Subgrid Parameterization Research Articles

Convective initiation and storm life cycles in convection‐permitting simulations of the Met Office Unified Model over South Africa

Convective initiation is a challenge for convection‐permitting models due to its sensitivity to sub‐km processes. We evaluate the representation of convective storms and their initiation over South Africa during four summer months in Met Office Unified Model simulations at a 1.5‐km horizontal grid length. Storm size distributions from the model compare well with radar observations, but rainfall in the model is predominantly produced by large storms (50 km in diameter or larger) in the evening, whereas radar observations show that most rainfall occurs throughout the afternoon, from storms 10–50 km in diameter. In all months, the modelled maximum number of storm initiations occurs at least 2 hr prior to the radar‐observed maximum. However, the diurnal cycle of rainfall between the model and observations compares well, suggesting that the numerous storm initiations in the simulations do not produce much rainfall. Modelled storms are generally less intense than those in radar observations, especially in early summer. In February, when tropical influences dominate, the simulated storms are of similar intensity to observed storms. Simulated storms tend to reach their peak intensity in the first 15 min after initiation, then gradually become less intense as they grow. In radar observations, storms reach their peak intensity 15 min into their life cycle, stay intense as they grow larger, then gradually weaken after they have reached their maximum diameter. Two November case studies of severe convection are analysed in detail. A higher resolution grid length initiates convection slightly earlier (300 m as opposed to 1.5 km) with the same scientific settings. Two 1.5 km simulations that apply more subgrid mixing have delayed convective initiation. Analysis of soundings indicates little difference in the convective indices, suggesting that differences in convection may be attributed to the choice of subgrid mixing parameters.

Quasi steady-state hurricanes revisited

We revisit the theoretical possibility of long-term, sustained tropical cyclone solutions using a state-of-the-art numerical model that incorporates the most recent observational guidance for subgrid scale parameters and airsea exchange coefficients of heat and momentum. Emphasis is placed on the realism of such solutions and the sources of cyclonic relative angular momentum (RAM) that are necessary to replenish that lost by friction at the surface. For simplicity, we confine our attention to strictly axisymmetric numerical experiments.We are able to replicate Hakim’s long-term simulation of a quasi-steady state cyclone in a 1500 km radial domain. The structure of the wind field is found to be somewhat realistic compared to observations, but sustained by unrealistic processes. Artificial sources of cyclonic RAM are quantified and the lateral damping of the anticyclonic wind near the outer boundary is found to make the largest contribution to the source of cyclonic RAM. When the domain size is extended to 9,000 km radius and lateral damping is removed altogether, a quasi-steady vortex emerges, but the structure of this vortex has many unrealistic features. In this solution, the remaining upper-level Rayleigh damping contributes a major portion of the needed source of cyclonic RAM. In a simulation in which the upper-level damping is removed also, the solution is found to be neither quasi-steady nor realistic.These findings call into question the realism of long-term, sustained tropical cyclone simulations, which require a sufficiently large source of cyclonic RAM to facilitate the existence of a quasi-steady state.

Subgrid Parameterizations of the Eddy–Eddy, Eddy–Mean Field, Eddy–Topographic, Mean Field–Mean Field, and Mean Field–Topographic Interactions in Atmospheric Models

Abstract Parameterizations are developed for each of the subgrid turbulence interaction classes in fully three-dimensional global atmospheric flows over topography, typical of January and July climate states. Stochastic and deterministic parameterizations are developed for the eddy–eddy interactions and deterministic parameterizations for eddy–mean field, eddy–topographic, mean field–mean field, and mean field–topographic interactions. All parameterizations are calculated from the statistics of higher-resolution reference direct numerical simulations (DNSs) truncated into resolved and subgrid scales and employed without tuning coefficients. This parameterization framework is validated by performing large-eddy simulations (LESs) that closely agree with the reference DNSs in terms of time-averaged kinetic energy spectra, zonal jet structure, and nonzonal streamfunction fields. Both the DNSs and LESs are formulated in such a way that the usual problem of a long artificial dissipation range does not occur. Successful LESs are produced with truncation wavenumbers 31 and 15, using, respectively, only 11.9% and 1.3% of the DNS computational effort at truncation wavenumber 63. The lower-resolution LESs show that the parameterizations are successful even when the energy injection due to baroclinic instability is not completely resolved. The contribution of each of the parameterized interaction classes to the quality of the LES is identified. The best agreement is achieved when all subgrid components are included. There is a very high level of agreement between the LESs and DNSs with typical streamfunction pattern correlations of r = 0.962 for the nonzonal components and r = 0.999 for the total fields when the complete sets of parameterizations are used.

