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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

The NASA-Goddard Multi-Scale Modeling Framework - Land Information System: Global Land/atmosphere Interaction with Resolved Convection

The present generation of general circulation models (GCM) use parameterized cumulus schemes and run at hydrostatic grid resolutions. To improve the representation of cloud-scale moist processes and landeatmosphere interactions, a global, Multi-scale Modeling Framework (MMF) coupled to the Land Information System (LIS) has been developed at NASA-Goddard Space Flight Center. The MMFeLIS has three components, a finite-volume (fv) GCM (Goddard Earth Observing System Ver. 4, GEOS-4), a 2D cloud-resolving model (Goddard Cumulus Ensemble, GCE), and the LIS, representing the large-scale atmospheric circulation, cloud processes, and land surface processes, respectively. The non-hydrostatic GCE model replaces the single-column cumulus parameterization of fvGCM. The model grid is composed of an array of fvGCM gridcells each with a series of embedded GCE models. A horizontal coupling strategy, GCE4fvGCM4Coupler4LIS, offered significant computational efficiency, with the scalability and I/O capabilities of LIS permitting landeatmosphere interactions at cloud-scale. Global simulations of 2007e2008 and comparisons to observations and reanalysis products were conducted. Using two different versions of the same land surface model but the same initial conditions, divergence in regional, synoptic-scale surface pressure patterns emerged within two weeks. The sensitivity of largescale circulations to land surface model physics revealed significant functional value to using a scalable, multi-model land surface modeling system in global weather and climate prediction.

cumulus schemes↗
DOE OSTI2020

Effects of Lateral Entrainment Mixing With Entrained Aerosols on Cloud Microphysics

The effects of entrained environment air and aerosols on cloud properties remain a critical yet understudied topic. This study first introduces a new entraining cloud parcel model considering entrained aerosols. With entrained aerosols represented by a newly introduced parameter, the impacts of entrainment rate and entrained aerosols on cloud microphysical properties are investigated. The results here show that the relationships between entrainment rate and cloud microphysical properties are highly nonlinear when the entrained aerosols vary. With the lateral entrainment mixing, a new phenomenon is revealed that the height of maximum parcel supersaturation cannot be reached when the entrainment rate is beyond a certain critical value. This new critical entrainment rate is different from the critical entrainment rate defined by Barahona and Nenes (2007, https://doi.org/10.1029/2007JD008473), beyond which clouds cannot form. This finding has important implications for developing parameterization of droplet activation, which is based primarily on the assumption of the existence of maximum supersaturation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1988

A parameterization of the evaporation of rainfall

A general theoretical expression for the rainfall rate and the total evaporation rate as a function of the distance below cloud base is developed, and is then specialized to the gamma raindrop size distribution. The theoretical framework is used to analyze the data of Rosenfeld and Mintz (1988) on the radar observations of the rainfall rate as a function of the distance below cloud base, for rain falling from continental convective cells in central South Africa, obtaining a parameterization for the evaporation of rainfall.

Schlesinger, Michael E.↗
DOE OSTI2023

Assessing Secondary Ice Production in Continental Clouds Based on AMF Synergistic Remote Sensing Observations

Ice crystals play an important role in radiation and precipitation formation. However, the prediction of ice number concentration has proven to be problematic, because the predicted concentration of ice nucleating particles is often smaller than the observed by several orders of magnitude. This difference between the observed and the predicted number concentration has been explained by so-called secondary ice production (SIP), which includes hypothesized mechanisms like rime splintering, shattering of large frozen drops, and ice-ice collision breakup. To better observe SIP and understand its frequency, production rate, and impact on cloud evolution, we developed a new method for retrieving microphysical properties of concurrent pristine ice and snow aggregates from X-band polarimetric radar observations. Compared to aircraft cloud probe measurements, our retrieved total number concentration and ice water content are overestimated by 98% and 44%, respectively, which outperforms other empirical relationships. The capability of quantifying pristine ice number concentration, which is the most essential observable in SIP studies, opens a new opportunity to build a long-term record of SIP from surface-based radar measurements. We have also conducted simulations using a cloud-resolving model to evaluate the representativeness of the parameterizations of three SIP mechanisms and for studying the impact of SIP on a frontal system. We found a surprisingly good agreement between the observed and retrieved pristine ice number concentrations. The good performance is attributed to the rime splintering process in the temperature zone between–3° and –8°C, and to the ice-ice collision breakup process at higher altitudes. The impact of the shattering of large frozen drops appears minimal. Apart from the enhancement of ice number concentration and increased horizontal coverage of pristine ice, the addition of three SIP processes does not change cloud evolutions dramatically in our simulations.

