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DOE OSTI2024

Evaluation of a practical approach for field scale moisture flow modeling in heterogeneous media at a semiarid site

Abstract A practical approach for modeling field‐scale moisture flow in a highly heterogeneous unsaturated medium is described in this study. The validity of this approach is demonstrated through comparison of the numerical simulations with field observations at a semiarid site located in southcentral Washington State. The methodology is based on upscaling the core scale hydraulic properties and combining power‐law and tensorial connectivity‐tortuosity (PA‐TCT) approaches to derive macroscopic anisotropy parameters for each hydrostratigraphic unit (HSU) identified in the field. Each heterogeneous HSU is approximated by an equivalent homogeneous medium (EHM) model for which PA‐TCT parameters are used in the flow simulations. The available field data on moisture content and matric potential are compared with steady‐state flow simulations based on the mean form of Richards' equation. While the homogenization or averaging of heterogeneities, embedded in the EHM modeling approximation, cannot capture all of the field‐scale variability, the simulated steady‐state moisture and matric potential profiles capture well the central tendency of the field data. This approach is deemed practical for assessing the fate and transport of contaminants in highly heterogeneous unsaturated media at the transport scale of hundreds of meters.

Khaleel, Raziuddin↗

DOE OSTI2022

Particle scale impacts on deconstruction energy of pine residues

The goal of this Case Study was to quantify the impacts of variable moisture and ash on hammer mill throughput and energy consumption and on generation of fines that are not able to be fed to conversion, as compared to a status quo Base Case system. Also considered was convertible carbon content (minimum carbon specification) and maximum ash content and the delivered feedstock cost impacts of not being able to feed residue not meeting both specifications to the conversion reactor. Laboratory data on the impacts of input particle size and moisture content on the exit particle size were received from FCIC Subtask 5.2 from their single particle impact population balance modeling study. Additional throughput and energy consumption data were obtained from FCIC Subtask 5.2 for the same grinder with a 6 mm screen in place. These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Because the ash contents in the separated fines had not been analyzed in the laboratory at the time of the model runs, we chose to assume that the ash distributed proportionally with total mass into the overs and unders in the disk screen following grinding. Key takeaways from this Case Study are that it is significantly more cost effective to hammer mill the residue prior to drying, even though the grinder throughput is lower and energy consumption is higher versus drying first before grinding. An effect of dry grinding versus high moisture grinding is the production of higher amounts of fines during dry grinding, leading to significantly more of the ground feedstock being rejected by conversion for being below a minimum particle size. With wet grinding the system is still able to produce more preprocessed feedstock meeting the minimum particle size specification even though the instantaneous throughput is lower than for the case of grinding dry feedstock. Additionally, even without the higher fines production from dry grinding, the status quo would still be more costly than wet grinding because the material is rejected after the drying energy has already been input for the dry grinding case. Finally, significant reductions in drying energy are obtained by drying after grinding, and those reductions are of far greater magnitude than the grinding energy increase.

09 BIOMASS FUELS↗

NASA NTRS2011

Hyperspectral Remote Sensing of Atmosphere and Surface Properties

Atmospheric Infrared Sounder (AIRS), Infrared Atmospheric Sounding Interferometer (IASI), and Cross-track Infrared Sounder (CrIS) are all hyper-spectral satellite sensors with thousands of spectral channels. Top of atmospheric radiance spectra measured by these sensors contain high information content on atmospheric, cloud, and surface properties. Exploring high information content contained in these high spectral resolution spectra is a challenging task due to computation e ort involved in modeling thousands of spectral channels. Usually, only very small fractions (4{10 percent) of the available channels are included in physical retrieval systems or numerical weather forecast (NWP) satellite data assimilations. We will describe a method of simultaneously retrieving atmospheric temperature, moisture, cloud, and surface properties using all available spectral channels without sacrificing computational speed. The essence of the method is to convert channel radiance spectra into super-channels by an Empirical Orthogonal Function (EOF) transformation. Because the EOFs are orthogonal to each other, about 100 super-channels are adequate to capture the information content of the radiance spectra. A Principal Component-based Radiative Transfer Model (PCRTM) developed at NASA Langley Research Center is used to calculate both the super-channel magnitudes and derivatives with respect to atmospheric profiles and other properties. There is no need to perform EOF transformations to convert super channels back to spectral space at each iteration step for a one-dimensional variational retrieval or a NWP data assimilation system. The PCRTM forward model is also capable of calculating radiative contributions due to multiple-layer clouds. The multiple scattering effects of the clouds are efficiently parameterized. A physical retrieval algorithm then performs an inversion of atmospheric, cloud, and surface properties in super channel domain directly therefore both reducing the computational need and preserving the information content of the IASI measurements. The inversion algorithm is based on a non-linear Levenberg-Marquardt method with climatology covariance matrices and a priori information as constraints. One advantage of this approach is that it uses all information content from the hyper-spectral data so that the retrieval is less sensitive to instrument noise and eliminates the need for selecting a sub-set of the channels.