Applications of Deep Learning to Ocean Data Inference and Subgrid Parameterization

AbstractOceanographic observations are limited by sampling rates, while ocean models are limited by finite resolution and high viscosity and diffusion coefficients. Therefore, both data from observations and ocean models lack information at small and fast scales. Methods are needed to either extract information, extrapolate, or upscale existing oceanographic data sets, to account for or represent unresolved physical processes. Here we use machine learning to leverage observations and model data by predicting unresolved turbulent processes and subsurface flow fields. As a proof of concept, we train convolutional neural networks on degraded data from a high‐resolution quasi‐geostrophic ocean model. We demonstrate that convolutional neural networks successfully replicate the spatiotemporal variability of the subgrid eddy momentum forcing, are capable of generalizing to a range of dynamical behaviors, and can be forced to respect global momentum conservation. The training data of our convolutional neural networks can be subsampled to 10–20% of the original size without a significant decrease in accuracy. We also show that the subsurface flow field can be predicted using only information at the surface (e.g., using only satellite altimetry data). Our results indicate that data‐driven approaches can be exploited to predict both subgrid and large‐scale processes, while respecting physical principles, even when data are limited to a particular region or external forcing. Our in‐depth study presents evidence for the successful design of ocean eddy parameterizations for implementation in coarse‐resolution climate models.

A Stochastic Lagrangian Basis for a Probabilistic Parameterization of Moisture Condensation in Eulerian Models

Abstract In this paper, we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a coarse-grained field on a grid cannot properly resolve regions of saturation—in which condensation occurs—that are smaller than the grid boxes. Thus, in the absence of a parameterization scheme, either the grid box must become saturated or condensation will be underestimated. On the other hand, in a stochastic Lagrangian model of moisture transport, trajectories of parcels tagged with humidity variables are tracked, and small-scale moisture variability can be retained; however, explicitly implementing such a scheme in a global model would be computationally prohibitive. One way to introduce subgrid-scale saturation into an Eulerian model is to assume the humidity within a grid box has a probability distribution. To close the problem, this distribution is conventionally determined by relating the required subgrid-scale properties of the flow to the grid-scale properties using a turbulence closure. Here, instead, we determine an assumed probability distribution by using the statistical moments from a stochastic Lagrangian version of the system. The stochastic system is governed by a Fokker–Planck equation, and we use that, rather than explicitly following the moisture parcels, to determine the parameters of the assumed distribution. We are thus able to parameterize subgrid-scale condensation in an Eulerian model in a computationally efficient and theoretically well-founded way. In two idealized advection–condensation problems, we show that a coarse Eulerian model with the subgrid parameterization is well able to mimic its Lagrangian counterpart.

Deep learning to represent subgrid processes in climate models

The representation of nonlinear subgrid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric subgrid processes in a climate model by learning from a multiscale model in which convection is treated explicitly. The trained neural network then replaces the traditional subgrid parameterizations in a global general circulation model in which it freely interacts with the resolved dynamics and the surface-flux scheme. The prognostic multiyear simulations are stable and closely reproduce not only the mean climate of the cloud-resolving simulation but also key aspects of variability, including precipitation extremes and the equatorial wave spectrum. Furthermore, the neural network approximately conserves energy despite not being explicitly instructed to. Finally, we show that the neural network parameterization generalizes to new surface forcing patterns but struggles to cope with temperatures far outside its training manifold. Our results show the feasibility of using deep learning for climate model parameterization. In a broader context, we anticipate that data-driven Earth system model development could play a key role in reducing climate prediction uncertainty in the coming decade.

