Discussion:
a model for hillbilly seyuns
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M***@kymhorsell.com
2018-11-08 08:44:46 UTC
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I was interested in anobba of those "science papers" a few days back.

Widespread and accelerated decrease of observed mean and extreme snow
depth over Europe
The amount of snow that accumulates across Europe each year is
"already dramatically decreasing", a new study finds. Analysing
observed records of snow depth across Europe, the researchers find
that average and maximum snow depth have decreased by around 12% and
11% per decade since 1951, respectively. These trends - which have
accelerated since the 1980s - have "strong implications for the
availability of freshwater in spring", the authors warn.
-- Geophysical Research Letters


So like many times in the past, we just have to get some data together
and try to reproduce something.

But this time, instead of reproducing the ostensible headline results
from the paper, I thought I'd like to reproduce how a hillbilly
"disproof of the paper" typically goes.

First we have to get some kind of data together.

Because I've done some work wid it in da past, I'll select the GRACE
data over Europe 2002-2017.

GRACE uses a pair of satellites to deduce nearby mass concentrations.
When the satellites travel over a region with a big fat glacier the
mass of the glacier sticking up above MSL a couple 100 km below ever
so slightly accelerates the lead sat in the train, and the delicate
measurement of the distance between the 2 sats that result over time
allows a modeler later to determine what the mass of ice weighs.

As the GRACE sats are in a polar orbit they return again and again to
the same region and allow changes in mass to be mapped.

Science gnomes in basements around the world process all the data and
boil it down to "equivalent water depths" which is a handy dandy way
to visualise what's happening to ice, oceans and water tables all over.

So we can select out the part of the data that applies to Europe in
winter over the lifetime of the GRACE (v1) sats and it boils down to:

Year Avg water-depth-equiv of mass over 1 mn km2 of W Europe
2002 3.5250974525843
2003 3.18467699271002
2004 0.949147695039959
2005 0.813106627260683
2006 1.26437778043749
2007 0.975124793055377
2008 0.225178838978584
2009 0.951917912005253
2010 5.55145592773663
2011 0.962508462386547
2012 0.0593164422530507
2013 0.944553679691897
2014 1.58655552502626
2015 1.74057310769486
2016 -0.426190505125377
2017 -0.179344306938506

The idea of measuring the mass variations over such a large area is to
filter out all the "little noises" such as changes in glaciers, and
try to boil it down to variations in whatever is happening in winter.
Mostly snowfall. We hope.

It's obvious by eye there is a decline, but we will need to get a
number on that.

A time series regression on the above gets:

(SERIAL CORR DETECTED; estimated rho = 0.322837)
y = -0.0866687*x + 175.026
beta in -0.0866687 +- 0.132414 95% CI
P(beta<0.000000) = 0.909573
r2 = 0.133302
calculated Spearman corr = -0.482143
Critical Spearman = 0.440500 2-sided at 5%; reject H0:no_trend

Model estimates:

Year Av depth model-est av depth
(cm water eq)
2002 3.5251 1.51552**(model -2s below obs)
2003 3.18468 1.42885**(")
2004 0.949148 1.34218
2005 0.813107 1.25551
2006 1.26438 1.16884
2007 0.975125 1.08218
2008 0.225179 0.995507*(model 1sd above obs)
2009 0.951918 0.908838
2011 0.962508 0.7355
2012 0.0593164 0.648832
2013 0.944554 0.562163
2014 1.58656 0.475494*(-1s)
2015 1.74057 0.388826*(-1s)
2016 -0.426191 0.302157
2017 -0.179344 0.215488


While the Spearman is 95% sure there is a trend (a -ve trend), the
T-test is only showing ~91% certainty.

This tells us to look at the residual plot:

Plot of residuals (centre of each sub-interval)
resid count
-2.5000: 0:
-1.5000: 0:
-0.5000: 8:********
0.5000: 4:****
1.5000: 3:***
2.5000: 1:*

Highly NON Gaussian (no bell curve).

