IOP PUBLISHING METROLOGIA Metrologia 44 (2007) L23–L30 doi:10.1088/0026-1394/44/3/N02 SHORT COMMUNICATION Evaluating the uncertainties of data rendered by computational models Raul R Cordero 1 , Gunther Seckmeyer 1 and Fernando Labbe 2 1 Leibniz Universit¨ at Hannover, Herrenh¨ auser Str. 2, 30419 Hannover, Germany 2 Universidad T´ ecnica Federico Santa Maria, Ave. Espa ˜ na 1680, Valpara´ ıso, Chile Received 30 January 2007 Published 21 May 2007 Online at stacks.iop.org/Met/44/L23 Abstract Computational models allow calculation of the value of an output quantity from a set of linked input quantities. The value of the output quantity yielded by a model is evidently influenced by errors in the determination of the input quantities. Therefore, the uncertainties of the output data can be expressed in terms of the uncertainties of the input quantities by using a Monte Carlo-based uncertainty propagation technique. As an example, we evaluated the uncertainty of the spectral UV irradiance rendered by a radiative transfer model under cloudless sky conditions. This model allows calculation of the spectrally resolved solar UV irradiance from some set of measured input quantities linked with the concentration of atmospheric constituents, the surface reflectivity as well as the spectral characteristics of the aerosol modulation. Although only a single model was used in this work, the methodology applied to evaluate the uncertainty is general and can be applied to any other computational model. 1. Introduction By international accord, the standard uncertainty associated with the best estimate of a measurand can be calculated from the standard deviation of the probability density function (PDF) that describes the state of knowledge about the measurand. The PDF of a non-varying stable quantity can be inferred by measuring directly and repeatedly under repeatability conditions the measurand with an instrument that shows negligible drift during the observation period [1, 2]. Frequently the measurand is not directly measured but is calculated through a measurement model that allows an output quantity (the value of the measurand) to be expressed in terms of linked input quantities (usually directly measured primary quantities). In this case, the standard uncertainty of the output quantity can be obtained from the standard uncertainties of the input quantities by using the well-known law of propagation of uncertainties (LPU) [2]. However, the LPU renders reliable standard uncertainties only if the involved measurement model is linear or weakly non-linear; otherwise, a general procedure based on a Monte Carlo simulation, known as the law of propagation of distributions (LPD) [3, 4], should be applied. The LPD is valid for both linear and non-linear models and yields the PDF of the output quantity, whose standard deviation can be in turn used to evaluate the standard uncertainty. The data rendered by a computational model depend on the values of the quantities needed to run the model. Then, if the calculated value corresponds to a measurand, the computational model becomes a measurement model that allows the output quantity (the value rendered by the model) to be evaluated from the values of the input quantities (those needed to run the model). Because a computational model can involve a set of strongly nonlinear equations, we argue that the uncertainty of the calculated values rendered by the model can be evaluated by applying the LPD. In this paper, we report on the application of a Monte Carlo-based uncertainty propagation technique to evaluate the uncertainties of the data rendered by a computational model. The uncertainty evaluation involves calculating the output of the selected model a large number of times by using sets of input data generated according to the PDFs attributed to the input quantities needed to run the model. Then, the mean and standard deviation of the outputs, obtained by the large number of calculations, are numerically computed and taken to be the best estimate and its associated standard uncertainty, respectively. 0026-1394/07/030023+08$30.00 © 2007 BIPM and IOP Publishing Ltd Printed in the UK L23