# Hydrological Analysis of a Dyke Pumping Station for the Purpose of Improving Its Functioning Conditions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{3}·s

^{−1}(3200 m

^{3}·h

^{−1}). Upstream of the pumping station, there is a retarding reservoir in the form of a widened (for a length of about 100 m) Łęgoń watercourse channel. The retarding reservoir is about 15 m wide at its bottom.

## 3. Methodologies of Flows Estimation

#### 3.1. Design Flows—The Spatial Regression Equation

^{2}. This equation, which is recommended by the Polish Hydrologists Association, is written in the following form [24]:

_{max p%}is the annual maximum flow with a probability of exceedance of p = 1% in m

^{3}·s

^{−1}and λ

_{p}is the quantile for the nondimensional regional curves of the maximal flows, which equals λ

_{p}= 1.224 for p = 0.3%.

_{max p=1%}is the maximum flow with a probability of exceedance equal to 1% in m

^{3}∙s

^{−1}; α

_{area}is the regional parameter of the formula, which is taken on the basis of the investigated area location in Poland and is equal to α

_{area}= 2.992 × 10

^{−3}; A is the river catchment area that amounts to A = 49.40 km

^{2}; H

_{1}is the maximum daily rainfall for a probability of exceedance of p = 1%, which is taken from the meteorological station in Raciborz and is equal to H

_{1}= 87.3 mm; and ϕ is the runoff coefficient for peak flows, which is equal to ϕ = 0.55 and qualified on the basis of “The map of Polish soils”. For a catchment with several soil groups with different values of runoff coefficient ϕ, a medium weight should be calculated for the whole catchment.

_{i}is an area covered with soil of a given group in km

^{2}and I

_{r}is the longitudinal river bed slope that is equal to I

_{r}= 0.73‰.

_{g}is the elevation of the watershed in the point crossing the axis of a dry valley of the longest watercourse in m a.s.l.; W

_{p}is the elevation of the calculated cross-section closing the catchment in m a.s.l.; L is the length of the longest watercourse in the catchment in km; l is the length of a dry valley in the lengthened part of the longest watercourse of the catchment in km; and ψ is the average slope of the river catchment, which is equal to ψ = 17.0‰.

_{max}is the maximal catchment elevation in m a.s.l.; A is the catchment area in km

^{2}; and lake is the lake index of the river catchment.

_{lake i}is an area of the lake i catchment that is equal to A

_{lake}= 2.5 km

^{2}and m is the number of lake catchments, which is equal to m = 1.

_{B I}is an area of i-succeeding swamp or peat land region in km

^{2}and k is the number of swamp regions.

^{2}, the maximum catchment length of 11.57 km, an average catchment gradient of 1.7%, and also a forestation ratio of 15%. Therefore, the maximum flows to the Ciechowice pumping station, with the specified probability of exceedance calculated using the spatial regression Formula (2), amounted to:

#### 3.2. The NRCS-CN Method

Fraction of precipitation time [h] | (0–0.3)T | (0.3–0.5)T | (0.5–1.0)T |

Percentage of total precipitation | 20 | 50 | 30 |

_{e}to cumulative total precipitation P minus initial losses I

_{α}is equal to the ratio of current cumulative infiltration F to maximum potential catchment storage S:

_{e}is the effective precipitation in mm; P is the total precipitation in mm; I

_{α}is the initial abstraction in mm; S is the potential catchment storage in mm; and F is the current infiltration in mm after runoff begins.

_{e}and P are the effective and the total precipitation amounts totalized over time from 0 to T [mm], λ is an empirical coefficient contingent on the CN (curve number) parameter, which is normally assumed as a constant value of 0.2 in order for S to be the only parameter of the method; and S is the maximum catchment storage [mm].

_{p}is the ponding time, K

_{s}is the saturated permeability coefficient of soil, t is the rainfall duration, and p is the rainfall intensity. Since the last three variables can be measured easily and t

_{p}is determined by any adequate formula, the uncertainty of the adopted infiltration models is reduced to a minimum.

_{α}. Parameter CN is determined as a weighted average for the whole catchment area on the basis of the adopted soil group, the catchment use, and the hydrologic conditions (14):

^{2}; CN

_{i}is the characteristic values of the particular areas A

_{i}; and n is the number of homogenous areas.

#### 3.3. Determination of Wave Hydrographs

^{−1}; t is the time from the coordinate system origin in h; k is the reservoir storage parameter in h determined using the empirical Formula (16); N is the number of reservoirs in the Nash model N = LAG/k, where runoff lag time (delay between the culmination of precipitation and the peak of the flood wave) is determined using Formula (17); and Γ(N) is the gamma function that is equal to (N − 1).

