Efficient methods for Isoline extraction from a TIN

Abstract

A data structure is presented to store a triangulated irregular network digital elevation model, from which isolines (contour lines) can be extracted very efficiently. If the network is based on n points, then for any elevation, the isolines can be obtained in O (logn + k) query time, where k is the number of line segments that form the isolines. This compares favourably with O(n) time by straightforward computation. When a structured representation of the isolines is needed, the same query time applies. For a fully topological representation (with adjacency), the query requires additional O(c log c) or O(c log logo) time, where c is the number of connected components of isolines. In all three cases, the required data structure has only linear size.     

Time series forecasting of river flow using an integrated approach of wavelet multi-resolution analysis and evolutionary data-driven models. A case study: Sebaou River (Algeria)

The complexity of hydrological processes and lack of data for modeling require the use of specific tools for non-linear natural phenomenon. In this paper, an effort has been made to develop a conjunction model – wavelet transformation, data-driven models, and genetic algorithm (GA) – for forecasting the daily flow of a river in northern Algeria using the time series of runoff. This catchment has a semi-arid climate and strong variability in runoff. The original time series was decomposed into multi-frequency time series by wavelet transform algorithm and used as inputs to artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) models. Several factors must be optimized to determine the best model structures. Wavelet-based data-driven models using a GA are designed to optimize model structure. The performances of wavelet-based data-driven models (i.e. WANFIS and WANN) were superior to those of conventional models. WANFIS (RMSE = 12.15 m³/s, EC = 87.32%, R = .934) and WANN (RMSE = 15.73 m³/s, EC = 78.83%, R = .888) models improved the performances of ANFIS (RMSE = 23.13 m³/s, EC = 54.11%, R = .748) and ANN (RMSE = 22.43 m³/s, EC = 56.90%, R = .755) during the test period.     

Modeling the morphology of gully cross sections in the Yuanmou Dry-hot Valley

Abstract

Characterizing gully cross sections (GCs) is essential for calculating the volume and erosion rate of the gully. However, little research has focused on modeling the morphology of GCs. This study investigated 456 GCs with a laser distance meter located at the mouth, middle, and head of 152 gullies in the Yuanmou Dry-hot Valley of China; mapped them with AutoCAD software; fitted them with 2nd–6th degree polynomial functions, and discussed the correlation between the coefficients and the morphology of GCs. The results showed that: (1) using a 2nd-degree polynomial function (y = ax² + bx + c) to describe the morphology of GCs produced a better result than other polynomial functions; (2) the coefficient a of 2nd-degree polynomial function was correlated with depth (r = ?0.226, p < 0.01), gradient (r = 0.545, p < 0.01), and activities; and (3) the symmetry axis (?b/2a) of 2nd-degree polynomial function increased with gully change from left-deflection to right-skewed, and the absolute value showed the asymmetrical degree (r = 0.216, p < 0.01). This study will not only help to understand the morphology and evolution of gullies, but will also provide a scientific basis for prevention of gully erosion.     

Spatial distribution and morphologic characteristics of gullies in the Black Soil Region of Northeast China: Hebei watershed

Gully erosion in the Black Soil Region of China has posed a threat to food security. This study aimed to determine the spatial distribution and morphologic characteristics of gullies in the region and their topographic thresholds. A 28 km² watershed was surveyed and 117 gullies measured. The results showed that: (1) Gullies were distributed equally on both hillslope and valley floor positions, with a total gully density of .66 km/km². (2) The mean depth, width, and cross-sectional area of gullies were .74 m, 2.39 m, and 2.43 m², respectively. These characteristics varied among gullies according to their topographic positions and slope gradients. Individual gully volume (V) was well predicted from gully length (L) by V = 2.08L^0.96 (r² = .66). Total gully volume (V) of each sub-watershed was predicted from mean slope gradient (S) and drainage area (A) as V = 275800S ? 8600A (r² = .73). (3) Gully erosion was more serious in steeper sub-watersheds and steeper hillslope positions. Gullies were wider in regions with relatively larger drainage areas, except for those developed in the main valley. The topographic threshold for gully initiation was S = .10A^?0.34, which indicated gully erosion was dominated by surface runoff. (4) Human activities, such as road construction, played a significant role in gully erosion.     

