Journal articles: 'Subgrid heterogeneity'

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Curasi, Salvatore R., Joe R. Melton, Elyn R. Humphreys, Txomin Hermosilla, and Michael A. Wulder. "Implementing a dynamic representation of fire and harvest including subgrid-scale heterogeneity in the tile-based land surface model CLASSIC v1.45." Geoscientific Model Development 17, no. 7 (April 12, 2024): 2683–704. http://dx.doi.org/10.5194/gmd-17-2683-2024.

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Abstract. Canada's forests play a critical role in the global carbon (C) cycle and are responding to unprecedented climate change as well as ongoing natural and anthropogenic disturbances. However, the representation of disturbance in boreal regions is limited in pre-existing land surface models (LSMs). Moreover, many LSMs do not explicitly represent subgrid-scale heterogeneity resulting from disturbance. To address these limitations, we implement harvest and wildfire forcings in the Canadian Land Surface Scheme Including Biogeochemical Cycles (CLASSIC) land surface model alongside dynamic tiling that represents subgrid-scale heterogeneity due to disturbance. The disturbances are captured using 30 m spatial resolution satellite data (Landsat) on an annual basis for 33 years. Using the pan-Canadian domain (i.e., all of Canada south of 76° N) as our study area for demonstration, we determine the model setup that optimally balances a detailed process representation and computational efficiency. We then demonstrate the impacts of subgrid-scale heterogeneity relative to standard average individual-based representations of disturbance and explore the resultant differences between the simulations. Our results indicate that the modeling approach implemented can balance model complexity and computational cost to represent the impacts of subgrid-scale heterogeneity resulting from disturbance. Subgrid-scale heterogeneity is shown to have impacts 1.5 to 4 times the impact of disturbance alone on gross primary productivity, autotrophic respiration, and surface energy balance processes in our simulations. These impacts are a result of subgrid-scale heterogeneity slowing vegetation re-growth and affecting surface energy balance in recently disturbed, sparsely vegetated, and often snow-covered fractions of the land surface. Representing subgrid-scale heterogeneity is key to more accurately representing timber harvest, which preferentially impacts larger trees on higher quality and more accessible sites. Our results show how different discretization schemes can impact model biases resulting from the representation of disturbance. These insights, along with our implementation of dynamic tiling, may apply to other tile-based LSMs. Ultimately, our results enhance our understanding of, and ability to represent, disturbance within Canada, facilitating a comprehensive process-based assessment of Canada's terrestrial C cycle.

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Huang, Meng, Po-Lun Ma, Nathaniel W. Chaney, Dalei Hao, Gautam Bisht, Megan D. Fowler, Vincent E. Larson, and L. Ruby Leung. "Representing surface heterogeneity in land–atmosphere coupling in E3SMv1 single-column model over ARM SGP during summertime." Geoscientific Model Development 15, no. 16 (August 29, 2022): 6371–84. http://dx.doi.org/10.5194/gmd-15-6371-2022.

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Abstract. The Earth's land surface features spatial and temporal heterogeneity over a wide range of scales below those resolved by current Earth system models (ESMs). State-of-the-art land and atmosphere models employ parameterizations to represent their subgrid heterogeneity, but the land–atmosphere coupling in ESMs typically operates on the grid scale. Communicating the information on the land surface heterogeneity with the overlying atmospheric boundary layer (ABL) remains a challenge in modeling land–atmosphere interactions. In order to account for the subgrid-scale heterogeneity in land–atmosphere coupling, we implement a new coupling scheme in the Energy Exascale Earth system model version 1 (E3SMv1) that uses adjusted surface variances and covariance of potential temperature and specific water content as the lower boundary condition for the atmosphere model. The new lower boundary condition accounts for both the variability of individual subgrid land surface patches and the inter-patch variability. The E3SMv1 single-column model (SCM) simulations over the Atmospheric Radiation Measurement (ARM) Southern Great Plain (SGP) site were performed to assess the impacts. We find that the new coupling parameterization increases the magnitude and diurnal cycle of the temperature variance and humidity variance in the lower ABL on non-precipitating days. The impacts are primarily attributed to subgrid inter-patch variability rather than the variability of individual patches. These effects extend vertically from the surface to several levels in the lower ABL on clear days. We also find that accounting for surface heterogeneity increases low cloud cover and liquid water path (LWP). These cloud changes are associated with the change in cloud regime indicated by the skewness of the probability density function (PDF) of the subgrid vertical velocity. In precipitating days, the inter-patch variability reduces significantly so that the impact of accounting for surface heterogeneity vanishes. These results highlight the importance of accounting for subgrid heterogeneity in land–atmosphere coupling in next-generation ESMs.

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Tesfa, Teklu K., and Lai-Yung Ruby Leung. "Exploring new topography-based subgrid spatial structures for improving land surface modeling." Geoscientific Model Development 10, no. 2 (February 22, 2017): 873–88. http://dx.doi.org/10.5194/gmd-10-873-2017.

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Abstract. Topography plays an important role in land surface processes through its influence on atmospheric forcing, soil and vegetation properties, and river network topology and drainage area. Land surface models with a spatial structure that captures spatial heterogeneity, which is directly affected by topography, may improve the representation of land surface processes. Previous studies found that land surface modeling, using subbasins instead of structured grids as computational units, improves the scalability of simulated runoff and streamflow processes. In this study, new land surface spatial structures are explored by further dividing subbasins into subgrid structures based on topographic properties, including surface elevation, slope and aspect. Two methods (local and global) of watershed discretization are applied to derive two types of subgrid structures (geo-located and non-geo-located) over the topographically diverse Columbia River basin in the northwestern United States. In the global method, a fixed elevation classification scheme is used to discretize subbasins. The local method utilizes concepts of hypsometric analysis to discretize each subbasin, using different elevation ranges that also naturally account for slope variations. The relative merits of the two methods and subgrid structures are investigated for their ability to capture topographic heterogeneity and the implications of this on representations of atmospheric forcing and land cover spatial patterns. Results showed that the local method reduces the standard deviation (SD) of subgrid surface elevation in the study domain by 17 to 19 % compared to the global method, highlighting the relative advantages of the local method for capturing subgrid topographic variations. The comparison between the two types of subgrid structures showed that the non-geo-located subgrid structures are more consistent across different area threshold values than the geo-located subgrid structures. Overall the local method and non-geo-located subgrid structures effectively and robustly capture topographic, climatic and vegetation variability, which is important for land surface modeling.

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Schymanski, Stanislaus J., Axel Kleidon, Marc Stieglitz, and Jatin Narula. "Maximum entropy production allows a simple representation of heterogeneity in semiarid ecosystems." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1545 (May 12, 2010): 1449–55. http://dx.doi.org/10.1098/rstb.2009.0309.

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Feedbacks between water use, biomass and infiltration capacity in semiarid ecosystems have been shown to lead to the spontaneous formation of vegetation patterns in a simple model. The formation of patterns permits the maintenance of larger overall biomass at low rainfall rates compared with homogeneous vegetation. This results in a bias of models run at larger scales neglecting subgrid-scale variability. In the present study, we investigate the question whether subgrid-scale heterogeneity can be parameterized as the outcome of optimal partitioning between bare soil and vegetated area. We find that a two-box model reproduces the time-averaged biomass of the patterns emerging in a 100 × 100 grid model if the vegetated fraction is optimized for maximum entropy production (MEP). This suggests that the proposed optimality-based representation of subgrid-scale heterogeneity may be generally applicable to different systems and at different scales. The implications for our understanding of self-organized behaviour and its modelling are discussed.

