Thursday, June 18, 2015

Anomaly base periods - monthly variation

It's easy to think of changing the base period for calculating temperature anomalies as having the effect of simply shifting the values up or down by a fixed amount. And for annual averages, this is true. But for monthly averages, it isn't, quite. Suppose, like HADCRUT, you express anomalies to a base 1961-90. That means that all Januarys are expressed relative to the January average for that time, etc. If you shift to a different period, those monthly bases will shift relative to each other. That is one reason for using a longish period (30 years). A long anomaly average will fluctuate less from month to month.

This effect was noted by commenter Olof, in relation to the April-May discrepancy between NCEP/NCAR and GISS of about 0.1°C. My NCEP index uses a base period 1994-2013 (where data is good); GISS uses 1961-90. If you extract GISS averages over 1994-2013, you get this:
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1994-20130.5070.5470.5680.5330.4980.5150.5040.5190.5280.5480.580.503

There is an expected drop from 0.568°C to 0.533°C of GISS relative to NCAR/NCEP on the latter's base period. In shifting to the later base, you would need to subtract these values for each month. That would raise May relative to April, and even more relative to March. This means that, because it seems May's were actually rather cool during this time, the NCEP index is always going to tend to give a higher anomaly.

This clearly explains only part of the discrepancy. But I thought it was worthwhile calculating all of the common indices on all base periods likely to be used, where possible (ie they have data). There is a table below the fold.

Here is is. You can generally recognise the native base period by a string of zeroes (for those periods I zeroed rounding discrepancies). BEST uses 1951-80, but for some reason doesn't give exactly zero. RSS uses 1979-98, which I haven't included.

