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At least 127 records · Page 7

The DESI N -body Simulation Project – II. Suppressing sample variance with fast simulations

ABSTRACT Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise three-dimensional map of our Universe. The survey effective volume reaches $\sim 20\, h^{-3}\, \mathrm{Gpc}^{3}$. It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. AbacusSummit is a suite of high-resolution dark-matter-only simulations designed for this purpose, with $200\, h^{-3}\, \mathrm{Gpc}^{3}$ (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide a more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi-N-body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variance than the expected DESI statistical variance at the scales we are interested in, e.g. $k \lt 0.3\, h\, \mathrm{Mpc}^{-1}$ for the halo power spectrum. In addition, it can significantly suppress the sample variance of the halo bispectrum. We further generalize the method for other cosmologies with only one realization in AbacusSummit suite to extend the effective volume ∼20 times. In summary, our proposed strategy of combining high-fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data.

cosmology: theory↗

The DESI N -body simulation project – I. Testing the robustness of simulations for the DESI dark time survey

ABSTRACT Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogues to validate data analysis pipelines and identify potential systematics. We compare three N-body simulation codes, abacus, gadget-2, and swift, to investigate the regimes in which their results agree. We run N-body simulations at three different mass resolutions, 6.25 × 108, 2.11 × 109, and 5.00 × 109 h−1 M⊙, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the Dark Energy Spectroscopic Instrument (DESI) statistical error for $s\ \gt\ 20\ h^{-1}$ Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of 2.1 × 109 h−1 M⊙ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than $20\ h^{-1}$ Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1 per cent for k ≤ 10 h Mpc−1. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi-N-body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy–halo relation will be presented in a follow-up study.

79 ASTRONOMY AND ASTROPHYSICS↗

Dark Energy Survey Year 3 results: Simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak lensing mass maps. II. cosmological results

Here, we present a simulation-based cosmological analysis using a combination of Gaussian and non-Gaussian statistics of the weak lensing mass (convergence) maps from the first three years of the Dark Energy Survey. We implement the following: (1) second and third moments; (2) wavelet phase harmonics; (3) the scattering transform. Our analysis is fully based on simulations, spans a space of seven 𝑤 Cold Dark Matter (𝑤⁢ CDM) cosmological parameters, and forward models the most relevant sources of systematics inherent in the data: masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration. We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a simulation-based inference approach. Including and combining different non-Gaussian statistics is a powerful tool that strongly improves constraints over Gaussian statistics (in our case, the second moments); in particular, the figure of merit (𝑆 8 , Ω m ) is improved by 70% (Λ ⁢CDM) and 90% (𝑤 ⁢CDM). When all the summary statistics are combined, we achieve a 2% constraint on the amplitude of fluctuations parameter 𝑆 8 ≡ 𝜎 8 ⁢(Ω m /0.3) 0.5 , obtaining 𝑆 8 = 0.794 ±0.017 (Λ⁢ CDM) and 𝑆 8 = 0.817 ±0.021 (𝑤 ⁢CDM), and a ∼10% constraint on Ω m , obtaining Ω m =0.259 ±0.025 (Λ ⁢CDM) and Ω m = 0.273 ±0.029 (𝑤⁢ CDM). In the context of the 𝑤⁢ CDM scenario, these statistics also strengthen the constraints on the parameter 𝑤, obtaining 𝑤 <−0.72. The constraints from different statistics are shown to be internally consistent (with a 𝑝-value>0.1 for all combinations of statistics examined). We compare our results to other weak lensing results from the first three years of the Dark Energy Survey data, finding good consistency; we also compare with results from external datasets, such as planck constraints from the cosmic microwave background, finding statistical agreement, with discrepancies no greater than <2.2⁢𝜎.

