The Arctic ionosphere exhibits highly variable electron density due to auroral precipitation, structured plasma convection, and large seasonal variability in daily photoionization . Accurate knowledge of electron density profiles is important for a wide range of space-weather applications and ionospheric research . Several measurement techniques allow continuous monitoring of the ionospheric electron density, including GNSS total electron content (TEC) e.g., and ionosondes . These methods are less accurate than incoherent scatter radar (ISR) measurements, which observe Thomson scatter from ionospheric electrons and allow estimation of electron density, plasma temperature, and ion velocity . However, ISRs provide significantly sparser coverage in time and space, compared to GNSS TEC and ionosonde measurements, often making continuous monitoring of electron density intractable.

Several methods have been developed to make use of ISR observations to facilitate the estimation of the ionospheric electron density. For example, and used a global network of ISRs to develop regional empirical electron-density models that successfully capture ionospheric climatology. They binned observations by altitude and time of day, then derived linear relationships between solar activity, geomagnetic activity, and electron density. The E-CHAIM model incorporates solar variability via the F10.7 cm flux and the Ionospheric Index (IG) . E-CHAIM uses information from ionosondes, ISRs, and radio-occultation experiments to generate an empirical model, providing improved plasma-density profiles in the auroral and polar regions compared with the International Reference Ionosphere (IRI) model .

Ionosondes measure the group delay of HF radio waves between a radar antenna and the point of reflection in the ionosphere across a range of frequencies e.g.,. Inferring the electron-density profile from these measurements is challenging because the inverse problem is nonlinear and ill-posed, as there are regions in the ionosphere that are not directly measured, such as the “valley region” between the E-region peak and the altitude where the F-region electron-density exceeds the peak E-region electron density, and the top-side ionosphere where the electron density decreases. Several methods have been developed to estimate the electron densities based on ionosonde measurements such as POLAN , ARTIST , NeXTYZ , Autoscala and the IGC method . These automated techniques perform well at mid-latitudes during conditions where the ionosphere is relatively unstructured, but are known to perform poorly during auroral precipitation, sporadic E and spread F conditions. Nevertheless, ionosonde measurements still contain information about the F-region scale height variation, the electron-density in the valley region between the E-region peak and the F-region, the presence of auroral precipitation in the form of complex E-region ionogram traces, or in the form of weak or non-existent traces indicating a presence of high E- and D-region ionization. This information is currently not used optimally as there is no simple analytic relationship that can be used.

Machine learning (ML) techniques can uncover complex relationships within data and have greatly impacted scientific research the last decade. In space physics, ML has been applied to a wide range of tasks , notably to classify auroral images , predict ground-induced currents , forecast substorm onset , predict local and global geomagnetic activity , model space-weather drivers , scale ionograms , perform time-series prediction of total electron content , predict electron-density distributions , and classify plasma regions in near-Earth space .

In this study, we present a novel approach for estimating electron-density profiles above the EISCAT Tromsø ISR facility. The goal is to find an empirical relationship between ISR-measured electron-density profiles and our input data: geophysical parameters and ionograms. We employ deep learning (DL) to approximate a mapping from 25 readily accessible geophysical parameters and/or ionogram images to the corresponding ISR measurements of electron density profile. This approach circumvents the need for algorithmic true-height inversion of ionograms and may capture more subtle information contained within ionograms when estimating electron density. Convolutional neural networks have already been shown to be powerful tools for automatic ionogram scaling e.g.,. Here, we adopt a similar approach for extracting features from ionograms, but instead of estimating scaling parameters, we directly predict the electron-density profile from each ionogram.

The remainder of this paper is organized as follows: Sect.  describes the dataset and preprocessing steps. Section  outlines the deep neural network architecture and training procedure. Section  presents our results and benchmarks them against established models. Section  discusses the implications of these findings and proposes directions for future work. Finally, in Sect.  we draw some conclusions from this work.

