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John C. Derber

Abstract

A variational four-dimensional analysis technique using quasi-geostrophic models as constraints is examined using gridded fields as data. The analysis method uses a standard iterative nonlinear minimization technique to find the solution to the constraining forecast model which best fits the data as measured by a predefined functional. The minimization algorithm uses the derivative of the functional with respect to each of the initial condition values. This derivative vector is found by inserting the weighted differences between the model solution and the inserted data into a backwards integrating adjoint model.

The four-dimensional analysis system was examined by applying it to fields created from a primitive equations model forecast and to fields created from satellite retrieval. The results show that the technique has several interesting characteristics not found in more traditional four-dimensional assimilation techniques. These features include a close fit of the model solution to the observations throughout the analysis interval and an insensitivity to the frequency of data insertion or the amount of data. The four-dimensional analysis technique is very versatile and can be extended to more complex problems with little theoretical difficulty.

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John C. Derber

Abstract

A variational assimilation technique is presented which continuously adjusts a model solution by introducing a correction term to the model equations. The technique is essentially a modification of the adjoint technique. The Variational Continuous Assimilation (VCA) technique optimizes the correction to the model equations rather than the initial conditions as is done in the adjoint technique.

The VCA-technique characteristics were examined by inserting independent analyses into a simple quasi- geostrophic model using both the VCA technique and the adjoint technique. Because the model equations do not have to be satisfied exactly in the VCA technique, some of the effects of systematic model errors can be removed from the assimilation. Thus, the VCA technique was able to consistently fit the data better than the adjoint technique. Predictions from the results from the assimilation techniques showed that the forecast from the adjoint technique's solution was consistently inferior to those from the VCA technique and those from the Geophysical Fluid Dynamics Laboratory's (GFDL's) First GARP (Global Atmospheric Research Program) Global Experiment (FGGE) IIIb analyses. As a by-product of the VCA technique, an empirical correction for the model's systematic error is produced. Application of this correction during a forecast produced substantially improved simulations.

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Kozo Okamoto and John C. Derber

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A technique for the assimilation of Special Sensor Microwave Imager (SSM/I) data in the National Centers for Environmental Prediction (NCEP) global data assimilation and forecast system is described. Because the radiative transfer model used does not yet allow for cloud/rain effects, it is crucial to properly identify and exclude (or correct) cloud/rain-contaminated radiances using quality control (QC) and bias correction procedures. The assimilation technique is unique in that both procedures take into account the effect of the liquid cloud on the difference between observed and simulated brightness temperature for each SSM/I channel. The estimate of the total column cloud liquid water from observed radiances is used in a frequency-dependent cloud detection component of the QC and as a predictor in the bias correction algorithm. Also, a microwave emissivity Jacobian model with respect to wind speed is developed for oceanic radiances. It was found that the surface wind information in the radiance data can be extracted through the emissivity model Jacobian rather than producing and including a separate SSM/I wind speed retrieval.

A two-month-long data assimilation experiment from July to August 2004 using NCEP’s Gridpoint Statistical Interpolation analysis system and the NCEP operational forecast model was performed. In general, the assimilation of SSM/I radiance has a significant positive impact on the analyses and forecasts. Moisture is added in the Northern Hemisphere and Tropics and is slightly reduced in the Southern Hemisphere. The moisture added appears to be slightly excessive in the Tropics verified against rawinsonde observations. Nevertheless, the assimilation of SSM/I radiance data reduces model spinup of precipitation and substantially improves the dynamic fields, especially in measures of the vector wind error at 200 hPa in the Tropics. In terms of hurricane tracks, SSM/I radiance assimilation produces more cases with smaller errors and reduces the average error. No disruption of the Hadley circulation is found from the introduction of the SSM/I radiance data.

