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(accuracy-precision)= | ||
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# Grasping accuracy and precision | ||
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Below, a small guide explaining what accuracy and precision are, and their relation to elevation data (or any spatial data!). | ||
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## Why do we need to understand accuracy and precision? | ||
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Elevation data comes from a wide range of instruments (optical, radar, lidar) acquiring in different conditions (ground, | ||
airborne, spaceborne) and relying on specific post-processing techniques (e.g., photogrammetry, interferometry). | ||
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While some complexities are specific to certain instruments and methods, all elevation data generally possesses: | ||
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- a [ground sampling distance](https://en.wikipedia.org/wiki/Ground_sample_distance), or footprint, **that does not necessarily represent the underlying spatial resolution of the observations**, | ||
- a [georeferencing](https://en.wikipedia.org/wiki/Georeferencing) **that can be subject to shifts, tilts or other deformations** due to inherent instrument errors, noise, or associated processing schemes, | ||
- a large number of [outliers](https://en.wikipedia.org/wiki/Outlier) **that remain difficult to filter** as they can originate from various sources (e.g., blunders, clouds). | ||
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All of these factors lead to difficulties in assessing the reliability of elevation data, required to | ||
perform additional quantitative analysis, which calls for defining the concepts relating to accuracy and precision for elevation data. | ||
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## Accuracy and precision of elevation data | ||
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### What are accuracy and precision? | ||
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[Accuracy and precision](https://en.wikipedia.org/wiki/Accuracy_and_precision) describe systematic and random errors, respectively. | ||
A more accurate measurement is on average closer to the true value (less systematic error), while a more precise measurement has | ||
less spread in measurement error (less random error), as shown in the simple schematic below. | ||
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*Note: sometimes "accuracy" is also used to describe both types of errors, while "trueness" refers to systematic errors, as defined | ||
in* [ISO 5725-1](https://www.iso.org/obp/ui/#iso:std:iso:5725:-1:ed-1:v1:en) *. Here, we use accuracy for systematic | ||
errors as, to our knowledge, it is a more commonly used terminology for remote sensing applications.* | ||
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:::{figure} imgs/precision_accuracy.png | ||
:width: 80% | ||
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Source: [antarcticglaciers.org](http://www.antarcticglaciers.org/glacial-geology/dating-glacial-sediments2/precision-and-accuracy-glacial-geology/), accessed 29.06.21. | ||
::: | ||
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### Translating these concepts for elevation data | ||
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However, elevation data rarely consists of a single independent measurement but of a **series of measurements** (image grid, | ||
ground track) **related to a spatial support** (horizontal georeferencing, independent of height), which complexifies | ||
the notion of accuracy and precision. | ||
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Due to this, spatially consistent systematic errors can arise in elevation data independently of the error in elevation itself, | ||
such as **affine biases** (systematic georeferencing shifts), in addition to **specific biases** known to exist locally | ||
(e.g., signal penetration in land cover type). | ||
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For random errors, a variability in error magnitude or **heteroscedasticity** is common in elevation data (e.g., | ||
large errors on steep slopes). Finally, spatially structured yet random patterns of errors (e.g., along-track undulations) | ||
also exist and force us to consider the **spatial correlation of random errors (sometimes called structured errors)**. | ||
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Translating the accuracy and precision concepts to elevation data, we can thus define: | ||
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- **Elevation accuracy** (systematic error) describes how close an elevation data is to the true elevation on the Earth's surface, both for errors **common to the entire spatial support** | ||
(DEM grid, altimetric track) and errors **specific to a location** (pixel, footprint), | ||
- **Elevation precision** (random error) describes the random spread of elevation error in measurement, independently of a possible bias from the true positioning, both for errors **structured over the spatial support** and **specific to a location**. | ||
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These categories are depicted in the figure below. | ||
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:::{figure} imgs/accuracy_precision_dem.png | ||
:width: 100% | ||
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Source: [Hugonnet et al. (2022)](https://doi.org/10.1109/jstars.2022.3188922). | ||
::: | ||
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### Absolute or relative elevation accuracy | ||
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Accuracy is generally considered from two focus points: | ||
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- **Absolute elevation accuracy** describes systematic errors to the true positioning, usually important when analysis focuses on the exact location of topographic features at a specific epoch. | ||
- **Relative elevation accuracy** describes systematic errors with reference to other elevation data that does not necessarily match the true positioning, important for analyses interested in topographic change over time. | ||
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## How to get the best out of your elevation data? | ||
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### Quantifying and improving accuracy | ||
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Misalignments due to poor absolute or relative accuracy are common in elevation datasets, and are usually assessed and | ||
corrected by performing **three-dimensional elevation coregistration and bias corrections to an independent source | ||
of elevation data**. | ||
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In the case of absolute accuracy, this independent source must be precise and accurate, such as altimetric data from | ||
[ICESat](https://icesat.gsfc.nasa.gov/icesat/) and [ICESat-2](https://icesat-2.gsfc.nasa.gov/) elevations, or coarser yet | ||
quality-controlled DEMs themselves aligned on altimetric data such as the | ||
[Copernicus DEM](https://portal.opentopography.org/raster?opentopoID=OTSDEM.032021.4326.3). | ||
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To use coregistration and bias correction pipelines in xDEM, see the **feature pages on {ref}`coregistration` and {ref}`biascorr`**. | ||
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### Quantifying and improving precision | ||
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While assessing accuracy is fairly straightforward as it consists of computing the mean differences (biases) between | ||
two or multiple datasets, assessing precision of elevation data can be much more complex. The spread in measurement | ||
errors cannot be quantified by a difference at single data point, and require statistical inference. | ||
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Assessing precision usually means applying **spatial statistics combined to uncertainty quantification**, | ||
to account for the spatial variability and the spatial correlation in errors. For this it is usually necessary, as | ||
for coregistration, to **rely on an independent source of elevation data on static surfaces similarly**. | ||
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To use spatial statistics for quantifying precision in xDEM, see **the feature page on {ref}`uncertainty`**. | ||
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Additionally, improving the precision of elevation data is sometimes possible by correcting random structured | ||
errors, such as pseudo-periodic errors (undulations). For this, one can **also use {ref}`biascorr`**. | ||
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---------------- | ||
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:::{admonition} References and more reading | ||
:class: tip | ||
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More background on structured random errors is available on the **{ref}`spatial-stats` guide page**. | ||
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**References:** | ||
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- [ISO 5725-1 (1994)](https://www.iso.org/obp/ui/#iso:std:iso:5725:-1:ed-1:v1:en), Accuracy (trueness and precision) of measurement methods and results — Part 1: General principles and definitions, | ||
- [Mittaz et al. (2019)](http://dx.doi.org/10.1088/1681-7575/ab1705), Applying principles of metrology to historical Earth observations from satellites, | ||
- [Hugonnet et al. (2022)](https://doi.org/10.1109/jstars.2022.3188922), Uncertainty analysis of digital elevation models by spatial inference from stable terrain. | ||
::: |
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