The parallel sum of matrices and its application in geodetic adjustments

Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can be used to simplify the algorithms applied for the estimation of those parameters. Received 15 December 1995; Accepted 24 September 1996     

Problems of accuracies in combined terrestrial and statellite control networks

Summary The combination of terrestrial and satellite aided network observations requires hybrid models of two kinds: a hybrid functional model and a stochastic model being able to process the heterogeneous observations approapriately. An appropriate combination of stochastic information means to adjoin proper weights to the various types of observations on one hand and on the other hand to separate the relelevant internal accuracy from that accuracy which is affected by a number of network external influences. The first task can be overcome by the technique of estimating variance components of the individual observation groups, the second one can be handled by applying S-transformations to covariance matrices. The paper deals with problems of the hybrid stochastic model. Examples are given.     

Can We Determine Electric Fields and Poynting Fluxes from Vector Magnetograms and Doppler Measurements?

The availability of vector-magnetogram sequences with sufficient accuracy and cadence to estimate the temporal derivative of the magnetic field allows us to use Faraday’s law to find an approximate solution for the electric field in the photosphere, using a Poloidal–Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined – Faraday’s law provides no information about the electric field that can be derived from the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler-flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections.     

The Global Context of Solar Activity During the Whole Heliosphere Interval Campaign

The Whole Heliosphere Interval (WHI) was an international observing and modeling effort to characterize the 3-D interconnected ??heliophysical?? system during this solar minimum, centered on Carrington Rotation 2068, March 20??C?April 16, 2008. During the latter half of the WHI period, the Sun presented a sunspot-free, deep solar minimum type face. But during the first half of CR 2068 three solar active regions flanked by two opposite-polarity, low-latitude coronal holes were present. These departures from the quiet Sun led to both eruptive activity and solar wind structure. Most of the eruptive activity, i.e., flares, filament eruptions and coronal mass ejections (CMEs), occurred during this first, active half of the interval. We determined the source locations of the CMEs and the type of associated region, such as active region, or quiet sun or active region prominence. To analyze the evolution of the events in the context of the global solar magnetic field and its evolution during the three rotations centered on CR 2068, we plotted the CME source locations onto synoptic maps of the photospheric magnetic field, of the magnetic and chromospheric structure, of the white light corona, and of helioseismological subsurface flows. Most of the CME sources were associated with the three dominant active regions on CR 2068, particularly AR 10989. Most of the other sources on all three CRs appear to have been associated with either isolated filaments or filaments in the north polar crown filament channel. Although calculations of the flux balance and helicity of the surface magnetic features did not clearly identify a dominance of one region over the others, helioseismological subsurface flows beneath these active regions did reveal a pronounced difference among them. These preliminary results suggest that the ??twistedness?? (i.e., vorticity and helicity) of subsurface flows and its temporal variation might be related to the CME productivity of active regions, similar to the relationship between flares and subsurface flows.     

A Snapshot of the Sun Near Solar Minimum: The Whole Heliosphere Interval

We present an overview of the data and models collected for the Whole Heliosphere Interval, an international campaign to study the three-dimensional solar?Cheliospheric?Cplanetary connected system near solar minimum. The data and models correspond to solar Carrington Rotation 2068 (20 March??C?16 April 2008) extending from below the solar photosphere, through interplanetary space, and down to Earth??s mesosphere. Nearly 200 people participated in aspects of WHI studies, analyzing and interpreting data from nearly 100 instruments and models in order to elucidate the physics of fundamental heliophysical processes. The solar and inner heliospheric data showed structure consistent with the declining phase of the solar cycle. A closely spaced cluster of low-latitude active regions was responsible for an increased level of magnetic activity, while a highly warped current sheet dominated heliospheric structure. The geospace data revealed an unusually high level of activity, driven primarily by the periodic impingement of high-speed streams. The WHI studies traced the solar activity and structure into the heliosphere and geospace, and provided new insight into the nature of the interconnected heliophysical system near solar minimum.     