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David F. Parrish and John C. Derber

Abstract

At the National Meteorological Center (NMC), a new analysis system is being extensively tested for possible use in the operational global data assimilation system. This analysis system is called the spectral statistical- interpolation (SSI) analysis system because the spectral coefficients used in the NMC spectral model are analyzed directly using the same basic equations as statistical (optimal) interpolation. Results from several months of parallel testing with the NMC spectral model have been very encouraging. Favorable features include smoother analysis increments, greatly reduced changes from initialization, and significant improvement of 1-5-day forecasts. Although the analysis is formulated as a variational problem, the objective function being minimized is formally the same one that forms the basis of all existing optimal interpolation schemes. This objective function is a combination of forecast and observation deviations from the desired analysis, weighted by the invent of the corresponding forecast- and observation-error covariance matrices. There are two principal differences in how the SSI implements the minimization of this functional as compared to the current OI used at NMC. First, the analysis variables are spectral coefficients instead of gridpoint values. Second, all observations are used at once to solve a single global problem. No local approximations are made, and there is no special data selection. Because of these differences, it is straightforward to include unconventional data, such as radiances, in the analysis. Currently temperature, wind, surface pressure, mixing, ratio, and Special Sensor Microwave/lmager (SSM/I) total precipitable water can be used as the observation variables. Soon to be added are the scatterometer surface winds. This paper provides a detailed description of the SSI and presents a few results.

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John C. Derber and Wan-Shu Wu

Abstract

With improved assimilation techniques, it is now possible to directly assimilate cloud-cleared radiances, rather than temperature and moisture retrievals, in objective analyses. The direct use of the cloud-cleared radiances became the operational technique for using satellite sounding data at the National Centers for Environmental Prediction (NCEP) in October 1995. The methodology for using the data (including bias correction, ozone analysis, skin temperature analysis, and quality control) are described in this paper. The impact of the direct use of the radiances compared to the previously operational use of satellite sounding data shows considerable improvement in NCEP’s forecast skill, especially in the Southern Hemisphere. It is anticipated that additional positive impacts will occur with application of the technique to other remotely sensed data.

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Masahiro Kazumori, Quanhua Liu, Russ Treadon, and John C. Derber

Abstract

The impact of radiance observations from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) was investigated in the National Centers for Environmental Prediction (NCEP) Global Data Assimilation System (GDAS). The GDAS used NCEP’s Gridpoint Statistical Interpolation (GSI) analysis system and the operational NCEP global forecast model. To improve the performance of AMSR-E low-frequency channels, a new microwave ocean emissivity model and its adjoint with respect to the surface wind speed and temperature were developed and incorporated into the assimilation system. The most significant impacts of AMSR-E radiances on the analysis were an increase in temperature of about 0.2 K at 850 hPa at the higher latitudes and a decrease in humidity of about 0.1 g kg−1 at 850 hPa over the ocean when the new emissivity model was used. There was no significant difference in the mean 6-h rainfall in the assimilation cycle. The forecasts made from the assimilation that included the AMSR-E data showed small improvements in the anomaly correlation of geopotential height at 1000 and 500 hPa in the Southern Hemisphere and reductions in the root-mean-square error (RMSE) for 500-hPa geopotential height in the extratropics of both hemispheres. Use of the new emissivity model resulted in improved RMSE for temperature forecasts from 1000 to 100 hPa in the extratropics of both hemispheres. The assimilation of AMSR-E radiances data using the emissivity model improved the track forecast for Hurricane Katrina in the 26 August 2005 case, whereas the assimilation using the NCEP operational emissivity model, FAST Emissivity Model, version 1 (FASTEM-1), degraded it.

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John C. Derber, David F. Parrish, and Stephen J. Lord

Abstract

At the National Meteorological Center (NMC), a new analysis system was implemented into the operational Global Data Assimilation System on 25 June 1991. This analysis system is referred to as Spectral Statistical Interpolation (SSI) because the spectral coefficients used in the NMC spectral model are analyzed directly using the same basic equations as statistical (optimum) interpolation. The major differences between the SSI analysis system and the conventional optimum interpolation (OI) analysis system previously used operationally at NMC are:

  • –The analysis variables are closely related to the coefficients of the NMC spectral model.

  • –Temperature observations are used, not heights as in the previous procedure. As a result, aircraft temperatures are being used for the first time at NMC.

  • –Nonstandard observations, such as satellite estimates of total precipitable water and ocean-surface wind speeds, can be easily included.

  • –No data selection is necessary. All observations are used simultaneously.

  • –The dynamical constraint between the wind and mass fields is more realistic and applied globally.

  • –Model initialization has been eliminated. The analysis is used directly as the forecast model initial condition.

