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Developers Corner / Test space
« on: February 05, 2019, 04:17:09 PM »
Thread used for testing images/animations. In my case an mp4 animation created with ffmpeg.

This image uses a -pix_fmt yuv420p option.

Developers Corner / Sentinel 2 Imagery
« on: August 02, 2015, 09:51:30 AM »
In the following I am assuming familiarity with the Sentinel 1A products.

Documenting attempts to use the new data.

Sample Sentinel 2 product(s) (only one appeared until now) are becoming available:

- enter S2A* in the search box of the Sentinel data-hub

The download url of the one available sample is:'a04ba2a6-352d-4b32-a5a8-367ede20ccbf')/$value

It is a 1.4 GB download

Unzipped, the images appear in 4 sub-directories:

<*> being 4 directories, corresponding to parts of the full image. In this case the original image is split in 4 granules (I would say tiles) each covering a quarter of the area.

The image data are JPEG 2000 images, one for each wavelength band (13 total). Blue (Band 2) has this filename:

S2A the satellite, L1C the data level, datetime and Band can be recognized.

I have not been able to open the image with normal tools:

ImageMagick just say's immediately cannot open:
: no decode delegate for this image format `JP2' @ error/constitute.c/ReadImage/501

[EDIT: this is a possible bug on my Debian Linux computer. See I will try the fix]

The Gimp says loading for a minute and then suggest the data is somehow "signed":
Image component 0 of image <filename>.jp2' is signed. This is currently not supported.
Signed as in signed/unsigned integers? Or signed as a form of encrypting/coding?

FIJI (= ImageJ) throws a Java exception. The interesting line in the stack trace says:

Caused by: File too long.
   at jj2000.j2k.fileformat.reader.FileFormatReader.readFileFormat(

Now there is a beta version of the Sentinel 2 toolbox available, although lack of functionality indicates the state is very alpha still.

The toolboxes are now known as SNAP (sentinel application toolbox) from which you can select the different toolboxes. You can download the latest SNAP by going to, enter name+email address to get the location of the real download pus username/password for retrieving them.

The latest toolbox (beta 5) is not able to open the zip file directly, looking through the forum messages you have to unzip manually and (with SNAP) open the main xml file in the main dir.
That works and you are able to see Bands 2,3,4 and 8. Probably blue,green,red and some infra red channel. Toolbox has the ability to view the RGB bands as a natural color image. It shows a part of north Italy, nice.

(to be continued)

Greenland and Arctic Circle / Svalbard / Spitsbergen
« on: July 18, 2015, 03:52:10 PM »
We discussed the surging glacier Austfonna last year in the Image of the Day thread:,416.msg42705.html#msg42705

It was a new item on ESA's website some months later:
Satellites catch Austfonna shedding ice

Finally the area comes out the clouds for a 2015 landsat image.
The surging of the glacier has continued (it extended). To the south-west a new smaller tongue has come down.

(must click)

Consequences / Mean European temperature in 2014 may be highest since 1500
« on: December 17, 2014, 06:07:36 PM »
Based on measurements and forecasts, year temperature for Europe is likely to be 10.5 oC, beating the previous record of 2007 by 0.3 oC.

A large number of European countries have reached a record year in 2014: Belgium, Bulgaria, Denmark, Germany, France, Iceland, Italy, Croatia, Luxembourg, Nederland, Norway, Austria,  Poland, Serbia, Slovakia, Slovenia, Czech, United Kingdom and likely Sweden.

Follow-up of a discussion in the "2014 sea ice area and extent data" thread about such calculations.

Arctic sea ice / New data set: Arctic Lead Area Fraction
« on: December 27, 2013, 10:08:24 AM »
The Integrated Climate Data Center, ICDC, from the Hamburg University distributes a lot of data of the the earth: land, ocean, atmosphere and cryosphere. Lots of it is freely accessible.

Now they have done it again,  based on the AMSR-E data they calculated the fraction of leads in a 6.25 km polar stereo-graphic grid:

New data: Arctic Lead Area Fraction
By: S. Kern

Data of the Advanced Scanning Microwave Radiometer aboard EOS: AMSR-E have been used to obtain a dataset of the Arctic winter-time lead area fraction. Leads are elongated areas of open water or thin ice which can be several hundreds to a few thousands of kilometers long and can be considered as windows through which the ocean looses large amounts of heat to the polar atmosphere during winter. The data set spans winters 2002/03 to 2010/2011 and is available here:

Hopefully they can extend the series using the AMSR2 data, I'd be most interested to see how the 2012/2013 stands in the series.

