Effects of MLS smearing on cloud ice measurements depend on cloud horizontal and vertical inhomogeneity, about which little was known priori to the launch of CloudSat (Figure 1). In the upper troposphere, statistics from in-situ measurements show that the ensemble mean of cloud IWC tends to decrease with height exponentially (McFarquhar and Heymsfield, 1997). This property leads to a simple, nearly-linear relation between MLS Tcir and IWC, because the Tcir–IWC sensitivity peaks near the pointing tangent height where Tcir is measured (Wu et al., 2005). It also serves as the basis of the MLS V2.2 IWC retrieval (Wu et al., 2008). As expected for the coarse horizontal resolution, cloud inhomogeneity may induce error when interpreting an MLS IWC measurement. However, this error appears to be mostly random and can be averaged down in a monthly or seasonal map (Wu et al., 2008).
If we restrict our study to the optically-thin situations at 215-83 hPa (that are used for the retrievals) where limb radiances are neither saturated by clouds nor by clear-sky gases, as shown in Figure 2, the MLS IWC weighting functions (WFs) from the linearized 2-D model are mostly positive. They extend horizontally over a 200-400 km along track and more than 3 km vertically due to the instrument FOV and the spherical geometry. In this calculation, we assume a 10 mg/m3 IWC uniformly distributed at pressures >83 hPa and force the IWC profile to drop sharply (with a scale height of 0.5 km) above 83 hPa since clouds rarely reach altitudes above 18 km. The 10 mg/m3 value is arbitrarily chosen to represent an optically-thin cloud field. As long as the Tcir-IWC relation remains in the linear regime (IWC < ~50 mg/m3), the WF morphology at 215-83 hPa does not vary significantly.
Although the WFs from a uniform 10 mg/m3 at 215-83 hPa extend relatively widely and deeply to high altitudes, only the altitudes near the tangent height are most significant because climatologically . In reality, each MLS IWC represents an average of an ensemble of clouds within the WF, of which the IWC statistics can be characterized by the exponential distribution. This consideration allows us to approximate the calculated WF with a rectangular box as shown in Figure 2 and ignore the contributions from upper left and right corners. Figure 2 also reveals some limitations of the simple IWC retrieval technique used in the V2.2 algorithm. The V2.2 IWC retrieval assumes that Tcir increase monotonically with IWC, which is only valid at tangent pressures < 261 hPa where the 2-D WFs are dominated by positive contributions. At 261 hPa and below, negative weights begin to make a significant contribution to Tcir, offsetting effects by the positive weights and causing reduced Tcir sensitivity to IWC. Depending on the amount of cloud ice in the path, the 240-GHz radiance generally has a poor sensitivity to cloud ice at these transition tangent pressures (383-261 hPa) [Wu and Jiang, 2004]. At tangent pressures >383 hPa, the WFs are dominated by negative contributions because clouds tend to scatter upwelling radiation out of the MLS LOS, reducing brightness temperature in limb radiance. The negative Tcir at these tangent heights can be used to retrieve a cloud ice column (above ~6 km).
To assess IWC uncertainties induced by cloud inhomogeneity, we need to know realistic distributions of the IWC inhomogeneity. This requires large statistics of IWC variability over hundreds of kilometers in distance with vertical resolution better than 1 km, which are not readily available with airborne and ground-based observations. Because MLS measurements involve large FOV and limb-view averaging, cloud spatial variability is more important than temporal variability for interpreting the results. Also, ground-based observations are not quite useful for our study since connection between spatial and temporal inhomogeneity requires additional assumptions about cloud variability. Thus, for this study we use CloudSat IWC observations to assess cloud inhomogeneity effects on MLS V2.2 IWC retrieval.
