Academic literature on the topic 'Subgrid heterogeneity'

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.

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.

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.

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.

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.

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.

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.

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.

[Truncated abstract] The balance equations of mass and momentum, defined at the scale of what has been defined as a Representative Elementary Watershed (REW) has been proposed by Reggiani et al. (1998, 1999). While it has been acknowledged that the REW approach and the associated balance equations can be the basis for the development of a new generation of distributed physically based hydrological models, four building blocks have been identified as necessary to transform the REW approach into, at the very least least, a workable modelling framework beyond the theoretical achievements. These are: 1) the development of reasonable closure relations for the mass exchange fluxes within and between various REW sub-regions that effectively parameterize the effects of sub-REW heterogeneity of climatic and landscape properties, 2) the design of numerical algorithms capable of generating numerical solutions of the REW-scale balance equations composed of a set of coupled ordinary differential and algebraic equations for the number of REWs constituting a study catchment and the sub-regions within the REWs, 3) applications of the resulting numerical model to real catchments to assess its performance in the prediction of any specified hydrological variables, and 4) the assessment of the model reliability through estimation of model predictive uncertainty and parameter uncertainty. This thesis is aimed at making substantial progress in developing each of these building blocks. Chapter 1 presents the background and motivation for the thesis, while Chapter 2 summarizes its main contributions. Chapter 3 presents a description of the closure problem that the REW approach faces, and presents and implements various approaches to develop closure relations needed for the completeness of balance equations of the REW approach. ... In addition, Chapter 4 also shows an initial application of CREW to a small catchment, Susannah Brook in the south-west of Western Australia. Chapter 5 presents the application of CREW to two meso-scale catchments in Australia, namely Collie and Howard Springs, located in contrasting climates. Chapter 6 presents results of the estimation of predictive uncertainty and parameter sensitivity through the application of CREW to two catchments in Australia, namely Susannah Brook and Howard Springs, by using the Generalized Likelihood Uncertainty Estimation (GLUE) methodology. Finally, Chapter 7 presents recommendations for future work for the further advancement of the REW approach. Through these exercises this PhD thesis has successfully transformed the REW-scale coupled balance equations derived by Reggiani et al. (1998, 1999) into a new, well tested numerical model blueprint for the development and implementation of distributed, physically based models applicable at the catchment, or REW scale.

