HOW DO WE DETERMINE a”? EMPIRICAL MECHANISTIC Data-based Process-based (Inductive, (Deductive Statistical) Mass-balance) Model Model
HOW DO WE DETERMINE “a”? EMPIRICAL Data-based (Inductive, Statistical) Model MECHANISTIC Process-based (Deductive Mass-balance) Model
EMPIRICAL MODELS 0
EMPIRICAL MODELS W c a 1
MECHANISTIC MODELS CONSERVATION OF MASS Mass Balance: For a finite volume over a unit time period: (accumulation)=(sources)-(sinks) source sink accumulation Volume
MECHANISTIC MODELS CONSERVATION OF MASS source sink Volume For a finite volume over a unit time period: (accumulation) = (sources) (sinks) accumulation Mass Balance:
MASS BALANCE FOR WELL-MIXED LAKE LOADING OUTFLOW REACTION SETTLING ACCUMULATION LOADING-OUTFLOW-REACTION-SETTLING
MASS BALANCE FOR WELL-MIXED LAKE LOADING REACTION SETTLING OUTFLOW ACCUMULATION = LOADING OUTFLOW REACTION SETTLING
PARAMETERIZE ACCUMULATION △M accumulation △t Substitute M=Vc △Ve accumulation △t If K=constant 公c accumulation =K △ Let△t →0 dc accumulation =D dt
accumulation = M t accumulation = Vc t Substitute M = Vc If V = constant Let t 0 PARAMETERIZE ACCUMULATION accumulation = V dc dt accumulation = V c t