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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!