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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Deep Convective Cloud Top Heights and Their Thermodynamic Control During CRYSTAL-FACE

Infrared (11 micron) radiances from GOES-8 and local radiosonde profiles, collected during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE) in July 2002, are used to assess the vertical distribution of Florida-area deep convective cloud top height and test predictions as to its variation based on parcel theory. The highest infrared tops (Z(sub 11)) reached approximately to the cold point, though there is at least a 1-km uncertainty due to unknown cloud-environment temperature differences. Since lidar shows that visible 'tops' are 1 km or more above Z(sub 11), visible cloud tops frequently penetrated the lapse-rate tropopause (approx. 15 km). Further, since lofted ice content may be present up to approx. 1 km above the visible tops, lofting of moisture through the mean cold point (15.4 km) was probably common. Morning clouds, and those near Key West, rarely penetrated the tropopause. Non-entraining parcel theory (i.e., CAPE) does not successfully explain either of these results, but can explain some of the day-to-day variations in cloud top height over the peninsula. Further, moisture variations above the boundary layer account for most of the day-today variability not explained by CAPE, especially over the oceans. In all locations, a 20% increase in mean mixing ratio between 750 and 500 hPa was associated with about 1 km deeper maximum cloud penetration relative to the neutral level. These results suggest that parcel theory may be useful for predicting changes in cumulus cloud height over time, but that parcel entrainment must be taken into account even for the tallest clouds. Accordingly, relative humidity above the boundary layer may exert some control on the height of the tropical troposphere.

Sherwood, Steven C.↗
NASA NTRS2010

The Characterization of Deep Convective Cloud Albedo as a Calibration Target Using MODIS Reflectances

There are over 25 years of historical satellite data available to climate analysis. The historical satellite data needs to be well calibrated, especially in the visible, where there is no onboard calibration on operational satellites. The key to the vicarious calibration of historical satellites relies on invariant targets, such as the moon, Dome C, and deserts. Deep convective clouds (DCC) also show promise of being a stable invariant or predictable target viewable by all satellites, since they behave as solar diffusers. However DCC have not been well characterized for calibration. Ten years of well-calibrated MODIS is now available. DCC can easily be identified using IR thresholds, where the IR calibration can be traced to the onboard black-bodies. The natural variability of DCC albedo will be analyzed geographically and seasonally, especially difference of convection initiated over land or ocean. Functionality between particle size and ozone absorption with DCC albedo will be examined. Although DCC clouds are nearly Lambertion, the angular distribution of reflectances will be sampled and compared with theoretical models. Both Aqua and Terra MODIS DCC angular models will be compared for consistency. Normalizing angular geostationary DCC reflectances, which were calibrated against MODIS, with SCIAMACHY spectral reflectances and comparing them to MODIS DCC reflectances will inspect the usage of DCC albedos as an absolute calibration target.

Doelling, David R.↗
NASA NTRSDate not supplied

Consistent Pixel Resolution Characterization of Deep Convective Clouds for Calibration

The NASA CERES project provides global TOA shortwave and longwave fluxes for climate monitoring and validation that spans over 20 years. CERES utilizes broadband fluxes derived from geostationary (GEO) imagers to estimate broadband fluxes between the CERES observations. In order for these fluxes to be viable, the GEO imager calibration must be stable over time. One such calibration method used by CERES is to evaluate ensemble sets of deep convective clouds (DCC) as invariant targets (IT) over time. DCC targets can also provide radiometric scaling between sensors. An international collaboration through GSICS is also evaluating the DCC-IT calibration methodology to provide consistent calibration coefficients across geostationary sensors. Tropical DCC are the coldest, brightest, and most Lambertian TOA Earth targets identified using a window channel brightness temperature threshold. The DCC-IT technique involves a large ensemble of TOA pixel-level reflectances, which are binned into probability density functions (PDF). The PDF structure dependency on sensor pixel resolution, which can vary greatly among sensors, is not well known. This study will identify the impact of pixel resolution on the DCC PDFs by aggregating VIIRS and Landsat OLI/TIRS pixel resolutions into various coarser pixel resolutions and comparing the shape and statistics of the resulting PDFs. This study should assist in mitigating the pixel resolution dependency in the DCC-IT approach for providing scaling factors between sensors.

