# A Novel Neural Network-Based Approach to Derive a Local Geomagnetic Baseline for Future Robust Characterization of Geomagnetic Indices at Mid-Latitude

Rungployphan Kieokaew, Veronika Haberle, Aurélie Marchaudon, Pierre-louis Blelly, Aude Chambodut

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## ► To cite this version:

Rungployphan Kieokaew, Veronika Haberle, Aurélie Marchaudon, Pierre-louis Blelly, Aude Chambodut. A Novel Neural Network-Based Approach to Derive a Local Geomagnetic Baseline for Future Robust Characterization of Geomagnetic Indices at Mid-Latitude. Space Weather: The International Journal of Research and Applications, 2025, 23, 10.1029/2024sw004192. [hal-05000893](https://hal.science/hal-05000893v1)

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Submitted on 21 Mar 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Space Weather®

RESEARCH ARTICLE

10.1029/2024SW004192

**Key Points:**

* We model daily quiet variation of geomagnetic field measured at Chambon-la-Forêt observatory using long short-term memory neural networks

* Our model robustly characterizes daily quiet sources regardless of solar activities and can be used for 1 hr, 1 day and 27 day forecasts

* Combined with extrapolation for above-diurnal variation, we propose an automated baseline for definition of geomagnetic indices

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

R. Kieokaew,
rkieokaew@irap.omp.eu

**Citation:**

Kieokaew, R., Haberle, V., Marchaudon, A., Blelly, P.-L., & Chambodut, A. (2025). A novel neural network-based approach to derive a local geomagnetic baseline for future robust characterization of geomagnetic indices at mid-latitude. *Space Weather*, 23, e2024SW004192. https://doi.org/10.1029/2024SW004192

Received 1 OCT 2024
Accepted 30 JAN 2025

**Author Contributions:**

**Conceptualization:**

Rungployphan Kieokaew,
Aurélie Marchaudon

**Data curation:** Veronika Haberle,
Aurélie Marchaudon, Aude Chambodut

**Formal analysis:**

Rungployphan Kieokaew, Pierre-Louis Blelly

**Funding acquisition:**

Aurélie Marchaudon, Pierre-Louis Blelly,
Aude Chambodut

**Investigation:** Rungployphan Kieokaew,
Aurélie Marchaudon

**Methodology:** Rungployphan Kieokaew,
Veronika Haberle

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

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# A Novel Neural Network-Based Approach to Derive a Local Geomagnetic Baseline for Future Robust Characterization of Geomagnetic Indices at Mid-Latitude

Rungployphan Kieokaew¹ ID, Veronika Haberle¹,² ID, Aurélie Marchaudon¹ ID, Pierre-Louis Blelly¹ ID, and Aude Chambodut³,⁴ ID

¹Institut de Recherche en Astrophysique et Planétologie, CNRS, CNES, Université de Toulouse, Toulouse, France, ²Conrad Observatory, GeoSphere Austria, Vienna, Austria, ³CNRS, ITES, Université de Strasbourg, Strasbourg, France, ⁴CNRS, EOST, Université de Strasbourg, Strasbourg, France

**Abstract** Geomagnetic indices derived from ground magnetic measurements characterize the intensity of solar-terrestrial interaction. Global magnetic indices derived from multiple magnetic observatories at mid-latitude have commonly been used for space weather operations. Yet, their temporal cadence is low and their intensity scale is crude. To derive a new generation of geomagnetic indices, it is desirable to establish a geomagnetic baseline that defines the quiet-level of activity without solar-driven perturbations. We present a new approach for deriving a baseline that represents the time-dependent quiet variations focusing on data from Chambon-la-Forêt, France. Using a filtering technique, the measurements are first decomposed into the above-diurnal (>24 hr) variation and the sum of 24, 12, 8, and 6 hr filters, called the daily variation. Using parameters that correlate with the ionospheric solar-quiet (Sq) currents, we predict the daily “quiet” variation that excludes the effects of solar-transient perturbations. Here, we train long short-term memory neural networks using at least 11 years of data at 1 hr cadence. This predicted daily quiet variation is combined with linear extrapolation of the secular trend associated with the intrinsic geomagnetic variability, which dominates the above-diurnal variation, to yield a local geomagnetic baseline. Unlike the existing baselines, our baseline is insensitive to geomagnetic storms. It is thus suitable for future definitions of geomagnetic indices that accurately reflect the intensity of solar-driven perturbations. Our methodology is quick to implement and scalable, making it suitable for real-time operation. Strategies for operational forecasting of our geomagnetic baseline 1 day and 27 days in advance are presented.

**Plain Language Summary** Geomagnetic indices, which characterize the magnitude of Sun-Earth interaction through ground magnetic measurements, are essential for research, operation, and warning in space weather. Existing geomagnetic indices derived from mid-latitude observations, particularly the Kp index, have rather insufficient time and intensity scales. To derive a new generation of geomagnetic indices, it is desirable to establish a geomagnetic “baseline” that represents the “quiet” level of activity without geomagnetic storms triggered by solar-origin perturbations (e.g., coronal mass ejections). We present a novel approach to derive a geomagnetic baseline at mid-latitude focusing on data from Chambon-la-Forêt, France. We first predict the daily quiet variation, mostly driven by the ionospheric Sq currents, 1 hour in advance using artificial neural networks with input variables indicative of the day-to-day, seasonal, and solar-cycle variations. Combining with linear extrapolation of the secular trend, driven by the internal geomagnetic variability, we propose a new local geomagnetic baseline. Unlike existing baselines, our baseline is insensitive to solar-driven perturbations. This presents a new opportunity to establish geomagnetic indices that accurately depict the magnitude of solar-driven perturbations. Our methodology is easy to put into practice for real-time operations and can also predict the baseline one day and 27 days in advance.

## 1. Introduction

Magnetic observatories at the ground level measure a superposition of magnetic fields of several sources at certain geographical locations. The dominant source is the Earth's intrinsic magnetic field, also called the “main field”, generated by geodynamo processes in the Earth's fluid inner core and contributing over 93% of the magnitude of the magnetic measurements at the surface, about tens of thousands of nano teslas (nT). Another internal source is the magnetized lithosphere which contributes with locally different but temporally nearly constant values (e.g., Thébault et al., 2010). Other sources contributing to the geomagnetic field are electric currents flowing in the
**Project administration:** Aurélie Marchaudon

**Resources:** Aurélie Marchaudon, Pierre-Louis Bleilly, Aude Chambodut

**Software:** Rungployphan Kieokaew

**Validation:** Rungployphan Kieokaew, Aude Chambodut

**Visualization:** Rungployphan Kieokaew

**Writing – original draft:** Rungployphan Kieokaew

**Writing – review & editing:** Rungployphan Kieokaew,

Veronika Haberle, Aurélie Marchaudon, Pierre-Louis Bleilly, Aude Chambodut

ionosphere and magnetosphere. In the ionosphere, the solar quiet (Sq) currents in low- and mid-latitudes in the E-region is a dominant source that gives rise to the regular daily (quiet) variations on the order of tens of nT (e.g., Yamazaki et al., 2016; Yamazaki & Maute, 2017). It forms on the sunlit side as powered by the solar irradiance. The Sq variations are believed to be affected by tidal waves of atmospheric origins, which are global-scale oscillations with harmonic periods of a day. Along the magnetic equator, a strong zonal current forms a belt known as the equatorial electrojet (EEJ; Chapman, 1951). The solar wind and the interplanetary magnetic field (IMF) interact with the Earth's environment and are external sources that drive perturbations in the geomagnetic field measurable at the ground level. In the magnetosphere, we can cite current systems such as the ring current and field-aligned currents which are significantly enhanced during solar events and modulate the geomagnetic field. At high latitudes in the ionosphere, depending on the solar wind energy input through convection and particle precipitation, the auroral ionospheric conductivities vary and induce the auroral electrojet (AEJ) current (Kamide & Akasofu, 1975; Rostoker, 1979) marking the auroral ovals in both hemispheres (e.g., Wang & Lühr, 2021, and references therein).

