Download - Uncertainties in early Central England temperatures

INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. 30: 1105–1113 (2010)Published online 25 June 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/joc.1967

Uncertainties in early Central England temperatures

David E. Parker*Met Office Hadley Centre, FitzRoy Road, Exeter EX1 3PB, UK

ABSTRACT: Uncertainties in historical climate records constrain our understanding of natural variability of climate,but estimation of these uncertainties enables us to place recent climate events and extremes into a realistic historicalperspective. Uncertainties in Central England temperature (CET) since 1878 have already been estimated; here we estimateuncertainties back to the start of the record in 1659, using Manley’s publications and more recently developed techniquesfor estimating spatial sampling errors. Estimated monthly standard errors are of the order of 0.5 °C up to the 1720s, but0.3 °C subsequently when more observing sites were used. Corresponding annual standard errors are up to nearly 0.4 °C inthe earliest years but around 0.15 °C after the 1720s. Daily standard errors from 1772, when the daily series begins, up to1877 are of the order of 1 °C because only a single site was used at any one time. Inter-diurnal variability in the daily CETrecord appears greater before 1878 than subsequently, partly because the sites were in the Midlands or southern Englandwhere day-to-day temperature variability exceeds that in the Lancashire part of Manley’s CET. Copyright 2009 RoyalMeteorological Society

KEY WORDS central England; temperature; uncertainty; biases; inter-diurnal variability

Received 5 February 2009; Revised 11 May 2009; Accepted 26 May 2009

1. Introduction

Natural climate variability is expected to continue, super-imposed on anthropogenic climate change. It is thereforenecessary to refine our knowledge and understanding ofhistorical natural variability, in order to properly inter-pret current events and to inform policy on adaptationto potential future events, especially extremes. However,our understanding of past variability needs to include esti-mates of uncertainty in the observations, to avoid naivetyin our application to the present day or to the future. Inthis paper, therefore, uncertainties in the Central Englandtemperature (CET) record are examined. Given the sub-stantial variability throughout the CET record from dailyup to multi-decadal timescales, it is clear that the futurecourse of CET will not be a monotonic anthropogenicwarming: the overall warming trend will appear erraticand there may be periods of stagnation, or even cool-ing, of multi-annual duration. We need to be preparedfor these irregularities and interpret them correctly.

The uncertainties in daily, monthly and annual max-imum, minimum and mean CET since 1878 have beenassessed by Parker and Horton (2005a). Here, therefore,we explore the uncertainties in the earlier CET record.This can be split into two sections: 1659–1771, whenwe have only Manley’s (1974) monthly mean series; and1772–1877, when we also have the daily mean CETseries developed by Parker et al. (1992) with the con-straint of matching Manley’s (1974) monthly averages.

* Correspondence to: David E. Parker, Met Office Hadley Centre,FitzRoy Road, Exeter EX1 3PB, UK.E-mail: [email protected]

There are no data for maximum or minimum CET before1878.

We do not have as detailed information on pre-1878 temperature measurements as for more recentobservations. However, the locations of the sites usedare in general recorded by Manley (1953, 1974) andby Parker et al. (1992), so we are able to estimatespatial sampling errors. We follow Parker and Horton(2005a) in using the method of Jones et al. (1997) (seealso Yevjevich (1972)) to calculate the areal samplingstandard error SE due to incomplete sampling of the CETregion:

SE2 = s2i r(1 − r)

1 + (n − 1)r(1)

where r = average correlation of each station with everyother stationn = number of stationsand the single-site temporal variance s2

i is given by

s2i = S2n

1 + (n − 1)r(2)

where S is the standard deviation of the combined series.Beyond that, we have Manley’s own expert opinion onthe uncertainties in his monthly series, expressed throughthe precision he accorded to the values.

In Section 2, we assess uncertainties in the monthlyCET record for 1659–1771 by combining Manley’sestimates with our calculated spatial sampling errors. InSection 3 we repeat this for 1772–1877, but we thenmake an alternative estimate in Section 4 using Manley’s

Copyright 2009 Royal Meteorological Society

1106 D. E. PARKER

(1946) Lancashire temperature series. In Section 5 weestimate uncertainties in daily CET for 1772–1877.However an additional concern affecting pre-1878 dailyCET is that Yan et al. (2001) found that its short-term (up to 3 days) variability showed a reduction in1877–1878 when the basis of the series changed froma single station to three stations. So we investigate thisproblem in Section 6 before drawing final conclusions inSection 7.

