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Abstract
Cloud-resolving models—in particular, large-eddy simulation (LES) models—are important tools to improve the understanding of cloud–radiation interactions. A method is presented for accurate, yet fast, three-dimensional calculation of surface shortwave irradiance within an LES model using the tilted independent column approximation with smoothing of the diffuse irradiance. The algorithm calculates a tilted optical thickness for each surface pixel that is then used as input to a one-dimensional radiative transfer code. In a sensitivity analysis, it is shown that this calculation can even be replaced by a simple precalculated lookup table that tabulates surface irradiance as a function of only solar zenith angle and cloud optical thickness. Because the vertical variability of the cloud is of little relevance for the surface irradiance, this approximation introduces little extra uncertainty. In a final step, surface irradiance is smoothed to account for horizontal photon transport between individual columns. The algorithm has been optimized for parallelization, which enhances its applicability in LES models. In this implementation, the total computational time of the LES model increased by only 3% relative to the reference run without radiation. Comparisons between the fast approximation and detailed three-dimensional radiative transfer calculations showed very good agreement for different cloud conditions and several solar zenith and azimuth angles, with a root-mean-square difference of 6%.
Abstract
Cloud-resolving models—in particular, large-eddy simulation (LES) models—are important tools to improve the understanding of cloud–radiation interactions. A method is presented for accurate, yet fast, three-dimensional calculation of surface shortwave irradiance within an LES model using the tilted independent column approximation with smoothing of the diffuse irradiance. The algorithm calculates a tilted optical thickness for each surface pixel that is then used as input to a one-dimensional radiative transfer code. In a sensitivity analysis, it is shown that this calculation can even be replaced by a simple precalculated lookup table that tabulates surface irradiance as a function of only solar zenith angle and cloud optical thickness. Because the vertical variability of the cloud is of little relevance for the surface irradiance, this approximation introduces little extra uncertainty. In a final step, surface irradiance is smoothed to account for horizontal photon transport between individual columns. The algorithm has been optimized for parallelization, which enhances its applicability in LES models. In this implementation, the total computational time of the LES model increased by only 3% relative to the reference run without radiation. Comparisons between the fast approximation and detailed three-dimensional radiative transfer calculations showed very good agreement for different cloud conditions and several solar zenith and azimuth angles, with a root-mean-square difference of 6%.
Abstract
Despite impressive advances in rain forecasts over the past decades, our understanding of rain formation on a microphysical scale is still poor. Droplet growth initially occurs through diffusion and, for sufficiently large radii, through the collision of droplets. However, there is no consensus on the mechanism to bridge the condensation coalescence bottleneck. We extend the analysis of prior methods by including radiatively enhanced diffusional growth (RAD) to a Markovian turbulence parameterization. This addition increases the diffusional growth efficiency by allowing for emission and absorption of thermal radiation. Specifically, we quantify an upper estimate for the radiative effect by focusing on droplets close to the cloud boundary. The strength of this simple model is that it determines growth-rate dependencies on a number of parameters, like updraft speed and the radiative effect, in a deterministic way. Realistic calculations with a cloud-resolving model are sensitive to parameter changes, which may cause completely different cloud realizations and thus it requires considerable computational power to obtain statistically significant results. The simulations suggest that the addition of radiative cooling can lead to a doubling of the droplet size standard deviation. However, the magnitude of the increase depends strongly on the broadening established by turbulence, due to an increase in the maximum droplet size, which accelerates the production of drizzle. Furthermore, the broadening caused by the combination of turbulence and thermal radiation is largest for small updrafts and the impact of radiation increases with time until it becomes dominant for slow synoptic updrafts.
