Development and Validation of Precipitation Enhanced Densities for the Empirical Canadian High Arctic Ionospheric Model

The Empirical Canadian High Artic Ionospheric Model (E‐CHAIM) provides the four‐dimensional ionosphere electron density at northern high latitudes (>50° geomagnetic latitude). Despite its emergence as the most reliable model for high‐latitude ionosphere density, there remain significant deficiencies in E‐CHAIM's representation of the lower ionosphere (below ∼200 km) due to a sparsity of reliable measurements at these altitudes, particularly during energetic particle precipitation events. To address this deficiency, we have developed a precipitation component for E‐CHAIM to be driven by satellite‐based far‐ultraviolet (FUV) imager data. Satellite observations of FUV emissions may be used to infer the characteristics of energetic particle precipitation and subsequently calculate the precipitation‐enhanced ionization rates and ionosphere densities. In order to demonstrate the improvement of E‐CHAIM's ionosphere density representation with the addition of a precipitation component, this paper presents comparisons of E‐CHAIM precipitation‐enhanced densities with ionosphere density measurements of three auroral region incoherent scatter radars (ISRs) and one polar cap ISR. Calculations for 29,038 satellite imager and ISR conjunctions during the years 2005–2019 revealed that the root‐mean‐square difference between E‐CHAIM and ISR measurements decreased by up to 2.9 × 1010 ele/m3 (altitude dependent) after inclusion of the precipitation component at auroral sites, and by 2.6 × 109 ele/m3 in the polar cap. Improvements were most substantial in the winter season and during active auroral conditions. The sensitivity of precipitation‐enhanced densities to uncertainties inherent to the calculation method was also examined, with the bulk of the errors due to uncertainties in FUV imager data and choice of distribution function for precipitation energy spectra.

morphology, evolution (temporal and spatial), and intensity. Because of this complexity, the development of models for high latitude ionosphere density has been a challenge. In addition, the development of empirical models has been hindered by the limited availability of reliable, direct, and widespread measurements of densities within the D, E, and lower F layers, particularly under precipitation conditions (Themens, Jayachandran, McCaffrey, Reid, & Varney, 2019). For example, ionosonde radars cannot provide electron density profiles during intense precipitation when E-region densities are larger than the F-region peak or when ionosonde transmissions are completely absorbed in the D and E layers. Additionally, inversions of satellite radio occultation measurements are impacted by cumulative downward propagation of errors which result in inaccurate lower ionosphere densities, particularly in regions with large horizontal density gradients (Yue et al., 2010).
Inaccurate high-latitude ionosphere models are problematic for radio propagation systems such as over-the-horizon-radar and long-range high-frequency radio communication, which depend on signal refraction in the ionosphere and thus accurate electron density representation for reliable operations (Jodalen et al., 2001;Zaalov et al., 2003). In addition, Global Navigation Satellite Systems (GNSS) require ionospheric correction for accurate positioning, and inaccurate ionosphere models can result in positioning errors of up to 100 m for single-frequency GNSS users (Hernández-Pajares et al., 2002). There are requirements for precision (centimeter-level) GNSS navigation in applications such as aviation, oil rig operation, agriculture, and automated mining and resource extraction (Perez-Ruiz & Upadhyaya, 2012;Sládková et al., 2011). With the widespread use of lower-cost single-frequency GNSS receivers and increasing infrastructure, resource exploration, and marine and aviation activity at high latitudes, access to accurate high latitude ionosphere densities is essential.
In recent years, the Empirical Canadian High Artic Ionospheric Model (E-CHAIM) (Themens et al., 2017(Themens et al., , 2018 has emerged as the most reliable representation of electron densities at northern high latitudes (>50° geomagnetic latitude; Maltseva & Nikitenko, 2020;Themens et al., 2020;Themens, Jayachandran, McCaffrey, Reid, & Varney, 2019). E-CHAIM is a significant improvement over other models such as the International Reference Ionosphere (IRI) at high latitudes, providing, for example, improvements of up to 60% in N m F 2 in the polar cap (Themens et al., 2017). Despite this improvement, E-CHAIM has limitations in its representation of the bottomside ionosphere, generally underestimating bottomside densities and performing poorly during energetic particle precipitation events . This poor performance is due to the limited availability of reliable datasets for bottomside densities, as discussed above.
To address this limitation, we examine the feasibility of deriving precipitation enhanced profiles for E-CHAIM based on auroral far ultraviolet (FUV) emission observations of the Defense Meteorological Satellite Program (DMSP) Special Sensor Ultraviolet Spectrographic Imager (SSUSI; Paxton et al., 1992) and the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) Global Ultraviolet Imager (GUVI; Humm et al., 1998). SSUSI and GUVI measurements of atmospheric emission intensities at Lyman-Birge-Hopfield (LBH) wavelengths may be used to estimate electron energy flux and mean energy of precipitating electron populations (Germany et al., 1990;Lummerzheim et al., 1991;Sotirelis et al., 2013;Strickland et al., 1983Strickland et al., , 1995. The energy flux and mean energy of precipitating electrons govern the atmospheric ionization rate and altitude of ionization, respectively, and are available as high-level GUVI and SSUSI data products. Given the high spatial resolution maps of GUVI and SSUSI data provided within a broad swath (thousands of kilometers) of the high-latitude region perpendicular to the spacecraft track, in addition to the multiple high latitude passes per day made by TIMED and DMSP satellites, the extensive historical GUVI and SSUSI datasets are a strong candidate to enhance E-CHAIM's performance in the presence of particle precipitation.
