OBJECTIVES: Coupling with LMDZ

The objective of this page is to present and discuss the existing coupling scheme between ORC and LMDZ and to propose new solution to improve physical/numerical consistency in the coupling.

The main points concern i) the treatment of the Evaporation and how the "beta" factor (soil water stress) is treated as well as how the potential evaporation is calculated and ii) the treatment of the radiation in ORC (longwave and shortwave) to ensure energy conservation when coupled with LMDz.

Several documents have been produced and are usefull to understand such coupling and the major points:

1. General Coupling with GCM (Polcher et al., 1998): ​Article on Coupling
2. Updated-note on the coupling by Polcher: ​Updated note (Polcher)
3. Note by Dufresne and Ghattas on coupling with LMDZ: ​Dufresne & Ghattas
4. New note by Fuxing on recent implementations: ​Fuxing note
5. Short note by Agnes on the "beta" coefficient showing how the energy budget formulation in the current ORC-TRUNK is not consistent with the implicit scheme of Polcher et al., 1998:​Agnes note.
6. Milly, 1992, Potential evaporation and Soil Moisture in GCMs: ​Milly's paper on Milly's correction
7. Derivation of Penman equation for the evaporation of a wet surface, based on the bulk aerodynamic approach and the linearization of qsat(Ts) around Ta: ​Penman equation
8. Evaporation and surface temperature, Monteith, J. L (1981) Quart. J. Roy. Meteor. Soc., 107, 1-27
9. Brusaert (2005). Hydrology, p124-135: ​Brutsaert 2005

EVAPO-TRANSPIRATION

Evaporation during coupling (beta problem)

1. Problem:

The derivation of the surface temperature as it is done in ORCHIDEE-TRUNK is not consistent with surface energy budget equation proposed by Polcher (Polcher et al. 1998; Document 1) for implicit coupling with the vertial diffusion in the boundary layer. Document 3 by Dufresne and Ghattas gives the corresponding equations in LMDZ.

In the trunk of ORCHIDEE, the stress factor beta is missing in the denominator in the sensitivity of the latent heat flux to the surface temperature at the old time step. This is coded in enerbil as:

larsub_old = chalsu0 * vbeta1 * (un - vbeta5) * (peqBcoef -  qsol_sat) / (zikq - peqAcoef)

This is not consistent with a fully implicit surface energy budget equation (cf Documents 4 and 5) and could lead to energy conservation problem.

2. Action decided

It has been decided to re-introduce the beta and take the following formulation for the ORCHIDEE-TRUNK:

larsub_old = chalsu0 * vbeta1 * (un - vbeta5) * (peqBcoef -  qsol_sat) / (zikq - vbeta1 * (un - vbeta5) * peqAcoef)

Note that the correction does not change significantly the results of ORC-LMDZ simulations.

3. Complementary notes

As mentioned in the Updated note by Polcher (Document 2), the current formulation can be seen as a mix between an implicit scheme for net radiation, H, potential ET (ETP), and an explicit scheme for beta. This has been introduced by Jan to support the implementation of a new energy budget based on a Penmann-Monteith ETP (). But introducing the virtual temperature of a wet surface (the hypothetically wet temperature of Milly, 1992, cf Document 6), further noted T* could be implemented in the standard implicit equations. The above change could also be reverted when the new energy budget will be implemented (which is not yet the case). Both option can be explored once we are ready to change the ETP formulation.

Overestimation of Potential Evaporation

The implementation of the potential evaporation formula based on a bulk formulation that considers qsat(Ts) is not satisfactory if one refers to Budyko's framework, which defines E=beta*Ep(T*), with T* defined as above, and the potential evaporation Ep = rau/ra*[qsat(T*)-qa].

Currently the code considers qsat(Ts) and not qsat(T*), and thus overestimates potential evaporation, since Ts becomes warmer than T* as the soil dries.

In the present version, this is only addressed when computing the bare soil evaporation, which is directly controlled by the potential evaporation, owing to a supply/demand approach. To do so, the demand is not the potential evaporation of ORCHIDEE based on qsat(Ts), but it is reduced by a corrective term following Milly, 1992 (Document 6). This does not create any water/energy conservation pb, since the difference between current ETP and Penman ETP is integrated in the beta which will be used in enerbil.

