Sampling biases in global temperature anomalies

Nick Stokes points out some fundamental problems with determining trends in surface temperatures. This is due to the changing distribution of stations within a grid cell with time. Consider a 5×5 degree grid cell which contains a 2 level plateau above a flat plain at sea level – as shown below. Temperature falls like -6.5C per 1000m in height so  the real temperatures at different locations will be  as shown. Therefore the correct average surface temperaure for that grid would be something like (3*20+2*14+7)/6 or about 16C. What you actually measure will depend on where your stations are located. Grid1Since the number of stations and their location is constantly changing  with time there is little hope of measuring any underlying trend of average temperature  in that cell. You might even argue that an average surface temperature, in this context, is a meaningless concept.

The mainstream answer to this problem is to use temperature anomalies instead. To do this we must define a monthly ‘normal’ temperature for each station over a 30 year period e.g. 1961-1990. Then in a second step we subtract these ‘normals’ from the measured temperatures to get DT or the ‘anomaly’ for that month. Then we average those values over the grid instead to get the average anomaly for that measurement month compared to 1961-1990. Next we can average over all months and all grid cells to derive the global annual temperature anomaly.  The sampling bias has not really disappeared but has been partly subtracted. There is still an  assumption that all stations react in synchrony to warming (or cooling) uniformly within a cell. This procedure introduces a new problem for those stations which have insufficient data  defined within the selected 30 year period, and this can invalidate some of the most valuable older stations. Are there other ways to approach this problem?

For the GHCN V1 and GHCN V3(uncorrected) datasets I wanted to use all stations so took a naive approach. I simply used monthly normals defined per grid cell rather than per station over the entire period.


Compare annual anomalies calculated per monthly grid cell. After 1900 the agreement of GHCN V3 with CRUTEM4 is good. The original GHCN1 data is shifted warmer than GHCN3 by up to 0.1C. This difference is real.

A novel approach to this problem was proposed first by Tamino, but then refined by RomanM and Nick Stokes. I will hopefully simplify their ideas without too much linear algebra. Corrections are welcome.

Each station is characterised by a fixed offset \mu_i  from the grid average. This remains constant in time because, for example,  it is due to its altitude. We can estimate \mu_i  by first calculating all the monthly average temperatures T_{av} for the particular grid cell in which it appears. Then by definition for any of the monthly averages

T_{av} = \frac{1}{N_{stations}} \sum{T_i - \mu_i}

so now in a second step, by averaging over all the ‘offsets’ for a given station we can estimate \mu_i .

\mu_i =\frac{1}{N_t}\sum_{time}{T_i -T_{av}}

So having found the set of all station ‘offsets’ in the database we can calculate temperature anomalies using all available stations in any month. I still think the anomalies  have to be normalised to some standard year, but at least the bias due to a changing set of stations will be reduced, especially in  the important early years.

P.S. I will try this out when time permits.


Posted in AGW, Climate Change, climate science, Science | Tagged | 3 Comments

A Ghost from the Past

I have located an original version of the Global Historical Climatology Network (GHCN) published around 1990. It contains raw temperature data from 6039 weather stations around the world. Quality control procedures corrected a few impossible values mainly due to typing mistakes, and removed any duplicate data. Otherwise they are the originally recorded temperatures. You are welcome to  download the metadata and the temperature data in re-formatted csv files, which I hope are self explanatory. The original ‘readme’ file with credits to authors can be downloaded here.  Since 1990 there have been a continuous set of  adjustments made to GHCN data for a variety of reasons. These include changes in station location, instruments and especially ‘data homogenisation’. These adjustments have had the net effect of cooling the past (pre-1930). The latest GHCN version is 3 which can be downloaded from NOAA.

So what I did next was to process the GHCN V1 data by first gridding the temperatures geographically in a 5×5 monthly degree grid, similar to CRUTEM4. I then calculated the monthly averages across all stations within one grid cell. The monthly temperature anomalies  are then just the differences from these average values. Averaging stations within a grid cell is essentially the same thing as data homogenisation, because it assumes that nearby stations have the same climate. The annual temperature anomalies are the geographically weighted averages of the monthly values. So what did the original V1 data say about past temperatures?



There is clearly a huge difference before about 1930. So let’s compare each hemisphere separately.



For the southern hemisphere I compare GHCN V1 with a contemporary version of CRU dated 1988 (see below).


GHCN V1 was available just before the first IPCC assessment report in 1990. At the time CRU had also collected a smaller set of station data from around the world which mostly were included in GHCN. I also have a copy of this data from around 1988 which we can compare directly with V1. The global average temperature anomalies are shown below.

