Space environmental sensors on polar-orbiting Defense Meteorological Satellite Program (DMSP) spacecraft occasionally encounter plasma density depletions when they cross the geomagnetic equator in the evening sector. These equatorial plasma bubbles (EPBs) are observed around the times and locations when equatorial spread F and radio scintillation phenomena tend to occur. The solar cycle, seasonal, and longitudinal variations in the observed frequency of these depletions (determined over the past 19 years) are indeed similar to those of scintillation. To test our understanding of EPB formation, we simulated the observations using PBMOD, a suite of first-principle models of the ambient ionosphere and EPB formation, driven by climatological models for its input parameters such as the plasma drift velocity. Maps of the model calculations of EPB frequencies at 840 km as functions of season and longitude exhibit patterns similar to the DMSP observations, including the expected peaks in EPB frequency near the equinoxes, an additional winter peak in the American sector, a summer peak in the Pacific sector, and the proper trends with solar cycle phase. Adjusting the model to reproduce the DMSP EPB occurrence frequencies in detail will allow us to fine tune PBMOD and provides a means for using the DMSP data to enhance the empirical drivers for the Communication/Navigation Outage Forecasting System (C/NOFS) mission.
 Equatorial plasma bubbles (EPBs) are the result of the nonlinear evolution of the generalized Rayleigh-Taylor (R-T) instability in the postsunset ionosphere in which the bottomside of the F layer is unstable to plasma interchanges, creating plasma depletions which rise through the peak of the F layer. Irregularities with scale sizes of meters to kilometers form within these density depletions, diffract radio waves and cause severe degradation of communication and navigation signals at low magnetic latitudes. The objective of the Communication/Navigation Outage Forecasting System (C/NOFS) mission [de La Beaujardière et al., 2004] is to better our understanding of these phenomena, leading to forecasts of the low-latitude ionospheric disturbances that cause these disruptions. In preparation for the C/NOFS mission, a suite of ionospheric forecast models was developed [Retterer, 2005] to predict the structure of the ambient ionosphere, identify locations of R-T instability, and perform a calculation of the nonlinear evolution of the plasma structure there to determine the strength of radio scintillation to be expected. One aspect of the validation of this model will be addressed here: does the model represent well the climatology, the average long-term conditions, of EPB occurrence. (A separate question, which is not considered here, is whether the model, with the assimilation of data from the satellite, can describe the day-to-day variability of the occurrence of scintillation: the weather of the phenomenon.)
 To validate the model climatology, we examined plasma density measurements from sensors on Defense Meteorological Satellite Program (DMSP) spacecraft and developed a global climatology of EPB occurrence. DMSP spacecraft fly in circular, Sun-synchronous polar orbits at an altitude of ∼840 km and an inclination of 98.7°. Burke et al. [2003, 2004a, 2004b] and Huang et al. [2001, 2002] developed a global climatology that demonstrated the utility of DMSP for EPB observations. Huang et al.  surveyed EPB activity during solar maximum years 1989 and 1991. Seasonal versus longitudinal EPB distributions were in general agreement with ground-based measurements of scintillation [Aarons, 1993] and the plasma drift model of Scherliess and Fejer . Huang et al.  also found that the number of EPBs increased during the early stages of solar storms, but was suppressed during recovery. Huang et al.  then extended their study to include seasonal and longitudinal distributions of EPBs from multiple DMSP spacecraft over a full solar cycle from 1989 to 2000. Burke et al.  compared DMSP EPB observations with coordinated ground measurements from the Jicamarca Unattended Long-Term Investigation of the Ionosphere and Atmosphere (JULIA) radar and a scintillation monitor in Ancon, Peru, and determined that the seasonally averaged occurrence rates of EPBs and scintillation correlated closely when the ionospheric disturbances that cause scintillation were expected to reach DMSP altitudes, e.g., at solar maximum.
