Process-based hydrological modelling

A 12-day intensive course offered through the University of Saskatchewan Centre for Hydrology (Geography 898.3)

May 9-20, 2020 - Barrier Lake Field Station, Kananaskis Valley, Alberta

Course Objectives

This course is designed to provide participants with the understanding and skills necessary to become experts in process-based hydrological modelling. The lectures will advance understanding of state-of-the-art modeling practices. The quantitative exercises will provide participants with the opportunity to build simple models, run complex models, make changes, and analyze model output. The practical exercises will require work in groups in order to develop the collaborative problem-solving skills that are required in both academia and industry.

By the conclusion of the course, students will be able to:

  • Explain the inner-workings of hydrological models, including their spatial discretization, flux parameterizations, and time stepping schemes;
  • Judge the relative merits of hydrological models of different type and complexity;
  • Construct hydrologic models to simulate dominant hydrological processes across a broad range of landscapes;
  • Construct hydrologic models to address applied questions, including scenarios of change (climate change; land use change) and predictions of streamflow;
  • Solve computationally intensive model simulations using massively parallel computers;
  • Use best practices in community hydrological modelling, including code sharing and code review, as well as fully documented and sharable model workflows.

Course Synopsis

The University of Saskatchewan Centre for Hydrology is offering an intensive course on the fundamentals of process-based hydrological modelling, including model development, model application, and model evaluation. The course will explain the model constructs that are necessary to simulate dominant hydrological processes, the assumptions that are embedded in models of different type and complexity, and best practices for model development and model applications. The course will cover the full model ecosystem, including the spatial discretization of the model domain, input forcing data generation, model evaluation, parameter estimation, post-processing, uncertainty characterization, data assimilation, and ensemble streamflow forecasting methods. The overall intent of the course is to provide participants with the understanding and tools that are necessary to develop and apply models across a broad range of landscapes. Specifically, the course will convey an understanding of how to represent existing process understanding in numerical models, how to devise meaningful model experiments, and how to evaluate these experiments in a systematic way. Along the way, participants will have the opportunity to build models, run models, make changes, and analyze model output.

Since the course is quantitative in nature, we recommend that participants have a firm foundation in calculus and physics at the first-year university level and some experience in computing (e.g., familiarity with python, R, matlab). We also recommend that participants have a strong background in hydrology, e.g., as obtained by taking Geography 827 “Principles of Hydrology” at the University of Saskatchewan or a similar graduate-level course in hydrology.

Course Format

The course will be held over a 12-day period at the Barrier Lake Field Station in the Canadian Rockies (approx. one hour drive west from Calgary, Alberta) and will be evenly split between lectures (mornings) and practical exercises (afternoons). The course will also include field excursions to learn about the landscape and understand how to best represent dominant processes in time stepping simulation models. If you have medical issues that will affect you on these field trips please contact Professor Clark to discuss beforehand.

Participants will complete a capstone project to apply a model to one or more locations, use observations to evaluate model performance, and answer a specific question.

The course will be taught by Prof. Martyn P. Clark, with guest lectures and practical exercises provided by internationally-renowned experts in process-based hydrological modelling.

The schedule for the course is as follows:

May 8-20, 2020 Intensive 12-day instruction 
(please arrive by 7pm on May 8th)
May 20, 2020 
at 9am MDT
Mid-term examination 
(3 hours)
May 31, 2020 Capstone project proposal due
June 19, 2020 Written project due
June 26, 2020 Final presentation  
(video conference will be available for non-local participants)

Note: The mid-term examination and capstone project are optional for participants auditing the course.

Dr. Clark will be available on site during the course; individual instructors will be available for portions of the course corresponding to their lecture day and at least one other day. Dr. Clark will be also available for in-person advising sessions at the University of Saskatchewan on a bi-weekly basis throughout May and June and via email/Skype/zoom throughout the spring term.

Course Topics

  1. Introduction to process-based hydrological modelling
    We will discuss alternative approaches to process-based hydrological modeling and summarize common uses of numerical models in hydrology. Participants will introduce their interests in hydrological modeling and explain what they hope to gain from the class.

  2. Model mechanics: From process understanding to model simulations
    In this theme we will explain how hydrologic models are constructed; how our understanding of dominant hydrological processes is represented in time-stepping mechanistic models. The theme will summarize the key ingredients of hydrological models, including state equations, flux parameterizations, and time stepping schemes. Participants will build a simple model “from scratch” to gain first-hand experience in model construction.

