A bug in CLM root distribution function

[chen1718@umn_edu]

Hi all,I was curious about the root distribution in CESM for different PFTs so I tried plot them in Matlab using the functions given in the Tech book. But I met error, so I found out the original paper of Zeng X., 2001 which gave a description of the original root distribution equation. I wrote the numerical equations myself, compared them to the code, and I found this bug.The root fraction rootfr in each soil layer currently is calculated as:         do lev = 1, nlevsoi-1
            rootfr(p,lev) = .5_r8*( exp(-roota_par(ivt(p)) * zi(c,lev-1))  &
                               + exp(-rootb_par(ivt(p)) * zi(c,lev-1))  &
                               - exp(-roota_par(ivt(p)) * zi(c,lev  ))  &
                               - exp(-rootb_par(ivt(p)) * zi(c,lev  )) )
         end do
         rootfr(p,nlevsoi) = .5_r8*( exp(-roota_par(ivt(p)) * zi(c,nlevsoi-1))  &
                                + exp(-rootb_par(ivt(p)) * zi(c,nlevsoi-1)) )
 However, given the equation that Zeng X.2001 gave, the calculation should be:         lev = 1         rootfr(p,lev) = 1 - .5_r8*( exp(-roota_par(ivt(p)) * zi(c,lev))  &
                               + exp(-rootb_par(ivt(p)) * zi(c,lev)) )         do lev = 2, nlevsoi
            rootfr(p,lev) = .5_r8*( exp(-roota_par(ivt(p)) * zi(c,lev-1))  &
                               + exp(-rootb_par(ivt(p)) * zi(c,lev-1))  &
                               - exp(-roota_par(ivt(p)) * zi(c,lev  ))  &
                               - exp(-rootb_par(ivt(p)) * zi(c,lev  )) )
         end doThe corrected equation will give a cumulative root fraction of 1 by adding all of the root fractions throughout the soil layers while the current equation does not. Hope this helps. Ming

 

[oleson]

It appears to be correct as coded.  I coded up the tech note equations in
NCL and it sums to one for all pfts.  I also checked the output of the
CLM4.5 code and it sums to one as well.
Here is the output for grassland, which sums to one:

(1)     0.1048206
(2)     0.1338198
(3)     0.1595498
(4)     0.1617819
(5)     0.138807
(6)     0.1124461
(7)     0.09343975
(8)     0.06386776
(9)     0.02640226
(10)    0.005065059<br /><br />You could check your calculations against this.<br /><br />

Keith Oleson<br />NCAR

 

[oleson]

It appears to be correct as coded.  I coded up the tech note equations in
NCL and it sums to one for all pfts.  I also checked the output of the
CLM4.5 code and it sums to one as well.
Here is the output for grassland, which sums to one:

(1)     0.1048206
(2)     0.1338198
(3)     0.1595498
(4)     0.1617819
(5)     0.138807
(6)     0.1124461
(7)     0.09343975
(8)     0.06386776
(9)     0.02640226
(10)    0.005065059<br /><br />You could check your calculations against this.<br /><br />

Keith Oleson<br />NCAR

 

[oleson]

It appears to be correct as coded.  I coded up the tech note equations in
NCL and it sums to one for all pfts.  I also checked the output of the
CLM4.5 code and it sums to one as well.
Here is the output for grassland, which sums to one:

(1)     0.1048206
(2)     0.1338198
(3)     0.1595498
(4)     0.1617819
(5)     0.138807
(6)     0.1124461
(7)     0.09343975
(8)     0.06386776
(9)     0.02640226
(10)    0.005065059<br /><br />You could check your calculations against this.<br /><br />

Keith Oleson<br />NCAR

 

[oleson]

It appears to be correct as coded.  I coded up the tech note equations in
NCL and it sums to one for all pfts.  I also checked the output of the
CLM4.5 code and it sums to one as well.
Here is the output for grassland, which sums to one:

(1)     0.1048206
(2)     0.1338198
(3)     0.1595498
(4)     0.1617819
(5)     0.138807
(6)     0.1124461
(7)     0.09343975
(8)     0.06386776
(9)     0.02640226
(10)    0.005065059<br /><br />You could check your calculations against this.<br /><br />

Keith Oleson<br />NCAR

 

[chen1718@umn_edu]

Dear Keith,
Thank you for your reply. NCL has the subscripts starting from 0, while in matlab subscripts start from 1 (that is why I got error message from the first equation). I remember that in CESM all the subscript start from 0 as well (This is a little bit confusing...) If that's true and there is a z0=0 in CESM, then the two coding are actually the same. Thank you for discussing with me.Best,Ming 

 

[chen1718@umn_edu]

Dear Keith,
Thank you for your reply. NCL has the subscripts starting from 0, while in matlab subscripts start from 1 (that is why I got error message from the first equation). I remember that in CESM all the subscript start from 0 as well (This is a little bit confusing...) If that's true and there is a z0=0 in CESM, then the two coding are actually the same. Thank you for discussing with me.Best,Ming 

 

[chen1718@umn_edu]

Dear Keith,
Thank you for your reply. NCL has the subscripts starting from 0, while in matlab subscripts start from 1 (that is why I got error message from the first equation). I remember that in CESM all the subscript start from 0 as well (This is a little bit confusing...) If that's true and there is a z0=0 in CESM, then the two coding are actually the same. Thank you for discussing with me.Best,Ming 

 

[chen1718@umn_edu]

Dear Keith,
Thank you for your reply. NCL has the subscripts starting from 0, while in matlab subscripts start from 1 (that is why I got error message from the first equation). I remember that in CESM all the subscript start from 0 as well (This is a little bit confusing...) If that's true and there is a z0=0 in CESM, then the two coding are actually the same. Thank you for discussing with me.Best,Ming