# A Multi-disciplinary Modelling Approach for Discharge Reconstruction in Irrigation Canals: The Canale Emiliano Romagnolo (Northern Italy) Case Study

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}(Simulation and Integration of Control for Canals) hydraulic software. Firstly, the methodology was developed and tested on a Pilot Segment (PS), characterized by a simple geometry and a quite significant historical hydraulic data availability. Then, it was applied on an Extended Segment (ES) of a more complex geometry and hydraulic functioning. Moreover, the available hydraulic data are scarce. The combination of these aspects represents a crucial issue in the irrigation networks in general.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the CER

^{2}. That area represents the 93% of the irrigated and the 22% of the agricultural land in the Emilia Romagna Region. The agricultural land covers the 60% of the regional territory [43], where different cultures are irrigated, among which extensive crops, vegetables, and orchards [44]. To convey and to distribute water, the CER hydraulic system uses seven pumping stations (the main one on the Po River) and 165 km of canal networks (Figure 1).

^{3}/s (from May to September) to 25 m

^{3}/s (the rest of the year). Moreover, discharges are also affected by the meteorological issues (e.g., long dry seasons), the type of cultivated crops, and the irrigation practices. The Consortium of the CER is in charge of: (1) maintenance operations (geometric and functioning repairs, periodic cleanings); (2) collection of quantitative and qualitative measurements; and, (3) supply of irrigation services to farmers (by means of several irrigation Associated Consortia that distributes water to final users).

#### 2.2. Investigation Period and Available Data

_{i}(Section 2.4.1).

^{3}/s), volume (m

^{3}), suction, and delivery tanks water level (m).

#### 2.3. Description of the Pilot Segment (PS)

^{2}and of 31.5 m

^{2}, respectively, and by submerged entrances and surface or/and piped-flow conditions. PS has three different trapezium cross sections with width ranges of 22.8–25.8 m (at the top) and 3.3–7 m (at the bottom). The side slopes are 3:1 and 1.5:1 for the first composite cross section and 2:1 for the other two simple sections. For the first 700 m along the segment, the bed altimetry goes from 12.81 m to 13.74 m above the sea level. After that part, the canal has a constant slope with a final value of 13.32 m above sea level.

#### 2.4. Elaboration of the Multi-Disciplinary Modelling Approach on PS

^{2}(5.38c, UMR G-eau IRSTEA, Montpellier, France) [49].

#### 2.4.1. Reconstruction of the Unmeasured Offtake Discharges

_{kCn}(m

^{3}/s) can be written as:

_{rDm}(m

^{3}/s) is the average discharge diverted from the reference offtake during the month m (m = 1, 2, 3), and w

_{kCn}is the weight of the offtake k during the decade n (n = 1, ..., 7).

_{rDm}was calculated as:

_{rDm}(m

^{3}) is the indirectly calculated cumulated volume of the reference offtake for the month m, while D

_{m}(s) is the duration of the month m.

_{kCn}, as follow:

_{kDm}(-) and w

_{kTn}(-) are the weights of the offtake k obtained using the D-data and the T-data, respectively, V

_{kDm}(m

^{3}) is the indirectly calculated volume of the offtake k during the month m, V

_{kTn}(m

^{3}), and V

_{rTn}(m

^{3}) are the volumes of the offtake k and of the reference offtake, respectively, calculated during the decade n using IRRINET.

_{kTn}) was determined by the expression [14]:

_{i}(m

^{2}) is the area covered by the crop i per each year, CWR

_{i}(mm) is the decadal cumulated optimum water requirement for the crop i, II

_{i}(-) is the irrigation intensity of the crop i, EI

_{i}(-) is the efficiency of the irrigation method for the crop i, and ED (-) is the efficiency of the delivery system.

_{rTn}.