In this study, we used three distinct data types acquired from multiple sources:

Electron-density profiles, ne(z), obtained from the EISCAT UHF incoherent-scatter radar at Ramfjordmoen, Tromsø

The EISCAT UHF profiles served as the “ground truth” for supervised training of our deep neural network (DNN). For each day with available EISCAT UHF measurements, we extracted the corresponding ionograms and geophysical parameters. Figure  shows the resulting data availability: between 2019 and 2022, 363 of 1452 d (25 %) yielded suitable data, providing 9040 of 139 392 possible hourly profiles (6.5 %), since many days contained data from experiments with partial daily coverage. The 2019–2022 data was selected due to the availability of simultaneous Digisonde and EISCAT data. Note that coverage is biased away from summer months due to reduced EISCAT usage during summer. This results in a dataset that is not balanced across all seasons. Furthermore, the training dataset is dominated by solar minimum and rising-phase conditions. To partially address this issue, we reserved data from the previous solar maximum and data from 2018 as an independent test set, containing 1177 samples. This enables evaluation of the model under contrasting solar cycle conditions. In future work, we aim to curate a more balanced dataset across both seasonal and solar-cycle variations to further improve model generalization. Our neural-network outputs were evaluated against ionogram-derived electron-density estimates from ARTIST 4.5 and E-CHAIM's ne(z) model predictions .

This section presents the multi-modal neural network designed to estimate the electron-density profiles, ne(z), from ionograms and geophysical parameters. We describe the machine-learning and pattern-recognition techniques employed and detail the network architecture, which processes both scalar geophysical inputs and ionogram images.

The global performance of KIAN-Net was evaluated by comparing its predictions ne(zi) with EISCAT UHF measurements from selected days in the years 2012, 2013, and 2018. The test dataset was entirely disjoint from the training dataset, using different years of data for training and testing. This approach ensures a fair evaluation of the model's ability to generalize to unseen geophysical conditions and solar cycle phases.

To determine how KIAN-Net's estimates of ne(zi) compare with existing methods, we included results from ARTIST 4.5 and E-CHAIM in our analysis. The E-CHAIM model was run with both the “storm” and “precip” flags enabled, meaning that global and auroral-zone information from the Ap, AE, and DST indices was used to estimate the electron density profile . We also generated estimates using each network component separately (Iono-CNN and Geo-DMLP) to assess their individual contributions and determine the relative influence of each input on the overall performance. To quantify goodness of fit, we used the testing dataset to compute the R2 score, the root-mean-square error (RMSE), the Pearson correlation coefficient rp, and the distance correlation rd. A summary of these performance metrics are presented in Table .

To illustrate model performances and further analyze the model outputs, we examine a four-day interval (13–17 January 2012) that captures full diurnal cycles and a representative range of geophysical activity. Results for this period are presented in Fig. , with corresponding relative errors in Fig. .

Visual inspection of Figs.  and shows that all deep-learning models successfully approximate the electron-density profiles and agree well with the EISCAT UHF measurements. By direct comparison, KIAN-Net, Iono-CNN, and Geo-DMLP outperform ARTIST 4.5 and E-CHAIM on the test dataset, with superior quantitative metrics, as shown in Table . Overall, KIAN-Net, Iono-CNN, and Geo-DMLP achieve R2 scores of 0.74, 0.66, and 0.62, respectively, while ARTIST 4.5 and E-CHAIM obtain R2 of -0.08 and 0.34. Figure  also highlights that all models, including the deep learning models, struggle to estimate nighttime electron densities during weak auroral precipitation. There are several reasons for this. First, during low-density periods in the F region, such as under the ionospheric trough, ionograms often contain limited information about the electron density profile, particularly above auroral heights. The trough is typically associated with strong horizontal gradients and tilts in the ionosphere, which inhibit vertical-incidence signals from returning to the ionosonde receiver . This limitation can be further enhanced by auroral absorption in the D-region, which reduces the signal-to-noise ratio of the ionosonde returns. Second, there is also a differences in sampling geometry, the EISCAT UHF radar provides altitude-resolved measurements within a narrow ∼ 1° field of view, whereas the Digisonde has a broader vertical field of view ∼ 30°. This difference, combined with the ionosonde's reduced sensitivity during trough and absorption conditions, makes direct comparisons between EISCAT profiles and ionogram-based estimates particularly challenging in the nighttime auroral region.