2. Monthly Temperatures for 1659–1771

Manley (1953, 1974) spliced together late 17th centuryand 18th century temperatures from individual observingsites to create a composite record. His basic techniquewas to use periods of overlap between records to bridgebackwards from more recent records. However there areperiods without adequate instrumental data, especiallyin the earlier years, so Manley also took somewhatsubjective account of other observations such as weatherand wind and the relative frequencies of snow versusrain. He also made use of temperatures observed between1707 and 1722 at Delft in the Netherlands (reduced to DeBilt (Utrecht) by Labrijn (1945)) – with the consequencethat agreement between the two series in this periodis imposed and cannot be used as validation (Jones,1999).

Manley (1974) described the earlier observations as“formidably open to doubt” and only estimated themonthly mean temperatures for 1659–1670 to the nearestdegree Celsius because the records were almost entirelynon-instrumental descriptions of the weather, which heinterpreted in terms of expected temperatures for particu-lar atmospheric circulation types or air masses accord-ing to modern instrumental data. For 1671–1698 and1707–1722 there were somewhat more instrumental data,including the Utrecht record, so Manley rounded to thenearest 0.5 °C. Owing to the availability of a better instru-mental record, Manley provided more precise estimatesfor 1699–1706; these are discussed separately below.

We take Manley’s precisions for 1659–1698 and1707–1722 as two standard errors. This is a strict inter-pretation because it implies that, even in the absence ofspatial sampling uncertainty, Manley would have cor-rectly rounded only 68% of the temperatures, because fora Gaussian distribution of errors, 32% lie outside ±1σ .We cautiously take Manley’s precisions to take account

of only calibration and record-splicing uncertainties, sowe augment them with spatial sampling uncertainties.These are estimated using Equation (1) with n = 1 andvalues of r and standard deviations based on Stonyhurst,Rothamsted and Ross-on-Wye (Table I), yielding typicalmonthly (annual) areal sampling standard errors SE of0.3 °C (0.1 °C). Adding the 0.3 °C areal sampling stan-dard error in quadrature yields overall monthly standarderrors of 0.6 °C for 1659–1670 and 0.4 °C for 1671–1698and 1707–1722. Owing to possible calibration biases,the calibration and record-splicing errors are likely tobe coherent between successive months so that annualcalibration and record-splicing standard errors will notbe as small as monthly calibration and record-splicingstandard errors divided by

√12. A more likely reduction

factor is√

2 because winter-half-year biases are likely tohave differed in nature from summer half-year biases asis true for many early unconventional instrumental expo-sures (Parker, 1994). Combination with the 0.1 °C annualareal sampling error yields overall annual standard errorsbetween 0.3 °C and 0.4 °C in 1659–1670 and 0.2 °C in1671–1698 and 1707–1722.

For 1699–1706 Manley (1953, 1974) used a three-times-daily instrumental record from Upminster, 15 mileseast of London and then outside the urban area. Giventhat he considered that the calibration and record-splicingerrors justified reporting monthly CET to the nearest0.1 °C and that standard errors of no more than 0.2 °Cwould justify this, we combine this with the 0.3 °Careal sampling standard error to estimate overall monthlystandard errors of between 0.3 °C and 0.4 °C. Using thesame assumption as above about the seasonal coherenceof calibration biases yields overall annual standard errorsof between 0.15 °C and 0.2 °C.

For 1723–1771 Manley (1953) used typically threewell-spaced locations, so the spatial sampling standarderrors are likely to have been similar to those for 1878onwards, namely 0.2 °C for monthly values and 0.06 °Cfor annual values (Parker and Horton, 2005a). If monthly(annual) calibration and record-splicing standard errorsare taken to be typically 0.2 °C (0.14 °C), then the overallstandard errors in monthly and annual CET are about0.3 °C and 0.15 °C respectively.