Abstract
Despite impressive advances in rain forecasts over the past decades, our understanding of rain formation on a microphysical scale is still poor. Droplet growth initially occurs through diffusion and, for sufficiently large radii, through the collision of droplets. However, there is no consensus on the mechanism to bridge the condensation coalescence bottleneck. We extend the analysis of prior methods by including radiatively enhanced diffusional growth (RAD) to a Markovian turbulence parameterization. This addition increases the diffusional growth efficiency by allowing for emission and absorption of thermal radiation. Specifically, we quantify an upper estimate for the radiative effect by focusing on droplets close to the cloud boundary. The strength of this simple model is that it determines growth-rate dependencies on a number of parameters, like updraft speed and the radiative effect, in a deterministic way. Realistic calculations with a cloud-resolving model are sensitive to parameter changes, which may cause completely different cloud realizations and thus it requires considerable computational power to obtain statistically significant results. The simulations suggest that the addition of radiative cooling can lead to a doubling of the droplet size standard deviation. However, the magnitude of the increase depends strongly on the broadening established by turbulence, due to an increase in the maximum droplet size, which accelerates the production of drizzle. Furthermore, the broadening caused by the combination of turbulence and thermal radiation is largest for small updrafts and the impact of radiation increases with time until it becomes dominant for slow synoptic updrafts.
Efficient Methods to Account for Cloud-Top Inclination and Cloud Overlap in Synthetic Visible Satellite ImagesAbstract
Visible satellite images contain high-resolution information about clouds that would be well suited for convective-scale data assimilation. This application requires a forward operator to generate synthetic images from the output of numerical weather prediction models. Only recently have 1D radiative transfer (RT) solvers become sufficiently fast for this purpose. Here computationally efficient methods are proposed to increase the accuracy and consistency of an operator based on the Method for Fast Satellite Image Synthesis (MFASIS) 1D RT. Two important problems are addressed: the 3D RT effects related to inclined cloud tops and the overlap of subgrid clouds. It is demonstrated that in a rotated frame of reference, an approximate solution for the 3D RT problem can be obtained by solving a computationally much cheaper 1D RT problem. Several deterministic and stochastic schemes that take the overlap of subgrid clouds into account are discussed. The impact of the inclination correction and the overlap schemes is evaluated for synthetic 0.6-μm SEVIRI images computed from operational forecasts of the German-focused COSMO (COSMO-DE) Model for a test period in May–June 2016. The cloud-top inclination correction increases the information content of the synthetic images considerably and reduces systematic errors, in particular for larger solar zenith angles. Taking subgrid cloud overlap into account is essential to avoid large systematic errors. The results obtained using several different 2D cloud overlap schemes are very similar, whereas small but significant differences are found for the most consistent 3D method, which accounts for the fact that the RT problem is solved for columns tilted toward the satellite.
Abstract
Visible satellite images contain high-resolution information about clouds that would be well suited for convective-scale data assimilation. This application requires a forward operator to generate synthetic images from the output of numerical weather prediction models. Only recently have 1D radiative transfer (RT) solvers become sufficiently fast for this purpose. Here computationally efficient methods are proposed to increase the accuracy and consistency of an operator based on the Method for Fast Satellite Image Synthesis (MFASIS) 1D RT. Two important problems are addressed: the 3D RT effects related to inclined cloud tops and the overlap of subgrid clouds. It is demonstrated that in a rotated frame of reference, an approximate solution for the 3D RT problem can be obtained by solving a computationally much cheaper 1D RT problem. Several deterministic and stochastic schemes that take the overlap of subgrid clouds into account are discussed. The impact of the inclination correction and the overlap schemes is evaluated for synthetic 0.6-μm SEVIRI images computed from operational forecasts of the German-focused COSMO (COSMO-DE) Model for a test period in May–June 2016. The cloud-top inclination correction increases the information content of the synthetic images considerably and reduces systematic errors, in particular for larger solar zenith angles. Taking subgrid cloud overlap into account is essential to avoid large systematic errors. The results obtained using several different 2D cloud overlap schemes are very similar, whereas small but significant differences are found for the most consistent 3D method, which accounts for the fact that the RT problem is solved for columns tilted toward the satellite.
