Holological study of lakes from an entropy viewpoint - Lake Mendota

Abstract

The monthly entropy fluxes associated with direct, diffuse and reflected solar radiation in Lake Mendota are calculated from the corresponding energy data of the lake. Also, the monthly entropy fluxes associated with infrared radiation, evaporation and sensible heat are estimated. The net entropy flow into the lake becomes negative; that is, the lake absorbs ‘negative entropy’ from its surroundings. In this respect, the lake can be regarded as a ‘superorganism’, which has ordered structures and functions in it similar to a biological organism. The change of entropy content is computed from the change of heat-storage and the mean temperature of the lake. From the net entropy flow and the change of entropy content, the entropy production is calculated. Entropy production is large in summer and small in winter; it oscillates with a period of 1 year. The monthly entropy production ( S prod) is a linear function of the monthly solar energy absorbed by the lake ( E solar): S prod= a+ bE solar, a=0.006 MJ m −3 month −1 K −1 and b=2.29 × 10 −4 m −1 K −1. The values ( a, b) are holistic indices which characterize the lake from an entropy viewpoint. Other indices of similar nature are also introduced. Comparison of these quantities in Lake Mendota (eutrophic) with those in the northern basin of Lake Biwa (oligo-mesotrophic) shows that processes of eutrophication or succession are accompanied by the increase of magnitudes of these indices that are related to entropy production. The increase of entropy production will be an entropy principle in some stage of ecological succession in lakes, and also in other ecological systems. A hypothesis is presented: the whole span of ecological succession consists of three phases: developmental stage (early stage) in which entropy production increases with time, stationary stage (intermediate stage) in which entropy production is kept constant, and senescent stage (later stage) in which entropy production decreases with time. These trends will be applied to Lotka-Odum's power and also Hirata-Ulanowicz's ascendency.