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At least 631 records · Page 35

BAYESIAN CALIBRATION OF SAFETY CODES USING DATA FROM SEPARATE-AND INTEGRAL EFFECTS TESTS

Large-scale system codes for simulation of safety performance of nuclear plants may contain parameters whose values are not known very accurately. In order to be able to use the results of these simulation codes with confidence, it is important to learn how the uncertainty on the values of these parameters affects the output of the codes. New information from tests or operating experience is incorporated into safety codes by a process known as calibration, which reduces uncertainty in the output of the safety code, and thereby improves its support for decision-making. Modern analysis capabilities afford very significant improvements on classical ways of doing calibration, and the work reported here implements some of those improvements. The key innovation has come from development of safety code surrogate model (code emulator) construction and prediction algorithms. A surrogate is needed for calibration of plant-scale simulation codes because the multivariate nature of the problem (i.e., the need to adjust multiple uncertain parameters at once to fit multiple pieces of new information) calls for multiple evaluations of performance, which, for a computation-intensive model, makes calibration very computation-intensive. Use of a fast surrogate makes the calibration processes used here with Markov Chain Monte Carlo (MCMC) sampling feasible. Moreover, most traditional surrogates do not provide uncertainty information along with their predictions, but the Gaussian Process (GP) based code surrogates used here do. This improves the soundness of the code calibration process. Results are demonstrated on a simplified scenario with data from Separate and Integral Effect Tests.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Calibration of a Passive Neutron Counter with {sup 242}Pu Standards - 16450

At the Los Alamos National Laboratory TA 55 facility, a large quantity of Heat Source (HS) and MT42 (primarily {sup 242}Pu) has been designated for disposal as TRU waste. The waste, to be packaged in either 55 gal drums or Pipe Overpack Containers (POCs), is scheduled to be assayed with the TA 55 HENC 3 system. The system is owned and operated by the Nuclear Waste Partnership (NWP) under a contract with the Carlsbad DoE field office. The HENC 3 is a combined passive neutron/gamma assay system. The neutron component of the system was previously calibrated up to 21.9 g of {sup 240}Pu effective. This corresponds to approximately 9 g of typical HS plutonium and 13 g of MT42 waste. In order to reduce packaging efforts and radiation dose for waste handling personnel, LANL has requested an increase in the HENC 3 calibration limit to approximate the maximum allowable shipping and storage limits for TRU waste. To increase the limits, NWP has obtained the use of well characterized MT42 source materials. The sources, developed and owned by LANL, range from to 5 g to 200 g of plutonium enriched to 86.6% {sup 242}Pu. Using these sources in combination, multiple measurements were performed with both 55-gal drums and POCs to determine their suitability for extending the neutron calibration range of the system. The results of the measurements were (1) compared to the existing calibration for consistency and (2) used to extend the calibration range to 307 g of {sup 240}Pu effective. This report will discuss the elements of the neutron component of the HENC 3 system, the calibration extension effort, problems encountered, and the results of the measurements. As a result of the extension, HS and MT42 materials can be assayed in 55-gal drums and POCs up to their allowable shipping limits. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

