Dear Dirk and Martin,
Thank you, Dirk, for checking again about these names and to Bruno for answering my questions!
> > (3a) sishevel Maximum shear strain rate of sea-ice velocity field (s-1)
> >
> > Maximum shear strain rate of sea-ice velocity field (second shear strain invariant: maximum is taken over coordinate rotations)
> >
> > sea_ice_horizontal_shear_strain_rate_maximum_over_coordinate_rotation
> > Help text: "Stress is the symmetric component of the tensor representing the gradient of internal forces (e.g. in ice). Shear stress refers to off-
> > diagonal element(s) of the stress tensor (a single element for horizontal shear stress). The
> > maximum over coordinate rotations of the shear strain rate, often referred to as the maximum shear strain [rate], represents the second
> > invariant of strain rate."
>
> I'm afraid I'm not expert enough to comment very usefully on these quantities. I note that the names sea_ice_x_internal_stress and
> sea_ice_y_internal_stress were agreed for Dirk's proposals 1.26 and 1.27. Would it be correct to describe the horizontal shear strain as also being
> 'internal'? If so, perhaps we should add it to the name.
BT>> Not really. The stress sigma in the momentum equation is the
integrated stresses from z=-hice to z=0. In that sense, they are the internal stresses. If we wanted to be exactly precise, we would say the vertically integrated internal stresses. But I dont think we should change the way they have always been referred to.
BT>> As for the strain rates. uice and vice are the velocity of a 2D
media. They are not vertically integrated since u and v are depth-independent. Or to be precise they are vertically integrated but since they are independent of depth, they end up being Uice h and Vice h. This is why you have in the momentum equation:
rho_i h du/dt + .... = ....
For this reason, I would not refer to uice and vice as internal velocity and the divergence/curl of (uice,vice) as the internal shear strain rate and internal divergence of ice velocity or divergence of internal sea ice velocity
Okay, so we shouldn't add 'internal' to the name.
> I'm not sure what 'horizontal' means here - is it parallel to the sea-surface or some other surface such as the sea ice base perhaps? Or does it
> mean it's in the same plane as the x and y coordinates in Dirk's names? I note that the definition of 3c says 'Horizontal stress refers to the stress
> in the horizontal plane' but that still doesn't really explain what is considered to be horizontal in this context.
BT>> The "horizontal" is the plane that is perpendicular to the gravity
vector - i.e. not the plane that is perpendicular to the local sea surface which can be tilted if there is a geostrophic current. This explains the sea surface tilt term in the momentum equation which is equal to m g times the gradient of the sea surface slopes.
Okay, thank you, that is clear.
> If you are including 'maximum' in
> the name, does that mean it's an intrinsic part of how the variable is calculated by the model, rather than a statistic representative of an area of
> sea ice? I'd welcome comments from anyone more knowledgeable than me about these quantities!
BT>> There is only 4 stress components at a point in a 2D tensor. It
reduces to 3 since the stress tensor is symmetric (sigma12 = sigma21).
Each of the stress components are defined with respect to a frame of reference. If this frame of reference is rotated (no reason why the frame of reference should have a specific orientation) we get other equivalent representation of the same stress. It is just a matter of how we position ourselves as an observer. So all these stresses are not independent measures of the same thing (if it were we could define the statistical mean, max, min); instead they are the same stress expressed in different frame of reference. In one frame of reference, they are maximum, in another they are minimum, etc. But again, they are not the statistical mean, max, etc.
I would not say either they are "an intrinsic part of how they are calculated", since they are not really "calculated". They are just rotated. Maybe this is just playing on words. I would personally say they are an "intrinsic property of a 2D tensor"
Okay, so maximum here is the largest value of strain rate that could result from any orientation of the frame of reference and, as you say, this is not a statistical maximum calculated along a coordinate axis of the data. In such a case we would use 'maximum' as part of the standard name and not a cell_method.
It has taken me a little while to understand this name, but I am beginning to grasp it!
sea_ice_horizontal_shear_strain_rate_maximum_over_coordinate_rotation (s-1)
'"Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs. Stress is the symmetric component of the tensor representing the gradient of internal forces (e.g. in ice). Shear stress refers to off-diagonal element(s) of the stress tensor (a single element for horizontal shear stress). "Horizontal" refers to the local horizontal in the location of the sea ice, i.e., perpendicular to the local gravity vector. Each of the stress components is defined with respect to a frame of reference. "Coordinate rotation" refers to the range of all possible orientations of the frame of reference. The shear stress has a maximum value relative to one of these orientations. The maximum over coordinate rotations of the shear strain rate, often referred to as the maximum shear strain [rate], represents the second invariant of strain rate.'