Liu, Xu↗

NASA NTRS2023

Impacts of Stratospheric Ozone Recovery on Southern Ocean Temperature and Heat Budget

The impacts of stratospheric ozone recovery on Southern Ocean surface and interior temperature, heat content, heat uptake, and heat transport are investigated by contrasting two ensemble chemistry-climate model simulations in 2005–2099: one with fixed ozone depleting substances (ODSs) and another with decreasing ODSs. In our simulations ozone recovery significantly affects Southern Ocean temperature, with large latitudinal and vertical variations. Ozone recovery causes a dipole change of the full-depth ocean heat content (OHC) with an increase south of 60°S and a decrease between 45°S and 60°S. Integrated over latitudes south of 40°S, OHC decreases in response to ozone recovery. This ocean heat loss is shown to be driven by weakened poleward ocean heat transport (OHT) across 40°S, which is partly canceled by enhanced heat uptake. The weakening of poleward OHT into the Southern Ocean is caused by the ozone-induced equatorward shift of the meridional overturning circulation.

stratospheric ozone↗

NASA NTRS1982

A statistical examination of Nimbus 7 SMMR data and remote sensing of sea surface temperature, liquid water content in the atmosphere and surfaces wind speed

Nimbus 7 Scanning Multichannel Microwave Radiometer (SMMR) brightness temperature measurements over the global oceans have been examined with the help of statistical and empirical techniques. Such analyses show that zonal averages of brightness temperature measured by SMMR, over the oceans, on a large scale are primarily influenced by the water vapor in the atmosphere. Liquid water in the clouds and rain, which has a much smaller spatial and temporal scale, contributes substantially to the variability of the SMMR measurements within the latitudinal zones. The surface wind not only increases the surface emissivity but through its interactions with the atmosphere produces correlations, in the SMMR brightness temperature data, that have significant meteorological implications. It is found that a simple meteorological model can explain the general characteristics of the SMMR data. With the help of this model methods to infer over the global oceans, the surface temperature, liquid water content in the atmosphere, and surface wind speed are developed. Monthly mean estimates of the sea surface temperature and surface winds are compared with the ship measurements. Estimates of liquid water content in the atmosphere are consistent with earlier satellite measurements.

Prabhakara, C.↗

NASA NTRS1983

A statistical examination of Nimbus-7 SMMR data and remote sensing of sea surface temperature, liquid water content in the atmosphere and surface wind speed

Nimbus 7 Scanning Multichannel Microwave Radiometer (SMMR) brightness temperature measurements over the global oceans have been examined with the help of statistical and empirical techniques. Such analyses show that zonal averages of brightness temperature measured by SMMR over the oceans on a large scale are primarily influenced by the water vapor in the atmosphere. Liquid water in the clouds and rain, which has a much smaller spatial and temporal scale, contributes substantially to the variability of the SMMR measurements within the latitudinal zones. The surface wind not only increases the surface emissivity, but through its interactions with the atmosphere produces correlations in the SMMR brightness temperature data that have significant meteorological implications. It is found that a simple meteorological model can explain the general characteristics of the SMMR data. With the help of this model, methods to infer over the global oceans, the surface temperature, liquid water content in the atmosphere, and surface wind speed are developed. Monthly mean estimates of the sea surface temperature and surface winds are compared with the ship measurements. Estimates of liquid water content in the atmosphere are consistent with earlier satellite measurements. Previously announced in STAR as N83-19187

Prabhakara, C.↗

NASA NTRS2009

Modeling Potential Carbon Monoxide Exposure Due to Operation of a Major Rocket Engine Altitude Test Facility Using Computational Fluid Dynamics

This viewgraph presentation reviews computational fluid dynamics as a tool for modelling the dispersion of carbon monoxide at the Stennis Space Center's A3 Test Stand. The contents include: 1) Constellation Program; 2) Constellation Launch Vehicles; 3) J2X Engine; 4) A-3 Test Stand; 5) Chemical Steam Generators; 6) Emission Estimates; 7) Located in Existing Test Complex; 8) Computational Fluid Dynamics; 9) Computational Tools; 10) CO Modeling; 11) CO Model results; and 12) Next steps.