HadCRUT
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.064-0.067-0.098-0.061-0.061-0.035-0.038-0.032-0.039-0.047-0.062-0.057
1961-1990000000000000
1971-20000.1230.1440.120.1180.1040.1090.110.110.0950.0840.0760.108
1981-20100.3250.340.3220.2990.2720.2810.2860.2970.270.2850.2670.27
1994-20130.4070.4480.4390.4390.3960.4230.4360.4430.4140.440.440.383
GISSlo
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980000000000000
1961-19900.1020.0960.1330.0920.0990.0780.0830.0740.0730.0650.0730.084
1971-20000.2420.2580.2620.2330.2210.2130.2090.1960.1840.1730.1820.219
1981-20100.4280.4470.4570.4050.3840.380.3770.3720.3730.3790.3820.386
1994-20130.5070.5470.5680.5330.4980.5150.5040.5190.5280.5480.580.503
NOAAlo
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.23-0.246-0.243-0.235-0.211-0.192-0.184-0.187-0.181-0.182-0.181-0.221
1961-1990-0.133-0.149-0.119-0.135-0.119-0.122-0.117-0.121-0.116-0.111-0.099-0.137
1971-2000000000000000
1981-20100.1760.1790.1890.1690.1630.1650.1620.1680.1580.1770.1730.14
1994-20130.2450.2740.2860.2920.2830.2980.3040.3080.3050.330.3360.239
UAH6.beta
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980NANANANANANANANANANANANA
1961-1990NANANANANANANANANANANANA
1971-2000NANANANANANANANANANANANA
1981-2010000000000000
1994-20130.0950.1020.080.1030.0860.1020.1180.120.1640.1260.0950.078
RSS.MSU
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980NANANANANANANANANANANANA
1961-1990NANANANANANANANANANANANA
1971-2000NANANANANANANANANANANANA
1981-20100.1160.1070.1050.1210.0840.0640.0940.0970.1110.0930.0940.075
1994-20130.2180.2120.1950.2460.1840.1780.2290.2320.280.2250.1890.162
TempLSgrid
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.091-0.093-0.118-0.082-0.077-0.06-0.061-0.056-0.056-0.059-0.075-0.08
1961-1990000000000000
1971-20000.130.150.1210.1310.1130.1160.1040.1040.0910.0940.0880.125
1981-20100.2990.3240.3030.2910.2690.2710.260.2680.2550.2770.2670.271
1994-20130.3560.4040.3940.4090.380.3950.3860.3970.3870.4220.4290.364
BESTlo
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-19800.0440.03-0.0130.021-0.007-0.001-0.023-0.022-0.0390.009-0.0090.043
1961-19900.1120.0920.0820.0820.0490.0330.020.0240.010.0510.040.096
1971-20000.2140.2190.1860.1950.1390.140.1310.1330.1050.1310.1190.196
1981-20100.3920.3970.3760.3590.2940.2980.2930.30.2740.3140.2870.341
1994-20130.4690.50.4870.4890.4120.4370.4270.4360.410.4570.4580.448
C.Wkrig
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.067-0.064-0.101-0.05-0.047-0.018-0.028-0.021-0.036-0.026-0.037-0.055
1961-1990000000000000
1971-20000.1170.1440.1240.1280.1040.1260.1280.1210.1070.0950.0960.103
1981-20100.3250.3480.3340.3120.2790.2960.3080.3150.2940.310.3030.287
1994-20130.4280.4660.4620.4640.4050.4450.4560.4730.4480.4860.5120.42
TempLSmesh
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.086-0.086-0.118-0.077-0.077-0.058-0.065-0.052-0.058-0.051-0.061-0.075
1961-1990000000000000
1971-20000.1230.1450.1210.1340.1070.1130.1050.1010.0870.090.0950.114
1981-20100.3030.330.310.3030.2680.2650.260.2670.2550.2830.2850.279
1994-20130.3830.4270.4130.4360.380.3930.3820.4080.3990.4440.4760.393
BESTla
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-19800.1160.022-0.0620.071-0.087-0.085-0.08-0.077-0.060.121-0.010.141
1961-19900.250.1460.1590.20.046-0.0260.0010.012-0.0010.1620.0720.234
1971-20000.4410.4040.3210.4140.1970.1660.1650.190.1340.2810.1690.424
1981-20100.7680.730.6780.6710.4350.410.3980.4290.4170.5980.4890.648
1994-20130.8670.8990.8550.8950.6410.670.6090.650.6890.8720.8360.795
GISS.Ts
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980000000000000
1961-19900.1410.1390.1830.1390.1530.1250.140.1220.1160.0960.0910.105
1971-20000.3290.3610.3620.340.3220.3220.3250.3090.2730.2470.2440.289
1981-20100.5840.6220.6160.5580.5260.5270.5260.5340.5210.5070.4970.517
1994-20130.7160.7680.7580.7080.6660.6960.6690.7030.7210.7230.7430.692
CRUTEM.4
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.105-0.129-0.196-0.11-0.111-0.054-0.072-0.062-0.042-0.057-0.085-0.074
1961-1990000000000000
1971-20000.2390.2870.2010.2140.1710.1880.1520.1630.1370.1390.0990.206
1981-20100.590.6170.5410.4930.4120.4350.4030.4340.4060.4670.4370.453
1994-20130.7270.7840.7180.7160.6060.6680.630.6550.660.740.7450.629
NOAAla
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.438-0.499-0.466-0.43-0.346-0.28-0.25-0.271-0.229-0.236-0.222-0.37
1961-1990-0.259-0.317-0.194-0.247-0.186-0.193-0.156-0.174-0.159-0.149-0.101-0.245
1971-2000000000000000
1981-20100.3590.3520.3710.2790.2460.2380.2470.2710.2540.3340.3460.233
1994-20130.4420.5230.5460.5220.4590.4780.4880.4860.520.6250.6870.375
HADSST3
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.033-0.027-0.032-0.033-0.032-0.026-0.015-0.008-0.031-0.036-0.038-0.034
1961-1990-0.01-0.01-0.008-0.011-0.01-0.0030.0090.008-0.004-0.009-0.011-0.012
1971-20000.0550.0590.0720.0610.0680.0720.0910.0860.0690.0510.0570.05
1981-20100.180.1860.2030.2010.2110.2210.2450.2470.2180.2020.1860.176
1994-20130.260.2760.2950.3020.3080.3260.3680.3750.3290.3160.3010.278
NOAAsst
Base periodJanFebMarAprMayJunJulAugSepOctNovDec
1951-1980-0.153-0.152-0.159-0.158-0.157-0.157-0.157-0.153-0.161-0.161-0.164-0.165
1961-1990-0.087-0.087-0.091-0.093-0.093-0.094-0.102-0.1-0.099-0.097-0.098-0.096
1971-2000000000000000
1981-20100.1080.1150.1220.1280.1310.1360.1290.1280.1210.1170.1080.105
1994-20130.1730.1830.1910.2060.2160.2280.2330.2390.2230.2180.2050.188

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