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![\begin{displaymath}
\frac{\partial Tcal}{\partial Trec} =
\frac{\partial Tcal}{...
...artial Tcal}{\partial Tau} \frac{\partial Tau}{\partial Trec}
\end{displaymath}](img70.png) |
(33) |
From Eq. (18)
![\begin{displaymath}
\frac{\partial Tcal}{\partial T_{emi}}
= \frac{Tcal}{T_{emi}-T_{load}}
\end{displaymath}](img71.png) |
(34) |
and from Eq. (20)
![\begin{displaymath}
\frac{\partial T_{emi}}{\partial Trec} = -1 + \frac{T_{emi}+Trec}
{T_{load}+Trec}
\end{displaymath}](img72.png) |
(35) |
thus
![\begin{displaymath}
\frac{\partial Tcal}{\partial T_{emi}} \frac{\partial T_{emi}}{\partial Trec}
= \frac{Tcal}{T_{load}+Trec}
\end{displaymath}](img73.png) |
(36) |
For the second term, from Eq. (18)
![\begin{displaymath}
\frac{\partial Tcal}{\partial Tau} = Air\_mass * Tcal
\end{displaymath}](img74.png) |
(37) |
and from Eq. (27)
![\begin{displaymath}
\frac{\partial Tau}{\partial Trec} =
\frac{\partial Tau}{\partial T_{emi}} \frac{\partial T_{emi}}{\partial Trec}
\end{displaymath}](img75.png) |
(38) |
![\begin{displaymath}
\frac{\partial Tau}{\partial Trec} =
\frac{1}{Air\_mass * T_{atm} * F_{eff}} \frac{\partial T_{emi}}{\partial Trec}
\end{displaymath}](img76.png) |
(39) |
![\begin{displaymath}
\frac{\partial Tcal}{\partial Tau} \frac{\partial Tau}{\part...
...cal}{T_{atm} * F_{eff}} \frac{T_{emi}-T_{load}}{T_{load}+Trec}
\end{displaymath}](img77.png) |
(40) |
giving finally
![\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial Trec} =
\frac{...
...eff} - T_{load} + T_{emi}}
{F_{eff}*T_{atm}*(T_{load} + Trec)}
\end{displaymath}](img78.png) |
(41) |
The typical numbers mentionned above, with
, yield
![\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial Trec} =
\frac{F_{eff}-1}{F_{eff}} \frac{1}{T_{load}+Trec}
\end{displaymath}](img80.png) |
(42) |
of the order of
per K. Note that this could be higher for
higher opacities (hence higher
).
Next: Relative to
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Gildas manager
2014-07-01