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add seperate page for cellular automata and physics update summary
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| /** | ||
| \page cellular_automata Cellular Automata Stochastic Convective Organization Scheme | ||
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| \b Scientific \b Background | ||
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| Cumulus clouds in the atmosphere can organize into a variety of sizes, ranging | ||
| from small fair‐weather cumulus clouds, rain showers and thunderstorms, to | ||
| larger scale weather systems. In weather and climate models, such organization | ||
| is traditionally not well-represented as the motions associated with cumulus | ||
| clouds are generally too small to be resolved by the numerical model. | ||
| In this scheme we use a stochastic cellular automaton (CA), a mathematical | ||
| model often used to describe self‐organizing behavior in physical systems to | ||
| represent the effects of convective organization. The scheme addresses the | ||
| effect of convective organization in a bulk-plume cumulus convection | ||
| parameterizations (saSAS), where this type of organization has to be | ||
| represented in terms of how the resolved flow would “feel” convection if | ||
| more coherent structures were present on the subgrid. | ||
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| In addition, for longer range forecasts (seasonal, decadal, climate), | ||
| the relevance of stochastic cumulus convection in numerical models can also | ||
| be discussed in terms of noise induced forcing. As an example, on the | ||
| time scale of organized convectively coupled waves, the small scale individual | ||
| convective plumes grow and decay so rapidly that they are not predictable | ||
| on time-scales longer than a few hours, whereas the organized larger scale | ||
| convectively coupled wave envelope can have a deterministic limit of | ||
| predictability of about two weeks. Thus, for longer range forecasts, | ||
| individual convective plumes can be viewed as stochastic noise - they can | ||
| have an impact on the convectively coupled waves (due to noise forcing), | ||
| but they are not predictable on their own. By providing the CA with a | ||
| stochastic initialization, the effect of stochastic cumulus convection | ||
| is also represented by the scheme. | ||
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| The scientific motivation for the scheme, the CA rulesets explored, and | ||
| the impact on convectively coupled equatorial waves can be found in the | ||
| following references; Bengtsson et al. 2011 \cite Bengtsson_2011, | ||
| Bengtsson et al. 2013 \cite bengtsson_et_al_2013, | ||
| Bengtsson and Kornich (2016) \cite bengtsson_and_kornich_2016, | ||
| Bengtsson et al 2019 \cite Bengtsson_2019, | ||
| and Bengtsson et al. 2021 \cite bengtsson_et_al_2021. | ||
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| \b Technical \b remarks | ||
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| The CA source code is located in the stochastic physics submodule in | ||
| the ufs-weather-model: https://github.com/noaa-psd/stochastic_physics . | ||
| In the UFS Weather Model, the main call to the CA routines are made | ||
| from FV3/stochastic_physics_driver.F90. | ||
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| There are currently two options to evolve the CA (can be done simultaneously); | ||
| (\p ca_global) a large scale global pattern which evolves the ruleset according | ||
| to game of life with cell history, or (\p ca_sgs) a sub-grid scale pattern | ||
| which is conditioned on a forcing from the atmospheric model. The two options | ||
| are controlled by namelist and are evolved in cellular_automata_globa.F90 | ||
| and cellular_automata_sgs.F90 respectively. Both approaches use the main | ||
| CA module update_ca.F90 to evolve the CA in time. Since the CA needs to know | ||
| about its neighborhood it uses the halo information to gather the state | ||
| in adjacent MPI domains and/or adjacent cube sphere interfaces. | ||
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| \b The \p ca_sgs \b option - \b Coupled \b to \b saSAS \b cumulus \b convection \b scheme | ||
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| The evolution of the CA is an extension to the automaton family known as “Generations,” | ||
| which in turn is based on the “Game of Life”(Chopard & Droz, 1998 \cite Chopard_1998) | ||
| but adds cell history to the rule set. It is a deterministic CA ruleset, initialized | ||
| with Gaussian white noise. Thus, when used in an ensemble system, each ensemble | ||
| member can provide a different seed to the random number generator governing | ||
| the initial state to then generate a different evolution for each member. | ||
| By cell history we refer to newborn cells being given a “lifetime,”τ, | ||
| that is incrementally reduced by 1 each time step where the rules are not met, | ||
| in contrast to going directly from 1 to 0. The CA is conditioned on a | ||
| forcing from the host model through the lifetime variable τ such that: | ||
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| \f[ | ||