58 GEOSCIENCES↗
NASA NTRS2010

Classification of Clouds and Deep Convection from GEOS-5 Using Satellite Observations

With the increased resolution of global atmospheric models and the push toward global cloud resolving models, the resemblance of model output to satellite observations has become strikingly similar. As we progress with our adaptation of the Goddard Earth Observing System Model, Version 5 (GEOS-5) as a high resolution cloud system resolving model, evaluation of cloud properties and deep convection require in-depth analysis beyond a visual comparison. Outgoing long-wave radiation (OLR) provides a sufficient comparison with infrared (IR) satellite imagery to isolate areas of deep convection. We have adopted a binning technique to generate a series of histograms for OLR which classify the presence and fraction of clear sky versus deep convection in the tropics that can be compared with a similar analyses of IR imagery from composite Geostationary Operational Environmental Satellite (GOES) observations. We will present initial results that have been used to evaluate the amount of deep convective parameterization required within the model as we move toward cloud system resolving resolutions of 10- to 1-km globally.

Putman, William↗
DOE OSTI2020

Effects of Cloud Liquid-Phase Microphysical Processes in Mixed-Phase Cumuli Over the Tibetan Plateau

Numerical simulations often overpredict precipitation over the Tibetan Plateau (TP). To examine the factors causing precipitation overprediction, different parameterizations of liquid-phase microphysical processes (accretion, autoconversion, and entrainment-mixing) are implemented into the Morrison microphysics scheme to simulate a TP precipitation event in summer with the Weather Research and Forecasting (WRF) model. The general spatial distribution and temporal trend of precipitation are captured by all simulations, but the precipitation rate is overpredicted. The results from sensitivity experiments suggest that compared to other examined liquid-phase processes, the accretion process is more important in precipitation simulation over the TP region. Further investigation with the Heidke skill scores reveals that accretion parameterization that takes into account the raindrop size produces the most accurate results in terms of the total surface precipitation. This parameterization suppresses spurious accretion and does not produce liquid-phase precipitation until cloud droplets are big enough. Here, it is also confirmed that increasing the model resolution can reduce precipitation overprediction. Results from the case study are confirmed by the use of a one-month simulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Evaluating Sea Breezes and Associated Convective Cloud Evolution in the Model Gray Zone

We characterize convective clouds associated with sea‐breeze circulations (SBC) using multi‐agency observations and multi‐case ensemble model simulations. The focus is on assessing convective cloud lifecycle properties and their merging behavior, as well as the environmental conditions they are embedded in, particularly SBC features. In total, 46 SBC days over the Houston‐Galveston region are selected and simulated using the Weather Research and Forecasting (WRF) model at a gray zone scale with a forecast‐like parameterization setup. Advanced techniques, including change‐point detection, a Lagrangian cloud tracking method, and a newly developed cell merging and splitting detection algorithm, are applied and/or developed for this study. Our findings indicate that the WRF model at 1 km grid spacing well represents the thermodynamic conditions over the region, as well as SBC timing and intensity. However, for the associated convective cells, WRF overestimates the 30‐dBZ echo top height, cell area, and maximum radar reflectivity compared to radar observations. This overestimation is potentially due to under‐resolved entrainment processes, an overestimated merging frequency, and the overestimation of updraft intensity. Furthermore, the model exhibits a deficiency in simulating congestus clouds, showing a more rapid transition from shallow to deep convection compared to observed behavior. Moreover, observations indicate stronger, deeper, and wider clouds when merging happens. Conversely, in simulations, the merging process does not necessarily lead to higher or longer‐lived cells, as many cases experience rapid and frequent merging and splitting which may result in more variance in convective updraft velocity during the convection lifetime.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2012

Sensitivity Studies of Dust Ice Nuclei Effect on Cirrus Clouds with the Community Atmosphere Model CAM5

