Recent developments on an interferometric multilateration measurement system for large volume coordinate metrology

A mobile multilateration measurement system developed at the Physikalisch-Technische Bundesanstalt (PTB) around 2010 has been thoroughly investigated and refined to gain better performance with smaller uncertainties even when applied to the calibration of large complex workpieces. The mathematical background of multilateration and the propagation of uncertainties for the algorithms involved is explained in detail. Using the example of simple 1D and 2D measuring tasks, the influence of certain parameters characterizing the setup of the measurement system on the overall uncertainty is quantified. A strategy is developed to incorporate multi-stylus measurements which are often inevitable when workpieces feature complex shapes. The findings are verified on a large involute gear which is 2 m in diameter. All measurements are performed on PTB's large coordinate measuring machine with a working range of 5 m x 4 m x 2 m.

Uncertainty assessment

Assessing uncertainties in measurements must become a standard practice in the field of urban drainage and stormwater management. This chapter presents three standard methods to estimate uncertainties: the Type A method (repeated measurements), the Type B method (law of propagation of uncertainties) and the MC method (Monte Carlo method). Each method is described with its fundamental principles and equations, various examples are presented in detail and Matlab® codes are given to facilitate the calculations for routine applications. An advanced method to account for partial autocorrelation in time series is presented. Lastly, typical orders of magnitude of standard uncertainties for usual sensors used in urban drainage and stormwater management are given.

TROPOMI glyoxal tropospheric column retrievals: description, inter-satellite comparison and validation

<p>The ESA S5p+Innovation programme aims at supporting the development of new TROPOMI scientific products. As part of this activity, a glyoxal tropospheric column algorithm, relying on heritage from SCIAMACHY, GOME-2 and OMI, has been adapted to TROPOMI and further developed. This product provides information on volatile organic compounds (VOC) emissions as glyoxal is mainly released in the atmosphere as an intermediate product of VOC oxidation, but also directly emitted from biomass burning events.</p><p>We present here the BIRA-IASB S5p glyoxal product, which relies on a DOAS approach: spectral fits in the 435-460 nm window provide glyoxal slant columns, which are then converted into tropospheric columns by means of air mass factors and application of a background correction. In particular, the algorithm has been improved to mitigate the impact of scene brightness inhomogeneity and of non-linearity in case of strong NO2 absorption. The retrieved columns are provided along with total error estimates resulting from the propagation of uncertainties at every step in the algorithm chain.</p><p>We also highlight the excellent consistency between the retrievals from TROPOMI and those from OMI and GOME-2A/B obtained with a similar algorithm. In addition, the good quality of the product is demonstrated with comparisons with MAX-DOAS glyoxal observations at a few stations in Asia and Europe.</p>

Scipp: Scientific data handling with labeled multi-dimensional arrays for C++ and Python

scipp is heavily inspired by the Python library xarray. It enriches raw NumPy-like multi-dimensional arrays of data by adding named dimensions and associated coordinates. Multiple arrays are combined into datasets. On top of this, scipp introduces (i) implicit handling of physical units, (ii) implicit propagation of uncertainties, (iii) support for histograms, i.e., bin-edge coordinate axes, which exceed the data’s dimension extent by one, and (iv) support for event data. In conjunction these features enable a more natural and more concise user experience. The combination of named dimensions, coordinates, and units helps to drastically reduce the risk for programming errors. The core of scipp is written in C++ to open opportunities for performance improvements that a Python-based solution would not allow for. On top of the C++ core, scipp’s Python components provide functionality for plotting and content representations, e.g., for use in Jupyter Notebooks. While none of scipp’s concepts in isolation is novel per-se, we are not aware of any project combining all of these aspects in a single coherent software package.

Uncertainty model for dual-Doppler retrievals of wind speed and wind direction

In this paper we present an analytical model for estimating the uncertainty of the horizontal wind speed based on dual-Doppler lidar measurements. The model follows the propagation of uncertainties method and takes into account the uncertainty of radial velocity estimation, azimuth and elevation pointing angles, and ranging. The model is achieved by coupling ranging and elevation angle to uncertainty of the probed wind speed through a simple power-law shear model. The model has been implemented in Python and made freely available through as the Python package YADDUM.

Matrix Presentation of Uncertainties Propagation in the Realization of ITS-90 Temperature Scale using Standard Platinum Resistance Thermometers

The paper presents a matrix approach to the propagation of uncertainties in the realization of the ITS-90 using Standard Platinum Resistance Thermometers (SPRT) calibrated at Defining Fixed Points (DFPs). The procedure allows correlations to be included between SPRT resistances measured during the calibration at the DFPs (i.e., the realization of the ITS-90) and the resistances measured during the subsequent use of the SPRT to measure temperature T90. The example also shows the possible contribution of these correlations to the overall temperature uncertainty measured by a calibrated SPRT.