79 ASTRONOMY AND ASTROPHYSICS↗

Networked HIL Simulation System for Modeling Large-scale Power Systems

This paper presents a networked hardware-in-the-loop (HIL) simulation system for modeling large-scale power systems. Researchers have developed many HIL test systems for power systems in recent years. Those test systems can model both microsecond-level dynamic responses of power electronic systems and millisecond-level transients of transmission and distribution grids. By integrating individual HIL test systems into a network of HIL test systems, we can create large-scale power grid digital twins with flexible structures at required modeling resolution that fits for a wide range of system operating conditions. This will not only significantly reduce the need for field tests when developing new technologies but also greatly shorten the model development cycle. In this paper, we present a networked OPAL-RT based HIL test system for developing transmission-distribution coordinative Volt-VAr regulation technologies as an example to illustrate system setups, communication requirements among different HIL simulation systems, and system connection mechanisms. Impacts of communication delays, information exchange cycles, and computing delays are illustrated. Simulation results show that the performance of a networked HIL test system is satisfactory.

Xie, Fuhong↗

Control and Simulation of a Grid-Forming Inverter for Hybrid PV-Battery Plants in Power System Black Start

Power system restoration is an important part of system planning. Power utilities are required to maintain black start capable generators that can energize the transmission system and provide cranking power to non-blackstart capable generators. Traditionally, hydro and diesel units are used as black start capable generators. With the increased penetration of bulk size solar farms, inverter based generation can play an important role in faster and parallel black start thus ensuring system can be brought back into service without the conventional delays that can be expected with limited black start generators. Inverter-based photovoltaic (PV) power plants have advantages that are suitable for black start. This paper proposes the modeling, control, and simulation of a grid-forming inverter-based PV-battery power plant that can be used as a black start unit. The inverter control includes both primary and secondary control loops to imitate the control of a conventional synchronous machine. The proposed approach is verified using a test system modified from the IEEE 9-bus system in the time-domain electromagnetic transient simulation tool PSCAD. The simulation results shows voltage and frequency stability during a multi-step black-start and network energization process.

Nguyen, Quan H.↗

BESTEST-GSR (Building Energy Simulation Test - Generation Simulation and Reporting) 2023 [SWR 18-23]

Building Energy Simulation Test (BESTEST) is an NREL-developed method to validate the qualitative performance of different whole building simulations engines relative to each other. https://www.nrel.gov/docs/legosti/old/6231.pdf The purpose of this repository is to generate BESTEST test case models, run simulations, and populate data for ASHRAE Standard 140 reporting spreadsheets for EnergyPlus® based whole building simulation tools. It was originally setup for 2014 version of Standard 140. In May of 2022 it was updated to the 2020 version of Standard 140. This update included updates and additions to existing test suites, the bulk of which was in Section 5.2 (Building Thermal Envelope and Fabric Load Tests). We did not add Section 5.5 Airside HVAC Equipment Performance, but we hope to add that later in 2022. At some point we also hope to add Section 5.2.4 ground modeling, which is currently excluded. Supported Tools The default IDF generation is based on the OpenStudio® CLI, but the workflow supports a 'Bring your own IDF' use case. Additionally, for non-EnergyPlus® based tools the post processing scripts can be used if simulation results are provided as a CSV file.The scripts on this repository should work on Mac, Windows, and Linux. Dependencies Install OpenStudio® 3.4.0 make sure command line can recognize the 'openstudio' command This includes EnergyPlus® 22.1 Install Ruby on your system if it isn't already setup. 2.7 is used for development but other versions may work Since OpenStudio has its own embedded Ruby, which is used for running measures, you don't necessarily have to use a version of Ruby supported by OpenStudio. Install RubyXL Ruby gem This is used to modify Microsoft Excel spreadsheets Install Parallel Ruby gem This allows the CLI to run simulations in parallel

Goldwasser, David↗

Intelligent resolution: Integrating Cryo-EM with AI-driven multi-resolution simulations to observe the severe acute respiratory syndrome coronavirus-2 replication-transcription machinery in action

