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DOE OSTI2019

Adsorption on transition metal surfaces: Transferability and accuracy of DFT using the ADS41 dataset

We present a benchmarking study of adsorption energies on transition metal surfaces computed with select functionals across different density functional theory codes. In addition to gradient corrected functionals, we evaluate the accuracies of representative metaGGAs, including MS2, SCAN, and SCAN+rVV10 , as well as a short-range screened hybrid functional, HSE06. The study shows that the challenge of finding a functional that can simultaneously capture both covalent and noncovalent molecule-surface interactions persists, with no single functional in the benchmarking study with average errors < 0.2 eV. We find that HSE06 on average does not improve the accuracy compared to PBE for the surface chemistry of transition metals. The BEEF-vdW dispersion-corrected generalized gradient approximation (GGA) and the MS2 metaGGA yield the lowest errors in both chemisorption and dispersion energies, demonstrating that moving up the Jacob's ladder of functionals to screened hybrids does not necessarily improve the description of transition metal surface chemistry.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Extending accurate spectral induced polarization measurements into the kHz range: modelling and removal of errors from interactions between the parasitic capacitive coupling and the sample holder

SUMMARY Spectral induced polarization (SIP), describing the measurement of the frequency domain electrical impedance magnitude and phase of porous materials, has been widely used to characterize subsurface hydrological/biogeochemical properties and processes. SIP data collected at frequencies higher than 100 Hz are expected to describe the polarization of small particles providing insights into the physicochemical properties of clays, nanoparticles and microorganisms. However, the phase measurements at these high frequencies are often contaminated by errors due to the parasitic capacitive coupling of the SIP instrument, especially for lower conductivity samples. We developed a model showing the measured phase is the sum of the true sample phase and an error term ωCinZx, where ω is the angular frequency; Cin is the instrument input capacitance and Zx is a measurable impedance function related to the sample holder properties and the reference resistor. Based on this model, a new phase correction method is proposed that results in highly accurate SIP data up to 20 kHz as well as the determination of Cin. We tested the correction method using electric circuits, NaCl fluids and three unconsolidated samples (sand, sand-clay and sand-pyrite mixtures). The corrected phase for the circuit and NaCl fluid experiments showed excellent agreement with the theoretical phase response across the studied frequency range (errors <1 mrad). For unconsolidated samples, removal of errors results in phase spectra more consistent with expected polarization mechanisms, as based on phase peaks recorded for small pyrite and clay particles at high frequencies. These phase peaks could not be identified in the uncorrected data. Our approach can substantially enhance the value of the SIP method for the characterization of fine-grained sediments and rocks.

58 GEOSCIENCES↗

DOE OSTI2026

Local Spin Density Approximation Strongly Improved by a Better-Informed Local Scaling of Its Self-Interaction Correction

The Perdew−Zunger self-interaction correction (PZSIC) makes density functional approximations (DFAs) exact for all one-electron densities. However, it overcorrects in manyelectron regions, introducing errors for the uniform-density limit, where uncorrected DFAs are exact. The locally scaled PZSIC (LSIC), based on the iso-orbital indicator zσ [which distinguishes single-orbital and slowly varying density regions and is used with the local spin density approximation (LSDA)], restores the uniform-density limit and significantly improves results for many properties, including chemical reaction barrier heights, atomization energies, and ionization potentials. Yet, LSIC performs poorly for weakly bonded systems, leaving many unbound, due to limitations of its iso-orbital indicator. To correct this, in this work we propose a new local scaling, LSIC-α, based on the iso-orbital indicator ασ (which additionally identifies regions of overlapping density tails). A two-parameter scaling function of ασ is fitted to a subset of the nonbonded appropriate norms for the SCAN and r2SCAN meta- GGAs, and tested on many properties of main-group atoms, molecules, and molecular complexes. LSIC-α greatly improves the interaction energies of weakly bonded systems in the S22 data set while retaining LSIC’s accuracy for other properties. This work shows that the errors of LSDA (and presumably of higher-level DFAs) can be largely but not entirely repaired by a proper “do no harm” self-interaction correction.

