A Thread for FCT's Explanations

[Abraham3]

FCT is going to explain to us how a ten minute average of wind-speed is more "accurate" than a one minute average of wind-speed. I thought it would be handy to have a thread just for this purpose here under Environment where it applies and won't interfere with the prayer meetings and what-not taking place in the Philippine thread now under Current Events.

So... standing by...

 

[flacaltenn]

Nope... Told you I want to do this in the BullRing.. Don't need to have trolls and partisians mucking up our little learning session...

And what do you propose to make it worth my while to do an exceptional job of making you look sillier for continuing to demand a confrontation?

 

[flacaltenn]

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
A request to OTHER USMB POSTERS ----

This poster has called me out PERSONALLY BY NAME in a thread. After recieving much stalking and badgering -- I've decided to address his complete misunderstanding of statistics, and sample mean estimation. MAYBE we'll get as far as how this applies to estimating the average wind speed of a hurricane.

I would APPRECIATE that we are left to discuss ONE ON ONE in this thread.. PLEASE respect that request.. Feel free to make a parallel thread if you simply cant resist.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

I am also participating in this thread under protest for the slight that Abraham offered up in the OP to people attempting to show compassion to the folks in the Phillipines following their disaster. It is no secret that Abraham is under the impression that anyone that dares to offer up a prayer in public or self-identifies as religious or conservative is of INFERIOR intelligience. AND he has lied about not making statements to that effect when indeed he has done so. NORMALLY -- I'd refuse a challenge that started out with slights to any group of people --- but we're gonna do this here and now.

 

[flacaltenn]

Abraham:

You chose to make the Current Events thread on the Phillipines cyclone disaster into a technical debate about AnthroGlobalWarming and wind speeds.. In that thread with reference to different methods of calculating AVERAGE wind speeds, you made this stupendously stupid comment...

http://www.usmessageboard.com/current-events/323191-philippine-catastrophe-10.html#post8123830

You don't even know the meaning of the word. The length of time over which the wind speed is averaged HAS NO BEARING WHATSOEVER on how accurate the measurement might be. It is simply a different measurement. We could average it over a day or a week or a month or a year.

And then you stalked and badgered me into this "tutorial" and explanation. The wrongness of that assertion in terms of math and statistics is so obvious -- that I was truly embarassed for you and wanted to avoid conflict. Here's what you have been DEMANDING OF ME...


You CLAIM to ace statistic courses. YET -- your statement above blatantly contradicts what every H.S. student learns about the accuracy of estimating mean values with respect to time series length or sample size. This is literally Chapter One of every Intro to Statistics course on this planet for centuries.

Before ANY discussion of how this applies to average wind speed calculations, we must first determine how you managed to mangle such a fundamentally basic math concept.. This is an example chosen quite at random that discusses sample size or time vector length effects on mean estimation accuracy.

Determining Sample Size for Estimating the Mean

Determining Sample Size for Estimating the Mean

Suppose we want to estimate the average GPA (u) of WMU undergraduates this school year. Historically, the SD of student GPA is known to be Sdev = .30. If a random sample of size n=25 yields a sample mean of Xavg = 3.05, then the population mean (u) is estimated as lying within the interval Xavg +/- 2(SDev/(sqrt n)) = 3.05 +/- 2(.30/sqrt(25)) with 95% confidence. The plus-or-minus quantity .12 is called the margin of error of the sample mean associated with a 95% confidence level. It is also correct to say ``we are 95% confident that is within .12 of the sample mean 3.05''. However, .12 is a large number. The value 3.05 +/- .12 can be as low as 2.93 or as high as 3.17. Is there some way to reduce the margin of error? Yes, and quite easily. Look at the formula for the margin of error: 2(SDev/sqrt(n)) . Observe that if sample size increases, the margin of error decreases.

