We now present and discuss results of DINAMO simulations in two distinct applications.
First, we use DINAMO to evaluate the ability of current climatological drivers (HWM14, IRI-2016, and NRLMSISE-00) to produce realistic ionospheric electrodynamics for different seasons and solar flux conditions (Sect. 3.1). We assess DINAMO results by comparing modeled zonal and vertical equatorial \({\mathbf {E}}\times {\mathbf {B}}\) drifts with observations. Next, we use DINAMO to quantify the contribution of the integrated vertical current (\(J_L\)) to the morphology of the drifts (Sect. 3.1.1).
Focus is given to results for the Peruvian longitude sector (\(\sim 284^\circ\)E), which allows a comparison of model drift results with mean plasma drifts derived from long-term Jicamarca ISR observations.
3.1 On DINAMO equatorial \(\mathbf{E }\times \mathbf{B }\) plasma drifts
Figures 2 and 3 show DINAMO results for the equatorial zonal and vertical \(\mathbf{E }\times \mathbf{B }\) plasma drifts, respectively. The DINAMO model results are represented by the blue curves. They show the behavior of the zonal and vertical plasma drifts as a function of local time for different seasons (rows) and solar flux conditions (columns) for the Peruvian sector at an altitude of 360 km. The top, middle, and bottom rows correspond to December solstice, equinox, and June solstice conditions, respectively. More specifically, DINAMO model results are for day-of-year 21 (December solstice), 172 (June solstice) and 264 (equinox). The left column in each Figure corresponds to low solar flux (LSF) conditions, and the right column corresponds to high solar flux (HSF) conditions. The solar and geomagnetic input conditions of the climatological models that were input for the DINAMO simulations were chosen to match the average conditions of Jicamarca ISR observations presented by Shidler et al. (2019) and available to this study. DINAMO simulations use climatological drivers set for \(F_{10.7}\) of 80 SFU and 150 SFU representing LSF and HSF conditions, respectively. During June solstice, however, we use 130 SFU to represent the HSF conditions. Finally, these simulations results are for geomagnetically quiet conditions with the climatological drivers set to Kp = 2 (Ap = 7).
For comparison purposes, Figs. 2 and 3 also show Jicamarca observations which are represented by the green curves. These observations were derived and first presented by Shidler et al. (2019). Shidler et al. (2019) estimated the mean behavior of geomagnetically quiet vertical and zonal plasma drifts as a function of local time and altitude (range between 200 and 600 km) from observations made by the Jicamarca ISR between 1986 and 2017. The mean drifts were derived for three seasonal bins: December solstice (Jan, Feb, Nov, Dec), equinox (Mar, Apr, Sep, Oct), and June solstice (May, Jun, Jul, Aug). The drifts were further split into a low solar flux bin with an average \(F_{10.7}\) of 80 SFU, for all seasons, and a high solar flux bin with an average \(F_{10.7}\) of 150 SFU for December solstice and equinox and an average of 130 SFU for June solstice. The difference in mean solar flux for June solstice was caused by lack of data. The average Kp index for the observations was approximately 2. Missing data points in the post-sunset sector are caused by coherent echoes from ESF events contaminating measurements of the background plasma drifts. Past studies have shown the occurrence rates for these events are directly proportional to the magnitude of the PRE (e.g., Fejer et al. 1999; Huang and Hairston 2015; Smith et al. 2015) which explains more prominent gaps in December and equinox during high solar flux periods. Additionally, missing values in the early morning are the result of low quality measurements (reduced signal-to-noise ratio) during that time due to decreased plasma densities.
Finally, for completeness, the red curves (in Fig. 3 only) represent the vertical drifts predicted by the Scherliess and Fejer (1999) climatological model (SF99). SF99 is a global model of the equatorial vertical drifts derived from in situ measurements made by the Atmospheric Explorer E (AE-E) satellite with additional measurements in the Peruvian sector made by the Jicamarca ISR between 1968 and 1992 (Scherliess and Fejer 1999).
A comparison of model results and measurements in Figs. 2 and 3 serve to show that DINAMO is capable of producing realistic estimates of the zonal and vertical plasma drifts. That is, it shows most of the features expected for the vertical and zonal drifts based on previous studies and observations. This is an indication of the fair representation of the ionospheric electrodynamics by the underlying driving conditions provided by the input climatological models (IRI2016, HWM14 and NRLMSISE-00).
