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ABSTRACT. The impact of utilizing additional densely spaced aircraft observations on the Goddard Earth Observing System. Data Assimilation System wind ...
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The Impact of Additional Aircraft Data on the Goddard Earth Observing System Analyses LEONID RUKHOVETS*

AND

JOEL TENENBAUM

State University of New York at Purchase, Purchase, New York

MARVIN GELLER State University of New York at Stony Brook, Stony Brook, New York (Manuscript received 19 June 1997, in final form 26 November 1997) ABSTRACT The impact of utilizing additional densely spaced aircraft observations on the Goddard Earth Observing System Data Assimilation System wind analyses is investigated. The additional data, the Global Aircraft Data Set (GADS), comes from flight data recordings of 30 British Airways Boeing 747-400 aircraft that are not used in operational analyses. The GADS experiment was created to provide data needed to improve analyses of strong winds near jet streams. All major operational centers underestimate such winds. The impact of including the GADS observations in the analyses is investigated using some cases from the 1995 Northern Hemisphere winter. The additional aircraft observations produce a substantial impact on the Goddard wind speed analyses in both sparse aircraft data regions (North Africa, Middle East, South America) and dense aircraft data regions (west Atlantic, east Asia, North America). Examples of the space and time extent of the impact are presented.

1. Introduction Four-dimensional data assimilation has many research and operational uses in atmospheric science (National Research Council 1991). For instance, operational weather centers assimilate real-time data to obtain optimal representations of the state of the atmosphere that can serve as initial conditions for numerical weather predictions. Also, extensive reanalysis activities are under way using retrospective data to serve as consistent datasets for climate analysis purposes (e.g., Kalnay et al. 1996; Schubert et al. 1993). These assimilation procedures use many kinds of observations: surface, rawinsondes, aircraft, ship, rocketsonde reports, satellite retrievals of geopotential thickness, pilot balloon, buoy, cloud-motion winds, and some others. The impact of regular aircraft wind data on analyses and forecasts was investigated during the 1980s in a number of studies (e.g., Baede et al. 1983; Barwell and Lorenc 1985; Barwell and Bromley 1988; Benjamin et al. 1991). This paper deals with the impact of using additional

*Current affiliation: General Science Corporation, Laurel, Maryland. Corresponding author address: Dr. Joel Tenenbaum, Division of Natural Sciences, State University of New York, Purchase NY 10577. E-mail: [email protected]

q 1998 American Meteorological Society

aircraft information on contemporary atmospheric assimilation products using the Goddard Earth Observing System Data Assimilation System (GEOS-1 DAS; Schubert et al. 1993; Pfaendtner et al. 1995). Currently, a new Data Assimilation System (GEOS-2) is being developed at the NASA/Goddard Data Assimilation Office (DAO 1996). The need for a critical examination of the impacts of current and potential future observing systems is highlighted in Emanuel et al. (1995). It is important to note that the Goddard effort differs from operational centers in its goal of producing the most accurate analyses, not necessarily the most accurate forecasts. In previous papers (Tenenbaum 1991, 1996) we have used independent aircraft data to estimate the wind speed errors in such analyses near strong jet streams. Unlike operational forecast systems, GEOS-1 can readily accept time-lagged flight data recorder information. In this paper we attempt to quantify the effect of substantial additional information from aircraft flight data recorders on the GEOS-1 analysis results. While aircraft observations are available mainly at flight levels, and have their main impact at these levels, their use may also improve analyses elsewhere. One reason why meteorological analyses at aircraft flight levels are of particular importance is that airlines use this information for both aircraft routing and payload determination (Tenenbaum 1992). Another is the current concern about

