L1-regularisation for ill-posed problems in variational data assimilation

We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.

Cyclic loss of open solar flux since 1868: the link to heliospheric current sheet tilt and implications for the Maunder Minimum

Open solar flux (OSF) variations can be described by the imbalance between source and loss terms. We use spacecraft and geomagnetic observations of OSF from 1868 to present and assume the OSF source, S, varies with the observed sunspot number, R. Computing the required fractional OSF loss, χ, reveals a clear solar cycle variation, in approximate phase with R. While peak R varies significantly from cycle to cycle, χ is surprisingly constant in both amplitude and waveform. Comparisons of χ with measures of heliospheric current sheet (HCS) orientation reveal a strong correlation. The cyclic nature of χ is exploited to reconstruct OSF back to the start of sunspot records in 1610. This agrees well with the available spacecraft, geomagnetic, and cosmogenic isotope observations. Assuming S is proportional to R yields near-zero OSF throughout the Maunder Minimum. However, χ becomes negative during periods of low R, particularly the most recent solar minimum, meaning OSF production is underestimated. This is related to continued coronal mass ejection (CME) activity, and therefore OSF production, throughout solar minimum, despite R falling to zero. Correcting S for this produces a better match to the recent solar minimum OSF observations. It also results in a cycling, nonzero OSF during the Maunder Minimum, in agreement with cosmogenic isotope observations. These results suggest that during the Maunder Minimum, HCS tilt cycled as over recent solar cycles, and the CME rate was roughly constant at the levels measured during the most recent two solar minima.

Predicting the arrival of high-speed solar wind streams at Earth using the STEREO Heliospheric Imagers

High-speed solar wind streams modify the Earth's geomagnetic environment, perturbing the ionosphere, modulating the flux of cosmic rays into the Earth atmosphere, and triggering substorms. Such activity can affect modern technological systems. To investigate the potential for predicting the arrival of such streams at Earth, images taken by the Heliospheric Imager (HI) on the STEREO-A spacecraft have been used to identify the onsets of high-speed solar wind streams from observations of regions of increased plasma concentrations associated with corotating interaction regions, or CIRs. In order to confirm that these transients were indeed associated with CIRs and to study their average properties, arrival times predicted from the HI images were used in a superposed epoch analysis to confirm their identity in near-Earth solar wind data obtained by the Advanced Composition Explorer (ACE) spacecraft and to observe their influence on a number of salient geophysical parameters. The results are almost identical to those of a parallel superposed epoch analysis that used the onset times of the high-speed streams derived from east/west deflections in the ACE measurements of solar wind speed to predict the arrival of such streams at Earth, assuming they corotated with the Sun with a period of 27 days. Repeating the superposed epoch analysis using restricted data sets demonstrates that this technique can provide a timely prediction of the arrival of CIRs at least 1 day ahead of their arrival at Earth and that such advanced warning can be provided from a spacecraft placed 40° ahead of Earth in its orbit.

Dilution of the Antarctic ozone hole into southern midlatitudes, 1998-2000

The reduction in southern midlatitude ozone is quantified by evaluating the trajectories of ozone-depleted air masses, assuming that photochemical recovery of ozone in advected air parcels can be ignored. This procedure is carried out for the 3 months from 15 October to 15 January for each of the years 1998, 1999, and 2000. Two distinct source regions, the vortex core and the vortex edge, are considered, and for each day, diabatic reverse domain filling calculations are performed for an ensemble of parcels between 30°S and 60°S and 400–700 K in altitude. In 1998, 1999, and 2000 the mean calculated ozone reduction is 16, 18, and 19 DU, respectively. Air parcels from the vortex edge region are significant contributors to the reduction, especially during spring. Results for four longitudinal and three latitudinal midlatitude subregions are also presented. A comparison with the Total Ozone Mapping Spectrometer measurements of total column ozone shows that without the dilution, ozone over Southern Hemisphere midlatitudes would be 5–6% higher during spring and summer. This result is probably an overestimate due to the neglect of photochemical recovery.

Incorporation of water vapour transfer in the JULES Land Surface Model: implications for key soil variables and land surface fluxes

This study focuses on the mechanisms underlying water and heat transfer in upper soil layers, and their effects on soil physical prognostic variables and the individual components of the energy balance. The skill of the JULES (Joint UK Land Environment Simulator) land surface model (LSM) to simulate key soil variables, such as soil moisture content and surface temperature, and fluxes such as evaporation, is investigated. The Richards equation for soil water transfer, as used in most LSMs, was updated by incorporating isothermal and thermal water vapour transfer. The model was tested for three sites representative of semi-arid and temperate arid climates: the Jornada site (New Mexico, USA), Griffith site (Australia) and Audubon site (Arizona, USA). Water vapour flux was found to contribute significantly to the water and heat transfer in the upper soil layers. This was mainly due to isothermal vapour diffusion; thermal vapour flux also played a role at the Jornada site just after rainfall events. Inclusion of water vapour flux had an effect on the diurnal evolution of evaporation, soil moisture content and surface temperature. The incorporation of additional processes, such as water vapour flux among others, into LSMs may improve the coupling between the upper soil layers and the atmosphere, which in turn could increase the reliability of weather and climate predictions.