In this study the effect of dust aerosol on upper tropospheric cirrus clouds through heterogeneous ice nucleation is investigated in the Community Atmospheric Model version 5 (CAM5) with two ice nucleation parameterizations. Both parameterizations consider homogeneous and heterogeneous nucleation and the competition between the two mechanisms in cirrus clouds, but differ significantly in the number concentration of heterogeneous ice nuclei (IN) from dust. Heterogeneous nucleation on dust aerosol reduces the occurrence frequency of homogeneous nucleation and thus the ice crystal number concentration in the Northern Hemisphere (NH) cirrus clouds compared to simulations with pure homogeneous nucleation. Global and annual mean shortwave and longwave cloud forcing are reduced by up to 2.0+/-0.1Wm (sup−2) (1 uncertainty) and 2.4+/-0.1Wm (sup−2), respectively due to the presence of dust IN, with the net cloud forcing change of −0.40+/-0.20W m(sup−2). Comparison of model simulations with in situ aircraft data obtained in NH mid-latitudes suggests that homogeneous ice nucleation may play an important role in the ice nucleation at these regions with temperatures of 205-230 K. However, simulations overestimate observed ice crystal number concentrations in the tropical tropopause regions with temperatures of 190- 205 K, and overestimate the frequency of occurrence of high ice crystal number concentration (greater than 200 L(sup-1) and underestimate the frequency of low ice crystal number concentration (less than 30 L(sup-1) at NH mid-latitudes. These results highlight the importance of quantifying the number concentrations and properties of heterogeneous IN (including dust aerosol) in the upper troposphere from the global perspective.

Liu, Xiaohong↗
NASA NTRS2005

Lightning NOx Production and Its Consequences for Tropospheric Chemistry

Cloud-resolving case-study simulations of convective transport and lightning NO production have yielded results which are directly applicable to the design of lightning parameterizations for global chemical transport models. In this work we have used cloud-resolving models (the Goddard Cumulus Ensemble Model (GCE) and MMS) to drive an off-line cloud-scale chemical transport model (CSCTM). The CSCTM, in conjunction with aircraft measurements of NO x in thunderstorms and ground-l;>ased lightning observations, has been used to constrain the amount of NO produced per flash. Cloud and chemistry simulations for several case studies of storms in different environments will be presented. Observed lightning flash rates have been incorporated into the CSCTM, and several scenarios of NO production per intracloud (IC) and per cloud-to-ground (CG) flash have been tested for each storm. The resulting NOx mixing ratios are compared with aircraft measurements taken within the storm (typically the anvil region) to determine the most likely NO production scenario. The range of values of NO production per flash (or per meter of lightning channel length) that have been deduced from the model will be shown and compared with values of production in the literature that have been deduced from observed NO spikes and from anvil flux calculations. Results show that on a per flash basis, IC flashes are nearly as productive of NO as CG flashes. This result simplifies the lightning parameterization for global models (ie., an algorithm for estimating the IC/CG ratio is not necessary). Vertical profiles of lightning NOx mass at the end of the 3-D storm simulations have been summarized to yield suggested profiles for use in global models. Estimates of mean NO production per flash vary by a factor of three from one simulated storm to another. When combined with the global flash rate of 44 flashes per second from NASA's Optical Transient Detector (OTD) measurements, these estimates and the results from other techniques yield global NO production rates of2-9 TgN/year. Simulations of the photochemistry over the 24 hours following a storm has been performed to determine the additional ozone production which can be attributed to lightning NO. Convective transport of HOx precursors leads to the generation of a HOx plume which substantially aids the downstream ozone production.

