Articles | Volume 28, issue 4
https://doi.org/10.5194/npg-28-565-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-28-565-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system
Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado, USA
Ian Grooms
Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado, USA
William Kleiber
Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado, USA
Related authors
No articles found.
Matthew LeDuc, Tomoko Matsuo, and William Kleiber
EGUsphere, https://doi.org/10.5194/egusphere-2025-5570, https://doi.org/10.5194/egusphere-2025-5570, 2025
This preprint is open for discussion and under review for Atmospheric Measurement Techniques (AMT).
Short summary
Short summary
We propose a new approach for inverse problems involving ratios of photon counts. We show that the method is computationally efficient and accurately handles the uncertainty introduced by count data. We demonstrate the method by estimating the temperature in the upper atmosphere in both calm and geomagnetically active conditions. We also present results that suggest this method can allow extension of these temperature retrievals to more times of day than current techniques.
Gokhan Danabasoglu, Frederic S. Castruccio, Burcu Boza, Alice M. Barthel, Arne Biastoch, Adam Blaker, Alexandra Bozec, Diego Bruciaferri, Frank O. Bryan, Eric P. Chassignet, Yao Fu, Ian Grooms, Catherine Guiavarc'h, Hakase Hayashida, Andrew McC. Hogg, Ryan M. Holmes, Doroteaciro Iovino, Andrew E. Kiss, M. Susan Lozier, Gustavo Marques, Alex Megann, Franziska U. Schwarzkopf, Dave Storkey, Luke van Roekel, Jon Wolfe, Xiaobiao Xu, and Rong Zhang
EGUsphere, https://doi.org/10.5194/egusphere-2025-5406, https://doi.org/10.5194/egusphere-2025-5406, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
A comparison of simulated and observed overturning transports across the Overturning in the Subpolar North Atlantic Program sections for the 2014–2022 period is presented. Eighteen ocean simulations participate in the study. The simulated transports are in general agreement with observations. Analyzing overturning circulations in both depth and density space together provides a more complete picture of the overturning properties. The study serves as a benchmark for evaluation of ocean models.
Edward H. Bair, Jeff Dozier, Karl Rittger, Timbo Stillinger, William Kleiber, and Robert E. Davis
The Cryosphere, 17, 2629–2643, https://doi.org/10.5194/tc-17-2629-2023, https://doi.org/10.5194/tc-17-2629-2023, 2023
Short summary
Short summary
To test the title question, three snow cover products were used in a snow model. Contrary to previous work, higher-spatial-resolution snow cover products only improved the model accuracy marginally. Conclusions are as follows: (1) snow cover and albedo from moderate-resolution sensors continue to provide accurate forcings and (2) finer spatial and temporal resolutions are the future for Earth observations, but existing moderate-resolution sensors still offer value.
Álvaro Ossandón, Manuela I. Brunner, Balaji Rajagopalan, and William Kleiber
Hydrol. Earth Syst. Sci., 26, 149–166, https://doi.org/10.5194/hess-26-149-2022, https://doi.org/10.5194/hess-26-149-2022, 2022
Short summary
Short summary
Timely projections of seasonal streamflow extremes on a river network can be useful for flood risk mitigation, but this is challenging, particularly under space–time nonstationarity. We develop a space–time Bayesian hierarchical model (BHM) using temporal climate covariates and copulas to project seasonal streamflow extremes and the attendant uncertainties. We demonstrate this on the Upper Colorado River basin to project spring flow extremes using the preceding winter’s climate teleconnections.
Cited articles
Anderson, J. L.: Localization and sampling error correction in ensemble Kalman
filter data assimilation, Mon. Weather Rev., 140, 2359–2371, 2012. a
Bannister, R. N.: A review of forecast error covariance statistics in
atmospheric variational data assimilation. I: Characteristics and
measurements of forecast error covariances, Q. J. Roy.
Meteor. Soc., 134, 1951–1970, https://doi.org/10.1002/qj.339, 2008. a
Bishop, C. H. and Hodyss, D.: Flow-adaptive moderation of spurious ensemble
correlations and its use in ensemble-based data assimilation, Q.
J. Roy. Meteor. Soc., 133, 2029–2044, 2007. a
Bolin, D. and Wallin, J.: Spatially adaptive covariance tapering, Spat.
Stat., 18, 163–178, https://doi.org/10.1016/j.spasta.2016.03.003, 2016. a, b, c, d
Buehner, M. and Shlyaeva, A.: Scale-dependent background-error covariance
localisation, Tellus A, 67, 28027,
https://doi.org/10.3402/tellusa.v67.28027, 2015. a
Burgers, G., van Leeuwen, P. J., and Evensen, G.: Analysis Scheme in the
Ensemble Kalman Filter, Mon. Weather Rev., 126, 1719–1724,
https://doi.org/10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2, 1998. a
Daley, D. J., Porcu, E., and Bevilacqua, M.: Classes of compactly supported
covariance functions for multivariate random fields, Stoch. Env.
