The nature and origins of the day-to-day variability in Earth’s surface magnetic field

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The nature and origins of the day-to-day variability in Earth’s surface magnetic field Jeffrey M. Forbes a,⇑, Astrid Maute b, Xiaoli Zhang a a

Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309, USA b High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80301, USA Received 31 January 2019; received in revised form 25 May 2019; accepted 27 May 2019

Abstract Numerical experiments are performed with the National Center for Atmospheric Research (NCAR) Thermosphere-Ionosphere-Elec trodynamics General Circulation Model (TIE-GCM) to reveal the characteristics and origins of daytime magnetic field variations on the ground (DB) at planetary-wave (PW) periods (2–20 days). Simulations are performed to separate the responses to forcing in the lower atmosphere from solar-magnetospheric forcing. Lower-atmosphere forcing is specified at the 97-km lower boundary of the TIE-GCM by NCAR’s Thermosphere-Ionosphere-Mesosphere Electrodynamics General Circulation Model (TIME-GCM), which itself is forced at 30 km by MERRA (Modern Era Retrospective-analysis for Research and Applications) outputs. Solar and magnetospheric inputs to the TIE-GCM are specified according to parameterizations based on F10.7 and Kp. The study focuses on latitudes 0°–65°N during October 1–31, 2009, when F10.7 (range 68–80), Kp (range 0–4), and Ap (range 0–13) are typical of quiet-time ‘‘weather”. Neutral dynamics in the dynamo region (ca. 100–150 km) during this period is dominated by winds due to PW modulated tides, where the PW include the quasi-6, 10 and 16-day westward-propagating normal modes with zonal wavenumber s = 1, and eastward-propagating ultra-fast Kelvin waves (UFKW) with s =
1 and periods between 2 and 5 days. Results and conclusions are as follows. PW-period perturbations in daytime DB at the ground are dominated by variability originating in the lower atmosphere. The only exception is the 45°–65° latitude regime around noon, where the DB variability due to lower atmospheric forcing exceeds that due to solar-magnetospheric forcing by only about 50%. Broadband zonally-symmetric oscillations also occur in DB due to dissipation of the tidal spectrum at PW periods in the E-region. These results raise the possibility that some level of contamination from the lower atmosphere may exist in magnetic indices such as ap, Kp, and Ap that are used as measures solarmagnetosphere-ionosphere coupling strength, under levels of geomagnetic activity similar to that characterizing October 2009. It is also found that variations in conductivities play a minor role compared with neutral winds in producing PW-period variations in DB, and that there is not a robust one-to-one correspondence between spectral peaks in DB and those in the neutral winds. Several factors contribute to this latter result, which are explained in the text. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Ionosphere; Magnetic perturbations; Tides and planetary waves; Dynamo

1. Introduction The day-to-day variability of the ionosphere that originates from dynamical coupling with the lower ⇑ Corresponding author.

E-mail address: [email protected] (J.M. Forbes).

(0–15  km) and middle atmosphere (ca. 15–100  km) has been a topic of interest since the 1990’s (e.g., Forbes et al., 2000; Rishbeth and Mendillo, 2001; Rishbeth, 2006; Rishbeth et al., 2009; Mendillo et al., 2002; Liu et al., 2013). Many observational studies (e.g., Altadill, 2000; Altadill et al., 1997, 2001, 2003; Altadill and Lastovicˇka, 1996; Apostolov et al., 1994, 1995; Borries

https://doi.org/10.1016/j.asr.2019.05.045 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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and Hoffmann, 2010; Borries et al., 2007; Forbes et al., 1997; Forbes and Leveroni, 1992; Forbes and Zhang, 1997; Lasˇtovicˇka et al., 2006; Lasˇtovicˇka and sˇauli, 1999; Liu et al., 2010, 2013; Pancheva, 1988; Pancheva and Lysenko, 1988; Pancheva et al., 1994; Parish et al., 1994) have focused on variability of foF2, NmF2, hmF2 and total electron content (TEC) at periods associated with ‘‘quasiresonant’’ or ‘‘normal-mode (NM)’’ planetary waves (PW) of the atmosphere (i.e., quasi-2, 6, 10 and 16-day waves (Salby, 1981); hereafter Q2DW, Q6DW, Q10DW, Q16DW, respectively). These types of studies contain some intrinsic shortcomings. With the exception of Borries and Hoffmann (2010), analyses are performed over limited longitudinal extents such that information on zonal wavenumber and direction of zonal propagation are absent. Studies often lack definitive connections with PW oscillations in the neutral atmosphere that are assumed responsible for the observed ionospheric variability, and furthermore several mechanisms through which PW variability is proposed to be transmitted to the ionosphere are not fully vetted (see further below). Finally, ionospheric variations due to recurrent magnetic activity and solar EUV radiation often occur around subharmonics of the 27-day solar rotation period (13.5, 9, 6.75 days) (e.g., Lei et al., 2008; Tulasi Ram et al., 2010) which are sufficiently close to NM periods to make separation of each effect problematic. The lunar M2 tide at a fixed local time also appears at a period of 14.75 days, close to that of the Q16DW (see, e.g., Forbes and Leveroni, 1992). Another line of investigation, insofar as PW coupling to the ionosphere is concerned, deals with the magnetic perturbations at the ground (hereafter (DB)) induced by the height-integrated wind-driven currents in the ionospheric E-region (ca. 100–150  km): Z Z b Jdz ¼ r  ½E þ U  B dz ð1Þ where U and B are the neutral wind and magnetic field vectors, respectively; b r is the conductivity tensor; and E is the electrostatic field that is set up near-instantaneously to force the total current to be non-divergent (r  J ¼ 0) in accord with Maxwell’s steady-state equations. Observational studies to detect PW periodicities in ground magnetic data (e.g., Parish et al., 1994; Kohsiek et al., 1995; Lawrence and Jarvis, 2003; Jarvis, 2006; Pancheva et al., 2006, 2008; Elhawary and Forbes, 2016) often suffer similar shortcomings to those noted above for studies of the Fregion; namely lack of longitudinal perspective (except for Pancheva et al., 2006, 2008; Elhawary and Forbes, 2016) and corroborating observations of neutral dynamics (except for Lawrence and Jarvis, 2003); uncertainties with regard to underlying mechanisms; and potential contamination by recurrent magnetic activity or EUV radiation as reflected in magnetic indices such as ap, Kp or Ap, or solar indices such as F10.7, respectively; or lunar effects. Concerning the physical mechanisms underlying PWionosphere coupling, the relative importance of several

