Patch scale aggregation of heterogeneous land surface cover for mesoscale meteorological models

Theoretical studies dealing with aggregation of surface parameters at small scale are reviewed. Finding effective parameters for surface resistance is possible for most cases by taking simple geometric or arithmetic averages of the component resistances. The use of more sophisticated techniques such as the blending height improves the calculations. Resistances for heat and water vapour behave differently in heterogeneous terrain. A simple surface energy balance model is adapted to show the behaviour of the roughness length of heat and water vapour in heterogeneous terrain. It is suggested that this simple parameterization can adequately take into account the effect of variation in surface cover on the fluxes of heat and water vapour.     

The scaling characteristics of remotely-sensed variables for sparsely-vegetated heterogeneous landscapes

With increasing interest in airborne and satellite-based sensors for mapping regional and global energy balance, there is a need to determine the uncertainty involved in aggregating remotely-sensed variables [surface temperature (T_k) and reflectance (π)] and surface energy fluxes [sensible (H) and latent (λE) heat flux] over large areas. This uncertainty is directly related to two factors: (1) the nonlinearity of the relation between the sensor signal and T_k, π, H orλE; and (2) the heterogeneity of the site. In this study, we compiled several remotely-sensed data sets acquired at different locations within a semi-arid rangeland in Arizona, at a variety of spatial and temporal resolutions. These data sets provided the range of data heterogeneities necessary for an extensive analysis of data aggregation. The general technique to evaluate uncertainty was to compare remotely-sensed variables and energy balance components calculated in two ways: first, calculated at the pixel resolution and averaged to the coarser resolution; and second, calculated directly at the coarse resolution by aggregating the fine-resolution data to the coarse scale. Results showed that the error in the aggregation of T_k and π was negligible for a wide range of conditions. However, the error in aggregation of H and λE was highly influenced by the heterogeneity of the site. Errors in H larger than 50% were possible under certain conditions. The conditions associated with the largest aggregation errors in H were:

• sites which are composed of a mix of stable and unstable conditions;

• sites which have considerable variations in aerodynamic roughness, especially for highly unstable conditions where the difference between surface and air temperature is large; and

• sites which are characterized by patch vegetation, where the pixel resolution is less than or nearly-equal to the diameter of the vegetation ‘element’ (in most cases, the diameter of the dominant vegetation type or vegetation patch).

Thus, knowledge of the surface heterogeneity is essential for minimizing error in aggregation of H and λE. Two schemes are presented for quantifying surface heterogeneity as a first step in data aggregation. These results emphasized the need for caution in aggregation of energy balance components over heterogeneous landscapes with sparse or mixed vegetation types.     

Sub‐grid scale parameterization of hillslope runoff and erosion processes for catchment‐scale models of semi‐arid landscapes

The processes of hillslope runoff and erosion are typically represented at coarse spatial resolution in catchment‐scale models due to computational limitations. Such representation typically fails to incorporate the important effects of topographic heterogeneity on runoff generation, overland flow, and soil erosion. These limitations currently undermine the application of distributed catchment models to understand the importance of thresholds and connectivity on hillslope and catchment‐scale runoff and erosion, particularly in semi‐arid environments. This paper presents a method for incorporating high‐resolution topographic data to improve sub‐grid scale parameterization of hillslope overland flow and erosion models. Results derived from simulations conducted using a kinematic wave overland flow model at 0.5 m spatial resolution are used to parameterize the depth–discharge relationship in the overland flow model when applied at 16 m resolution. The high‐resolution simulations are also used to derive a more realistic parameterization of excess flow shear stress for use in the 16 m resolution erosion model. Incorporating the sub‐grid scale parameterization in the coarse‐resolution model (16 m) leads to improved predictions of overland flow and erosion when evaluated using results derived from high‐resolution (0.5 m) model simulations. The improvement in performance is observed for a range of event magnitudes and is most notable for erosion estimates due to the non‐linear dependency between the rates of erosion and overland flow. Copyright © 2013 John Wiley & Sons, Ltd.     

