1. Statistical correction and downscaling of daily precipitation in the UK via a probability mixture model A ‘Model Output Statistics’ (MOS) approach for downscaling the full distribution of precipitation to station-level. Tom Kent – MSc Applied Meteorology and Climatology 23 rd July 2012

2. Central aim: To develop an eventwise GCM-based MOS model for downscaling the full distribution, including extremes, of daily precipitation at point locations (i.e. station level) using nudged GCM-simulated precipitation as the predictor. 2 Stages: Stationary model – fitting the mixture model to observations. Non-stationary model – development of a univariate VGLM mixture model

3. Location of transition from Gamma to GPD density Transition rate Weight function: Non-decreasing; takes values in (0,1]

4. Before downscaling…. Assessing the sensitivity of the mixture model parameters in a stationary setting Number of years = 44 (years 1958-2001) Leave one year out of the estimation procedure so that the model’s parameters are estimated from a 43 year subset of the data. Result: 44 sets of mixture model parameters are estimated from the 44 subsets of the observational data.

5. Data: Oxford DJF and JJA Daily observed precipitation 1958-2001. Dry threshold: >1mm

6. DJF: 90 th percentile (from obs.) = 10.9mm 95 th percentile = 14.4mm JJA: 90 th percentile (from obs.) = 13.2mm 95 th percentile = 18.5mm A closer look at the behaviour of m (the location of transition between Gamma and GPD)

7. A closer look at the behaviour of xi: when xi is positive, the upper tail of the distribution is unbounded when xi is negative, the upper tail is bounded When xi < 0, is a Gamma distribution alone more appropriate?

8. QQ Plots: Oxford JJA Mixture model distribution Gamma distribution

9. Mixture model distribution Gamma distribution QQ Plots: Oxford DJF

10. Histogram: wet (>1mm) precipitation measurements from Oxford. Red lines: mixture model pdfs determined by the different ‘leave-one-out’ subsets The effect of the sensitivity of the parameters on the mixture model pdfs:

11. Possible solution..? Remove tau from the estimation procedure, i.e. fix it beforehand so that the likelihood function is a function of 5 parameters only. MLE is then performed for a range of fixed tau values… The behaviour of the remaining 5 parameters can then be analysed for various fixed tau values

12. Spread/skill of the 5 mixture model parameters as a result of the leave-one-out estimation WITH TAU FIXED beforehand

13. Key points… relatively small spread (i.e. high skill) for tau close to zero relationship between m and tau: as tau decreases, m increases. For tau close to zero, m≈13; this seems reasonable as location transition between Gamma and GPD. But small tau implies “unsmoothness”; thus, it seems to be a trade-off between m and tau. Final (??) decision: Fix tau, leave m in the estimation procedure.

14. GPD Gamma distribution Weight function Fixed??

15. Thank you for listening… … any questions?