The impact of time‐averaging on the detectability of nonlinear empirical relations
Yuval, William W. Hsieh · Quarterly Journal of the Royal Meteorological Society · 2002
Abstract This paper studies how time‐averaging of observations can affect the detectable nonlinear empirical relations in the data. The example used is the simulation of the precipitation rate as a daily, weekly and monthly variable. The feedforward neural network (NN) model is employed to simulate the precipitation rate. A measure of the nonlinearity of the NN relation is introduced and is used to calculate the nonlinearity of the NNs. It is found that the use of data averaged over periods longer than the inherent time‐scale of the involved variables can result in a dramatic weakening of the detected nonlinearity. A suggested theoretical explanation asserts that averaging of independent samples of the data records yields distributions approaching the multi‐variate normal, in which case the relations among the variables are closer to linear. Copyright © 2002 Royal Meteorological Society.