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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2010

Separating Real and Apparent Effects of Cloud, Humidity, and Dynamics on Aerosol Optical Thickness near Cloud Edges

Aerosol optical thickness (AOT) is one of aerosol parameters that can be measured on a routine basis with reasonable accuracy from Sun-photometric observations at the surface. However, AOT-derived near clouds is fraught with various real effects and artifacts, posing a big challenge for studying aerosol and cloud interactions. Recently, several studies have reported correlations between AOT and cloud cover, pointing to potential cloud contamination and the aerosol humidification effect; however, not many quantitative assessments have been made. In this study, various potential causes of apparent correlations are investigated in order to separate the real effects from the artifacts, using well-maintained observations from the Aerosol Robotic Network, Total Sky Imager, airborne nephelometer, etc., over the Southern Great Plains site operated by the U.S. Department of Energy's Atmospheric Radiation Measurement Program. It was found that aerosol humidification effects can explain about one fourth of the correlation between the cloud cover and AOT. New particle genesis, cloud-processed particles, atmospheric dynamics, and aerosol indirect effects are likely to be contributing to as much as the remaining three fourth of the relationship between cloud cover and AOT.

Jeong, Myeong-Jae↗
NASA NTRS2010

Simulations of Aerosol Microphysics in the NASA GEOS-5 Model

Aerosol-cloud-chemistry interactions have potentially large but uncertain impacts on Earth's climate. One path to addressing these uncertainties is to construct models that incorporate various components of the Earth system and to test these models against data. To that end, we have previously incorporated the Goddard Chemistry, Aerosol, Radiation, and Transport (GOCART) module online in the NASA Goddard Earth Observing System model (GEOS-5). GEOS-5 provides a platform for Earth system modeling, incorporating atmospheric and ocean general circulation models, a land surface model, a data assimilation system, and treatments of atmospheric chemistry and hydrologic cycle. Including GOCART online in this framework has provided a path for interactive aerosol-climate studies; however, GOCART only tracks the mass of aerosols as external mixtures and does not include the detailed treatments of aerosol size distribution and composition (internal mixtures) needed for aerosol-cloud-chemistry-climate studies. To address that need we have incorporated the Community Aerosol and Radiation Model for Atmospheres (CARMA) online in GEOS-5. CARMA is a sectional aerosol-cloud microphysical model, capable of treating both aerosol size and composition explicitly be resolving the aerosol distribution into a variable number of size and composition groupings. Here we present first simulations of dust, sea salt, and smoke aerosols in GEOS-5 as treated by CARMA. These simulations are compared to available aerosol satellite, ground, and aircraft data and as well compared to the simulated distributions in our current GOCART based system.

Colarco, Peter↗
DOE OSTI2025

Investigating Aerosol and Meteorological Influences on Convective Clouds in Houston, Texas, during the TRACER/ESCAPE Field Campaigns

Aerosols serve as cloud condensation nuclei, shaping the microphysical properties of cloud droplets. Aerosol effects on convective clouds are complex and remain controversial. The debate centers around the process of aerosol-induced invigoration of deep convection, a phenomenon that could significantly affect convective cloud properties but lacks robust evidence due to methodological limitations in observational approaches and questions about the robustness of modeling studies. Resolving these discrepancies is crucial for understanding how aerosols affect the atmosphere. Here, this study examines the effects of meteorological and aerosol parameters in a weakly synoptic-driven convective environment, where the influence of aerosols may be more pronounced and observable. Daily atmospheric soundings and aerosol concentrations from several ground instruments collected during the summer of 2022 in Houston, Texas, as part of the Tracking Aerosol Convection interactions Experiment (TRACER) and Experiment of Sea Breeze Convection, Aerosols, Precipitation, and Environment (ESCAPE) field campaigns are analyzed. Statistical learning methods are applied to uncover the complex relationships between aerosols, meteorology, and convective cloud characteristics, such as cell area and echo-top height. The findings reveal that higher aerosol concentrations are associated with narrower convective cells, which we argue contradicts the idea of stronger convection with increased aerosol loading. However, once the data are clustered by the synoptic environment, the relationship between aerosol loading and convective cell area diminishes, indicating that the covariablity between synoptic-scale weather patterns, local thermodynamics, and aerosol loading makes it challenging to draw definitive conclusions about the specific impacts of aerosols on convective cloud properties.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Intense formation of secondary ultrafine particles from Amazonian vegetation fires and their invigoration of deep clouds and precipitation