Arctic sea ice / AMSR-E Slow Rotation Data has been released
« on: December 14, 2013, 03:36:05 PM »
Remember AMSR-E? The instrument, built by Jaxa, mounted on the NASA AQUA satellite provided us with the best Sea Ice Concentration data (as well as a multitude of other data, e.g. Sea Surface Temperature) from 2002 to 4 October 2011. At that time the instrument was switched off, due to the increased friction in the drive of its big rotating disk antenna.

Well, it seems the instrument is not quite dead yet and from December 4, 2011 has been collected data at a reduced rotational speed ( 2 instead of 40 rpm). Jaxa announced:

AMSR-E Slow Rotation Data has been released
The AMSR-E automatically halted its observations and rotation on October 4, 2011 (UTC) due to increased rotation friction. After then NASA and JAXA began to analyze the situation and had been seeking for the way to restart AMSR-E observation. And on December 4, 2012 (UTC,) the AMSR-E restarted its observations and rotation with slow rotation (2 rotations per minute). JAXA completed initial radiometric and geometric correction for slow rotation data, and now AMSR-E Slow Rotation Data is available to public users.
This data is useful for users who cross-calibrate AMSR-E with other radiometers and who try to research using new feature by slow rotation and so on. This data is not JAXA's standard product. AMSR2 Standard Product is available for general user.

Good news for the inter calibration of the AMSR-E and AMSR2 data.

Mainly of interest for those living in the Netherlands. Translated where needed.

The Platform Wiskunde Nederland (Dutch organization for mathematics), an organisation jointly founded by the the Koninklijk Wiskundig Genootschap (Royal Mathematics Society, KWG) and the Nederlandse Vereniging van Wiskundeleraren (Dutch Association of Mathematics Teachers, NvvW), makes an effort to improve the public image of  mathematics and mathematicians in the Netherlands.

As part of the MPE2013 (Mathematics of Planet Earth 2013) a public event is held:
time: 21st December 2013; 12:30-17:30
place: Educatorium Utrecht

Main speaker: Ken Golden

Mathematics and the melting polar ice caps

In September of 2012, the area of the Arctic Ocean covered by sea ice reached its lowest level ever recorded in more than three decades of satellite measurements. In fact, compared to the 1980's and 1990's, this represents a loss of more than half of the summer Arctic sea ice pack. While global climate models generally predict sea ice declines over the 21st century, the precipitous losses observed so far have significantly outpaced most projections.

Prof. Ken Golden (Dept. of Mathematics, Univ. of Utah, USA) will discuss how mathematical models of composite materials and statistical physics are being used to study key sea ice properties and advance how sea ice is represented in climate models. This work is helping to improve projections of the fate of Earth's ice packs, and the response of polar ecosystems. In addition, an exciting video from a 2012 Antarctic expedition where sea ice properties were measured will be shown.

The parallel sessions are interesting too:

Ute Ebert: How thunderstorms create antimatter

Carel Eijgenraam: Optimal dike heights in the Netherlands

Arjen Doelman: Climate change, desertification and billiard

Target is a general, non-mathematics audience. I am not associated with the PWN in any way, but for me there seem to be few excuses not to go. 

Information and reservations:

Developers Corner / Getting hi-res Landsat Images.
« on: November 06, 2013, 01:35:21 PM »

As discussed in the "NØIB (Norske Øer Ice Barrier)" thread, Landsat images available in viewers are not the best for those who like to be as close to the ice as possible (without going there):

- image format is JPEG. When zooming in to the details, the artifacts become apparent;
- resolution is far worse(180m)  than the native resolution from the Landsat imager (30 meters for most channels and one 15 meter pan-chromatic (B&W) channel);
- the images are false colors based on two infrared and one visible (red) channel. Fine for land images with vegetation, but not for images with lots of water, ice and snow.

Applicable pages from the USGS Landsat FAQ's:
What are the best spectral bands to use for my study?
What band combination is used for Landsat browse images?
How does Landsat 8 differ from previous Landsat satellites?

Step 0: Get a registration on the web site of the US Geological Survey.

This is required if you want to download image files in the process that I am now describing. If you just want to explore the images available, skip this step.
Registration is free, and takes entering email+password, and responding to the confirmation email. Save the password somewhere when you consider using the bulk downloading app, you need to enter the password there as well.