 Trajectories of the DMSP spacecraft chosen for this study all cross the magnetic equator in the postsunset local time (LT) sector (1900–2200 LT). DMSP spacecraft average 14 orbits of ∼104 min each per day, ∼5100 orbits per year. Satellites twice traverse all magnetic latitudes between ±20° MLat within a narrow LT range during every orbit and regress ∼25° in longitude between ascending nodes. We used data from the Special Sensor-Ions, Electrons, and Scintillation (SSIES) instruments which measure plasma densities, temperatures, and drift velocities. Since structure within the depletions made it difficult to count individual EPBs, we classified a cluster of EPBs as one occurrence. Also, data were sorted by the longitude of the spacecraft's equatorial crossing rather than the longitude of individual EPBs. EPB rates were calculated as the ratio of the number of orbits in which at least one EPB was detected divided by the total number of orbits for each month of the year in 24 longitude sectors of 15°. On average, there were ∼18 orbits per month for each satellite in each longitude bin.
 Solar cycle, seasonal, and longitudinal effects are evident in the DMSP EPB climatology. On the basis of the F10.7 index of solar radiation flux, we plotted data for solar maximum (2000–2002) and minimum (1994–1997) [Gentile et al., 2006]. The number of orbits with EPBs ranged from ∼1000 per year during solar maximum to <100 during solar minimum. In general, EPBs were more prevalent around the equinoxes in March–April and September–October and less likely near the solstices in June–July and December–January at DMSP altitudes. In all solar cycle phases DMSP observed more EPBs in the Atlantic-Africa sector than in the Pacific [Gentile et al., 2006].
 Because there is no climatology of ionospheric conditions during geomagnetically active times which we could model, we distinguished between depletions observed in quiet and active times using the Dst index as a discriminator and concentrated only on the quiet times. EPBs observed when Dst > −40 were included in the geomagnetically quiet category. This threshold value was chosen to prevent EPBs observed from the time of storm onset through early recovery from being counted in the statistics for quiet times.
Figure 1 presents both the quiet time (Figure 1a) and geomagnetically active (Figure 1b) EPB rates for the 2000–2002 solar maximum on a month-versus-longitude grid with longitude ranging from −180° to 180° in 24 bins of 15°. Colors represent the rates as indicated. Superimposed black lines mark the days when the evening terminator is aligned with the plane of geomagnetic field lines. These are expected to be days of maximum scintillation activity because both ends of the field line are in darkness, minimizing the early evening E region conductivity, which otherwise would short out the electric fields that promote the R-T instability [Tsunoda, 1985]. Both seasonal and longitudinal effects are evident with significantly higher EPB rates during the equinox months of March–April and from September–December in the America-Atlantic-Africa region. There are indications of higher stormtime EPB rates around the equinoxes that may be due to “preconditioning” of the ionosphere toward instability in the quiet condition. Overall, the stormtime climatology of EPBs from DMSP is extremely sparse; many individual events can be distinguished clearly, so it is hard to draw any general conclusions.
 The solar minimum climatology plots in Figure 2 present a striking contrast to the ones for solar maximum. EPB rates were generally less than 5% except in the America-Atlantic-Africa sector. Note that the depletions seen during geomagnetically active times are sporadic and show no systematic variation of occurrence with longitude because there is no obvious preferred universal time at which storms occur. The stormtime EPBs are roughly similar in frequency at solar max and min, but constitute a larger portion of the total number of EPBs at solar min because the quiet time EPBs are more infrequent.
 The suite of ionospheric models used in studying the ambient ionospheric plasma density, its R-T stability and the resulting plasma plumes and scintillation are described in detail by Retterer . The global ambient ionospheric model [Retterer et al., 2005], which will be used to calculate global ambient ionospheric structure, is based on the low-latitude ionospheric model of Anderson . It solves the continuity equation for plasma density in terms of the processes of production, loss, and transport of plasma density along and perpendicular to geomagnetic flux tubes in the vicinity of the geomagnetic equator. It requires specification of the solar UV flux, neutral densities, winds, and temperatures within the thermosphere, along with plasma drift velocity and temperature. For this climatological study, empirical models of these parameters were used: Hedin  Mass Spectrometer and Incoherent Scatter (MSIS) model for neutral densities and temperatures, Hedin et al.  Horizontal Wind Model (HWM) for neutral winds, Hinteregger  for the solar ultraviolet spectrum, Scherliess and Fejer  for plasma drifts, and Gulyaeva and Titheridge  for the plasma temperature. An altitude gradient is added to the plasma drift model through the time of the prereversal enhancement, with the velocities decreasing with altitude above the F layer [Eccles, 1998]. The plasma model also uses the International Geomagnetic Reference Field (IGRF) magnetic field.
