Relative to $\eta$

$Tcal$ has a slightly different definition in this case, and

  $$\frac{\partial Tcal}{\partial \eta} = \frac{Tcal}{\eta} + \frac{\... ...Tau} + \frac{\partial Trec}{\partial \eta} \frac{\partial Tcal}{\partial Trec}$$ (48)

  $$\frac{\partial Tau}{\partial \eta} = \frac{1}{T_{atm} * F_{eff}}\frac{\partial Temi}{\partial \eta}$$ (49)

  $$\frac{\partial Temi}{\partial \eta} = -\frac{T_{emi}+Trec}{\eta ^2} + \frac{\partial Trec}{\partial \eta} \frac{T_{emi}-T_{load}}{T_{load}+Trec}$$ (50)

In TREC mode, derivative with respect to $Trec$ must be omitted, and

  $$\frac{1}{Tcal} \frac{\partial Tcal}{\partial \eta} = \frac{\eta * T_{atm} * F{eff} - T_{emi} - Trec}{\eta ^2}$$ (51)

With a cold load, a corresponding equation could be derived using

  $$\frac{\partial Trec}{\partial \eta} = Trec \frac{Trec-T_{cold}}{T_{load}- \eta * T_{cold} + (1-\eta) * Trec}$$ (52)