^{2}; U is the fraction of impermeable surfaces in the whole catchment; P

_{e}is the amount of effective precipitation in mm; and D is the duration of effective precipitation in h. The time of growth amounts to ${t}_{p}=\left(N-1\right)k$ and the maximum of the unit hydrograph amounts to

_{e,j}is the partial effective precipitation in time interval j in mm; m is the number of the unit hydrograph ordinates; n is the number of effective precipitation time intervals; and h

_{k}is the unit hydrograph ordinates in m

^{3}∙s

^{−1}∙mm

^{−1}calculated using Equation (20), or if ${t}_{p}>3\Delta t$ using Equation (21):

_{1%}= 18.75 m

^{3}∙s

^{−1}and Q

_{0.3%}= 24.8 m

^{3}∙s

^{−1}.

_{m}= 0.923 M m

^{3}and V

_{k}= 1.182 M m

^{3}, respectively.

#### 3.4. Flood Waves Routing

^{3}s

^{−1}; x is a coordinate consistent with the direction of the water flow in m; A is the surface area of the flow in m

^{2}; and t is the time in s.

_{1}to x

_{2}and appropriately transformed, Equation (22) assumes the form of (23) in which the value of the integral expresses the volume of the water stored in the reservoir or that discharged from the reservoir:

_{1}coordinates at the beginning of the reservoir; x

_{2}coordinates at the end of the reservoir; Q(x

_{1}), Q(x

_{2}) represent the flow of water into and out of the reservoir in m

^{3}s

^{−1}, respectively; and ΔV/Δt is the change in water volume in the reservoir over time.

#### 3.5. Methodology Summary

- Selecting the methodology for estimating calculated flows with a specified probability of exceedance, which depends on whether the catchment is being controlled or not.
- Conducting hydrological calculations for designing flows estimation.
- Generating hydrographs to calculate flows.
- Evaluating terrain conditions in the localization of a dyke pumping station, which enables a retarding reservoir with a determined capacity and parameters to be constructed.
- Selecting the capacity of pumps in the dyke pumping station.
- Selecting computational scenarios that consider the variable capacity of pumps and the variable volume of a retarding reservoir.
- Estimating the functioning conditions of a dyke pumping station and a retarding reservoir during the occurrence of a flood wave.
- Estimating the costs of construction, exploitation, and maintenance for a dyke pumping station and a retarding reservoir with regards to different computational scenarios.

## 4. Pump Station Capacity Assumptions

- in each of the calculation cases, the retarding reservoir bottom is situated at 174.60 m a.s.l.,
- the retarding reservoir side slope is 1:2,
- the normal drainage level is 176.30 m a.s.l.,
- the maximum allowable water level in the upper dyke areas is 178.00 m a.s.l.,
- the dyke culvert flaps are closed (there is a flood on the main river),
- the initial water level in the retarding reservoir is situated at 176.00 m a.s.l.,
- the pump switching on/off levels: I-176.30/175.80; II-176.70/176.20; III-177.10/177.60; IV-177.50/177.00.

- Case 1: current (existing) state, retarding reservoir bottom dimensions of 15 × 100 m, pumps’ output of 4 × 0.9 = 3.60 m
^{3}s^{−1}, design flood wave routing; - Case 2: current state, retarding reservoir bottom dimensions of 15 × 100 m, pumps’ output after alteration of 4 × 1.05 = 4.20 m
^{3}s^{−1}, design flood wave routing; - Case 3: a total pumping station capacity of 18.75 m
^{3}s^{−1}, four pumps as is the case for the current state, four additional pumps with a capacity of 15.15 m^{3}s^{−1}, retarding reservoir bottom dimensions of 45 × 240 m, design flood wave routing; - Case 4: a total pumping station capacity of 18.75 m
^{3}s^{−1}, four pumps as is the case for the current state, four additional pumps with a total capacity of 15.15 m^{3}s^{−1}, retarding reservoir bottom dimensions of 45 × 240 m, control flood wave routing; - Case 5: a total pumping station capacity of 18.75 m
^{3}s^{−1}, four pumps after alteration 4 × 1.05 = 4.20 m^{3}s^{−1}, four additional pumps with a capacity of 14.55 m^{3}s^{−1}, retarding reservoir bottom dimensions of 45 × 240 m, design flood wave routing; - Case 6: a total pumping station capacity of 15.0 m
^{3}s^{−1}, four pumps, retarding reservoir bottom dimensions of 45 × 240 m, design flood wave routing; - Case 7: a total pumping station capacity of 15.0 m
^{3}s^{−1}, four pumps, retarding reservoir bottom dimensions of 55 × 910 m, design flood wave routing; - Case 8: a total pumping station capacity of 8.0 m
^{3}s^{−1}, four pumps, retarding reservoir bottom dimensions of 100 × 1700 m, design flood wave routing; - Case 9: a total pumping station capacity of 6.0 m
^{3}s^{−1}, four pumps, retarding reservoir bottom dimensions of 100 × 2150 m, design flood wave routing.

## 5. Calculation Results and Discussion

^{3}s

^{−1}(Case 1). The capacity of the retarding reservoir is insufficient to reduce the designed flood wave—the water level significantly exceeds the maximum permissible level of 178.00 m by 0.50 m. (Figure 5a). Similar results were obtained in the calculations of flood waves passing through a retarding reservoir while taking into account the change in the pumps’ capacity to the total capacity of 4.20 m

^{3}s

^{−1}(Case 2).