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the effects of aircraft exhaust products on atmospheric structure and climate (Stolarski and Wesoky 1993; Stolarski et al. 1995). The winds at flight levels play a particularly important role in redistributing aircraft exhaust products from their points of insertion near the tropopause. Better knowledge of the winds at these levels leads to a better knowledge of the fate of aircraft exhaust products. Also, a better representation of the atmosphere near the tropopause is an important component of current efforts in improving numerical weather predictions (Benjamin et al. 1996). Densely spaced aircraft observations are only partially used in operational practice. Such data are available from the flight recorders of wide-bodied long-haul aircraft. Using this type of data, Tenenbaum (1991, 1996) showed that all major operational centers underestimate winds near strong jet streams. The errors in the peak wind speed were about 11%–17% and 9%–13% of the observed value in the two studies. These estimates were obtained using the aircraft information as independent data; these aircraft data were not included in the assimilation process. The Global Aircraft Data Set (GADS) experiment was conceived to demonstrate how these data can be used to improve analyses of strong winds near jet streams. The first part of this experiment involves collecting up to 4000 additional aircraft reports per day from regions of strong wind shear. Data are taken from every flight of all British Airways Boeing 747-400 aircraft. Acquisition of GADS data began on 1 February 1995 and continues. To assess the impact of the GADS data, we used GEOS-1 DAS (Pfaendtner et al. 1995). First we carried out control GEOS-1 calculations not including GADS data. Then, we repeated the assimilation calculations including the GADS observations. Differences between results of these two calculations show the impact of the GADS observations on the GEOS-1 analyses. The outline of this paper is as follows. We briefly describe the basic properties of the GEOS-1 DAS in section 2 and the accuracy of various aircraft wind measurement systems in section 3. The details of the GADS experiment are described in section 4. To carry out the assimilation calculations using GADS information it is necessary to specify the GADS observation errors. This is done in section 5. The impacts of the GADS observations on the GEOS-1 analyses for different cases are discussed in section 6. Conclusions, based on these and other case studies, are presented in section 7. 2. A short description of the GEOS-1 DAS The GEOS-1 DAS includes three basic parts: quality control, an optimal interpolation (OI) analysis scheme, and an atmospheric general circulation model (GCM). Quality control is based on the inequality (Pfaendtner et al. 1995) D i2 # ((s oi ) 2 1 (s fi ) 2 )t ,

(1)

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where D i is the difference between an observation at a point i and the interpolated background first-guess value; (s oi ) 2 and (s fi ) 2 are the observation and forecast error variances, respectively; and t is a subjectively defined tolerance value. The OI scheme is based on the determination of analysis weights K, which are defined by the equation

K 5 P f H T (HP f H T 1 R)21 ,

(2)

where P f is the forecast error covariance matrix, H is a generalized interpolation operator that transforms model variables into observables, R is the observation error covariance matrix, R 5 [r ij ], r ij 5 s oi s oj m oij, m oij are the observation error correlations, and T is the transpose symbol. The correlation m oij for aircraft winds is set to d ij , the Kronecker delta function, so that errors from distinct observations are assumed to be uncorrelated (Pfaendtner et al. 1995). The GEOS-1 DAS assimilates data intermittently every 6 h. The OI scheme selects up to 75 observations from a cylinder of a radius approximately equal to 1600 km according to the methodology of Pfaendtner et al. (1995). The observations selected are then used to determine the analysis increments for all grid points within a minivolume. Each minivolume contains six horizontal grid points in low-latitude regions, eight horizontal grid points in midlatitude (between 308 and 828) regions, and an entire latitude band of grid points in polar regions. Each minivolume contains two vertical levels of grid points. There are nearly 12 000 minivolumes, with the same set of observations used for all grid points within the same minivolume. The GEOS-1 DAS analyzes global sea level pressure and near-surface wind over the oceans, geopotential heights, vector wind, and water vapor mixing ratio on constant pressure surfaces. The OI scheme uses a grid of 28 latitude by 2.58 longitude and 14 vertical levels (20, 30, 50, 70, 100, 150, 200, 250, 300, 400, 500, 700, 850, 1000 hPa). The GCM has the same horizontal resolution and 20 sigma levels in the troposphere and lower stratosphere. A detailed description of the GEOS-1 GCM is presented by Takacs et al. (1994). 3. Accuracy of aircraft winds The GADS experiment involves collecting data from every flight of all British Airways 747-400 aircraft. This process includes both the initial calculation of a ‘‘point’’ wind speed by the aircraft inertial navigation system and the subsequent transmission to the meteorological user. For typical aircraft speeds, the ‘‘point’’ is well under 4 km in horizontal extent. The absolute accuracy of such a measurement is of the order 1 m s21 (Axford 1968; Shapiro and Kennedy 1975). Given current computer, data recording, and VHF communications technology no further errors are introduced by automated transfers of such data to meteorological centers. This situation is in sharp contrast to errors introduced in the