  3. Process-based model development: Building models to simulate dominant processes across different landscapes
    In this theme we will discuss algorithmic descriptions of dominant processes across different landscapes, including glacier dynamics, snow energetics, frozen ground, forest-snow interactions, hillslope-riparian interactions, surface water – groundwater interactions, infiltration, evapotranspiration, runoff generation, surface water storage, and lakes and wetlands. A key focus will be on representing spatial heterogeneity in models, especially modelling how large-scale fluxes are shaped by small-scale heterogeneity. This theme will include a full-day field trip to observe the dominant hydrological processes in the Canadian Rockies. Participants will run models using alternative algorithms of dominant process and gain understanding of the differences among competing modeling approaches.

  4. Geospatial intelligence
    In this theme we will discuss methods to develop the spatial information required for model simulations (e.g., new geospatial data; hierarchal spatial organization of the landscape into GRUs/HRUs to represent spatial variability in topography, vegetation and soils). Participants will use terrain analysis methods to gain understanding of the importance of uncertainties in landscape structure.

  5. Meteorological forcing data
    This theme will discuss methods to generate spatial fields of meteorological inputs (e.g., spatial interpolation methods, empirical methods to estimate radiation/humidity from standard precipitation/temperature measurements, use of data from atmospheric model reanalyses, temporal disaggregation methods, and ensemble methods to explicitly characterize uncertainties in forcing inputs). Moreover, this theme will discuss methods to represent changes in time, specifically, use of information from Earth System models to produce scenarios of the impacts of climate change on water resources.

  6. Going big: The use massively parallel computers for computationally intensive model simulations
    In this theme we will introduce strategies used for computationally intensive model simulations, including parallelization of models and parallelization of analysis methods. This theme will also cover the common case where the problem is “embarrassingly parallel” and parallelization can be achieved using simple scripting procedures. Participants will run a suite of simulations on super-computers to gain experience with computationally-intensive modeling problems.

  7. Best practices in community hydrological modeling: transparent/extensible approach to model development and shareable model workflows.
    In this theme we will discuss methods for code sharing and code review (e.g., GitHub), fully documented and sharable model workflows (e.g., jupyter notebooks), and the use of containers to simplify porting of models (e.g., docker images). We will discuss coding conventions, modularity, approaches for intra-component and inter-component coupling, and workflow management. Participants will undertake exercises in collaborative model development, where different participants are working on individual model components. Participants will also develop prototypical model workflows for specific modeling applications.

  8. Use of multivariate data to understand/refine model simulations: Process-based model evaluation, sensitivity analysis, and parameter estimation.
    In this theme we will confront the model with data. We will discuss process-based model evaluation, i.e., the use of multivariate diagnostic signatures to independently evaluate internal model components, and compare against traditional model evaluation methods restricted to evaluating model simulations of streamflow. We will consider different local and global parameter sensitivity analysis methods to understand how model parameters affect model behavior. We will consider alternative single-objective and multiple-objective parameter estimation strategies, including regularization strategies necessary for high-dimensional modeling problems. Participants will run a suite of exercises to understand model behavior and refine model simulations.

  9. Ensemble methods: Uncertainty quantification, data assimilation, and probabilistic predictions.
    In this theme we will consider a suite of uncertainty quantification methods, including methods to quantify uncertainty in individual model components (e.g., model inputs; model states), methods to infer model uncertainty from observations, and ad-hoc methods to quantify uncertainty through ensembles of opportunity. We will consider ensemble data assimilation strategies, focusing on the ensemble Kalman filter and the particle filter to use snow data and streamflow data to update time stepping simulation models. We will consider ensemble streamflow forecasting methods to produce probabilistic depictions of risk. Participants will run a suite of predictability experiments to understand how forecast skill in different basins is shaped by both basin initial conditions and meteorological forecasts, taking advantage of uncertainty quantification methods and data assimilation methods to improve the statistical reliability of probabilistic streamflow predictions.

  10. Model philosophy: Understanding the relative merits of models of different type and complexity.
    In this final theme we will consider alternative typologies of hydrological models and explore the relative merits of models with varying levels of spatial complexity and process complexity. We will discuss some of the great historical debates on the “correct” approach to process-based hydrological modelling. We will explore how the hydrological sciences community is evolving to more unified hydrological modelling paradigms. Participants will discuss what they have learned in this course and how they will use the course material in their own work.


  1. Clark, M. P., Y. Fan, D. M. Lawrence, J. C. Adam, D. Bolster, D. J. Gochis, . . . X. Zeng, 2015a: Improving the representation of hydrologic processes in Earth System Models. Water Resources Research, 51, 5929-5956, doi: 10.1002/2015WR017096.

