Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun

A recent paper published in this journal considers the numerical integration of the shallow-water equations using the leapfrog time-stepping scheme [Sun Wen-Yih, Sun Oliver MT. A modified leapfrog scheme for shallow water equations. Comput Fluids 2011;52:69–72]. The authors of that paper propose using the time-averaged height in the numerical calculation of the pressure-gradient force, instead of the instantaneous height at the middle time step. The authors show that this modification doubles the maximum Courant number (and hence the maximum time step) at which the integrations are stable, doubling the computational efficiency. Unfortunately, the pressure-averaging technique proposed by the authors is not original. It was devised and published by Shuman [5] and has been widely used in the atmosphere and ocean modelling community for over 40 years.

Observational tracking of the 2D structure of coronal mass ejections between the sun and 1 AU

The Solar TErrestrial RElations Observatory (STEREO) provides high cadence and high resolution images of the structure and morphology of coronal mass ejections (CMEs) in the inner heliosphere. CME directions and propagation speeds have often been estimated through the use of time-elongation maps obtained from the STEREO Heliospheric Imager (HI) data. Many of these CMEs have been identified by citizen scientists working within the SolarStormWatch project ( www.solarstormwatch.com ) as they work towards providing robust real-time identification of Earth-directed CMEs. The wide field of view of HI allows scientists to directly observe the two-dimensional (2D) structures, while the relative simplicity of time-elongation analysis means that it can be easily applied to many such events, thereby enabling a much deeper understanding of how CMEs evolve between the Sun and the Earth. For events with certain orientations, both the rear and front edges of the CME can be monitored at varying heliocentric distances (R) between the Sun and 1 AU. Here we take four example events with measurable position angle widths and identified by the citizen scientists. These events were chosen for the clarity of their structure within the HI cameras and their long track lengths in the time-elongation maps. We show a linear dependency with R for the growth of the radial width (W) and the 2D aspect ratio (χ) of these CMEs, which are measured out to ≈ 0.7 AU. We estimated the radial width from a linear best fit for the average of the four CMEs. We obtained the relationships W=0.14R+0.04 for the width and χ=2.5R+0.86 for the aspect ratio (W and R in units of AU).

Long-term variations in the magnetic fields of the Sun and the heliosphere: their origin, effects, and implications

Recent studies of the variation of geomagnetic activity over the past 140 years have quantified the "coronal source" magnetic flux F-s that leaves the solar atmosphere and enters the heliosphere and have shown that it has risen, on average, by an estimated 34% since 1963 and by 140% since 1900. This variation of open solar flux has been reproduced by Solanki et al. [2000] using a model which demonstrates how the open flux accumulates and decays, depending on the rate of flux emergence in active regions and on the length of the solar cycle. We here use a new technique to evaluate solar cycle length and find that it does vary in association with the rate of change of F-s in the way predicted. The long-term variation of the rate of flux emergence is found to be very similar in form to that in F-s, which may offer a potential explanation of why F-s appears to be a useful proxy for extrapolating solar total irradiance back in time. We also find that most of the variation of cosmic ray fluxes incident on Earth is explained by the strength of the heliospheric field (quantified by F-s) and use observations of the abundance of the isotope Be-10 (produced by cosmic rays and deposited in ice sheets) to study the decrease in F-s during the Maunder minimum. The interior motions at the base of the convection zone, where the solar dynamo is probably located, have recently been revealed using the helioseismology technique and found to exhibit a 1.3-year oscillation. This periodicity is here reported in observations of the interplanetary magnetic field and geomagnetic activity but is only present after 1940, When present, it shows a strong 22-year variation, peaking near the maximum of even-numbered sunspot cycles and showing minima at the peaks of odd-numbered cycles. We discuss the implications of these long-term solar and heliospheric variations for Earth's environment.

