Climatological contingency probabilities of clouds

The ideas surrounding contingency co‐occurrence probabilities of cloud types are discussed with respect to two types of probability: firstly, that given a lower level cloud (L) there is also an upper level cloud (U), P(L ⇒ U), and secondly the probability that given an upper cloud layer there is a lower cloud layer, P(U ⇒ L). Particular emphasis is placed on the fact that analyses to date have considered the frequency of observation of co‐occurrence, not, the potentially more useful, coexistence probability. From four separate months of global surface observations the P(L ⇒ U) was calculated as a function of lower level cloud amount on a global, regional, and individual station basis for (i) stratiform and altiform and (ii) stratiform and cirriform cloud type combinations. Global patterns of P(L ⇒ U) behaviour are somewhat similar to regional patterns produced by previous work and are, on occasions, reproducible on a regional scale and, in some instances, by individual stations. Values of P(L ⇒ U) involving lower level overcasts are required in the calculation of the P(U ⇒ L) term, thus rendering climatological estimates of P(U ⇒ L) susceptible to biasing if an inappropriate value of P(L ⇒ U) for L = overcast is chosen. To demonstrate this effect, monthly global climatologies of P(U ⇒ L) were generated for several combinations of upper and lower cloud types using (i) an assumed mean value for the overcast case and (ii) a modification to the previously assumed overcast P(L ⇒ U) values, as suggested here. Comparison of these climatologies revealed differences, widely spread across the globe, of mostly within ± 10 per cent according to cloud type, but with a few larger changes in excess of 30 per cent.