Uncertainties in early Central England temperatures

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INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. 30: 11051113 (2010)Published online 25 June 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/joc.1967Uncertainties in early Central England temperaturesDavid E. Parker*Met Office Hadley Centre, FitzRoy Road, Exeter EX1 3PB, UKABSTRACT: 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 Manleys 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 Manleys CET. Copyright 2009 RoyalMeteorological SocietyKEY WORDS central England; temperature; uncertainty; biases; inter-diurnal variabilityReceived 5 February 2009; Revised 11 May 2009; Accepted 26 May 20091. IntroductionNatural 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: 16591771, whenwe have only Manleys (1974) monthly mean series; and17721877, when we also have the daily mean CETseries developed by Parker et al. (1992) with the con-straint of matching Manleys (1974) monthly averages.* Correspondence to: David E. Parker, Met Office Hadley Centre,FitzRoy Road, Exeter EX1 3PB, UK.E-mail: david.parker@metoffice.gov.ukThere 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 s2i is given bys2i =S2n1 + (n 1)r (2)where S is the standard deviation of the combined series.Beyond that, we have Manleys 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 16591771 by combining Manleysestimates with our calculated spatial sampling errors. InSection 3 we repeat this for 17721877, but we thenmake an alternative estimate in Section 4 using ManleysCopyright 2009 Royal Meteorological Society1106 D. E. PARKER(1946) Lancashire temperature series. In Section 5 weestimate uncertainties in daily CET for 17721877.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 in18771878 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 16591771Manley (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 asformidably open to doubt and only estimated themonthly mean temperatures for 16591670 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 16711698 and17071722 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 16991706; these are discussed separately below.We take Manleys precisions for 16591698 and17071722 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 1 .We cautiously take Manleys precisions to take accountof 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 16591670 and 0.4 C for 16711698and 17071722. 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 by12. A more likely reductionfactor is2 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 16591670 and 0.2 C in16711698 and 17071722.For 16991706 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 17231771 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 17721877For 17711814, Manley (1953) used four combinationsof sites. These generally consisted of five to sevenTable I. The constituent station variance (s2i ) (C2) and the average of the correlations of each of Stonyhurst, Rothamsted andRoss-on-Wye with each other station (r), for monthly and annual mean temperatures, 19311960, 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 Annuals2i 3.28 4.10 2.58 1.43 1.14 0.77 1.00 1.34 1.28 1.13 1.30 2.62 0.21r 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 0.10Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)UNCERTAINTIES IN EARLY CENTRAL ENGLAND TEMPERATURES 1107individual 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 17231771. 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 18151877, 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 0.210.34 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 0.30.4 C for monthly temperatures and 0.15 Cfor annual temperatures.These estimates for 17721877 are considered furtherin Section 4 below.4. An Alternative Estimate of Monthly andLonger-term Errors and Biases for 17721877Owing 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 Manleys 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-leys (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 18151877, 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)by2 will yield a standard error estimate for the averageof the independent Lancashire and Oxford annual series,Table II. Areal sampling standard errors in monthly and annual mean CET, 18151877 (C).Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual0.27 0.26 0.28 0.29 0.30 0.27 0.27 0.25 0.21 0.22 0.26 0.34 0.111750 1800 1850 1900 1950-2-1012deg CJanuary1750 1800 1850 1900 1950-2-1012deg CJuly1750 1800 1850 1900 1950-2-1012deg Cdeg CApril1750 1800 1850 1900 1950-2-1012October(a) (b)(c) (d)Figure 1. Mean temperature anomalies (relative to 19011930), Lancashire (Manley, 1946) minus Central England (Manley, 1974), 17721945:January, April, July and October.Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)1108 D. E. PARKER1750 1800 1850 1900 1950-0.6-0.4- CFigure 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 17826. Thisdoes not align with station changes in Manleys 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 17821786 and 9.47 C in 17771781(Barker, 17771789) Use of Barkers indoor temperaturein December 1786, when Barkers outdoor thermome-ter was broken, along with an average (17771785 with17871788) 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 Manleys Lancashire series. Exclusion of the Lan-cashire series from CET would reduce the cooling from17771781 to 17821786, implying that the remain-ing stations support Lyndon. However it is not possi-ble to compare CET, Lyndon and Lancashire recordsfor 17821786 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 Manleys CET. As anomalies of (Lancashireminus CET) from 1815 onwards are