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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

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 (

Creating A Consistent Historical NASA POWER Solar Radiation Dataset to Support Renewable Energy, Building Energy Efficiency and Agro-Climatology Decisions

Prediction of Worldwide Energy Resources (POWER) project provides irradiance dataset to support renewable energy, building energy efficiency and agricultural needs. These datasets are derived from Global Energy and Water Cycle Experiment Surface Radiation Budget (GEWEX SRB) and Clouds and the Earth’s Radiant Energy System (CERES SYN1Deg). A systematic bias has been reported between these two datasets for the years with overlapping observations. For obtaining a consistent climate data record spanning the entire time record of observations, it is crucial to understand and remove the bias in the irradiance dataset. Inconsistency in solar radiation data can lead to inaccurate conclusions about solar energy potential and obscure real trends in solar radiation patterns that would impact energy availability assessments. In this study, we adapt quantile mapping approach to remove the systematic bias and to improve reliability of shortwave and longwave irradiance data. We present a validation of the bias corrected data against ground truth. For each 1° latitude and 1° longitude grid box across the globe, we match the CDFs of the reference dataset (CERES SYN1Deg) to that of the SRB dataset, thereby, adjusting the irradiance values to match the empirical distribution of two different measurements. The performance of quantile mapping is evaluated by using the metrics such as Mean Absolute Deviation (MAD). The results indicate that the quantile mapping significantly improves the accuracy and reliability of solar irradiance dataset especially for the weather conditions associated with high cloud cover and extreme irradiance values. The initial range of MAD for the studied sites for daily data was 4 to 19 Wm-2. After correction these reduced to 3 to 7 Wm-2. The findings from this study have important implications for solar energy system design, agricultural planning, and climate modeling community. Reducing the inconsistency and biases in solar irradiance dataset can enable better planning and operation of solar energy systems, leading to increased efficiency and cost-effectiveness. Additionally, this work also contributes to the statistical post-processing techniques in the renewable energy domain and highlights the potential of historical and near-real-time NASA POWER dataset as a valuable resource for solar energy research and applications.

POWER