# Re: line integration

From: Dennis Shea <shea_at_nyahnyahspammersnyahnyah>
Date: Tue Aug 13 2013 - 15:10:54 MDT

Rather than:
L = sum((Qv1*dx_1)+Qu2*dy+(Qv2*dx_2)+Qu1*dy)

The 'x' and 'y' paths are not the same size.
Do a printVarSummary(...) of each term to verify.
That is what led to the error.
===

You should add each track separately.

Arrays dimensioned: [12] x [32] x [lon | 144] x [lat | 73]

Qu1 = Quu(:,:,{270},{60:80}) * dy ; (:,:,:)
Qu2 = Quu(:,:,{357},{60:80}) * dy
Qv1 = Qvv(:,:,{270:357},{60})* dx_1
Qv2 = Qvv(:,:,{270:357},{80})* dx_2

L1 = dim_sum_n(Qv1, 2) ; left->right
L2 = dim_sum_n(Qu2, 2) ; up
L3 = dim_sum_n(Qv2, 2) : right->left
L4 = dim_sum_n(Qu1, 2) ; down

L = L1 + L2+ L3 + L4 ; L(12,32)

==================================================

For a rectilinear grid and traversing in a counter-clockwise manner:

<= left

+ + + + 60

+ + 50
| ^
down + + lat | 40
up
+ + 30

+ + + + 20

lon =>

130 140 150 160

Q(time,lev,lat,lon)

Here is a crude approach for a rectilinear grid.
This assumes dx is he same at each latitude and dy
is constant

Q1 = dim_sum_n( Q(:,:,{20},{130:160})*dx({20}), 2) ; left->right
Q2 = dim_sum_n( Q(:,:,{20:60},{160}) *dy) , 2) ; up
Q3 = dim_sum_n( Q(:,:,{60},{130:160})*dx(60) , 2) : right->left
Q4 = dim_sum_n( Q(:,:,{20:60},{130}) *dy) , 2) ; down

QQ = Q1 + Q2+ Q3 + Q4 ; QQ(ntime,lev)

Circulation: U(time,lev,lat,lon), V(time,lev,lat,lon)

C1 = dim_sum_n( U(:,:,{20},{130:160})*dx({20}, 2) ; right->left
C2 = dim_sum_n( V(:,:,{20:60},{160}) *dy) , 2) ; up
C3 = dim_sum_n( U(:,:,{60},{130:160})*dx(60) , 2) : left->right
C4 = dim_sum_n( V(:,:,{20:60},{130}) *dy) , 2) ; down

C = C1 + C2+ C3 + C4 ; C(ntime)

On 8/13/13 2:07 PM, Bithi De wrote:
> Hi,
> Thanks Dennis for the reply.
> Let me explain my question clearly.
>
> * I have rectilinear grid.
> * I have U-component and V-component at each grid point , with print
> variable summary like this: (where 12= no. of months and 32= no. of
> years)
>
> Variable: Qvv
> Type: float
> Total Size: 16146432 bytes
> 4036608 values
> Number of Dimensions: 4
> Dimensions and sizes: [12] x [32] x [lon | 144] x [lat | 73]
> Coordinates:
> lon: [ 0..357.5]
> lat: [90..-90]
> Number Of Attributes: 1
> _FillValue : 9.96921e+36
>
>
> Variable: Quu
> Type: float
> Total Size: 16146432 bytes
> 4036608 values
> Number of Dimensions: 4
> Dimensions and sizes: [12] x [32] x [lon | 144] x [lat | 73]
> Coordinates:
> lon: [ 0..357.5]
> lat: [90..-90]
> Number Of Attributes: 1
> _FillValue : 9.96921e+36
>
>
>
> * I want to calculate line integration along the east, west boundary
> of an area for u component and line integration along the south and
> north boundary of an area for v component.
> I tried like the following:
>
> re = 6.37122e06
> rad = 4.0* atan(1.0) / 180.0
> con = re * rad
> clat = cos(lat * rad) ; cosine of latitude
>
> dlon = (lon(2) - lon(1))
> dlat = (lat(2) - lat(1))
> dx = con * dlon * clat ; dx at each latitude
> dy = con * dlat ; dy is constant
>
>
> dx1 = conform(Quu,dx,3)
> dx1!3 = "lat"
> dx1!2 = "lon"
> dx1&lat = lat
> dx1&lon = lon
> printVarSummary(dx1)
> printVarSummary(dy)
>
>
> ;***********************************************************************************
> ; transport across the boundary of the region
> ;***********************************************************************************
>
> Qu1 = Quu(:,:,{270},{60:80}) ;quu component value across east
> boundary at longitude 270
> printVarSummary (Qu1)
>
> Qu2 = Quu(:,:,{357},{60:80}) ;quu component value across west
> boundary at longitude 357.5
> printVarSummary (Qu2)
>
> Qv1 = Qvv(:,:,{270:357},{60}) ;Qvv component across
> south boundary at latitude 60
> Qv2 = Qvv(:,:,{270:357},{80}) ;Qvv component across
> north boundary at latitude 80
> printVarSummary (Qv1)
>
> printVarSummary (Qv2)
>
>
> dx_1=dx1(:,:,{270:357},{60})
> dx_2=dx1(:,:,{270:357},{80})
> printVarSummary (dx_1)
> printVarSummary (dx_2)
>
> L = sum((Qv1*dx_1)+Qu2*dy+(Qv2*dx_2)+Qu1*dy)
>
> For calculating L, I am getting an error like this:
> fatal:Plus: Dimension size, for dimension number 2, of operands does
> not match, can't continue
>
> Did I calculate dx and dy in wrong way? What should be the right approach?
> Bithi
>
>
> On 8/12/13, Dennis Shea <shea@ucar.edu> wrote:
>> Hi Bithi,
>>
>> This is offline. Respond to ncl-talk@ucar.edu only
>>
>> I hesitate to answer because I am very busy and I do
>> not have a lot of time to answer ncl-talk questions.
>>
>> What type of grid do you have? rectilinear or curvilinear?
>>
>> What have *you* tried? We at ncl-talk sometimes feel people
>> want us to write the code for them. We do not have the time.
>>
>>
>>
>> <= left
>>
>> + + + + 60
>>
>> + + 50
>> |
>> down + + lat up 40
>>
>> + + 30
>>
>> + + + + 20
>>
>> lon =>
>>
>> 130 140 150 160
>>
>> You have U and V at each grid point. Usually, you must go
>> counter clockwise around for the circulation theorm.
>>
>> U(time,lat,lon), V(time,lat,lon)
>>
>> Here is a crude approach for a rectilinear grid.
>>
>>
>> C = sum( U(:,{20},{130:160})*dx({20}) \
>> +V(:,{20:60},{160}) *dy) \
>> +U(:,{60},{130:160})*dx(60) \
>> +V(:,{20:60},{130}) +dy )
>>
>> C(ntim)
>>
>>
>>
>>
>> On 8/9/13 6:02 PM, Bithi De wrote:
>>> Hi All,
>>> Is it possible to calculate line integration using NCL? I need to
>>> calculate line integration along each boundary of an area.
>>>
>>> Thanks .
>>> Bithi
>>>
>>
>
>
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Received on Tue Aug 13 15:10:37 2013

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