generally in therange 0.2 C in the winter and summer half-years and0.1 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 2to yield a bias standard error estimate for the averageof 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 18151877 are probably within 0.1 C.The long-term biases may however approach 0.2 C inthe winter and summer half-years in 18151877, 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 17821786 biases mayreach 0.25 C.These estimates concur well with the more subjec-tive estimates of annual standard errors of 0.15 C for17721877 in Section 3.5. Daily Temperatures for 17721877:UncertaintiesFor 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 s2i , estimated daily areal sam-pling standard errors for a single station (n = 1) are in therange 0.871.00 C. When data for Stonyhurst, Rotham-sted and Cambridge Botanical Gardens are used, theestimated daily areal sampling standard errors are in therange 0.921.09 C. Thus we can anticipate daily arealsampling standard errors around 1 C for the 17721877CET; possibly more when London stations were usedthan when Thomas Barkers more central Rutland sta-tion was used (17771789). 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 (17771789) recorded temperatures to the nearest0.1 F. The daily standard errors in 17721877 comparewith typically 0.6 C for more recent daily mean CET(Parker and Horton, 2005a).6. Daily Temperatures for 17721877:Inter-diurnal VariabilityYan et al. (2001) analysed daily CET on dailytimescales (up to 3 days), weather timescales (5 daysto 2 months), and seasonal timescales (817 months).Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)UNCERTAINTIES IN EARLY CENTRAL ENGLAND TEMPERATURES 11091750 1800 1850 1900 1950-0.6-0.4- Cdeg Cdeg CApril to September1750 1800 1850 1900 1950-0.6-0.4- to March1750 1800 1850 1900 1950-0.6-0.4- 3. Mean April to September, October to March and annual temperature anomalies (relative to 19011930), Lancashire (Manley, 1946)minus Central England (Manley, 1974), 17721945. The series have been smoothed with a 21-point binomial filter, to show decadal andlonger-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 Decb 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 0.89Even 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 1 of the differences d1 betweensuccessive days mean CET anomalies relative to 11-term binomially filtered 19611990 daily normals (Joneset al., 1999). We calculated 1 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 1 as follows. First, inter-diurnaldifferences d1s were calculated for each of the constituentCET stations Rothamsted, Ross-on-Wye and Stonyhurstfor 19311960 when the data were complete and (Parkerand Horton, 2005a) unbiased. Then the correlation of d1sbetween 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 monthfrom 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 1 by bd1 instead ofby b would not lead to values much smaller than theoriginal 1, whereas plots of 1 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 1 for Rothamsted, Ross-on-Wye and Stonyhurst for 19311960 and found 1to be typically 1020% lower at Stonyhurst (Table IV).1 is also typically lower at Ringway and Squires Gatethan at the more southern stations used in 19611990(Table V). Local topography also affects 1 which willbe reduced at exposed sites where extreme cold nightsare less pronounced. But the real regional differencesCopyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)1110 D. E. PARKERJan1750 1800 1850 1900 1950 2000decade ending1. Cdeg Cdeg Cdeg Cdeg Cdeg Cdeg Cdeg Cdeg Cdeg Cdeg Cdeg CFeb1750 1800 1850 1900 1950 2000decade ending1. 1800 1850 1900 1950 2000decade ending1. 1800 1850 1900 1950 2000decade ending1. 1800 1850 1900 1950 2000decade ending1. 1800 1850 1900 1950 2000decade endingdecade endingdecade endingdecade endingdecade endingdecade endingdecade ending1. 1800 1850 1900 1950 20001. 1800 1850 1900 1950 20001. 1800 1850 1900 1950 20001. 1800 1850 1900 1950 20001. 1800 1850 1900 1950 20001. 1800 1850 1900 1950 20001. 4. Decadal standard deviations of differences between successive days CET anomalies, 17811790 through 19912000. 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 stationin the Midlands or southern England.Table IV. Standard deviations of inter-diurnal temperature differences (C) at CET stations and for the actual CET record,19311960.Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Deca) 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) 1south = (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 0.87Table V. Standard deviations of inter-diurnal temperature differences (C) at CET stations and composite stations, and for theactual CET record, 19611990.Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Deca) 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) 1south = (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 0.89Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)UNCERTAINTIES IN EARLY CENTRAL ENGLAND TEMPERATURES 1111Figure 5. Root-mean square differences (C) between successive daysmean temperatures in January (upper panel) and July (lower panel),19611990. Note the slightly different scales.in 1 are confirmed by the maps of 1 for Januaryand July 19611990 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, the19311960 values of 1 for the southern regions sam-pled by the pre-1878 daily stations were taken to bethe root-mean square of the 19311960 values of 1for Rothamsted and Ross-on-Wye (Table IV, row (d)),here denoted 1south. Then, the values of 1 for CETfor 19311960 were calculated (Table IV, row (e)), anddivided by 1south 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 1 by bs/b in