Hank's rule states that the 5400 m contour for the 1000-500 hPa thickness is a rough predictor for the rain-snow boundary, i.e. about 50% of the time the 5400 m contour corresponds to snow at low elevations. Calculate the mean temperature of a 1000-500 hPa layer that is 5400 m thick. Assuming that the temperature varies as T(z) = To-Tz and that the mean temperature occurs at the midpoint of the layer (2700 m), what lapse rate is required to produce a freezing temperature at the surface (z = 0)? How does this compare to typical lapse rates for the troposphere?