Ground magnetic measurements are valuable data sources for studying effects of the solar-driven disturbances on the magnetospheric and ionospheric systems. Transient solar-driven disturbances including solar storms affect the overall magnetospheric-ionospheric systems that enhance current systems and govern complex interaction among them, disturbing the Earth's magnetic field temporarily and triggering geomagnetic storms involving magnetic reconnection at the Earth's magnetopause and in the magnetotail. Interplanetary coronal mass ejection (ICME) is a major type of solar disturbances caused by an eruption on the solar surface. Earth-directed ICMEs have effects measurable on the ground from several hours up to a few days (e.g., Badruddin & Falak, 2016; Oliveira et al., 2017). Corotating interaction region (CIR) is another transient structure formed when the fast solar wind originated from the Sun's coronal holes takes over a slower wind. The compression region and high-speed wind embedded in CIRs can also disturb the geomagnetic field up to several days (e.g., Maggiolo et al., 2017; Sanchez-Garcia et al., 2017). Characterization of the intensity or effects of these solar storms on the various systems is a vital task of the space weather community.

Global geomagnetic indices characterizing the intensity of solar-terrestrial activities are derived from ground magnetic measurements. K-indices were first introduced by Bartels et al. (1939) to indicate the level of the perturbations with respect to a regular variation at a 3 hr range at mid-latitude, with a scale of 0 (quiet) to 9 (strongly disturbed). The Kp (K-planetary) index was later derived from a network of 13 mid-latitude observatories (Bartels, 1949). Since their first conception, more geomagnetic indices have been proposed and concretized. Other K-derived indices include aa that was derived from two antipodal observatories from which the longest time series are available (Mayaud, 1972). The am, an, and as indices were proposed by Mayaud (1968) to indicate sub-auroral magnetic activities at global, northern and southern scales. A comprehensive review of geomagnetic indices can be found in Menvielle et al. (2010). As an effort to improve the time resolution and scale of the Kp index, the Hpo indices were proposed at 30 min and 1 hr resolutions (Matzka et al., 2021; Yamazaki et al., 2022). Furthermore, new hemispheric geomagnetic indices α₁₅ with 15 min resolution derived from a network of 48 mid-latitude observatories in the northern and southern hemispheres were proposed (Chambodut et al., 2015).

To derive a new generation of geomagnetic indices, it is also desirable to establish a geomagnetic baseline that characterizes quiet magnetic variations in the absence of solar disturbances. The quiet magnetic variations, defined as "a smooth curve to be expected for that element on a magnetically quiet day, according to the season, the sunspot cycle and, in some cases, the phase of the Moon", traditionally involved hand-scaling by well-trained observers (Bartels et al., 1939). With the rise of the digital age, algorithms to automatically generate K indices were proposed (see Menvielle et al., 1995). These algorithms involved an estimation of the non-K variations that are the quiet variations according to the so-called Bartels-Mayaud rules (Mayaud, 1967). The Finnish Meteorological Institute (FMI) method (Sucksdorff et al., 1991) was found to be the most suitable for the continuation of K-indices series without any serious jump in the statistics when passing from analog to numerical determination at one magnetic observatory (Menvielle et al., 1995). Four algorithms including the FMI method have been endorsed by the IAGA (International Association of Geomagnetism and Aeronomy). Due to the lack of ground truth and clear identification of quiet sources, the subtraction of these empirically derived baselines from ground magnetic measurements may not reflect the real intensity of solar-driven perturbations. This can have serious impacts on space weather applications and warnings. More recently, alternative approaches have been developed to enable the derivation of geomagnetic baseline at mid-latitudes, such as that proposed by Cid et al. (2020) and
Nahayo et al. (2022) or that of Haberle et al. (2022, 2024). The former method has the advantage of being based on an algorithm that allows easy implementation for real-time operations. Nevertheless, relying on previous quiet days to replace the baseline during disturbed periods can reduce its accuracy, especially if the last quiet days are very distant in time. The latter method is based on automatic filtering of the magnetic signal, but again requires substitution from a previous quiet day during disturbed periods. In this work, we aim to derive the quiet magnetic variation without depending on previous quiet time intervals and, if possible, with high temporal resolution and fine scale in order to define a new generation of geomagnetic indices. As one of the first steps, we are focusing solely on the automated derivation of a local geomagnetic baseline; the definition of new local and global geomagnetic indices are left for future work.

To distinguish the perturbations of solar origin in the signals from other sources, establishing the geomagnetic baseline that robustly represents quiet periods is thus imperative. In an effort to derive a new magnetic activity index with a higher time resolution, Haberle et al. (2022) proposed to characterize the magnetic measurements during quiet periods by filtering the signals into the above-diurnal (>24 hr), diurnal (24 hr), and sub-diurnal variations to capture physical sources at specific time scales and combine them to determine the geomagnetic baseline. This approach works rather well during quiet periods. It is efficient; it does not need any a priori information, thus it is scalable and suitable for near-real time applications. However, in the presence of solar-driven disturbances, perturbations are still present in all of the filters. Consequently, the actual intensity of solar-driven perturbations can be underestimated. Comparing their results to the FMI method, it turns out that the baseline from the FMI method follows the geomagnetic-storm variation similar to the filtering approach. There is thus still a need to robustly establish a baseline that contains quiet variations with minimal influence of storm perturbations.

Machine learning neural networks have increasingly been used for space-weather related applications including prediction of magnetic activity indices (e.g., Collado-Villaverde et al., 2021; Gleisner & Lundstedt, 2001; Gruet et al., 2018; Iong et al., 2022; Lundstedt et al., 2002; Uwamahoro & Habarulema, 2014). In this work, we consider an application of neural networks for generation of a geomagnetic baseline that can be used regardless of the solar (active or quiet) conditions. Our goal is to automatically produce a local baseline that is not influenced by geomagnetic storms while robustly accounting for the main internal sources, the Sq variation and its possible day-to-day variability at mid-latitude. Additionally, we use magnetic measurements from an observatory only to demonstrate our prototype methodology for automatic derivation of a local geomagnetic baseline, which can later be applied to data from other mid-latitude observatories. Since Haberle et al. (2022) have already decomposed the ground magnetic measurements to several contributions, we take these data as a starting point with the aim to demonstrate the capability of machine-learning based approach. Specifically, we consider using neural networks for time-series prediction as they allow us to consider independent parameters associated with physical sources contributing to the magnetic measurements.

The organization of our paper is as follows. We first describe data and their pre-processing in Section 2. Next, we describe the neural network architecture and the training approach in Section 3. We then show the neural network results in Section 4. Finally, we discuss the production of our new geomagnetic baseline and address our forecast strategies in Section 5. The summary and perspectives are presented in Section 6.