Figure  presents the time-averaged performance metrics as a function of altitude. The metrics: R2, RMSE, Pearson correlation (rp), and distance correlation (rd) are systematically better for the DL models at all altitudes below 350 km. In this region, ARTIST 4.5 often failed and was replaced by a constant ne = 1 × 10⁸ m-3 to enable comparison with ISR observations. The performance gap is most pronounced in the E-region (100–160 km), where the KIAN-Net and Iono-CNN models achieve R2≳ 0.4 and RMSE≲ 0.2, whereas ARTIST 4.5 and E-CHAIM yield R2≪ 0 and RMSE≳ 0.2. This is further illustrated by the relative-error plots in Fig. d and e, which show that densities between 90 and 160 km are generally underestimated (blue shading). Correlation metrics also favour the DL models, with both rp and rd typically exceeding 0.90, and reaching ≥ 0.95 in the upper F-region for the KIAN-Net and Iono-CNN models, while ARTIST 4.5 and E-CHAIM exhibit correlations generally below 0.8.

The estimates produced by KIAN-Net closely match those of Iono-CNN, indicating that the ionogram inputs dominate over the geophysical parameters used by Geo-DMLP. This is expected, since the ionogram traces contain direct information about the electron densities, whereas the relationship between electron densities and geophysical parameters is more indirect. Nevertheless, Geo-DMLP captures both the daily variation of the F-region and the auroral variation of the E-region ne relatively well. At F-region heights, ne is governed by the balance between recombination and photoionization, which to first order depends on EUV flux (captured by F10.7) and the solar zenith angle. For the test days, Geo-DMLP tends to overestimate the duration of the F-region, predicting higher ne during both sunrise and sunset. We attribute this to significant day-to-day fluctuations of ne due to variable ionospheric horizontal convection during these periods. Remarkably, Geo-DMLP also predicts E-region enhancements due to auroral precipitation, despite its limited information about the local ionosphere. The geophysical parameters most sensitive to auroral activity are the local magnetic-field fluctuations driven by the auroral electrojet. However, these fluctuations arise from currents spanning a much larger region than the localized E-region echoes detected by the ionogram. To further assess their role, we performed a preliminary absolute gradient impact analysis of the geophysical inputs. This analysis indicates that solar zenith angle and F10.7 contribute most strongly, followed by AE and local magnetic-field variations, consistent with their expected influence on F-region ionization and auroral precipitation. Although ionogram data dominate model performance, these results suggest that the geophysical parameters provide complementary and physically meaningful information. Further, our results show that the DL-models successfully captured nighttime electron density profiles with both E and F-region peaks, as further discussed in Appendix .

ARTIST 4.5 systematically produced reasonable estimates of daytime bottom-side F-region densities. However, the quality of the topside densities is rather variable. This shortcoming stems from ARTIST's methodology, which derives an α-Chapman profile for the topside F-region peak using bottomside F-region densities. This approach is an oversimplification, especially during periods of high-energy deposition from the magnetosphere and loss of thermal equilibrium along the vertical column. During auroral activity, ARTIST 4.5 often fails to produce any ne(zi) estimates. When intense E-region ionization disrupts the ionosonde's ability to detect F-region echoes, ARTIST omits to make an electron density profile and instead scales the E-region as a sporadic E-layer.

In comparison, E-CHAIM, as an empirical mid- and high-latitude ionospheric model, generated continuous predictions throughout the test period. Using only the Ap, AE, and Dst indices as inputs, E-CHAIM does not respond to short-term or local variations, resulting in smoother ne(z) profiles. Consequently, E-CHAIM does not fully capture day-to-day local variations of F-region densities and the rapidly varying auroral E-region densities. Near the foF2 peak, where all models perform reasonably well, KIAN-Net and Iono-CNN remain slightly superior, with R2 scores typically above 0.95 and RMSE≈ 0.05. ARTIST 4.5 follows with R2≈ 0.75 and RMSE≈ 0.13, outperforming Geo-DMLP in this region. E-CHAIM shows weaker performance across most altitudes, except in the upper F-region (≥ 250 km), where its correlation coefficients reach ≳ 0.65.