Step 1: Find suitable Landsat images with the LandsatLook Viewer.

- Locate the spot of interest. You can use a name (Paris, France, or even Tobias, Greenland) or longitude,latitude coordinates.
- Zoom in sufficiently until a button "Select Scenes" appear in the selection box
- Press "Advanced Query". Make sure the OLI sensor is selected. OLI is Landsat 8, that is latest and greatest but only available in 2013 (and later, later). Select other sensors if pre-2013 data is of interest. Also set "Maximum Cloud Cover" to something high, sometimes partly clouded scenes have a clear view i just the thing that is interesting. Press Apply.
- Select "Only One" under the date slider.
-With the date slider, view the different images that are available in your area of interest.

Step 2. Order and download the Landsat data.

Convinced that the image in the viewer is worth doing some more effort on?  Has your computer enough RAM, physical and swap, installed to handle 800 MB images? Recommended is 16 GB physical RAM and perhaps double of that virtual.  Then you can continue for some serious computing.

Press the button "Metadata", a box appears with some detailed information on the selected image.
- Press "Add To Cart". You can do this actually several times before proceeding, but here I assume only one image is what we want;
- Press "View Cart"
- in the "Cart" select the image and press "Get Landsat Data";
- confirm that you go to " USGS EarthExplorer" (where you can check out);
- at some point you may be required to log in (see Step 0), unless like me you have selected the "keep logged in" option;
- a new browser window is opened with a list called "Pending Scenes". There should be only one "Scene", our image. Click on its "Entity Id";
- A new page opens with lots of details of our image, but at the bottom is a button "download". Just click on it, if you haven't yet done so (*);
- In the last page, click on the "download" button that says "Level 1 GeoTIFF Data Product";
- Select the location where you want the file and start the download;

 *) If the Level 1 data seems not available, look here

Step 3: Unpack the "Level 1 GeoTIFF Data Product"

The downloaded file is a compressed archive called something like LC80030042013267LGN00.tar.gz. I recommend unpacking the archive in to an empty directory. Use your favorite software, under Linux the command is:

  tar xzf LC80030042013267LGN00.tar.gz
Once unpacked you have a directory with these files:

-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B1.TIF
-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B2.TIF
-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B3.TIF
-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B4.TIF
-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B5.TIF
-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B6.TIF
-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B7.TIF
-rw-r--r-- 1 672931638 sep 24 20:14 LC80030042013267LGN00_B8.TIF
-rw-r--r-- 1 168288198 sep 24 20:14 LC80030042013267LGN00_B9.TIF
-rw-r--r-- 1 168288198 sep 24 20:15 LC80030042013267LGN00_B10.TIF
-rw-r--r-- 1 168288198 sep 24 20:15 LC80030042013267LGN00_B11.TIF
-rw-r--r-- 1 168288198 sep 24 20:15 LC80030042013267LGN00_BQA.TIF
-rw-r--r-- 1      7676 sep 24 20:15 LC80030042013267LGN00_MTL.txt

All files start with the image identifier, the Bxx means "spectral band xx". Bands, and their use are listed here For this discussion B2, B3 and B4 are important as they are the visible light bands Blue, Green and Red 30 m images.  The B8 is the panchromatic B&W hi-res image, with the 15 m resolution.
Of course all other bands can be experimented with for the more advanced studies. Here we aim at a simple natural looking image.

Step 4: Inspecting the image files and introducing ImageMagick.

At this stage you might fire up your favorite image editor (the Gimp, Photoshop etc.) to look what is in those files. When I was experimenting that is what I did myself. But because the processing of these "spectral band images" is highly repeatable, I use a command line tool for that.
The free tool is ImageMagick and available for Unix, Windows, Mac and even iOS. I am using these every day, for instance to produce the ice animations in the amsr2 thread.
Make sure the software is installed and open the terminal.
Imagemagick is a set of different programs, each with an unbelievable set of options. For introduction start with identify, used to describe the format and attributes of an image:

$ identify LC80030042013267LGN00_B2.TIF
LC80030042013267LGN00_B2.TIF TIFF 9171x9171 9171x9171+0+0 16-bit Grayscale DirectClass 168.3MB 0.010u 0:00.089

For now it is important to note that the file is a 16 bit TIF image, with size 9171 pixels width and height. Different Landsat scenes may have slightly different sizes, something that will slightly complicate out processing later on.

