# Tutorials

In addition to Python notebooks, GMDSI has developed a number of tutorials that demonstrate the use of utility support software that is supplied with the PEST suite. Some of these tutorials focus on issues such as model parameterization, objective function definition, and general PEST/PEST++ setup. 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.

Tutorials are listed below. Click on a tutorial to find out more about it, and to download tutorial files and documentation.

Some of the tutorials that are listed on this page can also be downloaded from a GMDSI tutorial GitHub repository.

## 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 uncertainty can be reduced through assimilating information from site characterisation on the one hand, and measurements of system behaviour on the other hand. But this

### 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 importantly, so-called “hyperparameters” are also ascribed to these points; these are used to characterise the nature of hydraulic property heterogeneity as it is likely to

## History-Matching

### 3D Ensemble Space Inversion and Nonstationary Geostats

This comprehensive tutorial demonstrates fast, efficient calibration of a complex 3D model. It complements a previous tutorial on a similar subject. However it shows how calibration results can be better, and can be achieved more easily, with recent software advances. Pilot points are used in an innovative way. They support

### 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 statistical model that can be used in place of the numerical model. This tutorial explores how new ideas from the petroleum industry can be explored

### 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 ENSI calibration. This provides estimates of parameter and predictive uncertainty at minimal numerical cost. This tutorial is a continuation of another GMDSI tutorial. These tutorials

### 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 of random parameter realisations as well as individual parameters. Realisations can be different for different parameter types. Regularisation seeks a minimum error variance solution within

### 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 (or necessarily the best) workflows; their purpose is to take the reader through the fundamentals of how to accomplish common tasks whilst also providing insights

## 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 of posterior parameter and predictive probability distributions. It has other uses as well. It can be used to demonstrate how the history-matching process bestows worth

### 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 suite. Data worth analysis is applied to a model which was calibrated in another GMDSI tutorial; this model was subjected to a suite of common

### 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. Given that such relationships are rarely linear, this is an important consideration. Nevertheless, non-linear methods are not free of assumptions, can sometimes incur a higher

### 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 linearised posterior covariance matrix Iterative ensemble smoother Data space inversion In doing this tutorial, you get to use the following programs: PEST PEST_HP PESTPP-IES DSI1

### 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 fields. The model run burden is extremely low, and unrelated to the complexity of the complex model’s construction or parameterisation. There is considerable overlap between

### 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 data space inversion (DSI).There is some overlap with a previous tutorial. However, there are also some important differences. Use of the PLPROC, TPL2PST and PESTPREP2

## 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 assist in automatic creation of PEST input datasets involving complex, multi-component objective functions. Starting from a set of field measurement data and model output files,

## 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. This tutorial offers a quick overview of PLPROC in pilot points parameterization of a MODFLOW-USG model. Other utility programs from the PEST suite are also

### 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 PEST in facilitating model-based decision-support which enshrines the principle that a model should encapsulate what we know and quantify what we do not. This tutorial

### 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, faults, or fracture networks. The hydraulic properties of these features may vary along their lengths. If this variability is relevant for a prediction of interest,

### 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. A covariance matrix of model parameters describes the variance of each parameter and the covariance of that parameter with that of every other parameter. For cases

### 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 into a model. These features can be assigned to one or many model layers. Hydraulic properties can vary along and within them. If appropriate, the

## 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 pages. LUMPREM is a simple, lumped-parameter recharge model. It generates time series of groundwater recharge using daily rainfall and potential evaporation as inputs. It can

## 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 by visualisation packages such as PARAVIEW, GIS packages such as QGIS, and display packages such as SURFER. Utilities supplied with the PEST suite can perform