Here, we must mention the good agreement of our results with those of the recent work of Eccles and Valladares (2021). They coincidentally also evaluated the impact of climatological models on producing realistic equatorial plasma drifts. However, they used the Electric Field Model–EFM (Eccles 2004) and focused on proper tide specification for a single solar flux condition (\(F_{10.7}\) = 110 SFU). More importantly, perhaps, is that their results reinforce the correctness of DINAMO and provide independent evidence of some of our findings. To avoid repetition, we highlight some aspects that were not addressed by Eccles and Valladares (2021).
3.1.1 On DINAMO F-region zonal drifts
Figure 2 shows that DINAMO, when driven by current climatological models (HWM14, IRI-2016 and NRLMSISE-00), is capable of reproducing the expected diurnal variability of the zonal drifts. More specifically, it is capable of producing the expected weak westward drifts during the day (e.g., Fejer et al. 2005, 1991), a rapid eastward acceleration in the post-sunset sector, and strong eastward plasma drifts at night. Therefore, current climatological drivers are capable of reproducing the main features of the equatorial zonal drifts including an eastward super-rotation of the ionosphere which is in good agreement with previous experimental studies (Pacheco et al. 2011).
There are, however, noticeable differences between model and observations. In all seasons and for all solar flux conditions, the reversal time for the modeled drifts occur at an earlier time in the morning, and at a later time in the evening compared to the observations. Additionally, the nighttime eastward modeled drifts tend to be weaker than the observations. Eccles and Valladares (2021) also found weaker model zonal drifts compared to observations. Here, we point out that our results indicate that the discrepancy between nighttime modeled and observed drifts is more accentuated during HSF conditions. Given the strong correlation between the motion of the plasma and neutrals during this time (e.g., Biondi et al. 1988; Chapagain et al. 2013; Fejer 1993; Fejer et al. 1985; Navarro and Fejer 2020), this behavior most likely stems from the specification of the F-region thermospheric neutral winds provided by HWM14. In a recent study, Navarro and Fejer (2019) compared quiet time values of the nighttime neutral winds predicted by HWM14 with observed neutral winds in the Peruvian sector during moderate solar flux conditions. They found, for example, that HWM14 significantly underestimates the eastward winds in the pre-midnight sector during equinox. Furthermore, HMW14 better represents moderate solar flux conditions. It does not include a solar flux dependency, and the observational database used in the derivation of HWM14 corresponds to measurements made during moderate solar activity with an average \(F_{10.7}\) of 107 SFU (Drob et al. 2015).
3.1.2 On DINAMO F-region vertical drifts
We now turn our attention to the vertical drifts output by DINAMO which are illustrated by the results shown in Fig. 3.
Similar to our findings for the zonal drifts, the results indicate that the climatological drivers can produce most of the features expected for equatorial vertical drifts based on previous theoretical and experimental studies. We start by pointing out that the drivers are capable of reproducing the PRE during equinox and December solstice. The model is also capable of reproducing the increase in the PRE magnitude with solar flux which has been observed in previous studies (e.g., Fejer et al. 2008, 1991). Additionally, the magnitude of the PRE modeled by DINAMO is in fair agreement with the observations (within around 10 m/s). More noticeable is the excellent agreement of the PRE peak times and of the times when the drifts revert from upward to downward.
Figure 3 also shows obvious differences between modeled and observed vertical drifts. For instance, the climatological drivers tend to produce daytime drifts that depart from the observations. More specifically, the results show weak peak values and downward vertical drifts in the afternoon. Additionally, the results show that these discrepancies are more evident during LSF (all seasons) and December solstice of HSF conditions. Eccles and Valladares (2021) also found that the tidal representation in HWM does not produce daytime drifts that match the predictions of the SF99 model. For instance, close inspection of their Fig. 4c shows the afternoon downward drifts for \(F_{10.7}\) = 110 SFU conditions as well.
Here, we must point out that our modeled daytime drifts resemble those seen by C/NOFS during the extreme solar flux conditions of 2008/2009. For instance, Stoneback et al. (2011) examined median values of the meridional plasma drifts using observations from the C/NOFS satellite and found downward afternoon drifts in all seasons for certain longitude sectors. Stoneback et al. (2011) proposed the increased role of the semi-diurnal tide in the E-region to explain downward afternoon drifts.
