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This paper is focused on the optimization approach to the solution of inverse problems. We introduce a stochastic dynamical system in which the parameter-to-data map is embedded, with the goal of employing techniques from nonlinear Kalman filtering to estimate the parameter given the data. The extended Kalman filter (which we refer to as ExKI in the context of inverse problems) can be effective for some inverse problems approached this way, but is impractical when the forward map is not readily differentiable and is given as a black box, and also for high dimensional parameter spaces because of the need to propagate large covariance matrices. Application of ensemble Kalman filters, for example use of the ensemble Kalman inversion (EKI) algorithm, has emerged as a useful tool which overcomes both of these issues: it is derivative free and works with a low-rank covariance approximation formed from the ensemble. In this paper, we work with the ExKI, EKI, and a variant on EKI which we term unscented Kalman inversion (UKI). The paper contains two main contributions. Firstly, we identify a novel stochastic dynamical system in which the parameter-to-data map is embedded. We present theory in the linear case to show exponential convergence of the mean of the filtering distribution to the solution of a regularized least squares problem. This is in contrast to previous work in which the EKI has been employed where the dynamical system used leads to algebraic convergence to an unregularized problem. Secondly, we show that the application of the UKI to this novel stochastic dynamical system yields improved inversion results, in comparison with the application of EKI to the same novel stochastic dynamical system. The numerical experiments include proof-of-concept linear examples and various applied nonlinear inverse problems: learning of permeability parameters in subsurface flow; learning the damage field from structure deformation; learning the Navier-Stokes initial condition from solution data at positive times; learning subgrid-scale parameters in a general circulation model (GCM) from time-averaged statistics. • A filtering-based method for inverse problems with novel stochastic dynamical systems. • Derive extended, ensemble, and unscented Kalman inversions for inverse problems. • The method induces a form of Tikhonov regularization to overcome ill-posedness. • Prove that the method features exponential convergence for linear inverse problems. • Test on 8 inverse problems, including calibrating a 3D climate model. [ABSTRACT FROM AUTHOR]

Abstract General Circulation Models with interactive physical and chemistry processes are the state-of-the-art tools for an integrated view and understanding of the Martian atmosphere and climate system. The GEM-Mars model currently includes 16 tracers for chemical composition and applies a fully online, interactive calculation of the photo- and gas phase chemistry of carbon dioxide (CO 2) and water vapor (H 2 O). These species largely control the chemical composition of the neutral Mars atmosphere through their photolysis products and their subsequent interactions. Water vapor undergoes a complex cycle on Mars as it is transported and interacts with ice reservoirs both at the planet's surface and at water ice clouds, which in turn provide radiative feedbacks. In the photochemical cycles involving CO 2 and H 2 O, the abundances of 5 species have been reported by previous investigations with significant spatio-temporal coverage: CO 2 , H 2 O, CO, O 3 and H 2 O 2. This paper presents the current status of the atmospheric chemistry simulations in GEM-Mars by comparing them to a selection of these observational datasets as well as to oxygen dayglow emission from O 2 (a1∆ g). The results are consistent with previous model-data comparisons and illustrate that the water cycle and the photochemistry are well implemented in the model. In particular, the simulation of the key reservoir species H 2 O 2 provides a good match to the available data. Model-data biases for ozone columns and oxygen airglow are related to the simulated water vapor vertical profile, as these species have important column contributions from vertical layers at the top of the hygropause. Highlights • GEM-Mars is a global Mars atmospheric model with online atmospheric chemistry. • Comparisons to a broad set of observations show good performance. • Good simulation of CO 2 , CO, H 2 O, H 2 O 2 , O 3 and O 2 (a1∆ g) airglow • Model-data bias for O 3 relates to biases in the simulated water vertical profile. • Middle-atmospheric water excess related to excessive heating by water ice clouds [ABSTRACT FROM AUTHOR]