Clearly, the 2*(SDev/sqrt(n)) error term goes DOWN as N (the number of samples or length of time) goes up.. In fact, I have several published papers that use a variation of this expression showing that the signal to noise ratio of any time series can be improved by lengthing the period of the averaging or filtering operation. You can double the Sig/Noise ratio by using 4 times the time series length (2 = (sqrt 4)) for example.

This is also key to the Central Limit Theorem and other corollary statements on Means. There are a few restrictions on this key theorem, the most important being the concept of a stationary mean value over the period of averaging. There are arguments to make that this INDEED DOES apply to the wind speed during cyclonic activity measurement.

Unless you have an excuse for this lapse of rigor -- you've already lost. HOWEVER, once we determine WHY you felt it so safe to ignore basic math we can explore that specific application..

Just for grins -- THIS is what you'll find..

http://www.wmo.int/pages/prog/www/tcp/Meetings/HC31/documents/Doc.3.part2.pdf

Although any period of time can be chosen for averaging the wind speed, shorter periods of averaging will typically produce more erratic values than the 10-min average. For example, ten 1-min averages taken during a 10-min period will produce values that lie both above and below the 10-min mean value. Any single 1-min random sample is an equally valid (unbiased) estimate of the mean wind but it is likely to be higher or lower than the true mean wind. Hence, while one estimate of the mean wind is (statistically) as good as another, in practice, mean winds measured over shorter periods will possess greater variance and will therefore be less reliable. Alternatively, if there was no turbulence in the wind, then all averaging periods would yield the same true mean wind speed.

World Meterological Org has the math correct. The argument over 10 or 1 minute averages thus doesn't hinge on which is a more ACCURATE estimation of the mean value -- but on other esoteric concerns that we can discuss AFTER you understand that the statement you made is COMPLETELY UNSUPPORTABLE IN terms of elementary math theory.

 

[Abraham3]

The length of time over which wind speed is averaged has no bearing on the accuracy of the result.

My reasoning is pretty simple.

When you change the length of time over which an average is taken, you change the identity, the nature, the character of the result. A one minute average and a ten minute average are apples and oranges. If you were to say "this one is more accurate", the obvious question you must satisfy is "It is more accurate at doing what?". The one minute average is not more accurate at approximating the actual ten minute average value and a ten minute average is not more accurate at approximating the actual one minute average value. Averages taken over differing time spans are measurements of different things. Neither is more or less accurate because, in fact, the attempted comparison is meaningless.

In his attempt to refute my contention, my opponent has altered the terms of the debate topic. He has freely replaced time with sample number. That replacement is NOT implicit in the statement of the debate topic that HE chose. That error invalidates his argument.

He has also implied that accuracy in this regard is somehow a measure of how well a specific averaged value characterizes some larger, abritrary entity; the storm, for instance. This also was neither implicit or explicit in the debate topic.

The debate topic statement can only be taken to indicate that my opponent believes that an average of windspeed measurements collected over ten minutes more accurately characterizes the actual ten minute average windspeed than an average of windspeeds collected over one minute characterizes the actual one minute average windspeed. He has presented NOTHING to support that statement. He has, instead, rather dramatically attempted to alter the terms and understandings of this 'debate' and padded his post with a great deal of ad hominem attacks and irrelevant observations.

 

[flacaltenn]

The length of time over which wind speed is averaged has no bearing on the accuracy of the result.

My reasoning is pretty simple.

When you change the length of time over which an average is taken, you change the identity, the nature, the character of the result. A one minute average and a ten minute average are apples and oranges. If you were to say "this one is more accurate", the obvious question you must satisfy is "It is more accurate at doing what?".

The exercise is to estimate the MEAN of the process.. It is NOT arbitrary. You have tossed both the basic math concept that states "a longer observation period is a more accurate estimation of the mean". And you tossed the VERIFICATION of that principle as it specifically to average wind measurements as stated by the WMO.. So I suppose you expect me to dive into the Rabbit Hole with you and ponder the UTILITY of a 1 minute average if it's not more accurate. Not required here.

