An improved method for single flow direction calculation in grid digital elevation models

This paper presents improvements to the global D8 (GD8) method for calculating single flow directions in a grid digital elevation model. Flow directions computed from grid digital elevation models serve as the foundation for much of the analysis and modeling of hydrological processes that are driven by topographic gradients. The literature includes both single flow direction methods, where flow goes to only one downslope cell, and multiple flow direction methods that apportion flow among multiple downslope cells. Among single flow direction methods, the standard D8 method, in which the flow direction is set based on the steepest local slope, results in bias on surfaces that do not align with the grid directions. Efforts to address this problem have led to the development of extended methods that account for elevation values further upslope in determining flow directions. We have identified discrepancies in one such method, GD8, and have examined ways to resolve these discrepancies. An improvement to GD8, named iGD8, is presented that allows replacing a reference cell from which path deviations are accumulated and that considers horizontal path deviation rather than global slope as a flow direction criterion. The improved method is found to be effective in resolving the problems encountered with GD8 and to be more efficient than a previously proposed alternative method (least transversal deviation (LTD) based D8, namely D8‐LTD) that uses recursive searching for the largest upstream area when multiple flow paths converge. The proposed improved GD8 method offers the opportunity for improved analysis and modeling of topographically driven hydrological processes by providing better foundational flow directions for these analyses.     

Improvement of surface run‐off in the hydrological model ParFlow by a scale‐consistent river parameterization

We propose an improvement of the overland‐flow parameterization in a distributed hydrological model, which uses a constant horizontal grid resolution and employs the kinematic wave approximation for both hillslope and river channel flow. The standard parameterization lacks any channel flow characteristics for rivers, which results in reduced river flow velocities for streams narrower than the horizontal grid resolution. Moreover, the surface areas, through which these wider model rivers may exchange water with the subsurface, are larger than the real river channels potentially leading to unrealistic vertical flows. We propose an approximation of the subscale channel flow by scaling Manning's roughness in the kinematic wave formulation via a relationship between river width and grid cell size, following a simplified version of the Barré de Saint‐Venant equations (Manning–Strickler equations). The too large exchange areas between model rivers and the subsurface are compensated by a grid resolution‐dependent scaling of the infiltration/exfiltration rate across river beds. We test both scaling approaches in the integrated hydrological model ParFlow. An empirical relation is used for estimating the true river width from the mean annual discharge. Our simulations show that the scaling of the roughness coefficient and the hydraulic conductivity effectively corrects overland flow velocities calculated on the coarse grid leading to a better representation of flood waves in the river channels.     

Comparison of the performance of flow‐routing algorithms used in GIS‐based hydrologic analysis

Flow direction and specific catchment area were calculated for different flow‐routing algorithms using TAPES‐G and TauDEM. A fuzzy classification was used along with eight topo–climatic attributes to delineate six landscape classes from a 10‐m USGS DEM. A series of maps and tabular outputs were produced to compare flow‐routing predictions in different parts of the study area in the Santa Monica Mountains of southern California. The matched pair t‐test was used to compare the performance of pairs of specific catchment area grids across six user‐defined fuzzy landscape classes. The results show that (1) the ‘source’ cells predicted with the D∞, DEMON, and FD8 algorithms were confined to hilltops; (2) two single flow‐routing algorithms (Rho8, D8) produced poor results; and (3) the choice of flow‐routing algorithm has potentially important consequences for the calculation of upslope contributing areas, sediment transport capacity, topographic wetness, and several other topographic indices. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of pit removal methods on river network position

Digital elevation models often contain depressions that result in areas described as having no drainage, referred to as sinks or pits. These depressions disrupt the drainage surface, which disrupt routing of flow over the surface. Most of the attributes that can be extracted from a digital elevation model rely on flow‐routing algorithms to calculate the upslope contributing area. There is little information on the influence of the various algorithms on the position and on the connectivity of the extracted networks. The aim of this study was to assess the effects of pit removal methods, data sources and flow‐routing algorithms on the position of river networks. The results show that all factors and methods have an impact on the position of the extracted networks. The pit removal method combining filling and carving extracted river networks closer to the reference, as well the elevation models with higher resolution. Single‐flow direction methods provided more accurate positioning of river network, in this test area where the drainage is generally well defined. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimization of Cell Parameterizations for Tomographic Inverse Problems

