HadAT uncertainty estimates

Users are strongly advised that uncertainties come in all shapes, sizes, and flavours. You should be extremely careful in comparing one group's estimate of uncertainties with another group's: Does it include the same factors? Are they calculated in the same manner? Are there other sources of uncertainty that they haven't considered? To our knowledge no-one has come up with an agreed protocol for assigning total uncertainty estimates to climate records - if you have we'd be absolutely delighted if you'd let us know. So, please be incredibly careful in how you interpret our uncertainty estimates and compare them with those of others. If you aren't and you over-interpret then you can't say that we didn't give you fair warning.

Uncertainty estimates are only available on seasonal products and up until the end of 2001. More details on the approach we use and its justification are available in Thorne et al., 2005 (PDF file). Details of uncertainty estimates gained through automating the HadAT procedure and creating ensembles of realizations are also available from the QUARC project website.

Sources of uncertainty which we DO NOT consider

Caution: this list is not necessarilly exhaustive.

• We do not consider the structural uncertainty which would result from another individual or group of experts having come in been given the same array of raw data and chosen to homogenise it in a different, but equally (im)plausible way. This uncertainty can begin to be understood by comparing the alternative datasets. Note that some (all?) of these, including HadAT, might be incorrect (defining "correct" as being statistically indistinguishable from the true climate system evolution, which is, of course, unknown). Equally we might not be truly sampling the full range of plausible results. So comparing existing datasets is a weak constraint - we may be over or under-estimating the true uncertainty through such a simple approach.
• We have not considered the effects of incomplete spatial sampling upon our large-scale average measures. HadAT2 is primarily a continental dataset - we poorly sample the oceans, and the Southern Hemisphere. At this stage we have decided against trying to account for this incomplete sampling effect, but it is sure to add uncertainty to our estimates of large scale means.
• In some of our estimates, temporal completeness of the record may be important, and we have not explicitly fully accounted for all its effects here. In particular we have not considered the effects of sub-monthly and sub-seasonal timescale sampling changes over time unless they caused a significant discontinuity in which case they will have been adjusted for.

Sources of uncertainty which we do consider

In contrast these lists are comprehensive.

For the individual stations we consider the effects of:

• Uncertainty in the seasonal climatology values which results from the effects of incomplete temporal sampling over 1966-95. These were estimated from those stations and levels with temporally complete coverage using a boot-strap approach. This effect would add a constant offset bias to all values for a given station for a given season.
• Uncertainty in the representativeness of the individual seasonal anomaly as we are sampling in most cases twice daily only and with instruments that are used only once (fire and forget) so are not recalibrated subsequent to their use. We assume that the difference series from the neighbour composite estimate provides a good parameterisation of this effect following the completion of the homogenisation process. The difference series is subjectively assumed to be indistinguishable from white noise (random normally distributed around zero) when a given station is accepted as having been homogenised. In reality this term will be a combination of sampling error and a true physical difference that results because our finite neighbour field will not be a perfect predictor of the station series.
• Uncertainty in the adjustments that were applied during the homogenisation process. Our adjustment calculation involved the calculation of 1,000 plausible adjustment factors at each suspected breakpoint which we identified. We saved from this distribution various percentiles of which we apply the 5th and 95th percentile range to yield an uncertainty in each adjustment applied. Of course, each adjustment will in reality have a unique absolute error (climate evolved in one way), but our best guess is a random error. If we actually knew the true sign and magnitude then we wouldn't have any uncertainty at all as we'd simply adjust for it.

We assumed that the sources of uncertainty (and the uncertainty in each adjustment) are independent of one another and therefore we summed them quadratically to gain an overall estimate of the uncertainty in each station record on each level for each timestep. The bounds for total uncertainty are 5th-95th percentile equivalent measures such that we would expect the true anomaly to fall within the reported anomaly +/- the given bounds on 90% of occasions.

Gaining uncertainty estimates over a range of space and time scales

To gain estimates of the uncertainty in the gridded product on a range of space and timescales we could have attempted to aggregate up our station timeseries uncertainty estimates to the required spatial and temporal resolution. However, there remains considerable debate within the scientific community as to the validity of such approaches. Hence we chose to calculate a population of "equi-probable" HadAT2 timeseries and use this to calculate our uncertainty estimates.

We started by calculating 100 realisations of each station timeseries. To do this for each realisation we took a randomised version of the scaled neighbour difference series and added it on to the original station timeseries. Then at each point that an adjustment was applied to the original station timeseries we created a small systematic increment to all earlier values by sampling from a random normal distribution with 1.64sigma derived from the 5th to 95th percentile range previously calculated from our 1000 adjustment estimates. No attempt was made to parameterise the effects of uncertainty in the climatology. The obvious way to do this would be to renormalise over the 1966-95 period but this makes the timeseries artificially similar over the climatology period and increasingly divergent away from this. We believe that our true uncertainty relative to the present day increases the further back in time we go.

Having gained a population of plausible station timeseries for each station we then created 1,000 realisations of the true gridded timeseries by randomly picking for each station a version of its timeseries and then combining these. These gridded realisations are available upon request (they would fill up the webserver). We proceeded to zonally average these gridded products. Every realisation of the zonal mean is available below in a tar file of netcdf files. Having created zonally averaged timeseries we then created global and tropical (defined as 20N to 20S) averages by cos(lat) weighting the zonal mean fields. Median of pairwise slopes trends were subsequently calculated for 1958-2002 (full period), 1958-1978 (pre-satellite period), and 1979-2002 (satellite period).

Trends files are denoted by pressure level followed by the HadAT2 trend over the period and then the trend for each of the 1,000 realisations in order. Timeseries files give the global (tropical) mean timeseries for HadAT2 and then each of the 1,000 realisations on each line in pressure level order. These are large files containing 177 values on each line.

Maintained by: Holly Titchner Last updated: 10/05/2010 Hosted by: Met Office Hadley Centre

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