Cold Kills: Rhode Island

sunshine hours

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Snow: They Are Going To Run Out of Room on the Graph

sunshine hours

I usually post Northern Hemisphere. But here is North America Snow Water Equivalent.

March 2000: According to Dr David Viner, a senior research scientist at the climatic research unit (CRU) of the University of East Anglia,within a few years winter snowfall will become “a very rare and exciting event”.

“Children just aren’t going to know what snow is,” he said.

Snow seems to be ignoring David Viner.

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Snow: Higher and Higher

Note on the chart:  The time series average and range between ±1 standard deviation (calculated for 1998/99 to 2011/12) shows how current conditions compare to historical variability.

Note 2:  Here’s the link to the Environment and Climate Change Canada site (they just had to throw in Climate Change): https://www.ccin.ca/ccw/snow/current

sunshine hours

March 2000: According to Dr David Viner, a senior research scientist at the climatic research unit (CRU) of the University of East Anglia,within a few years winter snowfall will become “a very rare and exciting event”.

“Children just aren’t going to know what snow is,” he said.

Snow seems to be ignoring David Viner.

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Influence of solar activity on European rainfall

Reblogged from Watts Up With That:

Press Release

Institute of Hydrography, Geoecology and Climate Sciences (IFHGK), www.ifhgk.org

15th February 2019

Influence of solar activity on European rainfall

A balanced level of precipitation provides the basis for a wide range of economic and social activities in Europe. Particularly agriculture, drinking water supply and inland waterway transport are directly affected. However, the amount of rain fluctuates strongly from year to year. While it may pour torrentially in one year, rain may remain absent for weeks in another year. The population is used to this variability and knows how to deal with it.

The chance discovery by an agricultural scientist from Münster, Germany, now suggests that in certain months rain over Germany and other parts of Europe follows a pattern that up to now has remained undetected. As part of agricultural consultation, Ludger Laurenz analyzed decades of rainfall records of his home weather station in Münster and noticed a constant up and down that followed an 11-year rhythm – especially in February. After detailed examination it was clear that this rhythm correlated closely with the activity of the sun: the well-documented 11-year sunspot cycle.

Laurenz next teamed up with two colleagues to examine the extent to which the observed pattern from Münster is reproducible in other parts of Germany and Europe, and whether the phenomenon also exists for the other months of the year. Horst-Joachim Lüdecke from the HTW University of Applied Sciences in Saarland gathered the precipitation data collected in Europe since the beginning of the 20th century. The physicist emeritus then developed a computer algorithm to determine the similarity of changes in rainfall and solar activity. All 39 European countries and every one of the 12 months of the year were quantified over a total of 115 years using mathematical correlations.

In order to include possible delay effects, the data series of rain and sunspots were systematically checked for shifts. For this purpose, the time series were gradually shifted in time against each other like combs and the respective change of the correlation quality was noted. The multidimensional data obtained in this way were evaluated for systematic trends by geoscientist Sebastian Lüning and visualized cartographically. Lüning is associated with the Swiss Institute of Hydrography, Geoecology and Climate Sciences (IFHGK) and is specialized in the research of solar climate effects.

The mapped out results show that the link between February precipitation and solar activity originally discovered in Münster is valid for large parts of Central and Northern Europe and has good statistical significance there. Towards southern Europe, however, the correlation weakens significantly.

The statistical investigation was also able to demonstrate systematic phase shifts across the continent. In Germany and neighboring countries, February precipitation was particularly low when the sun was very strong four years earlier. The delay seems to be due to the slow deep circulation of the Atlantic, as earlier work had already suggested. On the basis of the statistically-empirically determined correlation, February 2018 in Germany with particularly low precipitation can now also be explained, which followed a particularly high intensity peak of solar activity at the beginning of 2014.

Similar relationships between rainfall and solar activity have been observed in other months, although somewhat weaker, especially in April, June and July, which account for a large part of the vegetation period in Central Europe. The result was a complex interplay of sun and rain in Europe, which showed clear trends over 1000 km and varied strongly from month to month.