The production of digital elevation models for experimental model landscapes

Automated digital photogrammetry was used to produce digital elevation models of experimental model landscapes under controlled laboratory conditions as part of a series of rainfall erosion experiments looking at the evolution of landforms in response to erosion. The method allowed the elevations of the experimental landscapes to be studied in great detail on a regular grid digital terrain map with relatively very little effort. Digital photogrammetry produced elevation data at a resolution of 6 mm with a standard deviation of 2·0 mm over an experimental catchment relief of approximately 200 mm; this resolution is considerably better than that achievable by conventional manual photogrammetry. The density of grid points was sufficiently high that small‐scale details such as knickpoints developing in channels were represented. The method can facilitate the study of both experimental and natural landscapes in great detail. Copyright © 2001 John Wiley & Sons, Ltd.     

Partial analysis applied to scale problems in surface moisture fluxes

Partial analysis is applied to the problem of predicting the moisture fluxes of infiltraton and evaporation at land surfaces. The discussion covers the widely different scales of the soil particle, a soil pedon, a field, a basin and a biome. It is suggested that simplified models can be used at these different scales to provide bounding solutions to the integrated behaviour of land surface fluxes of interest in linking hydrologic models and general circulation climate models.     

DTM resolution controls the accuracy of estimating surface runoff indicators in flat,lowland landscapes

Surface runoff plays an important role in contaminant transport, nutrient loss, soil erosion and peak discharges in streams and rivers. Because it is the result of a variety of complex hydrological processes, estimating surface runoff using physically based hydrological models is challenging. Upscaling of physical soil properties is necessary to cope with the limits of computational power in surface runoff modelling. In flat landscapes, the (micro)topographic surface controls the onset and progression of surface runoff on saturated soils during rain events. Therefore, its proper representation is crucial when attempting to model and predict surface runoff. In this study, the influence of microtopography (centimetre scale) on estimations of maximum depression storage (MDS), random roughness (RR) and the connectivity threshold (CT) is explored. These properties are selected because they often serve as surface runoff indicators in hydrological modelling. To characterize microtopography, a terrestrial laser scanner (TLS) is used to generate a digital terrain model (DTM) of the study site with a horizontal spatial resolution of 5 cm. MDS, RR and CT are then calculated and compared to the values generated from the publicly available Dutch national DTM dataset with a resolution of 50 cm. Our results show considerable differences in MDS, RR and CT when calculated for the different input resolution datasets. Using DTMs that do not sufficiently capture microtopography leads to underestimation of MDS and RR, and to overestimation of CT. Our findings indicate that surface runoff indicators, and thereby the surface runoff response of a saturated surface to rainfall events, are defined at scales smaller than the scales of typically available DTMs. Understanding surface runoff through modelling studies therefore requires a framework that accounts for this lack of information arising from using coarser resolution DTMs. We demonstrate a linear relationship between MDS values generated from the different resolution DTMs. This opens the possibility of using empirical scaling relationships between high- and lower-resolution DTMs to account for microtopography. Repetition of our measurements on similar surfaces would contribute to establishing such empirical scaling relationships. Our results should be seen as indicative of flat landscapes and surfaces where centimetre scale microtopography is relevant.     

Modelling water fluxes for the analysis of diffuse pollution at the river basin scale

Diffuse pollution is a significant and sometimes even major component of surface water pollution. Diffuse inputs of pollutants to the surface water are related to runoff of precipitation. This means that the analysis of diffuse pollutant fluxes from the land surface to the surface water requires an analysis of water fluxes. In this paper we have modelled the average long‐term total runoff, groundwater recharge index and groundwater residence times for two large European river basins (Rhine and Elbe). We applied and compared two independently developed and recently published methods. We found that with the available large‐scale databases and methods we could simulate successfully the regional patterns of the average long‐term total runoff. The reported groundwater recharge indices and groundwater residence times should be interpreted as estimates based on available knowledge and databases. They do not represent absolute values, but illustrate the possible travel times and spatial patterns of the different runoff components that have to be taken into account for the analysis of diffuse pollution at large regional and temporal scales. Copyright © 2000 John Wiley & Sons, Ltd.     