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FIG. 1. Location of data from British Airways B747-400 flights for February 1995 exceeding 30 m s 21 (nearly continuous solid disks) and less than 30 m s21 in equatorial regions (solid disks with gaps).

reports manually transmitted by voice radio (AIREP1) where inaudibility, digit transposition, etc. can all introduce noise. The intrinsic 1 m s21 accuracy of the combined GADS measurement and transmission process can be contrasted with a value of 3–5 m s21 for the observational error to be associated with operational aircraft data (Daley 1991). Two reasons are the prevalence of manually transmitted data away from North America and the differences between the aircraft point measurements and winds that have been averaged over a grid point (50 km and up). In our subsequent studies of GEOS-1 analyses with and without automated GADS information, the question can still arise as to why analyses with GADS data should be treated as a very accurate depiction of the atmospheric state (small value of observation error as discussed in section 5). Here it is important to realize that densely spaced aircraft wind measurements [GADS away from North America and ARINC Communications Addressing and Report Systems (ACARS) over North America] also satisfy a constraint not available for other wind measurements (radiosondes, pilot balloons, cloudtracked winds). Over the North Atlantic, only aircraft capable of a certain minimum navigational accuracy are permitted into the airspace (Nolan 1990; National Air Traffic Services 1997). Such aircraft cross the North Atlantic as part of an organized track system with a longitudinal time interval of 15 min. As shown in the appendix, by examining the relation of airspeed errors to the safety

1

Aircraft reports transmitted by voice radio.

assumptions built into the design of the North Atlantic track system, we can independently set a bound on the accuracy of the average GADS wind at ;2 m s21 . In addition, GADS personnel have monitored more than 40 flights using flight deck instruments and verified that there are no significant local fluctuations, discrepancies, or substantial cancellations of large positive and negative errors during different parts of the crossing. 4. The Global Aircraft Data Set experiment For each flight of all British Airways Boeing 747400 aircraft, a special supplemental GADS message is appended to each regular flight data recording tape. These tapes are processed approximately 2–10 days after the flight and the GADS data are separated and transmitted via the Internet to the State University of New York (SUNY) at Purchase for quality checking and subsequent processing. Each GADS message consists of up to 90 GADS TABLE 1. Preliminary ensemble systematic errors of operational (ECMWF, NCEP, UKMO) and GEOS-1 DAS analyses compared with GADS observations during February 1995. The results include jet stream crossings in the vicinity of Egypt, Bombay, and Delhi. The peak wind speed error is defined as (peak analyzed wind speed minus peak observed wind speed)/(peak observed wind speed). An additional uncertainty of 6 3% common to all four analyses is introduced by the monthly mean averaging process. Center

Peak wind speed error (%)

ECMWF GEOS-1 NCEP UKMO

26.0 27.7 27.6 29.0

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FIG. 2. Locations of rawinsonde observations at 0000 UTC 4 February 1995.

FIG. 3. GEOS-1 DAS 200-hPa wind speed analysis at 0000 UTC 4 February 1995 for the Middle East: (a) control assimilation using regular data, (b) same experiment with GADS aircraft information added, (c) GADS impact [difference between (b) and (a)], (d) locations of GADS (triangles) and conventional (asterisks) aircraft observations. Contour intervals for (a)–(c) are 5 m s 21 , 5 m s21 , and 1 m s21 , respectively.

