The effect of the stochasticity of photoionization on 3D streamer simulations

Positive streamer discharges require a source of free electrons ahead of them for their growth. In air, these electrons are typically provided by photoionization. Here we investigate how stochastic fluctuations due to the discreteness of ionizing photons affect positive streamers in air. We simulate positive streamers between two planar electrodes with a 3D plasma fluid model, using both a stochastic and a continuum method for photoionization. With stochastic photoionization, fluctuations are visible in the streamer's direction, maximal electric field, velocity, and electron density. The streamers do not branch, and we find good agreement between the averaged stochastic results and the results with continuum photoionization. The streamers stay roughly axisymmetric, and we show that results obtained with an axisymmetric model indeed agree well with the 3D results. However, we find that positive streamers are sensitive to the amount of photoionization. When the amount of photoionization is doubled, there is even better agreement between the stochastic and continuum results, but with half the amount of photoionization, stochastic fluctuations become more important and streamer branching starts to occur

Why isolated streamer discharges hardly exist above the breakdown field in atmospheric air

We investigate streamer formation in the troposphere, in electric fields above the breakdown threshold. With fully three-dimensional particle simulations, we study the combined effect of natural background ionization and of photoionization on the discharge morphology. In previous investigations based on deterministic fluid models without background ionization, so-called double-headed streamers emerged. But in our improved model, many electron avalanches start to grow at different locations. Eventually the avalanches collectively screen the electric field in the interior of the discharge. This happens after what we call the `ionization screening time', for which we give an analytical estimate. As this time is comparable to the streamer formation time, we conclude that isolated streamers are unlikely to exist in fields well above breakdown in atmospheric air.Comment: Changed citation information. 6 pages, 4 figures, Geophysical Research Letters, Vol. 40, 2417-2422, 201

Testing of a new single-frequency GNSS carrier phase attitude determination method: land, ship and aircraft experiments

Global navigation satellite system (GNSS) ambiguity resolution is the process of resolving the unknown cycle ambiguities of the carrier phase data as integers. The sole purpose of ambiguity resolution is to use the integer ambiguity constraints as a means of improving significantly on the precision of the remaining GNSS model parameters. In this contribution, we consider the problem of ambiguity resolution for GNSS attitude determination. We analyse the performance of a new ambiguity resolution method for GNSS attitude determination. As it will be shown, this method provides a numerically efficient, highly reliable and robust solution of the nonlinearly constrained integer least-squares GNSS compass estimators. The analyses have been done by means of a unique set of extensive experimental tests, using simulated as well as actual GNSS data and using receivers of different manufacturers and type as well as different platforms. The executed field tests cover two static land experiments, one in the Netherlands and one in Australia, and two dynamic experiments, a low-dynamics vessel experiment and high-dynamics aircraft experiment. In our analyses, we focus on stand-alone, unaided, single-frequency, single epoch attitude determination, as this is the most challenging case of GNSS compass processing

Review and principles of PPP-RTK methods

PPP-RTK is integer ambiguity resolution-enabled precise point positioning. In this contribution, we present the principles of PPP-RTK, together with a review of different mechanizations that have been proposed in the literature. By application of S-system theory, the estimable parameters of the different methods are identified and compared. Their interpretation is essential for gaining a proper insight into PPP-RTK in general, and into the role of the PPP-RTK corrections in particular. We show that PPP-RTK is a relative technique for which the ‘single-receiver user’ integer ambiguities are in fact double-differenced ambiguities. We determine the transformational links between the different methods and their PPP-RTK corrections, thereby showing how different PPP-RTK methods can be mixed between network and users. We also present and discuss four different estimators of the PPP-RTK corrections. It is shown how they apply to the different PPP-RTK models, as well as why some of the proposed estimation methods cannot be accepted as PPP-RTK proper. We determine analytical expressions for the variance matrices of the ambiguity-fixed and ambiguity-float PPP-RTK corrections. This gives important insight into their precision, as well as allows us to discuss which parts of the PPP-RTK correction variance matrix are essential for the user and which are not

On the short-term temporal variations of GNSS receiver differential phase biases

As a first step towards studying the ionosphere with the global navigation satellite system (GNSS), leveling the phase to the code geometry-free observations on an arc-by-arc basis yields the ionospheric observables, interpreted as a combination of slant total electron content along with satellite and receiver differential code biases (DCB). The leveling errors in the ionospheric observables may arise during this procedure, which, according to previous studies by other researchers, are due to the combined effects of the code multipath and the intra-day variability in the receiver DCB. In this paper we further identify the short-term temporal variations of receiver differential phase biases (DPB) as another possible cause of leveling errors. Our investigation starts by the development of a method to epoch-wise estimate between-receiver DPB (BR-DPB) employing (inter-receiver) single-differenced, phase-only GNSS observations collected from a pair of receivers creating a zero or short baseline. The key issue for this method is to get rid of the possible discontinuities in the epoch-wise BR-DPB estimates, occurring when satellite assigned as pivot changes. Our numerical tests, carried out using Global Positioning System (GPS, US GNSS) and BeiDou Navigation Satellite System (BDS, Chinese GNSS) observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, suggest two major findings. First, epoch-wise BR-DPB estimates can exhibit remarkable variability over a rather short period of time (e.g. 6 cm over 3 h), thus significant from a statistical point of view. Second, a dominant factor driving this variability is the changes of ambient temperature, instead of the un-modelled phase multipath

