scholarly journals Connecting spatial moments and momentum densities

2020 ◽  
Vol 808 ◽  
pp. 135669
Author(s):  
M. Hoballah ◽  
M.B. Barbaro ◽  
R. Kunne ◽  
M. Lassaut ◽  
D. Marchand ◽  
...  
Keyword(s):  
Spatial Moments

scholarly journals Evidence of Preferential Flow Activation in the Vadose Zone via Geophysical Monitoring

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1358
Author(s):  
Lorenzo De Carlo ◽  
Kimberlie Perkins ◽  
Maria Clementina Caputo
Keyword(s):  
Preferential Flow ◽  
Water Movement ◽  
Test Site ◽  
Water Dynamics ◽  
Small Scale ◽  
Strong Impact ◽  
Aquifer Recharge ◽  
Spatial Moments ◽  
Artificial Rainfall ◽  
Preferential Pathways

Preferential pathways allow rapid and non-uniform water movement in the subsurface due to strong heterogeneity of texture, composition, and hydraulic properties. Understanding the importance of preferential pathways is crucial, because they have strong impact on flow and transport hydrodynamics in the unsaturated zone. Particularly, improving knowledge of the water dynamics is essential for estimating travel time through soil to quantify hazards for groundwater, assess aquifer recharge rates, improve agricultural water management, and prevent surface stormflow and flooding hazards. Small scale field heterogeneities cannot be always captured by the limited number of point scale measurements collected. In order to overcome these limitations, noninvasive geophysical techniques have been widely used in the last decade to predict hydrodynamic processes, due to their capability to spatialize hydrogeophysical properties with high resolution. In the test site located in Bari, Southern Italy, the geophysical approach, based on electrical resistivity tomography (ERT) monitoring, has been implemented to detect preferential pathways triggered by an artificial rainfall event. ERT-derived soil moisture estimations were obtained in order to quantitatively predict the water storage (m3m−3), water velocity (ms−1), and spread (m2) through preferential pathways by using spatial moments analysis.

scholarly journals Spatial variability and its scale dependency of observed and modeled soil moisture over different climate regions

2013 ◽  
Vol 17 (3) ◽  
pp. 1177-1188 ◽  
Author(s):  
B. Li ◽  
M. Rodell
Keyword(s):  
Soil Moisture ◽  
Spatial Variability ◽  
Land Surface ◽  
Large Scale ◽  
Warm Season ◽  
Scale Dependency ◽  
Convex Shape ◽  
Spatial Moments ◽  
Environmental Controls

Abstract. Past studies on soil moisture spatial variability have been mainly conducted at catchment scales where soil moisture is often sampled over a short time period; as a result, the observed soil moisture often exhibited smaller dynamic ranges, which prevented the complete revelation of soil moisture spatial variability as a function of mean soil moisture. In this study, spatial statistics (mean, spatial variability and skewness) of in situ soil moisture, modeled and satellite-retrieved soil moisture obtained in a warm season (198 days) were examined over three large climate regions in the US. The study found that spatial moments of in situ measurements strongly depend on climates, with distinct mean, spatial variability and skewness observed in each climate zone. In addition, an upward convex shape, which was revealed in several smaller scale studies, was observed for the relationship between spatial variability of in situ soil moisture and its spatial mean when statistics from dry, intermediate, and wet climates were combined. This upward convex shape was vaguely or partially observable in modeled and satellite-retrieved soil moisture estimates due to their smaller dynamic ranges. Despite different environmental controls on large-scale soil moisture spatial variability, the correlation between spatial variability and mean soil moisture remained similar to that observed at small scales, which is attributed to the boundedness of soil moisture. From the smaller support (effective area or volume represented by a measurement or estimate) to larger ones, soil moisture spatial variability decreased in each climate region. The scale dependency of spatial variability all followed the power law, but data with large supports showed stronger scale dependency than those with smaller supports. The scale dependency of soil moisture variability also varied with climates, which may be linked to the scale dependency of precipitation spatial variability. Influences of environmental controls on soil moisture spatial variability at large scales are discussed. The results of this study should be useful for diagnosing large scale soil moisture estimates and for improving the estimation of land surface processes.

scholarly journals Dispersion in doublet-type flows through highly anisotropic porous formations

2021 ◽  
Vol 931 ◽  
Author(s):  
Gerardo Severino
Keyword(s):  
Difficult Problem ◽  
Anisotropy Ratio ◽  
Spatial Moments ◽  
Spatial Moment ◽  
Dispersion Mechanism ◽  
Porous Formation ◽  
Perturbative Solution ◽  
Type Flow ◽  
Simplifying Assumptions ◽  
The Difference

