Module 2 motivation: downscaling





  1. Downscaling

  2. Downscaling: theory

  3. Project 1

We would like to accurately model precipitation at high spatial and temporal resolution

  • Stormwater management (long-term desigm)
  • Water resources management (subseasonal to multi-year planning)
  • Fire propagation (hourly to weekly)


  1. enhanced spatial detail
  2. mitigation of systematic ESM1 biases
  3. generation of variables not explicitly rendered by GCMs

(Lanzante et al., 2018)

Earth System Models



Challenges, summarized

  1. ESMs are tuned to get energy balance and large-scale circulation right, not local extremes
  2. ESMs average over space and time
  3. Local-scale precipitation can be tricky to model well

Downscaling: theory


  1. Downscaling

  2. Downscaling: theory

  3. Project 1

Supervised downscaling

  • Input: pairs \((X_i, y_i)\)
    • \(X_i\): predictors (e.g., gridded rainfall)
    • \(y_i\): predictand (e.g., gauge rainfall)
  • Goal: learn a function \(f\) such that \(f(X_i) \approx y_i\)
    • Measure quality of approximation through a loss function (more later)
  • Key point: the \(X_i\) and \(y_i\) are observed at the same time
    • Example: map satellite to radar data

Distributional downscaling

  • ESMs simulate from the distribution of weather, given climate boundary conditions. For example:
    • Run 100 ESM ensemble members over 20th century conditions
    • Study December 1, 1980 in all draws
    • Some will be rainy, some will be dry; some cool, some warm
    • Statistically meaningful, but not a forecast!
  • No pairs \((X_i, y_i)\). Instead we have samples \(\left\{X_1, \ldots, X_N \right\}\) and \(\left\{y_1, \ldots, y_K \right\}\)

Common datasets

  • Gauge data
  • Gridded observational products
    • For example: radar measurments are processed to produce gridded rainfall estimates
  • Reanalysis products
    • Use assimilation to “digest” observations using a model
    • Gridded reconstructions of past weather
    • State of the art is ERA5
  • ESM outputs
    • Historical runs
    • CMIP: compare multiple models on standardized scenarios (e.g., RCP 2.6, 4.5, 8.5)
    • Simulate from weather, conditional on boundary conditions

Bias correction

Simplest form of downscaling. Usually \(X\) are samples from a climate model and \(y\) are observations. \[ \begin{aligned} \text{bias} &= \mathbb{E}[X] - \mathbb{E}[y] \\ \hat{y} &= X - \text{bias} \end{aligned} \]


Is this a distributional or supervised method?

Quantile-quantile mapping



Stationarity means the relationship between \(X\) and \(y\) does not change over time

  • Supervised: \(p(y | X)\) or \(y = f(X)\) does not change over time
  • Distributional: Corrections to the distribution do not change over time

This is never a perfect assumption

Project 1


  1. Downscaling

  2. Downscaling: theory

  3. Project 1

Your task

  • Given:
    1. Hourly gridded rainfall data (small area)
    2. Hourly large-scale pressure and temperature fields
    3. Hourly gauge rainfall data at a single station
  • Develop a model to predict hourly gauge rainfall from the available datasets


  • Try and compare at least two different approaaches
  • Quantitative and qualitative evaluation of the models
  • You can use any methods you like:
    • Those we cover in class
    • Those you already know## References
Lanzante, J. R., Dixon, K. W., Nath, M. J., Whitlock, C. E., & Adams-Smith, D. (2018). Some Pitfalls in Statistical Downscaling of Future Climate. Bulletin of the American Meteorological Society, 99(4), 791–803.
Price, I., & Rasp, S. (2022, March 23). Increasing the accuracy and resolution of precipitation forecasts using deep generative models.