The one minute average is not more accurate at approximating the actual ten minute average value and a ten minute average is not more accurate at approximating the actual one minute average value. Averages taken over differing time spans are measurements of different things. Neither is more or less accurate because, in fact, the attempted comparison is meaningless.

No they are not "different things" they are different integration periods of observation of the mean. Taking a shorter time span will ALWAYS be less accurate. No moral relativism, no imagined utility for an inferior estimation.

In his attempt to refute my contention, my opponent has altered the terms of the debate topic. He has freely replaced time with sample number. That replacement is NOT implicit in the statement of the debate topic that HE chose. That error invalidates his argument.

Bullshit. You're lack of statistics knowledge is paralled with your lack of sampled data theory. As long as I assure that my sampling rate obeys Nyquist criterion --- MORE TIME SAMPLES IS LONGER TIME INTERVAL. The process that is being queried for the mean estimation doesnt even HAVE to be in the time domain. Applies to the Avg Sales of homes in Newark, the Avg Value of single dice throw, etc. All the same with regards to the confidence of the mean estimation.

He has also implied that accuracy in this regard is somehow a measure of how well a specific averaged value characterizes some larger, abritrary entity; the storm, for instance. This also was neither implicit or explicit in the debate topic.

No idea WTF this means.. Avg Wind speed is ONE measurement of storm intensity. Maximum gusts are another. I can produce charts and data backing the WMO 10 minute average with the distribution of the gust durations. There is significant energy in the frequency plot of gust durations between 1 minute and 10 minute.. Take a shorter period of observation then 10 minutes and you are no longer AVG wind speeds. You are rolling the dice that any shorter period will be biased by gust energy.

The debate topic statement can only be taken to indicate that my opponent believes that an average of windspeed measurements collected over ten minutes more accurately characterizes the actual ten minute average windspeed than an average of windspeeds collected over one minute characterizes the actual one minute average windspeed. He has presented NOTHING to support that statement. He has, instead, rather dramatically attempted to alter the terms and understandings of this 'debate' and padded his post with a great deal of ad hominem attacks and irrelevant observations.

That's right. I presented NOTHING EXCEPT a statement from the World Meteorological Org to that very effect you jackass. PLUS the elementary principle of mathematics that also states the GENERAL CASE of better mean estimation.. In YOUR opinion, that might be nothing.. Least you think that the WMO is a rare bird --- how about asking the Aussies who in the world is the odd ball?

Tropical Cyclone Intensity and Impacts

Mean Winds and Gusts
Mean Wind: In most of the world the mean wind speed is defined as the wind speed averaged over a period of 10 minutes. It should be measured at 10 m above the surface. The major exception is the USA where they use a 1-minute average.

Do not ask me to justify our domestic decision to use an inferior standard. It's NOT in the scope of debunking your silly assertion..

MORE from the WMO ---- Op Cit..

The mean wind estimate is therefore always of critical importance and should be based on the longest practical interval that can be regarded as stationary. In practice, the 10-min average generally satisfies this requirement. Once the mean wind is reliably measured or estimated, the effects of turbulence in typically producing higher but shorter-acting winds of greater significance for causing damage can be estimated using a gust factor.

Critically important. Because MOST of the work in this field is written in terms of "gust factors". These are EASILY applied to the more accurate 10 min mean, but only with great difficulty can they be applied to the US 1 minute mean standard. In order to expand a MEAN wind speed to a MAX GUST estimate using "gust factors" --- you cannot afford to have a Mean estimate that CONTAINS any portion of a valid gust. And 1 minute is too damn short.


So -- you understand the problem we're attempting to solve? Estimating the MEAN wind speed of a storm? Not trying to invent utility for inferior estimations of that key parameter?

No more accusations that I'm changing stuff. ASK ME WHY for instance, number of samples is the same as the length of a time series --- BEFORE you berate me --- Kay?