When ImageMagick reads the TIF files from LandSat it prints several warnings:

identify.im6: LC80030042013267LGN00_B2.TIF: unknown field with tag 33550 (0x830e) encountered. `TIFFReadDirectory' @ warning/tiff.c/TIFFWarnings/768.

As far as understand these warnings are harmless, concerning non image data embedded in the files, and can be suppressed by adding an option -quit on the command line.

Get the image information of the Panchromatic channel:

$ identify -quiet LC80030042013267LGN00_B8.TIF
LC80030042013267LGN00_B8.TIF TIFF 18341x18341 18341x18341+0+0 16-bit Grayscale DirectClass 672.9MB 0.000u 0:00.060

Because this channel is 15 m instead of 30 m, the width and height in pixels has doubled but not exacly! Actually one pixel is missing in both directions, a fact that we have to solve in the next section.

The last ImageMagick tool that I would like to introduce here is [ur=]convert[/url], the work horse of the set. With an almost infinite set of options it can convert between image formats as well as resize an image, blur, crop, despeckle, dither, draw on, flip, join, re-sample, and much more.

$ convert -quiet LC80030042013267LGN00_B8.TIF LC80030042013267LGN00_B8.png

Converting the TIFF file to a png file format. Png is much more efficient in disk space:
-rw-r--r-- 1 672931638 sep 24 20:14 LC80030042013267LGN00_B8.TIF
-rw-r--r-- 1 285094673 nov  6 12:53 LC80030042013267LGN00_B8.png

This is the file from which I showed selections in  the "NØIB (Norske Øer Ice Barrier)" thread.

Step 5: Process the image files with ImageMagick commands.

Ready for the magick? Here we go.

Combine the Read, Green and Blue images to one (composite) natural color image:
Code: [Select]
$ convert -quiet LC80030042013267LGN00_B4.TIF LC80030042013267LGN00_B3.TIF LC80030042013267LGN00_B2.TIF -channel RGB -combine out-nat-30.png
Producing an intermediate file out-nat-30.png, containing a perfectly usable natural color image with 30 m resolution.
But we go for the 15 m resolution, because it is there. In order to do that we must resample the image for the increased width and height:
Code: [Select]
$ convert out-nat-30.png -filter Point -resize 200% -crop 18341x18341+0+0 out-nat-15.tmp.png
The -filter option prevents that ImageMagick does some "smart" pixel interpolating when resizing and just doubles the number of pixels (in each direction).
The -crop option is nescessary because the 15 m panchromatic image had not exactly twice the size. The -crop  18341x18341+0+0, trims the result to the same size. The "+0+0" gives the offset from where to crop, this means count from the upper left corner which is what we want.

The result is a natural color image that has the correct number of pixels, but effectively the resolution is not changed because every cluster-of-four pixels has the same RGB value. The trick is to get the 15 m panchromatic information in.

Next step is to separate the RGB values into another color space called HSL, consisting of Hue,  Saturation and Lightness:

Code: [Select]
convert out-nat-15.tmp.png -colorspace HSL -separate separate_HSL_%d.png
Producing three (intermediate) files called separate_HSL_0.png, separate_HSL_1.png and separate_HSL_2.png. Each has 15 m pixels but an effective resolution of 30 m. The trick is to replace the Lightness image by our panchromatic (B8) channel. Here is the command to rebuild the image this way:
Code: [Select]
convert -quiet separate_HSL_0.png separate_HSL_1.png LC80030042013267LGN00_B8.TIF -set colorspace HSL -combine -colorspace RGB out-nat-15.png
Which produces the final result a 15 m hires natural color image. Only at the highest magnification where individual pixels are visible, the 30 m color resolution becomes visible.

The image is quite large:

-rw-r--r-- 1 716890168 nov  7 10:01 out-nat-15.png

A reflection of the amount of information in the image. Please don't convert to JPEG, or perhaps until you made the final cut and adjustments. Then convert with the highest quality settings.

Step 5a: Some optimizations.

In the previous section I have shown the procedure in a number of small steps. That is good for an explanation, showing what is done without the clobber of a number of simultanious things.
In this section are the commands that I actually use. You may skip it altogether if you like.

First there is the problem that I already mentioned that the size of the Landsat scenes are not always the same. Since we need it for the "-crop" option, we have to extract it form the files.