A Subgrid Approach for Modeling Microtopography Effects on Overland Flow

AbstractMicrotopography, or heterogeneities in the elevation across scales much smaller than the domain of interest, plays a critical role in surface water retention, surface/subsurface interactions, and runoff. Resolving microtopographic influences on flow requires high‐resolution simulations that are computationally demanding even when considering the surface system in isolation and even more so when surface flow is one component in integrated simulations that couple surface flow with unsaturated subsurface flow. There is thus significant motivation for models that allow the effects of subgrid microtopography to be better represented. Subgrid models modify coarsened models to capture the microtopography‐induced nonlinear effects on hydrologic processes. We present a subgrid model that alters the water storage and flow terms in the diffusion wave equation for surface flow. Stochastically generated microtopography with strongly contrasting spatial structure, high‐resolution digital elevation maps from a polygonal tundra site on the North Slope of Alaska and a hummocky microtopography from a field site in Northern Minnesota are used to assess the accuracy and applicability of the subgrid model to disparate landscapes. Approaches for determining subgrid model parameters are tested and simulation results using the subgrid model are compared to benchmark fine‐scale simulations and to coarse simulations that ignore microtopography. Our findings confirm that a properly parameterized subgrid model greatly improves the coarse‐scale representation of hydrographs and total water content in the system. Using the polygonal tundra example, we propose and test a strategy for moving to application‐relevant spatial scales by combining microtopography classification and a few fine‐scale simulations on small subdomains.

Simulation of stratified flows over a ridge using a lattice Boltzmann model

A three-dimensional thermal lattice Boltzmann model (TLBM) using multi-relaxation time method was used to simulate stratified atmospheric flows over a ridge. The main objective was to study the efficacy of this method for turbulent flows in the atmospheric boundary layer, complex terrain flows in particular. The simulation results were compared with results obtained using a traditional finite difference method based on the Navier–Stokes equations and with previous laboratory results on stably stratified flows over an isolated ridge. The initial density profile is neutral stratification in the boundary layer, topped with a stable cap and stable stratification aloft. The TLBM simulations produced waves, rotors, and hydraulic jumps in the lee side of the ridge for stably stratified flows, depending on the governing stability parameters. The Smagorinsky turbulence parameterization produced typical turbulence spectra for the velocity components at the lee side of the ridge, and the turbulent flow characteristics of varied stratifications were also analyzed. The comparison of TLBM simulations with other numerical simulations and laboratory studies indicated that TLBM is a viable method for numerical modeling of stratified atmospheric flows. To our knowledge, this is the first TLBM simulation of stratified atmospheric flow over a ridge. The details of the TLBM, its implementation of complex boundaries and the subgrid turbulence parameterizations used in this study are also described in this article.

Impact of air-sea drag coefficient for latent heat flux on large scale climate in coupled and atmosphere stand-alone simulations

The turbulent fluxes across the ocean/atmosphere interface represent one of the principal driving forces of the global atmospheric and oceanic circulation. Despite decades of effort and improvements, representation of these fluxes still presents a challenge due to the small-scale acting turbulent processes compared to the resolved scales of the models. Beyond this subgrid parameterization issue, a comprehensive understanding of the impact of air-sea interactions on the climate system is still lacking. In this paper we investigates the large-scale impacts of the transfer coefficient used to compute turbulent heat fluxes with the IPSL-CM4 climate model in which the surface bulk formula is modified. Analyzing both atmosphere and coupled ocean–atmosphere general circulation model (AGCM, OAGCM) simulations allows us to study the direct effect and the mechanisms of adjustment to this modification. We focus on the representation of latent heat flux in the tropics. We show that the heat transfer coefficients are highly similar for a given parameterization between AGCM and OAGCM simulations. Although the same areas are impacted in both kind of simulations, the differences in surface heat fluxes are substantial. A regional modification of heat transfer coefficient has more impact than uniform modification in AGCM simulations while in OAGCM simulations, the opposite is observed. By studying the global energetics and the atmospheric circulation response to the modification, we highlight the role of the ocean in dampening a large part of the disturbance. Modification of the heat exchange coefficient modifies the way the coupled system works due to the link between atmospheric circulation and SST, and the different feedbacks between ocean and atmosphere. The adjustment that takes place implies a balance of net incoming solar radiation that is the same in all simulations. As there is no change in model physics other than drag coefficient, we obtain similar latent heat flux between coupled simulations with different atmospheric circulations. Finally, we analyze the impact of model tuning and show that it can offset part of the feedbacks.

