The use of Lagrangian trajectories for the identification of the environmentally safe fairways

We propose and test a method for the optimisation of marine fairways to minimise the risk to high-value areas, based on statistical analysis of Lagrangian trajectories of current-driven pollution transport. The offshore areas are quantified according to the probability of pollution released in these areas to reach vulnerable regions. The method contains an eddy-resolving circulation model, a scheme for tracking of Lagrangian trajectories, a technique for the calculation of quantities characterising the potential of different sea areas to supply adverse impacts, and routines to construct the optimum fairway. The gain is expressed in terms of the probability of pollution transport to the nearshore and the associated time (particle age). The use of the optimum fairway would decrease the probability of coastal pollution by 40% or increase the average time of reaching the pollution to the coast from 5.3 to about 9 days in the Gulf of Finland, the Baltic Sea.     

Time evolution of orbital uncertainties for the impactor candidate 2004 AS1

We evaluate the asteroid impact risk from the discovery night onwards using six-dimensional statistical orbit computation techniques to examine the a posteriori probability density of the orbital elements. Close to the discovery moment the observational data of an object are typically exiguous: the number of observations is very small and/or the covered orbital arc is very short. For such data, the covariance matrices computed in the linear approximation (e.g., with the least-squares technique) are known to fail to describe the uncertainties in the orbital parameters. The technique of statistical ranging gives us rigorous means to assess the orbital uncertainties already on the discovery night. To examine the time evolution of orbital uncertainties, we make use of a new nonlinear Monte Carlo technique of phase-space sampling using volumes of variation, which complements the ranging technique for exiguous data and the least-squares technique for extensive observational data. We apply the statistical techniques to the near-Earth Asteroid 2004 AS₁, which grabbed the attention of asteroid scientists because, for one day, it posed the highest and most immediate impact risk so far recorded. We take this extreme case to illustrate the ambiguities in the impact risk assessment for short arcs. We confirm that the weighted fraction of the collision orbits at discovery was large but conclude that this was mostly due to the discordance of the discovery-night observations. This case study highlights the need to introduce a regularization in terms of an a priori probability density to secure the invariance of the probabilistic analysis especially in the nonlinear orbital inversion for short arcs. We remark that a predominant role of the a priori can give indications of the feasibility of the probabilistic interpretation, that is, how reliable the results derived from the a posteriori probability density are. Nevertheless, the strict mathematical definition of, e.g., the collision probability remains valid, and our nonlinear statistical techniques give us the means to always deduce, at the very least, order-of-magnitude-estimates for the collision probability.     

Extreme sea level events in the coastal waters of western Estonia

Extraordinarily low and high sea level events are analysed on the basis of historical data and their mechanisms of occurrence are studied with the 1 km grid size 2D hydrodynamic model in the two almost tideless semi-enclosed sub-basins of the Baltic Sea, the Gulf of Riga and the Väinameri. The sea level is modelled with realistic meteorological forcing and comparison data from 1999 and 2001. Resonance properties of the sub-basins are studied and their possible role in the formation of extraordinary sea level events is discussed. While the extremely low levels (−1.23 m below the mean sea level) in the Estonian coastal waters do not generally originate locally, the high levels (up to 2.53 m above the mean as measured in the Pärnu Bay) are short-term and local. They occur in combination with several forcing and morphometrical factors and are localised in the shallow and narrow bays exposed to the direction of the strongest possible storm winds, SW and W. Model simulations show that extremely high and low sea levels in some small bays of western Estonia can exceed the corresponding values in the Pärnu Bay.     

Identification of the environmentally safe fairway in the South-Western Baltic Sea and Kattegat

Application of the preventive techniques for the optimisation of fairways in the south-western Baltic Sea and the Kattegat in terms of protection of the coastal regions against current-driven surface transport of adverse impacts released from vessels is considered. The techniques rely on the quantification of the offshore domains (the points of release of adverse impacts) in terms of their ability to serve as a source of remote, current-driven danger to the nearshore. An approximate solution to this inverse problem of current-driven transport is obtained using statistical analysis of a large pool of Lagrangian trajectories of water particles calculated based on velocity fields from the Denmark’s Meteorological Institute (DMI)/BSH cmod circulation model forced by the DMI-HIRHAM wind fields for 1990–1994. The optimum fairways are identified from the spatial distributions of the probability of hitting the coast and for the time (particle age) it takes for the pollution to reach the coast. In general, the northern side of the Darss Sill area and the western domains of the Kattegat are safer to travel. The largest variations in the patterns of safe areas and the properties of pollution beaching occur owing to the interplay of water inflow and outflow. The gain from the use of the optimum fairways is in the range of 10–30?% in terms of the decrease in the probability of coastal hit within 10?days after pollution release or an increase by about 1–2?days of the time it takes for the hit to occur.     

Photometry and models of eight near-Earth asteroids

We present new observations and models of the shapes and rotational states of the eight near-Earth Asteroids (1580) Betulia, (1627) Ivar, (1980) Tezcatlipoca, (2100) Ra-Shalom, (3199) Nefertiti, (3908) Nyx, (4957) Brucemurray, and (5587) 1990 SB. We also outline some of their solar phase curves, corrected to common reference geometry with the models. Some of the targets may feature sizable global nonconvexities, but the observable solar phase angles were not sufficiently high for confirming these. None is likely to have a very densely cratered surface. We discuss the role of the intermediate topographic scale range in photometry, and surmise that this scale range is less important than large or small scale lengths.     