A complete classification of spatial relations using the Voronoi-based nine-intersection model

In this article we show that the Voronoi-based nine-intersection (V9I) model proposed by Chen et al. (2001, A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15 (3), 201–220) is more expressive than what has been believed before. Given any two spatial entities A and B, the V9I relation between A and B is represented as a 3 × 3 Boolean matrix. For each pair of types of spatial entities that is, points, lines, and regions, we first show that most Boolean matrices do not represent a V9I relation by using topological constraints and the definition of Voronoi regions. Then, we provide illustrations for all the remaining matrices. This guarantees that our method is sound and complete. In particular, we show that there are 18 V9I relations between two areas with connected interior, while there are only nine four-intersection relations. Our investigations also show that, unlike many other spatial relation models, V9I relations are context or shape sensitive. That is, the existence of other entities or the shape of the entities may affect the validity of certain relations.     

Accuracy of contour lines using 3D bands

This article describes a new methodology for the planimetric control of contour lines. The method is based on the generation of buffers around the contour lines which define a 3D buffer around the maximum slope line. After that we analyze the quantity of points from a more accurate source which is inside this buffer. As a result, we obtain a distribution function of the control points included when we apply several widths to the buffers. We have also determined the angularity and height differences of these points. The method has been applied to several sets of contour line intervals derived from a digital elevation model (DEM) and to the contour lines of one published topographic map using the DEM as the control source. We have also analyzed the representative behaviour of the contour lines, taking into account the contour line interval and the detection of an uncertainty model based on the slope variation. This study demonstrates the viability of the proposed method for obtaining the uncertainty of the contour lines depending on a given level of confidence and the variability of this uncertainty in the map. Finally, we propose a range of contour line intervals based on the scale and slopes.     

Sources of Uncertainty in Shear Stress and Roughness Length Estimates Derived from Velocity Profiles*

Shear stress is a fundamental parameter in many sediment transport expressions. It is commonly estimated from information contained in the velocity profile, specifically, shear velocity, u_*, and roughness length, z₀ Under ideal conditions, the functional relationship between elevation above the bed and flow velocity is log-linear, as expressed by the “law of the wall.” Unless the field data conform exactly to this ideal relationship, there is uncertainty in estimates of u_* and z₀. derived from velocity profiles. This uncertainty depends on the degree of scatter or deviation from the assumed log-linear model. Expressions are presented to quantify the error and to correct for it. Guidelines are suggested to minimize potential uncertainty, especially with regard to instrument deployment and velocity profile analysis. Calculation of confidence intervals around estimates of u_* and z₀, as proposed by Wilkinson (1984), is necessary and recommended.     

Sources of Uncertainty in Shear Stress and Roughness Length Estimates Derived from Velocity Profiles∗

Shear stress is a fundamental parameter in many sediment transport expressions. It is commonly estimated from information contained in the velocity profile, specifically, shear velocity, u _?, and roughness length, z ₀ Under ideal conditions, the functional relationship between elevation above the bed and flow velocity is log-linear, as expressed by the “law of the wall.” Unless the field data conform exactly to this ideal relationship, there is uncertainty in estimates of u _? and z ₀. derived from velocity profiles. This uncertainty depends on the degree of scatter or deviation from the assumed log-linear model. Expressions are presented to quantify the error and to correct for it. Guidelines are suggested to minimize potential uncertainty, especially with regard to instrument deployment and velocity profile analysis. Calculation of confidence intervals around estimates of u _? and z ₀, as proposed by Wilkinson (1984), is necessary and recommended.     

Multi-level method for discovery of regional co-location patterns

Regional co-location patterns represent subsets of feature types that are frequently located together in sub-regions in a study area. These sub-regions are unknown a priori, and instances of these co-location patterns are usually unevenly distributed across a study area. Regional co-location patterns remain challenging to discover. This study developed a multi-level method to identify regional co-location patterns in two steps. First, global co-location patterns were detected, and other non-prevalent co-location patterns were identified as candidates for regional co-location patterns. Second, an adaptive spatial clustering method was applied to detect the sub-regions where regional co-location patterns are prevalent. To improve computational efficiency, an overlap method was developed to deduce the sub-regions of (k + 1)-size co-location patterns from the sub-regions of k-size co-location patterns. Experiments based on both synthetic and ecological data sets showed that the proposed method is effective in the detection of regional co-location patterns.     

Computational reproducibility in geoscientific papers: Insights from a series of studies with geoscientists and a reproduction study

Reproducibility is a cornerstone of science and thus for geographic research as well. However, studies in other disciplines such as biology have shown that published work is rarely reproducible. To assess the state of reproducibility, specifically computational reproducibility (i.e. rerunning the analysis of a paper using the original code), in geographic research, we asked geoscientists about this topic using three methods: a survey (n = 146), interviews (n = 9), and a focus group (n = 5). We asked participants about their understanding of open reproducible research (ORR), how much it is practiced, and what obstacles hinder ORR. We found that participants had different understandings of ORR and that there are several obstacles for authors and readers (e.g. effort, lack of openness). Then, in order to complement the subjective feedback from the participants, we tried to reproduce the results of papers that use spatial statistics to address problems in the geosciences. We selected 41 open access papers from Copernicus and Journal of Statistical Software and executed the R code. In doing so, we identified several technical issues and specific issues with the reproduced figures depicting the results. Based on these findings, we propose guidelines for authors to overcome the issues around reproducibility in the computational geosciences.     

