An optimal inverse method using Doppler lidar measurements to estimate the surface sensible heat flux

Inverse methods are widely used in various fields of atmospheric science. However, such methods are not commonly used within the boundary-layer community, where robust observations of surface fluxes are a particular concern. We present a new technique for deriving surface sensible heat fluxes from boundary-layer turbulence observations using an inverse method. Doppler lidar observations of vertical velocity variance are combined with two well-known mixed-layer scaling forward models for a convective boundary layer (CBL). The inverse method is validated using large-eddy simulations of a CBL with increasing wind speed. The majority of the estimated heat fluxes agree within error with the proscribed heat flux, across all wind speeds tested. The method is then applied to Doppler lidar data from the Chilbolton Observatory, UK. Heat fluxes are compared with those from a mast-mounted sonic anemometer. Errors in estimated heat fluxes are on average 18 %, an improvement on previous techniques. However, a significant negative bias is observed (on average −63%) that is more pronounced in the morning. Results are improved for the fully-developed CBL later in the day, which suggests that the bias is largely related to the choice of forward model, which is kept deliberately simple for this study. Overall, the inverse method provided reasonable flux estimates for the simple case of a CBL. Results shown here demonstrate that this method has promise in utilizing ground-based remote sensing to derive surface fluxes. Extension of the method is relatively straight-forward, and could include more complex forward models, or other measurements.

Oscillations in the open solar magnetic flux with a period of 1.68 years: imprint on galactic cosmic rays and implications for heliospheric shielding

An understanding of how the heliosphere modulates galactic cosmic ray (GCR) fluxes and spectra is important, not only for studies of their origin, acceleration and propagation in our galaxy, but also for predicting their effects (on technology and on the Earth’s environment and organisms) and for interpreting abundances of cosmogenic isotopes in meteorites and terrestrial reservoirs. In contrast to the early interplanetary measurements, there is growing evidence for a dominant role in GCR shielding of the total open magnetic flux, which emerges from the solar atmosphere and enters the heliosphere. In this paper, we relate a strong 1.68- year oscillation in GCR fluxes to a corresponding oscillation in the open solar magnetic flux and infer cosmic-ray propagation paths confirming the predictions of theories in which drift is important in modulating the cosmic ray flux.

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.

Twenty-three cycles of changing open solar magnetic flux

This paper presents a comparison of various estimates of the open solar flux, deduced from measurements of the interplanetary magnetic field, from the aa geomagnetic index and from photospheric magnetic field observations. The first two of these estimates are made using the Ulysses discovery that the radial heliospheric field is approximately independent of heliographic latitude, the third makes use of the potential-field source surface method to map the total flux through the photosphere to the open flux at the top of the corona. The uncertainties associated with using the Ulysses result are 5%, but the effects of the assumptions of the potential field source surface method are harder to evaluate. Nevertheless, the three methods give similar results for the last three solar cycles when the data sets overlap. In 11-year running means, all three methods reveal that 1987 marked a significant peak in the long-term variation of the open solar flux. This peak is close to the solar minimum between sunspot cycles 21 and 22, and consequently the mean open flux (averaged from minimum to minimum) is similar for these two cycles. However, this similarity between cycles 21 and 22 in no way implies that the open flux is constant. The long-term variation shows that these cycles are fundamentally different in that the average open flux was rising during cycle 21 (from consistently lower values in cycle 20 and toward the peak in 1987) but was falling during cycle 22 (toward consistently lower values in cycle 23). The estimates from the geomagnetic aa index are unique as they extend from 1842 onwards (using the Helsinki extension). This variation gives strong anticorrelations, with very high statistical significance levels, with cosmic ray fluxes and with the abundances of the cosmogenic isotopes that they produce. Thus observations of photospheric magnetic fields, of cosmic ray fluxes, and of cosmogenic isotope abundances all support the long-term drifts in open solar flux reported by Lockwood et al. [1999a, 1999b].

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.

The evolution of the sun’s open magnetic flux: II. full solar cycle simulations

In this paper the origin and evolution of the Sun’s open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun’s open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.

