of DER. Chang and Li’s algorithm captures the trend of the vertical DER variation from observations of multi-NIR channels. A preliminary investigation was done using the rain flag defined in the AMSR-E ocean product to show the potential of the linear DER profile retrieval for warm rain detection.

Figure 8 shows the distribution of DER at cloud base and cloud top for raining and nonraining clouds, respectively, which are defined by the AMSR-E rain flag. Raining causes a DER increase of 3.5 μm at the cloud top (Fig. 8a) and a DER increase of 7 μm at the cloud base (Fig. 8b). So DER at cloud base is more effective for rain detection. For example, if we define a threshold of 14 μm for raining clouds (Rosenfeld and Gutman 1994), the DER at the cloud base correctly classifies 87.0% of AMSR-E–detected rains, while the DER at the cloud top classifies only 64.4% of AMSR-E–detected rains. For some AMSR-E–detected raining clouds, the DER at the cloud base can be as small as 10 μm. These clouds could be partially raining, while overall small DER is evident because of the effect of the nonraining part of the clouds. However, based on the same 14-μm raining threshold, the false raining detection rate is 22.7% using the DER at the cloud top and 30.6% using the cloud-bottom DER. If the DER threshold is increased to 20 μm, the false detection rate is considerably reduced, at the expense of missing some raining clouds. The false detection may be due to the AMSR-E sensitivity problem. Many of these AMSR-E–defined nonraining clouds could have very light rain or drizzle that evaporates before reaching the ground. Figure 9 shows the distribution of the DER differences between the cloud top and the cloud base. Raining clouds generally have larger DER at the cloud base than at the cloud top. This result is consistent with in situ observation (Martin et al. 1994). Use of −2 μm in the DER difference appears effective in separating the majority of raining and nonraining clouds, although there are some uncertainties. The uncertainties could be caused by partially raining clouds, as well as AMSR-E sensitivity problems. Development of a rain detection algorithm is beyond the scope of this study.