Additionally, perhaps the most striking difference between modeled and observed vertical drifts occur at night during LSF conditions, particularly in June solstice. Figure 3 shows that the climatological models driving DINAMO produce nighttime drifts that depart significantly from the observations during LSF conditions. In particular, large upward drifts are seen in June solstice when observations show downward drifts. Again, Fig. 4c in Eccles and Valladares (2021) also shows these abnormal drifts developing in May–July.
The section below presents results related to the sources of the unusual behavior in the model F-region drifts.
3.1.3 Abnormal nighttime F-region drifts
In order to identify the origin of the abnormal upward drifts described above, we follow the approach of previous studies (e.g., Eccles 2004; Maute et al. 2012) and isolate different source terms to evaluate their relative contribution to the overall vertical drifts. Figure 4 shows June solstice LSF vertical drifts decomposed into contributions from the gravitational dynamo (green curve), from the E-region neutral wind dynamo (blue curve), and from the F-region neutral wind dynamo (red curve). The total vertical drifts (all source terms included) is shown as the black curve. The contribution from the gravitational dynamo to the vertical drifts is found by setting the neutral winds to zero everywhere and solving Eq. 9. For the contribution from the E-region dynamo, gravity driven currents and neutral winds in the F-region are set to zero. Finally, the contribution from the F-region dynamo is found by setting gravity driven currents and neutral winds in the E-region to zero. Note that the E-region and F-region neutral wind dynamos are determined by decomposing the integrals in Eqs. 18d–18g (Appendix A) into a sum of integrals. Field line points below 200 km contribute to the E-region dynamo term, and points above 200 km contribute to the F-region dynamo. For instance, when determining the contribution of the F-region dynamo, the winds below 200 km and respective integrals are set to zero.
We start by pointing out that Fig. 4 shows that the gravitational term in DINAMO produces the same effect shown by the Eccles (2004) model. That is, the gravitational dynamo modifies the vertical drifts by 5 and 15 m/s near the solar terminators. During these times, the conductivity is rapidly changing, and zonal electric fields near the terminators are set up to keep currents divergence-free.
More importantly, Fig. 4 shows that the E-region neutral wind dynamo, as described by the input climatological models, is responsible for both the downward drifts in the late afternoon and upward drifts at night.
Finally, we point out that HWM14 does not include a solar flux dependency causing the neutral wind descriptions to be the same for both LSF and HSF conditions. Therefore, the reduction in downward drifts in the afternoon and upward drifts in the post-midnight sector from LSF to HSF conditions indicates that the E-region winds do play a role in these features, but their contribution is heavily modulated by the conductivities.
3.1.4 Height variation of F-region drifts
So far we focused on model results for a single height near the F-region peak (\(\sim\) 360 km). It is known, however, that vertical and zonal drifts can vary with height, particularly during evening and nighttime hours (Fejer et al. 2014; Hui and Fejer 2015; Kudeki and Bhattacharyya 1999; Lee et al. 2015; Nayar and Sreehari 2004; Richmond et al. 2015; Rodrigues et al. 2012; Shidler and Rodrigues 2019).
Previous results showed that the climatological drivers can produce the overall behavior of the observed drifts. We now examine the ability of the climatological drivers to produce realistic variations of the F-region drifts with height. Focus is given to equinox HSF model simulations as the previous results show that the model drifts at main F-region heights resemble the observations and, therefore, suggest better accuracy of the input drivers. During equinox, height variations in the zonal and vertical drifts are expected to develop at least near the sunset terminator (Shidler et al. 2019).
Figure 5 shows the local time versus height variability for the vertical (top) and zonal (bottom) plasma drifts produced by DINAMO for equinox HSF conditions. It serves to show that the climatological drivers can indeed produce the altitude variability associated with equatorial plasma drifts.
For example, DINAMO results for the zonal drifts (bottom panel) show the vertical shear observed around the time of the PRE that is associated with the evening plasma vortex (Eccles et al. 1999; Haerendel et al. 1992; Richmond et al. 2015; Rodrigues et al. 2012). Daytime westward drifts also show some height variability between 0900 and 1500 LT. This is in agreement with the analysis of Hui and Fejer (2015). They showed that daytime westward drifts observed at Jicamarca, between March and October, increase with height for altitudes below 300 km.