Derivation of precipitation-enhanced ionosphere densities from satellite ultraviolet imager (UVI) data has been previously examined by Aksnes et al. (2006), who added a precipitation component to IRI-95 ionosphere density profiles using UVI measurements of the Polar satellite. Atmospheric ionization rates were calculated from UVI-derived electron precipitation characteristics using the method introduced by Rees (1963). The authors found good agreement between precipitation-enhanced profiles and Tromsø incoherent scatter radar (ISR) measurements in the altitude range of 100-130 km during an interval of magnetospheric substorm activity on March 24, 1998. While the satellite UVI technique may only be used to characterize precipitating electron populations up to ∼20 keV, Aksnes et al. (2006) also used Polar satellite X-ray emission measurements to characterize the precipitating electron population up to ∼100 keV, allowing for the calculation of enhanced D-region densities as well.
In this study, we present the development and validation of a "precipitation scheme" for E-CHAIM based on GUVI and SSUSI electron precipitation energy flux and mean energy data products. GUVI and SUSSI data are used to characterize precipitating electron populations with mean energies of 0-20 keV, and subsequently calculate precipitation-enhanced ionosphere densities for E-CHAIM. This energy range primarily impacts altitudes in the range of 100-200 km. In the precipitation scheme, atmospheric ionization rates due to electron precipitation are calculated using the Fang-2010 parameterization scheme (Fang et al., 2010), which provides monoenergetic ionization rates based on first-principle model results. Ionosphere densities are calculated from ionization rates under the assumption of a steady state ionosphere and using the current E-CHAIM as a background ionosphere, resulting in a final "precipitation-enhanced" E-CHAIM ionosphere density profile. ISR measurements at Poker Flat ISR (PFISR; 65.1°N, 212.5°E), Tromsø (69.5°N, 19.1°E), Sondrestrom (67.0°N, 309.1°E), and Resolute ISR north face (RISR-N; 74.7°N, 265.1°E) stations, which can provide electron density profiles ranging from D-layer altitudes and well into the topside F-layer depending on operation mode (Evans, 1969;Mathews, 1984), are used to validate precipitation-enhanced densities. A total of 29,038 profiles were compared with ISR measurements, corresponding to measurements taken during conjunctions of SSUSI/GUVI and ISR field-of-views for the years 2005-2019.
We have also examined the sensitivity of calculated precipitation-enhanced E-CHAIM profiles to uncertainties inherent to the precipitation scheme. The sensitivity analysis provides insight into whether deviations from ISR measurements may be attributed to uncertainties in the calculated precipitation-enhanced densities, and provides the relative error contributions of each precipitation scheme input. Sources of error inherent to the precipitation scheme include uncertainties in energy flux and mean energy values, choice of distribution function to represent the shape of the energy spectrum of precipitating electrons, uncertainties in neutral atmosphere composition and temperature values (required for the Fang-2010 parameterization), errors inherent to the Fang-2010 parameterization itself, and uncertainties in the atmospheric recombination rates required to calculate ionosphere density. Sensitivity analysis was conducted for all 29,038 SSUSI/ GUVI-ISR conjunctions, by varying each input parameter within its respective uncertainty range and examining the subsequent variations in calculated precipitation-enhanced densities.
Section 2 describes the data sources and method used to calculated precipitation-enhanced densities for E-CHAIM. Section 3 presents comparisons of precipitation-enhanced densities with ISR measurements. Section 4 presents the sensitivity of calculated densities to uncertainties in precipitation scheme input parameters.

Data and Methodology
DSMP satellites have circular orbits at ∼860 km altitude with near-polar, sun-synchronous configurations. SSUSI data in this study are from four Block-5D3 DMSP satellites: F-16 (operational October 2003-August 2016), F-17 (operational November 2006-present), F-18 (operational October 2009-present), and F-19 (operational April 2014-February 2016. The TIMED satellite is in circular orbit at ∼630 km altitude and ∼74° inclination, with GUVI scan-mode data available for the period February 2002-December 2007. SUSSI and GUVI instruments employ scanning imaging spectrographs to measure multispectral FUV auroral emission intensities (Humm et al., 1998;Paxton et al., 1992). Each instrument is equipped with a cross-track scanning mirror to adjust the field-of-view of the telescope and optical elements, allowing for horizon-to-horizon scans perpendicular to satellite motion and thus a spatially broad picture of FUV emission intensity rates along the spacecraft track. Atmospheric N 2 emissions at LBH wavelength bands (140-152 nm 165-180 nm) respond to energetic particle precipitation, and measured emission rates at these wavelengths may be used to characterize the population of precipitating electrons (Germany et al., 1990;Sotirelis et al., 2013;Strickland et al., 1983Strickland et al., , 1995. Based on precipitating particle energy deposition rates, calculated theoretically using transport models such as Boltzmann 3-Constituent (Strickland et al., 1976), LBH emission rates may be used to infer the energy flux (Q 0 ) of precipitating electrons, while the average energy (E 0 ; 0-20 keV) of the precipitating population can be derived from the ratio of short and long wavelength LBH emission rates. SSUSI E 0 and Q 0 data values are gridded in bin sizes of ∼25 × 25 km, and are available as an "Auroral EDR" data product at https://ssusi.jhuapl.edu/. SSUSI data in this study are version 106, revision 0. GUVI E 0 and Q 0 data values are gridded in bin sizes of ∼25 × 25 km, and are available as a Level 2B "EDR Aurora" data product at http://guvitimed.jhuapl.edu/. GUVI data used in this study are version 106, revision 1. As noted by Aksnes et al. (2006), UVI-derived Q 0 may be unreliable when E 0 < 2 keV due to the lack of O 2 absorption of LBH emissions above ∼150 km. Q 0 values have thus been set to zero in grid elements where E 0 < 2 keV.