#### 2.4.2. Reconstruction of the Unmeasured Flowing Discharges

^{2}(Simulation and Integration of Control for Canals) was selected as the most appropriate irrigation canal modelling software. It has been developed at IRSTEA (previously CEMAGREF, Montpellier, France) [62] and it enables describing the dynamics of rivers, drainage networks, and irrigation canals [63]. For the latter, devices (i.e., sills and gates) and irrigation offtakes can be specified in geometric and functioning terms [49]. SIC

^{2}can run steady flow computations under boundary conditions for discharge and/or water level [64]. In fact, it can consider several combinations of settings for devices and offtakes. The software provides the water level and the discharge profiles along the analyzed hydraulic system [29]. SIC

^{2}models also unsteady flow for initial conditions that were obtained from steady state computations [64] in discharge and water level terms. It can be used for water demand and control operations [19,65]. SIC

^{2}describes the dynamic behavior of water (discharge and water level) with the complete one-dimensional (1-D) Saint Venant equations in a bounded system [49]. This is the case of the CER in which the flow can be considered as mono-dimensional with a direction sufficiently rectilinear.

^{3}/s) is the discharge, S (m

^{2}) is the wetted area, g (m/s

^{2}) is the acceleration due to gravity, Z (m) is the water level, J (m/m) is the friction slope, x (m) is the longitudinal abscissa, and t (s) is the time.

^{1/3}/s) is the Manning’s coefficient and R (m) is the hydraulic radius.

^{2}provides a large range of options. They can be imposed in discharge, elevation, or rating curve terms. Lateral inflows and weir and gate equations can also be inserted. For example, the flow through a gate structure can be expressed by several classical or advanced equations, such as the submerged flow equation:

_{d}(-) is the gate discharge coefficient, L (m) is the gate width, u (m) is the gate opening, Z

_{up}(m), and Z

_{dn}(m) are the water levels at the upstream and at the downstream of the gate, respectively.

^{2}[66,67,68].

^{2}. The hydraulic variables values were set according to the literature: The Manning’s coefficient presented a constant value of 0.013 (m

^{1/3}/s) along the segment and within the two culverts [68] and the gate discharge coefficient that characterizes the entrances of each culvert was 0.6 [16,49,69]. The offtakes were modelled as “nodes” and they were characterized in discharge terms. In particular, the q

_{kCn}values were inserted and were linearly interpolated in time.

_{obs,y}, Z2

_{obs,y}, Z3

_{obs,y}, and Z4

_{obs,y}can be defined. They contain the daily measured water levels at the four gauges: WL IN_1, WL OUT_1, WL IN_2, and WL OUT_2, respectively (Figure 2).

^{2}can compute the values of discharge and water level along PS under two boundary conditions only in water level terms; for PS they were represented by Z1

_{obs,y}, and Z4

_{obs,y}. The daily simulated water level values at WL OUT_1, and WL IN_2 (Z2

_{sim,y}and Z3

_{sim,y}) were compared to those that were measured (Z2

_{obs,y}and Z3

_{obs,y}) in order to demonstrate the reliability and accuracy of the hydraulic model, and therefore, of the computed discharge values. The vectors Z2

_{sim,y}and Z3

_{sim,y}can be defined as:

^{2}allows implementing a series of steady state simulations. The year 2015 was examined as a first test. The hydraulic model was run under a series of one-day steady state simulations and under one-day and 10-min unsteady state simulations.

^{2}and Matlab

^{®}(version 9.1, The MathWorks, Inc., Natick, MA, USA).

^{2}, the parameterized hydraulic variables were explicit Cd1 and Cd2, gate discharge coefficients of Culv_1 and Culv_2; n, n1 and n2, Manning’s coefficients along PS, within Culv_1 and Culv_2.

^{®}, this hydraulic set was recalled and the scaling factor Cq allowed multiplying the offtake discharge values from Section 2.4.1. In the math code, the criterion and the minimization function were implemented.

_{y}and diff3

_{y}can be defined as:

_{y}, and σ3

_{y}are the vectors containing the weights (values of 10 or 1), indicating whether a measure is affected by errors or not.

_{y}and diff3

_{y}, and consequently, the criterion J.

^{®}[70]. In Figure 3, the iterations on J are shown for the year 2015.

^{2}. The obtained model was called “optimized” and it returned the simulated discharges and water levels along PS. Finally, the optimization process was characterized by the cost of J that indicated the criterion value at the end of the iterations.

_{y}and σ3

_{y}. In particular, if a day j is affected by a suspicious measure, the weight (σ2

_{j}; σ3

_{j}) was set as 10; otherwise, it was equal to 1.

_{obs,y}, Z2

_{obs,y}, Z3

_{obs,y}, Z4

_{obs,y}, Q2

_{sim,y}, and Q3

_{sim,y}. The latter two contained simulated values of discharge (output of the optimized hydraulic model) at the Culv_1 and Culv_2, respectively.

