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DOE OSTI2021

Resolved gravity waves in the tropical stratosphere: Impact of horizontal resolution and deep convection parametrization

Convectively generated gravity waves (CGGWs) are important for numerical weather prediction due to their effect on the quasi-biennial oscillation (QBO) in the stratosphere. Here, using global ECMWF IFS simulations at TCo7999 (or 1.25 km), TCo2559 (or 3.9 km) and TCo1279 (or 7.8 km) horizontal resolutions, sensitivity of resolved CGGWs to the horizontal resolution and to the explicit versus parametrized representation of deep convection is elucidated during the westerly shear phase of the QBO. Parametrized deep convection is found to inhibit CGGWs, resulting in a twofold reduction in CGGW forcing. When deep convection is explicitly resolved, the total CGGW forcing is almost unchanged across the horizontal resolutions. However, the contribution of long and mesoscale CGGWs (with horizontal wavelengths 100 km ≤ $λ_h$ < $1,900$ km) to the total CGGW forcing decreases and the contribution of smaller-scale CGGWs (with $λ_h$ < $100$ km) increases as the horizontal resolution increases. At the maximum CGGW forcing altitude, at TCo7999 resolution 43% of the total CGGW forcing is due to long and mesoscale waves, whereas at TCo2559 and TCo1279 resolutions their contribution is 70% and 90%, respectively. While CGGW forcing from long and mesoscale waves is similar at TCo7999 resolution with explicit deep convection and at TCo1279 resolution with parametrized deep convection, CGGW forcing from these waves is artificially enhanced at TCo1279 and TCo2559 resolutions with explicit deep convection. This is due to the explicit deep convection being too strong and having too much variance for 100 km ≤ $λ_h$ < $1,900$ km. Therefore, parametrizations of deep convection and CGGWs (to account for forcing from waves with $λ_h$ < $100$ km) are required even at TCo2559 resolution. Additionally, resolved CGGW forcing at TCo7999 resolution is examined for the easterly shear phase of the QBO; similar to the westerly shear phase, the smaller-scale waves contribute 55% to the total CGGW forcing at the maximum CGGW forcing altitude.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Global Sensitivity Analysis Using the Ultra‐Low Resolution Energy Exascale Earth System Model

Abstract For decades, Arctic temperatures have increased twice as fast as average global temperatures. As a first step toward quantifying parametric uncertainty in Arctic climate, we performed a variance‐based global sensitivity analysis (GSA) using a fully coupled, ultra‐low resolution (ULR) configuration of version 1 of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SMv1). Specifically, we quantified the sensitivity of six quantities of interests (QOIs), which characterize changes in Arctic climate over a 75 year period, to uncertainties in nine model parameters spanning the sea ice, atmosphere, and ocean components of E3SMv1. Sensitivity indices for each QOI were computed with a Gaussian process emulator using 139 random realizations of the random parameters and fixed preindustrial forcing. Uncertainties in the atmospheric parameters in the Cloud Layers Unified by Binormals (CLUBB) scheme were found to have the most impact on sea ice status and the larger Arctic climate. Our results demonstrate the importance of conducting sensitivity analyses with fully coupled climate models. The ULR configuration makes such studies computationally feasible today due to its low computational cost. When advances in computational power and modeling algorithms enable the tractable use of higher‐resolution models, our results will provide a baseline that can quantify the impact of model resolution on the accuracy of sensitivity indices. Moreover, the confidence intervals provided by our study, which we used to quantify the impact of the number of model evaluations on the accuracy of sensitivity estimates, have the potential to inform the computational resources needed for future sensitivity studies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A multishock model for the density variance of anisotropic, highly magnetized, supersonic turbulence

ABSTRACT Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma ^2_{\rho /\rho _0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parametrizes the star formation (SF) rate of a cloud. However, models for $\sigma ^2_{\rho /\rho _0}$ all share a common feature – the variance is assumed to be isotropic. This assumption does not hold when a trans-/sub-Alfvénic mean magnetic field, ${B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma _{\rho /\rho _0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma _{\rho /\rho _0}^2$ in the high Mach number $(\mathcal {M})$ limit as small-scale density fluctuations become suppressed by the strong ${B}_0$. The model reduces to the isotropic $\sigma _{\rho /\rho _0}^2\!-\!\mathcal {M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma _{\rho /\rho _0}^2$ from 12 high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented overdensities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic ${B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

Beattie, James R.↗

NASA NTRS2018

Retrievals of Cloud Droplet Size from the Research Scanning Polarimeter Data: Validation Using In Situ Measurements

