Estimation of trends in rainfall extremes with mixed effects models

•Development of a model for the ratio of monthly maximum rainfall intensity•LME takes account of spatial and temporal correlation in hydrological records.•Applications of the lme to investigate evidence of a trend in extreme rainfall

Estimates of seasonal rainfall maxima at durations as short as 6 min are needed for many applications including the design and analysis of urban drainage systems. It is also important to investigate whether or not there is evidence of changes in these extremes, both as an indicator of the sensitivity of rainfall to anthropogenic and natural climate change and as an aid to the calibration of future scenarios. Estimation of trends in extreme values in a region needs to be based on all the available data if precision is to be achieved. However, extremes at different periods of accumulation at neighbouring sites are not independent because there are temporal and spatial correlations, respectively. A linear mixed effects (lme) model allows for this correlation structure, and can be fitted to unequal record lengths at different sites. The modelling technique is demonstrated with an analysis of monthly maximum rainfall, at nine aggregations between 6 min and 24 h, from six sites, with record lengths between 10 and 25 years, from a region in South Australia. In terms of mean value, there is no evidence of a trend or change in the seasonal distribution of the monthly extreme rainfall. However, there is a strong evidence of an increase in variability of monthly extreme rainfall, estimated as a 58% increase in absolute value of deviation from the mean over a 25 year period. Rainfall records are often only available as a daily accumulation. A formula for the ratio of the monthly maxima at durations shorter than 24 h, down to 6 min, to the 24 h monthly maximum, in terms of: duration, month of the year, and a site specific adjustment is estimated. There is a clear seasonal variation in the ratios and there is evidence of a difference between rainfall stations.

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