A Discussion on Uncertainty, Precision, Resolution of Global Temperature Measurements

[Crick]

This tppic comes up frequently. How can statisticians and scientists take data from analog thermometers which can only be read to a tenth of a degree and come up with a global value to a hundredth of a degree. The net has lots of good resources explaining the issue. So, here goes.

Did You Know? | National Centers for Environmental Information (NCEI)

A suite of notes that attempt to explain or clarify complex climate phenomena, Climate Monitoring products and methodologies, and climate system insights

www.ncei.noaa.gov

 

[Crick]

The linked document in the OP refers to a second document for further discussion. It is

Global Surface Temperature Anomalies | National Centers for Environmental Information (NCEI)

The Merged Land and Ocean Surface Temperature data are presented as anomalies (departures from a long-term average) on a five-degree by five-degree global grid. The period of record is January 1880 through the most recent month.

www.ncei.noaa.gov

It covers several topics but here is a concise description of how global average temperature is actually calculated.

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How is the average global temperature anomaly time-series calculated?
The global time series is produced from the Smith and Reynolds blended land and ocean data set (Smith et al., 2008). This data set consists of monthly average temperature anomalies on a 5° x 5° grid across land and ocean surfaces. These grid boxes are then averaged to provide an average global temperature anomaly. An area-weighted scheme is used to reflect the reality that the boxes are smaller near the poles and larger near the equator. Global-average anomalies are calculated on a monthly and annual time scale. Average temperature anomalies are also available for land and ocean surfaces separately, and the Northern and Southern Hemispheres separately. The global and hemispheric anomalies are provided with respect to the period 1901-2000, the 20th century average.

 

[CrusaderFrank]

I question integrity of a group that tells us they have statistically significant temperature readings prior to 1960, maybe even 1970, especially regarding any ocean temperatures

 

[CrusaderFrank]

https://www.ncei.noaa.gov/monitoring-content/monitoring-references/docs/smith-et-al-2008.pdf

"To illustrate this, annual averages of the LF and LF HF analysis anomalies are shown for a location in the tropical Pacific Ocean at 0°, 150°W (Fig. 1)"

This is literally the middle of NOWHERE!! Please show us the readings that form this dataset

 

[gfm7175]

It covers several topics but here is a concise description of how global average temperature is actually calculated.

It is calculated in a manner that violates the rules of statistical mathematics and is therefore invalid data.

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How is the average global temperature anomaly time-series calculated?
The global time series is produced from the Smith and Reynolds blended land and ocean data set (Smith et al., 2008).

Land and ocean data does not include any atmospheric data. Earth does include the atmosphere, you know... This data is already invalid because location bias has not been removed at the outset.

This data set consists of monthly average temperature anomalies

Monthly average temperature anomalies are calculated values, not measured values. What would be relevant would be any and all measured values, and those measured values would need to have location and time biases removed at the outset (cooking the data after the measurements are taken is not allowed).

on a 5° x 5° grid across land and ocean surfaces.

Such a grid across land and ocean is omitting the existence of the Earth's atmosphere, which is also a part of Earth and cannot be ignored with regard to measuring Earth's temperature. Omitting Earth's atmosphere means that there is location bias present in the data, and it is therefore invalid.

These grid boxes are then averaged to provide an average global temperature anomaly.

Averages and anomalies are calculated values, not measured values. Where are the measurements coming from? If only from land and sea thermometers in random locations, then there is still location bias present which renders any claim to "Earth's temperature" invalid.

An area-weighted scheme is used to reflect the reality that the boxes are smaller near the poles and larger near the equator.

Sounds like somethin' is cookin'......

Global-average anomalies are calculated on a monthly and annual time scale.

A BS number, since the measured data that it is calculated from is also BS due to location and time biases, for starters.

Average temperature anomalies are also available for land and ocean surfaces separately, and the Northern and Southern Hemispheres separately.

Still leaving out the atmosphere, I see...

The global and hemispheric anomalies are provided with respect to the period 1901-2000, the 20th century average.

Why is that specific time period "holier" than any other time period? Use a different base period and you'll get different results.

TLDR: Humans don't know as much as they think they know.

 

[Crick]

It is calculated in a manner that violates the rules of statistical mathematics and is therefore invalid data.

No, it is not.

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Standard error of the mean

The standard deviation measures the precision of a single typical measurement.
It is common experience that the mean of a number of measurements gives a more precise estimation than a single measurement. This experience is quantified by the standard error of the mean.

If each measurement has a standard deviation s and the measurements are all independent, then the mean of the N measurements has a standard deviation s/√N. This quantity is called the standard error of the mean. For a proof of this formula see the tutorial on expectations and estimators .

Thus, for the mean to be ten times more precise than a single measurement, 100 independent measurements need to be taken.

Estimating precision

web.chem.ox.ac.uk

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Land and ocean data does not include any atmospheric data. Earth does include the atmosphere, you know... This data is already invalid because location bias has not been removed at the outset.

All land data are the temperatures of the atmosphere immediately above the Earth's surface. Ocean data is SST data.