Approximation↗

DOE OSTI2015

Accurate ab initio vibrational energies of methyl chloride

Two new nine-dimensional potential energy surfaces (PESs) have been generated using high-level ab initio theory for the two main isotopologues of methyl chloride, CH{sub 3}{sup 35}Cl and CH{sub 3}{sup 37}Cl. The respective PESs, CBS-35{sup HL}, and CBS-37{sup HL}, are based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set (CBS) limit, and incorporate a range of higher-level (HL) additive energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms, scalar relativistic effects, and diagonal Born-Oppenheimer corrections. Variational calculations of the vibrational energy levels were performed using the computer program TROVE, whose functionality has been extended to handle molecules of the form XY {sub 3}Z. Fully converged energies were obtained by means of a complete vibrational basis set extrapolation. The CBS-35{sup HL} and CBS-37{sup HL} PESs reproduce the fundamental term values with root-mean-square errors of 0.75 and 1.00 cm{sup −1}, respectively. An analysis of the combined effect of the HL corrections and CBS extrapolation on the vibrational wavenumbers indicates that both are needed to compute accurate theoretical results for methyl chloride. We believe that it would be extremely challenging to go beyond the accuracy currently achieved for CH{sub 3}Cl without empirical refinement of the respective PESs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Atomic ionization: sd energy imbalance and Perdew–Zunger self-interaction correction energy penalty in 3d atoms

To accurately describe the energetics of transition metal systems, density functional approximations (DFAs) must provide a balanced description of s- and d- electrons. One measure of this is the sd transfer error, which has previously been defined as E ( 3 d n − 1 4 s 1 ) − E ( 3 d n − 2 4 s 2 ) . Theoretical concerns have been raised about this definition due to its evaluation of excited-state energies using ground-state DFAs. A more serious concern appears to be strong correlation in the 4s 2 configuration. Here, we define a ground-state measure of the sd energy imbalance, based on the errors of s- and d-electron second ionization energies of the 3d atoms, that effectively circumvents the aforementioned problems. We find an improved performance as we move from the local spin density approximation (LSDA) to the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) to the regularized and restored Strongly Constrained and Appropriately Normed (r 2 SCAN) meta-GGA for first-row transition metal atoms. However, we find large (∼2 eV) ground-state sd energy imbalances when applying a Perdew–Zunger 1981 self-interaction correction. This is attributed to an “energy penalty” associated with the noded 3d orbitals. A local scaling of the self-interaction correction to LSDA results in a balance of s- and d-errors.

Science & Technology - Other Topics↗

DOE OSTI2016

SDSS-IV/MaNGA: SPECTROPHOTOMETRIC CALIBRATION TECHNIQUE

Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), one of three core programs in the Sloan Digital Sky Survey-IV, is an integral-field spectroscopic survey of roughly 10,000 nearby galaxies. It employs dithered observations using 17 hexagonal bundles of 2″ fibers to obtain resolved spectroscopy over a wide wavelength range of 3600–10300 Å. To map the internal variations within each galaxy, we need to perform accurate spectral surface photometry, which is to calibrate the specific intensity at every spatial location sampled by each individual aperture element of the integral field unit. The calibration must correct only for the flux loss due to atmospheric throughput and the instrument response, but not for losses due to the finite geometry of the fiber aperture. This requires the use of standard star measurements to strictly separate these two flux loss factors (throughput versus geometry), a difficult challenge with standard single-fiber spectroscopy techniques due to various practical limitations. Therefore, we developed a technique for spectral surface photometry using multiple small fiber-bundles targeting standard stars simultaneously with galaxy observations. We discuss the principles of our approach and how they compare to previous efforts, and we demonstrate the precision and accuracy achieved. MaNGA's relative calibration between the wavelengths of Hα and Hβ has an rms of 1.7%, while that between [N ii] λ6583 and [O ii] λ3727 has an rms of 4.7%. Using extinction-corrected star formation rates and gas-phase metallicities as an illustration, this level of precision guarantees that flux calibration errors will be sub-dominant when estimating these quantities. The absolute calibration is better than 5% for more than 89% of MaNGA's wavelength range.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Addressing delayed case reporting in infectious disease forecast modeling