3. Monthly Temperatures for 1772–1877

For 1771–1814, Manley (1953) used four combinationsof sites. These generally consisted of five to seven

Table I. The constituent station variance (s2i ) (°C2) and the average of the correlations of each of Stonyhurst, Rothamsted and

Ross-on-Wye with each other station (r), for monthly and annual mean temperatures, 1931–1960, taken from Parker and Horton(2005b). From these are calculated the sampling standard error SE (°C) when only a single site is used (n = 1 in Equation (1)).

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual

s2i 3.28 4.10 2.58 1.43 1.14 0.77 1.00 1.34 1.28 1.13 1.30 2.62 0.21

r 0.97 0.96 0.97 0.96 0.90 0.88 0.91 0.95 0.93 0.94 0.93 0.96 0.95SE 0.31 0.40 0.27 0.23 0.32 0.29 0.29 0.25 0.29 0.25 0.29 0.32 0.10

Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 1105–1113 (2010)

UNCERTAINTIES IN EARLY CENTRAL ENGLAND TEMPERATURES 1107

individual sites or groups of sites, for example severalsites in London, and his own Lancashire series (Manley,1946). However he used some sites as cross-checksrather than as direct inputs to an areal average, so thespatial sampling standard errors are likely to have beencommensurate with those for three well-spaced sitesfor 1878 onwards cited above for 1723–1771. Givenmonthly (annual) calibration and record-splicing biasesof again typically 0.2 °C (0.14 °C), the overall monthlyand annual standard errors are again about 0.3 °C and0.15 °C.

For 1815–1877, Manley (1953, 1974) used 0.5 (Lan-cashire + Oxford Radcliffe Observatory). ApplyingEquation (1), with n = 2 stations, to the published Lan-cashire (Manley, 1946) and Oxford Radcliffe Observa-tory (Knox-Shaw and Balk, 1932) monthly and annualdata yields monthly areal sampling standard errors inthe range 0.21–0.34 °C and an annual sampling stan-dard error of 0.11 °C (Table II). Taking calibration andrecord-splicing biases of 0.15 °C and 0.1 °C on monthlyand annual timescales, given the more constant observ-ing sites and the improved instrumentation, especiallyat Oxford Radcliffe, the overall standard errors becomeabout 0.3–0.4 °C for monthly temperatures and 0.15 °Cfor annual temperatures.

These estimates for 1772–1877 are considered furtherin Section 4 below.

4. An Alternative Estimate of Monthly andLonger-term Errors and Biases for 1772–1877

Owing to the use of non-standard instruments and expo-sures, it is difficult to make and combine separate rig-orous estimates of calibration, precision, housing andsiting errors as was done for 1878 onwards by Parkerand Horton (2005a,b). So Sections 2 and 3 only gaveapproximate estimates based partly on Manley’s judge-ment in providing monthly CET to particular levels ofprecision. Here, however, we estimate the overall error ofCET on monthly, annual and longer timescales between1772 and 1877 by comparing CET anomalies with Man-ley’s (1946) Lancashire temperature anomalies. Manleyused his Lancashire series as a cornerstone in the devel-opment of his CET series. The differences are expectedto reflect a mixture of biases and areal sampling errorsin CET.

Figure 1 compares the monthly series for January,April, July and October; Figure 2 compares the annualseries. For 1815–1877, the anomaly of Oxford relative toCET is the mirror image of the anomaly for Lancashirebecause Manley (1953, 1974) used 0.5 (Lancashire +Oxford Radcliffe Observatory) in this period. So anoma-lies of (Lancashire minus Oxford) will be double the val-ues in the plots. Division of (Lancashire minus Oxford)by

√2 will yield a standard error estimate for the average

of the independent Lancashire and Oxford annual series,

Table II. Areal sampling standard errors in monthly and annual mean CET, 1815–1877 (°C).

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual

0.27 0.26 0.28 0.29 0.30 0.27 0.27 0.25 0.21 0.22 0.26 0.34 0.11

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Figure 1. Mean temperature anomalies (relative to 1901–1930), Lancashire (Manley, 1946) minus Central England (Manley, 1974), 1772–1945:January, April, July and October.