Surrogate-based model parameter optimization based on gas explosion experimental data

ABSTRACTThis article presents a method for optimizing the predictive capabilities of a computational fluid dynamics (CFD) tool used for consequence analysis in the process industries. A procedure for surrogate-based optimization of empirically determined sub-grid model parameters is implemented. The objective is to yield the best fit between certain outputs of a CFD model and corresponding experimental values. The present study investigates whether the optimization approach is applicable for improving the predictions of gas explosions when optimizing (i) only for experiments involving similar physical phenomena and (ii) for a wider range of experiments including symmetric modules as well as realistic offshore modules. Employing optimization may detect model limitations, supporting the further development of complex CFD models to represent a wider range of physical phenomena. The optimization process significantly improves the prediction of the maximum overpressure and pressure impulse at specific monitor points. Online supplemental data for this article can be accessed athttps://doi.org/10.1080/0305215X.2018.1450399.

New plume rise modeling in a turbulent atmosphere via hybrid RANS-LES numerical simulation

New plume rise formulas are developed to overcome the drawbacks of the conventional models in predicting the rise of buoyant jets in different atmospheric stability conditions. A hybrid Reynolds averaged Navier Stokes (RANS) and large eddy simulation (LES) approach with a mixed scale sub-grid parameterization technique is applied. By using the aforementioned simulation results, new plume rise formulas are derived. The direct effects of atmospheric turbulence intensity at stack height (IAir) and the vertical derivative of wind velocity are introduced in plume rise formulas. The quantile-quantile plots show that new formulas can predict the simulated plume rise in the turbulent crossflow with a deviation factor of 1.18, 1.0025 and 1.17 for stable, neutral and unstable conditions, respectively whereas the conventional models overestimate the final plume rise at least by a factor of 6.1, 3.4 and 2.7. Moreover, by applying the new plume rise formulas in Gaussian dispersion model, the accuracy of new formulas is evaluated. The results show that by applying the new plume rise formulas instead of the conventional Briggs formulas in the Gaussian model, the normalized mean square error reduces by 20% and the fraction of predictions within a factor of two increases by 50%.

Single‐Column Model Simulations of Subtropical Marine Boundary‐Layer Cloud Transitions Under Weakening Inversions

AbstractResults are presented of the GASS/EUCLIPSE single‐column model intercomparison study on the subtropical marine low‐level cloud transition. A central goal is to establish the performance of state‐of‐the‐art boundary‐layer schemes for weather and climate models for this cloud regime, using large‐eddy simulations of the same scenes as a reference. A novelty is that the comparison covers four different cases instead of one, in order to broaden the covered parameter space. Three cases are situated in the North‐Eastern Pacific, while one reflects conditions in the North‐Eastern Atlantic. A set of variables is considered that reflects key aspects of the transition process, making use of simple metrics to establish the model performance. Using this method, some longstanding problems in low‐level cloud representation are identified. Considerable spread exists among models concerning the cloud amount, its vertical structure, and the associated impact on radiative transfer. The sign and amplitude of these biases differ somewhat per case, depending on how far the transition has progressed. After cloud breakup the ensemble median exhibits the well‐known “too few too bright” problem. The boundary‐layer deepening rate and its state of decoupling are both underestimated, while the representation of the thin capping cloud layer appears complicated by a lack of vertical resolution. Encouragingly, some models are successful in representing the full set of variables, in particular, the vertical structure and diurnal cycle of the cloud layer in transition. An intriguing result is that the median of the model ensemble performs best, inspiring a new approach in subgrid parameterization.

