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DOE OSTI2022

Using probabilistic solar power forecasts to inform flexible ramp product procurement for the California ISO

How can independent system operators (ISOs) take advantage of probabilistic solar forecasts to lower generation costs and improve reliability of power systems? We discuss one three-step approach for doing so, focusing on how such forecasts might help the California Independent System Operator (CAISO) prepare unexpected net load ramps, where net load equals gross demand minus wind and solar production. First, we enhance an existing solar forecasting system to provide well-calibrated hours-ahead probabilistic forecasts. We then relate the degree of uncertainty reflected in the forecasted prediction intervals (independent variables) to error distributions for net load ramp forecasts for the CAISO real-time market (dependent variable) using machine learning and quantile regression. Projected ramp forecast errors conditioned on solar uncertainty are translated into flexible ramp requirements that therefore reflect real-time meteorological and solar conditions, improving on typical ISO procedures. Detailed descriptions are provided on the quantile regression and kth-nearest neighbor categorization methods for accomplishing that translation. Finally, a multiple time-scale look-ahead market simulation model is applied to a 118-bus IEEE Reliability Test System, modified to represent the CAISO generation mix and demand distributions. The model runs quantify how solar-conditioned ramp requirements can, first, decrease operating costs by reducing requirements compared to often conservative unconditional methods and, second, decrease generation scarcity events and consequently improve reliability by increasing flexibility requirements at times when unconditional forecast-based requirements understate actual ramp uncertainty. Solar-conditioned ramp requirements are found to reduce generation operating costs by about 2% for the test system (which would be equivalent to over $\$100$ million per year for a CAISO-size system).

14 SOLAR ENERGY↗

DOE OSTI2018

Nonparametric Prediction Intervals of Wind Power via Linear Programming

This letter proposes a machine learning-based linear programming model that quickly establishes the nonparametric prediction intervals of wind power by integrating extreme learning machine and quantile regression. The proportions of quantiles can be adaptively determined via sensitivity analysis. The proposed method has been proven to be significantly efficient and reliable, with a high application potential in power systems.

extreme learning machine↗

DOE OSTI2025

Joint Modeling of Wind Speed and Wind Direction Through a Conditional Approach

Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. In this work, we develop a conditional approach to model these two variables, where the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. To accommodate the circular nature of wind direction, a von Mises mixture model is used; the conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the dependence of the Weibull parameters on wind direction. A Monte Carlo simulation study indicates that our method outperforms two other approaches in estimation efficiency: one that utilizes periodic spline quantile regression and another that generates data from the commonly used Abe-Ley distribution for cylindrical data. We illustrate our method by using the output from a regional climate model to investigate how the joint distribution of wind speed and direction may change under some future climate scenarios. Our method indicates significant changes in the variation of wind speed with respect to some directions.

17 WIND ENERGY↗

DOE OSTI2018

Coherent Probabilistic Solar Power Forecasting

Solar power has been growing rapidly in recent years. Many countries have invested in solar energy technology, especially in Photovoltaic (PV) power generation. With the increased penetration level, solar power forecasting becomes more challenging. To cope with solar power uncertainties, probabilistic forecasting provides more information than traditional point forecasting. Moreover, multiple PV sites with spatial-temporal correlations need to be taken into account. To produce probabilistic forecasts, this paper applies quantile regression on top of time series models. Considering the coherency among multiple PV sites, a reconciliation is applied using a copula-based bottom-up method or proportion-based top-down method. Numerical results show that the proposed methods efficiently produce accurate and coherent probabilistic solar power forecasts.

quantile regression↗

DOE OSTI2024

A Data-Driven Exploration of the Impact of Renewable Energy on Inter-Area Oscillations in the U.S. Eastern Interconnection

As increasing amounts of renewable energy (RE) resources are incorporated into the bulk-power grid, power system oscillations are expected to change. This work investigates how RE generation impacts the frequency and damping ratio (DR) of two dominant inter-area modes in the U.S. Eastern Interconnection (EI) using regularly updated estimates collected over a 12-month period. Quantile regression is used to derive the correlation between operating conditions and mode properties, and a bootstrap method is used to quantify the uncertainty associated with the correlation estimates. Results show that with an increase in system load, the frequency of a mode decreases and DR increases. Evidence that increasing RE generation results in an increase in frequency and decline in DR was found for one of the two modes studied. This work shows that increasing RE levels will impact the properties of inter-area oscillations in the EI, but it does not indicate the presence of immediate threats to grid stability. The outlined approach can be used to periodically assess changing mode properties as RE levels continue to grow and flag stability concerns before they become serious reliability threats.

