Assimilation. Data assimilation is an analysis technique in which the observed information is accumulated into the model state by taking advantage of consistency constraints with laws of time evolution and physical properties.
3D-VAR:
4D-VAR:
Ensemble Kalmin Filter: Wikipedia Link
Model Resolution and Spherical Harmonics
Gridded data on a sphere can instead be represented by a series of spherical harmonic functions. This can both reduce data storage and computation as well as make some calculations easier to perform. The series is generally truncated to some zonal and meridional wavenumbers. The higher the numbers, the higher the spatial resoltuion retained. Two common truncations are triangular where the zonal and meridional wave numbers retained are the same and rhomboidal where the zonal and meridional add up to a constant. More information can be found in NCAR's description of the ERA-40 dataset, and a nice illustration from euromet.
The ECMWF spectral model is based on a triangular truncation (indicated by TLM where M is the maximum zonal wavenumber). The model employs reduced Gaussian grids for all computations in physical space. A Gaussian grid has a variable spacing of latitude circles which is optimized for transforms to and from physical space that are needed in the model calculations. In a reduced Gaussian grid the number of grid points per latitude circle is reduced as the distance from the equator increases, which results in a more uniform distribution of grid points on the sphere.
More details can be found in the ECMWF training course notes. For Gaussian grids, the resolution is indicated by NX where X is the number of latitude circles between equator and pole. Information about grid point spacing for various Gaussian grid resolutions used at ECMWF can be found here.
Homepage:
Reference:
The NCEP Climate Forecast System Reanalysis:
Suranjana Saha, Shrinivas Moorthi, Hua-Lu Pan, Xingren Wu, Jiande Wang, Sudhir Nadiga, Patrick Tripp, Robert Kistler, John Woollen, David Behringer, Haixia Liu, Diane Stokes, Robert Grumbine, George Gayno, Jun Wang, Yu-Tai Hou, Hui-ya Chuang, Hann-Ming H. Juang, Joe Sela, Mark Iredell, Russ Treadon, Daryl Kleist, Paul Van Delst, Dennis Keyser, John Derber, Michael Ek, Jesse Meng, Helin Wei, Rongqian Yang, Stephen Lord, Huug van den Dool, Arun Kumar, Wanqiu Wang, Craig Long, Muthuvel Chelliah, Yan Xue, Boyin Huang, Jae-Kyung Schemm, Wesley Ebisuzaki, Roger Lin, Pingping Xie, Mingyue Chen, Shuntai Zhou, Wayne Higgins, Cheng-Zhi Zou, Quanhua Liu, Yong Chen, Yong Han, Lidia Cucurull, Richard W Reynolds, Glenn Rutledge, Mitch Goldberg, 2010: The NCEP Climate Forecast System Reanalysis. Bull. Amer. Met. Soc. 91, 1015-1057. doi: 10.1175/2010BAMS3001.1
Dear Albeht,
It appears your comment was cut off. Please re-post.
thanks,
gil
Quantifying with definitive assurance the accuracy of a data point as defined by ISO 5725-1 (trueness and precision) requires an absolute reference. However, the atmosphere is not covered at all times and all locations with such a network of absolute measurement points. Please read the ERA-Interim page on the NCAR Climate Data Guide for a detailed qualitative discussion of all the difficulties in estimating accuracy in reanalyses ( https://climatedataguide.ucar.edu/reanalysis/era-interim ). However, with these limitations in mind, we can estimate quantitatively the relative accuracy (trueness and precision) of atmospheric reanalyses, with respect to unevenly distributed and imperfect observations. Of course, these metrics are only valid at the observation locations and times, but they may serve as guidance. First, look for example at Figure 16 by Poli et al. 2010 for regional vertical profile estimates of global relative accuracy (trueness estimated by bias, and precision estimated by standard deviation) of ERA-Interim temperatures, with respect to radiosondes. Bear in mind that these numbers are not an upper bound as errors could be correlated or present similar biases, as radiosondes are assimilated in reanalyses, so the errors in either radiosondes and in ERA-Interim could be larger than the difference between the two. These numbers are also not a lower bound for the relative accuracy of radiosondes and ERA-Interim, as in some locations and times the errors could be smaller than shown by these estimates covering large areas of the globe. The same Figure also shows comparison with aircraft measurements, which gives you a hint to appreciate the relative accuracy estimates using another observation reference. Second, depending on your application, the variation in time of the accuracy (trueness and precision) may also be of importance. Look at time-series, e.g. Figure 18 by Dee et al. 2011 (see Figure 19 for humidity), as well as Figures 6, 7, and 9 by Poli et al. 2010 to appreciate the magnitude of changes in relative accuracy (trueness and precision). Last, for a hint at how these relative accuracy estimates vary locally in the spatial domain, consider also that remote regions may present larger errors due to paucity of observational information in the reanalyses, such as shown in Figure 1 by Dee and Uppala 2009 for locations at latitudes greater than 70 degrees North.