The study thus confirms the concept of a solar participation in the European hydroclimatic development, which had already been indicated by a whole series of local case studies of other authors. The exact mechanism by which the solar signal influences precipitation is still largely unclear and requires further research.

The solar precipitation effect now mapped out across Europe for the first time opens up new possibilities for improved medium-term precipitation forecasts. Agriculture in particular, but also protection measures against extreme weather damage in connection with heavy rainfall and droughts could benefit from this. The next step in refining the forecasting methodology is a more precise quantification of the effects of Atlantic Ocean cycles, which also play an important role in rainfall, especially in Western Europe.

Original publication:

Laurenz, L., H.-J. Lüdecke, S. Lüning (2019): Influence of solar activity on European rainfall. J. Atmospheric and Solar-Terrestrial Physics, 185: 29-42, doi: 10.1016/j.jastp.2019.01.012

The pdf version can be downloaded free of charge at the following link until early March: https://authors.elsevier.com/a/1YXWZ4sIlkiVhv

Taking down the latest Washington Post Antarctic scare story on 6x increased ice melt

Reblogged from Watts Up With That:

Ice loss from Antarctica has sextupled since the 1970s, new research finds
An alarming study shows massive East Antarctic ice sheet already is a significant contributor to sea-level rise

Chris Mooney and Brady Dennis

January 14 at 3:00 PM (Washington Post)

Antarctic glaciers have been melting at an accelerating pace over the past four decades thanks to an influx of warm ocean water — a startling new finding that researchers say could mean sea levels are poised to rise more quickly than predicted in coming decades.

The Antarctic lost 40 billion tons of melting ice to the ocean each year from 1979 to 1989. That figure rose to 252 billion tons lost per year beginning in 2009, according to a study published Monday in the Proceedings of the National Academy of Sciences. That means the region is losing six times as much ice as it was four decades ago, an unprecedented pace in the era of modern measurements. (It takes about 360 billion tons of ice to produce one millimeter of global sea-level rise.)

“I don’t want to be alarmist,” said Eric Rignot, an Earth-systems scientist for the University of California at Irvine and NASA who led the work. But he said the weaknesses that researchers have detected in East Antarctica — home to the largest ice sheet on the planet — deserve deeper study.

“The places undergoing changes in Antarctica are not limited to just a couple places,” Rignot said. “They seem to be more extensive than what we thought. That, to me, seems to be reason for concern.”

The findings are the latest sign that the world could face catastrophic consequences if climate change continues unabated. In addition to more-frequent droughts, heat waves, severe storms and other extreme weather that could come with a continually warming Earth, scientists already have predicted that seas could rise nearly three feet globally by 2100 if the world does not sharply decrease its carbon output. But in recent years, there has been growing concern that the Antarctic could push that even higher.

That kind of sea-level rise would result in the inundation of island communities around the globe, devastating wildlife habitats and threatening drinking-water supplies. Global sea levels have already risen seven to eight inches since 1900.

The full drivel here


Why do I call it “drivel”? Three reasons:

1. Anything Chris Mooney writes about climate is automatically in that category, because he can’t separate his fear of doom from his writing.

2. The math doesn’t work in the context of the subheadline. Alarming? Read on.

3. Data back to 1972…where?

First, let’s get some data. Wikipedia, while biased towards alarmism in this reference, at least has the basic data.

https://en.wikipedia.org/wiki/Antarctic_ice_sheet

It covers an area of almost 14 million square kilometres (5.4 million square miles) and contains 26.5 million cubic kilometres (6,400,000 cubic miles) of ice.[2]A cubic kilometer of ice weighs approximately one metric gigaton, meaning that the ice sheet weighs 26,500,000 gigatons.

Now for the math.  