 

[flacaltenn]

Feel free to leap in with any quote that backs your statement that

The length of time over which the wind speed is averaged HAS NO BEARING WHATSOEVER on how accurate the measurement might be

SURELY you can supply just one link...

 

[Abraham3]

Just a few points. Getting late and I have another long day tomorrow.

1) If you wanted to debate the contention that an increase in samples increases accuracy, why didn't you say so? The point we're debating - that the contention concerns TIME - is the one YOU chose.

2) When you say a longer average is a more accurate representation, I have to ask (as I said I would) of WHAT you believe it to be a more accurate representation? And then you can point out where that appears in the debate topic you chose.

 

[flacaltenn]

Just a few points. Getting late and I have another long day tomorrow.

1) If you wanted to debate the contention that an increase in samples increases accuracy, why didn't you say so? The point we're debating - that the contention concerns TIME - is the one YOU chose.

2) When you say a longer average is a more accurate representation, I have to ask (as I said I would) of WHAT you believe it to be a more accurate representation? And then you can point out where that appears in the debate topic you chose.

1) ive already explained to you that for adequately sampled time series, there is no distinction between time extents and number of samples. The instrument world has gone digital. Continuous time measurements died with strip chart recoder. Thus a 1 second time series sampled every 10mseconds has a hundred samples. No deceit, no magic.. im just amazed that this bugs you.

2) Already told you that also. The task is to estimate averages. The intro to statistics chapter one knowledge I imparted to you says that larger and longer observations of averages are more accurate. No ifs ands buts. Thats why youve already lost. Your silly statement was that the length of the average had ABSOLUTELY NO EFFECT ON THE ACCURACY OF THE AVERAGE. Which is of course in conflict with high school statistics knowledge.

So how can you POSSIBLY DEFEND that statement? You cant.

The only way that longer isnt better is if the process that is being analyzed has a mean value that is not largely stationary over the chosen time period or there are no noise or interference components with fundamental freqs longer than a given observation window,

 

[flacaltenn]

Tell me.. Was that quoted statistics knowledge NEW to you? Now that youve been refreshed about the statistics you claimed to have taken ---- how could you ever make the statement thats under debate? What part of the math you know VALIDATES THAT IDIOTIC STATEMENT?


And why no comment about the statement from the WMO validating that h.s. math DOES apply to calculating avg wind speeds?

 

[Abraham3]

Then, per your rationale, an average of windspeed readings taken over a 96 hour period would be an even better estimate.

No? Why?

If I take a few one minute averages and an equal number of ten minute averages, what can I say about their respective standard deviations?

 

[Abraham3]

An explanation of standard deviation.

Let's say I have two sets of perfectly random numbers. The first set varies between 8 and 12. The second set varies between 0 and 20. The average, or mean, of both of these sets will be found to be 10. But if we look at the individual differences between each of these values (8-12 and 0-20) and their mean values (10 and 10), we see that the second set's values tend to be further away from their mean. The data in the second set are more scattered, less coherent.

Now let's think about windspeed. If we measure the wind for one minute, we will get a range of values. If we measure the wind for ten minutes, we will get a larger range of values. The standard deviation shows us that the data in the second set - the ten minute set - are more scattered, less coherent. The instantaneous windspeed at any point in that ten minutes is likely to be further from the mean than are the windspeeds during the one minute period.

So... which set is better characterized by its mean value? The set with the smaller deviation or the set with the larger deviation?

Take this to the extreme. Which is a more accurate representation of a set of measurements: an average of windspeed over one year or a single instantaneous measurement? The deviation of a year long average will be (relatively) enormous. The range of wind values will go from zero to whatever the maximum windspeed achieved that year. The single instantaneous measurement will have NO deviation. It will be, within the precision of the instrument used, a perfect representation of the parameter it measured.

