Incremental Analysis Update Research Articles

First simulations with a whole atmosphere data assimilation and forecast system: The January 2009 major sudden stratospheric warming

[1] A Whole atmosphere Data Assimilation System (WDAS) is used to simulate the January 2009 sudden stratospheric warming (SSW). WDAS consists of the Whole Atmosphere Model (WAM) and the 3-dimensional variational (3DVar) analysis system GSI (Grid point Statistical Interpolation), modified to be compatible with the WAM model. An incremental analysis update (IAU) scheme was implemented in the data assimilation cycle to overcome the problem of excessive damping by digital filter in WAM of the important tidal waves in the upper atmosphere. IAU updates analysis incrementally into the model, thus avoids the initialization procedure (i.e., digital filter) during the WAM forecast stage. The WDAS simulation of the January 2009 SSW shows a significant increase in TW3 (terdiurnal, westward propagating, zonal wave number 3) and a decrease in SW2 (semidiurnal, westward propagating, zonal wave number 2) wave amplitudes in the E region during the warming, which can be attributed likely to the nonlinear wave-wave interactions between SW2, TW3 and DW1 (diurnal, westward propagating, zonal wave number 1). There is a delayed increase in SW2 in the E region after the warming, indicating a modulation by the changing large-scale planetary waves in the loweratmosphere during the SSW. These tidal wave responses during SSW appeared to be global in scale. An extended WAM forecast initialized from WDAS analysis shows remarkably consistent tidal wave responses to SSW, indicating a potential forecasting capability of several days in advance of the effects of the large-scale tropospheric and stratospheric dynamics on the thermospheric and ionospheric variability.

Global Energy and Water Budgets in MERRA

Abstract Reanalyses, retrospectively analyzing observations over climatological time scales, represent a merger between satellite observations and models to provide globally continuous data and have improved over several generations. Balancing the earth’s global water and energy budgets has been a focus of research for more than two decades. Models tend to their own climate while remotely sensed observations have had varying degrees of uncertainty. This study evaluates the latest NASA reanalysis, the Modern Era Retrospective-Analysis for Research and Applications (MERRA), from a global water and energy cycles perspective, to place it in context of previous work and demonstrate the strengths and weaknesses. MERRA was configured to provide complete budgets in its output diagnostics, including the incremental analysis update (IAU), the term that represents the observations influence on the analyzed states, alongside the physical flux terms. Precipitation in reanalyses is typically sensitive to the observational analysis. For MERRA, the global mean precipitation bias and spatial variability are more comparable to merged satellite observations [the Global Precipitation and Climatology Project (GPCP) and Climate Prediction Center Merged Analysis of Precipitation (CMAP)] than previous generations of reanalyses. MERRA ocean evaporation also has a much lower value, which is comparable to independently derived estimate datasets. The global energy budget shows that MERRA cloud effects may be generally weak, leading to excess shortwave radiation reaching the ocean surface. Evaluating the MERRA time series of budget terms, a significant change occurs that does not appear to be represented in observations. In 1999, the global analysis increments of water vapor changes sign from negative to positive and primarily lead to more oceanic precipitation. This change is coincident with the beginning of Advanced Microwave Sounding Unit (AMSU) radiance assimilation. Previous and current reanalyses all exhibit some sensitivity to perturbations in the observation record, and this remains a significant research topic for reanalysis development. The effect of the changing observing system is evaluated for MERRA water and energy budget terms.