DINAMO results for the vertical drifts (top panel of Fig. 5) also show the expected weak height variation during most times. Height gradients, nevertheless, are positive in the morning and negative starting in the afternoon. Significant height gradients in the vertical drifts are only observed around 0400 LT and around the time of the PRE. This behavior is consistent with the curl-free condition for ionospheric electric fields and with previous observational studies that relate noticeable height variations of the equatorial vertical \({\mathbf {E}}\times {\mathbf {B}}\) drifts to the strong longitudinal variations in the zonal drifts occurring near dawn and dusk (e.g., Murphy and Heelis 1986; Pingree and Fejer 1987; Shidler and Rodrigues 2019; Shidler et al. 2019). More specifically, at the magnetic equator, \(\nabla \times {\mathbf {E}} = 0\) leads to \(\frac{2 W_i}{r} -\frac{\partial W_i}{\partial r} = \frac{1}{r} \frac{\partial U_i}{\partial \varphi }\), where \(W_i\) and \(U_i\) are the components of the ionospheric plasma drifts in the vertical (r) and zonal (\(\varphi\)) directions, respectively (Murphy and Heelis 1986).
3.2 On the vertical integrated current (\(J_L\))
We now present results related to our analysis of the integrated vertical current (\(J_L\)). More specifically, we evaluate the \(J_L\) contribution to the morphology of the zonal drifts. Again, we focus our analysis on DINAMO simulations for equinox HSF conditions for which the drivers seem to produce drifts that best match observations.
The expression for the integrated vertical current (Eq. 5) can be rearranged to solve for the zonal plasma drifts (\(U_i\)) at the magnetic equator:
$$\begin{aligned} U_i = U_{\varphi }^P + \frac{\Sigma _H}{\Sigma _P} U_L^H - \frac{\Sigma _H}{\Sigma _P} W_i - \frac{J_L}{B \Sigma _P} - \frac{g_0\Sigma _{Pg}}{B\Sigma _P}, \end{aligned}$$
(17)
where \(W_i\) is vertical plasma drift. Equation 17 has been used in the past (Haerendel et al. 1992) to describe the morphology of the zonal plasma drifts in terms of two-dimensional field line integrated quantities of the ionosphere.
A simplified version of Eq. 17 that only takes into consideration the \(U_{\varphi }^P\) and \(-\frac{\Sigma _H}{\Sigma _P}W_i\) terms has been commonly used to interpret observations of the zonal drifts (e.g., Chau and Woodman 2004; Hui and Fejer 2015; Richmond et al. 2015; Rodrigues et al. 2012). More recently, Shidler and Rodrigues (2021) analyzed the ability of Eq. 17 to reproduce observed zonal plasma drifts made at Jicamarca given field line integrated quantities specified by climatological models aided by mean vertical drifts derived from Jicamarca ISR observations. However, like in previous studies, the fourth term (\(-\frac{J_L}{B\Sigma _P}\)), however, had to be neglected since \(J_L\) could not be estimated from the models alone.
Haerendel et al. (1992) and Eccles et al. (2015) examined the impact of the \(-\frac{J_L}{B\Sigma _P}\) term, with emphasis on the period around 1900 LT when a shear in the zonal plasma drifts is commonly observed (e.g., Kudeki and Bhattacharyya 1999; Lee et al. 2015; Shidler et al. 2019). Additionally, it was simply assumed that \(J_L\) was positive and roughly constant with height having a magnitude of only a few mA/m. Therefore, the altitude variability was controlled by \(\Sigma _P\) which is significantly reduced in the bottomside and, therefore, the fourth term predicted strong westward drifts in the bottomside and weak drifts at higher altitudes. This behavior acts to enhance the vertical shear in the zonal plasma drifts.
DINAMO simulations now allow us to better estimate the contribution of the \(-\frac{J_L}{B\Sigma _P}\) term to the morphology F-region zonal drifts. Figure 6 shows the contributions from each term on the right-hand side of Eq. 17 to the zonal drifts as a function of local time and height. The results are for the Jicamarca longitude sector. While the total zonal drifts are shown in panel (a), the contribution from the five terms are shown in panels (b–f).
The magnitude and behavior of the first three terms panels (b–d) are in agreement with the results of Shidler and Rodrigues (2021). That is the Pedersen-weighted magnetic zonal winds (\(U_{\varphi }^P\)) in panel (b) are primarily responsible for most of the observed features of the zonal plasma drifts including the diurnal variability and the vertical shear commonly seen in the post-sunset sector. Shidler and Rodrigues (2021) also found that the contribution from the Hall-weighted meridional winds (\(U_L^H\)) in panel (c) was negligible throughout the day.
