Please note: Registration in this course is now closed for the 2020-2021 academic year.  Check back here for information about future offerings.

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.

Please note that the University of Saskatchewan is an English-speaking institution and it is expected that students registering in this course are proficient in written and spoken English.

Course Format

The course will be held online via 12 3-hour virtual learning modules and exercises. Participants will advance their understanding of how to best represent dominant processes in time stepping simulation models.

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. There will also be a midterm exam, written project and a final video conference presentation.

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.

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

Dr. Clark will be available via email for the duration of the course; individual instructors will be available for portions of the course corresponding to the timing of their virtual module. Dr. Clark will be also available via Skype or zoom throughout the fall term.

Course Topics

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.

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.

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. Participants will run models using alternative algorithms of dominant process and gain understanding of the differences among competing modeling approaches.

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.

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.

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.

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.

In this theme we will confront the model with data. We will consider global parameter screening and 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.

In this theme we evaluate the fidelity of the model simulations. This theme includes (a) synthetic test cases to ensure that the equations are implemented correctly, (b) process-based model evaluation, using multivariate data on spatial scales from hillslopes to continents, and (c) model benchmarking, to compare model simulations to a-priori expectations of model performance and to estimates of system-scale predictability. Participants will run a suite of exercises to gain experience with model evaluation.

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.

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.

Required Resources


  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. Video conference software such as Webex or Zoom will also be necessessary and may be available from the University of Saskatchewan once students are admitted.

Electronic Resources

Course administrators will facilitate 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 825 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.

Registration with the University of Saskatchewan, and Payment of Tuition Fees

All participants must apply for admission as a graduate student with the University of Saskatchewan.

Current Graduate Students in Canada

    • Students request permission to register in the course by emailing Dr. Martyn Clark ( and outlining how they meet the course prerequisites listed in the course synopsis
    • Students submit either a Canadian Universities Graduate Transfer Agreement (CUGTA) form or a Western Dean's Agreement (WDA) form, depending on the home institution.
Please note that each University has their own version of the CUGTA form, so students using this form should obtain it from their home institution.
  • Students will have their home institution sign the form and send it to The Department of Geography and Planning at the University of Saskatchewan ( They will be automatically registered in the course, but must pay student fees and tuition directly to the University of Saskatchewan.

Students outside of Canada or Professionals

  • Request permission to register in the course by emailing Dr. Martyn Clark ( and outlining how they meet the course prerequisites listed in the course synopsis
  • Apply for admission here (application type- non-degree).
    Note: Students and professionals DO NOT have to pay application fees, submit transcripts, or submit proof of English equivalency and should ignore these requests if prompted automatically by the form.
  • Students and professionals MUST submit a letter of support from their home institution or employer on official letterhead, listing the course, the term it will be taken, and the dates that the course will be held.  This letter should be submitted to 
  • Once an application has been processed, students will get access to a University of Saskatchewan PAWs account.  Students should monitor their admissions status on their PAWs account and, once they have been admitted, notify the Department of Geography and Planning ( that they have been admitted and provide their student number so that a registration permission can be entered.
  • After getting email confirmation from the department, students taking the course for credit can register themselves and pay their tuition on PAWs.  Students wishing to audit the course can contact Student Central at using their PAWs email account and request to be registered as an audit student in the course.  Tuition will still be paid on PAWs.  


Tuition and fees are payable by all participants, but vary depending on your citizenship and whether you are taking the course for credit or as an audit student.

Tuition and Fees for Canadian Students
Credit- $737.70 CAD   
Audit- $393.45 CAD

Tuition and Fees for non-Canadian Students
Credit- $1137.03 CAD   
Audit- $593.12 CAD

Further Information

  • For questions about course content - Prof. Martyn Clark (
  • For queries related to registration - Jolana Piercy (
  • For information related to switching from credit to audit - U of S Student Central (, 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.

This course has received the generous developmental support of the Pacific Institute for the Mathematical Sciences (click below to view the PIMS website):