GEM-Mars is a gridpoint-based three-dimensional general circulation model (GCM) of the Mars atmosphere extending from the surface to approximately 150 km based on the GEM (Global Environmental Multiscale) model, part of the operational weather forecasting and data assimilation system for Canada. After the initial modification for Mars, the model has undergone considerable changes. GEM-Mars is now based on GEM 4.2.0 and many physical parameterizations have been added for Mars-specific atmospheric processes and surface-atmosphere exchange. The model simulates interactive carbon dioxide-, dust-, water- and atmospheric chemistry cycles. Dust and water ice clouds are radiatively active. Size distributed dust is lifted by saltation and dust devils. The model includes 16 chemical species (CO 2 , Argon, N 2 , O 2 , CO, H 2 O, CH 4 , O 3 , O( 1 D), O, H, H 2 , OH, HO 2 , H 2 O 2 and O 2 (a 1 ∆ g )) and has fully interactive photochemistry (15 reactions) and gas-phase chemistry (31 reactions). GEM-Mars provides a good simulation of the water and ozone cycles. A variety of other passive tracers can be included for dedicated studies, such as the emission of methane. The model has both a hydrostatic and non-hydrostatic formulation, and together with a flexible grid definition provides a single platform for simulations on a variety of horizontal scales. The model code is fully parallelized using OMP and MPI. Model results are evaluated by comparison to a selection of observations from instruments on the surface and in orbit, relating to atmosphere and surface temperature and pressure, dust and ice content, polar ice mass, polar argon, and global water and ozone vertical columns. GEM-Mars will play an integral part in the analysis and interpretation of data that is received by the NOMAD spectrometer on the ESA-Roskosmos ExoMars Trace Gas Orbiter. The present paper provides an overview of the current status and capabilities of the GEM-Mars model and lays the foundations for more in-depth studies in support of the NOMAD mission. [ABSTRACT FROM AUTHOR]

Abstract: Current models of the general circulation of the global oceans employ a spatial discretization of the relevant hydrodynamic fields on Cartesian rectilinear grids. For many applications, significant benefit would be expected to accrue from the versatility offered by unstructured grids. However, until very recently, available numerical methods for performing integrations on unstructured grids could not conserve discrete dynamical invariants, a numerical model characteristic that is important for robust ocean simulations over large space and time scales (as needed, for instance, in climate modeling applications). Our purpose in this paper is to describe such a conservative discretization scheme for rotating hydrostatic Boussinesq fluid dynamics on general triangular tessellations of the sphere, and to demonstrate its properties in a number of simulations that incorporate realistic ocean basin geometry. Several different implicit time discretizations are possible, each of which exhibits a form of exact numerical energy conservation in the absence of dissipation. The properties of this new numerical methodology are validated through analysis of a sequence of unforced nonlinear dynamical problems, which clearly demonstrate the capacity of the model to resolve the geostrophic adjustment process and the onset of baroclinic instability in collapsing density fronts. As a final test, a number of ocean modeling experiments with realistic climatological and wind-stress forcing are performed in order to investigate the manner in which different mesh structures and resolutions influence the simulated phenomenology. As the theoretical properties of the numerical methodology suggest, it is thereby shown to be both robust and stable. The further work that will be required to implement this structure in a state-of-the-art oceanic general circulation model, as well as other potential applications of the techniques, are discussed in the concluding section of the paper. [Copyright &y& Elsevier]

There may be a chance of small-scale ephemeral liquid water formation on present-day Mars, even though the current climate does not support the existence of larger bodies of water. Through a process called deliquescence, hygroscopic salts can enter solution by absorbing water vapor directly from the atmosphere. Due to the absence of in-situ deliquescence experiments so far, the most reliable way to forecast deliquescence is through atmospheric modeling; however, the locations and times when salty liquid water could emerge are not yet well known. In this paper, we present our results of likely brine formation on Mars, its proposed locations and seasons, as well as the possible limiting factors. For our calculations we used the data of Laboratoire de Météorologie Dynamique Mars General Circulation Model version 5. The results show that from L s 3 5 ∘ - L s 16 0 ∘ , between 9 PM and 11 PM there is a good chance for calcium perchlorate deliquescence above 30 ∘ N, while in this zone the ideal regions are concentrated mostly to Acidalia Planitia and Utopia Planitia. We found that in the Southern Hemisphere, between L s 19 5 ∘ and L s 32 0 ∘ , there is a noticeable, but weaker, band in the vicinity of 60 ∘ S, and both Argyre Planitia and Hellas Planitia show some chance for brine formation. According to our results, the key limiting circumstance of deliquescence could be relative humidity in most cases, when the circumstances are nearly ideal (with the exception of one factor only). Our results suggest that during summer–early fall seasons, there could be deliquescence in both hemispheres in specific areas from the late evening until the early morning hours. There are only few studies detailing the geological and temporal distribution of brine formation through deliquescence; thus, this work could be used as a good guide for future landing site analysis or in choosing a specific location for further research. • We investigate seasonal and global chance for perchlorate deliquescence on Mars. • Good chance for deliquescence Ls 35 ∘ - Ls 160 ∘ above 30 ∘ N. • Ideal regions are concentrated mostly to Acidalia Planitia and Utopia Planitia. • Some deliquescence chance near 60 ∘ S from Ls 195 ∘ to Ls 320 ∘. • When conditions are almost ideal, relative humidity seems to be the limiting value. [ABSTRACT FROM AUTHOR]

