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Bradley A. Ballish

Abstract

A simple alternative formula for normal Mode initialization is shown to be exactly equivalent to Tribbia's procedure. It is then argued that although Tribbia's procedure gives excellent results for some problems, it can have convergence problems in other cases.

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Bradley A. Ballish

Abstract

The initialization schemes of Machenhauer (1977), Baer and Tribbia (1977), and one requiring the initial second time derivatives of gravity modes to be zero are tested by application to a simple differential equation, which partially simulates the behavior of gravity modes in a forecast model. These initialization schemes are tested to see under what conditions they converge, and they are tested on how well they eliminate future gravity wave oscillations. Preliminary results of initialization experiments with the National Meteorological Center's spectral forecast model are in support of the conclusions derived from analyzing this differential equation.

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Bradley A. Ballish and Ferdinand Baer

Abstract

Various normal-mode initialization techniques are applied to a simple 12-level linear model with boundary layer friction, and results are compared to exact solutions of the model. It is found that Machenhauer's initialization scheme gives an approximate solution to the initialization of ageostrophic circulations due to friction; however, all or almost all vertical modes must be initialized and a moderate number of iterations are required. Second-order Baer-Tribbia initialization is found to be less effective than several iterations of the Machenhauer procedure. An iterative initialization based on bounded derivative theory and requiring the second time derivatives of the gravity modes to vanish gives excellent results, but a simple iterative scheme to achieve this diverges with moderate friction. The successful application of these procedures to the initialization of ageostrophic circulations due to friction in numerical weather prediction models will require careful utilization of, and possibly improved, iterative methods to achieve convergence and stability.

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Systematic Differences in Aircraft and Radiosonde Temperatures

Implications for NWP and Climate Studies

Bradley A. Ballish and V. Krishna Kumar

Automated aircraft data are very important as input to numerical weather prediction (NWP) models because of their accuracy, large quantity, and extensive and different data coverage compared to radiosonde data. On average, aircraft mean temperature observation increments [MTOI; defined here as the observations minus the corresponding 6-h forecast (background)] are more positive (warmer) than radiosondes, especially around jet level. Temperatures from different model types of aircraft exhibit a large variance in MTOI that vary with both pressure and the phase of flight (POF), confirmed by collocation studies. This paper compares temperatures of aircraft and radiosondes by collocation and MTOI differences, along with discussing the pros and cons of each method, with neither providing an absolute truth.

Arguments are presented for estimating bias corrections of aircraft temperatures before input into NWP models based on the difference of their MTOI and that of radiosondes, which tends to cancel systematic errors in the background while using the radiosondes as truth. These corrections are just estimates because radiosonde temperatures have uncertainty and the NCEP background has systematic errors, in particular an MTOI of almost 2°C at the tropopause that is attributable in part to vertical interpolation errors, which can be reduced by increasing model vertical resolution. The estimated temperature bias corrections are predominantly negative, of the order of 0.5°–1.0°C, with relatively small monthly changes, and often have vertically deep amplitudes.

This study raises important issues pertaining to the NWP, aviation, and climate communities. Further metadata from the aviation community, field experiments comparing temperature measurements, and input from other NWP centers are recommended for refining bias corrections.

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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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