The \(-\frac{\Sigma _H}{\Sigma _P}W_i\) term (panel d) during daytime (when the Hall-to-Pedersen ratio is close to 1) makes a contribution to the zonal drifts with absolute values that are similar to those of the vertical drifts (\(W_i\)).
Perhaps more importantly, this term also makes significant contributions (\(\sim\)20 m/s) to the zonal drifts in the bottomside during nighttime acting as to enhance the shear around the time of the PRE (\(\sim\)1900 LT). Here, we must point out that recent studies linked the development of ESF to the Collisional Shear (CS) instability and to the strength of the vertical shear in the zonal drifts (Aveiro and Hysell 2010; Hysell and Kudeki 2004; Kudeki et al. 2007) The results, however, indicate that the strength of the shear is dictated by the magnitude of the PRE, which is more traditionally recognized as the most important driver of the Generalized Rayleigh–Taylor (GRT) instability leading to ESF.
The gravitational term is shown in panel (f), and has negligible contribution to the overall plasma drifts but is included here for completeness.
Finally, the contribution from the \(-\frac{J_L}{B\Sigma _P}\) term is shown in panel (e). Throughout most of the day, the contribution from this term is negligible. There are, however, a couple of times where this term predicts drifts with magnitudes greater than \(\sim\)5 m/s and that are a significant portion of the total zonal drifts. For example, between 0700 and 1000 LT at altitudes above about 500 km. Additionally, as suggested by Haerendel et al. (1992), the \(-\frac{J_L}{B\Sigma _P}\) term contributes with relatively strong (up to \(\sim\)16 m/s) westward plasma drifts between 1900 and 2100 LT at bottomside F-region heights (below \(\sim\)300 km) and weaker drifts (\(\sim\)10 m/s) at higher altitudes.
Figure 7 provides a closer look at the behavior and impact of \(J_L\) on zonal drifts. It shows (apex) height profiles of various parameters for 1900 LT (top) and 2000 LT (bottom). Panels (a1) and (a2) show altitude profiles of the modeled zonal drifts and three of the terms (right hand side of equation 17) contributing to them. The \(\frac{\Sigma _H}{\Sigma _P}U_L^H\) and \(-\frac{g_0\Sigma _{Pg}}{B\Sigma _P}\) terms are not shown since they do not make noticeable contributions at these times. Panels (b1) and (b2) show the height profile of \(J_L\). Finally, panels (c1) and (c2) show height profiles of the field line integrated conductances.
At 1900 LT the vertical drifts are still positive (upward). See Fig. 5. At this time, the Pedersen conductance also increases significantly with height up to \(\sim\)400 km, while the Hall conductance decreases moderately with height as shown in panel (c1). Therefore, the \(-\frac{\Sigma _H}{\Sigma _P}W_i\) term contributes with westward drifts more significantly in the bottomside F-region as indicated in panel (a1). Around this time, \(J_L\) increases with height (panel b1) and \(-\frac{J_L}{B\Sigma _P}\) contributes westward drifts that are nearly constant with height. Therefore, the \(-\frac{J_L}{B\Sigma _P}\) term acts to reduce the eastward F-region plasma drifts that are driven by the wind dynamo term (\(U_{\varphi }^P\)). The \(-\frac{J_L}{B\Sigma _P}\) term also increases the altitude of the transition height between westward and eastward plasma drifts from 200 km to about 245 km. The result is a strong vertical shear in the zonal drifts around the PRE time that can be seen in panel (a) of Fig. 6.
At 2000 LT the behavior of \(J_L\) more closely resembles the situation assumed by Haerendel et al. (1992). That is, \(J_L\) is positive (upward) and is nearly constant with altitude with a magnitude of a few mA/m. The overall behavior of the conductances do not change much from that of 1900 LT. Therefore, the \(-\frac{J_L}{B\Sigma _P}\) term continues to drive westward drifts with larger magnitudes at bottomside heights. At 2000 LT, however, the vertical drifts are downward (see Fig. 5). This causes the \(-\frac{\Sigma _H}{\Sigma _P}W_i\) to drive eastward drifts and nearly cancel the westward drifts driven by \(-\frac{J_L}{B\Sigma _P}\). Therefore, during this time the zonal drifts are more completely controlled by \(U_{\varphi }^P\).