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Adige modelling

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The concepts related of the New Model of River Adige, and especially an analysys of the existing OMS components ready and their interpretation on the basis of travel time approaches

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Adige modelling

  1. 1. Implementing a travel time model for the entire river Adige: the case of JGrass-NewAGE Riccardo Rigon, Marialaura Bancheri, Wuletawu Abera and Giuseppe Formetta Padova, 23-24 September 2015
  2. 2. !2 The River Adige, second longest, second largest in Italy R.F.B.A Introduction
  3. 3. !3 Subbasins or Hydrologic Response Units (HRUs) 1157 of ~ 10 square kilometres R.F.B.A Introduction
  4. 4. !4 Monitoring points R.F.B.A Introduction
  5. 5. !5 We are building a database containing all of this information There are several digital terrain data available which can be used as base: • The LIDAR data set (~2 m) from Provincia di Trento and Bolzano • SRTM data • ASTER data All the data are elaborated by means of our “Horton Machine” a set of specialised tools freely available at: http://abouthydrology.blogspot.it/2013/04/the-horton-machine.html R.F.B.A Introduction
  6. 6. !6 Modelling goals • Modelling the whole hydrological cycle, runoff, discharge, ET, snow but at an aggregated scale • Possibly at operational level • Giving travel time distributions • Introducing human management R.F.B.A Introduction
  7. 7. !7 Modelling goals We did it part of it a few times in the past 25 years and we had to rebuild everything from the scratch every time • This time we would like to build something that we should not rebuild entirely The design lines are in: http://www.slideshare.net/GEOFRAMEcafe/geoframe-a-system-for-doing-hydrology-by-computer R.F.B.A Introduction
  8. 8. !8 Just a slide on this CUAHSI BIANNUAL MEETING - BOULDER (CO) - JULY 14-16 2008 Object-oriented software development. O-O programming is nothing new, but it has proven to be a successful key to the design and implementation of modelling frameworks. Models and data can be seen as objects and therefore they can exploit properties such as encapsulation, polymorphism, data abstraction and inheritance. Component-oriented software development. Objects (models and data) should be packaged in components, exposing for re-use only their most important functions. Libraries of components can then be re-used and efficiently integrated across modelling frameworks.Yet, a certain degree of dependency of the model component from the framework can actually hinder reuse. NEW (well relatively) MODELING PARADIGMS ModifiedfromRizzolietal.,2005 MODELLING BY COMPONENTS http://www.slideshare.net/GEOFRAMEcafe/geoframe-a-system-for-doing-hydrology-by-computer R.F.B.A Introduction
  9. 9. !9 We use Object Modeling System v. 3 OMS R.F.B.A David et al., 2013; Formetta et al., EM&S, 2014 supporting parameter estimation and sensitivity/uncertainty anal- ysis, output analysis (e.g., statistical evaluation and graphical visu- alization) tools, modeling audit trails (i.e., reproducing model results for legal purposes), and miscellaneous technical/user documenta- tion. As with any EMF, fully embracing the OMS3 architecture requires a commitment to a structured model development process which may include the use of a version control system for model source code management or databases to store audit trails. Such features are important for institutionalized adoption of OMS3 but less critical for adherence by a single modeler. Most environmental modeling development projects do not have the luxury of employing experienced software engineers or computer scientists who are able to understand and apply complex design patterns, UML diagrams, and advanced object-oriented techniques such as parameterized types, higher level data struc- tures and/or object composition. The use of object-oriented design principles for modeling can be productive for a specific modeling project that has limited need for external reuse and extensibility. Extensive use of object-oriented design principles can be difficult for scientists to adopt in that adoption often entails a steep learning Fig. 1. OMS3 principle framework architecture.
