Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models

With the prospect of exascale computing, computational methods requiring only local data become especially attractive. Consequently, the typical domain decomposition of atmospheric models means horizontally-explicit vertically-implicit (HEVI) time-stepping schemes warrant further attention. In this analysis, Runge-Kutta implicit-explicit schemes from the literature are analysed for their stability and accuracy using a von Neumann stability analysis of two linear systems. Attention is paid to the numerical phase to indicate the behaviour of phase and group velocities. Where the analysis is tractable, analytically derived expressions are considered. For more complicated cases, amplification factors have been numerically generated and the associated amplitudes and phase diagnosed. Analysis of a system describing acoustic waves has necessitated attributing the three resultant eigenvalues to the three physical modes of the system. To do so, a series of algorithms has been devised to track the eigenvalues across the frequency space. The result enables analysis of whether the schemes exactly preserve the non-divergent mode; and whether there is evidence of spurious reversal in the direction of group velocities or asymmetry in the damping for the pair of acoustic modes. Frequency ranges that span next-generation high-resolution weather models to coarse-resolution climate models are considered; and a comparison is made of errors accumulated from multiple stability-constrained shorter time-steps from the HEVI scheme with a single integration from a fully implicit scheme over the same time interval. Two schemes, “Trap2(2,3,2)” and “UJ3(1,3,2)”, both already used in atmospheric models, are identified as offering consistently good stability and representation of phase across all the analyses. Furthermore, according to a simple measure of computational cost, “Trap2(2,3,2)” is the least expensive.

Geophysical characterization of the complex dynamics of groundwater and seawater exchange in a highly stressed aquifer system linked to a coastal lagoon (SE Spain)

Anthropogenic pressure influences the two-way interactions between shallow aquifers and coastal lagoons. Aquifer overexploitation may lead to seawater intrusion, and aquifer recharge from rainfall plus irrigation may, in turn, increase the groundwater discharge into the lagoon. We analyse the evolution, since the 1950s up to the present, of the interactions between the Campo de Cartagena Quaternary aquifer and the Mar Menor coastal lagoon (SE Spain). This is a very heterogeneous and anisotropic detrital aquifer, where aquifer–lagoon interface has a very irregular geometry. Using electrical resistivity tomography, we clearly identified the freshwater–saltwater transition zone and detected areas affected by seawater intrusion. Severity of the intrusion was spatially variable and significantly related to the density of irrigation wells in 1950s–1960s, suggesting the role of groundwater overexploitation. We distinguish two different mechanisms by which water from the sea invades the land: (a) horizontal advance of the interface due to a wide exploitation area and (b) vertical rise (upconing) caused by local intensive pumping. In general, shallow parts of the geophysical profiles show higher electrical resistivity associated with freshwater mainly coming from irrigation return flows, with water resources mostly from deep confined aquifers and imported from Tagus river, 400 km north. This indicates a likely reversal of the former seawater intrusion process.

Comparative Cluster/Double Star observations of the high and low latitude dayside magnetopause

The launch of the Double Star mission has provided the opportunity to monitor events at distinct locations on the dayside magnetopause, in coordination with the quartet of Cluster spacecraft. We present results of two such coordinated studies. In the first, 6 April 2004, both Cluster and the Double Star TC-1 spacecraft were on outbound transits through the dawn-side magnetosphere. Cluster observed northward moving FTEs with +/- polarity, whereas TC-1 saw -/+ polarity FTEs. The strength, motion and occurrence of the FTE signatures changes somewhat according to changes in IMF clock angle. These observations are consistent with ongoing reconnection on the dayside magnetopause, resulting in a series of flux transfer events (FTEs) seen both at Cluster and TC-1. The observed polarity and motion of each FTE signature advocates the existence of an active reconnection region consistently located between the positions of Cluster and TC-1, lying north and south of the reconnection line, respectively. This scenario is supported by the application of a model, designed to track flux tube motion, to conditions appropriate for the prevailing interplanetary conditions. The results from the model confirm the observational evidence that the low-latitude FTE dynamics is sensitive to changes in convected upstream conditions. In particular, changing the interplanetary magnetic field (IMF) clock angle in the model predicts that TC-1 should miss the resulting FTEs more often than Cluster, as is observed. For the second conjunction, on the 4 Jan 2005, the Cluster and TC-1 spacecraft all exited the dusk-side magnetosphere almost simultaneously, with TC-1 lying almost equatorial and Cluster at northern latitudes at about 4 RE from TC-1. The spacecraft traverse the magnetopause during a strong reversal in the IMF from northward to southward and a number of magnetosheath FTE signatures are subsequently observed. One coordinated FTE, studied in detail by Pu et al, [this issue], carries and inflowing energetic electron population and shows a motion and orientation which is similar at all spacecraft and consistent with the predictions of the model for the flux tube dynamics, given a near sub-solar reconnection line. This event can be interpreted either as the passage of two parallel flux tubes arising from adjacent x-line positions, or as a crossing of a single flux tube at different positions.