SISTec: Mathematical Calibration of Large Clearance Monitors - 18265

One major path for clearance of large amount of waste arising from the decommission of nuclear power plants is based on measurement with large clearance monitors (also known as free release measurement facilities). These devices utilize multi-detector plastic scintillator arrays (large clearance monitors can consist of up to 24 plastic scintillators) to offer both, extremely low minimum detectable activities (MDA) and short measurement times for waste packages weighing up to one metric ton. However, a major problem with these devices is to obtain nuclide specific efficiencies, especially for geometrically complex large waste packages. Normal procedure for estimating the efficiency is to device dummy waste packages and attach point sources with well-known activities to unfavourable positions in these packages. In accordance with this procedure, calibration factors can be derived in a radiological conservative way. Devising such test dummies is not always possible and the procedure is prone to generating large measurement uncertainties. In this publication, we propose a new method to derive calibration factors by means of the Los Alamos National Laboratory (LANL) simulation tool Monte Carlo N-Particle (MCNP) and a statistical-phenomenological model for the detector characterization. In a multi-step approach, first the detector response for a distribution of activity in a waste package is calculated and subsequently the detectors are mathematically characterized. Applying state of the art statistical and optimizing procedures, parameters for the detector response are derived in a self-consistent way. This also allows to rigorously propagate the uncertainties to the final calculated calibration factors according to the Guide to the Expression of Uncertainty in Measurement (GUM supplement 1). To validate the derived parameters for the detector characterization a minimally invasive experimental setup was devised and installed into the large clearance monitor. It consisted of an aluminum swivel arm which could position point sources to the relevant coordinates. The so collected measurement data not only allowed to investigate the precision of the calculated calibration factors, but also to probe the location of concentrated activity sources in the waste package. Furthermore, data on measurements with dummy waste packages were collected to test the reproducibility of well-known calibration factors. We present the software tool SIStec, which will provide an intuitive user-interface to generate and simulate waste package models and execute the above-mentioned method. Using SIStec, different scenarios for the distribution of activity in the waste package can be probed. This will also allow to optimize the clearance process on various levels. For example, measurement time for pre-measurements can be reduced in exchange for unfavourable calibration factors, which would still allow to meet the regulator limits for clearance. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Spatiotemporal Automatic Calibration of Infrastructure Lidar, Radar, and Camera with a Global Navigation Satellite System: Preprint

Robust and accurate perception is important for modern intelligent transportation systems (ITS), which use sensors of various modalities for data fusion to create a digital twin of an intersection. Sensor calibration is an important process that creates a unified coordinate frame for the sensor output data so that it can be used for data fusion. Classical approaches for sensor calibration are time-consuming, require an overlapping field of view for feature matching, and are not feasible for ITS application as they cause disruptions in the flow of traffic. In this paper, we present a spatiotemporal automatic calibration approach to calibrate multiple infrastructure lidar, radar, and cameras installed at a traffic intersection. The approach uses global navigation satellite system (GNSS) positioning information shared by connected vehicles, and when the vehicle is detected by the sensor, we match the sensor detections with the GNSS coordinates. The proposed algorithm is evaluated with a real-world dataset utilizing detections from two radars, cameras, and lidars with a test vehicle instrumented with a post-processing kinematic (PPK)-corrected GNSS driving past the sensors installed at a four-way traffic intersection. The experimental results show that the proposed automatic calibration approach can achieve the transformation with a root mean squared error of less than 0.5 for radar and lidar and less than 2 for camera detections. The ability to rapidly calibrate sensors not only benefits initial installations, but can also be used for system health monitoring, while utilizing available connected vehicle data to test the real-time sensor fidelity and operational status.

ADVANCED PROPULSION SYSTEMS↗

Application of Indirect Quantification of 133mXe to Calibration of HPGe Detector

The INL Noble Gas Laboratory provides intercomparison samples for the noble gas analysis laboratories as part of the CTBTO PrepCom IMS. Xe-133m is one of the four relevant radionuclides in nuclear explosion monitoring. Without commercially available Xe-133m calibration standards laboratories must create and improve calibration methods. Improvements in calibration methods at the INL NGL benefit the CTBTO PrepCom through better certified values for Xe-133m intercomparison samples. Calibration of High Purity Germanium detectors for Xe-133m quantification is complicated by the coexistence of Xe-133 in samples under analysis. Xe-133 is typically produced in larger quantities, has higher gamma emission probabilities, and its gammas are detected more efficiently than Xe-133m. Xe-133m activity of samples can be indirectly inferred through the 133:133m activity ratio of a batch of material, and the Xe-133 counts in the assay of a small aliquot of the same material. This indirect quantification method can be leveraged to perform detector calibrations for quantification of Xe-133m. Calibrations can be performed by inferring the Xe-133m to certify the sample, and direct counting to determine detector efficiency. A comparison of method results will be shown.

