No, I show how culling the nodes changes the results. When you decide the nodes, the triangle mesh is determined as the convex hull. And I show how varying the culling modifies the results within a limited range.

*“I dare you to submit this to a numerical analysis journal”*

It would be rejected for unoriginality. It is bog standard finite element integration. Triangle elements with piecewise linear basis functions. It is also, as I say there, the 2D equivalent of trapezoidal integration.

Every numerical integral is a weighted sum of values at the quadrature points (OK, maybe derivatives too). And those weights represent the area (or volume etc) of something. The task of numerical integration is to find the right weights.

]]>That includes John Christy and Roy Spencer, though they never publish their T-series with the error bars they reported in the more technical literature.

The major problem comes with the people compiling the air temperature record (GISS, UEA, UKMet, BEST). There’s an entirely tendentious and universal assumption, openly stated, that all measurement error is random and averages away.

The SST people assume that the data from every “platform,” i.e., ship, has a single constant error distribution. It’s incredible. One gets the impression that none of these people have ever made a measurement.

]]>Here is a quote from your web site:

“The average is formed by area-weighting, which I prefer to think of as a spatial integration method. ”

So you are stating that it is an approximation of an integral with variable weights that you can control. Oops.

I dare you to submit this to a numerical analysis journal claiming that it is accurate for general integration

giving your choice of triangulation (weights) and an error analysis.

Also I wanted an overlay of Olof’s curves with those of IPCC during the same years, not yours.

Jerry

]]>I’m only dealing with long-term large-scale changes in temperature. I suppose that these patterns are so smooth that it actually works with crude sampling/interpolation.

]]>On your own website you show how changing the number, size, and location of the triangles changes the result. That is exactly what one would expect as it changes the weights in the calculation of the mean. No error analysis when you

have clearly shown that that you are tuning the result just as climate models do so you can provide the answer you want. Where is your reviewed publication in a numerical analysis journal if you are so confident in your scheme (or in any reputable journal)? Numerical analysts would immediately see thru your game just as I have.

Jerry

]]>Do you trust the observational community (radiosondes, satellite, etc.) to be perfectly honest in their instrument accuracy estimates?

Jerry

]]>The 18 point subsampled UAH TLT are 18 gridcells (2.5×2.5 deg) in the center of 18 zones, 30 degrees heigh and 120 degrees wide. The points are area weighted by cosine of the latitude, which KNMI Climate explorer does automatically when I run the UAH field with such an 18 gridcell mask.

This was the first attempt. Next attempt was 36 points, filling the gaps in longitude between the first 18. This gave a clearly better result with reduced noise and a trend even more similar to the complete dataset.

Disclaimer, the chart was done in Nov 2016, so 2016 is only the year through Oct, but I dont think an update would change it very much.

I have done the same exercise with Hadcrut kriging through all 167 years. “18 points” surface temperature looks a little bit noiser than TLT, but there is no long-term bias compared to the complete global dataset.

]]>Here’s a set of citations to temp sensor accuracy I posted once, elsewhere:

**Radiosonde air temperature measurement uncertainty: ±0.3 C**:

R. W. Lenhard, Accuracy of Radiosonde Temperature and Pressure-Height Determination BAMS, 1970 51(9), 842-846.

F. J. Schmidlin, J.J. Olivero, and M.S. Nestler, Can the standard radiosonde system meet special atmospheric research needs? Geophys. Res. Lett., 1982 9(9), 1109-1112.

J. Nash Measurement of upper-air pressure, temperature and humidity WMO Publication-IOM Report No. 121, 2015.

The height resolution of modern radiosondes using radar or GPS = 15 m = (+/-)0.1 C due to lapse rate alone.

That makes the lower limit uncertainty of modern radiosonde temperatures (inherent + height) rmse = ±0.32 C.

**Satellite Microwave Sounding Units (MSU): ±0.3 C accuracy lower limit**:

Christy, J.R., R.W. Spencer, and E.S. Lobl, Analysis of the Merging Procedure for the MSU Daily Temperature Time Series Journal of Climate, 1998 11(8), 2016-2041 (MSU ≈±0.3 C mean inter-satellite difference)

Mo, T., Post-launch Calibration of the NOAA-18 Advanced Microwave Sounding Unit-A IEEE Transactions on Geoscience and Remote Sensing, 2007 45(7), 1928-1937.