proposed mechanisms remains unknown, thus impeding our understanding. Based on linear modeling (Hagan et al., 1993; Meyer, 1999; Forbes et al., 1995), PW are apparently unable to penetrate significantly above 100 km on their own, although there are pathways by which PW signals can be transmitted to the ionosphere and thermosphere through interactions with tides and gravity waves (GW). For instance, since tides are capable of penetrating to well into the dynamo region (ca. 100– 150  km), and PW-tide interactions are prevalent in mesosphere and lower thermosphere (MLT) observations (Beard et al., 1999; Kamalabadi et al., 1997; Pancheva et al., 2000, 2002, 2004; Forbes and Zhang, 2017), PW modulation of tides is a probable candidate for transmitting PW periodicities to the ionosphere E- and F-regions. This mechanism was in fact first proposed by Chen (1992). By the same token, PW can modulate the accessibility of GWs to the E-region, where GWs can dissipate and induce secondary excitation of PW-period wind oscillations (e.g., Meyer, 1999; Liu and Roble, 2002) capable of driving electric fields. The modulated GWs can also produce ionospheric variability at PW periods through mixing and composition effects in the lower thermosphere that spread to higher altitudes through molecular diffusion (Nguyen and Palo, 2014). While general circulation models have addressed atmosphere-ionosphere coupling in the context of the Q2DW (Chang et al., 2014; Yue et al., 2012, 2013, 2016; Yue and Wang, 2014; Gu et al., 2018) and Q6DW (Gan et al., 2016, 2017), insufficient attention has been devoted to their diagnosis in terms of separating the relative importance of the aforementioned physical coupling mechanisms, particularly those associated with GW. Comprehensive models of the atmosphere-ionosphere system, such as the National Center for Atmospheric Research (NCAR) Thermosphere Ionosphere Mesosphere Electrodynamics General Circulation Model (TIMEGCM) (see Section 2), offer the opportunity to provide new insights into some of the knowledge gaps noted above through numerical experiments. For instance, Yamazaki et al. (2016) devised numerical experiments with the TIME-GCM to separate solar-magnetospheric versus lower atmosphere origins of DB over the globe. They used a TIME-GCM simulation for April 2010, forced at its lower boundary at 30 km by output from MERRA (Modern-Era Retrospective analysis for Research and Applications) to introduce realistic variability due to tides, PW and Kelvin waves into the simulation; and highlatitude energy inputs parameterized by Kp to introduce variability of solar-magnetospheric origin. By performing numerical experiments with the above sources of variability introduced separately and together, their individual contributions were isolated. Yamazaki et al. (2016) arrived at the new and fundamentally important conclusion that the effects of magnetospheric forcing on DB variability equatorward of 60° latitude were much less than those due to lower-atmosphere forcing for Kp 4 (ap 27). In addition, they suggested that the main source of lower-atmosphere