## 2. Data

We describe datasets used in this work comprising mainly ground magnetic field measurements collected from an observatory at mid-latitude and then pre-processed them in order to capture and distinguish sources of their variation (Section 2.1). For geomagnetic measurements at low- and mid-latitudes by a local ground station, the Sq and EEJ current systems are the main contributor of the quiet variations. In this Section, we also describe features for these currents called “geometrical parameters”, which represent the daily and seasonal variations (Section 2.2), as well as the $F_{10.7}$ index (Section 2.3) which represents solar cycle irradiance variations. Indeed, the local time of measurements was generally found to correlate with these currents measurement as the Sq cells and the EEJ are formed on the sunlit-side (e.g., Stening, 2008). Moreover, the Sq and EEJ currents have seasonal dependency in terms of amplitude and position. During summer, their amplitude is higher than during winter due to prolonged solar irradiation, which also influences the ionospheric conductivity (e.g., Takeda, 1999). Finally, the daily 10.7 cm solar radio flux ($F_{10.7}$) is an excellent proxy of the solar activity indicative of the solar extreme ultraviolet radiation that influences the ionospheric conductivity. It is found to be highly linearly correlated with
the amplitude of Sq and EEJ currents (e.g., Haberle et al., 2022; Yamazaki & Kosch, 2014). Since we cannot model these currents directly, we use such driving parameters instead in the neural network (Section 3).

## 2.1. Ground Magnetic Field Data

We focus on definitive data from the magnetic observatory Chambon-la-Forêt (CLF) located at mid-latitude (48.0250 N, 2.2600 E) in France, Europe. The data are available at Bureau Central de Magnétisme Terrestre data repository from 1936 onwards. The data are replicated and associated with worldwide magnetic observatory data at the International Real-time Magnetic Observatory Network (INTERMAGNET, 2024) for the period from 1991 onwards. From Haberle et al. (2022), the definitive data were processed from 1991 to 2019. The measurements were made at 1 min cadence. The data are provided in a local cartesian coordinate system (NED: North, East, Down). The X-axis corresponds to the geographic north, the Y-axis corresponds to the geographic east, and the Z-axis completes the orthogonal system such that it directs toward the Earth's core.

In an effort to distinguish contributions from several sources to the ground magnetic measurements, Haberle et al. (2022) first applied signal processing techniques to filter the measurement data. Using Finite Impulse Response filters, they decomposed the measurement data into the contributions at various time-scales. For this, they use a window-size of 3 days with a Hamming-window. First, the above-diurnal contribution correspond to the variation in the signals above 24 ($f_{>24}$) hours and is obtained by applying a low-pass filter with cut-off period of 36 hr. Second, the other shorter time-scale contributions are extracted by a set of four band-pass filters with passing periods of 36–24 hr; 24–12 hr; 12–8 h and 8–6 hr. As such, the diurnal and semi-diurnal contributions correspond to the variation at 24 ($f_{24}$) and 12 ($f_{12}$) hours and the contributions at 8 ($f_8$) and 6 ($f_6$) hrs are also derived. To keep the same notation as Haberle et al. (2022), we call these various contributions as “filter data”. Using measurement data from observatories at low to mid latitudes in both hemispheres, they demonstrated that the derived filter data capture the physical sources contributing to the measurements reasonably well. The diurnal and semi-diurnal trends, in particular, are modulated by the season, the local time, and the day-to-day variation (see Campbell, 1989, and references therein). Haberle et al. (2022) combine all these filter data to determine a geomagnetic baseline during quiet periods.

Similar to Haberle et al. (2022), we compute the sum of $f_{24}, f_{12}, f_8$, and $f_6$, each obtained from the band-pass filter. This newly defined $f_D = f_{24} + f_{12} + f_8 + f_6$ called “daily filter”, comprises the day-to-day, seasonal, and solar cycle variations. For the $f_{>24}$ variation, we extract the secular trend using linear regression. This will be detailed in Section 5.1.

Since using the full resolution (1 min) data in the neural networks is computationally expensive, as a first step, we consider using the filter data at a lower time cadence as it allows us to progressively improve our approach. Taking the original 1 min filter data, we perform a decimation. In essence, the decimation consists of obtaining the data at every hour, that is, at every HH:00 where HH is a given hour from 01, 02, 03, ... to 23. To produce the ($f_D$) at 1 hr cadence, we first sum $f_{24}, f_{12}, f_8$, and $f_6$ at the original 1 min cadence before decimating them. The decimation is chosen instead of an averaging to avoid over-processing of the data as the latter can remove useful signals.

As a complementary analysis, in order to demonstrate that our approach also works for higher time-resolution, we also tested different time resolutions of 30, 15, 5, and 1 min in Supporting Information S1.

## 2.2. Geometrical Data

Measurements at a magnetic observatory are influenced by the geographical location of the station (i.e., northern/southern hemisphere), the local time (i.e., day/night), and the season (i.e., the inclination and position of Earth around the Sun). Thus, parameters that record these variabilities, so-called “geometrical parameters” are relevant. We derive the hourly local time (LT), from 0 to 23, from the time stamps of the data. To make the LT variation contiguous at the transition from 23 to 0, we transform it using sine and cosine functions to obtain $\sin(LT)$ and $\cos(LT)$. In addition, we chose the solar zenith angle (SZA) and the distance between the Sun and the Earth (DistSE). The SZA is the angle measured from directly above the observation point (zenith) to the elevation of the Sun in the sky, measured from the horizon and is dependent on the geographical position of the station and the season. The DistSE is given in astronomical units (AU). All these parameters are indicative of daily and seasonal variations.
## 2.3. Solar Radio Flux Data

$F_{10.7}$ is derived from a measurement of the flux density computed from the total emission at 10.7 cm wavelength from all sources present on the solar disk made over 1 hr period using two small radio telescopes (Tapping, 2013). We obtain the $F_{10.7}$ from CDAWeb (Coordinated Data Analysis Web); it is available as a part of the OMNI hourly product (Papitashvili & King, 2020). In particular, this $F_{10.7}$ data product from CDAWeb has been corrected to remove the atmospheric effects and interpolated to the Lagrangian L1 point upstream of the Earth.

# 3. Neural Network for the Daily Quiet Variation

We now turn our attention to the prediction of $f_D$ without the solar transient perturbations using neural networks. Since there is no ground truth for the daily quiet variation, we employ $f_D$ during quiet time as a proxy for it. Indeed, Haberle et al. (2022) demonstrated that $f_D$ can be used to produce a geomagnetic baseline at mid-latitudes in the absence of solar-driven perturbations as it comprises the ionospheric currents and atmospheric contributions. In the presence of solar-driven perturbations, $f_D$ can no longer be used as a proxy for the ground truth, and we expect that our results would deviate from it. As described in Section 2, the important parameters that correlate with the Sq currents, the key contributor to $f_D$, are the geometrical parameters and $F_{10.7}$. As a complementary analysis, we performed an assessment of contributions of these chosen variables, among others, on the $f_D$ variation using an explainable artificial intelligence (AI) method (SHapley Additive exPlanations; Lundberg & Lee, 2017) and a surrogate model in the SI. Our choice for the neural network along with its brief functioning are described in Section 3.1. We then outline its training in Section 3.2. Finally, we summarize the models and assess their performances during quiet time (Section 3.3) before providing the results (Section 4).