ISR electron density measurements are from the madrigal database (http://isr.sri.com/madrigal/). This study makes use of ISR data from the Tromsø, Sondrestrom, Poker Flat, and Resolute (north face only) systems. Data are processed in largely the same manner as Themens et al. (2018), where a probability distribution is created from 5 km vertical and 15-min temporal bins for each ISR and a log-normal distribution is fitted to estimate the appropriate electron density for each bin; however, compared to Themens et al. (2018), only a subset of configurations were used to better ensure the collocation of ISR profiles and GUVI/SSUSI pixel locations. ISR configurations are specified in Table 1.
At Resolute, there is a grating lobe near the radar vertical, so a beam off but close to vertical was selected instead of the vertical beam. The 75° elev., 26° azi. beam was chosen over the 85° elev., 26° azi. beam as the former has operated since initial deployment.
UVI-derived precipitation enhanced densities are compared with electron density measurements from four high-latitude ISRs, shown in Figure 1. Results are presented separately for auroral region and polar cap locations. ISR-SSUSI/GUVI conjunction events were considered when an ISR beam listed in Table 1 falls within one or more SSUSI/GUVI grid elements in the E-region or lower F-region (95-250 km), and when the time tags of SSUSI/GUVI and ISR measurements are within 7.5 min. For each such conjunction, SSU-SI/GUVI data were averaged over grid elements intersected by the ISR beam at 95-250 km altitude. The number of SSUSI/GUVI grid elements involved in each conjunction varied between 1 and 4. A number of selection criteria for SSUSI/GUVI grid elements during ISR conjunctions were tested, which had negligible impact on results.
The Fang-2010 parameterization provides ionosphere ionization rates q mono (E, h) at altitude h for electrons of energy E, and is based on solutions to Boltzmann transport equations, which describe where precipitating electrons deposit their energy in a neutral atmosphere. This parameterization has its heritage in a parameterization for auroral electron impact ionization proposed by Roble and Ridley (1987) and refined by Lummerzheim (1992). Inputs to the Fang-2010 scheme are electron precipitation energy, energy flux, and neutral atmospheric composition and temperature. In this study, altitude profiles of neutral atmosphere composition, density, and temperature data are from the empirical NRLMSISE-00 atmosphere model (Picone et al., 2002). The total population of precipitating electrons is specified based on SSUSI/GUVI E 0 and Q 0 data and the assumption of a particular distribution function to specify the shape of the energy spectrum for precipitating electrons. For model validation in this manuscript, we assume a Maxwellian distribution function. To investigate potential future improvements in implementation of the precipitation scheme, we also explore various spectral distribution functions for each ISR-UVI conjunction. Maxwellian, kappa, and Gaussian distributions are considered, which are the spectral shapes that best represent high latitude electron precipitation (Khazanov et al., 2014;Kletzing et al., 2003;Newell et al., 2009 where κ is a dimensionless parameter that characterizes the shape of the high-energy tail of the kappa distribution (κ = 3 is used in this work), and σ is the width of the Gaussian spectrum. Maxwell and kappa distributions are often used to characterize the electron precipitation associated with diffuse aurora, and are equivalent when E   . Gaussian shapes are often associated with monoenergetic-type electron precipitation and discrete auroral arcs.
The total ionization rate (q tot ) at height h is calculated by integrating monoenergetic ionization rates over all energies: A total of 3,000 logarithmically space energy bins are used in the integration, with bins progressively narrowing at lower altitudes. This total ionization rate can be related to the ionosphere electron density (N e ) via the continuity equation: where q 0 is the background ionization rate, α is the effective electron recombination rate in the ionosphere, and E v  is the bulk ionosphere plasma velocity. We assume a steady state ionosphere and no significant plasma transport over our time scales of interest, thus the precipitation-enhanced ionosphere density is: where N E-CHAIM is the background ionosphere density of E-CHAIM. Assumptions made in arriving at Equation 6 are discussed in Section 5. The additional ionization that results from the energy deposition of precipitating electrons combined with the "background" E-CHAIM densities produce a complete precipitation-enhanced electron density profile. This approach is similar in concept to that employed by Zhang et al. (2010) in their attempt to merge UVI-inferred NmE with that from the IRI. Effective recombination rates are from the empirical relationship of Gledhill (1986), which is based on 18 different data sources for electron density measurements and ionization rates. Given the limited data this relationship is based on, and the uncertainties associated with estimating ionization rates based on particle flux measurements of rockets and satellites, there is substantial uncertainty in the recombination rates, which is addressed in Section 4. Furthermore, this relationship is valid only between 50 and 150 km. In calculating precipitation-enhanced densities, we have included a smooth transition in the recombination rates above 150 km in order to suppress ionization at higher altitudes. Thus the precipitation scheme presented in this paper primarily modifies E-CHAIM densities below ∼200 km altitude.
