# Tutorials

In order to assist modellers in setting up and using model-partner software in ways that support the decision-support imperatives of data assimilation and uncertainty quantification, GMDSI is developing a series of tutorials.

GMDSI tutorials are designed to be modular and independent of each other. Each tutorial addresses its own specific modelling topic. Hence there is no need to work through them in a pre-ordained sequence. However, they also complement each other. Many employ variations of the same synthetic model, and are based on the same simulator (MODFLOW 6).

In these tutorials, utility software from the PEST suite is used extensively to assist in model parameterization, objective function definition, and general PEST/PEST++ setup. Some tutorials focus on the use of PEST and PEST++, while others focus on ancillary issues such as introducing transient recharge to a groundwater model, and translation of a model’s grid, parameterization, and calculated states to files that can be read by visualization, GIS and display packages.

All tutorials are hosted in a GitHub repository** here.** Individual tutorials can also be accessed through through the links below.

## Conceptualisation

### From Site Concepts to a 3D Site Model

Building and history-matching a three-dimensional model is a difficult procedure. The third dimension increases parameter requirements, model run times, and model output uncertainty. Ideally, predictive

### Conceptual Model to Numerical Model

This tutorial explores the use of “conceptual points” as a precursor to model parameterisation. Expected hydraulic properties are provided at these conceptual points. Just as

## History-Matching

### Optimization under Uncertainty using DSI

Optimization under uncertainty is notoriously numerically intensive. However its numerical burden can be reduced if data space inversion (DSI) is used to construct a surrogate

### ENSI and Linear Analysis

Ensemble space inversion (ENSI) enables efficient, regularisation-constrained calibration of complex, highly-parameterised models. This tutorial demonstrates how linear analysis can be undertaken in partnership with the

### Ensemble Space Inversion

Ensemble space inversion (ENSI) is implemented through the PEST_HP suite (version 18). Using ENSI you can calibrate a complex model quickly. The calibration subspace is comprised

### Calibration – A Simple Model

This is the first in a series of tutorials which demonstrate workflows for parameter estimation and uncertainty analysis with the PEST/PEST++ suites. These are not the only

## Uncertainty Analysis

### Linear Uncertainty Analysis

Linear uncertainty analysis is also known as “first order second moment” (or “FOSM”) analysis. It provides approximate mathematical characterisation of prior predictive probability distributions, and

### Data Worth Analysis

The present tutorial addresses the ability (or otherwise) of yet-ungathered data to reduce the uncertainties of decision-critical predictions using linear analysis utilities from the PEST

### Non-Linear Uncertainty Analysis

In contrast to linear uncertainty analysis, non-linear methods do not suffer from the limitation of assuming a linear relationship between model predictions and model parameters.

### Four Ways to Explore Model Predictive Uncertainty

This tutorial explains four ways to explore the uncertainties of two predictions made by a relatively simple, fast-running model. These are: Linear analysis Sampling a

### Data Space Inversion

This tutorial introduces data space inversion (DSI). DSI can be used to explore the uncertainties of predictions made by complex models with complicated hydraulic property

### Data Assimilation for a Simple Model

This tutorial explores construction of the interface between PEST/PEST++and a simple MODFLOW/MODPATH model, and how to then subject that model to history-matching and uncertainty analysis–including

## Observations

### OLPROC: Processing Observations Made Easy

OLPROC is a model dancing partner. Its role is to postprocess model outputs in order to match them with field measurements, as well as to

## Parameterisation

### PLPROC: Basics

PLPROC is a member of the PEST suite. Its primary use is for pilot points parameterization of models that use both structured and unstructured grids.

### PLPROC: a simple pilot point example

PLPROC allows a modeller to create and manipulate parameters that inform hydraulic properties that are represented in a numerical model. In doing this, PLPROC supports

### SEGLISTS: Interpolation along linear features

This tutorial demonstrates several options for spatial parameterization of linear and polylinear features. In a groundwater model, these may represent entities such as streams, rivers,

### Covariance Matrices: The PPCOV Suite

A variance-covariance matrix, often referred to as a covariance matrix, is a square matrix that provides covariances between pairs of elements of a random vector.

### Structural Overlay Parameters and PLPROC

Using the PLPROC parameter preprocessor supplied with the PEST suite, moveable polylinear and polygonal structural features such as faults and aquitard windows can be inserted

## LUMPREM

### LUMPREM: a Transient Recharge Model

Though it has nothing to do with parameter estimation, LUMPREM is a member of the PEST suite; it can be downloaded from the PEST web

## Other Tools & Utilities

### Model Visualisation and Display

This tutorial shows you how to extract data from MODFLOW 6 input and/or output files, and record that data in files that are easily read