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At least 163 records · Page 9

Investigation of Cloud Feedback in the GLAS Model

The theoretical and observational studies of cirrus clouds were reviewed to provide information for more realistic treatments of cirrus in the general circulation models. Based on the review, one time-step and ten-day model simulations were conducted to investigate the differences in the longwave radiation flux between the black and transparent cirrus treatment in the infrared. For both experiments substantial difference in the outgoing longwave flux at the top of the atmosphere is found. For the ten-day simulations, the differences in the convective, supersaturation and total cloudiness, temperature, and sensible and latent heat fluxes are also examined on various temporal and spatial scales. Although the cause-and-effect is difficult to identify, the results clearly suggest that on the time scale of a few days and longer cloud-radiation interactions play an important role. Sensitivity study of the longwave radiation flux to different longwave radiation parameterizations was performed by comparing the calculated fluxes between the Wu-Kaplan's scheme used in the present GLAS model and the Wang's schemes for climate studies.

Wang, W. C.↗

Evaluation of Methods to Estimate the Surface Downwelling Longwave Flux during Arctic Winter

Surface longwave radiation fluxes dominate the energy budget of nighttime polar regions, yet little is known about the relative accuracy of existing satellite-based techniques to estimate this parameter. We compare eight methods to estimate the downwelling longwave radiation flux and to validate their performance with measurements from two field programs in thc Arctic: the Coordinated Eastern Arctic Experiment (CEAREX ) conducted in the Barents Sea during the autumn and winter of 1988, and the Lead Experiment performed in the Beaufort Sea in the spring of 1992. Five of the eight methods were developed for satellite-derived quantities, and three are simple parameterizations based on surface observations. All of the algorithms require information about cloud fraction, which is provided from the NASA-NOAA Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) polar pathfinder dataset (Path-P): some techniques ingest temperature and moisture profiles (also from Path-P): one-half of the methods assume that clouds are opaque and have a constant geometric thickness of 50 hPa, and three include no thickness information whatsoever. With a somewhat limited validation dataset, the following primary conclusions result: (1) all methods exhibit approximately the same correlations with measurements and rms differences, but the biases range from -34 W sq m (16% of the mean) to nearly 0; (2) the error analysis described here indicates that the assumption of a 50-hPa cloud thickness is too thin by a factor of 2 on average in polar nighttime conditions; (3) cloud-overlap techniques. which effectively increase mean cloud thickness, significantly improve the results; (4) simple Arctic-specific parameterizations performed poorly, probably because they were developed with surface-observed cloud fractions; and (5) the single algorithm that includes an estimate of cloud thickness exhibits the smallest differences from observations.

Chiacchio, Marc↗

The Diurnal Cycle in TOGA-COARE: Regional Scale Model Simulations

The diurnal variation of precipitation processes over the tropics is a well-known phenomenon and has been studied using surface rainfall data, radar reflectivity data, and satellite-derived cloudiness and precipitation. Recently, Sui (1997) analyzed observations from TOGA COARE in the tropical western Pacific ocean to study the relevant mechanisms producing diurnal variation of precipitation. They found that the diurnal SST cycle is important for afternoon showers in the undisturbed periods and diurnal radiative processes for nocturnal rainfall. Takayabu (1996) found a quasi-2-day cycle in precipitation during TOGA COARE and they suggested that inertia-gravity waves may be associated with this 2-day cycle. Chen and Houze (1997), however, suggested that the quasi-2-day oscillation is mainly a function of the time required by the lower-tropospheric moisture field to recover from the drying caused by deep convection. In this study, the Penn State/NCAR Mesoscale Model (MM5) with improved physics (i.e., cloud microphysics, radiation, land-soil-vegetation-surface processes, and TOGA COARE flux scheme) and a multiple level nesting technique will be used to simulate two TOGA COARE convective espisodes, one convectively suppressed phase (mid to late January 1993) and one convectively active phase (mid to late December 1992). We will examine precipitation processes over the open ocean and over land by comparing MM5 simulated rainfall and out-going longwave radiation. By examining the OLR and precipitation, we can determine if there is a temporal lag between the maximum precipitation and the coldest upwelling longwave radiation (the time-lag between stratiform-cirrus and convective towers). The boundary layer response by (or recovery from) precipitation processes will also be shown by examining the PBL thermodynamic structure and the sensible and latent heat fluxes. A preliminary MM5 simulation showed a clear diurnal variation in rainfall over both land and open ocean for the convectively active phase. The results also indicated that a quasi-2-day cycle in precipitation was simulated only over part of the ocean.

