Modeling 429 



where 



r=mean water temperature in °C. 



The effect of temperature on physiological processes of the system 

 was expressed in the form of a ^lo function: 



where 



r^ = temperature effect on the process, and 

 7'r= reference temperature. 



It has been recognized that most organisms do not show clear Qio 

 responses as the rates do not increase exponentially over the entire range 

 of temperatures suitable for life. The models are built to cope only within a 

 narrow range, to 15°C. Temperature responses are frequently curvilinear 

 or linear for Lepidurus respiration and activity rates, for zooplankton 

 respiration and ingestion rates, and for algal P„tax, etc. The present 

 simplification in the models limits their accuracy at temperature extremes. 

 The simulation results were validated using real temperature data as input. 



Formulation of Process Rates 



One of our basic assumptions is that processes such as uptake of 

 nutrients and algal photosynthesis, uptake of carbon and nutrients by 

 bacteria, and ingestion of food by consumers can be characterized 

 approximately by Michaelis-Menten type functions. Thus, 



v=K„axX,/(x,+A:,) (11) 



where 



V = rate of photosynthesis, uptake of nutrients, ingestion, etc., 



Vmax = maximum uptake velocity, 



Xi = concentration of food, nutrient, etc., and 



^s = half saturation constant. 



This is based on our data on uptake of nutrients and primary 

 productivity from arctic ponds (Stanley 1974) and several published 

 reports (O'Brien 1974, Toerien et al. 1971, Golterman et al. 1969, Eppley 

 and Thomas 1969, Caperon 1968) which indicate this type of relationship 

 in the growth rate of phytoplankton. Experimental measurements from 

 these ponds and from lakes and estuaries also suggest that bacterial uptake 



