HadAT uncertainty estimates

This is a Met Office documentation. The BADC is not responsible for its content. "we" refers to Met Office.

      Introduction
1 - Sources of uncertainty which we DO NOT consider
2 - Sources of uncertainty which we do consider
3 - Gaining uncertainty estimates over a range of space and time scales

Introduction

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.

At present uncertainty estimates are only available on seasonal products and up until the end of 2001. In future we may extend our analyses and consider uncertainty on monthly timescales. More details on the approach we use and its justification are available in Thorne et al., 2005.

1 - Sources of uncertainty which we DO NOT consider

Caution: this list is not necessarilly exhaustive.

2 - Sources of uncertainty which we do consider

In contrast these lists are comprehensive.

For the individual stations we consider the effects of:

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.

Station uncertainty timeseries (total uncertainties as well as the three components) include:

3 - 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!