  10. 10. !10 So Any task is the combination of components that are “joined” at runtime R.F.B.A OMS Aberaetal.,2014
  11. 11. !11 Fields of hydrometerological forcings R.F.B.A OMS e.g. Garen and Marks, 2005; Tobin et al., 2014
  12. 12. !12 5.5 Semivariogram estimate and Krigings application and verification Figure 5.4: Workflow of kriging parameter estimation and interpolation. The red dashed lines represent the connections between the OMS3 models. The blue dashed lines represent the connection between components in each model. After computing the experimental variogram, the Particle Swarm algorithm is used to estimate the theoretical model parameters. Finally the kriging algorithm runs.R.F.B.A OMS A more complete view
  13. 13. !13 G. Formetta et al.: Modeling shortwave solar radiation using the JGrass-NewAge system 919 Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchart to model shortwave radiation at the terrain surface with generic sky conditions. Where not specified, quantity in input or output must be intended as a spatial field for any instant of simulation time. ”Mea- sured” refers to a quantity that is measured at a meteorological sta- tion. The components, besides the specfied files received in input, include an appropriate set of parameter values. figure Fig. 1. OMS3 SWRB components of JGrass-NewAge and flowchart to model shortwave radiation at the terrain surface with generic sky conditions. Where not specified, quantity in input or output must be intended as a spatial field for any instant of simulation time. “Measured” refers to a quantity that is measured at a meteorological station. The components, besides the specified files received in input, include an appropriate set of parameter values. 3 Applications The capability of the model was tested by combining four NewAge JGrass components within a OMS script: the SwRB, the (radiation decomposition model) DEC-MOD’s, The Little Washita River basin (611 km2) is located in southwestern Oklahoma, between Chickasha and Lawton and its main hydrological and geological features are pre- sented in Allen and Naney (1991). The elevation range is between 300 m and 500 m a.s.l., the main land uses are Radiation R.F.B.A OMS Formetta et al., GMD, 2013
  14. 14. !14 Radiation clearness index (black line in figure1). Model outputs are the raster maps or time-series of longwave radiation (DL and UL). Those data could be used by the evapotranspiration or the snow water equivalents components. Moreover, the LWRB component could be connected to the NewAge and OMS3 calibration algorithm in order to estimate the best model parameters values (red line in figure 1). Finally, the verification procedure is done connecting the LWRB component to verification component (red line in figure 1). Figure 1: OMS3 LWRB components of NewAge-JGrass and the flowchart to model longwave radiation. 5 R.F.B.A Formetta et al., to be submitted 2015 OMS
  15. 15. !15 Snowfall-Rainfall separation R.F.B.A Something new here !!! Abera et al., to be submitted 2015
  16. 16. !16 Snow Budget Fig. 12. The SWE-C integration in the NewAge System showing connections with the short wave radiation component and kriging interpolation algorithm. Connection with the Particle Swarm Opti- mization algorithm is in red dashed line. R.F.B.A OMS Formetta et al., GMD ,2013
  17. 17. !17 Runoff formation and aggregation is performed. Two river basins are used for the test and modeled in a three di↵erent delineations by using one (DL1), three (DL3) and twenty (DL20) HRU’s. Two modeling solutions were set up: Hymod and RHymod in fig.(7.9). Figure 7.9: Modelling solutions: Hymod (in red dashed line) and RHymod (in blued dashed line). The modeling solution RHymod includes: the Pristley-Taylor component for the evapo-R.F.B.A Formetta et al., GMD, 2011 OMS
  18. 18. The business as usual Riccardo Rigon, Marialaura Bancheri, Wuletawu Abera and Giuseppe Formetta Padova, 23-24 September 2015
  19. 19. !19 Each HRU is a control volume • No lateral fluxes • No deep losses and recharge terms supplying deep groundwater S(t) : Water storage in the control volume V M(t) : Solute storage in the control volume V Figure From Catchment travel times distributions and water flow in soils, Rinaldo et al. (2011) HRUs level example R.F.B.A
  20. 20. !20 Water Budget dS(t) dt = J(t) Q(t) AET (t) R.F.B.A HRUs level example
