Measuring CLAMP uncertainties

The position of any modern day sample in a CLAMP analysis used for calibration is dependent upon biological heterogeneity in response to local environmental factors and the quality of the sampling/scoring. All but 5 of the sites in the Physg3arc AZ data set have 20 or more taxa, and the minimum is 17. All leaf character states are present in all samples. This minimizes positional imprecision but nevertheless, strictly speaking, each site should actually be represented not by a point but a hyper-dimensional sphere, the diameter of which is proportional to the imprecision. Because aspects of ecological heterogeneity and failure to capture all aspects of morphological variation in scoring cannot be quantified, defining the position of each site by anything other than a point is impractical. What can be done, however, is to accept that such uncertainties exist and that they contribute to the scatter of the residuals about the 2nd order polynomial regression models used to calibrate CLAMP.

Uncertainties in climate measurements (see New et al. 1999 for a detailed account of these) lead to the positions of the climate vectors being only approximate. Uncertainties depend on site locations and the climate variable, but typically mean temperature errors could be as high as 1.3 °C. Such errors in the basic meterological data suggest that it is unrealistic to expect any proxy for temperature to be more precise than plus or minus 2-3 °C. This meteorological uncertainty is captured in the scatter of the CLAMP regression model residuals because the climate uncertainty for each site will be different, as will its positional relationship to the vector.  Note that such uncertainties apply to any climate-related proxy because the Earth’s climate is imperfectly characterised by station data that are the basis for gridded datasets.

Despite these uncertainties it is clear that the relationships between CLAMP leaf characters and climate are not due to chance. Monte Carlo methods available in CANOCO show that the various regressions are highly unlikely to be due to chance (p< 0.001 for many variables).

The statistical uncertainties encapsulating all sources other than taphonomic are estimated in CLAMP by means of the scatter seen in the regression models. This is the scatter of the residuals about a 2nd order polynomial regression line summarising the relationship between the climate vector scores (position along the climate vector) and the observed climate values for those sites. Thus within each calibration dataset each climate variable has its own specific uncertainty estimate. The scatter of the sites about the regression model line is usually expressed in terms of standard deviations, with ± 2 standard deviations encompassing 95% of the data. This measure, however, calculates uncertainty from the point of view of active samples and not passive ones as is the case with fossils, and only in respect of the vector score rather than the observed climate data.

To provide a more realistic assessment of CLAMP uncertainties we removed each modern sample in turn from the data set and treated it as passive. A new regression model was then constructed based on the passive positions of each modern site in a plot of observed climate against that predicted by CLAMP. Although this increases the uncertainty values it is a fairer reflection of the uncertainties relating to fossil data. This is what should be used as the measure of precision from now on. The results of this exercise are summarized in the figure and table below.

Plot of the Physg3brcAZ samples treated as passive. Vertical axis observed MAT, horizontal axis predicted MAT. The regression line is shown in red and the green lines show 1 s.d.. Sites are coded by geographical region.

Because each modern site has a complete suite of character scores (unlike often incomplete fossils) they represent the minimum uncertainties associated with the positioning of passive samples. In practice fossil leaves are often lacking in some features due to taphonomic or collecting losses. These losses can be shown to have minimal effect even in the most extreme situations of complete loss of characters suites across all taxa (Spicer et al. 2005; 2011) in that the predicted climates arising from such character loss lie within the uncertainty range of the full data set (Spicer et al. 2005; 2011). However, this is only true if the 'completeness statistic', that is calculated automatically on the scoresheets, remains above 0.66.

Table showing the standard deviations calculated for each climate variable and calibration data set by sequentially treating each modern vegetation sample as a passive and plotting the observed and predicted values as in the plot above. Note that these uncertainties are slightly larger than those used in the 'classic' CLAMP analyses. To download a copy of this table click here.

Tests of CLAMP reliability and inter-proxy comparisons

All proxies are subject to the uncertainties in measuring modern day climate and its inherent variability, as well as those arising from any methodology used for translating point observational data into a regular grid. This means that different gridded datasets will give different CLAMP results, so it is important when reporting CLAMP results to state which climate calibration was used. These differences in how modern climate is quantified will affect the calibration, and thus results, of all palaeoclimate proxies, not just CLAMP, so the calibration should always be stated for any proxy.

The only way of testing proxies in deep geological time is by comparison with results from other proxies. This is an important issue because of the possibility that atmospheric carbon dioxide concentrations could, conceivably, affect CLAMP calibration, although the multivariate character of CLAMP plus experimental testing suggests that this is unlilkely (Gregory, 1996; Herman and Spicer, 1997). So far CLAMP has yielded similar results to oxygen isotope proxies both for temperature (Kennedy et al., 2002; Spicer and Herman, 2010) and (via moist enthalpy) altitude (Spicer et al., 2003), although more comparisons are needed. Ufnar et al. (2004) used MAT values derived from LMA, and subsequently supported by CLAMP, to derive precipitation estimates from sideritic carbonates from the Late Cretaceous of Alaska. These precipitation estimates were in accordance with a variety of qualitative proxies as well as CLAMP. CLAMP also has been tested extensively against other plant-based proxies (e.g. Yang et al., 2007; Uhl et al., 2007) and generally found to give comparable results, albeit often temperatures are slightly cooler due to the way CLAMP is calibrated and evapotranspirational cooling in closed canopy environments.