Geomagnetic Storm Index Lab: Dst & Kp from Solar Wind (2D)

Quiet

Solar Wind Input

Speed v 450 km/s

Density n 6 cm⁻³

IMF Bz 0 nT

Ring-Current Model

Decay time τ 7.7 hr

Live Readout

Ring-current Dst*

0.0 nT

Observed Dst

0.0 nT

Kp proxy

0.0

Merging field Ey

0.00 mV/m

Injection Q

0.0 nT/hr

Sim. elapsed

0.0 hr

How it works

The ring current's contribution to the Dst index is modelled with the Burton et al. (1975) injection/decay equation, a real, empirically-calibrated ODE used in operational space-weather forecasting:

Bs  = max(0, -Bz)                 // southward IMF component
Ey  = v·Bs·10⁻³                   // dawn-dusk merging electric field, mV/m
Q   = -4.4·(Ey - Ec)  if Ey>Ec     // ring-current injection, nT/hr
      0                otherwise   (Ec = 0.49 mV/m coupling threshold)
dDst*/dt = Q - Dst*/τ              // injection minus exponential decay

Pdyn = 1.6726e-6·n·v²              // solar-wind dynamic pressure, nPa
Dst_obs = Dst* + b√Pdyn - c         (b=7.26 nT/√nPa, c=11 nT)

Southward Bz (negative) opens the magnetopause to reconnection, so a stronger, more negative Bz and faster wind both raise Ey and pump energy into the ring current, deepening Dst*. Higher density raises the dynamic pressure, which compresses the magnetopause and adds a separate, positive correction to the observed Dst — the two effects are independent, which is why a dense-but-northward-IMF wind barely dents Dst* yet still nudges the observed value.

Quiet — Dst above −20 nT.
Minor storm — −50 to −20 nT.
Moderate storm — −100 to −50 nT.
Intense storm — below −100 nT (real NOAA/space-weather classification thresholds).
Kp proxy — inverted from the empirical Dst_min≈−20·Kp−10 relation (Wang 2003 fit to storm statistics).

Dst* (ring current) Observed Dst Injection Q