A New System for Determining Global Temperature

Guest essay by Mike Jonas

Introduction

There are a number of organisations that produce estimates of global temperature from surface measurements. They include the UK Met Office Hadley Centre, the Goddard Institute of Space Studies (GISS) and Berkeley Earth, but there are others.

They all suffer from a number of problems. Here, an alternative method of deriving global temperature from surface measurements is proposed, which addresses some of those problems.

Note: The terms global temperature and regional temperature will be used here to refer to some kind of averaged surface temperature for the globe or for a region. It could be claimed that these would not be real temperatures, but I think that they would still be useful indicators.

The Problems

Some of the problems of the existing systems are:

· Some systems use temperature measurements from surrounding weather stations (or equivalent) to adjust a station’s temperature measurements or to replace missing temperature measurements. Those adjusted temperatures are then used like measured temperatures in ongoing calculations.

· The problem with this method is that surrounding stations are often a significant distance away and/or in very different locations, and their temperatures may be a poor guide to the missing temperatures.

· Some systems use a station’s temperature and/or the temperatures of surrounding stations over time to adjust a station’s temperature measurements, so that they appear to be consistent. (I refer to these as trend-based adjustments).

· There is a similar problem with this method. For example, higher-trending urban stations, which are unreliable because of the Urban Heat Effect (UHE), can be used to adjust more reliable lower-trending rural stations.

· Some systems do not make allowances for changes in a station, for example new equipment, a move to a nearby location, or re-painting. Such changes can cause a step-change in measured temperatures. Other systems treat such a change as creating a new station.

· Both these methods have problems. Systems that do not make allowance : These systems can make inappropriate trend-based adjustments, because the step-change is not identified. Systems that create a new station : These systems can also make inappropriate trend-based adjustments. For example, if a station’s paint detoriates, then its measurements may have an invalid trend. On re-painting, the error is rectified, but by regarding the repainted station as a new station the system then incorporates the invalid trend into its calculations.

There are other problems, of course, but a common theme is that individual temperature measurements are adjusted or estimated from other stations and/or other dates, before they get used in the ongoing calculations. In other words, the set of temperature measurements is changed to fit an expected model before it is used. [“model” in this sense refers to certain expectations of consistency between neighbouring stations or of temperature trends. It does not mean “computer model” or “computer climate model”.].

The Proposed New System

The proposed new system uses the set of all temperature measurements and a model. It adjusts the model to fit the temperature measurements. [As before, “model” here refers to a temperature pattern. It does not mean “computer model” or “computer climate model”.].

Over time, the model can be refined and the calculations can be re-run to achieve (hopefully) better results.

The proposed system does not on its own solve all problems. For example, there will be some temperature measurements that are incorrect or unreliable in some significant way and will genuinely need to be adjusted or deleted. This issue is addressed later in this article.

For the purpose of describing the system, I will begin by assuming that the basic time unit is one day. I will also not specify which temperature I mean by the temperature, but the entire system could for example be run separately for daily minimum and maximum temperatures. Other variations would be possible but are not covered here.

The basic system is described below under the two subheadings :The Model” and “The System”.

The Model

The model takes into account those factors which affect the overall pattern of temperature. A very simple initial model could use for example time of year, latitude, altitude and urban density, with simple factors being applied to each, eg. x degrees C per metre of altitude.

The model can then be used to generate a temperature pattern across the globe for any given day. Note that the pattern has a shape but it doesn’t have any temperatures.

So, using a summer day in the UK as an example, the model is likely to show Scottish lowlands as being warmer than the same-latitude Scottish highlands but cooler than the further-south English lowlands, which in turn would be cooler than urban London.

The System

On any given day, there is one temperature measurement for each weather station (or equivalent) active on that day. ie, there is a set of points (locations) each of which has one temperature measurement.

These points are then triangulated. That is, a set of triangles is fitted to the points, like this:

Note: the triangulation is optimised to minimise total line length. So, for example, line GH is used, not FJ, because GH is shorter.