So, if the Antarctic ice sheet weighs 26,500,000 gigatonnes or 26500000000000000 tonnes

252 billion tonnes is 252 gigatonnes

Really simple math says:  252gt/26,500,000gt x 100 = 9.509433962264151e-4 or 0.00095% change per year

But this is such a tiny loss in comparison to the total mass of the ice sheet, it’s microscopic…statistically insignificant.

In the email thread that preceded this story (h/t to Marc Morano) I asked people to check my work. Willis Eschenbach responded, corrected an extra zero, and pointed this out:

Thanks, Anthony. One small issue. You’ve got an extra zero in your percentage, should be 0.00095% per year loss.

Which means that the last ice will melt in the year 3079 …

I would also note that 250 billion tonnes of ice is 250 billion cubic meters. Spread out over the ocean, that adds about 0.7 mm/year to the sea level … that’s about 3 inches (7 cm) per century.

As you said … microscopic.

w.

Paul Homewood noted in the email thread:

Ice losses from Antarctica have tripled since 2012, increasing global sea levels by 0.12 inch (3 millimeters) in that timeframe alone, according to a major new international climate assessment funded by NASA and ESA (European Space Agency).

https://climate.nasa.gov/news/2749/ramp-up-in-antarctic-ice-loss-speeds-sea-level-rise/

0.5mm per year.

Not a lot to worry about.

“They attribute the threefold increase in ice loss from the continent since 2012 to a combination of increased rates of ice melt in West Antarctica and the Antarctic Peninsula, and reduced growth of the East Antarctic ice sheet.”

Translation: The volcano riddled West/Peninsula is melting bit more and the Eastern Sheet is growing a little less than usual.

Paul Homewood adds on his website:

Firstly, according to NASA’s own press release, the study only looks at data since 1992. The Mail’s headline (Taken from the Washington Post – Anthony) that “Antarctica is losing SIX TIMES more ice a year than it was in the 1970s “ is totally fake, as there is no data for the 1970s. Any estimates of ice loss in the 1970s and 80s are pure guesswork, and have never been part of this NASA IMBIE study, or previous ones.

image

Secondly, the period since 1992 is a ridiculously short period on which to base any meaningful conclusions at all. Changes over the period may well be due to natural, short term fluctuations, for instance ocean cycles. We know, as the NASA study states, that ice loss in West Antarctica is mainly due to the inflow of warmer seas.

The eruption of Pinatubo in 1991 is another factor. Global temperatures fell during the next five years, and may well have slowed down ice melt.

Either way, Pinkstone’s claim that the ice loss is due to global warming is fake. It is a change in ocean current that is responsible, and nothing to do with global warming.

Then there is his pathetic claim that “Antarctica is shedding ice at a staggering rate”. Alarmist scientists, and gullible reporters, love to quote impressive sounding numbers, like 252 gigatons a year. In fact, as NASA point out, the effect on sea level rise since 1992 is a mere 7.6mm, equivalent to 30mm/century.

Given that global sea levels have risen no faster since 1992 than they did in the mid 20thC, there is no evidence that Antarctica is losing ice any faster than then. To call it staggering is infantile.

NASA also reckon that ice losses from Antarctica between 2012 and 2017 increased sea levels by 3mm, equivalent to 60mm/century. Again hardly a scary figure. But again we must be very careful about drawing conclusions from such a short period of time. Since 2012, we have had a record 2-year long El Nino. What effect has this had?

But back to that previous NASA study, carried out by Jay Zwally in 2015, which found:

A new NASA study says that an increase in Antarctic snow accumulation that began 10,000 years ago is currently adding enough ice to the continent to outweigh the increased losses from its thinning glaciers.

The research challenges the conclusions of other studies, including the Intergovernmental Panel on Climate Change’s (IPCC) 2013 report, which says that Antarctica is overall losing land ice.