The deep convective cloud–environment feedback loop is likely important to Titan's global methane, energy, and momentum cycles, just as it is for Earth's global water, energy, and momentum budgets. General circulation models of Titan's atmosphere are unable to explicitly simulate deep convection and must instead parameterize the impact of this important subgrid-scale phenomenon on the model-resolved atmospheric state. The goal of this study is to better quantify through cloud resolving modeling the effects of deep convective methane storms on their environment and to feed that information forward to improve parameterizations in global models. Dozens of atmospheric profiles unstable with respect to deep moist convection are extracted from the global Titan Atmospheric Model (TAM) and used to initialize the cloud-resolving Titan Regional Atmospheric Modeling System (TRAMS). Mean profiles of heating/cooling and moistening/drying of the large-scale environment in TRAMS indicate that Titan's deep convection forces the environment in a manner analogous to Earth: Large-scale subsidence of the environmental air warms and dries the environment, but clouds can also moisten the environment through the detrainment and evaporation of condensate near cloud top. Relative humidity profiles and characteristic convective time scales are derived to guide the tuning of the deep convective parameterization implemented in TAM, as described in a companion paper. The triggering of convection, the dry convective mixing of the planetary boundary layer, and the entrainment of environmental air into rising air parcels are found to be critical to determining whether a deep convective cloud will form. Only profiles with relatively large convective available potential energy (CAPE) and well mixed planetary boundary layers with high relative humidity were found to produce storms. Environments with low-level thermal inversions and planetary boundary layers with low relative humidity or rapidly decreasing moisture with height failed to generate deep convection in TRAMS despite positive CAPE. • Cloud resolving simulations are initialized with soundings from a global atmospheric model of Titan. • The impact of deep convection on the large-scale environment is diagnosed. • Titan's large-scale environmental response to deep convection is analogous to Earth. • Tunable parameters for a deep convective parameterization in global models are derived. [ABSTRACT FROM AUTHOR]

In this paper we report new results concerning the seasonal atmospheric evolution near Titan's poles and equator in terms of temperature and composition using nadir spectra acquired by the Cassini Composite Infrared Spectrometer (CIRS) at high spectral resolution during the last year of the Cassini mission in 2017 complementing previous investigations covering almost two Titan seasons. In recent previous papers (Coustenis et al., 2016, 2018), we have reported on monitoring of Titan's stratosphere near the poles after the mid-2009 northern spring equinox. In particular we have reported on the observed strong temperature decrease and compositional enhancement above Titan's southern polar latitudes since 2012 and until 2014 of several trace species, such as complex hydrocarbons and nitriles, which were previously observed only at high northern latitudes. This effect accompanied the transition of Titan's seasons from northern winter in 2002 to northern summer in 2017, while at that latter time, the southern hemisphere was entering winter. Our new data, acquired in 2017 and analyzed here, are important because they are the only ones recorded since 2014 close to the south pole in the mid-infrared nadir mode at high resolution. A large temperature increase in the southern polar stratosphere (by 10–50 K in the 0.1 mbar–0.01 mbar pressure range) is found associated with a change in the temperature profile's shape. The 2017 observations also show a related significant decrease in most of the southern abundances which must have started sometime between 2014 and 2017. For the north, the spectra indicate a continuation of the decrease of the abundances which we first reported to have started in 2015 and small temperature variations. We discuss comparisons with other results and with current photochemical and dynamical models which could be updated and improved by the new constraints set by the findings presented here. • We have analyzed Cassini/CIRS Titan data acquired in 2017 at high spectral resolution. • We derive information on the thermal and chemical composition stratospheric structure. • We find a large temperature increase and a drop in abundances near the south pole. • Small thermal variations and continuing decrease in abundances are seen at the north. • This work brings new constraints to Global Circulation Models. [ABSTRACT FROM AUTHOR]

