S th i f i f ll ti i i hi h t l l ti t i hSynthesis of rainfall timeseries in a high temporal resolution – a parametric approachSynthesis of rainfall timeseries in a high temporal resolution – a parametric approachy g p p ppAna Claudia Callau Poduje & Uwe HaberlandtAna Claudia Callau Poduje & Uwe Haberlandt
d Parameters regionalization1 Motivation & Objectives 3 Study Area & Data Parameters regionalization1. Motivation & Objectives 3. Study Area & Data g. ot at o & Object es y
D i d ti f b d i t i S f L SDesign and operation of urban drainage systems require State of Lower SaxonyDesign and operation of urban drainage systems require State of Lower Saxonylong and continuous rain series Surface: 47 624 km2long and continuous rain series. ‐ Surface: 47,624 km2,g
bl Sh d il bili ( l d i l, ,
Problem: Short data availability (temporal and spatial ‐ Location: North‐westProblem: Short data availability (temporal and spatial ‐ Location: North‐west required resolutions) Grequired resolutions). Germany.required resolutions). Germany.Solution: Development of a precipitation model and Rainfallmeasurements:Solution: Development of a precipitation model and Rainfall measurements:p p p
ti f l th ti i (H b l d l 2008) 2 i ( i 3)generation of long synthetic series (Haberlandt et al 2008) ‐ 25 stations (Fig 3)generation of long synthetic series (Haberlandt et al.,2008). 25 stations (Fig. 3),Time resolution: 5 min 10 20 years of recordTime resolution: 5 min ‐ 10‐20 years of record ,
l l0 0 years of record ,
Spatial resolution: 1Km x 1Km ‐ 5 minute time resolutionSpatial resolution: 1Km x 1Km ‐ 5 minute time resolution.Figure 3: Location Rain Gauge StationsFigure 3: Location Rain Gauge Stations.ID OK OK Li R i OK EDK2 Methodolog 4 R ltID OK OK - Linear Regression OK, EDK2. Methodology 4. Results 0.152. Methodology 4. Results SUMMER
C id d d l) D fi iti f i f ll t 0 10Considered modelsa) Definition of rainfall events: 0.10
EConsidered modelsa) Definition of rainfall events:
MS
Model DSD WSD WSA WSI Bivariate modelVariable Unit Description Minimum RM
Model DSD WSD WSA WSI Bivariate modelVariable Unit Description Minimum 0.05
R
WSI 2*N D 1p
DSD i D S ll D ti 5 WSI 2*Ncop G li d SD 1 per seasonDSD min Dry Spell Duration 5 _ p
d f( ) Generalized WS 1 per seasonDSD min Dry Spell Duration 5
0 003 ed f(WSI,WSD) Generalized
‐WWSI Ncop 1 per yearWSD min Wet Spell Duration ‐ 0.00mu sigma gamma
n 3 ze o
f(WSI,WSD) Pareto SI‐WSI_Ncop 1 per yearWSD min Wet Spell Duration mu sigma gamma
on li to Pareto
WS
WSI 1cop 1 for all stationsWSTpeak min Time to peak Figure 7: Parameters and results ofso ra ret WWSI_1cop 1 for all stationsWSTpeak min Time to peak ‐
Fi re 8 R i li ti fFigure 7: Parameters and results of different interpolation techniq esar
s er arWSA 2*NCop D 1 per seasonWSA mm Wet Spell Amount 1 00 Figure 8: Regionalization of different interpolation techniques:
ea ne PaWSA_2*NCop
WS 1 per seasonWSA mm Wet Spell Amount 1.00 g g
parameters: DSD Summer eventsp q
DSD Summer events
Pe en P
K f(WSAWSD) W
pWSA N 1
pWSI / i W t S ll I t it 0 002
parameters: DSD Summer events.DSD Summer events.