Four examples of precipitation-enhanced densities (colored dashed lines) calculated for ISR-UVI conjunctions are shown in Figure 2, calculated for each spectral distribution function. Corresponding densities of non-precipitation E-CHAIM (dotted black lines) and ISR measurements (solid black lines) are also shown. Without the addition of the precipitation component, E-CHAIM underestimates densities below the F-region peak by up to three orders of magnitude, a common occurrence in the auroral region.
A total of 29,038 ISR-UVI conjunctions occurred from 2005 to 2019. Figure 3 shows the number of UVI observations binned according to E 0 or Q 0 (bins of 1 keV or 1 erg/cm 2 /s) and MLT (bins of 1 h) for auroral (a-f) and polar cap (g-l) ISRs, with number of observations in each bin indicated by color. Plots are organized horizontally according to auroral activity level, based on auroral electrojet (AE) indices taken from the OMNI database (https://cdaweb.gsfc.nasa.gov/index.html/).
Black dots are average E 0 or Q 0 for each 1 MLT bin. The bulk of SSUSI observations are from the morning and afternoon/evening due to the sun-synchronous DMSP orbits, and thus conjunctions are more concentrated in these MLT sectors. GUVI observations include all MLT sectors. E 0 or Q 0 for auroral region conjunctions generally increase away from local noon and with auroral activity level, where 49% of events for AE < 250 nT had no evident precipitation (Q 0 = 0.0 erg/cm 2 /s), and 15% of events for AE > 500 nT had no evident precipitation. As expected, electron precipitation is less common and less intense at Resolute in the polar cap, and thus instances of enhanced E-region ionization are relatively infrequent. At Resolute, E 0 and Q 0 are generally larger during quiet auroral periods, with 65% of Resolute conjunctions during AE < 250 nT having no evident precipitation compared to 89% when AE > 500 nT. The use of a polar cap index as opposed to AE index at Resolute had negligible impact on results.

Comparison of Precipitation-Enhanced Profiles With ISR Measurements
For results presented in Figures 4-7 As shown in Figure 4, auroral region E-CHAIM densities without precipitation enhancement tend to underestimate those of ISR measurements below ∼250 km altitude. These differences increase with AE index, 10.1029/2021SW002779 7 of 22 with an average difference of ∼1.2e11 ele/m 3 at ∼110 km when AE > 500 nT (Figure 4g). Precipitation-enhanced densities eliminate the bulk of this systematic underestimation, with average differences from ISR measurements significantly closer to zero. Precipitation densities have a tendency to overshoot those of ISR measurements in some cases, particularly in the E-region when AE > 500 nT, with a ∼2e10 ele/m 3 average overestimate at 100 km. RMS deviations in Figure 4 indicate a clear improvement in representation of ionosphere densities below ∼200 km with the precipitation scheme applied. Improvement is largest at ∼110-115 km altitude and increases with AE index. Possible reasons for these observed trends are discussed in Section 5.
Improvements with the addition of the precipitation component are more modest in the polar cap (Resolute), as shown in Figure 5. Note, however, that E-CHAIM RMS deviations are significantly smaller compared with auroral RMS in Figure 4. Below 200 km altitude, differences between ISR measurements and models are <4e10 ele/m 3 , on average, with a tendency for underestimation of ISR densities mainly in the  For all ISR-UVI auroral region conjunctions, Figures 6 and 7 show normalized histograms of the differences between log 10 (ISR N e ) and log 10 (E-CHAIM N e ) at 110 km altitude for 06:00-18:00 MLT (dayside) and 18:00- In Figures 6 and 7, OOM deviations from ISR measurements are largest and most common during the winter seasons, in the night sector, and increase with AE index. Without the precipitation component, E-CHAIM underestimates ISR measurements at 110 km by more than 1 OOM more than 60% of the time during daytime winter (Figures 6a-6c) and more than 90% of the time during nighttime winter (Figures 7a-7c). The most significant improvements during winter with addition of the precipitation component are during high AE intervals, with only 13% of events during daytime and 9% of events during nighttime resulting in differences larger than 1 OOM when AE > 500 nT.
During AE < 250 nT intervals in winter, a significant portion of E-region enhancements are not accounted for by SSUSI/GUVI observations, with a small leftward shift in the red distribution shown in Figure 6a, and a bi-modal type distribution shown in red in Figure 7a. These events involve enhancements in the lower ionosphere observed in ISR measurements, but little to no LBH emissions observed by SSUSI or GUVI. During equinox, E-CHAIM underestimates of E-region density are less common during daytime when less than 15% of events have OOM differences, and more common during night when more than 50% of events have OOM differences. The precipitation scheme provides improvement in most of these events, resulting in less than 3% with OOM differences during day, and less than 19% (6%) during night when AE < 250 nT (>500 nT). There are no OOM differences between E-CHAIM and ISR measurements during summer daytime (Figures 6g-6i), and few (<7%) OOM E-CHAIM underestimates of ISR measurements during summer nighttime (Figures 7g-7i), which are all accounted for by GUVI/SSUSI observations. In the Summer months, solar EUV is the dominant ionization mechanism at high latitudes, and ionization due to energetic particle precipitation may play a lesser role. Possible implications of these observations are discussed in Section 5.