I think the name and units are fine. I have expanded the definition somewhat by adding some of Bruno's explanation. Is this okay?
> (3b) sistremax Maximum shear stress in sea ice (N m-1)
> Maximum shear stress in sea ice (second stress invariant)
>
> sea_ice_horizontal_shear_stress_maximum_over_coordinate_rotation
>
> Help text: "Stress is the symmetric component of the tensor representing the gradient of internal forces (e.g. in ice). Shear stress refers to off-diagonal element(s) of the stress tensor (a single element for horizontal shear stress). The
> maximum over coordinate rotations of the shear stress, often referred to as the maximum shear stress, represents the second invariant of stress."
The name and units are fine. As with 3a I would suggest expanding the definition based on Bruno's explanation:
' "Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs. Stress is the symmetric component of the tensor representing the gradient of internal forces (e.g. in ice). Shear stress refers to off-diagonal element(s) of the stress tensor (a single element for horizontal shear stress). "Horizontal" refers to the local horizontal in the location of the sea ice, i.e., perpendicular to the local gravity vector. Each of the stress components is defined with respect to a frame of reference. "Coordinate rotation" refers to the range of all possible orientations of the frame of reference. The shear stress has a maximum value relative to one of these orientations. The maximum over coordinate rotations of the shear stress, often referred to as the maximum shear stress, represents the second invariant of stress.'
Okay?
> (3c) sistresave Average normal stress in sea ice (N m-1)
> Average normal stress in sea ice (first stress invariant: average of diagonal elements of the stress tensor)
>
> sea_ice_average_normal_horizontal_stress
> Help text: "Stress is the symmetric component of the tensor representing the gradient of internal forces (e.g. in ice). Horizontal stress refers to the stress in the horizontal plane. Average normal stress refers to the average of the
> diagonal elements of the stress tensor and represents the first invariant of stress."
The name and units are fine. I would suggest adding an explanation of 'horizontal' to the definition:
'"Sea ice" means all ice floating in the sea which has formed from freezing sea water, rather than by other processes such as calving of land ice to form icebergs. Stress is the symmetric component of the tensor representing the gradient of internal forces (e.g. in ice). Horizontal stress refers to the stress in the horizontal plane. "Horizontal" refers to the local horizontal in the location of the sea ice, i.e., perpendicular to the local gravity vector. Average normal stress refers to the average of the diagonal elements of the stress tensor and represents the first invariant of stress.'
Okay?
Best wishes,
Alison
------
Alison Pamment Tel: +44 1235 778065
NCAS/Centre for Environmental Data Archival Email: alison.pamment at stfc.ac.uk
STFC Rutherford Appleton Laboratory
R25, 2.22
Harwell Oxford, Didcot, OX11 0QX, U.K.
-----Original Message-----
From: CF-metadata <cf-metadata-bounces at cgd.ucar.edu> On Behalf Of Dirk Notz
Sent: 20 June 2018 06:47
To: CF-metadata (cf-metadata at cgd.ucar.edu) <cf-metadata at cgd.ucar.edu>
Subject: Re: [CF-metadata] SIMIP: 5 standard names and one area type for CMIP6
Dear Alison,
I have been in touch with Bruno Tremblay again, who is our SIMIP sea-ice dynamics guru. Regarding the questions on the sea-ice shear variables, he sent the replies copied below. I hope this clarifies the issues you raise.
Best,
Dirk
> 1. I note that the names sea_ice_x_internal_stress and sea_ice_y_internal_stress were agreed for Dirk's proposals 1.26 and 1.27. Would it be correct to describe the horizontal shear strain as also being 'internal'?
BT>> Not really. The stress sigma in the momentum equation is the
integrated stresses from z=-hice to z=0. In that sense, they are the internal stresses. If we wanted to be exactly precise, we would say the vertically integrated internal stresses. But I dont think we should change the way they have always been referred to.
BT>> As for the strain rates. uice and vice are the velocity of a 2D
media. They are not vertically integrated since u and v are depth-independent. Or to be precise they are vertically integrated but since they are independent of depth, they end up being Uice h and Vice h. This is why you have in the momentum equation:
rho_i h du/dt + .... = ....
For this reason, I would not refer to uice and vice as internal velocity and the divergence/curl of (uice,vice) as the internal shear strain rate and internal divergence of ice velocity or divergence of internal sea ice velocity
> 2. I'm not sure what 'horizontal' means here - is it parallel to the sea-surface or some other surface such as the sea ice base perhaps? Or does it mean it's in the same plane as the x and y coordinates in Dirk's names? I note that the definition of 3c says 'Horizontal stress refers to the stress in the horizontal plane' but that still doesn't really explain what is considered to be horizontal in this context.