Infectious disease forecasting is of great interest to the public health community and policymakers, since forecasts can provide insight into disease dynamics in the near future and inform interventions. Due to delays in case reporting, however, forecasting models may often underestimate the current and future disease burden. In this paper, we propose a general framework for addressing reporting delay in disease forecasting efforts with the goal of improving forecasts. We propose strategies for leveraging either historical data on case reporting or external internet-based data to estimate the amount of reporting error. We then describe several approaches for adapting general forecasting pipelines to account for under- or over-reporting of cases. We apply these methods to address reporting delay in data on dengue fever cases in Puerto Rico from 1990 to 2009 and to reports of influenza-like illness (ILI) in the United States between 2010 and 2019. Through a simulation study, we compare method performance and evaluate robustness to assumption violations. Our results show that forecasting accuracy and prediction coverage almost always increase when correction methods are implemented to address reporting delay. Some of these methods required knowledge about the reporting error or high quality external data, which may not always be available. Provided alternatives include excluding recently-reported data and performing sensitivity analysis. This work provides intuition and guidance for handling delay in disease case reporting and may serve as a useful resource to inform practical infectious disease forecasting efforts.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2013

Planck intermediate results (Corrigendum) : V. Pressure profiles of galaxy clusters from the Sunyaev-Zeldovich effect

Figure 7 of our original publication (Planck Collaboration 2013) is flawed. The correct figure is presented here and we stress that our original conclusion on the radial distribution of the gas fraction remains unchanged. There was an error in the reconstruction of the temperature profiles used to derive the gas mass distribution from the joint Planck and XMM-Newton pressure profile, and thereby a prediction for the gas fraction profiles. The error in the temperature profile reconstruction applies to this paper only. The predicted gas fraction profiles for both hypothesis on the temperature profiles, i.e., from hypothesis H1 and H2, were affected similarly. Now corrected, they are in better agreement at R 500 with the measurement by Pratt et al. (2009) on the REXCESS sample and with the expectations from the CMB. The Perseus profile (Simionescu et al. 2011) is still marginally compatible with our prediction within our large dispersion (shaded blue and red area on the figure).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Treatment Planning System Calculation Errors Are Present in Most Imaging and Radiation Oncology Core-Houston Phantom Failures

Purpose: The anthropomorphic phantom program at the Houston branch of the Imaging and Radiation Oncology Core (IROC-Houston) is an end-to-end test that can be used to determine whether an institution can accurately model, calculate, and deliver an intensity modulated radiation therapy dose distribution. Currently, institutions that do not meet IROC-Houston's criteria have no specific information with which to identify and correct problems. In the present study, an independent recalculation system was developed to identify treatment planning system (TPS) calculation errors. Methods and Materials: A recalculation system was commissioned and customized using IROC-Houston measurement reference dosimetry data for common linear accelerator classes. Using this system, 259 head and neck phantom irradiations were recalculated. Both the recalculation and the institution's TPS calculation were compared with the delivered dose that was measured. In cases in which the recalculation was statistically more accurate by 2% on average or 3% at a single measurement location than was the institution's TPS, the irradiation was flagged as having a “considerable” institutional calculation error. The error rates were also examined according to the linear accelerator vendor and delivery technique. Results: Surprisingly, on average, the reference recalculation system had better accuracy than the institution's TPS. Considerable TPS errors were found in 17% (n=45) of the head and neck irradiations. Also, 68% (n=13) of the irradiations that failed to meet the IROC-Houston criteria were found to have calculation errors. Conclusions: Nearly 1 in 5 institutions were found to have TPS errors in their intensity modulated radiation therapy calculations, highlighting the need for careful beam modeling and calculation in the TPS. An independent recalculation system can help identify the presence of TPS errors and pass on the knowledge to the institution.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2023