Can the Waves Generated by Fast Ferries be a Physical Model of Tsunami?

The potential of long ship-induced waves to serve as a physical model for tsunami waves (called simply tsunami below) is examined. Such waves (wavelengths more than 200 m at depths down to 10–20 m) are induced by high-speed ferries sailing at near-critical speeds in semisheltered, relatively shallow areas. It is shown based on experience from Tallinn Bay, Baltic Sea, that for many aspects these waves can model nearshore dynamics and runup of tsunami caused by landslides, including processes of wave refraction, diffraction, and sea-bottom interaction in bays and harbors. Many governing nondimensional parameters (such as the nonlinearity, dispersion, Reynolds and Ursell numbers, surf similarity parameter, breaking parameter, etc.) of the largest ship waves and landslide tsunamis have the same order of magnitude. It is especially important that use of ship waves for wave propagation and runup studies allows their spatial structure to be accounted for adequately. Near-critical ship waves can therefore be used as a natural substitute for tsunami, for study under controlled and safe conditions.     

OpenOrb: Open‐source asteroid orbit computation software including statistical ranging

Abstract— We are making an open‐source asteroid orbit computation software package called OpenOrb publicly available. OpenOrb is built on a well‐established Bayesian inversion theory, which means that it is to a large part complementary to orbit‐computation packages currently available. In particular, OpenOrb is the first package that contains tools for rigorously estimating the uncertainties resulting from the inverse problem of computing orbital elements using scarce astrometry. In addition to the well‐known least‐squares method, OpenOrb also contains both Monte‐Carlo (MC) and Markov‐Chain MC (MCMC; Oszkiewicz et al. [2009]) versions of the statistical ranging method. Ranging allows the user to obtain sampled, non‐Gaussian orbital‐element probability‐density functions and is therefore optimized for cases where the amount of astrometry is scarce or spans a relatively short time interval. Ranging‐based methods have successfully been applied to a variety of different problems such as rigorous ephemeris prediction, orbital element distribution studies for transneptunian objects, the computation of invariant collision probabilities between near‐Earth objects and the Earth, detection of linkages between astrometric asteroid observations within an apparition as well as between apparitions, and in the rigorous analysis of the impact of orbital arc length and/or astrometric uncertainty on the uncertainty of the resulting orbits. Tools for making ephemeris predictions and for classifying objects based on their orbits are also available in OpenOrb. As an example, we use OpenOrb in the search for candidate retrograde and/or high‐inclination objects similar to 2008 KV₄₂ in the known population of transneptunian objects that have an observational time span shorter than 30 days.     

The effect of the Baltic Sea level on gravity at the Metsähovi station

The loading effect of the Baltic Sea is immediately recognizable in the gravity record of the superconducting gravimeter T020 in Metsähovi, Finland, by simply inspecting residual gravity together with the tide gauge record at Helsinki 30 km away. The station is 10 km from the nearest bay of the Baltic Sea and 15 km from the open sea. Sea level variations in the Baltic are non-tidal and driven at short periods primarily by wind stress, at longer periods by water exchange through the Danish straits. Locally they can have a range of 2–3 m. Loading calculations show that a uniform layer of water covering the complete Baltic Sea increases the gravity in Metsähovi by 31 nm/s² per 1 m of water, and the vertical deformation is −11 mm. The observed gravity response to the local sea level is generally less, since the variations at short periods are far from uniform areally, the same water volume just being redistributed to different places. Regression of the whole gravity record (1994-2001) on local sea level gives 50–70% of the uniform layer response, as do loading calculations using actual water distributions derived from 11 tide gauges. However, both fits are dominated by some extreme values of short duration, and parts of the gravity record with long-period variations in sea level are close to the uniform layer response. The gravity observations can be used to test corrections for other co-located geodetic observations (GPS, satellite laser ranging) which are influenced by the load effect but not sensitive enough to discriminate between models.     

Combination of temporal gravity variations resulting from superconducting gravimeter (SG) recordings, GRACE satellite observations and global hydrology models

Gravity recovery and climate experiment (GRACE)-derived temporal gravity variations can be resolved within the μgal (10^?8 m/s ²) range, if we restrict the spatial resolution to a half-wavelength of about 1,500 km and the temporal resolution to 1 month. For independent validations, a comparison with ground gravity measurements is of fundamental interest. For this purpose, data from selected superconducting gravimeter (SG) stations forming the Global Geodynamics Project (GGP) network are used. For comparison, GRACE and SG data sets are reduced for the same known gravity effects due to Earth and ocean tides, pole tide and atmosphere. In contrast to GRACE, the SG also measures gravity changes due to load-induced height variations, whereas the satellite-derived models do not contain this effect. For a solid spherical harmonic decomposition of the gravity field, this load effect can be modelled using degree-dependent load Love numbers, and this effect is added to the satellite-derived models. After reduction of the known gravity effects from both data sets, the remaining part can mainly be assumed to represent mass changes in terrestrial water storage. Therefore, gravity variations derived from global hydrological models are applied to verify the SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. Such a comparison shows quite a good agreement between gravity variation derived from SG, GRACE and hydrology models, which lie within their estimated error limits for most of the studied SG locations. It is shown that the SG gravity variations (point measurements) are representative for a large area within the accuracy, if local gravity effects are removed. The individual discrepancies between SG, GRACE and hydrology models may give hints for further investigations of each data series.