Abstract
Abstract. In this paper we present a new description of statistical probability density functions (pdfs) of polar mesospheric clouds (PMCs). The analysis is based on observations of maximum backscatter, ice mass density, ice particle radius, and number density of ice particles measured by the ALOMAR Rayleigh–Mie–Raman lidar for all PMC seasons from 2002 to 2016. From this data set we derive a new class of pdfs that describe the statistics of PMC events that is different from previous statistical methods using the approach of an exponential distribution commonly named the g distribution. The new analysis describes successfully the probability distributions of ALOMAR lidar data. It turns out that the former g-function description is a special case of our new approach. In general the new statistical function can be applied to many kinds of different PMC parameters, e.g., maximum backscatter, integrated backscatter, ice mass density, ice water content, ice particle radius, ice particle number density, or albedo measured by satellites. As a main advantage the new method allows us to connect different observational PMC distributions of lidar and satellite data, and also to compare with distributions from ice model studies. In particular, the statistical distributions of different ice parameters can be compared with each other on the basis of a common assessment that facilitates, for example, trend analysis of PMC.
Highlights
In the derivation of the Z distribution we used the assumption that all ice parameters of maximum backscatter x = MBS, ice mass density y = IMD, ice particle radius r, and ice number density n are connected with one another by the power law given in Eq (5)
In this study we present a new method to describe statistical probability density functions for different ice parameters of polar mesospheric clouds (PMCs)
From this data set we derive ice cloud parameters of maximum backscatter, ice mass density, ice radius, and ice number density whose occurrence frequencies are investigated with respect to exponential distributions
Summary
First studies of probability distributions of polar mesospheric clouds (PMCs) were reported by Thomas (1995) using data from the UVS (ultraviolet spectrograph) instrument on board the Solar Mesosphere Explorer (SME) satellite and from the Solar Backscatter Ultraviolet (SBUV) instrument on the Nimbus-7 satellite over the period 1978–1986, measuring scattered limb albedo at 265 nm and nadir albedo at 273.5 nm, respectively. Thomas (1995) introduced empirical measures in the statistical analysis of PMC brightness distributions. Thomas (1995) introduced empirical measures in the statistical analysis of PMC brightness distributions. First studies of probability distributions of polar mesospheric clouds (PMCs) were reported by Thomas (1995) using data from the UVS (ultraviolet spectrograph) instrument on board the Solar Mesosphere Explorer (SME) satellite and from the Solar Backscatter Ultraviolet (SBUV) instrument on the Nimbus-7 satellite over the period 1978–1986, measuring scattered limb albedo at 265 nm and nadir albedo at 273.5 nm, respectively. He showed that the frequency distribution of PMC albedo derived from both SME and SBUV satellite data can be approximated by an (normalized) exponential probability function, see Fig. 3 in Thomas (1995). Model analyses have used the g function investigating trends and long-term changes in PMC parameters (Lübken et al, 2013; Berger and Lübken, 2015)
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