Notes: Abstract  The use of pattern correlations to compare observed temperature changes with predicted anthropogenic effects has greatly increased our confidence in the reality of these effects. Here we use synthetic observed data to determine the expected behavior of the pattern correlation statistic, R(t), and hence clarify some results obtained in previous studies. We show that, for the specific case considered here (near-surface temperature changes), even with a perfectly-known signal, expected values of R(t) currently should be only of order 0.3–0.5, as observed; that R(t) may show markedly non-linear variations in time; that the CO2-alone signal pattern should be difficult to detect today primarily because of data coverage deficiencies; and why the signal due to combined CO2-aerosol forcing is easier to detect than either the CO2-alone or aerosol-alone signals. Finally, we show that little is to be gained at present by searching for a time-dependent signal compared with a representative constant signal pattern.

Notes: Abstract This paper examines the success of various Markov-chain models of daily precipitation series in reproducing the characteristics of area-average rainfall in Britain. The first model considered is the standard twos-tate first-order Markov renewal process coupled to an amount model using the incomplete Γ-probability distribution. We find that variability of seasonal totals and autocorrelation of daily amounts are both too small in this model, compared with observations. These are serious deficiencies, often overlooked, and possibly related. We proceed to consider models involving Markov chains of higher (temporal) order and many states, both of which generalizations may increase autocorrelation. A second-order two-state model is no better than the first-order, but a first-order many-state model captures a high fraction of the seasonal variability, because use of many states improves the model's representation of spells of heavy precipitation, which appear to have a considerable influence on the seasonal variance. Better still is a second-order many-state model, a type which, to our knowledge, has not previously been investigated. We suggest that the best model would have a continuum of states, rather than a discrete set. Our conclusion is that a large proportion of seasonal variability may be explained in terms of the average daily structure, but there may be a residual component caused by processes operating on longer time-scales and possibly predictable with reference to these. Reproduction of long-period (e.g. monthly or seasonal) variance and of the structure of daily autocorrelation provide crucial tests of stochastic “weather generators”, and we recommend that models which fail to simulate these statistics realistically be used only with great caution.

Notes: Abstract A simple methane model is presented in which lifetime changes are expressed as a function of CH4 concentration and emissions of NOx CO and NMHCs. The model parameters define the relative sensitivities of lifetime to these determining factors. The parameterized model is fitted to results from five more complex atmospheric chemistry models and to 1990 IPCC concentration projections. The IPCC data and four of the five models are well fitted, implying that the models have similar relative sensitivities. However, overall sensitivities of lifetime to changes in atmospheric composition vary widely from model to model. The parameterized model is used to estimate the history of past methane emissions, lifetime changes and OH variations, with estimates of uncertainties. The pre-industrial lifetime is estimated to be 15–34% lower than today. This implies that 23–55% of past concentration changes are due to lifetime changes. Pre-industrial emissions are found to be much higher (220–330 TgCH4/y) than the best estimate of present natural emissions (155 TgCH4/y). The change in emissions since pre-industrial times is estimated to lie in the range 160–260 TgCH4/y, compared with the current best guess for anthropogenic emissions of 360 TgCH4/y. These results imply either that current estimates of anthropogenic emissions are too high and/or that there have been large changes in natural emissions. 1992 IPCC emissions scenarios are used to give projections of future concentration and lifetime changes, together with their uncertainties. For any given emissions scenario, these uncertainties are large. In terms of future radiative forcing and global-mean temperature changes over 1990–2100 they correspond to uncertainties of at least ±0.2 Wm−2 and ± 0.1° C, respectively.

Notes: Abstract This investigation addresses two general issues regarding the role of pattern similarity statistics in greenhouse warming detection studies: normalization, and the relative merits of centered versus uncentered statistics. A pattern correlation statistic is used to search for the greenhouse warming signals predicted by five different models in the observed records of land and ocean surface temperature changes. Two forms of this statistic were computed: R (t), which makes use of nonnormalized data, and $$\tilde R$$ (t), which employs point-wise normalized data in order to focus the search on regions where the signal-to-noise ratio is large. While there are no trends in the R (t) time series, the time series of $$\tilde R$$ (t) show large positive trends. However, it is not possible to infer from the $$\tilde R$$ (t) results that the observed pattern of temperature change is, in fact, becoming increasingly similar to the model-predicted signal. This is because point-wise normalization of the observed and simulated mean change fields by a single common field introduces a “common factor” effect, which means that the quantities being compared should show some similarity a priori. This does not necessarily make normalization inapplicable, because the detection test involves seeking a trend in the similarity statistic. We show, however, that trends in $$\tilde R$$ (t) must arise almost completely from the observed data, and cannot be an indicator of increasing observed data/signal similarity. We also compare the information provided by centered statistics such as R(t) and the uncentered C(t) statistic introduced by Barnett. We show that C(t) may be expressed as the weighted sum of two terms, one proportional to R(t) and the other proportional to the observed spatial mean. For near-surface temperatures, the spatial average term dominates over the R(t) term. In this case the use of C(t) is equivalent to the use of spatial-mean temperature. We conclude that at present, the most informative pattern correlation statistic for detection purposes is R(t), the standard product-moment correlation coefficient between the observed and model fields. Our failure to find meaningful trends in R(t) may be due to the fact that the signal is being obscured by the background noise of natural variability, and/or because of incorrect model signals or sensitivities.

Notes: Conclusions The arguments presented by Wood and his criticisms of the methods used by Jones et al. are largely fallacious and are generally based on misconceptions and unwarranted assumptions. This does not, of course, mean that the Jones et al. data are perfect. Jones et al. (1986a, b) have clearly stated that, at the regional level, there may be residual uncertainties in their gridded data set. Furthermore, they have noted that there is a residual uncertainty in the global-mean change since late last century of ±0.2 °C (Wigley et al., 1986), although the main reasons for this uncertainty do not relate to urban warming. Further studies of possible urban warming biases are certainly warranted, particularly at the regional scale. However, for averages over continental-scale areas upwards, it is unlikely that any significant urban warming bias remains.

Notes: Abstract The theory of heat and mass transfer in turbulent pipe flow is applied to a semi-infinite moist-walled cylindrical pipe to determine the longitudinal distributions of both temperature and moisture content as functions of external conditions, pipe radius and wall temperature, and flow velocity. Since many cave and mine passages approximate this model, the results are directly applicable to cave microclimate studies and mine ventilation problems. The results are found to agree well with previously published microclimate observations. The theory is also applicable to water flow in free-flow karst aquifers; specifically to the study of temperature variations and of solution kinetics under turbulent flow conditions.