_{y}-delta1

_{y}, and delta

_{y}-delta2

_{y}were used to evaluate in which vector the suspicious measures were located. The outliers of the data linear fitting were investigated. If the element j of delta

_{y}results as an outlier in both plots, a suspicious measure was in Z2

_{obsj}or in Z3

_{obsj}. If the element j of delta

_{y}results as an outlier in the first plot but not in the second, the suspicious measure was in Z1

_{obsj}. If the element j of delta

_{y}is an outlier in the second plot but not in the first, the suspicious measure was in Z4

_{obsj}. To evaluate if a suspicious measure is in Z2

_{obs}

_{j}or Z3

_{obsj}, Q2

_{sim,y}-delta1

_{y}, and Q3

_{sim,y}-delta2

_{y}were plotted. For both, a data quadratic fitting of data was considered. If the j-th element of delta1

_{y}results as an outlier, the suspicious measure was in Z2

_{obsj}while if the element j results as an outlier of delta2

_{y}, the suspicious measure was in Z3

_{obsj}.

#### 2.5. Description of the Extended Segment (ES)

^{3}/s and a maximum head of 4.5 m. For the first 33 m along the segment, the trapezium cross section top width is higher (85 m) and the bed altimetry varies from 10.79 m to 13.50 m above the sea level. Later, ES presents three different composite trapezium cross sections (top width from 26.4 m to 22.8 m; bottom width from 5.0 m to 3.3 m; side slope 3:1 and 1.5:1) and a constant slope (bed altimetry from 13.50 m to 12.81 m above the sea level). Four culverts under passing two roads (Road crossing_1 and Road crossing_2), the Navile Canal (Culv_3), and the Savena River (Culv_4) are characterized by a rectangular flow section of 36 m

^{2}(Figure 5). The road crossings present a modest length (about 20 m), while Culv_3 and Culv_4 are about 63 m and 86 m, respectively. The 12 occurring offtakes serve a total irrigated area of about 12,580 ha. The water gauges involved are only two at the ES extremities: WL OUT_0 (at the upstream) and WL IN_1 (at the downstream).

#### 2.6. Application of the Multi-disciplinary Modelling Approach on ES

_{totC,y}, the total offtake discharges vector:

_{totCj}was calculated as:

_{y}represented the ES upstream boundary conditions. It was obtained as:

_{obs,y}values reported were used as the downstream boundary conditions. The hydraulic model was implemented under a series of one-day steady state simulations. For every year, the vector Z0

_{obs,y}contains the daily measured water levels values at WL OUT_0. They were used for testing the model performances and for evaluating the optimization process. Z0

_{obs,y}can be defined as:

_{sim,y}contained the daily simulated water levels at WL OUT_0:

_{y}and σ0

_{y}. The former contained the values of the daily differences between simulated and measured water levels at WL OUT_0, as:

_{y}weighted the measures probably affected by errors (“suspicious”) located in Z0

_{obs,y}. The detection involved the Pieve di Cento pumps functioning data. In particular, for the year y, the vectors Z0

_{pmax,y}and Z0

_{pmin,y}contained the daily maximum and minimum values of the delivery tank water level that is registered by the pumps functioning, as:

_{pmaxj}-Z0

_{pminj}was identified. If Z0

_{obsj}do not belong to it, it is defined as a suspicious measure.

## 3. Results and Discussion

#### 3.1. Pilot Segment (PS)

#### 3.1.1. Unmeasured Offtake Discharges

_{kDm}, w

_{kTn}, and w

_{kCn}were calculated, as in Section 2.4.1. Out of these weights, the first one resulted generally higher than the second one; the V

_{rDm}-V

_{kDm}, in fact, differed considerably from V

_{rTn}-V

_{kTn}. When considering the year 2015 as an example, the maximum values were 23.04 × 10

^{4}m

^{3}and 13.68 × 10

^{4}m

^{3}, respectively. For the same year, Figure 6a underlines the monthly variability of w

_{kDm}as compared to the decadal one of w

_{kTn}for two offtakes: Offtake

_{1}(reference offtake) and Offtake

_{5}(Figure 2). The weights w

_{kCn}were obtained averaging D-data and T-data according to Equation (3), and they were reported in Figure 6b. The averaging of those values was needed to minimize the possible measurement errors in D-data, and also, to take into account that CWR from IRRINET are “optimal requirements”, when considering that water was always fully available.

