TY - JOUR
T1 - Accounting for variability in ULF wave radial diffusion models
AU - Thompson, Rhys
AU - Watt, Clare
AU - Williams, Paul
N1 - Funding Information:
R.?L.?T. was supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant EP/L016613/1. C.?E.?J.?W. is supported by Natural Environment Research Council (NERC) Grant NE/P017274/1 and Science and Technology Facilities Council (STFC) Grant ST/R000921/1.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - Many modern outer radiation belt models simulate the long‐time behavior of high‐energy electrons by solving a three‐dimensional Fokker‐Planck equation for the drift‐ and bounce‐averaged electron phase space density that includes radial, pitch‐angle and energy diffusion. Radial diffusion is an important process, often characterized by a deterministic diffusion coefficient. One widely‐used parameterization is based on the median of statistical ultra low frequency (ULF) wave power for a particular geomagnetic index Kp. We perform idealized numerical ensemble experiments on radial diffusion, introducing temporal and spatial variability to the diffusion coefficient through stochastic parameterization, constrained by statistical properties of its underlying observations. Our results demonstrate the sensitivity of radial diffusion over a long time period to the full distribution of the radial diffusion coefficient, highlighting that information is lost when only using median ULF wave power. When temporal variability is included, ensembles exhibit greater diffusion with more rapidly varying diffusion coefficients, larger variance of the diffusion coefficients and for distributions with heavier tails. When we introduce spatial variability, the variance in the set of all ensemble solutions increases with larger spatial scales of variability. Our results demonstrate that the variability of diffusion affects the temporal evolution of phase space density in the outer radiation belt. We discuss the need to identify important temporal and length scales to constrain variability in diffusion models. We suggest that the application of stochastic parameterization techniques in the diffusion equation may allow the inclusion of natural variability and uncertainty in modelling of wave‐particle interactions in the inner magnetosphere.
AB - Many modern outer radiation belt models simulate the long‐time behavior of high‐energy electrons by solving a three‐dimensional Fokker‐Planck equation for the drift‐ and bounce‐averaged electron phase space density that includes radial, pitch‐angle and energy diffusion. Radial diffusion is an important process, often characterized by a deterministic diffusion coefficient. One widely‐used parameterization is based on the median of statistical ultra low frequency (ULF) wave power for a particular geomagnetic index Kp. We perform idealized numerical ensemble experiments on radial diffusion, introducing temporal and spatial variability to the diffusion coefficient through stochastic parameterization, constrained by statistical properties of its underlying observations. Our results demonstrate the sensitivity of radial diffusion over a long time period to the full distribution of the radial diffusion coefficient, highlighting that information is lost when only using median ULF wave power. When temporal variability is included, ensembles exhibit greater diffusion with more rapidly varying diffusion coefficients, larger variance of the diffusion coefficients and for distributions with heavier tails. When we introduce spatial variability, the variance in the set of all ensemble solutions increases with larger spatial scales of variability. Our results demonstrate that the variability of diffusion affects the temporal evolution of phase space density in the outer radiation belt. We discuss the need to identify important temporal and length scales to constrain variability in diffusion models. We suggest that the application of stochastic parameterization techniques in the diffusion equation may allow the inclusion of natural variability and uncertainty in modelling of wave‐particle interactions in the inner magnetosphere.
KW - ULF waves
KW - space weather
KW - stochastic model
KW - wave-particle interactions
UR - http://www.scopus.com/inward/record.url?scp=85089909170&partnerID=8YFLogxK
U2 - 10.1029/2019JA027254
DO - 10.1029/2019JA027254
M3 - Article
SN - 0148-0227
VL - 125
JO - Journal of Geophysical Research
JF - Journal of Geophysical Research
IS - 8
M1 - e2019JA027254
ER -