Monthly average temperature anomalies are calculated values, not measured values.

No bias is introduced by the process.

What would be relevant would be any and all measured values, and those measured values would need to have location and time biases removed at the outset (cooking the data after the measurements are taken is not allowed).

Measured values are the recorded data and known biases ARE removed at the outset. You cannot remove all biases as measurements are taken simply because they are not all known.

Such a grid across land and ocean is omitting the existence of the Earth's atmosphere, which is also a part of Earth and cannot be ignored with regard to measuring Earth's temperature.

This is incorrect. As noted above, all land surface readings ARE atmospheric readings. The US CRN does not have thermometers stuck into the ground.

Omitting Earth's atmosphere means that there is location bias present in the data, and it is therefore invalid.

This comment is invalid. And since different locations on the Earth have different temperatures and those different temperatures are what scientistst are looking to measure, there is no such thing as "location bias" unless the geographical location of a measurement was in error, which is exceeedingly unlikely to be common, produce a bias or be a systemic error.

Averages and anomalies are calculated values, not measured values. Where are the measurements coming from? If only from land and sea thermometers in random locations, then there is still location bias present which renders any claim to "Earth's temperature" invalid.

Read the linked article. You have several erroneous ideas about how global temperatures are calculated. And you cannot refine tens of thousands of readings from the planet's surface into a single value representing the planet as a whole without performing a little math.

Sounds like somethin' is cookin'......

Turn up the fan and lower the thermostat.

A BS number, since the measured data that it is calculated from is also BS due to location and time biases, for starters.

Time bias was a known factors centuries ago and I haven't the faintest idea what you mean by "location bias". I suspect you don't either.

Still leaving out the atmosphere, I see...

Still speaking from ignorance.

Why is that specific time period "holier" than any other time period? Use a different base period and you'll get different results.

You would move the entire graph up or down but would make no other changes whatsoever. I'm sorry, but you are accomplishing nothing here but embarrassing yourself.

TLDR: Humans don't know as much as they think they know.

Some of us... yeah.

Just looked up TLDR. So... uh... yeah.

 

[Crick]

HOW GLOBAL AVERAGES CAN HAVE GREATER PRECISION THAN THE INDIVIDUAL TEMPERATURE READINGS

This is included in the post immediately above but it has come up on numerous occasions in these debates.

"Standard error of the mean

The standard deviation measures the precision of a single typical measurement.
It is common experience that the mean of a number of measurements gives a more precise estimation than a single measurement. This experience is quantified by the standard error of the mean.

If each measurement has a standard deviation s and the measurements are all independent, then the mean of the N measurements has a standard deviation s/√N. This quantity is called the standard error of the mean. For a proof of this formula see the tutorial on expectations and estimators .

Thus, for the mean to be ten times more precise than a single measurement, 100 independent measurements need to be taken."

Estimating precision

web.chem.ox.ac.uk

 

[gfm7175]

No, it is not.

Yes it is.

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---

Standard error of the mean

The standard deviation measures the precision of a single typical measurement.
It is common experience that the mean of a number of measurements gives a more precise estimation than a single measurement. This experience is quantified by the standard error of the mean.

If each measurement has a standard deviation s and the measurements are all independent, then the mean of the N measurements has a standard deviation s/√N. This quantity is called the standard error of the mean. For a proof of this formula see the tutorial on expectations and estimators .

Thus, for the mean to be ten times more precise than a single measurement, 100 independent measurements need to be taken.

Estimating precision

web.chem.ox.ac.uk

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Oh yes! Let's dive into temperature variance, shall we? This highlights yet ANOTHER issue with the temperature data that we have and people who are trying to apply it to the whole Earth.

Temperature can have a variance as high as 20degF/mile. If you really want to know the temperature of the Earth to any sort of usable accuracy, you would need over a billion UNIFORMALLY SPACED thermometers across all of the land, water, and atmosphere of the Earth. Anything less than that would lead to pure guesswork because temperature variance is so high (as much as 20degF/mile).

All land data are the temperatures of the atmosphere immediately above the Earth's surface. Ocean data is SST data.

... which excludes the temperatures of all of the atmosphere above what is immediately above the Earth's surface, and above that, and above that, and above that... ... ... This is called LOCATION BIAS. They also aren't uniformly spread across the Earth. That's also location bias.

No bias is introduced by the process.

... except for all the biases that I've been mentioning.

Measured values are the recorded data

This you have correct.

and known biases ARE removed at the outset.

No they aren't. If thermometers aren't uniformly spaced across the whole Earth, then there is location bias. This bias is known and is an issue.

You cannot remove all biases as measurements are taken simply because they are not all known.

Of course one cannot remove what one doesn't know about. I'm talking about known biases. As I've been bringing them up, they are most definitely known (at least by me).

This is incorrect. As noted above, all land surface readings ARE atmospheric readings. The US CRN does not have thermometers stuck into the ground.