From Zou, C.-Z. and W. Wang, Inter-satellite calibration of AMSU-A observations for weather and climate applications. J. Geophys. Res.: Atmospheres, 2011 116(D23), D23113.

Quoting from Zou (2011) “Although inter-satellite biases have been mostly removed, however, the absolute value of the inter-calibrated AMSU-A brightness temperature has not been adjusted to an absolute truth [i.e., the accuracy]. This is because the calibration offset of the reference satellite was arbitrarily assumed to be zero [i.e., the accuracy of the satellite temperature measurements is unknown].”

The inter-satellite calibrations and bias offset corrections that are used to improve precision do not improve accuracy.

**Infrared Satellite SST resolution: ±0.3 C**

W. Wimmer, I.S. Robinson, and C.J. Donlon, Long-term validation of AATSR SST data products using shipborne radiometry in the Bay of Biscay and English Channel. Remote Sensing of Environment, 2012. 116, 17-31.

**Land surface air temperature uncertainty,
Lower limit of measurement error: ±0.45 C** (CRS LiG thermometer prior to 1980); ±0.35 C (MMTS sensor after 1980, but only in the technologically advanced countries).

Hubbard, K.G. and X. Lin, Realtime data filtering models for air temperature measurements Geophys. Res. Lett., 2002 29(10), 1425; doi: 10.1029/2001GL013191.

Huwald, H., et al., Albedo effect on radiative errors in air temperature measurements Water Resources Res., 2009 45, W08431.

P. Frank Uncertainty in the Global Average Surface Air Temperature Index: A Representative Lower Limit Energy & Environment, 2010 21(8), 969-989.

X. Lin, K.G. Hubbard, and C.B. Baker, Surface Air Temperature Records Biased by Snow-Covered Surface. Int. J. Climatol., 2005 25, 1223-1236; doi: 10.1002/joc.1184.

**Sea Surface Temperature uncertainty: ±0.6-0.9 C** for ship engine intakes:

C. F. Brooks, C.F., Observing Water-Surface Temperatures at Sea Monthly Weather Review, 1926 54(6), 241-253.

J. F. T. Saur A Study of the Quality of Sea Water Temperatures Reported in Logs of Ships’ Weather Observations J. Appl. Meteorol., 1963 2(3), 417-425.

**SST uncertainty from buoys, including Argo: ±0.3-0.6 C**:

W. J. Emery, et al., Estimating Sea Surface Temperature from Infrared Satellite and In Situ Temperature Data. Bull. Am. Meteorol. Soc., 2001 82(12), 2773-2785.

R. E. Hadfield, et al., On the accuracy of North Atlantic temperature and heat storage fields from Argo. J. Geophys. Res.: Oceans, 2007 112(C1), C01009.

T.V.S. Udaya Bhaskar, C. Jayaram, and E.P. Rama Rao, Comparison between Argo-derived sea surface temperature and microwave sea surface temperature in tropical Indian Ocean. Remote Sensing Letters, 2012 4(2), 141-150.

Those are all 1-sigma uncertainties and none of them represent random error. They do not average away.

Anyone who understands measurement uncertainty must conclude from the above published calibrations that the 95% lower limit uncertainty bounds for air temperatures are:

**Surface air temperature: ±1 C
Radiosonde: ±0.6 C
Satellite: ±0.6 C**

The climate consensus people never produce plots with physically real error bars.

The entire field runs on false precision.

]]>The triangulation is the unique convex hull of nodes, determined just by node location. There are necessarily approximately twice as many triangles as nodes. As to manuscripts, there are plenty of published indices, which you apparently dismiss. If you want to see overlaid results, I show them here:

moyhu.blogspot.com.au/p/latest-ice-and-temperature-data.html#Drag

The triangle result is called TempLS mesh, and you can compare it over any period with any of the regular indices. If you want to compare numbers, there are tables here, with different anomaly base periods:

moyhu.blogspot.com.au/p/latest-ice-and-temperature-data.html#L1

The different integration methods that I use are shown by pressing the TempLS button.

Troposphere temperature measurements use a microwave range which is little affected by clouds.

]]>Where did you obtain the accuracy of the sat data? As you know tomography is also an ill posed problem (inversion of an integral) but works for the large scale features because they have so many different angles ( and lots of radiation for the patient). My experience has been that the sat temp data only works reasonably well in clear skies and when there is a ground based measurement to anchor the result. There should be different errors for the clear and cloudy sky cases with and without a land based measurement?

Jerry

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