Abstract
The resolution of numerical weather prediction models is constantly increasing, making it necessary to consider three-dimensional radiative transfer effects such as cloud shadows cast into neighboring grid cells and thus affecting radiative heating. For that purpose, fast approximations are needed since three-dimensional radiative transfer solvers are computationally far too expensive. For the solar spectral range, different approaches of how to consider three-dimensional effects were presented in the past—in particular, the tilted independent column approximation (TICA), which aims at improving the calculation of the direct radiation, and the nonlocal tilted independent column approximation (NTICA), which is used to additionally correct the diffuse radiation. Here a new version of NTICA is presented that—in contrast to earlier approaches—is applicable for a variety of cloud scenes and grid resolutions and for arbitrary solar zenith angles. This new parameterization for the diffuse irradiance is then applied to the two different TICA approaches and the results are compared with a full 3D Monte Carlo calculation. It is shown that both approaches strongly improve the calculation of radiation fluxes if the new parameterization for the diffuse irradiance—what the authors call “parameterized NTICA (paNTICA)”—is applied. It is found that the method in which TICA is only applied to direct radiation yields the better results. The studies show that consideration of three-dimensional effects is inevitable if higher model resolutions are used in the future. This paper proposes ways to consider these effects and, thus, to substantially reduce the errors made with one-dimensional radiative transfer solvers.
Abstract
The resolution of numerical weather prediction models is constantly increasing, making it necessary to consider three-dimensional radiative transfer effects such as cloud shadows cast into neighboring grid cells and thus affecting radiative heating. For that purpose, fast approximations are needed since three-dimensional radiative transfer solvers are computationally far too expensive. For the solar spectral range, different approaches of how to consider three-dimensional effects were presented in the past—in particular, the tilted independent column approximation (TICA), which aims at improving the calculation of the direct radiation, and the nonlocal tilted independent column approximation (NTICA), which is used to additionally correct the diffuse radiation. Here a new version of NTICA is presented that—in contrast to earlier approaches—is applicable for a variety of cloud scenes and grid resolutions and for arbitrary solar zenith angles. This new parameterization for the diffuse irradiance is then applied to the two different TICA approaches and the results are compared with a full 3D Monte Carlo calculation. It is shown that both approaches strongly improve the calculation of radiation fluxes if the new parameterization for the diffuse irradiance—what the authors call “parameterized NTICA (paNTICA)”—is applied. It is found that the method in which TICA is only applied to direct radiation yields the better results. The studies show that consideration of three-dimensional effects is inevitable if higher model resolutions are used in the future. This paper proposes ways to consider these effects and, thus, to substantially reduce the errors made with one-dimensional radiative transfer solvers.
Abstract
Marine cloud brightening (MCB) is a geoengineering approach to counteract climate change by the deliberate seeding of sea salt aerosol particles that, once they activated to cloud droplets, directly increase cloud reflectance and hence global albedo. However, a large fraction of the seeded aerosol may remain interstitial, i.e., unactivated particles among cloud droplets. Because the consideration of interstitial aerosol optical properties usually requires computationally expensive simulations of the entire particle spectrum and direct Mie calculations, we develop a simple parameterization to be used with computationally efficient bulk and even bin cloud microphysical schemes that do not treat the unactivated aerosol explicitly. Using parcel and large-eddy simulations with highly detailed Lagrangian cloud microphysics and direct Mie calculations as a reference, we show that the parameterization captures the variability in the interstitial aerosol extinction successfully. By applying the parameterization to typical MCB cases, we find that the consideration of interstitial aerosol extinction is important for the assessment of MCB in shallow clouds with weak updrafts, in which only a small fraction of aerosol particles is activated to cloud droplets.
Significance Statement
The optical properties of clouds are not only determined by the number and size of cloud droplets. Unactivated aerosol particles, so-called interstitial aerosol, can contribute substantially to the optical thickness of shallow clouds with weak updrafts in aerosol-laden conditions. The consideration of interstitial aerosol optical thickness has been computationally challenging, but the new parameterization presented here allows for an efficient representation in various types of cloud models. The parameterization is shown to be an important addition for the assessment of marine cloud brightening (MCB), a potential geoengineering technique to counteract global warming by increasing the cloud albedo through the deliberate seeding of aerosol.