Blotzer, Michael J.↗

NASA NTRS1981

Effect of fuel nitrogen and hydrogen content on emissions in hydrocarbon combustion

How the emissions of nitrogen oxides and carbon monoxide are affected by: (1) the decreased hydrogen content and (2) the increased organic nitrogen content of coal derived fuels is investigated. Previous CRT experimental work in a two stage flame tube has shown the effectiveness of rich lean two stage combustion in reducing fuel nitrogen conversion to nitrogen oxides. Previous theoretical work gave preliminary indications that emissions trends from the flame tube experiment could be predicted by a two stage, well stirred reactor combustor model using a detailed chemical mechanism for propane oxidation and nitrogen oxide formation. Additional computations are reported and comparisons with experimental results for two additional fuels and a wide range of operating conditions are given. Fuels used in the modeling are pure propane, a propane toluene mixture and pure toluene. These give hydrogen contents 18, 11 and 9 percent by weight, respectively. Fuel bound nitrogen contents of 0.5 and 1.0 percent were used. Results are presented for oxides of nitrogen and also carbon monoxide concentrations as a function of primary equivalence ratio, hydrogen content and fuel bound nitrogen content.

Bittker, D. A.↗

NASA NTRS1991

Detection of the greenhouse gas signal from space - A progress report

The spatial distribution of the expected changes in the atmospheric water vapor content and cloud cover, as predicted by the transient greenhouse gas (GHG) simulation of Hansen et al. (1988), are examined to determine whether the signals would be large enough and unique enough to be useful in a GHG detection study. The nature of the predicted GHG signal was first examined using the transient CO2 run from the GISS ocean/atmosphere general circulation model. Next, the remotely sensed irradiance characteristics data (as the measure of water vapor content) supplied by the HIRS/MSU sensors for the area of the equatorial cold tongue region (the region in which there are no measurement stations). It is shown that HIRS/MSU signals can provide data necessary for detecting GHS signals in atmospheric moisture for regions where ground observations are not possible.

Barnett, T. P.↗

NASA NTRS1987

Detecting forest structure and biomass with C-band multipolarization radar - Physical model and field tests

The ability of C-band radar (4.75 GHz) to discriminate features of forest structure, including biomass, is tested using a truck-mounted scatterometer for field tests on a 1.5-3.0 m pygmy forest of cypress (Cupressus pygmaea) and pine (Pinus contorta ssp, Bolanderi) near Mendocino, CA. In all, 31 structural variables of the forest are quantified at seven sites. Also measured was the backscatter from a life-sized physical model of the pygmy forest, composed of nine wooden trees with 'leafy branches' of sponge-wrapped dowels. This model enabled independent testing of the effects of stem, branch, and leafy branch biomass, branch angle, and moisture content on radar backscatter. Field results suggested that surface area of leaves played a greater role in leaf scattering properties than leaf biomass per se. Tree leaf area index was strongly correlated with vertically polarized power backscatter (r = 0.94; P less than 0.01). Field results suggested that the scattering role of leaf water is enhanced as leaf surface area per unit leaf mass increases; i.e., as the moist scattering surfaces become more dispersed. Fog condensate caused a measurable rise in forest backscatter, both from surface and internal rises in water content. Tree branch mass per unit area was highly correlated with cross-polarized backscatter in the field (r = 0.93; P less than 0.01), a result also seen in the physical model.

Westman, Walter E.↗

NASA NTRS1993

Comparison of cloud microphysical parameters derived from surface and satellite measurements during FIRE phase 2

Cloud microphysical properties are an important component in climate model parameterizations of water transport, cloud radiative exchange, and latent heat processes. Estimation of effective cloud particle size, liquid or ice water content, and optical depth from satellite-based instrumentation is needed to develop a climatology of cloud microphysical properties and to better understand and model cloud processes in atmospheric circulation. These parameters are estimated from two different surface data sets taken at Coffeyville, Kansas, during the First ISCCP Regional Experiment (FIRE) Phase-2 Intensive Field Observation (IFO) period (November 13 - December 7, 1991). Satellite data can also provide information about optical depth and effective particle size. This paper explores the combination of the FIRE-2 surface and satellite data to determine each of the cloud microphysical properties.