 Once the ambient ionosphere is calculated, the plasma structure is examined for regions susceptible to the R-T instability using the formulas of Sultan  and, where unstable, a calculation [Retterer, 2009] of the nonlinear development of the structure of the plasma, possibly into low-density plumes of plasma turbulence filling the F region, is launched. An additional input parameter into the plume calculation is the “seed” perturbation, from which the plume will develop if the plasma is unstable. The structure of the seed perturbation includes a sech(y/L) squared variation in the east-west direction (a depletion in density using a nonlinear function to produce a wide variety of spectral components), with a scale length L of 100 km, an altitude profile proportional to the gradient of the ambient density, and a peak magnitude of about 5 percent of the ambient density (J. M. Retterer, Forecasting low-latitude radio scintillation with 3-D ionospheric plume models: 2. Scintillation calculation, submitted to Journal of Geophysical Research, 2008, hereinafter referred to as Retterer, submitted manuscript, 2008). We took this seed perturbation to be the same, regardless of season or longitude. From the spectral density of the plasma irregularities within the plumes, an estimate of the intensity of scintillation strength, S4, is made, using a phase-screen calculation [Retterer, 2005; Retterer, submitted manuscript, 2008]. For comparisons with the DMSP observations, the output of the nonlinear model was probed for low-density plumes reaching an altitude of 840 km at the local time of the satellite orbit.
 Given a specification of all the input parameters on which it depends, this model is completely deterministic in that it calculates one outcome (which can be regarded as the most likely output given those inputs). Thus, to calculate the occurrence frequency of plasma depletions an ensemble of model runs was employed, with the probability of an outcome then being the probability of all the combinations of choices for the input parameters that lead to that outcome. For the occurrence of evening scintillation it has been recognized that the phenomenon is most sensitively dependent on one parameter: the magnitude of the prereversal peak of the upward plasma drift in the early evening [Fejer et al., 1999]. Thus the magnitude of the prereversal peak velocity will be the one parameter of our ensemble. The expected or mean value of this parameter is given by the empirical model of Scherliess and Fejer , and is shown in Figure 3 for two cases: solar maximum (F10.7 = 180) and solar minimum (F10.7 = 80). We estimate the probability distribution of this parameter by looking at the plots of plasma drift given by Scherliess and Fejer  that show the day-to-day variability of the upward plasma drift measured by the Jicamarca radar. There is a scatter of roughly ±10 m/s about the mean value of the velocity throughout the day, including the prereversal enhancement, with no apparent variation with season. If we assume a Gaussian distribution in which 98% of the variance is contained within a range of ±10 m/s, then we would assign the standard deviation of the distribution a value of ∼6 m/s.
 To build this variability into the model, we modified the Scherliess and Fejer  plasma drift model so that the velocity at the prereversal peak can be specified independently. Then to generate a member of our ensemble, we choose a prereversal velocity and run the plasma models to determine if depletions occur at the DMSP altitude. The threshold prereversal velocity for EPB formation is estimated from runs with several different prereversal velocities by looking for the run for which the magnitude of the peak density perturbation at the DMSP altitude first increases above zero. For example, Figure 4 gives the history of the vertical plasma drift for several members of the ensemble at longitude 330, day-of-year 335, showing the different prereversal velocity peaks (with corresponding subsequent negative overshoots), while Figure 5 gives the peak relative density perturbation at 840 km altitude (black points) and the perturbation in vertical total electron content (TEC) (red points) for the members of the ensemble at this location and day. We judge the threshold for DMSP density depletions at 10 percent of ambient density, so the threshold velocity is about 15 m/s larger than the mean value of the prereversal enhancement peak, while the threshold for TEC perturbations is near the mean prereversal enhancement drift (their occurrence at smaller velocities implies that they form at lower altitudes). The last step is determining the probability of EPB occurrence, which is the probability that any prereversal velocity exceeds the threshold prereversal velocity, using our characterization of the probability distribution as a Gaussian with mean equal to the Scherliess-Fejer result and a standard deviation of 6 m/s. This procedure is carried out for each of a complete set of longitudes and days of year to create a climatology comparable to the DMSP observations. (A tabulation every 10 days and fifteen degrees of longitude, with three different prereversal velocities at each point, requires approximately 2500 ionosphere/bubble calculations, which are performed on a Beowulf computer cluster.)
