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The modern flood forecasting


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This is the English translation, with some relevant corrections, of the talk I gave at University of Calabria, about the contemporary and post-contemporary flood forecasting.

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The modern flood forecasting

  1. 1. The modern flood forecasting Riccardo Rigon, Francesco Serafin, Marialaura Bancheri, Michele Bottazzi, and Giuseppe Formetta Cosenza 27 Luglio 2017 MichelangeloBuonarroti,CappellaSistema-IldiluvioUniversale,1508ca
  2. 2. “Prediction is very difficult, especially about the future!” Niels Bohr (1885-1962)
  3. 3. !3 Modern ? Much better: contemporary and smart Modern, on a closer inspection, is what is before contemporary. Modern: HEC-HMS SWAT SWMM *** I cannot forget the simple good old model of the instantaneous unit hydrography! Please see: http:// Rigon et al. A few digressions at the beginning
  4. 4. !4 The three tools above let you estimate, after an accurate estimation, flood wave. They are open source, supported by a wide community of developers and users. They work ! What else should we wish ? There are tens of good models of the hydrologic response*. Why are we here talking again about them ? One issue is the forecasting word *not all models are good. Some are better. Rigon et al. A few digressions at the beginning
  5. 5. !5 Forecasting means organisation of data, for instance To run, a good hydrological model needs data. The minimal set: • digital elevation models • precipitations (at sub hourly time scale fro small basins) • Some discharge mesurements (for models calibration) Many more data for accurate works: • temperature • radiation • snow measurements Rigon et al. A few digressions at the beginning
  6. 6. !6 DATA IN Robbed from Maurizio Napolitano Rigon et al. No data, no party
  7. 7. !7 Forecasting implies organization and interpretation of models of results DATA INFORMATION INFORMATION KNOWLEDGE DATA INFORMATION INFORMATION KNOWLEDGE Rigon et al. Data are just the beginning
  8. 8. !8 Sviluppare un adeguato sistema di modellistica per la pianificazione e la gestione; Sviluppare un adeguato sistema di previsione nelle applicazioni in tempo reale; Sostenere l’organizzazione in anticipo dei servizi di piena e di tutte le azioni di difesa del suolo, incluse le misure di protezione civile per la gestione delle emergenze. Gli obiettivi del progetto Rigon et al. A couple of examples @ARPAE CourtesybySilvanoPecoraeCinziaAlessandrini
  9. 9. !9 @ARPAE Rete osservativa Giornalmente il sistema acquisisce una serie di dati dalla rete osservativa Rete di monitoraggio : 919 Idrometri (blu) 1315 Pluviometri (verde) 167 Nivometri (verde) 928Termometri (verde) 193 Dighe RID (violetto) DATA INFORMATION INFORMATION KNOWLEDGE Rigon et al. CourtesybySilvanoPecoraeCinziaAlessandrini A couple of examples
  10. 10. !10 Forcasting means to choose the right models Rigon et al. Which is the best model ? Not the perfect ones, but those needed by the goal behind us, and also just in flood forecasting, objective can be different. 1. On the best model: model-is-better-q.html 2. Essentials for hydrologists: hydrologists.html 3. What can I estimate with this or the other ? : 2013/03/can-i-simulate-effects-of-changing.html 4. I am sick and tired to answer about those “standard” models: http:// 5. Again on the best model: hydrological-model-is-better.html
