Workshop ChoP-HM: Change of Paradigms in Hydrological Modelling; 3.-5. October 2003, Thurnau Castle, Germany The use of additional experimental data to educe the prediction uncertainty of models The solution? Stefan Uhlenbrook University of Freiburg, Institute of Hydrology, Germany
What do we need for a Change of Paradigms? Complete new insights gained, e.g. by: a new sensor/device? a really new modeling structure?... (Hydrology Einstein?) Maybe we should state the problem clearly, as... the mere formulation of a problem is far more often essential than its solution. (Einstein)
Problem: How predictions are done? - Hydrology - Ecology - Socio-economy????? Precip. [mm/h] Niederschlag [mm/h] 01.08.95 01.10.95 01.12.95 31.01.96 01.04.96 01.06.96 0 10 20 30 20 discharge [mm/h] Abfluss [m³/s] 18 16 14 12 10 8 6 gemessener Abfluss observ ed simulat ed simulierter Abfluss 4 2
Predictive Uncertainty: (PUB 2003) Links to Heterogeneity
Objectives (1) Multiple-response validation using a process-based model (2) Prediction uncertainty of modeled floods (3) Ways to reduce the uncertainty by incorporation additional field data
rugga Basin (Black Forest Mountains, Germany) P = Q + ET : 1750 mm = 1230 mm + 520 mm
(6) Runoff routing: Kinematic wave The model TAC D (tracer aided catchment model, distributed) Evapotranspiration: Penman-Monteith approach (1) Regionalization of input data: IDW, elevation gradients, topography and rainfall radar (2) Snow melt: Temperature index model (3) Interception: after Hoyningen-Heune (4) Soil water: BETA-function (HBV model) (5) Runoff generation: Designed reservoirs
Results Modelling of the main basin and a sub-basin 80 0 Abfluss [m³/s] 70 60 50 40 30 20 10 0 01.11.1995 26.11.1995 21.12.1995 15.01.1996 09.02.1996 05.03.1996 30.03.1996 24.04.1996 30 0 Zeit observed simulated 25 Niederschlag gemessener Abfluss simulierter Abfluss Dreisam (258 km 2 ) Abfluss [m³/s] 20 15 10 10 20 30 40 50 60 Niederschlag [mm] Brugga (40 km 2 ) 10 20 30 40 5 50 0 60 01.11.1995 26.11.1995 21.12.1995 15.01.1996 09.02.1996 05.03.1996 30.03.1996 24.04.1996 Zeit
Simulation of Dissolved Silica: Snow melt in spring 1996 precipitation [mm/h] discharge [mm/h] 3 2 1 0 5 4 3 2 1 simulated runoff observed runoff 20 10 0-10 0 7 6 Silikat Si [mg/l] 5 4 3 2 Si observed Si simulated 1 3000 3200 3400 3600 3800 4000 4200
Using TAC D in an extrapolation mode (2) uncertainty analysis of flood predictions Parameter uncertainy Model uncertainty uncertain predictions Incomplete process understanding Error in observed data Error due to regionalization
Results of runoff simulations Statistical measures: R eff and logr eff ummer vents winter vents R eff Oberried R eff St. Wilhelm (40 km 2 ) (15.2 km 2 ) Min Max Min Max Event 1-4.7 0.98 0.1 0.96 Event 2-9.4 0.97-12.7 0.96 Event 3-14.8 0.95-20.5 0.87 Event 4-5.2 0.97-30.7 0.97
Results of runoff simulations tatistical measures: R eff (Nash and Sutcliffe 1970) ummer vents winter vents R eff Oberried R eff St. Wilhelm (40 km 2 ) (15.2 km 2 ) Min Max Min Max Event 1-4.7 0.98 0.1 0.96 Event 2-9.4 0.97-12.7 0.96 Event 3-14.8 0.95-20.5 0.87 Event 4-5.2 0.97-30.7 0.97
Uncertainty Analysis Generalized Likelihood Uncertainty Estimation (GLUE) probability (-) mean accumulated probability (-) mean 5%-quantile 95%-quantile discharge (m 3 /s) discharge (m 3 /s)
Uncertainty of runoff prediction event no. 2, summer event 10.0 5 %-Quantil 95 %-Quantil R eff Oberried fuzzy-transf. discharge (m 3 /s) Abfluss [m 3 /s] 7.5 5.0 R eff Oberried / R 2 Silikat R eff Oberried / R eff St.Wilhelm observed gemessener Abfluss runoff 2.5 0.0 23.08.98 24.08.98 24.08.98 24.08.98 25.08.98 25.08.98
Reducing the uncertainty bounds by integrating additional information (1/2) 10.0 5 %-Quantil 95 %-Quantil R eff Oberried fuzzy-transf. discharge (m 3 /s) Abfluss [m 3 /s] 7.5 5.0 R eff Oberried / R 2 Silikat R eff Oberried / R eff St.Wilhelm observed gemessener Abfluss runoff 2.5 0.0 23.08.98 24.08.98 24.08.98 24.08.98 25.08.98 25.08.98
discharge (m 3 /s) Reducing the uncertainty bounds by integrating additional information (2/2) 5 Abfluss [m 3 /s] 4 3 2 5 %-Quantil 95 %-Quantil R eff Oberried fuzzy-transf. R eff Oberried / R 2 Silikat R eff Oberried / R eff St.Wilhelm R eff Oberried / R 2 Silikat / R eff St.Wilhelm observed gemessener Abfluss runoff 1 0 21.03.96 23.03.96 25.03.96 27.03.96 29.03.96 31.03.96 02.04.96
Conclusions from the case study (1) Well-validated model give uncertain predictions (2) Value of additional data to reduce uncertainty can be large, but is not warranted (additional parameters) (3) Spatial and temporal variability of uncertainties
Should we wait for the mega-multi-super probe/sensor? Now I understand hydrological processes!
Should we wait for a single flash light? (PUB 2003)
PUB: Research Targets (PUB 2003)
Do you agree???