A.P. Siebesma
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An open boundary setup is presented in which a high-resolution (high-res) large eddy simulation (LES) is one-way nested in a low-resolution (low-res) LES. The high-res nested LES is compared to the periodic LES from Savazzi et al. (2023, https://doi.org/10.1175/jas-d-23-0098.1). Both simulations are forced by the regional weather model HARMONIE-AROME: the periodic LES via domain-averaged tendencies, and the open boundary setup via the boundaries of the low-res nested LES. The open boundary simulations inherit the full atmospheric state from the larger domains through frequent boundary updates, including developed cloud structures and their environmental states. Cloud structures are refined as they transition to higher-resolution simulations, with clouds breaking into smaller fragments while retaining their large-scale distribution. This results in larger, more organized clouds in the high-res nested LES compared to the periodic LES when cloud fractions are similar. The periodic LES has a stronger daily cycle in cloudiness, with days starting very cloudy and ending with clear skies, producing deeper and more intermittent clouds accompanied by more intense rainfall. This leads to greater variation in cloud structures, ranging from large clouds during cloudy periods to fewer, smaller clouds during low cloud cover. In contrast, the high-res nested LES maintains more constant cloud cover, with cloud top and size varying more gradually. The intermittent behavior of the periodic LES is explained by the applied horizontally averaged tendencies, which drive the domain toward stable or unstable conditions. Inheritance of the full atmospheric state allows the high-res nested LES to maintain larger, more organized clouds.
Plain Language Summary
In this study, we compare two types of computer simulations that model clouds in detail. One simulation (high-res nested large eddy simulation [LES]) is part of a series of models, where each smaller model gets its cloud patterns and atmospheric state from a larger model that covers a bigger area but with less detail. The other simulation (periodic LES) uses atmospheric background conditions from a larger weather model, but does not receive any clouds. The results show that the periodic LES creates clouds that change quickly, shifting between cloudy periods with large clouds and times with only a few small, scattered clouds. On the other hand, the high-res nested LES has more gradual changes in cloud patterns. In the setup consisting of a series of models, clouds tend to break into smaller fragments as they transition from larger models with less detail to smaller ones with more detail. The inheritance of clouds in the high-res nested LES results in larger, more clustered clouds during periods of similar cloud cover, compared to the periodic LES.
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Plain Language Summary
In this study, we compare two types of computer simulations that model clouds in detail. One simulation (high-res nested large eddy simulation [LES]) is part of a series of models, where each smaller model gets its cloud patterns and atmospheric state from a larger model that covers a bigger area but with less detail. The other simulation (periodic LES) uses atmospheric background conditions from a larger weather model, but does not receive any clouds. The results show that the periodic LES creates clouds that change quickly, shifting between cloudy periods with large clouds and times with only a few small, scattered clouds. On the other hand, the high-res nested LES has more gradual changes in cloud patterns. In the setup consisting of a series of models, clouds tend to break into smaller fragments as they transition from larger models with less detail to smaller ones with more detail. The inheritance of clouds in the high-res nested LES results in larger, more clustered clouds during periods of similar cloud cover, compared to the periodic LES.
...
An open boundary setup is presented in which a high-resolution (high-res) large eddy simulation (LES) is one-way nested in a low-resolution (low-res) LES. The high-res nested LES is compared to the periodic LES from Savazzi et al. (2023, https://doi.org/10.1175/jas-d-23-0098.1). Both simulations are forced by the regional weather model HARMONIE-AROME: the periodic LES via domain-averaged tendencies, and the open boundary setup via the boundaries of the low-res nested LES. The open boundary simulations inherit the full atmospheric state from the larger domains through frequent boundary updates, including developed cloud structures and their environmental states. Cloud structures are refined as they transition to higher-resolution simulations, with clouds breaking into smaller fragments while retaining their large-scale distribution. This results in larger, more organized clouds in the high-res nested LES compared to the periodic LES when cloud fractions are similar. The periodic LES has a stronger daily cycle in cloudiness, with days starting very cloudy and ending with clear skies, producing deeper and more intermittent clouds accompanied by more intense rainfall. This leads to greater variation in cloud structures, ranging from large clouds during cloudy periods to fewer, smaller clouds during low cloud cover. In contrast, the high-res nested LES maintains more constant cloud cover, with cloud top and size varying more gradually. The intermittent behavior of the periodic LES is explained by the applied horizontally averaged tendencies, which drive the domain toward stable or unstable conditions. Inheritance of the full atmospheric state allows the high-res nested LES to maintain larger, more organized clouds.
Plain Language Summary
In this study, we compare two types of computer simulations that model clouds in detail. One simulation (high-res nested large eddy simulation [LES]) is part of a series of models, where each smaller model gets its cloud patterns and atmospheric state from a larger model that covers a bigger area but with less detail. The other simulation (periodic LES) uses atmospheric background conditions from a larger weather model, but does not receive any clouds. The results show that the periodic LES creates clouds that change quickly, shifting between cloudy periods with large clouds and times with only a few small, scattered clouds. On the other hand, the high-res nested LES has more gradual changes in cloud patterns. In the setup consisting of a series of models, clouds tend to break into smaller fragments as they transition from larger models with less detail to smaller ones with more detail. The inheritance of clouds in the high-res nested LES results in larger, more clustered clouds during periods of similar cloud cover, compared to the periodic LES.
Plain Language Summary
In this study, we compare two types of computer simulations that model clouds in detail. One simulation (high-res nested large eddy simulation [LES]) is part of a series of models, where each smaller model gets its cloud patterns and atmospheric state from a larger model that covers a bigger area but with less detail. The other simulation (periodic LES) uses atmospheric background conditions from a larger weather model, but does not receive any clouds. The results show that the periodic LES creates clouds that change quickly, shifting between cloudy periods with large clouds and times with only a few small, scattered clouds. On the other hand, the high-res nested LES has more gradual changes in cloud patterns. In the setup consisting of a series of models, clouds tend to break into smaller fragments as they transition from larger models with less detail to smaller ones with more detail. The inheritance of clouds in the high-res nested LES results in larger, more clustered clouds during periods of similar cloud cover, compared to the periodic LES.
