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 period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1994-2013	0.507	0.547	0.568	0.533	0.498	0.515	0.504	0.519	0.528	0.548	0.58	0.503

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 period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1961-1990	0	0	0	0	0	0	0	0	0	0	0	0
1971-2000	0.123	0.144	0.12	0.118	0.104	0.109	0.11	0.11	0.095	0.084	0.076	0.108
1981-2010	0.325	0.34	0.322	0.299	0.272	0.281	0.286	0.297	0.27	0.285	0.267	0.27
1994-2013	0.407	0.448	0.439	0.439	0.396	0.423	0.436	0.443	0.414	0.44	0.44	0.383

GISSlo

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1951-1980	0	0	0	0	0	0	0	0	0	0	0	0
1961-1990	0.102	0.096	0.133	0.092	0.099	0.078	0.083	0.074	0.073	0.065	0.073	0.084
1971-2000	0.242	0.258	0.262	0.233	0.221	0.213	0.209	0.196	0.184	0.173	0.182	0.219
1981-2010	0.428	0.447	0.457	0.405	0.384	0.38	0.377	0.372	0.373	0.379	0.382	0.386
1994-2013	0.507	0.547	0.568	0.533	0.498	0.515	0.504	0.519	0.528	0.548	0.58	0.503

NOAAlo

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1971-2000	0	0	0	0	0	0	0	0	0	0	0	0
1981-2010	0.176	0.179	0.189	0.169	0.163	0.165	0.162	0.168	0.158	0.177	0.173	0.14
1994-2013	0.245	0.274	0.286	0.292	0.283	0.298	0.304	0.308	0.305	0.33	0.336	0.239

UAH6.beta

Base period

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

1951-1980

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

1961-1990

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

1971-2000

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

1981-2010

0

0

0

0

0

0

0

0

0

0

0

0

1994-2013

0.095

0.102

0.08

0.103

0.086

0.102

0.118

0.12

0.164

0.126

0.095

0.078

RSS.MSU

Base period

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

1951-1980

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

1961-1990

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

1971-2000

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

1981-2010

0.116

0.107

0.105

0.121

0.084

0.064

0.094

0.097

0.111

0.093

0.094

0.075

1994-2013

0.218

0.212

0.195

0.246

0.184

0.178

0.229

0.232

0.28

0.225

0.189

0.162

TempLSgrid

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1961-1990	0	0	0	0	0	0	0	0	0	0	0	0
1971-2000	0.13	0.15	0.121	0.131	0.113	0.116	0.104	0.104	0.091	0.094	0.088	0.125
1981-2010	0.299	0.324	0.303	0.291	0.269	0.271	0.26	0.268	0.255	0.277	0.267	0.271
1994-2013	0.356	0.404	0.394	0.409	0.38	0.395	0.386	0.397	0.387	0.422	0.429	0.364

BESTlo

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1951-1980	0.044	0.03	-0.013	0.021	-0.007	-0.001	-0.023	-0.022	-0.039	0.009	-0.009	0.043
1961-1990	0.112	0.092	0.082	0.082	0.049	0.033	0.02	0.024	0.01	0.051	0.04	0.096
1971-2000	0.214	0.219	0.186	0.195	0.139	0.14	0.131	0.133	0.105	0.131	0.119	0.196
1981-2010	0.392	0.397	0.376	0.359	0.294	0.298	0.293	0.3	0.274	0.314	0.287	0.341
1994-2013	0.469	0.5	0.487	0.489	0.412	0.437	0.427	0.436	0.41	0.457	0.458	0.448

C.Wkrig

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1961-1990	0	0	0	0	0	0	0	0	0	0	0	0
1971-2000	0.117	0.144	0.124	0.128	0.104	0.126	0.128	0.121	0.107	0.095	0.096	0.103
1981-2010	0.325	0.348	0.334	0.312	0.279	0.296	0.308	0.315	0.294	0.31	0.303	0.287
1994-2013	0.428	0.466	0.462	0.464	0.405	0.445	0.456	0.473	0.448	0.486	0.512	0.42

TempLSmesh

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1961-1990	0	0	0	0	0	0	0	0	0	0	0	0
1971-2000	0.123	0.145	0.121	0.134	0.107	0.113	0.105	0.101	0.087	0.09	0.095	0.114
1981-2010	0.303	0.33	0.31	0.303	0.268	0.265	0.26	0.267	0.255	0.283	0.285	0.279
1994-2013	0.383	0.427	0.413	0.436	0.38	0.393	0.382	0.408	0.399	0.444	0.476	0.393

BESTla

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1951-1980	0.116	0.022	-0.062	0.071	-0.087	-0.085	-0.08	-0.077	-0.06	0.121	-0.01	0.141
1961-1990	0.25	0.146	0.159	0.2	0.046	-0.026	0.001	0.012	-0.001	0.162	0.072	0.234
1971-2000	0.441	0.404	0.321	0.414	0.197	0.166	0.165	0.19	0.134	0.281	0.169	0.424
1981-2010	0.768	0.73	0.678	0.671	0.435	0.41	0.398	0.429	0.417	0.598	0.489	0.648
1994-2013	0.867	0.899	0.855	0.895	0.641	0.67	0.609	0.65	0.689	0.872	0.836	0.795

GISS.Ts

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1951-1980	0	0	0	0	0	0	0	0	0	0	0	0
1961-1990	0.141	0.139	0.183	0.139	0.153	0.125	0.14	0.122	0.116	0.096	0.091	0.105
1971-2000	0.329	0.361	0.362	0.34	0.322	0.322	0.325	0.309	0.273	0.247	0.244	0.289
1981-2010	0.584	0.622	0.616	0.558	0.526	0.527	0.526	0.534	0.521	0.507	0.497	0.517
1994-2013	0.716	0.768	0.758	0.708	0.666	0.696	0.669	0.703	0.721	0.723	0.743	0.692

CRUTEM.4

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1961-1990	0	0	0	0	0	0	0	0	0	0	0	0
1971-2000	0.239	0.287	0.201	0.214	0.171	0.188	0.152	0.163	0.137	0.139	0.099	0.206
1981-2010	0.59	0.617	0.541	0.493	0.412	0.435	0.403	0.434	0.406	0.467	0.437	0.453
1994-2013	0.727	0.784	0.718	0.716	0.606	0.668	0.63	0.655	0.66	0.74	0.745	0.629

NOAAla

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1971-2000	0	0	0	0	0	0	0	0	0	0	0	0
1981-2010	0.359	0.352	0.371	0.279	0.246	0.238	0.247	0.271	0.254	0.334	0.346	0.233
1994-2013	0.442	0.523	0.546	0.522	0.459	0.478	0.488	0.486	0.52	0.625	0.687	0.375

HADSST3

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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	-0.003	0.009	0.008	-0.004	-0.009	-0.011	-0.012
1971-2000	0.055	0.059	0.072	0.061	0.068	0.072	0.091	0.086	0.069	0.051	0.057	0.05
1981-2010	0.18	0.186	0.203	0.201	0.211	0.221	0.245	0.247	0.218	0.202	0.186	0.176
1994-2013	0.26	0.276	0.295	0.302	0.308	0.326	0.368	0.375	0.329	0.316	0.301	0.278

NOAAsst

Base period	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
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
1971-2000	0	0	0	0	0	0	0	0	0	0	0	0
1981-2010	0.108	0.115	0.122	0.128	0.131	0.136	0.129	0.128	0.121	0.117	0.108	0.105
1994-2013	0.173	0.183	0.191	0.206	0.216	0.228	0.233	0.239	0.223	0.218	0.205	0.188