EGS-AGU-EUG Joint Assembly, Nice, France, 6 - 11 April 2003 Session: Hydrological Sciences HS12 Rainfall modelling: scaling and non-scaling approaches A CASE STUDY OF SPATIAL-TEMPORAL RAINFALL DISAGGREGATION AT THE TIBER RIVER, ITALY Paola Fytilas1 , Demetris Koutsoyiannis2, Francesco Napolitano1 1 Department of Hydraulics, University of Rome “La Sapienza”, 2 Department of Water Resources, National Technical University of Athens 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 io riv F b . m A Si ni . e T ne 4.PONTE SALARIO F . A n F i . A e n i e 5.ROMA FLAMINIO ne ne 7.PANTANO BORGHESE 6.ROMA MACAO 3. FRASCATI The Methodology 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) Parameter Estimation 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: m (rij)h = (rij)d Preservation of marginal statistics 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 Preservation of cross correlation coefficients 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 Preservation of autocorrelation coefficients 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 Preservation of probability distribution functions at gauge Ponte Salario Hourly rainfall depths 10 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 Preservation of historical hyetographs 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 6 5 H6 4 S6 3 2 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.