1. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si A Method for Daily Temperature Data Interpolation and Quality Control Based on the Selected Past Events Presentation for the 6 th Seminar for Homogenization and Quality Control in Climatological Databases Gregor Vertačnik Budapest, May 2008

2. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Overview Purpose Description The selection of similar days Interpolation Examples Issues and disadvantages Conclusion

3. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Purpose Missing data interpolation and quality control of daily air temperature series at climatological stations (T7, T14, T21, Tmin, Tmax) In simple methods (e.g. with monthly correction factors) the same climate statistics regardless the weather type at given day is used Typical temperature diurnal ranges and spatial patterns in complex terrain (Slovenia): –Northeasterly föhn wind, Bora (warm and windy littoral, cold interior) –Temperature inversion in valleys and basins (colder nights, fog, larger/smaller diurnal range) Aim of a new method: the use of climate statistics for the corresponding weather type Interpolation improvement: –Reduction of interpolation error (standard deviation) –Better mean values for longer periods (month)

4. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Climatological stations in the complex terrain of northwestern Slovenia, 1980: mountain-, plateau-, slope-, valley/basin-stations

5. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si An example of strong horizontal temperature (Tmax, yellow) gradient due to daily precipitation gradient (blue), August 29, 2003 (Val Canale flood). Stations below 1000 m are marked by a red circle.

6. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Description Temperature interpolation at the target station on the chosen (target) day Two-step method: –Selection of the most similar days to the interpolated one –Interpolation Use of temperature ranges and the spatial pattern: –Measurements before/after and at the interpolation time (e.g. for Tmin, T21 the day before, Tmin, T7, T14) –User-defined or the best-correlated nearby stations

7. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si The selection of similar days Minimum weighted Euclidean distance Input: temperature data at reference stations at the target and a similar day Weights based on Pearson correlation coefficient Two types of similarity: –Range and spatial pattern (weather phenomena) –Absolute values (air mass) Temperature time series on Rudno polje (Pokljuka) 18-19 July, 2007 (T0) and arbitrary similar series (T1, T2)

8. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Basic weights: Normalized (standardized) average temperature deviation of a similar day from the target day: Normalized (standardized) weighted Euclidean distance between a similar and the target day:

9. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Interpolation Basis: mean differences between the values of the reference variable at a reference station and the interpolated variable at the target station in the set of similar days Temperature estimation for each reference station Weighted mean of estimations Corrected for the number of days with the data An example of temp. estimatations at the reference stations, the final result and the measured value (in brackets)

10. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Minimum temperature in Portorož 2006-2007: –Reference stations: 1)Bilje 2)Bilje, Postojna –Reference variable: Tmin –Var. for the selection of simil. days: a)Tmin b)Tmin, T21_y, T14 c)T14_y, T21_y, T7, Tmin, T14, Tmax –30 similar days –Reference period: 1991-2005 –p 1 =1, p 2 =1, p 3 =2,k dev =0.5 Topography in western Slovenia with marked station locations Stat \ Vara)b)c) 1)1.691.651.63 2)1.571.521.50 Standard deviation of the error in °C (Bilje + monthly correct. 1.80, Postojna + monthly correct. 2.35) Examples

11. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Minimum temperature at Ljubljana Airport, 2003-2007: –5 reference stations (highest correlation) –Reference variable: minimum temperature –Reference period: 1995-2002 –Var. for the selection of similar days: T21 (the day before), T7, Tmin, T14, Tmax –p 1 =1, p 2 =1, p 3 =2,k dev =0.97 Standard deviation of the error series Standard deviation depending on the value of k dev Result comparison, March 2004

12. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Issues and disadvantages The choice of the weighting factors (depend on variables, stations) How many days to select and variables to include? Homogenous series strongly prefered! (possible solution iterative process?) Time consuming Sometimes impossible to infer on local phenomena (lack of stations): –wind (e.g. Karavanke föhn) –valley/basin fog –showers and thunderstorms  the reason for a large part of the variance remained unexplained (other meteorological variables and data at the target station should be included)

13. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Conclusion Lower interpolation error compared to the most simple method (monthly correction factors) More stations and variables for the selection of similar days usually improve interpolation results The method is unable to recognize some local weather phenomena → other meteorological variables should be included Optimal parameter values vary from case to case Homogenous series strongly prefered!

14. ENVIRONMENTAL AGENCY OF THE REPUBLIC OF SLOVENIA www.arso.gov.si Many thanks for your attention!