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Application of Normal-Mode Function Decomposition in Weather and Climate Research. in: Modal VIew of Atmospheric Variability

The book introduces the theory and computation of the normal-mode functions, reviews the applications of the normal modes in data assimilation and initialization of numerical weather prediction models, and for predictability research, and offers an up-to-date overview of research of atmospheric variability and energy transfers in terms of the Rossby and inertia-gravity waves across scales. Full reference: Application of Normal-Mode Function Decomposition in Weather and Climate Research. in: Modal VIew of Atmospheric Variability, Eds.: N. Žagar, and J. Tribbia. Mathematics of Planet Earth (8), Springer (2020), ISBN 978-3-030-60963-4, https://doi.org/10.1007/978-3-030-60963-4

Inferring atmospheric dynamics from aerosol observations in 4D-Var

In current 4D-Var systems for Numerical Weather Prediction (for example, at ECMWF), aerosols are treated as passive scalars meaning that their impact on the analysis increments of other variables, for example, wind, is turned off. This study assessed the potential of aerosol observations to improve wind analyses in 4D-Var systems. The potential impact strongly depends on the tracer relative spatial gradients in the background field. We showed, using CAMS (Copernicus Atmosphere Monitoring Service) data, that the mean magnitude of the relative horizontal gradients of the total aerosol mass mixing ratio is more than twice as large as the specific humidity relative gradients throughout the troposphere and stratosphere. In the stratosphere, aerosol relative gradients are comparable to ozone relative gradients (figure). The main result is that a combined assimilation of the aerosol and humidity data in 4D-Var improves the analysis with respect to only humidity data, while assimilating also temperature data additionally improves the wind analysis. The improvement is significantly smaller with respect to that obtained by assimilating direct wind observations, meaning that direct wind observations are indispensable. However, in the global observing system missing direct wind observations and with an increasing number of observations of atmospheric composition, the aerosol effects in 4D-Var are worth further investigation for the purpose of operational weather forecasting. Full reference: Zaplotnik Ž, Žagar N, Benedetti A, Semane N, 2020: Inferring atmospheric dynamics from aerosol observations in 4D-Var. Q.J.R. Meteorol. Soc.,146, 1403–1422, https://doi.org/10.1002/qj.3743

Atmospheric Subseasonal Variability and Circulation Regimes: Spectra, Trends, and Uncertainties

The globally integrated subseasonal variability associated with the two main atmospheric circulation regimes, the balanced (or Rossby) and unbalanced (or inertia–gravity) regimes, is evaluated for the four reanalysis datasets: ERA-Interim, JRA-55, MERRA, and ERA5. The results quantify amplitudes and trends in midlatitude traveling and quasi-stationary Rossby wave patterns as well as in the equatorial wave activity across scales. A statistically significant reduction of subseasonal variability is found in Rossby waves with zonal wavenumber k = 6 along with an increase in variability in wavenumbers k = 3–5 in the summer seasons of both hemispheres. The four reanalyses also agree regarding increased variability in the large-scale Kelvin waves, mixed Rossby–gravity waves, and westward-propagating inertio-gravity waves with the lowest meridional mode. The amplitude and sign of trends in inertia–gravity modes with smaller zonal scales and greater meridional modes differ between the ERA-Interim and JRA-55 datasets on the one hand and the ERA5 and MERRA data on the other. An increased variability in the ERA-Interim and JRA-55 accounts for positive trends in their total subseasonal variability. Full reference: Žagar, N., Ž. Zaplotnik, and K. Karami, 2020: Atmospheric Subseasonal Variability and Circulation Regimes: Spectra, Trends, and Uncertainties. J. Climate, 33 (21), 9375–9390, https://doi.org/10.1175/JCLI-D-20-0225.1

Energy spectra in inertio-gravity waves

MODES has provided a novel approach for the spatial filtering of the inertia-gravity (IG) waves in global analysis data.
The method is applied to the ECMWF interim reanalysis and the operational 2014–16 analysis fields. The derived spectrum of IG wave energy is divided into three regimes: a part associated with the large-scale unbalanced circulations that has a slope close to −1 for zonal wavenumbers up to k=6, a synoptic-scale range between 3000 and around 500 km that is characterized by a nearly −5/3 slope, and a mesoscale range below 500 km where the slope of the IG energy spectrum in the 2015/16 analyses is steeper.
In contrast, the energy spectrum of the Rossby waves has a −3 slope for all zonal wavenumbers greater than k=6.
Presented results suggest that energy associated with the IG modes exceeds the level of energy associated with the Rossby waves around zonal wavenumber 35. The exact wavenumber depends on the season and considered atmospheric depth and it is suggested as a cutoff scale for studies of gravity waves. Full J. Atmos. Sci. paper is available here .