According to the new analysis of satellite data, the Antarctic ice sheet showed a net gain of 112 billion tons of ice a year from 1992 to 2001. That net gain slowed   to 82 billion tons of ice per year between 2003 and 2008.

https://www.nasa.gov/feature/goddard/nasa-study-mass-gains-of-antarctic-ice-sheet-greater-than-losses 

Far from losing ice, as the new study thinks, Zwally’s 2015 analysis found the opposite, that the ice sheet was growing.

OK, Zwally’s data only went up to 2008, but there are still huge differences. Whereas Zwally estimates ice gain of between 82 and 112 billion tonnes a year between 1992 and 2008, the new effort guesses at a loss of 83 billion tonnes a year.

It is worth pointing out that Zwally’s comment about the IPCC 2013 report refers to the 2012 IMBIE report, which was the forerunner to the new study, the 2018 IMBIE.

Quite simply, nobody has the faintest idea whether the ice cap is growing or shrinking, never mind by how much, as the error margins and uncertainties are so huge.

The best guide to such matters comes from tide gauges around the world. And these continue to show that sea levels are rising no faster then mid 20thC, and at a rate of around 8 inches per century.

Disentangling California Drought

Reblogged from Watts Up With That:

Here is Jim Steele’s newest column article for the Tribune and 5 other Marin papers,~ctm

Pacifica Tribune column, January 16, 2019

What’s Natural?

Disentangling California Drought

clip_image001

Devastating droughts are a great concern. Droughts disrupt ecosystems, agriculture, and drinking water supplies. Contrary to headlines suggesting we have only 12 years before descending into climate hell with more severe droughts, historically, Californians are not experiencing more severe droughts. Despite low stream flows and withering plants, there’s no agreement on how to best define drought. Different methods suggest different severities for the same drought. Thus, the Intergovernmental Panel on Climate Change’s recent assessment, downgraded their ability to detect the causes of drought to “low confidence”.

Ocean circulation determines how much rain reaches the land. Each summer, California naturally experiences months of drought because storms carrying ocean moisture are blocked. Every few years, a rainy El Niño year alternates with drought producing La Niñas. But 20 years of more frequent La Niñas can cause 20 years of drought. To address natural precipitation shifts, California constructed ~1400 dams, storing water during wet years that can be released during drought years. Yosemite’s Hetch Hetchy reservoir supplies about 25% of San Francisco’s drinking water and 17% of its electricity. Misguided attempts to remove its dam would be disastrous for humans with scant environmental benefits.

NOAA scientists analyzed California’s 2011-2014 drought concluding it was dominated by a La Niña and natural variability. In contrast, their models suggested any greenhouse contribution was “very small”. Similarly, drought-sensitive tree rings suggested the extremely low precipitation was not unprecedented nor “outside the range of natural variability”. For 1200 years, extremely low rainfall happens a few times every century.

However, because higher temperatures can theoretically increase evaporation and dry the land, some researchers define drought by calculating the Palmer Drought Severity Index (PDSI). Despite using the same tree rings, the PDSI transformed a natural California drought into the worst in 1200 years, evoking global warming fears.

What to trust?

Most scientists agree the PDSI is biased towards worse droughts, because it assumes higher temperatures always dry the land. However, the opposite is also true! Without moisture to absorb heat, drier conditions produce higher temperatures. Studies using more accurate measurements than the PDSI find no increase in global droughts.

Before significant CO2 warming was possible, Dust Bowl years from 1928-1939 and the 1950s drought were the most severe 20th century American droughts. La Niña-like ocean temperatures blocked rain storms and triggered the Dust Bowl while plowing up native grasses made it worse. More concerning is 2 century-long megadroughts between 900 AD and 1400 AD. Trying to survive increasing dryness Native Americans created dams and irrigation canals. But those droughts finally led to the demise of once thriving Pueblo Cultures such as Mesa Verde.

Will our modern water infrastructure protect us if drought history repeats?

Reducing our carbon foot print or whacky plans to shade the earth from the sun to lower global temperatures will have no effect. Lower temperatures may in fact increase major droughts. Droughts during the 1750s, 1820s, and 1850s-1860s were similar to the 1950s. During the cool 1500s, the southwestern United States and Mexico suffered decades long droughts of “epic proportions”.

