1. Other components stakeholders Andrea Castelletti Politecnico di Milano NRML14

2. 2 The models of the water users We saw that the step indicator g t () is a component of the output of the model either of a water user or of an environmental service. Different typologies of water users exist as well as different models are available to describe them. We will present just a few examples: a hydropower plant an irrigation district the river environment

3. 3 Hydropower plant

4. 4 P SG M SL MEF Fucino MEF Vomano PIAGANINI CAMPOTOSTO PROVVIDENZA VILLA VOMANO Irrigation district (CBN) P_pomp SG+P_pomp Water works Ruzzo MEF Montorio Schema logico corretto(centraliPR)

5. 5 Run-off river power plant 45 o q min q max

6. 6 Run-off river power plant: causal network Maximum divertable flow MEF downstream

7. 7 Run-off river power plant: mechanistic model Energy production [kWh] in [t, t+1)  coefficient (  /3.6 10 6 )  g turbine efficiency [-] g gravity (9.81 m/s 2 )  water density ( 1000 kg/m 3 ) H hydraulic head (constant)  coefficient (  /3.6 10 6 )  g turbine efficiency [-] g gravity (9.81 m/s 2 )  water density ( 1000 kg/m 3 ) H hydraulic head (constant)

8. 8 A storage power plant

9. 9 receiving water body plant reservoir Storage power plant causal network

10. 10 receiving water body plant reservoir Storage power plant mechanistic model  coefficient (  /3.6 10 6 )  g turbine efficiency [-] g gravity (9.81 m/s 2 )  water density ( 1000 kg/m 3 ) H hydraulic head  coefficient (  /3.6 10 6 )  g turbine efficiency [-] g gravity (9.81 m/s 2 )  water density ( 1000 kg/m 3 ) H hydraulic head

11. 11 Storage power plant model It’s a non- dynamic model

12. 12 P SG M SL MEF Fucino MEF Vomano PIAGANINI CAMPOTOSTO PROVVIDENZA VILLA VOMANO Irrigation district (CBN) P_pomp SG+P_pomp Water works Ruzzo MEF Montorio Schema logico corretto(centraliPR)

13. 13 Reversible storage power plant Reversibile: the power comes from the grid, the alternator works as engine for the turbines, which run in inverse mode and pump the water back to the upstream reservoir.

14. 14 Reversible storage power plant Only pumping, two distinct power plants Downstream reservoir Upstream reservoir

15. 15 Pumping plant causal network Downstream reservoir Upstream reservoir downstream reservoir plant upstream reservoir Energy supplied by the network during the night Flow rate potentially liftable The effective flow rate depends upon penstock capacity maximum upstream storage flow available for pumping downstream as a function of the water available

16. 16 Pumping plant causal network Downstream reservoir Upstream reservoir downstream reservoir plant upstream reservoir Upstream active storage

17. 17 Power plant step-indicator The step-indicator G t () is the energy produced (or comsumed for the pumping plant): it is a physical indicator. Sometime an econimic indicator might be preferable: income availability to pay social cost Cost Benefit Analysis is usually adopted Can be obtained by manipulating G t () appropriately. Can be obtained by multiplying G t () per the energy price (which can be a function of G t ()).

18. 18 Average annual revenue Hyd1 Indicators Hydropower revenue Time intervalWinter Summ er August + Sat and Sun 00:00-06:30 06:30-08:30 08:30-10:30 10:30-12:00 12:00-16:30 16:30-18:30 18:30-21:30 21:30-00:00 25.3 46.7 116.3 46.7 116.3 46.7 25.3 46.7 25.3 Energy prices (€/Mwh) R t (E c (q t c )) Fascia F1 Fascia F2Fascia F4

19. 19 Irrigation district

20. 20 P SG M SL MEF Fucino MEF Vomano PIAGANINI CAMPOTOSTO PROVVIDENZA VILLA VOMANO Irrigation district (CBN) P_pomp SG+P_pomp Water Works Ruzzo MEF Montorio Schema logico corretto(centraliPR)

21. 21 The irrigation district The most natural indicator for an irrigation district is the harvested biomass (harvest) or the lost harvest with respect to the potential harvest: from both one can easily obtain the economic return associated to the agriculture production not easily computable! Proxy indicator: average annual potential damage from the stress f () is the potential damage; F a is the maximum stress occurred in the year a water demand at time t it depends on field capacity water supply at time t deficit at time t It is not separable! Enlarge the state! It is not separable! Enlarge the state! ! ! The model of the irrigation district must provide the water demands W t for all the crops at time t.