Abstract
Marine cloud brightening (MCB) is a geoengineering approach to counteract climate change by the deliberate seeding of sea salt aerosol particles that, once they activated to cloud droplets, directly increase cloud reflectance and hence global albedo. However, a large fraction of the seeded aerosol may remain interstitial, i.e., unactivated particles among cloud droplets. Because the consideration of interstitial aerosol optical properties usually requires computationally expensive simulations of the entire particle spectrum and direct Mie calculations, we develop a simple parameterization to be used with computationally efficient bulk and even bin cloud microphysical schemes that do not treat the unactivated aerosol explicitly. Using parcel and large-eddy simulations with highly detailed Lagrangian cloud microphysics and direct Mie calculations as a reference, we show that the parameterization captures the variability in the interstitial aerosol extinction successfully. By applying the parameterization to typical MCB cases, we find that the consideration of interstitial aerosol extinction is important for the assessment of MCB in shallow clouds with weak updrafts, in which only a small fraction of aerosol particles is activated to cloud droplets.
Significance Statement
The optical properties of clouds are not only determined by the number and size of cloud droplets. Unactivated aerosol particles, so-called interstitial aerosol, can contribute substantially to the optical thickness of shallow clouds with weak updrafts in aerosol-laden conditions. The consideration of interstitial aerosol optical thickness has been computationally challenging, but the new parameterization presented here allows for an efficient representation in various types of cloud models. The parameterization is shown to be an important addition for the assessment of marine cloud brightening (MCB), a potential geoengineering technique to counteract global warming by increasing the cloud albedo through the deliberate seeding of aerosol.
Abstract
Estimates of the global radiative forcing (RF) of line-shaped contrails and contrail cirrus exhibit a high level of uncertainty. In most cases, 1D radiative models have been used to determine the RF on a global scale. In this paper the effect of neglecting the 3D radiative effects of realistic contrails is quantified. Calculating the 3D effects of an idealized elliptical contrail as in the work of Gounou and Hogan with the 3D radiative transfer model MYSTIC (for “Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) produced comparable results: as in Gounou and Hogan’s work the 3D effect (i.e., the difference in RF between a 3D calculation and a 1D approximation) on contrail RF was on the order of 10% in the longwave and shortwave. The net 3D effect, however, can be much larger, since the shortwave and longwave RF largely cancel during the day. For the investigation of the 3D effects of more realistic contrails, the microphysical input was provided by simulations of a 2D contrail-to-cirrus large-eddy simulation (LES) model. To capture some of the real variability in contrail properties, this paper examines two contrail evolutions from 20 min up to 6 h in an environment with either high or no vertical wind shear. This study reveals that the 3D effects show a high variability under realistic conditions since they depend strongly on the optical properties and the evolutionary state of the contrails. The differences are especially large for low elevations of the sun and contrails spreading in a sheared environment. Thus, a parameterization of the 3D effects in climate models would need to consider both geometry and microphysics of the contrail.
Abstract
Estimates of the global radiative forcing (RF) of line-shaped contrails and contrail cirrus exhibit a high level of uncertainty. In most cases, 1D radiative models have been used to determine the RF on a global scale. In this paper the effect of neglecting the 3D radiative effects of realistic contrails is quantified. Calculating the 3D effects of an idealized elliptical contrail as in the work of Gounou and Hogan with the 3D radiative transfer model MYSTIC (for “Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) produced comparable results: as in Gounou and Hogan’s work the 3D effect (i.e., the difference in RF between a 3D calculation and a 1D approximation) on contrail RF was on the order of 10% in the longwave and shortwave. The net 3D effect, however, can be much larger, since the shortwave and longwave RF largely cancel during the day. For the investigation of the 3D effects of more realistic contrails, the microphysical input was provided by simulations of a 2D contrail-to-cirrus large-eddy simulation (LES) model. To capture some of the real variability in contrail properties, this paper examines two contrail evolutions from 20 min up to 6 h in an environment with either high or no vertical wind shear. This study reveals that the 3D effects show a high variability under realistic conditions since they depend strongly on the optical properties and the evolutionary state of the contrails. The differences are especially large for low elevations of the sun and contrails spreading in a sheared environment. Thus, a parameterization of the 3D effects in climate models would need to consider both geometry and microphysics of the contrail.