With the CloudSat IWC profiles along the A-Train track, we can simulate MLS 240-GHz Tcir using the MLS 2-D RT model and compared the derived Tcir-IWC relations with those used by V2.2. We randomly selected 2000 cases from CloudSat data in January 2007, binned the CloudSat IWC profiles into the input grid sizes (0.5° horizontally and ~0.67 km vertically) of MLS 2-D model, computed MLS Tcir, and compared the Tcir to the IWC averaged over the volume boxes in Figure 4. The resulting Tcir-IWC relations are shown in Figure 11 and compared to the V2.2 relations. As shown in Figure 3, the selected CloudSat cases cover a broad range of IWC values. The Tcir-IWC scatter reflects the uncertainty of individual V2.2 IWC measurements due to cloud inhomogeneity. As discussed above, interpreting V2.2 IWC as an average in the volume box near the tangent point may induce error. However, to first order, the inhomogeneity-induced IWC uncertainty appears to be random and can be reduced by averaging (e.g., monthly maps). For example, on a grid box of 5º×10º latitude-longitude, Aura MLS typically has a total of ~80 samples in the tropics during a month, which could reduce inhomogeneity-induced uncertainty by a factor of 9 if averaged. The inhomogeneity-induced percentage error tends to increase at smaller Tcir values or at higher pressures, but less scatter is found for the simulations at 147 and 177 hPa than at other pressure levels. The inhomogeneity error can be corrected properly with a 2-D tomographic IWC retrieval on MLS Tcir, the technique currently used in MLS clear-sky gas retrievals [Livesey et al., 2006]. Such an IWC retrieval is currently being developed for a future version of MLS retrieval algorithm.
Figure 3 also reveals an inhomogeneity-induced scaling error in the V2.2 Tcir-IWC relations, which cannot be reduced by averaging. The scaling error is pressure-dependent, generally less than 30% at 177-121 hPa but can be as large as -70% at 100-83 hPa for the retrieved IWC. It is also latitude-dependent, especially at 177 and 215 hPa, showing that the Tcir-IWC relations have a smaller slope in the extratropical bin. At 215 hPa, ignoring cloud inhomogeneity, the V2.2 retrieval would overestimate IWC by 80% in the tropics but underestimate it by 40% in the extratropics, and the underestimation becomes worse for large IWC values. At 147 and 177 hPa, the V2.2 retrieval tends to underestimate IWC at values < 10 mg/m3 but overestimate it at values > 10 mg/m3, and the overestimation appears to increase with IWC at large values.
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| Figure 1. Diagram to illustrate the MLS smearing on the IWC measured by CloudSat. The dashed lines are the MLS tangential beams. At high tangent heights, the beams penetrate through the limb and become sensitive to a volume-averaged IWC, whereas at low tangent heights the MLS beams cannot penetrate through the limb due to strong gaseous absorption and become only sensitive to a partial column of IWP, namely, hIWP, with a shallow angle (~3°). Note that the actual volume of the hIWP locates at ~300 km away from the tangent point, or ~2 profiles towards MLS |
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| Figure 2. IWC weighting functions (in K•g-1m3), or , for the 2-D RT model linearized at IWC0=10 mg/m3. The 2-D model has 21 IWC profiles (of which the location is indicated by the vertical dotted lines) and 35 vertical levels (24 levels per decade pressure in hPa). Solid-red (Blue-dotted) contours show the positive (negative) weights with the contour interval (in K•g-1m3) indicated in the title of each panel. In this example, MLS views from the negative-distance side and is only sensitive to clouds on the MLS side of tangent point at low ht where the radiance cannot penetrate through the limb. For this calculation a uniform distribution (IWC0 =10 mg/m3) is assumed up to ~83 hPa but drops to zero sharply above that pressure level. Contributions at pressures < 74 hPa (~18 km) are zeroed in these plots because clouds rarely exceed that altitude. |
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| Figure 3. Comparison of the V2.2 Tcir-IWC relations (black curves) with those modeled by the 2-D RT model using CloudSat IWC profiles (dots). A total of 2000 randomly-selected CloudSat cases are used for the simulation: 1229 (red) from the tropics (20°S-20°N) and 771 (blue) from the extratropics. The IWC is averaged over the rectangular boxes as depicted in Figure 4. The colored curves correspond to the polynomial fit to the simulated Tcir-IWC relations in each latitude bin, and only data with IWC > 0.1 mg/m3 are used in the fitting. |