Young, David F.↗

NASA NTRS1996

Calbindins decreased after space flight

Exposure of the body to microgravity during space flight causes a series of well-documented changes in Ca2+ metabolism, yet the cellular and molecular mechanisms leading to these changes are poorly understood. Calbindins, vitamin D-dependent Ca2+ binding proteins, are believed to have a significant role in maintaining cellular Ca2+ homeostasis. In this study, we used biochemical and immunocytochemical approaches to analyze the expression of calbindin-D28k and calbindin-D9k in kidneys, small intestine, and pancreas of rats flown for 9 d aboard the space shuttle. The effects of microgravity on calbindins in rats from space were compared with synchronous Animal Enclosure Module controls, modeled weightlessness animals (tail suspension), and their controls. Exposure to microgravity resulted in a significant and sustained decrease in calbindin-D28k content in the kidney and calbindin-D9k in the small intestine of flight animals, as measured by enzyme-linked immunosorbent assay (ELISA). Modeled weightlessness animals exhibited a similar decrease in calbindins by ELISA. Immunocytochemistry (ICC) in combination with quantitative computer image analysis was used to measure in situ the expression of calbindins in the kidney and the small intestine, and the expression of insulin in pancreas. There was a large decrease of immunoreactivity in renal distal tubular cell-associated calbindin-D28k and in intestinal absorptive cell-associated calbindin-D9k of space flight and modeled weightlessness animals compared with matched controls. No consistent difference in pancreatic insulin immunoreactivity between space flight, modeled weightlessness, and controls was observed. Regression analysis of results obtained by quantitative ICC and ELISA for space flight, modeled weightlessness animals, and their controls demonstrated a significant correlation. These findings after a short-term exposure to microgravity or modeled weightlessness suggest that a decreased expression of calbindins may contribute to the disorders of Ca2+ metabolism induced by space flight.

Non-NASA Center↗

NASA NTRS2001

Buckets: Smart Objects for Digital Libraries

Current discussion of digital libraries (DLs) is often dominated by the merits of the respective storage, search and retrieval functionality of archives, repositories, search engines, search interfaces and database systems. While these technologies are necessary for information management, the information content is more important than the systems used for its storage and retrieval. Digital information should have the same long-term survivability prospects as traditional hardcopy information and should be protected to the extent possible from evolving search engine technologies and vendor vagaries in database management systems. Information content and information retrieval systems should progress on independent paths and make limited assumptions about the status or capabilities of the other. Digital information can achieve independence from archives and DL systems through the use of buckets. Buckets are an aggregative, intelligent construct for publishing in DLs. Buckets allow the decoupling of information content from information storage and retrieval. Buckets exist within the Smart Objects and Dumb Archives model for DLs in that many of the functionalities and responsibilities traditionally associated with archives are pushed down (making the archives dumber) into the buckets (making them smarter). Some of the responsibilities imbued to buckets are the enforcement of their terms and conditions, and maintenance and display of their contents.

Nelson, Michael L.↗

NASA NTRS1991

Microwave backscattering and emission model for grass canopies

A two-layer model is developed that treats the grass canopy as a collection of randomly oriented elliptical dielectric discs over a layer of thatch with underlying soil surface. The distorted Born approximation in conjunction with the Peake formulation is used to calculate the backscattering coefficient and the emissivity from the canopy. Two particular features of this model which are unique for grass canopies are the variation of the canopy structure and the presence of the thatch layer. The basic parameters in the model such as the size and orientation of grass blades, dielectric constant of soil and vegetation, and thickness and water content of the thatch layer have been obtained from ground truth data. To interpret the available experimental observations of grasslands, numerical results from both passive and active models at L-band (1.4 GHz) are generated and various scattering and emission properties of the grass canopies are discussed.