New particle formation (NPF) in fire smoke is thought to be unlikely due to large condensation and coagulation sinks that scavenge molecular clusters. We analyze aircraft measurements over the Amazon and find that fires significantly enhance NPF and ultrafine particle (UFP < 50 nm diameter) numbers compared to background conditions, contrary to previous understanding. We identify that the nucleation of dimethylamine with sulfuric acid, which is aided by the formation of extremely low volatility organics in biomass-burning smoke, can overcome the large condensation and coagulation sinks and explain aircraft observations. We show that freshly formed clusters rapidly grow to UFP sizes through biomass-burning secondary organic aerosol formation, leading to a 10-fold increase in UFP number concentrations. Here, we find a contrasting effect of UFPs on deep convective clouds compared to the larger particles from primary emissions for the case investigated here. UFPs intensify the deep convective clouds and precipitation due to increased condensational heating, while larger particles delay and reduce precipitation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Strong Sensitivity of Simulated Biomass Burning Aerosol Transport and Radiative Effects Over the South Atlantic to Carbonaceous Aerosol Aging and Particle Density

Biomass burning aerosol (BBA) impacts climate through aerosol‐cloud‐radiation interactions, but models disagree on the sign and magnitude of BBA radiative effects. We quantify the sensitivity of BBA radiative effects and transport to three BBA‐relevant processes and properties: parameterized oxidative aging of organic aerosol (OA), a combined change to black carbon (BC) density and the method for calculating aerosol refractive index, and reduction in OA density. We evaluate Unified Model simulations against two aircraft campaigns from summer 2017 over the Southeast Atlantic. The model generally performs well, such that discrepancies between the observational data sets may sometimes limit the precision of the evaluation. Our newly developed aging parameterization reproduces observed OA:BC mass ratios well and allows modeled OA:BC to decrease with smoke age, but increases bias in aerosol extinction and changes the BBA radiative effect little (+0.12 W m -2 ). We calculate aerosol refractive index using either a volume‐weighted component average or the Maxwell‐Garnett (MG) mixing assumption, which represents BC as small inclusions in a host material. Compared to MG mixing, the volume‐weighted average refractive index and reduced BC density increase aerosol absorption, substantially increasing the total BBA radiative effect (+2.66 W m -2 ) and amount of BBA transported across the ocean through BC self‐lofting. Reducing OA density to better match literature values changes the total BBA radiative effect by −1.96 W m -2 . Changes to direct radiative effects exceed changes to cloud radiative effects. Our findings emphasize the sensitivity of aerosol radiative effects and transport to these processes and properties, which we suggest could be improved in climate models.

Southeast Atlantic↗
NASA NTRS2012

Stochastic Convection Parameterizations

computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts

atmospheric models↗
NASA NTRS2016

Neural Network (NN) Retrievals of Stratocumulus Cloud Properties Using Multiangle Polarimetric Observations During ORACLES

The ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) campaign is taking place in the SouthEast Atlantic during the Austral Spring for three consecutive years from 20162018. The study area encompasses one of the Earths three semipermanent subtropical Stratocumulus (Sc) cloud decks,and experiences very large aerosol optical depths, mainly biomass burning, originating from Africa. Over time, cloud optical depth (COD), lifetime and cloud microphysics (number concentration, effective radii Reff and precipitation) are expected to be influenced by indirect aerosol effects. These changes play a key role in the energetic balance of the region, and are part of the core investigation objectives of the ORACLES campaign, which acquires measurements of clean and polluted scenes of above cloud aerosols (ACA). Simultaneous retrievals of aerosol and cloud optical properties are being developed (e.g. MODIS, OMI), butstill challenging, especially for passive, single viewing angle instruments. By comparison, multiangle polarimetric instruments like RSP (Research Scanning Polarimeter) show promise for detection and quantification of ACA, however, there are no operational retrieval algorithms available yet. Here we describe anew algorithm to retrieve cloud and aerosol optical properties from observations by RSP flown on the ER2and P3 during the 2016 ORACLES campaign. The algorithm is based on training a NN, and is intended to retrieve aerosol and cloud properties simultaneously. However, the first step was to establish the retrievalscheme for low level Sc cloud optical properties. The NN training was based on simulated RSP total and polarized radiances for a range of COD, Reff, and effective variances, spanning 7 wavelength bands and 152 viewing zenith angles. Random and correlated noise were added to the simulations to achieve a morerealistic representation of the signals. Before introducing the input variables to the network, the signals are projected on a principle component plane that retains the maximal signal information but minimizes the noise contribution. We will discuss parameter choices for the network and present preliminary results of cloudretrievals from ORACLES, compared with standard RSP low-levelcloud retrieval method that has been validated against in situ observations.

Cloud-aerosol↗
DOE OSTI2025

Enhanced Convective Microphysics Scheme and Its Impacts on Mean Climate in E3SM

Abstract To improve the representation of microphysical processes in convective clouds and their interaction with aerosol and stratiform clouds, a two‐moment convective microphysics parameterization (CMP) scheme developed by Song and Zhang (2011, https://doi.org/10.1029/2010jd014833 ) is upgraded and implemented in E3SM. The new developments include: (a) implementing a parameterization for graupel to enhance the representation of ice‐phase microphysical processes; (b) representing the impact of spatial inhomogeneity of cloud droplets in cumulus ensembles on autoconversion and accretion processes to improve the representation of warm‐rain microphysical processes; (c) implementing a comprehensive Bergeron process parameterization to better represent mixed‐phase microphysical processes; and (d) representing the interactions between ice‐phase microphysics and cloud thermodynamics. Simulations show that the cloud microphysical properties simulated by the CMP are generally in good agreement with observations. It reasonably simulates the changes in droplets effective radius related to precipitation formation in convective clouds, as identified from satellite observations. It also successfully simulates the contrast in these processes between maritime and continental clouds, demonstrating its capability to simulate the impact of aerosols on convection. Analyses of the impact of CMP on climate mean state simulation demonstrate that the CMP slightly improves the simulations of precipitation, cloud macrophysical properties, longwave cloud radiative forcing, zonal wind, and temperature. However, a degradation in shortwave cloud radiative forcing occurs.

GCM↗
DOE OSTI2025

New Particle Formation Event Dataset at the Southern Great Plains (SGP) Observatory from 2018 to 2023

This data set contains observations of new particle formation (NPF) events collected at the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) observatory from 2018 to 2023. Measurements include particle number size distributions, radiance measurements, and associated meteorological variables from onsite instrumentation relevant for identifying and characterizing NPF events. Events were identified using standardized criteria and documented to support investigations of aerosol nucleation, growth dynamics, and their interactions with local atmospheric conditions. The data set provides a multi-year record that enables evaluation of seasonal and interannual variability in NPF occurrence and intensity at a mid-continental site. These data are intended to support studies of aerosol-cloud-climate interactions and model evaluation within both ARM and the broader atmospheric science community. More information can be found within the README_NPF_SGP_2018_2023.docx file.

event↗
NASA NTRS2004

Scientific Objectives, Measurement Needs, and Challenges Motivating the PARAGON Aerosol Initiative

Aerosols are involved in a complex set of processes that operate across many spatial and temporal scales. Understanding these processes, and ensuring their accurate representation in models of transport, radiation transfer, and climate, requires knowledge of aerosol physical, chemical, and optical properties and the distributions of these properties in space and time. To derive aerosol climate forcing, aerosol optical and microphysical properties and their spatial and temporal distributions, and aerosol interactions with clouds, need to be understood. Such data are also required in conjunction with size-resolved chemical composition in order to evaluate chemical transport models and to distinguish natural and anthropogenic forcing. Other basic parameters needed for modeling the radiative influences of aerosols are surface reflectivity and three-dimensional cloud fields. This large suite of parameters mandates an integrated observing and modeling system of commensurate scope. The Progressive Aerosol Retrieval and Assimilation Global Observing Network (PARAGON) concept, designed to meet this requirement, is motivated by the need to understand climate system sensitivity to changes in atmospheric constituents, to reduce climate model uncertainties, and to analyze diverse collections of data pertaining to aerosols. This paper highlights several challenges resulting from the complexity of the problem. Approaches for dealing with them are offered in the set of companion papers.

