# Doesn't the sublimation rate on glaciers depend on the (specific) latent heat of sublimation of water ice?

There is an expression for sublimation rate as a function of latent heat flux $L$ and (specific) latent heat of sublimation (of water ice) $\lambda$.
But then $L$ itself is given as a function of the latent heat of sublimation ($\lambda$):
So... doesn't $\lambda$ cancel out!? This would imply that the latent heat of sublimation doesn't matter at all here, which I guess is possible since it's a kinetically controlled process.