You can use the following code to convert the coordinates, it automatically takes the projection from your raster as the source and the projection from your Basemap object as the target coordinate system.
Imports
from mpl_toolkits.basemap import Basemap
import osr, gdal
import matplotlib.pyplot as plt
import numpy as np
Coordinate conversion
def convertXY(xy_source, inproj, outproj):
# function to convert coordinates
shape = xy_source[0,:,:].shape
size = xy_source[0,:,:].size
# the ct object takes and returns pairs of x,y, not 2d grids
# so the the grid needs to be reshaped (flattened) and back.
ct = osr.CoordinateTransformation(inproj, outproj)
xy_target = np.array(ct.TransformPoints(xy_source.reshape(2, size).T))
xx = xy_target[:,0].reshape(shape)
yy = xy_target[:,1].reshape(shape)
return xx, yy
Reading and processing the data
# Read the data and metadata
ds = gdal.Open(r'albers_5km.tif')
data = ds.ReadAsArray()
gt = ds.GetGeoTransform()
proj = ds.GetProjection()
xres = gt[1]
yres = gt[5]
# get the edge coordinates and add half the resolution
# to go to center coordinates
xmin = gt[0] + xres * 0.5
xmax = gt[0] + (xres * ds.RasterXSize) - xres * 0.5
ymin = gt[3] + (yres * ds.RasterYSize) + yres * 0.5
ymax = gt[3] - yres * 0.5
ds = None
# create a grid of xy coordinates in the original projection
xy_source = np.mgrid[ymax+yres:ymin:yres, xmin:xmax+xres:xres]
Plotting
# Create the figure and basemap object
fig = plt.figure(figsize=(12, 6))
m = Basemap(projection='robin', lon_0=0, resolution='c')
# Create the projection objects for the convertion
# original (Albers)
inproj = osr.SpatialReference()
inproj.ImportFromWkt(proj)
# Get the target projection from the basemap object
outproj = osr.SpatialReference()
outproj.ImportFromProj4(m.proj4string)
# Convert from source projection to basemap projection
xx, yy = convertXY(xy_source, inproj, outproj)
# plot the data (first layer)
im1 = m.pcolormesh(xx, yy, data[0,:,:], cmap=plt.cm.jet, shading='auto')
# annotate
m.drawcountries()
m.drawcoastlines(linewidth=.5)
plt.savefig('world.png',dpi=75)
If you need the pixels location to be 100% correct you might want to check the creation of the coordinate arrays really careful yourself (because i didn't at all). This example should hopefully set you on the right track.