  11. 11. !11 Le catene modellistiche HEC-HMS DHI-NAM TOPKAPI HEC-RAS DHI – M11 SOBEK HMS/NAM/TOPKAPI RAS/MIKE11/SOBEK Prima catena Seconda catena Terza catena Catena configurabile dall’utente PRECIPITAZIONI TEMPERATURE LIVELLI/PORTATE MODELLI METEOROLOGICI Osservati/Telemisura LM/Ensemble VALIDAZIONE, INTERPOLAZIONE E TRANSFORMAZIONE DATI @ARPAE DATA INFORMATION INFORMATION KNOWLEDGE Rigon et al. Meteo countsCourtesybySilvanoPecoraeCinziaAlessandrini
  12. 12. !12 Le catene modellistiche HEC-HMS DHI-NAM TOPKAPI HEC-RAS DHI – M11 SOBEK HMS/NAM/TOPKAPI RAS/MIKE11/SOBEK Prima catena Seconda catena Terza catena Catena configurabile dall’utente PRECIPITAZIONI TEMPERATURE LIVELLI/PORTATE MODELLI METEOROLOGICI Osservati/Telemisura LM/Ensemble VALIDAZIONE, INTERPOLAZIONE E TRANSFORMAZIONE DATI DATA INFORMATION INFORMATION KNOWLEDGE @ARPAE Rigon et al. Hydrology countsCourtesybySilvanoPecoraeCinziaAlessandrini
  13. 13. !13 I modelli idrologici • HEC – HMS (SMA model, Bennett, 1985) • DHI – NAM (NAM model, S.A. Nielsen and E. Hansen, 1973) • TOPKAPI (TOPKAPI model, Todini 1995) DATA INFORMATION INFORMATION KNOWLEDGE @ARPAE Rigon et al. Hydrology counts. It is usually a bunch of reservoirsCourtesybySilvanoPecoraeCinziaAlessandrini
  14. 14. !14 Le catene modellistiche HEC-HMS DHI-NAM TOPKAPI HEC-RAS DHI – M11 SOBEK HMS/NAM/TOPKAPI RAS/MIKE11/SOBEK Prima catena Seconda catena Terza catena Catena configurabile dall’utente PRECIPITAZIONI TEMPERATURE LIVELLI/PORTATE MODELLI METEOROLOGICI Osservati/Telemisura LM/Ensemble VALIDAZIONE, INTERPOLAZIONE E TRANSFORMAZIONE DATI DATA INFORMATION INFORMATION KNOWLEDGE @ARPAE Rigon et al. Flood wave propagation (does it matters ?)CourtesybySilvanoPecoraeCinziaAlessandrini
  15. 15. !15 Let me say that maybe ARPAE is not contemporary, but for sure post- modern. DATA INFORMATION INFORMATION KNOWLEDGE @ARPAE Rigon et al. Post - modern
  16. 16. !16 Some traits: •Real time (with real time flowing of information) •Multimodels ( based on Delt-Fews) •Uses meteo models and data (for real time) DATA INFORMATION INFORMATION KNOWLEDGE @ARPAE Rigon et al. The post modern Let me say that maybe ARPAE is not contemporary, but for sure post- modern.
  17. 17. !17 Connec9ng Rainfall to Flooding Connec9ng Rainfall to Flooding @IOWAINFORMATION KNOWLEDGE Witold F. Krajewski, Daniel Ceynar, Ibrahim Demir, Radoslaw Goska, Anton Kruger, Carmen Langel, Ricardo Mantilla, James Niemeier, Felipe Quintero, Bong-Chul Seo, Scott J. Small, Larry J. Weber, and Nathan C. Young, Real-Time Flood Forecasting and Information System for the State of Iowa, Real-time flood forecasting and information system for the State of Iowa, Bull. Am. Meteorol. Soc., doi:10.1175/BAMS-D-15-00243.1, 2017. Rigon et al. The contemporary ?CourtesybyRicardoMantilla
  18. 18. !18 @IOWAINFORMATION KNOWLEDGE Hyperresolution Rigon et al. CourtesybyRicardoMantilla The contemporary ?
  19. 19. !19 @IOWAINFORMATION KNOWLEDGE However, using high resolution spatola data is not all the story. Making hydrology at high resolution is. Rigon et al. CourtesybyRicardoMantilla The contemporary ?
  20. 20. !20 Radar rainfall coverage of Iowa Radar Information @IOWAINFORMATION KNOWLEDGE Rigon et al. CourtesybyRicardoMantilla The contemporary ?
  21. 21. !21 Statewide implementa9on of the HLM-Async Model Our distributed hydrological model provides streamflow predic9ons everywhere in Iowa @IOWAINFORMATION KNOWLEDGE Further information @ AboutHydrology Rigon et al. CourtesybyRicardoMantilla The contemporary ?