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Figure 2. As Figure 1, but annual.

i.e. CET. The plots scaled up by 2/√

2 after 1814 aregenerally consistent with the overall monthly and annualCET standard errors of 0.3 °C and 0.15 °C derived inSection 3. There are however a few outlier differencesthroughout the record, suggesting greater sampling errorsor station-specific biases in a few individual months.These outliers are generally not readily attributable toatmospheric circulation, but may sometimes be a result ofsea surface temperature anomaly patterns (Appendix 1).

The annual (Lancashire minus CET) series suggests acold bias in the Lancashire record, or warm bias in theremaining CET stations, of up to 0.4 °C in 1782–6. Thisdoes not align with station changes in Manley’s Lan-cashire or CET series and is unexplained. There wereno Royal Society London measurements in this period(Manley, 1946), but Manley had recourse to other Lon-don observations along with records for Lyndon (Rut-land) and Stroud extending from before until after thisperiod. Table IV of Manley (1946) shows that Lancashirewas less warm than usual compared with Edinburgh inthe 1780s, but Manley regarded that as typical of colddecades – implicitly, therefore, as an areal sampling phe-nomenon. The annual average temperature at Lyndonwas 8.40 °C in 1782–1786 and 9.47 °C in 1777–1781(Barker, 1777–1789) Use of Barker’s indoor temperaturein December 1786, when Barker’s outdoor thermome-ter was broken, along with an average (1777–1785 with1787–1788) December outdoor minus indoor tempera-ture, causes an uncertainty of no more than 0.02 °C forthe 5-year average. The difference 8.40 °C − 9.47 °C =−1.07 °C compares with −1.21 °C in CET and −1.59 °Cin Manley’s Lancashire series. Exclusion of the Lan-cashire series from CET would reduce the cooling from1777–1781 to 1782–1786, implying that the remain-ing stations support Lyndon. However it is not possi-ble to compare CET, Lyndon and Lancashire recordsfor 1782–1786 and subsequent years in a similar way,because Barker broke his thermometer in December 1786and its replacement is likely to have been biased relativeto the instrument used until December 1786 (Manley,1952; see also Appendix 2).

The low-pass filtered plots of anomalies of (Lancashireminus CET) in Figure 3 offer an insight into long-termbiases in Manley’s CET. As anomalies of (Lancashireminus CET) from 1815 onwards are generally in therange ±0.2 °C in the winter and summer half-years and±0.1 °C annually, then anomalies of (Lancashire minusOxford) will be in the range ±0.4 °C in the winter andsummer half-years and ±0.2 °C annually. Division by

√2

to yield a bias standard error estimate for the average

of the independent Lancashire and Oxford annual series,i.e. annual CET, yields ±0.14 °C. However there maybe real anomaly gradients, so annually-averaged long-term biases in 1815–1877 are probably within ±0.1 °C.The long-term biases may however approach ±0.2 °C inthe winter and summer half-years in 1815–1877, and theannual biases may also approach ±0.2 °C between 1772and 1814 when (Lancashire minus CET) is sometimes aslow as −0.2 °C annually. Around 1782–1786 biases mayreach ±0.25 °C.

These estimates concur well with the more subjec-tive estimates of annual standard errors of 0.15 °C for1772–1877 in Section 3.

5. Daily Temperatures for 1772–1877:Uncertainties

For daily mean CET, a sequence of single stations isused between 1772 and 1877, in contrast to the use ofthree or four sites thereafter (Parker et al., 1992). Whenrecent data for Stonyhurst, Rothamsted and Ross-on-Wyeare used to calculate r and s2

i , estimated daily areal sam-pling standard errors for a single station (n = 1) are in therange 0.87–1.00 °C. When data for Stonyhurst, Rotham-sted and Cambridge Botanical Gardens are used, theestimated daily areal sampling standard errors are in therange 0.92–1.09 °C. Thus we can anticipate daily arealsampling standard errors around 1 °C for the 1772–1877CET; possibly more when London stations were usedthan when Thomas Barker’s more central Rutland sta-tion was used (1777–1789). The total errors will remainaround 1 °C after in-quadrature combination of the dailysampling errors with the monthly bias errors becausethese are estimated to be at most 0.25 °C up to 1814 andat most 0.2 °C thereafter (Sections 3 and 4). These resultsare in accord with the discussion of the late 18th centurydaily data in the Appendix of Parker et al. (1992). Thereading precision error (see also Section 2.2 of Parker andHorton, 2005a) is likely to be very small: for example,Barker (1777–1789) recorded temperatures to the nearest0.1 °F. The daily standard errors in 1772–1877 comparewith typically 0.6 °C for more recent daily mean CET(Parker and Horton, 2005a).