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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variability occurred in connection with the diurnal and semidiurnal migrating tides, which varied at PW periods (mostly 6–7.5 days). It was beyond the scope of their work to determine whether the tidal variability is mainly caused by the tidal source or by PW modulation, although much evidence exists that indicates the latter mechanism to account for much of the observed tidal variability in the MLT (Beard, 1999; Nystrom et al., 2018; Pancheva et al., 2000, 2002, 2004; Forbes and Zhang, 2017). Two very recent studies (Forbes et al., 2018a, 2018b) isolated the ionosphere-thermosphere effects of a tidal spectrum varying at PW periods by performing numerical experiments with a MERRA-forced TIME-GCM for 2009 (hereafter TIME-GCM/MERRA2009, as described in Ha¨usler et al., 2014, 2015), and TIE-GCM v2.0 (Maute, 2017). By forcing the TIE-GCM at its 97-km lower boundary with TIME-GCM/MERRA2009, they were able to filter different parts of the upward-propagating wave spectrum at 97 km to isolate their effects aloft. The 2018a study (hereafter Paper I) focused on the neutral atmosphere response, and the 2018b study (hereafter Paper II) focused on the ionospheric response. Among their results, they demonstrated that a tidal spectrum modulated at PW periods produces (a) ± 40 m/s PW-period wind oscillations between 110 and 150 km at low to middle latitudes; and (b) perturbations in topside F-region electron density (Ne) of order ± 30–50% with respect to the mean at PW periods. The topside Ne variations are mainly connected with oscillations in hmF2, driven in part by in-situ neutral winds and by E  B drifts arising from dynamo action in the E-region. A significant and new aspect of these results is that the E-region neutral winds, E  B drifts, hmF2 and Ne variations, all contain a significant component that is broadband (3–20 day periods) and zonally-symmetric, and appears to largely originate from dissipation of the tidal spectrum at PW periods. Using a term from middleatmosphere dynamics, Forbes et al. (2018b) articulate that the ionosphere-thermosphere system ‘‘vacillates” in response to dissipation of the PW-modulated tidal spectrum, and also note that a similar response should be evident in ground magnetic data. In combination the works of Yamazaki et al. (2016), and Papers I and II, raise some interesting questions regarding PW-period oscillations in DB1: What do their longitudeUT structures look like? Do PW-period oscillations in DB due to lower-atmosphere sources include zonallysymmetric2 (hereafter, S0) oscillations, and if so, are they large or small compared with those of solarmagnetospheric origin? To what extent do oscillations in DB due to lower-atmosphere forcing reflect the characteristics of the driving dynamics? What role do conductivities play in producing DB longitude-UT structures? Are day1 Hereafter DB refers to magnetic perturbations during certain daytime sectors to be defined in Section 3. 2 In this paper zonally symmetric refers to longitude-mean but not local time-mean.

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time DB variations of solar-magnetospheric origin purely zonally-symmetric in magnetic coordinates, or might they also occur at s–0 and thus potentially be interpreted in data as variations of PW origin? These issues impact the ability to draw conclusions about atmosphereionosphere coupling and the underlying neutral dynamics based on global observations of DB, and may hold some relevance to the interpretation of magnetic activity indices such as Kp, ap, and Ap, which are assumed to largely reflect S0 components of DB. It is the purpose of this paper to answer these questions. We will furthermore use a spectral approach focused on longitude-UT variability of DB, and illuminate the important conclusions of Yamazaki et al. (2016) in a way that complements that work and deepens our understanding of atmosphere-ionosphere (A-I) coupling and its contributions to magnetic field variability. The following section provides a description of the model configuration and numerical experiments that were conducted to answer the questions posed above. Section 3 provides our results, and concluding remarks are found in Section 4. 2. Model description and numerical experiments The model configuration employed in the present investigation is described in Papers I and II, so only a brief description is provided here. The TIME-GCM solves the equations governing the energetics, dynamics, chemical composition, and electrodynamics of the neutral and ionized components of the atmosphere from a constant pressure level near 30 km to about 500–800 km depending on level of solar activity (see, e.g., Roble et al., 1988; Richmond et al., 1992; Roble and Ridley, 1994; and references therein). MERRA (Rienecker et al., 2011) is a physics-based weather prediction model constrained by global assimilated data, and thus inputs realistic variability of meteorological origin (i.e., diurnal and semidiurnal tides, Kelvin waves, planetary Rossby waves and stationary planetary waves) into the TIME-GCM. As noted previously, the TIE-GCM is forced at its 97 km lower boundary by output from TIME-GCM/ MERRA2009. This provides the flexibility to isolate the thermosphere-ionosphere effects of lower atmosphere forcing by different parts of the wave spectrum, i.e., tides, eastward- and westward propagating PW with periods between 3 and 7 days, and longer-period PW. However, the TIE-GCM does not resolve or parameterize GW, and thus does not include the potential macroscopic effects of GW that were mentioned in the Introduction. In order to capture the waves of interest both the TIME-GCM and TIE-GCM employ 2.5°  2.5° latitude-longitude grids, four grid points per scale height in the vertical direction, and 60-s time step. As in Papers I and II, it is sufficient to achieve our stated objectives, in this case to answer the questions posed in the introduction, by focusing on October 2009.

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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In the simulations reported here, solar and geomagnetic forcing of the thermosphere and ionosphere is provided by geophysical index (gpi) based parameterizations: spectral irradiances defined according to F10.7 values (Richards et al., 1994), and auroral particle precipitation (Emery et al., 2012; Roble and Ridley, 1987) and electric potential patterns (Weimer, 2005) based on 3-hourly Kp values. Fig. 1 illustrates F10.7 and Kp during October 2009, which is a solar minimum period with F10.7 ranging between 68 and 80. Kp values range between 0 and 4, and are typical of quiet-time ‘‘weather”. The TIE-GCM outputs analyzed in Section 3 are defined as follows: ‘‘gpi + MERRA” is obtained with TIME-GCM/MERRA2009 forcing at the lower boundary, and variable gpi forcing as defined by F10.7 and Kp values in Fig. 1. ‘‘cgpi + MERRA” is similarly defined, except that gpi is replaced with constant gpi forcing (cgpi) specified by mean values of Kp = 1.0 and F10.7 = 71 during