The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) replication transcription complex (RTC) is a multi-domain protein responsible for replicating and transcribing the viral mRNA inside a human cell. Attacking RTC function with pharmaceutical compounds is a pathway to treating COVID-19. Conventional tools, e.g., cryo-electron microscopy and all-atom molecular dynamics (AAMD), do not provide sufficiently high resolution or timescale to capture important dynamics of this molecular machine. Consequently, we develop an innovative workflow that bridges the gap between these resolutions, using mesoscale fluctuating finite element analysis (FFEA) continuum simulations and a hierarchy of AI-methods that continually learn and infer features for maintaining consistency between AAMD and FFEA simulations. We leverage a multi-site distributed workflow manager to orchestrate AI, FFEA, and AAMD jobs, providing optimal resource utilization across HPC centers. Our study provides unprecedented access to study the SARS-CoV-2 RTC machinery, while providing general capability for AI-enabled multi-resolution simulations at scale.

Trifan, Anda↗

Broadband (0–5 Hz) Fully Deterministic 3D Ground‐Motion Simulations of a Magnitude 7.0 Hayward Fault Earthquake: Comparison with Empirical Ground‐Motion Models and 3D Path and Site Effects from Source Normalized Intensities

We report on high‐performance computing (HPC) fully deterministic simulation of ground motions for a moment magnitude (⁠Mw⁠) 7.0 scenario earthquake on the Hayward fault resolved to 5 Hz using the SW4 finite‐difference code. We computed motions obeying physics‐based 3D wave propagation at a regional scale with an Mw 7.0 kinematic rupture model generated following Graves and Pitarka (2016). Both plane‐layered (1D) and 3D Earth models were considered, with 3D subsurface material properties and topography interpolated from a model of the U.S. Geological Survey (USGS). The resulting ground‐motion intensities cover a broader frequency range than typically considered in regional‐scale simulations, including higher frequencies relevant for engineering analysis of structures. Median intensities for sites across the domain are within the reported between‐event uncertainties (⁠τ⁠) of ground‐motion models (GMMs) across spectral periods 0.2–10 s (frequencies 0.1–5 Hz). The within‐event standard deviation ϕ of ground‐motion intensity measurement residuals range 0.2–0.5 natural log units with values consistently larger for the 3D model. Source‐normalized ratios of intensities (3D/1D) reveal patterns of path and site effects that are correlated with known geologic structure. These results demonstrate that earthquake simulations with fully deterministic wave propagation in 3D Earth models on HPC platforms produce broadband ground motions with median and within‐event aleatory variability consistent with empirical models. Systematic intensity variations for the 3D model caused by path and site effects suggest that these epistemic effects can be estimated and removed to reduce variation in site‐specific hazard estimates. This study motivates future work to evaluate the validity of the USGS 3D model and investigate the development of path and site corrections by running more scenarios.

Rodgers, Arthur J.↗

Investigation of Hydrometeor Distributions in Continental and Maritime Storm Systems: Application of Cloud-Resolving Simulations, a Polarimetric Scanning Radar Simulator and Polarimetric Radar Observations

Detailed observations from DOE ARM field campaigns were used to evaluate and improve microphysical and dynamic fields simulated by 3D Cloud Resolving Models (CRMs), employing both bulk and size-resolved bin microphysics. One of the main challenges in bridging the gap between observations and models is placing the analysis in a common framework. To address this, a polarimetric radar simulator was built, consisting of a forward operator to calculate model-consistent polarimetric radar fields, and an analysis package to calculate microphysical and dynamic fields from radar data in a self-consistent manner. The assumptions required for the transformation from model output to radar parameters were carefully considered and tested. It was found that although rain is fairly well captured by the forward model, ice characteristics are difficult to constrain. This polarimetric radar simulator, POLArimetric Radar Retrieval and Instrument Simulator (POLARRIS), was then applied to WRF simulations and polarimetric C-band radar observations from Darwin, Australia and the SGP site in Oklahoma. These two locations contrast maritime and mid-latitude continental convection respectively. POLARRIS was used with NASA Unified WRF simulations of the same storms in order to compare the observed land and ocean contrasts in microphysics and dynamics. An improved model framework for dynamic downscaling of large-scale aerosol products was also developed and applied to the NASA Unified WRF (NU-WRF) cloud resolving model. This improved framework was used to explore the effects of thermodynamic and aerosol invigoration in deep land and ocean convection through a series of sensitivity studies by perturbating aerosol (CCN) and convective available potential energy (CAPE). It was found that increases in aerosol concentrations yielded increases in low-density graupel in the maritime case and high-density hail in the continental case through riming by increased supercooled water. This result implies that native differences in aerosol concentrations may enhance the inherent contrast in riming effects between deep convective systems in the maritime and continental conditions. Formal publications were generated describing this research.