Robustness and cost effectiveness are major concerns for sustainable stormwater management under deep uncertainty of climate change. Given that many traditional static planning strategies are not working with unpredictable future conditions, the possibility of system failure, and the lock-in effects, the Adaptation Pathway (AP) approach was adopted for dynamically robust and cost-effective planning in this paper. In order to increase optimization accuracy of multi-staged planning, a continuous definition of the AP optimization problem was raised by improving the simplified versions in existing studies. A case study in Suzhou, a provincial pilot Sponge City in China undergoing increasing annual rainfall and severe water environment deterioration, was included by integrating Long-Term Hydrologic Impact Assessment-Low Impact Development model with optimization methods, aiming to persistently control the non-point source total phosphorus loading below an acceptable amount in the following unforeseen 20 years via multi-staged low-impact development (LID) construction. A novel optimization method developed by the authors in a companion paper, namely marginal-cost-based greedy strategy (MCGS), was successfully applied to efficiently solve the continuous version of the AP optimization problem. The popular genetic algorithm (GA) was used as a contrast. A weather generator was elaborated based on four Representative Concentration Pathway scenarios and 17 spatial downscaled general circulation models to simulate the unforeseen future annual rainfalls that helped with evaluating cost effectiveness of each prospective LID plan. Results showed that the adaptation pathways optimized by MCGS could save the whole life net present cost of an LID plan by 1%–60% compared with those optimized by GA, and the computational efficiency of MCGS was over 13 times faster than GA. • Deep uncertainty of climate change requires dynamically robust LID planning. • The Adaptation Pathway (AP) approach guarantees robustness and cost effectiveness. • The AP optimization problem was redefined in a continuous manner. • A greedy strategy was designed to optimize the adaptation pathway of LID placement. • The greedy strategy prevailed over the popular genetic algorithm significantly. [ABSTRACT FROM AUTHOR]

Abstract: In present-day forward time stepping ocean-climate models, capturing both the wind-driven and thermohaline components, a substantial amount of CPU time is needed in a so-called spin-up simulation to determine an equilibrium solution. In this paper, we present methodology based on Jacobian-Free Newton–Krylov methods to reduce the computational time for such a spin-up problem. We apply the method to an idealized configuration of a state-of-the-art ocean model, the Modular Ocean Model version 4 (MOM4). It is shown that a typical speed-up of a factor 10–25 with respect to the original MOM4 code can be achieved and that this speed-up increases with increasing horizontal resolution. [ABSTRACT FROM AUTHOR]

Abstract: Our understanding of Mercury’s sodium exosphere has improved considerably in the last 5years thanks to new observations (Schleicher, H., Wiedemann, G., Wöhl, H., Berkefeld, T., Soltau, D. [2004]. Astron. Astrophys. 425, 1119–1124) and to the publication of a summary of the large set of ground based observations (Potter, A.E., Killen, R.M., Morgan, T.H. [2007]. Icarus 186, 571–580; Potter, A.E., Killen, R.M. [2008]. Icarus 194, 1–12; ). In particular, the non-uniformity in longitude of the dayside sodium distribution (the dawn/dusk asymmetry) has now been clearly observed. This suggests that Mercury’s sodium exosphere is partly driven by a global day to nightside migration of the volatiles. One of the key questions remaining is the nature of the prevailing sodium ejection mechanisms. Because of the uncertain parameters for each ejection mechanisms, solving this problem has been difficult as indicated by the numerous papers over the last 15years with very different conclusions. In addition, the variation of the size and of the spatial distribution of the surface reservoir (Leblanc, F., Johnson, R.E. [2003]. Icarus 164, 261–281) varies with distance from the Sun affecting the importance of each ejection mechanism on Mercury’s orbital position. We here present an updated version of the Leblanc and Johnson (Leblanc, F., Johnson, R.E. [2003]. Icarus 164, 261–281) model. We take into account the two populations of sodium in the surface reservoir (Hunten, D.M., Morgan, T.M., Shemansky, D.M. [1988]. The Mercury atmosphere. In: Vilas, F., Chapman, C., Matthews, M. (Eds.), Mercury. University of Arizona Press, Tucson, pp. 562–612), one ambient population (physisorbed in the regolith with low binding energy) and one source population (chemisorbed coming from grain interior or from fresh dust brought to the surface and characterized by a higher binding energy). We also incorporate a better description of the solar wind sputtering variation with solar conditions. The results of a large number of simulations of the sodium exosphere are compared with the measured annual cycle of Mercury sodium emission brightness. These measurements were obtained from the published data by Potter et al. (Potter, A.E., Killen, R.M., Morgan, T.H. [2007]. Icarus 186, 571–580) as well as from our own data obtained during the last 2years using THEMIS solar telescope. These data show that: the annual cycle in the emission brightness is roughly the same from 1year to another; there are significant discrepancies between what would be observed if the exospheric content were constant; and the annual cycle of Mercury’s sodium exosphere strongly depends on its position in its orbit so that there are seasons in Mercury’s exosphere. Based on these comparisons we derived the principal signatures for each ejection mechanism during a Mercury year and show that none of the ejection mechanisms dominates over the whole year. Rather, particular features of the annual cycle of the sodium intensity appear to be induced by one, temporarily dominant, ejection mechanism. Based on this analysis, we are able to roughly explain the annual cycle of Mercury’s exospheric sodium emission brightness. We also derive a set of parameters defining those ejection mechanisms which best reproduce this cycle. For our best case, Mercury’s exosphere content varies from ∼1.6±0.1×1028 Na atoms at TAA=140° and 70° respectively to ∼4.5±0.3×1028 Na atoms at TAA=180° and 0°. In addition, Mercury’s exospheric surface reservoir contains ∼1×1031 Na atoms at TAA=300° and at TAA=170° with up to three times more sodium atoms trapped in Mercury’s nightside than in its dayside surface. [Copyright &y& Elsevier]