Jan proposed improved approaches based on the Penman-Monteith method to calculate the ETP (formulation that provide smaller ETP than the bulk formulation that is used). They have been developed by Anais Barella during her PhD thesis and tested in forced mode. The correct surface energy budget equation for the implicit coupling is not yet available and work has to be done before implementing this approach in Orchidee.trunk. ​http://www.lmd.polytechnique.fr/~intro/Files/2014_These_Barella.pdf).

It is stressed by all the participants that improvements on the ETP are important and that Anais work is a first step in this direction. However, this new approach will create a step change for ORCHIDEE as all stress functions will need to be updated and the process must be well documented.

Note that other GCM groups also faced the same issues and have used various approaches not to overestimate ETP.

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 Penman-Monteith, i.e. Ep = rau/ra*[qsat(T*)-qa], or Ep(T*).

This potential evaporation gets smaller than the one of ORCHIDEE, which is Ep(Ts)=rau/ra*[qsat(Ts)-qa] as the moisture stress increases.

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* Ta³

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.

RADIATION

The problem of energy conservation

In order to save computing time, the time step of the radiation code is longer than that of the other components of the model (rest of the atmospheric physics and call to LSM). If the radiation budget of each component is updated at a shorter time step, the energy is not conserved in the coupled system. This is the case in the ORCHIDEE.trunk/LMDZ version where the LWnet (through lwup) is calculated separately in LMDZ and ORCHIDEE.

Note that the same is true for the SWnet. To ensure energy conservation, SWnet should be constant between two calls of the RT model of LMDZ. This implies that the surface albedo does not vary between these two calls or that the correct average albedo is used in the atmosphere. However, currently, the net SW flux computed by LMDZ is used by ORCHIDEE for the surface energy budget. The albedo computed by ORCHIDEE is used by LMDZ when radiation is computed (LMDZ uses the instantaneous value of the albedo, albedo change is of second order compared to other changes, in particular clouds). THUS, currently in a coupled mode the albedo computed by ORCHIDEE is not used by ORCHIDEE to update the net SW flux used in the surface energy budget equation therefore the energy is conserved.

An option which favours the energy conservation has been introduced by Fuxing and Jean-Louis: Practically the LWup is updated only when the radiative code is called. Note that in this case, fixing the Lwup is equivalent to fix the surface temperature between two call of the RT model.

=> It is recognized that none of the option is satisfactory and that improvement is needed. Accurate simulations of the diurnal cycle of the surface temperature and fluxes requires to be able to change the surface temperature each time ORCHIDEE is called and also to change the albedo (maybe less critical)

A satisfactory level of energy conservation an also be achieved if the Trad provided by ORCHIDEE to LMDZ (and which describes the evolution of the surface radiative temperature) is averaged properly (see Polcher et al.) and used at the radiation time steps of LMDZ. This method was used in LMD6 and gave good results in terms of diurnal cycle and energy conservation.

However, in the mean time it is required that both option are available in Orchidee.trunk to be able to check for energy conservation problems (the option favoring energy conservation has to be committed in the trunk).

Anticipated Improvements

To go further some work is necessary on the LMDZ and ORCHIDEE sides as well as on the interface.

• LMDZ is currently implementing a new radiation code (RRTM) for the SW radiation, which will allow to increase the number of spectral bands for the albedo (expecting that the spectral bands are consistent with the one adopted for the albedo calculation in Orchidee). A post-doc student is working at LMD on the implementation of the new radiative code.

• A proposition is to follow the approach described in Polcher et al. 1998 (see above link): ORCHIDEE would provide to LMDZ an averaged (over the time-steps at which the radiation is not called) radiative temperature (averaged to the power 4), emissivity and albedo (simple averages). ORCHIDEE would thus be able to have varying albedo and temperature between calls to RT model but it will still provide to LMDz the mean

• The interface variables have to be redefined and they should include : net LW and net SW radiations, in several bands ?; emissivity and albedo (several bands ?) and the mean radiative temperature. Exchanging the net LW flux allows the atmosphere to diagnose the error done by using an average Trad at its radiation time step.

But first these changes have to be documented very clearly. It is stressed that these developments would suppress the backward compatibility (should we keep the backward compatibility with a flag ?)

This calls for redefining between ORCHIDEE and LMDZ the interface variables. From the ORCHIDEE side this will enable to simplify the intersurf.f90 code. Because it breaks the backward compatibility the timing has to be well selected.