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FIG. 4. Cross section of the GEOS-1 DAS 200-hPa wind speed analyses for the Middle East at 0000 UTC 4 February 1995: (a)–(c) Longitude–pressure along 308N and (d)–(f ) latitude–pressure along 588E. Contour intervals for (a) and (d), (b) and (e), and (c) and (f ) are 5 m s21 , 5 m s21 , and 2 m s21 , respectively.

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FIG. 5. Horizontal 200-hPa wind speed shears (gradients) of GEOS-1 DAS analysis calculated as a fraction of the local Coriolis parameter, f, at 0000 UTC 4 February 1995, Middle East. (a)–(c) As in Fig. 3. Contour interval is 0.1.

reports whose primary initial trigger criteria are wind speed .30 m s21 and at increments of 2.5 m s21. An example of the geographical distribution of data for February 1995 is shown in Fig. 1. Using these criteria, we received about 1000–1500 readings per day during February 1995. In the GEOS-1 DAS, the GADS observations are averaged, like closely spaced conventional data, creating so-called superobservations (Lorenc 1981; Baker et al. 1987). As noted above, the previous studies using flight data recording information (Tenenbaum 1991, 1996) showed analyzed jet stream winds for southwest Asia that were systematically too weak (ranging from 11%–17% too weak in the 1989 data to 9%–13% too weak in the 1992 data). These discrepancies existed even after correction for the distinction between point measurements and grid-box averages. The total number of jet crossing cases for each winter in these previous studies ranged from 15 (1989) to 35 (1992). Initial processing of the GADS experiment permitted an approximately sixfold increase in the number of jet crossings that can be used to estimate biases and explore the impact of additional aircraft data. Preliminary results using data for February 1995 are summarized in Table 1. The jet stream analyses range from 6% to 9% too weak for the operational cen-

ters [European Centre for Medium-Range Forecasts (ECMWF), National Centers for Environmental Prediction (NCEP), U.K. Meteorological Office (UKMO)] and GEOS-1 DAS with an additional common uncertainty of 63% due to the monthly mean averaging. Thus the operational centers and the GEOS-1 DAS analyses differ in the precise biases shown but demonstrate the same general behavior. Given that the GEOS-1 DAS (with coarser resolution) biases are similar to those of the operational centers, we conclude that these biases are not merely due to resolution effects. 5. Specification of the GADS observation errors In order to successfully use any kind of observations in a modern atmospheric data assimilation system, it is important to get appropriate estimates of observation error statistics. The statistics are necessary both for quality control and for the OI procedure [see Eqs. (1) and (2)]. The observation errors were first specified for interpolation purposes by Drozdov and Shepelevsky (1946) and then by Gandin (1963) for the OI procedure. This procedure was turned into an empirical method using extrapolation to zero separation of the observations

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FIG. 6. GEOS-1 DAS 250-hPa wind speed analysis at 0000 UTC 3 February 1995 for North Africa. (a)–(d) As in Fig. 3. Contour intervals for (a)–(c) are 5 m s21 , 5 m s21 , and 1 m s21 , respectively.

based on a homogeneous and isotropic structure function that is connected with the correlation function (Gandin 1963, 30). Then, the observation errors were obtained for data assimilation systems (e.g., Rutherford 1972; Hollett 1975; Bergman 1978; Hollingsworth and Lonnberg 1986; Baker et al. 1987; Shaw et al. 1987). More recently, theoretical models have been developed for the estimation of both forecast and observation errors (Daley 1991; Bartello and Mitchell 1992; Dee 1995; Dee et al. 1997). In the present study, we carried out assimilation experiments using different values of the GADS observation errors. The GEOS-1 DAS uses two different sets of observation error standard deviations: AIREP (11.2– 11.4 m s21 ) or ASDAR (aircraft to satellite data relay) [6–10 m s21 depending on the altitude of the levels of interest, 100–400 hPa; Pfaendtner et al. (1995)]. The substantially greater observation errors assumed for AIREPs in comparison with ASDAR follow from the manual processing for AIREPs compared with the completely automated procedure for ASDAR. It should be