Pickering, Kenneth E.↗
NASA NTRS2005

Lightning NO(x) Production and Its Consequences for Tropospheric Chemistry

Cloud-resolving case-study simulations of convective transport and lightning NO production have yielded results which are directly applicable to the design of lightning parameterizations for global chemical transport models. In this work we have used cloud-resolving models (the Goddard Cumulus Ensemble Model (GCE) and MMS) to drive an off-line cloud-scale chemical transport model (CSCTM). The CSCTM, in conjunction with aircraft measurements of NO(x) in thunderstorms and ground-based lightning observations, has been used to constrain the amount of NO produced per flash. Cloud and chemistry simulations for several case studies of storms in different environments will be presented. Observed lightning flash rates have been incorporated into the CSCTM, and several scenarios of NO production per intracloud (IC) and per cloud-to-ground (CG) flash have been tested for each storm. The resulting NO(x) mixing ratios are compared with aircraft measurements taken within the storm (typically the anvil region) to determine the most likely NO production scenario. The range of values of NO production per flash (or per meter of lightning channel length) that have been deduced from the model will be shown and compared with values of production in the literature that have been deduced from observed NO spikes and from anvil flux calculations. Results show that on a per flash basis, IC flashes are nearly as productive of NO as CG flashes. This result simplifies the lightning parameterization for global models (ie., an algorithm for estimating the ICKG ratio is not necessary). Vertical profiles of lightning NOx mass at the end of the 3-D storm simulations have been summarized to yield suggested profiles for use in global models. Estimates of mean NO production per flash vary by a factor of three from one simulated storm to another. When combined with the global flash rate of 44 flashes per second from NASA's Optical Transient Detector (OTD) measurements, these estimates and the results from other techniques yield global NO production rates of 2-9 TgN/year. Simulations of the photochemistry over the 24 hours following a storm has been performed to determine the additional ozone production which can be attributed to lightning NO. Convective transport of HO(x), precursors leads to the generation of a HO(x), plume which substantially aids the downstream ozone production.

Pickering, Kenneth E.↗
NASA NTRS1980

Interaction of a cumulus cloud ensemble with the large-scale environment. II

The closure assumption of the Arakawa-Schubert (1974) cumulus parameterization is examined with attention to the kinetic energy budget of a cumulus subensemble. It is concluded that dissipation should depend primarily on cloud type, and that cloud-work functions calculated under different synoptic conditions should consequently be quasi-constant for each cloud type. Observational evidence for the cloud-work function quasi-equilibrium is presented. Cloud-work functions are calculated from a variety of data sets in the tropics and subtropics. The results demonstrate that the cloud-work functions fall into a well-defined narrow range for each subensemble, although the thermodynamical vertical structures for each data set are quite different.

Lord, S. J.↗
NASA NTRS1993

New parameterizations and sensitivities for simple climate models

This paper presents a reexamination of the earth radiation budget parameterization of energy balance climate models in light of data collected over the last 12 years. The study consists of three parts: (1) an examination of the infrared terrestrial radiation to space and its relationship to the surface temperature field on time scales from 1 month to 10 years; (2) an examination of the albedo of the earth with special attention to the seasonal cycle of snow and clouds; (3) solutions for the seasonal cycle using the new parameterizations with special attention to changes in sensitivity. While the infrared parameterization is not dramatically different from that used in the past, the albedo in the new data suggest that a stronger latitude dependence be employed. After retuning the diffusion coefficient the simulation results for the present climate generally show only a slight dependence on the new parameters. Also, the sensitivity parameter for the model is still about the same (1.25 C for a 1 percent increase of solar constant) for the linear models and for the nonlinear models that include a seasonal snow line albedo feedback (1.34 C). One interesting feature is that a clear-sky planet with a snow line albedo feedback has a significantly higher sensitivity (2.57 C) due to the absence of smoothing normally occurring in the presence of average cloud cover.

