The eMLR approach and a
sensitivity analysis.
Toste Tanhua
Arne Körtzinger
Karsten Friis
Darryn W. Waugh
Douglas W.R. Wallace
extended Multiple
Linear Regression
(eMLR)
DIC  a0  a1  p1 .....an  pn  R
DIC bio  DIC  0.746  AOU  0.5  (Alk  NO3 )
This eMLR is based on
potential temperature
alkalinity
silicate
nitrate
AOU
Two methods to calculate the
decadal change in DIC
Sensetivity of the eMLR
determined with Monte Carlo
analysis
We used the M60/5 data
as the „historic“ data set,
and created a „modern“ data
set by adding Cant.
To this we added noise
and biases.
Testing the sensetivity of the
eMLR
Adding 2 noise
temperature 0.005°C
alkalinity 4.2 mol kg-1
DIC 1.4 mol kg-1
nitrate 0.2 mol kg-1
silicate 0.2 mol kg-1
AOU 0.6 mol kg-1
Adding bias
5 mol kg-1 too high Alk
5 mol kg-1 too low AOU
5 % too high Si
Same thing for the Western Basin
eMLR seems to be
water mass sensitive,
i.e. ideally one eMLR
for each water mass
should be done,
but this is impractical.
The systematic errors
plotted as a section
We also introduced a 20  random noise.....
The eMLR should be performed on the data set with
the „best“ data set.
Can we extend the decadal change in Cant to
the full anthropogenic period?
Cant is increasing exponentially, i.e. the
Transient Steady State assumption is valid.
c0 (t 2 )c(r )
c( r , t ) 
c0
Small sensitivity to non-exponential
growth of Cant, and to different buffer
factors for the carbonate system.
Another way of calculating Cant.
The eMLR approach compares well with a
tracer based approach.