noted that much smaller observation errors are used in the GEOS-2 (DAO 1996). We started our GEOS-1 experiments using AIREPs and ASDAR observation errors for the GADS observations. Our experiments showed that, in spite of substantial improvements of the wind speed analysis near GADS flight trajectories in comparison with the control experiments, there were still significant underestimates of the wind speeds near strong jet streams by the GEOS1 analyses using the GADS data [not shown; see Tenenbaum et al. (1996)]. Therefore, given the values implied by the results in section 3 and the appendix, we carried out further assimilation experiments, in which GADS observation errors for u and y wind components have values half that of the GEOS-1 ASDAR observation errors. These results are discussed in section 6. Further reduction of the observation errors produced a better analysis of the jet stream wind speeds in some experiments. However, in other experiments, the analyses showed some overestimation of wind speed values, perhaps because of the ill-conditioning of the OI equa-

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FIG. 7. GEOS-1 DAS 200-mb wind speed analysis at 1800 UTC 8 February 1995 for South America. (a)–(d) As in Fig. 3. Contour intervals for (a)–(c) are 5 m s21 , 5 m s21 , and 2 m s21 , respectively.

tion systems when excessively small observation errors are used. 6. GADS impact on the GEOS-1 DAS analyses We considered the GADS impact for different regions, both with sparse (Middle East, North Africa, South America) and with dense conventional aircraft coverage (northwest Atlantic, east Asia, North America). a. Sparse aircraft data areas 1) MIDDLE EAST

REGION

We consider a case for 0000 UTC 4 February 1995. Figure 2 shows the locations of rawinsondes for this date. The coverage can be considered as typical for 0000 UTC rawinsonde observations and we will not show rawinsonde coverage for other dates. The GADS impact on the GEOS-1 DAS wind speed analysis for the pressure level 200 hPa and the locations of the GADS and conventional aircraft data (AIREP,

ASDAR, ACARS) are shown in Fig. 3, which consists of four panels: Fig. 3a: the GEOS-1 DAS wind speed analysis at 200 hPa (the nearest standard level to the flight level) for the control experiment; Fig. 3b: the GEOS-1 DAS experiment with the GADS observations added (the GADS experiment); Fig. 3c: the GADS impact, that is, the difference between Fig. 3b and Fig. 3a (GADS minus control); and Fig. 3d: locations of the GADS (triangles) and conventional aircraft (asterisks) data. The trajectory of the GADS flight goes near the Persian Gulf parallel to the jet axis. We see a rather big impact over this region, up to 16 m s21 (or more then 30% of the wind speed value). The new center of the jet stream appears with maximum wind speed 62 m s21 . The maximum wind speed over this area in the control experiment is 46 m s21 . The maximum according to the aircraft observation is 66 m s21 (at the level 216 hPa). Given that the GADS data are confined to flight levels

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FIG. 8. GEOS-1 DAS 200 hPa wind speed analysis at 0600 UTC 9 February 1995 for the northwest Atlantic. (a)–(d) As in Fig. 3. Contour intervals for (a)–(c) are 5 m s21 , 5 m s21 , and 2 m s21 , respectively.