The dynamics and relationships of precipitation, temperature and convection boundaries in the dayside auroral ionosphere

A continuous band of high ion temperature, which persisted for about 8 h and zigzagged north-south across more than five degrees in latitude in the dayside (07:00– 15:00MLT) auroral ionosphere, was observed by the EISCAT VHF radar on 23 November 1999. Latitudinal gradients in the temperature of the F-region electron and ion gases (Te and Ti , respectively) have been compared with concurrent observations of particle precipitation and field-perpendicular convection by DMSP satellites, in order to reveal a physical explanation for the persistent band of high Ti , and to test the potential role of Ti and Te gradients as possible markers for the open-closed field line boundary. The north/south movement of the equatorward Ti boundary was found to be consistent with the contraction/expansion of the polar cap due to an unbalanced dayside and nightside reconnection. Sporadic intensifications in Ti , recurring on _10-min time scales, indicate that frictional heating was modulated by time-varying reconnection, and the band of high Ti was located on open flux. However, the equatorward Ti boundary was not found to be a close proxy of the open-closed boundary. The closest definable proxy of the open-closed boundary is the magnetosheath electron edge observed by DMSP. Although Te appears to be sensitive to magnetosheath electron fluxes, it is not found to be a suitable parameter for routine tracking of the open-closed boundary, as it involves case dependent analysis of the thermal balance. Finally, we have documented a region of newly-opened sunward convecting flux. This region is situated between the convection reversal boundary and the magnetosheath electron edge defining the openclosed boundary. This is consistent with a delay of several minutes between the arrival of the first (super-Alfv´enic) magnetosheath electrons and the response in the ionospheric convection, conveyed to the ionosphere by the interior Alfv´en wave. It represents a candidate footprint of the low-latitude boundary mixing layer on sunward convecting open flux

Nightside studies of coherent HF Radar spectral width behaviour

A previous case study found a relationship between high spectral width measured by the CUTLASS Finland HF radar and elevated electron temperatures observed by the EISCAT and ESR incoherent scatter radars in the postmidnight sector of magnetic local time. This paper expands that work by briefly re-examining that interval and looking in depth at two further case studies. In all three cases a region of high HF spectral width (>200 ms−1) exists poleward of a region of low HF spectral width (<200 ms^{−1}). Each case, however, occurs under quite different geomagnetic conditions. The original case study occurred during an interval with no observed electrojet activity, the second study during a transition from quiet to active conditions with a clear band of ion frictional heating indicating the location of the flow reversal boundary, and the third during an isolated substorm. These case studies indicate that the relationship between elevated electron temperature and high HF radar spectral width appears on closed field lines after 03:00 magnetic local time (MLT) on the nightside. It is not clear whether the same relationship would hold on open field lines, since our analysis of this relationship is restricted in latitude. We find two important properties of high spectral width data on the nightside. Firstly the high spectral width values occur on both open and closed field lines, and secondly that the power spectra which exhibit high widths are both single-peak and multiple-peak. In general the regions of high spectral width (>200 ms−1) have more multiple-peak spectra than the regions of low spectral widths whilst still maintaining a majority of single-peak spectra. We also find that the region of ion frictional heating is collocated with many multiplepeak HF spectra. Several mechanisms for the generation of high spectral width have been proposed which would produce multiple-peak spectra, these are discussed in relation to the data presented here. Since the regions of high spectral width are observed both on closed and open field lines the use of the boundary between low and high spectral width as an ionospheric proxy for the open/closed field line boundary is not a simple matter, if indeed it is possible at all.