Long-term variations in the magnetic field of the Sun and possible implications for terrestrial climate

Recent studies of the variation of geomagnetic activity over the past 140 years have quantified the "coronal source" or "open" magnetic flux F-s that leaves the solar atmosphere and enters the heliosphere and have shown that it has risen, on average, by 34% since 1963 and by 140% since 1900. This variation is reflected in studies of the heliospheric field using isotopes deposited in ice sheets and meteorites by the action of galactic comic rays. The variation has also been reproduced using a model that demonstrates how the open flux accumulates and decays, depending on the rate of flux emergence in active regions and on the length of the solar cycle. The cosmic ray flux at energies > 3 GeV is found to have decayed by about 15% during the 20(th) century (and by about 4% at > 13 GeV). We show that the changes in the open flux do reflect changes in the photospheric and sub-surface field which offers an explanation of why open flux appears to be a good proxy for solar irradiance extrapolation. Correlations between F-s, solar cycle length, L, and 11-year smoothed sunspot number, R-11, explain why the various irradiance reconstructions for the last 150 years are similar in form. Possible implications of the inferred changes in cosmic ray flux and irradiance for global temperatures on Earth are discussed.

The Sun-Earth connection in time scales from years to decades and centuries

The Sun-Earth connection is studied using long-term measurements from the Sun and from the Earth. The auroral activity is shown to correlate to high accuracy with the smoothed sunspot numbers. Similarly, both geomagnetic activity and global surface temperature anomaly can be linked to cyclic changes in the solar activity. The interlinked variations in the solar magnetic activity and in the solar irradiance cause effects that can be observed both in the Earth's biosphere and in the electromagnetic environment. The long-term data sets suggest that the increase in geomagnetic activity and surface temperatures are related (at least partially) to longer-term solar variations, which probably include an increasing trend superposed with a cyclic behavior with a period of about 90 years.

The effect of drying and urea treatment on nutritional and anti-nutritional components of browses collected during wet and dry seasons

Fibre, crude protein and tannin concentrations were measured in browse species from the semi-arid region of Northeast Brazil during the dry and wet seasons. The effects of oven-, sun- and shade-drying and of urea treatment were also determined. Crude protein (CP) content varied from 103 to 161 g/kg dry matter (DM) and the browses had similar CP content in the two seasons (during 2002) (102-161 and 107-153 g/kg DM in the wet and dry seasons, respectively). Total tannin concentrations ranged from 13 to 201 g/kg DM amongst the browses and were higher in the dry season. A 30-d treatment with urea reduced extractable tannins significantly (P < 0.05). The urea treatment was also most effective at reducing the in vitro effects of tannins compared to the other drying treatments. This was demonstrated by measuring the effect of polyethylene glycol (PEG) on gas production. Addition of PEG increased gas production of oven- (81.4%), sun- (78.5%) and shade-dried (76.7%) samples much more compared to urea treated samples (10.9%). (c) 2005 Elsevier B.V. All rights reserved.

Integrated optics for nulling interferometry in the thermal infrared: progress and recent achievements

The search for Earth-like exoplanets, orbiting in the habitable zone of stars other than our Sun and showing biological activity, is one of the most exciting and challenging quests of the present time. Nulling interferometry from space, in the thermal infrared, appears as a promising candidate technique for the task of directly observing extra-solar planets. It has been studied for about 10 years by ESA and NASA in the framework of the Darwin and TPF-I missions respectively. Nevertheless, nulling interferometry in the thermal infrared remains a technological challenge at several levels. Among them, the development of the "modal filter" function is mandatory for the filtering of the wavefronts in adequacy with the objective of rejecting the central star flux to an efficiency of about 105. Modal filtering takes benefit of the capability of single-mode waveguides to transmit a single amplitude function, to eliminate virtually any perturbation of the interfering wavefronts, thus making very high rejection ratios possible. The modal filter may either be based on single-mode Integrated Optics (IO) and/or Fiber Optics. In this paper, we focus on IO, and more specifically on the progress of the on-going "Integrated Optics" activity of the European Space Agency.