October 2009. Finally, the variable part of the TIE-GCM response to gpi forcing is isolated by analyzing a model output consisting of the difference between the ‘‘gpi + MERRA” and ‘‘cgpi + MERRA” TIE-GCM outputs at every grid point and time step. Since this model output only differs from the response to gpi forcing by a constant offset, and we are only considering residuals from mean values in the following, we will in the interest of simplicity refer to results connected with this difference field as ‘‘gpionly”. By the same reasoning we will simply refer to the ‘‘cgpi + MERRA” results as ‘‘MERRA-only”. The calculation of DB in these simulations, including contributions due to induced ground currents, follows the methodology described in Richmond and Maute (2014). Unless otherwise specified, all data processing is performed in magnetic coordinates. The reader is referred to Paper I and Nystrom et al. (2018) for extensive comparisons between TIMEGCM/MERRA2009 and ground-based and space-based measurements between about 90–110 km which justify the suitability of these models to provide a realistic framework for investigating the impacts of PW-tide interactions on the ionosphere-thermosphere system.

3. Results and discussion 3.1. Variability due to lower-atmosphere forcing versus solarmagnetospheric forcing

Fig. 1. Top to bottom: Kp, Ap and F10.7 indices for the month of October 2009. Mean values and standard deviations are Kp = 0.76 ± 0.89, Ap = 3.5 ± 3.0, F10.7 = 71 ± 3.3.

Ground magnetic variations are strongly modulated by the local time variation in ionospheric conductivity, and which therefore must be considered in any study of DB. Fig. 2 illustrates the geomagnetic longitude- and monthly-mean magnetic latitude versus local time (LT) distributions of the magnetic eastward (dBe) and magnetic northward (dBn) components of DB for the three simulations described previously: gpi + MERRA (2(a) and 2 (d)), MERRA-only (2(b) and 2(e)), and gpi-only (2(c) and 2(f)). Distinctive features of the magnetic perturbations in Fig. 2 are the equatorial daytime positive dBn in Fig. 2(e) corresponding to the equatorial electrojet (EEJ); the daytime negative dBn in Fig. 2(e) at middle to high latitudes of both hemispheres; and the positive and negative dBe cellular structures in Fig. 2(b). The combined effects of these dBn and dBe features are indicated by the notional current flow patterns in Fig. 2(b), which emulate the wellknown Sq (solar quiet) current system, and which confirm the climatological veracity of the TIE-GCM current system. It is furthermore immediately obvious that the gpi + MERRA and MERRA-only results are quantitatively very similar, and that dBn and dBe for MERRA-only are more than an order of magnitude larger than for gpi, at least equatorward of 60° magnetic latitudes. In this monthly-mean depiction, the effects of variable solar and geomagnetic activity effects are averaged out. We now turn

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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Fig. 2. Magnetic latitude versus local time (LT) distributions of the dBe (left) and dBn (right) components of magnetic longitude- and monthly-mean DB for the three simulations described in the text: from top to bottom, gpi + MERRA, MERRA-only, and gpi-only. Notional current flow patterns are drawn in Fig. 2(b) to demonstrate qualitative consistency of the dBn and dBe patterns in the model with the well-known Sq (solar quiet) current system, confirming qualitatively the climatological veracity of the TIE-GCM current system.

to depictions of the day-to-day variability attributable to each of these sources. In the following, we seek to examine the longitude-UT variability of dBe and dBn so that the questions posed in the Introduction can be addressed. Since the space-time variability at single points in latitude versus LT space may not be representative of the broader picture, longitude-UT variability is depicted for the following latitude-LT ranges that are representative of the global current system: for dBn, LT = 1000–1400 between 45°–65°N (NoonHi), 10°–30°N (NoonLo), and 2.5°S–2.5°N (NoonEq); for dBe, 10°–50°N at LT = 0600–1000 (Morn) and LT = 1400–1800 (Aft). These choices are not solely based on Fig. 2, but also on examination of similar latitude versus LT plots for individual days and longitudes throughout the month. These individual plots also revealed significant asymmetries between hemispheres, which are likely due to interhemispheric differences in the magnetic field configurations and neutral wind fields. Understanding the origins of inter-hemispheric asymmetries requires specialized numerical experiments beyond those needed to answer

the questions posed in the Introduction. Therefore, we limit the scope of the present work to the simulations results for the Northern (N.) Hemisphere. The longitude-UT structures of dBn and dBe for October 2009, are shown in Figs. 3 and 4, respectively, for the gpi + MERRA, MERRA-only and gpi-only cases. As might be expected based on the proximity to the auroral electrojet, the contributions of currents associated with magnetospheric coupling (Fig. 3(g)) are visually apparent in the gpi + MERRA NoonHi depiction for dBn (Fig. 3 (a)), particularly around days 4, 11, 15, 21–24, and 29 of October (refer to Fig. 1). On the other hand, these features are much less evident in NoonLo and NoonEq for dBn (Fig. 3(b)–(i)), and Morn and Aft for dBe (Fig. 4). It is notable that the dBn in Fig. 3(g) and (h) exhibit notable deviations from zonal symmetry. In addition, visual inspection of Figs. 3(i) and 4(f) (and perhaps Fig. 4(e)) reveals a 6–9 day period standing (non-zonally-propagating) oscillation with s = 1 (Fig. 3(i)) or s = 2 (Fig. 4(f)). (Note that in a longitude-UT plot, perturbations associated with an eastward-propagating wave would tilt to the right, and