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Kunstmann, H. "Upscaling of land-surface parameters through direct moment propagation." Advances in Geosciences 5 (December 16, 2005): 127–31. http://dx.doi.org/10.5194/adgeo-5-127-2005.

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Abstract. A new methodology is presented that allows the upscaling of land surface parameters of a Soil-Vegetation-Atmosphere-Transfer (SVAT) Model. Focus is set on the proper representation of latent and sensible heat fluxes on grid scale at underlying subgrid-scale heterogeneity. The objective is to derive effective land surface parameters in the sense that they are able to yield the same heat fluxes on the grid scale as the averaged heat fluxes on the subgrid-scale. A combination of inverse modelling and Second-Order-First-Moment (SOFM) propagation is applied for the derivation of effective parameters. The derived upscaling laws relate mean and variance (first and second moment) of subgrid-scale heterogeneity to a corresponding effective parameter at grid-scale. Explicit upscaling relations are exemplary derived for a) roughness length, b) wilting point soil moisture, and c) minimal stomata resistance. It is demonstrated that the SOFM-Method yields congruent results to corresponding Monte Carlo simulations. Effective parameters were found to be independent of driving meteorology and initial conditions.

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de Vrese, Philipp, and Stefan Hagemann. "Explicit Representation of Spatial Subgrid-Scale Heterogeneity in an ESM." Journal of Hydrometeorology 17, no. 5 (April 19, 2016): 1357–71. http://dx.doi.org/10.1175/jhm-d-15-0080.1.

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Abstract In present-day Earth system models, the coupling of land surface and atmosphere is based on simplistic assumptions. Often the heterogeneous land surface is represented by a set of effective parameters valid for an entire model grid box. Other models assume that the surface fluxes become horizontally homogeneous at the lowest atmospheric model level. For heterogeneity above a certain horizontal length scale this is not the case, resulting in spatial subgrid-scale variability in the fluxes and in the state of the atmosphere. The Max Planck Institute for Meteorology’s Earth System Model is used with three different coupling schemes to assess the importance of the representation of spatial heterogeneity at the land surface as well as within the atmosphere. Simulations show that the land surface–atmosphere coupling distinctly influences the simulated near-surface processes with respect to different land-cover types. The representation of heterogeneity also has a distinct impact on the simulated gridbox mean state and fluxes in a large fraction of land surface.

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Efendiev, Y., and L. J. Durlofsky. "Numerical modeling of subgrid heterogeneity in two phase flow simulations." Water Resources Research 38, no. 8 (August 2002): 3–1. http://dx.doi.org/10.1029/2000wr000190.

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Ke, Y., L. R. Leung, M. Huang, and H. Li. "Enhancing the representation of subgrid land surface characteristics in land surface models." Geoscientific Model Development 6, no. 5 (September 27, 2013): 1609–22. http://dx.doi.org/10.5194/gmd-6-1609-2013.

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Abstract. Land surface heterogeneity has long been recognized as important to represent in the land surface models. In most existing land surface models, the spatial variability of surface cover is represented as subgrid composition of multiple surface cover types, although subgrid topography also has major controls on surface processes. In this study, we developed a new subgrid classification method (SGC) that accounts for variability of both topography and vegetation cover. Each model grid cell was represented with a variable number of elevation classes and each elevation class was further described by a variable number of vegetation types optimized for each model grid given a predetermined total number of land response units (LRUs). The subgrid structure of the Community Land Model (CLM) was used to illustrate the newly developed method in this study. Although the new method increases the computational burden in the model simulation compared to the CLM subgrid vegetation representation, it greatly reduced the variations of elevation within each subgrid class and is able to explain at least 80% of the total subgrid plant functional types (PFTs). The new method was also evaluated against two other subgrid methods (SGC1 and SGC2) that assigned fixed numbers of elevation and vegetation classes for each model grid (SGC1: M elevation bands–N PFTs method; SGC2: N PFTs–M elevation bands method). Implemented at five model resolutions (0.1°, 0.25°, 0.5°, 1.0°and 2.0°) with three maximum-allowed total number of LRUs (i.e., NLRU of 24, 18 and 12) over North America (NA), the new method yielded more computationally efficient subgrid representation compared to SGC1 and SGC2, particularly at coarser model resolutions and moderate computational intensity (NLRU = 18). It also explained the most PFTs and elevation variability that is more homogeneously distributed spatially. The SGC method will be implemented in CLM over the NA continent to assess its impacts on simulating land surface processes.

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Malyshev, Sergey, Elena Shevliakova, Ronald J. Stouffer, and Stephen W. Pacala. "Contrasting Local versus Regional Effects of Land-Use-Change-Induced Heterogeneity on Historical Climate: Analysis with the GFDL Earth System Model." Journal of Climate 28, no. 13 (July 1, 2015): 5448–69. http://dx.doi.org/10.1175/jcli-d-14-00586.1.

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Abstract The effects of land-use and land-cover change (LULCC) on surface climate using two ensembles of numerical experiments with the Geophysical Fluid Dynamics Laboratory (GFDL) comprehensive Earth System Model ESM2Mb are investigated in this study. The experiments simulate historical climate with two different assumptions about LULCC: 1) no land-use change with potential vegetation (PV) and 2) with the CMIP5 historical reconstruction of LULCC (LU). Two different approaches were used in the analysis: 1) the authors compare differences in LU and PV climates to evaluate the regional and global effects of LULCC and 2) the authors characterize subgrid climate differences among different land-use tiles within each grid cell in the LU experiment. Using the first method, the authors estimate the magnitude of LULCC effect to be similar to some previous studies. Using the second method, the authors found a pronounced subgrid signal of LULCC in near-surface temperature over majority of areas affected by LULCC. The signal is strongest on croplands, where it is detectable with 95% confidence over 68.5% of all nonglaciated land grid cells in June–July–August, compared to 8.3% in the first method. In agricultural areas, the subgrid signal tends to be stronger than LU–PV signal by a factor of 1.3 in tropics in both summer and winter and by 1.5 in extratropics in winter. This analysis for the first time demonstrates and quantifies the local, subgrid-scale LULCC effects with a comprehensive ESM and compares it to previous global and regional approaches.

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Essery, R. L. H., M. J. Best, R. A. Betts, P. M. Cox, and C. M. Taylor. "Explicit Representation of Subgrid Heterogeneity in a GCM Land Surface Scheme." Journal of Hydrometeorology 4, no. 3 (June 2003): 530–43. http://dx.doi.org/10.1175/1525-7541(2003)004<0530:eroshi>2.0.co;2.

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Landry, Jean-Sébastien, Navin Ramankutty, and Lael Parrott. "Investigating the Effects of Subgrid Cell Dynamic Heterogeneity on the Large-Scale Modeling of Albedo in Boreal Forests*." Earth Interactions 20, no. 5 (February 1, 2016): 1–23. http://dx.doi.org/10.1175/ei-d-15-0022.1.

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Abstract Stand-clearing disturbances, which remove most of the tree cover but are followed by forest regrowth, affect extensive areas annually, yet each event is usually much smaller than a typical grid cell in Earth system climate models. This study argues that the approach taken to account for the resulting subgrid cell dynamic heterogeneity substantially affects the computation of land–atmosphere exchanges. The authors investigated in a simplified model the effects of three such approaches on the computation of albedo over boreal forests. It was found that the simplest approach—in which any new disturbance-created patch was immediately merged with the rest of the grid cell—underestimated the annual reflected solar radiation by ~3 W m−2 on average (a relative error of 15%) compared with the most accurate approach—in which albedo computations were performed for each individual subgrid patch. This study also investigated an intermediate approach, in which each patch was tracked individually, but albedo was estimated from a much smaller number of subgrid tiles grouping patches having a similar amount of tree cover. Results from this third approach converged quickly toward the most accurate results as the number of tiles increased and were robust to changes in the thresholds used to assign patches to specific tiles. When computing time prevents implementing the most accurate approach in Earth system climate models, the results advocate for using strategies similar to the intermediate approach in order to avoid biasing the net radiative forcing of stand-clearing disturbances toward a warming impact, at least over boreal forests.