Under a Unix compatible shell (Linux, Mac and Windows using CygWin) it goes like this:
Code: [Select]
cropsize=`identify -quiet LC80030042013267LGN00_B8.TIF | cut -d ' ' -f 4`
This creates from the output of the identify command a variable named cropsize  with a value:
$ echo $cropsize

A further complication is that I wrote the commands with full file names. If these files are the only similar named files, we can use wildcards. So instead of:

This makes the command independent from the actual Landsat scene.

Lastly, not all intermediate files are needed. I have not tried (yet) to squeeze everything on a single line but this is the current script (three lines):

Code: [Select]
cropsize=`identify -quiet *_B8.TIF | cut -d ' ' -f 4`
convert -quiet *_B4.TIF *_B3.TIF *_B2.TIF -channel RGB -combine  -filter Point  -resize 200% -crop $cropsize -colorspace HSL -separate separate_HSL_%d.png
convert -quiet separate_HSL_0.png separate_HSL_1.png *_B8.TIF -set colorspace HSL -combine -colorspace RGB out-nat-15.png

The script takes about 5 minutes here. I see the memory monitor for the process convertspike at 13 GB. This will give problems when you thought 8 GB was plenty or RAM.

Step 6: Final processing.

The conversion is done, but if we look at it the image is not very brilliant, lacking contrast. It is also far too big to share on the web.
The final edit are currently done in the image editor, I am using the Gimp , but I don't expect that is critical (provided it is 64 bits and can handle the sizes).

In the Gimp, I enhance the image with the automatic white balancing tool:
   Colors->Auto->White Balance
The cutting can be done with the crop tool or use a selection tool followed by choosing "Crop to Selection" from the image menu.


The procedure described above, is not finished. I am thinking:
- the HSL color separation is just one of several slightly different possibilities. HSL is the first one I tried, I have no idea if it is the best one;
- What about other spectral bands? Does infrared carry useful information that helps understanding the scenes;
- The "white balance" solution to get brilliant colors should be explored further;
- perhaps there are other ideas, I'd like to hear them.

Arctic sea ice / Daily SMOS Ice Thickness available: season 2015/2016
« on: September 24, 2013, 09:25:05 AM »
From the Uni Hamburg Integrated Climate Data Center:

New Data: SMOS Sea Ice Thickness 20.09.2013
By: Stefan Kern

Now, after almost 4 years of operation of the Soil Moisture and Ocean Salinity (SMOS) satellite, we can offer daily sea ice thickness estimates calculated from SMOS data for the Arctic for freezing seasons 2010/11 to 2012/13 via the ICDC web portal:

SMOS is European Space Agency’s (ESA) Soil Moisture and Ocean Salinity mission measuring the Earth radio emission at 1.4GHz. At this frequency ice is semi transparent, so the measured brightness can be used to calculate thickness.

Important disadvantages are 1) only measures thin ice up to about 0.5m 2) not usable in the melting season (15 April-15 Oktober).

Do read the "Data Quality" section in the link given above when interpreting the SMOS data.

Arctic sea ice / Home brew AMSR2 extent & area calculation
« on: June 17, 2013, 05:00:34 PM »
The nice guys at the University of Hamburg have provided the results of their unfinished sea ice concentration calculation based on L1(R) AMSR2 data from JAXA  online in some very handy NetCDF files.

Citation of source data:
Beitsch, A., L. Kaleschke and S. Kern (2013), "AMSR2 ASI 3.125 km Sea Ice Concentration Data, V0.1", Institute of Oceanography, University of Hamburg, Germany, digital media
(, [BEGIN Jan 2013- present];
Spreen, G., L. Kaleschke, G. Heygster (2008), "Sea Ice Remote Sensing Using AMSR-E 89
GHz Channels", J. Geophys. Res., 113, C02S03, doi:10.1029/2005JC003384.

Kaleschke, L., C. Lüpkes, T. Vihma, J. Haarpaintner, A. Bochert, J. Hartmann, G. Heygster,
"SSM/I Sea Ice Remote Sensing for Mesoscale Ocean-Atmosphere Interaction Analysis",
Can. J. Rem. Sens., 27(5), 526-537, 2001.
see also:
[EDIT 2017-03-30: source adress change]

The data is provided at a 3.125x3.125 km grid.

Summing the area of the grid cells that have an ice concentration of 15% (or some other value) should give a measure of the extent that can be compared with the well known Jaxa/Ice, NSIDC and others that do similar calculations.

Here I present the first results.