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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Fig. 3. Longitude-UT structures of dBn respectively, for gpi + MERRA (left), MERRA-only (middle) and gpi-only (right) cases for LT = 1000–1400 for 45°–65°N (top) 10°–30°N (middle) and 2.5°S–2.5°N (bottom).

westward-propagating wave to the left; as in these plots, a standing wave shows no tilt.). To further quantify the relative contributions of solarmagnetospheric forcing and forcing by waves from below 100 km to DB variances, variances of the magnetic perturbations plotted in Figs. 3 and 4 are listed in the top rows of Table 1. In the bottom rows, variances are provided for only the S0 oscillations. There are a few main points to take away from these results. First, in all cases except for dBn at 45°–65°N, the MERRA-only results account for almost all of the total (gpi + MERRA) variances with gpi-only making relatively small contributions. At 45°– 65°N, the MERRA-only variance in dBn (20.3 nT2) exceeds that due to gpi forcing alone (14.4 nT2) by almost 50%. Focusing on the s = 0 results for 45°–65°N, variances in dBn are 5.20 nT2 for MERRA-only and 9.61 nT2 for gpi-only. Put another way, day-to-day variability in S0 oscillations in dBn at 45°–65°N due to lower-atmosphere

forcing is about half that due to solar-magnetospheric forcing from above. 3.2. Interpretation of the response to lower-atmosphere forcing Figs. 5 and 6 provide the zonal wavenumber versus period spectra of the magnetic perturbations shown in Figs. 3 and 4. A distinguishing feature of the gpi-only results (as compared to MERRA-only) is the predominance of S0 components of dBe and dBn at all latitudes, although there are some distinct weak peaks at s – 0 as well as noticeable broadening across zonal wavenumbers. The latter may be the manifestation of longitude variations in the magnetic field as noted by Yue et al. (2013) in connection with their study of Q2DW-ionosphere coupling. Concerning the standing wave features noted in connection with the gpionly results in Figs. 3 and 4, a standing wave with period

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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Fig. 4. Same as Fig. 3, except for dBe for LT = 0600–1000 (top) and LT = 1400–1800 (bottom) for 10°–50°N.

Table 1 Variances (nT2) corresponding to the longitude-UT structures in Figs. 3 and 4. All oscillations

gpi + MERRA

gpi only

MERRA only

dBn, LT = 1000–1400, 45°–65°N dBn, LT = 1000–1400, 10°–30°N dBn, LT = 1000–1400, 2.5°S–2.5°N dBe, LT = 0600–1000, 10°–50°N dBe, LT = 1400–1800, 10°–50°N

34.3 51.4 202. 19.3 21.3

14.4 0.81 2.07 0.20 1.35

20.3 51.8 199. 19.4 19.3

s = 0 oscillations dBn, LT = 1000–1400, dBn, LT = 1000–1400, dBn, LT = 1000–1400, dBe, LT = 0600–1000, dBe, LT = 1400–1800,

gpi + MERRA 11.6 7.90 38.7 2.22 3.46

gpi only 9.61 0.36 1.32 0.08 0.72

MERRA only 5.20 8.29 39.6 2.19 2.04

45°–65°N 10°–30°N 2.5°S–2.5°N 10°–50°N 10°–50°N

T and zonal wavenumber s is represented by A cos ð2p=T Þ cos sk where k is magnetic longitude, which is equal to A=2  cos ½2p=T þ sk þ A=2  cos ½2p=T
sk; in other words, two oppositely-traveling waves with equal amplitudes, periods and zonal wavenumbers. This is a common feature in the gpi-only spectra across a range of periods and zonal wavenumbers, mostly in the form of wavenumber broadening, and which gives rise to standing zonal asymmetries in the gpi magnetic perturbations. In contrast to the gpi-only results, the MERRA-only spectra contain a number of non-S0 peaks. It is noteworthy that the MERRA-only magnetic perturbations in Figs. 3 and 4 do not show any zonal propagation (i.e., eastward or westward tilt) either, despite the fact that distinct spectral peaks corresponding to propagating waves exist in the corresponding spectra in Figs. 5 and 6. Similar to the

gpi-only spectra, some of the peaks do appear as sum and difference zonal wavenumber pairs at or near the same period (i.e., near 6 days in Figs. 5(e), 6(c) and (d)). In principle, these could also be associated with wavenumber broadening due to the geomagnetic field, and thus lead to standing wave-like behavior in dB. We now turn to our quest to ascertain the connection between the peaks in the MERRA-only spectra in Figs. 5 (d)–(f), 6(c) and (d), and those represented in the neutral dynamics. The single example presented in Fig. 7 suffices to reveal the difficulties that are involved. Fig. 7(a) duplicates the dBn spectrum from Fig. 5(e), which corresponds to LST = 1000–1400 between 10°–30°N magnetic latitude. Fig. 7(b) and (c) represent the zonal wavenumber vs. wave period spectra of the zonal wind at 97 km and 120 km altitude, respectively, at +20° geographic latitude, while Fig. 7

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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Fig. 5. Zonal wavenumber vs. period spectra corresponding to the Fig. 3 longitude-UT structures.

