[daip] Re: Question about DELZN

[Leonia Kogan]

Amy,

The following is the message I have prepared to answer on the today (one 
of everyday) Richard's message.
Is it written clearly?
Can you please read it and tell me your comments.

Thanks

Leonia

Richard Dodson wrote:

>Leonid,
>
>  I am, we are, trying to extend DELZN into new modes of use. Please
>be patient.
>
> You said many messages ago:
>
>  
>
>>Lets note that VAL_IANT -VAL_RANT are the values picked up from the SN
>>table as a function of time.
>>    
>>
>
>   I.e. which was exactly as I expected. I.e. that Value in the SN
>table is the difference. Now you have made a little clearer what you
>meant. I.e. (if I have understood your latest mail) that VAL is that
>which is found in the SN table. Not VAL_i-VAL_ref.
>  
>

I do not rememeber now who of us wrote this or that.
So let me start from the scratch what DELZN plots.

The value picked up from the SN table at the time 'time' (including 
calibrator observation at the set of times) is determined as:

VAL(time)  = ATMZEN_ant(time) * MAP_ant(time) - ATMZEN_ref(time) * 
MAP_ref(time) + CLOCK(time)    (1)

where
'ant' is antenna at the list of ,  'ref' is the antenna used as a 
reference during creation of  the SN table.
consider that the same 'ref'; used always, although DELZN can handle the 
case of variable 'ref' ;
ATMZEN_ant(time)  is the thickness of the zenith atmosphere at the time 
'time' above antenna 'ant' ;
ATMZEN_ref(time)  is the thickness of the zenith atmosphere at the time 
'time' above antenna 'ref' ;
CLOCK(time) is the residual of the clock difference ant-ref as a 
function of time.

DELZN finds the solution for
ATMZEN_ant(time) =POLYN_ant(time),
ATMZEN_ref(time) 
=POLYN_ref(time),                                                                                                              
(2)
CLOCK(time)  = POLYN_clock(time)

The solution is found using all antennas, reference antennas, times 
together!! (If it is important for your understanding)

Using equatioins (2) we can rewrite the equation (1):

VAL(time)  = POLYN_ant(time) * MAP_ant(time) - POLYN_ref(time) * 
MAP_ref(time) + POLYN_clock(time)    (3)

Solving (3) for  POLYN_ant(time)  (for example)  we can find relation 
between fitted polynomial of the ant zenith atmosphere
POLYN_ant(time)  and VAL(time)-SN table values:

POLYN_ant(time)  = [VAL(time)  + POLYN_ref(time) * MAP_ref(time) 
-POLYN_clock(time) ]  /  MAP_ant(time)   (3)

The right part of the equation (3) is plotted as points of data;   the 
left part of the equation (3) is plotted as the curve.of the polynomial.

Pay attention that the right part of the equation (3) is not SN table 
data (VAL). It includes the other two fitted polynomial as well.!!!

When I was creating DELZN I did not plan to plot anything. Then I 
decided to add plotting although it is  a big job.
The help file includes brief explanation of the plots and people stoped 
askinge me what is plotted.

I hope this detail explanation helps you to understand completely what 
is plotted!


>   As you have hinted there have been many people unable to interpret
>the plots. I am just more stubborn and demanding than most, for which
>I apologize -- but I am unable to change and will continue to ask
>questions.
>
>  I would be able to understand better if I could see the plots of the
>calculated atmosphere -- for a dataset we are sure works (i.e. the
>test one you have been using) -- under various changes of parameters.
>If it is too much work to make the plots I asked for could I run the
>tests myself? I would be happy to and it would be less work for you.
>
> So. Are we making progress? I believe so. You have demonstrated to
>yourself that the VLBA can solve for the atmosphere on a single source
>tracked for a day, which is exactly what we need for the VERA case. We
>have a VERA experiment on the 22nd of March and we plan to combine the
>usual operation with a more normal DELZN strategy. Then we will be
>able to compare the results. This is why we need to sort out these
>questions.
>
> Perhaps it would be useful to list the outstanding questions?
>
> I would like to see the similar plot that you sent, but with a lower
>order polynomial fitted. I know I am asking for more work -- but it
>should be quick to run. Alternatively I can run these tests on the
>test data myself. This I think would be the more profitable.
>
>>From your mail of March 3rd.
>-----------------------------
>  
>
>>>If one alters the number
>>>of parameters fitted for ATM one gets wildly different answers.
>>>      
>>>
>
>  
>
>>Of cource. You can fit the linear polynomial to these data with
>>    
>>
>different >parameters.
>  
>
>>The fitting will be a little bit worse but still reasonable. So your
>>    
>>
>following >statement isong.
>-----------------------------
>
>With the clearer explanation of what the DELZN plots of the Zenith
>delay are really showing I have a better understanding. However I
>still would like to see the linear polynomial fit to the data file.
>
>
>  
>
>>I have looked at your plots and see that the elevation differences are
>>less than 15 degrees. May be it is too small.
>>    
>>
>
>  Why is the elevation difference important to the solutions? Or do
>you mean that the atmosphere over the antennae will be the same
>therefore solutions derived from the differences will be degenerate?
>  
>

IF THE ELEVATIONS OF ALL ANTENNAS ARE IDENTICAL THEN THE DIFFERENCES 
ANT_REF
ARE EQUAL ZERO FOR ANY TIME/CALIBTATORS ARE EQUAL ZERO AND THEREFORE 
NOTHING CAN BE SOLVED.

YOU ARE RIGHT SAYING:  "Or do you mean that the atmosphere over the 
antennae will be the same therefore solutions derived from the 
differences will be degenerate?
Yes I mean this.


>  For the code: For the phase referenced experiment (I.e. VERA image
>of the target and the similar program on Sgr A). Do you agree that a
>new mapping function is required? 
>
I do not think so, at least now when there is no full understanding of 
DELZN.

>Really we need to also fit for
>position at the same time
>
I do not understand this: what position? this is not about DELZN concept

>, but that can be added later once we are
>sure that the new mapping function is really required.
>
>                Richard
>  
>
Leonid Kogan