Coincident with the Pueblo Culture’s demise, drought is detected in sediments of San Francisco Bay. Droughts reduce stream flows that normally flush the bay, allowing salty ocean water to encroach deeper into the Bay’s delta. Past droughts caused the Bay’s Suisun Marsh to become 40% saltier. Suisun Marsh is now considered the only sustainable habitat for a critically endangered fish, the Delta Smelt. The current theory for the Delta Smelt’s demise is agricultural diversions of freshwater raised salinity to intolerable levels. That perceived competition for freshwater has pitted farmers against efforts to save the smelt. Learning how the smelt survived a thousand years of much higher salinity might provide a win-win solution.

Agricultural and urban needs also compete with salmon survival. One promising win-win solution is having juvenile salmon develop in irrigated rice fields after hatching. Experiments show young salmon grow much bigger in rice fields. Additionally, low stream flows hamper salmon migration. But when enough water is naturally stored as groundwater, seasonal groundwater release can maintain adequate summer stream flows. Unfortunately, landscape changes have caused stream channels to cut downwards, draining local groundwater and drying the land. Restoring streams and groundwater would provide great benefits.

During my research in the Sierra Nevada, a meadow we were monitoring began to dry; willows died, and bird populations crashed. Many suggested it was just what global warming models predict. However, we determined a railroad track built over 100 years ago had caused the meadow’s stream channel to cut downwards, draining its groundwater. I initiated a watershed restoration. Vegetation quickly recovered, and wildlife increased. Despite California’s years of extreme drought, the restored meadow remained wetter than it had before restoration and before the drought.

So, I warn: knee-jerk reactions simply blaming climate change for devastating dryness, blind us to real causes and real environmental solutions.

Jim Steele authored Landscapes and Cycles: An Environmentalist’s Journey to Climate Skepticism.

Contact: naturalclimatechange@earthlink.net

Finding: Jet aircraft trails create extra rain and snow from clouds

Reblogged from Watts Up With That:

WASHINGTON—Planes flying over rain or snow can intensify the precipitation by as much as 10-fold, according to a new study.

The rain- and snow-bursts are not caused by emissions from the aircraft but are the peculiar consequence of the aircrafts’ wings passing though clouds of supercooled water droplets in cloud layers above a layer of active rain or snow.

Under the right conditions, this effect can boost rain and snow storms over airports, where many planes intersect the cloud layer on approach and descent.

“The interesting thing about this feature is that it is caused by aircraft, but it is not caused by pollution,” said Dimitri Moisseev, a researcher at the University of Helsinki and the Finnish Meteorological Institute and the lead author of the new study in AGU’s Journal of Geophysical Research: Atmospheres. “Even if there would be absolutely ecological airplanes, which don’t have any combustion, no fuel or anything, it would still happen.”

Although the bands of enhanced precipitation are artificially created, the physical process jump-started by the passage of planes can occur naturally, which makes them useful laboratories for studying the formation of precipitation, according to Moisseev. Observing them may help meteorologists “nowcast” natural rain and snow conditions 2 to 6 hours into the future, which is essential for airport operations.

“When you, like myself, look at the radar data every day there is always something interesting going on,” Moisseev said. “Surprisingly enough, there’s always new things that we cannot explain still.”

Moisseev discovered curious streamers of heightened precipitation in scans from the campus radar antenna at the University of Helsinki Kumpula. The unnaturally straight patches of intense precipitation appeared against a background of lighter rain or snow and seemed to bend toward the nearby Helsinki-Vantaa airport.

Their shapes looked intriguingly like the inverse of cloud formations known as fallstreaks, hole-punch or canal clouds, phenomena which can occur when aircraft fly through clouds of water droplets that are colder than 0 degrees Celsius (32 degrees Fahrenheit) —but aren’t freezing.

