Open solar flux estimates from near-Earth measurements of the interplanetary magnetic field: comparison of the first two perihelion passes of the Ulysses spacecraft

Results from all phases of the orbits of the Ulysses spacecraft have shown that the magnitude of the radial component of the heliospheric field is approximately independent of heliographic latitude. This result allows the use of near- Earth observations to compute the total open flux of the Sun. For example, using satellite observations of the interplanetary magnetic field, the average open solar flux was shown to have risen by 29% between 1963 and 1987 and using the aa geomagnetic index it was found to have doubled during the 20th century. It is therefore important to assess fully the accuracy of the result and to check that it applies to all phases of the solar cycle. The first perihelion pass of the Ulysses spacecraft was close to sunspot minimum, and recent data from the second perihelion pass show that the result also holds at solar maximum. The high level of correlation between the open flux derived from the various methods strongly supports the Ulysses discovery that the radial field component is independent of latitude. We show here that the errors introduced into open solar flux estimates by assuming that the heliospheric field’s radial component is independent of latitude are similar for the two passes and are of order 25% for daily values, falling to 5% for averaging timescales of 27 days or greater. We compare here the results of four methods for estimating the open solar flux with results from the first and second perehelion passes by Ulysses. We find that the errors are lowest (1–5% for averages over the entire perehelion passes lasting near 320 days), for near-Earth methods, based on either interplanetary magnetic field observations or the aa geomagnetic activity index. The corresponding errors for the Solanki et al. (2000) model are of the order of 9–15% and for the PFSS method, based on solar magnetograms, are of the order of 13–47%. The model of Solanki et al. is based on the continuity equation of open flux, and uses the sunspot number to quantify the rate of open flux emergence. It predicts that the average open solar flux has been decreasing since 1987, as Correspondence to: M. Lockwood (m.lockwood@rl.ac.uk) is observed in the variation of all the estimates of the open flux. This decline combines with the solar cycle variation to produce an open flux during the second (sunspot maximum) perihelion pass of Ulysses which is only slightly larger than that during the first (sunspot minimum) perihelion pass.

Relationship between the near-Earth interplanetary field and the coronal source flux: dependence on timescale

The Ulysses spacecraft has shown that the radial component of the heliospheric magnetic field is approximately independent of latitude. This has allowed quantification of the total open solar flux from near-Earth observations of the interplanetary magnetic field. The open flux can also be estimated from photospheric magnetograms by mapping the fields up to the ‘‘coronal source surface’’ where the field is assumed to be radial and which is usually assumed to be at a heliocentric distance r = 2.5R_{S} (a mean solar radius, 1R_{S} = 6.96x10^{8} m). These two classes of open flux estimate will differ by the open flux that threads the heliospheric current sheet(s) inside Earth’s orbit at 2.5R_{S} < r < 1R{1} (where the mean Earth-Sun distance, 1R_{1} = 1 AU = 1.5 x 10^{11} m). We here use near-Earth measurements to estimate this flux and show that at sunspot minimum it causes only a very small (approximately 0.5%) systematic difference between the two types of open flux estimate, with an uncertainty that is of order ±24% in hourly values, ±16% in monthly averages, and between -6% and +2% in annual values. These fractions may be somewhat larger for sunspot maximum because of flux emerging at higher heliographic latitudes.

An evaluation of the correlation between open solar flux and total solar irradiance

The correlation between the coronal source flux F_{S} and the total solar irradiance I_{TS} is re-evaluated in the light of an additional 5 years' data from the rising phase of solar cycle 23 and also by using cosmic ray fluxes detected at Earth. Tests on monthly averages show that the correlation with F_{S} deduced from the interplanetary magnetic field (correlation coefficient, r = 0.62) is highly significant (99.999%), but that there is insufficient data for the higher correlation with annual means (r = 0.80) to be considered significant. Anti-correlations between I_{TS} and cosmic ray fluxes are found in monthly data for all stations and geomagnetic rigidity cut-offs (r ranging from −0.63 to −0.74) and these have significance levels between 85% and 98%. In all cases, the t is poorest for the earliest data (i.e., prior to 1982). Excluding these data improves the anticorrelation with cosmic rays to r = −0:93 for one-year running means. Both the interplanetary magnetic field data and the cosmic ray fluxes indicate that the total solar irradiance lags behind the open solar flux with a delay that is estimated to have an optimum value of 2.8 months (and is within the uncertainty range 0.8-8.0 months at the 90% level).

Long-term drift of the coronal source magnetic flux and the total solar irradiance

We test the method of Lockwood et al. [1999] for deriving the coronal source flux from the geomagnetic aa index and show it to be accurate to within 12% for annual means and 4.5% for averages over a sunspot cycle. Using data from four solar constant monitors during 1981-1995, we find a linear relationship between this magnetic flux and the total solar irradiance. From this correlation, we show that the 131% rise in the mean coronal source field over the interval 1901-1995 corresponds to a rise in the average total solar irradiance of {\Delta}I = 1.65 +/- 0.23 Wm^{-2}.