Cross ValidationP Ge Kappa f(WSA,WSD) A‐WWSA Ncop 1 per yearWSI mm/min Wet Spell Intensity 0.002 Cross‐ValidationG pp f( , )
SA
_ p p yWSA 1
WSI mm/min Wet Spell Intensity 0.002/ WWSA 1cop 1 for all stationsWSPeak mm/5min Wet Spell Peak Intensity ‐ WWSA_1cop 1 for all stationsWSPeak mm/5min Wet Spell Peak Intensity
b) A l i f l (Fi 1) Bivariate modelsb) Analysis of external structure (Fig 1); Bivariate modelsb) Analysis of external structure (Fig. 1);WSI WSDc) Analysis of internal structure (Fig 2) WSI‐WSD:c) Analysis of internal structure (Fig. 2); WSI WSD:c) Analysis of internal structure (Fig. );Normal CopulaNormal Copula
Fi re 4K d ll‘ T ( ) 0 43Observed Rainfall - 5 minutes Rainfall Events 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101
Observed Rainfall Rainfall Events Theoretical Shape Figure 4: Kendall‘s Tau (mean):‐0.435 9
0.20.20g
Pairs of( )
n) WSA = WSDxWSI 0.180.18n)
Pairs of observedWSA‐WSD:/m
i
0.160.16/mi observed WSA‐WSD:
mm
/
WSI 0.140.14
mm
/
WSPeakWSPeak andHü l R i C ly
(m
WSD0.120.12y
(m WSPeakWSPeakArea = WSA
and pseudoHüsler‐Reiss Copula ns
ity WSD0.10.10
nsity pseudo‐p
d ll‘ ( )nten 0.080.08
nten observedKendall‘s Tau (mean): 0 38In 0.060.06In
observed variables of Figure 10: Comparison of test ofKendall s Tau (mean): 0.380.040.04 variables of Figure 10: Comparison of test of
fit for extreme values0.020.02 the 25 Figure 9: Error in simulations using parameters fit for extreme values.00.00
the 25 stations
Figure 9: Error in simulations using parameters d i d f b i d i li iWSD DSD WSD
WSTpeakWSTpeakstations. derived from observations and regionalization.
Time TimeWSTpeakWSTpeak g
Validation of the precipitation modelFi 1 E t l t t f t Fi 2 I t l t t f t Validation of the precipitation model 5 Summary and ConclusionsFigure 1: External structure of events. Figure 2: Internal structure of events.E (%) [S th ti Ob d]*100/Ob d 5. Summary and Conclusionsg gError (%) = [Synthetic – Observed]*100/Observed y
d) l f( ) [ y ] /
d) Regionalization of parameters:Selected Model: Generation WSA with 1 copula
d) Regionalization of parameters:Selected Model: Generation WSA with 1 copula I t l ti th d ID (I Di t ) OK pInterpolation methods: ID (Inverse Distance) , OKparameter for all stations;
Interpolation methods: ID (Inverse Distance) , OK parameter for all stations;(Ordinary Kriging) EDK (External Drift Kriging) Good performance in reproducing WSA and total yearly rainfall(Ordinary Kriging), EDK (External Drift Kriging) Good performance in reproducing WSA and total yearly rainfall( y g g) ( g g)
C id ti f l ti b t tp p g y y
B t f i d i E t V lConsideration of correlation between parameters Best performance in reproducing Extreme ValuesConsideration of correlation between parameters p p ge) Cross Validation: Competitive performance in reproducing flood eventse) Cross‐Validation: Competitive performance in reproducing flood events.)
I t l ti I l di l ti i ltPrecipitation model Interpolation: Including correlation improves results;Precipitation model Figure 5: Interpolation: Including correlation improves results;Si l ti f fl di i fi ti l b
Figure 5: Error in Cross Validation: Acceptable for some variablesSimulation of floodings using fictional urban cases – Error in Cross‐Validation: Acceptable for some variables.Simulation of floodings using fictional urban cases simulating p
SWMM (Storm Water Management Model EPA)simulating some basicSWMM (Storm Water Management Model, EPA) some basic
References: Haberlandt U Ebner von Eschenbach A D and Buchwald I (2008): A( g , )
statistics, Figure 6: Test of fit: synthetic vs References: Haberlandt, U., Ebner von Eschenbach, A.‐D., and Buchwald, I. (2008): A statistics, total yearly
Figure 6: Test of fit: synthetic vs. b d t l i space‐time hybrid hourly rainfall model for derived flood frequency analysis Hydroltotal yearly
i f ll dobserved extreme values series. space time hybrid hourly rainfall model for derived flood frequency analysis, Hydrol.
/rainfall and
Earth Syst. Sci., 12, 1353‐1367, doi:10.5194/hess‐12‐1353‐2008.rainfall andfloodings Earth Syst. Sci., 12, 1353 1367, doi:10.5194/hess 12 1353 2008.floodings.
Institute of Water Resources ManagementEGU General Assembly April 28 May 2 2014 Vienna Institute of Water Resources Management, EGU General Assembly, April 28 – May 2, 2014, Vienna Hydrology and Agricultural Hydraulic Engineeringy, p y , , Hydrology and Agricultural Hydraulic [email protected]‐hannover.deca au@ .u a o e .de
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