It is known that there exists a linear relationship between the maximum velocity of the prereversal enhancement (PRE) of the E × B drift and the strength of the equatorial ionization anomaly (EIA) crests at night. This can be a particularly useful relationship in the event that only one of the quantities is observed. But it is important to understand the drivers of the linear relationship in order to determine its range of validity. In this study, we use the SAMI2 model of the ionosphere together with measurements of vertical E × B drift velocity at Jicamarca to show that daytime drifts significantly affect the slope and linearity of the relationship. To validate the model, nighttime O I 135.6 nm radiances measured with the Tiny Ionospheric Photometer (TIP) aboard the Constellation Observing System for Meteorology, Ionosphere, and Climate (FORMOSAT-3/COSMIC) are used in coincidence with the E × B drift measurements at Jicamarca. From the observations, we derive a linear relationship between the crest-to-trough ratio of the EIA NmF2 and the PRE under solar minimum conditions. The model simulations demonstrate that the influence of daytime drifts on the nighttime ionosphere varies with longitude and solar cycle conditions; and therefore the linear relationship also varies with these parameters. In particular, we show that the late afternoon drifts at solar minimum have the effect of steepening the slope of the linear relationship. On the other hand, the extended effect of daytime drifts under solar maximum conditions, including contributions from midmorning hours, tends to weaken the relationship.
 A dominant feature of the tropical F region ionosphere is the Equatorial Ionization Anomaly (EIA), consisting of two regions of enhanced plasma density at ∼15° north and south of the magnetic dip equator. The EIA forms as a result of the upward E × B drift of plasma near the magnetic equator due to the eastward zonal electric field. This upward E × B drift, in combination with ambipolar diffusion along the geomagnetic field lines, transports ionization away from the magnetic equator toward higher latitudes. The plasma rises until pressure forces and gravity cause the plasma to descend along the field lines to tropical latitudes. At dusk, the interaction of the E and F region dynamos results in an enhancement of the eastward electric field before it turns westward at night, prompting the prereversal enhancement (PRE) of the upward E × B drift. As a result of the increased vertical drift caused by the PRE, the densities in the EIA are enhanced and can persist well into the evening. The density and latitudinal extent of the nighttime EIA is strongly associated with the vertical drift velocity during the day, at dusk, and in the evening hours.
 Observations and modeling studies have shown that there exists a linear relationship between the maximum velocity of the PRE and the strength of the EIA crests. Whalen [2001, 2003] used arrays of ionospheric sounders to infer that the maximum strength of the F2 layer electron density (NmF2) of the anomaly crests is linearly related to the PRE. Subsequent work [Whalen, 2004] expanded the study to include the relationship between the NmF2 and PRE at all levels of solar flux using eight ionospheric sounders across the globe. Whalen found that the NmF2 at each station varied linearly with the monthly average solar flux. He then used the linear relationship between the PRE and solar flux from Fejer et al.  to derive a linear relationship between NmF2 and the PRE. In an averaged sense, the linear relationship is not dependent on the solar flux level. Because the relationship with solar flux varied with longitude, the relationship with the PRE was inferred to vary in the same way. Whalen found that the relationship did not vary with season. More recently, Li et al.  used in situ data from DMSP, ROCSAT-1 and CHAMP to study the relationship between plasma bubbles, the EIA and PRE at solar maximum. Figure 3 from this study shows a direct comparison of the crest-to-trough ratio of the EIA NmF2 to the PRE that suggests a linear relationship during the solstices, but not during equinox months. Longitudinal variations in the relationship were not analyzed. In a theoretical study, Basu et al.  used 14 days during the solar maximum year 2002 to study the relationship between the PRE and the crest-to-trough ratio of the total electron content (TEC) using drift measurements from the Jicamarca incoherent scatter radar to drive an ionosphere model. The study showed that a linear relationship starts to develop at 2000 LT and persists for at least three hours, though the slope of the relationship changes as a function of time.