  22. 22. !22 HPC Cluster University of Iowa Data Center Virtual Servers IFC Central Database Server Model Forecasted Discharge River Network Topology, Rainfall Maps IFIS Underlying Cyber-Infrastructure: System Overview Rainfall Maps HTTP Data Transfer Reading from DB (TCP 5432) Wri-ng into DB (TCP 5432) Push Informa-on Pull Informa-on Model Forecasted and Real Stage and Discharge IFC Real Time Flood Forecas9ng Model Iowa Flood Informa9on System IFC Rainfall System @IOWAINFORMATION KNOWLEDGE Smart = Cyberinfrastructure + realtime measurements* *Iy must be clear: ARPAE too has a complex and similar cyberinfrastructure. Rigon et al. CourtesybyRicardoMantilla The contemporary - smart
  23. 23. !23 Predic9ons from The Model @IOWAINFORMATION KNOWLEDGE Rigon et al. Great resultsCourtesybyRicardoMantilla
  24. 24. !24 Hyperresolution* (~1 km2) Multiobjective -Multipurpose (at least for discharges) -Multiprocesses (describes multiple processes) Open (I will be back on this in a couple of slides) Coming with confidence of estimates Rigon et al. The post-contemporary ;-) The Manifest of Contemporary flood models, IMO*: * In My Opinion * Wood, E. F., Roundy, J. K., Troy, T. J., van Beek, L. P. H., Bierkens, M. F. P., Blyth, E., et al. (2011). Hyperresolution global land surface modeling: Meeting a grand challenge for monitoring Earth's terrestrial water. Water Resources Research, 47(5). CourtesybyRicardoMantilla
  25. 25. !25 So now, the poor hydrologists go home: all has been already done all is in the hands of (big) institutions all is too big, too complex, out of singles capacity Rigon et al. Sigh!
  26. 26. !26 Is not exactly like this The forecasting quality is not everywhere accurate. On the contrary, usually, is usually poor at the small scale. There is a problem of verification that the big guys cannot pursue alone. Environmental engineers does not necessario need that real-time knowledge. Planning requires statistical analysis. Water management, for the common good, implies the verification and balancing of many factors, to highlighten alternative answers, which corresponds to different need s of local and global societies. Laws and norms count. Rigon et al. Gulp!
  27. 27. !27 Fran Orford Supermodel Having a supermodel infrastructure does not solve, alone, the problems Rigon et al. Cartoons !
  28. 28. !28 Open Rigon et al. IMO, a contemporary and smart approach should allow collaborative work in which the capacity of single actors to go deeper are harmonised and contribute to Institution work. Institutions efforts, in turn, looks towards to share and avoid asymmetry in information.
  29. 29. !29 Studying floods is not only calculate a flood and, not even, many floods hazards defense works landslides forest agricolture glacier melting permafrost degradation agricolture ecology fishing drinking water hunting water withdraw A. Zisch, 2013 Besides Rigon et al.
  30. 30. !30 Flood forecasting in the contest of engineers work require more complex thinking that just estimatin flood wave. As European norms remark Rigon et al. Norms and laws
  31. 31. !31 It is needed to move from estimating floods in a catchment “as is” to forecasting “in which certain characteristics are modified (by climate change or human intervention)” while other are kept fixed. To do this it is necessary that the varying characteristics have been described explicitly in models. A tipica question: does increase of forest or changing agricolture management change floods (water yeld)? Rigon et al. Flood forecasting in a more wider context
  32. 32. !32 P Q S = 0 t ⇠ 10 anni Per una discussione più dettagliata sul tema: Rigon et al. Quantitative studies
  33. 33. !33 that could account explicitly for atrophic actions and a full set of feedbacks at multiple scales Entropy 2014, 16 3484 Figure 1. Quantification of the entropy or exergy budgets in the Critical Zone at different spatial scales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uijanooandLin,Entropy,2014 They require a new modeling approach Rigon et al.
