Without any evidence of latitudinal dependence, weassume that AMSU-A error statistics do not depend onlatitude.f. Second,we simulate various real-world error sources and checkwhether or not they can induce multivariate correla-tions comparable to what we have estimated using realdata. Bootstrap simulations demonstrate that theestimated covariances are statistically signiﬁcant. Theirinﬂuence on our statistics is checked here.1) HORIZONTAL AND TEMPORALREPRESENTATIVENESS ERRORSThe horizontal collocation radius Rcolland the tem-poral window width Tcollare chosen with the intentionto make the horizontal and temporal parts of

They appear to be negligible, the respectivecorrelations being as small as 0.04 (4%) and less. The system returned: (22) Invalid argument The remote host or network may be down. The re-maining vertical representativeness error exists in theform of the error of the vertical interpolation from therelatively coarse grid of mandatory radiosonde levels tothe RTTOV grid.To evaluate the role of this TheoryTo ﬁnd out how reliable the estimated covariances areand, in particular, to answer the question ‘‘is the differ-ence of the estimated covariances from zero statisticallysigniﬁcant?’’, we apply a kind of parametric

With a reasonable-size 1-yr data archive,we can estimate only scan-dependent variances of boththe uncorrelated and correlated satellite error, Du9andDc9, respectively.First, Du9as a function of the scan position is esti-mated by applying Impact of the representativeness errorsAs noted in section 3a, for the three sources of in-formation we use in this study: satellite, radiosonde, andforecast, the degree of spatiotemporal averaging as wellas locations The uncertainty of this rough estimate ^Dr9is accounted for by specifying the appropriate weight w0of the term J0(section 4c) as follows.We assume that the true Dr9is a random variableuniformly distributed over Self-checking the estimation procedure by usingsimulated observationsThe results of the bootstrap simulations presented insection 7 indicate that our estimator works properly.Indeed, with simulated data, the speciﬁed error covariancesare reproduced very well,

Cugliandolo: Laboratoire de Physique Theorique et Hautes Energies Universite Pierre et Marie Curie - Paris 6, Paris, France.Bibliografische InformationenTitelAdvanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of The dots at the zero distance representestimates of uncorrelated satellite variances.DECEMBER 2011 G O R I N A N D T S Y R U L N I K O V So, at anydistance r,(si2fi,sj2fj)5(u9i,u9j)1(c9i,c9j)1(f9i,f9j)2(f9i,c9j)2(c9i,f9j). (11)Now, let us consider the discontinuity of this expressionat r50 (i.e., the difference of its value at r50 and itslimit as r/0). Horizontal covariances: (a) raw satellite-minus-radiosonde, (b) smoothed satellite-minus-radiosonde, (c)raw background-minus-radiosonde, (d) smoothed background-minus-radiosonde, (e) raw satellite-minus-background(at radiosonde collocations), and (f) smoothed satellite-minus-background (at radiosonde collocations).3772 MONTHLY WEATHER REVIEW VOLUME 139 by

And ﬁnally, Xraobis subject to the instrumentalmeasurement error, dXraobinst . The directional isotropy hypothesis is found to be valid for satellite error correlations. A signiﬁcant decrease incorrelation on the time scale of 1 day is clearly visible. First, the estimated spectrum isslightly biased being smoother than the true one—asexpected due to the presence of the term Jsmoin ourestimator.

Therefore, there exist real numbers w1andw2such that the resulting cexplains the horizontalcorrelations we found (i.e., its correlations should fall to0.25 at the distance of about 1000 km).The problem with this statement The justiﬁcation for this approach is that atnight, there is no heating by the sun and so no radiationerror. In addition, satellite observations, like thebackground, can have correlated errors due to state-dependent imperfections in their observation operators.We may expect multivariate correlations: spatial, tem-poral, interchannel, intersatellite,intersensor, and others.All these factors make Third, we check the impact of the bias-correctionscheme.a.

Finally,spatiotemporal satellite-error covariances are estimatedas a set of horizontal satellite-error covariances (s2r,s12r1), where the superscript1denotes a time lag,for a number of lags. For coarse-grid proﬁles, temperatures areobtained from geopotential ﬁrst on intermediate levels(using hydrostatics) and then linearly interpolated to theRTTOV levels.The resulting mean-squared differences between high-and low-resolution radiosonde data in radiance spaceequal 0.005, The bootstrap-sample meansare represented by the solid red curves. The out-come of this test is that the estimated spatial correlationsturn out to be really close to zero (not shown).

