A phenomenological relationship between vertical air motion and disdrometer derived A-b coefficients

Abstract: Using the well-known Z-R power law, Z = A R^b, A-b parameters derived from a single disdrometer are readily found and can provide useful information to study rainfall drop size distributions (DSDs). However, large variations in values are often seen when comparing A-b sets from various researchers. Values of b typically range from 1.25 to 1.55 for both stratiform and convective events. The values of A approximately fall into three groups: 150 to 200 for convective, 200 to 400 for stratiform, and 400 to 500 for convective. Computing the A-b parameters using the gamma DSD, coupled with a modified drop terminal velocity model, vD(D) = vT(D) - w, where D is drop diameter, vT(D) is still air drop terminal velocity, and w is an estimate of vertical velocity of the air well above the disdrometer, shows an interesting result. This model predicts three regions of A, corresponding to w < 0, w = 0, and w > 0. Additional models that incorporate a constant vertical air velocity are also investigated. A-b sets derived from a Joss Waldvogel (JW) disdrometer and DSD data acquired near Athalassa, Cyprus, using selected 24 hour data sets from 2011 to 2014, are compared to the above models. The data is separated into two main groups: stratiform events defined by rainfall rates that did not exceed 10 mm/h at any time during the 24-hour period, and convective events defined by rainfall rates not flagged as stratiform. The convective rainfall is further separated into two groups: A-b pairs that fall to the left of the stratiform pairs and pairs that fall to the right. This procedure is repeated with data from other researchers that corresponds to seasonal averages. In all cases, the three vertical groupings of the A-b parameter plot seem to correlate to DSD simulations where various values of positive and negative vertical velocities are used.