References
Dee, D. P. and Uppala, S. (2009), Variational bias correction of satellite radiance data in the ERA-Interim reanalysis. Q.J.R. Meteorol. Soc., 135: 1830–1841. doi: 10.1002/qj.493
Poli, P., Healy, S. B. and Dee, D. P. (2010), Assimilation of Global Positioning System radio occultation data in the ECMWF ERA–Interim reanalysis. Q.J.R. Meteorol. Soc., 136: 1972–1990. doi: 10.1002/qj.722
Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A. C. M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A. J., Haimberger, L., Healy, S. B., Hersbach, H., Hólm, E. V., Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M., McNally, A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park, B.-K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.-N. and Vitart, F. (2011), The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q.J.R. Meteorol. Soc., 137: 553–597. doi: 10.1002/qj.828
Uppala, S.M., Kållberg, P.W., Simmons, A.J., Andrae, U., da Costa Bechtold, V., Fiorino, M., Gibson, J.K., Haseler, J., Hernandez, A., Kelly, G.A., Li, X., Onogi, K., Saarinen, S., Sokka, N., Allan, R.P., Andersson, E., Arpe, K., Balmaseda, M.A., Beljaars, A.C.M., van de Berg, L., Bidlot, J., Bormann, N., Caires, S., Chevallier, F., Dethof, A., Dragosavac, M., Fisher, M., Fuentes, M., Hagemann, S., Hólm, E., Hoskins, B.J., Isaksen, L., Janssen, P.A.E.M., Jenne, R., McNally, A.P., Mahfouf, J.-F., Morcrette, J.-J., Rayner, N.A., Saunders, R.W., Simon, P., Sterl, A., Trenberth, K.E., Untch, A., Vasiljevic, D., Viterbo, P., and Woollen, J. 2005: The ERA-40 re-analysis. Quart. J. R. Meteorol. Soc., 131, 2961-3012.doi:10.1256/qj.04.176
North American Regional Reanalysis.
Mesinger, Fedor; Dimego, Geoff; Kalnay, Eugenia; Mitchell, Kenneth; Shafran, Perry C.; Ebisuzaki, Wesley; Jovi, DuAn; Woollen, Jack; Rogers, Eric; Berbery, Ernesto H.; Ek, Michael B.; Fan, Yun; Grumbine, Robert; Higgins, Wayne; Li, Hong; Lin, Ying; Manikin, Geoff; Parrish, David; Shi, Wei
Bulletin of the American Meteorological Society, vol. 87, Issue 3, pp.343-360, http://dx.doi.org/10.1175/BAMS-87-3-343
Kanamitsu, Masao, Wesley Ebisuzaki, Jack Woollen, Shi-Keng Yang, J. J. Hnilo, M. Fiorino, G. L. Potter, 2002: NCEP–DOE AMIP-II Reanalysis (R-2). Bull. Amer. Meteor. Soc., 83, 1631–1643. doi:10.1175/BAMS-83-11-1631
Megha,
Please obtain a login for reanalyses.org at https://reanalyses.org/atmosphere/ncep2-references . Then the paper authors can contact you directly.
You may also be able to access the paper at the digital object identifier (doi) http://dx.doi.org/10.1175/BAMS-83-11-1631.
best wishes,
gil compo
, E., , , , , , , , , , , , , , , , , , , , , , 1996: The NCEP/NCAR 40-year reanalysis project, Bull. Amer. Meteor. Soc., 77, 437-470, doi: 10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2.
, R., , , , , , , , , , H., , and The NCEP–NCAR 50–Year Reanalysis: Monthly Means CD–ROM and Documentation, Bull. Amer. Meteor. Soc., 82, 247-267, doi:10.1175/1520-0477(2001)082<0247:TNNYRM>2.3.CO;2.
Dear sir/ma'am
I am interested in using the NCEP reanalysis wind data to generate wind stress fields in my region of interest. I would like to know if there is there any scaterometer data assimilation for the NCEP reanalysis I or II. I found a report on NCEP/NCAR reanalysis on the website describing the assimilation of SSMI satellite data for wind speeds, but this works for me because this satellite acquires data from microwaves. If so, could you specify which satellite is used ? Are there any dataset that do not assimilate scaterometer data ?
Thank you for your help.
Sincerely,
Igor
ERa-Interim resolutions
Dear Sr.
How is the 0.5, 0.25 and other degree resoltution from N128 reduced Gaussian grid in ERa-Interim. Where