『Abstract
　From published runoff measurements in catchments with a wide range of climatic conditions it is found that long-term mean annual runoff (R) can be closely fitted (r²=0.94) to measured climatic data by R = P * exp(-PET/P), where P is the mean annual precipitation and PET is the mean annual potential evapotranspiration (in mm) calculated via the Holland equation. PET = 1.2×10¹⁰* exp(-4620/Tk), which is solely a function of the mean annual temperature in Kelvin, Tk. Application of the chain rule for partial differentiation to the combined equations gives the following equation for estimating the change in runoff due to changes in P and Tk:
dR = exp(-PET/P) * [1 + PET/P] * dP - [5544×10¹⁰* exp(-PET/P) * exp(-4620/Tk) * Tk^-2] * dTk
　By setting dR equal to zero, this equation can be used to estimate the increase in P required to maintain constant runoff for a small increase in T. It can also be used to estimate the decrease in runoff in a scenario with constant precipitation and increased temperature. It is shown herein that predictions of annual runoff changes for various climate change scenarios based on this simple model compare favorably with those based on more complex, calibrated hydrological models, as well as with those based on long-term historical observations of runoff and climate change. Application of the equation above also indicates that the IPCC projections for climate change under the a1B emissions scenario may underestimate the area of North America that is likely to suffer decreases in runoff.

Keywords: Runoff; Evapotranspiration; Climate change』

Introduction
The models
Methods and data
Results
Effect of climate change on runoff
Climate elasticity
Runoff maintenance
Discussion
Acknowledgements
References