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Jouhaud, J., J. ‐L Dufresne, J. ‐B Madeleine, F. Hourdin, F. Couvreux, N. Villefranque, and A. Jam. "Accounting for Vertical Subgrid‐Scale Heterogeneity in Low‐Level Cloud Fraction Parameterizations." Journal of Advances in Modeling Earth Systems 10, no. 11 (November 2018): 2686–705. http://dx.doi.org/10.1029/2018ms001379.

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Ke, Y., L. R. Leung, M. Huang, and H. Li. "Enhancing the representation of subgrid land surface characteristics in land surface models." Geoscientific Model Development Discussions 6, no. 1 (March 28, 2013): 2177–212. http://dx.doi.org/10.5194/gmdd-6-2177-2013.

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Abstract. Land surface heterogeneity has long been recognized as important to represent in the land surface models. In most existing land surface models, the spatial variability of surface cover is represented as subgrid composition of multiple surface cover types. In this study, we developed a new subgrid classification method (SGC) that accounts for the topographic variability of the vegetation cover. Each model grid cell was represented with a number of elevation classes and each elevation class was further described by a number of vegetation types. The numbers of elevation classes and vegetation types were variable and optimized for each model grid so that the spatial variability of both elevation and vegetation can be reasonably explained given a pre-determined total number of classes. The subgrid structure of the Community Land Model (CLM) was used as an example to illustrate the newly developed method in this study. With similar computational burden as the current subgrid vegetation representation in CLM, the new method is able to explain at least 80% of the total subgrid Plant Functional Types (PFTs) and greatly reduced the variations of elevation within each subgrid class compared to the baseline method where a single elevation class is assigned to each subgrid PFT. The new method was also evaluated against two other subgrid methods (SGC1 and SGC2) that assigned fixed numbers of elevation and vegetation classes for each model grid with different perspectives of surface cover classification. Implemented at five model resolutions (0.1°, 0.25°, 0.5°, 1.0° and 2.0°) with three maximum-allowed total number of classes Nclass of 24, 18 and 12 representing different computational burdens over the North America (NA) continent, the new method showed variable performances compared to the SGC1 and SGC2 methods. However, the advantage of the SGC method over the other two methods clearly emerged at coarser model resolutions and with moderate computational intensity (Nclass = 18) as it explained the most PFTs and elevation variability among the three subgrid methods. Spatially, the SGC method explained more elevation variability in topography-complex areas and more vegetation variability in flat areas. Furthermore, the variability of both elevation and vegetation explained by the new method was more spatially homogeneous regardless of the model resolutions and computational burdens. The SGC method will be implemented in CLM over the NA continent to assess its impacts on simulating land surface processes.

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Xu, Zexuan, Erica R. Siirila-Woodburn, Alan M. Rhoades, and Daniel Feldman. "Sensitivities of subgrid-scale physics schemes, meteorological forcing, and topographic radiation in atmosphere-through-bedrock integrated process models: a case study in the Upper Colorado River basin." Hydrology and Earth System Sciences 27, no. 9 (May 5, 2023): 1771–89. http://dx.doi.org/10.5194/hess-27-1771-2023.

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Abstract. Mountain hydrology is controlled by interacting processes extending from the atmosphere through the bedrock. Integrated process models (IPMs), one of the main tools needed to interpret observations and refine conceptual models of the mountainous water cycle, require meteorological forcing that simulates the atmospheric process to predict hydroclimate then subsequently impacts surface–subsurface hydrology. Complex terrain and extreme spatial heterogeneity in mountainous environments drive uncertainty in several key considerations in IPM configurations and require further quantification and sensitivity analyses. Here, we present an IPM using the Weather Research and Forecasting (WRF) model which forces an integrated hydrologic model, ParFlow-CLM, implemented over a domain centered over the East River watershed (ERW), located in the Upper Colorado River basin (UCRB). The ERW is a heavily instrumented 300 km2 region in the headwaters of the UCRB near Crested Butte, CO, with a growing atmosphere-through-bedrock observation network. Through a series of experiments in the water year 2019 (WY19), we use four meteorological forcings derived from commonly used reanalysis datasets, three subgrid-scale physics scheme configurations in WRF, and two terrain shading options within WRF to test the relative importance of these experimental design choices for key hydrometeorological metrics including precipitation and snowpack, as well as evapotranspiration, groundwater storage, and discharge simulated by the ParFlow-CLM. Our hypothesis is that uncertainty from synoptic-scale forcings produces a much larger spread in surface–subsurface hydrologic fields than subgrid-scale physics scheme choice. Results reveal that the WRF subgrid-scale physics configuration leads to larger spatiotemporal variance in simulated hydrometeorological conditions, whereas variance across meteorological forcing with common subgrid-scale physics configurations is more spatiotemporally constrained. Despite reasonably simulating precipitation, a delay in simulated discharge peak is due to a systematic cold bias across WRF simulations, suggesting the need for bias correction. Discharge shows greater variance in response to the WRF simulations across subgrid-scale physics schemes (26 %) rather than meteorological forcing (6 %). The topographic radiation option has minor effects on the watershed-average hydrometeorological processes but adds profound spatial heterogeneity to local energy budgets (±30 W m−2 in shortwave radiation and 1 K air temperature differences in late summer). This is the first presentation of sensitivity analyses that provide support to help guide the scientific community to develop observational constraints on atmosphere-through-bedrock processes and their interactions.

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Eliseev, A. V., and D. E. Sergeev. "Impact of subgrid-scale vegetation heterogeneity on the simulation of carbon-cycle characteristics." Izvestiya, Atmospheric and Oceanic Physics 50, no. 3 (May 2014): 225–35. http://dx.doi.org/10.1134/s0001433814020030.

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Kabat, P., R. W. A. Hutjes, and R. A. Feddes. "The scaling characteristics of soil parameters: From plot scale heterogeneity to subgrid parameterization." Journal of Hydrology 190, no. 3-4 (March 1997): 363–96. http://dx.doi.org/10.1016/s0022-1694(96)03134-4.

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Eliseev, A. V., and D. E. Sergeev. "Impact of Subgrid-Scale Vegetation Heterogeneity on the Simulation of Carbon-Cycle Characteristics." Известия Российской академии наук. Физика атмосферы и океана 50, no. 3 (2014): 259–70. http://dx.doi.org/10.7868/s0002351514020035.

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Chen, Baozhang, Jing M. Chen, Gang Mo, Chiu-Wai Yuen, Hank Margolis, Kaz Higuchi, and Douglas Chan. "Modeling and Scaling Coupled Energy, Water, and Carbon Fluxes Based on Remote Sensing: An Application to Canada’s Landmass." Journal of Hydrometeorology 8, no. 2 (April 1, 2007): 123–43. http://dx.doi.org/10.1175/jhm566.1.

