Based on the 99% LWC value assessed

Based on the 99% LWC value assessed at 0℃, the LWC temperature curves shown in figures 11 and 12 were computed using the following methodology.The mean temperature and pressure of all the 30-s SLD data observed was -4.2℃ and 865 mb, respectively.These values were used to modify the U.S. standard atmosphere, which provides a relationship between temperature and pressure, so that the U.S. standard atmosphere temperature at 865 mb was also equal to -4.2℃.The modification required was a systematic reduction of the temperature profile by 11.0℃, which represents a cooler atmosphere than the U.S. standard atmosphere.This is consistent with the winter nature of the SLD observations.The modified U.S. standard atmosphere equation for computing pressure from temperature iswhere P is the pressure in Pascals and T is the temperature in Kelvin.The 11.0℃ modification can be clearly seen in the equation.Selected values of temperature and pressure for the modified U.S. standard atmosphere are given in table 4.These can be computed from the previous equation.The 0℃ LWC values from table 3 were assigned a pressure of 939 mb, which is consistent with the pressure at 0℃ in the modified U.S. standard atmosphere described above.For temperatures between 0° and -25℃, the corresponding pressures were determined using the equation provided above.For each temperature-pressure pair, the LWC was computed by assuming that the the liquid water mixing ratio remained constant for the changes in temperature and pressure from 0℃ and 939 mb.The LWC calculation is given by the following equationThe subscript “0C” refers to the values at 0℃ and 939 mb while the subscript “SA” refers to the values at temperature-pressure pairs of the modified U.S. Standard Atmosphere.The LWC0C values are taken from table 3.Note that the LWC values in the curves in figures 1 and 3 in the proposed Appendix X, which are identical to the curves in figures 11 and 12, should not be further normalized or adjusted for pressure by an applicant, since that would not be consistent with their derivation as just described.The values of LWC obtained directly from table 3 are valid only for the reference distances of 17.4 nmi(32.2 km).When considering longer(or shorter)exposure distances, the LWC originally selected may be reduced(or increased)for some applications by the SF shown in figure 7 of the proposed Appendix X. This SF is valid for each of the four SLD environments contained within Appendix X. It is also valid for different LWC probabilities such as the 99.9% LWC values.The derivation of the horizontal extent SF is discussed below.For each averaging interval, including the 30-s, 60-s, 120-s, and 300-s averages that corresponded to horizontal extents of 3, 6, 12, and 30 km, respectively, the collective SLD LWC observations, normalized to 0℃, were used to compute the 99% LWC value following the extreme value analysis described in section 3.21.It is important to note that all four Appendix X categories were grouped together for this analysis.In addition, there was no separation by temperature or MVD.Table 5 gives the sample size for 3, 6, 12, and 30 km data.The SLD 99% LWC values and the 95% confidence limits are plotted against the averaging distance in figure 13.Length ScaleLWC=0.553 - 0.089 log10(Distance)Averaging Length(km)The data in figure 13 were fit to a linear best fit aswhere dHkm is the horizontal averaging distance in km and LWC99 is the 99% LWC in g m-3 at the averaging distance dHkm.Based on equation 1, at a horizontal extent of 17.4 nmi the LWC is 0.418 g m-3.