Conor Haney↗
NASA NTRSDate not supplied

Deep Convective Cloud Calibration Sensitivity Studies in Support of Radiometrically Scaling GEO Imagers With VIIRS

The NASA CERES SYN1deg product provides the scientific community regional hourly TOA and surface broadband fluxes and clouds. For consistent geostationary (GEO) derived fluxes and clouds the GEO imagers are radiometrically scaled to the Aqua-MODIS calibration reference. The CERES project utilizes GEO and MODIS analogous channel coincident, collocated, and co-angled radiance pairs as the primary method to inter-calibrate the GEO imagers. Deep convective clouds (DCC) are bright tropical, near Lambertian, top of atmosphere pseudo invariant Earth targets that do not rely on coincident radiance pairs to radiometrically scale sensors to a common calibration reference. DCC pixels are identified by cold IR window channel brightness temperatures (BT). Successful DCC inter-calibration relies on sufficient sampling of comparable identified DCC pixels between sensors. The DCC identification thresholds, pixel resolution, local time, and geographical sampling should be consistent between sensors. Over 20 GEO imagers during the span of the CERES record have various visible and IR pixel resolutions. Unlike the MODIS and VIIRS imagers, where the visible and IR pixel resolutions are similar, the GEO visible pixel resolution is much finer than the IR pixel resolution. The study will examine the pixel resolution impact on the DCC calibration methodology. The resulting DCC calibration coefficients can be validated against the sensor pair calibration methodology. Accounting for the DCC calibration imager resolution differences will allow the CERES project to utilize the future CLARREO observations as the calibration reference for all GEO, MODIS, and VIIRS imagers across the CERES record.

Conor Haney↗
NASA NTRS2020

MODIS Detector Differences Using Deep Convective Clouds and Desert Targets

An accurate on-orbit characterization of the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors onboard the Terra and Aqua satellites is essential to satisfy the requirements from the scientific community for high-quality operational and research products. In this study, NASA’s C6.1 L1B data are utilized to assess the stability of the calibrated top of atmosphere reflectance retrieved from individual detectors within a spectral band over deep convective clouds (DCCs) and desert sites. The results from these invariant Earth targets show detector-to-detector (D2D) differences in the L1B reflectance products for select MODIS reflective solar bands. For Aqua MODIS, the D2D differences have no significant change over time for the bands studied. However, the D2D differences exhibit an increase in magnitude over time for Terra MODIS bands 1, 3-7, and 26, which can induce noticeable striping and higher uncertainties in the downstream data products. The D2D stability assessment results over DCCs are consistent with those observed over desert sites. In addition, the view-angle dependence of the D2D differences is investigated by separating the frames along scan into five zones. The D2D assessment is performed for each of the five zones, and the results will further benefit any improvements in the calibration of a detector-dependent response versus scan angle that can be considered for future MODIS Level 1B Collections.

MODIS↗
NASA NTRS2014

Initial Stability Assessment of S-NPP VIIRS Reflective Solar Band Calibration Using Invariant Desert and Deep Convective Cloud Targets

The latest CERES FM-5 instrument launched onboard the S-NPP spacecraft will use the VIIRS visible radiances from the NASA Land Product Evaluation and Analysis Tool Elements (PEATE) product for retrieving the cloud properties associated with its TOA flux measurement. In order for CERES to provide climate quality TOA flux datasets, the retrieved cloud properties must be consistent throughout the record, which is dependent on the calibration stability of the VIIRS imager. This paper assesses the NASA calibration stability of the VIIRS reflective solar bands using the Libya-4 desert and deep convective clouds (DCC). The invariant targets are first evaluated for temporal natural variability. It is found for visible (VIS) bands that DCC targets have half of the variability of Libya-4. For the shortwave infrared (SWIR) bands, the desert has less variability. The brief VIIRS record and target variability inhibits high confidence in identifying any trends that are less than 0.6yr for most VIS bands, and 2.5yr for SWIR bands. None of the observed invariant target reflective solar band trends exceeded these trend thresholds. Initial assessment results show that the VIIRS data have been consistently calibrated and that the VIIRS instrument stability is similar to or better than the MODIS instrument.