Model Selection: Using Information Measures from Ordinal Symbolic Analysis to Select Model Subgrid-Scale Parameterizations

Abstract The use of information measures for model selection in geophysical models with subgrid parameterizations is examined. Although the resolved dynamical equations of atmospheric or oceanic global numerical models are well established, the development and evaluation of parameterizations that represent subgrid-scale effects pose a big challenge. For climate studies, the parameters or parameterizations are usually selected according to a root-mean-square error criterion that measures the differences between the model-state evolution and observations along the trajectory. However, inaccurate initial conditions and systematic model errors contaminate root-mean-square error measures. In this work, information theory quantifiers, in particular Shannon entropy, statistical complexity, and Jensen–Shannon divergence, are evaluated as measures of the model dynamics. An ordinal analysis is conducted using the Bandt–Pompe symbolic data reduction in the signals. The proposed ordinal information measures are examined in the two-scale Lorenz-96 system. By comparing the two-scale Lorenz-96 system signals with a one-scale Lorenz-96 system with deterministic and stochastic parameterizations, the study shows that information measures are able to select the correct model and to distinguish the parameterizations, including the degree of stochasticity that results in the closest model dynamics to the two-scale Lorenz-96 system.

Towards improved parameterization of a macroscale hydrologic model in a discontinuous permafrost boreal forest ecosystem

Abstract. Modeling hydrological processes in the Alaskan sub-arctic is challenging because of the extreme spatial heterogeneity in soil properties and vegetation communities. Nevertheless, modeling and predicting hydrological processes is critical in this region due to its vulnerability to the effects of climate change. Coarse-spatial-resolution datasets used in land surface modeling pose a new challenge in simulating the spatially distributed and basin-integrated processes since these datasets do not adequately represent the small-scale hydrological, thermal, and ecological heterogeneity. The goal of this study is to improve the prediction capacity of mesoscale to large-scale hydrological models by introducing a small-scale parameterization scheme, which better represents the spatial heterogeneity of soil properties and vegetation cover in the Alaskan sub-arctic. The small-scale parameterization schemes are derived from observations and a sub-grid parameterization method in the two contrasting sub-basins of the Caribou Poker Creek Research Watershed (CPCRW) in Interior Alaska: one nearly permafrost-free (LowP) sub-basin and one permafrost-dominated (HighP) sub-basin. The sub-grid parameterization method used in the small-scale parameterization scheme is derived from the watershed topography. We found that observed soil thermal and hydraulic properties – including the distribution of permafrost and vegetation cover heterogeneity – are better represented in the sub-grid parameterization method than the coarse-resolution datasets. Parameters derived from the coarse-resolution datasets and from the sub-grid parameterization method are implemented into the variable infiltration capacity (VIC) mesoscale hydrological model to simulate runoff, evapotranspiration (ET), and soil moisture in the two sub-basins of the CPCRW. Simulated hydrographs based on the small-scale parameterization capture most of the peak and low flows, with similar accuracy in both sub-basins, compared to simulated hydrographs based on the coarse-resolution datasets. On average, the small-scale parameterization scheme improves the total runoff simulation by up to 50 % in the LowP sub-basin and by up to 10 % in the HighP sub-basin from the large-scale parameterization. This study shows that the proposed sub-grid parameterization method can be used to improve the performance of mesoscale hydrological models in the Alaskan sub-arctic watersheds.

A novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows

This paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models. The approximate deconvolution (AD) procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the Smagorinsky and Leith models. The novel idea here is to estimate the modeling parameters using the AD method rather than the traditionally used test filtering approach. First, a-priori and a-posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem. The proposed model is then applied to a wind-driven quasigeostrophic four-gyre ocean circulation problem, which is a standard prototype of more realistic ocean dynamics. Results show that the proposed model captures the quasi-stationary ocean dynamics and provides the time averaged four-gyre circulation patterns. Taking locally resolved flow characteristics into account, the model dynamically provides higher eddy viscosity values for lower resolutions.