There are several potential directions for future development of this method. First, incorporating additional EISCAT data from solar-maximum and summer conditions would balance the current dataset. Due to data availability, the considered dataset is weighted toward autumn, winter, and spring during the rising phase of the recent solar cycle. Dedicated summer campaigns should be conducted in the coming years to collect these missing observations. Second, extending this technique to include data from other ISR facilities, both across magnetic local time in the northern auroral zone (Sondre Strømfjord, Resolute Bay, Poker Flat, and EISCAT Svalbard) and at lower latitudes (Millstone Hill, Sanya, Arecibo, and Jicamarca), would broaden geographic and temporal coverage. For this task, it is not obvious if a single deep learning model should be trained with all available data to provide a global ionogram-inversion scheme, or if it is preferable with separate models for each IS-radar followed by an interpolation scheme, such as those used in and . Although KIAN-Net can operate using only ionograms or only geophysical parameters, we have not yet systematically evaluated how its performance degrades when one or more geophysical inputs are unavailable. Such “reduced-input” Geo-DMLP variants may effectively transition toward empirical models like E-CHAIM, this might make it possible to justify and make such models more responsive to geophysical conditions. Moreover, as computational resources increase, processing higher-resolution ionogram images with larger virtual-height ranges should further improve the quality of the estimates. Furthermore, E-CHAIM also includes an assimilative mode, A-CHAIM, which ingests ionosonde and GNSS-TEC data to adjust its output away from climatology, comparing A-CHAIM's assimilative performance with KIAN-Net would be of interest. In addition, incorporating further geophysical inputs into KIAN-Net, such as vertical TEC, the Polar Cap Index, and solar indices (e.g., F30 and MG II ), may improve its accuracy. Finally, because ionograms may contain information about other plasma parameters, training KIAN-Net to predict electron and ion temperature profiles could extend its utility beyond density estimation.

We have presented a multi-modal neural-network, named KIAN-Net, to estimate ionospheric electron-density profiles from both ionogram images and geophysical parameters. The model was trained to learn the mapping from 25 readily available geophysical inputs and ionogram images to simultaneous electron-density profiles measured by the EISCAT UHF incoherent scatter radar in Tromsø. Its two subnetworks, Iono-CNN and Geo-DMLP, extract complementary features from the ionograms and geophysical state parameters, respectively. KIAN-Net and its two subnetworks performs favorably compared to the industry-standard ionogram-inversion algorithm (ARTIST 4.5) and the state-of-the-art high-latitude empirical ionospheric model (E-CHAIM). Notably, Geo-DMLP, which is trained only on geophysical parameters, effectively captures high-latitude spatial and temporal variability, caused by dynamic auroral precipitation and complex plasma convection, suggesting its utility as a local ionospheric model for Tromsø.

In total, over 10 000 ionogram–geophysical-parameter sample pairs were used to train and evaluate KIAN-Net. On an independent test set spanning multiple years, KIAN-Net achieved an R2 of 0.74 against EISCAT observations, compared to R2 = -0.08 for ARTIST 4.5 and R2 = 0.34 for E-CHAIM. KIAN-Net also obtains RMSE≤ 0.17, Pearson correlation rp≥0.92, and distance correlation rd≥ 0.92. Detailed analysis shows that KIAN-Net provides robust and reliable electron density estimates (R2 > 0.5) across diverse ionospheric conditions, including periods with significant auroral activity. Future work includes expanding the network to different latitudes and longitudes where ISR data are available and training it to predict additional plasma parameters (e.g., electron and ion temperatures) from the input data, further expanding the capabilities of the model.