 Such a linear relationship is useful in that it can be used to approximately derive one quantity when the other cannot be measured. For example, measurements of the EIA from a chain of ionosondes or space-based instruments can be used to infer the PRE when vertical drift data is unavailable. The PRE is a useful parameter in that there is evidence it can be used to predict the occurrence of plasma depletions, or equatorial spread F (ESF) that lead to scintillation [Anderson et al., 2004b]. Various studies suggest the PRE must exceed a threshold velocity in order for ESF to occur [e.g., Fejer et al., 1999; Basu et al., 1996; Whalen, 2001; Anderson et al., 2004a]. Basu et al.  demonstrated that the linear relationship could indeed be used to estimate the strength of the PRE. In order for a measurement of the linear relationship to be useful, however, knowledge of its drivers is necessary to understand its range of validity. The goal of this work is to investigate the relative roles of the daytime and PRE drifts in the linear relationship between the PRE and EIA strength and to determine to what extent the relationship varies with longitude and solar cycle conditions.
 The study by Whalen  suggests that a linear relationship holds for all levels of solar flux. Basu et al.  showed that this relationship holds at solar maximum, but until now it has not been directly observed at solar minimum. In section 2, we use daytime and evening vertical plasma drift measurements at Jicamarca along with space-based ultraviolet (UV) measurements of the nighttime equatorial anomaly to establish that this linear relationship holds under solar minimum conditions (F10.7 = 80). In section 3, we use a physics-based model of the ionosphere to investigate the drivers of the slope and linearity of the relationship and how these quantities vary with longitude and solar cycle conditions. The UV measurements of the EIA, along with linear relationship established by the data, are used to validate the model. We discuss our results and present our conclusions in sections 4 and 5.
2.1. Vertical Drifts at Jicamarca
 We use vertical plasma drifts measured from the Jicamarca Radio Observatory. The daytime drifts between 0700 to 1700 LT are obtained using ΔH-inferred E × B velocities from two magnetometers located at Jicamarca (11.92°S, 283.13°E, 0.8°N dip latitude and Piura (5.18°S, 80.64°W, 6.8°N dip latitude) [Anderson et al., 2002, 2004a, 2006]. The evening drifts from approximately 1730 LT to 2000 LT are derived from the Jicamarca digital sounder by measuring the height-rise-with-time of the 4 MHz contour (corresponding to ∼2 × 105 electrons cm–3) after sunset. At the magnetic equator, the primary causes for this altitude to increase at dusk are the decay of the bottomside ionosphere in the absence of production by solar ionizing radiation and the increase in the upward E × B drift. The meridional neutral wind is of secondary importance because the geomagnetic field lines are horizontal at the magnetic equator. The height rise due to the decay mechanism is about 5 m s−1, which is much smaller than the tens of meters per second increase due to the prereversal enhancement in vertical E × B drift. This technique has been described in detail by Anderson et al. [2004b]. For this study, the maximum velocity measured between 1800 and 2000 LT is used as the PRE velocity.
2.2. TIP Data Set
 To obtain the peak electron densities in the EIA crests, we use satellite measurements of the O I 135.6 nm airglow feature measured by the Tiny Ionospheric Photometer (TIP) aboard the Constellation Observing System for Meteorology, Ionosphere, and Climate (FORMOSAT-3/COSMIC). COSMIC consists of six identical microsatellites that were initially launched into the same orbit at 500 km, which is the configuration they were in during the timeframe of this study. The satellites eventually moved into individual orbits at a higher altitude of 800 km. Each TIP instrument is a compact, narrowband, ultraviolet photometer operating at the 135.6 nm wavelength [Dymond et al., 2000; Kalmanson et al., 2004] that is used to characterize the nighttime ionosphere directly below the spacecraft. TIP is orders of magnitude more sensitive than its FUV predecessors, such as SSULI, LORAAS, SSUSI, GUVI and IMAGE [Thonnard et al., 1999; Budzien et al., 2002; Paxton et al., 2003; Mende et al., 2000], and provides remarkable detail of the latitudinal profile of the EIA [Coker et al., 2009; Dymond et al., 2009].