_{kCn}) was mainly coherent with the yearly meteo-climatic conditions (i.e., average daily rainfall). The reference offtake discharge values ranged from 0 m

^{3}/s to 0.24 m

^{3}/s. q

_{kCn}of all other offtakes varied from 0 m

^{3}/s to 0.17 m

^{3}/s.

_{1}and Offtake

_{5}) had the lowest values in 2014 (mean values of 0.021 m

^{3}/s and 0.032 m

^{3}/s, respectively) and the highest mainly in 2012 (mean values of 0.137 m

^{3}/s and 0.082 m

^{3}/s, respectively). If the month of July is considered, the discharge values of the reference offtake were lower in 2012 than in 2013 and 2015. This can be explained not only by meteo-climatic conditions (that resulted in crop stress), but also by insufficient machine, manpower, or energy availability at the field. Moreover, among the years that were analysed, the cultivated crops differ.

#### 3.1.2. Steady State Flow Condition

^{−4}m, respectively.

^{3}/s and 0.279 m

^{3}/s, respectively.

^{2}computes 73 steady state simulations; one for every day of the irrigation period. The hydraulic variables on a daily basis are not function of time.

#### 3.1.3. PS optimized Model

_{sim,y}values are reported (values at the upstream of PS). For every year, they are grouped into two vectors: Q2

_{simc}(output from measured water levels not affected by errors) and Q2

_{sims}(output from measured water levels probably affected by errors, Section 2.4.2).

^{3}/s (Q2

_{sim,}

_{2014}) and 16.660 m

^{3}/s (Q3

_{sim,}

_{2014}), with standard deviations of 2.694 m

^{3}/s and 3.204 m

^{3}/s, respectively. When considering Q2

_{sim,y}as an example, the years 2013 and 2015 were characterized by higher flowing discharge mean values (23.930 m

^{3}/s and 21.710 m

^{3}/s) and standard deviation values (4.230 m

^{3}/s and 4.841 m

^{3}/s) as compared to those of the year 2012 (20.700 m

^{3}/s and 2.538 m

^{3}/s, respectively). This can be justified by the limiting factors that are mentioned in Section 3.1.1. Therefore, the years with extreme climatic conditions (2014 and 2012) presented less variability in relation to flowing discharge mean values when compared to the years 2013 and 2015 characterized by the alternation of dry and rainy intervals.

^{3}/s and 12.88 m

^{3}/s, respectively, while the reference offtake discharge ranged from 0.24 m

^{3}/s (0.81% of the flowing discharge maximum) to 0.07 m

^{3}/s (0.24% of the flowing discharge minimum). Cq cannot be considered as one of the parameters for the optimization process since it did not have any influence on it.

_{up}-Z

_{dn}) reported maximum and minimum values of 0.13 m and 0.03 m, respectively. They were higher than those at Culv_2 that were 0.07 m and 0.01 m, respectively. Due to the modest impact of the offtakes, the values of the discharges at the two culverts were similar, and therefore the gate discharge coefficient at Culv_1 has to be lower than the one at Culv_2. Within Culv_1, both flow types (surface and piped) occurred. The years 2012 and 2015 were characterized by 39 days of surface and 34 days of piped flows. The years 2013 and 2014, on the other hand, presented mainly surface flow (57 and 59 days, respectively).

^{1/3}/s) [68]. Over the last four years, the mean value was 0.0147 m

^{1/3}/s and the maximum difference attested was 0.002 m

^{1/3}/s (2012–2013). The n1 and n2 values were coherent with the literature range for concrete culverts (0.010–0.014 m

^{1/3}/s) [74] and both had a mean of 0.012 m

^{1/3}/s. When considering the analysis period, the maximum difference among the years was 0.005 m

^{1/3}/s (between 2012 and 2013 for n1, and between 2012 and 2014 for n2). The Manning’s coefficient is the result of many factors: Basic value (roughness of the material that was used to line the canal), irregularities of the canal bed, cross sections variations, obstacles, vegetation growth, and meandering [75,76]. Along the PS, the Manning’s coefficient was stable; its variations can be related to the presence of obstacles (debris, downed plants, and dropped obstacles) and algae growth. For the culverts, it showed more variability and it was the result of many possible factors, such as the grids at the culverts entrances, which involve head losses, the gates modelling approximations, and the additional head losses due to the change of geometry between open and closed flow cross sections.