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Abstract Land surface models (LSMs) need to be coupled with atmospheric general circulation models (GCMs) to adequately simulate the exchanges of energy, water, and carbon between the atmosphere and terrestrial surfaces. The heterogeneity of the land surface and its interaction with temporally and spatially varying meteorological conditions result in nonlinear effects on fluxes of energy, water, and carbon, making it challenging to scale these fluxes accurately. The issue of up-scaling remains one of the critical unsolved problems in the parameterization of subgrid-scale fluxes in coupled LSM and GCM models. A new distributed LSM, the Ecosystem–Atmosphere Simulation Scheme (EASS) was developed and coupled with the atmospheric Global Environmental Multiscale model (GEM) to simulate energy, water, and carbon fluxes over Canada’s landmass through the use of remote sensing and ancillary data. Two approaches (lumped case and distributed case) for handling subgrid heterogeneity were used to evaluate the effect of land-cover heterogeneity on regional flux simulations based on remote sensing. Online runs for a week in August 2003 provided an opportunity to investigate model performance and spatial scaling issues. Comparisons of simulated results with available tower observations (five sites) across an east–west transect over Canada’s southern forest regions indicate that the model is reasonably successful in capturing both the spatial and temporal variations in carbon and energy fluxes, although there were still some biases in estimates of latent and sensible heat fluxes between the simulations and the tower observations. Moreover, the latent and sensible heat fluxes were found to be better modeled in the coupled EASS–GEM system than in the uncoupled GEM. There are marked spatial variations in simulated fluxes over Canada’s landmass. These patterns of spatial variation closely follow vegetation-cover types as well as leaf area index, both of which are highly correlated with the underlying soil types, soil moisture conditions, and soil carbon pools. The surface fluxes modeled by the two up-scaling approaches (lumped and distributed cases) differ by 5%–15% on average and by up to 15%–25% in highly heterogeneous regions. This suggests that different ways of treating subgrid land surface heterogeneities could lead to noticeable biases in model output.

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Pflug, Justin M., Yiwen Fang, Steven A. Margulis, and Ben Livneh. "Interactions between thresholds and spatial discretizations of snow: insights from estimates of wolverine denning habitat in the Colorado Rocky Mountains." Hydrology and Earth System Sciences 27, no. 14 (July 24, 2023): 2747–62. http://dx.doi.org/10.5194/hess-27-2747-2023.

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Abstract. Thresholds can be used to interpret environmental data in a way that is easily communicated and useful for decision-making purposes. However, thresholds are often developed for specific data products and time periods, changing findings when the same threshold is applied to datasets or periods with different characteristics. Here, we test the impact of different spatial discretizations of snow on annual estimates of wolverine denning opportunities in the Colorado Rocky Mountains, defined using a snow water equivalent (SWE) threshold (0.20 m) and threshold date (15 May) from previous habitat assessments. Annual potential wolverine denning area (PWDA) was thresholded from a 36-year (1985–2020) snow reanalysis model with three different spatial discretizations: (1) 480 m grid cells (D480), (2) 90 m grid cells (D90), and (3) 480 m grid cells with implicit representations of subgrid snow spatial heterogeneity (S480). Relative to the D480 and S480 discretizations, D90 resolved shallower snow deposits on slopes between 3050 and 3350 m elevation, decreasing PWDA by 10 %, on average. In years with warmer and/or drier winters, S480 discretizations with subgrid representations of snow heterogeneity increased PWDA, even within grid cells where mean 15 May SWE was less than the SWE threshold. These simulations increased PWDA by upwards of 30 % in low-snow years, as compared to the D480 and D90 simulations without subgrid snow heterogeneity. Despite PWDA sensitivity to different snow spatial discretizations, PWDA was controlled more by annual variations in winter precipitation and temperature. However, small changes to the SWE threshold (±0.07 m) and threshold date (±2 weeks) also affected PWDA by as much as 82 %. Across these threshold ranges, PWDA was approximately 18 % more sensitive to the SWE threshold than the threshold date. However, the sensitivity to the threshold date was larger in years with late spring snowfall, when PWDA depended on whether modeled SWE was thresholded before, during, or after spring snow accumulation. Our results demonstrate that snow thresholds are useful but may not always provide a complete picture of the annual variability in snow-adapted wildlife denning opportunities. Studies thresholding spatiotemporal datasets could be improved by including (1) information about the fidelity of thresholds across multiple spatial discretizations and (2) uncertainties related to ranges of realistic thresholds.

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Arola, Antti, and Dennis P. Lettenmaier. "Effects of Subgrid Spatial Heterogeneity on GCM-Scale Land Surface Energy and Moisture Fluxes." Journal of Climate 9, no. 6 (June 1996): 1339–49. http://dx.doi.org/10.1175/1520-0442(1996)009<1339:eossho>2.0.co;2.

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Liang, Xu, and Zhenghui Xie. "A new surface runoff parameterization with subgrid-scale soil heterogeneity for land surface models." Advances in Water Resources 24, no. 9-10 (November 2001): 1173–93. http://dx.doi.org/10.1016/s0309-1708(01)00032-x.

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Avissar, Roni. "A statistical-dynamical approach to parameterize subgrid-scale land-surface heterogeneity in climate models." Surveys in Geophysics 12, no. 1-3 (March 1991): 155–78. http://dx.doi.org/10.1007/bf01903417.

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Kreye, Phillip, and Günter Meon. "Subgrid spatial variability of soil hydraulic functions for hydrological modelling." Hydrology and Earth System Sciences 20, no. 6 (July 1, 2016): 2557–71. http://dx.doi.org/10.5194/hess-20-2557-2016.

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Abstract. State-of-the-art hydrological applications require a process-based, spatially distributed hydrological model. Runoff characteristics are demanded to be well reproduced by the model. Despite that, the model should be able to describe the processes at a subcatchment scale in a physically credible way. The objective of this study is to present a robust procedure to generate various sets of parameterisations of soil hydraulic functions for the description of soil heterogeneity on a subgrid scale. Relations between Rosetta-generated values of saturated hydraulic conductivity (Ks) and van Genuchten's parameters of soil hydraulic functions were statistically analysed. An universal function that is valid for the complete bandwidth of Ks values could not be found. After concentrating on natural texture classes, strong correlations were identified for all parameters. The obtained regression results were used to parameterise sets of hydraulic functions for each soil class. The methodology presented in this study is applicable on a wide range of spatial scales and does not need input data from field studies. The developments were implemented into a hydrological modelling system.

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Pimentel, Rafael, Javier Herrero, and María José Polo. "Subgrid parameterization of snow distribution at a Mediterranean site using terrestrial photography." Hydrology and Earth System Sciences 21, no. 2 (February 10, 2017): 805–20. http://dx.doi.org/10.5194/hess-21-805-2017.

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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.

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Salmun, Haydee, Andrea Molod, and Andreea Ira. "Observational validation of an extended mosaic technique for capturing subgrid scale heterogeneity in a GCM." Tellus B: Chemical and Physical Meteorology 59, no. 3 (January 2007): 622–32. http://dx.doi.org/10.1111/j.1600-0889.2007.00257.x.

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Mölders, Nicole, and Armin Raabe. "Numerical Investigations on the Influence of Subgrid-Scale Surface Heterogeneity on Evapotranspiration and Cloud Processes." Journal of Applied Meteorology 35, no. 6 (June 1996): 782–95. http://dx.doi.org/10.1175/1520-0450(1996)035<0782:niotio>2.0.co;2.

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Wang, Dagang, and Guiling Wang. "Toward a Robust Canopy Hydrology Scheme with Precipitation Subgrid Variability." Journal of Hydrometeorology 8, no. 3 (June 1, 2007): 439–46. http://dx.doi.org/10.1175/jhm585.1.