 The 135.6 nm emission is produced primarily by recombination of O+ ions and electrons, with some contribution due to neutralization of O+ ions by ambient O− ions. Meléndez-Alvira et al.  showed that mutual neutralization contributes up to 11% of the total intensity at altitudes near 275 km in the early evening, but that it is lower at higher altitudes. For the purposes of this study, we neglect contamination due to O+ – O− mutual neutralization so that the observed nadir intensity I (in Rayleighs) is given by
where ne is the electron density at altitude z, dz is the differential altitude, h is the altitude of the satellite, and α1356 is the radiative recombination rate at electron temperature Te given by 7.3√(1160/Te) × 10−13 cm3 s–1 [Meléndez-Alvira et al., 1999]. We further assume that the O+ density equals the electron density, which is a good approximation below the H+/O+ transition height at night in the F region. To calculate the O I 135.6 nm radiance, the TIP counts are first divided by the integration time, 1.18 s, and then by the detector sensitivity ∼600 ± 120 counts s–1 Rayleigh–1. The TIP instruments use a filter wheel to block the input light and measure the particle radiation and dark count background or “dark data.” As these noise sources are very smooth, the data are filtered to identify the dark data. A polynomial function is then interpolated through the dark data and subtracted to correct the radiance data. Last, the dark data are removed by replacing them with a polynomial interpolation of the corrected radiances. We derive the NmF2 by assuming a three parameter Chapman profile ionosphere with a constant scale height of 50 km for atomic oxygen as determined from NRLMSISE-00 [Picone et al., 2002] and a radiative recombination rate coefficient (α135.6) of 8.3 × 10−13 cm3 s–1 at an electron temperature of ∼900 K. We note that an important constraint on the TIP instrument is the requirement of new moon or moon-down conditions in order to avoid the instrument's residual sensitivity to visible light.
 As mentioned above, in 2006 to 2007, several of the COSMIC spacecraft were in the same orbital plane with a local time ∼2000 – 2100 LT. Over this period we found 18 moon-down days where the TIP observations crossed within 7° longitude of Jicamarca and for which there were measurements of the daytime and evening E × B drifts. Specifically, the days in the study include May 27–29, 31, September 13–15, 17 and November 8, 10 in 2006; and April 17–20 and June 11–14 in 2007. TIP measured both northern and southern anomaly crests on 13 of these days. During this solar minimum period, the daily F10.7 solar index ranged from 68.9 to 89.3, with an average of 78.15. Geomagnetic activity was also quite low with an average daily Ap index of 5.
 To investigate the relationship between the anomaly crests and the maximum velocity of the PRE, we use the crest-to-trough ratio, defined as the maximum NmF2 of the northern or southern anomaly crest divided by the minimum NmF2 between the crests. Scatterplots of the crest-to-trough ratio of NmF2 at ∼2030 LT versus the maximum velocity of the PRE are shown in Figure 1; the dashed line shows the least squares fit to the points. The correlation coefficient (r) and the slope of the regression line are also indicated. Figures 1a and 1b show the crest-to-trough ratio of the northern and southern anomaly crests, respectively. There is generally more plasma density in the northern crest than in the southern, but the slope of the highly linear relationship to the PRE is nearly the same in both cases. A better measure of the strength of the EIA is obtained by averaging the peak densities in the EIA crests such that the crest-to-trough ratio is (NmF2north + NmF2south)/2(NmF2trough) [Mendillo et al., 2000], which effectively averages out the hemispheric asymmetries introduced by the F region field-aligned neutral winds. By using this index, the linear correlation with the PRE is even better (Figure 1c). We also find that the NmF2 in each anomaly crest is linear with the maximum PRE velocity, though there is slightly more spread in the points (Figure 2), quantified by the smaller correlation coefficients.
3. SAMI2 Simulations
 We use the SAMI2 (Sami2 is Another Model of the Ionosphere) to investigate the linear relationship between the anomaly crests and the PRE. In the first modeling study, the Jicamarca drift measurements are used to specify the vertical drift in SAMI2; the calculated O I 135.6 nm radiances are then directly compared with the TIP radiances. We also show that the model reproduces the linear relationship shown in Figure 1. Having validated the model, we undertake a second study to investigate the role of the PRE versus daytime drifts. In a third study, we consider how the linear relationship varies with longitude and solar cycle conditions.
 SAMI2 is a two-dimensional model of the low-latitude and midlatitude ionosphere that covers altitudes from 85 km to 20,000 km and latitudes between ±62.5° about the magnetic equator, and models the dynamics and chemistry of seven ion species: H+, He+, N+, O+, N2+, NO+, and O2+ [Huba et al., 2000]. The SAMI2 code includes the E × B drift of the plasma as well as ion inertia for motion along a flux tube specified by a dipole fit to the International Geomagnetic Reference Field (IGRF). The code uses a fixed, nonorthogonal grid in which one coordinate axis is aligned with the geomagnetic field. Neutral thermospheric winds in SAMI2 are given by the Horizontal Wind Model (HWM07) [Drob et al., 2008]; the neutral composition and temperature are specified by the NRLMSISE-00 model [Picone et al., 2002].