only, we may ask what is the vertical extent of the GADS impact? A longitude–pressure cross section along latitude 308N (the latitude of the maximum impact) and a latitude–pressure cross section along longitude 588E are shown in Fig. 4. The GADS impact extends over the 50–500-hPa layer with the maximum GADS impact being within the 200–250-hPa layer. Horizontal wind shear is an important meteorological parameter for aviation. One indicator of it is the horizontal gradient of the wind speed. Figure 5 shows the magnitudes of the horizontal wind speed gradients, calculated as a fraction of the local Coriolis parameter f. We see that the horizontal wind shear increases up to 0.3 f when the GADS observations are taken into consideration. Thus, the GADS-induced increase of the wind shear is approximately twofold. 2) NORTH AFRICA

REGION

We consider the case for 0000 UTC 3 February 1995. The trajectory of the GADS flight goes through central North Africa perpendicular to the jet axis. The GADS

impact on the GEOS-1 DAS 250-hPa wind speed analysis and locations of the GADS and conventional aircraft data for the North Africa region are shown in Fig. 6. The impact of the GADS observations change the maximum wind speed in the center of the jet stream from 58 m s21 in the control experiment to 63 m s21 in the GADS experiment. The aircraft observations show that the maximum wind speed is equal to 70 m s21 at the 238-hPa level. We should take into consideration some decrease of the real wind by vertical interpolation, however. Figure 6c shows two centers of the maximum impact located along the GADS flight trajectory (see Fig. 6d). They do not coincide with the center of the jet stream. The maximum impacts are equal to 10 m s21 (25% and 40% of observed values). It is greater than the change seen in the center of the jet stream (5 m s21 ). 3) SOUTH AMERICA

REGION

The British Airways flights over South America occur only twice weekly. Therefore, there are relatively few observations over this region. We consider the case for

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FIG. 9. GEOS-1 DAS 200-hPa wind speed analysis at 0600 UTC 11 February 1995 for east Asia. (a)–(d) As in Fig. 3. Contour intervals for (a)–(c) are 5 m s21 , 5 m s21 , and 1 m s21 , respectively.

1800 UTC 8 February 1995. Figure 7 shows the GADS impact on the GEOS-1 200-hPa wind speed analysis and locations of the GADS and other aircraft data. We see rather large changes of the wind speeds in the region surrounding the GADS data because of the small number of conventional observations. The maximum impact is 18 m s21 (90% of the observed value). The maximum wind speed increases from 38 m s21 in the control experiment to 46 m s21 . Aircraft observations give a maximum wind speed of 47 m s21 . b. Dense aircraft data areas 1) NORTHWEST ATLANTIC

REGION

The previous cases concerned regions with sparse aircraft observations. Now we consider cases when the GADS observations are added to dense aircraft observations. First we consider the northwest Atlantic area, adjoining the east coast of the United States for the case 0600 UTC 8 February 1995. The GADS flight track was almost parallel to the jet axis and provided numerous observations. The GADS impacts for the wind speed field at the 200-hPa level and locations of the GADS

and other aircraft data are shown in Fig. 8. There are substantial changes of the wind speed pattern in comparison with the control experiment. The western jet streak is moved northward by about 28 of latitude. The maximum wind speed in the center of the jet stream is changed from 72 m s21 in the control experiment to 77 m s21 . The observations give a maximum value equal to 82 m s21 for the point 348N, 708W at the 217-hPa pressure level. The eastern jet streak becomes stronger by about 4 m s21 and is moved to the west. Thus the largest impact is seen in the region between the two jet streak maxima and is 26 m s21 (70% of analyzed value). The point of maximum impact does not coincide with any jet stream center. The impact changes its sign along the GADS flight. As examined in detail in the initial evaluation of the GEOS-1 system, a likely reason for such an effect is the OI selection procedure using the minivolumes (Pfaendtner et al. 1995). A transfer from one minivolume to another can produce a complete change in the observation set selected and, as a consequence, large gradients of the analysis field. Effects of the data selection are investigated in Cohn et al. (1998). The new

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FIG. 10. GEOS-1 DAS 250-hPa wind speed analysis at 0600 UTC 8 March 1995 for North America. (a)–(d) As in Fig. 3. Contour intervals for (a)–(c) are 5 m s21 , 5 m s21 , and 1 m s21 , respectively.