We have also tested the accuracy of UVI-based precipitation enhanced densities by taking best-fits of all ISR measurements to infer the ideal input E 0 and Q 0 , and comparing with SSUSI/GUVI measurements. "Ideal" input E 0 and Q 0 refer to the inputs to the precipitation scheme that best reproduce ISR observations. This procedure involves iterations through input E 0 values of 0.0-20.0 keV and Q 0 values of 0.0-100.0 erg/cm 2 /s. E-CHAIM is used as the background ionosphere density, as in Equation 6. A precipitation enhanced density is calculated for each iteration, along with a least-squares-fit to ISR densities at altitudes of 95-140 km. The ideal input E 0 and Q 0 are based on the iteration that results in the best fit to ISR measurements. The bulk of conjunctions at all sites show E 0 and Q 0 differences concentrated within ±5 keV and ±5 erg/ cm 2 /s, with a larger portion of auroral region UVI data deviating from ideal ISR values during high AE intervals (Figures 8c and 8f). It is noted that low energy and flux events are more common during low AE intervals (see Figure 3), and that deviations from ideal ISR E 0 and Q 0 tend to be larger for higher energy and flux events. Thus larger differences are expected during high AE intervals. In the morning sector in the auroral region, there are a significant number of events where UVI E 0 is less than ideal, particularly during quiet auroral periods (Figure 8a). These events are in large part associated with the OOM winter underestimates of ISR densities by the precipitation scheme during quiet times in Figures 6a and 7a. A smaller number of events resulted in larger than ideal UVI E 0 values in the morning sector, while UVI E 0 data in the afternoon/evening sector was generally closer to ideal for all auroral activity levels. The UVI Q 0 data generally preformed quite well in the auroral region (Figures 8d-8f) compared with the UVI E 0 data,  with a tendency for UVI Q 0 to overshoot the ideal ISR values in both the morning and afternoon/evening sectors. Notably in the polar cap, there is a tendency for UVI Q 0 values to be less than ideal (Figures 8j-8l), consistent with the underestimation of ISR densities in the lower ionosphere shown in Figure 5 by both E-CHAIM and the precipitation enhanced densities.
For potential future improvements in implementation of the precipitation scheme, we also explore ideal spectral distribution functions to apply in Equation 4. Again we refer to an "ideal" spectral distribution as the one which results in the best fit to ISR measurements. For all ISR-UVI conjunctions, we again iterate through E 0 and Q 0 as described above, but also add an iteration through Maxwellian, Kappa, and Gaussian distribution functions (Equations 1-3). The ideal spectral distributions is based on the iteration that results in the best fit to ISR measurements. Figure 9 shows the ideal energy spectra according to ISR best fits. Note that results shown only include events with nonzero ideal E 0 and Q 0 values. Results for auroral (a-c) and polar cap (d-f) events are organized horizontally according to AE index, with the percentage of events corresponding to each spectral shape plotted in bins of 2 MLT for auroral events and 4 MLT for polar cap events. A Maxwellian or kappa distribution is ideal in most cases in both polar cap and auroral regions. In the auroral region, the Kappa distribution is more often ideal in the morning and early afternoon sector, while the Maxwellian is the preferred spectral shape in the late afternoon and evening sectors. These local time trends become more pronounced as auroral activity increases. Cases where a Gaussian distribution is ideal also increases with auroral activity, where up to 40% of events in the 14:00-16:00 MLT sector are best characterized by a Gaussian distribution when AE > 500 nT (Figure 9c). Newell et al. (2009) showed an increase in the occurrence of monoenergetic-type aurora in the afternoon sector during high solar wind-magnetosphere coupling intervals, based on DMSP SSJ particle data. This increase in discrete auroral occurrence Figure 9. For auroral (a-c) and polar cap (d-f) regions, the percentage of events that resulted in incoherent scatter radar (ISR) best fits for each test energy spectrum shape. AE, auroral electrojet. may contribute to the increased occurrence of Gaussian best fits in this sector. Kappa distributions are most often ideal in the polar cap, particularly during active auroral periods, with the exception of the early morning sector (Figure 9f). Gaussian distributions are less often ideal in the polar cap, with up to 10% occurrence of such cases in the dayside when AE < 250 nT (Figure 9d).

Error Analysis
There are a number of sources of error associated with the calculation of precipitation-enhanced densities. This analysis addresses whether errors inherent to the precipitation scheme may account for differences between ISR measurements and precipitation-enhanced densities. We also examine the sensitivity of precipitation-enhanced densities to uncertainties of each input parameter of the precipitation scheme, which may be used to improve the implementation of the precipitation scheme in E-CHAIM in the future.