3.1. Jicamarca Comparisons
 To simulate the 18 days used in this study, the measured E × B drift are used to drive SAMI2 for local times from 0700 to 2000 LT at 283.1°E, whereas the nighttime and early morning hour drifts are specified by the Scherliess-Fejer climatology model [Scherliess and Fejer, 1999]. Additional inputs to the model include the year, day of year, daily Ap, F10.7 and the 81-day average F10.7 solar flux index. At very low F10.7, comparisons with data have shown that NRLMSIS-00 overestimates the neutral oxygen content by more than 30% [Emmert et al., 2008]; thus to account for this discrepancy, we reduce the MSIS neutral oxygen content by a factor of 0.7. The model radiances are calculated using equation (1) above, where the integration is performed from the bottom of the SAMI2 ionosphere (∼85 km) to the satellite altitude (∼500 km). Figure 3 shows a comparison of the square root of the TIP radiances at 135.6 nm, which is proportional to electron density, to SAMI2 at the anomaly crests and the equatorial trough. SAMI2 matches the TIP measurements fairly well at the trough, but generally overestimates the density in the anomaly crests by ∼20%. Reasons for the differences in ionospheric content between the model and the data include neutral concentrations, F region winds, and uncertainties associated with chemical reaction rates.
 We next consider the relationship between the EIA crests and the maximum PRE velocity. Figure 4 shows the SAMI2 crest-to-trough ratio as a function of the PRE at the times of the TIP observations (∼2030 LT). Also shown (in green) are the results of SAMI2 simulations performed using a model vertical drift in which only the PRE is varied and the day of year is held constant; these results will be discussed in more detail in section 3.2 below. We find that the PRE is better correlated with the crest-to-trough ratio than the crest NmF2, which is consistent with the TIP results in the previous section. There is a stronger linear relationship to the PRE in the southern anomaly crest-to-trough ratio than in the northern anomaly; this is also the case with the data (Figure 1), but it is much more pronounced in the SAMI2 simulations. We find that the SAMI2 results have a lower correlation coefficient than the data; for example, in the northern anomaly, the model yields r = 0.59, whereas r = 0.87 for the data. This result is somewhat unexpected in that the model ionosphere does not capture the day-to-day variability of the thermospheric composition and winds, and thus we would anticipate less variation in the model. We were able to better match the observations by removing the seasonal variation of the background thermosphere, which was accomplished by holding the day of year constant but allowing all other inputs including Ap, F10.7, and vertical drifts to vary as before. Figure 5 shows the results for day of year held fixed at 150, which was chosen because it represents the season with the highest percentage of measurements. By removing the seasonal effects, the correlation between the crest-to-trough ratio and the PRE increases, especially in the northern anomaly (r = 0.85). The slopes of the linear fit also come into better agreement with the measurements. The consistent results provide reassurance that the model is correctly capturing the physical processes responsible for the linear relationship between the anomaly crest and the PRE and allow us to now use the model as a tool to investigate the relative contributions of the daytime and evening drifts.
3.2. PRE Variation
 We are now interested in gaining insight into the drivers of the linear relationship. We first look at the contributions from the PRE itself by performing a series of simulation runs where the PRE velocity is varied and the daytime drifts are held constant. We use a sine wave that approximately fits the average daytime pattern of the Jicamarca drifts used in our study, which are shown in gray in Figure 6. The red curve shows the mean drift and the blue dashed line is a sine wave with maximum amplitude of 24 m s−1 at 1200 LT and a Gaussian PRE of 13 m s−1 centered at 1830 LT. We then vary the amplitude of the PRE while holding the daytime drifts constant, as shown in Figure 7, and use these vertical drift velocities in SAMI2.
