Liquid water fade margin requirements for infrared and millimeter wave runway imaging sensors in fog

Liquid water content and particle size distribution at each ten meters in the vertical for a deep advection fog and a shallow radiation fog are analyzed to determine the liquid water loss at millimeter and infrared wavelengths. The liquid water fade margin is calculated along a three degree glideslope in each fog from the current height above the runway to the touchdown point. Millimeter wave fade margin requirements are calculated from the vertical distribution of bulk liquid water content and infrared fade margin requirements are predicted from the vertical distribution of dropsize. Fog dropsize distributions for both fog layers are well fitted to a gamma distribution with a median drop diameter of approximately 9 microns. Millimeter wave imaging sensors operating in a shallow radiation fog are shown to require less than 1 dB of one-way liquid water fade margin. In the deep advection fog, one-way liquid water fade margin requirements at 8.6 mm, 6.8 mm, and 3.2 mm are predicted to be 1, 2, and 6.7 dB respectively. In comparison, the one-way liquid water fade margin requirements at near, middle, and far infrared wavelengths are two orders of magnitude greater than at millimeter wavelengths and indicate the fog layers are opaque to infrared imaging sensors even near the touchdown point. The specific attenuations predicted in the two fogs are consistent with previously reported values.