Gaussian approximations in filters and smoothers for data assimilation

We present mathematical arguments and experimental evidence that suggest that Gaussian approximations of posterior distributions are appropriate even if the physical system under consideration is nonlinear. The reason for this is a regularizing effect of the observations that can turn multi-modal prior distributions into nearly Gaussian posterior distributions. This has important ramifications on data assimilation (DA) algorithms in numerical weather prediction because the various algorithms (ensemble Kalman filters/smoothers, variational methods, particle filters (PF)/smoothers (PS)) apply Gaussian approximations to different distributions, which leads to different approximate posterior distributions, and, subsequently, different degrees of error in their representation of the true posterior distribution. In particular, we explain that, in problems with medium' nonlinearity, (i) smoothers and variational methods tend to outperform ensemble Kalman filters; (ii) smoothers can be as accurate as PF, but may require fewer ensemble members; (iii) localization of PFs can introduce errors that are more severe than errors due to Gaussian approximations. In problems with strong' nonlinearity, posterior distributions are not amenable to Gaussian approximation. This happens, e.g. when posterior distributions are multi-modal. PFs can be used on these problems, but the required ensemble size is expected to be large (hundreds to thousands), even if the PFs are localized. Moreover, the usual indicators of performance (small root mean square error and comparable spread) may not be useful in strongly nonlinear problems. We arrive at these conclusions using a combination of theoretical considerations and a suite of numerical DA experiments with low- and high-dimensional nonlinear models in which we can control the nonlinearity.Office of Naval Research [N00173-17-2-C003, PE-0601153N]; Alfred P. Sloan Research Fellowship; National Science Foundation [DMS-1619630]Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Ion Funnel Augmented Mars Atmospheric Pressure Photoionization Mass Spectrometry for In Situ Detection of Organic Molecules

Laser desorption is an attractive technique for in situ sampling of organics on Mars given its relative simplicity. We demonstrate that under simulated Martian conditions (~2.5 Torr CO_2) laser desorption of neutral species (e.g., polycyclic aromatic hydrocarbons), followed by ionization with a simple ultraviolet light source such as a discharge lamp, offers an effective means of sampling organics for detection and identification with a mass spectrometer. An electrodynamic ion funnel is employed to provide efficient ion collection in the ambient Martian environment. This experimental methodology enables in situ sampling of Martian organics with minimal complexity and maximum flexibility

Dissolution geology of organic materials on Saturn’s moon Titan: alien analogs of terrestrial karst