So that explains why the T-test gets "the wrong answer".

And we proceed assuming the Spearman rank is good and there *is* a
declining trend of around 87 mm/decade of water equiv.

Now the first thing to note is that snow and water are not the same.
If we're trying to guesstimate changes in av winter snow depth we have
to multiply by an appropriate factor.

Since we're looking at winter snow we can assume "fresh snow" which is
around 1/2 the density of water.

I.e. the change in "average winter snow depth" we've apparently 95%
found is around 170 mm/decade.

Unfortunately, since we're using an ANOMALY measure (i.e. the GRACE
data just shows a deviation from normal in water depth equiv -- not
one nailed to a mean sea level) we need to search around to find what
kind of NORMAL SNOW depth some ground stations read.

Fortunately, the met people out in Eastern Europe keep track of that
kind of thing.

Averaging the daily winter readings from a dozen snow depth gauges
gives an average over the stations and days of winter of around 16 cm
avg depth. (And -- we'll need it later -- the average of the MAX
depth is about 32 cm).

So we end up with a change per decade of 1.7 cm with an expected
average near 16 cm -- 11%.

Now we have to go back and get an estimate from the GRACE data
about the "maximum snow depth" over winter.

There are a whole bunch of ways this could be defined -- the max of
the averages for each grid box; the average of the maxes from each
grid box; various combinations of same.

We'll just select one based on how easy it is to calculate.

Here's the data:

Year max mass anom for Europe in winter
(cm water equiv)
2002 11.2261
2003 16.255
2004 10.8912
2005 7.82793
2006 9.57811
2007 12.4522
2008 6.10066
2009 7.65856
2010 13.9344
2011 14.9452
2012 8.69216
2013 9.10115
2014 6.15802
2015 16.5383
2016 13.7045
2017 7.64518

Which gives a TS model:

(No serial corr detected).
y = -0.0428101*x + 96.8211
beta in -0.0428101 +- 0.418849 95%
P(beta<0.000000) = 0.585177
r2 = 0.0034208
calculated Spearman corr = -0.114706
|r| <= rc (0.425000 2-sided) at 5%; accept H0:no_trend

2002 11.2261 11.1154
2003 16.255 11.0726*
2004 10.8912 11.0297
2005 7.82793 10.9869
2006 9.57811 10.9441
2007 12.4522 10.9013
2008 6.10066 10.8585*
2009 7.65856 10.8157
2010 13.9344 10.7729
2011 14.9452 10.7301*
2012 8.69216 10.6873
2013 9.10115 10.6445
2014 6.15802 10.6016*
2015 16.5383 10.5588*
2016 13.7045 10.516
2017 7.64518 10.4732

Plot of residuals (centre of each sub-interval)
resid count
-5.0000: 2:**
-3.0000: 3:***
-1.0000: 4:****
1.0000: 2:**
3.0000: 2:**
5.0000: 3:***

The resid plot shows why the T-test says "no". A 58% chance it's just
a lucky -ve trend. The Spearman also says no.

But let's ignore that and just look at the central measurement.

The decline in max winter snow depth is around .43 cm/dec.

This then can be divided by the prev-noted "max snow depth" from the
snow gauges (32 cm) to get .42/32 == 1.3%.

OBVIOUSLY THE PAPER IS WRONG!

(This is the model hillbilly refutation part of the exercise; a real
hillbilly refutation would not have bother to discover the difference
between water and snow density either).

~ ~ ~ ~ ~ ~ ~ ~ ~


But we must go on.

First, we note, the change in the "average snow depth" is very close
to the number published in the paper (12% for average since 1951).

But the paper says after 1980 (which our GRACE data is) the rate of
decline should be "higher".

So instead of simply dropping the ball we have to try to decide what
might be the possible explanation for the difference.