CompareJones-V1The agreement  after 1900 is very good, but  they disagree strongly in the 19th century. Now you can also see why the IPCC first assessment report (FAR) was so cagey about any global warming signal (“yet to emerge”).  That was because  there wasn’t any signal in the temperature data available at that time!


Posted in AGW, Climate Change, climate science, Science | Tagged , , | 46 Comments

Untangling UK Wind power production

There are currently 6044 operational wind turbines in the UK with a total capacity of 12.133 GW. Do we know how much electrical power they generate? The answer is not simple. These 6044 turbines are installed in over 700 sites, some of which are very large while others are only a single turbine.  There are 3 ways to connect them to the Grid.

1. Direct transmission line to the Grid. This is suitable only for large wind farms especially off-shore. The output of such wind farms is metered through the ‘balancing mechanism’, from which Gridwatch and this site get their live updates. A full list of these directly connected wind farms are given below.

Wind Farm Capacity (MW)
Arecleogh 120
Clyde 462
Carraig Gheal 46
Crystal Rig 138
Greater Gabbard Offshore 501
Griffin Wind Farm 204
Gwynt y Mor offsgore 592
Hadyard Hill 130
Humber Offshore 220
Harestanes 126
London Array 720
Lincs Offshore 540
Ormonde 160
Sherringham Shoal Offshore 315
Thanet Offshore 300
West of Duddon Sands 382
Whitelee 511
Walney Offshore 369
Westermost Rough 205

Total Capacity = 7.1 GW

I had thought that these were all the ‘metered’ wind farms included in the Balancing Mechanism BM reports. However I later discovered that those in category 2 are also metered because they receive constraint payments.

2. Secondly there are wind farms that are registered  with the Balancing Mechanism, but are ‘BM embeded’ in the local distribution network. These large to medium wind farms are still visible to the Balancing Mechanism and their output is metered. We know this as they receive constraint paayments to disconnect when there is too much wind. This is the list of such wind farms

Baillie Wind Farm 52.5
BETHW-1 29.75
Braes of Doune 74
Berry Burn Wind Farm 66.7
Beinn An Tuirc 2 43.7
Burbo Offshore Wind 90
CLDRW-1 37
Clachan Flats 15
Dalswinton Windfarm 30
Gordonstown 13
Goole Fields Wind Farm 34.476
Glens of Foudland 26.7
Gunfleet Sands Demo 11.7
Great Yarmouth Power Limited 405
Hill of Towie 48
Minsca Wind Farm 36.8
E_RHEI-1 52
Tullo Extension 25

Total capacity = 1.1GW

Therefore the total metered capacity of wind farms within the BM system is simply the sum of category 1 and category 2.

Total Metered Capacity = 8.2 GW

The real-time output from category 1 and 2  wind farms is shown below:

3. Now there are about 600 smaller wind farms ranging from 1 up to to 40 turbines that have a connection to the regional Distribution Network Operator (DNO) and are paid ‘Feed-In Tariffs’ (FITS). These smaller wind farms are not part of the balancing mechanism and are therefore not metered centrally. Their net effect on the National Grid is to reduce demand slightly via the local distribution network. They must have an on-site transformer to convert generated DC to 3-phase AC and connect to the local DNO. They may also use generated energy locally and then get paid a discount because it is ‘green’. The exported electricity  is metered locally and receives the FIT as shown below.


The estimated total FIT capacity of these 600 farms =  3.8 GW (the difference of 12GW and the metered total).

Unfortunately the output from wind farms in category 3 is never made public. It is impossible to know the real-time power from these wind farms. What I originally set out to discover was  what percentage of  total wind power is measured by the Balancing Mechanism. It has been a headache to get all this information together, but I think we can now estimate the total output from all UK wind farms. To do this we can simply assume that the load capacity for the  feed-in wind farms is the same as that for the metered farms, (which may be optimisitic as the largest farms are off-shore). Under this assumption  the correction factor to be applied to the BM reports values is 12/8.2 = 1.46.  So the actual wind power  from all UK wind farms to electricity generation in the UK right now is:

Therefore I will in future increase the BM reports values for wind power output by this factor to better reflect the actual situation.


  1. UK Wind Energy Database (UKWED)
  2. Elexon
  3. Variable Pitch
  4. Renewable Energy Foundation
Posted in Energy, renewables, Science, wind farms | Tagged | 17 Comments