_{sim,}

_{y}and Z3

_{sim,y}(Figure 9).

_{y}and σ3

_{y}vectors, as shown in Table 3. The maximum difference for the cost of the criterion was 0.1319 m (0.2799–0.1480 m) for 2013.

_{sim,y}were plotted versus those of the vector Z2

_{obs,y}. The former were reported for optimized (Opt) and non-optimized (Non-Opt) models.

_{sim,y}and Z3

_{obs,y}(Figure 11). Also, in this case, the optimized model shows an excellent fit, reporting mean values of intercept and slope line of 0.105 and 0.994, respectively.

^{−4}m and 8.150 × 10

^{−3}m, respectively. They significantly differ from those of the non-optimized one (mean value of 0.0302 m at WL OUT_1 and 0.0285 m at WL IN_2).

#### 3.2. Extended Segment (ES)

_{kCn}obtained were mainly coherent with the yearly meteo-climatic condition. In particular, the ES reference offtake reported minimum (0.02 m

^{3}/s) and maximum (1.17 m

^{3}/s) values during the rainy and the dry years, respectively. Moreover, q

_{kCn}for all other offtakes varied from 0 m

^{3}/s (2014) to 0.87 m

^{3}/s (2012). This range was larger than those of PS (0–0.24 m

^{3}/s for the reference offtake and 0–0.17 m

^{3}/s for all other offtakes). In fact, the ES irrigated land supplied is 1.5 times larger (12,580 ha) than that of PS.

_{s}and Q0

_{c}vectors in order to distinguish the flowing discharge values that are based on Q2

_{sims}and Q2

_{simc}, respectively.

^{3}/s (standard deviation of 2.70 m

^{3}/s); the highest values were related to 2012 (24.13 m

^{3}/s on average with a standard deviation of 3.22 m

^{3}/s) and 2013 (25.81 m

^{3}/s on average, standard deviation of 4.569 m

^{3}/s).

^{1/3}/s [68]. Over the three years, the mean value was 0.015 m

^{1/3}/s (very similar to PS n) and the maximum difference of 0.009 m

^{1/3}/s was between the years 2012 and 2015 (0.002 m

^{1/3}/s in PS). The n3, n4, n5 and n6 values were coherent with the range 0.010–0.014 m

^{1/3}/s for concrete culverts [74], except for the year 2015, for which the values were higher (0.019 m

^{1/3}/s maximum). As said before, the Manning’s coefficient differences can be attributed to several factors, such as geometric irregularities or variations of the canal bed and of cross sections, obstacles, vegetation growth, and meandering. Moreover, the field survey estimated the accuracy of Z0

_{obs,y}values (±0.10 m) to be lower than those in PS.

_{y}, diff3

_{y}and diff0

_{y}can justify these results. In fact, considering the year 2015 as an example, the maximum absolute values (only for days not affected by suspicious measures) are 0.015 m at WL OUT_1 (diff2

_{y}) and 0.011 m at WL IN_2 (diff3

_{y}), while at WL OUT_0 (diff0

_{y}), it was much higher and very close to the accuracy threshold (0.102 m). In any case, Figure 13 shows that all the single elements of Z0

_{sim,y}are within the Z0

_{obs,y}accuracy range (±0.10 m), except for few days (eight for 2012, nine for 2013, and two for 2015) that are related to Z0

_{obsj}or Q2

_{simj}and that were probably affected by errors.

_{sim,y}and Z0

_{obs,y}were plotted (Figure 14) in order to detect the modelling impacts of the diff0

_{y}elements. The intercept and the slope of the linear correlation were evaluated, and they were compared with the optimum values (i.e., perfect fitting) and with those reported for PS.

^{−5}), a backwater flow occurred affecting the optimization process and leading to a poor representation of the reality. The multi-disciplinary modelling approach developed in this study presented satisfying results for the two remaining years (2013 and 2015).

