Generalized Haber's Law for Exponential Concentration Decline, with Application to Riparian-Aquatic Pesticide Ecotoxicity

A simple analytic solution to the dynamic version of Haber's law was derived, conditional on a specified toxic load exponent (n) and on exponential decline in environmental toxicant concentration. Such conditions are particularly relevant to assessing ecotoxicity risk posed (e.g., to juvenile salmonids) by agricultural organophosphate (OP) pesticides that are subject to degradation and/or dissipation. A dynamic Haber's law model was fit to previously published detailed data on lethality for two aquatic species induced by six agricultural OP pesticides, and more crude fits were obtained to less detailed data on five other OP and on two non-OP pesticides, indicating that for lethality, a range of 0.5 ≤n≤ 1.5 may be typical for OP pesticides. The AgDRIFT^® stream deposition model was next used to establish that first-order or exponential loss, with dilution half-times on the order of ≤0.01 days, pertains approximately to pesticide residues in streams that arise after aerial application of agricultural pesticides 100 feet upwind. The analytic model was then applied to demonstrate that pesticide concentrations deposited in downwind streams following an aerial application are effectively diluted by about 50- to 300-fold from their initial concentration. Riparian ecotoxicity risk assessment models that ignore this effective dilution, and base pesticide-specific estimates of reduced survival on the initial concentrations, are therefore unrealistically conservative.