We present a proof of concept for the probabilistic emulation of the Ring current-Atmosphere interactions Model with Self-Consistent magnetic field (RAM-SCB) particle flux. We extend the workflow developed by Licata and Mehta (2023) by applying it to the ring current and further developing its uncertainty quantification methodology. We introduce a novel approach for sampling over 20 years of solar and geomagnetic activity to identify 30 simulation periods, each one week long, to generate the training, validation, and test datasets. Large-scale physics-based simulation models for the ring current can be computationally expensive. This work aims at creating an emulator that is more efficient, capable of forecasting, and provides an estimate on the uncertainty of its predictions, all without requiring large computational resources. We demonstrate the emulation process on a subset of particle flux: a single energy channel of omnidirectional flux. A principal component analysis (PCA) is used for the dimensionality reduction into the reduced-space, and the dynamic modeling is performed with a recurrent neural network. A hierarchical ensemble of Long-Short Term Memory (LSTM) neural networks provides the statistics needed to produce a probabilistic output, resulting in a reduced-order probabilistic emulator (ROPE) that performs time-series forecasting of the ring current’s particle flux with an estimate on its uncertainty distribution. The resulting ROPE from this smaller subset of RAM-SCB particle flux provides dynamic predictions with errors less than 11% and calibration scores under 10%, demonstrating that this workflow can provide a probabilistic emulator with a robust and reliable uncertainty estimate when applied to the ring current.

The Wang-Sheeley-Arge (WSA) model estimates the solar wind speed and interplanetary magnetic field polarity at any point in the inner heliosphere using global photospheric magnetic field maps as input. WSA employs the Potential Field Source Surface (PFSS) and Schatten Current Sheet (SCS) models to determine the Sun’s global coronal magnetic field configuration. The PFSS and SCS models are connected through two radial parameters, the source surface and interface radii, which specify the overlap region between the inner SCS and outer PFSS model. Though both radii are adjustable within the WSA model, they have typically been fixed to 2.5 R sol. Our work highlights how the solar wind predictions improve when the radii are allowed to vary over time. Data assimilation using particle filtering (sequential Monte Carlo) is used to infer the optimal values over a fixed time window. The Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model generates an ensemble of photospheric maps that are used to drive WSA. When the solar wind model predictions and satellite observations are used in a newly-developed quality-of- agreement metric, sets of metric values are generated. These metric values are assumed to roughly correspond to the probability of the two key model radii. The highest metric value implies the optimal radii. Data assimilation entails additional choices relating to input realization and timeframe, with implications for variation in the solar wind over time. We present this work in its theoretical context and with practical applications for prediction accuracy.

We present a new data assimilation algorithm known as the Continuous Data Assimilation (CDA) algorithm that has been tested extensively in the mathematical literature and, most recently, in a downscaling simulation in the atmospheric literature. Unlike more common data assimilation methods, the CDA algorithm has an exponential convergence rate and is computationally efficient. This work is the first attempt to demonstrate the viability of the data assimilation algorithm in large-scale ocean models. We implement the CDA algorithm in the Model for Prediction Across Scales - Ocean in an idealized mesoscale eddy test case, demonstrating the ability of the data assimilation algorithm to capture the net effects of unresolved processes in low-resolution models.