Sorry. I'd didn't realize you'd be a prick about it, so I should rephrase. The existence of ALMOST ALL of Earth's atmosphere is being ignored (except for a little bit just above the surface where the thermometers are).

Because you couldn't resist being a prick, you've just brought up yet ANOTHER problem. There are no thermometers stuck into the ground. The ground is also a part of Earth, and thus should also be included in measurements of Earth's temperature. This includes going underground, all the way to Earth's core. Leaving those areas out is location bias with regard to claiming to know "Earth's temperature".

This comment is invalid.

Childish.

And since different locations on the Earth have different temperatures and those different temperatures are what scientistst are looking to measure, there is no such thing as "location bias"

That is exactly WHY there is location bias dude... holy crap... Different locations have different temperatures, and those locations can easily vary by as much as 20degF/mile. If you don't have thermometers uniformly spaced all within a mile of each other, then your calculated results for "Earth's temperature" could be (and are) WAYYYYYYYYYYYY off due to the existence of this very high variance. Remember, the Earth has almost 200 million sq miles of surface area, and that's just the surface area, let alone all of the atmospheric area and all of the underground area.

TLDR: You (and "the experts") are taking too few pinpoint locations of Earth and are attempting to calculate the temperature of the entirety of Earth from them.

unless the geographical location of a measurement was in error, which is exceeedingly unlikely to be common, produce a bias or be a systemic error.

I'm assuming that the geographical location is correct. The issue is that many geographical locations are being left out, and having a thermometer just a mile over from another potential location means that the snapshot temperature data, at any given time, could vary from the potential location by as much as 20degF.

Read the linked article. You have several erroneous ideas about how global temperatures are calculated.

Your issue, not mine.

And you cannot refine tens of thousands of readings from the planet's surface into a single value representing the planet as a whole without performing a little math.

Of course not, but the point is that tens of thousands of readings (which have location bias because they aren't uniformly spaced -- and also have time bias if they aren't simultaneously read by the same observer) aren't nearly enough readings given how high temperature variance is. You would need over a billion uniformly spaced and simultaneously read thermometers to know Earth's temperature to any usable accuracy.

Time bias was a known factors centuries ago and I haven't the faintest idea what you mean by "location bias". I suspect you don't either.

Now you're in paradox. First you claim that it isn't an issue. Now you claim to not even know what it is. I've already identified it and explained it to you.

Still speaking from ignorance.

Your issue, not mine. All of the atmosphere above the surface level area is being completely ignored. That's location bias, as not all locations are being taken into consideration.

You would move the entire graph up or down but would make no other changes whatsoever.

Wrong.

I'm sorry, but you are accomplishing nothing here but embarrassing yourself.

Your issue, not mine.

Some of us... yeah.

Just looked up TLDR. So... uh... yeah.

Your issue, not mine.

 

[Crick]

There is no requirement for uniformly spaced weather stations.

The several thousand stations used by each of the four major datasets (HadCRUT4, GISTEMP, MLOST and JMA) are more than adequate. A billion would be nice, but it would cost a lot of money and is not needed.

There is no such thing as location bias in the temperature datasets.

We record temperatures at human scale heights because it is where almost all of our historical temperatures were recorded and because it is where we live. Temperatures from higher altitudes gets collected by radiosonde-equipped weather balloons and by satellites.

I'm sorry, but you really don't know what you're talking about.

 

[ding]

This tppic comes up frequently. How can statisticians and scientists take data from analog thermometers which can only be read to a tenth of a degree and come up with a global value to a hundredth of a degree. The net has lots of good resources explaining the issue. So, here goes.

Did You Know? | National Centers for Environmental Information (NCEI)

A suite of notes that attempt to explain or clarify complex climate phenomena, Climate Monitoring products and methodologies, and climate system insights

www.ncei.noaa.gov

When their reconstruction reaches the opposite conclusion of the data from the region most affected by changes in temperature they don’t pass the smell test so to speak.

 

[Crick]

When their reconstruction reaches the opposite conclusion of the data from the region most affected by changes in temperature they don’t pass the smell test so to speak.

Would you care to explain what you're trying to say here?

 

[ding]

Would you care to explain what you're trying to say here?

converting solar radiation into electricity is solar radiation that does not warm the surface of the planet.

 

[Crick]

converting solar radiation into electricity is solar radiation that does not warm the surface of the planet.

That is not what you were trying to say.

 

[ding]

That is not what you were trying to say.

Actually it was. You don’t understand the disagreement between Todd and I.

 

[Crick]

Actually it was. You don’t understand the disagreement between Todd and I.

Carry on MacDuff.

 

[ding]

Carry on MacDuff.

 

[Crick]

There is the point that you weren't having a conversation in this thread and the topic of your prior conversation has nothing to do with this one's topic.

 

[ding]

There is the point that you weren't having a conversation in this thread and the topic of your prior conversation has nothing to do with this one's topic.

See it however you want to see it. I couldn’t careless.

 

[Crick]

See it however you want to see it. I couldn’t careless.

Still hurting?

 

[ding]

Still hurting?

Not at all. Feeling pretty good today.