Now, I have not abandoned my position that averages across different time spans are different entities and are apples and oranges. But my opponent's contention that a longer measurement period leads to a more accurate characterization is patently false. It might work with a static, unchanging value for which one is attempting to gain a precise measure. But the wind is not static. The more time you spend measuring it, the more it will vary and the further, on average, your mean will come to fall from your instantaneous measurements.

 

[flacaltenn]

Then, per your rationale, an average of windspeed readings taken over a 96 hour period would be an even better estimate.

No? Why?

If I take a few one minute averages and an equal number of ten minute averages, what can I say about their respective standard deviations?

You're not listening or you're not following are you?

Do you know what STATIONARY MEAN refers to? IF the object is find an accurate mean, you need to assure that the MEAN VALUE is not varying over the chosen period.. Do the math (if you can).. A storm moving at 18mph, observed for 10 minutes travels HOW FAR? it's about the size of one embedded thunderstorm aint it?

In many cases, the req for a stationary mean disappears if you simply agree that the mean reading will INCLUDE any traveling of the true avg value.. For AVG sale prices of homes in Phoenix --- you are ignoring whether the market is going UP or DOWN to make that measurement over a month or a year.

Same with a hurricane. Your goal might be to average the wind field within 20 miles of eye. If that's the measurement -- it should be STATED that it is averaged over a particular distance.

You have so many misconceptions that are beyond the scope of this free tutoring..
AND ---- you're NOT LEARNING or answering questions. Since you've already caused me to repeat stuff..

 

[flacaltenn]

An explanation of standard deviation.

Let's say I have two sets of perfectly random numbers. The first set varies between 8 and 12. The second set varies between 0 and 20. The average, or mean, of both of these sets will be found to be 10. But if we look at the individual differences between each of these values (8-12 and 0-20) and their mean values (10 and 10), we see that the second set's values tend to be further away from their mean. The data in the second set are more scattered, less coherent.

Now let's think about windspeed. If we measure the wind for one minute, we will get a range of values. If we measure the wind for ten minutes, we will get a larger range of values. The standard deviation shows us that the data in the second set - the ten minute set - are more scattered, less coherent. The instantaneous windspeed at any point in that ten minutes is likely to be further from the mean than are the windspeeds during the one minute period.

So... which set is better characterized by its mean value? The set with the smaller deviation or the set with the larger deviation?

Take this to the extreme. Which is a more accurate representation of a set of measurements: an average of windspeed over one year or a single instantaneous measurement? The deviation of a year long average will be (relatively) enormous. The range of wind values will go from zero to whatever the maximum windspeed achieved that year. The single instantaneous measurement will have NO deviation. It will be, within the precision of the instrument used, a perfect representation of the parameter it measured.

Now, I have not abandoned my position that averages across different time spans are different entities and are apples and oranges. But my opponent's contention that a longer measurement period leads to a more accurate characterization is patently false. It might work with a static, unchanging value for which one is attempting to gain a precise measure. But the wind is not static. The more time you spend measuring it, the more it will vary and the further, on average, your mean will come to fall from your instantaneous measurements.

You trying to reinvent basic statistics here? This is unacceptable. You made 5 errors in the post above.. I will not even address them. Because you refer to me as "your opponent". This is not a ******* game. And we are NOT inventing ALTERNATE TEXTBOOKS on math techniques..

What really REALLY PISSES ME OFF is the statement ---

But my opponent's contention that a longer measurement period leads to a more accurate characterization is patently false.

I am not gonna wait while you skip High School math and invent your own.. So I want a link or a couple quotes to back that up.. Your ability to even FOLLOW this discussion is in doubt. So no more TUTORING..

What needs to be done is for you to PRODUCE a reference that NEGATES the 1st quote I supplied in this thread. The quote needs to apply to the estimation of mean for any process and SHOW that irrespective of the length of observation -- ALL estimates of mean are equally precise.

You've called me and every Intro to Statistics prof liars.... I think you owe us all some proof...

 

[flacaltenn]

Just when I thought you couldn't make a more STUPENDOUSLY STUPID statement than the one that got us here... You produce it....