Mesoscale numerical weather prediction models currently operate at kilometer-scale and even sub-kilometer-scale resolutions. Although shallow cumulus convection is partly resolved at these resolutions, it is still common to use a shallow cumulus parameterization (SCP). Within the context of the EUREC4A model intercomparison project, we evaluate how the modeled mesoscale cloud field in the trades responds to parameterized or explicit shallow convection in the mesoscale model HARMONIE-AROME. We simulate a region of 3,200 × 2,025 km2 east of Barbados using a grid spacing of 2.5 km for a 2 months period (1 January to 29 February 2020). We compare three configurations of HARMONIE-AROME: (a) one with an active SCP (control), (b) one without parameterized momentum transport by shallow convection, and (c) one with an inactive SCP. The experiments produce different responses in the cloud field that are not incremental. With the SCP inactive, the model produces a warmer lower troposphere with many smaller but deeper clouds that precipitate more. Along with stronger resolved eddy kinetic energy, wider and stronger shallow meridional overturning circulations develop. In the configuration without parameterized momentum transport by shallow convection, the eddy-diffusivity scheme effectively takes over the missing transport in the sub-cloud layer up to ~800 m. Above that level, horizontal wind variance increases as the total momentum flux decreases, enhancing eddy kinetic energy at scales of 2.5 km and larger. In contrast to the configuration with an inactive SCP, cloud top heights hardly deepen, but stratiform cloudiness below the inversion and mean cloud size increase.
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Mesoscale numerical weather prediction models currently operate at kilometer-scale and even sub-kilometer-scale resolutions. Although shallow cumulus convection is partly resolved at these resolutions, it is still common to use a shallow cumulus parameterization (SCP). Within the context of the EUREC4A model intercomparison project, we evaluate how the modeled mesoscale cloud field in the trades responds to parameterized or explicit shallow convection in the mesoscale model HARMONIE-AROME. We simulate a region of 3,200 × 2,025 km2 east of Barbados using a grid spacing of 2.5 km for a 2 months period (1 January to 29 February 2020). We compare three configurations of HARMONIE-AROME: (a) one with an active SCP (control), (b) one without parameterized momentum transport by shallow convection, and (c) one with an inactive SCP. The experiments produce different responses in the cloud field that are not incremental. With the SCP inactive, the model produces a warmer lower troposphere with many smaller but deeper clouds that precipitate more. Along with stronger resolved eddy kinetic energy, wider and stronger shallow meridional overturning circulations develop. In the configuration without parameterized momentum transport by shallow convection, the eddy-diffusivity scheme effectively takes over the missing transport in the sub-cloud layer up to ~800 m. Above that level, horizontal wind variance increases as the total momentum flux decreases, enhancing eddy kinetic energy at scales of 2.5 km and larger. In contrast to the configuration with an inactive SCP, cloud top heights hardly deepen, but stratiform cloudiness below the inversion and mean cloud size increase.
Journal article
(2025)
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Victor J.H. Trees, Ping Wang, Piet Stammes, Lieuwe G. Tilstra, David P. Donovan, A. Pier Siebesma
Cloud shadows can be detected in the radiance measurements of the TROPOspheric Monitoring Instrument (TROPOMI) on board the Sentinel-5P satellite due to its high spatial resolution and could possibly affect its air quality products. The cloud-shadow-induced signatures are, however, not always apparent and may depend on various cloud and scene parameters. Hence, the quantification of the cloud shadow impact requires the analysis of large data sets. Here we use the cloud shadow detection algorithm DARCLOS to detect cloud shadow pixels in the TROPOMI absorbing aerosol index (AAI) product over Europe during 8 months. For every shadow pixel, we automatically select cloud- and shadow-free neighbour pixels in order to estimate the cloud-shadow-induced signature. In addition, we simulate the measured cloud shadow impact on the AAI with our newly developed three-dimensional (3D) radiative transfer algorithm MONKI. Both the measurements and simulations show that the average cloud shadow impact on the AAI is close to zero (0.06 and 0.16, respectively). However, the top-of-atmosphere reflectance ratio between 340 and 380 nm, which is used to compute the AAI, is significantly increased in 95 % of the shadow pixels. So, cloud shadows are bluer than surrounding non-shadow pixels. Our simulations explain that the traditional AAI formula intrinsically already corrects for this cloud shadow effect via the lower retrieved scene albedo. This cancellation of cloud shadow signatures is not always perfect, sometimes yielding second-order low and high biases in the AAI which we also successfully reproduce with our simulations. We show that the magnitude of those second-order cloud shadow effects depends on various cloud parameters which are difficult to determine for the shadows measured with TROPOMI. We conclude that a potential cloud shadow correction strategy for the TROPOMI AAI would therefore be complicated if not unnecessary.
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Cloud shadows can be detected in the radiance measurements of the TROPOspheric Monitoring Instrument (TROPOMI) on board the Sentinel-5P satellite due to its high spatial resolution and could possibly affect its air quality products. The cloud-shadow-induced signatures are, however, not always apparent and may depend on various cloud and scene parameters. Hence, the quantification of the cloud shadow impact requires the analysis of large data sets. Here we use the cloud shadow detection algorithm DARCLOS to detect cloud shadow pixels in the TROPOMI absorbing aerosol index (AAI) product over Europe during 8 months. For every shadow pixel, we automatically select cloud- and shadow-free neighbour pixels in order to estimate the cloud-shadow-induced signature. In addition, we simulate the measured cloud shadow impact on the AAI with our newly developed three-dimensional (3D) radiative transfer algorithm MONKI. Both the measurements and simulations show that the average cloud shadow impact on the AAI is close to zero (0.06 and 0.16, respectively). However, the top-of-atmosphere reflectance ratio between 340 and 380 nm, which is used to compute the AAI, is significantly increased in 95 % of the shadow pixels. So, cloud shadows are bluer than surrounding non-shadow pixels. Our simulations explain that the traditional AAI formula intrinsically already corrects for this cloud shadow effect via the lower retrieved scene albedo. This cancellation of cloud shadow signatures is not always perfect, sometimes yielding second-order low and high biases in the AAI which we also successfully reproduce with our simulations. We show that the magnitude of those second-order cloud shadow effects depends on various cloud parameters which are difficult to determine for the shadows measured with TROPOMI. We conclude that a potential cloud shadow correction strategy for the TROPOMI AAI would therefore be complicated if not unnecessary.