(e) is the corresponding spectrum for the meridional wind at 120 km and +20° geographic latitude. Fig. 7(d) and (f) illustrate the wind variations that correspond to the spectra in Fig. 7(c) and (e), respectively and are discussed a little later in this section. The 120 km altitude is chosen since it is representative of the maximum tidal-driven response, and it is between the altitudes of the peak Hall (rH ) and Pedersen (rP ) conductivities, roughly about 112 km and 125 km, respectively, in the TIE-GCM (note: rP ¼ rH at about 125 km). Also, the waves seen at 120 km are likely to possess relatively large vertical wavelengths and thus are more efficient generators of electric current and ground magnetic variations. The latitude of +20° is chosen since it is representative of those corresponding to the dBn in Fig. 7(a), which in

turn reflect the predominantly eastward-flowing R height-integrated currents ( Jdz) around noon that are characteristic of the Sq current system, just poleward of the equatorial electrojet: J k ¼
rH ½Et
UB þ rP ½Ek þ VB sin I 

ð2Þ

(e.g., Takeda, 1991) where k denotes longitude (positive east), t denotes the direction transverse to B (positive downward/equatorward), and U and V are the eastward and southward wind speeds. Expression (2) was derived assuming an aligned dipole configuration, i.e., magnetic and geographic longitudes coincide and the magnetic declination is neglected. Here the terms proportional to UB and VB sin I correspond to the wind-driven currents and Et and Ek correspond to the polarization field-driven referred to in

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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Fig. 6. Zonal wavenumber vs. period spectra corresponding to the Fig. 4 longitude-UT structures.

connection with (1). The reader is reminded that in the following we seek to establish the connection between DB at the ground and the wind dynamo forcing terms in (2), realizing that DB consists of an additional contribution from Et and Ek : Furthermore, we note that comparison between the spectrum in Fig. 7(a) and those in Fig. 7(c) and (e) is valid even though there is not exact geographical correspondence between them; the dBn are averaged over 10-30°N and we know that the wind spectra at 20°N geographic are representative of those over a similar latitude range, so comparison of their spectra is a valid means of informing us if they share the same periodicities. As revealed in Paper I, there are some important differences between the characteristics and origins of MERRAforced TIE-GCM PW-period wind spectra at 97 km and 120 km. The spectrum at 97 km in Fig. 7(b) contains spectral peaks at [wave periods, zonal wavenumbers] near [5– 7d, s = +1], [8–10d, s = +1], [12–16d, s = +1], [4–5d, s = +2, +3], [3–5d, s =
1]. (See also spectrum at other latitudes in the Supplementary Information accompanying Paper I). Of these the s = +1 waves can be identified as the Q6DW, Q10DW, and Q16DW normal modes discussed in the Introduction. The [4–6d, s = +2] wave is consistent with a NM as well (Salby, 1981), but has not been discussed in connection with prior data analyses or model results to date. The [3–5d, s =
1] peaks correspond to

UFKWs. The 12–20 days S0 oscillations could arise from interactions between the Q16DW and a SPW1 (Pancheva et al., 2007, 2009). Concerning the Q6DW and Q10DW seen in both Fig. 7 (b) and (c), it is shown in Paper I (their Fig. 7) that at 110 km (near the maximum of rH ) the signatures of these waves arise from direct vertical PW propagation, whereas above about 115 km (which encompasses the maximum of rP ) the signatures of the Q6DW and Q10DW primarily arise as a result of tidal forcing alone. That is, the Q6DW and Q9DW above 115 km are the result of PW-modulated tides, and these authors proposed a two-stage nonlinear interaction to explain this result. In addition, the presence of a broadband (6–20 day) S0 oscillation at 120 km (Fig. 7 (c)) is due to the deposition of zonal-mean momentum by the dissipating tidal spectrum. Some remnants of the [4– 5d, s = +2, +3] and [3–5d, s = –1] at 97 km (Fig. 7(b)) still appear at 120 km (Fig. 7(c)), while signatures of new waves located near [6d, s =
2], [10
12d, s =
3], [10–14d, s = +2] have emerged which we have confirmed are not consistent with the two secondary waves that would arise from nonlinear interaction between two primary waves according to the theory of Teitelbaum and Vial (1991). One of these secondary waves would possess the sum of the frequencies and zonal wavenumbers of the interacting primary waves; the other would possess their differences.

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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J.M. Forbes et al. / Advances in Space Research xxx (2019) xxx–xxx

Fig. 7. (a) Spectrum of dBn, LT = 1000–1400, 10°–30°N, duplicated from Fig. 5(e). (b) Spectrum of zonal wind, U, +20° latitude, 97 km. (c) Spectrum of U, +20° latitude, 120 km. (d) longitude-UT values of U corresponding to spectrum in (c). (e) Spectrum of meridional wind, V, +20° latitude, 120 km. (f) longitude-UT values of V corresponding to spectrum in (e).

