Your value is however an instantaneous number, while you'd indispensably be required to use an integrated value which reflects the counterbalancing long - term effects of
the strong volcanic forcing pulses (which remain in the system, yet unaccounted in your analysis).
The Hansen paper is an extreme case, combining
a strong volcanic forcing with a model with high sensitivity, and so probably provides an upper bound for the volcanic influence on temperature.
Not exact matches
There are various possible explanations for this discrepancy, but it is interesting to speculate that it could indicate that the models employed may have a basic inadequacy that does not allow a sufficiently
strong AO response to large - scale
forcing, and that this inadequacy could also be reflected in the simulated response to
volcanic aerosol loading.
Are they still valid, if an external
forcing leads to a very
strong but rather short - term disturbance (e.g. a very
strong volcanic eruption) that either acts regionally (high - latitude eruption) or hemispherically (tropical eruption)?
There was a
strong role for
volcanic forcing during the LIA — a fact which the «sun does everything» crowd seems to not fully grasp.
The chapter 9 summary also conceded the discrepancy, but attributed it «to a substantial degree» to natural variability, with «possible» contributions from
forcing — mentioning aerosols as well as solar and
volcanics — and, «in some models», to too
strong a response to greenhouse
forcing:
There is medium confidence that this difference between models and observations is to a substantial degree caused by unpredictable climate variability, with possible contributions from inadequacies in the solar,
volcanic, and aerosol
forcings used by the models and, in some models, from too
strong a response to increasing greenhouse - gas
forcing.
Then I constructed an XY plot of temperature vs.
forcings by year (with
volcanic eruptions removed), fitted a line and got a
strong linear relationship (R = 0.98) with a gradient of 0.32 C per watt / sq m and no sign of any change with time.