MONKI
A three-dimensional Monte Carlo simulator of total and polarised radiation reflected by planetary atmospheres
Preprint
(2025)
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Victor J.H. Trees, Ping Wang, Job I. Wiltink, Piet Stammes, Daphne M. Stam, David P. Donovan, A. Pier Siebesma
Spectropolarimetry is a powerful tool for characterising planetary atmospheres and surfaces. For the design and operation of spectro(polari)metric instrumentation, numerically simulated signals of the measured radiation are essential. Here we present MONKI (Monte Carlo KNMI), an efficient and accurate radiative transfer code written in Fortran, based on the Monte Carlo method. MONKI computes both total and polarised radiances reflected and transmitted by a planetary atmosphere, fully accounting for the polarisation of light in all orders of scattering. MONKI can handle atmospheres that are horizontally homogeneous, as well as those with horizontal inhomogeneities, such as three-dimensional (3D) patchy clouds. We validate MONKI through comparisons with various other radiative transfer codes and demonstrate that it converges reliably even for optically thick and strongly polarising atmospheres. Finally, we present sample simulations of sunlight reflected by the Earth and Venus, and explain the total and polarised radiance features by analysing the altitudes at which the photons are scattered. We conclude that MONKI is a versatile and accurate tool, suitable for simulations and detailed analyses of locally reflected light by the Earth, Venus, and, in principle, any other planet.
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Spectropolarimetry is a powerful tool for characterising planetary atmospheres and surfaces. For the design and operation of spectro(polari)metric instrumentation, numerically simulated signals of the measured radiation are essential. Here we present MONKI (Monte Carlo KNMI), an efficient and accurate radiative transfer code written in Fortran, based on the Monte Carlo method. MONKI computes both total and polarised radiances reflected and transmitted by a planetary atmosphere, fully accounting for the polarisation of light in all orders of scattering. MONKI can handle atmospheres that are horizontally homogeneous, as well as those with horizontal inhomogeneities, such as three-dimensional (3D) patchy clouds. We validate MONKI through comparisons with various other radiative transfer codes and demonstrate that it converges reliably even for optically thick and strongly polarising atmospheres. Finally, we present sample simulations of sunlight reflected by the Earth and Venus, and explain the total and polarised radiance features by analysing the altitudes at which the photons are scattered. We conclude that MONKI is a versatile and accurate tool, suitable for simulations and detailed analyses of locally reflected light by the Earth, Venus, and, in principle, any other planet.
We investigate if mesoscale self-organisation of trade cumuli in 150 km-domain large-eddy simulations modifies the top-of-atmosphere radiation budget relative to 10 km-domain simulations, across 77 characteristic, idealized environments. In large domains, self-generated mesoscale circulations produce fewer, larger and deeper clouds, raising the cloud albedo. Yet they also precipitate more than small-domain cumuli, drying and warming the cloud layer, and reducing cloud cover. Consequently, large domains cool slightly less through the shortwave cloud-radiative effect, and slightly more through clear-sky outgoing longwave radiation, for a net cooling (−0.5 W (Formula presented.)). This cooling is generally smaller than the large-domain radiation's sensitivity to large-scale meteorological variability, which is similar in small-domain simulations and observations. Hence, mesoscale self-organisation would not alter weak trade-cumulus feedback estimates previously derived from small-domain simulations. We explain this with a symmetry hypothesis: ascending and descending branches of mesoscale circulations symmetrically increase and reduce cloudiness, weakly modifying the mean radiation budget.
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We investigate if mesoscale self-organisation of trade cumuli in 150 km-domain large-eddy simulations modifies the top-of-atmosphere radiation budget relative to 10 km-domain simulations, across 77 characteristic, idealized environments. In large domains, self-generated mesoscale circulations produce fewer, larger and deeper clouds, raising the cloud albedo. Yet they also precipitate more than small-domain cumuli, drying and warming the cloud layer, and reducing cloud cover. Consequently, large domains cool slightly less through the shortwave cloud-radiative effect, and slightly more through clear-sky outgoing longwave radiation, for a net cooling (−0.5 W (Formula presented.)). This cooling is generally smaller than the large-domain radiation's sensitivity to large-scale meteorological variability, which is similar in small-domain simulations and observations. Hence, mesoscale self-organisation would not alter weak trade-cumulus feedback estimates previously derived from small-domain simulations. We explain this with a symmetry hypothesis: ascending and descending branches of mesoscale circulations symmetrically increase and reduce cloudiness, weakly modifying the mean radiation budget.
Journal article
(2024)
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Victor J. H. Trees, Stephan R. de Roode, Job I. Wiltink, Jan Fokke Meirink, Ping Wang, Piet Stammes, A. Pier Siebesma
Clouds affected by solar eclipses could influence the reflection of sunlight back into space and might change local precipitation patterns. Satellite cloud retrievals have so far not taken into account the lunar shadow, hindering a reliable spaceborne assessment of the eclipse-induced cloud evolution. Here we use satellite cloud measurements during three solar eclipses between 2005 and 2016 that have been corrected for the partial lunar shadow together with large-eddy simulations to analyze the eclipse-induced cloud evolution. Our corrected data reveal that, over cooling land surfaces, shallow cumulus clouds start to disappear at very small solar obscurations (~15%). Our simulations explain that the cloud response was delayed and was initiated at even smaller solar obscurations. We demonstrate that neglecting the disappearance of clouds during a solar eclipse could lead to a considerable overestimation of the eclipse-related reduction of net incoming solar radiation. These findings should spur cloud model simulations of the direct consequences of sunlight-intercepting geoengineering proposals, for which our results serve as a unique benchmark.
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Clouds affected by solar eclipses could influence the reflection of sunlight back into space and might change local precipitation patterns. Satellite cloud retrievals have so far not taken into account the lunar shadow, hindering a reliable spaceborne assessment of the eclipse-induced cloud evolution. Here we use satellite cloud measurements during three solar eclipses between 2005 and 2016 that have been corrected for the partial lunar shadow together with large-eddy simulations to analyze the eclipse-induced cloud evolution. Our corrected data reveal that, over cooling land surfaces, shallow cumulus clouds start to disappear at very small solar obscurations (~15%). Our simulations explain that the cloud response was delayed and was initiated at even smaller solar obscurations. We demonstrate that neglecting the disappearance of clouds during a solar eclipse could lead to a considerable overestimation of the eclipse-related reduction of net incoming solar radiation. These findings should spur cloud model simulations of the direct consequences of sunlight-intercepting geoengineering proposals, for which our results serve as a unique benchmark.