  34. 34. !34 We actually do not know how to put this stuff all together in models H067:Hydrologic Dynamics, Complexity and Predictability: Physical and Analytical Approaches for Improving System Understanding and Prediction Session ID#: 23200 Session URL and Abstract Submission (deadline 3 August): Session Description: Hydrology is a rich multidisciplinary field encompassing a complex process network involving interactions of diverse nature and scales. Still, it abides to core dynamical principles regulating individual and cooperative processes and interactions, ultimately relating to the overall Earth System dynamics. This session focuses on advances in theoretical and applied studies in hydrologic dynamics, regimes, transitions and extremes along with their physical understanding, predictability and uncertainty. Moreover, it welcomes research on dynamical co-evolution, feedbacks and synergies among hydrologic and other earth system processes at multiple spatiotemporal scales. The session further encourages discussion on physical and analytical approaches to hydrologic dynamics ranging from traditional stochastic, information-theoretical and dynamical analysis to general frameworks addressing non-ergodic and thermodynamically unstable processes and interactions.   This session is further complemented by an ongoing special issue at the EGU journal Earth System Dynamics: Grateful for your attention and consideration, we look forward to your contributions. With warm regards, The Conveners: Rui A. P. Perdigão and Julia Hall TU Wien, Austria Rigon et al. It is a topic for research
  35. 35. !35 H023 "Balancing the Water Budget: A Physical Basis for Quantifying Water Fluxes Using Data and Models"  at the 2017 Fall Meeting of the American Geophysical Union.  We are excited to explore the emerging challenges of balancing the water budget through a fusion of mechanistic and statistical approaches to hydrology. Session Description: Mass balance is the governing principle in the characterization of hydrologic processes. The water budget, ΔStorage = Input – Output, is a “first principles lens” that can be used to guide exploration, observations, and process representation of hydrologic fluxes. Furthermore, it constitutes the framework in which we integrate and evaluate hydrologic models at multiple spatio-temporal scales (from single events to multi-decadal cycles, and from watersheds to continents). Given its fundamental importance, an important question is to what degree and with how much confidence can the water budget be balanced. This session solicits studies exploring this question at multiple spatial and temporal scales using both data-driven and model-based approaches. We especially welcome efforts to incorporate a broad understanding of conservation of mass into the evaluation or integration of hydrologic models. Improved system-wide understanding is paramount as the globalization of water and trade of “virtual” water stocks become the status quo. Confirmed Invited Speakers Jim Kirchner, ETH Zürich, Zurich, Switzerland Richard Hooper, Tufts University, Medford, MA Best regards, William Farmer Jessica Driscoll Christopher Tennant Dino Bellugi Rigon et al. It is a topic for research
  36. 36. !36 (4.1) k @t = Jk(t)+ i Qki(t)° ETk(t)°Qk(t) for an appropriate set of elementary control volumes connected together. In Eq.(5.1), S [L3 ] represents the total water storage of the basin, J [L3 T°1 ], ET [L3 T°1 ], and Q [L3 T°1 ] are precipitation, evapotranspiration, and runoff (surface and groundwater) respectively. The Qis represent input fluxes, of the same nature of Q, coming from adjacent control volumes. a b Figure 4.1: The location of the Posina basin in the Northeast of Italy (a) and DEM elava- tion, location of rain gauges and hydrometer stations, subbasin-channel link partitions used for this modelling (b). It is clear that Eq.(5.1) is governed by two types of terms, which can be easily identi- fied as “inputs" and “outputs". The outputs are certainly evapotranspiration, ET, and discharges, Q, including the Qis, because they come from the assembly of control volumes. The inputs are J(t), but this term has to be split into rainfall and snowfall. Moreover, other inputs are ancillary to the estimation of outputs, in particular temperature, T and radiation Rn. Another input of the equation is the definition of the domain of integration and its“granularity", i.e. its partition into elements for which a singe value of the state variables is produced. In this paper we discuss the estimation of all of these input quantities, with the A starting point Abera et al., HESS, 2017 Posina A small basin of 114 km2 in Vicenza province, that flows into the As Bacchiglione-Brenta system. The model is JGrass-NewAGE Rigon et al.