133mXe↗

Radioxenon detector calibration spike production and delivery systems

Abstract Beta-Gamma coincidence radioxenon detectors must be calibrated for each of the four-radioxenon isotopes (135Xe, 133Xe, 133mXe, and 131mXe). Without a proper calibration, there is potential for the misidentification of the amount of each isotope detected. It is important to accurately determine the amount of each radioxenon isotope, as the ratios can be used to distinguish between an anthropogenic source and a nuclear explosion. We have developed a xenon calibration system (XeCalS) that produces calibration spikes of known activity and pressure for field calibration of detectors. The activity concentrations of these calibration spikes are measured using a beta-gamma coincidence detector and a high purity germanium (HPGe) detector. We will present the results from the development and commissioning of XeCalS, along with the future plans for a portable spike implementation system.

beta-gamma coincidence detector↗

Absolute mass calibration of fission product distributions measured with the E-$v$ method

The mass calibration of fission product distributions measured with the energy–velocity (E-v) method constitutes a technical challenge. The energy loss of the fission fragments in the various dead layers of the spectrometer and other sources of pulse-height defects of the energy detectors are a significant source of systematic uncertainty in the mass calculations used to determine the measured fission product yields. Here, in this study, the absolute calibration of the fission mass distributions is accomplished by measuring prompt γ-rays in coincidence with the fission fragments. This allows for the direct calibration of the mass spectra and eliminates any dependence on potentially complicated energy corrections. The first test measurement was performed at the Los Alamos Neutron Science Center employing the SPectrometer for Ion DEtermination in fission Research (SPIDER). SPIDER is a 2E-2v spectrometer designed for measuring independent fission product yields from neutron-induced fission. In this test, the single-arm SPIDER (E-v) system and an array of 252 Cf sources were used. The single-arm system consisted of two time pick-off detectors for measuring the time-of-flight of the fission fragments and a double-sided silicon strip detector (DSSD) for measuring the kinetic energy. Characteristic γ-rays from fission fragments were detected using three high-purity germanium (HPGe) detectors. For the mass calibration, γ–mass coincidence events from twelve product isotopes were used. The measured FPYs from 252 Cf spontaneous fission were found to be in excellent agreement with the evaluated data after applying the absolute mass calibration. From the γ–mass coincidence events, the mass resolution of the system was also extracted. An average mass resolution of ~1.4 AMU (FWHM) for the light fragments and ~2.4 AMU (FWHM) for the heavy fragments were found. This was the first in-situ calibration and characterization of the SPIDER spectrometer, which paves the way for high-quality FPY measurements with this instrument.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Emulator-based Bayesian calibration of a subglacial drainage model

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

58 GEOSCIENCES↗

Machine Learning Calibration of Groundwater Table Depth in ELM: Impact on Land Surface Hydrology and Land‐Atmosphere Fluxes

Accurate representation of groundwater table depth (GWTD) is crucial for simulating hydrological cycling in Earth system models (ESM). Nevertheless, there is a notable gap in the literature regarding the validation of GWTD simulations in ESMs and their subsequent impact on downstream hydrological components. This study explores the calibration of parameterization of global GWTD using machine learning within the Energy Exascale Earth System Model (E3SM) Land Model (ELM). Despite achieving significant gains in simulating GWTD through calibration, offline ELM simulations unexpectedly show that these improvements do not translate to substantial enhancements in model performance for other key hydrological variables, including soil moisture (SM), runoff, groundwater contribution to runoff or base flow index (BFI), and evapotranspiration and its partitioning. The performance in SM and runoff was even degraded in some regions, while BFI was mostly overestimated. Although there is significant improvement in GWTD within the critical range of 1–5 m, where groundwater traditionally influences land surface energy fluxes, these improvements occurred mostly in humid areas where the impact of GWTD on surface processes is minimal. Although the impacts of model calibration are generally small in offline ELM simulations, coupled land-atmosphere simulations exhibit much stronger responses to GWTD calibration, highlighting the role of land-atmosphere feedbacks in Earth system modeling. These findings underscore the need for integrated calibration strategies that simultaneously optimize multiple hydrological variables. However, if a single-variable approach is necessary, it is crucial to establish clear priorities for calibration, identifying the most critical variables that have the greatest impact on overall model performance.