The evolution of the Sun's open magnetic flux: I. a single bipole

In this paper the origin and evolution of the Sun’s open magnetic flux are considered for single magnetic bipoles as they are transported across the Sun. The effects of magnetic flux transport on the radial field at the surface of the Sun are modeled numerically by developing earlier work by Wang, Sheeley, and Lean (2000). The paper considers how the initial tilt of the bipole axis (α) and its latitude of emergence affect the variation and magnitude of the surface and open magnetic flux. The amount of open magnetic flux is estimated by constructing potential coronal fields. It is found that the open flux may evolve independently from the surface field for certain ranges of the tilt angle. For a given tilt angle, the lower the latitude of emergence, the higher the magnitude of the surface and open flux at the end of the simulation. In addition, three types of behavior are found for the open flux depending on the initial tilt angle of the bipole axis. When the tilt is such that α ≥ 2◦ the open flux is independent of the surface flux and initially increases before decaying away. In contrast, for tilt angles in the range −16◦ < α < 2◦ the open flux follows the surface flux and continually decays. Finally, for α ≤ −16◦ the open flux first decays and then increases in magnitude towards a second maximum before decaying away. This behavior of the open flux can be explained in terms of two competing effects produced by differential rotation. Firstly, differential rotation may increase or decrease the open flux by rotating the centers of each polarity of the bipole at different rates when the axis has tilt. Secondly, it decreases the open flux by increasing the length of the polarity inversion line where flux cancellation occurs. The results suggest that, in order to reproduce a realistic model of the Sun’s open magnetic flux over a solar cycle, it is important to have accurate input data on the latitude of emergence of bipoles along with the variation of their tilt angles as the cycle progresses.

Long-term variations in the open solar flux and possible links to Earth’s climate

Recent paleoclimate studies provide strong evidence for an association between cosmogenic isotope production and Earth’s climate throughout the holecene. These isotopes are generated by the bombardment of Earth’s atmosphere by galactic cosmic rays, the fluxes of which vary in approximately inverse proportion to the total open magnetic flux of the Sun. This paper discusses how results from the Ulysses spacecraft allow us to quantify the open solar flux from observations of near-Earth interplanetary space and to study its long-term variations using the homogeneous record of geomagnetic activity. A study of the results and of their accuracy is presented. The two proposed mechanisms that could lead to the open solar flux being a good proxy for solar-induced climate change are discussed: the first is the modulation of the production of some types of cloud by the air ions produced by cosmic rays; the second is a variation in the total or spectral solar irradiance, in association with changes in the open flux. Some implications for our understanding of anthropogenic climate change are discussed.

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 changes in the solar photosphere associated with changes in the coronal source flux

Using sunspot observations from Greenwich and Mount Wilson, we show that the latitudinal spread of sunspot groups has increased since 1874, in a manner that closely mirrors the long-term (similar to 100 year) changes in the coronal source flux, F-s, as inferred from geomagnetic activity. This latitude spread is shown to be well correlated with the flux emergence rate required by the model of the coronal source flux variation by Solanki er al. [2000]. The time constant for the decay of this open flux is found to be 3.6 +/-0.8 years. Using this value, and quantifying the photospheric flux emergence rate using the latitudinal spread of sunspot groups, the model reproduces the observed coronal source flux variation. The ratio of the 100-year drift to the solar cycle amplitude for the flux emergence rate is found to be half of the same ratio for F-s.

Reconfiguration and closure of lobe flux by reconnection during northward IMF: possible evidence for signatures in cusp/cleft auroral emissions

Observations are presented of the response of the dayside cusp/cleft aurora to changes in both the clock and elevation angles of the interplanetary magnetic field (IMF) vector, as monitored by the WIND spacecraft. The auroral observations are made in 630 nm light at the winter solstice near magnetic noon, using an all-sky camera and a meridian-scanning photometer on the island of Spitsbergen. The dominant change was the response to a northward turning of the IMF which caused a poleward retreat of the dayside aurora. A second, higher-latitude band of aurora was seen to form following the northward turning, which is interpreted as the effect of lobe reconnection which reconfigures open flux. We suggest that this was made possible in the winter hemisphere, despite the effect of the Earth's dipole tilt, by a relatively large negative X component of the IMF. A series of five events then formed in the poleward band and these propagated in a southwestward direction and faded at the equatorward edge of the lower-latitude band as it migrated poleward. It is shown that the auroral observations are consistent with overdraped lobe flux being generated by lobe reconnection in the winter hemisphere and subsequently being re-closed by lobe reconnection in the summer hemisphere. We propose that the balance between the reconnection rates at these two sites is modulated by the IMF elevation angle, such that when the IMF points more directly northward, the summer lobe reconnection site dominates, re-closing all overdraped lobe flux and eventually becoming disconnected from the Northern Hemisphere.