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Along the CER | |

Culv_1, Culv_2 | Culverts of Pilot Segment passing under rivers |

Culv_3, Culv_4 | Culverts of Extended Segment passing under rivers |

ES | Extended Segment |

PS | Pilot Segment |

WL OUT_0 | Water gauge at the exit of the pumping station Pieve di Cento |

WL IN_1 | Water gauge at the entrance of Culv_1 |

WL OUT_1 | Water gauge at the exit of Culv_1 |

WL IN_2 | Water gauge at the entrance of Culv_2 |

WL OUT_2 | Water gauge at the exit of Culv_2 |

Measured data | |

Z0_{obs,y} | Vector containing daily water levels at WL OUT_0 for the year y |

Z0_{pmax,y} | Vector containing maximum daily water levels from the functioning of Pieve di Cento pumps |

Z0_{pmin,y} | Vector containing minimum daily water levels from the functioning of Pieve di Cento pumps |

Z1_{obs,y} | Vector containing daily water levels at WL IN_1 for the year y |

Z2_{obs,y} | Vector containing daily water levels at WL OUT_1 for the year y |

Z3_{obs,y} | Vector containing daily water levels at WL IN_2 for the year y |

Z4_{obs,y} | Vector containing daily water levels at WL OUT_2 for the year y |

Offtakes | |

Ai | Irrigable area; area covered by the crop i |

C-data | Calculated data |

CWR_{i} | Decadal cumulated optimum crop water requirement for the crop i |

D-data | Declared data provided by the Associated Consortia |

D_{m} | Duration of the month m |

ED | Coefficient of the efficiency of the delivery system CER-irrigable area |

EI_{i} | Coefficient of the efficiency of the irrigation method of the crop i |

II_{i} | Coefficient of irrigation intensity of the crop i |

q_{kCn} | Calculated discharge exiting from the offtake k during the decade n |

q_{kC,y} | Vector containing daily calculated discharge values of the offtake k for the year y |

q_{rDm} | Discharge value exiting from the reference offtake during the month m |

q_{totC,y} | Vector containing daily calculated offtake discharges from the segment (i.e., ES) for the year y |

T-data | Estimated data provided by IRRINET |

V_{kDm} | Monthly cumulated volume of the offtake k from D-data |

V_{kTn} | Decadal cumulated volume of the offtake k from T-data |

V_{rDm} | Monthly cumulated volume of the reference offtake from the D-data |

V_{rTn} | Decadal cumulated volume of the reference offtake from the T-data |

w_{kCn} | Weight of the offtake k during the decade n |

w_{kDm} | Weight of the offtake k during the month m from D-data |

w_{kTn} | Weight of the offtake k during the decade n from T-data |

Optimization | |

Cd1, Cd2 | Gate discharge coefficients at the entrances of Culv_1 and Culv_2 |

Cd3, Cd4 | Gate discharge coefficients at the entrances of Culv_3 and Culv_4 |

Cd5, Cd6 | Gate discharge coefficients at the entrances of 2 road crossings (ES) |

Cq | Scaling factor of the offtake discharges |

J | Criteria to be minimized |

n | Manning’s coefficient on the CER open-flow sections (along PS or ES) |

n1, n2 | Manning’s coefficients within Culv_1 and Culv_2 |

n3, n4 | Manning’s coefficients within Culv_3 and Culv_4 |

n5, n6 | Manning’s coefficients within the 2 road crossings |

Q0_{y} | Vector containing daily calculated flowing discharges at WL OUT_0 for the year y |

Q2_{sim,y} | Vector containing daily simulated flowing discharges at WL OUT_1 for the year y |

Q3_{sim,y} | Vector containing daily simulated flowing discharges at WL IN_2 for the year y |

Z0_{sim,y} | Vector containing daily simulated water levels at WL OUT_0 for the year y |

Z2_{sim,y} | Vector containing daily simulated water levels at WL OUT_1 for the year y |

Z3_{sim,y} | Vector containing daily simulated water levels at WL IN_2 for the year y |

σ0_{y} | Vector containing the daily weights of the suspicious measures located in Z0_{obs,y} |

σ2_{y} | Vector containing the daily weights of the suspicious measures located in Z1_{obs,y}, Z2_{obs,y} and Z4_{obs,y} |

σ3_{y} | Vector containing the daily weights of the suspicious measures located in Z1_{obs,y}, Z3_{obs,y} and Z4_{obs,y} |

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**Figure 2.**The scheme of Pilot Segment (PS): The six irrigation offtakes, the two culverts passing under the Idice River (Culv_1) and the Quaderna River (Culv_2), the four water gauges (WL) at the IN and OUT of both the culverts.

