Changes between Version 23 and Version 24 of Documentation/CouplingLMDZ

Timestamp:

2014-10-29T12:05:22+01:00 (10 years ago)

Author:

aducharne

Comment:

--

Documentation/CouplingLMDZ

@@ -69 +69 @@
 Agnes is not fully convinced yet by the above analysis on potential evaporation, since the evaporation formulation in ORCHIDEE perfectly fits the developments of Brutsaert (see Document 8, p133-135), showing how to introduce a surface evaporation based on qsat(Ts) and a surface resistance into the standard bulk aerodynamic formulation of E. In this framework, the maximum rate at each time step is different from the potential evaporation of Budyko, but is it really a pb ?
 
+
+== Milly's correction ==
+
+This correction is presently introduced in the code to estimate the potential evaporation of Budyko (or Penman-Monteith, or Thornthwaite), i.e. Ep = rau/ra*[qsat(T*)-qa], or Ep(T*).
+
+This potential evaporation is smaller than the one of ORCHIDEE, which is Ep(Ts)=rau/ra*[qsat(T*)-qa].
+
+Milly, 1992 (Document 6) applies a first-order linearisation of qsat(T) around Ta (like in the derivation of the Penman formula for wet surface evaporation, see Document 7) for qsat(T*) and qsat(Ts). The expressions of Ep(T*) and Ep(Ts) are then found by using the unstressed/stressed energy budget equation respectively (in which the upward LW term is also linearized). 
+
+The resulting link between Ep(T*) and Ep(Ts) is given by Equation 17 of Milly, 1992, which is equivalent to equation E14 of Patricia's de Rosnay's PhD thesis. They can be written as: 
+        Ep(T*) = Ep(Ts)*b/(a+b),
+
+        a = rau*cp_air/ra + chalev0*rau*delta*vbeta/ra + 4*emis*c_stefan* Ta^3
+
+        b = chalev0*rau*delta*(1-vbeta)/ra
+
+        delta is the derivative of qsat(T) at Ta
+
+This is equivalent to the equations in the code (in enerbil_flux), if one replaces vbeta by vevapp(ji)/evapot(ji), delta by grad_qsat(ji), and ra by 1/qc.
+
+In this development, one (= Agnès) can question the validity of linearizing qsat(T*) around Ta, as T* can become very different from Ta, especially in dry areas/period.
+
 [[BR]]