Nedjeljka Zagar - Dynamics of data assimilation in the tropics
An important information source for understanding the tropical climate system, the global hydrological cycle and stratospheric transports are (re)analysis fields (e.g. NCEP/NCAR or ERA-40 reanalyses) produced by combining observations and prior information coming from numerical weather prediction (NWP) models (a short-range forecast). Two pieces of information are weighted according to their error characteristic in the process of data assimilation.
Analysis fields in the tropics are characterized by significant uncertainties; for example, differences between the tropical wind field in reanalysis datasets are of the order of natural variability. Reducing uncertainties in the tropical analyses, especially in the tropical wind field, should lead not only to better tropical forecasts, but also to improved understanding of the tropical climate system as well as extratropical medium and extended-range forecasting. My research aims at contributing to this process.
Tropical data assimilation research has to address three important issues of greater
relevance in the tropics than in the mid-latitudes: a non-homogeneous observation
coverage, the relative importance of wind- and mass-field information and balance
relationships. The global observing system is dominated by observations of the mass
field variables while direct wind observations are relatively few,
especially in the tropics.
At the same time, fundamental adjustment theory provides arguments that wind-field
information has greater importance for numerical weather prediction (NWP) than
information about the mass field at small horizontal scales and low latitudes.
Finally, balance relationships, such as geostrophy which enable a more efficient
use of existing observations of the mass field, are questionable in the tropics.
Of special importance in data assimilation is the forecast-error covariance matrix because of its role of spreading the observed information in space and to unobserved variables. Variational data assimilation schemes presently used in NWP analyze motions primarily in terms of Rossby waves and they assume that the forecast-error covariances are stationary. A stationary covariance model is most often also assumed homogeneous and isotropic and it is modeled globally.
In reality, forecast-error covariances are flow dependent in space and time. This fact is taken into account in the Ensemble Kalman filter (EnKF) assimilation approach in which forecast-error covariances are estimated from a finite ensemble of forecasts at each analysis step.
My research aims at improving tropical analysis procedures by improved modelling of the forecast-error term for the assimilation and by understanding the flow dependency of model forecast errors. I am addressing these questions in collaboration with scientists in NCAR's CGD, IMAGE and MMM divisions and by using both simple models, suitable to study particular aspects of the problem, and full-scale global and regional models (CAM and WRF models). The derived information about the flow-dependency of tropical forecast errors can then be applied also to improve the background-error covariance modelling and balance relationships in variational systems which presently dominate the operational NWP applications.
The analysis of large-scale tropical motion has to take into account equatorial inertio-gravity waves in addition to Rossby waves. Also, the change of sign of the Coriolis parameter at the equator gives rise to important types of large-scale non- rotational motions, which are absent in the mid-latitude atmosphere: the Kelvin and mixed Rossby-Gravity (MRG) modes.
In one of my projects, a simple model has been developed to compare three and
four-dimensional variational assimilation and EnKF in idealized tropical cases.
Another study involves collaboration within the DART project (Data Assimilation Research
Testbed, http://www.image.ucar.edu/DAReS) to study the flow dependency of the tropical
background errors on both the large-scale and mesoscales.
The question asked is about the characteristic structures of the forecast-error
covariances in terms of various global and equatorially-trapped motions
in time and space, the propagation of tropical errors and their impact on the
extratropics.
Figure 1 illustrates the flow dependencies of the 6-hour zonal wind errors along the latitude circle located at 1 degree N in the Community Atmospheric model 3.0 in January 2003. One persistent region of increased forecast errors can be seen over the Indonesian region and errors spread westward in the mean easterly flow. The errors over the eastern Pacific and Atlantic seem trapped within the areas of strong westerlies embedded within the predominatly eastery winds. An important mode of temporal variability in the tropics is the stratospheric quasi-biennial oscillation (QBO). Its impact on the background-error covariances and resulting analysis has been studied based on the European Centre for Medium-Range Weather Forecasts (ECMWF) model tropical errors. By comparing the forecast-error proxy data from two different phases of QBO, it was shown that the phase of the QBO has an effect on the distribution of tropical forecast-error variances between various equatorial waves. In the easterly QBO phase, the percentage of error variance in Kelvin waves is significantly increased in comparison with the westerly phase. In the westerly phase, westward-propagating inertio-gravity waves become more important at the expense of Kelvin modes, eastward-propagating mixed Rossby-gravity waves and inertio-gravity modes.
The impact of the phase of the QBO on stratospheric analysis is illustrated
in Figure 2. 
Here, single-wind observations are located at the equator in cases when the background-error variance spectrum is taken from the two QBO phases at approximately 30 hPa. This figure illustrates that the mass-wind coupling is significantly stronger in the easterly QBO phase than in the westerly phase as a consequence of a greater contribution from Kelvin waves in the easterly phase. Obtained results suggest that background-error statistics from the easterly QBO period may be on average more useful for the multivariate variational assimilation, as a consequence of an increased impact of Kelvin waves in the easterly phase.
ASP Spotlight August 2007
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