Articles | Volume 30, issue 3
Research article
19 Sep 2023
Research article |  | 19 Sep 2023

How far can the statistical error estimation problem be closed by collocated data?

Annika Vogel and Richard Ménard

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Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Cited articles

Anthes, R. and Rieckh, T.: Estimating observation and model error variances using multiple data sets, Atmos. Meas. Tech., 11, 4239–4260,, 2018. a, b, c, d
Crow, W. T. and van den Berg, M. J.: An improved approach for estimating observation and model error parameters in soil moisture data assimilation, Water Resour. Res., 46, W12519,, 2010. a, b
Crow, W. T. and Yilmaz, M. T.: The Auto-Tuned Land Data Assimilation System (ATLAS), Water Resour. Res., 50, 371–385,, 2014. a
Daley, R.: The Effect of Serially Correlated Observation and Model Error on Atmospheric Data Assimilation, Mon. Weather Rev., 120, 164–177,<0164:TEOSCO>2.0.CO;2, 1992a. a
Daley, R.: The Lagged Innovation Covariance: A Performance Diagnostic for Atmospheric Data Assimilation, Mon. Weather Rev., 120, 178–196,<0178:TLICAP>2.0.CO;2, 1992b. a, b
Short summary
Accurate estimation of the error statistics required for data assimilation remains an ongoing challenge, as statistical assumptions are required to solve the estimation problem. This work provides a conceptual view of the statistical error estimation problem in light of the increasing number of available datasets. We found that the total number of required assumptions increases with the number of overlapping datasets, but the relative number of error statistics that can be estimated increases.