[GRASS-user] how to calculate area of voronoi polygons considering the boundary of the catchment

[Micha Silver]

Hi Daljeet


daljeet wrote:

> Hi Micha,
>
> I could create isohyetal lines using the suggested steps:
>
>   
... clipped...
>
> Following are the doubts/questions
>
> 1. I saw the details of the raster created from v.surf.rst
>
>   
>> r.info rainraster
>>     
>
> zmin_data=0.000000, zmax_data=141.322000                                |
> zmin_int=-13.588332, zmax_int=52.589905 
>
> zmin_data and zmax_data seems to be correct but I do not understand 
> a) why the interpolated value zmin_int=-13.588332 is -ve
> b) and what is meaning of zmax_int equal to  52.58990
>   
If I understand correctly, the zmax_int and zmin_int are the max and min 
displacements of the interpolated values vs. the actual data points. The 
RST method creates an interpolation which does not usually go thru the 
actual data points, but rather "smooths" over them. These numbers show 
the drift above and below actual data points. So you have one point 
where the interpolated rainfall is 13 mm (or whatever the rain units 
are) below the actual data, and one point where the interpolation is 52 
mm above.
> 2. The target is to be able to calculate the area between two isohyetal
> lines and multiplying that area with the average rainfall within the two
> isohyets. This is to be done for all isohyetal lines. 
>
> Average can be calculated by averaging the value of rainfall of the two
> isohyetal lines.
>
> But how to calculate the area b/w the two isohyetal lines?
>   
Well I can think of two approaches to this.
1- Using vectors:  You might try to convert the isolines to closed 
boundaries, then add centroids and find some way to get the rainfall 
values into the centroids. This would require first to create an "edge" 
line all around the region (v.in.region will do this) to close the ends 
of the isolines,  then run v.clean with the "break" tool to get nodes 
where each contour line crosses this region line. Then you should be 
able to convert the lines to closed boundaries (v.type) and finally 
v.centroids to create centroids in each of the resulting strips between 
isohyetal lines.

But this procedure looks way to convoluted to me. Instead maybe you 
could try:
2- Using rasters:  You already have the rainfall raster. Perhaps create 
a reclass raster map of the rainfall raster using discrete values 
instead of the continuous range. So your reclass rules would look 
something like:
0 thru 20 = 10
21 thru 40 = 30
41 thru 60 = 50
...
This will group together all values in the interval between 0-20 and 
give them the value midway between, etc. Then you could do r.to.vect 
fea=area to create a vector map, and finally v.db.addtable and v.to.db 
to get the areas of each strip into the vector attribute table. (Note 
that r.reclass requires an integer raster)

After that long-winded response, I should add one more comment: Rainfall 
is not a continuous phenomena across a geographic area. There's no 
reason to expect that between the 40 mm line and the 60 mm line the 
average rainfall is 50 mm. If you stay with the original, continuous 
rainfall raster, and use v.rast.stats then the statistics are totalled 
on a cell by cell basis, and you avoid the "unnatural" results that 
might pop up when forcing the data into a framework of arbitrary intervals.

Regards,
Micha
>