Extensive pre-implementation testing demonstrated that the SSI consistently produced superior analyses and forecasts when compared to the previous OI system. Improvement in skill is shown not only for the 3–5-day forecasts, but also in one-day aviation forecasts.

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Yanqiu Zhu, John C. Derber, R. James Purser, Bradley A. Ballish, and Jeffrey Whiting

Abstract

Various studies have noted that aircraft temperature data have a generally warm bias relative to radiosonde data around 200 hPa. In this study, variational aircraft temperature bias correction is incorporated in the Gridpoint Statistical Interpolation analysis system at the National Centers for Environmental Prediction. Several bias models, some of which include information about aircraft ascent/descent rate, are investigated. The results show that the aircraft temperature bias correction cools down the atmosphere analysis around 200 hPa, and improves the analysis and forecast fits to the radiosonde data. Overall, the quadratic aircraft ascent/descent rate bias model performs better than other bias models tested here, followed closely by the aircraft ascent/descent rate bias model.

Two other issues, undocumented in previous studies, are also discussed in this paper. One is the bias correction of aircraft report (AIREP) data. Unlike Aircraft Meteorological Data Relay (AMDAR) data, where unique corrections are applied for each aircraft, bias correction is applied indiscriminately (without regard to tail numbers) to all AIREP data. The second issue is the problem of too many aircraft not reporting time in seconds, or too infrequently, to be able to determine accurate vertical displacement rates. In addition to the finite-difference method employed to estimate aircraft ascent/descent rate, a tensioned-splines method is tested to obtain more continuously smooth aircraft ascent/descent rates and mitigate the missing time information.

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Daryl T. Kleist, David F. Parrish, John C. Derber, Russ Treadon, Wan-Shu Wu, and Stephen Lord

Abstract

At the National Centers for Environmental Prediction (NCEP), a new three-dimensional variational data assimilation (3DVAR) analysis system was implemented into the operational Global Data Assimilation System (GDAS) on 1 May 2007. The new analysis system, the Gridpoint Statistical Interpolation (GSI), replaced the Spectral Statistical Interpolation (SSI) 3DVAR system, which had been operational since 1991. The GSI was developed at the Environmental Modeling Center at NCEP as part of an effort to create a more unified, robust, and efficient analysis scheme. The key aspect of the GSI is that it formulates the analysis in model grid space, which allows for more flexibility in the application of the background error covariances and makes it straightforward for a single analysis system to be used across a broad range of applications, including both global and regional modeling systems and domains.

Due to the constraints of working with an operational system, the final GDAS package included many changes other than just a simple replacing of the SSI with the new GSI. The new GDAS package contained an upgrade to the Global Forecast System model, including a new vertical coordinate, as well as new features in the GSI that were never developed for the SSI. Some of these new features included changes to the observation selection, quality control, minimization algorithm, dynamic balance constraint, and assimilation of new observation types. The evaluation of the new system relative to the SSI-based system was performed for nearly an entire year of analyses and forecasts. The objective and subjective evaluations showed that the new package exhibited superior forecast performance relative to the old SSI-based system. The new system has been shown to improve forecast skill in the tropics and substantially reduce the short-term forecast error in the extratropics. This implementation has laid the groundwork for future scientific advancements in data assimilation at NCEP.

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Thomas L. Koehler, John C. Derber, Brian D. Schmidt, and Lyle H. Horn

Abstract

Evaluations of operational TIROS-N and NOAA-6 temperature soundings over North America are presented for an early January 1980 period one month after completion of the First GARP Global Experiment. In addition to collocated comparisons, synoptic analyses derived only from satellite data and model forecasts initialized from these analyses are compared with those obtained from conventional data. The collocated results, similar to those presented by Phillips et al. (1979) and Schlatter (1981) from TIROS-N soundings, show maximum sounding errors new the surface and tropopause. The analysis comparisons further illustrate that thermal gradients inferred from satellite soundings are too weak, with NOAA-6 gradients slightly weaker than TIROS-N gradients. Difference fields between satellite and conventional thickness analyses propagate eastward with the synoptic patterns, strongly suggesting a correlation of satellite sounding errors to synoptic patterns. These anomalies are also retained in model forecasts started from satellite analyses. These results stress the importance of properly defining the error characteristics of satellite soundings before incorporating them into analysis-forecast systems.

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