From: Dennis Shea <shea_at_nyahnyahspammersnyahnyah>

Date: Mon Oct 07 2013 - 11:47:18 MDT

Date: Mon Oct 07 2013 - 11:47:18 MDT

As noted the function is an approximation.

The surface area of a sphere is

A = 4*pi*R^2 ; area of sphere; R is radius of earth

Area of a hemisphere:

diff = 90-0.0

Ahem = A*(diff/180.0) = A*0.5

Area of the 'cap'

diff = 90-88.92773

A889 = A*(diff/180.0)

On 10/2/13 7:37 PM, Soumik Basu wrote:

*> Hi,
*

*>
*

*> I am trying to calculate the sea ice extent from sea ice fraction data
*

*> for CAM3.1 in T85 grid.
*

*> I used the area_global_rectilinear_grid function to calculate the area
*

*> of each of the grid box. But I am trying to estimate the area over the
*

*> pole as the latitudes ends at 88.92773. For doing that I tried
*

*> calculating in the following way. But what confused me is that why the
*

*> sum of the grid areas calculated using the function is greater than the
*

*> surface area of the earth. Is there any better way to estimate the area
*

*> of the small circle over the pole?
*

*>
*

*>
*

*> ;****************************************************
*

*> ; Calculate area at each grid point
*

*> ;****************************************************
*

*> ; T85
*

*>
*

*> nlat = 128
*

*> lat = latGau(nlat, "lat", "latitude", "degrees_north")
*

*> mlon = 256
*

*> lon = lonGlobeF(mlon, "lon", "longitude", "degrees_east")
*

*> print(lat)
*

*> area = area_global_rectilinear_grid (lat, lon, False)
*

*>
*

*> areaa = dble2flt(area)
*

*>
*

*> printVarSummary(areaa)
*

*> printMinMax(areaa, True)
*

*>
*

*> R = 6371.220 ; in km
*

*>
*

*> pi = 4d0*atan(1d0)
*

*>
*

*> S_Area = 4d0*pi*R^2 ;Total surface area of the earth
*

*>
*

*> print(S_Area)
*

*>
*

*> Area_total = sum(areaa) ; Total area from the grid boxes
*

*>
*

*> print(Area_total)
*

*>
*

*> Pole_area = (S_Area - Area_total)/(10^6)*2 ; Area over the pole in 10^6
*

*> sq km
*

*>
*

*> print(Pole_area)
*

*>
*

*> Here are the printVarSummary results:
*

*>
*

*> Variable: areaa
*

*> Type: float
*

*> Total Size: 131072 bytes
*

*> 32768 values
*

*> Number of Dimensions: 2
*

*> Dimensions and sizes: [lat | 128] x [lon | 256]
*

*> Coordinates:
*

*> lat: [-88.92773..88.92773]
*

*> lon: [ 0..358.5938]
*

*> Number Of Attributes: 8
*

*> long_name : area of each grid cell
*

*> units : km^2
*

*> area_total : 5.101007e+08
*

*> area_lat : <ARRAY of 128 elements>
*

*> rearth : 6371.22
*

*> area_sphere : 5.100997e+08
*

*> area_ratio : 1.000002
*

*> typeConversion_op_ncl : double converted to float
*

*> (0)
*

*> (0) area of each grid cell: min=451.99 max=24355.4
*

*>
*

*>
*

*> Variable: S_Area
*

*> Type: double
*

*> Total Size: 8 bytes
*

*> 1 values
*

*> Number of Dimensions: 1
*

*> Dimensions and sizes: [1]
*

*> Coordinates:
*

*> (0) 510099745.7121028
*

*>
*

*>
*

*> Variable: Area_total
*

*> Type: float
*

*> Total Size: 4 bytes
*

*> 1 values
*

*> Number of Dimensions: 1
*

*> Dimensions and sizes: [1]
*

*> Coordinates:
*

*> (0) 5.101245e+08
*

*>
*

*>
*

*> Variable: Pole_area
*

*> Type: double
*

*> Total Size: 8 bytes
*

*> 1 values
*

*> Number of Dimensions: 1
*

*> Dimensions and sizes: [1]
*

*> Coordinates:
*

*> (0) -0.04953257579445839
*

*>
*

*>
*

*> Thanks,
*

*> Soumik
*

*>
*

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Received on Mon Oct 7 11:47:13 2013

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