each calendarmonth. The pre-1878 1 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 19611990 using the different set of stations in use inthat period (Table V) the effect on pre-1878 1 is a littleweaker. The differences between bs and bsa are likely tohave arisen from real differences in weather and climatebetween 19311960 and 19611990, as well as from themicroclimatic effects of using different stations. Becausethree stations were used in 19311960, the use of bs inthe scaling is the preferred choice for adjusting pre-18781 to be equivalent to a three-station record.The residual enhanced 1 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 17721877 thanin 18782007 (Table VI). The slightly reduced positiveskewness in summer in 17721877 (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. ConclusionsMonthly CET up to 1722 has a standard error of estimateof the order of 0.5 C, except for 16991706 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 onwardsTable VI. Skewness of daily CET, g = n1(t m)3/(n1(t m)2)3/2. Here t is the daily CET anomaly (C) relative to11-term binomially filtered 19611990 daily normals, m is the sample average which may not be zero outside 19611990, and nis 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 17721877, and 0.101 (0.084) for 18782007 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 ofconfidence.Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Deca) 17721877 0.27 0.34 0.05 0.00 0.04 0.28 0.38 0.14 0.02 0.15 0.07 0.23b) 18782007 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 0.02Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)1112 D. E. PARKERTable VII. Skewness of daily CET at constituent CET stations, 19311960 and 19611990. 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.Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecRoss-on-Wye 19311960 0.19 0.21 0.01 0.09 0.20 0.48 0.50 0.26 0.06 0.09 0.07 0.26Rothamsted 19311960 0.12 0.17 0.07 0.27 0.34 0.50 0.43 0.26 0.12 0.04 0.15 0.09Stonyhurst 19311960 0.27 0.13 0.05 0.21 0.23 0.73 0.69 0.49 0.01 0.11 0.16 0.18Malvern 19611990 0.66 0.10 0.09 0.02 0.42 0.60 0.65 0.56 0.07 0.01 0.03 0.32Rothamsted 19611990 0.53 0.20 0.09 0.09 0.35 0.42 0.44 0.32 0.09 0.07 0.07 0.09Ringway 19611990 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 19611990 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 19611990 0.50 0.16 0.03 0.14 0.54 0.61 0.95 0.74 0.10 0.09 0.15 0.41are mainly supported by comparison with ManleysLancashire series, but there is an uncertainty of the orderof a quarter of a degree in the intensity of the cold interval17821786. Annual average biases for 18151877 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 Manleys CET. A furthercontribution may have been non-standard instrumentalexposure.AcknowledgementsDaily 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 MonthsManleys 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 eachLamb type for 18781958 (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 Lambs (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 19161917 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 BarkersTemperature RecordManley (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 Barkers 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 toManleys monthly CET.A2.1 Annual average indoor and outdoor temperatures (C) at Lyndon, Rutland, and their differences, 17771788.1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788a) 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 0.60Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)UNCERTAINTIES IN EARLY CENTRAL ENGLAND TEMPERATURES 1113ReferencesBarker T. 17771789. Meteorological Register made at LyndonHall, Rutland. Unpublished manuscript available in NationalMeteorological Library and Archive: Exeter, UK, 371.Fisher RA. 1931. The moments of the distribution for normal samplesof measures of departure from normality. 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Central England temperatures: monthly means 1659to 1973. Quarterly Journal of the Royal Meteorological Society 100:389405.Parker DE. 1994. Effects of changing exposure of thermometers at landstations. International Journal of Climatology 14: 131.Parker DE, Horton EB. 2005a. Uncertainties in Central EnglandTemperature 18782003 and some improvements to the maximumand minimum series. International Journal of Climatology 25:11731188.Parker DE, Horton EB. 2005b. Uncertainties in Central England Tem-perature 1878-2003 and some improvements to the maximum andminimum series. Hadley Centre Technical Note 63: This documentis available at http://www.metoffice.gov.uk/publications/HCTN/index.html.Parker DE, Legg TP, Folland CK. 1992. A new daily CentralEngland Temperature series. International Journal of Climatology12: 317342.Rayner NA, Parker DE, Horton EB, Folland CK, Alexander LV,Rowell DP, Kent EC, Kaplan A. 2003. Global analyses of seasurface temperature, sea ice, and night marine air temperaturesince the late nineteenth century. Journal of Geophysical Research108(D14): 4407. DOI:10.1029/2002JD002670.Trenberth KE. 1984. Some effects of finite sample size and persistenceon meteorological statistics. Part II: potential predictability. MonthlyWeather Review 112: 23692379.Yan Z, Jones PD, Moberg A, Bergstrom H, Davies TD, Yang C. 2001.Recent trends in weather and seasonal cycles: an analysis of dailydata from Europe and China. Journal of Geophysical Research 106:51235138.Yevjevich V. 1972. Probability and Statistics in Hydrology. WaterResources Publications, Fort Collins, Co.: USA; 302.Copyright 2009 Royal Meteorological Society Int. J. Climatol. 30: 11051113 (2010)


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