Derivation of GUVI and SSUSI E 0 and Q 0 data involve a number of steps including instrument calibration, subtraction of dayglow emissions, removal of MeV noise, and subtraction of precipitating proton contributions (Germany et al., 1990;Paxton et al., 1992;Strickland et al., 1995). Based on these calibration and modeling steps, Germany et al. (1997) estimated a 72% 1-sigma uncertainty level in UVI E 0 and Q 0 data. We use this 72% uncertainty level in our error analysis. For comparison to the Germany et al. uncertainty, we have also carried out comparisons of SUSSI E 0 and Q 0 data with corresponding values derived from DMSP Special Sensor J (SSJ) particle data (Redmon et al., 2017), which provides precipitating electron flux in 20 energy bands between 30 eV and 30 keV. Comparisons were done for all ISR-UVI conjunctions where the spacecraft magnetically mapped to within 100 km of the respective ISR station, and where SSJ data were available. Based on these comparisons we found 1-sigma uncertainty levels of 68% for UVI E 0 values and 79% for UVI Q 0 , where discrepancies between SSJ and UVI values increased with energy and flux. These comparisons roughly agree with the uncertainty levels of Germany et al. (1997), although E 0 and Q 0 values derived from SSJ data also inherit some uncertainty due to the 30 keV upper limit in observable energy.
Mass density and neutral temperatures of the NRLMSISE-00 model are used as inputs to the Fang-2010 parameterization for atmospheric ionization rates. Based on extensive model comparisons with measurements of the neutral atmosphere, Picone et al. (2002) found uncertainty ranges of −8.35%-16.21% and −30.85-1.48 K for NRLMSISE-00 density and temperature, respectively. Fang et al. (2010) indicated that monoenergetic ionization rates of the Fang-2010 parameterization scheme contained 5% uncertainty, at most, based on comparisons with model runs. Although some of this maximum 5% may be attributed to atmosphere inputs, we test the sensitivity of precipitation-enhanced profiles to NRLMSISE-00 uncertainties and the 5% Fang-2010 uncertainty separately.
Sensitivity of UVI-derived densities to uncertainty in effective recombination rates is estimated by testing the recombination rates of various sources. In addition to the Gledhill (1986) rates, we also test the empirical relationship of Vickrey et al. (1982), which is based on ISR and rocket sounding data, and the electron temperature dependent expressions for dissociative recombination rates of Schunk and Nagy (2009)  , and NO + recombination rates. We obtain ionosphere electron temperatures from the IRI-2016 (Bilitza et al., 2017).
The choice of distribution function to construct precipitating electron populations also impacts final precipitation-enhanced density profiles. A Maxwellian function (Equation 1) was used for results presented in Section 4. The sensitivity of calculated densities to choice of distribution function is evaluated by applying Kappa and Gaussian distributions (Equations 2 and 3) to the precipitation scheme, and comparing with densities calculated using the Maxwellian distribution. Table 2 summarizes the input parameters to the precipitation scheme and associated uncertainties.
The sensitivity of the precipitation scheme to uncertainties in input parameters has been tested for all ISR-UVI conjunctions. Figure 10 shows the average variability in precipitation enhanced densities associated with the uncertainty range of each input parameter (color coded), or associated with the various choices of input option in the case of recombination rates and energy spectrum shape. The cumulative uncertainty range (maximum possible variability in calculated density) is shown in black. Uncertainties are shown at 8 different altitudes (centered on the total uncertainty ranges in black), and for four different Q 0 ranges based on the SSUSI/GUVI Q 0 data. Dashed gray line contours indicate the percentage of ISR density-precipitation-enhanced density differences that fall within each respective contour pair. For example, the two 98% contours in each panel enclose the range of density differences observed in 98% of the ISR-UVI conjunctions. So at 120 km altitude in Figure 10a, 98% of the time the difference between ISR and precipitation-enhanced densities is between −1.0e11 m −3 and 1.1e11 m −3 . These contours are included as a guide to indicate the percentage of density differences that fall within the total uncertainty ranges. Positive ΔN e values indicate an increase in the precipitation enhanced density when a particular input parameter is varied, as well as an underestimate of ISR measurements by precipitation enhanced densities in the case of gray contours.
Sensitivity of precipitation enhanced densities to variations in input parameters generally increases with SSUSI/GUVI Q 0 , given that the contribution of the precipitation component to the overall density will be larger when there is more precipitating particle flux. For lowest flux events in Figure 10a, sensitivity to each input parameter is relatively small, with variations in UVI Q 0 and E 0 data having the largest contribution depending on altitude. Total uncertainty ranges are within ±1e11 m −3 , which is relatively small compared to larger flux situations, but still a large uncertainty range for ionosphere density. Seventy-five percent of the ISR-UVI-derived density differences fall within the total uncertainty bounds at most altitudes, indicating that uncertainties of the precipitation scheme in Table 1 can account for the bulk of the differences observed in ISR measurements and UVI-derived densities in Figures 4-7. An exception is at higher altitudes >200 km, where the precipitation scheme uncertainty accounts for <50% of observed density differences, and where errors in the E-CHAIM model itself are likely more dominant.