Ground-based and satellite observations of high-latitude auroral activity in the dusk sector of the auroral oval

On 7 December 2000, during 13:30-15:30 UT the MIRACLE all-sky camera at Ny Alesund observed auroras at high-latitudes (MLAT similar to 76) simultaneously when the Cluster spacecraft were skimming the magnetopause in the same MLT sector (at similar to 16:00-18:00 MLT). The location of the auroras (near the ionospheric convection reversal boundary) and the clear correlation between their dynamics and IMF variations suggests their close relationship with R1 currents. Consequently, we can assume that the Cluster spacecraft were making observations in the magnetospheric region associated with the auroras, although exact magnetic conjugacy between the ground-based and satellite observations did not exist. The solar wind variations appeared to control both the behaviour of the auroras and the magnetopause dynamics. Auroral structures were observed at Ny Alesund especially during periods of negative IMF B-Z. In addition, the Cluster spacecraft experienced periodic (T similar to 4 - 6 min) encounters between magnetospheric and magnetosheath plasmas. These undulations of the boundary can be interpreted as a consequence of tailward propagating magnetopause surface waves. Simultaneous dusk sector ground-based observations show weak, but discernible magnetic pulsations (Pc 5) and occasionally periodic variations (T - 2 - 3 min) in the high-latitude auroras. In the dusk sector, Pc 5 activity was stronger and had characteristics that were consistent with a field line resonance type of activity. When IMF BZ stayed positive for a longer period, the auroras were dimmer and the spacecraft stayed at the outer edge of the magnetopause where they observed electromagnetic pulsations with T similar to 1 min. We find these observations interesting especially from the viewpoint of previously presented studies relating poleward-moving high-latitude auroras with pulsation activity and MHD waves propagating at the magnetospheric boundary layers.

A multipoint study of a substorm occurring on 7 December, 1992, and its theoretical implications

On 7 December 1992, a moderate substorm was observed by a variety of satellites and ground-based instruments. Ionospheric flows were monitored near dusk by the Goose Bay HF radar and near midnight by the EISCAT radar. The observed flows are compared here with magnetometer observations by the IMAGE array in Scandinavia and the two Greenland chains, the auroral distribution observed by Freja and the substorm cycle observations by the SABRE radar, the SAMNET magnetometer array and LANL geosynchronous satellites. Data from Galileo Earth-encounter II are used to estimate the IMF B-z component. The data presented show that the substorm onset electrojet at midnight was confined to closed field lines equatorward of the preexisting convection reversal boundaries observed in the dusk and midnight regions. No evidence of substantial closure of open flux was detected following this substorm onset. Indeed the convection reversal boundary on the duskside continued to expand equatorward after onset due to the continued presence of strong southward IMF, such that growth and expansion phase features were simultaneously present. Clear indications of closure of open flux were not observed until a subsequent substorm intensification 25 min after the initial onset. After this time, the substorm auroral bulge in the nightside hours propagated well poleward of the pre-existing convection reversal boundary, and strong flow perturbations were observed by the Goose Bay radar, indicative of flows driven by reconnection in the tail.