Goddard data assimilation system (GEOS-2) is free from problems with minivolumes. 2) EAST ASIA

REGION

Figure 9 shows maps of the GADS and conventional aircraft data for 0600 UTC 11 February 1995. In east Asia there is one GADS flight (between Seoul and Hong Kong) and many regular flights for this date. The GADS impact is shown in Fig. 9c. The magnitude of the impact is up to 12 m s21 (15% of the observed value) and results in an expansion of the zone of strong wind speeds (more than 85 m s21 ) to the west. 3) NORTH AMERICA

REGION

We consider the case 0600 UTC 8 March 1995, when the GADS flight was over the North American continent. Figure 10 shows the GADS impact and the locations of the GADS and other aircraft observations for this case. We see a substantial strengthening of the wind speed in the center of the jet stream up to 9 m s21 (about 9% of observed value). The maximum wind speed in

the center of the jet stream is changed from 77 m s21 in the control experiment to 86 m s21 . The aircraft observations also give a maximum value equal to 86 m s21 . The second center of substantial impact is located in the southwest part of the United States. Here, there are a lot of other aircraft observations, but the GADS impact still reaches about 7 m s21 . c. Persistence of the GADS impact In the previous sections we considered the spatial features of the GADS impacts. Now we examine how long in time the impact can exist. We return again to the case of 3 February 1995 for North Africa. For the next observation time (window) in Fig. 11, 0600 UTC 3 February 1995, there is just one GADS observation in the northern part of Africa (triangle in Fig. 11d). Figure 11c shows the GADS impact on the GEOS-1 250-hPa wind speed analysis for this case. We see two maxima in the impact pattern. The northern maximum is explained by the single GADS observation.

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FIG. 11. GEOS-1 DAS 250-hPa wind speed analysis at 0600 UTC 3 February 1995 for North Africa. (a)–(d) As in Fig. 3. Contour intervals for (a)–(c) are 5 m s21 , 5 m s21 , and 1 m s21 , respectively.

The appearance of the southern maximum is explained by the influence of the first guess. In order to trace how long this pattern exists, we consider the next few observation times. We did not include any GADS observations after 0000 UTC 3 February 1995 in the GADS experiment. Thus the GADS impact on the GEOS-1 analysis is produced exclusively by the first guess from the previous observation time. Figure 12 depicts the sequence of the GADS impacts on the GEOS-1 wind speed analyses. We find that the pattern is maintained up to 1800 UTC 5 February 1995 and is moving to the east. The impact, created by the GADS observations of 0000 UTC 3 February 1995, disappears gradually and is completely gone by 0000 UTC 6 February 1995, that is, after 3 days. Thus for this case, the GADS impact extends for at least several days. 7. Conclusions Our primary conclusions are based on case studies. We consider the impact of British Airways observations on the GEOS-1 DAS analyses for areas with sparse

(North Africa, Middle East, South America) and dense (west Atlantic, east Asia, North America) conventional data. We show the impact using the cases from the winter of 1995 although we have many other examples confirming our conclusions. Our conclusions are as follows. R The additional GADS information produces a substantial impact on the GEOS-1 wind speed analyses both in sparse (North Africa, Middle East, South America) and dense (west Atlantic, east Asia, North America) aircraft data regions. R The assimilations including GADS information bring the resulting analyses near jet streams significantly closer to the actual state of the atmosphere (as indicated by available observations). R The GADS impact extends throughout the 50–500hPa layer. R The GADS observations can produce horizontal wind shears (calculated by the magnitude of the horizontal wind speed gradient) that are enhanced by a factor of 2. R The GADS impact can persist for several days. This

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FIG. 12. Impact of GADS aircraft information on GEOS-1 DAS 250-hPa wind speed analyses from 0600 UTC 3 February through 0000 UTC 6 February 1995. Contour interval is 1 m s 21 .