Landscape structure,groundwater dynamics,and soil water content influence soil respiration across riparian–hillslope transitions in the Tenderfoot Creek Experimental Forest,Montana

Variability in soil respiration at various spatial and temporal scales has been the focus of much research over the last decade aimed to improve our understanding and parameterization of physical and environmental controls on this flux. However, few studies have assessed the control of landscape position and groundwater table dynamics on the spatiotemporal variability of soil respiration. We investigated growing season soil respiration in a ～393 ha subalpine watershed in Montana across eight riparian–hillslope transitions that differed in slope, upslope accumulated area (UAA), aspect, and groundwater table dynamics. We collected daily‐to‐weekly measurements of soil water content (SWC), soil temperature, soil CO₂ concentrations, surface CO₂ efflux, and groundwater table depth, as well as soil C and N concentrations at 32 locations from June to August 2005. Instantaneous soil surface CO₂ efflux was not significantly different within or among riparian and hillslope zones at monthly timescales. However, cumulative integration of CO₂ efflux during the 83‐day growing season showed that efflux in the wetter riparian zones was ～25% greater than in the adjacent drier hillslopes. Furthermore, greater cumulative growing season efflux occurred in areas with high UAA and gentle slopes, where groundwater tables were higher and more persistent. Our findings reveal the influence of landscape position and groundwater table dynamics on riparian versus hillslope soil CO₂ efflux and the importance of time integration for assessment of soil CO₂ dynamics, which is critical for landscape‐scale simulation and modelling of soil CO₂ efflux in complex landscapes. Copyright © 2010 John Wiley & Sons, Ltd.     

Global Forces in Eruptive Solar Flares: The Lorentz Force Acting on the Solar Atmosphere and the Solar Interior

We compute the change in the Lorentz force integrated over the outer solar atmosphere implied by observed changes in vector magnetograms that occur during large, eruptive solar flares. This force perturbation should be balanced by an equal and opposite force perturbation acting on the solar photosphere and solar interior. The resulting expression for the estimated force change in the solar interior generalizes the earlier expression presented by Hudson, Fisher, and Welsch (Astron. Soc. Pac. CS-383, 221, 2008), providing horizontal as well as vertical force components, and provides a more accurate result for the vertical component of the perturbed force. We show that magnetic eruptions should result in the magnetic field at the photosphere becoming more horizontal, and hence should result in a downward (toward the solar interior) force change acting on the photosphere and solar interior, as recently argued from an analysis of magnetogram data by Wang and Liu (Astrophys. J. Lett. 716, L195, 2010). We suggest the existence of an observational relationship between the force change computed from changes in the vector magnetograms, the outward momentum carried by the ejecta from the flare, and the properties of the helioseismic disturbance driven by the downward force change. We use the impulse driven by the Lorentz-force change in the outer solar atmosphere to derive an upper limit to the mass of erupting plasma that can escape from the Sun. Finally, we compare the expected Lorentz-force change at the photosphere with simple estimates from flare-driven gasdynamic disturbances and from an estimate of the perturbed pressure from radiative backwarming of the photosphere in flaring conditions.     

Photospheric Magnetic Evolution in the WHI Active Regions

Sequences of line-of-sight (LOS) magnetograms recorded by the Michelson Doppler Imager are used to quantitatively characterize photospheric magnetic structure and evolution in three active regions that rotated across the Sun??s disk during the Whole Heliosphere Interval (WHI), in an attempt to relate the photospheric magnetic properties of these active regions to flares and coronal mass ejections (CMEs). Several approaches are used in our analysis, on scales ranging from whole active regions, to magnetic features, to supergranular scales, and, finally, to individual pixels. We calculated several parameterizations of magnetic structure and evolution that have previously been associated with flare and CME activity, including total unsigned magnetic flux, magnetic flux near polarity-inversion lines, amount of canceled flux, the ??proxy Poynting flux,?? and helicity flux. To catalog flare events, we used flare lists derived from both GOES and RHESSI observations. By most such measures, AR 10988 should have been the most flare- and CME-productive active region, and AR 10989 the least. Observations, however, were not consistent with this expectation: ARs 10988 and 10989 produced similar numbers of flares, and AR 10989 also produced a few CMEs. These results highlight present limitations of statistics-based flare and CME forecasting tools that rely upon line-of-sight photospheric magnetic data alone.