**Figure 3.**For 2015, the values of J (

**a**) and of the parameterized hydraulic variables contained in the vector X (

**b**) during the iterations of the optimization process that resulted in the minimization of the criterion.

**Figure 4.**For 2015, Cd1 (

**a**), Cd2 (

**b**), n (

**c**), n1 (

**d**), n2 (

**e**), the cuts of J around the minimum values of the parameterized hydraulic variables. In all cases they represent real minimum for the criterion.

**Figure 5.**The scheme of ES: The 12 irrigation offtakes, the three culverts under passing the Idice River (Culv_1), the Navile Canal (Culv_3), and the Savena River (Culv_4), the two water gauges (WL OUT_0 and WL IN_1) at the OUT of the pumping station Pieve di Cento and at the IN of Culv_1, the two road crossings.

**Figure 6.**For the year 2015, the values of the weights w

_{kDm}and w

_{kTn}(

**a**) and w

_{kCn}(

**b**) for the reference offtake (Offtake

_{1}) and for a generic one (Offtake

_{5}).

**Figure 7.**For every year, the variability of the diverted discharges for the reference offtake (Offatake

_{1}) (

**a**) and for a generic offtake (Offtake

_{5}) (

**b**).

**Figure 8.**For every year: 2012 (

**a**); 2013 (

**b**); 2014 (

**c**) and 2015 (

**d**), the values of Q2

_{sim}obtained from the optimized model.

**Figure 9.**For every year: 2012 (

**a**); 2013 (

**b**); 2014 (

**c**) and 2015 (

**d**), the simulated water level values contained in Z2

_{sim}and Z3

_{sim}.

**Figure 10.**For every year: 2012 (

**a**); 2013 (

**b**); 2014 (

**c**) and 2015 (

**d**), the linear interpolation of Z2

_{obs}and Z2

_{sim}for both optimized and non-optimized models.

**Figure 11.**For every year: 2012 (

**a**); 2013 (

**b**); 2014 (

**c**) and 2015 (

**d**), the linear interpolation of Z3

_{obs}and Z3

_{sim}for both optimized and non-optimized models.

**Figure 12.**For every year: 2012 (

**a**); 2013 (

**b**), 2014 (

**c**) and 2015 (

**d**), the values of discharge (Q0) calculated at WL OUT_0.

**Figure 13.**The simulated water level values contained in Z0

_{sim}for the years 2012 (

**a**), 2013 (

**b**) and 2015 (

**c**).

**Figure 14.**The linear interpolation of Z0

_{obs}and Z0

_{sim}for the optimized model for the years 2012 (

**a**), 2013 (

**b**) and 2015 (

**c**).

Available Data | Type | Unit | Time Step | Source |
---|---|---|---|---|

Offtake Volumes | Indirectly calculated | m^{3} | Monthly (cumulated values) | Associated Consortia |

CWR_{i} | Estimated | mm | Decadal (cumulated values) | IRRINET |

Water Levels | Measured | m | Daily (average values) | CER |

Water Levels at Suction/Delivery Tanks | Measured | m | Pumps on/off (single values) | CER |

**Table 2.**The values of the coefficients intensity of irrigation (II) and efficiency of the irrigation method (EI) for the irrigated crops served by PS and extended segment (ES).

Irrigated Crops | II_{i} (-) | EI_{i} (-) |
---|---|---|

Extensive crops | ||

Maize | 0.75 | 0.75 |

Soy | 0.50 | 0.75 |

Alfa-Alfa | 0.25 | 0.75 |

Vegetables | ||

Beet | 0.60 | 0.75 |

Onion | 1.00 | 0.75 |

Melon | 1.00 | 0.85 |

Potato | 1.00 | 0.75 |

Tomato | 1.00 | 0.85 |

Orchards | ||

Pear | 1.00 | 0.85 |

Peach | 1.00 | 0.85 |

Vine | 0.50 | 0.85 |

**Table 3.**The values of the five parameterized variables and the cost of the criterion obtained from the optimization process: Without (above) and with the weights of suspicious measures (below).