River profile evolution by plucking in lithologically heterogeneous landscapes: Uniform uplift vs. tilting

Recent studies provide a theoretical framework for understanding the incision of bedrock rivers by plucking. These studies motivated the development of a numerical model that simulates plucking to explore the evolution of channel profiles in lithologically diverse terrain. In the main governing equation, the incision rate is calculated as a function of the difference between the boundary shear stress and a threshold shear stress needed to entrain blocks from the bed. Because an earlier study suggested that plucking is the primary incisional process in the northern Sierra Nevada (CA), the model was calibrated to approximate the conditions in the region. The profiles of the simulated rivers are stair-stepped, with sharp breaks-in-slope at lithological boundaries. This characteristic is common to rivers draining the northern Sierra Nevada, suggesting that the size of blocks available for plucking, as mediated by the fracture density, may be the primary control on their gradients. Moreover, the numerical experiments highlight the role of threshold shear stresses in the post-orogenic persistence of steep reaches and relict terrain. Finally, comparisons of profiles evolved under tilting or uniform uplift scenarios provide insights into how these different uplift modes affect profile evolution. For example, whereas uniform uplift generates a single migrating knickpoint at the range front, multiple migrating knickpoints can form simultaneously along a river in a tilting landscape. © 2020 John Wiley & Sons, Ltd.     

An improved approach for assigning pumping rates to heterogeneous aquifer models

A common assumption of ground water models formulated using a block-centered finite-difference method is that a well is located at the center of a cell regardless of its actual location. Due to this assumption, errors are introduced in the spatial distribution of simulated heads. This paper presents an alternative approach for assigning the pumping rates of wells that are located off cell centers. This approach consists of assigning the pumping rate not only to the cell in which the well is located but also to adjacent cells, taking into account the length of the well screen, the hydraulic conductivity, and the distance from the well to the center of its cell. The advantage of this alternative approach over the conventional one is illustrated with a test problem of a synthetic aquifer. Statistical measures of error indicate a much better model fit when pumping rates of wells are distributed over several cells.     

Regional estimation of catchment‐scale soil properties by means of streamflow recession analysis for use in distributed hydrological models

The estimation of catchment‐scale soil properties, such as water storage capacity and hydraulic conductivity, is of primary interest for the implementation of distributed hydrological models at the regional scale. This estimation is generally performed on the basis of information provided by soil databases. However, such databases are often established for agronomic uses and generally do not document deep‐weathered rock horizons (i.e. pedologic horizons of type C and deeper), which can play a major role in water transfer and storages. Here, we define the Drainable Storage Capacity Index (DSCI), an indicator that relies on the comparison between cumulated streamflow and precipitation to assess catchment‐scale storage capacities. DSCI is found to be reliable to detect underestimation of soil storage capacities in soil databases. We also use the streamflow recession analysis methodology defined by Brutsaert and Nieber in 1977 to estimate water storage capacities and lateral saturated hydraulic conductivities of the nondocumented deep horizons. The analysis is applied to a sample of 23 catchments (0.2–291 km²) located in the Cévennes‐Vivarais region (south of France). For regionalization purposes, the obtained results are compared with the dominant catchment geology and present a clear hierarchy between the different geologies of the area. Hard crystalline rocks are found to be associated with the thickest and less conductive deep soil horizons. Schist rocks present intermediate values of thickness and of saturated hydraulic conductivity, whereas sedimentary rocks and alluvium are found to be less thick and most conductive. These results are of primary interest in view of the future set‐up of distributed hydrological models over the Cévennes‐Vivarais region. Copyright © 2013 John Wiley & Sons, Ltd.     

Variations in the solar fluxes of helium and protons on the long-term scale

A reconstruction of data on ancient (to ～600 Ma ago) solar fluxes of protons and helium has been performed on the basis of isotopic investigations of helium and neon in lunar soil samples from columns delivered by the automatic stations Luna-16 and Luna-24 in 1970 and 1976. Recent investigations have shown the presence of long-term climate variations, which can be explained in the context of solar-terrestrial links. However, the “space” impact, simultaneously with the Sun’s influence on the Earth, takes place in the form of cosmic ray irradiation and as an influence on the Earth that is exerted by the flux of cosmic dust and meteorites (including the very large ones at the early stage of the Earth evolution). Therefore the existence of long-term variability of solar corpuscular fluxes may serve as direct evidence of the manifestation of solar-terrestrial links. The possibility of finding these links appears on the basis of the revealed variations of solar wind fluxes with an age from the contemporary level to the level of ～600 Ma ago.     

Two-dimensional models of elastic tides in a horizontally heterogeneous medium

The possibility of determining local horizontal inhomogeneities of the shear and bulk moduli from data on amplitudes and phases of tidal tilts and strains is considered. Simple analytical formulas determining the sought effects are derived by the perturbation method, and their numerical estimates are determined for the simplest 2-D models. It is shown that relative variations in the shear and bulk moduli affect not only the amplitudes and phases of variations in tidal parameters but also the shape of curves of tidal amplitude anomalies versus the horizontal coordinate. Given adequate spatial resolution, this can significantly facilitate the elastic moduli inversion from tidal data.     

