## 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 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.

 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
 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