We present comparisons of cloud droplet size distributions (DSDs) retrieved from the research scanning polarimeter (RSP) data with correlative in situ measurements made during the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES). The airborne portion of this field experiment was based out of St. John's airport, Newfoundland, Canada with the focus of this paper being on the deployment in May - June 2016. RSP was onboard the NASA C-130 aircraft together with an array of in situ and other remote sensing instrumentation. The RSP is an along-track scanner measuring the polarized and total reflectance in 9 spectral channels. Its uniquely high angular resolution allows for characterization of liquid water droplet sizes using the rainbow structure observed in the polarized reflectance over the scattering angle range from 135 to 165.degrees The rainbow is dominated by single scattering of light by cloud droplets, so its structure is characteristic specifically of the droplet sizes at cloud top (within unit optical depth into the cloud, equivalent to approximately 50m). A parametric fitting algorithm applied to the polarized reflectance provides retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, the Rainbow Fourier Transform (RFT), which allows us to retrieve the droplet size distribution itself. The latter is important in the case of clouds with complex microphysical structure, or multiple layers of cloud, which result in multi-modal DSDs. During NAAMES the aircraft performed a number of flight patterns specifically designed for comparisons between remote sensing retrievals and in situ measurements. These patterns consisted of two flight segments above the same straight ground track. One of these segments was flown above clouds allowing for remote sensing measurements, while the other was near the cloud top where cloud droplets were sampled. We compare the DSDs retrieved from the RSP data with in situ measurements made by the Cloud Droplet Probe (CDP). The comparisons generally show good agreement (better than 1 micron for effective radius and in most cases better than 0.02 for effective variance) with deviations explainable by the position of the aircraft within the cloud, or by the presence of additional cloud layers between the cloud being sampled by the in situ instrumentation and the altitude of the remote sensing segment. In the latter case, the multi-modal DSDs retrieved from the RSP data were consistent with the multi-layer cloud structures observed in the correlative High Spectral Resolution Lidar (HSRL) profiles. The results of these comparisons provide a rare validation of polarimetric droplet size retrieval techniques, demonstrating their accuracy and robustness and the potential of satellite data of this kind on a global scale.

Remote Sensing↗

NASA NTRS2016

Polarized View of Supercooled Liquid Water Clouds

Supercooled liquid water (SLW) clouds, where liquid droplets exist at temperatures below 0 C present a well known aviation hazard through aircraft icing, in which SLW accretes on the airframe. SLW clouds are common over the Southern Ocean, and climate-induced changes in their occurrence is thought to constitute a strong cloud feedback on global climate. The two recent NASA field campaigns POlarimeter Definition EXperiment (PODEX, based in Palmdale, California, January-February 2013) and Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS, based in Houston, Texas in August- September 2013) provided a unique opportunity to observe SLW clouds from the high-altitude airborne platform of NASA's ER-2 aircraft. We present an analysis of measurements made by the Research Scanning Polarimeter (RSP) during these experiments accompanied by correlative retrievals from other sensors. The RSP measures both polarized and total reflectance in 9 spectral channels with wavelengths ranging from 410 to 2250 nm. It is a scanning sensor taking samples at 0.8deg intervals within 60deg from nadir in both forward and backward directions. This unique angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135deg and 165deg. Simple parametric fitting algorithms applied to the polarized reflectance provide retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT),which allows retrieval of the droplet size distribution without assuming a size distribution shape. We present an overview of the RSP campaign datasets available from the NASA GISS website, as well as two detailed examples of the retrievals. In these case studies we focus on cloud fields with spatial features varying between glaciated and liquid phases at altitudes as high as 10 km, which correspond to temperatures close to the homogeneous freezing temperature of pure water drops (about -35 C or colder). The multimodal droplet size distributions retrieved from RSP data in these cases are consistent with the multi-layer cloud structure observed by correlative Cloud Physics Lidar (CPL) measurements.