The single instantaneous measurement will have NO deviation. It will be, within the precision of the instrument used, a perfect representation of the parameter it measured.

Got to hand it to --- that's a belly buster. About 9.9 on the 10 pt. mathematically dysfunctional scale. Outdoes your original gaff by MILES...

You need to stop winging it on your own and use MATH AND SCIENCE. NOT BELIEFS, and NOT FEELINGS... I'm not taking on the MOUNTAIN of math ignorance that you have..

Either REFUTE the textbook quote I provided -- or WE (the world of math and science) WINS !!!!!!

 

[Abraham3]

I don't need references because I've proven you incorrect with my own resources. The longer the measurement span, the larger the variance and the standard deviation and the LESS accurate of a representation is the average. Your contention that more data makes for increased accuracy only works if you're attempting to measure a static value. You've admitted so yourself.

You ought to learn to control your temper. And I appreciate the offer, but I really have no need of any of your 'tutoring'.

 

[flacaltenn]

I don't need references because I've proven you incorrect with my own resources. The longer the measurement span, the larger the variance and the standard deviation and the LESS accurate of a representation is the average. Your contention that more data makes for increased accuracy only works if you're attempting to measure a static value. You've admitted so yourself.

You ought to learn to control your temper. And I appreciate the offer, but I really have no need of any of your 'tutoring'.

You screwed up the concept of "stationary mean" and distorted it into me saying "static value".. which I did not. No points. Penalty for the foul. You still on the THIRD TRY aren't getting that point or most of the OTHER POINTS, but you sure are confident that you are "winning". But you're not..

What references are those? You are incorrect. The POPULATION Variance is an non-varying number. By looking at only SOME of the data -- which is all scientists ever generally do --- you will get BETTER estimates of this truth value the longer you look.

Same deal in estimating the true or PROCESS variance as in estimating the true or PROCESS mean. Longer is better. That's what the math says..

And here's why....

What you're missing is that the values are distributed in accordance with some distribution function --- like a Normal or Rayleigh distribution. For a Normal distribution, 95% of the time, the samples will fall within +/- 2 sigma of the mean. Since the variance or SDEV is the AVERAGE DISTANCE from the mean --- ESTIMATED variances will all cluster within that range. The AVERAGE DISTANCE from the mean does not change drastically for LARGE Number samples because the effect of say 1 erratically large value which is a 1% probability event DOES NOT INFLUENCE THE TOTAL variance hardly at all.

Instead of longer sample periods giving EVER INCREASING VARIANCE (The Abraham3 Intro to Estimation theory) -- what longer periods do is to CONVERGE the estimate of variance to the true Average DISTANCE from the mean in the distribution... Does not work like you state.
((I'd like to say that the convergence point is at the 50% percent confidence point -- but I'd have to check.. That would place it somewhere around the 0.7 or 0.8 sigma point))


Longer and Larger time estimates of the TRUE variance therefore more represent the variance for the total process.. And it's more LIKELY that any shorter observation window will produce extremely high (or low) ESTIMATES of that variance at any observation.

Let me give you an example.. In a 100 point estimation, an outlier will account for 0.01 times its distance. And that will occur maybe say 5% of the time. If you estimated variance with 2 points. That outlier will contribute 0.5 times it's distance 5% of the time.

Certainly every test of these 2 choices would yield wildly varying variances for the 2 point case and the 100 point case would be a better predictor.

Now realize that your latest theory about shorter sample tests having LOWER variances is based on the fallacy that you are ACCURATELY ESTIMATING THE ONE TRUE PROCESS variance with that shorter sample test. And that's simply not true. As i said in the beginning the PROCESS only has one true variance. That variance is defined by the shape and type of its distribution function. And the only way you ACCURATELY CONFIRM that variance with an estimation is to use a fairly LONG observation time.

