Research Projects
Estimating temperature and precipitation uncertainties with quantile neural networks | Article • Code
Due to the risks that climate variability and extremes pose, quantifying risks and uncertainties under given conditions is a general goal of many climate science problems. One approach to quantifying uncertainties in regression tasks which has gained traction in recent years is to train neural networks on the Gaussian maximum likelihood to predict the mean and standard deviation of a normal distribution. These mean-variance estimation networks have been used to add uncertainty in stochastic parametrizations, to identify sources of predictability, and to estimate the time remaining until critical global warming thresholds are reached. However, this approach assumes that uncertainties can be represented through normal distributions, which may not hold for highly non-Gaussian quantities such as precipitation or daily temperature maxima. On the other hand, linear quantile regression allows for the prediction of any non-Gaussian distribution, but it assumes linear functional dependencies.
In this study, we propose a quantile regression neural network for quantifying uncertainties. Our proposed quantile regression neural network includes two straightforward modifications to the loss function to (1) enforce equal accuracy for different quantiles of the distribution and to (2) minimize the occurence of degenerate predicted probability distributions. We evaluate this approach for estimating uncertainties on a suite of synthetic and observational datasets, comparing the predicted distributions against those made by linear quantile regression and mean-variance estimation networks to assess the relative importance of the linearity and Gaussianity assumptions. On synthetic datasets, we demonstrate that our quantile regression neural network better represents uncertainties than linear quantile regression or mean-variance estimation networks, contains advantages over other quantile neural network techniques, and exhibits robust convergence properties. Using NOAA Global Summary of the Day (GSOD) station observations, we find that daily temperature maxima are relatively well-described using Gaussian statistics, though conditional dependencies on pressure observations are significantly nonlinear.
In this study, we propose a quantile regression neural network for quantifying uncertainties. Our proposed quantile regression neural network includes two straightforward modifications to the loss function to (1) enforce equal accuracy for different quantiles of the distribution and to (2) minimize the occurence of degenerate predicted probability distributions. We evaluate this approach for estimating uncertainties on a suite of synthetic and observational datasets, comparing the predicted distributions against those made by linear quantile regression and mean-variance estimation networks to assess the relative importance of the linearity and Gaussianity assumptions. On synthetic datasets, we demonstrate that our quantile regression neural network better represents uncertainties than linear quantile regression or mean-variance estimation networks, contains advantages over other quantile neural network techniques, and exhibits robust convergence properties. Using NOAA Global Summary of the Day (GSOD) station observations, we find that daily temperature maxima are relatively well-described using Gaussian statistics, though conditional dependencies on pressure observations are significantly nonlinear.
Learning Propagators for Sea Surface Height Forecasts Using Koopman Autoencoders | Publication • Code
Sea surface height forecasts are impacted by many different sources of uncertainty due to the highly nonlinear and chaotic dynamics of the climate system. In light of these uncertainties, many different approches are commonly taken to developing forecasts, such as by using computationally intensive numerical models which directly simulate physics or through data-driven approaches trained on observational products to model dynamics.
Over the past few decades, Linear Inverse Modeling (LIM) has become an eminent statistical-dynamical technique for building forecasts directly from data in the climate sciences, at times producing forecasts that can outperform numerical simulations. Implementing LIM generally involves applying a linear dimensionality reduction to spatiotemporal datasets (for example, using principal component analysis) and then inferring the best-fit propagator in the latent space from the time-lagged covariance statistics of the latent state variables. However, it assumes that the modeled system is described by linear dynamics, an assumption which may not hold for the chaotic and complex climate system, posing challenges for LIM.
Recent data-driven approaches based on the operator-theoretic perspective of nonlinear dynamics have offered an alternative approach to modeling dynamics. In particular, in Koopman operator theory, nonlinear dynamical systems can be represented through the linear (but infinite-dimensional) Koopman operator which advances measurements of a dynamical system forward in time. In this study, we showed it was possible to develop a better low-dimensional propagator for regional sea surface height forecasts using a convolutional neural network autoencoder architecture inspired by Koopman operator theory, originally proposed by Lusch et al (2018). By learning the dimensionality reduction and dynamics simultaneously, the Koopman autoencoder produces better forecasts than when learning the dimensionality reduction and propagator separately.
