# Other components canals and diversions Andrea Castelletti Politecnico di Milano NRML13.

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Other components canals and diversions Andrea Castelletti Politecnico di Milano NRML13

2 Schema fisicoSchema fisico Adriatic Sea Fucino VILLA VOMANO PIAGANINI PROVVIDENZA CAMPOTOSTO MONTORIO (M) SAN GIACOMO (SG) Irrigation District (CBN) S. LUCIA (SL) PROVVIDENZA (P)

3 Canal the peaks propagation velocity w is greater than the average velocity v; the difference (w-v) increases with the depth H of the stream. space instantaneous flow

4 The peak time increases with the distance; The peak flow decreases with the distance; Hydrographs are a-symmetrical and widen; Canal: storing effect sec. 1 sec. 2 sec. 3 control sections elementary unit time instantaneous flow storing effect (flow buffering)

5 Example: the Po river l1l1 l2l2 l3l3 l4l4 l5l5 t SEPOCTNOV Hydrometric plots for 5 stations (l i ) h

6 Canal: causal network

7 Canal: mechanistic model Travel time state internal representation plug-flow

8 Canal: the delay If = 0 the system is a non- dynamic one: the state does not exist. To reduce the computing time in solving the design problem, the more convenient solution would be to fix in a way that be equal to zero. But how to determine ?.... plug-flow

9 Canal: how to determine If one is able to observe a flood wave.. … but if this is not possible? use the cross-correlogram t t t t upstreamdownstream computed using whitened series

10 correlation ρ ρ xy is a statistics of x and y measuring the strenghtness of the link between x and y if x = α y |ρ xy | = 1 Correlation if x = α y + ε white |ρ xy | < 1 if x = ε white ρ xy = 0 provides an estimate of

11 (Self)correlogram It measures the correlation of the pair 1 … separated by different time intervals … τ Pairs of variables ( y t, y t+τ ) as a function of τ : … of which we are interested in the strenghtness of the link.

12 Canal: leakage If the leakage does not change with the time If the leakage changes with the time In this way is never negative even for very small value of the entring flow. plug-flow

13 Detention areas Structural interventions that create a storage upstream where part of the inflow is retained when the flow rate is partuclarly high. They can be of 3 types:: detention areas Produce a narrowing of the riverbed Produce an increase in the canal section when the flow is above a given value They can be modeled as the aggregation of two components: a reservoir and a canal detention basin dry dams

14 Detention areas canal reservoir If travel times can be neglected Recession phase Concentration phase

15 Detention areas canal reservoir By assuming that: stage-discharge curve of the canal is linear, vale a dire ; the reservoir is cylindirc, i.e. ; The stage-discharge curve between the canal and the reservois is linear in the difference of the levels

16 The model of a planned canal If the canal is going to be planned its model should include u p. Each value of u p correspond to a different alternative. Typical situation: the canal has to be sized In that case u p is the maximum flow conveyable into the canal u p = 0 is the business as usual alternative: do not do nothing !

17 Step-indicator of a canal A step indicator is often associated to the canal For example: the damage produced by floods along the canal shores the environmental cost due to low flow rates

18 Diversion (dam): structure A branch point is usually an artificial work called diversion dam. back-flow profile spillway crest bank of the water course inlet dam

19 q max Diversion (dam) Features: entirely or partly channels the flow into a diversion canal can be equipped with mobile parts (usually sluice gates) for regulating the channelled flow. riverbed canal the diversion canal flow rate ( q max ) is limited thorugh a crest spillways. A branch point is usually an artificial work called diversion dam.

20 Diversion (dam): causal network

21 Diversion (dam): mechanistic model Non-regulated diversion Regulated diversion: … diversion with a MEF: only if:

22 Schema fisicoSchema fisico Adriatic Sea Fucino VILLA VOMANO PIAGANINI PROVVIDENZA CAMPOTOSTO MONTORIO (M) SAN GIACOMO (SG) Irrigation district (CBN) S. LUCIA (SL) PROVVIDENZA (P)

23 Features of the reservoirs 4.954 950 000 Piaganini 5.585 1 690 000 Provvidenza 975.461.8 217 000 000 Campotosto T s [hours] q max [m 3 /sec] V active [m 3 ] time for emptying 3.530 380 000 V. Vomano

24 Piaganini

25 Schema fisico (bacini)Schema fisico (bacini) Adriatic Sea Fucino VILLA VOMANO PIAGANINI PROVVIDENZA CAMPOTOSTO MONTORIO (M) SAN GIACOMO (SG) Irrigation district (CBN) S. LUCIA (SL) PROVVIDENZA (P)

26 Schema logico erratoSchema logico errato Adriatic Sea VILLA VOMANO PROVVIDENZA (M) (P) (SG) Irrigation district (SL) PIAGANINI CAMPOTOSTO

27 Schema logico erratoSchema logico errato Adriatic Sea VILLA VOMANO PROVVIDENZA (M) (P) (SG) Irrigationdistrict (SL) PIAGANINI CAMPOTOSTO P pumping SG pumping Problems: only ENEL is interested in the internal water cycling; a daily modelling time step is too large to accurately describe the phenomenon. Problems: only ENEL is interested in the internal water cycling; a daily modelling time step is too large to accurately describe the phenomenon.

28 P SG M SL DMV Fucino MEF Vomano PIAGANINI CAMPOTOSTO PROVVIDENZA VILLA VOMANO Distretto irriguo (CBN) P_pomp SG+P_pomp Acquedotto del Ruzzo DMV Montorio Schema logico corretto Advantages: only the minimun value of release and pumping are decided, while ENEL is let free to increase these value to cope with the availability/demand of the national grid. Advantages: only the minimun value of release and pumping are decided, while ENEL is let free to increase these value to cope with the availability/demand of the national grid.

29 Pumping: Hydroelectric constraints P SG M SL MEF2 Fucino MEF1 Vomano Irrigation district (CBN) P_pump SG+P_pump Ruzzo Water Works MEF Montorio u2u2 u1u1

30 Confluence point The model of a confluence point is a simple algebraic expression. Being i=1,...,n in coming canals, the model has the following form:

31 P SG M SL MEF Fucino MEF Vomano PIAGANINI CAMPOTOSTO PROVVIDENZA VILLA VOMANO Irrigation district (CBN) P_pump SG+P_pump Ruzzo water works MEF Montorio