Stochastic modelling approach for future flood risk modelling

Transcription

1 Stochastic modelling approach for future flood risk modelling S. Patidar1 1Institute H. Haynes1 Ji Li1 R. Haynes2 for Infrastructure and Environment, Heriot-Watt University, Edinburgh, Scotland, UK 2Scottish Environmental Protection Agency, SEPA

2 Motivation Climate change is playing a key role in the manifestation of the extreme climatic events, Eg. Flooding, hurricanes, cyclones, etc. Ø For the UK one of the most challenging issue is: ü increased risk of frequent and severe flooding in the future Ø Mostly flood risk management project involves: ü Use of single 1:N year extreme flow/rainfall event. Ø This approach does not accounts for: ü effect of flood clustering on channel cross-section ü effect of change in channel capacity on flood risk Ø Future climate change scenarios indicate that: ü storm and flood frequency will increase the UK s susceptibility to storm clusters will also be magnified.

3 Aim To develop an efficient modelling approach that combines: Ø stakeholder knowledge (Scottish Environment Protection Agency, SEPA) with cross-disciplinary academic expertise (statistical modelling, river process, climate change & flood modelling) Ø to refine mathematical modelling approaches in flood risk. Our approach includes: Ø Statistical modelling Ø sediment transport processes & related flood risk Ø multi-event simulation Ø flood sequence/cluster risk-recovery processes Ø but, able to work within the constraints of limited data & run times

4 Methodology Stochastic modelling of 15 min mean flow Generate multiple (e.g.100) synthetic flow sequences Hidden Markov Model + Generalised Pareto (HMM- GP) 1D/2D sediment transport modelling of flow sequences 100 future channel configurations Define worst-case channel 1D/2D flood hazard modelling using worst-case channel Quantify change in inundation Pender, D., Patidar, S., Pender, G. & Haynes, H. (2016) Stochastic simulation of daily streamflow sequences using a hidden Markov model. Hydrology Research, Vol. 47, no. 1, pp

5 Methodology Previous Work: Ø EPSRC s FloodMEMORY:Multi-Event Modelling Of Risk & RecoverY (EP/K013513/1) project as part of FCERM.net (EP/L000180/1) project has HMM-GP modelling framework for simulating synthetic daily flood sequences. Present work: Ø investigated suitability of HMM-GP modelling approach for simulating streamflow at a much finer temporal resolution of 15 minutes. Ø Ø Ø Validated for 14 distinct gauging stations across 4 cases study rivers Don, Nith, Dee and Tweed. Developed a systematic approach that exploits STL: a Seasonal-Trend decomposition procedure based on Loess for reframing HMM-GP modelling framework to allow integration of climate impact. Utilise 2D sediment transport and flood inundation modelling.

6 Why do we need stochastic model?

7 Why do we need stochastic model? Ø Computationally efficient at generating multiple realisations for uncertainty analysis Ø Provide realistic realisations of river flows Ø Can be used for long-term modelling Ø Allows estimation of sediment transport and loading on flood defences Ø Ensure long-term sustainability of flood defence assets Ø Easily applicable at multiple sites Ø Limits error accumulation that occurs using rainfall and hydrological models

8 Catchment geographical characteristics Ø The gauging stations were selected for the availability of 15-minutely data, the length of records and the minimal amount of missing data (less than 5%). The 15 minutely gauged dataset is provided by the Scottish Environmental Protection Agency (SEPA). Ø Ø All the selected river catchments have both the urban development areas (limited to less than 0.5%.) and headwater agricultural areas. The average daily flow located furthermost upstream of the rivers are below 13 m 3 /s and the downstream gauging stations show a variability within a range from 28 m 3 /s to 81 m 3 /s.

9 Catchment geographical and Statistical characteristics Catchment geographical characteristics Don Nith Dee Tweed Catchment area (km 2 ) River slope (m/km) Urban extent (%) River mobility Gauging station statistics High deposition high erosion Don (Houghton) Nith (Friars Carse) Dee (Woodend) Tweed (Norham) Time Period Mean (µ) Standard Deviation (s) Minimum (Q0) th Percentile (Q5) th Percentile (Q10) th Percentile (Q25) th Percentile (Q50) th Percentile (Q75) th Percentile (Q90) th Percentile (Q95) th Percentile (Q100)

10 Catchment statistical characteristics Case study rivers: ØDon at Haughton, ØNith at Friars Carse, ØDee at Woodend ØTweed at Norham. Ordered monthly box plot illustrating five summary statistics (5 th percentile, 25 th percentile, 50 th percentile, 75 th percentile and 95 th percentile; maximum values are specified at top of each box plot).

11 Stochastic Modelling of stream flow Ø to produce desired number of the synthetic flow-series our approach combines Hidden-Markov Model with extreme value distribution [Generalised Pareto (GP)]. Hidden Markov Model Ø Based on the evolution of process/system in time from a given state to another state, i.e. Ø Exploits the probability of the system to jump from one state to another Ø Accounts for the transition of system through hidden states

12 Hidden Markov Model A HMM model is comprised of five elements: 1. Set of distinct observed states - Percentile analysis of all observed values using increment of 10% to define eleven distinct observed states (A,B,C,D,E,F,G,H,I,J,K) Ø Ø Ø Ø Ø Ø State A flow between the minimum and 10 th Percentile State B flow between the10 th and 20 th percentile So on.