—?We develop algorithms for the construction of irregular cell (block) models for parameterization of tomographic inverse problems. The forward problem is defined on a regular basic grid of non-overlapping cells. The basic cells are used as building blocks for construction of non-overlapping irregular cells. The construction algorithms are not computationally intensive and not particularly complex, and, in general, allow for grid optimization where cell size is determined from scalar functions, e.g., measures of model sampling or a priori estimates of model resolution. The link between a particular cell j in the regular basic grid and its host cell k in the irregular grid is provided by a pointer array which implicitly defines the irregular cell model. The complex geometrical aspects of irregular cell models are not needed in the forward or in the inverse problem. The matrix system of tomographic equations is computed once on the regular basic cell model. After grid construction, the basic matrix equation is mapped using the pointer array on a new matrix equation in which the model vector relates directly to cells in the irregular model. Next, the mapped system can be solved on the irregular grid. This approach avoids forward computation on the complex geometry of irregular grids. Generally, grid optimization can aim at reducing the number of model parameters in volumes poorly sampled by the data while elsewhere retaining the power to resolve the smallest scales warranted by the data. Unnecessary overparameterization of the model space can be avoided and grid construction can aim at improving the conditioning of the inverse problem. We present simple theory and optimization algorithms in the context of seismic tomography and apply the methods to Rayleigh-wave group velocity inversion and global travel-time tomography.     

Impact of grid resolution on the integrated and distributed response of a coupled surface–subsurface hydrological model for the des Anglais catchment,Quebec

Digital elevation models (DEMs) at different resolutions (180, 360, and 720 m) are used to examine the impact of different levels of landscape representation on the hydrological response of a 690‐km² catchment in southern Quebec. Frequency distributions of local slope, plan curvature, and drainage area are calculated for each grid size resolution. This landscape analysis reveals that DEM grid size significantly affects computed topographic attributes, which in turn explains some of the differences in the hydrological simulations. The simulations that are then carried out, using a coupled, process‐based model of surface and subsurface flow, examine the effects of grid size on both the integrated response of the catchment (discharge at the main outlet and at two internal points) and the distributed response (water table depth, surface saturation, and soil water storage). The results indicate that discharge volumes increase as the DEM is coarsened, and that coarser DEMs are also wetter overall in terms of water table depth and soil water storage. The reasons for these trends include an increase in the total drainage area of the catchment for larger DEM cell sizes, due to aggregation effects at the boundary cells of the catchment, and to a decrease in local slope and plan curvature variations, which in turn limits the capacity of the watershed to transmit water downslope and laterally. The results obtained also show that grid resolution effects are less pronounced during dry periods when soil moisture dynamics are mostly controlled by vertical fluxes of evaporation and percolation. Copyright © 2010 John Wiley & Sons, Ltd.     

Hydraulic model tests for evaluating sediment control function with a grid-type Sabo dam in mountainous torrents

There are two kinds of Sabo dams in order to control sediment transport by debris flow and flash floods in mountainous area, which are closed and open-type＇s dams. In Japan, open-type＇s Sabo dams are constructed taking into account the continuity of sediment routing from upstream to downstream reach in a basin. A plan to construct a 20 m high grid-type Sabo dam which can capture a sediment volume of 400,000 m3 is proposed in the Amahata river basin in Japan. Hydraulic model tests are conducted to decide on the section for a dam （Section A, B） and the grid size such as clearance of vertical/horizontal bars for evaluating the plan. Several runs of flume tests are conducted and the sediment control function of the Sabo darn is discussed using several experimental data such as dimensionless sediment runoff rate from Sabo dam, temporal changes of bed profile and mean diameter and so on. It was found that sediment deposition in sediment storage area of Sabo dam was affected by curved channel, and that next the grid size of steel bars and thirdly the section of a dam was able to capture sediment in storage area of Sabo dam. Sediment was controlled well in the section B and in the grid size of 1.0×d95, and the problems related to sediment runoffafter sediment capturing in Sabo dam are pointed out.     

Simulating the surface waters of the Amazon River basin: impacts of new river geomorphic and flow parameterizations