Year | Parameterized Hydraulic Variables | Cost of the Criterion | ||||
---|---|---|---|---|---|---|

Cd1 (-) | Cd2 (-) | n (m^{1/3}/s) | n1 (m^{1/3}/s) | n2 (m^{1/3}/s) | J Cost (m) | |

Without Suspicious Measures Weights | ||||||

2012 | 0.37 | 0.64 | 0.014 | 0.015 | 0.015 | 0.1742 |

2013 | 0.68 | 0.76 | 0.015 | 0.009 | 0.011 | 0.2799 |

2014 | 0.39 | 0.82 | 0.016 | 0.015 | 0.008 | 0.2331 |

2015 | 0.49 | 0.69 | 0.015 | 0.012 | 0.013 | 0.1036 |

With Suspicious Measures Weights | ||||||

2012 | 0.37 | 0.65 | 0.014 | 0.014 | 0.015 | 0.1460 |

2013 | 0.71 | 0.74 | 0.016 | 0.009 | 0.011 | 0.1480 |

2014 | 0.44 | 0.80 | 0.015 | 0.013 | 0.010 | 0.1101 |

2015 | 0.50 | 0.71 | 0.014 | 0.012 | 0.012 | 0.0808 |

**Table 4.**The root mean square error (RMSE) values for both optimized and non-optimized models at WL OUT_1 and WL IN_2.

Year | RMSE (m) | |
---|---|---|

Non-Optimized Hydraulic Model | Optimized Hydraulic Model | |

WL OUT_1 | ||

2012 | 0.0586 | 2.9 × 10^{−4} |

2013 | 0.0220 | 6.1 × 10^{−4} |

2014 | 0.0216 | 5.8 × 10^{−4} |

2015 | 0.0185 | 3.9 × 10^{−4} |

WL IN_2 | ||

2012 | 0.0318 | 6.1 × 10^{−3} |

2013 | 0.0340 | 11.2 × 10^{−3} |

2014 | 0.0316 | 8.3 × 10^{−3} |

2015 | 0.0265 | 7.0 × 10^{−3} |

**Table 5.**The values of the nine parameterized variables and of the cost of the criterion obtained from the optimization process.

Year | Parameterized Hydraulic Variables | Cost of the Criterion | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Cd3 (-) | Cd4 (-) | Cd5 (-) | Cd6 (-) | n (m^{1/3}/s) | n3 (m^{1/3}/s) | n4 (m^{1/3}/s) | n5 (m^{1/3}/s) | n6 (m^{1/3}/s) | J Cost (m) | |

2012 | 0.60 | 0.45 | 0.62 | 0.52 | 0.020 | 0.020 | 0.013 | 0.011 | 0.010 | 0.5057 |

2013 | 0.58 | 0.60 | 0.58 | 0.58 | 0.014 | 0.013 | 0.013 | 0.013 | 0.013 | 0.4667 |

2015 | 0.42 | 0.59 | 0.43 | 0.45 | 0.011 | 0.019 | 0.019 | 0.019 | 0.010 | 0.3465 |

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**MDPI and ACS Style**

Luppi, M.; Malaterre, P.-O.; Battilani, A.; Di Federico, V.; Toscano, A.
A Multi-disciplinary Modelling Approach for Discharge Reconstruction in Irrigation Canals: The Canale Emiliano Romagnolo (Northern Italy) Case Study. *Water* **2018**, *10*, 1017.
https://doi.org/10.3390/w10081017

**AMA Style**

Luppi M, Malaterre P-O, Battilani A, Di Federico V, Toscano A.
A Multi-disciplinary Modelling Approach for Discharge Reconstruction in Irrigation Canals: The Canale Emiliano Romagnolo (Northern Italy) Case Study. *Water*. 2018; 10(8):1017.
https://doi.org/10.3390/w10081017

**Chicago/Turabian Style**

Luppi, Marta, Pierre-Olivier Malaterre, Adriano Battilani, Vittorio Di Federico, and Attilio Toscano.
2018. "A Multi-disciplinary Modelling Approach for Discharge Reconstruction in Irrigation Canals: The Canale Emiliano Romagnolo (Northern Italy) Case Study" *Water* 10, no. 8: 1017.
https://doi.org/10.3390/w10081017