Guest essay by Tom Quirk
The convention in meteorology is to report mean temperatures as the average of minimum and maximum temperatures. This assumption has been tested using temperatures recorded every 30 minutes through the 24 hour day at various locations in Australia by the Bureau of Meteorology and made available on their website. The period examined is from the middle of March 2013 to the end of April 2013. Analysis shows that distortions are introduced by the use of thermometers that measure minimum and maximum temperatures and more importantly that the averaging of minimum and maximum temperatures does not represent the mean for the period examined. Whether this is also true for the entire year should be tested.
The Bureau of Meteorology (BOM) on its website (http://www.bom.gov.au/australia/index.shtml) provides temperatures recorded every 30 minutes through the 24 hour day at various locations in Australia, an example, Canberra is at http://www.bom.gov.au/products/IDN60903/IDN60903.94926.shtml.
The convention in meteorology is to report daily, monthly or yearly mean temperatures as the average of minimum and maximum temperatures. This assumption can be tested using the BOM data.
13 locations around Australia have been selected for analysis. Figure 1 shows the average of the 30 minute intervals for 43 days in March and April for Cairns and Alice Springs. The figures show errors on the mean, not standard deviations. The data for the 13 sites divided into continental and coastal locations are shown in the Appendix.
The measurements at Alice Springs and Cairns are a perfect illustration that the mean is not always the average of minimum and maximum temperatures. For Alice Springs the average of the minimum and maximum temperatures is 0.12 +/- 0.12 above the average of all 48 30 minute readings while for Cairns the average of all 48 30 minute readings is 0.45 +/- 0.07 below the average of the minimum and maximum temperatures.
Figure 1: Temperatures measured at 30 minute intervals through a 24 hour day. The sample is for 37 days in March and April and the errors not the standard deviations are shown. The difference for Mean (30 minute Tmin & Tmax) – Mean (all 30 minute T) is -0.13 +/- 0.10 for Alice Springs and 0.46 +/- 0.07 for Cairns.
The minimum and maximum temperatures that are reported by the BOM are a result of readings from the two thermometers at 9.00 am each morning. This gives a record of the minimum temperature for the day of the reading since minima in general occur between midnight and about 7.30 am local time. This can be seen in Figure 1. The maximum temperature is a record from 9.00 am on the previous day. In general this maximum occurs before midnight.
As a test of the 30 min readings, the temperature differences of the 24 hour minimum thermometer and the 30 minute thermometer minimum value and likewise the temperature differences of the 24 hour maximum thermometer and the 30 minute thermometer maximum value were calculated. The results are shown in Figure 2. There are biases with the 24 hour readings being equal to or below the 30 minute minimum and the 24 hour maximum readings being equal to or above the 30 minute readings.
Figure 2: Maximum or minimum temperature differences for the 24 hour and 30 minute measurements as a function of the maximum or minimum 30 minute temperature measurement.
However these thermometer differences are not dependent on temperature as shown in Figure 2 where there are no significant trends. Note that there are a number of large differences. Some are due to the 24 hour record assumption that minimum temperatures occur between midnight and 9.00 am where in fact the minimum comes from the previous day after 9.00 am but before midnight. Other measurements may not to date have had a quality control check.
There is evidence of a systematic error in Figure 2 that is more obvious in Figure 3 and detailed in Table 1.
Figure 3: Maximum or minimum temperature differences for 24 hour thermometer temperatures and 30 minute temperature measurements
This bias is not unexpected as an extreme might occur in the 30 minute interval between regular measurements. A measure of this is to look at the temperature differences that occur in the 30 minute interval before and after the extreme minimum or maximum. The scatter is 0.6 0C for the maximum readings and -0.2 0C for the minimum readings, the same magnitude as the difference in Figure 3 and Table 1.