In higher flux situations (Figures 10b-10d), precipitation enhanced densities are most sensitive to variations in Q 0 , E 0 , and choice of energy distribution function, with smaller increases in the uncertainty contributions of other inputs. Largest uncertainties due to recombination rates, atmosphere mass density, atmosphere temperature and the Fang-2010 ionization rates are ∼7e10 m −3 at 115 km, ∼4e10 m −3 at 100 km, ∼9e10 m −3 at 100 km, and ∼1e10 m −3 at 100 km, respectively, when Q 0 > 10 erg/cm 2 /s. UVI E 0 is the dominant uncertainty source at higher altitudes >130 km, with a primarily positive uncertainty range of up to 2.5e11 m −3 for Q 0 > 10 erg/cm 2 /s events. Uncertainty due to UVI E 0 is primarily negative at E-region altitudes, up to −4e11 m −3 . Uncertainties in UVI Q 0 becomes increasingly important toward lower F and E-region altitudes, as large as ±2.5e11 m −3 at 100 km, and choice of spectral shape is most impactful on E-region densities, with uncertainties as large as ±2.5e11 m −3 . Total uncertainty in precipitation enhanced densities is as large as ±6.0e11 m −3 at E-region altitudes when Q 0 > 10 erg/cm 2 /s. For the most part, 75% and often 90% contours fall within the total uncertainty levels in Figures 10b-10d, again with the exception of higher altitudes >200 km. Figure 11 shows the average variability of precipitation enhanced densities, but as a percentage of the initial precipitation-enhanced density (before any input parameter modification). These are plotted in a single panel since, as density increases with input precipitation flux, the percent variability remains largely consistent for all Q 0 levels. Again, Figure 11, shows the dominant sources of error to be UVI Q 0 and E 0 at most altitudes, with choice of energy spectrum increasingly important at lower altitudes. Recombination rates Gledhill (1986), Vickrey et al. (1982), Sheehan and St. Maurice (2004), Schunk and Nagy (2009) Distribution function Maxwellian, Kappa, Gaussian (Equations 1-3) Note. GUVI, Global Ultraviolet Imager; SSUSI, Special Sensor Ultraviolet Spectrographic Imager.  Figure 12 presents sensitivity of peak E-region density (NmE) and altitude of peak density (hmE) of precipitation enhanced profiles to variations in precipitation scheme parameters. A comparison between ISR NmE and hmE values and those derived from the precipitation scheme showed no significant correlation (Figure 13), which is not surprising given the uncertainty levels involved. Dashed gray lines show contours below which the respective percentages of NmE or hmE differences (ISR minus precipitation scheme) fall. to the corresponding power law. Uncertainties in Q 0 and spectral shape are the largest factors in NmE uncertainties, approaching 7e11 m −3 and 4.5e11 m −3 at UVI Q 0 = 30 erg/cm 2 /s, respectively. Note that the bulk of events involve UVI Q 0 values less than 10 erg/cm 2 /s, corresponding to cumulative NmE uncertainties of up to ∼8e11 m −3 , however more extreme UVI Q 0 events result in NmE uncertainties surpassing 1.5e12 m −3 . The bulk of cumulative percent NmE uncertainties (relative to NmE without modification of input parameters) are in the range of 60%-95%. Similar to Knight et al. (2018), who compared NmE derived from SUSSI LBH measurements with NmE of high latitude digisonde measurements, precipitation NmE and ISR NmE show modest agreement in Figure 12. They are not statistically correlated, however, with a Pearson correlation coefficient of 0.52. Figure 12b is the hmE uncertainty as a function of SSUSI/GUVI E 0 , which is the primary factor in determining the altitude of the enhanced ionization layer. Small dots show results for each individual ISR-UVI conjunctions and large dots are binned averages. Uncertainty in UVI E 0 inputs are the dominant factor in hmE uncertainty, which increases with UVI E 0 at lower E 0 values up to ∼22 km at 7 keV, and gradually decreases with E 0 for higher energies as the ionization layer narrows in the lower ionosphere. Uncertainties due to spectral shape are also significant at lower energies when the precipitation layer is at higher altitudes, peaking at 11 km at 3 keV and decreasing gradually with energy. Cumulative uncertainties follow roughly the same pattern as those due to E 0 uncertainties, peaking at ∼26 km at 7 keV. Likely due to the large hmE uncertainties of precipitation-enhanced densities, there is no correlation between UVI and ISR hmE in Figure 13. Results of Knight et al. (2018) also showed no agreement between SSUSI LBH hmE and digisonde hmE values.

Discussion and Ongoing Work
As demonstrated in Section 3, E-CHAIM's auroral region performance below 200 km altitude is substantially improved with the addition of a SSUSI/GUVI-based precipitation component. Improvements are often a few orders of magnitude during winter and equinox seasons. However, there remains substantial room for further improvement given lingering OOM underestimates of ISR measurements by precipitation-enhanced densities during low AE periods, some tendency for precipitation-enhanced densities to overshoot those of ISR measurements, particularly in the E-region, and an inability to accurately capture NmE and hmE of enhanced E-layers. Some of these deficiencies may be a result of the large uncertainties associated with the precipitation scheme.