Tao, W.-K.↗

Sensitivity of Arctic Surface Temperature to Including a Comprehensive Ocean Interior Reflectance to the Ocean Surface Albedo Within the Fully Coupled CESM2

Abstract Almost all current climate models simplify the ocean surface albedo (OSA) by assuming the reflected solar energy without the ocean interior contribution. In this study, an improved ocean surface albedo scheme is incorporated into the Community Earth System Model version 2 (CESM2) to assess the sensitivity of Arctic surface temperature to including ocean interior reflectance to the OSA. Fully coupled CESM2 simulations with and without ocean interior reflectance are subsequently performed, we focus on the analysis of Arctic surface temperature responses. Incorporating ocean interior reflectance increases absorbed solar radiation and warms the ocean, enhancing seasonal heat storage and release across the Arctic Ocean, and increasing sea ice reduction and positive climate feedbacks that elevates Arctic surface temperature. Seasonal variations in air‐surface temperature differences induce changes in turbulent heat flux patterns, concurrently modifying dynamic advection and moisture processes that affect boundary layer humidity and low clouds, especially in winter. Based on partitioning physical processes in the thermodynamic energy equation, surface air warming is induced primarily through positive heating anomalies of vertical advection, latent heat release, and longwave radiative forcing. Through an examination of the surface energy budget, skin temperature warming is driven predominantly by increased downward longwave radiation, positive surface albedo feedback in summer, and increased conductive heat transport from the ocean particularly in winter. Significant effects of ocean interior reflectance on the Arctic Ocean, including sea surface warming and sea ice reduction, justify the importance of ocean interior reflectance in climate models for better understanding of ongoing Arctic climate changes.

Meteorology & Atmospheric Sciences↗

The role of global cloud climatologies in validating numerical models

Reliable estimates of the components of the surface radiation budget are important in studies of ocean-atmosphere interaction, land-atmosphere interaction, ocean circulation and in the validation of radiation schemes used in climate models. The methods currently under consideration must necessarily make certain assumptions regarding both the presence of clouds and their vertical extent. Because of the uncertainties in assumed cloudiness, all these methods involve perhaps unacceptable uncertainties. Here, a theoretical framework that avoids the explicit computation of cloud fraction and the location of cloud base in estimating the surface longwave radiation is presented. Estimates of the global surface downward fluxes and the oceanic surface net upward fluxes were made for four months (April, July, October and January) in 1985 to 1986. These estimates are based on a relationship between cloud radiative forcing at the top of the atmosphere and the surface obtained from a general circulation model. The radiation code is the version used in the UCLA/GLA general circulation model (GCM). The longwave cloud radiative forcing at the top of the atmosphere as obtained from Earth Radiation Budget Experiment (ERBE) measurements is used to compute the forcing at the surface by means of the GCM-derived relationship. This, along with clear-sky fluxes from the computations, yield maps of the downward longwave fluxes and net upward longwave fluxes at the surface. The calculated results are discussed and analyzed. The results are consistent with current meteorological knowledge and explainable on the basis of previous theoretical and observational works; therefore, it can be concluded that this method is applicable as one of the ways to obtain the surface longwave radiation fields from currently available satellite data.

HARSHVARDHAN↗

Monthly Mean In Situ Surface Flux Observations Paired with Satellite-Derived and Reanalysis-Based Flux Data for the Great Lakes Region, 2001–2020