Long-term acclimation of leaf production, development, longevity and quality following 3 yr exposure to free-air CO2 enrichment during canopy closure in Populus

The effects of elevated CO2 on leaf development in three genotypes of Populus were investigated during canopy closure, following exposure to elevated CO2 over 3 yr using free-air enrichment.• Leaf quality was altered such that nitrogen concentration per unit d. wt (Nmass) declined on average by 22 and 13% for sun and shade leaves, respectively, in elevated CO2. There was little evidence that this was the result of ‘dilution’ following accumulation of nonstructural carbohydrates. Most likely, this was the result of increased leaf thickness. Specific leaf area declined in elevated CO2 on average by 29 and 5% for sun and shade leaves, respectively.• Autumnal senescence was delayed in elevated CO2 with a 10% increase in the number of days at which 50% leaf loss occurred in elevated as compared with ambient CO2.• These data suggest that changes in leaf quality may be predicted following long-term acclimation of fast-growing forest trees to elevated CO2, and that canopy longevity may increase, with important implications for forest productivity.

Solar cycle 24: implications for energetic particles and long-term space climate change

The recent solar minimum was the longest and deepest of the space age, with the lowest average sunspot numbers for nearly a century. The Sun appears to be exiting a grand solar maximum (GSM) of activity which has persisted throughout the space age, and is headed into a significantly quieter period. Indeed, initial observations of solar cycle 24 (SC24) continue to show a relatively low heliospheric magnetic field strength and sunspot number (R), despite the average latitude of sunspots and the inclination of the heliospheric current sheet showing the rise to solar maximum is well underway. We extrapolate the available SC24 observations forward in time by assuming R will continue to follow a similar form to previous cycles, despite the end of the GSM, and predict a very weak cycle 24, with R peaking at ∼65–75 around the middle/end of 2012. Similarly, we estimate the heliospheric magnetic field strength will peak around 6nT. We estimate that average galactic cosmic ray fluxes above 1GV rigidity will be ∼10% higher in SC24 than SC23 and that the probability of a large SEP event during this cycle is 0.8, compared to 0.5 for SC23. Comparison of the SC24 R estimates with previous ends of GSMs inferred from 9300 years of cosmogenic isotope data places the current evolution of the Sun and heliosphere in the lowest 5% of cases, suggesting Maunder Minimum conditions are likely within the next 40 years.

Reconstruction and prediction of variations in the open solar magnetic flux and interplanetary conditions

Historic geomagnetic activity observations have been used to reveal centennial variations in the open solar flux and the near-Earth heliospheric conditions (the interplanetary magnetic field and the solar wind speed). The various methods are in very good agreement for the past 135 years when there were sufficient reliable magnetic observatories in operation to eliminate problems due to site-specific errors and calibration drifts. This review underlines the physical principles that allow these reconstructions to be made, as well as the details of the various algorithms employed and the results obtained. Discussion is included of: the importance of the averaging timescale; the key differences between “range” and “interdiurnal variability” geomagnetic data; the need to distinguish source field sector structure from heliospherically-imposed field structure; the importance of ensuring that regressions used are statistically robust; and uncertainty analysis. The reconstructions are exceedingly useful as they provide calibration between the in-situ spacecraft measurements from the past five decades and the millennial records of heliospheric behaviour deduced from measured abundances of cosmogenic radionuclides found in terrestrial reservoirs. Continuity of open solar flux, using sunspot number to quantify the emergence rate, is the basis of a number of models that have been very successful in reproducing the variation derived from geomagnetic activity. These models allow us to extend the reconstructions back to before the development of the magnetometer and to cover the Maunder minimum. Allied to the radionuclide data, the models are revealing much about how the Sun and heliosphere behaved outside of grand solar maxima and are providing a means of predicting how solar activity is likely to evolve now that the recent grand maximum (that had prevailed throughout the space age) has come to an end.