The Romulus cosmological simulations: a physical approach to the formation, dynamics and accretion models of SMBHs

We present a novel implementation of supermassive black hole (SMBH) formation, dynamics, and accretion in the massively parallel tree+SPH code, ChaNGa. This approach improves the modeling of SMBHs in fully cosmological simulations, allowing for a more de- tailed analysis of SMBH-galaxy co-evolution throughout cosmic time. Our scheme includes novel, physically motivated models for SMBH formation, dynamics and sinking timescales within galaxies, and SMBH accretion of rotationally supported gas. The sub-grid parameters that regulate star formation (SF) and feedback from SMBHs and SNe are optimized against a comprehensive set of z = 0 galaxy scaling relations using a novel, multi-dimensional parameter search. We have incorporated our new SMBH implementation and parameter optimization into a new set of high resolution, large-scale cosmological simulations called Romulus. We present initial results from our flagship simulation, Romulus25, showing that our SMBH model results in SF efficiency, SMBH masses, and global SF and SMBH accretion histories at high redshift that are consistent with observations. We discuss the importance of SMBH physics in shaping the evolution of massive galaxies and show how SMBH feedback is much more effective at regulating star formation compared to SNe feedback in this regime. Further, we show how each aspect of our SMBH model impacts this evolution compared to more common approaches. Finally, we present a science application of this scheme studying the properties and time evolution of an example dual AGN system, highlighting how our approach allows simulations to better study galaxy interactions and SMBH mergers in the context of galaxy-BH co-evolution.

Spatial and temporal CCN variations in convection-permitting aerosol microphysics simulations in an idealised marine tropical domain

Abstract. A convection-permitting limited area model with periodic lateral boundary conditions and prognostic aerosol microphysics is applied to investigate how concentrations of cloud condensation nuclei (CCN) in the marine boundary layer are affected by high-resolution dynamical and thermodynamic fields. The high-resolution aerosol microphysics–dynamics model, which resolves differential particle growth and aerosol composition across the particle size range, is applied to a domain designed to match approximately a single grid square of a climate model. We find that, during strongly convective conditions with high wind-speed conditions, CCN concentrations vary by more than a factor of 8 across the domain (5–95th percentile range), and a factor of ∼ 3 at more moderate wind speed. One reason for these large sub-climate-grid-scale variations in CCN is that emissions of sea salt and dimethyl sulfide (DMS) are much higher when spatial and temporal wind-speed fluctuations become resolved at this convection-permitting resolution (making peak wind speeds higher). By analysing how the model evolves during spin-up, we gain new insight into the way primary sea salt and secondary sulfate particles contribute to the overall CCN variance in these realistic conditions, and find a marked difference in the variability of super-micron and sub-micron CCN. Whereas the super-micron CCN are highly variable, dominated by strongly fluctuating sea spray emitted, the sub-micron CCN tend to be steadier, mainly produced on longer timescales following growth after new particle formation in the free troposphere, with fluctuations inherently buffered by the fact that coagulation is faster at higher particle concentrations. We also find that sub-micron CCN are less variable in particle size, the accumulation-mode mean size varying by ∼ 20 % (0.101 to 0.123 µm diameter) compared to ∼ 35 % (0.75 to 1.10 µm diameter) for coarse-mode particles at this resolution. We explore how the CCN variability changes in the vertical and at different points in the spin-up, showing how CCN concentrations are introduced both by the emissions close to the surface and at higher altitudes during strong wind-speed conditions associated to the intense convective period. We also explore how the non-linear variation of sea-salt emissions with wind speed propagates into variations in sea-salt mass mixing ratio and CCN concentrations, finding less variation in the latter two quantities due to the longer transport timescales inherent with finer CCN, which sediment more slowly. The complex mix of sources and diverse community of processes involved makes sub-grid parameterisation of CCN variations difficult. However, the results presented here illustrate the limitations of predictions with large-scale models and the high-resolution aerosol microphysics–dynamics modelling system shows promise for future studies where the aerosol variations will propagate through to modified cloud microphysical evolution.

