My current work has been focused on using MOD10A1 albedo data to quantify albedo change in the 21st century across the High Arctic. Data has been collected daily between May – September, to ensure a full melt season is viewed, and has been processed and filtered using various open source software (GDAL, NumPy, QGIS, RSGISLib). Over 10,000 images were analysed across three sites in the Arctic (Austfonna, Humboldt and Agassiz Ice Cap), detailing how albedo has changed daily, monthly and yearly, both spatially and with respect to elevation. Below are some preliminary results for Austfonna glacier in Svalbard with future posts analysing the other sites.

Figure 1 shows the data filtering hierarchy that was utilised for each image (SZA = solar zenith angle).

The daily albedo for each year was plotted to both gain an understanding of melt season characteristics, and see whether the amplitude is increasing throughout the time-series. If so, this would infer that albedo values are dropping lower through the melt season (e.g. 2008 – 2013). Melt season length can also be deduced from the width of the quadratic curves.

Finally, moving images were created to investigate the spatial patterns in albedo change. Two years were analysed to provide comparison with 2008 (top) seeing a relatively stable melt season and 2013 (bottom) witnessing a more erratic trend with very low albedo values.

Appendix: Below is the code used for filtering the data based on different thresholds for the SZA’s presented in figure 1. Open source software was used throughout its development.

