Venus Modeling Workshop (2017) 8017.pdf

STOCHASTIC MODELS OF LIGHTNING AND LIGHTNING DETECTION ON . R. D. Lorenz 1, 1Johns Hopkins Applied Physics Laboratory, Laurel, MD 20723, USA ([email protected])

Introduction: Observations regarding lightning on Even with very poor statistics (7 flashes), the opti- Venus are mutually discrepant, with positive and nega- cal survey by Hansell et al. [3] found ‘an indication tive reports. A model of lightning as a pure random that Venus undergoes quiet times and noisy times ’ process with a uniform rate appears to be incompatible since on four nights of observation the counts were with the observation set. While a plausible thesis is [2,2,0,3], with the last 3 occurring within 10 minutes of that one or more observations are 'wrong' in asserting each other. On the other hand, in part such an interpretation, here I explore models of possible stochasticity may also be due to variations in the detec- temporal and/or spatial variability of lightning in an tion efficiency (such as the claimed dependence of Ve- attempt to maximize agreement with observations nus Express magnetometer signatures of lightning on while minimizing the number of model parameters. the geometry of the magnetic field lines) : Russell et al. Clustered Occurrences: The first-order analysis [4] note only 61 detections in some 12,223s of obser- of any phenomenon not unreasonably posits a Poisson vation, but consider that the observations only access process with a single, uniform occurrence rate λ. An Venus 1/4 of the time, and over only a few hundred km observation is then a set T of Bernouilli trials (detect ? (0.027% of the planet's area) : their extrapolation of a Y/N) which attempt to constrain λ as ~Y/T. A major 18/s global flash rate (20% of ) based on the challenge in reconciling observations to date is that the wholly unsupported assumption that the flash rate is detection threshold (typically, a top-of-atmosphere uniform. light flash energy) is not always accurately quantified, Although ultimately it may be necessary to develop and is typically different for different searches, and a spatial variability model to explicitly track the migra- without taking this into account (wherein the popula- tion of "storms" and the intersection of those lightning- tion of lightning events has some distribution that favorable regions with an observation process, a first yields different counts for different thresholds) the step is simply to posit two additional variable – a char- comparisons are largely meaningless. acteristic duration S of a storm, and an occurrence rate Some progress has been made in recent years in R, and to adopt λ as a conditional quantity (i.e. λ=λo addressing analogous challenges in planetary meteor- during a storm, λ=0 otherwise). If (as is presently the ology, namely assessing the population of dust devils case) the observation duty cycle is small, it is possible on Earth and . A simple and physically-based ob- to find many nondetections that are not inconsistent servation-dependent threshold detection with a plausi- with a few high-rate detections. ble (power law) distribution of dust devil diameters [1] Conclusions: Efforts are underway to develop a was able to reconcile reported dust devil occurrence reasonably parsimonious model of lightning variability rates (devils/km2/day) which differed by four orders of and detection on Venus to reconcile at least some ob- magnitude! These surveys were all conducted, howev- servation claims. This modeling will help interpret er, at locations/times expected a priori to have dust results from the Lightning and Airglow Camera (LAC) devils, and typically with long enough periods that day- on the Venus Climate Orbiter. to-day variations were averaged out. Acknowledgement: This work was supported by Inspection of dust devil occurrences (e.g. the num- NASA Venus Climate Orbiter Participating Scientist ber of devils in single orbital Mars images) shows a Grant NNX16AC78G. strongly non-Poisson distribution, with the number of References: [1] Lorenz, R. (2009), Power Law of 'many-devil' images disproproportionate to an extrapo- Dust Devil Diameters on Earth and Mars, Icarus, 203, lation given the number of single- and few-devil imag- 683-684 [2] Lorenz, R., and B. Jackson (2016) Dust es. In other words, there is at least one 'hidden variable' Devil Populations and Statistics, Space Science Re- determining whether conditions are favorable for dust views, 10.1007/s11214-016-0277-9 [3] Hansell, S. et devils or not (typically the ambient wind speed). al., (1995) Optical Detection of Lightning on Venus, This paradigm seems appropriate for lightning on Icarus, 117, 345-351 [4] Russell, C. et al. (2008) Venus, if it exists, as indeed it seems to be true for Whistler mode waves from lightning on Venus: Mag- lightning on Earth. Casual observation indicates that if netic control of ionospheric access, J. Geophys. Res., one sees one lightning flash, one is likely to see many, 113, E00B05, doi:10.1029/2008JE003137 because there is a storm, whereas overall storms are rare.