Temporal and spatial variability of auroral forms in the 10–14 MLT sector: Relationship to plasma convection and solar wind-magnetosphere coupling

Ground-based observations of dayside auroral forms and magnetic perturbations in the arctic sectors of Svalbard and Greenland, in combination with the high-resolution measurements of ionospheric ion drift and temperature by the EISCAT radar, are used to study temporal/spatial structures of cusp-type auroral forms in relation to convection. Large-scale patterns of equivalent convection in the dayside polar ionosphere are derived from the magnetic observations in Greenland and Svalbard. This information is used to estimate the ionospheric convection pattern in the vicinity of the cusp/cleft aurora. The reported observations, covering the period 0700-1130 UT, on January 11, 1993, are separated into four intervals according to the observed characteristics of the aurora and ionospheric convection. The morphology and intensity of the aurora are very different in quiet and disturbed intervals. A latitudinally narrow zone of intense and dynamical 630.0 nm emission equatorward of 75 degrees MLAT, was observed during periods of enhanced antisunward convection in the cusp region. This (type 1 cusp aurora) is considered to be the signature of plasma entry via magnetopause reconnection at low magnetopause latitudes, i.e. the low-latitude boundary layer (LLB I,). Another zone of weak 630.0 nm emission (type 2 cusp aurora) was observed to extend up to high latitudes (similar to 79 degrees MLAT) during relatively quiet magnetic conditions, when indications of reverse (sunward) convection was observed in the dayside polar cap. This is postulated to be a signature of merging between a northward directed IMF (B-z > 0) and the geomagnetic field poleward of the cusp. The coexistence of type 1 and 2 auroras was observed under intermediate circumstances. The optical observations from Svalbard and Greenland were also used to determine the temporal and spatial evolution of type 1 auroral forms, i.e. poleward-moving auroral events occurring in the vicinity of a rotational convection reversal in the early post-noon sector. Each event appeared as a local brightening at the equatorward boundary of the pre-existing type 1 cusp aurora, followed by poleward and eastward expansions of luminosity. The auroral events were associated with poleward-moving surges of enhanced ionospheric convection and F-layer ion temperature as observed by the EISCAT radar in Tromso. The EISCAT ion flow data in combination with the auroral observations show strong evidence for plasma flow across the open/closed field line boundary.

Relationship of dayside auroral precipitations to the open-closed separatrix and the pattern of convective flow

The implications are discussed of acceleration of magnetospheric ions by reflection off two magnetopause Alfvén waves, launched by the reconnection site into the inflow regions on both sides of the boundary. The effects of these waves on the ion populations, predicted using the model described by Lockwood et al. [1996], offer a physical interpretation of all the various widely used classifications of precipitation into the dayside ionosphere, namely, central plasma sheet, dayside boundary plasma sheet (BPS), void, low-latitude boundary layer (LLBL), cusp, mantle, and polar cap. The location of the open-closed boundary and the form of the convection flow pattern are discussed in relation to the regions in which these various precipitations are typically found. Specifically, the model predicts that both the LLBL and the dayside BPS precipitations are on newly opened field lines and places the convection reversal within the LLBL, as is often observed. It is shown that this offers solutions to a number of paradoxes and problems that arise if the LLBL and BPS precipitations are thought of as being on closed field lines. This model is also used to make quantitive predictions of the longitudinal extent and latitudinal width of the cusp, as a function of solar wind density.

Variability of dayside high latitude convection associated with a sequence of auroral transients

10 second resolution ionospheric convection data covering the invariant latitude range from 71° to 76°, obtained by using the EISCAT UHF and VHF radars, are combined with optical data from Ny Ålesund during a sequence of auroral transients in the post-noon sector (∼ 15 MLT). Satellite observations of polar cap convection patterns suggest negative BZ and BY components of the interplanetary magnetic field. Burst-like enhancements of westward (sunward) post-noon convection were accompanied by eastward moving auroral forms at higher latitudes, above the convection reversal boundary. In this case the background convection was weak, whereas the integrated potential drop across the radar field-of-view associated with the westward flow bursts was typically ∼ 20-35 kV. The auroral phenomenon consists of a series of similar events with a mean repetition period of 8 min. A close correlation between the auroral activity and convection enhancements in the cleft ionosphere is demonstrated.