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Abstract Representation of the canopy hydrological processes has been challenging in land surface modeling due to the subgrid heterogeneity in both precipitation and surface characteristics. The Shuttleworth dynamic–statistical method is widely used to represent the impact of the precipitation subgrid variability on canopy hydrological processes but shows unwanted sensitivity to temporal resolution when implemented into land surface models. This paper presents a canopy hydrology scheme that is robust at different temporal resolutions. This scheme is devised by applying two physically based treatments to the Shuttleworth scheme: 1) the canopy hydrological processes within the rain-covered area are treated separately from those within the nonrain area, and the scheme tracks the relative rain location between adjacent time steps; and 2) within the rain-covered area, the canopy interception is so determined as to sustain the potential evaporation from the wetted canopy or is equal to precipitation, whichever is less, to maintain somewhat wet canopy during any rainy time step. When applied to the Amazon region, the new scheme establishes interception loss ratios of 0.3 at a 10-min time step and 0.23 at a 2-h time step. Compared to interception loss ratios of 0.45 and 0.09 at the corresponding time steps established by the original Shuttleworth scheme, the new scheme is much more stable under different temporal resolutions.

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Rouholahnejad Freund, Elham, Ying Fan, and James W. Kirchner. "Global assessment of how averaging over spatial heterogeneity in precipitation and potential evapotranspiration affects modeled evapotranspiration rates." Hydrology and Earth System Sciences 24, no. 4 (April 16, 2020): 1927–38. http://dx.doi.org/10.5194/hess-24-1927-2020.

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Abstract. Accurately estimating large-scale evapotranspiration (ET) rates is essential to understanding and predicting global change. Evapotranspiration models that are applied at a continental scale typically operate on relatively large spatial grids, with the result that the heterogeneity in land surface properties and processes at smaller spatial scales cannot be explicitly represented. Averaging over this spatial heterogeneity may lead to biased estimates of energy and water fluxes. Here we estimate how averaging over spatial heterogeneity in precipitation (P) and potential evapotranspiration (PET) may affect grid-cell-averaged evapotranspiration rates, as seen from the atmosphere over heterogeneous landscapes across the globe. Our goal is to identify where, under what conditions, and at what scales this “heterogeneity bias” could be most important but not to quantify its absolute magnitude. We use Budyko curves as simple functions that relate ET to precipitation and potential evapotranspiration. Because the relationships driving ET are nonlinear, averaging over subgrid heterogeneity in P and PET will lead to biased estimates of average ET. We examine the global distribution of this bias, its scale dependence, and its sensitivity to variations in P vs. PET. Our analysis shows that this heterogeneity bias is more pronounced in mountainous terrain, in landscapes where spatial variations in P and PET are inversely correlated, and in regions with temperate climates and dry summers. We also show that this heterogeneity bias increases on average, and expands over larger areas, as the grid cell size increases.

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Liu, Chongxuan, Jianying Shang, Huimei Shan, and John M. Zachara. "Effect of Subgrid Heterogeneity on Scaling Geochemical and Biogeochemical Reactions: A Case of U(VI) Desorption." Environmental Science & Technology 48, no. 3 (January 13, 2014): 1745–52. http://dx.doi.org/10.1021/es404224j.

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Liu, Yuanyuan, Chongxuan Liu, Changyong Zhang, Xiaofan Yang, and John M. Zachara. "Pore and continuum scale study of the effect of subgrid transport heterogeneity on redox reaction rates." Geochimica et Cosmochimica Acta 163 (August 2015): 140–55. http://dx.doi.org/10.1016/j.gca.2015.04.039.

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Kröniger, Konstantin, Gabriel G. Katul, Frederik De Roo, Peter Brugger, and Matthias Mauder. "Aerodynamic Resistance Parameterization for Heterogeneous Surfaces Using a Covariance Function Approach in Spectral Space." Journal of the Atmospheric Sciences 76, no. 10 (September 30, 2019): 3191–209. http://dx.doi.org/10.1175/jas-d-18-0150.1.

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Abstract Simulating the influence of heterogeneous surfaces on atmospheric flow using mesoscale models (MSM) remains a challenging task, as the resolution of these models usually prohibits resolving important scales of surface heterogeneity. However, surface heterogeneity impacts fluxes of momentum, heat, or moisture, which act as lower boundary conditions for MSM. Even though several approaches for representing subgrid-scale heterogeneities in MSM exist, many of these approaches rely on Monin–Obukhov similarity theory, preventing those models from resolving all scales of surface heterogeneity. To improve upon these residual heterogeneity scales, a novel heterogeneity parameterization is derived by linking the heterogeneous covariance function in spectral space to an associated homogeneous one. This covariance function approach is subsequently used to derive a parameterization of the aerodynamic resistance to heat transfer of the surface layer. Here, the effect of surface heterogeneity enters as a factor applied to the stability correction functions of the bulk similarity approach. To perform a first comparison of the covariance function approach against the conventional bulk similarity and tile approaches, large-eddy simulations (LESs) of distinct surface heterogeneities are conducted. The aerodynamic resistances from these three parameterizations are subsequently tested against the LES reference by resolving the surface heterogeneities with six different test-MSM grids of varying cell dimension. The results of these comparisons show that the covariance function approach proposed here yields the smallest deviations from the LES reference. In addition, the smallest deviation of the covariance function approach to the reference is observed for the LES with the largest surface heterogeneity, which illustrates the advantage of this novel parameterization.

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Janzon, Erik, Heiner Körnich, Johan Arnqvist, and Anna Rutgersson. "Single Column Model Simulations of Icing Conditions in Northern Sweden: Sensitivity to Surface Model Land Use Representation." Energies 13, no. 16 (August 17, 2020): 4258. http://dx.doi.org/10.3390/en13164258.

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In-cloud ice mass accretion on wind turbines is a common challenge that is faced by energy companies operating in cold climates. On-shore wind farms in Scandinavia are often located in regions near patches of forest, the heterogeneity length scales of which are often less than the resolution of many numerical weather prediction (NWP) models. The representation of these forests—including the cloud water response to surface roughness and albedo effects that are related to them—must therefore be parameterized in NWP models used as meteorological input in ice prediction systems, resulting in an uncertainty that is poorly understood and, to the present date, not quantified. The sensitivity of ice accretion forecasts to the subgrid representation of forests is examined in this study. A single column version of the HARMONIE-AROME three-dimensional (3D) NWP model is used to determine the sensitivity of the forecast of ice accretion on wind turbines to the subgrid forest fraction. Single column simulations of a variety of icing cases at a location in northern Sweden were examined in order to investigate the impact of vegetation cover on ice accretion in varying levels of solar insolation and wind magnitudes. In mid-winter cases, the wind speed response to surface roughness was the primary driver of the vegetation effect on ice accretion. In autumn cases, the cloud water response to surface albedo effects plays a secondary role in the impact of in-cloud ice accretion, with the wind response to surface roughness remaining the primary driver for the surface vegetation impact on icing. Two different surface boundary layer (SBL) forest canopy subgrid parameterizations were tested in this study that feature different methods for calculating near-surface profiles of wind, temperature, and moisture, with the ice mass accretion again following the wind response to surface vegetation between both of these schemes.

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Nose, Takehiko, Takuji Waseda, Tsubasa Kodaira, and Jun Inoue. "Satellite-retrieved sea ice concentration uncertainty and its effect on modelling wave evolution in marginal ice zones." Cryosphere 14, no. 6 (June 24, 2020): 2029–52. http://dx.doi.org/10.5194/tc-14-2029-2020.