Ionospheric and geomagnetic responses to changes in IMF B_Z: a superposed epoch study

Superposed epoch studies have been carried out in order to determine the ionospheric response at mid-latitudes to southward turnings of the interplanetary magnetic field (IMF). This is compared with the geomagnetic response, as seen in the indices K p, AE and Dst. The solar wind, IMF and geomagnetic data used were hourly averages from the years 1967–1989 and thus cover a full 22-year cycle in the solar magnetic field. These data were divided into subsets, determined by the magnitudes of the southward turnings and the concomitant increase in solar wind pressure. The superposed epoch studies were carried out using the time of the southward turning as time zero. The response of the mid-latitude ionosphere is studied by looking at the F-layer critical frequencies, f o F2, from hourly soundings by the Slough ionosonde and their deviation from the monthly median values, δf o F2. For the southward turnings with a change in B z of δB z > 11.5 nT accompanied by a solar wind dynamic pressure P exceeding 5 nPa, the F region critical frequency, f o F2, shows a marked decrease, reaching a minimum value about 20 h after the southward turning. This recovers to pre-event values over the subsequent 24 h, on average. The Dst index shows the classic storm-time decrease to about −60 nT. Four days later, the index has still to fully recover and is at about −25 nT. Both the K p and AE indices show rises before the southward turnings, when the IMF is strongly northward but the solar wind dynamic pressure is enhanced. The average AE index does register a clear isolated pulse (averaging 650 nT for 2 h, compared with a background peak level of near 450 nT at these times) showing enhanced energy deposition at high latitudes in substorms but, like K p, remains somewhat enhanced for several days, even after the average IMF has returned to zero after 1 day. This AE background decays away over several days as the Dst index recovers, indicating that there is some contamination of the currents observed at the AE stations by the continuing enhanced equatorial ring current. For data averaged over all seasons, the critical frequencies are depressed at Slough by 1.3 MHz, which is close to the lower decile of the overall distribution of δf o Fl values. Taking 30-day periods around summer and winter solstice, the largest depression is 1.6 and 1.2 MHz, respectively. This seasonal dependence is confirmed by a similar study for a Southern Hemisphere station, Argentine Island, giving peak depressions of 1.8 MHz and 0.5 MHz for summer and winter. For the subset of turnings where δB z > 11.5 nT and P ≤ 5 nPa, the response of the geomagnetic indices is similar but smaller, while the change in δf o F2 has all but disappeared. This confirms that the energy deposited at high latitudes, which leads to the geomagnetic and ionospheric disturbances following a southward turning of the IMF, increases with the energy density (dynamic pressure) of the solar wind flow. The magnitude of all responses are shown to depend on δB z . At Slough, the peak depression always occurs when Slough rotates into the noon sector. The largest ionospheric response is for southward turnings seen between 15–21 UT.

Variability of the interplanetary medium at 1 A.U. over 24 years: 1963–1986

A survey is presented of hourly averages of observations of the interplanetary medium, made by satellites close to the Earth (i.e. at l a.u.) in the years 1963-1986. This survey therefore covers two complete solar cycles (numbers 20 and 21). The distributions and solar-cycle variations of IMF field strength, B, and its northward component (in GSM coordinates), B(z), and of the solar-wind density, n, speed, v, and dynamic pressure, P, are discussed. Because of their importance to the terrestrial magnetosphere/ionosphere, particular attention is given to B(z) and P. The solar-cycle variation in the magnitude and variability of B(z) previously reported for cycle 20, is also found for cycle 21. However, the solar-wind data show a number of differences between cycles 20 and 21. The average dynamic pressure is found to show a solar-cycle variation and a systematic increase over the period of the survey. The minimum of dynamic pressure at sunspot maximum is mainly due to reduced solar-wind densities in cycle 20, but lower solar-wind speed in cycle 21 is a more significant factor. The distribution of the duration of periods of stable polarity of the IMF B(z) component shows that the magnetosphere could achieve steady state for only a small fraction of the time and there is some evidence for a solar-cycle variation in this fraction. It is also found that the polarity changes in the IMF B(z) fall into two classes: one with an associated change in solar-wind dynamic pressure, the other without such a change. However, in only 20% of cases does the dynamic pressure change exceed 50%.