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}.

On the cause of a magnetospheric flux transfer event

We present a detailed investigation of a magnetospheric flux transfer event (FTE) seen by the Active Magnetospheric Tracer Explorer (AMPTE) UKS and IRM satellites around 1046 UT on October 28, 1984. This event has been discussed many times previously in the literature and has been cited as support for a variety of theories of FTE formation. We make use of a model developed to reproduce ion precipitations seen in the cusp ionosphere. The analysis confirms that the FTE is well explained as a brief excursion into an open low-latitude boundary layer (LLBL), as predicted by two theories of magnetospheric FTEs: namely, that they are bulges in the open LLBL due to reconnection rate enhancements or that they are indentations of the magnetopause by magnetosheath pressure increases (but in the presence of ongoing steady reconnection). The indentation of the inner edge of the open LLBL that these two models seek to explain is found to be shallow for this event. The ion model reproduces the continuous evolution of the ion distribution function between the sheath-like population at the event center and the surrounding magnetospheric populations; it also provides an explanation of the high-pressure core of the event as comprising field lines that were reconnected considerably earlier than those that are draped over it to give the event boundary layer. The magnetopause transition parameter is used to isolate a field rotation on the boundaries of the core, which is subjected to the tangential stress balance test. The test identifies this to be a convecting structure, which is neither a rotational discontinuity (RD) nor a contact discontinuity, but could possibly be a slow shock. In addition, evidence for ion reflection off a weak RD on the magnetospheric side of this structure is found. The event structure is consistent in many ways with features predicted for the open LLBL by analytic MHD theories and by MHD and hybrid simulations. The de Hoffman-Teller velocity of the structure is significantly different from that of the magnetosheath flow, indicating that it is not an indentation caused by a high-pressure pulse in the sheath but is consistent with the motion of newly opened field lines (different from the sheath flow because of the magnetic tension force) deduced from the best fit to the ion data. However, we cannot here rule out the possibility that the sheath flow pattern has changed in the long interval between the two satellites observing the FTE and subsequently emerging into the magnetosheath; thus this test is not conclusive in this particular case. Analysis of the fitted elapsed time since reconnection shows that the core of the event was reconnected in one pulse and the event boundary layer was reconnected in a subsequent pulse. Between these two pulses is a period of very low (but nonzero) reconnection rate, which lasts about 14 mins. Thus the analysis supports, but does not definitively verify, the concept that the FTE is a partial passage into an open LLBL caused by a traveling bulge in that layer produced by a pulse in reconnection rate.

The contribution of flux transfer events to convection

It is shown from flux transfer event (FTE) occurrence statistics, observed as a function of MLT by the ISEE satellites, that recent 2-dimensional analytic theories of the effects of pulsed Petschek reconnection predict FTEs to contribute between 50 and 200 kV to the total reconnection voltage when the magnetosheath field points southward. The upper limit (200 kV) allows the possibility that FTEs provide all the antisunward transport of open field lines into the tail lobe. This range is compared with the voltages associated with series of FTEs signatures, as inferred from ground-based observations, which are in the range 10–60 kV. We conclude that the contribution could sometimes be made by a series of single, large events; however, the voltage is often likely to be contributed by several FTEs at different MLT.

On the quasi-periodic nature of magnetopause flux transfer events

The recurrence rate of flux transfer events (FTEs) observed near the dayside magnetopause is discussed. A survey of magnetopause observations by the ISEE satellites shows that the distribution of the intervals between FTE signatures has a mode value of 3 min, but is highly skewed, having upper and lower decile values of 1.5 min and 18.5 min, respectively. The mean value is found to be 8 min, consistent with previous surveys of magnetopause data. The recurrence of quasi-periodic events in the dayside auroral ionosphere is frequently used as evidence for an association with magnetopause FTEs, and the distribution of their repetition intervals should be matched to that presented here if such an association is to be confirmed. A survey of 1 year's 15-s data on the interplanetary magnetic field (IMF) suggests that the derived distribution could arise from fluctuations in the IMF Bz component, rather than from a natural oscillation frequency of the magnetosphere-ionosphere system.