6. Daily Temperatures for 1772–1877:Inter-diurnal Variability

Yan et al. (2001) analysed daily CET on ‘daily’timescales (up to 3 days), ‘weather’ timescales (5 daysto 2 months), and ‘seasonal’ timescales (8–17 months).



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Figure 3. Mean April to September, October to March and annual temperature anomalies (relative to 1901–1930), Lancashire (Manley, 1946)minus Central England (Manley, 1974), 1772–1945. The series have been smoothed with a 21-point binomial filter, to show decadal and

longer-term changes.

Table III. Standard-deviation-reduction factors for daily CET anomalies from Parker et al. (1992) (b) and for inter-diurnal CETchanges (bd1).

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

b 0.90 0.90 0.90 0.89 0.88 0.86 0.86 0.86 0.89 0.89 0.89 0.90bd1 0.91 0.88 0.85 0.86 0.84 0.85 0.84 0.82 0.85 0.86 0.87 0.89

Even though Parker et al. (1992) reduced the overallexcessive variability pre-1878 to compensate for the useof a sequence of single sites, Yan et al. (2001) foundthat ‘daily’ variability in CET was greater pre-1878 thansubsequently.

To investigate this, we define daily variability as thestandard deviation σ1 of the differences d1 betweensuccessive days’ mean CET anomalies relative to 11-term binomially filtered 1961–1990 daily normals (Joneset al., 1999). We calculated σ1 from the Parker et al.(1992) daily series, as a function of month and year.Then we calculated the influence of the change in thenumber of stations on σ1 as follows. First, inter-diurnaldifferences d1s were calculated for each of the constituentCET stations Rothamsted, Ross-on-Wye and Stonyhurstfor 1931–1960 when the data were complete and (Parkerand Horton, 2005a) unbiased. Then the correlation of d1s

between each possible pair of stations was calculated andused to find the average inter-station correlation rd1s foreach calendar month, from which a standard-deviation-reduction factor bd1 = √

[(1 + 2rd1s)/3] (Equation (2)and Yevjevich, 1972) was calculated. The top rowof Table III gives the temperature anomaly standard-deviation-reduction factors b for each calendar month

from Parker et al. (1992) and the lower row gives bd1.bd1 is generally little smaller than b, and in January itexceeds b, so scaling the pre-1878 σ1 by bd1 instead ofby b would not lead to values much smaller than theoriginal σ1, whereas plots of σ1 based on the Parkeret al. (1992) series (Figure 4, solid lines) suggest that anadjustment of up to 20% is required, especially in winter.So the variation of the spatial coherence of temperaturechanges with timescale is not the main reason for theexcess inter-diurnal variability in the pre-1878 daily CETrecord.

The stations used for pre-1878 daily CET were con-fined to London, Rutland and Oxford (Parker et al.(1992)). In particular no Lancashire station was used,whereas Stonyhurst was used in the three-station seriesfrom 1878 onwards. To assess the effects of this, we com-pared climatological values of σ1 for Rothamsted, Ross-on-Wye and Stonyhurst for 1931–1960 and found σ1

to be typically 10–20% lower at Stonyhurst (Table IV).σ1 is also typically lower at Ringway and Squires Gatethan at the more southern stations used in 1961–1990(Table V). Local topography also affects σ1 which willbe reduced at exposed sites where extreme cold nightsare less pronounced. But the real regional differences


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Figure 4. Decadal standard deviations of differences between successive days’ CET anomalies, 1781–1790 through 1991–2000. The solid linesare based on the original Parker et al. (1992) series. The dashed lines are scaled down before 1878 to compensate for the use of a single station

in the Midlands or southern England.

