The shortest distance between two points isn't always a great circle: getting around landmasses in the calibration of marine geodisparity

Paleobiology ◽  
10.1666/13015 ◽  
2014 ◽  
Vol 40 (3) ◽  
pp. 428-439 ◽  
Author(s):  
Shuang-Ye Wu ◽  
Arnold I. Miller
Keyword(s):  
Temporal Trends ◽  
Great Circle ◽  
Planar Surface ◽  
Cost Distance ◽  
Shortest Distance ◽  
Temporal Intervals ◽  
Global Biodiversity ◽  
Great Circle Distance ◽  
Distance Approach ◽  
Faunal Similarity

In the assessment of Phanerozoic marine global biodiversity, there has been longstanding interest in quantifying compositional similarities among sampling points as a function of their distances from one another (geodisparity). Previous research has demonstrated that faunal similarity between any two locations tends to decrease significantly as the great circle distance (GCD) between the locations increases, but the rate of decrease begins to stabilize at transoceanic distances. The accuracy of these assessments, and comparisons among different temporal intervals, may suffer, however, because of intervening landmasses that are not accounted for when distance is calibrated simply as GCD. Here, we present a new method for determining the shortest overwater distance (WD) between two marine locations, and we use the method to recalibrate for several Phanerozoic intervals previous measures of global geodisparity in the taxonomic compositions of marine biotas. WD was determined by using a cost-distance approach in ArcGIS, modified to work on a spherical, as opposed to a planar, surface. Results demonstrate two notable effects of using WD. First, mean compositional similarity between locations tends to decrease more continuously as a function of distance with WD than with GCD. Second, pairs of locations with WDs that are at least 50% greater than their GCDs tend to have lower compositional similarity to one another than those with more closely matching WDs and GCDs. These differences are expected as WD better represents the “true” distance between locations; they diminish at GCDs of 5000 km or more when clear, transoceanic paths between locations become more common. Despite these effects, using WD does not alter fundamental temporal trends in global geodisparity through the Phanerozoic observed in previous research, but it is likely to have more significant ramifications for more confined paleobiogeographic investigations.

Empirical Estimation of Shortest Route Length along U.S. Interstate Highways Based on Great Circle Distance

2021 ◽  
pp. 036119812110152
Author(s):  
Nawei Liu ◽  
Fei Xie ◽  
Zhenhong Lin ◽  
Mingzhou Jin
Keyword(s):  
Linear Regression ◽  
State Level ◽  
Distance Matrix ◽  
Great Circle ◽  
The State ◽  
Empirical Estimation ◽  
Interstate Highways ◽  
Shortest Route ◽  
Route Length ◽  
Great Circle Distance

In this study, 98 regression models were specified for easily estimating shortest distances based on great circle distances along the U.S. interstate highways nationwide and for each of the continental 48 states. This allows transportation professionals to quickly generate distance, or even distance matrix, without expending significant efforts on complicated shortest path calculations. For simple usage by all professionals, all models are present in the simple linear regression form. Only one explanatory variable, the great circle distance, is considered to calculate the route distance. For each geographic scope (i.e., the national or one of the states), two different models were considered, with and without the intercept. Based on the adjusted R-squared, it was observed that models without intercepts generally have better fitness. All these models generally have good fitness with the linear regression relationship between the great circle distance and route distance. At the state level, significant variations in the slope coefficients between the state-level models were also observed. Furthermore, a preliminary analysis of the effect of highway density on this variation was conducted.

scholarly journals Aviation

MRS Bulletin ◽  
2008 ◽  
Vol 33 (4) ◽  
pp. 445-447 ◽  
Author(s):  
Dipankar Banerjee
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Energy Use ◽  
Great Circle ◽  
Load Factor ◽  
Propulsion Systems ◽  
Technological Factors ◽  
Great Circle Distance ◽  
Passenger Load Factor ◽  
Global Energy Consumption

Aviation accounts for about 3% of the current global energy consumption of 15 terawatts (TW). The global annual growth of energy use in the aviation sector is likely to be around 2.15% and will exceed that in other transportation sectors, although land transport will continue to consume the largest amounts of fuel. Figure 1 displays the historical improvements in energy efficiency in the aviation sector. Fuel use is determined by both operational and technological factors. The former includes the passenger load factor, ground efficiencies, taxi procedures, take-off and landing paths and circuitry (actual distance traveled versus a great-circle distance), and changes in the mixture of old and new aircraft and propulsion systems with time. Technology factors, focusing on materials issues, are described in greater detail herein.

scholarly journals Simple Single and Multi-Facility Location Models using Great Circle Distance