Statistical Tool Size Study for Computer-Controlled Optical Surfacing

Over the past few decades, computer-controlled optical surfacing (CCOS) systems have become more deterministic. A target surface profile can be predictably achieved with a combination of tools of different sizes. However, deciding the optimal set of tool sizes that will achieve the target residual error in the shortest run time is difficult, and no general guidance has been proposed in the literature. In this paper, we present a computer-assisted study on choosing the proper tool size for a given surface error map. First, we propose that the characteristic frequency ratio (CFR) can be used as a general measure of the correction capability of a tool over a surface map. Second, the performance of different CFRs is quantitatively studied with a computer simulation by applying them to guide the tool size selection for polishing a large number of randomly generated surface maps with similar initial spatial frequencies and root mean square errors. Finally, we find that CFR = 0.75 achieves the most stable trade-off between the total run time and the number of iterations and thus can be used as a general criterion in tool size selection for CCOS processes. To the best of our knowledge, the CFR is the first criterion that ties tool size selection to overall efficiency.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Enthalpies of formation for Criegee intermediates: A correlation energy convergence study

Criegee intermediates, formed from the ozonolysis of alkenes, are known to have a role in atmospheric chemistry, including the modulation of the oxidizing capacity of the troposphere. Although studies have been conducted since their discovery, the synthesis of these species in the laboratory has ushered in a new wave of investigations of these structures, both theoretically and experimentally. In some of these theoretical studies, high-order corrections for correlation energy are included to account for the mid multi-reference character found in these systems. Many of these studies include a focus on kinetics; therefore, the calculated energies should be accurate (<1 kcal/mol in error). In this research, we compute the enthalpies of formation for a small set of Criegee intermediates, including higher-order coupled cluster corrections for correlation energy up to coupled cluster with perturbative quintuple excitations. The enthalpies of formation for formaldehyde oxide, anti-acetaldehyde oxide, syn-acetaldehyde oxide, and acetone oxide are presented at 0 K as 26.5, 15.6, 12.2, and 0.1 kcal mol−1, respectively. Additionally, we do not recommend the coupled cluster with perturbative quadruple excitations [CCSDT(Q)] energy correction, as it is approximately twice as large as that of the coupled cluster with full quadruple excitations (CCSDTQ). Half of the CCSDT(Q) energy correction may be included as a reliable, cost-effective estimation of CCSDTQ energies for Criegee intermediates.

Chemistry↗

DOE OSTI2024

Relating flow resistance to equivalent roughness

Describing flow resistance using the physical properties of an underlying surface is a recalcitrant problem in overland flow models. If discharge measurements are available, an equivalent roughness (e.g., Manning’s n) can be calibrated to represent the effects of surface properties within the domain with a single numerical value. Alternatively, the flow resistance can be estimated from discharge and velocity measured at a point, typically a runoff plot outlet. However, such experimental estimates are often inconsistent with the equivalent roughness determined from calibration to discharge, even if both derive from the same dataset. For example, if Manning’s equation is used to parameterize flow resistance, the Manning’s n obtained by calibrating a model to discharge differs from the value of n calculated from measured flow and velocity at the hillslope outlet. Here, this discrepancy is resolved by deriving a correction factor relating experimentally-determined flow resistance to the equivalent roughness. The derived correction factor is tested for four commonly-used resistance formulations using 129 rainfall simulator experiments. The correction factor is necessary to reproduce measured velocities, and yields minor improvements in discharge prediction. Plain Language Summary: Accurate runoff prediction is needed for land and water management in dryland regions, where sporadic and limited rainfall necessitate efficient water use and drought mitigation strategies. The skill of runoff models is known to be hindered by out ability to estimate flow resistance, which is the quantity that describes how energy is lost from flowing water to the underlying surface. Typically, models represent flow resistance with an equivalent roughness, e.g., Manning’s n, that is adjusted until the model can reproduce available discharge observations at watershed scale. However, the flow resistance measured in plot-scale experiments (1–10 m) often exceeds equivalent roughness coefficients by a factor of 10. This means that the direct use of plot-scale experimental data to parameterize runoff models could cause errors in discharge and runoff velocity predictions. Here, we resolve these differences by deriving an analytic correction factor that relates flow resistance to the equivalent roughness required for models to reproduce experimental velocity and discharge data. This correction factor is tested using rainfall simulator data from 129 experiments performed in the US Southwest covering a wide range of precipitation intensities, soil textures and vegetation types. Use of the correction factor substantially improves model prediction of flow velocity, which is needed for reproducing the timing of flood events and the estimation of erosion.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Inverse Volume Scaling of Finite-Size Error in Periodic Coupled Cluster Theory