This paper describes the impacts of new river geomorphic and flow parameterizations on the simulated surface waters dynamics of the Amazon River basin. Three major improvements to a hydrologic model are presented: (1) the river flow velocity equation is expanded to be dependent on river sinuosity and friction in addition to gradient forces; (2) equations defining the morphological characteristics of the river, such as river height, width and bankfull volume, are derived from 31 622 measurements of river morphology and applied within the model; (3) 1 km resolution topographic data from the Shuttle Radar Topography Mission (SRTM) are used to provide physically based fractional flooding of grid cells from a statistical representation of sub‐grid‐scale floodplain morphology. The discharge and floodplain inundation of the Amazon River is simulated for the period 1968–1998, validated against observations, and compared with results from a previous version of the model. These modifications result in considerable improvement in the simulations of the hydrological features of the Amazon River system. The major impact is that the average wet‐season flooded area on the Amazon mainstem for the period 1983–1988 is now within 5% of satellite‐derived estimates of flooded area, whereas the previous model overestimates the flooded area by about 80%. The improvements are a consequence of the new empirical river geomorphologic functions and the SRTM topography. The new formulation of the flow velocity equation results in increased river velocity on the mainstem and major tributaries and a better correlation between the mean monthly simulated and observed discharge. Copyright © 2007 John Wiley & Sons, Ltd.     

A comparison of hillslope drainage area estimation methods using high-resolution DEMs with implications for topographic studies of gullies

Topographic models provide a useful tool for understanding gully occurrence in the landscape but require reliable estimates of gully head drainage areas. Modern high-resolution topography data (collected using structure from motion photogrammetry or light detection and ranging) is increasingly used for topographic studies of gullies, but little work has been done to assess the variability of gully head drainage area estimates using different methods. This study evaluated alternative approaches to using high-resolution digital elevation models (DEMs) so that gully topographic models can be more readily applied to any area with suitably high-resolution data. Specifically, we investigated the impact of single- or multiple-direction flow routing algorithms, DEM hydrologic-enforcement procedures and spatial resolution on gully head drainage area estimation. We tested these methods on a 40 km² site centred on Weany Creek, a low-relief semi-arid landscape draining towards the Great Barrier Reef, Australia. Using a subroutine to separate gully heads into those with divergent or convergent flow patterns upslope, we found that divergent flow conditions occurred at half of 484 studied gullies. Drainage areas estimated by different flow routing algorithms were more variable in these divergent cases than for convergent cases. This variation caused a significant difference between topographic threshold parameters (slope b and intercept k) derived from single- or multiple-direction flow routing algorithms, respectively. Different methods of hydrologic enforcement (filling or breaching) also affected threshold analysis, resulting in estimates of the exponent b being ~188% higher if the DEM was filled than if breached. The testing of the methods to date indicates that a finer resolution (≤2 m) DEM and a multiple-direction flow routing algorithm achieve the most realistic drainage area estimates in low-relief landscapes. For Weany Creek we estimated threshold parameters k = 0.033 and b = 0.189, indicating that it is highly susceptible to gully erosion.     

The variability in the morphological active width: Results from physical models of gravel‐bed braided rivers

The morphological active width, defined as the lateral extent of bed material displacement over time, is a fundamental parameter in multi‐threaded gravel‐bed rivers, linking complex channel dynamics to bedload transport. Here, results are presented from five constant discharge experiments, and three event hydrographs, covering a range of flow strengths and channel configurations for which morphological change, bedload transport rates, and stream power were measured in a physical model. Changes in channel morphology were determined via differencing of photogrammetrically‐derived digital elevation models (DEMs) of the model surface generated at regular intervals over the course of ~115 h of experimental runs. Independent measures of total bedload output were made using downstream sediment baskets. Results indicate that the morphological active width increases with total and dimensionless stream power and is strongly and positively correlated with bulk change (total volume of bed material displaced over time) and active braiding intensity (ABI). Although there is considerable scatter due to the inherent variability in braided river morphodynamics, the active width is positively correlated with independent measurements of bedload transport rate. Active width, bulk change, and bedload transport rates were all negligible below a dimensionless stream power threshold value of ~ 0.09, above which all increase with flow strength. Therefore, the active width could be used as a general predictor of bulk change and bedload transport rates, which in turn could be approximated from total and dimensionless stream power or ABI in gravel‐bed braided rivers. Furthermore, results highlight the importance of the active width, rather than the morphological active depth, in predicting volumes of change and bedload transport rates. The results contribute to the larger goals of better understanding braided river morphodynamics, creating large high‐resolution datasets of channel change for model calibration and validation, and developing morphological methods for predicting bedload transport rates in braiding river systems. Copyright © 2018 John Wiley & Sons, Ltd.     