Surface radiative and turbulent heat fluxes over the Great Lakes strongly influence regional hydrological and meteorological processes, and their accurate representation is critical for numerical weather prediction and coupled atmosphere–lake modeling. However, direct flux observations are spatially sparse across the region, so gridded reanalysis and satellite-derived products are often used for climatological analyses and model evaluation despite differences in their flux representations. This dataset provides processed, quality-controlled, monthly mean surface flux observations from the Great Lakes Evaporation Network (GLEN), AmeriFlux, and the National Data Buoy Center, paired with spatiotemporally matched flux estimates from two reanalysis products, the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis dataset (ERA5) and the Modern Era Reanalysis for Research and Applications, version 2 (MERRA-2), and two satellite-derived products, the Clouds and Earth's Radiant Energy Systems Energy Balanced and Filled (CERES-EBAF) and the Cloud, Albedo and Surface Radiation dataset from AVHRR data - Edition 3 (CLARA-A3). The dataset includes sixteen observational stations with variable temporal coverage within 2001–2020. For each station, a CSV file contains monthly time series of available flux variables, including surface downwelling shortwave radiation (SW), surface downwelling longwave radiation (LW), sensible heat (SH) flux, and latent heat flux (LH), alongside matched gridded product values where available. Columns in the CSV file correspond to different variables sourced from each dataset, with column titles structured as "{dataset}_{variable}". Columns with relevant metadata are also provided in each CSV file, including station latitude and longitude, monthly timestamps, and the name of the sourced observational data. These files are structured for direct use in common analysis tools, including Microsoft Excel, Python pandas, and Python matplotlib. This dataset supports climatological analysis of the Great Lakes regional surface energy budget, evaluation of satellite-derived and reanalysis-based flux products, and development or validation of flux representations in numerical weather prediction and coupled atmosphere–lake models.

Great Lakes↗

TPSAS-NF1676L-17940-DND

The NASA/GEWEX SRB (Global Energy and Water Exchanges, Surface Radiation Budget) project produces and archives shortwave and longwave radiation budget flux estimates at the top of the atmosphere and at the Earth's surface. The latest version in the archive, Release 3.0, is available as 3-hourly, 3-hourly-monthly, daily and monthly means continuously over the period from July 1983 to December 2007 on a quasi-equal-area grid system of 44016 grid boxes. SRB Release 4 with further improvements in data quality and higher spatial resolution is being developed. The SRB shortwave/longwave fluxes at the Earth's surface from the algorithm GSW(V3.0)/GLW(V3.1) have been extensively validated against high-quality ground-based observations, in particular observed data from the Baseline Surface Radiation Network (BSRN). Comparisons with nearly 6000 site-months of both shortwave and longwave data from 52 BSRN sites show generally good agreement. In addition, the GEWEX SRB data have also been found to compare favorably with the World Radiation Data Centre (WRDC) data and the Global Energy Balance Archive (GEBA) data. In spite of the fact that the BSRN sites are scattered on all seven continents, the validation of the SRB data over the vast oceans had not been done until recently. In this paper, we present comparisons of the GEWEX-SRB data shortwave/longwave data with observations made on arrays moored in tropical oceans. Specifically, we have data from 21 buoys, or moorings, from Predictions and Research Moored Array in the Atlantic (PIRATA), 14 buoys from the Research Moored Array for African-Asian-Australian Monsoon Analysis and Prediction (RAMA) in the Indian Ocean, 20 buoys from the Tropical Atmosphere Ocean (TAO) array in the Pacific, and 3 buoys from the Woods Hole Oceanographic Institute (WHOI) (2 in the Pacific and 1 in the Atlantic). The data from these buoys span 12 years from 2000 to 2011, though not necessarily continuously. It is found that except for occasional outliers, the majority of the comparable pairs of data points agree well. Further examination of the outliers is necessary to determine whether they can be attributed to wind-driven tilt and/or aerosol accumulation on the instruments. In order to see how the ocean-based validation compares with land-based validation, we made SRB-BSRN monthly mean shortwave/longwave radiation comparisons in the tropical region only, where all the buoys are moored. The results show that in the case of shortwave radiation, the bias error from the ocean-based validation is somewhat larger than its land-based counterpart, but their RMS errors are not significantly different. In the case of longwave radiation, the ocean-based and land-based validations show nearly identical comparison statistics.