Graves, Charles E.↗
NASA NTRSDate not supplied

Boundary-Layer Cloud Modeling Challenges on the North Slope of Alaska

The accurate modeling and prediction of cloud base heights is critical for energy balance calculations and aviation operations, alike. Low-level (i.e., boundary-layer) Arctic clouds can be difficult to model, making prediction of formation and dissipation challenging. Primarily mixed-phase, these clouds typically contain low quantities of supercooled liquid water and often slowly precipitate relatively small amounts of moderately and heavily rimed snow particles. While this appears to be the predominant cloudy state on the North Slope of Alaska (NSA), the delicate balance of microphysical, dynamical, radiative, surface coupling, and advective processes can rapidly shift to heavy snow (with various degrees of riming) or to a complete dissipation of the cloud layer without any precipitation, depending on the dominant processes. Here we strive to disentangle these various processes. First, we compare the predictive performances of four different numerical weather models in forecasting the presence and base-heights of low-level clouds: the High-Resolution Rapid Refresh - Alaska (HRRR-AK) model, the Polar Weather Research and Forecasting (Polar WRF) model, the Unified Model (UM), and the European Centre for Medium-range Weather Forecasting (ECMWF) model. Initial results comparing model output at two U.S. Department of Energy Atmospheric Radiation Measurement (AMT) NSA sites, during the fall season in 2019 and 2022, show that the UM slightly outperforms the HRRR-AK in terms of accurately forecasting the presence of a low-level cloud layer (89% of the time). All models have a significant bias of 300 to 800 meters in forecasting cloud base height (lower than is observed); however, the UM and ECMWF models have the lowest biases. Finally, a case study for a particularly challenging April 2017 thin-cloud event is presented, wherein we compare the performance of four different bulk microphysical parameterization schemes using a higher-resolution large eddy simulation (LES) model, the WRF-LES. Initial results show that the Thompson scheme was the only one able to reproduce and sustain a substantial supercooled liquid layer, but it was unable to reproduce the transition from a deep, liquid-rich cloud to a thin layer with moderately and heavily rimed precipitation. This is the first step in linking simulated LES-scale riming processes with those parameterized at a coarser mesoscale model scale. This has important implications for forecasting low-level clouds in an operational environment, given the efficiency of the riming process.

cloud base heights↗
DOE OSTI2023

Long-term variability in immersion-mode marine ice-nucleating particles from climate model simulations and observations

Abstract. Ice-nucleating particles (INPs) in the Southern Ocean (SO) atmosphere have significant impacts on cloud radiative and microphysical properties. Yet, INP prediction skill in climate models remains poorly understood, in part because of the lack of long-term measurements. Here we show, for the first time, how model-simulated INP concentrations compare with year-round INP measurements during the Macquarie Island Cloud Radiation Experiment (MICRE) campaign from 2017–2018. We simulate immersion-mode INP concentrations using the Energy Exascale Earth System Model version 1 (E3SMv1) by combining simulated aerosols with recently developed deterministic INP parameterizations and the native classical nucleation theory (CNT) for mineral dust in E3SMv1. Because MICRE did not collect aerosol measurements of super-micron particles, which are more effective ice nucleators, we evaluate the model's aerosol fields at other high-latitude sites using long-term in situ observations of dust and sea spray aerosol. We find that the model underestimates dust and overestimates sea spray aerosol concentrations by 1 to 2 orders of magnitude for most of the high-latitude sites in the Southern Hemisphere. We next compare predicted INP concentrations with concentrations of INPs collected on filter samples (typically for 2 or 3 d) and processed offline using the Colorado State University ice spectrometer (IS) in immersion freezing mode. We find that when deterministic parameterizations for both dust and sea spray INPs are used, simulated INPs are within a factor of 10 of observed INPs more than 60 % of the time during summer. Our results also indicate that the E3SM's current treatment of mineral dust immersion freezing in the SO is impacted by compensating biases – an underprediction of dust amount was compensated by an overprediction of its effectiveness as INPs. We also perform idealized droplet freezing experiments to quantify the implications of the time-dependent behavior assumed by the E3SM's CNT-parameterization and compare with the ice spectrometer observations. We find that the E3SM CNT 10 s diagnostic used in this study is a reasonable approximation of the exact formulation of CNT, when applied to ice spectrometer measurements in low-INP conditions similar to Macquarie Island. However, the linearized 10 s diagnostic underestimates the exact formula by an order of magnitude or more in places with high-INP conditions like the Sahara. Overall, our findings suggest that it is important to correct the biases in E3SM's simulated dust life cycle and update E3SM's INP parameterizations. INP prediction errors of 2 to 3 orders of magnitude can have considerable impacts on the simulated cloud and radiative properties in global climate models. On comparing INP concentrations during MICRE against ship-based campaigns, Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS) and Antarctic Circumnavigation Expedition (ACE), we find that INPs from the latter are significantly higher only in regions closer to Macquarie Island. This alludes to the fact that physical, chemical and biological processes affecting INP concentrations as stimulated by the island could be partly responsible for the high INP concentrations observed at Macquarie Island during the MICRE campaign. Therefore, improvements to both aerosol simulation and INP parameterizations are required to adequately simulate INPs and their cloud impacts in E3SM. It will be helpful to include a parallel measurement of the size-resolved aerosol composition and explore opportunities for long-term measurement platforms in future field campaigns studying INP sources in remote marine regions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Dependence of CCN closure relationship with organic fraction from two airborne field campaigns over mid-latitude land and ocean