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Abstract. Ocean surface waves are known to decay when they interact with sea ice. Wave–ice models implemented in a spectral wave model, e.g. WAVEWATCH III® (WW3), derive the attenuation coefficient based on several different model ice types, i.e. how the model treats sea ice. In the marginal ice zone (MIZ) with sea ice concentration (SIC) < 1, the wave attenuation is moderated by SIC: we show that subgrid-scale processes relating to the SIC and sea ice type heterogeneity in the wave–ice models are missing and the accuracy of SIC plays an important role in the predictability. Satellite-retrieved SIC data (or a sea ice model that assimilates them) are often used to force wave–ice models, but these data are known to have uncertainty. To study the effect of SIC uncertainty ΔSIC on modelling MIZ waves during the 2018 R/V Mirai observational campaign in the refreezing Chukchi Sea, a WW3 hindcast experiment was conducted using six satellite-retrieved SIC products based on four algorithms applied to SSMIS and AMSR2 data. The results show that ΔSIC can cause considerable wave prediction discrepancies in ice cover. There is evidence that bivariate uncertainty data (model significant wave heights and SIC forcing) are correlated, although off-ice wave growth is more complicated due to the cumulative effect of ΔSIC along an MIZ fetch. The analysis revealed that the effect of ΔSIC can overwhelm the uncertainty arising from the choice of model ice types, i.e. wave–ice interaction parameterisations. Despite the missing subgrid-scale physics relating to the SIC and sea ice type heterogeneity in WW3 wave–ice models – which causes significant modelling uncertainty – this study found that the accuracy of satellite-retrieved SIC used as model forcing is the dominant error source of modelling MIZ waves in the refreezing ocean.

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Hu, Zhenglin, and Shafiqul Islam. "Effects of subgrid-scale heterogeneity of soil wetness and temperature on grid-scale evaporation and its parameterization." International Journal of Climatology 18, no. 1 (January 1998): 49–63. http://dx.doi.org/10.1002/(sici)1097-0088(199801)18:1<49::aid-joc224>3.0.co;2-u.

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Schneiderbauer, Simon, and Stefan Pirker. "Filtered and heterogeneity-based subgrid modifications for gas-solid drag and solid stresses in bubbling fluidized beds." AIChE Journal 60, no. 3 (December 26, 2013): 839–54. http://dx.doi.org/10.1002/aic.14321.

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36

Riley, W. J. "Using model reduction to predict the soil-surface C<sup>18</sup>OO flux: an example of representing complex biogeochemical dynamics in a computationally efficient manner." Geoscientific Model Development Discussions 5, no. 4 (November 2, 2012): 3469–91. http://dx.doi.org/10.5194/gmdd-5-3469-2012.

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Abstract. Earth System Models (ESMs) must calculate large-scale interactions between the land and atmosphere while accurately characterizing fine-scale spatial heterogeneity in water, carbon, and nutrient dynamics. We present here a high-dimensional model representation (HDMR) approach that allows detailed process representation of a coupled carbon and water tracer (the δ18O value of the soil-surface CO2 flux (δFs)) in a computationally tractable manner. δFs depends on the δ18O value of soil water, soil moisture, soil temperature, and soil CO2 production (all of which are depth-dependent), and the δ18O value of above-surface CO2. We tested the HDMR approach over a growing season in a C4-dominated pasture using two vertical soil discretizations. The difference between the HDMR approach and the full model solution in the three-month integrated isoflux was less than 0.2% (0.5 mol m−2‰), and the approach is up to 100 times faster than the full numerical solution. This type of model reduction approach allows representation of complex coupled biogeochemical processes in regional and global climate models and can be extended to characterize subgrid-scale spatial heterogeneity.

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Uvarov, Vyacheslav. "Accounting for Subgrid Scale Heterogeneity in the Frames of Numerical Model for Global Distribution of Electric Fields in the Earth Ionosphere." Proceedings of Petersburg Transport University 19, no. 3 (September 25, 2022): 600–608. http://dx.doi.org/10.20295/1815-588x-2022-3-600-608.

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Purpose: Creation of a global numerical model of ionospheric electric fields with the possibility of more detailed description of their small-scale features in some limited subareas. Methods: Formulation of a boundary value task with accounting for underlined subdomain for to describe subgrid scale features and the task solution by modern numerical method. Results: Model testing was conducted. In particular, stable numerical solution was obtained for the case of small-scale localized conductivity increase due to additional ionization of the ionosphere by an auroral ray. Practical significance: The model will make it possible to qualify the picture of ionospheric electric field global distribution in those limited subareas which for, there is fuller set of experimental data on the distribution of conductivity and field-aligned currents.

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Shaffer, Stephen R., Mohamed Moustaoui, Alex Mahalov, and Benjamin L. Ruddell. "A Method of Aggregating Heterogeneous Subgrid Land-Cover Input Data for Multiscale Urban Parameterization." Journal of Applied Meteorology and Climatology 55, no. 9 (September 2016): 1889–905. http://dx.doi.org/10.1175/jamc-d-16-0027.1.

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AbstractA method of representing grid-scale heterogeneous development density for urban climate models from probability density functions of subgrid-resolution observed data is proposed. Derived values are evaluated in relation to normalized Shannon entropy to provide guidance in assessing model input data. Urban fraction for dominant-class and mosaic urban contributions is estimated by combining analysis of 30-m-resolution National Land Cover Database 2006 data products for continuous impervious surface area and categorical land cover. The aim of the method is to reduce model error through improvement of urban parameterization and representation of observations employed as input data. The multiscale variation of parameter values is demonstrated for several methods of utilizing input. This approach provides multiscale and spatial guidance for determining where parameterization schemes may be misrepresenting heterogeneity of input data, along with motivation for employing mosaic techniques that are based upon assessment of input data. The proposed method has wider potential for geographic application and complements data products that focus on characterizing central business districts. It utilizes observations to obtain a parameterization of urban fraction that is dependent upon resolution and class-partition scheme, thus providing one means of influencing simulation prediction at various aggregated grid scales.

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Nitzbon, Jan, Moritz Langer, Léo C. P. Martin, Sebastian Westermann, Thomas Schneider von Deimling, and Julia Boike. "Effects of multi-scale heterogeneity on the simulated evolution of ice-rich permafrost lowlands under a warming climate." Cryosphere 15, no. 3 (March 19, 2021): 1399–422. http://dx.doi.org/10.5194/tc-15-1399-2021.

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Abstract. In continuous permafrost lowlands, thawing of ice-rich deposits and melting of massive ground ice lead to abrupt landscape changes called thermokarst, which have widespread consequences on the thermal, hydrological, and biogeochemical state of the subsurface. However, macro-scale land surface models (LSMs) do not resolve such localized subgrid-scale processes and could hence miss key feedback mechanisms and complexities which affect permafrost degradation and the potential liberation of soil organic carbon in high latitudes. Here, we extend the CryoGrid 3 permafrost model with a multi-scale tiling scheme which represents the spatial heterogeneities of surface and subsurface conditions in ice-rich permafrost lowlands. We conducted numerical simulations using stylized model setups to assess how different representations of micro- and meso-scale heterogeneities affect landscape evolution pathways and the amount of permafrost degradation in response to climate warming. At the micro-scale, the terrain was assumed to be either homogeneous or composed of ice-wedge polygons, and at the meso-scale it was assumed to be either homogeneous or resembling a low-gradient slope. We found that by using different model setups and parameter sets, a multitude of landscape evolution pathways could be simulated which correspond well to observed thermokarst landscape dynamics across the Arctic. These pathways include the formation, growth, and gradual drainage of thaw lakes; the transition from low-centred to high-centred ice-wedge polygons; and the formation of landscape-wide drainage systems due to melting of ice wedges. Moreover, we identified several feedback mechanisms due to lateral transport processes which either stabilize or destabilize the thermokarst terrain. The amount of permafrost degradation in response to climate warming was found to depend primarily on the prevailing hydrological conditions, which in turn are crucially affected by whether or not micro- and/or meso-scale heterogeneities were considered in the model setup. Our results suggest that the multi-scale tiling scheme allows for simulating ice-rich permafrost landscape dynamics in a more realistic way than simplistic one-dimensional models and thus facilitates more robust assessments of permafrost degradation pathways in response to climate warming. Our modelling work improves the understanding of how micro- and meso-scale processes affect the evolution of ice-rich permafrost landscapes, and it informs macro-scale modellers focusing on high-latitude land surface processes about the necessities and possibilities for the inclusion of subgrid-scale processes such as thermokarst within their models.