Taiping Zhang↗

Understanding the Biases in Global Monsoon Simulations from the Perspective of Atmospheric Energy Transport

Understanding global monsoon (GM) variability and projecting its future changes rely heavily on climate models. However, climate models generally show pronounced biases in GM simulations, and the reasons for this remain unclear. Here, in this study, we evaluate the performance of 20 pairs of climate models that participated in both phase 5 of the Coupled Model Intercomparison Project (CMIP5) and phase 6 of CMIP (CMIP6) and identify the sources of their GM simulation biases from an energy transport perspective. The multimodel mean improvement in CMIP6 compared to CMIP5 is demonstrated by the increasing skill scores for various GM metrics from 0.20–0.79 to 0.48–0.83. More specifically, the dry biases in the Northern Hemisphere Summer Monsoon (NHSM) precipitation in CMIP5 [root-mean-square error (RMSE): 1.85 mm day −1 ] are reduced in CMIP6 (RMSE: 1.66 mm day −1 ). This higher simulation skill is associated with higher skill in simulating the precipitation-solstitial mode, monsoon intensity, and monsoon domains. The improvement in the NHSM precipitation simulation results from that in the meridional transport of atmospheric energy. Atmospheric energy budget analysis shows that the negative biases in downward surface longwave radiation and northward energy transport are smaller in CMIP6 than in CMIP5 in the boreal summer, resulting in a more realistic interhemispheric thermal contrast and meridional gradient of moist static energy. However, a major weakness of the CMIP6 models is found in the Southern Hemisphere Summer Monsoon precipitation simulation due to the positive bias in the top-of-the-atmosphere downward longwave radiation. This study shows that reasonably reproducing the meridional global atmospheric energy transportation is necessary for skillful GM simulation.

54 ENVIRONMENTAL SCIENCES↗

A More Transparent Infrared Window

The infrared window region (780–1,250 cm –1 , 12.8 to 8.0 μm) is of great importance to Earth's climate due to its high transparency and thermal energy. We present here a new investigation of the transparency of this spectral region based on observations by interferometers of downwelling surface radiance at two DOE Atmospheric Radiation Measurement program sites. We focus on the dominant source of absorption in this region, the water vapor continuum, and derive updated values of spectral absorption coefficients for both the self and foreign continua. Our results show that the self continuum is too strong in the previous version of Mlawer-Tobin_Clough-Kneizys-Davies (MT_CKD) water vapor continuum model, a result that is consistent with other recent analyses, while the foreign continuum is too weak in MT_CKD. In general, the weaker self continuum derived in this study results in an overall increase in atmospheric transparency in the window, although in atmospheres with low amounts of water vapor the transparency may slightly decrease due to the increase in foreign continuum absorption. These continuum changes lead to a significant decrease in downwelling longwave flux at the surface for moist atmospheres and a modest increase in outgoing longwave radiation. The increased fraction of surface-leaving radiation that escapes to space leads to a notable increase (~5–10%) in climate feedback, implying that climate simulations that use the new infrared window continuum will show somewhat less warming than before. This study also points out the possibly important role that aerosol absorption may play in the longwave radiative budget.

58 GEOSCIENCES↗

Data/code for Mlawer et al. 2024 (A more transparent infrared window)

The infrared window region (780–1,250 cm –1 , 12.8 to 8.0 μm) is of great importance to Earth's climate due to its high transparency and thermal energy. We present here a new investigation of the transparency of this spectral region based on observations by interferometers of downwelling surface radiance at two DOE Atmospheric Radiation Measurement program sites. We focus on the dominant source of absorption in this region, the water vapor continuum, and derive updated values of spectral absorption coefficients for both the self and foreign continua. Our results show that the self continuum is too strong in the previous version of Mlawer-Tobin_Clough-Kneizys-Davies (MT_CKD) water vapor continuum model, a result that is consistent with other recent analyses, while the foreign continuum is too weak in MT_CKD. In general, the weaker self continuum derived in this study results in an overall increase in atmospheric transparency in the window, although in atmospheres with low amounts of water vapor the transparency may slightly decrease due to the increase in foreign continuum absorption. These continuum changes lead to a significant decrease in downwelling longwave flux at the surface for moist atmospheres and a modest increase in outgoing longwave radiation. The increased fraction of surface-leaving radiation that escapes to space leads to a notable increase (~5–10%) in climate feedback, implying that climate simulations that use the new infrared window continuum will show somewhat less warming than before. This study also points out the possibly important role that aerosol absorption may play in the longwave radiative budget.

