1. Analysis of rainfall fields in Southern Italy
University of Calabria, 26th June 2014
Davide Luciano DE LUCA

2. High resolution rainfall data
PRAISE
(HESS, 2007)
Hydrological scale
Rainfall nowcasting models
PRAISEST
(HESS, 2009)
PRAISE-ME
(Nova Publishers, 2013)
Rain gauges
Downscaling techniques (HSJ, in press)

3. Topics What’s the meaning of downscaling? Adopted procedure
Results and conclusions

4. What’s the meaning of downscaling?

5. What’s the meaning of downscaling?b)

6. Canonical model Microcanonical model c) W is defined as
cascade generator W1 W2

7. Canonical Model mn(1) ≠ mn+1(1)+ mn+1(2) mn(1) mn+1(1) mn+1(2)
Intermittent lognormal b-model
(Gupta & Waymire,1993; Over & Gupta, 1994, 1996, Molnar & Burlando, 2005)
W is a iid random variable, its distribution is non-negative with
E[W]=1, that is the mass is, on the average, preserved at all the levels
mn(1)
mn(1) ≠
mn+1(1)+ mn+1(2)
mn+1(1)
mn+1(2)

8. Canonical Model
Intermittent lognormal b-model
(Gupta & Waymire,1993; Over & Gupta, 1994, 1996, Molnar & Burlando, 2005)
W is a iid random variable, its distribution is non-negative with
E[W]=1, that is the mass is, on the average, preserved at all the levels
mn(1)

9. Microcanonical Model mn(1) = mn+1(1)+ mn+1(2) mn(1) mn+1(1) mn+1(2)
It exactly preserves mass between levels
(Menadbe & Sivalapan, 2000, Molnar & Burlando, 2005)
mn(1)
mn(1) =
mn+1(1)+ mn+1(2)
mn+1(1)
mn+1(2)

10. P0,L=P(WL=0 and WR=1) Microcanonical Model mn(1) = mn+1(2) We define…

11. P0,R=P(WL=1 and WR=0) Microcanonical Model mn(1) = mn+1(1) We define…

12. Microcanonical Model mn(1) = mn+1(1)+ mn+1(2) If 0<W<1… mn(1)

13. Innovation in this work
Notation
TYPE: a particular analytical structure of a random cascade model
CLASS: parameter dependency on time scale and rainfall height at coarser resolution
Class I: parameters are independent on both time scale and rainfall height at coarser resolution;
Class II: dependency on time scale is only allowed;
Class III: parameters depend on both time scale and rainfall height at coarser resolution.
Innovation in this work
Class IV: parameters depend on rainfall height at coarser resolution, and dependency on time scale is allowed for selected temporal resolutions only.
The goal is to improve the evaluation of the main features of rainfall time series, such as frequency distribution and extreme values, especially for areas where the rainfall fields preserve some characteristics into a particular range of temporal resolutions, and exhibit a variability into other temporal ranges.

14. Innovation in this work
Notation
TYPE: a particular analytical structure of a random cascade model
CLASS: parameter dependency on time scale and rainfall height at coarser resolution
Summer: rainfall heights, aggregated into 5-40 min, are similar to the values cumulated on 1 or 3 h time scale (due to convective phenomena)
rainfall breakdown can be assumed as stationary into a range of time scales, and variable into other ranges (for example 6 h – 1 day).
Class I: parameters are independent on both time scale and rainfall height at coarser resolution;
Class II: dependency on time scale is only allowed;
Class III: parameters depend on both time scale and rainfall height at coarser resolution.
Innovation in this work
Class IV: parameters depend on rainfall height at coarser resolution, and dependency on time scale is allowed for selected temporal resolutions only.

15. Data B T C J
5-min resolution rain series with at least 10 years of data
The monthly scale was chosen as seasonal scale of analysis

16. Data From the finest to the coarsest resolution… 5 min 10 min 20 min
1280 min (21.33 h)
Day centered data
00:00
01:20
12:00
22:40
00:00

17. Adopted procedure For each class of models: For each rain gauge
intermittency P0
frequency distribution of positive rainfall height R
E[R] and E[H]
in order to increase the sample size of extreme values, a Peak Over a Threshold (POT) analysis was carried out, in which the adopted threshold was E[R]. In this context, the reproduction of median and 90 % percentile values was tested.
For each rain gauge
For each month
1280 min series
Monte Carlo simulations (5-640 min)
97.5 %
Mean of simulations
2.5 %

18. Adopted procedure CLASS IV CLASS III a SCA ALL resolution
Magari fare grafici qualitativi
resolution

19. Adopted procedure CLASS IV a CT SCA resolution
Magari fare grafici qualitativi
resolution

20. Adopted procedure CLASS IV a CT CT resolution
Magari fare grafici qualitativi
resolution

21. Adopted procedure CLASS IV a CT ALL resolution
Magari fare grafici qualitativi
resolution

22. Adopted procedure CLASS IV
SCA ALL (a is scale-dependent for all the resolutions)
SCA – CT 80-5 (a is scale-dependent until 160 min, and then it assumes a constant value between 80 and 5 min)
SCA – CT 40-5 (a is scale-dependent until 80 min, and then it assumes a constant value between 40 and 5 min)
CT – CT 80-5 (a assumes constant values in two ranges of resolution, respectively min and 80-5 min)
CT – CT 40-5 (a assumes constant values in two ranges of resolution, respectively min and 40-5 min)
CT ALL (a assumes a constant value into the whole range of resolutions)
combination with the highest percentage of rain gauges with observed E[H] inside their uncertainty bands, for 5 min resolution
Magari fare grafici qualitativi

23. Some Results B C J T HSJ, in press Month B T C J January SCA ALL
February
SCA
CT 40-5
March
April CT
May CT
CT 80-5
SCA
June
CT ALL
July
August
September
October
November
December B T C J
Magari fare grafici qualitativi

24. Some Results
HSJ, in press I II
III IV

25. Some Results
HSJ, in press I II
III IV

26. Some Results
HSJ, in press I II
III IV

27. Conclusions
Extreme values: the best performances are obtained with the proposed new class of models.
Validation results are consistent with the climatology of the study area.
In summer months, convective phenomena originates heavy rain that preserves this property at finer temporal levels. For this reason, a modeling which considers the breakdown process as similar as for a set of finer resolutions improves the reconstruction of this feature.
On the contrary, frontal storms occur in the winter months and there are shorter values of rainfall amount: therefore, models with the breakdown process dependent on scale are more suitable.