Inter-area oscillation, mode meters, quantile regr↗

DOE OSTI2025

Quantifying spatial and vertical variations in soil C:N relationships in permafrost-affected landscapes

Permafrost regions are experiencing rapid changes that affect carbon (C) and nitrogen (N) cycles, with implications for vegetation dynamics and gas exchanges with the atmosphere. Soil C:N ratio is a key indicator of organic matter quality, yet spatial estimates of N stocks and C:N ratios lag behind those for C. We used quantile regression forests to compare direct and indirect digital soil mapping approaches for predicting soil C:N ratios at 0–30, 30–60, and 60–100 cm depths across a latitudinal transect in Alaska. The indirect approach – deriving C:N from separately predicted C and N stocks – outperformed direct mapping for the surface layer (0–30 cm), while direct mapping was marginally better at greater depths. However, prediction accuracy decreased with depth for both methods. Temperature and topography were the most important predictors. Both approaches overestimated low and underestimated high C:N ratios, with direct mapping showing greater bias. Our results underscore the challenges of modeling C:N ratios in heterogeneous, data-sparse permafrost soils, but also suggest that indirect mapping holds promise if supported by more extensive datasets.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

What Shapes Transportation Charging Infrastructure Availability? Evidence from Tennessee

This study examines how community, travel, and freight characteristics relate to public charging infrastructure availability across Tennessee ZIP codes. We link Alternative Fuels Data Center station locations with traffic, socioeconomic, demographic, commuting, and freight employment data to build a ZIP code-level dataset. Ordinary least squares regression captures variation in chargers per 10,000 residents (R2=0.311). Quantile regressions at the 25th, 50th, and 75th percentiles, with pseudo R2 values up to 0.099, show that the determinants of infrastructure availability differ across low-, medium-, and high-availability areas. Percent female, percent car commuters, average household size, and median age are negatively associated with charging availability across much of the distribution. Truck traffic is positively associated only in lower-availability ZIP codes, while vehicle miles traveled shifts from a negative association at the lower end of the distribution to a positive association at the upper end. The results provide insight into how public charging deployment aligns with community characteristics, mobility demand, and freight activity across Tennessee. Future work can distinguish charger types and power levels, incorporate land-use and temporal rollout patterns, and examine how charging infrastructure needs differ across urban and rural contexts.

Calderón, Oriana [University of Tennessee, Knoxvil↗

NASA NTRS2024

Multi-Agency Ensemble Forecast of Wildfire Air Quality in the United States: Toward Community Consensus of Early Warning

Wildfires pose increasing risks to human health and properties in North America. Due to large uncertainties in fire emission, transport, and chemical transformation, it remains challenging to accurately predict air quality during wildfire events, hindering our collective capability to issue effective early warnings to protect public health and welfare. Here we present a new real-time Hazardous Air Quality Ensemble System (HAQES) by leveraging various wildfire smoke forecasts from three U.S. federal agencies (NOAA, NASA, and Navy). Compared to individual models, the HAQES ensemble forecast significantly enhances forecast accuracy. To further enhance forecasting performance, a weighted ensemble forecast approach was introduced and tested. Compared to the unweighted ensemble mean, the multilinear regression weighted ensemble reduced fractional bias by 34% in the major fire regions, false alarm rate by 72%, and increased hit rate by 17%. Finally, we improved the weighted ensemble using quantile regression and weighted regression methods to enhance the forecast of extreme air quality events. The advanced weighted ensemble increased the PM2.5 exceedance hit rate by 55% compared to the ensemble mean. Our findings provide insights into the development of advanced ensemble forecast methods for wildfire air quality, offering a practical way to enhance decision-making support to protect public health.

