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NASA NTRSDate not supplied

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗
NASA NTRS2022

Combining Machine Learning and Numerical Simulation for High-Resolution PM2.5 Concentration Forecast

Forecasting ambient PM2.5 concentrations with spatiotemporal coverage is key to alerting decision-makers of pollution episodes and preventing detrimental public exposure, especially in regions with limited ground air monitoring stations. The existing methods either rely on chemical transport models (CTMs) to forecast spatial distribution of PM2.5 with nontrivial uncertainty or statistical algorithms to forecast PM2.5 concentration time-series at air monitoring locations without continuous spatial coverage. In this study, we developed a PM2.5 forecast framework by combining the robust Random Forest algorithm with a publicly accessible global CTM forecast product – NASA’s Goddard Earth Observing System “Composition Forecasting” (GEOS-CF), providing spatiotemporally continuous PM2.5 concentration forecasts for the next five days at a 1-km spatial resolution. Our forecast experiment was conducted for a region in Central China including the populous and polluted Fenwei Plain. The forecast for the next two days had overall validation R2 of 0.76 and 0.64, respectively; the R2 was around 0.5 for the following three forecast days. Spatial cross-validation showed similar validation metrics. Our forecast model, with validation normalized mean bias close to zero, substantially reduced the large biases in GEOS-CF. The proposed framework requires minimal computational resources compared to running CTMs at urban scales, enabling near-real-time PM2.5 forecast in resource-restricted environments.

PM2.5↗
NASA NTRSDate not supplied

Numerical Simulation of No Vent Chill and Fill of a Large Liquid Hydrogen Tank

On orbit transfer of cryogenic liquids is necessary for many future space missions. The techniques required to transfer cryogens in micro gravity are quite different from ground system applications. In normal gravity, cryogenic tanks are usually filled from the bottom at nearly atmospheric pressure. The vapor generated due to heat transfer from warm tank walls, is allowed to vent from the top of the tank while the tank is being filled. If the normal gravity technique is used on orbit, the uncertainty of liquid and vapor distributions in unsettled condition may result in dumping of large amounts of liquid propellant overboard. The Vented Chill and No Vent Fill (VCNVF) process is a methodology [1] used to reduce propellant loss by holding the vent valve open during initial wall chilldown, preventing over-pressurization of the tank and stalling of the incoming flow, but closing the tank vent valve after chilling the tank wall sufficiently. An accurate simulation of no vent tank chill and fill is necessary to estimate the amount of propellant necessary to chill the tank, determine the maximum sustainable flowrate to fill the tank without stalling, and establish a timeline for the filling process. Numerical modeling of filling a cryogenic tank is complex because the flow is two-phase and the process involves both boiling and condensation with heat transfer between solid and fluid. In recent years, progress has been made to develop a numerical modeling technique [2,3,4] that has been verified by comparing with the test data from a small flight tank using liquid nitrogen [5]. The purpose of the present paper is to apply this technique in a larger tank with liquid hydrogen and compare with the test data of Chato [1]. The K-site Test Facility [1], shown in Figure 1, consists of a Test Tank, spray system, instrumentation, and the vacuum chamber. The test tank selected was ellipsoidal with an 87 inch major diameter and a 1.2 to 1 major to minor axis ratio. The two ends are joined by a short 1.5 inch cylindrical section. The tank is made of 2219 aluminum chemically milled to a nominal thickness of 0.087 inches. The tank weighs 329.25 pounds, and the tank volume is 175 ft 3 . The GFSSP model of the Test Tank is shown in Figure 2. Node 13 is a boundary node that represents the supply tank which is supplying liquid hydrogen at a given pressure and temperature. The total measured flowrate is evenly distributed through Branches 131 through 139. Nodes 1 through 9 represent the test tank and they are connected with metal solid nodes 14 through 22 through fluid-to-solid conductors that allow convective heat transfer between the solid and fluid nodes. The predicted tank pressure, filling rate, wall temperature and fluid temperature will be compared with test data.