Saatchi, Sasan S.↗

DOE OSTI2025

Effect of particle size and moisture on flow performance of loblolly pine anatomical fractions: Experimental findings and model predictions

The rising energy demand has highlighted biomass as a promising next-generation energy source. However, commercializing biomass-derived energy faces challenges, particularly in handling biomass feedstock. Factors like particle size, shape, moisture content, and surface roughness significantly impact biomass flowability. This study addresses a crucial knowledge gap by examining the effects of particle size and moisture content on the flow behavior and shear properties of different anatomical fractions of loblolly pine (Pinus taeda). The bulk shear behavior was examined using a Schulze ring shear tester, while flow performance was tested through gravity-driven flow experiments in a variable wedge-shape hopper. Results were incorporated into empirical and machine learning-based flow prediction models to evaluate their accuracy and limitations. The study found that samples with higher moisture content show higher unconfined yield strength. The critical arching distance increased with particle size, e.g., from approximately 13 and 33 mm for 2- and 6-mm whole chips, respectively at a 32-degree inclination angle. Conversely, the flow rate decreased for a given hopper opening as particle size increased. For instance, at a 60-mm hopper opening and a 32-degree inclination angle, the mass flow rates for 2- and 6-mm whole chips were 7.83 and 6.42 tonne/h, respectively. The empirical model consistently overpredicted the mass flow rate for all anatomical fractions, while the machine learning model more accurately predicted the central tendency of flow rate but was insensitive to varying tissue proportions. These novel findings provide comprehensive characterization of anatomical fractions, reveal significant combined effects of particle size and moisture content on biomass flow behavior, and demonstrate a better predictive accuracy of a machine learning model, all of which are useful for optimizing material handling strategies and biomass utilization technologies in the industry.

09 - BIOMASS FUELS↗

NASA NTRS2016

Connecting Paleo and Modern Oceanographic Data to Understand Atlantic Meridional Overturning Circulation Over Decades to Centuries

Modeling is an important tool for understanding AMOC on all timescales. Mechanistic studies of modern AMOC variability have been hampered by a lack of consistency between free-running models and the sensitivity of AMOC to resolution and parameterization. Recent work within the framework of the phase two Coordinated Ocean- Reference Experiments (CORE-II) addresses this issue head on, looking at model differences of AMOC mean state and interannual variability. One consistent feature across the models is that AMOC mean transport is related to mixed layer depths and Labrador Sea salt content, whereas interannual variability is primarily associated with Labrador Sea temperature anomalies. This is consistent with the hypothesized importance of salt balance for AMOC variability on geological timescales. The simulated relationships between AMOC and subsurface temperature anomalies in fully coupled climate models reveal subsurface AMOC fingerprints that could be used to reconstruct historical AMOC variations at low frequency.With the lack of long-term AMOC observations, models of ocean state that assimilate observational data have been explored as a way to reconstruct AMOC, but comparisons between models indicate they are quite variable in their AMOC representations. Karspeck et al. (2015) found that historical reconstructions of AMOC in such models are sensitive to the details of the data assimilation procedure. The ocean data assimilation community continues to address these issues through improved models and methods for estimating and representing error information.Two objectives of paleoclimate modeling are 1) to provide mechanistic information for interpretation of paleoclimate observations, and 2) to test the ability of predictive models to simulate Earth's climate under different background forcing states. In a good example of the first objective, Schmittner and Lund (2015) and Menviel et al. (2014) provided key information about the proxy signals expected under freshwater disturbance of AMOC, which were used to support the paleoclimate observations made by Henry et al. (2016). In an example of the second objective, Muglia and Schmittner (2015) analyzed Third Paleoclimate Modeling Intercomparison Project (PMIP3) models of the Last Glacial Maximum (LGM) and found consistently more intense and deeper AMOC transports relative to preindustrial simulations, counter to the paleoclimate consensus of LGM conditions, indicating that some processes are not well represented in the PMIP3 models. One challenge is to find adequate paleo observations against which to test these models. PMIP is now in phase 4 (part of CMIP6), which includes experiments covering five periods in Earth's history: the last millennium, last glacial maximum, last interglacial, and the mid-Pliocene. Newly compiled paleoclimate datasets from the PAGES2k project, more transient simulations, and participation of isotope enabled models planned for CMIP6PMIP4 will enable richer paleo data-model comparisons in the near future.

