Long-range dependence and extreme values of precipitation, phosphorus load, and Cyanobacteria.

Extreme daily values of precipitation (1939-2021), discharge (1991-2021), phosphorus (P) load (1994-2021), and phycocyanin, a pigment of Cyanobacteria (June 1-September 15 of 2008-2021) are clustered as multi-day events for Lake Mendota, Wisconsin. Long-range dependence, or memory, is the shortest for precipitation and the longest for phycocyanin. Extremes are clustered for all variates and those of P load and phycocyanin are most strongly clustered. Extremes of P load are predictable from extremes of precipitation, and precipitation and P load are correlated with later concentrations of phycocyanin. However, time delays from 1 to 60 d were found between P load extremes and the next extreme phycocyanin event within the same year of observation. Although most of the lake's P enters in extreme events, blooms of Cyanobacteria may be sustained by recycling and food web processes.