54 ENVIRONMENTAL SCIENCES↗

The Extraordinary March 2022 East Antarctica “Heat” Wave. Part II: Impacts on the Antarctic Ice Sheet

Abstract Between 15 and 19 March 2022, East Antarctica experienced an exceptional heat wave with widespread 30°–40°C temperature anomalies across the ice sheet. In Part I, we assessed the meteorological drivers that generated an intense atmospheric river (AR) that caused these record-shattering temperature anomalies. Here, we continue our large collaborative study by analyzing the widespread and diverse impacts driven by the AR landfall. These impacts included widespread rain and surface melt that was recorded along coastal areas, but this was outweighed by widespread high snowfall accumulations resulting in a largely positive surface mass balance contribution to the East Antarctic region. An analysis of the surface energy budget indicated that widespread downward longwave radiation anomalies caused by large cloud-liquid water contents along with some scattered solar radiation produced intense surface warming. Isotope measurements of the moisture were highly elevated, likely imprinting a strong signal for past climate reconstructions. The AR event attenuated cosmic ray measurements at Concordia, something previously never observed. Last, an extratropical cyclone west of the AR landfall likely triggered the final collapse of the critically unstable Conger Ice Shelf while further reducing an already record low sea ice extent. Significance Statement Using our diverse collective expertise, we explored the impacts from the March 2022 heat wave and atmospheric river across East Antarctica. One key takeaway is that the Antarctic cryosphere is highly sensitive to meteorological extremes originating from the midlatitudes and subtropics. Despite the large positive temperature anomalies driven from strong downward longwave radiation, this event led to huge amounts of snowfall across the Antarctic interior desert. The isotopes in this snow of warm airmass origin will likely be detectable in future ice cores and potentially distort past climate reconstructions. Even measurements of space activity were affected. Also, the swells generated from this storm helped to trigger the final collapse of an already critically unstable Conger Ice Shelf while further degrading sea ice coverage.

Wille, Jonathan D.↗

Gridded Sub-daily Climate Forcings for North America Based on Daymet and ERA5 (Daymet-ERA5)

To support high spatial and temporal resolution land surface modeling, this dataset provides hourly time step historic weather forcing at 1-km spatial resolution for the entire North America. The latest Daymet V4 data provides gridded historic daily weather observations at 1-km spatial resolution from 1980 to 2024. Using sub-daily temporal information from the ECMWF ERA5 reanalysis, Daymet was further temporally downscaled to hourly time steps and provided in the format required for land surface model simulations. The process of temporal downscaling preserves the relative magnitude in each hourly time step from ERA5 while maintaining the total and average values from Daymet for each day. This results in a blended 1980-2024 Daymet-ERA5 dataset. Available variables include surface air temperature, precipitation, specific humidity, shortwave and longwave radiation, wind speed, and pressure. These data can be used as a high-resolution meteorological forcing dataset to support high-resolution land surface modeling where accurate meteorological forcing datasets built from historic observations and/or reanalysis datasets are desirable.

54 ENVIRONMENTAL SCIENCES↗

Linear Response Function Reveals the Most Effective Remote Forcing in Causing September Arctic Sea Ice Melting in CESM

We apply the linear response function method to investigate the most excitable mode of the September Arctic sea ice and its corresponding remote oceanic forcing in climate models. The method is useful in identifying the fundamental, dynamical and causal relationship between the remote forcing and sea ice response. We find that the most excitable mode of the September Arctic sea ice preferentially takes place over the Pacic side of the Arctic and its remote forcing corresponds to a dipole pattern of precipitation anomaly in the tropics with an increase of precipitation over the western and central tropical and subtropical Pacic ocean while a decrease over the Maritime Continent. The tropical precipitation anomaly likely drives a Rossby wave train propagating toward higher latitudes and leads to a ridge anomaly over the Pacic side of the Arctic, resulting in poleward atmospheric heat transport, enhanced downward longwave radiation and thus melting of the sea ice. In addition, a good agreement is found with the leading tropical Arctic teleconnection mode detected in a pre-industrial control simulation, which supports the usefulness and robustness of the linear response function method and the importance of tropical forcing in shaping the sea ice variability.