2021 ◽  
Vol 37 ◽  
pp. 01001
Author(s):  
A Baskar
Keyword(s):  
Facility Location ◽  
Operations Research ◽  
Euclidean Distance ◽  
Great Circle ◽  
Location Problems ◽  
Optimal Point ◽  
Facility Location Problems ◽  
The Earth ◽  
Facility Location Models ◽  
Great Circle Distance

Facility location problems (FLP) are widely studied in operations research and supply chain domains. The most common metric used in such problems is the distance between two points, generally Euclidean distance (ED). When points/ locations on the earth surface are considered, ED may not be the appropriate distance metric to analyse with. Hence, while modelling a facility location on the earth, great circle distance (GCD) is preferable for computing optimal location(s). The different demand points may be assigned with different weights based on the importance and requirements. Weiszfeld’s algorithm is employed to locate such an optimal point(s) iteratively. The point is generally termed as “Geometric Median”. This paper presents simple models combining GCD, weights and demand points. The algorithm is demonstrated with a single and multi-facility location problems.

scholarly journals Reconstructing geographic range-size dynamics from fossil data

Paleobiology ◽  
2018 ◽  
Vol 44 (1) ◽  
pp. 25-39 ◽  
Author(s):  
Simon A. F. Darroch ◽  
Erin E. Saupe
Keyword(s):  
Convex Hull ◽  
Spatial Data ◽  
Fossil Record ◽  
Geographic Range ◽  
Great Circle ◽  
Range Size ◽  
Data Set ◽  
Reconstruction Methods ◽  
Point Data ◽  
Great Circle Distance

AbstractEcologists and paleontologists alike are increasingly using the fossil record as a spatial data set, in particular to study the dynamics and distribution of geographic range sizes among fossil taxa. However, no attempts have been made to establish how accurately range sizes and range-size dynamics can be preserved. Two fundamental questions are: Can common paleo range-size reconstruction methods accurately reproduce known species’ ranges from locality (i.e., point) data? And, are some reconstruction methods more reliable than others? Here, we develop a methodological framework for testing the accuracy of commonly used paleo range-size reconstruction methods (maximum latitudinal range, maximum great-circle distance, convex hull, and alpha convex hull) in different extinction-related biogeographic scenarios. We use the current distribution of surface water bodies as a proxy for “preservable area,” in which to test the performance of the four methods. We find that maximum great-circle distance and convex-hull methods most reliably capture changes in range size at low numbers of fossil sites, whereas convex hull performs best at predicting the distribution of “victims” and “survivors” in hypothetical extinction scenarios. Our results suggest that macroevolutionary and macroecological patterns in the relatively recent past can be studied reliably using only a few fossil occurrence sites. The accuracy of range-size reconstruction undoubtedly changes through time with the distribution and area of fossiliferous sediments; however, our approach provides the opportunity to systematically calibrate the quality of the spatial fossil record in specific environments and time intervals, and to delineate the conditions under which paleobiologists can reconstruct paleobiogeographical, macroecological, and macroevolutionary patterns over critical intervals in Earth history.

scholarly journals Do Nearctic Northern Wheatears (Oenanthe Oenanthe Leucorhoa) Migrate Nonstop to Africa?

The Condor ◽  
2006 ◽  
Vol 108 (2) ◽  
pp. 446-451 ◽  
Author(s):  
Kasper Thorup ◽  
Kasper Thorup ◽  
Troels Eske Ortvad ◽  
JØrgen RabØl
Keyword(s):  
West Africa ◽  
Western Europe ◽  
Great Circle ◽  
Wintering Grounds ◽  
Oenanthe Oenanthe ◽  
West Greenland ◽  
Flight Costs ◽  
Body Weights ◽  
Direct Flight ◽  
Great Circle Distance

Abstract We present data suggesting that Northern Wheatears (Oenanthe oenanthe leucorhoa) breeding in West Greenland and Canada may be able to accomplish migration to their wintering grounds in West Africa in one direct, transatlantic crossing of more than 4000 km (great circle distance). This conclusion is based on analyses of wing lengths, body weights, and timing of departure from West Greenland and arrival on an island 350 km off the coast of Morocco. Previously, it has been suggested that Nearctic wheatears migrate to Africa by a two-step journey, the first leg comprising a shorter transatlantic crossing to western Europe. A long, direct flight has previously been considered unfeasible as the predicted flight costs were considered to be too high. However, recent insights in aerodynamic theory make these long ocean crossings appear more feasible, especially when taking the use of tailwinds into account.

