Looking now at Jim Pettit's admirable 3D interactives of monthly and weekly PIOMAS in #1055 (works in Firefox but not latest Opera) but not thrilled with lack of grayscale 'floor' and use of gregorian calendar (winter solstice off, lunar cycle off and irrelevant, weeks and months arbitrary units), I chased down the original

daily data set at UW (which consists of 38 years x 365 days in three columns year-day#-km

^{3} covering 1979-2016.

http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/data/Bringing this into a year by day rectangular array, fleshing out the missing months of 2016 based on July 2016's average fraction of 2015 (0.884), normalizing by multiplying every entry by the quotient of the global maximum in 255 and rounding to integers in [0.255] or rather in this data set [85,255], this text file can be imported as a 32-bit grayscale using Import --> Text Image... in ImageJ, which converts correctly to 8-bit (provided Edit --> Options --> Conversions has 'Scale when converting' de-checked, preventing rescaling to [0.255]).

The txt attachment below provides the final numerical array used to make the initial image.

Back in olden times, everyone was familiar with the exact 1-1 correspondence of numerical data arrays and pixel arrays of the same dimensions (pictures) as numbers in the graphics engine drove the monitor display voltages. Today however it is surprisingly hard to find software other than matlab and imageJ comfortable with the back-and-forth (which extends with three array stacks to RGB, HSV etc).

To reiterate, all 38 years of daily Piomas data can be displayed as a simple 14k grayscale that is 365 pixels wide and 38 pixels high (UW drops day 366 of leap years). The grayscale value of each pixel is proportional to the volume of ice in the year of its row and day of its column.

If you read out the grayscale value by mousing over it, say 246 gray for day 71 of 1979, and divided by scaling normalization used (7.719), you recover UW's tabled ice volume for that day and year, 31.839 km

^{3}.

The Piomas data scarcely has the level of precision indicated so 2

^{32 } values ranging 0 to 4,294,967,295 is also excessive. The actual ice volume on that day might have been somewhere between 30 and 33 instead of the 31.839 km

^{3} reported. But let's play along in 32-bit because day to day relative values might be better and then drop to 8-bit at the end.

When should a numeric array be recast as an image? Always: it's far easier and faster to manipulate data using image tools and see patterns and trends. For example, the Piomas data can be contoured in interactive 3D right from ImageJ's Analyze --> 3D surface Plot --> Isolines.

The initial image is quite small at 13,870 = 38 x 365 pixels and a little tricky to faithfully enlarge without unwanted interpolation: chose 'none' instead of bicubic etc and restrict to integral multiples to say triple the size of individual pixels without them being affected by neighboring values, as in the 3rd image below (which had to be removed because its width was throwing off forum display of the other images).

You can always drop down to the underlying spreadsheet and replicate an image operation with numbers (eg for line graphs or statistical analysis) but when was the last time you looked at the numerical array underlying a Landsat image or built a 36 layer spreadsheet for the Modis channels?

The animation shows a simple pattern analysis. The 3rd image was blurred slightly and posterized to two levels, then rescaled to forum limits. This shows as the years went by, ice volume really started shrinking in the summer months (darker grays).