Analytical Model of Magnetospheric Whistler Mode Waves Based on Cubic Splines

We model the behavior of long-term averages of whistler mode waves in the inner magnetosphere as a function of position and geomagnetic activity. We analyze a combined data set of the Van Allen Probes and Cluster missions to construct empirical analytic expressions defined in a 4-dimensional parametric space of magnetic local time, absolute value of magnetic latitude, McIlwain's L parameter, and Kp index. We use a simple but sufficiently general functional form based on polynomial cubic splines with linear extrapolation outside of the approximation interval. The model clearly reproduces the strong influence of external driving in the equatorial region and a weak response of chorus amplitudes at high latitudes to the geomagnetic activity.