Do Monin-Obukhov or local similarity theory apply in these conditions? To address this question, I analyzed eddy correlation data collected from several forested sites, one heather site and two grassland sites, and data collected in offshore flow of warm air over cooler water. The analysis is complicated by a tendency for increased nonstationarity (mesoscale meandering) and increased random flux errors in very stable conditions. A modified similarity theory is constructed and related to existing modifications of traditional similarity theory. Conditions are identified where existing approaches and the new approach fail. One example is failure over weak slopes, typical of much of the earthÂ’s surface, where shallow intermittent drainage flows are generated on clear nights with weak ambient flow.