Aim and terms¶
This atlas is written in the language of metrology: the International Vocabulary of Metrology (VIM, JCGM 200) and the Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100 and its supplements). This page states its aim in those terms and says how each part of the atlas maps onto them.
The aim¶
For every variable in the dataset, the atlas states
- the measurand (VIM 2.3): the quantity a record is meant to represent. A record has two: the time of what it describes and the value of it. For a numeric that summarises a window of signal, the measurand is the value over that window, so its time is an interval, not an instant;
- the measurement model (VIM 2.48) that links the measurand to the recorded pair (recorded time, recorded value): clocks, delays and windows on the time side; rounding, heaping and instrument error on the value side;
- what is known about the measurand given a record, as a probability distribution: in the GUM's terms, the state of knowledge about the output quantities. Because there are two output quantities, time and value, and they are not always independent, this is the multivariate case of GUM Supplement 2 (JCGM 102:2011);
- the evidence for every part of the model: the studies, with how each number was evaluated.
With the distribution known, the measurement uncertainty (VIM 2.26) of anything computed from the data can be found by propagating distributions, as in GUM Supplement 1 (JCGM 101:2008, by Monte Carlo): draw true times and values from each record's distribution, compute, and read the spread of the result.
This is a metrology of recorded data. Classical metrology designs and calibrates a measurement before it is made; here the measurements were made long ago, so each part of the model is reconstructed from the records themselves.
How the atlas maps onto the vocabulary¶
| In the atlas | Metrology | Note |
|---|---|---|
| A variable's "What it measures" | measurand (VIM 2.3) | Includes, for windowed values, the window: a vague window is definitional uncertainty (VIM 2.27). |
| Time accuracy: clock offset, drift, delay | systematic measurement error (VIM 2.17), measurement bias (VIM 2.18), instrumental drift (VIM 4.21) | Corrections remove the known part; what is left is uncertainty. |
| Time and value resolution: sampling grids, stamp grids, rounding, heaping | resolution (VIM 4.14) | Heaping is a mixture of resolutions, each with its share of the records. |
| Value accuracy: instrument error | measurement accuracy (VIM 2.13), measurement trueness (VIM 2.14), measurement precision (VIM 2.15) | Mostly still to be described. |
| A clock's "Route to UTC" | metrological traceability chain (VIM 2.42) | Each link adds uncertainty. Where a link is assumed, the chain is broken and the time is not metrologically traceable (VIM 2.41). |
| Status measured | Type A evaluation (VIM 2.28) | Evaluated from the data by a study. |
| Status estimated or assumed | Type B evaluation (VIM 2.29) | From documentation, the literature or judgement. |
| Status derived | propagation | Computed from other evaluated quantities. |
| The measurement-space figure | the joint distribution of the output quantities | A schematic: each part drawn as uniform over its range. |
| The synchronisation planner | a screening uncertainty budget | Combines standard uncertainties of the time side for several variables (uniform parts, independent). |
Words used here¶
- Accuracy and resolution are used as the two kinds of error on each axis: how far the record is from the truth (bias, drift, delay, instrument error), and how finely it was recorded (sampling, rounding, heaping). The VIM uses accuracy as a qualitative term; where a number is given, it is a bias or a standard uncertainty and the page says which.
- True value: the value of the measurand. The GUM treats it as unknowable and describes knowledge of it by a distribution; so does the atlas.
- Working reference: the clock that times are compared against in the planner. It is a practical reference, not a reference quantity value (VIM 5.18) in the strict sense.
Anchors¶
A recorded value stands for an interval of true values. The anchor says where the recorded value sits in that interval: at the nearest step (the interval is centred on it), at the floor (the true value lies at or above it, as for completed years or a clock that truncates), or at the ceiling (at or below it). A wrong anchor shifts every value by up to half a step, always the same way, so it biases averages rather than adding noise. For a count, the counting rule plays the same role.
Windows of time are always anchored at their end. A value that summarises a stretch of time (an averaged numeric, a duration, a beat-to-beat estimate over 30 s) is stamped when its window ends: the data lie before the stamp, never after it, so no value is placed before the data it was made from existed. The atlas keeps to this for every derived value, and its timing results say how far each device's stamps depart from it.
Every variable's anchor, and whether it is tested, a convention, an assumption or open, is listed under Anchor decisions.