Clouds↗

NASA NTRS2016

Retrievals of Cloud Droplet Size from the RSP Data: Validation Using in Situ Measurements

We present comparisons of cloud droplet size distributions retrieved from the Research Scanning Polarimeter (RSP) data with correlative in situ measurements made during the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES). This field experiment was based at St. Johns airport, Newfoundland, Canada with the latest deployment in May - June 2016. RSP was onboard the NASA C-130 aircraft together with an array of in situ and other remote sensing instrumentation. The RSP is an along-track scanner measuring polarized and total reflectances in9 spectral channels. Its unique high angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135 and 165 degrees. A parametric fitting algorithm applied to the polarized reflectances provides retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT), which allows us to retrieve the droplet size distribution (DSD) itself. The latter is important in the case of clouds with complex structure, which results in multi-modal DSDs. During NAAMES the aircraft performed a number of flight patterns specifically designed for comparison of remote sensing retrievals and in situ measurements. These patterns consisted of two flight segments above the same straight ground track. One of these segments was flown above clouds allowing for remote sensing measurements, while the other was at the cloud top where cloud droplets were sampled. We compare the DSDs retrieved from the RSP data with in situ measurements made by the Cloud Droplet Probe (CDP). The comparisons show generally good agreement with deviations explainable by the position of the aircraft within cloud and by presence of additional cloud layers in RSP view that do not contribute to the in situ DSDs. In the latter case the distributions retrieved from the RSP data were consistent with the multi-layer cloud structures observed in the correlative High Spectral Resolution Lidar (HSRL) profiles. The comparison results provide a rare validation of polarimetric droplet size retrieval techniques, which can be used for analysis of satellite data on global scale.

cloud droplets↗

NASA NTRSDate not supplied

A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty

When allocating redundant effectors to virtual control commands, linear (generalized inverse) allocators have historically been used on aircraft and spacecraft. While simple to implement, generalized inverses are unable to realize a significant portion of the attainable moments. To address this drawback, the control allocation problem can also be formulated as a linear programming or quadratic programming problem and solved using convex optimization based solvers. These approaches have been shown to access a larger set of attainable moments, however, little work has been done to understand the performance of convex optimization-based control allocation in the presence of parametric model uncertainty. This paper seeks to compare the performance of several control allocation approaches, including two forms of generalized inverse allocators, the pseudo inverse and minimum-variance, and the linear programming and quadratic programming approach in the presence of parametric model uncertainty. The performance of these four allocators were tested on an aircraft model in the presence of realistic parametric model uncertainty and the convex optimization approaches were shown to outperform the generalized inverses.

Luke J Miller↗

DOE OSTI2021

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Region and cloud regime dependence of parametric sensitivity in E3SM atmosphere model

Abstract The Department of Energy (DOE)’s Energy Exascale Earth System Model (E3SM), including its atmosphere model (EAM), has many relatively new features. In a previous study we conducted a systematic parametric sensitivity analysis for EAM based on short, perturbed parameter ensemble (PPE) simulations, mainly focusing on global mean climate features and metrics. While parameter values in global climate models are generally invariant in space and time, model response to parameters perturbation may vary by regions and climate regimes, which motivates the need to better understand the EAM model behaviors and physics at regional scale and process level. In this study, using the same set of PPE simulations and a similar sensitivity analysis framework, we identify parameters that cause largest sensitivities over different regions and compare model responses in fast atmospheric processes to the parameters across different cloud regimes for several important cloud-related fidelity metrics. We find that cloud forcing has opposite response to some parameters over mid-latitude vs. tropical land. We also analyze how the parametric sensitivity varies as stratocumulus transitions to shallow convection and to deep convection over ocean. Low cloud forcing and shortwave cloud forcing in the subtropical eastern Pacific are most sensitive to the parameters controlling the width of the probability density function (PDF) of the subgrid vertical velocity ( w’ ) ( gamma ) and the damping of the w’ skewness ( c8 ) near the coast but become more sensitive to the parameter affecting the damping of the w’ variance ( c1 ) further offshore. Detailed interpretation of the spatial dependence of parametric sensitivity is provided. We also investigate how the parametric sensitivity evolves with prediction duration. This study improves our process-level understanding of cloud physics and parameterization and provides insights for developing more advanced regime-aware parameterization schemes in global climate model.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1988

On the simultaneous improvement of a satellite orbit and determination of sea surface topography using altimeter data

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface toography with minimum wavelengths of about 500 km and to reduce the radial orbit errors caused by geopotential uncertainties. The modeling of these errors is made using the linearized Lagrangian perturbation theory. Observation equations are developed using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information can then provide estimates of parametrs representing the sea surface topography and corrections to the orbit. The potential of the method is demonstrated in a solution where simulated geopotential errors and the Levitus sea surface topography are used to generate the observables for a Seasat 3 day arc. The simulation results suggest that the method can be used to efficiently process real altimeter data.

Engelis, Theodossios↗

NASA NTRS2006

When Will the Antarctic Ozone Hole Recover?