Simulating low flows over a heterogeneous landscape in southeastern Poland

This paper presents a scheme describing low flow formation processes in areas with different environmental conditions, including the impact of the selection and explanatory power of predictors for a probabilistic model based on the Logit model. The research was carried out using 29 daily streamflow gauges located in the Lublin region of southeastern Poland for the hydrological period 1976–2018. Analysis resulted in two distinct low flow schemes. In the lowland rivers, low flows occur during the warm season and are related to evaporation exceeding precipitation. In the upland rivers, hydrogeological factors related to water levels in the local Cretaceous aquifers determine the occurrence of low flows. This differentiation affects the quality of the predictive models. For lowland rivers, models based on the climatic water balance with a monthly shift have a better fit, while these models used for upland rivers are characterized by an approximately 10% decrease in accuracy. For upland rivers, the combined C_tH_t models without shifts produce the best model fit. The generalized precision of the Logit models is around 80%–90%.     

Field scale impacts of spatially correlated relative permeability in heterogeneous multiphase systems

Two-dimensional numerical simulations of two-phase (DNAPL-water) flow in spatially correlated random fields demonstrate the influence of nonwetting phase (NWP) relative permeability–saturation (k_r,N–S_W) relationships correlated to porous media intrinsic permeability (k). Both the volume of porous media invaded by the NWP and the length of time during which the NWP is migrating are under predicted if k_r,N–k correlation is not accounted for in the model formulation. Not accounting for the k_r,N–k correlation resulted in under predicting the volume of porous media invaded by up to approximately 10%, which is likely not significant for many practical applications. However, not accounting for the k_r,N–k correlation resulted in under predicting field scale migration times by up to a factor of 4, which is likely significant in that the migration times are on the order of years to several decades for the DNAPL (1,2-DCE) considered in this study. The under prediction of migration times was greater for lower permeability aquifers.     

三维非均匀地质模型中的逐段迭代射线追踪

地震射线追踪是地震定位、层析成像、偏移等领域的重要正演环节.随着这些领域研究的深入,针对传统的网格结构和层状结构在描述复杂地质模型遇到的很大困难,我们采用大小不等、形状各异的地质块组成的集合体来描述三维复杂地质模型,并用三角形面片来描述地质块之间的物性间断面,理论上可以描述任意复杂的地质模型.为适应任意非均匀速度分布的地质模型,基于费马原理,本文发展了与之相适应的逐段迭代射线追踪方法.该方法属于弯曲法范畴,对路径点采用一阶显式增量修正,相对于传统的迭代法,高效省时.数值试验表明,联合逐段迭代法和伪弯曲法的射线追踪扰动修正方案在三维复杂非均匀块状模型中有适用性和高效性.     

Propagation of love waves in a medium containing a heterogeneous layer lying over a heterogeneous half space

Summary Propagation and the dispersion equation of love waves for a few generalised models of heterogeneous crust over a heterogeneous mantle have been investigated. Dispersion equations obtained by a few earlier authors have been shown to be the special cases of the above results.     

Determination of regional land surface heat fluxes over a heterogeneous landscape of the Jiddah area of Saudi Arabia by using Landsat‐7 ETM data

In this study, a parameterization method based on Landsat‐7 Enhanced Thematic Mapper (ETM) data and field observations is presented and tested for deriving the regional land surface variables, vegetation variables and land surface heat fluxes over a heterogeneous landscape. As a case study, the method and two Landsat‐7 ETM images are applied to the Jiddah area of Saudi Arabia. The regional distribution maps of surface reflectance, normalized difference vegetation index, modified soil adjusted vegetation index (MSAVI), vegetation coverage, leaf area index, surface temperature, net radiation flux, soil heat flux, sensible heat flux and latent heat flux have been determined over the Jiddah area. The derived results have been validated by using the ‘ground truth’. The results show that the more reasonable regional distributions of land surface variables (surface reflectance, surface temperature), vegetation variables (MSAVI and vegetation coverage), net radiation, soil heat flux and sensible heat flux can be obtained by using the method proposed in this study. Further improvement of the method is also discussed. Copyright © 2006 John Wiley & Sons, Ltd.