optical depth↗
NASA NTRS2001

Remote Sensing of Non-Aerosol (anomalous) Absorption in Cloud Free Atmosphere

The interaction of sunlight with atmospheric gases, aerosols and clouds is fundamental to the understanding of climate and its variation. Several studies questioned our understanding of atmospheric absorption of sunlight in cloudy or in cloud free atmospheres. Uncertainty in instruments' accuracy and in the analysis methods makes this problem difficult to resolve. Here we use several years of measurements of sky and sun spectral brightness by selected instruments of the Aerosol Robotic Network (AERONET), that have known and high measurement accuracy. The measurements taken in several locations around the world show that in the atmospheric windows 0.44, 0.06, 0.86 and 1.02 microns the only significant absorbers in cloud free atmosphere is aerosol and ozone. This conclusions is reached using a method developed to distinguish between absorption associated with the presence of aerosol and absorption that is not related to the presence of aerosol. Non-aerosol absorption, defined as spectrally independent or smoothly variable, was found to have an optical thickness smaller than 0.002 corresponding to absorption of sunlight less than 1W/sq m, or essentially zero.

Kaufman, Yoram J.↗
NASA NTRS2022

Seasonal Updraft Speeds Change Cloud Droplet Number Concentrations in Low Level Clouds Over the Western North Atlantic

To determine the impact of dynamic and aerosol processes on marine low clouds, we examine the seasonal impact of updraft speed w and cloud condensation nuclei concentration at 0.43 % supersaturation () on the cloud droplet number concentration (N(C)) of low-level clouds over the western North Atlantic Ocean. Aerosol and cloud properties were measured with instruments on board the NASA LaRC Falcon HU-25 during the ACTIVATE (Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment) mission in summer (August) and winter (February–March) 2020. The data are grouped into different loadings, and the density functions of NC and w near the cloud bases are compared. For low updrafts (w < 1.3 m s−1), NC in winter is mainly limited by the updraft speed and in summer additionally by aerosols. At larger updrafts (w > 3 m s−1), NC is impacted by the aerosol population, while at clean marine conditions cloud nucleation is aerosol-limited, and for high it is influenced by aerosols and updraft. The aerosol size distribution in winter shows a bimodal distribution in clean marine environments, which transforms to a unimodal distribution in high due to chemical and physical aerosol processes, whereas unimodal distributions prevail in summer, with a significant difference in their aerosol concentration and composition. The increase of is accompanied with an increase of organic aerosol and sulfate compounds in both seasons. We demonstrate that NC can be explained by cloud condensation nuclei activation through upwards processed air masses with varying fractions of activated aerosols. The activation highly depends on w and thus supersaturation between the different seasons, while the aerosol size distribution additionally affects NC within a season. Our results quantify the seasonal influence of w and on NC and can be used to improve the representation of low marine clouds in models.

Simon Kirschler↗
NASA NTRS2024

Maximizing the Volume of Collocated Data from Two Coordinated Suborbital Platforms

Suborbital (e.g., airborne) campaigns that carry advanced remote sensing and in situ payloads provide detailed observations of atmospheric processes, but can be challenging to use when it is necessary to geographically collocate data from multiple platforms that make repeated observations of a given geographic location at different altitudes. This study reports on a data collocation algorithm that maximizes the volume of collocated data from two coordinated suborbital platforms and demonstrates its value using data from the NASA Aerosol Cloud Meteorology Interactions Over the western Atlantic Experiment (ACTIVATE) suborbital mission. A robust data collocation algorithm is critical for the success of the ACTIVATE mission goal to develop new and improved remote sensing algorithms, and quantify their performance. We demonstrate the value of these collocated data to quantify the performance of a recently developed vertically resolved lidar + polarimeter–derived aerosol particle number concentration (Na ) product, resulting in a range-normalized mean absolute deviation (NMAD) of 9% compared to in situ measurements. We also show that this collocation algorithm increases the volume of collocated ACTIVATE data by 21% compared to using only nearest-neighbor finding algorithms alone. Additional to the benefits demonstrated within this study, the data files and routines produced by this algorithm have solved both the critical collocation and the collocation application steps for researchers who require collocated data for their own studies. This freely available and open-source collocation algorithm can be applied to future suborbital campaigns that, like ACTIVATE, use multiple platforms to conduct coordinated observations, e.g., a remote sensing aircraft together with in situ data collected from suborbital platforms.

