Università degli Studi di Napoli "Parthenope"

Teaching schedule

Academic year: 
Belonging course: 
Course of Master's Degree Programme on CIVIL ENGINEERING
Disciplinary sector: 
Year of study: 
Second semester
Hours of front activity: 



Course description

The design and the management of the interventions for the hydraulic risk reduction require a basic knowledge of flow propagation models and extreme hydrology. The course is intended to help the students in acquiring the theoretical foundation and the practical skills required for the hydraulic modelling of flow propagation in rivers and on flooded areas. In addition, the course gives the principles of extreme hydrology, with a project application.

***Learning outcomes***

1) Knowledge and understanding

The student must demonstrate knowledge and understanding of the fundamentals of the following topics:
- Advanced topics in Hydraulics- Mathematical models for the simulation of flow propagation in rivers and on flooded areas- Principles of Probability- Principles of Hydrology.
The student will be able to implement methodologies appropriate for solving complex problems, both systematically and creatively.

2) Ability to apply knowledge and understanding

The student will acquire the ability to use their knowledge to critically, independently and creatively solve problems with some originality in new contexts. In particular, the following abilities are developed:
- physical and mathematical characterisation of flooding problems;
- critical use of mathematical and numerical flow propagation models.
These abilities are concretely trained by means of a project exercise.

3) Autonomy of judgement

The student will be able to make sound judgments about hydraulic risk reduction problems, even on the basis of incomplete information:
- evaluation of project characteristics;
-benchmarking of different and competitive projects;
- evaluation hydraulic softwares performance;
- evaluation of project outcomes, also with reference to social and environmental impacts.

4) Communication skills

The students will be able to communicate clearly and unambiguously about the main issues in the field of the hydraulic risk management. In particular, the students will be able to:
- communicate properly during the oral examination;
- collaborate with their peers in a working group, defining objectives, activities, and tools;
- present and discuss a project with both specialist and non-specialist audiences.

5) Learning skills

The students willl be able to identify and address learning needs for further knowledge, take responsibility for further professional development.


The following courses and competencies are prerequisites:
- Hydraulics
- Hydraulic works



- Advanced topics in Hydraulics and Fluid Mechanics (16 hours class)

The Saint-Venant Equations. Steady flow profiles. Kinematic wave. One- and two-dimensional Shallow water Equations.

- Mathematical models for the simulation of flow propagation in rivers and on flooded areas (18 hours class)
Introduction to the Hyperbolic partial differential equations. The color equation: analytic solution with the method of characteristics. Inviscid Burger’s equations. Analytic solution of the Burger’s equation with the method of characteristics. Integral form of conservation laws and weak solutions. Vanishing viscosity solutions. Linearization of non-linear equations Rankine-Hugoniot theorem. Self-similar solutions of the Riemann problem: moving finite-amplitude discontinuities, Riemann fan. Stability of moving finite-amplitude discontinuities (shocks). Hyperbolic systems of partial differential equations. Riemann problem for linear hyperbolic systems. Characteristic fields in the SWEs. Propagation celerity of finite and infinitesimal amplitude discontinuities in the SWEs. Froude number and physical interpretation. Method of characteristics for the SWEs. Boundary conditions. Shock curves. Rarefaction curves. Solution of the Riemann problem. Special cases: the dam-break problem. Introduction to the Finite Volume method. Riemann problem at the interface between cells.

- Principles of Probability (15 hours class)

Events space, probability axioms, corollaries. Continuous random variables. Probability distributions. Density function. Expected value. Expectation operator. Moments. Variance. Uniform distribution, exponential distribution, normal distribution, lognormal distribution. Extreme value distribution. Function of random variables. Discrete random variables. Probability mass function. Bernoulli, geometric, binomial, and Poisson distributions. Risk and return period. Gumbel distribution.

- Principles of Hydrology (15 hours class +8 hours of class exercise)

Rain gauges. Hydrologic data. Intensity-duration-frequency curves. Regularization of hydrologic data. Regionalization of intensity-duration-frequency curves. Linear rainfall-runoff models. IUH. Convolution integral. Lag-time. S curve. Unit step response. Rectangular pulse response. Discretization of the convolution integral. The linear reservoir. Nash IUH. The time-area rainfall-runoff model. Variational approach for the calculatio nof annual extrema. The time-area method in urban catchments. The linear reservoir and the the time-area method seen as consequence of the kinematic wave linearization. Inverse of the Gumbel distribution. Hydrologic similarity. Growth factor in the Gumbel distribution. TCEV distribution. Growth factor in the TCEV distribution. Hydrologic regionalization. Lag-time in Campania region, Rossi-Villani formula. Geomorphoclimatic approach. Evaluation of lreservoir coefficien and concentration time. VAPI approach for the evaluation of annual extreme flow rates. Project exercise.

Teaching Methods

During the course, learning is mainly subdivided in the following activities:
- class (theory)
- group (not individual) project exercise at home
- class (numerical exercises, and verification of home project exercise).
The reference texts can be downloaded from the teacher's website.


- AA.VV. Estratti dalla pubblicazione “Valutazione delle piene in Campania”, CNR
- V. Comincioli, Metodi Numerici e Statistici per le Scienze Applicate, CEA
- Chow V.T., Maidment D.R., Mays L.W., Applied hydrology, McGraw-Hill.
- Cozzolino L, Modelli semplificati dell’idraulica.
- J.A. Cunge, F.M. Holly Jr., A. Verwey, Practical aspects of computational river hydraulics, Institute of Hydraulic Research, Iowa University
- LeVeque R.J., Finite-volume methods for hyperbolic problems, Cambridge University Press.
- U. Moisello, Idrologia Tecnica, La Goliardica Pavese
- C. Montuori, Complementi di Idraulica, Liguori - Mood A.M., Graybill F.A., Boes D.C., Introduzione alla statistica, McGraw-Hill.
- Rossi F., Appunti di probabilità ciclostilati.
- Rossi F., Fiorentino M., Versace P. (1984) Two-Component Extreme Value Distribution for Flood Frequency Analysis, Water Resources Research 20(7), 847-856.
- Rossi F., Villani P., Alcune considerazioni sul metodo dell’invaso e della corrivazione.

Learning assessment

The final examination is in oral form. The student is scrutinized with respect to the theoretical content of the course, and the project exercise is discussed.
The student must prove of having understood the theoretical and practical issues related to the project exercise, and his/her ability to use the numerical tools.
On request by the student, the oral exam can be conducted in English language.

More information

Office hours for students:
Thursday, 11:00-13:00
By appointment (e-mail)