22. 22 Not always such a simplified model is acceptable. For instance: If for several days a crop is not irrigated, the water demand becomes greater than that of regularly irrigated crop. The irrigation district is a dynamic system. If at the beginning of the year farmers decide to plant dry crops, the water supplied would not have any influence on the harvest. The harvest depends on human expectations and decisions. crop characteristics; irrigation system; current agricultural practice in the area. The simplest way is to rely on an expert estimating the water demand scenario on the basis of: How to determine the water demand W t ?

23. 23 Not always such a simplified model is acceptable. For instance: If for several days a crop is not irrigated, the water demand becomes greater than that of regularly irrigated crop. The irrigation district is a dynamic system. If at the beginning of the year farmers decide plant dry crops, the water supplied would not have any influence on the harvest. The harvest depends on human expectations and decisions. crop characteristics; irrigation system; current agricultural practice in the area. The simplest way is to rely on an expert estimating the water demand scenario on the basis of: How to determine the water demand W t ? The expert’s estimate is a description of the water demand in normal conditions, including a normal water supply. It’s an accurate model for small variations in the water supply. It’s not acceptable when variations are significant, such as: during exceptional droughts; when a change in the status quo is planned. What can we do else?

24. 24 Irrigation system-soil-vegetation (SSV) model

25. 25 Irrigation system-soil-vegetation (SSV) model

26. 26 conveyance drainage soil-vegetation model GW flow model Interface with GW model river irrigation rainfallET withdrawals run off recharge river-GW exchange o re-use return-flows diversion irrigation network interception distribution Irrigation system-soil-vegetation (SSV) model seepage from canals

27. 27 root zone CANOPY INTERCEPTION: Hoyningen-Hune (1983), Braden (1985) RAINFALL AND IRRIGATION INFILTRATION: Green&Ampt model (1911) or CN-SCS method (1972) EVAPORATION: FAO-56 Allen et al. (1998) TRASPIRATION: FAO-56 Allen et al. (1998) PERCOLATION: RESERVOIR CASCADE (DARCY FLUX WITH UNIT VERTICAL GRADIENT) CAPILLARY RISE PROCESSES 16560 cells

28. 28 Groundwater flow model (map of aquifer trasmissivity)

29. 29 Example of output: irrigation supply

30. 30 Example of output: ET deficit (ETpotential-ETactual)

31. 31 Example of output: crop production index

32. 32 Single cell outputs (daily time-step) Maize cell in Mulazzano GW recharge ETa rainfall + irrigation

33. 33 Irrigation water requirements

34. 34 Irrigation district: the farmers’ behaviour It is not always so easy!

35. 35 The Vomano Project The Consorzio di Bonifica Nord (CBN) would like to assess the opportunities for extending its irrigation district from 7000 ha to 14 000 ha. Therefore CBN needs an estinmate of the water demand for the enlarged district. CBN Irrigation district

36. 36 Irrigation district: block diagram extension expectation incentives supply to the district t temperature t solar radiation t precipitation t irrigation district

37. 37 DistributionGrowth crop areas supply t Irrigation district: block diagram extension expectation incentives supply to the district t temperature t solar radiation t precipitation t Potential Evapotransp. irrigation techs. Farmers Causal net

38. 38 The farmers’ behaviour: causal network extensionexpectationincentives extensionexpectationincentives Choice between: - dry crops and 1 irrigated crop - sprinklers and microirrigation Choice between: - dry crops and 2 irrigated crops (cauliflower + tomato&maize) - sprinklers and microirrigation