Abstract: This paper reports on the results from an extensive study of all nadir-looking spectra acquired by Cassini/CIRS during the 44 flybys performed in the course of the nominal mission (2004–2008). With respect to the previous study (Coustenis, A., and 24 colleagues [2007]. Icarus 189, 35–62, on flybys TB–T10) we present here a significantly richer dataset with, in particular, more data at high northern and southern latitudes so that the abundances inferred here at these regions are more reliable. Our enhanced high-resolution dataset allows us to infer more precisely the chemical composition of Titan all over the disk. We also include improved spectroscopic data for some molecules and updated temperature profiles. The latitudinal distributions of all of the gaseous species are inferred. We furthermore test vertical distributions essentially for acetylene (C2H2) from CIRS limb-inferred data and from current General Circulation Models for Titan and compare our results on all the gaseous abundances with predictions from 1-D photochemical-radiative models to check the reliability of the chemical reactions and pathways. [Copyright &y& Elsevier]

Abstract: A study of the dynamics of the second largest anticyclone in Jupiter, Oval BA, and its red colour change that occurred in late 2005 is presented in a three part study. The first part, this paper, deals with its long-term kinematical and dynamical behaviour monitored since its formation in 2000 to September 2008 using ground-based observations archived at the public International Outer Planet Watch (IOPW) database. The vortex changed its zonal drift velocity from 1.8ms−1 in the period 2000–2002 to 0.8ms−1 in 2002–2003, and to 2.5ms−1 since late 2003. It also migrated southwards by 1.0±0.5° in latitude between 2000 and 2004, remaining afterwards at an almost fixed latitude position. During the period 2000–2007, the oval also changed its triangular-like shape to a more symmetrical one. No latitudinal change was found in the months before the development of a red annulus in its interior. The colour change took place in less than 5months in 2005–2006 and no red colour feature was observed to have been present or entrained by BA months before the annulus development. After detailed examination of the four encounters between BA and GRS that took place during this 9 year period, we did not detect any noticeable change in its drift rate or in apparent structure associated with the encounters at cloud level. Also, the area of BA did not significantly change in this period. Additionally, we found that BA displays a long-term oscillation of ∼160days in its longitude position with peak to peak amplitude of 1.2°. Numerical experiments using the global circulation model EPIC reproduce accurately the shape, connecting it to its latitude migration, and morphology of the oval and confirm that no strong interaction between BA and the GRS is possible at least in the current situation. [Copyright &y& Elsevier]

Groundwater is key to economic growth in the Mediterranean region. This is particularly true of areas such as southern Spain, where aquifers underpin social development by supplying water to a booming tourist industry. Intensive groundwater use raises sustainability concerns, as pumping often exceeds the long-term recharge rate. Climate change and population growth are likely to exacerbate the water supply challenge in the coming years, due to the expected decrease in rainfall and to increasing competition among users. This paper examines some of the main aquifers in the Costa del Sol region, one of Spain's leading tourist destinations, where intensive groundwater extraction has led to water table drawdowns and the desiccation of all major springs. A numerical model was developed and calibrated for the purpose of evaluating the likely evolution of the system in the future. Downscaled scenarios from global circulation models were coupled with population growth forecasts to establish a range of plausible water management scenarios. Given the relatively small size of the aquifers and the limited recharge rate, the current pumping patterns appear unsustainable. Results suggest that drawdowns in excess of 150 m could take place within the next decade, thus compromising domestic supplies. Image 103287324 • A distributed model was applied to simulate water level evolution in Mijas range. • Three management scenarios were developed and tested for the 2015–2035 interval. • Climate change and current water management will produce an unsustainable situation. • New sources of water supply are needed to guarantee drinking water in Mijas area. [ABSTRACT FROM AUTHOR]