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result is obtained from an experiment in which no further GADS observations are input after the initial insertions. R Assigning GADS error standard deviations to be half that of the ASDAR error standard deviations used in the GEOS-1 analyses improves the realism of the jet stream analysis (as measured by comparison with the GADS observations) without obvious negative impacts in other regions. This result occurs without giving rise to overestimates of the core wind speeds. Acknowledgments. We would like to thank, from British Airways, G. Fever, J. Rankin, G. Selves; from NASA, G. Brin, R. Govindaraju, Y. Kondratyeva, D. Lamich, R. Rood, M. Sienkiewicz; and from SUNY Purchase, E. Branca, M. Oztunali, M. Wisniewski. This research was supported in part by NASA Grant NAG52700 and by a SUNY research leave (JT). APPENDIX

Operational Constraints and GADS accuracy Because of the density and diurnal nature of the air traffic (up to 700 flights each way per day during the summer), the North Atlantic has had a highly organized track structure for more than two decades (Attwooll 1966). Five or more parallel tracks are established twice per day in advance of the diurnal aircraft flows. The tracks are centered on the forecast wind-corrected optimal great circle routing with horizontal spacings of 18 in latitude and vertical spacings of 1000 ft (2000 ft before March 1997). Longitudinal time intervals are at least 15 min and are monitored via high-frequency (HF) radio transmission at 108 intervals. All aircraft on a given track fly at a constant Mach number (set to a value in the range 0.82–0.86). Only in the presence of geomagnetic storms that interfere with HF radio transmissions are minimum time intervals increased to 20 min. This along-track spacing gives an indication of the assumed accuracy within which aircraft airspeeds can be maintained and, by inference, measured. Errors in the airspeed produce the dominant error in wind speeds derived from inertial navigation systems. Assume for simplicity a westbound flight proceeding directly into a head wind. Let s5 ya 5 yo 5 yf 5 to 5 tf 5

length of North Atlantic track airspeed averaged over the track observed wind speed averaged over the track forecast wind speed averaged over the track observed time on track forecast time on track.

The observed wind averaged over the crossing is

yo 5 ya 2 Typical winter values are

s . to

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s 5 1600 nm (2963 km), t o 5 4 hr (1.44 3 10 4 s),

y a 5 480 kt (2.47 3 10 2 m s21 ), yielding

y o 5 4.1 3 101 m s21 (80 kt). For practical purposes, the errors in s and t o are negligible and the error in y a determines the error in y o . Note that errors in y a can be magnified because y o is the difference of two relatively large numbers (an effect that decreases with increasing wind speed, the opposite of radiosonde wind speed errors). To estimate the error in y a , we replace the observed quantities, y o and t o , with the forecast quantities, y f and t f , and solve for the forecast time of the crossing: tf 5

s . ya 2 yf

For y f , in practice the aircraft flight plans almost all use the same UKMO forecasts implying that to a good approximation, errors in y f are common to almost all aircraft. Solving for y a , we obtain

ya 5 yf 1

s . tf

To estimate the magnitude of errors in y a , assume that an error on the order of 15% in t f would be the highest acceptable value that would not compromise safety; that is, the track system could tolerate errors of t f 5 (15%)(15 min) 5 135 s. Then Dy a 5 2

s Dt f , tf tf

and substituting the typical winter values we obtain Dy a 5

2.96 3 10 6 m 1.35 3 10 2 s 1.44 3 10 4 s 1.44 3 10 4 s

Dy a 5 1.98 3 10 0 m s21 independent of y f . The corresponding error for y o would be Dy o 5 D y a , since both s and t o are effectively precisely known quantities from the inertial navigation system. Thus Dy o ; 2 m s21 , which is well below the observation error that is used for GADS data as discussed in section 5. REFERENCES Attwooll, V. W., 1966: The parallel-route system for North Atlantic subsonic jet traffic. Navigation, 9, 187–197.

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