An assembly model for simulation of large-scale ground water flow and transport

When managing large-scale ground water contamination problems, it is often necessary to model flow and transport using finely discretized domains--for instance (1) to simulate flow and transport near a contamination source area or in the area where a remediation technology is being implemented; (2) to account for small-scale heterogeneities; (3) to represent ground water-surface water interactions; or (4) some combination of these scenarios. A model with a large domain and fine-grid resolution will need extensive computing resources. In this work, a domain decomposition-based assembly model implemented in a parallel computing environment is developed, which will allow efficient simulation of large-scale ground water flow and transport problems using domain-wide grid refinement. The method employs common ground water flow (MODFLOW) and transport (RT3D) simulators, enabling the solution of almost all commonly encountered ground water flow and transport problems. The basic approach partitions a large model domain into any number of subdomains. Parallel processors are used to solve the model equations within each subdomain. Schwarz iteration is applied to match the flow solution at the subdomain boundaries. For the transport model, an extended numerical array is implemented to permit the exchange of dispersive and advective flux information across subdomain boundaries. The model is verified using a conventional single-domain model. Model simulations demonstrate that the proposed model operated in a parallel computing environment can result in considerable savings in computer run times (between 50% and 80%) compared with conventional modeling approaches and may be used to simulate grid discretizations that were formerly intractable.     

Improving hydrodynamic modeling of an estuary in a mixed tidal regime by grid refining and aligning

Water levels and flows in the Singapore coastal waters are driven by the complex interactions of the Indian and Pacific Ocean tides, seasonal monsoon-driven contributions and also forced by local winds. The Singapore Regional Model was developed to simulate hydrodynamics in the Strait of Singapore which produces representative sea level variation in this region. However, resolution and alignment of the grid system of the model with respect to depth contours in some of its subregions, i.e., the Johor Estuary area require further improvement. For this, the grid system of the model was modified and compared the simulated results with field measurements. The computed flow velocities agreed better with field observations when the grid resolution was increased. However, improving the alignment of the grid with the channel boundary (with a much lower increase in grid resolution) provided a substantially larger improvement of the model performance. The grid modification greatly influenced the computed salinity in the estuary, while water levels are slightly affected. Further analysis of model results showed a pronounced ebb tidal asymmetry generated by the O1–K1–M2 tidal constituents in the estuary.     

Multiple flow direction algorithms for runoff modelling in grid based elevation models: An empirical evaluation

When pathways for groundwater flow are defined in grid based elevation models, the grid structure creates some obstacles as it only allows for eight flow directions. Earlier algorithms have used arbitrarily designed flow distributions, which have resulted in either too diverging or too converging flow patterns. This study defines a computationally simple distribution function, where the converging nature (x) can be altered. A material of reference flow distributions was produced through simulation in four elevation models. The distribution function was tested for different values on x, against the reference. The results show a stable correlation pattern between the tested function and the reference. Optimum values on x were found, which suggest that the flow distribution from a grid cell should be weighted with the slope gradient raised to the power of 4–6.     

One‐ and two‐dimensional modelling of overland flow in semiarid shrubland,Jornada basin,New Mexico

Two distributed parameter models, a one‐dimensional (1D) model and a two‐dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event‐based and represent each watershed by an array of 1‐m² cells, in which the cell size is approximately equal to the average area of the shrubs. Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite‐difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second‐order predictor–corrector finite‐difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions. The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large‐scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration. Copyright © 2006 John Wiley & Sons, Ltd.     

积分方程法复杂介质可控源电磁勘探快速正反演研究现状及发展方向

复杂介质可控源电磁勘探数值模拟及反演算法的研究一直是国内外地球物理学者研究的热点。本文对复杂介质可控源电磁勘探快速正反演算法研究进行综述,重点对复杂介质快速正反演算法及应用进行分析,指出高效并行、特殊边界条件或将是其真正实用化的关键,当前仍然是极具挑战的研究方向。着重对未受关注的可控源电磁法复杂介质积分方程法正反演算法及其应用研究,如二维、2.5维快速正反演算法;地面、井筒电磁勘探实例、起伏地形异常场模拟等进行讨论。指出国内积分方程法的研究相对滞后,但应用前景较可观;特别是大尺度隐伏资源勘探领域,高精度、高效电磁勘探正反演需求较迫切。通过体积分方程法快速正反演算例分析,表明该方法可适用于大尺度勘探生产,具有较好实用性。复杂地形模拟,高效正反演算法等是积分方程法实用化的关键。      

Smoothing of digital elevation models and the alteration of overland flow path length distributions