54 ENVIRONMENTAL SCIENCES↗

Developing and testing capabilities for simulating cases with heterogeneous land/water surfaces in a novel atmospheric large eddy simulation code

Large eddy simulations (LES) are the primary computational tool used to simulate high Reynolds number three-dimensional turbulent flows. In the context of earth system sciences, particularly atmospheric science, LES are uniquely able to resolve the scales of atmospheric motion that are key for building process-level understanding of boundary layer turbulence, atmosphere-surface interaction, clouds, and cloud-aerosol-chemistry interaction, and are a core limited-area modeling capability. Increasing demands are being placed on LES code bases as growing high performance computing resources allow LES to address a wider range of scientific problems. In addition, LES are emerging as a source of high-quality machine learning training data. These demands necessitate an agile and extensible code base that allows the model to quickly adapt to emergent needs. However, LES have largely relied on legacy Fortran code bases that lack flexibility. A new, Python-based LES capability called Predicting INteractions of Aerosol and Clouds in Large Eddy Simulation (PINACLES) has been developed as part of the Department of Energy’s Earth System Model Development (ESMD) program area’s Enabling Aerosol-cloud interactions at Global convection-permitting scalES (EAGLES) project. PINACLES was developed from the ground up with a philosophy of maximizing scientific throughput, by attempting to optimize for both model throughput and software extensibility. The initial development of PINACLES delivered a state-of-the-art idealized LES capability solving the non-hydrostatic anelastic equations of motion with doubly periodic boundary conditions and idealized homogenous surface boundary conditions. Here we provide a final report on the outcomes of a fiscal year 2021 Seed Laboratory Directed Research Project that extended PINACLES in two key ways. First, PINACLES was coupled to a state-of-the-art land surface model enabling it to simulate spatially inhomogeneous land-atmosphere interactions that are known to control key atmospheric processes. Second, the dynamical core of PINACLES was modified to permit non-periodic boundary conditions. This model enhancement enables simulation of realistic cases with boundary conditions prescribed from atmospheric reanalysis and enables nested simulations conducted on a hierarchy of computational domains with increasing resolution. Together, these extensions to PINACLES make it a formidable modeling capability and expand its potential application to diverse components of DOE’s atmospheric science portfolio.

42 ENGINEERING↗

High-Performance Simulation of Dynamic Hydrologic Exchange and Implications for Surrogate Flow and Reactive Transport Modeling in a Large River Corridor

Hydrologic exchange flows (HEFs) have environmental significance in riverine ecosystems. Key river channel factors that influence the spatial and temporal variations of HEFs include river stage, riverbed morphology, and riverbed hydraulic conductivity. However, their impacts on HEFs were often evaluated independently or on small scales. In this study, we numerically evaluated the combined interactions of these factors on HEFs using a high-performance simulator, PFLOTRAN, for subsurface flow and transport. The model covers 51 square kilometers of a selected river corridor with large sinuosity along the Hanford Reach of the Columbia River in Washington, US. Three years of spatially distributed hourly river stages were applied to the riverbed. Compared to the simulation when riverbed heterogeneity is not ignored, the simulation using homogeneous riverbed conductivity underestimated HEFs, especially upwelling from lateral features, and overestimated the mean residence times derived from particle tracking. To derive a surrogate model for the river corridor, we amended the widely used transient storage model (TSM) for riverine solute study at reach scale with reactions. By treating the whole river corridor as a batch reactor, the temporal changes in the exchange rate coefficient for the TSM were derived from the dynamic residence time estimated from the hourly PFLOTRAN results. The TSM results were evaluated against the effective concentrations in the hyporheic zone calculated from the PFLOTRAN simulations. Our results show that there is potential to parameterize surrogate models such as TSM amended with biogeochemical reactions while incorporating small-scale process understandings and the signature of time-varying streamflow to advance the mechanistic understanding of river corridor processes at reach to watershed scales. However, the assumption of a well-mixed storage zone for TSM should be revisited when redox-sensitive reactions in the storage zones play important roles in river corridor functioning.

