Where is Ben Nevis?

This repository contains the first files for a fun(?) project that tests optimisation methods on Ordnance Survey (OS) data for Great Britain.

Requirements

Python 3.6 or higher, with pip-installable dependencies listed in requirements.txt (you can install these with pip install -r requirements.txt). The additional package convertbng is recommended, but not required.

When first run, this script will download the data from the OS (about 160MB) and then convert it to a NumPy array stored on disk (about 1.5GB).

Usage

First run: plot a map of GB

After downloading, run gb.py to download and unpack the data and test that all went well by plotting a map of great brittain. (Don't worry, it'll be a lot faster the 2nd time.)

The amount of downscaling can be set using the variable downsampling. An example with downsampling=32 is shown below.

Running a fit

Next, you can start fit.py to run a fit. Results will be stored in the results directory. This directory will also contain some other files, such as an .npy file storing a cached numpy representation of the downloaded terrain data (and optionally a file called spline that stores a cached spline).

Data set

Height information is from the Terrain 50 data set made available by the UK's Ordnance Survey. More information can be found here.

The data is divided into squares indicated with a two letter code, and several data files per square. However, each data file contains its absolute "eastings" and "northings", so we can ignore the letter codes. Eastings and northings are defined by the "National Grid", or OSGB36. In easier terms, they are x and y coordinates, in meters, relative to the bottom-left point of the grid (which is the bottom left of the square "SV", which contains the Isles of Scilly).

As an example, the header from the NN17 file is:

ncols 200
nrows 200
xllcorner 210000
yllcorner 770000
cellsize 50

Here ncols and nrows indicate the number of grid points in the file, the Lower Left corner of the data in the file is given by xllcorner and yllcorner, and the distance between any two data points is given as cellsize. In the Terrain 50 data set, the cellsize is always 50 (giving it its name). There is a more accurate Terrain 5 set that costs money.

According to wikipedia, the approximate coordinates for Ben Nevis are 216600, 771200 (which is in the NN17 square).

An easy way to find places on the grid is with https://britishnationalgrid.uk. Another nice map with BNG coordinates is https://explore.osmaps.com. A a great map without BNG coordinates can be found at https://opentopomap.org.

The sea

The sea is a bit messy in these files, as the values depend on mean sea level in each 10x10 km^2 area (OS Tile) relative to OS datum (0m) level which is mean sea level in Newlyn, Cornwall.

Hill tops

Names of hill and mountain tops are taken from The Database of British and Irish Hills v17.2, which is made available under a CC-BY license.

Lattitude and longitude 🐇🕳️

What about longitude (east-west) and lattitude (north-south)? These are defined, it seems, by WGS 84, although there is a Europe-specific version called ETRS89 which "for most purposes ... can be considered equivalent to WGS84" ("Transformations and OSGM15 User Guide"). Transforming from national grid coordinates to longitude and lattitude is hard, and the Ordnance Survey have released a thing called OSTN15 to do this. Although this still seems to result in x, y coordinates, not degrees. Luckily, somebody's made a tool for it. Unfortunately, some people have issues installing this, so that we rely on a less accurate fallback for the time being. If you can, please manually install convertbng too (BenNevis will try using this first, before switching to bnglonglat).

Interpolation

To get heights for arbitrary points, we need to interpolate. By default, we use a linear interpolant. We also experimented with a scipy RectBiVariateSpline. This takes some time (~30 seconds on a fast machine) and uses considerable memory (~3GB). Most importantly, the spline shows some very serious (and unrealistic) artefacts near high gradients (e.g. at the sea side), so that the linear interpolation seems the way to go for now.

Tiny API docs

Proper API docs might be added at some point. For now, there are only a handful of public objects:

data utilities (see _data.py for details):
- ben returns grid coordinates (Coords) for Ben Nevis
- Coords represents grid coordinates and can convert to various forms
- dimensions returns the physical dimensions (in meters) of the GB height data
- fen returns grid coordinates for Holme Fen, the lowest point (inland)
- gb loads and returns the heights data for GB
- Hill represents a hill from the hills database
- linear_interpolant returns a linear interpolant over the GB height data
- pub returns grid coordinates for a random pub, selected from a very short list
- spacing returns the physical distance (in meters) between grid points
- spline returns a spline defined over the GB height data
- squares returns the coordinates of major BNG squares
plotting utilities (see _plot.py for details)
- plot creates a plot of a map, with optional labels etc.
- plot_line creates a plot of the height profile between two points
- png_bytes turns a matplotlib figure into a bytes string
- save_plot stores a plot and checks its size (only for paranoid people)
others (see _util.py for details)
- Timer times and formats intervals

EricWay1024 / BenNevis