1. Correction of daily values for inhomogeneities P. Štěpánek Czech Hydrometeorological Institute, Regional Office Brno, Czech Republic E-mail: petr.stepanek@chmi.cz COST-ESO601 meeting, Tarragona, 9-11 March 2009

2. Using daily data for inhomogeniety detection, is it meaningful?

3. Homogenization of daily values – precipitation series working with individual monthly values (to get rid of annual cycle) It is still needed to adapt data to approximate to normal distribution One of the possibilities: consider values above 0.1 mm only Additional transformation of series of ratios (e.g. with square root)

4. Original values - f ar from normal distribution (ratios tested/reference series)Frequencies Homogenization of precipitation – daily values

5. Limit value 0.1 mm (ratios tested/reference series)Frequencies

6. Limit value 0.1 mm, square root transformation (of ratios) (ratios tested/reference series)Frequencies Homogenization of precipitation – daily values

7. Problem of independence, Precipitation above 1 mm August, Autocorrelations

8. Problem of independece, T emperature August, Autocorrelations

9. Problem of independece, T emperature differences (reference – candidate) August, Autocorrelations

10. Homogenization Detection (preferably on monthly, seasonal and annual values) Correction – for daily values

11. WP1 SURVEY (Enric Aguilar) Daily data - Correction (WP4) Very few approaches actually calculate special corrections for daily data. Most approaches either –Do nothing (discard data) –Apply monthly factors –Interpolate monthly factors The survey points out several other alternatives that WG5 needs to investigate

12. Daily data correction methods „Delta“ methods Variable correction methods – one element Variable correction methods – several elements

13. Daily data correction methods Interpolation of monthly factors –MASH –Vincent et al (2002) - cublic spline interpolation Nearest neighbour resampling models, by Brandsma and Können (2006) Higher Order Moments (HOM), by Della Marta and Wanner (2006) Two phase non-linear regression (O. Mestre) Modified percentiles approach, by Stepanek Using weather types classifications (HOWCLASS), by I. Garcia-Borés, E. Aguilar,...

14. Adjusting daily values for inhomogeneities, from monthly versus daily adjustments („delta“ method)

15. Adjusting from monthly data monthly adjustments smoothed with Gaussian low pass filter (weights approximately 1:2:1) smoothed monthly adjustments are then evenly distributed among individual days

16. Adjusting straight from daily data Adjustment estimated for each individual day (series of 1 st Jan, 2 nd Jan etc.) Daily adjustments smoothed with Gaussian low pass filter for 90 days (annual cycle 3 times to solve margin values)

17. Air temperature etc.: differences between individual observation hours: be careful when appliying straight to daily AVG

18. Adjustments ( Delta method ) The same final adjustments may be obtained from either monthly averages or through direct use of daily data (for the daily-values-based approach, it seems reasonable to smooth with a low-pass filter for 60 days. The same results may be derived using a low-pass filter for two months (weights approximately 1:2:1) and subsequently distributing the smoothed monthly adjustments into daily values) (1 – raw adjustments, 2 – smoothed adjustments, 3 – smoothed adjustments distributed into individual days), b) daily-based approach (4 – individual calendar day adjustments, 5 – daily adjustments smoothed by low-pass filter for 30 days, 6 – for 60 days, 7 – for 90 days)

19. Spline through monthly temperature adjustments („delta“ method) Easy to implement No assumptions about changes in variance Integrated daily adjustments = monthly adjustments But, is it natural?

20. Variable correction f(C(d)|R), function build with the reference dataset R, d – daily data cdf, and thus the pdf of the adjusted candidate series C*(d) is exactly the same as the cdf or pdf of the original candidate series C(d)

21. Trewin & Trevitt (1996) method: Use simultaneous observations of old and new conditions Variable correction

22. 1996

23. The HOM method concept: Fitting a model Locally weighted regression (LOESS) (Cleveland & Devlin,1998) HSP2 HSP1

24. The HOM method concept: Calculating the binned difference series Decile 1, k=1 Decile 10, k=10

25. The HOM method concept: The binned differences DELLA-MARTA AND WANNER, JOURNAL OF CLIMATE 19 (2006) 4179-4197

26. SPLIDHOM ( ), Olivier Mestre SPLIDHOM (SPLIne Daily HOMogenization), Olivier Mestre direct non-linear spline regression approach (x rather than a correction based on quantiles), cubic smoothing splines for estimating regression functions

27. Variable correction, q-q function Michel Déqué, Global and Planetary Change 57 (2007) 16–26

28. Our modified percentiles based approach

29. Our percentiles based approach

30. Variable correction methods – complex approach (several elements) not yet available …

31. Comparison of the methods, ProClimDB software

34. Correction methods comparison

35. Correction methods comparison, different parameters settings 0 051015202530

36. Correction methods comparison, different parameters settings

37. Correction of daily values We have some methods … - but we have to validate them -> benchmark dataset on daily data Do we know how inhomogeneites in daily data behave? we should analyse real data who and when?, what method for data comparison?