Res. Risk A., 29, 1249–1263,
https://doi.org/10.1007/s00477-014-0996-y, 2015. a, b, c, d
Dormand, J. and Prince, P.: A family of embedded Runge-Kutta formulae,
J. Comput. Appl. Math., 6, 19–26,
https://doi.org/10.1016/0771-050X(80)90013-3, 1980. a
El Gharamti, M.: Enhanced Adaptive Inflation Algorithm for Ensemble
Filters, Mon. Weather Rev., 146, 623–640,
https://doi.org/10.1175/MWR-D-17-0187.1, 2018. a, b
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic
model using Monte Carlo methods to forecast error statistics, J.
Geophys. Res.-Oceans, 99, 10143–10162, https://doi.org/10.1029/94JC00572,
1994. a
Frolov, S., Bishop, C. H., Holt, T., Cummings, J., and Kuhl, D.: Facilitating
Strongly Coupled Ocean–Atmosphere Data Assimilation with an
Interface Solver, Mon. Weather Rev., 144, 3–20,
https://doi.org/10.1175/MWR-D-15-0041.1, 2016. a, b, c, d
Frolov, S., Reynolds, C. A., Alexander, M., Flatau, M., Barton, N. P., Hogan,
P., and Rowley, C.: Coupled Ocean–Atmosphere Covariances in Global
Ensemble Simulations: Impact of an Eddy-Resolving Ocean, Mon.
Weather Rev., 149, 1193–1209, https://doi.org/10.1175/MWR-D-20-0352.1, 2021. a, b
Gaspari, G. and Cohn, S. E.: Construction of correlation functions in two and
three dimensions, Q. J. Roy. Meteor. Soc., 125,
723–757, https://doi.org/10.1002/qj.49712555417, 1999. a, b, c, d
Genton, M. G. and Kleiber, W.: Cross-Covariance Functions for
Multivariate Geostatistics, Stat. Sci., 30, 147–163,
https://doi.org/10.1214/14-STS487, 2015. a, b, c
Gneiting, T.: Compactly Supported Correlation Functions, J.
Multivariate Anal., 83, 493–508, https://doi.org/10.1006/jmva.2001.2056, 2002. a, b
Gottwald, G. A. and Majda, A. J.: A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks, Nonlin. Processes Geophys., 20, 705–712, https://doi.org/10.5194/npg-20-705-2013, 2013. a
Greybush, S. J., Kalnay, E., Miyoshi, T., Ide, K., and Hunt, B. R.: Balance and
Ensemble Kalman Filter Localization Techniques, Mon. Weather
Rev., 139, 511–522, https://doi.org/10.1175/2010MWR3328.1, 2011. a
Houtekamer, P. L. and Mitchell, H. L.: Data Assimilation Using an
Ensemble Kalman Filter Technique, Mon. Weather Rev., 126,
796–811, https://doi.org/10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2, 1998. a
Houtekamer, P. L. and Mitchell, H. L.: A Sequential Ensemble Kalman
Filter for Atmospheric Data Assimilation, Mon. Weather Rev.,
129, 123–137, https://doi.org/10.1175/1520-0493(2001)129<0123:ASEKFF>2.0.CO;2, 2001. a
Houtekamer, P. L. and Zhang, F.: Review of the Ensemble Kalman Filter for
Atmospheric Data Assimilation, Mon. Weather Rev., 144, 4489–4532,
https://doi.org/10.1175/MWR-D-15-0440.1, 2016. a
Kelly, D., Majda, A. J., and Tong, X. T.: Concrete ensemble Kalman filters
with rigorous catastrophic filter divergence, P. Natl.
Acad. Sci. USA, 112, 10589–10594, https://doi.org/10.1073/pnas.1511063112,
2015. a
Lu, F., Liu, Z., Zhang, S., and Liu, Y.: Strongly Coupled Data
Assimilation Using Leading Averaged Coupled Covariance (LACC).
Part I: Simple Model Study, Mon. Weather Rev., 143,
3823–3837, https://doi.org/10.1175/MWR-D-14-00322.1, 2015. a, b, c, d
Morss, R. E. and Emanuel, K. A.: Influence of added observations on analysis
and forecast errors: Results from idealized systems, Q. J.
Roy. Meteor. Soc., 128, 285–321,
https://doi.org/10.1256/00359000260498897, 2002. a
Ménétrier, B., Montmerle, T., Michel, Y., and Berre, L.: Linear Filtering
of Sample Covariances for Ensemble-Based Data Assimilation.