Feasibility Study of Wing-In-Ground for Marine Rescue Operation

2014 ◽  
Vol 69 (7) ◽  
Author(s):  
Jaswar Koto ◽  
E. Prayetno
Keyword(s):  
Feasibility Study ◽  
Standard Error ◽  
Visual Basic ◽  
Great Circle ◽  
International Maritime Organization ◽  
Spherical Trigonometry ◽  
Simulation Code ◽  
Rescue Operation ◽  
Optimal Position ◽  
Great Circle Distance

This study aims to investigate performance of current rescue facilities and position based on statistic data of sea accident between 2010 and 2011 in Kepulauan Riau. Current rescue facilities are located at the latitude 0.93105 and longitude 104.44359. Using the statistic data, an optimal recue location and facilities in Kepulauan Riau are determine based on International Maritime Organization (IMO) standard. International Maritime Organization requirement, an emergency, passengers should be able to leave the ship with time 60 minutes. The optimal position and rescue facilities are determined using Great Circle Distance-Spherical Trigonometry and Statistical of Standard Error methods. In this study, simulation code is developed using visual basic 2010 language. Results of simulation show current rescue facility requires a lot of time to reach the accident location which is up to 12.5 hours. In order to meet IMO requirement, this study proposes wing in ground for rescue operation. Using current rescue location, wing in ground also does not meet the IMO standard which is up to 3.04 hours. Additional, this study divides the Kepulauan Riau into two regions of rescue operation. The optimal for rescue facilities of region 1, at the latitude 0.74568 and longitude 104.36256, and based on the distribution of the accidents in Kepulauan Riau 2010-2011, current rescue facility required up to 5.6 hours to reach the accident area, while the wing in ground facilities required up to 1.3 hours. The optimal for rescue facilities of region 2, at the latitude 3.00338 and longitude 107.79373, current rescue facility required up to 5 hours to reach the accident area, while the wing in ground facilities required shorter time that is up to 1.2 hour.

scholarly journals Practical Considerations with Radar Data Height and Great Circle Distance Determination

2020 ◽  
Author(s):  
Mark A. Askelson ◽  
Chris J. Theisen ◽  
Randall S. Johnson
Keyword(s):  
Constant Curvature ◽  
Taylor Series ◽  
Radar Data ◽  
The United States ◽  
Great Circle ◽  
Earth Model ◽  
Spatial Transformation ◽  
Taylor Series Approximation ◽  
Series Approximation ◽  
Great Circle Distance

AbstractOwing to their ease of use, “simplified” propagation models, like the Equivalent Earth model, are commonly employed to determine radar data locations. With the assumption that electromagnetic rays follow paths of constant curvature, which is a fundamental assumption in the Equivalent Earth model, propagation equations that do not depend upon the spatial transformation that is utilized in the Equivalent Earth model are derived. This set of equations provides the true constant curvature solution and is less complicated, conceptually, as it does not depend upon a spatial transformation. Moreover, with the assumption of constant curvature, the relations derived herein arise naturally from ray tracing relations.Tests show that this new set of equations is more accurate than the Equivalent Earth equations for a “typical” propagation environment in which the index of refraction n decreases linearly at the rate dn/dh = -1/4a, where h is height above ground and a is the Earth’s radius. Moreover, this new set of equations performs better than the Equivalent Earth equations for an exponential reference atmosphere, which provides a very accurate representation of the average atmospheric n structure in the United States. However, with this n profile the equations derived herein, the Equivalent Earth equations, and the relation associated with a flat Earth constant curvature model produce relatively large height errors at low elevations and large ranges.Taylor series approximations of the new equations are examined. While a second-order Taylor series approximation for height performs well under “typical” propagation conditions, a convenient Taylor series approximation for great circle distance was not obtained.

scholarly journals Sphere to Spheroid Comparisons

2006 ◽  
Vol 59 (3) ◽  
pp. 491-496 ◽  
Author(s):  
Michael A. Earle
Keyword(s):  
Great Circle ◽  
Positioning Accuracy ◽  
The Earth ◽  
Satellite Positioning ◽  
The Difference ◽  
Great Circle Distance ◽  
Spheroidal Model

The notion of the earth as a perfect sphere has served navigators quite well over the centuries and it continues to provide a basis for instruction and practical navigation. Aside from the fact that modern navigators employ refined models of the earth such as the WGS84 ellipsoid, which together with satellite positioning gives unprecedented positioning accuracy, the question arises as to just how good are the spherical results for distance when compared to the results for distance obtained from the spheroidal model. In this document a comparison is made of great circle distance (GCD) on the sphere with great ellipse distance (GED) on the spheroid. This comparison is then repeated for rhumbline distances. In each case it is concluded that the difference in using the sphere when compared to the spheroid is near 0·5%.

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