The model is then fitted to all the points. The triangles are used to estimate the temperatures at all other points by reference to the three corners of the triangle in which they are located. In simple terms, within each triangle the model retains its shape while its three corners are each moved up or down to match their measured temperatures. (For points on one of the lines, it doesn’t matter which triangle is used, the result is the same).

I can illustrate the system with a simple 1D example (ie. along a line). On a given day, suppose that along the line between two points the model looks like:

If the measured temperatures at the two points on that day were say 12 and 17 deg C, then the system’s estimated temperatures would use the model with its ends shifted up or down to match the start and end points:

Advantages

There are a number of advantages to this approach:

· All temperature measurements are used unadjusted. (But see below re adjustments).

· The system takes no notice of any temperature trends and has no preconceived ideas about trends. Trends can be obtained later, as required, from the final results. (There may be some kinds of trend in the model, for example seasonal trends, but they are all “overruled” at every measured temperature.).

· The system does not care which stations have gaps in their record. Even if a station only has a single temperature measurement in its lifetime, it is used just like every other temperature measurement.

· No estimated temperature is used to estimate the temperature anywhere else. So, for example, when there is a day missing in a station’s temperature record then that station is not involved in the triangulation that day. The system can provide an estimate for that station’s location on that day, but it is not used in any calculation for any other temperature.

· No temperature measurement affects any estimated temperature outside its own triangles. Within those triangles, its effect decreases with distance.

· No temperature measurement affects any temperature on any other day.

· The system can use moving temperature measurement devices, eg. on ships, provided the model or the device caters for things like time of day.

· The system can “learn”, ie. its results can be used to refine the model, which in turn can improve the system (more on this later). In particular, its treatment of UHE can be validated and re-tuned if necessary.

Disadvantages

Disadvantages include:

· Substantial computer power may be needed.

· There may be significant local distortions on a day-to-day basis. For example, the making or missing of one measurement from one remote station could significantly affect a substantial area on that day.

· The proposed system does not solve all the problems of existing systems.

· The proposed system does not completely remove the need for adjustments to measured temperatures (more on this later).

System Design

There are a number of ways in which the system could be designed. For example, it could use a regular grid of points around the globe, and estimate the temperature for each point each day, then average the grid points for global and regional temperatures. Testing would show which grid spacings gave the best results for the least computer power.

Better and simpler designs may well be possible.

Note : Whenever long distances are involved in the triangulation process, Earth’s surface curvature could matter.

Discussion

One of the early objectives of the new system would be to refine the model so that it better matched the measured temperatures, thus giving better estimated temperatures. Most model changes are expected to make very little difference to the global temperature, because measured temperatures override the model. After a while, the principal objective for improving the model would not be a better global temperature, it would be … a better model. Eventually, the model might contribute to the development of real climate models, that is, models that work with climate rather than with weather (see Inside the Climate Computer Models).

Oceans would be a significant issue, since data is very sparse over significant ocean areas. The model for ocean areas is likely to affect global averages much more than the model for land areas. Note that ocean or land areas with sparse temperature data will always add to uncertainty, regardless of the method used.

I stated above (“Disadvantages”) that the proposed system does not completely remove the need for adjustments to measured temperatures. In general, individual station errors don’t matter provided they are reasonably random and not systemic, because they will average out over time and because each error impacts only a limited area (its own triangles) on one day only. So, for example, although it would be tempting to delete obviously wrong measurements, it is better to leave them in if there are not too many of them, because they have little impact and their removal would then not have to be justified and documented. The end result would be a simpler system, easier to follow, to check and to replicate, and less open to misuse (see “Misuse” below), although there would be more day-to-day variation. Systemic errors do matter because they can introduce a bias, so adjustments to these should be made, and the adjustments should be justified and documented. An example of a systemic error could be a widespread change to the time of day that max-min thermometers are read. Many of the systemic errors have already been analysed by the various temperature organisations. It would be very important to retain all original data so that all runs of the system using adjusted measurements can be compared to runs with the original data in order to quantify the effect of the adjustments and to assist in detecting bias.

Some stations may be so unreliable or poorly sited that they are best omitted. For example, stations near air-conditioner outlets, or at airports where they receive blasts from aircraft engines.