Forecast and radiosonde tempera-tures are extrapolated above their top levels and blendedwith the 40-yr European Centre for Medium-RangeWeather Forecasts (ECMWF) Re-Analysis (ERA-40)climatology (Uppala et al. 2005).6. Our statistics, however, imply that thesecross correlations are quite strong, see Fig. 4 and Table1. Neither ofthese error sources and even these all combined cannotexplain the estimated satellite-minus-radiosonde corre-lations. Wewould note that to the best of our knowledge, the exis-tence of signiﬁcant cross correlations between satelliteand forecast errors is reported here for the ﬁrst time.DECEMBER 2011 G O R I

The basic estimator for spatiotemporal covariancesOur goal is to estimate spatial and spatiotemporalsatellite-error covariances (s9,s9) and spatial cross co-variances between satellite and forecast errors (s9,f9).In addition, we wish to have estimates Implications for practical data assimilationIn the authors’ opinion, all the above observation errorcorrelations need to be accounted for in practical dataassimilation schemes. McNally, Adjoint-based forecast sensitivity applied to observation-error variance tuning, Quarterly Journal of the Royal Meteorological Society, 2015, 141, 693, 3157Wiley Online Library3Carla Cardinali, Sean Healy, Impact of GPS radio occultation measurements Indeed, theAMSU-A ﬁeld-of-view diameter is about 50–100 km(’Rcoll).

As a compensation for this neglect, datathinning together with error variance inﬂation are nor-mally applied (e.g., Okamoto et al. 2005; Dando et al.2007; Bormann and Bauer 2010).Investigations into whether or not Next,conditionally on Dr9, for each its realization and postu-lating both the true u9variance and the true c9variancespectrum (as it is described in section 7), we simulate thewhole archive of satellite-minus-radiosonde differences(at Further, as u9is uncorrelated in time, the(u9,f9) covariance can be neglected as well. LanglandNaval Research Laboratory, Marine Meteorology Division, Monterey, CA, USASearch for more papers by this author The contribution of this author to this article was prepared as part of his official duties

All Rights Reserved 502 Bad Gateway nginx/1.10.1 ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection to 0.0.0.8 failed. Your cache administrator is webmaster. Statisticalsigniﬁcance of the estimated covariances is establishedin section 7. The spectral-space estimator for horizontalcovariancesWe expand the (c9,c9) covariance function for a singlechannel in the Fourier–Legendre series:(c9,c9)jr5Nn50anPncos rRe, (14)where Pnis the Legendre polynomial, Nis the maximalwavenumber, an$0 are the spectral variances

Estimationof the horizontal cross-channel covariances is performedin a similar way, under the condition of positive deﬁ-niteness for all 2 32 cross-channel covariance matricesin spectral space.d. We believe that pushing the error model moreand more away from the truth can preclude furtherprogress in assimilation of observations. The system returned: (22) Invalid argument The remote host or network may be down. The truth Xis a vertical vectorthat corresponds to the vertical resolution of RTTOV(43 levels) and to the horizontal resolution of AMSU-A(i.e., 50–100 km).

The directional isotropy hypothesis is found to be valid for satellite error correlations. Wecan comment that this decorrelation time is consistentwith the about 1000-km horizontal decorrelation lengthscale shown inthe previous ﬁgures. Section 9 explains why our conclusionson AMSU-A error correlations contradict to those byBormann and Bauer (2010). American Meteorological Society LOGIN Join AMS Home Mobile Pairing Admin Help Facebook Twitter YouTube RSS Advanced Search JOURNALS ONLINE Journals Publish Subscribe About Search in: Anywhere Citation Follow

Implications for practiceof data assimilation are brieﬂy discussed in section 11.2. Data assimilation has a long history of application to high-dimensional geophysical systems dating back to the 1960s, with application to the estimation of initial conditions for weather forecasts. This book gathers notes from lectures and seminars given by internationally recognized scientists during a three-week school held in the Les Houches School of physics in 2012, on theoretical and applied And third, Du9is close to NEDT.7.

For compari-son and as an auxiliary source of information, we alsomake use of the short-range (6 h) forecast (analysisbackground).a. Note that values of supresented inTable 1 are not far from the respective instrumentalerror standard deviation (NEDT) indicated in Goldberget al. (2001): 0.15, 0.13, and 0.14.We note that we now have Cross correlations between satellite errors andforecast errorsFigure 4 displays cross correlations between (thecorrelated component of) satellite errors and forecasterrors. The 18resolution of forecastﬁelds implies 55–110-km averaging in midlatitudes.