Part I: Optimality Criteria and Application to Variance
Filtering and Covariance Localization, Mon. Weather Rev., 143,
1622–1643, https://doi.org/10.1175/MWR-D-14-00157.1, 2015. a
Penny, S. G., Bach, E., Bhargava, K., Chang, C.-C., Da, C., Sun, L., and
Yoshida, T.: Strongly Coupled Data Assimilation in Multiscale
Media: Experiments Using a Quasi-Geostrophic Coupled Model,
J. Adv. Model. Earth Sy., 11, 1803–1829,
https://doi.org/10.1029/2019MS001652, 2019. a
Porcu, E., Daley, D. J., Buhmann, M., and Bevilacqua, M.: Radial basis
functions with compact support for multivariate geostatistics, Stoch.
Env. Res. Risk A., 27, 909–922,
https://doi.org/10.1007/s00477-012-0656-z, 2013. a, b
Roh, S., Jun, M., Szunyogh, I., and Genton, M. G.: Multivariate localization methods for ensemble Kalman filtering, Nonlin. Processes Geophys., 22, 723–735, https://doi.org/10.5194/npg-22-723-2015, 2015. a, b, c, d
Shampine, L. F. and Reichelt, M. W.: The MATLAB ODE Suite, SIAM J.
Sci. Comput., 18, 1–22, https://doi.org/10.1137/S1064827594276424, 1997.
a
Shen, Z., Tang, Y., Li, X., Gao, Y., and Li, J.: On the localization in strongly coupled ensemble data assimilation using a two-scale Lorenz model, Nonlin. Processes Geophys. Discuss. [preprint], https://doi.org/10.5194/npg-2018-50, 2018. a
Sluka, T. C., Penny, S. G., Kalnay, E., and Miyoshi, T.: Assimilating
atmospheric observations into the ocean using strongly coupled ensemble data
assimilation, Geophys. Res. Lett., 43, 752–759,
https://doi.org/10.1002/2015GL067238, 2016. a
Smith, P. J., Lawless, A. S., and Nichols, N. K.: Estimating Forecast Error
Covariances for Strongly Coupled Atmosphere–Ocean 4D-Var
Data Assimilation, Mon. Weather Rev., 145, 4011–4035,
https://doi.org/10.1175/MWR-D-16-0284.1, 2017. a, b
Smith, P. J., Lawless, A. S., and Nichols, N. K.: Treating Sample
Covariances for Use in Strongly Coupled Atmosphere-Ocean Data
Assimilation, Geophys. Res. Lett., 45, 445–454,
https://doi.org/10.1002/2017GL075534, 2018. a, b, c
Smith, P. J., Lawless, A. S., and Nichols, N. K.: The role of cross-domain
error correlations in strongly coupled 4D-Var atmosphere–ocean data
assimilation, Q. J. Roy. Meteor. Soc., 146,
2450–2465, https://doi.org/10.1002/qj.3802, 2020. a
Stanley, Z.: zcstanley/Multivariate_Localization_Functions: Code for resubmission (2.0), Zenodo [code], https://doi.org/10.5281/zenodo.4973844, 2021. a
Wang, X., Chipilski, H. G., Bishop, C. H., Satterfield, E., Baker, N., and
Whitaker, J. S.: A Multiscale Local Gain Form Ensemble Transform
Kalman Filter (MLGETKF), Mon. Weather Rev., 149, 605–622,
https://doi.org/10.1175/MWR-D-20-0290.1, 2021. a
Wilks, D. S.: Effects of stochastic parametrizations in the Lorenz '96 system,
Q. J. Roy. Meteor. Soc., 131, 389–407,
https://doi.org/10.1256/qj.04.03, 2005. a
Ying, Y., Zhang, F., and Anderson, J. L.: On the Selection of Localization
Radius in Ensemble Filtering for Multiscale Quasigeostrophic
Dynamics, Mon. Weather Rev., 146, 543–560,
https://doi.org/10.1175/MWR-D-17-0336.1, 2018. a, b
Yoshida, T. and Kalnay, E.: Correlation-Cutoff Method for Covariance
Localization in Strongly Coupled Data Assimilation, Mon. Weather
Rev., 146, 2881–2889, https://doi.org/10.1175/MWR-D-17-0365.1, 2018. a, b, c
Short summary
In weather forecasting, observations are incorporated into a model of the atmosphere through a process called data assimilation. Sometimes observations in one location may impact the weather forecast in another faraway location in undesirable ways. The impact of distant observations on the forecast is mitigated through a process called localization. We propose a new method for localization when a model has multiple length scales, as in a model spanning both the ocean and the atmosphere.
In weather forecasting, observations are incorporated into a model of the atmosphere through a...