The Moisture Budget of the Polar Atmosphere in MERRA

Abstract The atmospheric moisture budget from the Modern Era Retrospective-Analysis for Research and Applications (MERRA) is evaluated in polar regions for the period 1979–2005 and compared with previous estimates, accumulation syntheses over polar ice sheets, and in situ Arctic precipitation observations. The system is based on a nonspectral background model and utilizes the incremental analysis update scheme. The annual moisture convergence from MERRA for the north polar cap is comparable to previous estimates using 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) and earlier reanalyses but it is more than 50% larger than MERRA precipitation minus evaporation (P − E) computed from physics output fields. This imbalance is comparable to earlier reanalyses for the Arctic. For the south polar cap, the imbalance is 20%. The MERRA physics output fields are also found to be overly sensitive to changes in the satellite observing system, particularly over data-sparse regions of the Southern Ocean. Comparisons between MERRA and prognostic fields from two contemporary reanalyses yield a spread of values from 6% of the mean over the Antarctic Ice Sheet to 61% over a domain of the Arctic Ocean. These issues highlight continued problems associated with the representation of cold-climate physical processes in global data assimilation models. The distribution of MERRA surface fluxes over the major polar ice sheets emphasizes larger values along the coastal escarpments, which agrees more closely with recent assessments of ice sheet accumulation using regional models. Differences between these results and earlier assessments illustrate a continued ambiguity in the surface moisture flux distribution over Greenland and Antarctica. The higher spatial and temporal resolution as well as the availability of all budget components, including analysis increments in MERRA, offer prospects for an improved representation of the high-latitude water cycle in reanalyses.

Observation and numerical simulations with radar and surface data assimilation for heavy rainfall over central Korea

This study investigated the impact of multiple-Doppler radar data and surface data assimilation on forecasts of heavy rainfall over the central Korean Peninsula; the Weather Research and Forecasting (WRF) model and its three-dimensional variational data assimilation system (3DVAR) were used for this purpose. During data assimilation, the WRF 3DVAR cycling mode with incremental analysis updates (IAU) was used. A maximum rainfall of 335.0 mm occurred during a 12-h period from 2100 UTC 11 July 2006 to 0900 UTC 12 July 2006. Doppler radar data showed that the heavy rainfall was due to the back-building formation of mesoscale convective systems (MCSs). New convective cells were continuously formed in the upstream region, which was characterized by a strong southwesterly low-level jet (LLJ). The LLJ also facilitated strong convergence due to horizontal wind shear, which resulted in maintenance of the storms. The assimilation of both multiple-Doppler radar and surface data improved the accuracy of precipitation forecasts and had a more positive impact on quantitative forecasting (QPF) than the assimilation of either radar data or surface data only. The back-building characteristic was successfully forecasted when the multiple-Doppler radar data and surface data were assimilated. In data assimilation experiments, the radar data helped forecast the development of convective storms responsible for heavy rainfall, and the surface data contributed to the occurrence of intensified low-level winds. The surface data played a significant role in enhancing the thermal gradient and modulating the planetary boundary layer of the model, which resulted in favorable conditions for convection.

Radar data assimilation for the simulation of mesoscale convective systems

A heavy rainfall case related to Mesoscale Convective Systems (MCSs) over the Korean Peninsula was selected to investigate the impact of radar data assimilation on a heavy rainfall forecast. The Weather Research and Forecasting (WRF) three-dimensional variational (3DVAR) data assimilation system with tuning of the length scale of the background error covariance and observation error parameters was used to assimilate radar radial velocity and reflectivity data. The radar data used in the assimilation experiments were preprocessed using quality-control procedures and interpolated/thinned into Cartesian coordinates by the SPRINT/CEDRIC packages. Sensitivity experiments were carried out in order to determine the optimal values of the assimilation window length and the update frequency used for the rapid update cycle and incremental analysis update experiments.

A mollified ensemble Kalman filter

AbstractIt is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high‐frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow–fast extension of the popular Lorenz‐96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter. Copyright © 2010 Royal Meteorological Society

Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations

A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and constant Coriolis frequency. The filtered solution is obtained by retaining only the eigenvectors corresponding to the geostrophic equilibrium and by discarding explicitly the eigenvectors corresponding to the fast moving inertia-gravity waves. An alternative formulation is derived using a variational approach. Both filtering methods are tested numerically for a periodic domain with constant depth and the variational approach is implemented for a closed domain with large topographic variations. The filtering methods significantly reduce the amplitudes of the inertia-gravity waves while preserving the mean flow. The variational method is compared to the Incremental Analysis Update technique and the benefits of the variational filter are presented.

