Description

Error propagation equations combine two or more random Errors together and propagate uncertainty according to a standard set of rules. For example, in the Manning equation:

N: Manning Roughness A: Area P: Wetted Perimenter S: Slope V: Velocity

With the assumption that the Manning surface roughness, the area and the wetted perimeter are uncertain, the Error could be quantified as:

Standard rules for the error propagation equations can be found in many standard handbooks on statistics and measurement error analysis.

Software

none

Advantages

• Requires very little resources Most computation can be performed on a piece of paper and requires only minimal computations.

• Very Quick There is no major additional computational burden involved besides the derivation of the error equation

Disadvantages

• Assumes Gaussian and independent errors In the basic version it is assumed that the error around the measurements is normal, which is not always the case in nature. For example, many thermostats measure temperature more accurately at room temperature than at low temperatures. In such a case the distribution would be skewed and non-gaussian. However, the method can be extended to allow for non-Gaussian distributions and covariance (Goodman, 1960; Ku, 1966).

• Difficult to apply in complex calculations The more complex and non-linear the equations are the more difficult is it to apply all the rules for error propagation.

• Assumes correct model structure The error equations are based on the assumption that the underlying model is correct. However, for example, there is a large variety of alternatives to the Manning equation, for which this methodology could not take account for.

References and Further Reading

Kunstmann H., Kastens, M., Direct propagation of probability density functions in hydrological equations, Journal of Hydrology 325 (2006) 82–95

van der Sluijs, J., J. Risbey, P. Kloprogge, J. Ravetz, S. Funtowicz, S. Quintana, A. Pereira, B. De Marchi, A. Petersen, P. Janssen, R. Hoppe, and S. Huijs, RIVM/MNP Guidance for uncertainty Assessment and Communication. 2003, University of Utrecht & RIVM: Utrecht. (download from http://www.nusap.net/)

Benjamin, J.R. and Cornell, C.A., 1993. Probability, Statistics, and Decision for Civil Engineers. McGraw?. Hill, New York.

Goodman, L., 1960. On the Exact Variance of Products. Journal of the American Statistical Association: 708-713.

Ku, H., 1966. Notes on the Use of Propagation of Error Formulas. J Research of National Bureau of Standards-C. Engineering and Instrumentation, 70(4): 263-273.