Estimation of temperature and precipitation uncertainties using quantile neural networks

TL;DR

This paper introduces a novel quantile neural network framework, RBLQNN, for accurately estimating uncertainties in climate variables like temperature and precipitation, outperforming existing methods on synthetic and real datasets.

Contribution

The paper presents RBLQNN, a new loss function modification for neural networks that improves uncertainty estimation in geophysical data, especially for nonlinear and non-Gaussian distributions.

Findings

RBLQNN accurately predicts conditional distributions on synthetic data.

It outperforms linear quantile regression and MVE neural networks on precipitation data.

Temperature distributions are well modeled by Gaussian assumptions, with nonlinear dependencies identified.

Abstract

Extreme events pose significant risks and are challenging to predict. Assessing climate hazards requires placing quantitative constraints on geophysical fields under observable but fluctuating conditions. We propose a framework for estimating uncertainties -- a ReLU-bias loss quantile neural network (RBLQNN) -- with two novel modifications to the loss function to enforce uniform quantile accuracy and reduce degenerate predicted probability distributions. We evaluate the RBLQNN against other probabilistic baselines on a suite of datasets: synthetic datasets, observed daily temperature maxima from 1,501 NOAA Global Surface Summary of the Day (GSOD) weather stations, and altimetry-observed precipitation from the Tropical Rainfall Measuring Mission (TRMM). On synthetic datasets, the RBLQNN accurately predicts conditional distributions where more restrictive methods like linear quantile regression (LQR) or mean-variance estimation (MVE) neural networks fail, mitigates shortcomings of some other quantile neural networks, and converges stably under a range of hyperparameters. When applied to daily temperature maxima, the RBLQNN reveals that temperature distributions are relatively well described by Gaussian statistics, though nonlinear dependencies on local sea level pressure and geopotential heights appear important. For precipitation statistics, the RBLQNN strongly outperforms both LQR and MVE baselines, demonstrating its capacity to capture highly nonlinear and non-Gaussian conditional distributions. The RBLQNN's performance across varied datasets demonstrates it is a flexible and general approach for constraining uncertainties in geophysical quantities with nonlinear or non-Gaussian conditional dependencies.