Events of enhanced convection and related dayside auroral activity

In this paper we study the high-latitude plasma flow variations associated with a periodic (∼8 min) sequence of auroral forms moving along the polar cap boundary, which appear to be the most regularly occuring dayside auroral phenomenon under conditions of southward directed interplanetary magnetic field. Satellite data on auroral particle precipitation and ionospheric plasma drifts from DMSP F10 and F11 are combined with ground-based optical and ion flow measurements for January 7, 1992. Ionospheric flow measurements of 10-s resolution over the range of invariant latitudes from 71° to 76° were obtained by operating both the European incoherent scatter (EISCAT) UHF and VHF radars simultaneously. The optical site (Ny Ålesund, Svalbard) and the EISCAT radar field of view were located in the postnoon sector during the actual observations. The West Greenland magnetometers provided information about temporal variations of high-latitude convection in the prenoon sector. Satellite observations of polar cap convection in the northern and southern hemispheres show a standard two-cell pattern consistent with a prevailing negative By component of the interplanetary magnetic field. The 630.0 nm auroral forms located poleward of the persistent cleft aurora and the flow reversal boundary in the ∼1440–1540 MLT sector were observed to coincide with magnetosheath-like particle precipitation and a secondary population of higher energy ions, and they propagated eastward/tailward at speeds comparable with the convection velocity. It is shown that these optical events were accompanied by bursts of sunward (return) flow at lower latitudes in both the morning and the afternoon sectors, consistent with a modulation of Dungey cell convection. The background level of convection was low in this case (Kp =2+). The variability of the high-latitude convection may be explained as resulting from time-varying reconnection at the magnetopause. In that case this study indicates that time variations of the reconnection rate effectively modulates ionospheric convection.

The response of ionospheric convection in the polar cap to substorm activity

We report multi-instrument observations during an isolated substorm on 17 October 1989. The EISCAT radar operated in the SP-UK-POLI mode measuring ionospheric convection at latitudes 71°-78°. SAMNET and the EISCAT Magnetometer Cross provide information on the timing of substorm expansion phase onset and subsequent intensifications, as well as the location of the field aligned and ionospheric currents associated with the substorm current wedge. IMP-8 magnetic field data are also included. Evidence of a substorm growth phase is provided by the equatorward motion of a flow reversal boundary across the EISCAT radar field of view at 2130 MLT, following a southward turning of the interplanetary magnetic field (IMF). We infer that the polar cap expanded as a result of the addition of open magnetic flux to the tail lobes during this interval. The flow reversal boundary, which is a lower limit to the polar cap boundary, reached an invariant latitude equatorward of 71° by the time of the expansion phase onset. A westward electrojet, centred at 65.4°, occurred at the onset of the expansion phase. This electrojet subsequently moved poleward to a maximum of 68.1° at 2000 UT and also widened. During the expansion phase, there is evidence of bursts of plasma flow which are spatially localised at longitudes within the substorm current wedge and which occurred well poleward of the westward electrojet. We conclude that the substorm onset region in the ionosphere, defined by the westward electrojet, mapped to a part of the tail radially earthward of the boundary between open and closed magnetic flux, the “distant” neutral line. Thus the substorm was not initiated at the distant neutral line, although there is evidence that it remained active during the expansion phase. It is not obvious whether the electrojet mapped to a near-Earth neutral line, but at its most poleward, the expanded electrojet does not reach the estimated latitude of the polar cap boundary.

EISCAT observations of unusual flows in the morning sector associated with weak substorm activity

