### Re: [arts-users] O3 Jacobians

```Thanks, Patrick!

On Fri, Apr 5, 2019 at 2:14 PM Patrick Eriksson <
patrick.eriks...@chalmers.se> wrote:

> Hi,
>
>
> > so, logrel and rel only make a difference in a (externally coupled)
> > retrieval, e.g. with qpack, not with plain ARTS. is that correct?
>
> Yes.
>
>
>
> > so, when I'd like to label a (logrel) O3 Jacobians plot, I could use K /
> > 100% O3? or what would you suggest?
>
> Yes, that labeling looks OK, besides that the value of the Jacobian also
> depends on the layer thickness. The original values are per layer. One
> option is to divide the Jacobian with the layer thickness in km to write
> e.g. "K/(100%O3*km)"
>
> /P
>

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=
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Email: jana.mend...@gmail.com
Phone : +46 (0)708 860 729
=
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### Re: [arts-users] O3 Jacobians

```
Hi,

so, logrel and rel only make a difference in a (externally coupled)
retrieval, e.g. with qpack, not with plain ARTS. is that correct?

Yes.

so, when I'd like to label a (logrel) O3 Jacobians plot, I could use K /
100% O3? or what would you suggest?

Yes, that labeling looks OK, besides that the value of the Jacobian also
depends on the layer thickness. The original values are per layer. One
option is to divide the Jacobian with the layer thickness in km to write
e.g. "K/(100%O3*km)"

/P
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### Re: [arts-users] O3 Jacobians

```Hi Patrick, Hi all,

On Fri, Apr 5, 2019 at 6:16 AM Patrick Eriksson <
patrick.eriks...@chalmers.se> wrote:

>
> Are you just interested in the Jacobian or will you also perform
> retrievals (by Qpack?)?
>

for now, just in the Jacobians.

though, the setup for the O3 Jacobians as we used so far comes from Uwe's
O3 retrieval processing. I start thinking that the logrel setting is
probably not the best when trying to understand the meaning and the role of
Jacobians, and when comparing the O3 Jacobians, e.g. to the wind Jacobians
(@Mathias, @Rita, we should probably discuss this...).

later this shall result in retrievals (of wind, actually), likely using
qpack (for the simple reason that we use Uwe's O3 retrieval as
example/proxy/base and this is using qpack).

>
> > our main issue here is to understand what unit logrel(O3) implies.
> > following Patrick's advice from the previous (wind) thread, I checked
> > the AUG (and the correct one for that matter - cause we're still using
> > arts2.2; 'logrel' retrieval unit seems to be gone in arts2.3) - et voila!
> > (it's sec. 16.4 for all others interested in the matter)
>  >
> > so, according to my understanding of Sec16.4, 'logrel' is (at least
> > regarding the Jacobian output) identical to 'rel', which in turn for the
> > (semi-)analytical jacobians corresponds (or, is scaled) to a 100% change
> > in the abs species (here, O3) with respect to the species' VMRs (as
> > given by the vmr_field interpolated to the species' Jacobian p_grid). Is
> > that understanding correct?
>
> I would say yes. In my words: If we denote "logrel" as z, then
> z=log(x/xa). That is you retrieve the log of ratio with respect to a
> priori.
>
> logrel and rel give identical results for the first iteration of a
> retrieval. But differ for later iterations (handled by Qpack).
>

so, logrel and rel only make a difference in a (externally coupled)
retrieval, e.g. with qpack, not with plain ARTS. is that correct?

so, when I'd like to label a (logrel) O3 Jacobians plot, I could use K /
100% O3? or what would you suggest?
(well, just for this sake it's probably more straight-forward to use 'vmr'
units and label them K/1 or rescale them to K/ppm...)

>
> > and how is that for 'vmr' then? would the jacobians correspond to a '1'
> > (or 10^6 ppm) change in the species? or a 1ppm change? (i'm unsure what
> > VMR's SI unit is...).
>
> All Jacobians are for a unit change, so here it is "1!. That is, what
> change would you get if you add a full atmosphere of the gas of concern.
>

Ok, thanks for the confirmation!

Best wishes,
Jana

--
=
Jana Mendrok, Ph.D. (Geoscience)

Email: jana.mend...@gmail.com
Phone : +46 (0)708 860 729
=
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### Re: [arts-users] O3 Jacobians

```
Hi Jana,

Are you just interested in the Jacobian or will you also perform
retrievals (by Qpack?)?

our main issue here is to understand what unit logrel(O3) implies.
the AUG (and the correct one for that matter - cause we're still using
arts2.2; 'logrel' retrieval unit seems to be gone in arts2.3) - et voila!