The new study demonstrates that a similar phenomenon can enhance or elicit rain or snowfall from cloud layers underlying these supercooled cloud layers.

SUPERCOOL

Air pressure changes from passing aircraft can trigger these supercooled water droplets to freeze into ice crystals. Air expands abruptly in the wake of wing and propeller tips, causing a dramatic local drop in pressure and temperature. Inside a cloud of water droplets that is already supercooled between -15 to -20 degrees Celsius (5 to -4 degrees Fahrenheit), the passing aircraft can drop the temperature below -40 degrees Celsius (-40 degrees Fahrenheit) and instigate the formation of ice crystals.Both tiny water droplets and ice crystals form clouds. Pure water can stay liquid down to -40 degrees Celsius (-40 degrees Fahrenheit) without dust particles or other suitable surfaces present to seed crystallization into ice. So water droplets that condense into clouds can be much colder than the typical freezing point of 0 degrees Celsius (32 degrees Fahrenheit). Such supercooled liquid clouds are common in low- to mid-level cloud layers.

The new ice crystals help freeze more supercool water droplets, setting off a chain reaction of crystal formation in a widening circle around the path of the aircraft. When the crystals fall, they create holes or streaks of clear air in the cloud, sometimes opening a window of blue sky if the cloud layer is thin. In most cases, the ice crystals evaporate before they reach the ground.

Meteorologists have known that passing aircraft can freeze water droplets into ice crystals and previous work had suggested that the process could enhance rain and snow in underlying clouds, but the effect had not been captured in detail.

Andrew Heymsfield, a senior scientist at the National Center for Atmospheric Research’s Mesoscale and Microscale Meteorology Laboratory in Boulder, Colorado, and a researcher unaffiliated with the new study, had noted the potential for inadvertent seeding of supercooled clouds over airports in a previous paper about the formation and spread of aircraft-induced holes in clouds. He observed similar arcs of heightened snowfall in radar data collected near Denver, Colorado’s former Stapleton Airport in 1992.

“We know that planes can trigger precipitation. The authors of this study have a lot of cases, with wonderful data from ground-based instruments—radar, lidar—good information about particle size and concentration, and radiosonde data to show the likely temperature for formation,” Heymsfield said. “They succeeded in documenting the phenomenon.”

To find out if the streamers of heightened precipitation could be caused by aircraft, Moisseev and his colleagues reviewed 11 years of the University of Helsinki’s weather radar data and found 17 days with repeat cases of the characteristic linear streamers between December 2008 and January 2018.

They examined flightpaths near the airport to see whether the streamers could be caused by passing aircraft. Flightpaths archived to 2011 confirmed aircraft passed within 2-10 kilometers (1-6 miles) of the intense precipitation streamers in most of the cases observed.

“The intensified precipitation basically follows the track of an airplane above the cloud,” Moisseev said. “It could extend over hundreds of kilometers, but the cross-section would be maybe 100 meters. So it’s a very narrow, long feature.”

SEEDING SNOW

The additional ice crystals raise the rate at which crystals collide to form larger snowflakes, intensifying snowfall, according to the authors.

This could happen if an airplane flies directly through a precipitating cloud, but the authors suspect something more complicated is going on, because their data locates the starting height of rain and snow enhancement far above the layer that is already precipitating.

The new study concludes the airplane-generated ice crystals most likely fall from a supercooled upper cloud layer into a lower layer that is actively raining or snowing, begetting more rain or snow from the lower cloud layer.

Satellite data support this scenario, showing a top layer of clouds composed of supercool droplets or a mix of ice and water, poised at about the right temperature to turn to ice crystals under the influence of aircraft. This upper, supercool layer floats at the typical approach altitude of planes flying into the Helsinki-Vantaa airport.

Rain and snow artificially enhanced by air traffic has useful clues for natural precipitation and the factors affecting the efficiency of formation, according to Moisseev. The streamers are accidental experiments that allow the researchers to observe the effect along the path of the aircraft, and just outside it, and ask questions the kinds of microphysical processes taking place.

