About this module
Every water-resources decision rests on incomplete, noisy measurements — a well hydrograph, a rain-gauge record, a single satellite scene are each a partial, uncertain window onto a continuous process, not the process itself. This module builds the statistical reasoning that the rest of the course leans on: how to describe a hydrological record honestly, which probability distribution actually fits the physics of a variable, how to test whether a trend is real, and how similarity decays across space and time in a well network or a satellite pixel stack.
How AI tools fit into how you learn here
Statistics is where sloppy prompting shows up fastest — an LLM will happily fit a normal distribution to a variable that can never be negative if you don't push back. This module is where we deliberately practise that: asking a tutor model to justify a distribution choice or a trend test, then checking its reasoning against the underlying theory rather than accepting the first plausible-sounding answer. It's a habit worth building here, before Week 4's models make the stakes of a wrong assumption higher.
Topics covered
- ✓ What data really is: population vs. sample, deterministic vs. stochastic processes
- ✓ Where uncertainty comes from: measurement error, sampling error, natural variability, structural uncertainty
- ✓ Descriptive statistics for a hydrological record: mean, median, variance, coefficient of variation
- ✓ Choosing a distribution that fits the physics — normal, log-normal, Gumbel/GEV
- ✓ From estimate to evidence: confidence intervals, hypothesis testing, the Mann–Kendall trend test
- ✓ Spatial variability and geostatistics: autocorrelation, semivariograms, kriging
- ✓ Temporal variability: trend, seasonality, autocorrelation, stationarity
- ✓ Bringing space and time together — the space-time cube behind a satellite image stack
Preparation notebooks
- Platform & environment check — Colab, shared drive, library imports
- Descriptive statistics on a real well hydrograph
- Fitting and comparing distributions — normal vs. log-normal on hydraulic conductivity
- Trend testing with Mann–Kendall across a well network
- Semivariogram basics across a well network
Optional: MATLAB Self-Paced Track
Provided by our technology partner MathWorks as a free, self-paced complement to this week's session. Budget around 20–30% more time than the stated duration.
Explore Convolutional Neural Networks — this week's course ~1 hMATLAB Online access and GPU credits are provided free to registered participants during the course period (August 2026).
Where to find the rest of the material
The five preparation notebooks referenced above are distributed through the course platform ahead of the live session. If you can't find them, reach the course team via the enquiries section on the main course page.