Journal article
(2024)
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Pouriya Alinaghi, Martin Janssens, Goutam Choudhury, Tom Goren, A. Pier Siebesma, Franziska Glassmeier
Shallow trade cumuli over subtropical oceans are a persistent source of uncertainty in climate projections. Mesoscale organization of trade cumulus clouds has been shown to influence their cloud radiative effect (CRE) through cloud cover. We investigate whether organization can explain CRE variability independently of cloud-cover variability. By analyzing satellite observations and high-resolution simulations, we show that more clustered cloud fields feature geometrically thicker clouds with larger domain-averaged liquid water paths, smaller cloud droplets, and consequently larger cloud optical depths. The relationships between these variables are shaped by the mixture of deep cloud cores and shallower interstitial clouds or anvils that characterize cloud organization. Eliminating cloud-cover effects, more clustered clouds reflect up to 20 W/m2 more instantaneous shortwave radiation back to space.
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Shallow trade cumuli over subtropical oceans are a persistent source of uncertainty in climate projections. Mesoscale organization of trade cumulus clouds has been shown to influence their cloud radiative effect (CRE) through cloud cover. We investigate whether organization can explain CRE variability independently of cloud-cover variability. By analyzing satellite observations and high-resolution simulations, we show that more clustered cloud fields feature geometrically thicker clouds with larger domain-averaged liquid water paths, smaller cloud droplets, and consequently larger cloud optical depths. The relationships between these variables are shaped by the mixture of deep cloud cores and shallower interstitial clouds or anvils that characterize cloud organization. Eliminating cloud-cover effects, more clustered clouds reflect up to 20 W/m2 more instantaneous shortwave radiation back to space.
Preprint
(2024)
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Pouriya Alinaghi, Pier Siebesma, Fredrik Jansson, Martin Janssens, Franziska Glassmeier
Recent observations of the trade-wind regions highlight the covariability between cold-pool properties and mesoscale cloud organization. Given the covariability of organization with cloud cover and albedo, this suggests a potential impact of cold pools on the cloud radiative effect (CRE). To explore this, we use an ensemble of 103 large-domain, high-resolution, large-eddy simulations and investigate how the variability in cold pools is determined by large-scale external cloud-controlling factors (CCFs) and shaped by processes within the mesoscale. It is demonstrated that the size and frequency of occurrence of cold pools are strongly influenced by the near-surface horizontal wind speed and large-scale subsidence. The temporal evolution of cold pools is strongly correlated with the diurnality in radiation. Even without external variability, we find a strong intermittent behaviour in the evolution of cold pools, governed by a complex interplay between cold pools and clouds which expresses itself in the form of shallow squall lines. These squall lines result from precipitating downdrafts, cold pool outflows and the resulting gust fronts, reinforcing parent clouds. Cold pools influence the CRE of trade cumuli, but only when they exist during the day. This emphasizes the importance of the synchronization between cold-pool events and the diurnal cycle of insolation for the dependence of the CRE on cold pools.
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Recent observations of the trade-wind regions highlight the covariability between cold-pool properties and mesoscale cloud organization. Given the covariability of organization with cloud cover and albedo, this suggests a potential impact of cold pools on the cloud radiative effect (CRE). To explore this, we use an ensemble of 103 large-domain, high-resolution, large-eddy simulations and investigate how the variability in cold pools is determined by large-scale external cloud-controlling factors (CCFs) and shaped by processes within the mesoscale. It is demonstrated that the size and frequency of occurrence of cold pools are strongly influenced by the near-surface horizontal wind speed and large-scale subsidence. The temporal evolution of cold pools is strongly correlated with the diurnality in radiation. Even without external variability, we find a strong intermittent behaviour in the evolution of cold pools, governed by a complex interplay between cold pools and clouds which expresses itself in the form of shallow squall lines. These squall lines result from precipitating downdrafts, cold pool outflows and the resulting gust fronts, reinforcing parent clouds. Cold pools influence the CRE of trade cumuli, but only when they exist during the day. This emphasizes the importance of the synchronization between cold-pool events and the diurnal cycle of insolation for the dependence of the CRE on cold pools.
Journal article
(2024)
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Alessandro C.M. Savazzi, Louise Nuijens, Wim De Rooy, Martin Janssens, A. Pier Siebesma
This study investigates momentum transport in shallow cumulus clouds as simulated with the Dutch Atmospheric Large Eddy Simulation (DALES) for a 150 3 150 km2 domain east of Barbados during 9 days of EUREC4A. DALES is initialized and forced with the mesoscale weather model HARMONIE-AROME and subjectively reproduces observed cloud patterns. This study examines the evolution of momentum transport, which scales contribute to it, and how they modulate the trade winds. Daily-mean momentum flux profiles show downgradient zonal momentum transport in the subcloud layer, which turns countergradient in the cloud layer. The meridional momentum transport is nontrivial, with mostly downgradient transport throughout the trade wind layer except near the top of the surface layer and near cloud tops. Substantial spatial and temporal heterogeneity in momentum flux is observed with much stronger tendencies imposed in areas of organized convection. The study finds that while scales < 2 km dominate momentum flux at 200 m in unorganized fields, submesoscales O(2-20) km carry up to 50% of the zonal momentum flux in the cloud layer in organized fields. For the meridional momentum flux, this fraction is even larger near the surface and in the subcloud layer. The scale dependence of the momentum flux is not explained by changes in convective or boundary layer depth. Instead, the results suggest the importance of spatial heterogeneity, increasing horizontal length scales, and countergradient transport in the presence of organized convection.
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This study investigates momentum transport in shallow cumulus clouds as simulated with the Dutch Atmospheric Large Eddy Simulation (DALES) for a 150 3 150 km2 domain east of Barbados during 9 days of EUREC4A. DALES is initialized and forced with the mesoscale weather model HARMONIE-AROME and subjectively reproduces observed cloud patterns. This study examines the evolution of momentum transport, which scales contribute to it, and how they modulate the trade winds. Daily-mean momentum flux profiles show downgradient zonal momentum transport in the subcloud layer, which turns countergradient in the cloud layer. The meridional momentum transport is nontrivial, with mostly downgradient transport throughout the trade wind layer except near the top of the surface layer and near cloud tops. Substantial spatial and temporal heterogeneity in momentum flux is observed with much stronger tendencies imposed in areas of organized convection. The study finds that while scales < 2 km dominate momentum flux at 200 m in unorganized fields, submesoscales O(2-20) km carry up to 50% of the zonal momentum flux in the cloud layer in organized fields. For the meridional momentum flux, this fraction is even larger near the surface and in the subcloud layer. The scale dependence of the momentum flux is not explained by changes in convective or boundary layer depth. Instead, the results suggest the importance of spatial heterogeneity, increasing horizontal length scales, and countergradient transport in the presence of organized convection.