A global view of the limits of prediction skill of NWP models

The scale-dependent growth of the global forecast uncertainties simulated by the operational ensemble prediction system of the European Centre for Medium-Range Weather Forecasts. It is shown that the initial uncertainties are largest in the tropics and have biggest amplitudes at the large scales. The growth of forecast uncertainties (ensemble spread) takes place at all scales from the beginning of forecasts. The growth is nearly uniform in the zonal wavenumbers 1–5 and strongly scale-dependent in the larger wavenumbers. Moreover, the growth from initial uncertainties at large scales appears dominant over the impact of errors cascading up from small scales.
The growth of uncertainties is found to be faster in the balanced than in the unbalanced modes and after 0.5–1 day of forecasts the balanced errors become dominant except at the subsynoptic scales. Full Tellus A paper is available here .

Information Content of Observations in the Global EnKF Data Assimilation

Modal approach has been developed to estimate the efficiency of data assimilation to reduce the prior uncertainties in the global data assimilation systems.
The approach has been applied to the ensemble Kalman filter data assimilation system DART/CAM. Observing ssytem simulation experiments employed the perfect-model framework and a globally homogeneous network of wind and temperature profiles.
The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully.
It is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is associated with the applied radius for the covariance localization. Full Mon. Wea. Rev. paper is available here

Scale-dependent estimates of the growth of global forecast uncertainties

MODES has been applied for a scale-dependent estimates of the growth of forecast uncertainties in a global prediction system.
A new parametric model for the representation of the forecast error growth is formulated and applied independently to every zonal wavenumber. In contrast to the standard fitting method, the new fitting function involves no time derivatives and provides the asymptotic values of the forecast errors as a function of the fitting parameters.
The new model is easily transformed to the widely used model of Dalcher and Kalnay (1987) to discuss the scale-dependent growth as a sum of two terms, the so-called alpha and beta terms. Their comparison shows that at planetary scales their contributions to the growth in the first two days are similar whereas at small scales the term describes most of a rapid exponential growth of errors towards saturation. Full Tellus A paper is available here .

Short-term forecast errors and balance issues

Some properties of the short-term forecast errors are modelled in the background-error covariance matrix for data assimilation. The three-dimensional decomposition of forecast errors derived from the ensemble of analyses and forecasts of the ECMWF system suggests that a significant part of the short-term forecast errors (as modelled by the ensemble spread) is associated with the inertio-gravity mods.
Full reference: Žagar, N. , L. Isaksen, D. Tan and J. Tribbia, 2013: Balance properties of the short-range forecast errors in the ECMWF 4D-Var ensemble. Q. J. R. Meteorol. Soc., 139, 1229-1238. DOI: 10.1002/qj.2033. Paper is available on request.

Modal view of the global predictability with application to ECMWF ensemble prediction system

A new methodology for the analysis of atmospheric predictability has been developed and applied to the ECMWF operational ensemble prediction system. It is based on the representation of atmospheric dynamical variables in terms of normal mode functions and the computation of the ensemble spread in modal space.
Full reference: N. Žagar, R. Buizza and J. Tribbia, 2015: A Three-Dimensional Multivariate Modal Analysis of Atmospheric Predictability with Application to the ECMWF Ensemble. J. Atmos. Sci., 72, 4423–4444. Paper is available here or as pdf on request.

Description of the MODES software

Paper on the theory and technical development of the MODES software has been published in Geoscientific Model Development
N. Žagar, A. Kasahara, K. Terasaki, J. Tribbia and H. Tanaka, 2015: Normal-mode function representation of global 3-D data sets: open-access software for the atmospheric research community. Full text and pdf are available here .
MODES is compiled by using gfortran although other options have been succesfully tested. The application requires the use of the netcdf and (optionally) grib-api libraries.

Representation of MJO in terms of 3D normal-mode functions

MODES has been applied for a three-dimensional multivariate decomposition of the Madden-Julian Oscillation into balanced and inertio-gravity components. The decomposition provides a quantitative comparison between the roles of the Kelvin mode and the equatorial Rossby mode as well as the MJO teleconnections.
Full reference: N. Žagar and C. Franzke, 2015: Systematic decomposition of the Madden-Julian Oscillation into balanced and inertio-gravity components, Geophys. Res. Lett., 42, 6829–6835. Paper text and pdf are available here .