DEM smoothing is a common pre-processing technique used to remove undesirable roughness from a DEM. However, it is hypothesized that smoothing straightens and reduces the length of overland flow paths, which is an important factor controlling modelled time-to-peak flow. Currently, there is a lack of research comparing how different smoothing techniques alter the distribution of overland flow path length. Four low-pass filtering techniques were applied to three fine-resolution LiDAR DEMs of varying relief: the mean filter, the median filter, the Gaussian filter, and the feature-preserving DEM smoothing (FPDEMS) filter, each with different degrees of smoothing. Downslope-distance-to-stream distributions were then derived using D8 and D∞ flow directions and statistically compared to distributions derived from the unsmoothed DEM for each study site. The results indicate that the alteration of flow path length distributions as a result of smoothing is complex. Mean flow path lengths may decrease or increase in response to smoothing, depending on landscape relief and the derivation of flow directions, and generalized flow paths may become longer. The largest increase in mean flow path lengths was 19.2 m using the 21 × 21 median filter and D8 flow directions in the high-relief study site, relative to an unsmoothed mean length of 138.6 m in this site. The largest decrease in mean flow path length was 48.9 m using the 21 × 21 mean filter and D∞ flow directions in the low-relief study site, relative to an unsmoothed mean length of 290.9 m in this site. Furthermore, minimal flow path length alterations were achieved with the Gaussian filter when gentle smoothing is required, and with the FPDEMS filter when moderate to aggressive smoothing is required. These results suggest that an appropriate smoothing method should be chosen based on the relief of the landscape and the degree of smoothing required.     

The effects of topographic depressions on multiscale overland flow connectivity: A high‐resolution spatiotemporal pattern analysis approach based on connectivity statistics

In watershed modelling, the traditional practice of arbitrarily filling topographic depressions in digital elevation models has raised concerns. Advanced high‐resolution remote sensing techniques, including airborne scanning laser altimetry, can identify naturally occurring depressions that impact overland flow. In this study, we used an ensemble physical and statistical modelling approach, including a 2D hydraulic model and two‐point connectivity statistics, to quantify the effects of depressions on high‐resolution overland flow patterns across spatial scales and their temporal variations in single storm events. Computations for both models were implemented using graphic processing unit‐accelerated computing. The changes in connectivity statistics for overland flow patterns between airborne scanning laser altimetry‐derived digital elevation models with (original) and without (filled) depressions were used to represent the shifts of overland flow response to depressions. The results show that depressions can either decrease or increase (to a lesser degree and shorter duration) the probability that any two points (grid locations) are hydraulically connected by overland flow pathways. We used macro‐connectivity states (Φ) as a watershed‐specific indicator to describe the spatiotemporal thresholds of connectivity variability caused by depressions. Four states of Φ are identified in a studied watershed, and each state represents different magnitudes of connectivity and connectivity changes (caused by depressions). The magnitude of connectivity variability corresponds to the states of Φ, which depend on the topological relationship between depressions, the rising/recession limb, and the total rainfall amount in a storm event. In addition, spatial distributions of connectivity variability correlate with the density of depression locations and their physical structures, which cause changes in streamflow discharge magnitude. Therefore, this study suggests that depressions are “nontrivial” in watershed modelling, and their impacts on overland flow should not be neglected. Connectivity statistics at different spatial scales and time points within a watershed provide new insights for characterizing the distributed and accumulated effects of depressions on overland flow.     

Sub-grid scale parameterisation of 2D hydrodynamic models of inundation in the urban area

This paper presents preliminary results from a study considering the parameterisation of coarse-grid 2D flood models to take into account sub-grid scale flow patterns occurring in the urban area. A simulation of a severe flood in an urbanized coastal floodplain is first run using a fine grid that can resolve the flow around and between buildings. Next, the same model is run again using the same underlying topography, although stripped from any buildings, and a set of 7 values of the roughness parameter (Manning’s n), all larger than (or equal to) the value used in the original run. A further set of simulations is carried out using a five-fold increased grid cell size. It is found that while it may be possible to model the overall effects of the buildings using strongly increased roughness parameter values, using a coarse grid otherwise has implications related to the loss of information about the site topography that results in flood flow routes being incorrectly modelled.     

计算断层自发破裂过程的离散网格划分研究

离散化网格的空间步长选取在各种数值算法中都是一个很受关注的问题,在全空间均匀介质模型和简单离散化方案下,利用边界积分方程方法研究在自发破裂求解过程中动力学参数组合Dc和Te (Dc为临界滑动弱化位移,Te为有效的断层破裂面上的初始应力)对计算网格划分的影响,初步得到了Dc和Te参数空间中的有效计算网格的选取规律,对合理、有效地运用边界积分方程方法计算地震震源的破裂过程具有重要的指导意义.