The hectometric modelling challenge
Gaps in the current state of the art and ways forward towards the implementation of 100-m scale weather and climate models
Review
(2024)
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Humphrey W. Lean, Natalie E. Theeuwes, Michael Baldauf, Jan Barkmeijer, Geoffrey Bessardon, Lewis Blunn, Jelena Bojarova, Ian A. Boutle, Pier Siebesma, More authors...
For a number of years research has been carried out in several centres which has demonstrated the potential benefits of 100-m scale models for a range of meteorological phenomena. More recently, some meteorological services have started to consider seriously the operational implementation of practical hectometric models. Many, but by no means all, of the applications are likely to relate to urban areas, where the enhanced resolution has obvious benefits. This article is concerned with the issues that need to be addressed to bridge the gap between research at 100-m scales and practical models. We highlight a number of key issues that need to be addressed, with suggestions of important avenues for future development. An overarching issue is the high computational cost of these models. Although some ideas to reduce this are presented, it will always be a serious constraint. This means that the benefits of these models over lower resolution ones, or other techniques for generating high-resolution forecasts, will need to be clearly understood, as will the trade-offs with resolution. We discuss issues with model dynamical cores and physics–dynamics coupling. There are a number of challenges around model parameterisations, where some of the traditional problems (e.g., convection) become easier but a number of new challenges (e.g., around surface parameterisations) appear. Observational data at these scales present a challenge and novel types of observations will need to be considered. Data assimilation will be needed for short-range forecasts, but there is currently little knowledge of this, although some of the likely issues are clear. An ensemble approach will be essential in many cases (e.g., convection), but research is needed into ensembles at these scales and significant work on post-processing systems is required to make the best use of models at these grid lengths.
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For a number of years research has been carried out in several centres which has demonstrated the potential benefits of 100-m scale models for a range of meteorological phenomena. More recently, some meteorological services have started to consider seriously the operational implementation of practical hectometric models. Many, but by no means all, of the applications are likely to relate to urban areas, where the enhanced resolution has obvious benefits. This article is concerned with the issues that need to be addressed to bridge the gap between research at 100-m scales and practical models. We highlight a number of key issues that need to be addressed, with suggestions of important avenues for future development. An overarching issue is the high computational cost of these models. Although some ideas to reduce this are presented, it will always be a serious constraint. This means that the benefits of these models over lower resolution ones, or other techniques for generating high-resolution forecasts, will need to be clearly understood, as will the trade-offs with resolution. We discuss issues with model dynamical cores and physics–dynamics coupling. There are a number of challenges around model parameterisations, where some of the traditional problems (e.g., convection) become easier but a number of new challenges (e.g., around surface parameterisations) appear. Observational data at these scales present a challenge and novel types of observations will need to be considered. Data assimilation will be needed for short-range forecasts, but there is currently little knowledge of this, although some of the likely issues are clear. An ensemble approach will be essential in many cases (e.g., convection), but research is needed into ensembles at these scales and significant work on post-processing systems is required to make the best use of models at these grid lengths.
Journal article
(2024)
-
Pouriya Alinaghi, A. Pier Siebesma, Fredrik Jansson, Martin Janssens, Franziska Glassmeier
Recent observations of the trade-wind regions highlight the covariability between cold-pool properties and mesoscale cloud organization. Given the covariability of organization with cloud cover and albedo, this suggests a potential impact of cold pools on the cloud radiative effect (CRE). To explore this, we use an ensemble of 103 large-domain, high-resolution, large-eddy simulations and investigate how the variability in cold pools is determined by large-scale external cloud-controlling factors and shaped by processes within the mesoscale. It is demonstrated that the size and frequency of occurrence of cold pools are strongly influenced by the near-surface horizontal wind speed and large-scale subsidence. The temporal evolution of cold pools is strongly correlated with the diurnality in radiation. Even without external variability, we find a strong intermittent behavior in the evolution of cold pools, governed by a complex interplay between cold pools and clouds which expresses itself in the form of shallow squall lines. These squall lines result from precipitating downdrafts, cold pool outflows and the resulting gust fronts, reinforcing parent clouds. Cold pools influence the CRE of trade cumuli, but only when they exist during the day. This emphasizes the importance of the synchronization between cold-pool events and the diurnal cycle of insolation for the dependence of the CRE on cold pools.
...
Recent observations of the trade-wind regions highlight the covariability between cold-pool properties and mesoscale cloud organization. Given the covariability of organization with cloud cover and albedo, this suggests a potential impact of cold pools on the cloud radiative effect (CRE). To explore this, we use an ensemble of 103 large-domain, high-resolution, large-eddy simulations and investigate how the variability in cold pools is determined by large-scale external cloud-controlling factors and shaped by processes within the mesoscale. It is demonstrated that the size and frequency of occurrence of cold pools are strongly influenced by the near-surface horizontal wind speed and large-scale subsidence. The temporal evolution of cold pools is strongly correlated with the diurnality in radiation. Even without external variability, we find a strong intermittent behavior in the evolution of cold pools, governed by a complex interplay between cold pools and clouds which expresses itself in the form of shallow squall lines. These squall lines result from precipitating downdrafts, cold pool outflows and the resulting gust fronts, reinforcing parent clouds. Cold pools influence the CRE of trade cumuli, but only when they exist during the day. This emphasizes the importance of the synchronization between cold-pool events and the diurnal cycle of insolation for the dependence of the CRE on cold pools.
Open boundary conditions were developed for atmospheric large-eddy simulation (LES) models and implemented into the Dutch Atmospheric Large-Eddy Simulation model. The implementation was tested in a “Big Brother”-like setup, in which the simulation with open boundary conditions was forced by an identical control simulation with periodic boundary conditions. The results show that the open boundary implementation has minimal influence on the solution. Both the mean state and the turbulent structures are close to the control simulation, and disturbances at the in- and outflow boundaries are negligible. To emulate a setup in which the LES is coupled to a coarser model, the influence of coarse boundary input was tested by smoothing the output of the periodic control simulation both temporally and spatially before feeding it as input to the simulation with open boundary conditions. When smoothing is applied over larger spatial and longer temporal scales, disturbances start to form at the inflow boundary and an area exists where turbulence needs to develop. Adding synthetic turbulence to the smoothed input reduces the size of this area and the magnitude of the disturbances.