  21. 21. !21 Water Budget Volume of water in the control volume Total precipitation = rainfall + snow melting Discharge Actual Evapotranspiration dS(t) dt = J(t) Q(t) AET (t) R.F.B.A HRUs level example
  22. 22. !22 The business as usual dS(t) dt = J(t) Q(t) AET (t) AET(t) = S(t) Smax ET (t) where ET(t) is potential evapotranspiration (maybe space-averaged) and a,b,Smax are parameters (in principle different for any HRU) Q(t) = k S(t)b R.F.B.A HRUs level example
  23. 23. !23 In this case: Let for a moment b=1, then the equation is linear and has a solution dS(t) dt = J(t) kS(t)b S(t) Smax ET (t) S(t) = e ( t k + 1 Smax R t 0 ET (t0 )dt0 ) Z t 0 e(s k + 1 Smax R s 0 ET (t0 )dt0 )J(s)ds if S(0) = 0 which is known, as soon as, ET(t) and J(t) are known R.F.B.A HRUs level example
  24. 24. !24 If we define S(t) := Z t 0 S(t, ⌧)d⌧ Storage at time t generated by precipitation at time Z t 0 S(t, s)ds = Z t 0 e (t s k + 1 Smax R t s 0 ET (t0 )dt0 )J(s)ds we have S(t, s) = e (t s k + 1 Smax R t s 0 ET (t0 )dt0 )J(s) R.F.B.A HRUs level example
  25. 25. !25 Q(t) := Z t 0 Q(t, ⌧)d⌧ AET (t) := Z t 0 AET (t, ⌧)d⌧ Discharge at time t generated by precipitation at time Actual evapotranspiration generated by precipitation at time We can also define R.F.B.A HRUs level example
  26. 26. !26 Is also Q(t, s) = ke (t s k + 1 Smax R t s 0 ET (t0 )dt0 )J(s) AET (t, s) = S 1 max h e (t s k + 1 Smax R t s 0 ET (t0 )dt0 )J(s) i ET (t) Given S(t, s) = e (t s k + 1 Smax R t s 0 ET (t0 )dt0 )J(s) R.F.B.A HRUs level example
  27. 27. Travel/Residence times do we need it ? Riccardo Rigon, Marialaura Bancheri, Wuletawu Abera and Giuseppe Formetta Padova, 23-24 September 2015 A.Bonomi
  28. 28. !28 Let’s introduce the (forward) conditional probability: The kinematic of probabilities: mostly from Botter, Rinaldo, Bertuzzo et al. 2010-2011 which defines the probability that a water molecule, injected at time ti is inside the control volume at time t. Then, by construction: J(ti)P(t ti|ti) is the volume of water inside the control volume that was injected at time ti or, R.F.B.A
  29. 29. !29 And therefore, the fraction of water of a certain age over the total, at a certain time is: we obtain then: * R.F.B.A B.R.B. with some variations
  30. 30. !30 we can reflect further on the meaning of the fraction: S(t ⌧, t) S(t) By definition is itself a probability, if t is kept fixed and is left varying⌧ p (t ⌧|t) := S(t ⌧, t) S(t) It is a conditional probability then, and it is “backward” since, it looks at time t what happened before. ** R.F.B.A B.R.B. with some variations
  31. 31. !31 From the two relations * and **, we can obtain: S(t) p (t ⌧|t) = P(t ⌧|⌧)J(⌧) Which seems a version of the Niemi’s theorem (1977) which reads instead Q(t) p (t ⌧|t) = p(t ⌧|⌧)J(⌧) REALLY TRUE ? I CONFESS I DERIVE IT TWO DAYS AGO, AND IT COULD BE WRONG R.F.B.A B.R.B. with some variations
  32. 32. !32 If we consider two output fluxes, i.e. Q(t) and E(t), we must consider that the probability of exit time must be split in two components. The formal way to do it is to introduce a partition function: from which: Bancheri and Rigon Volumes and Probabilities B.R.B. with no variations
  33. 33. !33 If we consider the mixing hypothesis, from which: and Then the Master equation reduces to: R.F.B.A B.R.B. with no variations
  34. 34. !34 Is a linear partial differential equation which is integrable. [If we make the assumptions explicated before, Q(t), ET(t) and S(t) can be assumed to be known] The logical initial condition is: And the solution is: R.F.B.A B.R.B. with no variations
  35. 35. Is !35 Consequently using some of the hypotheses, also the other probabilities can be derived. From R.F.B.A B.R.B. with no variations
  36. 36. !36 From Is R.F.B.A B.R.B. with no variations
  37. 37. !37 A quantity is still to be determined, which is the coefficient of partition It can be actually be determined, by imposing the normalisation of the probability This finally implies: R.F.B.A B.R.B. with no variations
  38. 38. !38 NOTE This: actually bothers me a little, since it implies you have to wait infinite time to know it. Wander if a finite time version of it can work !
  39. 39. NAHymod the Hymod implementation of JGrass-NewAGE September, 2015 R. Rigon, G. Formetta, M. Bancheri, W.Abera S.Bertoni,2006?