Fang, Yilin [Pacific Northwest National Laboratory↗

Planck 2015 results: VIII. High Frequency Instrument data processing: Calibration and maps

This paper describes the processing applied to the cleaned, time-ordered information obtained from the Planck High Frequency Instrument (HFI) with the aim of producing photometrically calibrated maps in temperature and (for the first time) in polarization. The data from the entire 2.5-year HFI mission include almost five full-sky surveys. HFI observes the sky over a broad range of frequencies, from 100 to 857 GHz. To obtain the best accuracy on the calibration over such a large range, two different photometric calibration schemes have been used. The 545 and 857 GHz data are calibrated using models of planetary atmospheric emission. The lower frequencies (from 100 to 353 GHz) are calibrated using the time-variable cosmological microwave background dipole, which we call the orbital dipole. This source of calibration only depends on the satellite velocity with respect to the solar system. Using a CMB temperature of T CMB = 2.7255 ± 0.0006 K, it permits an independent measurement of the amplitude of the CMB solar dipole (3364.3 ± 1.5 μK), which is approximatively 1σ higher than the WMAP measurement with a direction that is consistent between the two experiments. We describe the pipeline used to produce the maps of intensity and linear polarization from the HFI timelines, and the scheme used to set the zero level of the maps a posteriori. We also summarize the noise characteristics of the HFI maps in the 2015 Planck data release and present some null tests to assess their quality. Lastly, we discuss the major systematic effects and in particular the leakage induced by flux mismatch between the detectors that leads to spurious polarization signal.

79 ASTRONOMY AND ASTROPHYSICS↗

Calibrating Microscopic Car-Following Models for Adaptive Cruise Control Vehicles: Multiobjective Approach

Adaptive cruise control (ACC) vehicles are the first step toward comprehensive vehicle automation. However, the impacts of such vehicles on the underlying traffic flow are not yet clear. Therefore, it is of interest to accurately model vehicle-level dynamics of commercially available ACC vehicles so that they may be used in further modeling efforts to quantify the impact of commercially available ACC vehicles on traffic flow. Importantly, not only model selection but also the calibration approach and error metric used for calibration are critical to accurately model ACC vehicle behavior. In this work, we explore the question of how to calibrate car following models to describe ACC vehicle dynamics. Specifically, we apply a multi-objective calibration approach to understand the tradeoff between calibrating model parameters to minimize speed error vs. spacing error. Three different car-following models are calibrated for data from six vehicles. The results are in line with recent literature and verify that targeting a low spacing error does not compromise the speed accuracy whether the opposite is not true for modeling ACC vehicle dynamics.

33 ADVANCED PROPULSION SYSTEMS↗

High precision tilt stage as a key element to a universal test mirror for characterization and calibration of slope measuring instruments

The ultimate performance of surface slope metrology instrumentation, such as long trace profilers and auto-collimator based deflectometers, is limited by systematic errors that are increased when the entire angular range is used for metrology of significantly curved optics. At the ALS X-Ray Optics Laboratory, in collaboration with the HZB/BESSY-II and PTB (Germany) metrology teams, we are working on a calibration method for deflectometers, based on a concept of a universal test mirror (UTM) [V. V. Yashchuk et al., Proc. SPIE 6704, 67040A (2007)]. Potentially, the UTM method provides high performance calibration and accounts for peculiarities of the optics under test (e.g., slope distribution) and the experimental arrangement (e.g., the distance between the sensor and the optic under test). At the same time, the UTM calibration method is inherently universal, applicable to a variety of optics and experimental arrangements. In this work, we present the results of tests with a key component of the UTM system, a custom high precision tilt stage, which has been recently developed in collaboration with Physik Instrumente, GmbH. The tests have demonstrated high performance of the stage and its capability (after additional calibration) to provide angular calibration of surface slope measuring profilers over the entire instrumental dynamic range with absolute accuracy better than 30 nrad. The details of the stage design and tests are presented. We also discuss the foundation of the UTM method and calibration algorithm, as well as the possible design of a full scale UTM system.