VIIRS↗
NASA NTRSDate not supplied

Performance Assessment of the NOAA-20 VIIRS RSB Using Deep Convective Clouds

The Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the NOAA-20 (N20) satellite was launched on November 18, 2017. The N20 VIIRS reflective solar bands (RSBs) are calibrated on-orbit using a solar diffuser. An accurate on-orbit calibration is crucial to the high-quality downstream products facilitating atmosphere, ocean and land applications. In this study, the stability of the Level 1B (L1B) reflectance product is investigated using measurements over deep convective clouds (DCCs) for M-bands M1-M5, M7-M11, and I-bands I1-I3. The methodologies developed previously for Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) sensors and Suomi National Polar-orbiting Partnership (SNPP) VIIRS are extended and applied to the N20 RSB to derive DCC-based trends. The Collection 2 L1B data produced by NASA Land Science Investigator-led Processing Systems (SIPS) is used to evaluate the performance of the N20 VIIRS RSB calibration. At nadir, the reflectance trends for M1, M5, M8-M11, and I3 are insignificant compared to their corresponding variations (STDs) except for bands M2-M4, M7, and I1-I2, whose trends are larger than or equivalent to their STDs. The reflectance is relatively stable compared to their STDs for all the study RSBs at six aggregation zones across the entire scan angle range. Also discussed in this paper are the detector-to-detector differences and half-angle mirror side differences using the DCCs. Future applications using DCCs, which include an intercomparison with SNPP VIIRS, are also discussed.

N20 VIIRS↗
NASA NTRS2013

Investigating the Use of Deep Convective Clouds (DCCT) to Monitor On-orbit Performance of the Geostationary Lightning Mapper (GLM) using Lightning Imaging Sensor (LIS) Measurements

There is a need to monitor the on-orbit performance of the Geostationary Lightning Mapper (GLM) on the Geostationary Operational Environmental Satellite R (GOES-R) for changes in instrument calibration that will affect GLM's lightning detection efficiency. GLM has no onboard calibration so GLM background radiance observations (available every 2.5 min) of Deep Convective Clouds (DCCs) are investigated as invariant targets to monitor GLM performance. Observations from the Lightning Imaging Sensor (LIS) and the Visible and Infrared Scanner (VIRS) onboard the Tropical Rainfall Measuring Mission (TRMM) satellite are used as proxy datasets for GLM and ABI 11 m measurements.

Buechler, Dennis E.↗
NASA NTRS2008

Evaluation of Cloud Physical Properties of ECMWF Analysis and Re-Analysis (ERA-40 and ERA Interim) against CERES Tropical Deep Convective Cloud Object Observations

This study presents an approach that converts the vertical profiles of grid-averaged cloud properties from large-scale models to probability density functions (pdfs) of subgrid-cell cloud physical properties measured at satellite footprints. Cloud physical and radiative properties, rather than just cloud and precipitation occurrences, of assimilated cloud systems by the European Center for Medium-range Weather Forecasts (ECMWF) operational analysis (EOA) and ECMWF Re-Analyses (ERA-40 and ERA Interim) are validated against those obtained from Earth Observing System satellite cloud object data for January-August 1998 and March 2000 periods. These properties include ice water path (IWP), cloud-top height and temperature, cloud optical depth and solar and infrared radiative fluxes. Each cloud object, a contiguous region with similar cloud physical properties, is temporally and spatially matched with EOA and ERA-40 data. Results indicate that most pdfs of EOA and ERA-40 cloud physical and radiative properties agree with those of satellite observations of the tropical deep convective cloud-object type for the January-August 1998 period. There are, however, significant discrepancies in selected ranges of the cloud property pdfs such as the upper range of EOA cloud top height. A major discrepancy is that the dependence of the pdfs on the cloud object size for both EOA and ERA-40 is not as strong as in the observations. Modifications to the cloud parameterization in ECMWF that occurred in October 1999 eliminate the clouds near the tropopause but shift power of the pdf to lower cloud-top heights and greatly reduce the ranges of IWP and cloud optical depth pdfs. These features persist in ERA-40 due to the use of the same cloud parameterizations. The downgrade of data assimilation technique and the lack of snow water content information in ERA-40, not the coarser horizontal grid resolution, are also responsible for the disagreements with observed pdfs of cloud physical properties although the detection rates of cloud object occurrence are improved for small size categories. A possible improvement to the convective parameterization is to introduce a stronger dependence of updraft penetration heights with grid-cell dynamics. These conclusions will be rechecked using the ERA Interim data, due to recent changes in the ECMWF convective parameterization (Bechtold et al. 2004, 2008). Results from the ERA Interim will be presented at the meeting.