^{3}and the pumping station capacity is increased to the capacity determined by the hydrological calculations in both Case 3 (Figure 5b) and Case 5 (Figure 5d).

^{3}s

^{−1}with the replacement of the pumps in the existing pumping station in order to obtain a total capacity of 4 × 1.05 = 4.20 m

^{3}s

^{−1}, and the building of another pumping station in order to obtain a capacity of 14.55 m

^{3}s

^{−1}. The required retarding reservoir capacity is 31,590 m

^{3}and its bottom dimensions are 45 × 240 m. Moreover, Case 3, which can be executed at a lower cost, can also be considered as it does not require the reconstruction of the existing pumping station, but only requires the replacement of the pumps due to their condition.

## 6. Conclusions

- The designed flood wave of p = 1% cannot be safely passed through the pumping station for the existing specifications—the total pumping station capacity of 3.60 m
^{3}s^{−1}and the retarding reservoir capacity of 7412 m^{3}. - On the basis of computer simulations, it should be indicated that the solution that involves reducing the required pumping station capacity leads to an increase in the required retarding reservoir capacity. The approach to ensure safe operation of the pumping station should not only take into consideration the capacity of the pumping station and volume of the retarding reservoir, but also the retention capacity of the riverbed. This will reduce the cost of rebuilding an existing facility.
- On the basis of the performed analysis, it was decided that Case 5 is the most beneficial for reconstructing the dyke pumping station, and in this case, the designed flood wave of p = 1% can be safely passed through the Ciechowice pumping station at the total pumping station capacity of 18.75 m
^{3}s^{−1}and the retarding reservoir capacity of 31,590 m^{3}.

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Hyetographs of the total and effective precipitation in the Łęgoń watercourse catchment for (

**a**) p = 0.3%, (

**b**) p = 1%.

**Figure 5.**Flood wave transformation in (

**a**) Case 1; (

**b**) Case 3; (

**c**) Case 4; (

**d**) Case 5; (

**e**) Case 6; (

**f**) Case 7; (

**g**) Case 8; and (

**h**) Case 9.

Soil | % Area | Hydrologic Soil Group |
---|---|---|

Sediments | 12.8 | A |

Peat | 13.58 | C |

Sand | 31.39 | B |

Sandy loam | 28.9 | C |

Loess and silt | 8.23 | B |

Water | 5.1 | - |

Type | A (km^{2}) | % Area |
---|---|---|

Agricultural areas | 29.37 | 59.45 |

Grasslands | 1.71 | 3.47 |

Mixed forest | 8.22 | 16.65 |

Coniferous forest | 1.44 | 2.92 |

Settlement | 6.15 | 12.44 |

Water | 2.50 | 5.07 |

Total catchment area | 49.4 | 100 |

Case | Bottom Dimensions [m × m] | Reservoir Capacity [m^{3}] | Reservoir Depth [m] | Max. Water Elevation in the Reservoir [m a.s.l.] | Capacity of the Pumping Station [m^{3} s^{−1}] |
---|---|---|---|---|---|

1 | 15 × 100 | 7412 | - | above 178.00 | 4 × 0.9 = 3.60 |

2 | 15 × 100 | 7412 | - | above 178.00 | 4 × 1.05 = 4.20 |

3 | 45 × 240 | 31,724 | 2.63 | 177.23 | 4 × 0.9 + 15.16 = 18.76 |

4 | 45 × 240 | - | - | above 178.00 | 4 × 0.9 + 15.16 = 18.76 |

5 | 45 × 240 | 31,591 | 2.62 | 177.22 | 4 × 1.05 + 14.46 = 18.76 |

6 | 45 × 240 | - | - | above 178.00 | 4 × 3.75 = 15.00 |

7 | 55 × 910 | 191,209 | 3.40 | 178.00 | 4 × 3.75 = 15.00 |

8 | 100 × 1700 | 617,304 | 3.40 | 178.00 | 4 × 2.0 = 8.00 |

9 | 100 × 2150 | 778,266 | 3.39 | 177.99 | 4 × 1.5 = 6.00 |

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**MDPI and ACS Style**

Machajski, J.; Kostecki, S.
Hydrological Analysis of a Dyke Pumping Station for the Purpose of Improving Its Functioning Conditions. *Water* **2018**, *10*, 737.
https://doi.org/10.3390/w10060737

**AMA Style**

Machajski J, Kostecki S.
Hydrological Analysis of a Dyke Pumping Station for the Purpose of Improving Its Functioning Conditions. *Water*. 2018; 10(6):737.
https://doi.org/10.3390/w10060737

**Chicago/Turabian Style**

Machajski, Jerzy, and Stanisław Kostecki.
2018. "Hydrological Analysis of a Dyke Pumping Station for the Purpose of Improving Its Functioning Conditions" *Water* 10, no. 6: 737.
https://doi.org/10.3390/w10060737