 The set of SAMI2 runs are performed for the typical conditions of the observation days at the Jicamarca longitude (283.1°E). The day of year was chosen to be 150, with F10.7 = 80 and Ap = 5. We then look at how the crest-to-trough ratio of the anomaly crests at 2030 LT varies as only the PRE velocity is increased from 5 m s−1 to 30 m s−1. The results are overplotted on Figures 4 and 5 as the diamond symbols connected with dashed lines. The crest-to-trough ratio is not strictly linear with the PRE. We note, however, that the simulations indicate the maximum NmF2 of the anomaly crests is linear with the PRE velocity. A comparison with the simulations using the Jicamarca drifts shows that the PRE is the dominant driver of the linear relationship, but that other aspects of the E × B drift play an important role. In other words, the daytime drift, along with the timing and duration of the PRE contribute to the slope and spread of the points.
3.3. Local Time Contributions
 To determine the relative contributions of the daytime E × B drifts to the anomaly crest NmF2 at 2030 LT, we perform runs using two drift models: one double the amplitude of the other during the daytime, but with the same PRE. All other inputs are held constant between the two runs (DOY = 150, F10.7 = 80, Ap = 5, Longitude = 283.1°E). The larger drift is sinusoidal with a daytime maximum velocity of 30 m s−1 and a 20 m s−1 PRE, whereas the smaller drift as a daytime maximum velocity of 15 m s−1 and a 20 m s−1 PRE. A similar approach has been used by England et al.  to look at the local time effects of tropospheric forcing on the nighttime EIA.
 We define a series of drift patterns that apply the larger drifts from 0600 LT to a selected local time, and then revert back to the smaller drifts until 2400 LT. For each drift pattern in the series, the selected local time is incremented hourly from 0700 to 1800 LT. We then compare the crest-to-trough ratio in the anomaly crests at 2030 LT using the altered drift pattern to the crest-to-trough ratio resulting from the smaller drift pattern to determine the percent change. The solid black line in Figure 8 shows the percent change in the average NmF2 of the anomaly crests as a function of the local time until which the larger drift is applied. For example, when the larger drift is applied from 0600 to 1200 LT, the crest-to-trough ratio decreases by ∼2%, but when it is applied until 1800 LT the NmF2 increases by 80%, with half of the contribution coming from the afternoon hours between 1400 to 1700 LT.
 Based on the results shown in Figure 8, the afternoon drifts are contributing to the linear relationship found in the data. That the linear relationship between the PRE and the EIA persists despite the daytime day-to-day variation of the drifts, and that the relationship has a different slope than the PRE-only variation, suggests that there is a linear relationship between the afternoon drifts and the PRE. We take the mean of the afternoon Jicamarca vertical drift (between 1400 and 1700 LT) and plot it versus the PRE (Figure 9). The linear trend is not strong, but it has the effect of steepening the linear relationship between the PRE and the crest-to-trough ratio of the EIA. Average Jicamarca drifts at earlier times in the day show less or no correlation with the PRE.
3.4. Solar Cycle and Longitude Dependence
 We expand on our SAMI2 model runs from the previous sections in order to investigate solar cycle and longitudinal effects on the linear relationship between the crest-to-trough ratio and the maximum PRE velocity. The simulations discussed above (sections 3.1–3.3) are rerun for DOY = 150, Ap = 5, and with the F10.7 increased to 190. Overall, we find that the daytime drifts have a greater effect on the nighttime anomaly crests under solar maximum conditions than at solar minimum. The (red) dot-dashed line in Figure 8 shows that doubling the daytime drift velocity from 15 m s−1 to 30 m s−1 results in a nearly twofold increase of the crest-to-trough ratio at 2030 LT and that ∼50% of the change is due to the drifts before 1400 LT. The effect this has on the linear relationship between the EIA and the PRE is shown in Figure 10a. The correlation coefficient decreases from 0.90 (cf. Figure 5c) to 0.60 and the slope of the linear fit decreases from 0.10 to 0.04 due to the contribution of a larger percentage of the daytime drift.
 To look at the longitude dependence of the linear trend, we run the simulations at 120°E longitude at the solar minimum conditions (F10.7 = 80). The dashed line (blue) in Figure 8 shows that at this longitude, an increase in the daytime drift velocity before 1400 LT has a negative effect on the nighttime EIA crests; the crest-to-trough ratio at 2030 LT decreases when the daytime drift is larger. At this longitude the PRE has the largest positive influence on the EIA, which leads to a strong linear trend (r = 0.90) with a slightly reduced slope (Figure 10b) that more closely resembles the case where only the PRE is varied, as shown by the dashed green line in Figure 5c.
