Advanced(?) interpolation

[Nepomuk 0]

Hello Hifi-Team,on my flight departing from Madeira i noticed that the ground winds were quite strange. The (interpolated) station LPFU at the aiport showed 117/08 the (non-interpolated) station LPMA 2 miles away showed 040/09.There has to be something wrong with the weighting of the distances of interpolated stations!Interpolation details for LPFU:RegardsNepo

[JSkorna 137]

Hi,You have:90@1240@9300@5120@17I am not going to post the formulas, but the closest station did have the correct effect on the end result.

[Nepomuk 0]

but the closest station did have the correct effect on the end result.

Sorry, i dont get it. The end result at LPFU is 117/8, the closest station is 040/9.090@12 31 miles away040@ 9 2 miles away300@5 250 miles away120@17 486 miles away.I expect that the wind at LPFU is near 040/9 because its only 2 miles away. Why changes the wind direction 77°?RegardsNepo

[JSkorna 137]

Hi,Because all 4 stations are used, not just the closest one.

[Nepomuk 0]

Hello Jim,without any math, what do you think the winds should be at LPFU?

Quadrangle Distance-Weighted Interpolation TechnologyNew intelligent interpolation fills gaps in weather data more realistically than ever before. The 4 closest data stations in each 90-degree directional quadrant are analyzed and weighted against distance, significantly increasing depiction accuracy in areas with few (or no) reports.

If the distance of the surrounding stations is weighted, the result should be closer to the values of LPMA. GCLA and LPAZ should have little influence. Here is my simple but correct math for the weighting:d1, d2, d3, d4: distance to stationsw1, w2, w3, w4: weight factor, w1+w2+w3+w4=1wX = 1 / (dX * (1/d1 + 1/d2 + 1/d3 + 1/d4))S1: 090@12 31 miles awayS2: 040@ 9 2 miles awayS3: 300@5 250 miles awayS4: 120@17 486 miles away.w1 = 1 / ( 31 * (1/31 + 1/2 + 1/250 + 1/486)) = 0,059 = 6%w2 = 1 / ( 2 * (1/31 + 1/2 + 1/250 + 1/486)) = 0,929 = 93%w3 = 1 / (250 * (1/31 + 1/2 + 1/250 + 1/486)) = 0,007 = 0,7% roundedw4 = 1 / (486 * (1/31 + 1/2 + 1/250 + 1/486)) = 0,004 = 0,4% roundedIf S1 and S2 got 99% of 100%, how is it possilbe that the wind is 77° off station LPMA (S2)? You may use other formulas, but the results should be similar.Do you agree that there is something wrong with the weighted interpolation?RegardsNepo

[JSkorna 137]

Hi,You are assuming you know the calculations that ASE is actually using and no I will not agree that something is wrong with the weighted interpolation.Because the same calculations are used at every interpolated station, this would happen every time, at every location, for the past 3 years.Edit: Also, wouldn't you agree that in your example almost all of the data would be coming from 1 data station and then this wouldn't be advanced interpolation, but using the closest station data, just as ASv6.5 uses?

[JRBarrett 2,968]

Hi,You are assuming you know the calculations that ASE is actually using and no I will not agree that something is wrong with the weighted interpolation.

In mathematics, there are often many formulae/alogrithms which can be used to solve a particular problem. While the calculations may be very different between them, the end results should be pretty much the same. If, indeed, ASE specifically weights for distance (as the documentation specifically states), then the result should be much closer to what Nepo calculated, than to what the program appears to be coming up with.

Because the same calculations are used at every interpolated station, this would happen every time, at every location, for the past 3 years.

Not necessarily. In a case where there are an abundance of nearby "actual" METARS to use for the interpolation, (as would normally be the case in Europe, or the U.S.), then the end result would be quite close, even if the weighting algorithm is flawed - or even if no weighting was being used at all.The evidence of incorrect weighting would only manifest in an situation where the 3 of the 4 stations used for interpolation are quite far away, while one is rather close - as is the case in the Azores, or (as another user recently noted) in New Zealand.

Edit: Also, wouldn't you agree that in your example almost all of the data would be coming from 1 data station and then this wouldn't be advanced interpolation, but using the closest station data, just as ASv6.5 uses?

That's the entire point of weighting data in an application such as ASE - by FAR the majority of weight should be assigned to the station which is closest in terms of distance. In this particular example - where one station is only 2nm away, while the others are dozens to hundreds of miles farther away - the end result would (for all intents and purposes) be the same as AS6.5's use of only the closest station.I just ran the four data points in Nepo's example through a linear regression module in Wolfram Mathematica, and came up with almost exactly the same result as he did - 98.5% weighting to the data from LPMA.Now, I realize that there will be situations where no possible interpolation technique would be able to give an accurate result - i.e. an isolated island airport where all of the potential interpolation METAR sources are hundreds of miles away... in such a case, any interpolation is going to be far removed from reality - probably no better than a wild guess. That's an unavoidable fact of life.But, in the example Nepo showed, it is clear to me that ASE is either not weighting for distance (despite what the documentation says), or is not weighting properly.Jim Barrett

[Nepomuk 0]

Thank you Jim B. for your support!I dont know if the issue is related to the weighting. Its just a presumption - but there are interpolation errors.. Maybe its a problem related to northern winds?Another strange interpolation (northern winds reported, southern at the interpolated station):RegardsNepo

[Guest jahman]

I don't think linear interpolation should be used at all, rather a reasonably steep S-curve of weights is closer to nature. For example, if you use linear interpolation you would never have a front as they would be diffused away by the linear weights.Cheers,- jahman.

[kterz 49]

Take a look at thisAlso note that when hitting the Interpolation details button, it is sometimes necessary to leave the report page go to some other page (eg briefing) and then back to report, so that the interpolation details have a chance to get initialised.

[Nepomuk 0]

Hello Hifi-Team,same time, same station - the interpolation using B647 now looks much better:RegardsNepo