Ive been thinking about attempting to predict that part of the climate signal associated with initial conditions i.e. excluding or subtracting off the externally forced part in order to form the ANOMALY

This is what we want to assess when calculating the Anomaly correlation coefficient ACC for example, so that the “predictable” rising trend in global surface T in removed

We could define the externally forced variation in HadCM3 as accurately as we like by running the model N times and getting the ensemble mean of that over the period 1989-2001

Whenever we make a hindcast this ensemble mean is the expected values that the hindcast ensemble will converge back towards WHATEVER the initial anomalies we introduce This will ensure that the ACC for example will tend to zero for long lead times

However getting at the externally forced component of the ECMWF atmospheric data or the ocean field data (and hence the ANOMALIES) is not so easy

1) We can obviously assume the seasonal cycle is externally forced, hence we can derive the 12 monthly mean fields from 40 years or as much data as we have

2) The simplest way to DEFINE the next externally forced component in the data is to identify the LINEAR TREND. Obviously one could fit a more complicated curve (after all the CO2 is not increasing linearly and there is also the volcanic emissions as spikes) but to 1st order a linear trend should be OK

We could calculate the linear trend of every field formally with least squares fitting. This seems unnecessary. However we should probably allow the trend to be different for each month of the year (because climate change affects different seasons differently)

I suggest one possibility below

With 44 years of ECMWF ERA40 data (one would do the same for the ocean fields eg. EN3 or the ECMWF ocean)

Define seasonal climatology of years 0-22 (1956-1978??)

Define seasonal climatology for years 23-44

Total seasonal climatology is average of these 2 (assumed to be best representative of middle of period i.e. around 1978?)

Trend per year is difference between these 2 climatologies / 22 years Note you will have separate trend for Jan Feb March etc.

This should give nice smooth trend fields for each month

Can then define the final ECMWF evolving climatology as

mean climatology +/- some fraction of the trend this fraction is expected to be negative in early years but positive in later years

If we are dealing with 1989-2001 we expect it to mostly be warmer than the climatology for middle of the 44 year period

So this defines the ECMWF trending climatology

We remove this from the actual ECMWF data. This ANOMALY is then what we would want to assimilate

In order to assimilate this anomaly we would want to define the model climatology with its own trend in the same way

For the model climatology instead of using 1 run you can use the average of 5 ensemble runs by Leon over the period 1950-2001 in order to define the model trend

Then you define the model climatology in the same way

You then combine model climatology with observational anomaly and assimilate in the usual way.

Since you will always calculate the hindcast anomalies with respect to the evolving model climatology and then verify them against the evolving observational climatology this should have the effect of removing trends and allowing ACC to behave more like Matt Collins analysis