Alok Majumdar↗
NASA NTRS2019

POLARRIS: A POLArimetric Radar Retrieval and Instrument Simulator

This paper introduces a synthetic polarimetric radar simulator and retrieval package, POLArimetric Radar Retrieval and Instrument Simulator (POLARRIS), for evaluating cloud‐resolving models (CRMs). POLARRIS is composed of forward (POLARRIS‐f) and inverse (retrieval and diagnostic) components (iPOLARRIS) to generate not only polarimetric radar observables (Zh, Zdr, Kdp, ρhv) but also radar‐consistent geophysical parameters such as hydrometeor identification, vertical velocity, and rainfall rates retrieved from CRM data. To demonstrate its application and uncertainties, POLARRIS is applied to simulations of a mesoscale convective system over the Southern Great Plains on 23 May 2011, using the Weather Research and Forecasting model with both spectral bin microphysics (SBM) and the Goddard single‐moment bulk 4ICE microphysics. Statistical composites reveal a significant dependence of simulated polarimetric observables (Zdr, Kdp) on the assumptions of the particle axis ratio (oblateness) and orientation angle distributions. The simulated polarimetric variables differ considerably between the SBM and 4ICE microphysics in part due to the differences in their ice particle size distributions as revealed by comparisons with aircraft measurements. Regardless of these uncertainties, simulated hydrometeor identification distributions overestimate graupel and hail fractions, especially from the simulation with SBM. To minimize uncertainties in forward model, the particle shape and orientation angle distributions of frozen particles should be predicted in a microphysics scheme in addition to the size distributions and particle densities.

Toshi Matsui↗
NASA NTRS2017

A Method for Obtaining High Frequency, Global, IR-Based Convective Cloud Tops for Studies of the TTL

Models of varying complexity that simulate water vapor and clouds in the Tropical Tropopause Layer (TTL) show that including convection directly is essential to properly simulating the water vapor and cloud distribution. In boreal winter, for example, simulations without convection yield a water vapor distribution that is too uniform with longitude, as well as minimal cloud distributions. Two things are important for convective simulations. First, it is important to get the convective cloud top potential temperature correctly, since unrealistically high values (reaching above the cold point tropopause too frequently) will cause excessive hydration of the stratosphere. Second, one must capture the time variation as well, since hydration by convection depends on the local relative humidity (temperature), which has substantial variation on synoptic time scales in the TTL. This paper describes a method for obtaining high frequency (3-hourly) global convective cloud top distributions which can be used in trajectory models. The method uses rainfall thresholds, standard IR brightness temperatures, meteorological temperature analyses, and physically realistic and documented corrections IR brightness temperature corrections to derive cloud top altitudes and potential temperatures. The cloud top altitudes compare well with combined CLOUDSAT and CALIPSO data, both in time-averaged overall vertical and horizontal distributions and in individual cases (correlations of .65-.7). An important finding is that there is significant uncertainty (nearly .5 km) in evaluating the statistical distribution of convective cloud tops even using lidar. Deep convection whose tops are in regions of high relative humidity (such as much of the TTL), will cause clouds to form above the actual convection. It is often difficult to distinguish these clouds from the actual convective cloud due to the uncertainties of evaluating ice water content from lidar measurements. Comparison with models show that calculated cloud top altitudes are generally higher than those calculated by global analyses (e.g., MERRA). Interannual variability in the distribution of convective cloud top altitudes is also investigated.

hydration↗
NASA NTRSDate not supplied

Consequences of Asteroid Characterization on the State of Knowledge about Inferred Physical Properties and Impact Risk

Physical characteristics of Near-Earth Objects (NEOs) are essential inputs to planetary defense assessments. The size, density, and strength of an NEO are critical inputs to modeling behavior during atmospheric entry as well as assessing the risk of impact. Similarly, knowledge of the physical characteristics of an object are necessary to evaluate the probable result of a mitigation mission. Usually, these attributes cannot be directly measured, but increasingly sophisticated methods have been developed to infer physical properties from related measurements of asteroids, meteors, and/or meteorites. Fortuitously, some of these measurements have been obtained for enough NEOs to elucidate the distribution of values across the sampled population. However, the situation becomes more challenging when considering a specific asteroid, since it is unlikely that all the relevant measurements have been made for any given object. We have developed a Bayesian network that can combine available information about a particular NEO with knowledge of the larger population to infer probabilistic values and uncertainties for physical characteristics of interest. Distributions of asteroid population albedos, taxonomic classes, and macroporosities, along with meteorite density distributions and associations between taxonomic classes and meteorite classes, provide the default distributions for the network’s parameter nodes. The inference network links parameters for each virtual asteroid either deterministically or probabilistically as appropriate, and eliminates any unphysical combinations of parameters. Within the context of planetary defense, our Bayesian network can be used to constrain the ranges of likely impactor properties, which can subsequently reduce the uncertainty in modelling of atmospheric entry, mitigation efficacy, and impact risk assessment. When additional measurements become available for a specific object, the network incorporates those measurements to generate virtual asteroids with property distributions that are consistent with the measurements. We will use the 2023 PDC scenario to demonstrate how the inference network can be combined with plausible characterization measurements to refine the state of knowledge about likely combinations of physical parameters and the resulting impact risk.

