A statistical analysis of Martian dust storms using the Landau probability distribution

Introduction

Dust is an essential part of the Martian atmosphere, and the notable dynamic phenomena of dust storms are quite intriguing on the planet. These storms significantly modify the dynamics and thermodynamics of the Martian atmosphere. Due to the lifted dust in the atmosphere, a layer is created that blocks the sunlight from reaching the surface and consequently generates a cooling effect. At the same time, it heats the atmosphere at higher altitudes due to the absorption and scattering of solar radiation [1]. Dust storms can also alter the atmospheric circulation and vertical structure [2, 3]. Thus, studying Martian dust storms can help us understand the comprehensive behavior of the Martian atmosphere. Studies have used both observational and numerical modeling datasets to analyze the characteristics of dust storms [3, 4]. The dust availability, dust lifting centers, trajectories, and several other features of the dust storms are identified through such analysis. But they are a bit time-consuming and often require high computational resources. However, several characteristics of dust storms can be statistically interpreted through probability distributions or polynomial functions. This study uses the Landau distribution to analyze several dust storms and investigate the peak, dust availability, duration, etc.

Data and Methodology

During the growth phase of a dust storm, a rapid increase in dust is observed, which continues till the peak, followed by an elongated decay phase. So, a time series analysis of dust opacity will indicate a right-skewed variation. Thus, right-skewed probability distribution, like the Landau type, is used here to fit the time series plot and get a statistical interpretation of dust storms. The dust opacity (d) for a storm can be fitted using the distribution as:

                                                                                                                                                      d = τ + αL( μ, σ)                                                                                                                                   (1)

where L is the Landau distribution. τ, α, μ, and σ are constants that signify several physical characteristics of the storm. Column dust optical depth (CDOD) is a measure of the total amount of dust over the entire atmospheric column, and it is used in the current analysis as it incorporates all the pressure levels. CDOD data obtained from the Montabone dust scenario [5, 6] is used to fit the probability distribution.

Results

The dust availability is determined by the background dust (τ). The strength and maximum opacity during the storm are determined through the intensity parameter (α). The peak of the dust storm is specified by the location parameter (μ). The duration of the storm is signified by the scale parameter (σ). In this study, four storms are considered across different Martian years (MY) and seasons. The storms happened around L_S=180°-270° in MY 34 (DS1); L_S=310°-340° (DS2) in MY 35; L_S=150°-170° (DS3), and L_S=250°-280° (DS4) in MY 36. DS1 is a global dust storm, and DS2 is a large regional storm. Notably, DS3 is a small regional storm, and DS4 is a regional storm near the southern polar cap. The Landau distribution fit seems to capture the growth of the dust storm very well (Figure 1). However, there are slight deviations around the peak, and underestimation is observed in most instances. The exact peak for all the storms is not properly realized. The distribution usually overestimates in the early stage of the decay phase and underestimates in the later stages. However, if the decay phase is prolonged, like that for a global dust storm (DS1), it follows closely the Landau distribution (Figure 1a). However, if the dust storm has a slow growth phase (Figure 1d), it fails to capture the trend completely, as the slow-growth dust storms show a symmetrical distribution.

Figure 1. The Landau distribution fits (red line) with the actual data (black dots) for DS1 (a), DS2 (b), DS3 (c), and DS4 (d).

The background dust (τ) is strictly dependent on the season and provides an idea about the dust availability (Table 1). For the global storm (DS1), the τ value is greater, hinting at higher dust availability, which is the probable reason for the growth of the storm into a global one. A high τ value for DS4 signifies the greater dust availability due to the southern summer. As DS3 happens in the early part of the dust season, it shows the lowest τ. The larger value of α indicates a higher intensity of the storm, which is realized through the maximum CDOD values. DS1, being a global event, shows the highest α. And DS3, being an early-season storm with lower dust availability, shows the lowest α. However, any empirical relationship between the peak CDOD and α could not be established. The peak of the dust storms can be estimated as  , which is found to match with peaks of DS2 and DS3, but deviates a lot for DS1 and DS4. The Landau distribution fit captured the peak of DS1 much earlier (Figure 1a), and it did not show a good fit for DS4, indicating a mismatch. The higher σ value represents the longer duration of the storm. As DS1 is a global storm, it has the longest duration, and with DS4, a storm with a slow growth phase, an overall extended duration is realized. In terms of L_S, the approximate duration (initiation to decay) is estimated to be 4.338σ.

Table 1. The parameters for the dust storms obtained from the Landau distribution.

 

Conclusions

The Landau distribution greatly helps in understanding several characteristics of the Martian dust storms. The growth phase is captured well, and the decay phase is more or less followed, whereas the exact peak is not properly captured. The proposed approach can be useful to study the dust storms alongside the conventional analysis. Although this study has used CDOD values, the distribution is expected to work with dust opacity for different pressure levels. However, altitudes near the surface would not perform well due to non-uniform dust-lifting.

References

[1] Panda et al. (2025). New Astronomy Reviews, 101723. [2] Haberle (1986). Science, 234(4775). [3] Kass et al. (2016). GRL, 43(12). [4] Bertrand et al. (2020). JGR: Planets, 125(7). [5] Montabone et al. (2015). Icarus, 251, 65-95. [6] Montabone et al. (2020). JGR: Planets, 125(8).