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DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗

DOE OSTI2025

Bias correcting regional scale Earth system model projections: novel approach using empirical mode decomposition

Bias correction is a crucial step in using Earth system model outputs for assessments, as it adjusts systematic errors by comparing the model to observations. However, standard methods – ranging from mean-based linear scaling to distribution-based quantile mapping typically treat bias correction as a single-scale process, overlooking the fact that biases can manifest differently across daily, seasonal, and annual timescales. In this study, we propose a novel, timescale-aware bias-correction approach built on Empirical Mode Decomposition. By decomposing the meteorological signal into multiple oscillatory components and aggregating them to represent distinct timescales, we apply targeted corrections to each component, thereby preserving both short- and long-term structure in the data. Experimental illustrations show that the timescale-aware EMDBC framework matches the performance of conventional quantile-delta mapping (QDM) at the native daily scale and achieves progressively larger bias reductions at bi-weekly, seasonal, and annual scales. As a result, the proposed approach offers a more robust path to accurate and reliable Earth system projections, strengthening their utility for resilience and adaptation planning.

Ganguli, Arkaprabha [Argonne National Laboratory (↗

DOE OSTI2019

Spatial Predictions and Associated Uncertainty of Annual Soil Respiration at the Global Scale

Abstract Soil respiration (Rs), the soil‐to‐atmosphere CO 2 flux produced by microbes and plant roots, is a critical but uncertain component of the global carbon cycle. Our current understanding of the variability and dynamics is limited by the coarse spatial resolution of existing estimates. We predicted annual Rs and associated uncertainty across the world at 1‐km resolution using a quantile regression forest algorithm trained with observations from the global Soil Respiration Database spanning from 1961 to 2011. This model yielded a global annual Rs estimate of 87.9 Pg C/year with an associated global uncertainty of 18.6 (mean absolute error) and 40.4 (root mean square error) Pg C/year. The estimated annual heterotrophic respiration (Rh), derived from empirical relationships with Rs, was 49.7 Pg C/year over the same period. Predicted Rs rates and associated uncertainty varied widely across vegetation types, with the greatest predicted rates of Rs in evergreen broadleaf forests (accounting for 20.9% of global Rs). The greatest prediction uncertainties were in northern latitudes and arid to semiarid ecosystems, suggesting that these areas should be targeted in future measurement campaigns. This study provides predictions of Rs (and associated prediction uncertainty) at unprecedentedly high spatial resolution across the globe that could help constrain local‐to‐global process‐based models. Furthermore, it provides insights into the large variability of Rs and Rh across vegetation classes and identifies regions and vegetation types with poor model performance that should be prioritized for future data collection.

Warner, D. L.↗