Breeding success in Brent in relation to individual feeding opportunities during spring staging in the Wadden Sea

Brent Geese Branta bernicla individually marked with inscribed leg rings were intensively watched from permanent towers on the saltings of the island Schiermonnikoog in the Dutch Wadden Sea during the spring staging period April- May 1982 when 3,000 used the area. By observing geese on plots with enhanced vegetation (biomass, protein content) as a result of fertilizer treatment, it was found that individuals on the improved sites fought more and walked more slowly. The position of the marked individuals in relation to the total feeding minutes accumulated by the flock as the group grazed past the tower was determined by making use of a radial system of counting plots. Individuals tended to be consistent in their relative timing in the grazing sequence, and the highest rate of interaction and lowest pacing rate was found just behind the leading edge of the flock, in the second quartile of feeding minutes, and by inference birds in this sector experienced the best feeding conditions. Status of the males (proportion of interactions won) was highest for individuals habitually in this sector, and observation of the same birds in the fall revealed the highest incidence of breeding success (pairs accompanied by young) for this group. A number of measures reflecting a good food supply (low pace rate, highest percentage feeding times, and highest number of bites per step) were found to correlate positively with male status supporting the conclusions from the grouped data presented in relation to the grazing sequence. Though a causal relation cannot be proved from such correlations, we interpret these findings to indicate that males of high status can provide their mates with enhanced feeding opportunities, resulting in accumulation of more body reserves in the spring, and a heightened probability of successful breeding. Females subsequently found to prove successful had a larger proportion of Triglochin maritima in their spring diet but a larger sample of droppings will be needed to substantiate this hint of a difference of diet in birds of the same flock

Integer Least-squares Theory for the GNSS Compass

Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory presented is generally valid and it is not restricted to any particular GNSS or combination of GNSSs. Its general applicability also applies to the measurement scenarios (e.g. single-epoch vs. multi-epoch, or single-frequency vs. multi-frequency). In particular it is applicable to the most challenging case of unaided, single frequency, single epoch GNSS attitude determination. The success rate performance of the different methods is also illustrated

The effect of the stochasticity of photoionization on 3D streamer simulations

Positive streamer discharges require a source of free electrons ahead of them for their growth. In air, these electrons are typically provided by photoionization. Here we investigate how stochastic fluctuations due to the discreteness of ionizing photons affect positive streamers in air. We simulate positive streamers between two planar electrodes with a 3D plasma fluid model, using both a stochastic and a continuum method for photoionization. With stochastic photoionization, fluctuations are visible in the streamer's direction, maximal electric field, velocity, and electron density. The streamers do not branch, and we find good agreement between the averaged stochastic results and the results with continuum photoionization. The streamers stay roughly axisymmetric, and we show that results obtained with an axisymmetric model indeed agree well with the 3D results. However, we find that positive streamers are sensitive to the amount of photoionization. When the amount of photoionization is doubled, there is even better agreement between the stochastic and continuum results, but with half the amount of photoionization, stochastic fluctuations become more important and streamer branching starts to occur

Breeding success in Brent in relation to individual feeding opportunities during spring staging in the Wadden Sea

Brent Geese Branta bernicla individually marked with inscribed leg rings were intensively watched from permanent towers on the saltings of the island Schiermonnikoog in the Dutch Wadden Sea during the spring staging period April- May 1982 when 3,000 used the area. By observing geese on plots with enhanced vegetation (biomass, protein content) as a result of fertilizer treatment, it was found that individuals on the improved sites fought more and walked more slowly. The position of the marked individuals in relation to the total feeding minutes accumulated by the flock as the group grazed past the tower was determined by making use of a radial system of counting plots. Individuals tended to be consistent in their relative timing in the grazing sequence, and the highest rate of interaction and lowest pacing rate was found just behind the leading edge of the flock, in the second quartile of feeding minutes, and by inference birds in this sector experienced the best feeding conditions. Status of the males (proportion of interactions won) was highest for individuals habitually in this sector, and observation of the same birds in the fall revealed the highest incidence of breeding success (pairs accompanied by young) for this group. A number of measures reflecting a good food supply (low pace rate, highest percentage feeding times, and highest number of bites per step) were found to correlate positively with male status supporting the conclusions from the grouped data presented in relation to the grazing sequence. Though a causal relation cannot be proved from such correlations, we interpret these findings to indicate that males of high status can provide their mates with enhanced feeding opportunities, resulting in accumulation of more body reserves in the spring, and a heightened probability of successful breeding. Females subsequently found to prove successful had a larger proportion of Triglochin maritima in their spring diet but a larger sample of droppings will be needed to substantiate this hint of a difference of diet in birds of the same flock