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Galmarini, S., J. F. Vinuesa, and A. Martilli. "Modelling the impact of sub-grid scale emission variability on upper-air concentration." Atmospheric Chemistry and Physics Discussions 7, no. 4 (August 20, 2007): 12289–326. http://dx.doi.org/10.5194/acpd-7-12289-2007.

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Abstract. The long standing issue of sub-grid emission heterogeneity and its influence to upper air concentration is addressed here and a subgrid model proposed. The founding concept of the approach is the assumption that average emission acts as source terms of average concentration, while emission fluctuations are source for the concentration variance. The model is based on the derivation of the sub-grid contribution of emission and the use of the concentration variance equation to transport it in the atmospheric boundary layer. The model has been implemented in an existing mesoscale model and the results compared with Large-Eddy Simulation data for ad-hoc simulation devised to test specifically the parametrization. The results show and excellent agreement of the models. For the first time a time evolving error bar reproducing the sub-grid scale heterogeneity of the emissions and the way in which it affects the concentration has been shown. The concentration variance is presented as an extra attribute to better define the mean concentrations in a Reynolds-average model. The model has applications from meso to global scale and that go beyond air quality.

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41

Riley, W. J. "Using model reduction to predict the soil-surface C<sup>18</sup>OO flux: an example of representing complex biogeochemical dynamics in a computationally efficient manner." Geoscientific Model Development 6, no. 2 (March 12, 2013): 345–52. http://dx.doi.org/10.5194/gmd-6-345-2013.

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Abstract. Earth system models (ESMs) must calculate large-scale interactions between the land and atmosphere while accurately characterizing fine-scale spatial heterogeneity in water, carbon, and other nutrient dynamics. We present here a high-dimension model representation (HDMR) approach that allows detailed process representation of a coupled carbon and water tracer (the δ18O value of the soil-surface CO2 flux (δ Fs)) in a computationally tractable manner. δ Fs depends on the δ18O value of soil water, soil moisture and temperature, and soil CO2 production (all of which are depth dependent), and the δ18O value of above-surface CO2. We tested the HDMR approach over a growing season in a C4-dominated pasture using two vertical soil discretizations. The difference between the HDMR approach and the full model solution in the three-month integrated isoflux was less than 0.2% (0.5 mol m−2 ‰), and the approach is up to 100 times faster than the full numerical solution. This type of model reduction approach allows representation of complex coupled biogeochemical processes in regional and global climate models and can be extended to characterize subgrid-scale spatial heterogeneity.

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42

Galmarini, S., J. F. Vinuesa, and A. Martilli. "Modeling the impact of sub-grid scale emission variability on upper-air concentration." Atmospheric Chemistry and Physics 8, no. 2 (January 15, 2008): 141–58. http://dx.doi.org/10.5194/acp-8-141-2008.

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Abstract. The long standing issue of sub-grid emission heterogeneity and its influence to upper air concentration is addressed here and a subgrid model proposed. The founding concept of the approach is the assumption that average emission act as source terms of average concentration, emission fluctuations are source for the concentration variance. The model is based on the derivation of the sub-grid contribution of emission and the use of the concentration variance equation to transport it in the atmospheric boundary layer. The model has been implemented in an existing mesoscale model and the results compared with Large-Eddy Simulation data for ad-hoc simulation devised to test specifically the parametrization. The results show an excellent agreement of the models. For the first time a time evolving error bar reproducing the sub-grid scale heterogeneity of the emissions and the way in which it affects the concentration has been shown. The concentration variance is presented as an extra attribute to better define the mean concentrations in a Reynolds-average model. The model has applications from meso to global scale and that go beyond air quality.

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43

JIA, Yangwen, Nobuyuki TAMAI, and Norio TANAKA. "INFLUENCES OF SUBGRID HETEROGENEITY OF LAND USE AND GRID SIZE ON WATER AND HEAT BUDGETS IN THE SHUTOKEN AREA." PROCEEDINGS OF HYDRAULIC ENGINEERING 43 (1999): 115–20. http://dx.doi.org/10.2208/prohe.43.115.

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Cao, Xuejian, Guangheng Ni, Youcun Qi, and Bo Liu. "Does Subgrid Routing Information Matter for Urban Flood Forecasting? A Multiscenario Analysis at the Land Parcel Scale." Journal of Hydrometeorology 21, no. 9 (September 1, 2020): 2083–99. http://dx.doi.org/10.1175/jhm-d-20-0075.1.

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AbstractThe accessibility of high-resolution surface data enables fine distributed modeling for urban flooding. However, the surface routing processes between nonhomogeneous land cover components remain in most grid units, due to the high spatial heterogeneity of urban surfaces. Limited by the great difficulty in the acquisition, subgrid routing information (SRI) is always ignored in high-resolution urban flood modeling, and more importantly, the potential impacts of missing SRI on flood forecasting are still less understood. In this study, 54 urban-oriented scenarios of subgrid routing schemes are designed at an isolated grid, including three types of land parcels, two routing directions, and nine routing percents. The impacts of missing SRI are evaluated comprehensively under 60 different rainfall scenarios, in terms of the peak runoff (PR) and the runoff coefficient (RC). Furthermore, the influence mechanism is revealed as well to explain the discrepancy of the impacts under different conditions. Results show the missing of the routing process from impervious to pervious areas leads to significant impacts on the simulation of both PR and RC. Overestimated RC is detected, however, the impacts on PR are bidirectional depending on the rainfall intensity. Overestimation of PR due to missing SRI is observed in light rainfall events, but the opposite effect is identified under heavy rainfall conditions. This study highlights the importance of incorporating the SRI for urban flood forecasting to avoid underestimating the hazard risk in heavy rainfall. Simultaneously, it identifies that blindly utilizing infiltration-based green infrastructure is not feasible in urban stormwater management, due to the possible increase in peak runoff.

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Li, Cathy W. Y., Guy P. Brasseur, Hauke Schmidt, and Juan Pedro Mellado. "Error induced by neglecting subgrid chemical segregation due to inefficient turbulent mixing in regional chemical-transport models in urban environments." Atmospheric Chemistry and Physics 21, no. 1 (January 14, 2021): 483–503. http://dx.doi.org/10.5194/acp-21-483-2021.

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Abstract. We employed direct numerical simulations to estimate the error on chemical calculation in simulations with regional chemical-transport models induced by neglecting subgrid chemical segregation due to inefficient turbulent mixing in an urban boundary layer with strong and heterogeneously distributed surface emissions. In simulations of initially segregated reactive species with an entrainment-emission configuration with an A–B–C second-order chemical scheme, urban surface emission fluxes of the homogeneously emitted tracer A result in a very large segregation between the tracers and hence a very large overestimation of the effective chemical reaction rate in a complete-mixing model. This large effect can be indicated by a large Damköhler number (Da) of the limiting reactant. With heterogeneous surface emissions of the two reactants, the resultant normalised boundary-layer-averaged effective chemical reaction rate is found to be in a Gaussian function of Da, and it is increasingly overestimated by the imposed rate with an increased horizontal scale of emission heterogeneity. Coarse-grid models with resolutions commensurable to regional models give reduced yet still significant errors for all simulations with homogeneous emissions. Such model improvement is more sensitive to the increased vertical resolution. However, such improvement cannot be seen for simulations with heterogeneous emissions when the horizontal resolution of the model cannot resolve emission heterogeneity. This work highlights particular conditions in which the ability to resolve chemical segregation is especially important when modelling urban environments.