Wu, Yutian↗

The impact of forest-controlled snow variability on late-season streamflow varies by climatic region and forest structure

Previous studies have documented how forests influence snow at fine spatial scales, but none have documented the influence that existing forest-snow variability has on streamflow. Here to test how much forest-controlled snow variability influences streamflow, a tiling parameterization based on classifications from high-resolution (1–3 m) vegetation maps was incorporated into the Distributed Hydrology and Soil Vegetation Model (DHSVM). Within each grid cell (90–150 m), the tiling parameterization simulated forest-snow variability with four independently evolving snowpacks. Each tile had unique radiation conditions to represent conditions underneath the canopy, in exposed areas, and along north- and south-facing forest edges. This tiled parameterization was used to test where and when detailed forest-snow modelling should be considered further and where and when the impacts are too small to be worth the effort. To test this, tiled model simulations of streamflow were compared to non-tiled model simulations in the Sierra Nevada, CA, the Jemez Mountains, NM, and the Eastern Cascades, WA. In Tuolumne, CA, the tiled model simulated little difference in grid cell average SWE, and late-season streamflow decreased by only 3%–4% compared to the non-tiled model. In Jemez, NM, the tiled model decreased late-season streamflow by 18% due to increased sublimation. In Chiwawa, WA, the tiled model increased late-season streamflow by 15% due to high shortwave radiation attenuation and less longwave radiation enhancement from the forest. Furthermore, within the Chiwawa, a substantial silvicultural practice was synthetically implemented to increase the north-facing edge's fractional area. This silvicultural experiment, which used the same fractional forest area in all simulations increased late-season streamflow by 35% compared to tiled model simulations that did not represent forest edges. In conclusion, representing forest-SWE variability had an effect on late-season streamflow in some watersheds but not in others based on the fractional area of the forest edges, forest characteristics, and climate conditions.

54 ENVIRONMENTAL SCIENCES↗

Machine Learning Eliminates Reanalysis Warm Bias and Reveals Weaker Winter Surface Cooling Over Arctic Sea Ice

The surface energy budget governs Arctic sea-ice growth/melt, yet observations are sparse, and reanalysis data sets suffer from systematic biases. Here, we train a neural network with observational data to bias-correct hourly ERA5 fluxes over Arctic ice-covered regions (≥70°N; sea-ice concentration >80%) for 1994–2024. Training data cover two full seasonal cycles and different sea-ice regimes. The neural network reduces RMSE for net shortwave radiation by ∼40%, downward longwave radiation by ∼16% and the total surface energy budget by ∼55%, eliminating the wintertime warm bias of ∼4 K in ERA5. Wintertime surface cooling is reduced by ∼50%, yielding thermodynamic ice-growth estimates of ∼80–120 cm, consistent with SMOS–CryoSat satellite thickness increases and in contrast to the 150–200 cm growth implied by ERA5. Our bias-corrected data capture the observed clear/cloudy states of the winter boundary layer and can be used to study Arctic climatology, evaluate climate models and drive sea-ice-ocean models.

Hossain, Akil [Alfred Wegener Institute for Polar ↗

Generation of available potential energy and the energy cycle during the global weather experiment

Two major themes were pursued during this research period. The first of these involved examining the impacts of satellite-based data and the forecast model used by the Goddard Laboratory for Atmospheres (GLA) on general circulation statistics. For the other major topic, the diabatic heating fields produced by GLA were examined for one month during the FGGE First Special Observing Period. As part of that effort, the three-dimensional distribution of the four component heating fields were studied, namely those due to shortwave radiation, Q sub SW, longwave radiation, Q sub LW, sensible heating, Q sub S, and latent heating, Q sub L. These components were calculated as part of the GLA analysis/forecast system and archived every quarter day; from these archives cross products with temperature were computed to enable the direct calculation of certain terms of the large-scale atmospheric energy cycle, namely those involving the generation of available potential energy (APE). The decision to archive the diabatic heating components separately has enabled researchers to study the role of the various processes that drive the energy cycle of the atmosphere.

Salstein, D. A.↗

Longwave cloud radiative forcing at the surface from ISCCP-C1 data

A method for deriving one component of the total cloud forcing picture, namely, the LW cloud forcing at the surface, is presented. The method is based on a validated radiative transfer technique and utilizes meteorological data available from the International Satellite Cloud Climatology Project. The radiative transfer model used was validated earlier and the TOVS-derived temperature and water vapor data used were generally reasonable. On a monthly-average basis, random error was estimated to be in the 5-10 W/sq m range, but biases as large as 10-20 W/sq m can occur in some regions. The lack of information on cloud-base heights were found to be the largest source of errors in the models and the meteorological data.

Gupta, Shashi K.↗