plaintext partial derivatives in docs

docs/getting_started/why_pdemtools.md

@@ -8,7 +8,6 @@ As Earth Science has moved into the 'big data' era, increasing amounts of Arctic
 
 The `pdemtools` `search()` tool and `load` module allow for convenient access to the ArcticDEM and REMA datasets. Mosaics can be downloaded from a one-line `load.mosaic()` function, whilst the `search()` function allows for convenient filtering of a locally downloading ArcticDEM/REMA strip index according to variables such as date, region of interest, spatial coverage, temporal baseline, source sensors, accuracy, and cross-track data. The results of searches are returned as a [`geopandas`](https://geopandas.org) dataframe, and can be downloaded using the `load.from_search()` function. Elevation models are returned as [`xarray`](https://docs.xarray.dev) DataArrays [Hoyer _et al. 2017](https://doi.org/10.5334/jors.148) with geospatial metadata via the [`rioxarray`](https://corteva.github.io) extension - a standard format for storing and processing n-dimensional geospatial data within the geospatial Python community. By utilising standardised formats, the aim is to allow the user to quickly move beyond `pdemtools` into their own analysis in whatever format they desire, be that `xarray`, `numpy` or `dask` datasets, DEM analysis Python packages such as [`xdem`](https://xdem.readthedocs.io/) for advanced coregistration or [`richdem`](https://richdem.readthedocs.io) for flow analysis, or exporting to geospatial file formats for analysis beyond Python.
 
-After download, there exist a number of (pre-)processing steps that are near universally common in topographic analyses. These include geoid-correction, co-registration of time-series data, and/or the construction of terrain parameters such as hillshade, slope, aspect, and curvature. `pdemtools` contains pre-built functions to perform these processing steps, as well as further functionality specific to ArcticDEM and REMA use cases. For instance, we include functions to quickly extract the EIGEN-6C4 geoid [Foerste _et al._ 2014](https://doi.org/10.5880/icgem.2015.1) and Greenland/Antarctic bedrock masks directly from local versions of the Greenland and Antarctic BedMachine datasets ([Morlighem _et al_, [2022a](https://doi.org/10.5067/GMEVBWFLWA7X), [2022b](https://doi.org/10.5067/FPSU0V1MWUB6)), reprojecting and resampling the data to match the target DEM. Options for ingesting user-provided mask and geoid data are also provided. Additionally, partial derivatives of the surface used to calculate terrain parameters (∂z/∂x, ∂z/∂y, ∂<sup>2</sup>z/∂x<sup>2</sup>, ∂<sup>2</sup>z/∂y<sup>2</sup>, ∂<sup>2</sup>z/∂x∂y
-) are calculated following [Florinsky (2009)](https://doi.org/10.1080/13658810802527499), as opposed to more common methods such as [Zevenbergen and Thorne (1987)](https://doi.org/10.1002/esp.3290120107). The newer approach computes partial derivatives of elevation based on fitting a third-order polynomial, by the least-squares approach, to a 5 $\times$ 5 window as opposed to the more common 3 $\times$ 3 window. This is more appropriate for high-resolution DEMs: curvature over a 10 m window for the 2 m resolution ArcticDEM/REMA strips will lead to a local denoising effect that limits the impact of noise common in high-resolution photogrammetric products. These methods are also adapted into a co-registration routine, which otherwise follows the commonly used approach of [Nuth & Kääb (2011)](https://doi.org/10.5194/tc-5-271-2011).
+After download, there exist a number of (pre-)processing steps that are near universally common in topographic analyses. These include geoid-correction, co-registration of time-series data, and/or the construction of terrain parameters such as hillshade, slope, aspect, and curvature. `pdemtools` contains pre-built functions to perform these processing steps, as well as further functionality specific to ArcticDEM and REMA use cases. For instance, we include functions to quickly extract the EIGEN-6C4 geoid [Foerste _et al._ 2014](https://doi.org/10.5880/icgem.2015.1) and Greenland/Antarctic bedrock masks directly from local versions of the Greenland and Antarctic BedMachine datasets ([Morlighem _et al_, [2022a](https://doi.org/10.5067/GMEVBWFLWA7X), [2022b](https://doi.org/10.5067/FPSU0V1MWUB6)), reprojecting and resampling the data to match the target DEM. Options for ingesting user-provided mask and geoid data are also provided. Additionally, partial derivatives of the surface used to calculate terrain parameters (∂z/∂x, ∂z/∂y, ∂<sup>2</sup>z/∂x<sup>2</sup>, ∂<sup>2</sup>z/∂y<sup>2</sup>, ∂<sup>2</sup>z/∂x∂y) are calculated following [Florinsky (2009)](https://doi.org/10.1080/13658810802527499), as opposed to more common methods such as [Zevenbergen and Thorne (1987)](https://doi.org/10.1002/esp.3290120107). The newer approach computes partial derivatives of elevation based on fitting a third-order polynomial, by the least-squares approach, to a 5 $\times$ 5 window as opposed to the more common 3 $\times$ 3 window. This is more appropriate for high-resolution DEMs: curvature over a 10 m window for the 2 m resolution ArcticDEM/REMA strips will lead to a local denoising effect that limits the impact of noise common in high-resolution photogrammetric products. These methods are also adapted into a co-registration routine, which otherwise follows the commonly used approach of [Nuth & Kääb (2011)](https://doi.org/10.5194/tc-5-271-2011).
 
 We aim to grow `pdemtools` by implementing new methods developed by the ArcticDEM and REMA research community. For instance, we currently include sea-level-filtering and iceberg detection routines outlined by @shiggins_automated_2023, and invite community contributions or requests of other routines that will be of use to users of `pdemtools`. Ongoing research projects making use of `pdemtools` are applying ArcticDEM and REMA data to the mapping of crevasses, ice cliff heights, and subglacial lakes, as well as the initiation of ice sheet models. It has also been used within training exercises at the 2024 Polar Geospatial Center Data Workshop, contributing to a growing international network of `pdemtools` users.