Yunyao Li↗

DOE OSTI2020

The Evolving Distribution of Relative Humidity Conditional Upon Daily Maximum Temperature in a Warming Climate

Abstract The impacts of heat waves in a warming climate depend not only on changing temperatures but also on changing humidity. Using 35 simulations from the Community Earth System Model Large Ensemble (CESM LENS), we investigate the long‐term evolution of the joint distribution of summer relative humidity (RH) and daily maximum temperature ( Tmax ) near four U.S. cities (New York City, Chicago, Phoenix, and New Orleans) under the high‐emissions Representative Concentration Pathway (RCP) 8.5. We estimate the conditional quantiles of RH given Tmax with quantile regression models, using functions of temperature for each city in July for three time periods (1990–2005, 2026–2035, and 2071–2080). Quality‐of‐fit diagnostics indicate that these models accurately estimate conditional quantiles for each city. As expected, each quantile of Tmax increases from 1990–2005 to 2071–2080, while mean RH decreases modestly. Conditional upon a fixed quantile of Tmax , the median and high quantiles of RH decrease, while those of the Heat Index (HI) and dew point both increase. This result suggests that, despite a modest decrease in median relative humidity, heat stress measured by metrics considering both humidity and temperature in a warming climate will increase faster than that measured by temperatures alone would indicate. For a fixed Tmax , the high quantiles of RH (and thus of HI and dew point) increase from 1990–2005 to 2071–2080 in all four cities. This result suggests that the heat stress of a day at a given Tmax will increase in a warming climate due to the increase of RH.

Yuan, Jiacan↗

NASA NTRS2013

Modeling Longitudinal Data Containing Non-Normal Within Subject Errors

The mission of the National Aeronautics and Space Administration’s (NASA) human research program is to advance safe human spaceflight. This involves conducting experiments, collecting data, and analyzing data. The data are longitudinal and result from a relatively few number of subjects; typically 10 – 20. A longitudinal study refers to an investigation where participant outcomes and possibly treatments are collected at multiple follow-up times. Standard statistical designs such as mean regression with random effects and mixed–effects regression are inadequate for such data because the population is typically not approximately normally distributed. Hence, more advanced data analysis methods are necessary. This research focuses on four such methods for longitudinal data analysis: the recently proposed linear quantile mixed models (lqmm) by Geraci and Bottai (2013), quantile regression, multilevel mixed–effects linear regression, and robust regression. This research also provides computational algorithms for longitudinal data that scientists can directly use for human spaceflight and other longitudinal data applications, then presents statistical evidence that verifies which method is best for specific situations. This advances the study of longitudinal data in a broad range of applications including applications in the sciences, technology, engineering and mathematics fields.

Feiveson, Alan↗

DOE OSTI2025

Uncertainty quantification for neural network potential foundation models

Abstract For neural network potentials (NNPs) to gain widespread use, researchers must be able to trust model outputs. However, the blackbox nature of neural networks and their inherent stochasticity are often deterrents, especially for foundation models trained over broad swaths of chemical space. Uncertainty information provided at the time of prediction can help reduce aversion to NNPs. In this work, we detail two uncertainty quantification (UQ) methods. Readout ensembling, by finetuning the readout layers of an ensemble of foundation models, provides information about model uncertainty, while quantile regression, by replacing point predictions with distributional predictions, provides information about uncertainty within the underlying training data. We demonstrate our approach with the MACE-MP-0 model, applying UQ to the foundation model and a series of finetuned models. The uncertainties produced by the readout ensemble and quantile methods are demonstrated to be distinct measures by which the quality of the NNP output can be judged.

36 MATERIALS SCIENCE↗

DOE OSTI2019

A two-step short-term probabilistic wind forecasting methodology based on predictive distribution optimization

With increasing wind penetrations into electric power systems, probabilistic wind forecasting becomes more critical to power system operations because of its capability of quantifying wind uncertainties. In this paper, a two-step probabilistic wind forecasting approach based on pinball loss optimization is developed. First, a multimodel machine learning-based ensemble deterministic forecasting framework is adopted to generate deterministic forecasts. The deterministic forecast is assumed to be the mean value of the predictive distribution at each forecasting time stamp. Then, the optimal unknown parameter (i.e., standard deviation) of the predictive distribution is estimated by a support vector regression surrogate model based on the deterministic forecasts. Lastly, probabilistic forecasts are generated from the predictive distribution. Numerical results of case studies at eight locations show that the developed two-step probabilistic forecasting methodology has improved the pinball loss metric score by up to 35% compared to a baseline quantile regression forecasting model.

