Matthew Mazloff mmazloff at ucsd.edu
Wed May 3 13:13:09 EDT 2017

```My comment is that I highly suspect the ADJtheta value is correct and you just need to figure out why. The code is complex and you can either follow it through or try what I suggest: just make the costfunction one box. When it becomes one box, I suspect the costfinal will be about the same but ADJtheta will be much larger because it is theta at one time step and one box that contributes to it. Currently it is many boxes and many timesteps that contribute and that is why I think you get 10^-7. The costfinal is a weighted sum — it is not an “average" in the code as it is in your head

-Matt

> On May 3, 2017, at 10:04 AM, Peng Zhan <peng.zhan at kaust.edu.sa> wrote:
>
> Hi Matthew,
>
> I found the file of "costfinal" gives 25.60, which is reasonable for a daily averaged SST over a box.
> This suggests the cost function is defined without unknown weights that may change the scale, right?
>
> If yes, then we still need to figure out where is the 10^-6 from. Any comment?
>
> Thanks, Peng
>
> On Wed, May 3, 2017 at 7:50 PM, Matthew Mazloff <mmazloff at ucsd.edu <mailto:mmazloff at ucsd.edu>> wrote:
> ps> Though its an average the costfunction will accumulate. So I think it should be divided by secs per day and number of boxes in the average, making 10^-7 sounds about right!
>
>
>
>
>> On May 3, 2017, at 9:37 AM, Matthew Mazloff <mmazloff at ucsd.EDU <mailto:mmazloff at ucsd.edu>> wrote:
>>
>> Hello
>>
>> Essentially yes, though weighted by your cost function design. So ADJtheta will have volume and timestep weigthing in it.
>>
>> Its linear so your average is essentially the sum of grid cell costfunctions. Try letting your costfunction be SST for one grid cell and one time step and figuring out the weighting from that.
>>
>> Matt
>>
>>
>>> On May 3, 2017, at 9:29 AM, Peng Zhan <peng.zhan at kaust.edu.sa <mailto:peng.zhan at kaust.edu.sa>> wrote:
>>>
>>> Dear all,
>>>
>>> I am doing the adjoint sensitivity analysis, but get confused about the values' physical meaning in the ADJ* results.
>>>
>>> For instance, the cost function J is defined using daily average SST over a box, the ADJ* results are about 10^-7 to 10^-6 in magnitude.
>>>
>>> 1. Is the surface ADJtheta the sensitivity to SST it self?
>>> 2. If yes, the sum of ADJtheta over the box right before the target day should be close to 1?
>>>
>>>
>>>
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