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Open boundary conditions were developed for atmospheric large-eddy simulation (LES) models and implemented into the Dutch Atmospheric Large-Eddy Simulation model. The implementation was tested in a “Big Brother”-like setup, in which the simulation with open boundary conditions was forced by an identical control simulation with periodic boundary conditions. The results show that the open boundary implementation has minimal influence on the solution. Both the mean state and the turbulent structures are close to the control simulation, and disturbances at the in- and outflow boundaries are negligible. To emulate a setup in which the LES is coupled to a coarser model, the influence of coarse boundary input was tested by smoothing the output of the periodic control simulation both temporally and spatially before feeding it as input to the simulation with open boundary conditions. When smoothing is applied over larger spatial and longer temporal scales, disturbances start to form at the inflow boundary and an area exists where turbulence needs to develop. Adding synthetic turbulence to the smoothed input reduces the size of this area and the magnitude of the disturbances.
Abstract
(2024)
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Pouriya Alinaghi, Martin Janssens, Fredrik Jansson, A. Pier Siebesma, Franziska Glassmeier
Recent observations of the trades highlight the covariability between cold pool (CP) properties and cloud cover, suggesting a potential impact of CPs on the cloud radiative effect (CRE). To explore this, we use an ensemble of 103 large-domain, high-resolution, large-eddy simulations (Cloud Botany). We investigate the extent to which the variability in CPs is driven by external conditions or convective self-organization. Our findings show that CPs are notably controlled by large-scale conditions, specifically (horizontal) wind speed and subsidence. The temporal evolution of CPs is tightly related to the diurnality in radiation. To understand the extent to which CPs vary with self-organization, we switch off the diurnality in radiation. Despite the absence of the diurnal cycle, CP time series still exhibit fluctuations. These fluctuations result from the recharge-discharge of thermodynamic and dynamic properties of the sub-cloud layer owing to CP-cloud interactions. Our results demonstrate that circulations induced by CPs reinforce the parent clouds, resulting in deepening and scale growth, followed by mesoscale arcs enclosing clear-sky areas. Finally, we show that CPs influence CRE, but only when they exist during the day. Our findings emphasize the importance of the relationship between the timescales of self-organization and the diurnal cycle of external conditions, greatly influencing the CRE dependency on self-organizing CPs.
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Recent observations of the trades highlight the covariability between cold pool (CP) properties and cloud cover, suggesting a potential impact of CPs on the cloud radiative effect (CRE). To explore this, we use an ensemble of 103 large-domain, high-resolution, large-eddy simulations (Cloud Botany). We investigate the extent to which the variability in CPs is driven by external conditions or convective self-organization. Our findings show that CPs are notably controlled by large-scale conditions, specifically (horizontal) wind speed and subsidence. The temporal evolution of CPs is tightly related to the diurnality in radiation. To understand the extent to which CPs vary with self-organization, we switch off the diurnality in radiation. Despite the absence of the diurnal cycle, CP time series still exhibit fluctuations. These fluctuations result from the recharge-discharge of thermodynamic and dynamic properties of the sub-cloud layer owing to CP-cloud interactions. Our results demonstrate that circulations induced by CPs reinforce the parent clouds, resulting in deepening and scale growth, followed by mesoscale arcs enclosing clear-sky areas. Finally, we show that CPs influence CRE, but only when they exist during the day. Our findings emphasize the importance of the relationship between the timescales of self-organization and the diurnal cycle of external conditions, greatly influencing the CRE dependency on self-organizing CPs.
Journal article
(2024)
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Andrés Yarce Botero, Michiel van Weele, Arjo Segers, Pier Siebesma, Henk Eskes
Meteorological fields calculated by numerical weather prediction (NWP) models drive offline chemical transport models (CTMs) to solve the transport, chemical reactions, and atmospheric interaction over the geographical domain of interest. HARMONIE (HIRLAM ALADIN Research on Mesoscale Operational NWP in Euromed) is a state-of-The-Art non-hydrostatic NWP community model used at several European weather agencies to forecast weather at the local and/or regional scale. In this work, the HARMONIE WINS50 (cycle 43 cy43) reanalysis dataset at a resolution of 0.025°ĝ€¯×ĝ€¯0.025° covering an area surrounding the North Sea for the years 2019-2021 was coupled offline to the LOTOS-EUROS (LOng-Term Ozone Simulation-EURopean Operational Smog model, v2.2.002) CTM. The impact of using either meteorological fields from HARMONIE or from ECMWF on LOTOS-EUROS simulations of NO2 has been evaluated against ground-level observations and TROPOMI tropospheric NO2 vertical columns. Furthermore, the difference between crucial meteorological input parameters such as the boundary layer height and the vertical diffusion coefficient between the hydrostatic ECMWF and non-hydrostatic HARMONIE data has been studied, and the vertical profiles of temperature, humidity, and wind are evaluated against meteorological observations at Cabauw in The Netherlands. The results of these first evaluations of the LOTOS-EUROS model performance in both configurations are used to investigate current uncertainties in air quality forecasting in relation to driving meteorological parameters and to assess the potential for improvements in forecasting pollution episodes at high resolutions based on the HARMONIE NWP model.
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Meteorological fields calculated by numerical weather prediction (NWP) models drive offline chemical transport models (CTMs) to solve the transport, chemical reactions, and atmospheric interaction over the geographical domain of interest. HARMONIE (HIRLAM ALADIN Research on Mesoscale Operational NWP in Euromed) is a state-of-The-Art non-hydrostatic NWP community model used at several European weather agencies to forecast weather at the local and/or regional scale. In this work, the HARMONIE WINS50 (cycle 43 cy43) reanalysis dataset at a resolution of 0.025°ĝ€¯×ĝ€¯0.025° covering an area surrounding the North Sea for the years 2019-2021 was coupled offline to the LOTOS-EUROS (LOng-Term Ozone Simulation-EURopean Operational Smog model, v2.2.002) CTM. The impact of using either meteorological fields from HARMONIE or from ECMWF on LOTOS-EUROS simulations of NO2 has been evaluated against ground-level observations and TROPOMI tropospheric NO2 vertical columns. Furthermore, the difference between crucial meteorological input parameters such as the boundary layer height and the vertical diffusion coefficient between the hydrostatic ECMWF and non-hydrostatic HARMONIE data has been studied, and the vertical profiles of temperature, humidity, and wind are evaluated against meteorological observations at Cabauw in The Netherlands. The results of these first evaluations of the LOTOS-EUROS model performance in both configurations are used to investigate current uncertainties in air quality forecasting in relation to driving meteorological parameters and to assess the potential for improvements in forecasting pollution episodes at high resolutions based on the HARMONIE NWP model.