### 3.1. Neural Network Description

We develop a neural network with multiple input features and multiple output targets. The multiple input features are to accommodate the independent variables: sin(LT), cos(LT), SZA, DistSE, and $F_{10.7}$. The multiple output targets are set to accommodate the dependent variables consisting in the three components ($X_D$, $Y_D$, $Z_D$) of the daily filter. Since the ground magnetic measurements comprise the responses from the Sun and atmospheric conditions influencing the magnetospheric and ionospheric currents, the neural network must be able to account for the history of such conditions and/or physical processes. For this reason, we choose a recurrent neural network (RNN). Long Short-Term Memory networks (LSTM) are a variant of RNNs designed to overcome the vanishing gradient problems which typically arise with the long temporal dependencies (Hochreiter & Schmidhuber, 1997). In principle, this type of neural network can keep track of the dependencies in the input sequences. Through the learning process, the neural network can memorize past input sequences that will likely affect the future data. Thanks to their efficiency, LSTM networks have commonly been used in natural language processing and time series forecasting. Further description of the LSTM networks can be found in Appendix A.

We now outline the concept for the daily quiet variation prediction. The purpose is to predict $f_D$ based on history of the input variables. Given the time $t_N$, where $N$ is a running index within a sequence, for instance, we want to predict $X_D$, $Y_D$, $Z_D$ at time $t_{N+1}$ using the past sequences of the input variables, which are available up to $t_N$. Figure 1a shows an example of sin(LT), cos(LT), SZA, DistSE, and $F_{10.7}$ during June 1 and 5, 2009. In the green shade, we highlight, for instance, a time interval that would be taken as sequential inputs for the neural network. With these sequential inputs, we aim to predict $X_D$, $Y_D$, and $Z_D$ for the next hour adjacent to the highlighted interval as illustrated in Figure 1b, marked by red dots. The prediction step can be repeated by advancing through the sequence from left to right in Figures 1a and 1b to generate continuous prediction of $f_D$, as will be employed in Section 4.

To build a neural network, we start with a simple architecture consisting of an input layer, a hidden layer, and an output layer. The input layer consisting of LSTM cells is to accommodate the sequential inputs of sin(LT), cos(LT), SZA, DistSE, and $F_{10.7}$ with a certain length; the output layer is to predict $X_D$, $Y_D$, $Z_D$ at a next time step. We set up experiments using training data in 1991–2001 (11 years), validation data in 2002, and test data in 2003. The input and output data are rescaled to the range [0, 1] by finding the minimum and maximum values of each feature for the data in 1991–2001 using the formula:

$$x_{\text{scaled}} = \frac{x - x_{\text{min}}}{x_{\text{max}} - x_{\text{min}}}, \qquad (1)$$
<figure><img src="image_4.png" /><figcaption>**Figure 1.** (a) sin(LT), cos(LT), SZA, DistSE, and $F_{10.7}$ during 1 and 5 June, 2009, highlighted in green as an example for the sequential inputs to the neural network. (b) $X_D$, $Y_D$, and $Z_D$ for the same interval, marked with red dots for the expected prediction. (c) Schematic of the neural network consisting of stacked layers and multiple RNN units (nodes), taken here as LSTM cells. The neural network takes in 12 hr sequences (green) of the variables in (a) up to the current time stamp $t_N$ and predicts the daily quiet variations (red) at the next adjacent hour $t_{N+1}$.</figcaption></figure>
where *x* represents values of the individual input and output variables. The scaling values (e.g., *x*<sub>min</sub>, *x*<sub>max</sub>) are saved for rescaling the output from the neural network in the final step. The same scaling is applied throughout this work. As for the architecture, first, we vary the number of the nodes in the input and output layers to find satisfactory results. Second, we add more hidden layers to improve the neural network performance. For each layer, a nonlinear “activation function” is applied to the output to introduce nonlinearity. Here, the Rectified Linear Unit (Glorot et al., 2011) is used as the activation function as it overcomes the vanishing gradient problem in multiple-layer networks. Third, to prevent the neural network from overfitting, a dropout layer is introduced to drop units along with their connections during the training (Srivastava et al., 2014). Several sets of different architectures with different numbers of hidden layers and neurons were tested (see Table S1 in Supporting Information S1). Besides, a set of varying time windows of the sequential inputs was also tested (see Table S2 in Supporting Information S1); the best results are found using 12 hr.

Figure 1c summarizes the architecture that yields the minimum loss, taken as the mean-squared error (MSE). It consists of stacked layers of multiple LSTM nodes, represented as RNNs unit in the diagram. The input layer (i.e., the first hidden layer) has 100 nodes. There are three additional hidden layers (orange shade) including one LSTM output layer with 50 nodes each. Then, a dropout layer with 50 nodes (gray shade) is placed with a dropout ratio of 0.3. In essence, this layer randomly drops 30% of the nodes and connections from the previous layer to prevent overfitting before yielding the predicted outputs (see SI for tests with different dropout ratios). This neural network takes 17 min of CPU time to train for 11 years of data. We further optimize its training so that it is appropriate for our applications next.

## 3.2. Neural Network Training

For the model training, we set up the neural network to learn in batches where it learns from a certain amount of data at a time. Here, the batch size is set to 256 for the training data at 1 hr cadence (95,945 data points for 11 years). The weights and biases in the neural network nodes and connections are initialized with random numbers and then updated through several cycles. The number of training cycles is known as “epoch”. The learning process is optimized and tracked through the loss function, which evaluates the model performance during each training epoch. Here, the loss function is set to be the MSE. The optimization during its learning, that is, the iterative process for updating weights in the neural network, is performed using the stochastic gradient descent. Here, we employ the adaptive moment estimation (Kingma & Ba, 2014), known as “Adam” optimization algorithm, as it is rather computationally efficient for deep neural network training. The learning rate (the step size in the stochastic gradient descent) is set to be 0.001. We monitor the learning process through the validation loss. The learning process is stopped once there is no improvement in the validation loss for five consecutive epochs. The best model is saved when the validation loss reaches a minimum value before the training stops.

To effectively train the neural network model, we split the datasets as the following. Overall, we split the sequential data into the training, validation, and test sets. The validation set is used for evaluating and monitoring the model performance during the learning over several epochs. The ground magnetic measurements have temporal dependencies coming from the solar wind and solar dynamo (influencing the solar activities or phases). Therefore, the choice of training and validation data can introduce biases. First, the neural network must be trained using a sufficient amount of data, in this case a complete solar cycle, so that it learns as much as possible. Second, since a best model is chosen based on the validation data, the choice of validation data can also introduce a bias. For example, if the model is validated and selected using an interval of data with active solar activities, that is, during a solar maximum where the occurrence of ICMEs is high, the model may not be appropriate for use during the quiet solar activities, that is, during a solar minimum where the occurrence of ICMEs is low. To minimize such a bias, we propose a new strategy for the model training as follows.

To best capture the different nature of solar activities in the various phases of the solar cycle, we propose an adaptive training method called “Walk Forward Validation” (also called “Sliding Window” or “Rolling Forecast”) approach (e.g., Brownlee, 2017). This approach has been used in economy and stock market predictions where the model is retrained once newer data become available (e.g., Kaastra & Boyd, 1996). The advantage is that the model would be the most up-to-date, making it more relevant to the current situation and thus the near future situation. Essentially, the neural network is trained in several steps while moving forward along the time series. Figure 2 illustrates the walk forward training for the data starting from 1991 onwards. In each panel, we
<figure><img src="image_5.png" /><figcaption>**Figure 2.** The walk forward training approach. The $F_{10.7}$ (black) indicative of the solar variability is shown for context. (a) Step 1 consists in training of the neural network with a specified training window (blue shade) and validating it with the adjacent data with a specified validation window (green shade). (b) Step 2 consists in updating the training with the next, shifted training and validation windows. The process is repeated up until to the test year. (c) The model is tested after the final training and validation step.</figcaption></figure>

show $F_{10.7}$ indicative of the solar activity. We summarize our neural network training with the walk forward approach as follows.