Response surfaces for advanced consequence models: Two approaches

This paper reports the approximation quality of response surfaces as metamodels for key results from computational fluid dynamics (CFD) gas explosion simulations. The response surfaces constitute smooth approximations to variations in the CFD output with respect to perturbing empirically determined sub-grid model parameters. Two response surface approaches are tested – polynomial response surfaces (PRSs) created from Taylor polynomials via finite differences of the model output, and response surfaces based on neural networks (RSNNs) generated on the basis of Latin hypercube samplings. First, results for selected examples of medium- and large-scale gas explosions are presented in detail. It was found that in order to achieve the same approximation quality with RSNNs as with PRSs, a higher number of simulations may be required. However, in contrast to the polynomial approach, the number of simulations required for an RSNN can be adapted to the non-linearity of the model output. For the scenarios for which a PRS approximates the model output poorly, an RSNN built from an increased number of simulations is found to yield a significantly more reliable approximation. Second, the paper investigates the general applicability of the RSNNs for industrial-scale gas explosion simulations. Based on the results from the detailed analysis, the extended analysis is only conducted for the RSNN approach, including 37 experiments from 5 experimental campaigns commonly used for model validation.

Subgrid parameterization of snow distribution at a Mediterranean site using terrestrial photography

Abstract. Subgrid variability introduces non-negligible scale effects on the grid-based representation of snow. This heterogeneity is even more evident in semiarid regions, where the high variability of the climate produces various accumulation melting cycles throughout the year and a large spatial heterogeneity of the snow cover. This variability in a watershed can often be represented by snow accumulation–depletion curves (ADCs). In this study, terrestrial photography (TP) of a cell-sized area (30 × 30 m) was used to define local snow ADCs at a Mediterranean site. Snow-cover fraction (SCF) and snow-depth (h) values obtained with this technique constituted the two datasets used to define ADCs. A flexible sigmoid function was selected to parameterize snow behaviour on this subgrid scale. It was then fitted to meet five different snow patterns in the control area: one for the accumulation phase and four for the melting phase in a cycle within the snow season. Each pattern was successfully associated with the snow conditions and previous evolution. The resulting ADCs were associated to certain physical features of the snow, which were used to incorporate them in the point snow model formulated by Herrero et al. (2009) by means of a decision tree. The final performance of this model was tested against field observations recorded over four hydrological years (2009–2013). The calibration and validation of this ADC snow model was found to have a high level of accuracy, with global RMSE values of 105.8 mm for the average snow depth and 0.21 m2 m−2 for the snow-cover fraction in the control area. The use of ADCs on the cell scale proposed in this research provided a sound basis for the extension of point snow models to larger areas by means of a gridded distributed calculation.

Subgrid parameterization for snow depth over mountainous terrain from flat field snow depth

AbstractSnow depth is an important variable for a variety of models including land‐surface, meteorological, and climate models. Various measurement networks were therefore developed to measure snow depth on the ground. Measurement stations are generally located in gentle terrain (flat field measurements) most often at lower or mid elevation. While these sites have provided a wealth of information, various studies have questioned the representativity of such flat field measurements for the surrounding topography, especially in alpine regions. Using highly resolved snow depth maps at the peak of winter from two distinct climatic regions in Switzerland and in the Spanish Pyrenees, we developed two parameterizations to estimate domain‐averaged snow depth in coarse‐scale model applications over complex topography using easy to derive topographic parameters. The first parameterization uses a commonly applied linear lapse rate. Removing the dominant elevation gradient in mean snow depth revealed remaining underlying correlations with other topographic parameters, in particular the sky view factor. The second parameterization combines a power law elevation trend scaled with the subgrid parameterized sky view factor. Using a variety of statistic measures showed that the more complex parameterization performs better when using mean high‐resolution flat field snow depth. The performances slightly decreased when formulating the parameterizations for a single flat field snow depth measurement. Nevertheless, the more complex parameterization still outperformed the linear lapse rate model. As the parameterization was developed independently of a specific geographic region, we suggest it could be used to assimilate flat field snow depth or snowfall into coarse‐scale snow model frameworks.