A discussion is given of plasma flows in the dawn and nightside high-latitude ionospheric regions during substorms occurring on a contracted auroral oval, as observed using the EISCAT CP-4-A experiment. Supporting data from the PACE radar, Greenland magnetometer chain, SAMNET magnetometers and geostationary satellites are compared to the EISCAT observations. On 4 October 1989 a weak substorm with initial expansion phase onset signatures at 0030 UT, resulted in the convection reversal boundary observed by EISCAT (at \sim0415 MLT) contracting rapidly poleward, causing a band of elevated ionospheric ion temperatures and a localised plasma density depletion. This polar cap contraction event is shown to be associated with various substorm signatures; Pi2 pulsations at mid-latitudes, magnetic bays in the midnight sector and particle injections at geosynchronous orbit. A similar event was observed on the following day around 0230 UT (\sim0515 MLT) with the unusual and significant difference that two convection reversals were observed, both contracting poleward. We show that this feature is not an ionospheric signature of two active reconnection neutral lines as predicted by the near-Earth neutral model before the plasmoid is “pinched off”, and present two alternative explanations in terms of (1) viscous and lobe circulation cells and (2) polar cap contraction during northward IMF. The voltage associated with the anti-sunward flow between the reversals reaches a maximum of 13 kV during the substorm expansion phase. This suggests it to be associated with the polar cap contraction and caused by the reconnection of open flux in the geomagnetic tail which has mimicked “viscous-like” momentum transfer across the magnetopause.

Multiple, discrete arcs on sunward convecting field lines in the 14-15 MLT region

Ionospheric plasma flow measurements and simultaneous observations of thin (∼0.2° invariant latitude (ILAT)), multiple, longitudinally extended auroral arcs of transient nature within 74°-76° ILAT and 1030-1130 UT (∼14-15 MLT) on January 12, 1989, are reported. The auroral structures appeared within the luminous belt of strong 630.0-nm emissions located predominantly on sunward convecting field lines equatorward of the convection reversal boundary as identified by the European Incoherent Scatter UHF radar. The events occurred during a period of several hours quasi-steady solar wind speed (∼ 700 km s−1) and a radially orientated interplanetary magnetic field (IMF) with a weak northward tilt (IMF Bz>0). These typical dayside auroral features are related to previous studies of auroral activity related to the upward region 1 current in the postnoon sector. The discrete auroral events presented here may result from magnetosheath plasma injections into the low-latitude boundary layer (LLBL) and an associated dynamo mechanism. An alternative explanation invokes kinetic Alfvén waves, triggered either by Kelvin-Helmholtz instability at the inner (or outer) edge of the LLBL or by pressure pulse induced magnetopause surface waves.

Auroral bright spot sequence near 1400 MLT: Coordinated optical and ion drift observations

Optical observations of a dayside auroral brightening sequence, by means of all-sky TV cameras and meridian scanning photometers, have been combined with EISCAT ion drift observations within the same invariant latitude-MLT sector. The observations were made during a January 1989 campaign by utilizing the high F region ion densities during the maximum phase of the solar cycle. The characteristic intermittent optical events, covering ∼300 km in east-west extent, move eastward (antisunward) along the poleward boundary of the persistent background aurora at velocities of ∼1.5 km s−1 and are associated with ion flows which swing from eastward to westward, with a subsequent return to eastward, during the interval of a few minutes when there is enhanced auroral emission within the radar field of view. The breakup of discrete auroral forms occurs at the reversal (negative potential) that forms between eastward plasma flow, maximizing near the persistent arc poleward boundary, and strong transient westward flow to the south. The reported events, covering a 35 min interval around 1400 MLT, are embedded within a longer period of similar auroral activity between 0830 (1200 MLT) and 1300 UT (1600 MLT). These observations are discussed in relation to recent models of boundary layer plasma dynamics and the associated magnetosphere-ionosphere coupling. The ionospheric events may correspond to large-scale wave like motions of the low-latitude boundary layer (LLBL)/plasma sheet (PS) boundary. On the basis of this interpretation the observed spot size, speed and repetition period (∼10 min) give a wavelength (the distance between spots) of ∼900 km in the present case. The events can also be explained as ionospheric signatures of newly opened flux tubes associated with reconnection bursts at the magnetopause near 1400 MLT. We also discuss these data in relation to random, patchy reconnection (as has recently been invoked to explain the presence of the sheathlike plasma on closed field lines in the LLBL). In view of the lack of IMF data, and the existing uncertainty on the location of the open-closed field line boundary relative to the optical events, an unambiguous discrimination between the different alternatives is not easily obtained.