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Stoll, Rob, and Fernando Porté-Agel. "Surface Heterogeneity Effects on Regional-Scale Fluxes in Stable Boundary Layers: Surface Temperature Transitions." Journal of the Atmospheric Sciences 66, no. 2 (February 1, 2009): 412–31. http://dx.doi.org/10.1175/2008jas2668.1.

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Abstract Large-eddy simulation, with recently developed dynamic subgrid-scale models, is used to study the effect of heterogeneous surface temperature distributions on regional-scale turbulent fluxes in the stable boundary layer (SBL). Simulations are performed of a continuously turbulent SBL with surface heterogeneity added in the form of streamwise transitions in surface temperature. Temperature differences between patches of 6 and 3 K are explored with patch length scales ranging from one-half to twice the equivalent homogeneous boundary layer height. The surface temperature heterogeneity has important effects on the mean wind speed and potential temperature profiles as well as on the surface heat flux distribution. Increasing the difference between the patch temperatures results in decreased magnitude of the average surface heat flux, with a corresponding increase in the mean potential temperature in the boundary layer. The simulation results are also used to test existing models for average surface fluxes over heterogeneous terrain. The tested models fail to fully represent the average turbulent heat flux, with models that break the domain into homogeneous subareas grossly underestimating the heat flux magnitude over patches with relatively colder surface temperatures. Motivated by these results, a new parameterization based on local similarity theory is proposed. The new formulation is found to correct the bias over the cold patches, resulting in improved average surface heat flux calculations.

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Graham, L. P., and S. Bergström. "Land surface modelling in hydrology and meteorology – lessons learned from the Baltic Basin." Hydrology and Earth System Sciences 4, no. 1 (March 31, 2000): 13–22. http://dx.doi.org/10.5194/hess-4-13-2000.

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Abstract. By both tradition and purpose, the land parameterization schemes of hydrological and meteorological models differ greatly. Meteorologists are concerned primarily with solving the energy balance, whereas hydrologists are most interested in the water balance. Meteorological climate models typically have multi-layered soil parameterisation that solves temperature fluxes numerically with diffusive equations. The same approach is carried over to a similar treatment of water transport. Hydrological models are not usually so interested in soil temperatures, but must provide a reasonable representation of soil moisture to get runoff right. To treat the heterogeneity of the soil, many hydrological models use only one layer with a statistical representation of soil variability. Such a hydrological model can be used on large scales while taking subgrid variability into account. Hydrological models also include lateral transport of water – an imperative if' river discharge is to be estimated. The concept of a complexity chain for coupled modelling systems is introduced, together with considerations for mixing model components. Under BALTEX (Baltic Sea Experiment) and SWECLIM (Swedish Regional Climate Modelling Programme), a large-scale hydrological model of runoff in the Baltic Basin is used to review atmospheric climate model simulations. This incorporates both the runoff record and hydrological modelling experience into atmospheric model development. Results from two models are shown. A conclusion is that the key to improved models may be less complexity. Perhaps the meteorological models should keep their multi-layered approach for modelling soil temperature, but add a simpler, yet physically consistent, hydrological approach for modelling snow processes and water transport in the soil. Keywords: land surface modelling; hydrological modelling; atmospheric climate models; subgrid variability; Baltic Basin

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Huang, Maoyi, Xu Liang, and L. Ruby Leung. "A Generalized Subsurface Flow Parameterization Considering Subgrid Spatial Variability of Recharge and Topography." Journal of Hydrometeorology 9, no. 6 (December 1, 2008): 1151–71. http://dx.doi.org/10.1175/2008jhm936.1.

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Abstract Subsurface flow is an important hydrologic process and a key component of the water budget. Through its direct impacts on soil moisture, it can affect water and energy fluxes at the land surface and influence the regional climate and water cycle. In this study, a new subsurface flow formulation is developed that incorporates the spatial variability of both topography and recharge. It is shown through theoretical derivation and case studies that the power-law and exponential subsurface flow parameterizations and the parameterization proposed by Woods et al. are all special cases of the new formulation. The subsurface flows calculated using the new formulation compare well with values derived from observations at Tulpehocken Creek, Pennsylvania, and Walnut Creek, Iowa. Sensitivity studies show that when the spatial variability of topography or recharge, or both is increased, the subsurface flows increase at the two aforementioned sites and at the Maimai hillslope, New Zealand. This is likely due to enhancement of interactions between the groundwater table and the land surface that reduce the flow path. An important conclusion of this study is that the spatial variability of recharge alone, and/or in combination with the spatial variability of topography can substantially alter the behaviors of subsurface flows. This suggests that in macroscale hydrologic models or land surface models, subgrid variations of recharge and topography can make significant contributions to the grid mean subsurface flow and must be accounted for in regions with large surface heterogeneity. This is particularly true for regions with humid climate and a relatively shallow groundwater table where the combined impacts of spatial variability of recharge and topography are shown to be more important. For regions with an arid climate and a relatively deep groundwater table, simpler formulations, for example, the power law, for subsurface flow can work well, and the impacts of subgrid variations of recharge and topography may be ignored.

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RUBIN, Y., A. SUN, R. MAXWELL, and A. BELLIN. "The concept of block-effective macrodispersivity and a unified approach for grid-scale- and plume-scale-dependent transport." Journal of Fluid Mechanics 395 (September 25, 1999): 161–80. http://dx.doi.org/10.1017/s0022112099005868.

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We present a new approach for modelling macrodispersivity in spatially variable velocity fields, such as exist in geologically heterogeneous formations. Considering a spectral representation of the velocity, it is recognized that numerical models usually capture low-wavenumber effects, while the large-wavenumber effects, associated with subgrid block variability, are suppressed. While this suppression is avoidable if the heterogeneity is captured at minute detail, that goal is impossible to achieve in all but the most trivial cases. Representing the effects of the suppressed variability in the models is made possible using the proposed concept of block-effective macrodispersivity. A tensor is developed, which we refer to as the block-effective macrodispersivity tensor, whose terms are functions of the characteristic length scales of heterogeneity, as well as the length scales of the model's homogenized areas, or numerical grid blocks. Closed-form expressions are developed for small variability in the log-conductivity and unidirectional mean flow, and are tested numerically. The use of the block-effective macrodispersivities allows conditioning of the velocity field on the measurements on the one hand, while accounting for the effects of unmodelled heterogeneity on the other, in a numerically reasonable set-up. It is shown that the effects of the grid scale are similar to those of the plume scale in terms of filtering out the effects of portions of the velocity spectrum. Hence it is easy to expand the concept of the block-effective dispersivity to account for the scale of the solute body and the pore-scale dispersion.

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Bonan, Gordon B., David Pollard, and Starley L. Thompson. "Influence of Subgrid-Scale Heterogeneity in Leaf Area Index, Stomatal Resistance, and Soil Moisture on Grid-Scale Land–Atmosphere Interactions." Journal of Climate 6, no. 10 (October 1993): 1882–97. http://dx.doi.org/10.1175/1520-0442(1993)006<1882:iosshi>2.0.co;2.

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Journal articles on the topic 'Subgrid heterogeneity'

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