[MITgcm-devel] more seaice blues for the adjoint

Martin Losch Martin.Losch at awi.de
Fri Jun 8 07:08:22 EDT 2007 

In the code:
zmax = 2.5e8 * P, and P = Pstar*HEFF*exp(-20*(1-AREA)), so NOT  
constant if HEFF and AREA are not constant.
I don't get this zmin thing either, I'll check again ...

Martin

On 8 Jun 2007, at 12:58, Jinlun Zhang wrote:

> Martin, I am in Japan, so I catch this email of yours quick.
> Good to know B-grid also has this problem. But I thought if the  
> motion gets smaller and smaller, then delta approaches zero, and  
> zeta would hit maximum, and eventually, everything is constant,  
> thus dp/dx is zero. This would not be related to zmin. Am I wrong  
> here?
> Jinlun
>
>> Hi Jinlun,
>>
>> I check with the b-code and at first I got zero motion!!! But why?  
>> the reason is not the grid, but this line:
>> zmin = 4e8
>> if I set this to
>> zmin = 0
>> as we have agree a few days/weeks ago, I do get motion.
>>
>> So it's not the C-grid, but this lower limit for zeta, that makes  
>> zeta = constant if delta = 0, and thus P = zeta*2*delt2 = const,  
>> so no dP/dx -> no motion. if zmin = 0, then zeta is not constant,  
>> neither P and we have motion.
>> so if zmin = 0, then I need to do something else to ensure P =  
>> constant if delta = 0., eg. P = P * delta/delt2
>>
>> Martin
>>
>> On 8 Jun 2007, at 08:38, Jinlun Zhang wrote:
>>
>>> Hi Martin,
>>> Before your fix, is it occurring with both LSR and EVP C-grid  
>>> codes? Also, would it be possible for you to try the B-grid that  
>>> I put in originally (if it is still one of the options)? It is OK  
>>> for not trying if you don't have time. I remember I tested this  
>>> thing with B-grid years ago without finding similar problem, but  
>>> I am not sure now after so many years without dealing with it  
>>> again. I just hope this is not one of the differences between B  
>>> and C. Your explanation certainly indicates that this thing does  
>>> not depend on grid. But a test on B-grid would clear any residual  
>>> doubts.
>>> Thanks, Jinlun
>>>
>>>
>>> Martin Losch wrote:
>>>> Chris,
>>>> when there is no strain (in the absence of any forcing), the ice  
>>>> should not move, right? Unless you expect it to spread like a  
>>>> pile of sand with time, but I don't know what the time scale for  
>>>> that would be, very slow.
>>>> If delta = 0, we reset it to delta_min, because we have to  
>>>> devide by it zeta = press/(2*delta), this effictively makes zeta  
>>>> <= zeta_max = press/(2*delta_min), after capping zeta, we  
>>>> recompute press_replace = zeta*2*delta, if delta has been  
>>>> replaced by delta_min, this give non zero pressure and thus a  
>>>> forcing due to internal stress. That's the numerical issue. I am  
>>>> not shure that I solved it very well (the adjoint breaks), but  
>>>> this way the ice does not move in the absence of forcing.
>>>>
>>>> Martin
>>>> On 7 Jun 2007, at 18:05, chris hill wrote:
>>>>
>>>>> Martin,
>>>>>
>>>>>  Quick ice question.
>>>>>
>>>>> Is it just a numerical issue i.e. is it clear what the  
>>>>> underlying equations are, since ice is neither a classical  
>>>>> fluid or a classical solid. What time scale does it spread on?
>>>>>
>>>>> Chris
>>>>> Martin Losch wrote:
>>>>>> No, but it's a numerical issure. I did not pay any attention  
>>>>>> to this before and maybe this was no problem in the original  
>>>>>> code that you supplied but if you have zero strain, Delta = 0,  
>>>>>> and this is replaced by some Delta_min (SEAICE_EPS in the  
>>>>>> code) in order to avoid division by zero (and infinite  
>>>>>> viscosities). P however is still non-zero and divergence 
>>>>>> (stress) end up being (dP/dx, dP/dy) .NE. 0, so that you have  
>>>>>> a forcing of down the slope of P. This does not make sense  
>>>>>> (why would ice spontaneously spread?), so that the pressure is  
>>>>>> replaced by P = P*Delta/max(Delta,SEAICE_EPS), so that in the  
>>>>>> (rare) case of no strain P = zeta = eta = 0 and thus no  
>>>>>> forcing by stress. Makes sense to me (and is really only  
>>>>>> relevant in idealized test case, just like the spurious motion  
>>>>>> of sigma coordinates vs. z-coordinates in ocean models).
>>>>>> Hope I did not misunderstand anything here.
>>>>>> Martin
>>>>>> On 7 Jun 2007, at 13:40, Jinlun Zhang wrote:
>>>>>>> Hi Martin,
>>>>>>> Would this be due to some kind of finite differencing problem?
>>>>>>> Jinlun
>>>>>>>
>>>>>>> Martin Losch wrote:
>>>>>>>> Hi Patrick,
>>>>>>>>
>>>>>>>> I have found (or rather, was pointed to) a problem with the  
>>>>>>>> seaice solvers: The start to move spontaneously (in the  
>>>>>>>> absence of forcing), if the sea ice distribution is NOT  
>>>>>>>> uniform.
>>>>>>>> I have implemented a fix but this will cause problems with  
>>>>>>>> the adjoint: I need terms like
>>>>>>>> SQRT(deltaC), which used to be SQRT(MAX 
>>>>>>>> (deltaC,SEAICE_EPS_SQ)), so that the derivate code will be  
>>>>>>>> involve 1/sqrt(deltaC). Should I put this into #ifdefs?
>>>>>>>>
>>>>>>>> Martin
>>>>>>>
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