Xu, Kuan-Man↗
NASA NTRSDate not supplied

Deep Convective Cloud Calibration Sensitivity Studies in Support of Radiometrically Scaling GEO Imagers With VIIRS

The NASA CERES SYN1deg product provides the scientific community regional hourly TOA and surface broadband fluxes and clouds. For consistent geostationary (GEO) derived fluxes and clouds the GEO imagers are radiometrically scaled to the Aqua-MODIS calibration reference. The CERES project utilizes GEO and MODIS or VIIRS analogous channel coincident, collocated, and co-angled radiance pairs as the primary method to inter-calibrate the GEO imagers. Tropical deep convective clouds (DCC) are bright, near Lambertian, top of atmosphere pseudo invariant Earth targets that do not rely on coincident ray-matched radiance pairs to radiometrically scale sensors to a common calibration reference. The DCC invariant target (DCC-IT) methodology collectively analyzes all tropical DCC identified pixel radiances by way of probability density function (PDF) distributions. Perfectly inter-calibrated sensor pairs should reveal nearly identical PDF distributions given the same DCC identification criterion. The PDF median, mean, mode, and inflection point statistics were tested as a function of DCC identification criterion using SNPP-VIIRS and Himawari-8 AHI 0.65μm channel radiances during January 2019. It was found that the PDF inflection point provided inter-calibration factors within 0.25% that were nearly independent of DCC identification criterion. The PDF median provided inter-calibration factors within 0.25% for the coldest BT and most stringent homogeneity factors. The PDF mean and mode statistics were inadequate under any DCC conditions. It is critical for the DCC pixel radiances to be anisotropically corrected. The DCC-IT methodology will also be tested for other visible and SWIR bands.

DCC↗
NASA NTRS2016

Response Versus Scan-Angle Corrections for MODIS Reflective Solar Bands Using Deep Convective Clouds

The absolute radiometric calibration of the reflective solar bands (RSBs) of Aqua- and Terra-MODIS is performed using on-board calibrators. A solar diffuser (SD) panel along with a solar diffuser stability monitor (SDSM) system, which tracks the performance of the SD over time, provides the absolute reference for calibrating the MODIS sensors. MODIS also views the moon and deep space through its space view (SV) port for lunar-based calibration and computing the zero input radiance, respectively. The MODIS instrument views the Earths surface through a two-sided scan mirror, whose reflectance is a function of angle of incidence (AOI) and is described by response versus scan-angle (RVS). The RVS for both MODIS instruments was characterized prior to launch. MODIS also views the SD and the moon at two different assigned RVS positions. There is sufficient evidence that the RVS is changing on orbit over time and as a function of wavelength. The SD and lunar observation scans can only track the RVS variation at two RVS positions. Consequently, the MODIS Characterization Support Team (MCST) developed enhanced approaches that supplement the onboard calibrator measurements with responses from pseudo-invariant desert sites. This approach has been implemented in Level 1B (L1B) Collection 6 (C6) for selected short-wavelength bands. This paper presents an alternative approach of characterizing the mirror RVS to derive the time-dependent RVS correction factors for MODIS RSBs using tropical deep convective cloud (DCC) targets. An initial assessment of the DCC response from Aqua-MODIS band 1 C6 data indicates evidence of RVS artifacts, which are not uniform across the scans and are more prevalent in the left side Earth-view scans.

Bhatt, Rajendra↗
NASA NTRS2016

Response Versus Scan-Angle Corrections for MODIS Reflective Solar Bands Using Deep Convective Clouds

The absolute radiometric calibration of the reflective solar bands (RSBs) of Aqua- and Terra-MODIS is performed using on-board calibrators. A solar diffuser (SD) panel along with a solar diffuser stability monitor (SDSM) system, which tracks the performance of the SD over time, provides the absolute reference for calibrating the MODIS sensors. MODIS also views the moon and deep space through its space view (SV) port for lunar-based calibration and computing the zero input radiance, respectively. The MODIS instrument views the Earth's surface through a two-sided scan mirror, whose reflectance is a function of angle of incidence (AOI) and is described by response versus scan-angle (RVS). The RVS for both MODIS instruments was characterized prior to launch. MODIS also views the SD and the moon at two different assigned RVS positions. There is sufficient evidence that the RVS is changing on orbit over time and as a function of wavelength. The SD and lunar observation scans can only track the RVS variation at two RVS positions. Consequently, the MODIS Characterization Support Team (MCST) developed enhanced approaches that supplement the onboard calibrator measurements with responses from pseudo-invariant desert sites. This approach has been implemented in Level 1B (L1B) Collection 6 (C6) for selected short-wavelength bands. This paper presents an alternative approach of characterizing the mirror RVS to derive the time-dependent RVS correction factors for MODIS RSBs using tropical deep convective cloud (DCC) targets. An initial assessment of the DCC response from Aqua-MODIS band 1 C6 data indicates evidence of RVS artifacts, which are not uniform across the scans and are more prevalent in the left side Earth-view scans.

