Metric Optimisation for Analogue Forecasting based on Simulated Annealing. EGU General Assembly, April 2009, Vienna* bearbeiten

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1 Metric Optimisation for Analogue Forecasting based on Simulated Annealing EGU General Assembly, April 2009, Vienna* J. Bliefernicht and A. Bárdossy University of Stuttgart durch Klicken Institute of Hydraulic Engineering Chair for Hydrology and Geohydrology *:slightly updated version for publication; October /28/2015 1

2 Objective Niederschlagsvorhersage Weather Forecasting Basic Overview global numerical weather prediction (NWP) deterministic and ensemble-based approaches Titelmasterformat using downscaling techniques durch Klicken dynamical approaches (limited area model) adaptation of the NWP output statistical approaches durch Klicken Forecasting of meteorological surface variables e.g. precipitation, air temperature regression-based approach classification analogue method needed as input information for subsequent forecasting systems 2/28/2015 e.g. hydrological prediction models 2 This talk is about the analogue method

3 Analogue Method (e.g. Lorenz, 1969) past analogue (reanalysis) forecast (global NWP model) Titelmasterformat weather information durch Klicken P = 5 mm/d T = 8 C The local surface of the past analogue is used as forecast durch Klicken normalised geopotential height normalised geopotential height 2/28/2015 3

4 Analogue Method (e.g. Lorenz, 1969) Model performance depends on various subjective criteria: Distance function (metric) for measuring the closeness between Titelmasterformat meteorological fields durch Klicken Location and size of predictor domain (embedding dimension) Predictor variable Number of analogues durch Klicken To tackle the first two issues: novel algorithm for an optimisation of the distance function and predictor domain evaluation of the novel algorithm for daily areal precipitation extremes crucial information for hydrological prediction 2/28/2015 4

5 Spatial Distribution of the Metric Weights Traditional way: uniform Symmetric durch Klicken 2/28/2015 5

6 What is the Optimum Distribution of the Weights? Uniform Symmetric? durch Klicken approximate the distribution of the weights optimisation algorithm 2/28/2015 6

7 Distance Function weighted Euclidean distance: n Titelmasterformat durch 2 d( t Klicken 1, t2) gi xi ( t1) xi ( t 2) i 1 g i: weight at grid point i specific durch case: Euclidean Klicken distance with traditional way of defining the weights in analogue forecasting g 1 = g 2 = = g n 2/28/2015 7

8 Study Region, Niederschlagsvorhersage Target Variable, Model Development study region German Rhine basin Titelmasterformat external durch drift kriging Klicken Pruem Ruhr predictor Upper similar to perfect prog Sieg Upper Main durch Klicken Nahe F. Saale predictand daily areal precipitation gridded data set geopotential height NCEP/NCAR reanalysis investigation period model development training period: cross-validation validation period: independent data set 2/28/2015 8

9 Objective Function I - Precipitation daily precipitation amount (intuitive choice) highly skewed!!! durch Klicken objective function indicator time series (0,1) of daily areal precipitation with a focus on extremes 2/28/2015 9

10 Objective Niederschlagsvorhersage Function II Discharge Changes durch Klicken 2/28/

11 Objective Niederschlagsvorhersage Function II Discharge Changes small daily discharge changes durch Klicken 2/28/

12 Objective Function II Discharge Changes small daily discharge changes almost symmetric durch Klicken indicator time series of daily flow changes which focus on small flow changes 2/28/

13 Objective Function II Discharge Changes small daily discharge changes Optimisation algorithm define the weight at each grid point almost symmetric simulated annealing (e.g. Aarts & Korst, 1989) step-by-step durch optimisation Klicken indicator time series of daily flow changes which focus on small flow changes 2/28/

14 Optimised Weights using Precipitation objective function I precipitation study region durch Klicken 2/28/

15 Optimised Weights using Discharge Changes objective function II discharge changes study region durch Klicken 2/28/

16 Modell Improvement* - Training Period (34 years) durch Klicken *:Baseline is a symmetric distribution of weights 2/28/

17 Modell Improvement* - Validation Period (10 years) durch Klicken *:Baseline is a symmetric distribution of weights 2/28/

18 Summary and Conclusions optimisation algorithm for analogue forecasting to define the optimum distance and the predictor domain replaces a time consuming manual calibration tested for intensive daily areal precipitation transferrable to other local surface variables durch Klicken model predictions indicate that the methodology can improve the traditional way of analogue forecasting but be careful with the selection of the objective function 2/28/

19 Further Readings and References Further information Bliefernicht (2010): Probability Forecasts of Daily Areal Precipitation for Small River Basins: Chapter 5: Metric Optimisation, Dissertation, Institut für Wasserbau, Universität Stuttgart, Germany. Analogue Method Lorenz, E.: Atmospheric predictability as revealed by naturally occurring analogues, Journal of the Atmospheric Sciences, 26, , Zorita, E. and von Storch, H.: The analog method as a simple statistical downscaling technique: Comparison with more complicated methods, Journal of Climate, 12, , durch Klicken Obled, C., Bontron, G., and Garcon, R.: Quantitative precipitation forecasts: a statistical adaptation of model outputs through an analogues sorting approach, Atmospheric Research, 63, , Bliefernicht, J. and Bárdossy, A.: Probabilistic forecast of daily areal precipitation focusing on extreme events, Natural Hazards and Earth System Sciences, 7, , Metric optimisation in analog forecasting: Fraedrich, K. and Rückert, B.: Metric adaption for analog forecasting, Physica A: Statistical Mechanics and its Application, 253, , /28/

20 Training Period durch Klicken 2/28/

21 Validation Period durch Klicken 2/28/