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A Method for D aily T emperature D ata I nterpolation and Q uality C ontrol B ased on the S elected P ast E vents Presentation for the 6 th Seminar for Homogenization and Quality Control in Climatological Databases Gregor Vertačnik Budapest, May 2008. Overview. Purpose

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A Methodfor Daily Temperature Data Interpolationand Quality Control Basedonthe Selected Past Events

Presentation for the 6th Seminar for Homogenization and Quality Control in Climatological Databases

Gregor Vertačnik

Budapest, May 2008



  • Purpose

  • Description

  • The selection of similar days

  • Interpolation

  • Examples

  • Issues and disadvantages

  • Conclusion



  • 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)


Climatological stations in the complex terrain of northwestern Slovenia, 1980: mountain-, plateau-, slope-, valley/basin-stations


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.



  • 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

The selection of similar days

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)


  • 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:



  • 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)



  • Minimum temperature in Portorož 2006-2007:

    • Reference stations:

      • Bilje

      • Bilje, Postojna

    • Reference variable: Tmin

    • Var. for the selection of simil. days:

      • Tmin

      • Tmin, T21_y, T14

      • T14_y, T21_y, T7, Tmin, T14, Tmax

    • 30 similar days

    • Reference period: 1991-2005

    • p1=1, p2=1, p3=2,kdev=0.5

Standard deviation of the error in °C (Bilje + monthly correct. 1.80, Postojna + monthly correct. 2.35)

Topography in western Slovenia with marked station locations


  • 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

    • p1=1, p2=1, p3=2,kdev=0.97

Standard deviation depending on the value of kdev

Standard deviation of the error series

Result comparison, March 2004

Issues and disadvantages

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)



  • 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!

Many thanks for your attention

Many thanks for your attention!

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