oval (Neubert & Christiansen, 2003; Rother et al., 2007; McGranaghan et al., 2017). Electric field, Poynting flux, and density irregularities follow a similar spatial distribution (Cousins & Shepherd, 2012; Prikryl et al., 2015; Hatch et al., 2018), while the distribution of the electric field variability is highly dependent on IMF conditions, and the energy flux in the nightside can be larger on the nightside, likely due to substorms. Also, the probability distribution of mesoscale/small‐scale structures does not have a discrete peak but has a broad spectrum that varies in regions (Golovchanskaya, 2008; Lühr et al., 2015). Consideration of mesoscale/small‐scale electric fields and their variability can substantially increase the Joule heating (Codrescu et al., 1995; Deng et al., 2009; Yigit & Ridley, 2011; Zhu et al., 2018). These studies show that statistical parameterization is a possible pathway for specifying distribution of mesoscale/small‐scale quantities that are difficult to resolve over a large spatial scale at each instance. However, currently parameterizations have been conducted only during limited geomagnetic and geographic conditions, and statistical averaging tends to underestimate actual amplitude of multiscale parameters due to smoothing over their localized and transient structures. As studies above have shown, mesoscale/small‐scale features (such as flows) are not necessarily random fluctuations around a large‐scale mean, but are often oriented in a certain direction, and thus do not average out but have net effects on the large‐scale. Moreover, coherent structures and physical connections among the quantities are missed by statistical averaging, because information of size, orientation, and duration is lost, and individual parameters are processed without considering behavior of other parameters. Although parameterization is a useful and promising approach, those cautions should be noted when using such parameterization for model input, and a challenge to data analysis is to create an approach of comprehensive parameterization without underestimating mesoscale and small‐scale features.
Figure 3.5 Representative statistical distributions of mesoscale/small‐scale quantities mapped to the high‐latitude ionosphere: (a) Electric field from SuperDARN; (b) FAC (Swarm); (c) GPS phase scintillation as a proxy of small‐scale density irregularities; (d,e) electron energy flux and Poynting flux by the FAST satellite; and (f) Joule heating (GITM simulation). The Sun is to the top of each plot
(a: Cousins & Shepherd, 2012. Reproduced with permission of John Wiley & Sons; b: McGranaghan et al., 2017. Licensed under CC‐BY 3.0; c: Prikryl et al., 2015. Licensed under CC‐BY 3.0; d,e: Hatch et al. (2018). Reproduced with permission of Elsevier; f: Yigit & Ridley, 2011. Reproduced with permission of Elsevier).
3.6 SUMMARY
This chapter has provided a review of multiscale processes in the high‐latitude ionosphere. A large amount of existing data, high‐resolution observations, and modeling capabilities have revealed key properties and their importance in understanding large‐scale processes. As summarized in Figure 3.2, such processes include cusp, PMAFs, polar cap patches/TOIs, auroral arcs, PBIs, streamers, substorm, surges, diffuse aurora, and related flow channels, field‐aligned currents (FACs), and precipitation/conductance. Those can be comparable or larger in magnitude than the large‐scale background, and thus substantially affect local processes. Moreover, mesoscale/small‐scale processes can propagate over long distances and affect processes in adjacent regions. Possible influence of small‐scale processes on global processes has also been indicated. Such feedback studies are still limited and further studies are desired to understand multiscale processes. Particularly, more systematic studies of mesoscale/small‐scale features are necessary to understand how multiscale interaction processes occur.
This chapter also presented an approach to specify instantaneous distribution of mesoscale precipitation over a regional scale. We found that mesoscale precipitation is dynamic and has a substantial impact (~25%–50%) compared with the total precipitation energy input. It is potentially a useful method to provide event‐specific high‐resolution information of precipitation without statistical averaging. On the other hand, measurement capabilities are limited for resolving convection, currents, and density over a similar scale. It is even more challenging to identify distributions of small‐scale parameters. Further advances are necessary to quantify instantaneous distributions of mesoscale/small‐scale features.
From a modeling standpoint, inclusion of mesoscale/small‐scale features would be critically important for improving understanding of local and global processes. However, it is currently not feasible to resolve all scales globally. Statistical parameterization and mesh refinement techniques are necessary and are fast developing. It is also necessary to treat physics in global models such as inertial and time‐dependent momentum effects, kinetic effects, and inductive processes; however, care should be taken when statistical parameterization is used because of their limitations.
ACKNOWLEDGMENTS
This work was supported by NASA grant 80NSSC18K0657, 80NSSC20K0604 and 80NSSC20K0725, NSF grant AGS-1401822 and AGS-1907698, and AFOSR grant FA9559‐16‐1‐0364. The THEMIS mission is supported by NASA contract NAS5-02099 and Canadian Space Agency. We thank support from the CEDAR workshop “Grand Challenge: Multi scale I‐T system dynamics” and ISSI workshops “Multiple-Instrument Observations and Simulations of the Dynamical Processes Associated With Polar Cap Patches/Aurora and Their Associated Scintillations” and “Multi-Scale Magnetosphere‐Ionosphere‐Thermosphere Interaction”.
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