Table IV. Standard deviations of inter-diurnal temperature differences (°C) at CET stations and for the actual CET record,1931–1960.


a) Ross-on-Wye 2.24 2.13 1.99 1.89 1.93 2.02 1.79 1.76 1.99 2.13 2.15 2.17b) Rothamsted 2.12 2.01 1.98 1.99 1.99 1.99 1.89 1.78 2.11 2.07 2.06 1.99c) Stonyhurst 1.93 1.67 1.68 1.69 1.77 1.79 1.64 1.59 1.74 1.74 1.74 1.84d) σ1south = √

(a2 + b2) 2.18 2.07 1.99 1.94 1.96 2.01 1.84 1.77 2.05 2.10 2.11 2.08e) CET 1.92 1.74 1.62 1.62 1.61 1.66 1.51 1.41 1.66 1.72 1.75 1.80f) bs = (e)/(d) 0.88 0.84 0.81 0.84 0.82 0.83 0.82 0.80 0.81 0.82 0.83 0.87

Table V. Standard deviations of inter-diurnal temperature differences (°C) at CET stations and composite stations, and for theactual CET record, 1961–1990.


a) Malvern 2.08 1.89 1.91 1.87 1.74 1.85 1.80 1.65 1.88 1.97 2.18 2.20b) Rothamsted 1.99 1.80 1.92 2.01 1.92 1.95 1.91 1.89 1.96 2.03 2.18 2.10c) Ringway 1.92 1.81 1.82 1.84 1.79 1.89 1.73 1.75 1.84 1.82 2.13 2.04d) Squires Gate 1.90 1.77 1.77 1.87 1.81 1.80 1.56 1.72 1.90 1.93 2.10 2.06e) Composite = 0.5 (Ringway + Squires Gate) 1.82 1.70 1.68 1.71 1.64 1.67 1.47 1.58 1.73 1.75 2.00 1.95f) σ1south = √

(a2 + b2) 2.04 1.85 1.92 1.94 1.83 1.90 1.86 1.77 1.92 2.00 2.18 2.15g) CET 1.82 1.63 1.64 1.64 1.53 1.59 1.48 1.46 1.62 1.70 1.92 1.91h) bsa = (g)/(f) 0.89 0.88 0.85 0.85 0.84 0.84 0.80 0.82 0.84 0.85 0.88 0.89



Figure 5. Root-mean square differences (°C) between successive daysmean temperatures in January (upper panel) and July (lower panel),

1961–1990. Note the slightly different scales.

in σ1 are confirmed by the maps of σ1 for Januaryand July 1961–1990 in Figure 5, based on the 5 kmresolution gridded daily maximum and minimum tem-perature datasets created in support of the UKCIP08project (Jenkins et al., 2007). So we have developeda new standard-deviation-reduction factor bs. First, the1931–1960 values of σ1 for the southern regions sam-pled by the pre-1878 daily stations were taken to bethe root-mean square of the 1931–1960 values of σ1

for Rothamsted and Ross-on-Wye (Table IV, row (d)),here denoted σ1south. Then, the values of σ1 for CETfor 1931–1960 were calculated (Table IV, row (e)), anddivided by σ1south to yield bs (Table IV, row (f)) whichis slightly smaller than bd1. Because it relates the inter-diurnal variability of a single southern station directlyto that of CET, bs compensates for both the spatialcorrelation and the geographic variation of inter-diurnalvariability. This direct calculation also circumvents theassumption of equal station variances made in the aboveuse of the Yevjevich (1972) formula. Comparison of b,bd1 and bs suggests that the southern location of the pre-1878 daily CET stations is a greater contributor to theexcess inter-diurnal variability, than the mere use of asingle station, especially in winter. Figure 4 shows theoverall impact of scaling σ1 by bs/b in each calendar

month. The pre-1878 σ1 has been reduced but there is stillenhanced inter-diurnal variability before 1878 betweenNovember and January and to a lesser extent in February.If bs is replaced by the alternative values bsa calculatedfor 1961–1990 using the different set of stations in use inthat period (Table V) the effect on pre-1878 σ1 is a littleweaker. The differences between bs and bsa are likely tohave arisen from real differences in weather and climatebetween 1931–1960 and 1961–1990, as well as from themicroclimatic effects of using different stations. Becausethree stations were used in 1931–1960, the use of bs inthe scaling is the preferred choice for adjusting pre-1878σ1 to be equivalent to a three-station record.