  40. 40. !40 What Hymod does Moore, 1985 The basin is assumed to be composed by a group of storages which follow a distribution F(C) where C is the value of the storage which can vary from 0 to Cmax. If Cmax is exceeded, that water in excellence goes directly into runoff. If we call precipitation P, this is: RH = P + C(t) Cmax if P + C(t) > Cmax Generically, it is: RH = max(0, P(t) + C(t) Cmax) Which is true even if P(t)+C(t) < Cmax R.F.B.A Hymod
  41. 41. !41 There is a residual runoff RS produced by using the curve, which is valid even if C(t)+P(t) < Cmax: F(C) = 1 ✓ 1 C Cmax ◆b The volume below the curve goes into this residual runoff R.F.B.A Storage (probability) function
  42. 42. !42 Van Delft et al. 2009 figure said it properly for runoff R.F.B.A Generating runoff What Hymod does
  43. 43. !43 In figure C(t)=2 P=2 Cmax =10. Therefore for a correct interpretation of the figure in previous slides, the area below a curve is the runoff produced. A correct interpretation of the plot says that all the precipitation below the curve is produced as R, the rest remaining stored at time t+1 . Let’s represent the curves in the right direction R.F.B.A Storage (probability) function
  44. 44. !44 The area below each one of the curve is The integral result can be written as: Z C(t)+P (t) C(t) F(C)dC = Z C(t)+P (t) C(t) 1 ✓ 1 C Cmax ◆b dC F(P(t), C(t), Cmax, b) = P(t) 1 Cb max(b + 1) h (Cmax C(t))) b+1 (Cmax C(t) P(t))) b+1 i R.F.B.A Storage (probability) function So:
  45. 45. !45 1) Update C* Summarizing 2) Update the Rs 3) Update S R.F.B.A The algorithm of separation
  46. 46. !46 Introducing AET S(t) continuously increases unless ET acts. In this case there is a fourth step: Where the left arrow means assignment, and AET is the actual ET AET(t) = S(t) Smax ET (t) R.F.B.A The algorithm of separation
  47. 47. Say ↵ is coefficient to be calibrated R = Rsub + Rsup R.F.B.A Runoff volumes is then split into surface runoff and subsurface storm runoff
  48. 48. !48 Therefore, we have three LINEAR systems of reservoirs. The quick system SQ(t) = S1(t) + S2(t) + S3(t) R.F.B.A Runoff volumes
  49. 49. !49 The subsurface system: The groundwater system: R.F.B.A Runoff volumes and groundwater
  50. 50. !50 It seems a quite complicate system, but every hydrologist knows it can be “exactly” solved. For the quick system R.F.B.A Three little reservoirs
  51. 51. !51 And: And: R.F.B.A Other two linear reservoirs
  52. 52. !52 For what regards the numerics Is certainly dubious that using the convolutions would be faster that integrating directly the differential equations. However, they can be used to test some simplified case, and that’s nice. R.F.B.A
  53. 53. Travel/Residence times after Hymod Riccardo Rigon, Marialaura Bancheri, Wuletawu Abera and Giuseppe Formetta Padova, 23-24 September 2015
  54. 54. !54 has the structure for some function f and input I, and, therefore, the storage part injected at time is: These formulas and their companions for Qi(t) and AET(t) can be used to estimate the various residence times. R.F.B.A It seems simple !
  55. 55. !55 Putting all together by convolutions this is NOT Adige BTW R.F.B.A Rigonetal.,ESP&L2016
  56. 56. So what we expect from all of this ? Riccardo Rigon, Marialaura Bancheri, Wuletawu Abera and Giuseppe Formetta Padova, 23-24 September 2015 MichelangeloB.
