The Lumina Observer Aurora Probability Model

The Lumina probability model is a chance-of-rain-style forecast for aurora visibility. First it computes a short-term probability from current conditions, using the IMF field strength as the primary metric. Then it updates a storm-memory state driven by normalised Newell coupling, which rises during sustained driving and decays more slowly afterward. Finally it combines the short-term probability and storm memory in log-odds space, then maps back to a value of 0-1 (represented as a percentage in the app interface). It applies geomagnetic-latitude dependence, so the same conditions can yield different viewing odds by location, ie. a user in Tasmania will see increased odds versus a user in Adelaide at the same point in time.

The model is designed to be physically informed, responsive to real-time conditions, and to carry forward storm loading so the probability doesn't drop to zero during brief lulls.

Model summary

• The model has three layers:
  1. raw Newell coupling input;
  2. storm memory state; and
  3. final displayed probability.
• The short-term layer estimates aurora probability with a logistic equation: it adds several physically meaningful inputs, then converts the result into a probability between 0 and 1.
• Inputs are: solar wind coupling strength (Newell), cumulative southward IMF influence (a southward-Bz integral score), NOAA hemispheric power, solar wind dynamic pressure, and geomagnetic local time (with a midnight boost).
• The local time term uses a cosine falloff to midnight, which gives a smooth taper from peak weighting near midnight to zero at the window edge.
• Each input is soft-saturated with x / (x + a) , so very large values still help but with diminishing returns. This prevents one extreme metric from dominating unrealistically.
• The weighted sum is:

  \[ z = b_0 + w_1 f_{\text{Newell}} + w_2 f_{\text{Bz}} + w_3 f_{\text{Power}} + w_4 f_{\text{Pressure}} + w_5 f_{\text{Midnight}} \]

  and probability is:

  \[ p = \sigma(z) = \frac{1}{1 + e^{-z}} \]

• Storm memory is driven by normalised Newell coupling, where Newell is mapped into 0-1 with soft saturation and updated as a charge/decay process (faster rise, slower relaxation).
• The final displayed aurora probability blends short-term probability with storm memory in log-odds space:

  \[ \operatorname{logit}(p_{\mathrm{final}}) = \operatorname{logit}(p_{\mathrm{short}}) + k \cdot m \]

  \[ p_{\mathrm{final}} = \sigma\big(\operatorname{logit}(p_{\mathrm{short}}) + k \cdot m\big) \]

  where \(m \in [0,1]\) is storm memory and \(k\) is a tuning gain.

Latitude-aware adjustment

• A second step adjusts odds (not raw probability) by geomagnetic latitude, because identical solar conditions are more likely to produce visible aurora at higher geomagnetic latitudes.
• It applies a linear shift in log-odds relative to a baseline latitude, then clamps that shift to a minimum/maximum multiplier so latitude influence stays bounded and realistic.

Summary

• Strong southward IMF and coupling matter most;
• Pressure and hemispheric power add context;
• Nighttime geometry and latitude set viewing favourability;
• Storm memory carries sustained activity forward so the model doesn't give too negative a signal during brief lulls.