scholarly journals A practical two-phase approach to improve the reliability and efficiency of Markov chain Monte Carlo directed hydrologic model calibration

2020 ◽  
Author(s):  
Brian Skahill ◽  
Jeffrey Baggett
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Model Calibration ◽  
Hydrologic Model ◽  
Two Phase ◽  
Phase Approach ◽  
Hydrologic Model Calibration

Enceladus geyser study using Markov Chain Monte Carlo fits of DSMC simulations

2020 ◽  
Author(s):  
David Goldstein ◽  
Arnaud Mahieux ◽  
Philip Varghese ◽  
Laurence Trafton
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Saline Water ◽  
Flow Characteristics ◽  
Density Field ◽  
Flow Density ◽  
Number Density ◽  
Two Phase

<p>The two-phase water plumes arising from the Enceladus South pole and extending hundreds of km from the moon are a key signature of what lies below the surface. Multiple Cassini instruments measured the gas-particle plume over the warm Tiger Stripe region during several close flybys. A lot of work has been put into constraining the vent and flow characteristics, such the vent positions and orientations, the mass flows, speeds and temperatures.<br>The most likely source for these extensive geysers is a subsurface liquid reservoir of somewhat saline water and oth-er volatiles boiling off through crevasse-like conduits into the vacuum of space. The plumes thus provide a window for understanding Enceladus’ subsurface composition and geysering.<br>We used a DSMC code to simulate the plume, as it exits a vent, under axisymmetric conditions, in a vertical domain extending up to 10 km, where the flows become collisionless. We performed a DSMC parametric study of the flow parameters considering the following eight parameters: vent diameter, outgassed flow density, water vapor/ice mass ratio, gas and ice speed, ice grain diameter, temperature and vent exit angle.<br>We constructed parametric expressions for the plume characteristics – number density, temperature, velocity compo-nents – using simple analytic expressions to depict the constrained surfaces of these parameter values, at the 10 km upper boundary.<br>We use these parametrizations to propagate the plumes to higher altitudes – up to thousands of km – assuming free-molecular conditions. The density field at higher altitude is determined from the parametrizations described above, and explicit analytical expressions for the various force fields that the plumes are experiencing: Enceladus and Saturn gravity fields, Coriolis and centripetal accelerations due to Enceladus rotation.<br>This split domain approach enables rapid numerical computations – ~10 minutes – and tabulations of the density and velocity fields in space.<br>We then performed a formal Monte Carlo sensitivity analysis of twelve vent parameters – the ones cited above plus vent latitude, longitude, azimuth and zenith angles of the venting direction – conditioned on the number density field measured by the INMS instrument, considering the 98-vent geometry reported in Porco et al. (2014). The sensitivity analysis is used to determine which vent parameters should be considered for a subsequent fit of the INMS observa-tion. We present an advanced way to constrain the vent parameters by performing a Markov Chain Monte Carlo search that returns probability values for the preselected vent parameters, considering a few INMS observations. This ap-proach allows us to constrain many vent parameters (up to a few hundreds), and, uniquely, return probability distri-bution for each of them.</p>

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