Atmosphere↗
DOE OSTI2025

A Data Library of Liquid Clouds Modelled With a Large Eddy Simulation Framework

We describe a library of atmospheric large eddy simulations (LES) of liquid-phase boundary layer clouds constructed to enable aerosol–cloud–turbulence interaction studies, support parameterization evaluation and development, and provide training data for machine learning applications. The simulations use a modern LES framework designed for high numerical accuracy, coupled to a detailed spectral bin microphysical scheme. Case studies are configured to represent observed conditions in four key global cloud regions—the Northeastern Atlantic, Northeastern Pacific, Continental United States and Southern Ocean—following a semi-idealised approach. The library also includes aerosol concentration halving and doubling experiments to expose the sensitivities of the case studies to aerosol perturbations. Simulation results are compared to observations on a case-by-case basis, then the library's coverage is evaluated in terms of spreads in meteorological factors and atmospheric boundary layer attributes.

aerosol↗
DOE OSTI2025

Examining the Ice-Nucleating Particles from the North Slope of Alaska (ExINP-NSA) (Final Campaign Report)

The Examining the Ice-Nucleating Particles from the North Slope of Alaska (ExINP-NSA) campaign was conducted at the National Oceanic and Atmospheric Administration’s (NOAA) Barrow Atmospheric Baseline Observatory (71.3230° N, 156.6114° W, “BRW” hereafter), next to the Atmospheric Radiation Measurement (ARM) user facility NSA site and ~ 6 km northeast of the town of Utqiaġvik. The location of the NSA site is shown in Figure 1. Our observing period began in October 2021 and continued until May 2024. This campaign was funded by the U.S. Department of Energy (DOE) Office of Science Early Career Research Program through grant number DE-SC001879. This grant contains funding for three ARM field campaigns. The previous field campaigns were performed at ARM’s Southern Great Plains atmospheric observatory in Oklahoma (SGP; 36.6073° N, 97.4876° W) and the ARM’s Eastern North Atlantic atmospheric observatory on Graciosa Island, Azores (ENA; 39.0916° N, 28.0257° W). The ExINP-NSA campaign aims included: • Determining the number concentration of ice-nucleating particles (n INPs ) active at temperatures spanning the range of heterogeneous freezing processes (from ≈−30 °C to 0 °C) using a combination of online and offline measurements, • Determining whether local meteorological conditions and/or synoptic scale air mass transport impact INP abundance and/or ice nucleation efficiency, • Examining if the physicochemical properties of INPs relate to aerosol chemistry, and • Assessing if there is a similarity in INP properties across three ARM sites Multi-seasonal datasets of INP abundance in the NSA region were delivered from this campaign. This campaign also allowed researchers to perform a comprehensive analysis of atmospheric INPs based on long- term ground-based measurements in the Alaskan Arctic. Our data and results from the ExINP-NSA campaign will help refine current earth system models. One of the stated goals of ARM is to advance aerosol-cloud ice interaction, which will be a direct result of this campaign. Current earth system models poorly represent INPs, and the 15-minute time resolution data over several seasons generated during this campaign will provide an invaluable resource, especially combined with the datasets generated during two previous ARM ExINP campaigns. These datasets will allow for a greater understanding of ice nucleation processes as they may (or may not) relate to local meteorological processes and aerosol chemistry and will eventually help further the understanding of the Earth’s atmospheric processes and energy balance.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Model Intercomparison of the Impacts of Varying Cloud Droplet–Nucleating Aerosols on the Life Cycle and Microphysics of Isolated Deep Convection