Variable complexity of the US Continental Divide trace

Abstract

Map-view complexity of 65 contiguous segments of the conterminous US Continental Divide trace was evaluated by the divider method, with each segment’s geometry approximated by a fractal dimension (D) value, or two D values applying to fine and coarse scales of inspection. Results support a generalization that D values in the range 1.05–1.12 are typical for drainage divides viewed at regional to national scales. However about 20% of cases reviewed in this study are smoother (D = 1.01–1.04) or more complex (D = 1.13–1.18) traces. Complexities of these watershed boundary segments show no significant correlation with physiographic province or local relief. The primary influence of bedrock lithology and surface process is seen in zones of Quaternary volcanism, where uncommonly smooth and highly complex divide trace segments are more the rule than exception. Uncommonly smooth divide traces are also found descending mountain pediments in areas of parallel drainage, and some of the most tortuous traces are associated with drainage patterns disrupted by non-fluvial processes. Divide trace segments crossing terrain with uniform lithology show decreased complexity, but traces with the broadest range of complexity, including highest D values, occur in areas with moderate, not extreme, degrees of bedrock diversity.     

The Implementation and Sustainability of Village Conservation Agreements Around Kerinci Seblat National Park,Indonesia

We investigated the implementation and sustainability of village conservation agreements and village conservation grants facilitated by an integrated conservation and development project (ICDP) around the Kerinci Seblat National Park, Sumatra, Indonesia, 5 years after the project closed. Forty-three percent of agreement actions (n = 180) and 30% of grant activities (n = 74) were sustained. Informants identified numerous factors influencing success, but statistical tests failed to detect simple explanations. Conservation-livelihood agreements have a greater chance of success when preexisting factors are understood and the purpose of the agreement itself is clearly defined.     

Mapping illegal domestic waste disposal potential to support waste management efforts in Queensland,Australia

Illegal disposal of waste is a significant management issue for contemporary governments because of the hazards posed to both human and ecosystem health. Understanding the complex distribution pattern of illegal waste and the range of economic, environmental and social factors influencing this distribution is valuable for improving the effectiveness and efficiency of waste management efforts. This article examines the applicability of mapping illegal waste disposal in the Sunshine Coast (Queensland, Australia) through the identification and integration of predictive spatial data in a geographic information system. A statistical model of illegal waste disposal was developed using a binary logistic regression analysis to identify explanatory variables suitable for predicting the distribution of illegal waste. Five statistically significant explanatory variables were identified through this analysis: population density, primary land use, distance to the nearest road, waste facility and roadside amenity. The generated statistical model had a predictive success of 86.1% with all indicators suggesting good model fit (χ² = 474.3, P = 0 with df = 22) across the study area. Standardised spatial data on each explanatory variable were combined using a weighted linear combination analysis and the results were classified into five categories from very low to very high illegal waste disposal potentials using the equal interval method. The resultant mapping identified 6.9% of the study area as having very high illegal waste disposal potential, and subsequent validation indicated that 32.9% of known illegal waste disposal sites were located within these areas.     

The Role of Community Identity in Cattlemen Response to Florida Panther Recovery Efforts

The concept of community identity has often been employed to explain ways in which communities respond to agents that impact community well-being. Using a case study of the Florida cattlemen community, we examine how cattlemen understand and perceive regulatory efforts to recover the Florida panther on private ranch lands. The data comes from participants in the Florida cattlemen community, and was collected through in-depth interviews (n = 13), group interviews (n = 32), and written comments associated with a survey about panther conservation (n = 78). Our findings indicate that some cattlemen in Florida have a strong sense of community identity. Perceptions of government actions and variation in economic risks are critical factors in understanding how this community responds to federal interventions. Our findings suggest that the concept of community identity can be used to explain the responses of agricultural landowners to governmental policies that are perceived as a threat to collective identity.     