Fang, Yilin↗

A nonlinear propulsion system simulation technique for piloted simulators

A real time digital simulation technique providing the capabilities needed to evaluate propulsion system performance and aircraft system interaction on NASA manned flight simulators, is discussed. A parameter correlation technique is used with real and pseudo dynamics in a stable integration convergence loop. The cycle time reported was 2.0 ms on one computer and 5.7 ms on the simulator computer. The model was found to be stable and accurate with time up to 50 ms. It is concluded that the program has generated a valuable simulation technology and flight simulator experience by providing an adequate level of detail to evaluate propulsion systems in a simulated flight environment.

Mihaloew, J. R.↗

Materials Requirements for Standard Lunar Highlands Regolith Simulants as Defined by the NASA Simulant Development Program

The development of surface technologies for NASA's human and robotic lunar program beyond 2010 has begun. The multitude of projects underway and future ones will soon rely on the availability of lunar regolith simulant materials chosen to simulate the characteristics of lunar regoliths in order to design, test and qualify prototype hardware and flight equipment. The selection and development of standard lunar regolith simulants (SLRS) for the use of NASA technology programs was one of the main recommendations of the 2005 Workshop on Lunar Regolith Simulant Materials at Marshall Space Flight Center. The realization of that objective is now underway through the NASA simulant development program at the Marshall Space Flight Center. The approach adopted to define materials requirements for standard simulants of regolith from the Highlands regions of the Moon will be presented along with a discussion of limitations inherent to such an endeavor.

Sibille, Laurent↗

An Orion/Ares I Launch and Ascent Simulation: One Segment of the Distributed Space Exploration Simulation (DSES)

This paper describes the architecture and implementation of a distributed launch and ascent simulation of NASA's Orion spacecraft and Ares I launch vehicle. This simulation is one segment of the Distributed Space Exploration Simulation (DSES) Project. The DSES project is a research and development collaboration between NASA centers which investigates technologies and processes for distributed simulation of complex space systems in support of NASA's Exploration Initiative. DSES is developing an integrated end-to-end simulation capability to support NASA development and deployment of new exploration spacecraft and missions. This paper describes the first in a collection of simulation capabilities that DSES will support.

Chung, Victoria I.↗

Validation of Multibody Program to Optimize Simulated Trajectories II Parachute Simulation with Interacting Forces

A capability to simulate trajectories of multiple interacting rigid bodies has been developed, tested and validated. This capability uses the Program to Optimize Simulated Trajectories II (POST 2). The standard version of POST 2 allows trajectory simulation of multiple bodies without force interaction. In the current implementation, the force interaction between the parachute and the suspended bodies has been modeled using flexible lines, allowing accurate trajectory simulation of the individual bodies in flight. The POST 2 multibody capability is intended to be general purpose and applicable to any parachute entry trajectory simulation. This research paper explains the motivation for multibody parachute simulation, discusses implementation methods, and presents validation of this capability.