The Antarctic ozone hole demonstrates large-scale, man-made affects on our atmosphere. Surface observations now show that human produced ozone depleting substances (ODSs) are declining. The ozone hole should soon start to diminish because of this decline. In this talk we will demonstrate an ozone hole parametric model. This model is based upon: 1) a new algorithm for estimating 61 and Br levels over Antarctica and 2) late-spring Antarctic stratospheric temperatures. This parametric model explains 95% of the ozone hole area's variance. We use future ODS levels to predict ozone hole recovery. Full recovery to 1980 levels will occur in approximately 2068. The ozone hole area will very slowly decline over the next 2 decades. Detection of a statistically significant decrease of area will not occur until approximately 2024. We further show that nominal Antarctic stratospheric greenhouse gas forced temperature change should have a small impact on the ozone hole.

Newman, Paul A.↗

NASA NTRS2006

When Will the Antarctic Ozone Hole Recover?

The Antarctic ozone hole demonstrates large-scale, man-made affects on our atmosphere. Surface observations now show that human produced ozone depleting substances (ODSs) are declining. The ozone hole should soon start to diminish because of this decline. Herein we demonstrate an ozone hole parametric model. This model is based upon: 1) a new algorithm for estimating C1 and Br levels over Antarctica and 2) late-spring Antarctic stratospheric temperatures. This parametric model explains 95% of the ozone hole area s variance. We use future ODS levels to predict ozone hole recovery. Full recovery to 1980 levels will occur in approximately 2068. The ozone hole area will very slowly decline over the next 2 decades. Detection of a statistically significant decrease of area will not occur until approximately 2024. We further show that nominal Antarctic stratospheric greenhouse gas forced temperature change should have a small impact on the ozone hole.

Newman, Paul A.↗

DOE OSTI2023

Sensitivity of Near-Surface Variables in the RUC Land Surface Model in the Weather Research and Forecasting Model

In this study, we investigate the parametric sensitivity of near-surface variables, such as sensible heat flux, latent heat flux, ground heat flux, hub-height wind speed and land surface temperature, to the parameters used in the Rapid Update Cycle (RUC) land surface model (LSM) during a wintertime and summertime period. The model simulations are compared with observations collected from the second Wind Forecast Improvement Project (WFIP2) field campaign. The results suggest that parameters related to snow/ice and thermal processes can have significant impact on the simulated near-surface variables. Out of the 11 examined parameters, only 6 of them have considerable influences on the model behaviors and explain about 60 ~ 80 % of the estimated total variance of the simulated variables. In addition, the magnitude of the parametric sensitivity varies with season. For instance, parameters associated with snow/ice processes are dominant during the wintertime whereas those associated with thermal processes are more important during the summertime. Furthermore, the impact of the identified parameters on the simulated variables is highly related to the topography. There is a high degree of sensitivity to the parameter values over the slope region. This points out the importance of collecting field observations over steep areas to better quantity the appropriate values of key parameters. Overall, our findings provide a better understanding of the RUC LSM behavior associated with parameter uncertainties and can be used to improve the forecasting skill of land surface processes via calibration of the most uncertain model parameters.

17 WIND ENERGY↗

DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗

NASA NTRS1981

Statistics of some atmospheric turbulence records relevant to aircraft response calculations

Methods for characterizing atmospheric turbulence are described. The methods illustrated include maximum likelihood estimation of the integral scale and intensity of records obeying the von Karman transverse power spectral form, constrained least-squares estimation of the parameters of a parametric representation of autocorrelation functions, estimation of the power spectra density of the instantaneous variance of a record with temporally fluctuating variance, and estimation of the probability density functions of various turbulence components. Descriptions of the computer programs used in the computations are given, and a full listing of these programs is included.