Le transfert radiatif est crucial dans la modélisation de l’atmosphère, du climat, et pour la simulation du changement climatique. Les calculs de flux radiatifs au sommet de l’atmosphère et en surface permettent notamment d’estimer le bilan énergétique de la planète, grandeur dont la bonne estimation est une contrainte importante dans les simulations climatiques. De nombreux éléments interagissent avec le rayonnement dans l’atmosphère : gaz, aérosols, nuages, et différents types de surfaces (végétation, océans, neige...). Ces différents composants ne se comportent pas de la même façon avec le rayonnement solaire, dont la source est le soleil, et avec le rayonnement infrarouge, dont la source est la surface terrestre ainsi que l’atmosphère elle-même. Dans ces deux situations, les nuages, composés de gouttelettes d’eau liquide et/ou de cristaux d’eau solide, représentent une difficulté importante de modélisation. Les nuages sont des objets complexes, de part leur composition, leur géométrie, et leurs interactions multiples avec le rayonnement. L’interaction nuage-rayonnement est étudiée depuis de nombreuses années, et il a été démontré qu’elle représente un des obstacles les plus importants à l’amélioration des modèles globaux de simulation du climat. Dans cette thèse, nous nous intéressons à un des aspects clé dans la représentation de l’effet des nuages sur le rayonnement : le recouvrement vertical des nuages. Cette notion est en effet liée de manière directe à la couverture nuageuse, grandeur de premier ordre dans le calcul de l’albedo d’une scène nuageuse. Dans le cadre du recouvrement vertical des nuages, nous mettons en place un formalisme permettant d’explorer en profondeur différentes hypothèses de recouvrement des nuages, en particulier le recouvrement exponentiel-aléatoire. Nous montrons que cette hypothèse de recouvrement peut, sous certaines conditions, permettre une très bonne représentation des propriétés des nuages, à la fois géométriques et radiatives, même à partir d’un profil vertical nuageux de résolution grossière. Nous démontrons que la variabilité verticale sous-maille de la fraction nuageuse, bien que non prise en compte par les modèles atmosphériques grande échelle, peut avoir un impact significatif sur les flux solaires calculés au sommet de l’atmosphère. La prise en compte rigoureuse de la résolution verticale par le recouvrement est également un facteur important. Dans un second temps, nous incorporons ces résultats dans un code de transfert radiatif par Monte Carlo (RadForce). L’utilisation de ce nouvel algorithme, qui utilise par ailleurs une approche raie-par-raie pour les différents gaz atmosphériques, nous permet d’estimer l’altitude d’émission de chaque composant présent dans l’atmosphère. Ces nouveaux outils nous permettent d’analyser de manière nouvelle des forçages radiatifs liés aux gaz à effet de serre, ainsi que l’impact de la prise en compte du recouvrement vertical des nuages<br>Radiative transfer is a crucial process in atmospheric and climate modelling, as well as for climate change simulations. Computations of radiative fluxes at the top of the atmosphere and at the surface allow us to estimate the radaitive budget of the planet, which is very important to represent correctly when it comes to climate simulations. Many elements interact with the radiation in the atmosphere : gases, aerosols, clouds, and different types of surfaces (vegetation, oceans, snow...). These different components do not interact in the same way with solar radiation, that comes from the sun, and with infrared radiation, that comes from the earth’s surface and the atmosphere itself. In both situations, clouds, composed of liquid water droplets and/or solid water crystals, represent an important modeling difficulty. Clouds are complex objects, because of their composition, their geometry, and their multiple interactions with the radiation field. Cloud-radiation interaction has been studied for many years, and it has been shown that it represents one of the most important obstacles to the improvement of global climate models. In this work, we focus on one of the key aspects in the representation of the effect of clouds on radiation : vertical cloud overlap. This notion is indeed directly linked to the cloud cover, which is a quantity of first order importance in the calculation of the albedo of a cloud scene. Within the framework of the vertical cloud overlap, we develop a formalism allowing us to explore in depth various hypotheses of cloud overlap, in particular exponential-random overlap. We show that this overlap hypothesis can, under certain conditions, allow a very good representation of cloud properties, both geometric and radiative, even from a coarse resolution vertical cloud profile. We show that the vertical subgrid variability of the cloud fraction, although not taken into account by large-scale atmospheric models, can have a significant impact on the solar fluxes calculated at the top of the atmosphere. The rigorous consideration of vertical resolutions by the overlap is also an important factor. We then focus on incorporating these overlap results into a Monte Carlo radiative transfer code (RadForce). The use of this new algorithm, which also uses a line-by-line approach for the different atmospheric gases, allows us to model the emission altitudes of each atmospheric component. These new tools allow us to analyze in a new way the radiative forcings linked to greenhouse gases, as well as the impact of taking into account the vertical overlap of clouds and their vertical subgrid heterogeneity

This chapter deals with computing the velocity fields in heterogeneous media. This is a broad area, and we shall concentrate here on upscaling, on the spatial correlation pattern of the velocity, and on accuracy measures for techniques that compute velocity fields. Numerical simulations of velocity fields in heterogeneous media (Ababou et al., 1988, 1989; Bellin et al., 1992, 1994; Bellin and Rubin, 1996; Dykaar and Kitandis, 1992a,b; Hassan et al., 1998a,b; Salandin and Fiorotto, 1998) indicate that to capture accurately the effects of the spatial variability of the conductivity on the velocity field, the conductivity field should be modeled with high resolution. Techniques for generating highly detailed realizations of rock properties were reviewed earlier. Because of the huge level of detail included in these realizations, large-scale flow simulations can become computationally intensive. However, the need for fine detail varies over the aquifer. For example, a high level of detail is needed where the velocity field may vary rapidly, such as near wells, or over areas traversed by a contaminant plume, or for describing small-scale features which dominate the flow, such as high-conductivity channels. Coarsening the grid over areas where high resolution is unnecessary can reduce the computational effort. To be able to do that, a procedure is needed for assigning properties such as conductivity on a coarser scale which is more appropriate for simulation, while avoiding the loss of important details. Such a procedure is called upscaling (also scale-up). Upscaling assigns properties to blocks based on subgrid-scale heterogeneity. Upscaling leads to block-effective properties. Unlike effective properties, block-effective properties depend on the size of the block. In the limit of block dimensions much larger than the integral scale of the heterogeneity, the block-effective properties become equal to the media's effective properties. Unlike the case of effective conductivities, there is no consensus about the definition of block conductivity. For example, Rubin and Gomez-Hernandez (1990) defined the block conductivity as the coefficient of proportionality between the block-averaged flux and the gradient. Indelman and Dagan (1993a, b) stipulated that the block-effective conductivity should dissipate energy at a rate equal to the dissipation due to the small-scale heterogeneity.

