Use ifelse in liquid_fraction, plus a comment

src/relations.jl

@@ -968,7 +968,7 @@ end
 
 # we may be hitting a slow path:
 # https://stackoverflow.com/questions/14687665/very-slow-stdpow-for-bases-very-close-to-1
-pow_hack(x, y) = exp(y * log(x))
+@inline pow_hack(x, y) = exp(y * log(x))
 
 function saturation_vapor_pressure(
     param_set::APS,
@@ -1290,24 +1290,26 @@ is a function that is 1 above `T_freeze` and goes to zero below `T_icenuc`.
 function liquid_fraction(
     param_set::APS,
     T::FT,
-    ::Type{phase_type},
+    ::Type{State},
     q::PhasePartition{FT} = q_pt_0(FT),
-) where {FT <: Real, phase_type <: ThermodynamicState}
-    _T_freeze::FT = TP.T_freeze(param_set)
-    _T_icenuc::FT = TP.T_icenuc(param_set)
-
-    if T > _T_freeze
-        return FT(1)
-    elseif T > _T_icenuc
-        _pow_icenuc::FT = TP.pow_icenuc(param_set)
-        if _pow_icenuc == 1
-            return (T - _T_icenuc) / (_T_freeze - _T_icenuc)
-        else
-            return ((T - _T_icenuc) / (_T_freeze - _T_icenuc))^_pow_icenuc
-        end
-    else
-        return FT(0)
-    end
+) where State <: ThermodynamicState
+
+    Tᶠ = TP.T_freeze(param_set)   # freezing temperature
+    Tⁿ = TP.T_icenuc(param_set)   # temperature of homogeneous ice nucleation
+    α  = TP.pow_icenuc(param_set) # power law partial ice nucleation parameter
+
+    # Model for cloud water condensate probabilty when temperature is below
+    # freezing (all liquid condensate), but above the temperature of homogeneous
+    # ice nucleation (all ice condensate). In it's simplest form, this is simply
+    # a number that varies between 0 and 1. For example, see figure 6 in 
+    # Hu et al., https://doi.org/10.1029/2009JD012384, JGR (2010).
+    λᵖ = ((T - Tⁿ) / (Tᶠ - Tⁿ))^α
+
+    above_freezing = T > Tᶠ
+    supercooled_liquid = (T ≤ Tᶠ) & (T > Tⁿ)
+
+    return ifelse(above_freezing, one(FT),
+           ifelse(supercooled_liquid, λᵖ, zero(FT)))
 end
 
 function liquid_fraction(
@@ -2776,8 +2778,7 @@ relative_humidity(
     PhasePartition(param_set, ts),
 )
 
-relative_humidity(param_set::APS, ts::AbstractPhaseDry{FT}) where {FT <: Real} =
-    FT(0)
+@inline relative_humidity(::APS, ::AbstractPhaseDry{FT}) where FT = zero(FT)
 
 """
     total_specific_enthalpy(e_tot, R_m, T)