Further speculation about their origins is beyond the scope of the present work, which is to ascertain the level of compatibility between the wind field spectrum and dBn spectrum in Fig. 7(a). Comparing now the zonal wind peaks in Fig. 7(c) with the dBn peaks in Fig. 7(a), we see that (i) the Q6DW is prominent in both spectra with some extension from s = +1 to s = +2; (ii) [10–14d, s = +2] and broadband S0 signatures appear in both spectra; and (iii) the Q9DW, [4–5d, s = +2, +3] and [10–12d, s =
3] are missing in Fig. 7(a). There is also a lot of activity around [4–9d, s =
1,
2] in Fig. 7(a) that is missing in the Fig. 7(c) spectrum. Referring to expression (2), the commonality of features between the spectra in Fig. 7(a) and (c) is interpreted as reflecting the contributions of Hall currents. Expression (2) also suggests that the meridional wind spectrum, shown in Fig. 7(e), be examined in light of these results. Fig. 7(e) shows the following peaks in common with the zonal wind spectrum: Q6DW, [10–14d, s = +2], Q10DW, [4–5d, s = +2, +3] and [10–12d, s = -3]; but only the first two of these are reflected albeit approximately in the dBn spectrum of Fig. 7(a). The spectrum of 7(e) shows some activity around [4–9d, s = –1,
2], that in combination with contributions around [4–9d, s = –1,
2] from the zonal winds reflected in Fig. 7(c), can in principle fill in the amplitudes in this part of the spectrum in Fig. 7 (a). The V-spectrum in Fig. 7(e), apart from the Q6DW, also possesses several signatures at periods <8 days that

are symmetric in zonal wavenumber about s = 0. As noted earlier in connection with gpi-only results, these correspond to standing oscillations in the longitude-UT structures as shown in Fig. 7(f). However, for the most part these spectral features do not appear in Fig. 7(a). In comparison with the 100 m/s range of values depicted in the longitude-UT plot for U in Fig. 7(d), the range of values in Fig. 7(f) is only 50 m/s. The additional sin I factor of order 0.35 suggests that the meridional winds could be less than 20% as effective as zonal winds in producing dBn perturbations on the ground at magnetic latitudes 10°–30°, possibly explaining in part the absence of these Vspectrum features in the dBn spectrum. In addition, the dBn spectrum is also determined by the electric field, which is determined in part by winds between ± 30° magnetic latitude (Maute et al., 2012), but also by winds at higher latitudes. The combination of these factors likely explains the differences in spectral features noted above between Fig. 7 (a) and (f). The longitude-UT structures and spectra of noontime height-integrated rH and rP were also examined in connection with the interpretation of results in Fig. 7. Percent residuals from October-mean values at each longitude were used to create longitude-UT plots and spectra similar to those analyzed above for dBn and winds. The residuals revealed typical ranges of order ±4%, which when multiplied by a mean value of dBn of order 10 nT across LST = 1000–1400 and 10°–30° magnetic latitude, yielded

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

J.M. Forbes et al. / Advances in Space Research xxx (2019) xxx–xxx

a range of order 0.4 nT, which contributes negligibly to the
8 nT to +20 nT dBn variability in Fig. 3(e). In other words, longitude and day-to-day variability at PW periods in conductivity contribute negligibly to the dB variability as compared with the contributions from winds. Similar conclusions regarding the secondary importance of longitude variability of conductivities were made by Maute et al. (2012). The example explored in Fig. 7 is typical of other comparisons between dB and wind spectra that were examined. That is, similar levels of correspondence (or lack thereof) as above exist between the dB spectra in Fig. 5(d)–(f) and (c)– (d), and those of the corresponding neutral winds (not shown). While the major peaks such as Q6DW, Q10DW, Q16DW and UFKW all occur in subsets of the dB and neutral wind spectra, their relative prominence is not always consistent in the dB spectra as compared with the wind spectra at a given latitude. This should perhaps not be surprising, since the dB variations underlying the dB spectra are induced by a combination of wind-driven currents and electrostatic field-driven currents (cf. Expression (1)), which may possess different spatial and temporal distributions. The wind-driven currents in turn reflect the influence of height-integrated conductivity-weighted winds, and thus depend on the vertical amplitude and phase structures of zonal and meridional winds and how they correlate with the vertical profiles of Hall and Pedersen conductivities; these factors also determine the relative efficiency of different wave components to drive currents resulting in electrostatic fields. Spectral features in dB that do not exist in the wind spectra can arise from zonal and interhemispheric asymmetries in the magnetic field. In addition, there are spectral peaks whose origins remain to be identified in both the dB and wind spectra. It is conjectured that these arise from the fact that much of the PW-period wind variability arises in connection with PW-modulated tides, perhaps involving second-order nonlinear interactions that complicate the picture. More theoretical and modeling work is needed to understand this facet of the dynamics. In summary, unequivocal connections between peaks in the dBe and dBn spectra and those of the neutral winds do not universally occur within the simulations, and similar results are expected to be a characteristic of observational data. 4. Summary and conclusions In this study we present magnetic eastward (dBe) and magnetic northward (dBn) magnetic perturbations at the ground from MERRA-forced TIME-GCM numerical experiments designed to separate contributions of lower-atmosphere origin from those arising from solar-magnetospheric variability. The emphasis is on longitude-UT variability between 0°–65°N magnetic latitude at PW periods (2–20 days) during the October 2009, simulation interval, where the level of geomagnetic activity is measured according to the Kp and Ap indices plotted in

