# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Estimating area of vector polygons on spherical and ellipsoidal earth models with application in estimating regional carbon flows

(2017) In Student thesis series INES NGEM01 20171
Dept of Physical Geography and Ecosystem Science
Abstract
Estimating area of polygons on the Earth’s surface is required in many fields in earth science. In the field of carbon modelling, one application of estimating polygons’ area is to estimate carbon flows for regions. This thesis aims to develop a methodology to estimate area of a polygon on a spherical/ellipsoidal surface applied to the problem to estimate carbon flows in regions.

It is common that field data are stored in grid which covers the Earth’s surface in earth science. Region area estimation is inevitable for computation of sum of field data or density of data in regions. Region area can be computed by summing up the whole or partial area of grid cells covered by the region. The Earth is usually modelled as a sphere or an... (More)
Estimating area of polygons on the Earth’s surface is required in many fields in earth science. In the field of carbon modelling, one application of estimating polygons’ area is to estimate carbon flows for regions. This thesis aims to develop a methodology to estimate area of a polygon on a spherical/ellipsoidal surface applied to the problem to estimate carbon flows in regions.

It is common that field data are stored in grid which covers the Earth’s surface in earth science. Region area estimation is inevitable for computation of sum of field data or density of data in regions. Region area can be computed by summing up the whole or partial area of grid cells covered by the region. The Earth is usually modelled as a sphere or an ellipsoid. Area of the overlay polygon on spherical/ellipsoidal surface can be considered as the product of cell area and fraction (partial value) of overlay area in the grid cell. Three methodologies to estimate partial value of overlay area in a grid cell were proposed and tested: 1) using latitude-longitude plane, 2) using cylindrical area-preserving projection and 3) using the area of corresponding of spherical polygons. Cell sizes were estimated by cylindrical equal-area projection method. Tests show that area-preserving projection method is a suitable method to estimate area of a polygon on the Earth’s surface for the application of regional carbon flow estimation because it trades off the quality of estimates and computational demands.

Estimation of carbon flows in regions is interesting in many research domains. Atmospheric inversion is one technique of carbon flux modelling to provide carbon flux data in grid with various resolutions. Regional carbon flows can be estimated as the sum of fluxes in grid cells overlapped by the polygonal region. In most models, flux is modelled constant everywhere in each grid cell. A case study was performed to estimate carbon flow in Sweden using the methodology developed to estimate area of polygon. The uncertainties in the estimation of carbon flow in Sweden are influenced by the estimation of geographic extent of Sweden and the flux data in grid provided by atmospheric inversions. Four groups of test were done to test the effects of different factors on the flow estimation: partial values, earth model, interpolation and inversion systems. The test result illustrates partial value, earth model and interpolation have less than 1% effect on final result. The region flow is mainly influenced by flux data modeled by different inversions. (Less)
Popular Abstract
Estimating area of polygons on the Earth’s surface is required in many fields in earth science, especially for the problems requiring as precise area of regions as possible. In the field of carbon modelling, one application of estimating polygons’ area is to estimate carbon flows in regions. The result of regional carbon flows estimation is influenced by the region area estimation. However, in current scientific work about regional carbon estimation, the method to estimate region area is not clear and how many uncertainties introduced by area estimation to the final result is not investigated.

This thesis aims to develop a methodology to estimate area of a polygon on the Earth’s surface, which is applied to estimate carbon flows in... (More)
Estimating area of polygons on the Earth’s surface is required in many fields in earth science, especially for the problems requiring as precise area of regions as possible. In the field of carbon modelling, one application of estimating polygons’ area is to estimate carbon flows in regions. The result of regional carbon flows estimation is influenced by the region area estimation. However, in current scientific work about regional carbon estimation, the method to estimate region area is not clear and how many uncertainties introduced by area estimation to the final result is not investigated.

This thesis aims to develop a methodology to estimate area of a polygon on the Earth’s surface, which is applied to estimate carbon flows in regions, and to test the uncertainties propagated to the final result by the area estimated by the methodology developed. For method development, three methodologies to estimate area were proposed and tested. Tests show that cylindrical area-preserving projection method is a suitable method to estimate area of a polygon on the Earth’s surface for the application of regional carbon flow estimation because it trades off the quality of estimates and computational demands. To assess the uncertainties, a case study was performed to estimate carbon flow in Sweden using the cylindrical equal-area projection method to estimate area of polygon. A regional carbon flow is computed by the product of area of the region and carbon flux in that region. Three atmospheric inversion systems: CTE, CAMS and Jena CarboScope were chosen to provide carbon flux data. The test illustrates the most uncertainties come from the flux data modeled by different inversions. Compared to the uncertainties from flux data, the uncertainties (less than 1%) in polygon area estimation by the projection method is too small to worry about. (Less)
author
supervisor
organization
course
NGEM01 20171
year
type
H2 - Master's Degree (Two Years)
subject
keywords
spherical/ellipsoidal earth model, regional carbon flows, map projection, area of a polygon, atmospheric inversions
publication/series
Student thesis series INES
report number
436
language
English
id
8921924
2017-07-26 12:29:04
date last changed
2017-07-26 12:29:04
```@misc{8921924,
abstract     = {Estimating area of polygons on the Earth’s surface is required in many fields in earth science. In the field of carbon modelling, one application of estimating polygons’ area is to estimate carbon flows for regions. This thesis aims to develop a methodology to estimate area of a polygon on a spherical/ellipsoidal surface applied to the problem to estimate carbon flows in regions.

It is common that field data are stored in grid which covers the Earth’s surface in earth science. Region area estimation is inevitable for computation of sum of field data or density of data in regions. Region area can be computed by summing up the whole or partial area of grid cells covered by the region. The Earth is usually modelled as a sphere or an ellipsoid. Area of the overlay polygon on spherical/ellipsoidal surface can be considered as the product of cell area and fraction (partial value) of overlay area in the grid cell. Three methodologies to estimate partial value of overlay area in a grid cell were proposed and tested: 1) using latitude-longitude plane, 2) using cylindrical area-preserving projection and 3) using the area of corresponding of spherical polygons. Cell sizes were estimated by cylindrical equal-area projection method. Tests show that area-preserving projection method is a suitable method to estimate area of a polygon on the Earth’s surface for the application of regional carbon flow estimation because it trades off the quality of estimates and computational demands.

Estimation of carbon flows in regions is interesting in many research domains. Atmospheric inversion is one technique of carbon flux modelling to provide carbon flux data in grid with various resolutions. Regional carbon flows can be estimated as the sum of fluxes in grid cells overlapped by the polygonal region. In most models, flux is modelled constant everywhere in each grid cell. A case study was performed to estimate carbon flow in Sweden using the methodology developed to estimate area of polygon. The uncertainties in the estimation of carbon flow in Sweden are influenced by the estimation of geographic extent of Sweden and the flux data in grid provided by atmospheric inversions. Four groups of test were done to test the effects of different factors on the flow estimation: partial values, earth model, interpolation and inversion systems. The test result illustrates partial value, earth model and interpolation have less than 1% effect on final result. The region flow is mainly influenced by flux data modeled by different inversions.},
author       = {Huang, Huiting},
keyword      = {spherical/ellipsoidal earth model,regional carbon flows,map projection,area of a polygon,atmospheric inversions},
language     = {eng},
note         = {Student Paper},
series       = {Student thesis series INES},
title        = {Estimating area of vector polygons on spherical and ellipsoidal earth models with application in estimating regional carbon flows},
year         = {2017},
}

```