As demonstrated in Section 4, the primary error sources for precipitation-enhanced densities are uncertainties in SUSSI/GUVI E 0 and Q 0 data and the choice of distribution function for precipitation energy spectrum. Uncertainties in the E-CHAIM model used for the background ionization of the precipitation-enhanced density will also contribute to deviations from ISR measurements and could be a factor in some of the lower ionosphere discrepancies observed during low AE intervals when UVI Q 0 tends to be low. E-CHAIM errors will play less of a role in high Q 0 situations when the precipitation component dominates at low altitudes <200 km.
In arriving at Equation 6 from the continuity equation for ionosphere density, it was necessary to neglect time dependence and assume a steady state. This is a necessary assumption since E-CHAIM is an empirical model that generates an instantaneous 3D representation of ionospheric electron density and as such does not accommodate time dependence. As discussed in Semeter and Kamalabadi (2005), the steady-state assumption is valid when the response time of the ionosphere is smaller than the time scales over which significant variability in electron precipitation is observed. Ionospheric response times can be <1 second up Figure 11. Sensitivity of precipitation enhanced densities (in percent change in N e ) to uncertainties associated with each input parameter (color coded), along with total uncertainty in final precipitation enhanced densities (in black). Sensitivity ranges at each altitude are averaged over all incoherent scatter radar-ultraviolet image conjunctions. to 10s of seconds depending on the ionosphere density (Figure 3 in Semeter & Kamalabadi, 2005), and thus there will be cases where the precipitation flux varies on time scales smaller than the ionospheric response time. In these cases, the steady state assumption will inevitability produce errors in calculated precipitation-enhanced densities.

% Uncertainty in Precipitation Enhanced
An additional source of error may be the precipitation of energetic protons into the auroral ionosphere, the effects of which are removed from SSUSI and GUVI E 0 and Q 0 data products. According to Newell et al. (2009), DMSP particle sensors have observed significant auroral ion precipitation across late afternoon/evening and early morning sectors at auroral ISR latitudes, which may contribute to some of the precipitation scheme underestimation of ISR densities. In addition, Knight et al. (2018) predicted that  satellite LBH-derived NmE may be biased by up to 20% in the presence of proton precipitation (if assuming only electron precipitation), however Knight (2019) found no such bias when comparing LBH-derived NmE with NmE of ionosonde radars. To potentially account for ion precipitation contributions and as an aid to electron precipitation contributions, we plan on testing the OVATION-Prime Model (Newell et al., 2014), an empirical model for auroral ion and electron precipitation characteristics based on DMSP SSJ data, to support UVI inputs to the precipitation scheme for E-CHAIM. Statistical comparison of DMSP SSJ particle data and SSUSI data may also provide an additional constraint for precipitation scheme inputs. We are also working on a method to integrate optimal spectral shape into the precipitation scheme. This may involve a climatological model to describe ideal spectrum based on AE index and local time, as in Figure 9.

Conclusions
We have used satellite-based UVI imager data (DMSP SSUSI and TIMED GUVI) and the Fang-2010 parameterization of atmospheric ionization rates to develop a precipitation enhanced density component for the E-CHAIM model at high latitudes. Precipitation enhanced densities were tested by comparison with ISR ionosphere density measurements during conjunctions between ISR and satellite UVI fields of view. Twenty-nine thousand and thirty-eight such conjunctions from 2005 to 2019 have revealed substantial improvements in E-CHAIM's representation of auroral region densities at altitudes of 90-200 km with inclusion of the precipitation component, where the RMS difference between E-CHAIM and ISR measurements decreased by up to 2.9 × 10 10 ele/m 3 . Largest improvements were observed in the E-region ionosphere. Minor improvements were also observed in the polar cap after inclusion of the precipitation component, where the RMS difference between E-CHAIM and ISR measurements decreased by up to 2.6 × 10 9 ele/m 3 . Improvements were most substantial, often multiple orders of magnitude, during active auroral periods, and during the winter season. E-CHAIM precipitation enhanced densities show best agreement with ISR measurements in the afternoon-evening sector, with a tendency to underestimate ISR densities in the morning sector. These morning sector underestimations are characterized by enhanced E-region densities in ISR measurements, but no substantial Q 0 in the corresponding UVI data, and mainly occurred during quiet auroral intervals.
To determine the main potential sources of error in the precipitation component, the sensitivity of precipitation-enhanced densities to uncertainties in input parameters was also tested. Precipitation enhanced densities were most sensitive to uncertainties associated with UVI E 0 , UVI Q 0 , and the choice of energy distribution function for precipitating electrons. Estimated total uncertainties in precipitation-enhanced densities were less than 1 × 10 11 ele/m 3 for Q 0 < 2 erg/cm 2 /s and as large as 6 × 10 11 ele/m 3 for Q 0 > 10 erg/ cm 2 /s, and generally increased with Q 0 and with decreasing altitude. Methods of applying the empirical Ovation-PRIME model and DMSP SSJ particle data to constrain E 0 and Q 0 inputs are being investigated, while a climatological model for ideal energy distribution function is also being developed. The precipitation scheme has been implemented into the E-CHAIM model as part of the E-CHAIM v3.0 software update, and is freely available at https://chain-new.chain-project.net/index.php/chaim/e-chaim (with the creation of a free account). A paper describing this implementation is forthcoming.