Dynamic linear models for forecasting of radiation belt electrons and limitations on physical interpretation of predictive models

Abstract

Key Points:• Static models are ill equipped to model dynamics in radiation belt • Models with many inputs are often nonuniquely interpretable • DLMs are attractive models for forecasting radiation belt dynamics Abstract Relationships exist between radiation belt electron flux intensities and solar drivers such as solar wind speed, ion density, and magnetic fields. The particulars of these relationships, however, are not well understood. Many forecasting models have been developed in the last 25 years, attempting to make sense of these relationships and produce accurate forecasts for electron flux intensities. We discuss some of the inherent limitations that many forecasting models (e.g., static models) possess when trying to untangle the intricate and dynamic relationships between electron flux levels and solar wind drivers. Dynamics related to the solar cycle limit physical interpretations for static forecasting models to customized and narrow time windows. Furthermore, the interrelatedness of solar drivers severely limit the ability to uniquely partition and describe the relationship between any one solar driver with electron flux levels. We suggest an alternate approach using dynamic linear models (DLMs). DLMs avoid some of the inherent limitations of physical understanding static models possess. We compare the 1 day ahead forecast accuracy of a relatively simple DLM to the current NOAA relativistic electron forecast model (REFM). The REFM does produce a more favorable prediction efficiency averaged across years when compared to the relatively simple DLM (0.749 to 0.721). However, the competitiveness of the DLM suggests that further development may lead to more accurate and interpretable models in the future.

Radiation belt electron dynamics at low L (<4): Van Allen Probes era versus previous two solar cycles

“…It has been known for decades that the intensity of the outer belt is positively correlated with solar wind speed [e.g., Paulikas and Blake , ; Baker et al ., ; Li et al ., ; Lyatsky and Khazanov , ; Reeves et al ., ; Kellerman et al ., ; Osthus et al ., ]. Also required for the enhancement of outer belt electrons is geomagnetic activity, which requires a southward component of the interplanetary magnetic field (IMF) [e.g., Miyoshi and Kataoka , ; McPherron et al ., ; Li et al ., ; Miyoshi et al ., ; Jaynes et al ., ].…”

The System Science Development of Local Time‐Dependent 40‐keV Electron Flux Models for Geostationary Orbit

“…An alternative approach to first principles‐based forecast models is the system identification or machine learning approach, where the models are automatically derived from input‐output data by computer algorithms. These algorithms include linear prediction filters (Baker et al, ; Rigler et al, ), dynamic linear models (Osthus et al, ), neural networks (Freeman et al, ; Koons & Gorney, ; Ling et al, ), and Nonlinear AutoRegressive Moving Average with eXogenous (NARMAX) inputs (Boynton, Balikhin, Billings, & Amariutei, ; Boynton et al, ; Wei et al, ). Neural networks and NARMAX methodologies are more suited to modeling the radiation belts, as the system is nonlinear with respect to the solar wind input.…”

Electron flux models for different energies at geostationary orbit

“…In this approach, models are automatically deduced from input‐output data by the system identification algorithms. The system identification methodologies include linear prediction filters [ Baker et al , ], dynamic linear models [ Osthus et al , ], neural networks [ Koons and Gorney , ; Freeman et al , ; Ling et al , ], and Nonlinear Autoregressive Moving Average with Exogenous inputs (NARMAX) [ Wei et al , ; Boynton et al , , ]. While linear prediction filters and dynamic linear models are suitable for linear systems, the main advantage of NARMAX and neural networks is that they are capable of modeling nonlinear dynamics within the system.…”