Raiszadeh, Behzad↗

Effect of Simulant Type on the Absorptance and Emittance of Dusted Thermal Control Surfaces in a Simulated Lunar Environment

During the Apollo program the effects of lunar dust on thermal control surfaces was found to be more significant than anticipated, with several systems overheating due to deposition of dust on them. In an effort to reduce risk to future missions, a series of tests has been initiated to characterize the effects of dust on these surfaces, and then to develop technologies to mitigate that risk. Given the variations in albedo across the lunar surface, one variable that may be important is the darkness of the lunar dust, and this study was undertaken to address that concern. Three thermal control surfaces, AZ-93 white paint and AgFEP and AlFEP second surface mirrors were dusted with three different lunar dust simulants in a simulated lunar environment, and their solar absorptivity and thermal emissivity values determined experimentally. The three simulants included JSC 1AF, a darker mare simulant, NU-LHT-1D, a light highlands simulant, and 1:1 mixture of the two. The response of AZ-93 was found to be slightly more pronounced than that of AgFEP. The increased with fractional dust coverage in both types of samples by a factor of 1.7 to 3.3, depending on the type of thermal control surface and the type of dust. The of the AZ-93 decreased by about 10 percent when fully covered by dust, while that of AgFEP increased by about 10 percent. It was found that alpha/epsilon varied by more than a factor of two depending on the thermal control surface and the darkness of the dust. Given that the darkest simulant used in this study may be significantly lighter than the darkest dust that could be encountered on the lunar surface, it becomes apparent that the performance degradation of thermal control surfaces due to dust on the moon will be strongly dependent on the and of the dust in the specific locality.

Gaier, James R.↗

Effect of Simulant Type on the Absorptance and Emittance of Dusted Thermal Control Surfaces in a Simulated Lunar Environment

During the Apollo program the effects of lunar dust on thermal control surfaces was found to be more significant than anticipated, with several systems overheating due to deposition of dust on them. In an effort to reduce risk to future missions, a series of tests has been initiated to characterize the effects of dust on these surfaces, and then to develop technologies to mitigate that risk. Given the variations in albedo across the lunar surface, one variable that may be important is the darkness of the lunar dust, and this study was undertaken to address that concern. Three thermal control surfaces, AZ-93 white paint and AgFEP and AlFEP second surface mirrors were dusted with three different lunar dust simulants in a simulated lunar environment, and their integrated solar absorptance ( ) and thermal emittance ( ) values determined experimentally. The three simulants included JSC-1AF, a darker mare simulant, NU-LHT-1D, a light highlands simulant, and 1:1 mixture of the two. The response of AZ-93 was found to be slightly more pronounced than that of AgFEP. The increased with fractional dust coverage in both types of samples by a factor of 1.7 to 3.3, depending on the type of thermal control surface and the type of dust. The of the AZ-93 decreased by about 10 percent when fully covered by dust, while that of AgFEP increased by about 10 percent. It was found that / varied by more than a factor of two depending on the thermal control surface and the darkness of the dust. Given that the darkest simulant used in this study may be lighter than the darkest dust that could be encountered on the lunar surface, it becomes apparent that the performance degradation of thermal control surfaces due to dust on the Moon will be strongly dependent on the and of the dust in the specific locality

Gaier, James R.↗

Reconciling Simulated and Observed Views of Clouds: MODIS, ISCCP, and the Limits of Instrument Simulators in Climate Models

The properties of clouds that may be observed by satellite instruments, such as optical depth and cloud top pressure, are only loosely related to the way clouds are represented in models of the atmosphere. One way to bridge this gap is through "instrument simulators," diagnostic tools that map the model representation to synthetic observations so that differences between simulator output and observations can be interpreted unambiguously as model error. But simulators may themselves be restricted by limited information available from the host model or by internal assumptions. This work examines the extent to which instrument simulators are able to capture essential differences between MODIS and ISCCP, two similar but independent estimates of cloud properties. We focus on the stark differences between MODIS and ISCCP observations of total cloudiness and the distribution of cloud optical thickness can be traced to different approaches to marginal pixels, which MODIS excludes and ISCCP treats as homogeneous. These pixels, which likely contain broken clouds, cover about 15% of the planet and contain almost all of the optically thinnest clouds observed by either instrument. Instrument simulators can not reproduce these differences because the host model does not consider unresolved spatial scales and so can not produce broken pixels. Nonetheless, MODIS and ISCCP observation are consistent for all but the optically-thinnest clouds, and models can be robustly evaluated using instrument simulators by excluding ambiguous observations.

Pincus, Robert↗