# Re: area_global_rectilinear_grid

From: Dennis Shea <shea_at_nyahnyahspammersnyahnyah>
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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