Abstract
Operational numerical weather prediction systems currently only assimilate infrared and microwave satellite observations, whereas visible and near-infrared reflectances that comprise information on atmospheric clouds are not exploited. One of the reasons for that is the absence of computationally efficient observation operators. To remedy this issue in anticipation of the future regional Kilometer-Scale Ensemble Data Assimilation (KENDA) system of Deutscher Wetterdienst, we have developed a version that is fast enough for investigating the assimilation of cloudy reflectances in a case study approach. The operator solves the radiative transfer equation to simulate visible and near-infrared channels of satellite instruments based on the one-dimensional (1D) discrete ordinate method. As input, model output of the operational limited-area Consortium for Small-Scale Modeling (COSMO) model of Deutscher Wetterdienst is used. Assumptions concerning subgrid-scale processes, calculation of in-cloud values of liquid water content, ice water content, and cloud microphysics are summarized, and the accuracy of the 1D simulation is estimated through comparison with three-dimensional (3D) Monte Carlo solver results. In addition, the effects of a parallax correction and horizontal smoothing are quantified. The relative difference between the 1D simulation in “independent column approximation” and the 3D calculation is typically less than 9% between 0600 and 1500 UTC, computed from four scenes during one day (with local noon at 1115 UTC). The parallax-corrected version reduces the deviation to less than 6% for reflectance observations with a central wavelength of 810 nm. Horizontal averaging can further reduce the error of the 1D simulation. In all cases, the bias is less than 1% for the model domain.
Abstract
Operational numerical weather prediction systems currently only assimilate infrared and microwave satellite observations, whereas visible and near-infrared reflectances that comprise information on atmospheric clouds are not exploited. One of the reasons for that is the absence of computationally efficient observation operators. To remedy this issue in anticipation of the future regional Kilometer-Scale Ensemble Data Assimilation (KENDA) system of Deutscher Wetterdienst, we have developed a version that is fast enough for investigating the assimilation of cloudy reflectances in a case study approach. The operator solves the radiative transfer equation to simulate visible and near-infrared channels of satellite instruments based on the one-dimensional (1D) discrete ordinate method. As input, model output of the operational limited-area Consortium for Small-Scale Modeling (COSMO) model of Deutscher Wetterdienst is used. Assumptions concerning subgrid-scale processes, calculation of in-cloud values of liquid water content, ice water content, and cloud microphysics are summarized, and the accuracy of the 1D simulation is estimated through comparison with three-dimensional (3D) Monte Carlo solver results. In addition, the effects of a parallax correction and horizontal smoothing are quantified. The relative difference between the 1D simulation in “independent column approximation” and the 3D calculation is typically less than 9% between 0600 and 1500 UTC, computed from four scenes during one day (with local noon at 1115 UTC). The parallax-corrected version reduces the deviation to less than 6% for reflectance observations with a central wavelength of 810 nm. Horizontal averaging can further reduce the error of the 1D simulation. In all cases, the bias is less than 1% for the model domain.
Abstract
The Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres (MYSTIC) three-dimensional radiative transfer model was used in a parametric study to determine the strength of longwave radiative heating and cooling in atmospheres enclosed in idealized valleys and basins. The parameters investigated included valley or basin shape, width, and near-surface temperature contrasts. These parameters were varied for three different representative atmospheric temperature profiles for different times of day. As a result of counterradiation from surrounding terrain, nighttime longwave radiative cooling in topographic depressions was generally weaker than over flat terrain. In the center of basins or valleys with widths exceeding 2 km, cooling rates quickly approached those over flat terrain, whereas the cooling averaged over the entire depression volume was still greatly reduced. Valley or basin shape had less influence on cooling rates than did valley width. Strong temperature gradients near the surface associated with nighttime inversion and daytime superadiabatic layers over the slopes significantly increased longwave radiative cooling and heating rates. Local rates of longwave radiative heating ranged between −30 (i.e., cooling) and 90 K day−1. The effects of the near-surface temperature gradients extended tens of meters into the overlying atmospheres. In small basins, the strong influence of nocturnal near-surface temperature inversions could lead to cooling rates exceeding those over flat plains. To investigate the relative role of longwave radiative cooling on total nighttime cooling in a basin, simulations were conducted for Arizona’s Meteor Crater using observed atmospheric profiles and realistic topography. Longwave radiative cooling accounted for nearly 30% of the total nighttime cooling observed in the Meteor Crater during a calm October night.