Journal article
(2023)
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Martin Janssens, Jordi Vilà-Guerau De Arellano, Chiel C. Van Heerwaarden, Stephan R. De Roode, A. Pier Siebesma, Franziska Glassmeier
Condensation in cumulus clouds plays a key role in structuring the mean, nonprecipitating trade wind boundary layer. Here, we summarize how this role also explains the spontaneous growth of mesoscale [.O(10) km] fluctuations in clouds and moisture around the mean state in a minimal-physics, large-eddy simulation of the undisturbed period during BOMEX on a large [O(100) km] domain. Small, spatial anomalies in condensation in cumulus clouds, which form on top of small moisture fluctuations, power circulations that transport moisture, but not heat, from dry to moist regions, and thus reinforce the condensation anomaly. We frame this positive feedback as a linear instability in mesoscale moisture fluctuations, whose time scale depends only on (i) a vertical velocity scale and (ii) the mean environment's vertical structure. In our minimal-physics setting, we show both ingredients are provided by the shallow cumulus convection itself: it is intrinsically unstable to length scale growth. The upshot is that energy released by clouds at kilometer scales may play a more profound and direct role in shaping the mesoscale trade wind environment than is generally appreciated, motivating further research into the mechanism's relevance.
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Condensation in cumulus clouds plays a key role in structuring the mean, nonprecipitating trade wind boundary layer. Here, we summarize how this role also explains the spontaneous growth of mesoscale [.O(10) km] fluctuations in clouds and moisture around the mean state in a minimal-physics, large-eddy simulation of the undisturbed period during BOMEX on a large [O(100) km] domain. Small, spatial anomalies in condensation in cumulus clouds, which form on top of small moisture fluctuations, power circulations that transport moisture, but not heat, from dry to moist regions, and thus reinforce the condensation anomaly. We frame this positive feedback as a linear instability in mesoscale moisture fluctuations, whose time scale depends only on (i) a vertical velocity scale and (ii) the mean environment's vertical structure. In our minimal-physics setting, we show both ingredients are provided by the shallow cumulus convection itself: it is intrinsically unstable to length scale growth. The upshot is that energy released by clouds at kilometer scales may play a more profound and direct role in shaping the mesoscale trade wind environment than is generally appreciated, motivating further research into the mechanism's relevance.
Cloud Botany
Shallow Cumulus Clouds in an Ensemble of Idealized Large-Domain Large-Eddy Simulations of the Trades
Journal article
(2023)
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F.R. Jansson, Martin Janssens, Johanna H. Grönqvist, A.Pier Siebesma, Franziska Glassmeier, Jisk Attema, Victor Azizi, Masaki Satoh, Yousuke Sato, More authors...
Small shallow cumulus clouds (less-than 1 km) over the tropical oceans appear to possess the ability to self-organize into mesoscale (10–100 km) patterns. To better understand the processes leading to such self-organized convection, we present Cloud Botany, an ensemble of 103 large-eddy simulations on domains of 150 km, produced by the Dutch Atmospheric Large Eddy Simulation model on supercomputer Fugaku. Each simulation is run in an idealized, fixed, larger-scale environment, controlled by six free parameters. We vary these over characteristic ranges for the winter trades, including parameter combinations observed during the EUREC4A (Elucidating the role of clouds–circulation coupling in climate) field campaign. In contrast to simulation setups striving for maximum realism, Cloud Botany provides a platform for studying idealized, and therefore more clearly interpretable causal relationships between conditions in the larger-scale environment and patterns in mesoscale, self-organized shallow convection. We find that any simulation that supports cumulus clouds eventually develops mesoscale patterns in their cloud fields. We also find a rich variety in these patterns as our control parameters change, including cold pools lined by cloudy arcs, bands of cross-wind clouds and aggregated patches, sometimes topped by thin anvils. Many of these features are similar to cloud patterns found in nature. The published data set consists of raw simulation output on full 3D grids and 2D cross-sections, as well as post-processed quantities aggregated over the vertical (2D), horizontal (1D) and all spatial dimensions (time-series). The data set is directly accessible from Python through the use of the EUREC4A intake catalog.
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Small shallow cumulus clouds (less-than 1 km) over the tropical oceans appear to possess the ability to self-organize into mesoscale (10–100 km) patterns. To better understand the processes leading to such self-organized convection, we present Cloud Botany, an ensemble of 103 large-eddy simulations on domains of 150 km, produced by the Dutch Atmospheric Large Eddy Simulation model on supercomputer Fugaku. Each simulation is run in an idealized, fixed, larger-scale environment, controlled by six free parameters. We vary these over characteristic ranges for the winter trades, including parameter combinations observed during the EUREC4A (Elucidating the role of clouds–circulation coupling in climate) field campaign. In contrast to simulation setups striving for maximum realism, Cloud Botany provides a platform for studying idealized, and therefore more clearly interpretable causal relationships between conditions in the larger-scale environment and patterns in mesoscale, self-organized shallow convection. We find that any simulation that supports cumulus clouds eventually develops mesoscale patterns in their cloud fields. We also find a rich variety in these patterns as our control parameters change, including cold pools lined by cloudy arcs, bands of cross-wind clouds and aggregated patches, sometimes topped by thin anvils. Many of these features are similar to cloud patterns found in nature. The published data set consists of raw simulation output on full 3D grids and 2D cross-sections, as well as post-processed quantities aggregated over the vertical (2D), horizontal (1D) and all spatial dimensions (time-series). The data set is directly accessible from Python through the use of the EUREC4A intake catalog.
