= Accelerate Spinup jobs in ORCHIDEE =

This page presents a work which consists to implement a numerical method that
can accelerate the convergence of the SPINUP. ORCHIDEE usually use a iterativ 
and specific method based on forcesoil, consisting by running the module 
stomate_soilcarbon.f90 stand alone between 5000 and 10000 times.Before 
forcesoil, you have to run ORCHIDEE a given length just to have the litter pools 
at equilibrium. The problem with the FORCESOIL job is that you got some biaises
and takes longer at the global scale.
That's why we implement a new method for accelerating the spinup. 
This method is based used by the model PASIM(see paper and description below).

== Description of the method used by PASIM ==

PASIM is a model of prairial management developped by the INRA institute.
The soil module of PASIM is based on the CENTURY model like ORCHIDEE. It 
consists on 5 carbon which are linked by fluxes : litter structural,
litter metabolic, carbon active, carbon slow and carbon passive.(See flow chart below).
we can represent symbolically the fluxes between the pools by a matrix of size (5,5).

Each line of the matrix represents a pool and each row the fluxes received (or leaving) by 
the pool. We can consider the following equation (for more details see papers below).

Using the approximation of the derivative in time and two sequences, we obtain a equation
with the carbon stock and these two sequences. 

Mathematically, equilibrium means that carbon stock is a fixed point of the previous equation.
So we obtain a linear system which can be solved by a direct algebraic method like gauss-jordan.
The solution is the carbon stock at equilibrium.
In PASIM, we got one linear system for each point grid. The method is stopped when a criterion is
reached (relative error on the current total carbon stock calculated and the previous one).

PS : PASIM takes into account the nitrogen cycle and a similar method is used for calculating the 
nitrogen stock. This method can be easily extended.


== Adaptation to the method for ORCHIDEE ==

As it is written above, the soil module of ORCHIDEE is based on the CENTURY model like PASIM.
There are three main differences between PASIM and ORCHIDEE :

1. ORCHIDEE takes into account 7 pools. The metabolic litter and the structural litter are
both divided in 2 sub-pools : above and below. So the method for ORCHIDEE consists to search
the following solution (litter structural above, litter structural below, litter metabolic above,
litter metabolic below, carbon active, carbon slow, carbon passive)

2. There are no PFTs in PASIM. So we have to have NVM systems per each grid cell.

3. ORCHIDEE considers fire (module lpj_fire.f90). Some part of the above litter (structural + metabolic) is burned.
So we have to take into account 2 more fluxes in the matrix.		

We decided not to have the same stopping condition used by PASIM. We want for the moment to evaluate 
the relative error for each carbon pool and to consider the maximum of all these errors.

== Implementation of the method in ORCHIDEE ==

Here you find a text file which explains the implementation in ORCHIDEE (compare with the original papers) :


== Validation of the method ==

The most difficult part is the validation of the method. We have to solve many problems to find the good
setup. Moreover, we want ORCHIDEE to stop when the stopping criterion is reached even if the job is not
finished. 

Finally, we consider the following reference job :[[BR]]

- Full Orchidee (sechiba + stomate, no forcesoil)[[BR]]

- Calendar type : no_leap (we modify a forcing file for the year 1982)

- One grid cell ((6°-7°lon,49°-50°lat + IMPOSE_VEG=y (20% bare soil, 80% C3 grass)) + no fire

- Length of the simulation : 7000Y

- loop on the same forcing file (option norestart=y in COMP/driver.card + modification in readdim2.f90)

- Annual outputs

The results are accessible on /dmnfs12/cont003/p529sol/IGCM_OUT/OL2/OOL_SEC_STO7000Y. The results obtained
are (gC/m²) :

|| Pools                  ||       || 
||                        ||       ||   
||litter structural above || 2339  || 
||litter structural below || 559.2 || 
||litter metabolic above  || 142   || 
||litter metabolic below  || 55    || 
||carbon active           || 253   || 
||carbon slow             || 5873  || 
||carbon passive          || 9226  ||



=== Results obtained by the matrix method ===

Here we list the results for each pool at different lenght of simulation for the matrix method :

|| Pools                  || 50Y   || 100Y  ||  200Y || 300Y  || 400Y  || 500Y  || 1000Y || 1500Y || 2000Y || 7000Y ||
||                        ||       ||       ||       ||       ||       ||       ||       ||       ||       ||       ||
||litter structural above || 2333  || 2339  || 2339  || 2339  || 2339  || 2339  || 2339  || 2339  || 2339  || 2339  ||
||litter structural below || 558.9 || 559.3 || 559.2 || 559.2 || 559.3 || 559.1 || 559.2 || 559.3 || 559.2 || 559.2 ||
||litter metabolic above  || 142.2 || 142.3 || 142.2 || 142   || 142.3 || 142   || 142.2 || 142.3 || 142.4 || 142.1 ||
||litter metabolic below  || 55.03 || 55.09 || 55.03 || 54.96 || 55.09 || 55.09 || 55.03 || 55.09 || 55.1  || 55    ||
||carbon active           || 250.4 || 252.9 || 252.8 || 253   || 253.2 || 252.8 || 252.9 || 253.2 || 253.2 || 253   ||
||carbon slow             || 5706  || 5856  || 5873  || 5873  || 5873  || 5873  || 5873  || 5873  || 5873  || 5873  ||
||carbon passive          || 8728  || 8980  || 9111  || 9155  || 9176  || 9190  || 9215  || 9223  || 9226  || 9229  ||

We notice that the convergence of the method is controlled by the carbon passive pool. We focus on the evolution of the 
relative error of the carbon passive obtained by the matrix method to the reference one :

|| 100Y  || 200Y  || 300Y  || 400Y  || 500Y  || 1000Y || 1500Y || 2000Y || 7000Y ||
|| 2.66% || 1.24% || 0.76% || 0.54% || 0.39% || 0.14% || 0.05% || 0.0%  || 0.05% ||


We obtained the following time series :






=== Comparison with Forcesoil ===

We want to compare now with the forcesoil job. In ORCHIDEE, it consists to run soilcarbon
a certain number of times after and before running full ORCHIDEE. 
We consider the same point, we loop over the same forcing file and we use a noleap calendar. This
is the spinup configuration we use :

{{{
    # SPINUP configuration : 
    # ----------------------
# Initialisation for spin-up :
# sechiba alone (!!! only if ok_stomate == n !!!)
duree_nostomate=0
# sechiba and stomate
duree_inistomate=250
# teststomate (only if duree_nostomate or duree_inistomate > 0)
duree_offlineini=0

# Loop configuration for spin-up :
# The whole job is restarted n_iter times
n_iter=1
# orchidee with sechiba (and stomate if ok_stomate=y below)
duree_sechiba=10
# teststomate
duree_stomate=0
# forcesoil
duree_carbonsol=10000

# Finalization for spin-up :
# all orchidee
duree_final=250
# This last parameter must be non-zero.

}}}

We obtain the following results at the end of the simulation:  	

|| Pools                  ||       || 
||                        ||       ||   
||litter structural above || 2339  || 
||litter structural below || 559.2 || 
||litter metabolic above  || 142   || 
||litter metabolic below  || 54.9  || 
||carbon active           || 253   || 
||carbon slow             || 5873  || 
||carbon passive          || 9223  ||
 	
The output files can be found at : /dmnfs12/cont003/p529sol/IGCM_OUT/OL2/SpinUp_classic_setup_nofire