Steady doublet-type flow takes place in a porous formation, where the log-transform $Y = \ln K$ of the spatially variable hydraulic conductivity $K$ is regarded as a stationary random field of two-point autocorrelation $\rho _Y$ . A passive solute is injected at the source in the porous formation and we aim to quantify the resulting dispersion process between the two lines by means of spatial moments. The latter depend on the distance $\ell$ between the lines, the variance $\sigma ^2_Y$ of $Y$ and the (anisotropy) ratio $\lambda$ between the vertical and the horizontal integral scales of $Y$ . A simple (analytical) solution to this difficult problem is obtained by adopting a few simplifying assumptions: (i) a perturbative solution, which regards $\sigma ^2_Y$ as a small parameter, of the velocity field is sought; (ii) pore-scale dispersion is neglected; and (iii) we deal with a highly anisotropic formation ( $\lambda \lesssim 0.1$ ). We focus on the longitudinal spatial moment, as it is of most importance for the dispersion mechanism. A general expression is derived in terms of a single quadrature, which can be straightforwardly carried out once the shape of $\rho _Y$ is specified. Results permit one to grasp the main features of the dispersion processes as well as to assess the difference with similar mechanisms observed in other non-uniform flows. In particular, the dispersion in a doublet-type flow is observed to be larger than that generated by a single line. This effect is explained by noting that the advective velocity in a doublet, unlike that in source/line flows, is rapidly increasing in the far field owing to the presence there of the singularity. From the standpoint of the applications, it is shown that the solution pertaining to $\lambda \to 0$ (stratified formation) provides an upper bound for the dispersion mechanism. Such a bound can be used as a conservative limit when, in a remediation procedure, one has to select the strength as well as the distance $\ell$ of the doublet. Finally, the present study lends itself as a valuable tool for aquifer tests and to validate more involved numerical codes accounting for complex boundary conditions.

scholarly journals Spatial variability and its scale dependency of observed and modeled soil moisture under different climate conditions

2012 ◽  
Vol 9 (9) ◽  
pp. 10245-10276 ◽  
Author(s):  
B. Li ◽  
M. Rodell
Keyword(s):  
Soil Moisture ◽  
Spatial Variability ◽  
Warm Season ◽  
Weather Conditions ◽  
Data Sets ◽  
Scale Dependency ◽  
Convex Shape ◽  
Climate Conditions ◽  
Spatial Moments

Abstract. Past studies on soil moisture spatial variability have been mainly conducted in catchment scales where soil moisture is often sampled over a short time period. Because of limited climate and weather conditions, the observed soil moisture often exhibited smaller dynamic ranges which prevented the complete revelation of soil moisture spatial variability as a function of mean soil moisture. In this study, spatial statistics (mean, spatial variability and skewness) of in situ soil moisture measurements (from a continuously monitored network across the US), modeled and satellite retrieved soil moisture obtained in a warm season (198 days) were examined at large extent scales (>100 km) over three different climate regions. The investigation on in situ measurements revealed that their spatial moments strongly depend on climates, with distinct mean, spatial variability and skewness observed in each climate zone. In addition, an upward convex shape, which was revealed in several smaller scale studies, was observed for the relationship between spatial variability of in situ soil moisture and its spatial mean across dry, intermediate, and wet climates. These climate specific features were vaguely or partially observable in modeled and satellite retrieved soil moisture estimates, which is attributed to the fact that these two data sets do not have climate specific and seasonal sensitive mean soil moisture values, in addition to lack of dynamic ranges. From the point measurements to satellite retrievals, soil moisture spatial variability decreased in each climate region. The three data sources all followed the power law in the scale dependency of spatial variability, with coarser resolution data showing stronger scale dependency than finer ones. The main findings from this study are: (1) the statistical distribution of soil moisture depends on spatial mean soil moisture values and thus need to be derived locally within any given area; (2) the boundedness of soil moisture plays a pivoting role in the dependency of soil moisture spatial variability/skewness on its mean (and thus climate conditions); (3) the scale dependency of soil moisture spatial variability changes with climate conditions.

scholarly journals Spatial structure arising from chase-escape interactions with crowding

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Anudeep Surendran ◽  
Michael J. Plank ◽  
Matthew J. Simpson
Keyword(s):  
Spatial Structure ◽  
Cell Biology ◽  
Scale Up ◽  
Interaction Strength ◽  
Distinct Species ◽  
Interspecies Interactions ◽  
Individual Based Model ◽  
Directional Bias ◽  
Spatial Moments ◽  
Individual Level

Abstract Movement of individuals, mediated by localised interactions, plays a key role in numerous processes including cell biology and ecology. In this work, we investigate an individual-based model accounting for various intraspecies and interspecies interactions in a community consisting of two distinct species. In this framework we consider one species to be chasers and the other species to be escapees, and we focus on chase-escape dynamics where the chasers are biased to move towards the escapees, and the escapees are biased to move away from the chasers. This framework allows us to explore how individual-level directional interactions scale up to influence spatial structure at the macroscale. To focus exclusively on the role of motility and directional bias in determining spatial structure, we consider conservative communities where the number of individuals in each species remains constant. To provide additional information about the individual-based model, we also present a mathematically tractable deterministic approximation based on describing the evolution of the spatial moments. We explore how different features of interactions including interaction strength, spatial extent of interaction, and relative density of species influence the formation of the macroscale spatial patterns.

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