1. In Figure 2a, the first step consists in the neural network training using the data within a specified minimum training window (11 years) as shaded in blue. It is then validated with the unseen data adjacent to the training data defined within a specified validation window (1 year) as shaded in green.

2. In Figure 2b, the trained neural network from step 1 is trained again using the data in a next, shifted 11 year window. The validation data in the previous step are included in the training data. The model is then validated with the unseen data, defined within a specified validation window, adjacent to the newly shifted training window. Technically, the weights and biases in the neural network are updated through this learning process using new data.

3. The process is repeated until the end of all the training data excluding the test set. Figure 2c shows the final training step with the test data shaded in purple. Here, for instance, the final model is validated with the data during low solar activities in 2008, therefore, it should be appropriate for the test using data in 2009 which also has low solar activities.

For our purpose, we define a minimum training window to be 11 years and a validation training window to be 1 year. Table 1 summarizes all the models we used for producing model prediction from 2003 to 2019. Data in 2009 and 2012 are taken as representative test datasets for the quiet and active solar periods, respectively. As shown in Figure 2, the neural network was originally trained from 1991 to 2001 (i.e., model V00: initial model), validated in 2002, and tested in 2003. Using the walk forward approach, we update the training up to 2009 with year 2008 being the validation data (model V06). Likewise for 2012, we update the training until 2012 with year 2011 being the validation data (model V09). Here, the model is most relevant to the time closer to the end of the training window as it is trained several times using the newer data, while being less relevant to the older data. This approach would offer optimum results for the time-dependent prediction.
<table><caption>**Table 1**

Description of the Model Training and Validation for Each Test Year and the RMSE, Evaluated for the Prediction in Each Year in Comparison to the Daily Filter, Selected for Only CK48 Really Quiet Days</caption><thead><tr><th>Models</th><th>(Update) training data</th><th>Validation year</th><th>Test year</th><th># Of CK48 days</th><th>RMSE [x, y, z] (nT)</th><th>RMSE (nT)</th></tr></thead><tbody><tr><td>V00 (initial model)</td><td>1991–2001</td><td>2002</td><td>2003</td><td>20</td><td>[3.3, 5.3, 1.4]</td><td>6.4</td></tr><tr><td>V01 (V00 updated)</td><td>1992–2002</td><td>2003</td><td>2004</td><td>77</td><td>[4.9, 5.3, 1.5]</td><td>7.4</td></tr><tr><td>V02 (V01 updated)</td><td>1993–2003</td><td>2004</td><td>2005</td><td>92</td><td>[3.9, 5.6, 1.9]</td><td>7.1</td></tr><tr><td>V03 (V02 updated)</td><td>1994–2004</td><td>2005</td><td>2006</td><td>145</td><td>[3.9, 5.6, 1.4]</td><td>7.0</td></tr><tr><td>V04 (V03 updated)</td><td>1995–2005</td><td>2006</td><td>2007</td><td>164</td><td>[3.0, 4.1, 1.2]</td><td>5.2</td></tr><tr><td>V05 (V04 updated)</td><td>1996–2006</td><td>2007</td><td>2008</td><td>171</td><td>[2.9, 3.8, 1.4]</td><td>5.0</td></tr><tr><td>V06 (V05 updated)</td><td>1997–2007</td><td>2008</td><td>2009</td><td>277</td><td>[3.8, 4.2, 1.4]</td><td>5.9</td></tr><tr><td>V07 (V06 updated)</td><td>1998–2008</td><td>2009</td><td>2010</td><td>212</td><td>[3.6, 3.9, 1.6]</td><td>5.5</td></tr><tr><td>V08 (V07 updated)</td><td>1999–2009</td><td>2010</td><td>2011</td><td>156</td><td>[4.1, 6.2, 1.4]</td><td>7.6</td></tr><tr><td>V09 (V08 updated)</td><td>2000–2010</td><td>2011</td><td>2012</td><td>122</td><td>[4.9, 6.6, 2.4]</td><td>8.6</td></tr><tr><td>V10 (V09 updated)</td><td>2001–2011</td><td>2012</td><td>2013</td><td>175</td><td>[4.9, 6.0, 1.9]</td><td>8.0</td></tr><tr><td>V11 (V10 updated)</td><td>2002–2012</td><td>2013</td><td>2014</td><td>129</td><td>[4.0, 6.0, 2.3]</td><td>7.6</td></tr><tr><td>V12 (V11 updated)</td><td>2003–2013</td><td>2014</td><td>2015</td><td>75</td><td>[3.4, 5.4, 2.4]</td><td>6.9</td></tr><tr><td>V13 (V12 updated)</td><td>2004–2014</td><td>2015</td><td>2016</td><td>94</td><td>[3.2, 3.5, 1.4]</td><td>4.9</td></tr><tr><td>V14 (V13 updated)</td><td>2005–2015</td><td>2016</td><td>2017</td><td>108</td><td>[4.2, 3.5, 1.7]</td><td>5.8</td></tr><tr><td>V15 (V14 updated)</td><td>2006–2016</td><td>2017</td><td>2018</td><td>180</td><td>[3.4, 3.0, 1.3]</td><td>4.7</td></tr><tr><td>V16 (V15 updated)</td><td>2007–2017</td><td>2018</td><td>2019</td><td>199</td><td>[3.5, 3.2, 1.3]</td><td>4.9</td></tr></tbody></table>

### 3.3. Model Performance for 1-hr Lead Time

Due to the lack of the ground truth of the daily quiet variation, it is non-trivial to evaluate our model performance. To overcome this challenge, we choose to calculate and present root-mean-square error (RMSE) for magnetically quiet days only. The International Service of Geomagnetic Indices (ISGI, 1906) characterizes magnetic quietness with regard to the irregular geomagnetic activity and provides the “Really Quiet (C)” and “Quiet (K)” days over 24 hr (CK24) or 48 hr (CK48). CK24 and CK48, deduced from *aa* index (Mayaud, 1972), are IAGA-endorsed data products. Here we focus only on CK48 really quiet days. In Haberle et al. (2022), they have shown that the FB follows well the quiet variations of the magnetic field when only looking at these CK48 really quiet days; therefore comparing the results of the daily filter with our model is relevant. We present these results in Table 1.

To produce the results in Table 1, we first compute the RMSE for the 1 hr lead time forecasting from each model, producing for 1 year of test data consecutively for all days in that test year. The RMSE computed for all days in each test year is in the range from 7.8 nT (2009, solar minimum) to 18 nT (2003, solar maximum). Next, we select only the CK48 really quiet days in each test year and compute the RMSE. We note that, in 2003, there are only 20 CK48 really quiet days. All the RMSEs for these magnetically really quiet days are in the range from 4.7 nT (2018) to 8.6 nT (2012).

### 4. Neural Network Prediction of the Geomagnetic Daily Quiet Variation

In this Section, we show prediction results for the daily quiet variation based on the neural network in Figure 1, trained with the walk forward approach (see Figure 2 and Table 1). On one hand, we expect our modeling results to be rather similar to the daily filter data during quiet days where the influence from solar-driven perturbations is minimal. On the other hand, we expect that our modeling results should be insensitive to solar-driven perturbations. These qualities are essential for characterizing a geomagnetic baseline, excluding the long-term secular variation, representative of the regular (daily) quiet variation in the absence of external drivers. In the following, we show first results during quiet period, that is, during the solar minimum in 2009, and then results during non-quiet period, that is, during the solar maximum in 2012. The results in 2009 and 2012 are generated from the models V06 and V09 in Table 1, respectively.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Comparison between the daily filter (black) and the neural network prediction of the daily quiet variation (red) during the consecutive CK48 really quiet days between 18 May and 6 June 2009, shown for (a) $X_D$, (b) $Y_D$, and (c) $Z_D$ components. Passages of CIRs on 20–21, and 28 May are shaded in gray.</figcaption></figure>

As described in Section 3.1 (Figure 1), the neural network provides 1 hr lead time prediction. For practical reasons, the results below are produced by running the neural network model consecutively over all days for each test year consecutively to generate continuous prediction.