Journal article
(2023)
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Martin Janssens, Jordi Vilà-Guerau de Arellano, Chiel C. van Heerwaarden, Bart J.H. van Stratum, Stephan R. de Roode, A. Pier Siebesma, Franziska Glassmeier
Numerical simulations of the tropical mesoscales often exhibit a self-reinforcing feedback between cumulus convection and shallow circulations, which leads to the self-aggregation of clouds into large clusters. We investigate whether this basic feedback can be adequately captured by large-eddy simulations (LESs). To do so, we simulate the non-precipitating, cumulus-topped boundary layer of the canonical “BOMEX” case over a range of numerical settings in two models. Since the energetic convective scales underpinning the self-aggregation are only slightly larger than typical LES grid spacings, aggregation timescales do not converge even at rather high resolutions (<100 m). Therefore, high resolutions or improved sub-filter scale models may be required to faithfully represent certain forms of trade-wind mesoscale cloud patterns and self-aggregating deep convection in large-eddy and cloud-resolving models, and to understand their significance relative to other processes that organize the tropical mesoscales.
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Numerical simulations of the tropical mesoscales often exhibit a self-reinforcing feedback between cumulus convection and shallow circulations, which leads to the self-aggregation of clouds into large clusters. We investigate whether this basic feedback can be adequately captured by large-eddy simulations (LESs). To do so, we simulate the non-precipitating, cumulus-topped boundary layer of the canonical “BOMEX” case over a range of numerical settings in two models. Since the energetic convective scales underpinning the self-aggregation are only slightly larger than typical LES grid spacings, aggregation timescales do not converge even at rather high resolutions (<100 m). Therefore, high resolutions or improved sub-filter scale models may be required to faithfully represent certain forms of trade-wind mesoscale cloud patterns and self-aggregating deep convection in large-eddy and cloud-resolving models, and to understand their significance relative to other processes that organize the tropical mesoscales.
Atmospheric delay has a profound impact on synthetic aperture radar (SAR) interferometry, inducing a spatial signal that significantly devaluates interferometric products. While the wide-scale variability of the atmosphere can be adequately modeled with global or regional weather models, it is especially the turbulent and convective part of the atmosphere at smaller spatial and temporal scales that is typically poorly captured. Due to the high resolution and precision of InSAR, there is a need for a realistic modeling of the 3-D distribution of turbulent refractivity in the boundary layer. This would enable assessment of the impact of a temporal or spatial model misalignment on the interferometric products, and contribute to studying the impact for future SAR missions. Here we test the feasibility of an advanced large Eddy simulation (LES) model to simulate a time-series refractivity distribution with a high spatio-temporal resolution to show the spatio-temporal variability of the troposphere on short time scales. We found for a fair-weather situation that the LES model produces realistic atmospheric simulations that match stochastically with results found in interferometric studies and that tropospheric delay variation leads to significant phase gradients within several minutes. This implies that even when using an (unrealistic) perfect weather model with resolutions similar to the SAR image, realizations that are several minutes apart from the time of the SAR acquisition will lead to significant phase errors. We propose the use of LES models as a realistic instrument to perform InSAR quality-assessments and for the development and simulation for future missions.
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Atmospheric delay has a profound impact on synthetic aperture radar (SAR) interferometry, inducing a spatial signal that significantly devaluates interferometric products. While the wide-scale variability of the atmosphere can be adequately modeled with global or regional weather models, it is especially the turbulent and convective part of the atmosphere at smaller spatial and temporal scales that is typically poorly captured. Due to the high resolution and precision of InSAR, there is a need for a realistic modeling of the 3-D distribution of turbulent refractivity in the boundary layer. This would enable assessment of the impact of a temporal or spatial model misalignment on the interferometric products, and contribute to studying the impact for future SAR missions. Here we test the feasibility of an advanced large Eddy simulation (LES) model to simulate a time-series refractivity distribution with a high spatio-temporal resolution to show the spatio-temporal variability of the troposphere on short time scales. We found for a fair-weather situation that the LES model produces realistic atmospheric simulations that match stochastically with results found in interferometric studies and that tropospheric delay variation leads to significant phase gradients within several minutes. This implies that even when using an (unrealistic) perfect weather model with resolutions similar to the SAR image, realizations that are several minutes apart from the time of the SAR acquisition will lead to significant phase errors. We propose the use of LES models as a realistic instrument to perform InSAR quality-assessments and for the development and simulation for future missions.
Poster
(2022)
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Martin Janssens, Jordi Vilà-Guerau de Arellano, Chiel C. van Heerwaarden, Bart J.H. van Stratum, A.P. Siebesma, S.R. de Roode, F. Glassmeier
A new generation of operational atmospheric models operating at horizontal resolutions in the range 200 m up to ~ 2 km is becoming increasingly popular for operational use in numerical weather prediction and climate applications. Such grid spacings are becoming sufficiently fine to resolve a fraction of the turbulent transports. Here we analyze LES results of a convective boundary layer obtained by coarsening horizontal grid spacings up to 800 m. The aim is to explore the dependency of the mean state and turbulent fluxes on the grid resolution. Both isotropic and anisotropic eddy diffusion approaches are evaluated, where in the latter case the horizontal and vertical eddy diffusivities differ in accord with their horizontal and vertical grid spacings. For coarsening horizontal grid sizes entrainment at the top of the boundary layer tends to get slightly enhanced for isotropic diffusion. An analysis of the energy spectrum shows that anisotropic diffusion causes relatively more dissipation of variance at smaller length scales. This leads, in turn, to a shift of spectral energy towards larger length scales. This can also be clearly seen from the different kinds of spatial organization. The present study therefore suggests that details with regards to the representation of processes at small scales might impact the organization at length scales much larger than the smallest scales that can be resolved by the model.
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A new generation of operational atmospheric models operating at horizontal resolutions in the range 200 m up to ~ 2 km is becoming increasingly popular for operational use in numerical weather prediction and climate applications. Such grid spacings are becoming sufficiently fine to resolve a fraction of the turbulent transports. Here we analyze LES results of a convective boundary layer obtained by coarsening horizontal grid spacings up to 800 m. The aim is to explore the dependency of the mean state and turbulent fluxes on the grid resolution. Both isotropic and anisotropic eddy diffusion approaches are evaluated, where in the latter case the horizontal and vertical eddy diffusivities differ in accord with their horizontal and vertical grid spacings. For coarsening horizontal grid sizes entrainment at the top of the boundary layer tends to get slightly enhanced for isotropic diffusion. An analysis of the energy spectrum shows that anisotropic diffusion causes relatively more dissipation of variance at smaller length scales. This leads, in turn, to a shift of spectral energy towards larger length scales. This can also be clearly seen from the different kinds of spatial organization. The present study therefore suggests that details with regards to the representation of processes at small scales might impact the organization at length scales much larger than the smallest scales that can be resolved by the model.