A Case Study of Spatial-Temporal Rainfall Disaggregation at the Tiber River Basin, Italy

1 TEMPORAL TEMPORAL - -

al Technical University of Athens

, Francesco Napolitano 2 HS12 TIBER RIVER, ITALY TIBER RIVER, ITALY

, Demetris Koutsoyiannis Hydrological Sciences 1 RAINFALL DISAGGREGATION AT THE RAINFALL DISAGGREGATION AT THE

EGS-AGU-EUG Assembly, Nice, France, 6 - Joint 11 April 2003 Session: Rainfall modelling: scaling and non-scaling approaches A CASE STUDY OF SPATIAL A CASE STUDY OF SPATIAL Department of Hydraulics, University of Rome “La Sapienza”, University Department of Hydraulics, Department of Water Resources, Nation

Paola Fytilas 1 2 Study Area:Area Aniene River Catchment-Tiber River-Central Italy Data period:January 1994-December 1999 • Raingauges with hourly data used in the generation phase • Raingauges with hourly data used to evaluate the effectiveness of the methodology • Raingauges with daily data only

F . . A nie ne

1.TIVOLI F 8.ROMA ACQUA ACETOSA . A n ie ne 2.L UNGHEZZA

riv

b F . m A Si n . i e T ne

4.PONTE SALARIO F . An F . A i n e i e n ne 5.ROMA FLAMINIO e 7.PANTANO BORGHESE

6.ROMA MACAO

3. FRASCATI TheThe MethodologyMethodology

Observed DAILY data at Observed several points HOURLY data at several points

Marginal statistics (d) Marginal statistics (h) Temporal Correlation(d) Temporal Correlation(h) Spatial Correlation (d) Spatial Correlation (h)

Spatial-temporal Multivariate Simplified COUPLING Rainfall model or Point rainfall model TRANSFORMATION empirical expression AR(1) disaggregation for cross-correlation coefficients

Synthetic Hourly Synthetic Hourly Data at several Data at several points points (not consistent (consistent with daily with daily amounts) amounts) ParameterParameter EstimationEstimation

Essential statistics to preserve in the generated hourly series : 1.the means, variances and coefficients of skewness; 2.the temporal correlation structure (autocorrelations); 3.the spatial correlation structure (lag zero cross-correlations); and 4.the proportions of dry intervals. Daily time scale:estimated directly using the data set available for all raingauges Hourly time scale:All the statistics, including the cross-correlations coefficients between gages 1,2,3 can be estimated directly from the data set available at these locations. The unknown cross-correlation coefficients at hourly level were estimated indirectly using the empirical relationship:

(rij)h = (rij)d PreservationPreservation ofof marginalmarginal statisticsstatistics

Mean Proportion dry Standard deviation

0.16 0.92 0.76 historical 0.74 0.16 value used on disaggregation 0.90 0.15 synthetic 0.88 0.72 0.15 0.86 0.70 0.14 0.84 0.68 0.66 Mean 0.14 0.82 0.13 0.64

Proportion dry 0.80 0.13 0.62

0.78 Standard deviation 0.12 0.76 0.60 0.12 12345678 0.58 12345678 12345678 raingauges raingauges raingauges

Skewness Maximum hourly rainfall depths Lag1 autocorrelation coefficients

0.70 14.00 25 0.60 12.00 20 0.50 10.00 15 0.40 8.00 0.30 c 6.00 10

Skewness 0.20

4.00 valueMaximum 5

Lag1 autocorrelation 0.10 2.00 0 0.00 0.00 12345678 12345678 12345678 raingauges raingauges raingauges PreservationPreservation ofof crosscross correlationcorrelation coefficientscoefficients

Lag0 cross-correlation coefficients-gauge 1 Lag0 cross-correlation coefficients-gauge 2 Lag0 cross-correlation coefficients-gauge 3

1.00 1.00 1.00 0.90 0.90 0.90 0.80 0.80 0.80 0.70 0.70 0.70 0.60 0.60 0.60 0.50 0.50 0.50 0.40 0.40 0.40 0.30 0.30 0.30 cross-correlations 0.20 cross-correlations 0.20 cross-correlations 0.20 0.10 0.10 0.10 0.00 0.00 0.00 12345678 12345678 12345678 raingages raingages raingauges

Lag0 cross-correlation coefficients-gauge 4 Lag0 cross-correlation coefficients-gauge 5 Lag0 cross-correlation coefficients-gauge 6

1.00 1.00 1.00 0.90 0.90 0.90 0.80 0.80 0.80 0.70 0.70 0.70 0.60 0.60 0.60 0.50 0.50 0.50 0.40 0.40 0.40 0.30 0.30 0.30 cross-correlations

0.20 cross-correlations 0.20 cross-correlations 0.20 0.10 0.10 0.10 0.00 0.00 0.00 12345678 12345678 12345678 raingauges raingauges raingauges PreservationPreservation ofof autocorrelationautocorrelation coefficientscoefficients

Ponte Salario Roma Flaminio

1.00 1.00 0.90 0.90 H5 S5 Markov 0.80 H4 S4 Markov 0.80 0.70 0.70 0.60 0.60 0.50 0.50 0.40 0.40 0.30 0.30 Autocorrelation Autocorrelation 0.20 0.20 0.10 0.10 0.00 0.00 012345678910 012345678910 Lag Lag

Roma Macao 1.00 0.90 0.80 H6 S6 Markov 0.70 0.60 0.50 0.40

Autocorrelation 0.30 0.20 0.10 0.00 012345678910 Lag PreservationPreservation ofof probabilityprobability distributiondistribution functionsfunctions atat gaugegauge PontePonte SalarioSalario

Hourly rainfall depths

Historical Simulated Length of dry intervals 1

250

200 hourly rainfall depth[mm/h] Historical 0.1 Simulated 0.7 0.8 0.9 0.95 0.99 0.999 0.9999 150 Non exceedence probability 100

50 length of dry intervals [h] intervals dry of length

0 0.001 0.01 0.1 1 Exceedence probability PreservationPreservation ofof historicalhistorical hyetographshyetographs

Ponte Salario Roma Flaminio

6 6

5 5 H4 H5 4 S4 4 S5

3 3

2 2

1 1 hourly rainfall depths [mm] hourly rainfall depths [mm] depths rainfall hourly 0 0 3/12/1998 3/12/1998 4/12/1998 4/12/1998 5/12/1998 5/12/1998 3/12/1998 3/12/1998 4/12/1998 4/12/1998 5/12/1998 5/12/1998 0:00 12:00 0:00 12:00 0:00 12:00 0:00 12:00 0:00 12:00 0:00 12:00

Roma Macao

5 H6 4 S6

1 hourly rainfall depths[mm] 0 3/12/1998 3/12/1998 4/12/1998 4/12/1998 5/12/1998 5/12/1998 0:00 12:00 0:00 12:00 0:00 12:00