## 4.1. Quiet Period

The year 2009 has the most CK48 really quiet days among the period between 1991 and 2019 (see Table 1). Here, we focus on an interval with consecutive CK48 days from May 18 to 6 June 2009. Figure 3 shows a comparison between the neural network prediction for $X_D$, $Y_D$, and $Z_D$ (red) and the daily filter (black) in panels (a) - (c). During this period, there were two CIR arrivals on 20–21 May and 28 May (Jian et al., 2006) as shaded in gray. Overall, we find that the neural network results are qualitatively similar to the daily filter especially for $Y_D$. There are, however, some differences at small scales as well as for daily extrema. In fact, since the daily filter includes all signals at 24, 12, 8, and 6 hr harmonics, all effects from atmospheric and tidal waves can be present. The absence of these features from the neural network prediction implies that there is no such information in the inputs or that these features cannot be learned. For $X_D$, the filter data show rather irregular variation although with some periodicity; our neural network shows rather different variation especially for the smaller-scale features. For $Z_D$, there are also some differences although less important than $X_D$.

On May 21, 22, and 28, the daily filter shows some enhanced extrema especially on the $X_D$ and $Y_D$ components, most-likely driven by the CIR passages. It is known that during ICME/CIR storms, ionospheric currents can be altered from the normal quiet pattern. Two processes are known to be mainly responsible for magnetic disturbances at mid-latitudes, and thus at CLF. One is the “prompt penetration” of the polar electric fields to lower latitudes, and the other is the “disturbance dynamo” electric field driven by storm-time winds (see Yamazaki et al., 2016, for details). These effects can influence all components. As the daily filter was derived from the signal
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Comparison between the daily filter (black) and the neural network prediction (red) from 13 to 27 July, 2012 for (a) $X_D$, (b) $Y_D$, and (c) $Z_D$ components. An ICME passage between 14 July at 18:09 and 17 July at 05:00, 2012, is shaded in blue. CK48 really quiet days are marked with “C” in panel (b) on 13, 18, and 26 July.</figcaption></figure>

decomposition, such perturbations can still persist in the data. For our neural network prediction, we find that the amplitudes of our daily quiet variation remain regular and do not vary with such solar-origin perturbations. This suggests that our neural network can be used to predict the daily quiet variation. Nevertheless, as discussed above, our neural network prediction may not include smaller-scale variations likely driven by atmospheric origins.

## 4.2. Perturbed Period

We now turn our attention to the neural network prediction during non-quiet days. We select the interval from July 13 to 27, 2012, where a few CK48 really quiet days were present near a geomagnetic storm. Figure 4 shows the daily filter (black) and the neural network prediction for the daily quiet variation (red) for $X_D$, $Y_D$, and $Z_D$ in panels (a) - (c). During this period, a geomagnetic storm was triggered following an Earth-directed ICME passage between July 14 at 18:09 and July 17 at 05:00, 2012 (Richardson & Cane, 2024), as shaded in blue. In addition, July 13, 18, and 26 are characterized by ISGI as CK48 really quiet days. They are marked by letter “C” in Figure 4b.

During the ICME passage as shaded in blue, a clear perturbation is visible in the daily filter for all components, especially for $X_D$ and $Z_D$. Regarding the neural network prediction, our daily quiet variation shows regular variation that is insensitive to the geomagnetic storm for all components. Outside the storm time, in particular for CK48 really quiet days, our neural network prediction shows rather similar variation to the daily filter especially for $Y_D$ and $Z_D$. These demonstrate that our approach can be used to provide the daily quiet variation regardless of the presence of solar-origin perturbations unlike the filter method. Nevertheless, as discussed in Section 4.1, the neural network prediction does not include smaller-scale features (especially for $X_D$) and their extrema are not as enhanced as those of the daily filter. This may suggest again that our prediction does not include variation of atmospheric origins.
With the implementation in Section 3, our method can yield the daily quiet variation 1 hr in advance. In Section 5, we consider extending the lead time of the forecast. In combination with the secular trend extrapolation, we also consider providing a new prototype for geomagnetic baseline forecast.

# 5. Geomagnetic Baseline Forecasting

To produce a geomagnetic baseline, we need two elements: (a) the daily quiet variation, and (b) the secular trend variation. For a geomagnetic baseline similar to the existing filter baseline or the FMI baseline, we need only X and Y components. In Section 4, we demonstrated that the neural network can be used to provide the daily quiet variation 1 hr in advance. To provide a complete geomagnetic baseline, we also need to know the secular trend variation 1 hr in advance. We first consider this aspect in Section 5.1. Then, we propose a method to extend the forecast horizon to 1 day and 27 days in Section 5.2. In particular, we compare our proposed baseline with the filter baseline and FMI baseline. Finally, we discuss the operational aspects and future work in Section 5.3.

## 5.1. Extrapolation of the Above-Diurnal Secular Trend

In addition to the daily quiet variation, we need to characterize the secular variation, that is, excluding the solar-driven perturbation, in $X_{>24}$ and $Y_{>24}$. The secular trend variation is driven by the internal sources of the geomagnetic field including those originating in the core and lithosphere of the Earth (e.g., Mandea & Cham-bodut, 2020). The secular trend variation varies on the time scale between a month to a few thousand of years. On time scales of between a month and 100 years, the secular variation is entirely caused by the rigidly coupled movement of the magnetic field lines with the fluid motion in the liquid outer core (advection).

The secular variation has been recorded since mid 1,500s at CLF (Mandea & Le Mouël, 2016). Figures 5a and 5b show $X_{>24}$ and $Y_{>24}$ between 1991 and 2020 derived from the measurements at CLF. One can see that the secular trend appears rather linear to the first order. Over this time scale, $X_{>24}$ has increased for about 400 nT while $Y_{>24}$ has increased for about 1400 nT. On top of the secular variation, there are smaller-scale fluctuations owing to the solar-driven perturbations. For instance, one can see more-frequent drops in $X_{>24}$ in 1998–2006 during the high solar activity and less-frequent drops in $X_{>24}$ in 2008–2010 during the solar minimum. It would be desirable if we can characterize and project the secular trend based on physical understandings. For instance, we may use main geomagnetic field model outputs together with constants on each component, to take into consideration the local crustal biases at the considered magnetic observatory location. The IGRF model (International Geomagnetic Reference Field; Alken et al., 2017), updated every 5 years, in conjunction with constant values to consider the crustal field due to remnant rocks within the crust may be considered. The CHAOS-7 model of the geomagnetic field derived from observations from low-Earth orbit satellites, updated every 4–6 months, may also be used. Yet, these approaches will downgrade the capacity of real-time calculation and lead to use of a priori information, making it less convenient for operational implementation.