Table 1: 24 hour thermometer reading – 30 minute temperature readings
|24 hour value – 30 minute value||-0.18||0.51||-0.26||0.60|
The effect that these systematic errors have on the mean temperature is given in Table 2 and shown in Figure 4. The average systematic error from the 24 hour thermometer readings is an increase in mean temperature of 0.14 +/- 0.04 0C.
Table 2: Difference for mean temperature for 24 hour thermometer reading – 30 minute temperature readings
|Latitude0S||Longitude0E||24 hour value – 30 minute value0C||+/- Error0C|
Figure 4: Location differences of mean temperature for 24 hour thermometer reading – 30 minute temperature readings. The overall difference is 0.14 +/- 0.01 0C.
The corrections to the mean temperatures are therefore increased if the BOM 24 hour thermometer measurements are used rather than the 30 minute measurements.
This systematic error is a consequence of the “one-way” temperature recording where, for example, a 10 minute 10C fluctuation in temperature would give a 0.50C increase in mean temperature rather than the properly weighted 0.010C change.
Summary of comparison
The results of the analysis of mean temperatures are presented in Table 3 and Figure 5. The comparison of the average of the minimum and maximum temperatures with a mean of 48 measurements throughout the day shows an overestimate of the mean temperature from averaging minimum and maximum temperatures. All the differences are equal or increased with the use of the BOM 24 hour thermometer measurements. The values highlighted in yellow are over 2 standard deviations from no difference of mean and “mean”. If the distribution were normal this is a probability of 98% that the difference is real.
The variations in temperature difference are a function of latitude and longitude. For this analysis the locations have been grouped as coastal and continental. The map of Australia shows the locations selected for temperature analysis.
Table 3: Temperature differences comparing the average of Tmin and Tmax with a 24 hour mean.
Figure 5: Temperature differences comparing the average of Tmin and Tmax with a 24 hour mean.
These temperature variations are complicated as shown by the correlation coefficients for locations where the correlation coefficients for Wangaratta and Canberra are significantly different to other coastal locations while the continental locations are no different to the remaining coastal locations (Table 4 and Figure 6).
Table 4: Correlation coefficients for Tmin and Tmax
|Latitude 0S||Longitude0E||Numberof days||CorrelationMin & Max T||Error|
Figure 6: Correlation coefficients for Tmin and Tmax by latitude.
The data and analysis covers up to 45 days of 48 temperature measurements made every 30 minutes. The results indicate significant systematic distortion of the reported mean temperature. Variations in this difference should be expected as the daylight hours are longer in summer than in winter with the extremes being in January and July. This is also a function of latitude where in Melbourne the extremes are 10 to 15 hours of daylight and Darwin 11 to 13 hours of daylight. However the period covered is from mid March to the end of April and lies between the extremes. It may well represent the average result.
However a full year is needed to establish the extent of the systematic distortions.
There is a systematic error using minimum and maximum recording thermometers. This is a consequence of the “one-way” temperature recording where, for example, a 10 minute 10C fluctuation in temperature would give a 0.50C increase in mean temperature rather than the properly weighted 0.010C change.
This preliminary analysis shows that around the Australian coast the mean temperature has been overestimated by 0.6 0C. If this is the general case throughout the year then the overall Australian temperature has been over estimated.
There is clearly a need to re-examine the reported Australian temperature record in the light of this analysis rather than the seemingly endless reworking of minimum and maximum temperature by adjustments.
If the mean land temperatures are overstated from averaging minimum and maximum temperatures and the air temperatures over the oceans are measured mean values then the blending of the two data sets creates a systematic distortion.
Computer models tuned by back-casting to reported measurements will in turn overstate feedback effects. This could be particularly the case for regional modelling and consequent projections.
Selected locations show the average of the 30 minute intervals for over 43 days from 18th March to 30th April. The figures show local times and errors on the mean, not standard deviations.
|Continental||Latitude 0S||Longitude0E||Numberof days|
|Coastal||Latitude 0S||Longitude0E||Numberof days|