Estimation of drift and diffusion functions from time series data: A maximum likelihood framework

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This contribution develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem this contribution solves important problems concerning the applicability and the accuracy of estimated parameters.Comment: 18 pages, 2 figure

Catastrophic ice lake collapse in Aram Chaos, Mars

Hesperian chaotic terrains have been recognized as the source of outflow channels formed by catastrophic outflows. Four main scenarios have been proposed for the formation of chaotic terrains that involve different amounts of water and single or multiple outflow events. Here, we test these scenarios with morphological and structural analyses of imagery and elevation data for Aram Chaos in conjunction with numerical modeling of the morphological evolution of the catastrophic carving of the outflow valley. The morphological and geological analyses of Aram Chaos suggest large-scale collapse and subsidence (1500 m) of the entire area, which is consistent with a massive expulsion of liquid water from the subsurface in one single event. The combined observations suggest a complex process starting with the outflow of water from two small channels, followed by continuous groundwater sapping and headward erosion and ending with a catastrophic lake rim collapse and carving of the Aram Valley, which is synchronous with the 2.5 Ga stage of the Ares Vallis formation. The water volume and formative time scale required to carve the Aram channels indicate that a single, rapid (maximum tens of days) and catastrophic (flood volume of 9.3?104 km3) event carved the outflow channel. We conclude that a sub-ice lake collapse model can best explain the features of the Aram Chaos Valley system as well as the time scale required for its formation.Comment: 20 pages, 17 figures. Icarus, 201

Groundwater seepage landscapes from distant and local sources in experiments and on Mars

© 2014 Author(s). Valleys with theater-shaped heads can form due to the seepage of groundwater and as a result of knickpoint (waterfall) erosion generated by overland flow. This ambiguity in the mechanism of formation hampers the interpretation of such valleys on Mars, particularly since there is limited knowledge of material properties. Moreover, the hydrological implications of a groundwater or surface water origin are important for our understanding of the evolution of surface features on Mars, and a quantification of valley morphologies at the landscape scale may provide diagnostic insights on the formative hydrological conditions. However, flow patterns and the resulting landscapes produced by different sources of groundwater are poorly understood. We aim to improve the understanding of the formation of entire valley landscapes through seepage processes from different groundwater sources that will provide a framework of landscape metrics for the interpretation of such systems. We study groundwater seepage from a distant source of groundwater and from infiltration of local precipitation in a series of sandbox experiments and combine our results with previous experiments and observations of the Martian surface. Key results are that groundwater flow piracy acts on valleys fed by a distant groundwater source and results in a sparsely dissected landscape of many small and a few large valleys. In contrast, valleys fed by a local groundwater source, i.e., nearby infiltration, result in a densely dissected landscape. In addition, valleys fed by a distant groundwater source grow towards that source, while valleys with a local source grow in a broad range of directions and have a strong tendency to bifurcate, particularly on flatter surfaces. We consider these results with respect to two Martian cases: Louros Valles shows properties of seepage by a local source of groundwater and Nirgal Vallis shows evidence of a distant source, which we interpret as groundwater flow from Tharsis

Laboratory and telescope use of the NICMOS2 128 x 128 HgCdTe array

The second generation of Hubble Space Telescope (HST) instruments will include a near-infrared instrument. This choice has driven the development of near-infrared arrays to larger sizes and lower read noises. Rockwell International has delivered an array for use in the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) instrument; this array has been dubbed NICMOS2. NICMOS2 is a 128x128 array of HgCdTe diodes In-bonded to a switched MOSFET readout. The readout was specifically designed for astronomical use with the HST requirement of low read noise a prime goal. These arrays use detector material which is similar to that used by Rockwell in previous arrays (e.g., HgCdTe produced on a sapphire substrate), but the NICMOS2 devices differ substantially from other 128x128 arrays produced by Rockwell in having a read noise of only 30 electrons when read out using appropriate correlated sampling. NICMOS2 has now been characterized in the laboratory, and it has been used on groundbased telescopes