Coupled cluster theory is one of the most popular post-Hartree-Fock methods for molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we review the current understanding of finite-size error in quantum chemistry methods for periodic systems. We introduce new tools that elucidate the mechanisms behind this phenomenon in the context of coupled cluster doubles calculations. This reconciles some seemingly paradoxical statements related to finite-size scaling. Our findings also show that singularity subtraction can be a powerful method to effectively reduce finite-size errors in practical quantum chemistry calculations for periodic systems. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A data-driven framework for error estimation and mesh-model optimization in system-level thermal-hydraulic simulation

We report over the past decades, several computer codes have been developed for simulation and analysis of thermal-hydraulics and system response in nuclear reactors under operating, abnormal transient, and accident conditions. However, simulation errors and uncertainties still inevitably exist even while these codes have been extensively assessed and used. In this work, a data-driven framework (Optimal Mesh/Model Information System, OMIS) is formulated and demonstrated to estimate simulation error and suggest optimal selection of computational mesh size (i.e., nodalization) and constitutive correlations (e.g., wall functions and turbulence models) for low-fidelity, coarse-mesh thermal-hydraulic simulation, in order to achieve accuracy comparable to that of high-fidelity simulation. Using results from high-fidelity simulations and experimental data with many fast-running low-fidelity simulations, an error database is built and used to train a machine learning model that can determine the relationship between local simulation error and local physical features. This machine learning model is then used to generate insight and help correct low-fidelity simulations for similar physical conditions. The OMIS framework is designed as a modularized six-step procedure and accomplished with state-of-the-art methods and algorithms. A mixed-convection case study was performed to illustrate the entire framework.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

An adaptive Gaussian process-based method for efficient Bayesian experimental design in groundwater contaminant source identification problems: ADAPTIVE GAUSSIAN PROCESS-BASED INVERSION

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose a Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.

Zhang, Jiangjiang↗

DOE OSTI2015

DARHT Radiographic Grid Scale Correction

Recently it became apparent that the radiographic grid which has been used to calibrate the dimensional scale of DARHT radiographs was not centered at the location where the objects have been centered. This offset produced an error of 0.188% in the dimensional scaling of the radiographic images processed using the assumption that the grid and objects had the same center. This paper will show the derivation of the scaling correction, explain how new radiographs are being processed to account for the difference in location, and provide the details of how to correct radiographic image processed with the erroneous scale factor.