Assuming that the secular trend would remain linear in our time scale of consideration, for example, for 1 hr up to 27 days, we may employ linear regression as follows. To obtain a projection for the next hour up to next 27 days, we perform linear fitting on $X_{>24}$ and $Y_{>24}$ individually, on the past data with a length of more than a month. Since the presence of solar-origin perturbations, typically lasting from a day up to a week, can deviate the trend, we take a longer interval in order to smooth such effects. We decide to take the data length of about 3 months or 90 days as the interval of $X_{>24}$ and $Y_{>24}$ to perform a linear fitting in order to project the secular trend. As an example, we perform linear fitting on the data preceding 18 May 2009, in Figures 5c and 5d for $X_{>24}$ and $Y_{>24}$, respectively. The linear fitting on the past 90 days data is denoted by a red solid line. Next, we can project the same trend, using the same slope and intercept, up to 27 days as depicted by a red dashed line. Both the linear fitting and linear projection qualitatively agree with the global trend of the filter $X_{>24}$ and $Y_{>24}$. Similarly, we can perform the same linear fitting for the data preceding 13 July 2012, in Figures 5e and 5f. These two examples demonstrate that the simple linear regression may be used to forecast the secular trend present in the above-diurnal filter locally.

## 5.2. Forecast and Comparison With FMI Baseline

Using the neural network for the daily quiet variation and the extrapolation method for the above-diurnal secular variation, we can combine them to obtain prediction of the geomagnetic baseline. From Section 3.2, we obtain a neural network model that produces the daily quiet variation 1 hr in advance based on 12 hr history of $\sin(LT)$, $\cos(LT)$, SZA, DistSE, and $F_{10.7}$. Here, we employ the model V09 in Table 1 for the test data in 2012 as will be
<figure><img src="image_8.png" /><figcaption>**Figure 5.** The above-diurnal filter derived from the measurements at CLF (blue). (a) $X_{>24}$ and (b) $Y_{>24}$ from 1991 to 2020. (c)–(f) Examples of linear fitting (red solid line) on $X_{>24}$ and $Y_{>24}$ and 27 day linear projection (red dashed line) for the chosen intervals in 2009 and 2012.</figcaption></figure>

shown below. In order to advance the lead time, we need to have $F_{10.7}$ forecast. Several approaches for forecasting $F_{10.7}$ exist (e.g., Henney et al., 2012; Lei et al., 2019; Warren et al., 2017; Wei et al., 2024; Yaya et al., 2017). Nevertheless, to keep our approach ergonomic, we may simply use the standard $F_{10.7}$ data product with the following consideration. To obtain a forecast for the next day, we may assume that $F_{10.7}$ is similar to that of the current day. To provide a longer lead time of the forecast, the community often employs a recurrence model where the next solar rotation is assumed to have the solar irradiance similar to the past solar rotation (e.g., Fröhlich, 2003; Owens et al., 2013). With this consideration, we can use the $F_{10.7}$ over the past 27 days to provide a prediction over the next 27 days.

For the above-diurnal secular trend, we may also project the trend for the next hour, next day and next 27 days using the past 90 days of the data as shown in Section 5.1. In practice, all these procedures can be done daily to provide geomagnetic baseline forecast 1 and 27 day in advance, in addition to the 1 hr baseline prediction using real-time $F_{10.7}$. Figure 6a shows an example of the 27 day forecast of the neural network (NN) produced baseline (red) combined with the secular trend projection for July 1 - 27, 2012. This is done by projecting the $F_{10.7}$ forecast
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Comparison between the filter baseline (black) and (a) the 27 day baseline forecast based on the neural network (using time-shifted $F_{10.7}$) combined with the $f_{24}$ trend linear projection (red), and (b) the 1 day baseline forecast produced daily for 27 consecutive days represented by different colors. Intervals during ICME passages are shaded in blue and an interval during a CIR passage is shaded in gray.</figcaption></figure>

to be similar to the past 27 days. During this period, there are four ICME passages (Richardson & Cane, 2024) as shaded in blue. Also, there is a CIR passage (Hajra & Sunny, 2022) as shaded in gray embedded in the third ICME. Our baseline, labeled as “NN” (red), is shown in comparison to the filter baseline (black) for the *Y*-component. Similar to Section 4, we find that our approach produces a variation that is insensitive to the solar-origin perturbations, seen as enhanced extrema of the filter baseline. In Figure 6b, we produce the 1 day baseline forecast that is updated daily at midnight for 27 consecutive days represented using different colors. This approach yields rather similar results as in Figure 6a (red) albeit some differences in the extrema. Therefore, our approach can be used to yield a new geomagnetic baseline forecast in advance for 1 day or 27 days, in addition to the real-time calculation.

Finally, we compare our approach to the existing methods. Figure 7 shows the hourly measurements (black), the filter baseline (FB, yellow), the FMI baseline (cyan), and our NN baseline (red) produced for the Halloween 2003 event. Here, the NN daily quiet prediction is produced from the model V00 (see Table 1). Figures 7a and 7b show the *X*- and *Y*-components at CLF, respectively. The NN baseline is produced daily with the lead time of 1 day similar to Figure 6b. The geomagnetic storm perturbations are clearly visible from 28 October to 1 November, with a maximum drop in *X* of about 1,000 nT and a maximum enhancement in *Y* of about 500 nT compared to the quiet-level variation preceding the event. During the quietest days of this period (23–24 October and 2–3 November), we find that the three baselines (FMI, FB, and NN) follow closely the hourly measurements of the magnetic field. However, as soon as some magnetospheric activity is recorded, for example, on 26–27 October for which the Dst index reaches –50 nT (see https://wdc.kugi.kyoto-u.ac.jp/dst_final/200310/index.html), which could be regarded as a minor storm, the FMI and FB baselines still follow to closely the hourly measurements, while the NN remains unperturbed and follows the expected quiet-time variations linked to the Sq currents,
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Comparison between the hourly measurements at CLF (black) and the various geomagnetic baselines: filter (FB; yellow), FMI (cyan), and NN (red) for the Halloween 2003 geomagnetic storm shown for (a) X and (b) Y components. The NN baseline is produced from the secular trend projection combined with the V00 model prediction using time-shifted $F_{10.7}$ (see text).</figcaption></figure>

similar to the earlier and later quiet days. This seems to confirm that the NN baseline best represents the expected quiet-time magnetic field when moderate activity is occurring.

During the Halloween event from 28 October to 1 November, the three baselines differ significantly. The FB and FMI baselines follow the storm variation with the FB being more sensitive to the perturbation compared to the FMI baseline. Regarding the global extrema in Y (at about 67 nT) preceding 31 October in Figure 7b, for instance, the FB extrema is about 1/3 while the FMI extrema is about 20% of the Y magnitude. Meanwhile, our NN baseline remains insensitive to the storm variation throughout the event. When characterizing the magnitude of the storm perturbation by subtracting the baseline from the measurement, one would underestimate the actual magnitude if the FB or the FMI baseline is used. In contrast, a better estimate can be obtained using our approach. This result shows that our baseline can robustly characterize the quiet variations during storm perturbation as long as we assume that quiet variations are the same even during a storm.

### 5.3. Operational Aspects and Future Work

We highlight that our approach presented here is a prototype only. To move toward real-time operation, there are certain aspects that deserve to be addressed. For instance, here, we have used INTERMAGNET definitive data for CLF, in order to model the magnetic field baseline as accurately as possible. The definitive data are the cleanest and most reliable magnetic data, to train and validate the neural network. This is mainly to avoid integrating artifacts which could be contained in not fully validated data sets, such as quasi-definitive or provisional data. We can however argue that quasi-definitive data are in general following a processing which is very similar to the one used to produce definitive data, except that the time interval for the baseline calculation is shorter (a few months instead of 1 year or more). Thus, we cannot expect a strong deviation between quasi-definitive data and definitive ones. As such, we are confident that our neural network model will still provide reliable results if tested on quasi-definitive data, even with training and validation done on definitive data. The challenge will be to test it on
provisional data which are the only one available in real-time. However, we believe there are methods to pre-
process these provisional data (smoothing, removing spikes) which would allow applying our neural network
model. This latter aspect is out of the scope of this paper which has solely for purpose to prove that neural network
model can reproduce quiet baseline variations.