The heliospheric magnetic field over the Hale cycle

The concept that open magnetic flux of the Sun (rooted with one and only one footpoint at the Sun) is a conserved quantity is taking root in the heliospheric community. Observations show that the Sun's open magnetic flux returns to the baseline from one solar minimum to the next. The temporary enhancement in the 1 AU heliospheric magnetic flux near solar maximum can be accounted for by the temporary creation of closed magnetic flux (with two footpoints at the Sun) during the ejection of coronal mass ejections (CMEs), which are more frequent near solar maximum. As a part of the International Heliophysical Year activities, this paper reviews two recently discussed consequences of open flux conservation: the reversal of open magnetic flux over the solar cycle driven by Coronal Mass Ejections and the impacts of open flux conservation on the global structure of the heliospheric magnetic field. These studies demonstrate the inherent linkages between coronal mass ejections, footpoint motions back at the Sun, and the global structure and evolution of the heliospheric magnetic field.

Predictions of the arrival time of coronal mass ejections at 1AU: an analysis of the causes of errors

Three existing models of Interplanetary Coronal Mass Ejection (ICME) transit between the Sun and the Earth are compared to coronagraph and in situ observations: all three models are found to perform with a similar level of accuracy (i.e. an average error between observed and predicted 1AU transit times of approximately 11 h). To improve long-term space weather prediction, factors influencing CME transit are investigated. Both the removal of the plane of sky projection (as suffered by coronagraph derived speeds of Earth directed CMEs) and the use of observed values of solar wind speed, fail to significantly improve transit time prediction. However, a correlation is found to exist between the late/early arrival of an ICME and the width of the preceding sheath region, suggesting that the error is a geometrical effect that can only be removed by a more accurate determination of a CME trajectory and expansion. The correlation between magnetic field intensity and speed of ejecta at 1AU is also investigated. It is found to be weak in the body of the ICME, but strong in the sheath, if the upstream solar wind conditions are taken into account.

First imaging of corotating interaction regions using the STEREO spacecraft

Plasma parcels are observed propagating from the Sun out to the large coronal heights monitored by the Heliospheric Imagers (HI) instruments onboard the NASA STEREO spacecraft during September 2007. The source region of these out-flowing parcels is found to corotate with the Sun and to be rooted near the western boundary of an equatorial coronal hole. These plasma enhancements evolve during their propagation through the HI cameras’ fields of view and only becoming fully developed in the outer camera field of view. We provide evidence that HI is observing the formation of a Corotating Interaction Region(CIR) where fast solar wind from the equatorial coronal hole is interacting with the slow solar wind of the streamer belt located on the western edge of that coronal hole. A dense plasma parcel is also observed near the footpoint of the observed CIR at a distance less than 0.1AU from the Sun where fast wind would have not had time to catch up slow wind. We suggest that this low-lying plasma enhancement is a plasma parcel which has been disconnected from a helmet streamer and subsequently becomes embedded inside the corotating interaction region.

The Heliospheric Imagers onboard the STEREO mission

Mounted on the sides of two widely separated spacecraft, the two Heliospheric Imager (HI) instruments onboard NASA’s STEREO mission view, for the first time, the space between the Sun and Earth. These instruments are wide-angle visible-light imagers that incorporate sufficient baffling to eliminate scattered light to the extent that the passage of solar coronal mass ejections (CMEs) through the heliosphere can be detected. Each HI instrument comprises two cameras, HI-1 and HI-2, which have 20° and 70° fields of view and are off-pointed from the Sun direction by 14.0° and 53.7°, respectively, with their optical axes aligned in the ecliptic plane. This arrangement provides coverage over solar elongation angles from 4.0° to 88.7° at the viewpoints of the two spacecraft, thereby allowing the observation of Earth-directed CMEs along the Sun – Earth line to the vicinity of the Earth and beyond. Given the two separated platforms, this also presents the first opportunity to view the structure and evolution of CMEs in three dimensions. The STEREO spacecraft were launched from Cape Canaveral Air Force Base in late October 2006, and the HI instruments have been performing scientific observations since early 2007. The design, development, manufacture, and calibration of these unique instruments are reviewed in this paper. Mission operations, including the initial commissioning phase and the science operations phase, are described. Data processing and analysis procedures are briefly discussed, and ground-test results and in-orbit observations are used to demonstrate that the performance of the instruments meets the original scientific requirements.