47 OTHER INSTRUMENTATION↗

DOE OSTI2015

Evaluation of in vivo quantification accuracy of the Ingenuity-TF PET/MR

Purpose: The quantitative accuracy of standardized uptake values (SUVs) and tracer kinetic uptake parameters in patient investigations strongly depends on accurate determination of regional activity concentrations in positron emission tomography (PET) data. This determination rests on the assumption that the given scanner calibration is valid in vivo. In a previous study, we introduced a method to test this assumption. This method allows to identify discrepancies in quantitative accuracy in vivo by comparison of activity concentrations of urine samples measured in a well-counter with activity concentrations extracted from PET images of the bladder. In the present study, we have applied this method to the Philips Ingenuity-TF PET/MR since at the present stage, absolute quantitative accuracy of combined PET/MR systems is still under investigation. Methods: Twenty one clinical whole-body F18-FDG scans were included in this study. The bladder region was imaged as the last bed position and urine samples were collected afterward. PET images were reconstructed including MR-based attenuation correction with and without truncation compensation and 3D regions-of-interest (ROIs) of the bladder were delineated by three observers. To exclude partial volume effects, ROIs were concentrically shrunk by 8–10 mm. Then, activity concentrations were determined in the PET images for the bladder and for the urine by measuring the samples in a calibrated well-counter. In addition, linearity measurements of SUV vs singles rate and measurements of the stability of the coincidence rate of “true” events of the PET/MR system were performed over a period of 4 months. Results: The measured in vivo activity concentrations were significantly lower in PET/MR than in the well-counter with a ratio of the former to the latter of 0.756 ± 0.060 (mean ± std. dev.), a range of 0.604–0.858, and a P value of 3.9 ⋅ 10{sup −14}. While the stability measurements of the coincidence rate of “true” events showed no relevant deviation over time, the linearity scans revealed a systematic error of 8%–11% (avg. 9%) for the range of singles rates present in the bladder scans. After correcting for this systematic bias caused by shortcomings of the manufacturers calibration procedure, the PET to well-counter ratio increased to 0.832 ± 0.064 (0.668 –0.941), P = 1.1 ⋅ 10{sup −10}. After compensating for truncation of the upper extremities in the MR-based attenuation maps, the ratio further improved to 0.871 ± 0.069 (0.693–0.992), P = 3.9 ⋅ 10{sup −8}. Conclusions: Our results show that the Philips PET/MR underestimates activity concentrations in the bladder by 17%, which is 7 percentage points (pp.) larger than in the previously investigated PET and PET/CT systems. We attribute this increased underestimation to remaining limitations of the MR-based attenuation correction. Our results suggest that only a 2 pp. larger underestimation of activity concentrations compared to PET/CT can be observed if compensation of attenuation truncation of the upper extremities is applied. Thus, quantification accuracy of the Philips Ingenuity-TF PET/MR can be considered acceptable for clinical purposes given the ±10% error margin in the EANM guidelines. The comparison of PET images from the bladder region with urine samples has proven a useful method. It might be interesting for evaluation and comparison of the in vivo quantitative accuracy of PET, PET/CT, and especially PET/MR systems from different manufacturers or in multicenter trials.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Uncertainty of Rotating Shadowband Irradiometers and Si-Pyranometers Including the Spectral Irradiance Error

Concentrating solar power projects require accurate direct normal irradiance (DNI) data including uncertainty specifications for plant layout and cost calculations. Ground measured data are necessary to obtain the required level of accuracy and are often obtained with Rotating Shadowband Irradiometers (RSI) that use photodiode pyranometers and correction functions to account for systematic effects. The uncertainty of Si-pyranometers has been investigated, but so far basically empirical studies were published or decisive uncertainty influences had to be estimated based on experience in analytical studies. One of the most crucial estimated influences is the spectral irradiance error because Si-photodiode-pyranometers only detect visible and color infrared radiation and have a spectral response that varies strongly within this wavelength interval. Furthermore, analytic studies did not discuss the role of correction functions and the uncertainty introduced by imperfect shading. In order to further improve the bankability of RSI and Si-pyranometer data, a detailed uncertainty analysis following the Guide to the Expression of Uncertainty in Measurement (GUM) has been carried out. The study defines a method for the derivation of the spectral error and spectral uncertainties and presents quantitative values of the spectral and overall uncertainties. Data from the PSA station in southern Spain was selected for the analysis. Average standard uncertainties for corrected 10 min data of 2% for global horizontal irradiance (GHI), and 2.9% for DNI (for GHI and DNI over 300 W/m2) were found for the 2012 yearly dataset when separate GHI and DHI calibration constants were used. Also the uncertainty in 1 min resolution was analyzed. The effect of correction functions is significant. The uncertainties found in this study are consistent with results of previous empirical studies.

14 SOLAR ENERGY↗