Quantile Regression

BACKGROUND

Figure 1: Quantile regression applied to dewpoint temperature at one station at the Army Test and Evaluation Command at the Dugway Testing Range in Utah, providing a probabilistic range that the dew point may fall within at a lead-time of 42-hr.
Figure 1: Quantile regression applied to dewpoint temperature at one station at the Army Test and Evaluation Command at the Dugway Testing Range in Utah, providing a probabilistic range that the dew point may fall within at a lead-time of 42-hr.

Post-processing ensemble forecasts is generally a necessary requirement to provide meaningful probabilistic guidance to users.  One approach that has been used for a variety of applications is quantile regression (QR). RAL scientists are applying a novel statistical correction approach by combining QR with other post-processing approaches (e.g. analog, logistic regression) to calibrate at the specific probability intervals required by the user. Some of the benefits of this approach are that no assumptions are required on the form of the forecast probability distribution function to attain optimality; the resultant forecast skill is no worse than a forecast of either climatology or persistence; and the generated ensembles have dispersive properties directly related to the uncertainty in the forecast that one would expect.

QR is also a powerful approach for combining different forecast model outputs to generate one coherent and reliable probability distribution function of what the future weather will be. RAL scientists have merged medium-range ensemble rainfall forecasts from five global weather centers (Canada, China, ECMWF, US, Brazil) to calibrate and enhance the accuracy of rainfall forecasts over both East Africa and the Indian subcontinent, gaining 2- to 3-days in additional forecasting skill in the process.

ACCOMPLISHMENTS IN FY2017

  • A combined QR-analog approach was further refined in the application of numerical wind speed prediction in the optimal management of wind turbines and wind power resource within China
  • A combined QR-logistic regression approach has been further refined in the application of post-processing of numerical weather forecasts for the Army Test and Evaluation Command at the Dugway Testing Range in Utah
  • QR was also applied to blend ensemble rainfall forecasts from eight weather forecasting centers for the Indian Bihar State to optimize rainfall prediction ensembles that feed into hydrologic models for the Kosi and Bagmati river basins
  • QR was also applied to generate improved ensemble predictions of river flow and height at hydrologic gauging stations in the Ganges and Brahmaputra river basins within India
  • QR has also been utilized to provide ensemble rainfall and streamflow forecasts at a variety of time scales for Sudan utilizing ensemble rainfall data from a variety of global circulation models and geophysical regressors
Figure 2: Quantile regression applied to Kosi river (India) basin-wide rainfall forecasts during 2015-6, blending forecasts from five global weather centers into one “grand global ensemble” for this particular basin, enhancing forecast skill out 2 to 3 additional days longer.
Figure 2: Quantile regression applied to Kosi river (India) basin-wide rainfall forecasts during 2015-6, blending forecasts from five global weather centers into one “grand global ensemble” for this particular basin, enhancing forecast skill out 2 to 3 additional days longer.

PLANS FOR FY2018

  • Merge QR with geophysical predictors to further optimize rainfall and streamflow prediction at time-scales of 1-15 days, 2-6 weeks, and 1-6 months in advance for the optimal management of flow releases from hydro-electric reservoirs within Ethiopia and the greater East Africa region
  • Expand the prediction of river water level across the Brahmaputra and Ganges catchments utilizing QR with a combination of river width measurements and hydrologic multi-model forecasting.