The residual enhanced σ1 is centred on the wintersolstice, not on the meteorological winter (Figure 4). Thismay imply enhanced radiative cooling of instrumentswith non-standard exposure on clear, and therefore cold,days and nights. During the rest of the year theremay be less effect on daily mean CET because night-time radiative cooling may be balanced by daytimeheating from reflected insolation. For example, the overallbiases in temperatures measured from Glaisher standsare negative at night throughout the year, and negative(positive) by day in winter (summer) (Parker, 1994).However, spurious cooling on cold winter days and nightsis not borne out by the skewness of daily CET in winter,which is not systematically different in 1772–1877 thanin 1878–2007 (Table VI). The slightly reduced positiveskewness in summer in 1772–1877 (Table VI) is likelyto have arisen from the absence of northwestern stationswhich have slightly greater skewness in summer thanmidland and southern stations (Table VII; see also theAppendix of Parker et al., 1992).

7. Conclusions

Monthly CET up to 1722 has a standard error of estimateof the order of 0.5 °C, except for 1699–1706 when agood instrumental record reduced the estimated standarderror below 0.4 °C. From 1722 to 1877 the standard erroris typically 0.3 °C. Corresponding annual standard errorsare up to nearly 0.4 °C in the earliest years but around0.15 °C after 1722. The estimates from 1772 onwards

Table VI. Skewness of daily CET, g = n−1∑

(t − m)3/(n−1∑

(t − m)2)3/2. Here t is the daily CET anomaly (°C) relative to11-term binomially filtered 1961–1990 daily normals, m is the sample average which may not be zero outside 1961–1990, and n

is the sample size in days. The standard errors of g are sg = [6n′(n′ − 1)(n′ − 2)−1(n′ + 1)−1(n′ + 3)−1]0.5 (Fisher, 1931) wheren′ is an effective sample size of 4.5 (6.5) days per month in winter (summer) to allow for lag 1 day autocorrelation 0.75 (0.65)(Equation 4.11 of Trenberth, 1984). This gives sg = 0.112 (0.093) for 1772–1877, and 0.101 (0.084) for 1878–2007 in winter(summer). The standard errors of the differences between periods are, by combining in quadrature, approximately 0.15 (0.13)in winter (summer). Therefore differences outside ±0.30 (0.26) in winter (summer) (bold) are significant at the 95% level of

confidence.


a) 1772–1877 −0.27 −0.34 −0.05 −0.00 0.04 0.28 0.38 0.14 −0.02 −0.15 0.07 −0.23b) 1878–2007 −0.40 −0.29 −0.12 0.11 0.21 0.44 0.52 0.48 0.08 −0.08 −0.09 −0.25a) – b) 0.13 −0.05 0.07 −0.11 −0.17 −0.16 −0.14 −0.34 −0.10 −0.07 0.16 0.02


1112 D. E. PARKER

Table VII. Skewness of daily CET at constituent CET stations, 1931–1960 and 1961–1990. Standard errors sg are approximately0.21 (0.17) in winter (summer), so differences need to be 0.59 (0.48) or more in winter (summer) to be significant at the 95%

level of confidence.


Ross-on-Wye 1931–1960 −0.19 −0.21 0.01 0.09 0.20 0.48 0.50 0.26 −0.06 −0.09 −0.07 −0.26Rothamsted 1931–1960 −0.12 −0.17 −0.07 0.27 0.34 0.50 0.43 0.26 0.12 0.04 0.15 −0.09Stonyhurst 1931–1960 −0.27 −0.13 0.05 0.21 0.23 0.73 0.69 0.49 0.01 −0.11 −0.16 −0.18Malvern 1961–1990 −0.66 −0.10 −0.09 0.02 0.42 0.60 0.65 0.56 0.07 0.01 0.03 −0.32Rothamsted 1961–1990 −0.53 −0.20 0.09 0.09 0.35 0.42 0.44 0.32 0.09 0.07 0.07 −0.09Ringway 1961–1990 −0.39 −0.07 0.12 0.21 0.50 0.60 0.79 0.74 0.16 −0.00 −0.07 −0.21Squires Gate 1961–1990 −0.61 −0.26 −0.20 −0.00 0.46 0.55 1.00 0.48 −0.44 −0.23 −0.25 −0.62(Ringway + Squires Gate)/2 1961–1990 −0.50 −0.16 −0.03 0.14 0.54 0.61 0.95 0.74 −0.10 −0.09 −0.15 −0.41