risk assessment↗
NASA NTRSDate not supplied

Consequences of Asteroid Characterization on the State of Knowledge about Inferred Physical Properties and Impact Risk

Physical characteristics of Near-Earth Objects (NEOs) are essential inputs to planetary defense assessments. The size, density, and strength of an NEO are critical inputs to modeling behavior during atmospheric entry as well as assessing the risk of impact. Similarly, knowledge of the physical characteristics of an object are necessary to evaluate the probable result of a mitigation mission. Usually, these attributes cannot be directly measured, but increasingly sophisticated methods have been developed to infer physical properties from related measurements of asteroids, meteors, and/or meteorites. Fortuitously, some of these measurements have been obtained for enough NEOs to elucidate the distribution of values across the sampled population. However, the situation becomes more challenging when considering a specific asteroid, since it is unlikely that all the relevant measurements have been made for any given object. We have developed a Bayesian network that can combine available information about a particular NEO with knowledge of the larger population to infer probabilistic values and uncertainties for physical characteristics of interest. Distributions of asteroid population albedos, taxonomic classes, and macroporosities, along with meteorite density distributions and associations between taxonomic classes and meteorite classes, provide the default distributions for the network’s parameter nodes. The inference network links parameters for each virtual asteroid either deterministically or probabilistically as appropriate, and eliminates any unphysical combinations of parameters. Within the context of planetary defense, our Bayesian network can be used to constrain the ranges of likely impactor properties, which can subsequently reduce the uncertainty in modelling of atmospheric entry, mitigation efficacy, and impact risk assessment. When additional measurements become available for a specific object, the network incorporates those measurements to generate virtual asteroids with property distributions that are consistent with the measurements. We will use the 2023 PDC scenario to demonstrate how the inference network can be combined with plausible characterization measurements to refine the state of knowledge about likely combinations of physical parameters and the resulting impact risk.

risk assessment↗
NASA NTRS2003

Probabilistic Analysis of Solid Oxide Fuel Cell Based Hybrid Gas Turbine System

The emergence of fuel cell systems and hybrid fuel cell systems requires the evolution of analysis strategies for evaluating thermodynamic performance. A gas turbine thermodynamic cycle integrated with a fuel cell was computationally simulated and probabilistically evaluated in view of the several uncertainties in the thermodynamic performance parameters. Cumulative distribution functions and sensitivity factors were computed for the overall thermal efficiency and net specific power output due to the uncertainties in the thermodynamic random variables. These results can be used to quickly identify the most critical design variables in order to optimize the design and make it cost effective. The analysis leads to the selection of criteria for gas turbine performance.

Gorla, Rama S. R.↗
NASA NTRS1995

Uncertainty in cloud optical depth estimates made from satellite radiance measurements

The uncertainty in optical depths retrieved from satellite measurements of visible wavelength radiance at the top of the atmosphere is quantified. Techniques are briefly reviewed for the estimation of optical depth from measurements of radiance, and it is noted that these estimates are always more uncertain at greater optical depths and larger solar zenith angles. The lack of radiometric calibration for visible wavelength imagers on operational satellites dominates the uncertainty retrievals of optical depth. This is true for both single-pixel retrievals and for statistics calculated from a population of individual retrievals. For individual estimates or small samples, sensor discretization can also be significant, but the sensitivity of the retrieval to the specification of the model atmosphere is less important. The relative uncertainty in calibration affects the accuracy with which optical depth distributions measured by different sensors may be quantitatively compared, while the absolute calibration uncertainty, acting through the nonlinear mapping of radiance to optical depth, limits the degree to which distributions measured by the same sensor may be distinguished.

Pincus, Robert↗
NASA NTRS1980

Uncertainty in estimates of the number of extraterrestrial civilizations

Estimation of the number N of communicative civilizations by means of Drake's formula involves the combination of several quantities, each of which is to some extent uncertain. The uncertainty in any quantity may be represented by a probability distribution function, even if that quantity is itself a probability. The uncertainty of current estimates of N is derived principally from uncertainty in estimates of the lifetime of advanced civilizations. It is argued that this is due primarily to uncertainty concerning the existence of a "Galactic Federation" which is in turn contingent upon uncertainty about whether the limitations of present-day physics are absolute or (in the event that there exists a yet-undiscovered "hyperphysics") transient . It is further argued that it is advantageous to consider explicitly these underlying assumptions in order to compare the probable numbers of civilizations operating radio beacons, permitting radio leakage, dispatching probes for radio surveillance or dispatching vehicles for manned surveillance.