Abstract
The Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres (MYSTIC) three-dimensional radiative transfer model was used in a parametric study to determine the strength of longwave radiative heating and cooling in atmospheres enclosed in idealized valleys and basins. The parameters investigated included valley or basin shape, width, and near-surface temperature contrasts. These parameters were varied for three different representative atmospheric temperature profiles for different times of day. As a result of counterradiation from surrounding terrain, nighttime longwave radiative cooling in topographic depressions was generally weaker than over flat terrain. In the center of basins or valleys with widths exceeding 2 km, cooling rates quickly approached those over flat terrain, whereas the cooling averaged over the entire depression volume was still greatly reduced. Valley or basin shape had less influence on cooling rates than did valley width. Strong temperature gradients near the surface associated with nighttime inversion and daytime superadiabatic layers over the slopes significantly increased longwave radiative cooling and heating rates. Local rates of longwave radiative heating ranged between −30 (i.e., cooling) and 90 K day−1. The effects of the near-surface temperature gradients extended tens of meters into the overlying atmospheres. In small basins, the strong influence of nocturnal near-surface temperature inversions could lead to cooling rates exceeding those over flat plains. To investigate the relative role of longwave radiative cooling on total nighttime cooling in a basin, simulations were conducted for Arizona’s Meteor Crater using observed atmospheric profiles and realistic topography. Longwave radiative cooling accounted for nearly 30% of the total nighttime cooling observed in the Meteor Crater during a calm October night.
Abstract
For passive satellite imagers, current retrievals of cloud optical thickness and effective particle size fail for convective clouds with 3D morphology. Indeed, being based on 1D radiative transfer (RT) theory, they work well only for horizontally homogeneous clouds. A promising approach for treating clouds as fully 3D objects is cloud tomography, which has been demonstrated for airborne observations. However, more efficient forward 3D RT solvers are required for cloud tomography from space. Here, we present a path forward by acknowledging that optically thick clouds have “veiled cores” (VCs). Sunlight scattered into and out of this deep region does not contribute significant information about the inner structure of the cloud to the spatially detailed imagery. We investigate the VC location for the MISR and MODIS imagers. While MISR provides multiangle imagery in the visible and near-infrared (IR), MODIS includes channels in the shortwave IR, albeit at a single view angle. This combination will enable future 3D retrievals to disentangle the cloud’s effective particle size and extinction fields. We find that, in practice, the VC is located at an optical distance of ~5, starting from the cloud boundary along the line of sight. For MODIS’s absorbing wavelengths the VC covers a larger volume, starting at smaller optical distances. This concept will not only lead to a reduction in the number of unknowns for the tomographic reconstruction but also significantly increase the speed and efficiency of the 3D RT solver at the heart of the algorithm by applying, say, the photon diffusion approximation inside the VC.
Abstract
For passive satellite imagers, current retrievals of cloud optical thickness and effective particle size fail for convective clouds with 3D morphology. Indeed, being based on 1D radiative transfer (RT) theory, they work well only for horizontally homogeneous clouds. A promising approach for treating clouds as fully 3D objects is cloud tomography, which has been demonstrated for airborne observations. However, more efficient forward 3D RT solvers are required for cloud tomography from space. Here, we present a path forward by acknowledging that optically thick clouds have “veiled cores” (VCs). Sunlight scattered into and out of this deep region does not contribute significant information about the inner structure of the cloud to the spatially detailed imagery. We investigate the VC location for the MISR and MODIS imagers. While MISR provides multiangle imagery in the visible and near-infrared (IR), MODIS includes channels in the shortwave IR, albeit at a single view angle. This combination will enable future 3D retrievals to disentangle the cloud’s effective particle size and extinction fields. We find that, in practice, the VC is located at an optical distance of ~5, starting from the cloud boundary along the line of sight. For MODIS’s absorbing wavelengths the VC covers a larger volume, starting at smaller optical distances. This concept will not only lead to a reduction in the number of unknowns for the tomographic reconstruction but also significantly increase the speed and efficiency of the 3D RT solver at the heart of the algorithm by applying, say, the photon diffusion approximation inside the VC.