17 WIND ENERGY↗

DOE OSTI2022

Uncertainty quantification for Bayesian active learning in rupture life prediction of ferritic steels

Abstract Three probabilistic methodologies are developed for predicting the long-term creep rupture life of 9–12 wt%Cr ferritic-martensitic steels using their chemical and processing parameters. The framework developed in this research strives to simultaneously make efficient inference along with associated risk, i.e., the uncertainty of estimation. The study highlights the limitations of applying probabilistic machine learning to model creep life and provides suggestions as to how this might be alleviated to make an efficient and accurate model with the evaluation of epistemic uncertainty of each prediction. Based on extensive experimentation, Gaussian Process Regression yielded more accurate inference ( $$Pearson\;correlation\;coefficent> 0.95$$ P e a r s o n c o r r e l a t i o n c o e f f i c e n t > 0.95 for the holdout test set) in addition to meaningful uncertainty estimate (i.e., coverage ranges from 94 to 98% for the test set) as compared to quantile regression and natural gradient boosting algorithm. Furthermore, the possibility of an active learning framework to iteratively explore the material space intelligently was demonstrated by simulating the experimental data collection process. This framework can be subsequently deployed to improve model performance or to explore new alloy domains with minimal experimental effort.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2026

Beyond Point Estimates: Benchmarking Uncertainty Quantification Methods on the AION-1 Astronomical Foundation Model

Foundation models for astronomical surveys offer powerful learned representations that can be transferred to downstream regression tasks such as galaxy property estimation. However, point predictions alone are insufficient for scientific inference; reliable uncertainty quantification (UQ) is essential. We compare seven UQ methods on galaxy property regression using frozen AION-1 foundation-model embeddings, predicting redshift, stellar mass, stellar-population age, gas-phase metallicity, and specific star-formation rate, from Legacy Survey photometry/imaging and DESI spectra, with PROVABGS-derived labels. Distribution-free conformal methods achieve marginal coverage within $\sim$1 pp of the nominal 90% across all properties, while non-conformal baselines (Deep Ensembles, MC~Dropout) fail to calibrate reliably. Among conformal approaches, Conformalized Quantile Regression (CQR) delivers the best coverage in the bin with the poorest model predictions. More importantly, only the Locally Valid and Discriminative (LVD) framework -- particularly when operating on AION-1 embeddings -- also provides finite-sample \emph{local validity}, producing intervals that adapt to each galaxy's local prediction difficulty rather than relying on marginal guarantees alone. These results establish conformal prediction, and LVD in particular, as the preferred UQ framework for uncertainty-aware inference on foundation-model embeddings in astrophysics.

Tame-Narvaez, Karla [Fermilab] (ORCID:000000022249↗

DOE OSTI2016

Trends and sensitivities of low streamflow extremes to discharge timing and magnitude in Pacific Northwest mountain streams

Abstract Path analyses of historical streamflow data from the Pacific Northwest indicate that the precipitation amount has been the dominant control on the magnitude of low streamflow extremes compared to the air temperature‐affected timing of snowmelt runoff. The relative sensitivities of low streamflow to precipitation and temperature changes have important implications for adaptation planning because global circulation models produce relatively robust estimates of air temperature changes but have large uncertainties in projected precipitation amounts in the Pacific Northwest U.S. Quantile regression analyses indicate that low streamflow extremes from the majority of catchments in this study have declined from 1948 to 2013, which may significantly affect terrestrial and aquatic ecosystems, and water resource management. Trends in the 25th percentile of mean annual streamflow have declined and the center of timing has occurred earlier. We quantify the relative influences of total precipitation and air temperature on the annual low streamflow extremes from 42 stream gauges using mean annual streamflow as a proxy for precipitation amount effects and streamflow center of timing as a proxy for temperature effects on low flow metrics, including 7q10 summer (the minimum 7 day flow during summer with a 10 year return period), mean August , mean September , mean summer , 7q10 winter , and mean winter flow metrics. These methods have the benefit of using only readily available streamflow data, which makes our results robust against systematic errors in high elevation distributed precipitation data. Winter low flow metrics are weakly tied to both mean annual streamflow and center of timing .