Seasonal climate inferences from high-resolution modern diatom data along a climate gradient: a case study

This study represents a step towards developing seasonal climate inferences by using high-resolution modern data sets. The importance of seasonal climate changes is highlighted by the instrumental record of a meteorological station close to our study site (lac du Sommet in the Laurentian Mountains, Québec, Canada): Between 1966 and 2001, May temperatures increased significantly by 3.1°C (r = 0.41, n = 35, p < 0.01) but annual mean temperatures only by 0.6°C (r = 0.21, n = 35, p > 0.05). Comparison of this instrumental record with fossil diatom assemblages in a sediment core from lac du Sommet showed that axis one of a principal component analysis (PCA) of the fossil diatoms was best correlated with wind velocity in June (r = 0.62, n = 19, p < 0.005) and that past diatom production was significantly enhanced in periods with colder July temperatures (r =  ?0.77, n = 19, p < 0.0005) and higher wind velocity in June (r = 77, n = 19, p < 0.0005). The strong impact of the spring and summer conditions on overall diatom composition and productivity suggests that seasonal lake responses to climate are more important than annual mean temperatures. However, the seasonal dynamics of diatom communities are not well understood, and seasonality is rarely inferred effectively from lake sediment studies. Our research presents a pilot study to answer a twofold question: Is it possible to identify diatom communities which are typical for warmer or colder seasonal climate using sediment traps, and if it is, can this knowledge be used to infer seasonal climate conditions from fossil diatom assemblages? To address these questions, the seasonal dynamics of diatom communities and water chemistry were studied using sediment traps and water samples at biweekly intervals in four lakes distributed along an altitudinal gradient in the Laurentian Mountains from May through October 2002. Date of ice break-up was significantly related to the diatom assemblages taken in spring and uncorrelated to other significant environmental variables. Summer water temperature, circulation of the water column and pH explained a significant part of the biological variance in summer, and total nitrogen (TN) explained most of the biological variance in autumn. To infer these variables, weighted averaging partial least squares models were applied to the seasonal data sets. Inferred ice break-up dates were significantly correlated with number of days below 0°C in April (r = 0.52, n = 19, p < 0.025), inferred circulation of the water column was significantly related to measured wind velocity in June (r = 0.64, n = 19, p < 0.005), inferred summer water temperature and inferred pH was significantly related to measured July air temperature (r = 0.50, r =  ?53, n = 19, p < 0.025) and inferred TN autumn concentrations had an inverse relationship to August temperatures (r =  ?0.53, n = 19, p < 0.01). This comparison of the historical record with diatom-inferred seasonal climate signals, based on the comparison of fossil diatom assemblages with modern sediment trap data of high temporal resolution, provides a promising new approach for the reconstruction of seasonal climate aspects in paleolimnological studies.     

Computation of the third‐order partial derivatives from a digital elevation model

Loci of extreme curvature of the topographic surface may be defined by the derivation function (T) depending on the first‐, second‐, and third‐order partial derivatives of elevation. The loci may partially describe ridge and thalweg lines. The first‐ and second‐order partial derivatives are commonly calculated from a digital elevation model (DEM) by fitting the second‐order polynomial to a 3×3 window. This approach cannot be used to compute the third‐order partial derivatives and T. We deduced formulae to estimate the first‐, second‐, and third‐order partial derivatives from a DEM fitting the third‐order polynomial to a 5×5 window. The polynomial is approximated to elevation values of the window. This leads to a local denoising that may enhance calculations. Under the same grid size of a DEM and root mean square error (RMSE) of elevation, calculation of the second‐order partial derivatives by the method developed results in significantly lower RMSE of the derivatives than that using the second‐order polynomial and the 3×3 window. An RMSE expression for the derivation function is deduced. The method proposed can be applied to derive any local topographic variable, such as slope gradient, aspect, curvatures, and T. Treatment of a DEM by the method developed demonstrated that T mapping may not substitute regional logistic algorithms to detect ridge/thalweg networks. However, the third‐order partial derivatives of elevation can be used in digital terrain analysis, particularly, in landform classifications.     

Terrestrial Laser Scanning of grain roughness in a gravel-bed river

This paper demonstrates the application of Terrestrial Laser Scanning (TLS) to determine the full population of grain roughness in gravel-bed rivers. The technique has the potential to completely replace the need for complex, time-consuming manual sampling methods. Using TLS, a total of 3.8 million data points (mean spacing 0.01 m) were retrieved from a gravel bar surface at Lambley on the River South Tyne, UK. Grain roughness was extracted through determination of twice the local standard deviation (2σ_z) of all the elevations in a 0.15 m radius moving window over the data cloud. 2σ_z values were then designated to each node on a 5 cm regular grid, allowing fine resolution DEMs to be produced, where the elevation is equivalent to the grain roughness height. Comparisons are made between TLS-derived grain roughness and grid-by-number sampling for eight 2 m² patches on the bar surface. Strong relationships exist between percentiles from the population of 2σ_z heights with measured a-, b-, and c-axes, with the closest matches appearing for the c-axis. Although strong relationships exist between TLS-derived grain roughness (2σ_z), variations in the degree of burial, packing and imbrication, results in very different slope and intercept exponents. This highlights that conventional roughness measurement using gravel axis length should be used with caution as measured axes do not necessarily represent the actual extent to which the grain protrudes into the flow. The sampling error inherent in conventional sampling is also highlighted through undertaking Monte Carlo simulation on a population of 2000 clasts measured using the grid-by-number method and comparing this with the TLS-derived population of grain roughness heights. Underestimates of up to − 23% and overestimates of up to + 50% were found to occur when considering the D₈₄, and − 20% and overestimates of up to + 36% were found to occur when considering the D_50.     

