Stochastic Hydrology

Module aims

To introduce statistical methods used for hydrological design; some standard time series methods applied to the modelling of hydrological variables; the use of Monte Carlo simulation in quantifying uncertainty; some stochastic models used for the rainfall input to hydrological systems.

Learning outcomes

On successfully completing this course unit, students will: 

  • Be able to use standard time-series models for hydrological modelling.
  • Know about the range of approaches to rainfall modelling.
  • Know how to estimate the frequency of extreme hydrological events.
  • Have an understanding of tools available to estimate and model uncertainty.
  • Have an ability to use software for the analysis and modelling of time-series.
  • Have skills in rainfall modelling, ARIMA modelling, extreme-value estimation.

Module syllabus

Topics covered will include:  

  • Time-series analysis: model definition and identification.
  • Particular ARMA models of use in hydrology.
  • Time-series analysis: forecasting, goodness-of-fit.
  • Extreme-value analysis: annual maxima and partial duration series.
  • Poisson-cluster modelling of rainfall time-series
  • Multi-fractal modelling in hydrology 

Week No.




Time series modelling: Motivation and the main Linear Models

Dr C. Onof


Time series modelling: ARIMA models

Dr C. Onof


Time-series modelling: Physical basis of ARIMA modelling + focus on the AR(1) model

Dr C. Onof


Time-series modelling: Goodness-of-fit and Forecasting

Dr C. Onof


Extreme-value estimation for hydrological design (I)

Dr C. Onof


Extreme value estimation for hydrological design (II)

David Cross


Stochastic Rainfall Modelling with Poisson cluster processeses

Dr C. Onof/Ben Guo


Stochastic Rainfall Modelling with Generalised Linea Models

Barbara Orellana


Stochastic Rainfall Modelling with multifractal processes

Dr A. Gires

Teaching methods

A combination of lectures and tutorials.


Assessment of the module is by examination only.

Reading list


Module leaders

Dr Christian Onof