Peter A Sturrock↗
NASA NTRS2022

Estimating pixel-level uncertainty in ocean color retrievals from MODIS

The spectral distribution of marine remote sensing reflectance, R(rs), is the fundamental measurement of ocean color science, from which a host of bio-optical and biogeochemical properties of the water column can be derived. Estimation of uncertainty in these derived properties is thus dependent on knowledge of the uncertainty in satellite-retrieved R(rs) (u(c)(R(rs))) at each pixel. Uncertainty in R(rs), in turn, is dependent on the propagation of various uncertainty sources through the R(rs) retrieval process, namely the atmospheric correction (AC). A derivative-based method for uncertainty propagation is established here to calculate the pixel-level uncertainty in R(rs), as retrieved using NASA’s multiple-scattering epsilon (MSEPS) AC algorithm and verified using Monte Carlo (MC) analysis. The approach is then applied to measurements from the Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite, with uncertainty sources including instrument random noise, instrument systematic uncertainty, and forward model uncertainty. The uc(Rrs) is verified by comparison with statistical analysis of coincident retrievals from MODIS and in situ Rrs measurements, and our approach performs well in most cases. Based on analysis of an example 8-day global products, we also show that relative uncertainty in R(rs) at blue bands has a similar spatial pattern to the derived concentration of the phytoplankton pigment chlorophyll-a (chl-a), and around 7.3%, 17.0%, and 35.2% of all clear water pixels (chl-a ≤ 0.1 mg/cu.m) with valid u(c)(R(rs)) have a relative uncertainty ≤ 5% at bands 412 nm, 443 nm, and 488 nm respectively, which is a common goal of ocean color retrievals for clear waters. While the analysis shows that u(c)(R(rs)) calculated from our derivative-based method is reasonable, some issues need further investigation, including improved knowledge of forward model uncertainty and systematic uncertainty in instrument calibration.

Pixel-level uncertainty↗
NASA NTRS2012

New Approaches to Quantifying Transport Model Error in Atmospheric CO2 Simulations

In recent years, much progress has been made in observing CO2 distributions from space. However, the use of these observations to infer source/sink distributions in inversion studies continues to be complicated by difficulty in quantifying atmospheric transport model errors. We will present results from several different experiments designed to quantify different aspects of transport error using the Goddard Earth Observing System, Version 5 (GEOS-5) Atmospheric General Circulation Model (AGCM). In the first set of experiments, an ensemble of simulations is constructed using perturbations to parameters in the model s moist physics and turbulence parameterizations that control sub-grid scale transport of trace gases. Analysis of the ensemble spread and scales of temporal and spatial variability among the simulations allows insight into how parameterized, small-scale transport processes influence simulated CO2 distributions. In the second set of experiments, atmospheric tracers representing model error are constructed using observation minus analysis statistics from NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA). The goal of these simulations is to understand how errors in large scale dynamics are distributed, and how they propagate in space and time, affecting trace gas distributions. These simulations will also be compared to results from NASA's Carbon Monitoring System Flux Pilot Project that quantified the impact of uncertainty in satellite constrained CO2 flux estimates on atmospheric mixing ratios to assess the major factors governing uncertainty in global and regional trace gas distributions.

Ott, L.↗
NASA NTRSDate not supplied

Impacts of aerosol size-dependent below-cloud scavenging on tropospheric aerosol in the NASA GEOS model

Cloud scavenging is the major sink for a suite of tropospheric aerosols, and thus largely affects the global distribution and lifetime of aerosols as well as the formation of clouds. Simplified model parameterizations of cloud scavenging of aerosols substantially contribute to large uncertainties in the simulated aerosol burdens, spatial distributions, lifetimes, as well as aerosol radiative forcing. Here we evaluate the wet scavenging scheme in the current NASA GEOS model, develop more physically-based parameterizations of below-cloud scavenging, and assess the impacts of the new scavenging parameterizations on the GEOS simulations of aerosols. The current below-cloud scavenging (BCS; washout) scheme uses a first-order removal with a constant scavenging coefficient. We replaced the current scheme with a size-dependent parameterization of Croft et al.(Atmos. Chem. Phys., 2009; hereafter referred to as C09). The C09 BCS parameterizations calculate aerosol below-cloud scavenging coefficients based on a size-dependent collision efficiency between aerosol particles and raindrops (or snow crystals). A look-up table of compiled collision efficiencies provides values for sixty aerosol sizes and nine rain flux rates. Snow-aerosol collision efficiencies are a function of the sixty aerosol sizes only. We assume a log-normal size distribution for aerosols (bulk) in GOCART. The collision efficiencies are then calculated online using a bilinear interpolation from the look-up table for the given aerosol sizes and precipitation flux rates in the model.