Neural population models and cortical field theory: overview

The term neural population models (NPMs) is used here as catchall for a wide range of approaches that have been variously called neural mass models, mean field models, neural field models, bulk models, and so forth. All NPMs attempt to describe the collective action of neural assemblies directly. Some NPMs treat the densely populated tissue of cortex as an excitable medium, leading to spatially continuous cortical field theories (CFTs). An indirect approach would start by modelling individual cells and then would explain the collective action of a group of cells by coupling many individual models together. In contrast, NPMs employ collective state variables, typically defined as averages over the group of cells, in order to describe the population activity directly in a single model. The strength and the weakness of his approach are hence one and the same: simplification by bulk. Is this justified and indeed useful, or does it lead to oversimplification which fails to capture the pheno ...

Methane emissions from cattle: estimates from short-term measurements using a Green Feed system compared with measurements obtained using respiration chambers or sulphur hexafluoride tracer

The Green Feed (GF) system (C-Lock Inc., Rapid City, USA) is used to estimate total daily methane emissions of individual cattle using short-term measurements obtained over several days. Our objective was to compare measurements of methane emission by growing cattle obtained using the GF system with measurements using respiration chambers (RC)or sulphur hexafluoride tracer (SF6). It was hypothesised that estimates of methane emission for individual animals and treatments would be similar for GF compared to RC or SF6 techniques. In experiment 1, maize or grass silage-based diets were fed to four growing Holstein heifers, whilst for experiment 2, four different heifers were fed four haylage treatments. Both experiments were a 4 × 4 Latin square design with 33 day periods. Green Feed measurements of methane emission were obtained over 7 days (days 22–28) and com-pared to subsequent RC measurements over 4 days (days 29–33). For experiment 3, 12growing heifers rotationally grazed three swards for 26 days, with simultaneous GF and SF6 measurements over two 4 day measurement periods (days 15–19 and days 22–26).Overall methane emissions (g/day and g/kg dry matter intake [DMI]) measured using GF in experiments 1 (198 and 26.6, respectively) and 2 (208 and 27.8, respectively) were similar to averages obtained using RC (218 and 28.3, respectively for experiment 1; and 209 and 27.7, respectively, for experiment 2); but there was poor concordance between the two methods (0.1043 for experiments 1 and 2 combined). Overall, methane emissions measured using SF6 were higher (P<0.001) than GF during grazing (186 vs. 164 g/day), but there was significant (P<0.01) concordance between the two methods (0.6017). There were fewer methane measurements by GF under grazing conditions in experiment 3 (1.60/day) com-pared to indoor measurements in experiments 1 (2.11/day) and 2 (2.34/day). Significant treatment effects on methane emission measured using RC and SF6 were not evident for GF measurements, and the ranking for treatments and individual animals differed using the GF system. We conclude that under our conditions of use the GF system was unable to detectsignificant treatment and individual animal differences in methane emissions that were identified using both RC and SF6techniques, in part due to limited numbers and timing ofmeasurements obtained. Our data suggest that successful use of the GF system is reliant on the number and timing of measurements obtained relative to diurnal patterns of methane emission.

Infrared and millimetre-wave scintillometry in the suburban environment – Part 1: Structure parameters

Scintillometry, a form of ground-based remote sensing, provides the capability to estimate surface heat fluxes over scales of a few hundred metres to kilometres. Measurements are spatial averages, making this technique particularly valuable over areas with moderate heterogeneity such as mixed agricultural or urban environments. In this study, we present the structure parameters of temperature and humidity, which can be related to the sensible and latent heat fluxes through similarity theory, for a suburban area in the UK. The fluxes are provided in the second paper of this two-part series. A millimetre-wave scintillometer was combined with an infrared scintillometer along a 5.5 km path over northern Swindon. The pairing of these two wavelengths offers sensitivity to both temperature and humidity fluctuations, and the correlation between wavelengths is also used to retrieve the path-averaged temperature–humidity correlation. Comparison is made with structure parameters calculated from an eddy covariance station located close to the centre of the scintillometer path. The performance of the measurement techniques under different conditions is discussed. Similar behaviour is seen between the two data sets at sub-daily timescales. For the two summer-to-winter periods presented here, similar evolution is displayed across the seasons. A higher vegetation fraction within the scintillometer source area is consistent with the lower Bowen ratio observed (midday Bowen ratio < 1) compared with more built-up areas around the eddy covariance station. The energy partitioning is further explored in the companion paper.

