## Monday, December 10, 2012

### Raster calculations with GDAL and numpy: calculating GFS wid speed

Performing raster calculations is a frequent need. GDAL python bindings come with a utility program,  gdal_calc.py, that does that, but many times is useful to code them.
In this example, we will be able to calculate the wind speed field from the GFS model, from the given u and v speed.
The calculated wind field. America is easily seen at the right side of the image

### The data

In this example, we will use the GFS global model data, which is available at their web site. Just navigate to a date that pleases you and download a .grb file.
Files are in grib format, with a little problem when trying to view them in QGis: Coordinates are from 0 to 360º in longitude, while the usual thing is to put them from -180º to 180º. Everything will work without changing this, but you can do it after taking a look to this post.

Inside the grib file, there are many bands (hundreds). You can see their definition using the gdal command gdalifo, or the file with the extension *inv at the same place you downloaded the grib file. There are many wind fields, that correspond to different altitudes, all them indicated as u (east) and v components (north). Just take note of the band number of both at the desired level.

### NumPy

The best of using the python gdal bindings, compared from those of the other programs, is that converting a raster file to a NumPy matrix is now very easy.
NumPy is a python extension that allows to perform matrix calculations in a really easy and efficient way. It should be installed in your computer if GDAL python is installed.
Once you have two matrices A and B in NumPy, adding element by element to a C matrix would be as easy as:
C = A + B
and multiplying:
C = A * B
Note that is not a matrix multiplication (more info here), but this is what we usually need when working with raster images.

### The code

The wind speed is the modulus of the two components, so
spd = sqrt(u^2+v^2)
The "traditional way" to calculate it would be opening two bands and loop all the elements to create the new band. Instead, this can be done:
from osgeo import gdal
from osgeo.gdalnumeric import *
from osgeo.gdalconst import *

fileName = "gfs.tiff"
bandNum1 = 199
bandNum2 = 200

outFile = "out.tiff"

#Open the dataset
band1 = ds1.GetRasterBand(bandNum1)
band2 = ds1.GetRasterBand(bandNum2)

#Read the data into numpy arrays

#The actual calculation
dataOut = numpy.sqrt(data1*data1+data2*data2)

#Write the out file
driver = gdal.GetDriverByName("GTiff")
dsOut = driver.Create("out.tiff", ds1.RasterXSize, ds1.RasterYSize, 1, band1.DataType)
CopyDatasetInfo(ds1,dsOut)
bandOut=dsOut.GetRasterBand(1)
BandWriteArray(bandOut, dataOut)

#Close the datasets
band1 = None
band2 = None
ds1 = None
bandOut = None
dsOut = None


Note that:
1. gdalnumeric is used, because it's the easiest way to dump a raster into a NumPy matrix using BandReadAsArray and the inverse function with BandWriteArray.
2. In this case, we are reading the bands 199 and 200, but you should check which bands are the ones to read in the file you download.
3. CopyDatasetInfo will copy all the input file metadata into the output file. This includes the geotransform, the projection, the GCPs (there aren't in this case) and the other metadata.
4. Don't forget to set the bands and datasets to None at the end to free them. In longer scripts this may be critical.

### gdal_calc.py

If you want to use the command line function to do the same, you can try with:
gdal_calc.py -A gfs.tiff --A_band 199 -B gfs.tiff --B_band 200 --outfile out.tiff --calc="sqrt(A*A+B*B)"
It gives the same result.