  57. 57. !57 Inputs of this type (with errors estimate) (a) Time 0 Oct 15 Oct 16 Oct 17 Oct 18 (b) SB1 SB4 SB13 SB37 0 5 10 15 0 5 10 15 Oct 15 Oct 16 Oct 17 Oct 18 Oct 15 Oct 16 Oct 17 Oct 18 Time Estimatedrainfallrate(mm/h) (c) Figure 10: Spatial rainfall variability in subbasin aggregated approach: (a) variability in the estimated total rainfall (the code number in the subbasin represents the subbasin number, while the color shows the total rainfall distribution), (b) comparison of four selected time series subbasin rainfall estimates, and (c) further analysis on the kriging estimation error used to estimate the confidence interval of the estimates for some selected subbasins. The analysis is based on Oct 16, 1996 event. R.F.B.A
  58. 58. !58 mperature an eleva- icated by etermined ers repre- ile range. aps sam- HRU 1 HRU 4 HRU 13 HRU 37 0 10 20 0 10 20 Sep 02 Sep 04 Sep 06 Sep 08 Sep 10 Sep 02 Sep 04 Sep 06 Sep 08 Sep 10 Time (h) Temprature(^(o)c/h) Figure 13: Estimated time-series temperature and associated kriging estimation and sampling errors for selected subbasins (1,4,13,37) for sept 1-10, 2002.The black solid line shows the estimated temperature values, while gray area is the estimation plus or minus of kriging stan- R.F.B.A Inputs of this type (with errors estimate)
  59. 59. !59 racy is considered acceptable for the long term water balance analysis in this study. This could also be due to di↵erence in the temporal and spatial scale between the model and MODIS data. HRU1 HRU4 HRU13 HRU37 0 2 4 6 0 2 4 6 Feb 21 06:00 Feb 21 12:00 Feb 21 18:00 Feb 22 00:00 Feb 22 06:00 Feb 21 06:00 Feb 21 12:00 Feb 21 18:00 Feb 22 00:00 Feb 22 06:00 time Rainfall/snowpartition(mm/hour) Precip Type Snowfall,Js Rainfall,JR Figure 15: Comparison of four selected HRUs (HRU 1, 4, 13, 37) time series snowfall separation estimates during Feb 21-22, 2004 event. Modeling at HRU level, as it is the aggregation of each point within the HRu that can be characterized by pure snowfall or pure rainfall or snow-water mix event, the water-snow mixing is more physically and statistically meaningful. portrays at figure 8 elevation have high elling than at low el responsible for high approach, could com cipitation during sn 5. Summary and o In this study a s oped and deployed get. These range fr umes at which the input forcings, to th each of the hydrolo the errors made (ass been performed. W ducible by sharing from information in Considering Pos Italy, this study test terpolation and sem rainfall anount and of semivariogram m main di↵erent in th R.F.B.A Inputs of this type (with errors estimate) This actually has to be interpreted
  60. 60. !60 0 100 200 300 2012−01−01 2012−02−01 2012−03−01 2012−04−01 2012−05−01 2012−06−01 2012−07−01 2012−08−01 2012−09−01 2012−10−01 2012−11−01 2012−12−01 monthly J(mm) −100 0 100 200 300 10-2011 11-2011 12-2011 01-2012 02-2012 03-2012 04-2012 05-2012 06-2012 07-2012 08-2012 09-2012 Months Watercomponent:Q,ET,S(mm) Q ET S components R.F.B.A Outputs of this type (with errors estimate) This is with respect to the average S
  61. 61. !61 0 1000 2000 1995−01−011996−01−011997−01−011998−01−011999−01−012000−01−012001−01−012002−01−012003−01−012004−01−012005−01−012006−01−012007−01−012008−01−012009−01−012010−01−012011−01−012012−01−01 yearly J(mm) −500 0 500 1000 1500 2000 94/95 95/96 96/97 97/98 98/99 99/00 00/01 01/02 02/03 03/04 04/05 05/06 06/07 07/08 08/09 09/10 10/11 11/12 Year Watercomponent:Q,ET,S(mm) Q ET S components R.F.B.A Outputs of this type (with errors estimate)
  62. 62. !62 NOTE We have problems with Evapotranspiration actually ! R.F.B.A At hourly time scale, just the fact that in Hymod withdraw ET from the lower storage, prevent us to have oscillating discharge. Penman-Monteith or Priestley-Taylor approaches cannot be applied “tout-court” to a coarse- grained model*. Some way to integrate them in space is needed. At yearly time, radiation driven approaches tend to underestimate ET variability (still respecting the global water budget). TO BE CONTINUED … A single BIG reservoir for each HRU is clearly not enough discriminating * See the good old and overlooked Bertoldi et al, JHM, 2006
  63. 63. !63 FINALLY We will be able to give proper total amounts of budget. But it will be pretty sure that travel times distributions given with HYMOD will be wrong. (But we have alternative ready) That’s actually a great result from which we can move on easily in JGrass-NewAGE, by adopting different partitions of the storages, and maybe by using some storage selection function. R.F.B.A
  64. 64. !64 Find this presentation at http://abouthydrology.blogspot.com Ulrici,2000? Other material at Questions ? R. Rigon

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