  2. Clark, M. P., B. Nijssen, J. D. Lundquist, D. Kavetski, D. E. Rupp, R. A. Woods, . . . R. M. Rasmussen, 2015b: A unified approach for process-based hydrologic modeling: 1. Modeling concept. Water Resources Research, 51, 2498-2514, doi: 10.1002/2015WR017198.

  3. Clark, M. P., B. Nijssen, J. D. Lundquist, D. Kavetski, D. E. Rupp, R. A. Woods, . . . D. G. Marks, 2015c: A unified approach for process-based hydrologic modeling: 2. Model implementation and case studies. Water Resources Research, 51, 2515-2542, doi: 10.1002/2015WR017200.

  4. Clark, M. P., B. Schaefli, S. J. Schymanski, L. Samaniego, C. H. Luce, B. M. Jackson, . . . S. Ceola, 2016: Improving the theoretical underpinnings of process-based hydrologic models. Water Resources Research, 52, 2350-2365, doi: 10.1002/2015WR017910

  5. Clark, M. P., M. F. P. Bierkens, L. Samaniego, R. A. Woods, R. Uijlenhoet, K. E. Bennett, . . . C. D. Peters-Lidard, 2017: The evolution of process-based hydrologic models: historical challenges and the collective quest for physical realism. Hydrology and Earth System Sciences, 21, 3427-3440, doi: 10.5194/hess-21-3427-2017

Textbooks are available from the University of Saskatchewan Bookstore

Other Required Materials
Students will require a computer (running Windows, Mac, linux). It will be advantageous for students to pre-install data analysis programs such as R, Python and matLab.

Electronic Resources
Students should arrange access to supercomputing facilities (e.g., computeCanada) before the start of the course.

Supplementary Resources
The course will use some existing hydrological models; students’ use of particular models will depend on their expertise and interests. These models will be provided to students during the course.


All students are required to enroll in Geography 898 at the University of Saskatchewan in either an audit or credit capacity. Options are available to switch between these for some time after the course.
Please note that both logistics fees and tuition fees are payable by all course participants, whether they are students or professionals, and attending for audit or credit. Registration is a two stage process.

Please note that both logistics fees and tuition fees are payable by all course participants, whether they are students or professionals, and attending for audit or credit.

The logistics fees, which cover the use of the facilities, meals and accommodation, are payable to the CSHS: tuition fees are payable to the U of S. Both vary with your status (e.g., student or professional), and are detailed below.

There are thus two stages involved in registering for the course, as follows:

Stage 1: Logistics Fees.

The mandatory logistics fees, which cover the use of facilities, meals and accommodation, as well as transportation to the Barrier Lake Field Station from the Calgary airport (if required) are $1500 per student and are non-negotiable.

Registration is not yet open - please check back here to pay your logistics fees.

Registrants who cancel will be refunded 85% of these logistics fees, but only if their cancellation is received in writing by the organizers at least one month prior to the start of the class.


Stage 2: Registration With the USask, and Payment of Tuition Fees.

All participants must apply for registration as a graduate student with the University of Saskatchewan, and must therefore satisfy the university's admission requirements, which are detailed here.

When registering, please use the following details:

Fees are payable by all participants, but vary with your status (student or professional, whether you are attending for audit or credit, and - if you are a student - the institution at which you are studying).

To see details of the appropriate process for registration and fee-payment,

  • If you are currently a student, and your institution is shown in the drop-down list below, selecting it will display the relevant information
  • If you are not a student, or your institution is not listed, please choose the Professional or Institution Not Listed option:


If you would like to request transfer of credit to your home institution, please order your transcript for the course directly through your PAWS account or this link.

Withdrawal from Course, or Switching from Credit to Audit
If after taking the course you decide to withdraw or switch from credit to audit, please contact U of S Student Central (e-mail, or phone 1-877-650-1212) for details. If you do so by 10th February 2020, you will receive a 50% reduction in the tuition fee. It is still possible to switch from credit to audit until 26th March 2020, but there will be no reduction in the tuition fee.

For further information..

  • For questions about course content - Prof. Martyn Clark (e-mail)

  • For queries related to registration - Jolana Piercy (e-mail

  • For information related to switching from credit to audit - U of S Student Central (e-mail, or phone 1-877-650-1212) If you would like to request transfer of credit to your home institution, please order your transcript for the course directly through your PAWS account or this link.

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