39. 39 DistributionGrowth crop areas supply t Irrigation district: causal network extension expectation incentives supply to the district t temperature t solar radiation t precipitation t Potential Evapotransp. irrigation techs. Farmers BBN

40. 40 Choice between: - dry crops and 2 irrigated crops (cauliflower + tomato&maize) - sprinklers and microirrigation incentives 0 S 7000 expectation 14000 7000 3500 10500 14000 0.90.70.5 0.10.30.5 0 0.4 0.1 0.4 0.3 0.10.5 0.200 0 0 0 0 00 000 extension LOWALTA MEDIUM LOWHIGH MEDIUM expectation The farmers’ behaviour: Bayesian Belief Network (BBN) extensionexpectationincentives constraint violation

41. 41 Choice between: - dry crops and 2 irrigated crops (cauliflower + tomato&maize) - sprinklers and microirrigation The farmers’ behaviour: Bayesian Belief Network (BBN) extensionexpectationincentives

42. 42 Choice between: - dry crops and 2 irrigated crops (cauliflower + tomato&maize) - sprinklers and microirrigation The farmers’ behaviour: Bayesian Belief Network (BBN) extensionexpectationincentives

43. 43 Calibration of the BBN The BBN parameters are the Conditional Probability Tables. To calibrate the BBN we need to estimate their elements (CPT population). Simple algebraic relation : S cav = S - S p&m extensionexpectationincentives

44. 44 Calibration of the BBN extensionexpectationincentives interviews

45. 45 DistributionGrowth crop areas supply t Irrigation district: BBN extension expectation incentives supply to the district t temperature t solar radiation t precipitation t Potential Evapotransp. irrigation techs. Farmers BBN SSV model ALGEBRAIC model FAO model time t

46. 46 t=0 t=1t=T-1... Irrigation district: BBN

47. 47 Model validation flow rate [m 3 /s] canal capacity model real

48. 48 The ecological status of a fluvial ecosystem

49. 49 HIERARCHY

50. 50 ECOLOGICAL STATUS General conditions Benthic macroinvertebrates LIM Biological quality (terrestrial and aquatic biota) Fish fauna Terrestrial flora Abundance Biodiversity (EPT) Community composition Population structure (key species) Autochthonous species Exotic species Age distribution structure Abundance Physico- chemical quality (water quality) Riparian vegetation Naturalness Cover Longitudinal continuity Width of riparian strip Corridor (zonal) vegetation Hydromorpholo gical quality Hydrological regime Characteristics of regime (annual, monthly flows; max, min annual flow; peak and period,…) Mean values Standard deviations Biodiversity-spring Biodiversity-summer Biodiversity-autumn Biodiversity-winter Total exotic species Presence of Silurus Glanis Naturalness of structural features Autochthony Naturalness (species) Cover Indicators not represented for lack of space HIERARCHY

51. 51 Dissolved oxygen previous 3 months (d) Median flow previous 3 months (Q) Minimum flow previous month (q) EVALUATION INDEX Cause-effect relations Pollutant loads reduction Setting lake release policy and water distribution policy Stress hydromorphol. conditions Prevailing hydromorphol. conditions Actions Macroinvertebrates (m) Biodiversity of the community (m 1 ) Abundance (of habitat) (m 2 ) Biodiv. winter (m 11 ) Biodiv. spring (m 12 ) Biodiv. summer (m 13 ) Biodiv. autumn (m 14 ) Causal factors Macroinvertebrates: causal network

52. 52 Median flow previous 3 months (Q) EVALUATION INDEX Setting lake release policy and water distribution policy Macroinvertebrates (m) Abundance (of habitat) (m 2 ) Flowrate Actions Cause-effect relations Wet area Macroinvertebrates: causal network

53. 53 Step 1 – Analysis of satellite images (Landsat TM 7) Example 1 empirical, deterministic model based on experimental data Macroinvertebrates: determining cause- effect relationships

