Classical Köhler Theory vs κ-Köhler Theory in A Study Accommodating Black Carbon (BC) heating - Which one/When to use
Excellent — you're using the classical Köhler theory to compute the equilibrium saturation ratio (Seq), and you’re asking how this compares to the κ-Köhler theory approach. Let’s explain the difference clearly and provide the equations. Note: As in Nenes (2002), there are 4 scenarios how the presence of BC affect the formed DSD: Scenario 1 (NoHeat scenario): just as the basic assumption in cloud parcel model - there's only latent heat release upon condensation. d T /dt = adiabatic cooling + latent heating Scenario 2 (Drop scenario): There's additional heat (reflected by ga value) caused by light absorption of BC in addition to the basic latent heat; this additional heat influence only the Seq of the water droplet. d T /dt = adiabatic cooling + latent heating (No change); but Seq change Scenario 3 (External Scenario); The BC is not part of the droplet, i.e. externally mixed particle with the hygroscopic or water absorbing particles, so the BC doesn't heat th...