 In the Introduction, we noted several previous studies of the relationship between the EIA crests and the PRE. Whalen  used the linear relationship of the EIA and E × B drifts to solar flux in order to infer a linear relationship between the EIA NmF2 and the PRE that does not depend on F10.7. His Figure 8 indicates that the slope of the relationship is the same for all seasons and levels of solar flux. Our results, however, demonstrate that the slope varies with F10.7. Additionally, a comparison of our Figure 2 with Whalen's results at Bogota shows that we obtain a much flatter slope. Better agreement is obtained if we consider our average results. Our study indicates that the average PRE is 13 m s−1 and the average NmF2 in the anomaly crests is 0.5 × 106 electrons cm−3 at solar minimum and 2.0 × 106 electrons cm−3 at solar maximum. These results are compared with Figure 8 from Whalen , where our solar minimum results fall on the dashed line for the December solstice months and our solar maximum results fall nearly at the first point on the solar maximum line.
 We also compare our results with that of Basu et al. , who conducted a similar study to our own, but at solar maximum. In their work, also at the Jicamarca longitude, the crest-to-trough ratio was found to be the only feature that showed a strong linear relationship with the PRE. Our results indicate that the NmF2 of the anomaly crests is also linear with the PRE, but that the crest-to-trough ratio does have a stronger linear relationship, with a correlation coefficient closer to one, especially when the anomaly crests are averaged. Because the Basu et al. study was conducted at solar maximum, we infer from our modeling study that the linear relationship should be weaker than at solar minimum, and indeed this is the case. The TEC measurements used in their study show a linear correlation coefficient of ∼0.5 and a slope of 0.05. This result can be directly compared with our solar maximum simulation (Figure 10a) for which we found a correlation coefficient of 0.6 and a slope of 0.04. Though the measured PRE velocities of each study do not cover the same range of values, our results indicate a PRE of 30 m s−1 corresponds to a crest-to-trough ratio of 2, which is in very good agreement with the Basu et al. results.
 We have used measurements of vertical E × B at Jicamarca and 135.6 nm radiances from TIP to show that there is a linear relationship between the PRE and the strength of the postsunset EIA crests at solar minimum. We have demonstrated that the linear relationship between the EIA crest-to-trough ratio of NmF2 and the maximum velocity of the PRE holds quite well on a day-to-day basis and is independent of season. The NmF2 of the anomaly crests is also linear with the PRE, but with a slightly weaker linear correlation. The linear correlation is strongest when the average of northern and southern anomaly crests is used to calculate the crest-to-trough ratio.
 The Jicamarca measurements were used to validate the SAMI2 model, and a number of simulations were performed to investigate the nature of the linear relationship in more detail. We found that the slope of the linear relationship is primarily determined by the influence of the PRE itself, but the daytime drifts also have an important impact on both the slope and linear fit of the PRE versus NmF2 relationship. At solar minimum, the daytime drifts between 1400 to 1700 LT have the largest impact the NmF2 of the anomaly crests at 2030 LT. Because these drifts are also correlated with the PRE, they have the effect of steepening the slope of the linear relationship. At solar maximum, however, even the morning daytime drifts contribute to the evening NmF2. These earlier drifts have little to no correlation to the PRE and thus have the effect of decreasing the slope and weakening the linear relationship. A comparison with a previous study [Basu et al., 2004] conducted at Jicamarca during solar maximum corroborates this result. In addition we showed that the contribution of the daytime drifts varies with longitude, and that the linear relationship varies with longitude. We found that the SAMI2 model predicts a stronger seasonal variation than is observed at Jicamarca; in fact, the model matches the data best when the thermospheric composition and winds are not varied with season within the model. A more extensive study involving additional data from each season and at different longitudes will need to be carried out in order to vigorously validate the model.
 In summary, our results indicate that the linear relationship between the crest-to-trough ratio of NmF2 can be used to determine information about the E × B drifts and the strength of the PRE when it cannot be measured directly. But the linear relationship may vary significantly from one longitude sector to the next and under different solar cycle conditions. Though a generally linear relationship holds on a day-to-day basis, variations in the daytime drift pattern can increase the noise, or scatter, in the relationship.
 This work was supported by the U.S. Office of Naval Research.