Bhatt, Rajendra↗
NASA NTRS2016

Assessment of MODIS On-Orbit Calibration Using a Deep Convective Cloud Technique

The MODerate Resolution Imaging Spectroradiometer (MODIS) sensors onboard Terra and Aqua satellites are calibrated on-orbit with a solar diffuser (SD) for the reflective solar bands (RSB). The MODIS sensors are operating beyond their designed lifetime and hence present a major challenge to maintain the calibration accuracy. The degradation of the onboard SD is tracked by a solar diffuser stability monitor (SDSM) over a wavelength range from 0.41 to 0.94 micrometers. Therefore, any degradation of the SD beyond 0.94 micrometers cannot be captured by the SDSM. The uncharacterized degradation at wavelengths beyond this limit could adversely affect the Level 1B (L1B) product. To reduce the calibration uncertainties caused by the SD degradation, invariant Earth-scene targets are used to monitor and calibrate the MODIS L1B product. The use of deep convective clouds (DCCs) is one such method and particularly significant for the short-wave infrared (SWIR) bands in assessing their long-term calibration stability. In this study, we use the DCC technique to assess the performance of the Terra and Aqua MODIS Collection-6 L1B for RSB 1 3- 7, and 26, with spectral coverage from 0.47 to 2.13 micrometers. Results show relatively stable trends in Terra and Aqua MODIS reflectance for most bands. Careful attention needs to be paid to Aqua band 1, Terra bands 3 and 26 as their trends are larger than 1% during the study time period. We check the feasibility of using the DCC technique to assess the stability in MODIS bands 17-19. The assessment test on response versus scan angle (RVS) calibration shows substantial trend difference for Aqua band 1between different angles of incidence (AOIs). The DCC technique can be used to improve the RVS calibration in the future.

Mu, Qiaozhen↗
NASA NTRSDate not supplied

Inter-Calibrating the CERES SW Instrument Fluxes Using Deep Convective Clouds(DCC) Within the Same Sun-Synchronous Orbit

The NASA CERES EBAF product provides the scientific community observed TOA fluxes to monitor the Earth’s energy imbalance and to validate climate models. To provide a seamless EBAF 24-year record, the CERES instrument calibration must be stable and consistent across satellite records. Once the Terra and Aqua spacecraft are decommissioned at the end of 2025, the CERES project will rely on CERES instrument observations on the SNPP and NOAA-20 1:30 PM sun-synchronous orbits. The SNPP and NOAA-20 satellite orbit placement will prevent any time matched observations for inter-calibration efforts. The future Libera instrument, which will continue the CERES record and scheduled for launch in 2028 onboard the NOAA-22 satellite, will also need to be inter-calibrated without the aid of time-matched observations. Deep convective clouds (DCC) are the most Lambertian, brightest, tropical Earth invariant targets located at the tropopause making them ideal to radiometrically scale the CERES SW observed radiance to a common reference. The SNPP, NOAA-20 and future NOAA-22 satellites are in the same 16-day repeatable orbits, allowing the DCC targets to be observed with the same angular configuration. The empirically derived SNPP CERES SW channel Bidirectional Reflectance Distribution Function (BRDF) can be easily be applied to the NOAA-20 CERES SW channel radiances since they observe the nearly the same DCC systems. The DCC BRDF corrected radiances are analyzed collectively into radiance probability distribution functions (PDF). By comparing the PDF statistics, the SNPP and NOAA-20 CERES SW channel can be inter-calibrated. The inter-calibration coefficients are validated with the CERES instrument calibration team coefficients to optimize the methodology.