You're right about my temper. Your insistence at creating your own version of math and statistics tests my patience. But since I've been chuckling all day about your bass-ackwards conclusive theory that contradicts EVERY MATH TEXTBOOK IN THE ******* world --- I've decided to join you in your dive down your Rabbit Hole of fictional math theory.. I cant bear to miss the next gem your "your references" come up with.

Lemme make it up to you and give you a "less snarky" retort to your yesterday post below.
Got to tell ya tho --- entertainment value or not --- unless you start producing references and stop channeling your math starved intuition --- you've got nothing.

 

[Abraham3]

Wind speed is not static and does not have a static mean.

Let's say you wanted to take ten minute averages but were unsure whether or not your mean was sufficiently static. How would you find out? You'd take shorter averages. And you've already admitted that it's not static on any scale - only that an observer could decide, arbitrarily, that it was sufficiently static.

Not one of this multitude of assumptions you've made was included in the point you chose to debate here. Leaves me feeling as if I've been treated unfairly.

Since your impatience led you to forego the official refereed debate you demanded, I see no stopping point save for one or both of us to say "I'm done".

Summation: Wind speed constantly varies. Increasing the length of time over which a sample is collected and a mean calculated will increase the sample's variance and deviation. Increasing sample length produces a less and less accurate estimate of the wind's actual behavior. My opponent's claims apply to an effort to determine a static value. It does not apply to windspeed.

I'm done.

You could wait for FCT to say something similar, but as far as I'm concerned, anyone that wants to put in their two cents may feel free to do so.

 

[flacaltenn]

Don't want to abandon the discussion without including EVIDENCE that for EITHER the 1min or 10min averaging --- the Process Mean of hurricanes CAN BE considered stationary (or static in Abraham3 mathspeak) for intervals at least up to 10minutes.

First pic is the core of this argument. Data of Hurricane Ike over a 2 day period..
Ignore the bottom grey squiggly plot. Authors were trying to show the effect of urban obstructions on lower mounted instruments. The top 2 plots are EXACTLY the 1min avgd wind speeds with the 10min avgd wind speeds superimposed.. THIS IS THE NUT CORE of our argument. NOTE ------

1) There is CONSIDERABLY MORE variance in the 1min avg data. It is a POORER PERFORMING PREDICTOR of the mean hurricane speed winds..

2) The 10min plot shows NO EFFECTS of deviating from the true MEAN SPEED of the storm. Meaning that over 10min averages, the process mean CAN be considered stationary with no noticeable loss of precision.

This evidence as well as the basic math theory behind estimation is proof that the assertion under discussion is PATENTLY false.

So WHY is there MORE VARIANCE in the 1min avg -- making it a POORER estimation of mean storm wind speeds? ((Besides the obvious PREDICTED decrease in precision from the math theory? ))
The next plot shows a graph of "gust factor" versus DURATION in seconds. Gust factor is a measure of the INCREASED PEAK ENERGY wrt the long term mean wind speed. Note here the difference in energy intensity between 1min and 10min.. So there IS a considerable amount of ERROR in any estimations at 1min.

Another look at the diff in energy between 1min and 10min---- this time in Frequency Space plot. Note the placement of the 95% confidence limit is WAAAAY above the 1sec energy components.

First chart is linked IN THE IMAGE. Last 2 charts are from the WMO reference already cited on Page 1 of this thread.

A VISUAL confirmation that despite your assertion that

You don't even know the meaning of the word. The length of time over which the wind speed is averaged HAS NO BEARING WHATSOEVER on how accurate the measurement might be. It is simply a different measurement. We could average it over a day or a week or a month or a year.

............. was never supportable. EVEN IN the specific case of measuring hurricane winds --- but more importantly --- it was never supportable in terms of every known Intro to Statistic Chapter One knowledge.

 

[flacaltenn]

Wind speed is not static and does not have a static mean.