| \tau =N\left( \frac{\int_{l=1}^{l=top}E\frac{dp }{g} }{\max\left( \int_{l=1}^{l=top} E\frac{d p}{g}\right)} \right) | ||
| \f] | ||
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| here, N is an integer that when multiplied by the model time-step represents | ||
| a physical time scale, such that τ is longer in regions where the forcing is larger, | ||
| E is the vertically integrated convective rain evaporation from the | ||
| saSAS cumulus convection scheme stored in Coupling%condition. The denominator is | ||
| the maximum value of the forcing in the global domain. While the grid-scale | ||
| forcing in practice could be any two-dimensional field, we choose here | ||
| to set it as the vertically integrated subgrid rain evaporation amount, | ||
| serving as an indicator of geographical regions where enhanced subgrid | ||
| organization may arise through convective cold-pools. | ||
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| The CA is evolved on a finer grid than the numerical prediction | ||
| host model (size controlled by namelist), and can be either coarse | ||
| grained back to the host model grid as a fraction, or (in case of \p nca_plumes = .true.) | ||
| give back the maximum number of connected “plumes” (represented by | ||
| connected CA cells), and their associated size within each numerical | ||
| prediction host model grid-box. nca_plumes is default true and the | ||
| maximum cluster size is passed to the saSAS cumulus convection scheme | ||
| in the Coupling%ca_deep container. | ||
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| Depending on the activated namelist options, the CA can feed back to | ||
| the saSAS convection scheme via the entrainment (\p ca_entr), closure | ||
| (\p ca_closure) or convective initiation (\p ca_trigger) in the following way: | ||
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| - Entrainment (\p ca_entr): In entraining plume model bulk mass-flux schemes, | ||
| the upward mass-flux is typically parameterized as a function of environmental | ||
| air being entrained into the rising plume (as well as parcel properties at | ||
| cloud base). The fractional entrainment is described as a function of the | ||
| plume radius. Larger thermals (plumes) have smaller fractional entrainment, | ||
| which is a consequence of the fact that larger areas have relatively smaller | ||
| perimeters. In this scheme, the assumption is that subgrid organization will | ||
| lead to a few larger plumes rather than several smaller plumes, such that | ||
| the grid-box average fractional entrainment is reduced. Thus, after | ||
| the CA is updated, we count the number of plumes, and their associated | ||
| size within each NWP grid-box (\p nca_plumes = true). If the largest | ||
| cluster of cells found on the subgrid is larger than a set radius, then the | ||
| fractional entrainment rate is reduced at that grid-point by 30% | ||
| (selected based on experimentation) | ||
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| - Triggering (\p ca_trigger): In NWP models physical processes are parameterized | ||
| in columns, and the horizontal interaction between physical processes takes | ||
| place only through advection and diffusion. As the CA can organize clusters | ||
| across adjacent NWP model grid-boxes, the method offers a novel approach to | ||
| enhance the probability of triggering of convection in nearby areas, | ||
| representing subgrid fluctuations in temperature and humidity, and triggering | ||
| in premoistened regions if convection is triggered in a cluster. The | ||
| stochastic nature of the CA may enhance organization in different | ||
| directions within the grid-box, and across grid-boxes, depending on the | ||
| initial seed. If the model is run as an ensemble, the convection scheme's | ||
| stochastic triggering function can help to improve uncertainty estimates | ||
| associated with subgrid fluctuations of temperature and humidity and | ||
| randomness in organization. In this work, model grid boxes in which the | ||
| CA's largest connecting plume exceeds a given threshold will be considered | ||
| as candidates for convective activation, in addition to saSAS’s current | ||
| triggering criteria. | ||
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| - Closure (\p ca_closure): We assume that convection that organizes into | ||
| plumes with larger radii tends to cover a larger area fraction of the | ||
| grid-box and thereby acts to enhance the cloud base mass flux. In this | ||
| coupling strategy, we again count the number of plumes (represented by | ||
| connected cellular automaton cells), and their associated size within | ||
| each NWP grid-box. If the largest cluster of cells found on the subgrid | ||
| is larger than a set radius, then the cloud base mass-flux is enhanced in | ||
| that grid-box by 25% (selected based on experimentation). This option is | ||
| being revisited by reformulating the entire closure using a prognostic | ||
| evolution of the updraft area fraction, and is in its current formulation | ||
| not recommended. | ||
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| */ |
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