Incremental Analysis Update Implementation into a Sequential Ocean Data Assimilation System

Abstract This study deals with the enhancement of a sequential assimilation method applied to an ocean general circulation model (OGCM). A major drawback of sequential assimilation methods is the time discontinuity of the solution resulting from intermittent corrections of the model state. The data analysis step can induce shocks in the model restart phase, causing spurious high-frequency oscillations and data rejection. A method called Incremental Analysis Update (IAU) is now recognized to efficiently tackle these problems. In the present work, an IAU-type method is implemented into an intermittent data assimilation system using a low-rank Kalman filter [Singular Evolutive Extended Kalman (SEEK)] in the case of an OGCM with a 1/3° North Atlantic grid. A 1-yr (1993) experiment has been conducted for different setups in order to evaluate the impact of the IAU scheme. Results from all of the different tests are compared with a specific interest in high-frequency output behaviors and solution consistency. The improvements brought up by the IAU implementation, such as the disappearance of spurious high-frequency oscillations and the time continuity of the solution, are shown. An overall assessment of the impact of this new approach on the assimilated runs is discussed. Advantages and drawbacks of the IAU method are pointed out.

Incremental Analysis Updates Initialization Technique Applied to 10-km MM5 and MM5 3DVAR

Abstract An incremental analysis updates (IAU) technique is implemented for 3-h updates of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) three-dimensional variational data assimilation (3DVAR) and model system with a 10-km resolution to remove spurious gravity waves. By gradually incorporating analysis increments, IAU affects only the removal of high frequencies, leaving the waves related to diurnal processes. IAU appears to be efficient in reducing the moisture spinup problem in the MM5 3DVAR cycling system. The advantage of the IAU is the most significant in improving precipitation forecasts. Rapid update cycle (RUC) with 1- and 2-h intervals in conjunction with the IAU indicates a rapid minimization and less spinup and -down problems because of greater balancing between the moisture and dynamic variables. Impact studies are performed on a heavy rainfall case that occurred in the Korean Peninsula. Verification results with a 3-h cycling system are presented on operational environments.

Ocean data assimilation using intermittent analyses and continuous model error correction

A new data insertion approach is applied to the Derber and Rosati ocean data assimilation (ODA) system, a system that uses a variational scheme to analyze ocean temperature and provide ocean model corrections continuously. Utilizing the same analysis component as the original system, the new approach conducts analyses to derive model corrections intermittently at once-daily intervals. A technique similar to the Incremental Analysis Update (IAU) method of Bloom et al. is applied to incorporate the corrections into the model gradually and continuously. This approach is computationally more economical than the original.

Preliminary estimation of horizontal fluxes of cloud liquid water in relation to subtropical moisture budget studies employing ISCCP, SSMI, and GEOS‐1/DAS data sets

Special Sensor Microwave/Imager (SSM/I) retrievals of cloud liquid water, International Satellite Cloud Climatology Project (ISCCP) cloud estimates, and winds from the Goddard EOS (GEOS‐1/DAS) assimilation are employed to evaluate vertically integrated cloud liquid water (CLW) transport for 1992. First, GEOS‐1/DAS multiyear data are used to confirm an earlier finding of a paradoxical net moisture sink over the Arabian‐Iraqi desert [Alpert and Shay‐El, 1993]. The negative vertically integrated moisture flux divergence over this region is balanced mainly by the negative incremental analysis updates (IAU) of moisture. Moisture fluxes reveal strong convection but without precipitation in a shallow Hadley‐type cell. Vertical profiles indicate that the moisture removal process is associated with middle and high clouds and probably with CLW flux divergence. The CLW fluxes are estimated explicitly and globally from ISCCP and SSM/I by using linear regression methods. Areas of significant CLW divergence are found over the eastern coasts of both the United States and Asia, in the vicinity of the Gulf Stream and Kuroshio currents, as earlier conjectured by Peixoto [1973]. In both the Arabian‐Iraqi desert and over the Sahara, divergence of a vertically integrated CLW flux opposes the convergence of a vertically integrated horizontal moisture flux, thus explaining at least partially the paradoxical net sink and source in these regions. However, the magnitude of the annual CLW flux estimates as calculated here is, in general, too small to play any significant role in the vertically integrated water budget, except perhaps along coastal regions and over dry subtropical deserts where precipitation minus evaporation is relatively small.