47 OTHER INSTRUMENTATION↗

A free-standing wire scattering technique to monitor calibration variations of the DIII-D density profile reflectometer

Real-time phase calibration of the ITER profile reflectometer is essential due to the long plasma duration and expected waveguide path length changes during a discharge. Progress has been recently made in addressing this issue by employing a phase calibration technique on DIII-D that monitors calibration variations that occur during each plasma discharge. By installing a thin free-standing metallic wire (1 mm diameter) near the end of the overmoded waveguide transmission system (oriented perpendicular to the waveguide axis), the round-trip phase shift from the wire is detected simultaneously with the plasma phase shifts. Variations in the reflectometer round trip path length (-26 m) are then calculated after each DIII-D plasma discharge, allowing the calibration phase to be accurately monitored and updated. The round-trip reflectometer path length is observed to vary by -3 mm (root mean square value) during a typical DIII-D discharge. Using the variations in calibration phase, the density profile measurement accuracy can be improved. Since the wire retro-reflected power is -0.01 of the plasma signal, minimal effect is observed on the reflected signal from the plasma. Importantly, through a suitable choice in wire diameter, the calibration signal can be made approximately independent of the V-band reflectometer launch polarization. Furthermore, this is particularly important on DIII-D since orthogonal X- and O-mode polarized beams are coupled into the same transmission waveguide and launch antenna.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Four-dimensional calibration turntable of the motional Stark effect diagnostic on EAST

The motional Stark effect (MSE) diagnostic is applied to measure the safety factor q and current density profile of a tokamak device, which are important parameters in realizing the high-performance and long-pulse steady state of a tokamak. A single-channel MSE diagnostic based on dual photoelastic modulators, whose sightline meets with the neutral beam injection at a major radius of R = 2.12 m, has been built for the D window of the Experimental Advanced Superconducting Tokamak (EAST). According to the requirements of MSE diagnostic polarimetric calibration, a high-precision four-dimensional calibration turntable, driven by four stepping motors and controlled by software running on the computer, was designed for EAST. The turntable allows us to rapidly calibrate the MSE diagnostic in a series of positions and angles during EAST maintenance. The turntable can move in four dimensions of translation, yaw, pitch, and roll of the polarizer and can create linearly polarized light at any given angle with accuracy of ~0.05° for the MSE system offline calibration. As a result, the experimental results of the MSE diagnostic calibration in the laboratory show that the turntable has the advantages of high positioning accuracy, flexible spatial movement, and convenient control and fully meets the calibration requirements of an MSE diagnosis system.

47 OTHER INSTRUMENTATION↗

Improving gas adsorption modeling for MOFs by local calibration of Hubbard U parameters

While computational screening with density functional theory (DFT) is frequently employed for the screening of metal–organic frameworks (MOFs) for gas separation and storage, commonly applied generalized gradient approximations (GGAs) exhibit self-interaction errors, which hinder the predictions of adsorption energies. We investigate the Hubbard U parameter to augment DFT calculations for full periodic MOFs, targeting a more precise modeling of gas molecule–MOF interactions, specifically for N2, CO2, and O2. We introduce a calibration scheme for the U parameter, which is tailored for each MOF, by leveraging higher-level calculations on the secondary building unit (SBU) of the MOF. When applied to the full periodic MOF, the U parameter calibrated against hybrid HSE06 calculations of SBUs successfully reproduces hybrid-quality calculations of the adsorption energy of the periodic MOF. The mean absolute deviation of adsorption energies reduces from 0.13 eV for a standard GGA treatment to 0.06 eV with the calibrated U, demonstrating the utility of the calibration procedure when applied to the full MOF structure. Furthermore, attempting to use coupled cluster singles and doubles with perturbative triples calculations of isolated SBUs for this calibration procedure shows varying degrees of success in predicting the experimental heat of adsorption. It improves accuracy for N2 adsorption for cases of overbinding, whereas its impact on CO2 is minimal, and ambiguities in spin state assignment hinder consistent improvements of O2 adsorption. Our findings emphasize the limitations of cluster models and advocate the use of full periodic MOF systems with a calibrated U parameter, providing a more comprehensive understanding of gas adsorption in MOFs.