Mark, W. D.↗

DOE OSTI2020

CONTROLLED END GAS AUTO IGNITION WITH EXHAUST GAS RECIRCULATION ON A STOICHIOMETRIC, SPARK IGNITED, NATURAL GAS ENGINE

The goal of this study is to address fundamental limitations to achieving diesel-like efficiencies in heavy duty on-highway natural gas (NG) engines. Engine knock and misfire are barriers to pathways leading to higher efficiency engines. This study explores enabling technologies for development of high efficiency stoichiometric, spark ignited, natural gas engines. These include design strategies for fast and stable combustion and higher dilution tolerance. Additionally, advanced control methodologies are implemented to maintain stable operation between knock and misfire limits. To implement controlled end- gas autoignition (C-EGAI) strategies a Combustion Intensity Metric (CIM) is used for ignition control with the use of a Woodward large engine control module (LECM). Tests were conducted using a single cylinder, variable compression ratio, cooperative fuel research (CFR) engine with baseline conditions of 900 RPM, engine load of 800 kPa indicated mean effective pressure (IMEP), and stoichiometric air/fuel ratio. Exhaust gas recirculation (EGR) tests were performed using a custom EGR system that simulates a high pressure EGR loop and can provide a range of EGR rates from 0 to 40%. The experimental measurements included the variance of EGR rate, compression ratio, engine speed, IMEP, and CIM. These five variables were optimized through a Modified Box- Benken design Surface Response Method (RSM), with brake efficiency as the merit function. A positive linear correlation between CIM and f-EGAI was identified. Consequently, CIM was used as the feedback control parameter for C-EGAI. As such, implementation of C-EGAI effectively allowed for the utilization of high EGR rates and CRs, controlling combustion between a narrower gap between knock and lean limits. The change from fixed to parametric ignition timing with CIM targeted select values of f-EGAI with an average coefficient of variance (COV) of peak pressure of 5.4. The RSM efficiency optimization concluded with operational conditions of 1080 RPM, 1150 kPa IMEP, 10.55:1 compression ratio, and 17.8% EGR rate with a brake efficiency of 21.3%. At this optimized point of peak performance, a f-EGAI for C-EGAI was observed at 34.1% heat release due to auto ignition, a knock onset crank angle value of 10.3° aTDC and ignition timing of - 24.7° aTDC. This work has demonstrated that combustion at a fixed f-EGAI can be maintained through advanced ignition control of CIM without experiencing heavy knocking events.

Cooperative Fuel Research Engine, Auto Ignition, E↗

DOE OSTI2025

Requirements on the gain calibration for LiteBIRD polarisation data with blind component separation

The detection of primordial B modes of the cosmic microwave background (CMB) could provide information about the early stages of the Universe's evolution. The faintness of this signal requires exquisite calibration accuracy and control of instrumental systematic effects which otherwise could bias the measurements. In this work, we study the impact of an imperfect relative polarisation gain calibration on the recovered value of the tensor-to-scalar ratio r for the LiteBIRD experiment, through the application of the blind Needlet Internal Linear Combination (NILC) foreground-cleaning method. We derive requirements on the relative calibration accuracy of the overall polarisation gain (Δg ν ) for each LiteBIRD frequency channel. Our results show that minimum variance techniques, as NILC, are less sensitive to systematic gain calibration uncertainties compared to a parametric approach, if the latter is not equipped with a proper modelling of these instrumental effects. In this study, the most stringent requirements are found in the channels where the CMB signal is relatively brighter, with the tightest constraints at 166 GHz (Δg ν ≈ 0.16%). This differs from the outcome of an analogous analysis performed with a parametric method, where the tightest requirements are obtained for the foreground-dominated channels. Gain calibration uncertainties, corresponding to the derived requirements, are then simultaneously propagated into all frequency channels. By doing so, we find that the overall impact on estimated r is lower than the total gain systematic budget for LiteBIRD approximately by a factor 5, due to the correlations of the impacts of gain calibration uncertainties in different frequency channels. In order to decouple the systematic effect from the specific choice of the model, we derive the requirements assuming constant spectral parameters for the foreground emission. To assess the robustness of the obtained results against more realistic scenarios, we repeat the analysis assuming sky models of intermediate and high complexity. In these further cases, we adopt an optimised NILC pipeline, called the Multi-Clustering NILC (MC-NILC). We find that the impact of gain calibration uncertainties on r is lower than the LiteBIRD gain systematics budget for the intermediate-complexity sky model. For the high-complexity case, instead, it would be necessary to tighten the requirements by a factor 1.8.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Near-Efficient and Non-Asymptotic Multiway Inference

We establish non-asymptotic efficiency guarantees for tensor decomposition–based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference , the estimation of the full distributional parameter tensor, and (ii) multiway analysis , the recovery of its canonical polyadic (CP) decomposition factors. Our main result shows that in the rank-one setting, a rank-constrained maximum-likelihood estimator achieves multiway analysis with variance matching the Cramér–Rao Lower Bound (CRLB) up to absolute constants and logarithmic factors. This provides a general framework for studying “near-efficient” multiway estimators in finite-sample settings. For higher ranks, we illustrate that our multiway estimator may not attain the CRLB; nevertheless, CP-based parametric inference remains nearly minimax optimal, with error bounds that improve on prior work by offering more favorable dependence on the CP rank. Numerical experiments corroborate near-efficiency in the rank-one case and highlight the efficiency gap in higher-rank scenarios.

97 MATHEMATICS AND COMPUTING↗