#!/usr/bin/env python ####################################### # An python class to calculate 11 day running statistics for each pixel # in the image and filtering according to criteria determined by median # and standard Deviation. Output is a new tiff file. # Author: Nathan Shaw ####################################### # import relevent modules import os.path import sys import math from osgeo import gdal import numpy as np import glob class Filtering(object): #function to collect 11 consectutive files for running statistics def elevens(startFile, num): return (startFile[pos - num: pos + num + 1] for pos in xrange(5, len(startFile)-5,1)) # a function to calculate the median of the 11 files def median(valueList): order = sorted(valueList) if len(order) % 2 == 0: return ((order[len(order)/2] + order[(len(order)/2) - 1]) / 2.0) else: return order[len(order)/2] # function which returns a tiff from a numpy array def createTiff(raster, File, folder, outputFile): #find raster projection for creation trans = File.GetGeoTransform() #find raster size for creation Ny, Nx = raster.shape format = "GTiff" driver = gdal.GetDriverByName( format ) dst_ds = driver.Create("//home//student//Desktop//DISSERTATION_DATA//" + str(folder.replace('_CLIP','_FILTER')) + "//" + str(outputFile), Nx, Ny, 1, gdal.GDT_Byte) dst_ds.GetRasterBand(1).WriteArray(raster) dst_ds.SetGeoTransform(trans) dst_ds = None print outputFile + ' complete' # a function to compare the statistics from the 11 files and the individual image in question discarding pixels as and when needed def pixelFiltering(inputFile, outputFile, folder, emptyAv, emptySD, emptyMed): data = gdal.Open("//home//student//Desktop//DISSERTATION_DATA//" + str(folder) + "//" + str(inputFile)) myArray2 = data.ReadAsArray() x = myArray2.shape #finding image number so different filtering criteria can be imposed for early/ late melt season. dataFind = inputFile[13:16] #locate days in melt season where SZA is greater than 70 degrees if (int(dataFind) <= 134 or int(dataFind) >= 237): for numRows2 in range(x[0]): for numCols2 in range(x[1]): pixelValue = myArray2[numRows2, numCols2] #sort through pixels only doing comparison on ones between 0 and 100 #select maximum albedo for time of year with 97 possible due to low SZA if (pixelValue >= 97 and pixelValue <= 100): myArray2[numRows2, numCols2] = 0 # define pixel to be zero (or Nan as long as outside 0 - 100) elif (pixelValue > 100 or pixelValue <= 0): pass #filter the pixel value based on median and SD values (unique for below/after 70 degree SZA - and for each glacier) else: if ((pixelValue > emptyAv[numRows2, numCols2] + 1.5*emptySD[numRows2,numCols2]) and (pixelValue > emptyMed[numRows2, numCols2] + 4)): # data outside 2*SD is removed but only if outside median +- 4 aswell. This is just for SZA > 70 myArray2[numRows2, numCols2] = 0 elif ((pixelValue < emptyAv[numRows2, numCols2] - 1.5*emptySD[numRows2, numCols2]) and (pixelValue > emptyMed[numRows2, numCols2] + 4)): myArray2[numRows2, numCols2] = 0 else: pass #output final numpy array to tiff createTiff(myArray2, data, folder, outputFile) #for all images where SZA is less than 70 degrees else: for numRows2 in range(x[0]): for numCols2 in range(x[1]): pixelValue = myArray2[numRows2, numCols2] #sort through pixels only doing compariosn on ones between 0 and 100 if (pixelValue >= 95 and pixelValue <= 100): # chose 95 for days when SZA < 70 as albedo never going to be higher myArray2[numRows2, numCols2] = 0 # define pixel to be zero (or Nan as long as outside 0 - 100) elif (pixelValue > 100 or pixelValue <= 0): pass else: if ((pixelValue > emptyAv[numRows2, numCols2] + 2*emptySD[numRows2,numCols2]) and (pixelValue > emptyMed[numRows2, numCols2] + 4)): # data outside 2*SD is removed but only if outside median +- 4 aswell. This is just for SZA < 70 myArray2[numRows2, numCols2] = 0 elif ((pixelValue < emptyAv[numRows2, numCols2] - 2*emptySD[numRows2, numCols2]) and (pixelValue > emptyMed[numRows2, numCols2] + 4)): myArray2[numRows2, numCols2] = 0 else: pass #output final numpy array to tiff createTiff(myArray2, data, folder, outputFile) # main function which will collect images, stack them, calculate statistics (mean, SD and median) before compare with image in question def convertToNumpy(inFile): images = [a for a in os.listdir(inFile) if a.endswith('CLIP')] for files in sorted(images): images2 = [a for a in os.listdir("//home//student//Desktop//DISSERTATION_DATA//" + str(files)) if a.endswith('.tif')] for group in elevens(sorted(images2),5): empty = [] for files2 in group: data = gdal.Open("//home//student//Desktop//DISSERTATION_DATA//" + str(files) + "//" + str(files2)) #could put os.change dir here myArray1 = data.ReadAsArray() empty.append(myArray1) #numpy function to stack all images array = np.dstack(empty) #calculate statistics for each pixel in stacked array #get image dimensions x = array.shape emptyAv = np.empty((x[0],x[1])) emptySD = np.empty((x[0],x[1])) emptyMed = np.empty((x[0],x[1])) for numRows in range(x[0]): for numCols in range(x[1]): pixel_list = array[numRows, numCols] #calculation of mean,SD and median # empty list for albedo values albedoList = [] for items in pixel_list: if (items < 95 and items > 0): # selcting pixels with no albedo higher than 95 in JJA, 97 in dates outside SZA of 70 albedoList.append(items) else: pass if len(albedoList) != 0: #calculate average average = sum(albedoList)/len(albedoList) #calculate SD standardDeviation = math.sqrt(sum([dev*dev for dev in [a - average for a in albedoList]]) / len(albedoList)) #append all values to empty numpy arrays to allow pixel by pixel comparison emptyAv[numRows, numCols] = sum(albedoList)/len(albedoList) emptySD[numRows, numCols] = standardDeviation emptyMed[numRows, numCols] = median(albedoList) else: emptyAv[numRows, numCols] = 0 emptySD[numRows, numCols] = 0 emptyMed[numRows, numCols] = 0 pixelFiltering(group[5],str(group[5].replace('.tif','_filter.tif')),files, emptyAv, emptySD, emptyMed) print group[5] + '\n' # executable function def run(self, initialDirectory): self.convertToNumpy(initialDirectory) if __name__ == "__main__": obj = Filtering() obj.run("//home//student//Desktop//DISSERTATION_DATA")