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Fig. 1. The reader is reminded that the main source of lower-atmosphere day-to-day variability in these simulations is associated with modulation of the full spectrum of vertically-propagating solar tides by multiple PWs. In keeping with monthly-mean climatological patterns of dBe and dBn, we focus on daytime longitude-UT variability of mean values of dBe and dBn in the following latitude-LT sectors: for dBn, LT = 1000–1400 between 45°–65°N (NoonHi), 10°–30°N (NoonLo), and 2.5°S–2.5° N (NoonEq); for dBe, 10°–50°N at LT = 0600–1000 (Morn) and LT = 1400–1800 (Aft). As articulated in the Introduction, the aim is to answer the following questions regarding PW-period oscillations in daytime DB: What do their longitude-UT structures look like? Do PW-period oscillations in DB due to loweratmosphere sources include zonally-symmetric (S0) oscillations, and if so, are they large or small compared with those of solar-magnetospheric origin? To what extent do oscillations in DB due to lower-atmosphere forcing reflect the characteristics of the driving dynamics? What role do conductivities play in producing DB longitude-UT structures? Are daytime DB variations of solar-magnetospheric origin purely zonally-symmetric in magnetic coordinates, or might they also occur at s–0 and thus potentially be interpreted in data as variations of PW origin? Our conclusions, which are restricted to latitudes <65° magnetic and the level of geomagnetic activity depicted in Fig. 1, are as follows PW-period magnetic perturbations at the ground are dominated by variability originating in the lower atmosphere except for NoonHi (LT = 1000–1400, 45°–65°N) where variability caused by the lower-atmosphere exceeds that caused by solar-magnetospheric variability by only 50%. For the case of only lower atmospheric forcing, about 25% of the NoonHi variability in dBn is zonallysymmetric, which is more than 50% of the s = 0 variability attributable to solar-magnetospheric forcing. The longitude-UT variability of conductivities at PW periods due to lower-atmosphere sources plays a negligible role compared to winds in producing longitude-UT variability of DB at PW periods. The height dependencies of Hall and Pedersen conductivities and their anisotropies do, however, play an important role in moderating the influences of the winds. Zonal wavenumber vs. period spectra of dBe and dBn for the simulation considering only lower atmosphere forcing usually contain expected PW peaks from neutral dynamics. However, in some cases periodicities in the neutral winds are missing from the DB spectra, and vice-versa; the correspondence between these spectra is not robust. This is attributed in part to the fact that the wind spectra in the zonal and meridional directions are not the same, and from one location to another convolve differently with Hall and Pedersen conductivities to generate wind-driven currents and electric fields.

Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045

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Longitudinal variations in geomagnetic field strength and orientation may also play a role in producing peaks in DB spectra that do not exist in the wind spectra. In some cases, the origins of periodicities in the neutral dynamics remain unexplained. This is in part due to the fact the PW periodicities in the neutral dynamics arise from modulation of the tidal spectrum, spanning a range of zonal wavenumbers, by multiple PW. The wave-wave interactions that occur have not been fully delineated or quantified, and multiple stages of interactions may be involved. Daytime DB variability due to solar-magnetospheric forcing is in general not purely zonally-symmetric in magnetic coordinates, and contains longitudinal wave1 and wave-2 standing wave structures that appear to arise from broadening of the zonal wavenumber spectrum, perhaps due to the spatial variations of the main magnetic field. Spatial variations in electric field and conductivity may also contribute. The first two items listed above raise the question as to whether magnetic variability driven by the lower atmosphere has the potential to introduce some level of contamination to the derivation of indices such as ap, Kp, Ap that are used as measures of activity associated with solarmagnetosphere-ionosphere interactions. This same basic question was raised in connection with gravity waves by Hines (1965). After removal of the regular Sq and L daily variations, derivation of ap, Kp and Ap depend on the maximum ranges of DB within 3-hour intervals at 11–13 ground stations between 45°–65° magnetic latitude that are spread out over longitude (see, e.g., Takahashi et al., 2001; Thomsen, 2004). These ranges are susceptible to additional contributions from lower-atmosphere forcing, which are potentially quite large (e.g., Larsen, 2002; Nystrom et al., 2018). However, the present results have not addressed sub-diurnal variability, which is also expected to be quite large, since the PW-period variability described here is associated with day-to-day changes in 24hour, 12-hour and 8-hour period tides, and secondary oscillations that are produced by tide-tide and PW-tide interactions (e.g., Nystrom et al., 2018) that add to the spatial-temporal complexity of the neutral wave spectrum. In addition to the day-to-day variability in DB addressed here, the effects of these sub-diurnal oscillations on DB variability over 1–3 hourly time scales and their implications for derivation of geomagnetic indices warrant further investigation.

Acknowledgements J. Forbes acknowledges support from NSF Award AGS-1552027 to conduct this research. X. Zhang was supported by NASA Grant NNX16AG64G to the University of Colorado and A. Maute was supported through sub-award 1554133 from this NASA Grant to the High

Altitude Observatory, National Center for Atmospheric Research, and through NASA Grant NNX16AK88G. TIME-GCM and TIE-GCM results are archived on the National Center for Atmospheric Research High Performance Storage System and are available on request. We would like to acknowledge high-performance computing support from Cheyenne (doi:10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. The National Center for Atmospheric Research is funded by the National Science Foundation. The Authors also thank A.D. Richmond for valuable comments on an earlier version of the manuscript.

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Please cite this article as: J. M. Forbes, A. Maute and X. Zhang, The nature and origins of the day-to-day variability in Earth’s surface magnetic field, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.05.045