Reassessment of the moisture source over the Sahara Desert based on NASA reanalysis

The components of the moisture balance equation are calculated for the Middle East/North Africa regions based on NASA/GEOS‐1 multiyear reanalysis data set. These include the Evaporation (E), Precipitation (P), moisture flux divergence (∇ · Q), and errors associated with the incremental analysis updates of the specific humidity, or IAU(q). The Annual mean ∇ · Q corresponds well to the results of Vitart et al. [1996], based on NCEP data. IAU (q) reveals a strong moisture source over the eastern Mediterranean and also confirms the paradoxical net moisture sink over the Arabian‐Iraqi desert found by Alpert and Shay‐El [1993]. Over the North African Sahara Desert the moisture flux was shown to converge through the northern and southern boundaries mainly at low levels (∼900 hPa) and to diverge through the eastern and western boundaries at higher levels (∼700 hPa). Starr and Peixoto [1958] have classified North Africa as a net moisture source. Area averaging of ∇ · Q over a box with varying dimensions reveals that it can be classified as a net sink if the box is small enough and located over the center of the desert. If the box is big enough to include the boundaries of the continent only then can it be classified as net source or divergence zone. Inspection of the intermonthly and diurnal variability, as well as the model biases, weakens also the net source argument. It is suggested that the earlier finding of a net source might be due to the smoothing of the water/land boundary, or due to various atmospheric diffusion processes such as the sea breeze cycle and cloud intrusion and evaporation.

Dynamics of Zonal-Mean Flow Assimilation and Implications for Winter Circulation Anomalies

Seasonally averaged 200-mb circulations for recent winters (1987/88 and 1988/89) that represent opposite phases of El Nino and a zonal-mean zonal flow index cycle are diagnosed using data assimilated by the Goddard Earth Observing System (GEOS) and operational analyses of the European Centre for Medium-Range Weather Forecasts (ECMWF). The comparison is undertaken to determine whether there are significant differences in the 200-mb vorticity dynamics implied by the mean meridional circulations in the two datasets and whether these differences can be related to the Incremental Analysis Update (IAU) method used in the GEOS assimilation. The two datasets show a high degree of similarity in their depictions of the large-scale rotational flow, but there are substantial differences in the associated divergent circulations. For the zonal-mean flow, the zonal winds are substantially the same, but the meridional wind in the Tropics and subtropics is considerably weaker in the GEOS assimilation than its counterparts in both the ECMWF data and the GEOS analyses used to produce the assimilation. The authors examine the assimilation of the Hadley circulation using a zonally symmetric f-plane model. For this model, the IAU method easily assimilates the rotational flow but fails to assimilate the divergent circulation. This deficiency of the IAU method may explain the weakness of the Hadley cell in the GEOS assimilation, at least in relation to the GEOS analysis. For this simple model, an alternative assimilation method, based on constraints imposed by the analyzed potential vorticity and mean meridional circulation fields, is proposed that simultaneously assimilates both rotational and divergent flow components. Barotropic modeling suggests that an accurate representation of mean meridional flow anomalies can be important for the diagnosis of both zonal-mean and eddy rotational flow perturbations, particularly during extreme phases of the zonal-mean zonal flow fluctuation.