54. 54 Step 2 - Classification and assignment of pixel “water” Macroinvertebrates: determining cause- effect relationships

55. 55 Step 3 – Estimation of the “flow rate-wet area” relationship Macroinvertebrates: determining cause- effect relationships y = 0,3397x + 30,406 R 2 = 0,8746 0 10 20 30 40 50 60 70 80 90 100 0,0020,0040,0060,0080,00100,00 Flow rate [m3/s] % Wet surface Real Linear regression

56. 56 FISH FAUNA (f) Community composition (f 1 ) Abundance key species (f 22 ) Longitudinal Continuity (l) Prevailing flow during minimum flow quarter (Q) Minimum daily flow during hatching period key species (s) EVALUATION INDEX Creating fish- passages / removing discontinuities Setting lake release policy and water distribution policy Stress hydromorphol. conditions Prevailing hydromorphol. conditions during minimum flow period (same year) Presence of autochthonous species (f 11 ) Presence of exotic species (f 12 ) Age distribution structure key species (f 21 ) Population structure (key species) (f 2 ) Minimum annual 3-days flow (q) Stress hydromorphol. conditions hatching period key species Prevailing hydromorphol. conditions during minimum flow period (last 3 years) Exotic species / tot (f 121 ) Presence of silurus (f 122 ) Actions Causal factors Triennial average of prevailing flow during minimum flow quarter (m) Cause-effect relations Fish fauna: causal network

57. 57 FISH FAUNA (f) Community composition (f 1 ) Longitudinal Continuity (l) EVALUATION INDEX Cause-effect relations Creating fish- passages / removing discontinuities Setting lake release policy and water distribution policy Presence of autochthonous species (f 11 ) Prevailing hydromorphol. conditions during minimum flow period (last 3 years) Actions Causal factors Triennial average of prevailing flow during minimum flow quarter (m ) Example 2 model based on expert judgment Fish fauna: determining cause-effect relationships

58. 58 For a given longitudinal stretch... Fish fauna: determining cause-effect relationships

59. 59 ? ? ? ? ? Q min flow quarter Hydromorphol. conditions (v, h, t...) Fish fauna: determining cause-effect relationships

60. 60 IF 5 < m ≤ 25 → f 11 = 6 + (8/20)*(f 11 -5)*m; IF 25 < m ≤75 → f 11 = 14 + (5/50)*(f 11 -25) *m; IF m > 75 → f 11 = 19  X X   Fish fauna: determining cause-effect relationships

61. 61 Disturbances The disturbances is so with respect to the component we are considering. It could be described by a modelas a function of other variables or its own past values. For example: The focus is now on the system. When the disturbance of a component is explained with a model, it is an internal variable of the system. The new “candidate” disturbance is the disturbance of the new model......... the sequence ends when all the disturbance to the global model are either deterministic or random..... However also this latter could be described with a model....

62. 62 Disturbances Therefore: The disturbance of a component is also a disturbance for the global model if and only if: It does not need to be “explained” through a model: it is a deterministic variable; It cannot be “explained” through a model: it is a purely random variable. Just check if its value is deterministically know at each time instant. Whiteness test

63. 63 Model of the disturbances Deterministic model (without inputs) Trajectory Deterministic disturbance w t : Purely random stochastic disturbance  t+1 : Marginal probability distribution  t ():  t+1 ~  t () If  t+1 is a vector then  t () is the joint distribution of its components.  t () can be conditional only to the planning decisions :  t+1 ~  t (|u p ). When  t () is time varying we will assume it as periodic Remarks: We will call  t () the model of the disturbance.

64. 64 Model of the disturbances Purely random uncertian disturbance  t+1 : The knowledge is not enough neither to express a probability  t (); We only know that the disturbance values belong to the data interval  t :  t+1   t  t can only depens upon the planning decisions :  t (u p ). When  t is time variant we can assume it as periodic : Remarks: We will call  t the model of the disturbance.

65. 65 Reading IPWRM.Theory Ch. 5