The calculations have the following features:

1) uses the actual area of the grid cells, which may deviate a few perecent from the nominal 3.125^2 km2;
2) Ice concentration of the "North Pole hole" is calculated to be the same as a small ring (width 25% of the radius of the hole itself) around the hole;
3) Spurious ice is removed from coastlines where there is open water within a "few" grid cells;
3a) pixels labeled as sea, separated from the world oceans are considered "lake" and discarded;
4) "phantom" ice fleets that appear and disappear randomly, especially at lower latitudes are detected and removed;
5) an ice mask is used to split the area into regions as closely as possible similar to those of the Cryosphere Today.

Of course it may be regarded as a foolish undertaking:

1) the 3.125 km grid cannot be compared with anything else available;
2) the 3.125 km ice concentration values are influenced by clouds and water vapor (as a consequence of using the hi-res 89 GHz microwave band);
3) The ice concentration data is unofficial and work-in-progress;
4) The data is only available for 2013, we cannot compare with any other year directly.

Well, it is fun to try and I was supprised when I saw the first result:

My calculations have been tracking Jaxa's quite close.
I expected a lot of noise as there is no filter (Jaxa filters 2 days), the unfiltered data looks quite usable.
Since end of May, the two have been diverging. This is to be expected, when hole fall in the ice cover the smaller grid will more likely pick them up than the wider grid.

Considering now:
1) extent per region;
2) area calculation;
3) compactness calculation (like CAPIE but from the same source)

[update put the area graph in the top post:]

[update put the compactness graph in the top post]

[update: add regional graphs]

Arctic sea ice / Latest PIOMAS update (Oktober, mid-monthly update)
« on: March 12, 2013, 05:07:20 PM »
Hello, PIOMAS has updated:
Latest value: 2013-3-1 19.945
Latest value: 2013-3-31 21.612
Latest value: 2013-4-30 21.273
Latest value: 2013-5-31 19.087
Latest value: 2013-6-30 13.002
Latest value: 2013-7-31 7.104
Latest value: 2013-8-31 5.077
Latest value: 2013-9-30 5.343
Latest value: 2013-10-31 8.218
Latest value: 2013-11-30 11.449
Latest value: 2013-12-31 15.225
Latest value: 2014-1-31 18.938  <- version 2.1 !
Latest value: 2014-2-28 20.86
Latest value: 2014-3-31 22.609
Latest value: 2014-4-30 22.94
Latest value: 2014-5-31 20.288
Latest value: 2014-6-30 14.632
Latest value: 2014-7-31 9.575
Latest value: 2014-8-31 7.22
Latest value: 2014-9-30 7.119 (minimum 2014  on 9-18: 6.810)
Latest value: 2014-10-31 9.701
Latest value: 2014-11-30 13.314
Latest value: 2014-12-31 16.842
Latest value: 2015-1-31 20.229
Latest value: 2015-3-8 22.813
Latest value: 2015-3-31 24.036
Latest value: 2015-4-30 24.066
Latest value: 2015-5-31 21.496
Latest value: 2015-6-30 15.263
Latest value: 2015-7-31 8.604
Latest value: 2015-8-31 5.975
Latest value: 2015-9-15 5.713
Latest value: 2015-9-30 6.032
Latest value: 2015-10-31 8.563
Latest value: 2015-11-30 11.999
Latest value: 2015-12-31 15.652
Latest value: 2016-1-31 18.536
Latest value: 2016-2-29 20.660
Latest value: 2016-4-1 22.337
Latest value: 2016-5-1 22.268
Latest value: 2016-6-1 19.201
Latest value: 2016-7-1 13.177
Latest value: 2016-8-1 7.448
Latest value: 2016-9-1 4.638
Latest value: 2016-10-1 4.869
Latest value: 2016-11-1 6.534
Latest value: 2016-12-1  9.515
Latest value: 2016-12-31 13.078
Latest value: 2017-1-31 16.162
Latest value: 2017-2-28 18.608
Latest value: 2017-3-31 20.398
Latest value: 2017-4-30 20.64
Latest value: 2017-5-31 18.11
Latest value: 2017-6-30 12.164
Latest value: 2017-7-31 6.725
Latest value: 2017-9-15 4.658
Latest value: 2017-11-30 10.871
Latest value: 2017-12-31 14.418
Latest value: 2018-01-31 17.57 (prelim)

I have updated my graphics at Arctische Pinguin for the latest data.

Monthly data:

Daily Anomalies:

Daily data with a "prediction" based on exponential trend:

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