  37. 37. !37 The scheme, for each subbasin could be represented as*: receive precipitation (the flux can be separated in rainfall and snowfall ) gives evapotranspiration and discharge this “reservoir, can be further “ e x p l o d e d ” i n m u l t i p l e reservoirs, according to various solutions a flux a quantity that varies The mathematical skeleton * Rigon et al.
  38. 38. !38 All us multiplied by the number of Hydrologic Response Units Here just 5 Rigon et al.
  39. 39. !39 The IOWA model covers thousands of basins like this Mass Conservation Equations Fluxes between control volumes dsp dt = P t( )− qpl − qpc − ep dsl dt = qpl − qls − el dss dt = qls − qsc − es qpc = k2sp 1.67 and qpl = kl sp qls = kisl and qsc = k3ss kl = kDRY 1− sl Sl ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ N Channel Routing dqc dt = voqc λ1 Aλ1 1− λ1( )l qpc + psc − qc + qu u∈c ∑ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Modeling the Land-Surface (Under the hood) CourtesyofRicardoMantilla Rigon et al. Which is also what the IOWA model does
  40. 40. !40 Going this way means to assume* that our catchment could be modeled (reduced to) a set of ordinary differential equations** Mathematical muscles tuple of water quantity in reservoirs tuple of inputs tuple of outputstuple of parameters tuple of initial conditions From a mathematical point of view, this is a dynamical system ** To which corresponds a view for travel time Rigon et al. * Here a trial to get ODEs from PDEs systems
  41. 41. !41 This mathematics is common to many other disciplines Rigon et al. I say that because there is plenty of literature treating with dynamical systems which can be easily borrowed to analyse catchments then. In particular, they are open (have inputs and outputs), non-linear (equations are often non linear), parametric (the “quality of equations depends on their parameters) dynamical systems. Since our system is open (but it could be potentially closed, speaking about mass flow) methods used to study Dynamical Systems and the related nomenclature were never used though.
  42. 42. !42 0 50 100 1994 1995 1996 1997 1998 1999 Time [h] Q[m3 /s] Measured Hymod Model Discharge Here a result with many comments to do* …. *Both simulations preserve the mass budget All this work … just for this ? Rigon et al.
  43. 43. !43 0 10 20 30 Jan 2005 Apr 2005 Jul 2005 Oct 2005 Jan 2006 Date Discharge(m3/s) 0.0 2.5 5.0 7.5 10.0 Jan 2005 Apr 2005 Jul 2005 Oct 2005 Jan 2006 Date Discharge(m3 /s) OBS SIM 0 5 10 15 20 25 Jan 2005 Apr 2005 Jul 2005 Oct 2005 Jan 2006 Date Discharge(m3 /s) 0 1 2 3 Jan 2005 Apr 2005 Jul 2005 Oct 2005 Jan 2006 Date Discharge(m3 /s) 0.0 0.2 0.4 0.6 Jan 2005 Apr 2005 Jul 2005 Oct 2005 Jan 2006 Date Discharge(m3/s) Link 14 Link 9 Link 32 Link 1 Link 3 1 Link 9 Figure 9: NewAGE model forecasting validation at internal links. Discharge is estimated for all links, here plotted for links 1,3, 9 (the outlet links), and 14, 27, and 32 as samples. When data is available at any internal point, model performances can be evaluated by comparison (e.g. for links 14 and 32). 12 Rigon et al. Projections inside the basin Abera,W.,Formetta,G.,Borga,M.,&Rigon,R.(2017).
  44. 44. !44 ation. It is highest in June er to February, as expected, nual budget. In 2012, from ation is sustained by the wa- recipitation, indicating that, tion of the catchment could in these months. HRUs, the monthly means of the 18 years of simulations monthly estimates for four October, one from each sea- result confirms the monthly ure 13). The trend in Q fol- arly proportional. River basin has been an- at hourly time-steps, using infall and temperature) and ude estimations of the four recipitation, discharge, rel- on) under the hypothesis of ne of the years where mea- ystem components are used ecast the water cycle. The and can be transposed to all a are available. Whilst pre- locations, part of the work lyse when they were liquid S). The upper graph shows the total available water, J, divided in its snow and rainfall parts. 0 100 200 300 400 500 01-2012 02-2012 03-2012 04-2012 05-2012 06-2012 07-2012 08-2012 09-2012 10-2012 11-2012 12-2012 Date(months) Q,ET,S(mm/month) Q ET S 0 100 200 300J(mm/month) Figure 13: The same as figure 12, but monthly variability for the year 2012. 14 What mass conservation implies, explained precipitation discharges storage variation evapotranspiration Rigon et al. Abera,W.,Formetta,G.,Borga,M.,&Rigon,R.(2017).