Another aspect is the time-resolution of the local geomagnetic baseline. Here, we have proposed a 1 hr resolution. As this may have fundamental implications for real-time operations to calculate magnetic indices with high temporal resolution, we nevertheless tested different temporal resolutions of 30, 15, 5, and 1 min for model features and outputs. The results are presented in the SI, and show that the metric remains very similar regardless of the time resolution, whereas the CPU time increases drastically with time resolution. This motivated our choice to use this 1 hr cadence for this study in order to progressively improve the analysis or optimize the model training, validation, and testing, while keeping the CPU time reasonable. As shown in the SI, it is possible to increase the temporal resolution without changing the RMSE of our NN model. Besides, since the baseline is essentially a smooth curve, it is reasonable to interpolate between the one-hour time stamps modeled by the NN model to increase the time resolution to a few minutes, especially when we forecast over one or several days. These operational aspects will be addressed in future work.

**6. Summary and Perspectives**

We propose a new approach for producing a local geomagnetic baseline for robust characterization of the quiet, time-dependent variation in the absence of solar-driven perturbations. As a first step, we demonstrate our approach using ground magnetic data from CLF. The method consists in the neural network prediction of the daily quiet variation, mostly driven by the Sq ionospheric currents at mid-latitude, and the extrapolation of the secular variation, owing to the internal geomagnetic field change, using linear regression based on the past 90 day variation. This geomagnetic baseline essentially represents the quiet variations that vary with the (local) intrinsic geomagnetic variability, solar cycles, seasons, and daily variability.

We choose key parameters consisting in geometrical parameters specific to CLF and the solar irradiance that
dominantly correlate to the daily variation. Using these parameters as inputs and the daily filter as outputs, we
develop a LSTM neural network that can robustly predict the daily quiet variation regardless of the solar activities.
The neural network is trained using at least 11 years of 1 hr cadence data and updated using the walk forward
approach. Our neural network can yield prediction of the daily quiet variation 1 hr in advance based on the past
12 hr history. Furthermore, using time-shifted F<sub>10.7</sub>, our prediction can be obtained 1 and 27 days in advance.
Combining with the linear extrapolation of the secular trend, our method yields a new local geomagnetic baseline
that could be convenient for operational implementation. As demonstrated for the Halloween 2003 event, our
baseline is insensitive to external perturbations unlike the FB and FMI baselines. Nevertheless, our baseline shows
some deviations from the measurements during the quiet time, likely due to the absence of the quiet atmospheric
sources and possible errors in the secular trend extrapolation. Future improvements should include such quiet
sources to better represent the daily quiet variation in the absence of solar-origin perturbations. For instance, the
effect of the semidiurnal lunar tide should be investigated. Besides, the secular trend prediction can be improved.
Finally, another avenue to explore would be to compare our NN baseline with the baseline developed for the LDi
and LCi indices for real-time operations (Cid et al., 2020; Nahayo et al., 2022), once we have validated our neural
network on other magnetic stations than CLF, such as SPT (San Pablo-Toledo magnetic observatory).

In conclusion, we present a new neural network-based approach for automatic generation of a new geomagnetic
baseline prediction that is robust against solar-origin perturbations. Our approach is convenient to implement and
is scalable to other magnetic observatories. It thus offers an alternative approach for development of a new
generation of geomagnetic indices with fine scale and high time resolution for operational space weather. Main
perspectives of this work are to validate our neural network-based approach to other magnetic observatories at
mid-latitudes and to use it on provisional magnetic data to ensure that the baseline prediction remains robust with
non-validated real-time data.

**Appendix A: Brief Description of LSTM Neural Networks**

The core of a LSTM unit is a cell where the short-term memory (called the activation) is stored and propagated
forward. Figure A1 shows the internal structure of a LSTM cell. The propagation of the activation vectors within
<figure><img src="image_11.png" /><figcaption>**Figure A1.** Schematic of the internal structure of a LSTM unit. $\sigma$ represents a layer of neurons with sigmoid activations, Tanh represents a layer of neurons with tanh activations, + represents vector addition, and $\times$ represents vector multiplication.</figcaption></figure>

the cell is controlled by the forget gate, the input gate, and the output gate. For each time step (t), the parameters within the cell are calculated as follows.

$$f_{(t)} = \sigma(W_{xf}^T X_{(t)} + W_{hf}^T h_{(t-1)} + b_f), \qquad (A1)$$

$$i_{(t)} = \sigma(W_{xi}^T X_{(t)} + W_{hi}^T h_{(t-1)} + b_i), \qquad (A2)$$

$$g_{(t)} = \tanh(W_{xg}^T X_{(t)} + W_{hg}^T h_{(t-1)} + b_g), \qquad (A3)$$

$$o_{(t)} = \sigma(W_{xo}^T X_{(t)} + W_{ho}^T h_{(t-1)} + b_o), \qquad (A4)$$

$$c_{(t)} = f_{(t)} \otimes c_{(t-1)} + i_{(t)} \otimes g_{(t)}, \qquad (A5)$$

$$y_{(t)} = h_{(t)} = o_{(t)} \otimes \tanh(c_{(t)}), \qquad (A6)$$

where $X_{(t)}$ is the input vector, $f_{(t)}$ is the forget gate's activation vector, $i_{(t)}$ is the input gate's activation vector, $g_{(t)}$ is the current entry vector, $h_{(t)}$, $y_{(t)}$ is the hidden state or output vector, $c_{(t)}$ is the cell state vector, $\otimes$ represents the element-wise multiplication, $\sigma$ is the sigmoid function (also known as logistic), $W_k$ where $k \in (f, i, g, o)$ are weights matrices, $b_k$ are bias vectors, and tanh is the hyperbolic tangent function. Indeed, a LSTM unit is a network in itself as it contains multiple layers of neurons as depicted in Figure A1.

## Data Availability Statement

The CLF magnetic observatory data are available from Bureau Central de Magnétisme Terrestre data repository (BCMT, 1921) and at INTERMAGNET data repository (INTERMAGNET, 2024). We acknowledge use of NASA/GSFC Space Physics Data Facility (Space physics data facility, 2024), CDAWeb (Cdaweb, 2023), OMNI hourly data (Papitashvili & King, 2020), and AMDA (Budnik et al., 2015; Génot et al., 2021). The results in this work were produced from version 0.1.1 of the Python code developed by RK (Kieokaew, 2024).
Acknowledgments

The authors acknowledge the support of the AID (Agence de l'Innovation et de la Défense) and the French ANR (Agence Nationale de la Recherche), under grant ANR-20-ASTC-0030 (project ANR ASTRID PRISMS). Work at IRAP is supported by Centre National de la Recherche Scientifique (CNRS) through the Programme National Soleil-Terre of the Institut National Terre et Univers (PNST/INSU), Centre National d'Etudes Spatiales (CNES) and the University of Toulouse III (UT3). Work at EOST is supported by CNRS, CNES and the University of Strasbourg. RK acknowledges the postdoctoral fellowship from CNES.

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