The first thing to understand is -- you are (in this simulation) a
barely-literate hillbilly. If there is any mistook going on it is VERY
VERY LIKELY to be yourun, not the autha(s) of the original
paper. Given the published paper is in a real journal, not a "vanity
journal" that charges authors to publish any rubbish they care to submit.

With no other information other than the clipping above we have to
decide is there a plausible explanation that shows how we get one
answer and the published paper gets another.

In this case there obviously is. The authors likely did not use GRACE
data (given it is an ANOMALY measurement). They most likely used data
from a possible large number of snow gauges or other direct or
indirect measurements of winter snow.

The GRACE data has averaged over the whole region. And most of the
region even in winter has no snow. Places with snow gauges -- guess
what -- USUALLY HAVE SNOW IN WINTER.

So we can try to convert our GRACE "the whole 1 mn km2" data into a
simulation of measuring a bunch of snow gauges.

And the easy way to do that is to take each (say) 1x1 deg grid box
over Europe, throw away all those grid boxes where there is never much
snow in winter, and only use the OTHER boxes to get our "average snow
depth" and "maximum snow depth".

Here is the data:

Average winter snow depth across Europe (ignoring locations with no snow):

2002 0.606795
2003 2.02086
2004 0.696911
2005 -0.250832
2006 1.01491
2007 0.675506
2008 0.138087
2009 1.5651
2010 4.07876
2011 0.612856
2012 -0.305182
2013 -0.593528
2014 2.04311
2015 0.140684
2016 -2.67473
2017 -3.1374

Model:

(SERIAL CORR DETECTED; estimated rho = 0.265994)
y = -0.262029*x + 526.725
beta in -0.262029 +- 0.163853 90% CI (just fer fun!)
P(beta<0.000000) = 0.992932
r2 = 0.381555

Rate of decline:

2.62 cm/dec

Percent decline:
2.62/16 ~ 16%/dec

Max winter snow depth across Europe:

Data:

2002 0.986783
2003 2.39532
2004 0.95843
2005 -0.0323647
2006 1.19959
2007 0.759098
2008 0.323841
2009 1.83873
2010 4.32521
2011 0.872369
2012 0.0110796
2013 -0.272827
2014 2.50562
2015 0.766749
2016 -2.14177
2017 -2.75462

Model:

(SERIAL CORR DETECTED; estimated rho = 0.266375)
y = -0.241848*x + 486.469
beta in -0.241848 +- 0.168781 90% CI
P(beta<0.000000) = 0.987617
r2 = 0.331255

Rate of decline:

2.42 cm/dec

Percent decline:

2.42/32 ~ 8%/dec.

Which has roughly demonstrated that the salient points in the paper
are likely valid.

* Both average and max snow depth across Europe seems to be declining.

* Decline in max snow is nominally less as a% than decline in
avg winter snow.

* The rate of snow decline seems to have accelerated post 2000
compared with post 1950.


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Wally W.
2018-11-08 13:06:01 UTC
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Post by M***@kymhorsell.com
Because I've done some work wid it in da past, I'll select the GRACE
data over Europe 2002-2017.
https://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment
Perigee 483 km (300 mi)
Post by M***@kymhorsell.com
Year Avg water-depth-equiv of mass over 1 mn km2 of W Europe
2004 0.949147695039959
No units given, but let's assume it is in meters.

0.949147695039959
0.000000000000001 = 1e-15 meters precision

https://en.wikipedia.org/wiki/Bohr_radius
The Bohr radius is a physical constant, approximately equal to the
most probable distance between the nucleus and the electron in a
hydrogen atom in its ground state.
Its value is 5.2917721067(12)e-11 m

1e-15 / 5e-11 = 0.00002

Let's use measurements from satellites 300 miles above the Earth to
calculate lengths that are precise to better than one thousandth of
the radius of the smallest atom.

It's truly amazing what one can do with Excel these days if they don't
fancy themselves to be a hillbilly.

https://simple.wikiquote.org/wiki/Robert_Burns
Simple: I wish for a power to give us this gift: Being able to see
ourselves the way other people see us.

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