  45. 45. !45 And then, perhaps, we can treat draughts also Why the water budget ? Rigon et al. Abera,W.,Formetta,G.,Borga,M.,&Rigon,R.(2017).
  46. 46. !46 So, perhaps, we avoid embarrassing situations (where water inputs are less than outputs) Rigon et al. StefanoTasin,2017 Why the water budget ?
  47. 47. !47 Multipurpose-Multiprocesses root zone ground canopy surface waters Rigon et al. neve A more reasonable representation of the processes in a HRU requires these storages sediment (and watered sediment)
  48. 48. !48 1 2 3 4 5 6 7 0 When we add them all together with fluxes snow root ground canopy surface waters Rigon et al. A
  49. 49. !49 This whole system must be added together with repeating this scheme for any of the HRU, but potentially it could be varied for each HRU. Scaling up Rigon et al.
  50. 50. !50 Introducing this complexity causes, obviously, issues about parameters identification, computational burden (to be performed in paralalle), issues about data acquisition and storage, representation and analysis of the data. Issues Rigon et al.
  51. 51. !51 All of this does not exists yet in a system. but is what my group is working on Composite Pattern - A very first idea COMPONENT . . . Leaf Local Node Ghost Node Node Abstra ctclass TRAVERSER 37 / 68 Answers Rigon et al.
  52. 52. !52 The representation of catchements and human infrastructures (and/or actions) with graphs*, allows not only the representation of the ordinary differenziali equazioni systems that are thought to rule the systems, but also a split of those systems in parts that can be implemented separately and assembled at the end, and eventually modeled in parallel, by means by smart graphs “traverser” that analyses and understand graphs interdipendencies. *with theirs mathematics The prototype “deployment” of this informatics is already used by the authors and will be soon openly released to all open source. Answers Rigon et al.
  53. 53. !53 Details of recent papers Abera, W., Formetta, G., Brocca, L., & Rigon, R. (2017). Modeling the water budget of the Upper Blue Nile basin using the JGrass-NewAge model system and satellite data. Hydrology and Earth System Sciences, 21(6), 3145–3165. Abera, W., Formetta, G., Borga, M., & Rigon, R. (2017). Estimating the water budget components and their variability in a pre-alpine basin with JGrass-NewAGE, 1–18. http:// Rigon, R., Bancheri, M., & Green, T. R. (2016). Age-ranked hydrological budgets and a travel time description of catchment hydrology. Hydrology and Earth System Sciences, 20(12), 4929– 4947. Formetta, G., Antonello, A., Franceschi, S., David, O., & Rigon, R. (2014). Hydrological modelling with components: A GIS-based open source framework, 55(C), 190–200. 10.1016/j.envsoft.2014.01.019 Rigon, R., Bancheri, M., Formetta, G., & de Lavenne, A. (2015). The geomorphological unit hydrograph from a historical-critical perspective. Earth Surface Processes and Landforms, n/a–n/a. The path so far Rigon et al.
  54. 54. !54 The great, important, and ofted debated question is: Hoe the events that happens in catchements, in soils, plants, forests, can be described by physics and chemistry (in a word by hydrology)? The preliminary answer that this talk would rise is the following: There is a partial ability of present hydrology to account for these events, and there is no reason to doubt that they can be even more in the next future development of this science.* * Paraphrasing What is life ? by E. Schroedinger R. Rigon The scope of hydrologists
  55. 55. !55 This presentation can be found at Ulrici,2000? Other material at Questions ? Stay tuned for future evolutions and releases of our open source softwares R. Rigon