Kilbourne, Hali↗

DOE OSTI2020

Frequency Analysis of Solar PV Power to Enable Optimal Building Load Control

In this paper, we present a flexibility estimation mechanism for buildings’ thermostatically controlled loads (TCLs) to enable the distribution level consumption of the majority of solar photovoltaic (PV) generation by local building TCLs. The local consumption of PV generation provides several advantages to the grid operation as well as the consumers, such as reducing the stress on the distribution network, minimizing voltage fluctuations and two-way power flows in the distribution network, and reducing the required battery storage capacity for PV integration. This would result in increasing the solar PV generation penetration levels. The aims of this study are twofold. First, spectral (frequency) analyses of solar PV power generation together with the power consumption of multiple building TCLs (such as heating, ventilation, and air conditioning (HVAC) systems, water heaters, and refrigerators) are performed. These analyses define the bandwidth over which these TCLs can operate and also describe the PV generation frequency bandwidth. Such spectral analyses, in frequency domain, can help identify the flexible components of PV generation that can be consumed by the various TCLs through optimal building load utilization. Second, a quadratic optimization problem based on model predictive control is formulated to allow consuming most of the low and medium frequency content of the PV power locally by building TCLs, while maintaining occupants’ comfort and TCLs’ physical constraints. The solution to the proposed optimization problem is achieved using optimal control strategies. Numerical results show that most of the low and medium frequency content of the PV generation can be consumed locally by building TCLs. The remaining high-frequency content of the PV generation can then be stored/offset using energy storage systems.

14 SOLAR ENERGY↗

NASA NTRS1994

Reionization in a cold dark matter universe: The feedback of galaxy formation on the intergalactic medium

We study the coupled evolution of the intergalactic medium (IGM) and the emerging structure in the universe in the context of the cold dark matter (CDM) model, with a special focus on the consequences of imposing reionization and the Gunn-Peterson constraint as a boundary condition on the model. We have calculated the time-varying density of the IGM by coupling our detailed, numerical calculations of the thermal and ionization balance and radiative transfer in a uniform, spatially averaged IGM of H and He, including the mean opacity of an evolving distribution of gas clumps which correspond to quasar absorption line clouds, to the linearized equations for the growth of density fluctuations in both the gaseous and dark matter components in a CDM universe. We use the linear growth equations to identify the fraction of the gas which must have collapsed out at each epoch, an approach similar in spirit to the so-called Press-Schechter formalism. We identify the IGM density with the uncollapsed baryon fraction. The collapsed fraction is postulated to be a source of energy injection into the IGM, by radiation or bulk hydrodynamical heating (e.g., via shocks) or both, at a rate which is marginally enough to satisfy the Gunn-Peterson constraint at z less than 5. Our results include the following: (1) We find that the IGM in a CDM model must have contained a substantial fraction of the total baryon density of the universe both during and after its reionization epoch. (2) As a result, our previous conclusion that the observed Quasi-Stellar Objects (QSOs) at high redshift are not sufficient to ionize the IGM enough to satisfy the Gunn-Peterson constraint is confirmed. (3) We predict a detectable He II Gunn-Peterson effect at 304(1 + z) A in the spectra of quasars at a range of redshift z greater than or approx. 3, depending on the nature of the sources of IGM reionization. (4) We find, moreover, that a CDM model with high bias parameter b (i.e., b greater than or approx. 2) cannot account for the baryon content of the universe at z approximately 3 observed in quasar absorption line gas unless Omega (sub B) significantly exceeds the maximum value allowed by big bang nucleocynthesis. (5) For a CDM model with bias parameter within the allowed range of (lower) values, the lower limit to Omega(sub B) imposed by big bang nucleosynthesis (Omega(sub B) h(sup 2) greater than or equal to 0.01) combines with our results to yield the minimum IGM density for the CDM fodel. For CDM with b = 1 (Cosmic Background Explorer (COBE) normalization), we find Omega(sub IGM)(sup min) (z approximately 4) approx. equal 0.02-0.03, and Omega(sub IGM)(sup min)(z approximately 0) approx. equal 0.005-0.03, depending upon the nature of the sources of IGM reionization. (6) In general, we find that self-consistent reionization of the IGM by the collapsed baryon fraction has a strong effect on the rate of collapse. (7) As a further example, we show that the feedback effect on the IGM of energy release by the collapsed baryon fraction may explain the slow evolution of the observed comoving QSO number density between z = 5 and z = 2, followed by the sharp decline after z = 2.

Shapiro, Paul R.↗