13 Hidden Markov Model 2. Set of unobserved (hidden) states within observed states account for all the discrete values with one decimal place within the range of each eleven distinct observed states. For example: Ø if state A corresponds to values between 0 to 1 then set of unobserved states corresponding to state A will be 0.1, 0.2, 0.3,, 0.9 Ø if state B corresponds to values between 1 to 2 then set of unobserved states corresponding to state B will be 1.1, 1.2, 1.3, 1.4,, 1.9 Ø so on

14 Hidden Markov Model 3. State transitional probability matrix probability of transition between different observed states. Ø Corresponding to eleven distinct states Þ11 11 matrix A B K A B K ém ê ê m ê... ê ê... ê ëm aa ba ka m m m ab bb kb m m m ak bk kk ù ú ú ú ú ú ú û

15 Hidden Markov Model 4. Emission probability matrix emission probability of underlying (hidden) states from discrete observed states. Ø Corresponding to eleven distinct states and nine underlying (hidden) state Þ11 9 matrix A B.... K! # # # # # # "# m a1 m a2... m a9 m b1 m b2... m b m k1 m k 2... m k 9 5. Set of eleven initial probability of observed states obtained from the analysis of time series data $ & & & & & & %&

16 Extreme Value Distribution

17 Stochastic modelling framework

18 Results: Comparing annual statistics Comparing: Probability Density Distribution (PDD); Quantiles (from 0 to 98 th percentile with a step size of 1); and Auto-Correlation Function (ACF) Statistics are estimated for entire 15 minutely streamflow dataset available over the observation period. for the observed (solid thick black lines) and 100 synthetic streamflow profiles (solid brown lines).

19 Results: Comparing annual statistics Comparing: 5 th, 25 th, 50 th, 75 th and 95 th percentiles for the observed (black dotted lines with solid circles) and 100 synthetic streamflow profiles (brown solid circles) for the case study river Don at Haughton. Percentiles are estimated for 15 minutely streamflow data for each year and over the period

20 Results: Comparing extreme percentiles Comparing 10 percentiles values from 99 th to 100 th percentile with a step size of 0.1 for the observed (black dotted lines with solid circles) and 100 synthetic streamflow profiles (brown solid circles) Percentiles are estimated for entire 15 minutely streamflow dataset available over the observation period. for the case study river Don at Haughton, Nith at Friars Carse, Dee at Woodend and Tweed at Norham.

21 Current uses within flood risk studies Sediment transport modelling: The two-dimensional hydro-morphological model (Telemac- 2D with SYSYPHE) is used to reproduce the floodplain inundation depth, areas and drying time. Flood cluster scenario design: Ø Case 1: 200 year RP followed by a 2 year RP Ø Case 2: 200 year RP followed by a 10 year RP Ø Case 3: 200 year RP followed by a 200 year RP

22 Current uses within flood risk studies The relationship between the maximum inundation area and the time between two events.

23 Current uses within flood risk studies The relationship between the maximum flow depth and the time between two events.

24 Current uses within flood risk studies The relationship between the drying time and the time between two events.

25 Conclusions

26 Future Work Aim to improve & constrain methods towards practitioner needs Objective 1: Climate change within the HMM-GP ü ü ü use of 15 minute gauge data which UKCIP scenarios? use of multiple gauges (pan-scotland & downstream translation of sensitivity) Objective 2: Constrain sequence clusters of influence ü use of 15 minute gauge data to run sequences ü describe/design clusters better (POT thresholds, event duration) ü compare cluster-in-sequence (CIS) to equivalent cluster-from-benchmark (CFB) ü minimum timeframe to capture change ( CFB?) ü compare hazard analysis Objective 3: Consider downstream translation of sensitivity

27 Integrating precipitation with HMM-GP model for synthesising flows sequences Percentile Distribution Model (PDM) to integrate precipitation information with the synthetic river flow series (generated by HMM-GP) Upper panel - HMM-GP Model has been trained using daily river flow and precipitation data. Clearly HMM-GP model follows closely with original flow data Lower Panel Model trained on data has been used to synthesis synthetic flow series for Demonstrate capabilities of PDM- HMM-GP modelling approach in effectively incorporating influence of precipitation with flow series.

28 Integrating precipitation with HMM-GP model for synthesising flows sequences Application of PDM-HMM-GP Model to generate future flow series using daily probabilistic precipitation projections (available from UKCP09) for two future time periods: Upper Panel 2030s 2020 to 2049 Lower Panel 2050s 2040 to 2069 Some notes Method need to be rigorously refined and possibilities for including other influencing variables need to be assessed.

29 Many thanks for attention J Journal papers Pender, D., Patidar, S., Pender, G. & Haynes, H. (2016) Stochastic simulation of daily streamflow sequences using a hidden Markov model. Hydrology Research, Vol. 47, no. 1, pp Pender, D., Patidar, S., Hassan, K. & Haynes, H. (2016). Method for Incorporating Morphological Sensitivity into Flood Inundation Modeling. Journal of Hydraulic Engineering, Vol. 142, Issue 6. Conference papers S. Patidar, K. Hassan, H. Haynes and G. Pender, Statistical modelling approach for integrating probabilistic climate projections with the river flow data, River Flow, St. Louis, Mo., July 12 15, S. Patidar, K. Hassan, H. Haynes, G. Pender and D. Pender, A model for stochastic simulation of daily streamflow, River Flow, St. Louis, Mo., July 12 15, Pender, D., Patidar, S. & Haynes, H. (2015) Incorporating River Bed Level Changes into Flood Risk Modelling, 36th IAHR World Congress, At The Hague, the Netherlands, Volume: E-proceedings of the 36th IAHR World Congress. Contact: S.Patidar@hw.ac.uk