David Doelling↗
NASA NTRS2017

Characterizing Response Versus Scan-Angle for MODIS Reflective Solar Bands Using Deep Convective Clouds

MODIS consists of a cross-track, two-sided scan mirror, whose reflectance is not uniform but is a function of angle of incidence (AOI). This feature, known as response versusscan-angle (RVS), was characterized for all reflective solar bands of both MODIS instruments prior to launch. The RVS characteristic has changed on orbit, which must be tracked precisely over time to ensure the quality of MODIS products. The MODIS characterization support team utilizes the onboard calibrators and the earth view responses from multiple pseudo invariant desert sites to track the RVS changes at different AOIs. The drawback of using deserts is the assumption that these sites are radiometrically stable during the monitoring period. In addition, the 16-day orbit repeat cycle of MODIS allows for only a limited set of AOIs over a given desert. We propose a novel and robust approach of characterizing the MODIS RVS using tropical deep convective clouds (DCC). The method tracks the monthly DCC response at specified sets of AOIs to compute the temporal RVS changes. Initial results have shown that the Aqua-MODIS collection 6 band 1 level 1B radiances show considerable residual RVS dependencies, with long-term drifts up to 2.3 at certain AOIs.

Clouds↗
DOE OSTI2020

A Bottom-up Approach to Improve the Representation of Deep Convective Clouds in Weather and Climate Models (Final Report)

A fundamental yet outstanding question about deep cumulus convection regards how convective updrafts, downdrafts, and surface-based cold pools are inter-related within organized storms, and how these three convective components are modulated by external and internal factors. We considered this question through numerical model simulations as well as data collected during the MC3E field campaign. One of our basic hypotheses was that deep cold pools are forced by wide downdrafts which arise from wide updrafts. This “bottom-up” perspective required consideration of the external controls on updraft width, and then the internal controls on cold-pool characteristics including depth. Model experiments showed that environmental vertical wind shear (an external factor) exerts a particularly strong control on updraft width; analyses of linear and nonlinear dynamic pressure forcing readily explain this control. The experiments also showed that increases in updraft width are accompanied by corresponding increases in downdraft width and cold-pool depth. The updraft–downdraft connection is through precipitation: the wide area of precipitation that will be initiated in a wide updraft will in turn lead to a wide downdraft. The downdraft–cold pool connection is through mass continuity: at the downdraft terminus, the large downdraft mass flux through a wide downdraft must lead to a deep cold pool. Model experiments also showed that the cold-pool depth and other characteristics can be significantly modulated by microphysical processes (internal factors). Specifically, the cold-pool expansion rate, depth, and intensity was found to depend most strongly on the amount of rain evaporation near the ground. However, the sustenance of the cold pool itself depended upon the downdrafts strengthened by sublimation of graupel higher in the storm. Finally, field campaign data revealed compelling inter-relationships between the cold-pool characteristics, and downdraft transience in terms of the microphysics. For example, pulses of hail and graupel (also internal factors) within downdrafts resulted in short-lived increases in the cold-pool depth. However, the cold-pool speed appeared to be relatively independent of the cold-pool depth and intensity, suggesting limitations of density current theory to convective cold pools in nature.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Factors Affecting Entrainment Rate in Deep Convective Clouds and Parameterizations

The parameterization of cloud entrainment rates has been problematic for many years, hindering the accurate representation of convective processes in large-scale models. Here, we extend our previous work on individual shallow convection to ensemble deep convection. Entrainment rates are estimated based on three-dimensional convective clouds from August 19-20 of 1999, during the Kwajalein Experiment, simulated using a high-resolution cloud-resolving model. They are found to be negatively correlated with both vertical velocity and buoyancy, and positively correlated with the vertical divergence of the vertical velocity and with the reciprocal of cloud radii. The physical mechanisms underlying these relationships are interpreted. It is found that the parameterizations with multiple properties perform better than those with a single property. Entrainment rates and relative humidity of entrained air are positively correlated at temperature higher than 0°C, but negatively correlated at temperature lower than 0°C. Relative humidity is also included in the parameterization of entrainment rates, which differs from our previous work on shallow cumulus clouds and other studies. Finally, two forms of parameterization for entrainment rate are recommended. The first treats the entrainment rate as a function of the vertical velocity and buoyancy for temperature higher than 0°C, but as a function of relative humidity and buoyancy for temperature lower than 0°C. The second involves an equation that relates entrainment rates to vertical velocity and buoyancy regardless of temperature.

54 ENVIRONMENTAL SCIENCES↗