Kormos, Patrick R.↗

DOE OSTI2018

A temperature threshold to identify the driving climate forces of the respiratory process in terrestrial ecosystems

Terrestrial ecosystem respiration (R e ) is the second largest carbon flux between the biosphere and atmosphere. Therefore, climate-driven changes of Re greatly impact on future atmospheric CO 2 concentration. The aim of this study was to derive an air temperature threshold to identify the driving climate forces of the respiratory process in terrestrial ecosystems within different temperature zones. A global dataset of 647 site-years of ecosystem flux data and related variables were collected at 152 sites. The quantile regression was applied to evaluate relationships between the maximum realizable Re rates and mean annual air temperature (MAT) as well as other micrometeorological factors (i.e., atmospheric CO 2 concentration, atmospheric water content, soil heat flux, sensible heat flux, latent heat flux, precipitation, relative humidity, and soil water content). Our analysis revealed an ecosystem threshold of MAT of 11 ± 2.3 °C. In ecosystems with MATs lower than the threshold, the maximum R e rates were primarily dependent on temperature and respiration was mainly a temperature-driven process. In ecosystems with MATs higher than the threshold, besides MAT, other factors, such as water availability and surface heat flux, became significant driving forces of the maximum Re rates and respiration was a multi-factor-driven process. Temperature played the key role in generation of the maximum R e rates in the terrestrial ecosystems, while other driving forces reduce the maximum R e rates and the temperature sensitivity of the respiratory process. According to a regression tree analysis, MAT was also the most influencing factor of mean R e rates among the climate forces. The information from this study should be useful to predict the respiratory process in terrestrial ecosystems with different temperatures under the climate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

What factors affect the prices of low-priced U.S. solar PV systems?

The price of solar PV systems has declined rapidly, yet there are some much lower-priced systems than others. This study explores the factors that determine prices in these low-priced (LP) systems. Using a data set of 42,611 residential-scale PV systems installed in the U.S. in 2013, we use quantile regressions to estimate the importance of factors affecting the installed prices for LP systems (those at the 10th percentile) in comparison to median-priced systems. We find that the value of solar to consumers-a variable that accounts for subsidies, electric rates, and PV generation levels-is associated with lower prices for LP systems but higher prices for median priced systems. Conversely, systems installed in new home construction are associated with lower prices at the median but higher prices for LP. Other variables have larger price-reducing effects on LP than on median priced systems: systems installed in Arizona and Florida, as well as commercial and thin film systems. In contrast, the following have a smaller effect on prices for LP systems than median priced systems: tracking systems, self-installations, systems installed in Massachusetts, the system size, and installer experience. Furthermore, these results highlight the complex factors at play that lead to LP systems and shed light into how such LP systems can come about.

14 SOLAR ENERGY↗

DOE OSTI2017

Constructing probabilistic scenarios for wide-area solar power generation

Optimizing thermal generation commitments and dispatch in the presence of high penetrations of renewable resources such as solar energy requires a characterization of their stochastic properties. In this study, we describe novel methods designed to create day-ahead, wide-area probabilistic solar power scenarios based only on historical forecasts and associated observations of solar power production. Each scenario represents a possible trajectory for solar power in next-day operations with an associated probability computed by algorithms that use historical forecast errors. Scenarios are created by segmentation of historic data, fitting non-parametric error distributions using epi-splines, and then computing specific quantiles from these distributions. Additionally, we address the challenge of establishing an upper bound on solar power output. Our specific application driver is for use in stochastic variants of core power systems operations optimization problems, e.g., unit commitment and economic dispatch. These problems require as input a range of possible future realizations of renewables production. However, the utility of such probabilistic scenarios extends to other contexts, e.g., operator and trader situational awareness. Finally, we compare the performance of our approach to a recently proposed method based on quantile regression, and demonstrate that our method performs comparably to this approach in terms of two widely used methods for assessing the quality of probabilistic scenarios: the Energy score and the Variogram score.

14 SOLAR ENERGY↗