are mainly supported by comparison with Manley’sLancashire series, but there is an uncertainty of the orderof a quarter of a degree in the intensity of the cold interval1782–1786. Annual average biases for 1815–1877 aremainly within ±0.1 °C, so are small enough to allow CETto be a very reliable monitor of climate variability andchange in that period.

Daily CET before 1878, being based on a single siteat any one time, has a standard error of about 1 °C; thisneeds to be taken into account when assessing recentextremes. Inter-diurnal variability in the daily CET recordappears greater before 1878 than subsequently, partlybecause the sites were in the Midlands or southern Eng-land where inter-diurnal temperature variability exceedsthat in the Lancashire part of Manley’s CET. A furthercontribution may have been non-standard instrumentalexposure.

Acknowledgements

Daily temperatures for Rothamsted were provided by GillTuck of Rothamsted Research. This paper was supportedby the Joint DECC, Defra and MoD Integrated ClimateProgramme – GA01101, CBC/2B/0417 Annex C5 and isBritish Crown copyright.

Appendix 1. Differences between Anomalies ofLancashire and CET in Specific Months

Manley’s Lancashire was anomalously cold relativeto his CET in January 1781, 1783, 1806 and 1809(Figure 1a). However daily Lamb atmospheric circula-tion types (Lamb, 1972) for January 1781 and 1783compiled by Kington (1988), along with average dailyCET and Stonyhurst (Lancashire) temperatures for each

Lamb type for 1878–1958 (the period of most reliableStonyhurst data Parker et al., (1992)), do not imply thatCET and Lancashire temperature anomalies should havediffered by more than 0.2 °C. In the other two Januariesdaily Lamb types are not available but the predominantflow was westerly or cyclonic (Lamb and Johnson, 1966)suggesting more frequent intrusions of cold Arctic airinto Lancashire than further south. The Kington (1988)Lamb types for April 1781 do not imply the relativelywarm Lancashire seen in Figure 1b. There are no dailyLamb types or Lamb and Johnson (1966) analyses of sealevel pressure for April 1817. The Lamb types for April1917 in Lamb’s (1972) catalogue do not imply that Lan-cashire should have been relatively less cold than CentralEngland, but sea surface temperature anomalies (Rayneret al., 2003) were more negative towards the east andsouth of England following the severe 1916–1917 win-ter. The Kington (1988) daily Lamb types for July 1781do not support a relatively warm Lancashire. The rel-atively cold October in Lancashire in 1783 (Figure 1d)is not supported by the Lamb types given by (Kington,1988).

Appendix 2. A Bias in Thomas Barker’sTemperature Record

Manley (1952) noted that when Thomas Barker brokehis outdoor thermometer in December 1786 and replacedit in January 1787, the difference between the indoorand outdoor readings underwent a systematic change,indicating a discontinuity in Barker’s outdoor record.Table A2.1 confirms this: the discontinuity is of the orderof 0.7 °C with the later outdoor data being relatively lesscold. The daily CET record (Parker et al., 1992) is notaffected by this discontinuity because it is anchored toManley’s monthly CET.

A2.1 Annual average indoor and outdoor temperatures (°C) at Lyndon, Rutland, and their differences, 1777–1788.

1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788

a) Indoor 10.07 10.36 11.56 10.19 11.31 9.34 11.02 9.36 9.92 9.58 10.26 10.34b) Outdoor 8.85 9.29 10.21 8.93 10.05 8.05 9.44 7.78 8.55 8.19 9.62 9.74b) – a) −1.22 −1.07 −1.35 −1.26 −1.26 −1.29 −1.58 −1.58 −1.37 −1.39 −0.64 −0.60



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