The effect of sub-alpine landslides on headwater stream gradient and beaver habitat

During previous work in the San Juan Mountains of Colorado, we observed that headwater (first-order) streams draining landslides were often characterized by the presence of beaver (Castor canadensis) dams whereas other headwater tributaries typically lacked evidence of beaver. Here, we hypothesize that hummocky landslide topography attracts beaver. To test the hypothesis, we examined 10 landslides and 11 adjacent headwater streams in the area, noting location, vegetation, elevation, and evidence of beaver activity, and then compared the landslide and non-landslide headwater streams using the G-test to determine whether or not variables were independent of one another. We reject the null hypothesis that beaver dam presence is unrelated to landslide deposits (p = 0.003). We further hypothesize that this relationship results from differences in stream gradient and concavity between landslide streams and other streams. We found streams on landslides to have a greater portion of their gradients below what geologic and ecologic literature suggests is a reasonable upper threshold (12%) for beaver dam maintenance. Additionally, streams on landslides are more concave. We conclude that the relationship between beaver presence and landslides results from a higher proportion of reaches below the 12% threshold and increased concavity of headwater streams on landslides.     

基于层次格网索引的图幅接边处等高线高程错误识别和自动修正研究

等高线蕴含的历史高程信息可有效延长地形研究的时间序列,有利于深入挖掘地形变化长期规律,然而,图幅接边处的高程属性错误降低了等高线的数据质量,制约着等高线高程信息的实际应用。针对这一问题,该文提出一种基于层次格网索引的图幅接边处等高线高程错误识别和自动修正方法:首先,将层次格网索引与方向性二邻域算法相结合,以减少数据重复计算;然后,利用等高线空间位置标签及快速排序算法构建强空间位置关系,解决图幅接边处等高线匹配的准确性问题;最后,以高程冲突位点为驱动因子进行逻辑判断,实现等高线高程错误的识别及自动修正。实验结果表明:该方法运算效率较未进行效率优化时提高了203倍,接边处等高线高程错误识别与修正精度的最大值分别达97.71%和91.40%;相较于现有方法,该方法在精度和效率方面表现更佳,对区域性错误和变形等高线具有更高的适用性。     

Characterizing Content Distributions of Impurities in a Limestone Mine Using a Feedforward Neural Network

The factors determining the suitability of limestone for industrial use and its commercial value are the amounts of calcium oxide (CaO) and impurities. From 244 sample points in 18 drillhole sites in a limestone mine, southwestern Japan, data on four impurity elements, SiO₂, Fe₂O₃, MnO, and P₂O₅ were collected. It generally is difficult to estimate spatial distributions of these contents, because most of the limestone bodies in Japan are located in the accretionary complex lithologies of Paleozoic and Mesozoic age. Because the spatial correlations of content data are not clearly shown by variogram analysis, a feedforward neural network was applied to estimate the content distributions. The network structure consists of three layers: input, middle, and output. The input layer has 17 neurons and the output layer four. Three neurons in the input layer correspond with x, y, z coordinates of a sample point and the others are rock types such as crystalline and conglomeratic limestones, and fossil types related to the geologic age of the limestone. Four neurons in the output layer correspond to the amounts of SiO₂, Fe₂O₃, MnO, and P₂O₅. Numbers of neurons in the middle layer and training data differ with each estimation point to avoid the overfitting of the network. We could detect several important characteristics of the three-dimensional content distributions through the network such as a continuity of low content zones of SiO₂ along a Lower Permian fossil zone trending NE-SW, and low-quality zones located in depths shallower than 50 m. The capability of the neural network-based method compared with the geostatistical method is demonstrated from the viewpoints of estimation errors and spatial characteristics of multivariate data. To evaluate the uncertainty of estimates, a method that draws several outputs by changing coordinates slightly from the target point and inputting them to the same trained network is proposed. Uncertainty differs with impurity elements, and is not based on just the spatial arrangement of data points.