Just handled this in the previous post with actual hurricane wind speed data. In all the research I did -- MULTITUDES of references cited 10 minute averaging as the preferred standard. What you are trying to assert is contrary to the guidance of almost EVERY METEROLOGICAL SOCIETY on the planet including the WORLD MET. ORG. And I've cited references to back this up. It's PREFERRED BECAUSE it is a better predictor of MEAN wind speeds. And I've cited references on that.

What good would it be to quote both a Maximum Gust for hurricanes along with a SHORT period average MEAN that ACTED like a gust indicator? That's what you are proposing. To make the accuracy of the means prediction PURPOSELY bad so that Gust energy is preserved and included in the mean value. The 2 statistics should be unique --- not similiar.. Thats the primary purpose of culling information with statistical tools.

Let's say you wanted to take ten minute averages but were unsure whether or not your mean was sufficiently static. How would you find out? You'd take shorter averages. And you've already admitted that it's not static on any scale - only that an observer could decide, arbitrarily, that it was sufficiently static.

Deciding HOW to use the tools of math is harder than learning the tools in the first place. In the case of means estimation with a non-stationary process mean, I told you that in most cases --- it can be ignored. Like in the case of AVG home prices, or Global Annual Mean Surface Temperature for Global Warming (a classic case of over-extended averaging). But in cases where the mean is varying SLOWER than the observation rate, it can be considered a means of non-destructive data reduction because it PRESERVES ACCURATELY the value of the mean over time. As the charts and references I produced show -- this is true in the hurricane wind case where non-stationary mean WOULD contribute bias if it existed over that observation length. It doesn't as the 1st figure in my last post clearly shows and by the WIDESPREAD ADOPTION of this standard all over the world. Asserting elsewise puts you at odds with the very "scientific authorities" that you defer to in OTHER cases of science debate.

Not one of this multitude of assumptions you've made was included in the point you chose to debate here. Leaves me feeling as if I've been treated unfairly.
Since your impatience led you to forego the official refereed debate you demanded, I see no stopping point save for one or both of us to say "I'm done".

Following this post and any editing --- I'm also done then. YOU decided to dive into the false assertions about "variance being less" for shorter periods --- I didn't. In my FIRST POST -- I referenced both a textbook example of the reasons your statement was false AND SPECIFICALLY a confirmation from the WMO that rejects your alternate theory. The dive into the Rabbit Hole was your initiative.. HOWEVER --- EVERYTHING I DISCUSSED was pertinent and neccessary to dissuade you of your "intuition". You produced NOT ONE link or reference in the COMPLETE debate.

Summation: Wind speed constantly varies. Increasing the length of time over which a sample is collected and a mean calculated will increase the sample's variance and deviation. Increasing sample length produces a less and less accurate estimate of the wind's actual behavior. My opponent's claims apply to an effort to determine a static value. It does not apply to windspeed.

I'm done.

You could wait for FCT to say something similar, but as far as I'm concerned, anyone that wants to put in their two cents may feel free to do so.

Per your summation: Yes, NO, NO, NO.

One more point --- You don't even know it --- but you REFUTED YOUR OWN ASSERTION -- thus defeating yourself without ANY help from me. Your original statement

"The length of time over which the wind speed is averaged HAS NO BEARING WHATSOEVER on how accurate the measurement might be."

........ was very specific. But when it came time for you to defend it --- You launched right into an ALTERNATE discussion of why SHORTER periods of observation were better !!! You bravely expended MOST ALL of your "gust energy" on that premise. Even going to the absurb, (but highly entertaining assertion) that A SINGLE OBSERVATION was a better predictor of statistical features than longer observations. (The "burn the textbooks" tactic) HOWEVER ---- if shorter periods of averaging are BETTER -- your original statement that it "HAS NO BEARING WHATSOEVER" is patently false.

Congrats. And thanks for the challenge. I don't feel better. I'm not a happier camper. And I didn't WANT to have to expose your inclinations to tear up the textbooks and wing your way thru the debate. I TRIED to avoid this.

Let's NOT do this again anytime soon... No grudges...