Over the past few decades, Linear Inverse Modeling (LIM) has become an eminent statistical-dynamical technique for building forecasts directly from data in the climate sciences, at times producing forecasts that can outperform numerical simulations. Implementing LIM generally involves applying a linear dimensionality reduction to spatiotemporal datasets (for example, using principal component analysis) and then inferring the best-fit propagator in the latent space from the time-lagged covariance statistics of the latent state variables. However, it assumes that the modeled system is described by linear dynamics, an assumption which may not hold for the chaotic and complex climate system, posing challenges for LIM.
Recent data-driven approaches based on the operator-theoretic perspective of nonlinear dynamics have offered an alternative approach to modeling dynamics. In particular, in Koopman operator theory, nonlinear dynamical systems can be represented through the linear (but infinite-dimensional) Koopman operator which advances measurements of a dynamical system forward in time. In this study, we showed it was possible to develop a better low-dimensional propagator for regional sea surface height forecasts using a convolutional neural network autoencoder architecture inspired by Koopman operator theory, originally proposed by Lusch et al (2018). By learning the dimensionality reduction and dynamics simultaneously, the Koopman autoencoder produces better forecasts than when learning the dimensionality reduction and propagator separately.
Identifying sources of sea level predictability using uncertainty permitting machine learning with explainable AI | Publication • Code
Reliable sea level forecasts on daily-to-seasonal timescales (1–180 days) are hindered by numerous sources of uncertainty from both the atmosphere and ocean. This time horizon is notoriously challenging for forecasting, as predictability from the atmosphere is lost but longer-term sources of predictability from the ocean have yet to emerge. Nevertheless, the daily-to-seasonal time horizon is critical for municipalities to mitigate potential damages from high-tide tide flooding.
One approach to improving forecasts on this time horizon is to focus on intial conditions which can extend predictability horizons. Identifying these initial conditions which are inherently more predictable can allow forecasts to be made on time horizons that would not normally be considered. In this study, we leverage mean-variance estimation networks to identify state-dependent sources of predictability for sea level using the Community Earth System Model (CESM2) Large Ensemble dataset (LENS2). Using these uncertainty-quantifying neural networks, we examine how the dominant drivers of predictability change over a range of different forecast leads at a variety of locations. For instance, while local persistence drives dynamic sea level predictability at Guam (14°N, 145°E) on shorter forecast lead times, as the forecast lead is extended to seasonal timescales, propagating Rossby waves emerge as a dominant source of predictability. This study shows how uncertainty-quantifying machine learning can be used to help identify sources of predictability on a range of forecasting leads and could help improve forecasts crucial to administrators.
One approach to improving forecasts on this time horizon is to focus on intial conditions which can extend predictability horizons. Identifying these initial conditions which are inherently more predictable can allow forecasts to be made on time horizons that would not normally be considered. In this study, we leverage mean-variance estimation networks to identify state-dependent sources of predictability for sea level using the Community Earth System Model (CESM2) Large Ensemble dataset (LENS2). Using these uncertainty-quantifying neural networks, we examine how the dominant drivers of predictability change over a range of different forecast leads at a variety of locations. For instance, while local persistence drives dynamic sea level predictability at Guam (14°N, 145°E) on shorter forecast lead times, as the forecast lead is extended to seasonal timescales, propagating Rossby waves emerge as a dominant source of predictability. This study shows how uncertainty-quantifying machine learning can be used to help identify sources of predictability on a range of forecasting leads and could help improve forecasts crucial to administrators.
Exploring the nonstationarity of sea level probability distributions | Publication
Changes in the shape of the probability distribution of geophysical variables can significantly impact the occurrence of extremes. Therefore, understanding and quantifying these changes is paramount to understanding changing risks under rising seas. In this study, we propose a theoretical framework for quantifying changes in probability distributions, modifying an approach by McKinnon and Rhines (2016) to improve interpretability.