aerosols↗
NASA NTRS2013

Modeling and Evaluation of the Global Sea-Salt Aerosol Distribution: Sensitivity to Emission Schemes and Resolution Effects at Coastal/Orographic Sites

One of the major sources of uncertainty in model estimates of the global sea-salt aerosol distribution is the emission parameterization. We evaluate a new sea-salt aerosol life cycle module coupled to the online multi-scale chemical transport model NMMB/BSC-CTM. We compare 5 year global simulations using five state-of-the-art sea-salt open-ocean emission schemes with monthly averaged coarse aerosol optical depth (AOD) from selected AERONET sun photometers, surface concentration measurements from the University of Miami's Ocean Aerosol Network, and measurements from two NOAA/PMEL cruises (AEROINDOEX and ACE1). Model results are highly sensitive to the introduction of sea-surface-temperature (SST)-dependent emissions and to the accounting of spume particles production. Emission ranges from 3888 teragrams per year to 8114 teragrams per year, lifetime varies between 7.3 hours and 11.3 hours, and the average column mass load is between 5.0 teragrams and 7.2 teragrams. Coarse AOD is reproduced with an overall correlation of around 0.5 and with normalized biases ranging from +8.8 percent to +38.8 percent. Surface concentration is simulated with normalized biases ranging from minus 9.5 percent to plus 28 percent and the overall correlation is around 0.5. Our results indicate that SST-dependent emission schemes improve the overall model performance in reproducing surface concentrations. On the other hand, they lead to an overestimation of the coarse AOD at tropical latitudes, although it may be affected by uncertainties in the comparison due to the use of all-sky model AOD, the treatment of water uptake, deposition and optical properties in the model and/or an inaccurate size distribution at emission.

Bias↗
NASA NTRS2017

Sensitivity Analysis of the Bone Fracture Risk Model

Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.

mathematical models↗
NASA NTRS1992

A statistical model for evaluating GOPEX uplink performance

This article describes a statistical model to analyze the signal intensity received at the solid-state imaging (SSI) camera of the Galileo optical communications system from an Earth-based transmitter (GOPEX) demonstration. The analytical model assumes that the optical beam possesses a Gaussian profile and the communication channel has a log-normal scattering characteristic. The atmospheric-induced jitter is modelled as two independent zero mean Gaussian random variables. By modelling the system parameters as a set of independent and identically distributed (iid) random variables, the combined impact of uncertainties due to system parameters and the turbulent atmosphere can be approximated by a log-normal distributed signal intensity at the spacecraft. A Monte-Carlo software simulation package was also developed to compute the confidence interval probabilities for general optical beam profiles. Numerical results show that the approximation is valid for a wide range of operation scenarios.

Kiesaleh, K.↗
NASA NTRS1987

Meteor velocity distribution and an optimum monitoring mathematical model

At present, there are a great number of radio meteor, ionosphere and rocket observation data for the altitude range of 80 to 100 km which indicate the existence of large scale circulation systems in the mesopause to low thermosphere range which change regularly with season and latitude. But the existing observation network and observation programs are not optimal for revealing the main factors forming the circulation mode at these altitudes. A generalized optimum monitoring mathematical model is offered for consideration. The model input data are distribution density, response function, individual measurement root mean square uncertainty and detection effectiveness function. The model makes it possible to obtain the observation distribution density, the minimal possible dispersion and optimized system effectiveness.

Volkov, N. G.↗
NASA NTRS1986

Penetration of sunlight into a canopy - Explicit models based on vertical and horizontal leaf projections

The projections of leaf areas onto a horizontal plane and onto a vertical plane are examined for their utility in characterizing canopies for sunlight penetration (direct beam only) models. These projections exactly specify the penetration if the projections on the principal plane of the normals to the top surfaces of the leaves are in the same quadrant as the sun. Inferring the total leaf area from these projections (and therefore the penetration as a function of the total leaf area) is possible only with a large uncertainty (up to + or - 32 percent) because the projections are a specific measure of the total leaf area only if the leaf angle distribution is known. It is expected that this uncertainty could be reduced to more acceptable levels by making an approximate assessment of whether the zenith angle distribution is that of an extremophile canopy.

Otterman, J.↗