###

This paper is freely available for 30 days. You can download a PDF copy of the article by clicking on this link:

https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018JD029449

There is no [statistically significant] snow cover trend due to global warming since 1972 in the Northern Hemisphere

Reblogged from Watts Up With That:

From the “alarmists and their cats are grumpy over this” department.

There’s been some recent hubbub over decreasing snowfall in the northern hemisphere by the usual suspects, who claim that AGW is reducing snow cover.

And then of course, there’s Dr. David Viner of CRU, who famously said in a story in the UK Independent titled: Snowfalls are now just a thing of the past:

However, the warming is so far manifesting itself more in winters which are less cold than in much hotter summers. According to Dr David Viner, a senior research scientist at the climatic research unit (CRU) of the University of East Anglia,within a few years winter snowfall will become “a very rare and exciting event”.

“Children just aren’t going to know what snow is,” he said.

It got disappeared from the Internet, but I saved a copy here: One of the longest running climate prediction blunders has disappeared from the Internet

That’s opinion, then there’s data, such as this data from the highly respected Rutgers Snow Lab, as plotted by climate scientists Ole Humlum.

No trend, period.

 

Don’t believe it? Plot it yourself: use this link to download the original data.

More here: http://www.climate4you.com/SnowCover.htm


Added: Willis Eschenbach writes in comments

Hmmm … I took you up on your invitation to plot it myself. Actually, there is a trend … in fact, there are two trends.

Here’s the first trend, starting in 1972 …

As you can see, there’s a slight negative trend overall, about a tenth of a million square km. per decade. However, an examination of the blue Gaussian average in the bottom panel shows a faster drop to 1990, then a slow rise to the present. So I took a closer look at the post 1990 data.

As you can see, since 1990 the snow area has been increasing at about a quarter million square km per decade.

Go figure …

w.


Steve Mosher writes in comments: (and I reply)

Jeez

You cant say there is NO trend or zero trend. FFS

Here

library(dplyr)
library(ggplot2)

nhURL <-“https://climate.rutgers.edu/snowcover/files/moncov.nhland.txt&quot;

N <- tbl_df(read.table(nhURL, header=F))
N % rename(Year=V1, Month=V2, Extent=V3) %>%
mutate(Extent=Extent/1000000)%>% dplyr::filter(Year > 1971)

A % group_by(Year) %>% summarise(Average=mean(Extent))

ggplot( A, aes(x=Year,y=Average))+geom_line()+geom_smooth(method=”lm”) +
ggtitle(“Global Snow Extent Annual Average”)+
labs(y= “Average Snow Extent (millions sq km”) +
scale_x_continuous(breaks=seq(min(A$Year),max(A$Year),2))+

theme( axis.text.x = element_text(angle=90, vjust=0.5, size=10))

Call:
lm(formula = Average ~ Year, data = A)

Residuals:
Min 1Q Median 3Q Max
-2.02403 -0.44104 0.03122 0.30382 1.91688

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 54.005641 15.978734 3.38 0.00151 **
Year -0.014501 0.008009 -1.81 0.07690 .

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7448 on 45 degrees of freedom
Multiple R-squared: 0.0679, Adjusted R-squared: 0.04718
F-statistic: 3.278 on 1 and 45 DF, p-value: 0.0769

  • Your p-value is 0.0769 or ~0.08

    A definition of p-values says:

    – A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

    – A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

    – p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions.

    Source: https://www.dummies.com/education/math/statistics/what-a-p-value-tells-you-about-statistical-data/

    So at 0.08 no statistically significant trend. I’ve added to the title to reflect that.

[UPDATE] I thought I might add one more plot. Here are the trends of the Rutgers snow data by quarter.

As you can see, there is no significant trend in the winter data. Snow in the fall has increased, snow in the spring and summer have decreased.

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