This study investigates the relationship between measured and calculated cloud condensation nuclei (CCN) number concentration and its dependence with organic fraction utilizing aircraft observations from The Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA, 2017–2018) and The Holistic Interactions of Shallow Clouds, Aerosols, and Land Ecosystems (HI-SCALE, 2016) campaigns, which represent midlatitude marine and continental environments, respectively. For the ACE-ENA marine region, aerosol and CCN concentrations were significantly higher in summer than in winter, whereas at continental site for HI-SCALE, aerosol and CCN concentrations showed no pronounced differences between spring and autumn. Using aerosol chemical composition and number size distribution data, CCN concentrations at various supersaturations are calculated based on Köhler theory and then compared with observations from CCN counter. The results show that CCN closure performs well at both sites with a slight overestimation, with mean closure ratio (CR) of 1.13 and 1.17, respectively. Further investigation reveals that CR at lower supersaturation perform better than that at higher supersaturation. The dependence of CR on organic mass fraction (MForg) varies by environment: for marine aerosols, CR decreases with increasing organic fraction at lower supersaturations, whereas continental aerosols exhibit a consistent overestimation, with CR decreasing as organic fraction increases at higher supersaturations. This study provides key insights into CCN characteristics over midlatitude marine and continental environments, emphasizing the necessity of incorporating size-resolved chemical composition and mixing states into future model parameterizations, and contributing to a better understanding of aerosol–cloud interactions.

ACE-ENA field campaign↗
NASA NTRS1986

Cloud and radiation experiments with a general circulation model

Interactions between cloud fields and radiation fields in GCM simulations were examined with June-July simulations with the UCLA/Goddard GCM. Modified radiation parameterizations for longwave and shortwave transfer were made to the GCM. The model generated supersaturation, boundary layer and convective clouds. The simulations were configured to consider the absence of water vapor absorption in the longwave parameterization, no appearance of anvils, and no detrainment of liquid water.

HARSHVARDHAN↗
NASA NTRS1991

Clouds-radiation interactions in a general circulation model - Impact upon the planetary radiation balance

Simultaneously conducted observations of the earth radiation budget and the cloud amount estimates, taken during the June 1979 - May 1980 Nimbus 7 mission were used to show interactions between the cloud amount and raidation and to verify a long-term climate simulation obtained with the latest version of the NCAR Community Climate Model (CCM). The parameterization of the radiative, dynamic, and thermodynamic processes produced the mean radiation and cloud quantities that were in reasonable agreement with satellite observations, but at the expense of simulating their short-term fluctuations. The results support the assumption that the inclusion of the cloud liquid water (ice) variable would be the best mean to reduce the blinking of clouds in NCAR CCM.

Smith, Laura D.↗
NASA NTRS1993

Surface Net Solar Radiation Estimated from Satellite Measurements: Comparisons with Tower Observations

A parameterization that relates the reflected solar flux at the top of the atmosphere to the net solar flux at the surface in terms of only the column water vapor amount and the solar zenith angle was tested against surface observations. Net surface fluxes deduced from coincidental collocated satellite-measured radiances and from measurements from towers in Boulder during summer and near Saskatoon in winter have mean differences of about 2 W/sq m, regardless of whether the sky is clear or cloudy. Furthermore, comparisons between the net fluxes deduced from the parameterization and from surface measurements showed equally good agreement when the data were partitioned into morning and afternoon observations. This is in contrast to results from an empirical clear-sky algorithm that is unable to account adequately for the effects of clouds and that shows, at Boulder, a distinct morning to afternoon variation, which is presumably due to the predominance of different cloud types throughout the day. It is also demonstrated that the parameterization may be applied to irradiances at the top of the atmosphere that have been temporally averaged by using the temporally averaged column water vapor amount and the temporally averaged cosine of the solar zenith angle. The good agreement between the results of the parameterization and surface measurements suggests that the algorithm is a useful tool for a variety of climate studies.

Li, Zhanqing↗