Karst or dissolution geology can occur whenever a circulating fluid can dissolve a geological material. On Earth, the “classical” karst definition is for limestone (CaCO3) in water (H2O), but other material/solvent combinations can create terrestrial dissolution terrain as well. These include so-called “evaporite karst materials” such as halite (NaCl)/H2O or gypsum (CaSO4)/H2O, dolomite (CaMg(CO3)2)/H2O, and even silica (SiO2)/H2O [Ford and Williams, 2007].  On Mars, there has been the suggestion of kieserite (MgSO4)/H2O system that may have formed in an earlier, wetter environment [Baroni and Sgavetta, 2013]. Saturn’s moon Titan extends the definition of karst to include non-aqueous liquids dissolving a landscape made of organic materials. The Cassini mission has provided evidence that Titan’s 1.5 bar nitrogen atmosphrere and cryogenic 94 K surface temperature supports a hydrocarbon-based cycle on Titan similar to the terrestrial water cycle. These circulating liquids may be capable of dissolving some of the surface organic molecules derived from Titan’s complex atmospheric photochemistry. Although under a different gravity, temperature, materials and fluid regime, many of the features on Titan’s surface bear striking resemblances to terrestrial karst terrains. Our investigations have focused on the labyrinth terrains of Titan. These are elevated plateaux of organic materials that appear similar to polygonal karst, tower karst, and fluviokarst on Earth [Malaska et al., 2010; 2017]. Remote sensing data is consistent with these plateaux being constructed of low-dielectric organic materials [Janssen et al. 2009; 2016; Malaska et al, 2016b]. Theoretical calculations followed by cryogenic laboratory experiments have shown that organic materials found on Titan’s surface will dissolve when subjected to Titan’s rainfall of methane-rich fluids [Raulin, 1987; Lorenz and Lunine, 1996; Malaska et al., 2010; 2011; Malaska and Hodyss, 2014; Cornet et al., 2015] and preliminary modelling has been able to reproduce some of the morphologies observed on Titan [Cornet et al., 2017]. Titan’s labyrinth terrains may originate as mixed organic windblown sediments that are later lithified in a process similar to calcite-cemented sandstone on Earth. Organic molecules and sediments produced by Titan’s rich organic photochemistry include organic molecules such as acetylene (C2H2), ethylene (C2H4), hydrogen cyanide (HCN),  benzene (C2H6), acrylonitrile (C2H3CN), acetonitrile (CH3CN), cyanoacetylene (HC2CN), other alkynes and nitriles, and a complex refractory organic materials similar to laboratory tholins. Once uplifted, the saturation equilibrium and kinetics of dissolution for each material and fluid combination affecting the plateau may play key roles in determining how the karstic system will evolve [Malaska et al., 2011; Cornet et al., 2015]. Some of the Titan organic minerals will dissolve, while some will be left behind as an insoluble lag deposit. Advanced laboratory investigations of organic materials on Titan is underway to further understand how these geological structures evolve and compare them with the formation processes of terrestrial analogs. We suggest that karst is a general planetary process wherever circulating fluids are capable of dissolving materials and developing subsurface drainage

A co-crystal between benzene and ethane: a potential evaporite material for Saturn’s moon Titan

Using synchrotron X-ray powder diffraction, the structure of a co-crystal between benzene and ethane formed in situ at cryogenic conditions has been determined, and validated using dispersion-corrected density functional theory calculations. The structure comprises a lattice of benzene molecules hosting ethane molecules within channels. Similarity between the intermolecular interactions found in the co-crystal and in pure benzene indicate that the C— H network of benzene is maintained in the co-crystal, however, this expands to accommodate the guest ethane molecules. The co-crystal has a 3:1 benzene:ethane stoichiometry and is described in the space group R3 with a = 15.977 (1) A˚ and c = 5.581 (1) A˚ at 90 K, with a density of 1.067 g cm3 . The conditions under which this co-crystal forms identify it is a potential that forms from evaporation of Saturn’s moon Titan’s lakes, an evaporite material

A Deeper Analysis of Center-Finding Techniques for Tropical Cyclones in Mesoscale Models. Part I: Low-Wavenumber Analysis

AbstractA deeper analysis of possible errors and inconsistencies in the analysis of vortex asymmetries owing to the placement of centers of tropical cyclones (TCs) in mesoscale models is presented. Previous works have established that components of the 2D and 3D structure of these TCs—primarily radial wind and vertical tilt—can vary greatly depending on how the center of a model TC is defined. This work will seek to expand the previous research on this topic, but only for the 2D structure. To be specific, this work will present how low-wavenumber azimuthal Fourier analyses can vary with center displacement using idealized, parametric TC-like vortices. It is shown that the errors associated with aliasing the mean are sensitive primarily to the difference between the peak of vorticity inside the radius of maximum winds and the average vorticity inside the core. Tangential wind and vorticity aliasing occur primarily in the core; radial wind aliasing spans the whole of the vortex. It is also shown that, when adding low-wavenumber asymmetries, the aliasing is dependent on the placement of the center relative to the location of the asymmetries on the vortex. It is also shown that the primary concern for 2D analysis when calculating the center of a TC is correctly resolving azimuthal wavenumber 0 tangential wind, because errors here will alias onto all higher wavenumbers, the specific structures of which are dependent on the structure of the mean vortex itself