BT>> The "horizontal" is the plane that is perpendicular to the gravity
vector - i.e. not the plane that is perpendicular to the local sea surface which can be tilted if there is a geostrophic current. This explains the sea surface tilt term in the momentum equation which is equal to m g times the gradient of the sea surface slopes.
> 3. If you are including 'maximum' in the name, does that mean it's an intrinsic part of how the variable is calculated by the model, rather than a statistic representative of an area of sea ice?
BT>> There is only 4 stress components at a point in a 2D tensor. It
reduces to 3 since the stress tensor is symmetric (sigma12 = sigma21).
Each of the stress components are defined with respect to a frame of reference. If this frame of reference is rotated (no reason why the frame of reference should have a specific orientation) we get other equivalent representation of the same stress. It is just a matter of how we position ourselves as an observer. So all these stresses are not independent measures of the same thing (if it were we could define the statistical mean, max, min); instead they are the same stress expressed in different frame of reference. In one frame of reference, they are maximum, in another they are minimum, etc. But again, they are not the statistical mean, max, etc.
I would not say either they are "an intrinsic part of how they are calculated", since they are not really "calculated". They are just rotated. Maybe this is just playing on words. I would personally say they are an "intrinsic property of a 2D tensor"
>> (3a) sishevel Maximum shear strain rate of sea-ice velocity field (s-1)
>>
>> Maximum shear strain rate of sea-ice velocity field (second shear
>> strain invariant: maximum is taken over coordinate rotations)
>>
>> sea_ice_horizontal_shear_strain_rate_maximum_over_coordinate_rotation
>> Help text: "Stress is the symmetric component of the tensor
>> representing the gradient of internal forces (e.g. in ice). Shear stress refers to off-diagonal element(s) of the stress tensor (a single element for horizontal shear stress). The maximum over coordinate rotations of the shear strain rate, often referred to as the maximum shear strain [rate], represents the second invariant of strain rate."
>
> I'm afraid I'm not expert enough to comment very usefully on these quantities. I note that the names sea_ice_x_internal_stress and sea_ice_y_internal_stress were agreed for Dirk's proposals 1.26 and 1.27. Would it be correct to describe the horizontal shear strain as also being 'internal'? If so, perhaps we should add it to the name. I'm not sure what 'horizontal' means here - is it parallel to the sea-surface or some other surface such as the sea ice base perhaps? Or does it mean it's in the same plane as the x and y coordinates in Dirk's names? I note that the definition of 3c says 'Horizontal stress refers to the stress in the horizontal plane' but that still doesn't really explain what is considered to be horizontal in this context. If you are including 'maximum' in the name, does that mean it's an intrinsic part of how the variable is calculated by the model, rather than a statistic representative of an area of sea ice? I'd welcome comments from anyone more knowledgeable than me about these quantiti
es!
>
> This name is still under discussion.
>
>> (3b) sistremax Maximum shear stress in sea ice (N m-1)
>> Maximum shear stress in sea ice (second stress invariant)
>>
>> sea_ice_horizontal_shear_stress_maximum_over_coordinate_rotation
>>
>> Help text: "Stress is the symmetric component of the tensor
>> representing the gradient of internal forces (e.g. in ice). Shear stress refers to off-diagonal element(s) of the stress tensor (a single element for horizontal shear stress). The maximum over coordinate rotations of the shear stress, often referred to as the maximum shear stress, represents the second invariant of stress."
>
> This name appears to be consistent with 3a and my comments and questions would be the same for this one.
>
> This name is still under discussion.
>
>> (3c) sistresave Average normal stress in sea ice (N m-1)
>> Average normal stress in sea ice (first stress invariant: average of
>> diagonal elements of the stress tensor)
>>
>> sea_ice_average_normal_horizontal_stress
>> Help text: "Stress is the symmetric component of the tensor
>> representing the gradient of internal forces (e.g. in ice). Horizontal stress refers to the stress in the horizontal plane. Average normal stress refers to the average of the diagonal elements of the stress tensor and represents the first invariant of stress."
>
> Again I'd ask similar questions to those for 3a and 3b. By 'average' here are we referring to the mean? If so, then I think we should say that in the name. By 'normal' is this one referring to the 'normal' to the horizontal? Am I being na?ve in thinking we should call that 'vertical'?
>
> This name is still under discussion.
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Received on Thu Jun 21 2018 - 00:43:53 BST