(it's sec. 16.4 for all others interested in the matter)

>
so, according to my understanding of Sec16.4, 'logrel' is (at least
regarding the Jacobian output) identical to 'rel', which in turn for the
(semi-)analytical jacobians corresponds (or, is scaled) to a 100% change
in the abs species (here, O3) with respect to the species' VMRs (as
given by the vmr_field interpolated to the species' Jacobian p_grid). Is
that understanding correct?

I would say yes. In my words: If we denote "logrel" as z, then
z=log(x/xa). That is you retrieve the log of ratio with respect to a
priori.

logrel and rel give identical results for the first iteration of a
retrieval. But differ for later iterations (handled by Qpack).

and how is that for 'vmr' then? would the jacobians correspond to a '1'
(or 10^6 ppm) change in the species? or a 1ppm change? (i'm unsure what
VMR's SI unit is...).

All Jacobians are for a unit change, so here it is "1!. That is, what
change would you get if you add a full atmosphere of the gas of concern.

Bye,

Patrick
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```

### Re: [arts-users] O3 Jacobians

```Hi,

On Thu, Apr 4, 2019 at 12:35 PM Richard Larsson
wrote:

> [...]
>
In your jacobianAddAbsSpecies, you set the unit of x to be logrel.  So, the
> unit in your case of J will be [iy_unit / logrel(O3)].
>

our main issue here is to understand what unit logrel(O3) implies.
AUG (and the correct one for that matter - cause we're still using arts2.2;
'logrel' retrieval unit seems to be gone in arts2.3) - et voila!
(it's sec. 16.4 for all others interested in the matter)

so, according to my understanding of Sec16.4, 'logrel' is (at least
regarding the Jacobian output) identical to 'rel', which in turn for the
(semi-)analytical jacobians corresponds (or, is scaled) to a 100% change in
the abs species (here, O3) with respect to the species' VMRs (as given by
the vmr_field interpolated to the species' Jacobian p_grid). Is that
understanding correct?

and how is that for 'vmr' then? would the jacobians correspond to a '1' (or
10^6 ppm) change in the species? or a 1ppm change? (i'm unsure what VMR's
SI unit is...).

best wishes,
Jana

--
=
Jana Mendrok, Ph.D. (Geoscience)

Email: jana.mend...@gmail.com
Phone : +46 (0)708 860 729
=
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```

### Re: [arts-users] O3 Jacobians

```Hi again Rita,

The ARTS approach to all this comes from the idealistic view of a computer
model as a simple linear algebra system,

J ยท x = y,

where J is 'the model', or the Jacobian matrix, x is the model input, i.e.,
O3, and y is the model output, i.e., the simulated radiation.  From this,
the units in J must, when multiplied by x, give the unit of y.  You have
iy_unit only in the individual *Standard iy-functions, like
to be logrel.  So, the unit in your case of J will be [iy_unit /
logrel(O3)].

Note that if you add more components to the Jacobian, such as wind or
temperature or whatnot, then these additions will have different units in
their respective positions of J and x.

With hope,
//Richard

Den tors 4 apr. 2019 kl 12:46 skrev Rita Kajtar :

> Hello!
>
>
> Since it is hard to trust that the e-mails sent from my LTU account are
> reaching everybody in the ARTS users list, I will, from now on, use my
> Gmail account.
>
> Thank you to those who helped out with my first problem.
>
> Below is another short question I addressed to the community yesterday,
> but I am not sure who received it or if anyone received it at all. If
> someone did, my apologies for spamming again.
>
> This time my question is related to the calculation of Jacobians for O3.
>
> I am considering a no winds, no specific atmospheric background case and
> the jacobianAddAbsSpecies in my control file is set as it follows:
>
>
>
>
>
>
>
>
>
>
> g3=gas1_jac_lon_grid,  species="O3",  method="analytical",  unit="logrel",
>   )*
>
> When looking at the change in Bt in my plots, in what units the change of
> O3 is being represented?
>
>
> Best regards,
>
> Rita Kajtar
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```