Chemistry↗

Calibrating a finite-strain phase-field model of fracture for bonded granular materials with uncertainty quantification

To study the mechanical behavior of mock high explosives, an experimental and simulation program was developed to calibrate, with quantified uncertainty, a material model of the bonded granular material Idoxuridine and nitroplasticized Estane-5703. This paper reports on the efficacy of such a framework as a generalizable methodology for calibrating material models against experimental data with uncertainty quantification. Additionally, this paper studies the effect of two manufacturing temperatures and three initial granular configurations on the unconfined compressive behavior of the resulting bonded granular materials. In each of these cases, the same calibration framework was used; in that, hundreds of high-fidelity direct numerical simulations using a new, graphics processing unit-enabled, high-performance finite element method software, Ratel, were run to calibrate a finite-strain phase-field fracture model against experimental data. It was found that manufacturing temperature influenced the elastic response of the mock high explosives, with higher temperatures yielding a stiffer response. By contrast, it was found that the initial configuration of the grains had a negligible impact on the overall behavior of the mock high explosives though it remains possible that local damage accumulation within the specimens could be altered by the initial configurations. Overall, the calibration framework was successful at creating well-calibrated models, showing its usefulness as an engineering and scientific tool.

36 MATERIALS SCIENCE↗

The Simons Observatory: gain, bandpass and polarization-angle calibration requirements for B-mode searches

We quantify the calibration requirements for systematic uncertainties for next-generation ground-based observatories targeting the large-angle B-mode polarization of the Cosmic Microwave Background, with a focus on the Simons Observatory (SO). We explore uncertainties on gain calibration, bandpass center frequencies, and polarization angles, including the frequency variation of the latter across the bandpass. We find that gain calibration and bandpass center frequencies must be known to percent levels or less to avoid biases on the tensor-to-scalar ratio r on the order of Δ r∼10-3, in line with previous findings. Polarization angles must be calibrated to the level of a few tenths of a degree, while their frequency variation between the edges of the band must be known to O(10) degrees. Given the tightness of these calibration requirements, we explore the level to which residual uncertainties on these systematics would affect the final constraints on r if included in the data model and marginalized over. We find that the additional parameter freedom does not degrade the final constraints on r significantly, broadening the error bar by O(10%) at most. We validate these results by reanalyzing the latest publicly available data from the collaboration within an extended parameter space covering both cosmological, foreground and systematic parameters. Finally, our results are discussed in light of the instrument design and calibration studies carried out within SO.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Full calibration of the tomographic redshift distribution from the HSC PDR3 Shape Catalog with DESI

The calibration of tomographic redshift distributionsis essential for cosmological analysis of weak lensing data.In this work, we calibrate all four tomographic bins of the Hyper Suprime Camera (HSC) weak lensing catalog with the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 and 2 using the clustering redshifts technique. We include z > 1.2 redshift sources such as emission line galaxies (ELG) and quasars (QSO) sources in our calibration, which were not available in the previous HSC calibration (Rau et al. (2022), Mon. Not. Roy. Astron. Soc. 524 (2023) 5109), allowing a complete calibration of all the redshift bins. We find the first tomographic bin exhibits a small shift towards low redshifts. The second bin is in good agreement with the photometric calibration, while third and fourth bin exhibit a shift towards higher redshifts. However, these shifts are considerably smaller than the shifts obtained in the HSC Year 3 cosmic shear analyses. We evaluate the impact of galaxy bias and magnification effects from all the samples on the measurements, finding them to be small, and we propose corrections to reduce them further. Specifically, we relax the assumption of linear bias and only assume no redshift evolution of the cross-correlation coefficient, allowing us to leverage smaller clustering scales. We model the redshift distributions with splines and compare our results to previous analyses as well as to other parameterizations found in literature. For the two high-redshift tomographic bins, we find the shifts to higher redshifts with respect to the measurements performed in Rau+2022 to be Δz$_{3}$ =-0.039$^{+0.020}$$_{-0.021}$ and Δz$_{4}$ = -0.048$^{+0.012}$$_{-0.012}$.

Choppin de Janvry, J. [LBL, Berkeley; UC, Berkeley↗