 Because of the scale of the computation, the faster two-dimensional bubble model is employed rather than the more complex three-dimensional model [Retterer, 2009]. The field-line integrated conductances in the two-dimensional model are estimates based on the local plasma density in the equatorial plane, which is followed dynamically, and the variation of the plasma density along the field lines in the ambient model. In both models, the contribution of the molecular species in the E region to the conductances is simply the field-line integral of the ambient conductivity, with the density given by a local chemistry calculation; that is, there is no transport of the molecular species.
Figure 6 presents the initial results calculated with the climatological drivers, showing the model bubble frequencies in Figure 6 (top) and the DMSP observations in Figure 6 (bottom) (replotted using the same color scale). Figure 6a shows the results for solar maximum (solar F10.7 = 180 in the model), and Figure 6b shows the results for solar minimum (F10.7 = 80). Overall the model frequencies exhibit patterns of EPB occurrence similar to the observations. For solar max, the model seems generally to overestimate the probability of bubble occurrence, with peak values close to 90% rather than the measured 75%. For solar min, the model correctly demonstrates the reduction in bubble frequency, although again the model frequencies are higher than observed. This excess of EPB frequency can be corrected by adjustment of the parameters of the model. An additional feature is apparent in the solar min model results which is not seen in the data: the enhancement in EPB frequency at the equinoxes at longitudes of 0° to 150°. An examination of the empirical plasma drift model shows that it, too, includes an enhancement at these longitudes. The DMSP EPB frequencies suggest that this feature in the plasma drift model should not be there.
 The model was modified with the aim of achieving better agreement with the DMSP climatology. The coefficient of the O+ contribution to the field-line integrated conductances was reduced by 10 percent. This increases the stabilizing effect of the molecular contribution to the conductances and should help lower the modeled EPB occurrence frequencies. The second modification was a reduction in the mean prereversal enhancement velocity at solar min at longitudes from 0° to 150°, as shown in Figure 7. This should lower the EPB frequency in this region and eliminate the false peak. Figure 8 shows the results, which are as we expected. Neither of the two differences from the observations is eliminated, but both are reduced, showing that with some effort the observed EPB frequencies could be reproduced by the first-principles model.
 The purpose of PBMOD in connection with C/NOFS is, of course, the prediction of radio scintillation, which it does using the irregularity spectra found in its plume calculations in a phase-screen calculation of S4 (Retterer, submitted manuscript, 2008), the amplitude scintillation statistic. With the ensemble of models refined here with the DMSP observations, we can estimate the probability of occurrence of scintillation above a given level by again looking for the threshold drift velocity for scintillation of that strength. Figure 9 gives the probability of S4 > 0.6 (the level at which 10 dB fades are common) under solar-minimum conditions for vertical signal propagation at 250 MHz. We see that the model predicts that in equinox seasons the probability of strong scintillation is still fairly high (40–50%) despite the weak prereversal enhancement velocities; this is probably due to low thresholds for the plasma instability because of the cool thermospheric conditions of solar minimum.
4. Discussion and Conclusions
 The primary objective of the DMSP studies has been to exploit global and continuous observations of plasma densities at low magnetic latitudes in the evening LT sector in preparation for the C/NOFS mission. These data allowed the climatological variations of EPB occurrence with longitude, season, and solar cycle to be estimated. Comparisons of the PBMOD system of ionospheric models with this data set are perhaps the most rigorous test of the model to date, demanding that the model produce correct results not merely for an individual case, but for an entire set of times and locations. This comparison showed that the model has the features of the data set basically right, but also suggests that some tuning of parameters could lead to even more accurate results. It was interesting to see that a simple model with a uniform seed was capable of reproducing the climatology of EPBs, although not too surprising because the R-T instability is a linear one that can grow from a perturbation of any amplitude. The comparisons with data also suggested that the models could indirectly enable such measurements as the DMSP EPB observations to act as constraints on empirically derived models such as the plasma drift model and provide global specification of parameters that can be easily measured from the ground in only a few places.
 This work was supported by the Air Force Office of Scientific Research and Air Force contracts F19628-04-C-0055 and FA8718-08-C-0012 with Boston College.