Towards improving the framework for probabilistic forecast evaluation

The evaluation of forecast performance plays a central role both in the interpretation and use of forecast systems and in their development. Different evaluation measures (scores) are available, often quantifying different characteristics of forecast performance. The properties of several proper scores for probabilistic forecast evaluation are contrasted and then used to interpret decadal probability hindcasts of global mean temperature. The Continuous Ranked Probability Score (CRPS), Proper Linear (PL) score, and IJ Good’s logarithmic score (also referred to as Ignorance) are compared; although information from all three may be useful, the logarithmic score has an immediate interpretation and is not insensitive to forecast busts. Neither CRPS nor PL is local; this is shown to produce counter intuitive evaluations by CRPS. Benchmark forecasts from empirical models like Dynamic Climatology place the scores in context. Comparing scores for forecast systems based on physical models (in this case HadCM3, from the CMIP5 decadal archive) against such benchmarks is more informative than internal comparison systems based on similar physical simulation models with each other. It is shown that a forecast system based on HadCM3 out performs Dynamic Climatology in decadal global mean temperature hindcasts; Dynamic Climatology previously outperformed a forecast system based upon HadGEM2 and reasons for these results are suggested. Forecasts of aggregate data (5-year means of global mean temperature) are, of course, narrower than forecasts of annual averages due to the suppression of variance; while the average “distance” between the forecasts and a target may be expected to decrease, little if any discernible improvement in probabilistic skill is achieved.

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics

To improve the quantity and impact of observations used in data assimilation it is necessary to take into account the full, potentially correlated, observation error statistics. A number of methods for estimating correlated observation errors exist, but a popular method is a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. The accuracy of the results it yields is unknown as the diagnostic is sensitive to the difference between the exact background and exact observation error covariances and those that are chosen for use within the assimilation. It has often been stated in the literature that the results using this diagnostic are only valid when the background and observation error correlation length scales are well separated. Here we develop new theory relating to the diagnostic. For observations on a 1D periodic domain we are able to the show the effect of changes in the assumed error statistics used in the assimilation on the estimated observation error covariance matrix. We also provide bounds for the estimated observation error variance and eigenvalues of the estimated observation error correlation matrix. We demonstrate that it is still possible to obtain useful results from the diagnostic when the background and observation error length scales are similar. In general, our results suggest that when correlated observation errors are treated as uncorrelated in the assimilation, the diagnostic will underestimate the correlation length scale. We support our theoretical results with simple illustrative examples. These results have potential use for interpreting the derived covariances estimated using an operational system.

Good practice for pupils learning English as an additional language; lessons from effective literacy teachers in inner city primary schools.

This article presents observations and discussion of the successful teaching of English to pupils, in English primary schools, for whom English is an additional language (EAL). It draws on research in Year 2 (6/7year old) classes in three inner-city primary schools carried out in 2003 and 2005. Three recognised, effective teachers of literacy were selected for case study; all worked in successful schools where results for literacy, measured by national tests, were in line with or better than national averages. Following analyses of lesson observations and interviews with the teachers, their Headteachers and the EAL co-ordinators in the schools, a number of common elements in their practice emerged. Discussion centres on how these pedagogical features supported effective learning environments for the early literacy development of bilingual children, and on the implications for the practice of teaching English to all pupils.

The timing of anthropogenic emergence in simulated climate extremes

Determining the time of emergence of climates altered from their natural state by anthropogenic influences can help inform the development of adaptation and mitigation strategies to climate change. Previous studies have examined the time of emergence of climate averages. However, at the global scale, the emergence of changes in extreme events, which have the greatest societal impacts, has not been investigated before. Based on state-of-the-art climate models, we show that temperature extremes generally emerge slightly later from their quasi-natural climate state than seasonal means, due to greater variability in extremes. Nevertheless, according to model evidence, both hot and cold extremes have already emerged across many areas. Remarkably, even precipitation extremes that have very large variability are projected to emerge in the coming decades in Northern Hemisphere winters associated with a wettening trend. Based on our findings we expect local temperature and precipitation extremes to already differ significantly from their previous quasi-natural state at many locations or to do so in the near future. Our findings have implications for climate impacts and detection and attribution studies assessing observed changes in regional climate extremes by showing whether they will likely find a fingerprint of anthropogenic climate change.

Diagnosing observation error correlations for Doppler radar radial winds in the Met Office UKV model using observation-minus-background and observation-minus-analysis statistics

With the development of convection-permitting numerical weather prediction the efficient use of high resolution observations in data assimilation is becoming increasingly important. The operational assimilation of these observations, such as Dopplerradar radial winds, is now common, though to avoid violating the assumption of un- correlated observation errors the observation density is severely reduced. To improve the quantity of observations used and the impact that they have on the forecast will require the introduction of the full, potentially correlated, error statistics. In this work, observation error statistics are calculated for the Doppler radar radial winds that are assimilated into the Met Office high resolution UK model using a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This is the first in-depth study using the diagnostic to estimate both horizontal and along-beam correlated observation errors. By considering the new results obtained it is found that the Doppler radar radial wind error standard deviations are similar to those used operationally and increase as the observation height increases. Surprisingly the estimated observation error correlation length scales are longer than the operational thinning distance. They are dependent on both the height of the observation and on the distance of the observation away from the radar. Further tests show that the long correlations cannot be attributed to the use of superobservations or the background error covariance matrix used in the assimilation. The large horizontal correlation length scales are, however, in part, a result of using a simplified observation operator.