The microphysical impacts of aerosol particles on scattered isolated deep convective cells near Houston, Texas, on 19 June 2013, are examined using multiple cloud-resolving model (CRM) simulations initialized with vertical profiles of low and high concentrations of cloud droplet–nucleating aerosols. These simulations formed part of the Model Intercomparison Project (MIP) conducted by the Deep Convective Working Group of the Aerosol, Cloud, Precipitation and Climate (ACPC) initiative. Each CRM generated a field of convective cells representing those observed during the case study with varying degrees of accuracy. The Tracking and Object-Based Analysis of Clouds (tobac) cell-tracking algorithm was applied to each MIP CRM simulation to track relatively long-lived convective cells (20–60 min). Most of the CRMs produced similar aerosol loading impacts on the warm phase of tracked cell properties with reduced autoconversion and accretion growth of rain, increased cloud water, reduced rainfall, and reduced near-surface evaporation of rain. The sign of aerosol impacts on the warm-phase properties of the convective cells was also quite consistent over cell lifetimes with the greatest magnitude of influence in the first half of the life cycle in most CRMs. In contrast, the ice-phase response to aerosol loading was highly variable among CRMs and included increases or decreases in ice amounts at inconsistent stages of the cell life cycle and midlevel versus upper-level changes in ice. This intermodel variability in ice is indicative both of the complex indirect interactions between aerosols and ice-phase processes in deep convection and their associated parameterizations.

Aerosol-cloud interaction↗
DOE OSTI2025

High sensitivity of simulated fog properties to parameterized aerosol activation in case studies from ParisFog

Aerosols influence fog properties such as visibility and lifetime by affecting fog droplet number concentrations (N d ). Numerical weather prediction (NWP) models often represent aerosol–fog interactions using highly simplified approaches. Incorporating prognostic size-resolved aerosol microphysics from climate models could allow them to simulate N d and aerosol–fog interactions without incurring excessive computational expense. However, microphysics code designed for coarse spatial resolution may struggle with sub-kilometer-scale grid spacings. Here, we test the ability of the UK Met Office Unified Model to simulate aerosol and fog properties during case studies from the ParisFog field campaign in 2011. We examine the sensitivity of fog properties to variations in N d caused by modifications to simulated aerosol activation. Our model, with a 500 m horizontal resolution and interactive aerosol and cloud microphysics, significantly underpredicts N d , although it only slightly underestimates the cloud condensation nuclei concentration. With an updated version of the Abdul-Razzak and Ghan (2000) activation scheme, we produce N d that are more consistent with those predicted by a cloud parcel model under fog-like conditions. We activate droplets only by adiabatic cooling. We incorporate more realistic hygroscopicities for sulfate and organic aerosols and explore the sensitivity of simulated N d to unresolved updrafts. We find that both N d and simulated fog liquid water content are very sensitive to the updated activation scheme but remain less affected by the update to hygroscopicities. Our improvements offer insights into the physical processes regulating N d in stable conditions, potentially laying foundations for improved operational fog forecasts that incorporate interactive aerosol simulations or aerosol climatologies.

Ghosh, Pratapaditya [Carnegie Mellon University, P↗
NASA NTRS2024

Summarizing Multiple Aspects of Triple Collocation Analysis in a Single Diagram

With the ongoing expansion of global observation networks, it is expected that we shall routinely analyze records of geophysical variables such as temperature from multiple collocated instruments. Validating datasets in this situation is not a trivial task because every observing system has its own bias and noise. Triple collocation is a general statistical framework to estimate the error characteristics in three or more observational-based datasets. In a triple colocation analysis, several metrics are routinely reported but traditional multiple-panel plots are not the most effective way to display information. A new formula of error variance is derived for connecting the key terms in the triple collocation theory. A diagram based on this formula is devised to facilitate triple collocation analysis of any data from observations, as illustrated using three aerosol optical depth datasets from the recent Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE). An observational-based skill score is also derived to evaluate the quality of three datasets by taking into account both error variance and correlation coefficient. Several applications are discussed and sample plotting routines are provided.

triple collocation↗