Spatial variability and the uncertainty in characterizing the flow domain play an important role in the transport of contaminants in porous media: they affect the pathlines followed by solute particles, the spread of solute bodies, the shape of breakthrough curves, the spatial variability of the concentration, and the ability to quantify any of these accurately. This chapter briefly reviews some basic concepts which we shall later employ for the analysis of solute transport in heterogeneous media, and also points out some issues we shall address in the subsequent chapters. Our exposition in chapters 8-10 on contaminant transport is built around the Lagrangian and the Eulerian approaches for analyzing transport. The Eulerian approach is a statement of mass conservation in control volumes of arbitrary dimensions, in the form of the advection-dispersion equation. As such, it is well suited for numerical modeling in complex flow configurations. Its main difficulties, however, are in the assignment of parameters, both hydrogeological and geochemical, to the numerical grid blocks such that the effects of subgrid-scale heterogeneity are accounted for, and in the numerical dispersion that occurs in advection-dominated flow situations. Another difficulty is in the disparity between the scale of the numerical elements and the scale of the samples collected in the field, which makes the interpretation of field data difficult. The Lagrangian approach focuses on the displacements and travel times of solute bodies of arbitrary dimensions, using the displacements of small solute particles along streamlines as its basic building block. Tracking such displacements requires that the solute particles do not transfer across streamlines. Since such mass transfer may only occur due to pore-scale dispersion, Lagrangian approaches are ideally suited for advection-dominated situations. Let us start by considering the displacement of a small solute body, a particle, as a function of time. “Small” here implies that the solute body is much smaller than the characteristic scale of heterogeneity. At the same time, to qualify for a description of its movement using Darcy’s law, the solute body also needs to be larger than a few pores. The small dimension of the solute body ensures that it moves along a single streamline and that it does not disintegrate due to velocity shear.

We study turbulent flow over surfaces with varying roughness scales, using large eddy simulation (LES). The goal is to use LES results to formulate effective boundary conditions in terms of effective roughness height and blending height, to be used for RANS. The LES are implemented with the dynamic Smagorinsky model based on the Germano identity. However, as is well-known, when this identity is applied locally, it yields a coefficient with unphysically strong fluctuations and averaging is needed for better realism and numerical stability. The traditional approach consists of averaging over homogeneous directions, for example horizontal planes in channel flow. This requirement for homogeneous directions in the flow field and the concomitant inability to handle complex geometries renders the use of this model questionable in studying the effect of surface heterogeneity. Instead, a new version of the Lagrangian dynamic subgrid-scale (SGS) model [1] is implemented. A systematic set of simulations of flow over patches of differing roughness is performed, covering a wide range of patch length scales and surface roughness values. The simulated mean velocity profiles are analyzed to identify the height of the blending layer and used to measure the effective roughness length. Extending ideas introduced by Miyake [2] and Claussen [3], we have proposed a simple expression for effective surface roughness and blending height knowing local surface patch roughness values and their lengths [4]. Results of the model agreed well with the LES results when the heterogeneous surface consisted of patches of equal sizes. The model is tested here for surfaces with patches of different sizes.