Near-bed and surface flow division patterns in experimental river bifurcations

Understanding channel bifurcation mechanics is of great importance for predicting and managing multichannel river processes and avulsion in distributary river deltas. To date, research on river channel bifurcations has focused on factors determining the stability and evolution of bifurcations. It has recently been shown that, theoretically, the nonlinearity of the relation between sediment transport and flow discharge causes one of the two distributaries of a (slightly) asymmetrical bifurcation to grow and the other to shrink. The positive feedback introduced by this effect results in highly asymmetrical bifurcations. However, there is a lack of detailed insight into flow dynamics within river bifurcations, the consequent effect on bed load flux through bifurcating channels, and thus the impact on bifurcation stability over time. In this paper, three key parameters (discharge ratio, width-to-depth ratio, and bed roughness) were varied in order to examine the secondary flow field and its effect on flow partitioning, particularly near-bed and surface flow, at an experimental bifurcation. Discharge ratio was controlled by varying downstream water levels. Flow fields were quantified using both particle image velocimetry and ultrasonic Doppler velocity profiling. Results show that a bifurcation induces secondary flow cells upstream of the bifurcation. In the case of unequal discharge ratio, a strong increase in the secondary flow near the bed causes a larger volume of near-bed flow to enter the dominant channel compared to surface and depth-averaged flow. However, this effect diminishes with larger width-to-depth ratio and with increased bed roughness. The flow structure and division pattern will likely have a stabilizing effect on river channel bifurcations. The magnitude of this effect in relation to previously identified destabilizing effects is addressed by proposing an adjustment to a widely used empirical bed load nodal-point partition equation. Our finding implies that river bifurcations can be stable under a wider range of conditions than previously thought. Key Points Secondary flow in symmetrical bifurcations causes strong near-bed flow curvature A disproportional amount of near-bed flow enters the dominant downstream channel Flow curvature adds a stabilizing feedback on bifurcation evolution

On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise

This article reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as well as dynamical noise which is an intrinsic part of the dynamical process can be quantified correctly, solely on the basis of measured times series and proper data analysis. Finally real world data sets are presented pointing out the relevance of the new approach

Subordination Pathways to Fractional Diffusion

The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a random walk along the line of space, happening in operational time;(rw_3), the inversion of (rw_1), namely a random walk along the line of operational time, happening in natural time. Via the general integral equation of CTRW and appropriate rescaling, the transition to the diffusion limit is carried out for each of these three random walks. Combining the limits of (rw_1) and (rw_2) we get the method of parametric subordination for generating particle paths, whereas combination of (rw_2) and (rw_3) yields the subordination integral for the sojourn probability density in space-time fractional diffusion.Comment: 20 pages, 4 figure

MODEX: Laboratory experiment exploring sediment spreading of a mound under waves and currents

The dispersal of sand from submerged mounds in the nearshore is driven by the interplay of processes such as converging and recirculating flows, changing roughness, bed slope effects and wave focusing/refraction. This morphological diffusivity is key to understanding sand bars in shallow seas, tidal inlets, estuaries, and the nearshore response to human interventions such as nourishments and dredging. Most of the work on the evolution of submerged mounds has been based on fluvial studies, focusing on flow without waves. In these cases, circular mounds tend to deform to crescentic (barchan) shapes. In contrast, observations of sandbars and berms in the nearshore subjected to waves show much more complex translation and deformation behavior. This contribution introduces the laboratory MOrphological Diffusivity Experiment (MODEX) aimed at examining morphological diffusivity under different forcing conditions. The experiment particularly addresses the linkages between small scale (local) effects (e.g. bed slope, bedforms) on the adjustment of sandy mounds.Peer ReviewedPostprint (published version

Palaeoflow and Sediment Delivery Reconstructions from Martian Delta Morphology by Combined Modelling and HRSC DTM Analysis

have been formed by sapping. On the left of the delta there is a second lobe that may have formed as an initial drowned delta or alluvial fan. Summary: The size and shape of alluvial fans and deltas contain information on their formative time scale, sediment supply and the amount of water involved. A new numerical morphological model is presented that allows quantitative comparison of morphological predictions and HRSC DTMdata of six deltas. As morphology is uniquely coupled to water and sediment flux, the model also discriminates between dense flows (slurries) and dilute flows (rivers). We demonstrate that two Gilbert (Fig. 1) and three stepped fan deltas may have formed by dilute flows into filling lakes in less than 10 years. Introduction: Alluvial fans and deltas on Mars record past hydrological conditions. Until now these conditions were inferre

On distributions of functionals of anomalous diffusion paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.Comment: 25 pages, 4 figure