Improving empirical relationships for predicting the effect of vegetation change on annual water yield

Continuing worldwide growth in results from paired-catchment vegetation-change experiments raises the possibility of improving empirical predictions of change in annual water yield. However, the results are variable, and a large amount of variation in change in annual yield is not explained by relationships derived from the results. We investigated causes of this unexplained variation (scatter), for relationships between change in annual yield and precipitation, and proposed procedures for improving the strength and accuracy of the relationships. Results from 35 New Zealand experiments were used to investigate three possible causes of the scatter: inter-annual variability of precipitation, heterogeneity arising from combining increases and decreases in annual yield, and heterogeneity from mixing different forms of reported change in annual yield. We also investigated the significance of data gaps (uneven distribution of results across the full range of precipitation values). Inter-annual variability of precipitation was the most important of the causes of scatter investigated. Scatter was reduced (44% increase in R2) by relating maximum change in annual yield to the annual precipitation for the year of the maximum, rather than to mean annual precipitation. Small sample size was found to be a more serious problem in the development of predictive relationships than heterogeneity of change in annual yield data; however, the accuracy of prediction can be increased by homogenisation of the change in annual yield data using transformation equations. We also found that data gaps can decrease the accuracy of the predictive relationships, but, in general, have no effect on the amount of variation explained. Our main conclusion was that annual precipitation in the year of maximum change in annual yield should be included as an explanatory variable in empirical predictive relationships. We also recommend that, before developing relationships, basic data from all experiments be re-analysed using a consistent methodology.