The issue of “significant local distortions on a day-to-day basis” should simply be accepted as a feature of the system. It is really only an artefact of the sparseness and variability of the temperature measurement coverage. The first aim of the system is to provide regional and global temperatures and their trends. Even a change to a station that caused a step change in its data (such as new equipment, a move to a nearby location, or re-painting) would not matter much, because each station influences only its own triangles. It would matter, however, if such step-changes were consistent and widespread, ie. they would matter if they could introduce a significant bias at a regional or global level.

It wouldn’t even matter if at a given location on a particular day the estimated maximum temperature was lower than the estimated minimum temperature. This could happen if, for example, among the nearby stations some had maximum temperatures missing while some other stations had minimum temperatures missing. (With a perfect model, it couldn’t happen, but of course the model can never be perfect.).

All the usual testing methods would be used, like using subsets of the data. For example, the representation of UHE in the model can be tested by calculating with and without temperature measurements on the outskirts of urban areas, and then comparing the results at those locations.

All sorts of other factors can be built into the model, some of which may change over time – eg. proximity to ocean, ocean currents, average cloud cover, actual hours of sunshine, ENSO and other ocean oscillations, and many more. Assuming that the necessary data is available, of course.

Evaluation

Each run of the system can produce ratings that give some indication of how reliable the results are:

· How much the model had to be adjusted to fit the temperature measurements.

· How well the temperature measurements covered the globe.

The ratings could be summarised globally, by region, and by period.

Some station records give measurement reliability. These could be incorporated into the ratings.

Misuse

Like all systems, the proposed system would be open to misuse, but perhaps not as much as existing systems.

Bias could still be introduced into the system by adjusting historical temperature measurements – eg. to increase the rate of warming by lowering past temperatures. The proposed system does make this a bit more difficult, because it removes some of the reasons for adjusting past temperature measurements. In particular, temperature measurements cannot be adjusted to fit surrounding measurements, and they cannot be adjusted to fit a model (deletion of “outliers” is an example of this). If such a bias was introduced, the ratings (see “Evaluation” above) would not be affected, so they would not be able to assist in detecting the bias. The bias could be detected by comparing results against results from unadjusted data, but proving it against a determined defence could be very difficult.

Bias could still be introduced into the system by exploiting large areas with no temperature measurements, such as the Arctic, but the proposed system also makes this a bit more difficult. In order to exploit such areas, the model would need to be designed to generate change within the unmeasured area. So, for example, a corrupt model could make the centre of the Arctic warmer over time relative to the outer regions where the weather stations are. It would be possible to detect this type of corruption via the ratings (a high proportion of the temperature trend would come from a region with a low coverage rating), but again proof would be difficult.

NB. In talking about misuse, I am not in any way suggesting that misuse does or would occur. I am simply checking the proposed system for weaknesses. There may be other weaknesses that I have not identified.

Conclusion

It would be very interesting to implement such a system, because it would operate very differently to current systems and would therefore provide a genuine alternative to and check against the current systems. Raising the necessary funding could be a major hurdle.

The system could also, I think, be used to check some weather and climate theories against historical temperature data, because (a) it handles incomplete temperature data, (b) it provides a structure (the model) in which such theories can be represented, and (c) it provides ratings for evaluation of the theories.

Provided that the system could be used without needing too much computer power, it could be suitable for open-source/cooperative environments where users could check each other’s results and develop cooperatively. The fact that the system is relatively easy to understand, unlike the current set of climate models, would be a big advantage.

Footnotes

1. I hope that the use of the word “model” does not cause confusion. I tried to make it clear that the model I refer to in this document is a temperature pattern, not a computer model. I tried some other words, but they didn’t really work.

2. I assume that unadjusted temperature data is available from the temperature organisations (weather bureaux etc). To any reasonable person, it is surely inconceivable that these organisations would not retain their original data.

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Mike Jonas (MA Maths Oxford UK) retired some years ago after nearly 40 years in I.T.

Abbreviations

C – Centigrade or Celsius

ENSO – El Niño Southern Oscillation

GISS – Goddard Institute of Space Studies

UHE – Urban Heat Effect

1D – 1-dimensional