3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 TP 2.3 Bonn Temporal downscaling of heavy precipitation Ralf Lindau

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 The task Soil erosion model within the LandCaRe „model chain“ needs rain input with a temporal resolution of 30 min. CLM output is available hourly. Downscaling technique is needed. First step: All model grid boxes with more than 20 mm daily precipitation are extracted from CLM output.

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 Two cases of downscaling Two principle cases: Data consists of averages (1 h rain sum  30 min rain sum). Downscaling should produce averages of smaller scale. The variance of each scale should be increased by a certain amount. The pdf should contain more extremes. Data consists of point measurements (DWD rain stations  rain map of Germany) Downscling should produce synthetic data in observation gaps. The variance and pdf should remain constant.

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 Principle of average downscaling Two coarse averages x i and x j are altered by a random  x. It results: The original covariance x i x j plus the added variance  x  x This is valid for each scale as x i and x j have an arbitrary time lag.

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 Determination of the variance to be added The original (1h) data variance is mm 2 /h 2 Averaging over 2,4,8 hours reduces the variance. A linear fit enables us to estimate the potential variance for 0.5 h time resolution: mm 2 /h 2

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 Effects on semi-variogram The total variance (horizontal lines) is increased (as desired) from to (mm/h) 2 This increase (as desired) is added equally to each scale (see dashed line for difference)

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 Effects on pdf Problem: Additive noise creates negative rain values Original pdfDownscaled pdf

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 Multiplicative noise Solution: Multiplicative noise instead of additive noise OriginalDownscaled (down – org) / (down + org)

3. Jahrestreffen LandCaRe 2020, Tharandt – 30. November 2009 Kriging of Rain Beispiel: Regen vom bis DWD OriginalErgebnis Varianzeigenschaften DWD Original Ergebnis BeobFehler: mm 2 /d 2 Konstante Varianz- reduktion um den BeobFehler