Applications of COSMIC to Meteorology and Climate 1

The GPSIMET (Global Positioning System/Meteorology, Ware et a1. 19996) project demonstrated atmospheric limb sounding from low-earth-orbit (LEO) with high vertical resolution, high accuracy, and global coverage in all weather. Based on the success and scientific results of GPS/MET, Taiwan’s National Space Program Office (NSPO), the University Corporation for Atmospheric Research (UCAR), the Jet Propulsion Laboratory (JPL), the Naval Research Laboratory (NRL), the University of Texas at Austin, the University of Arizona, Florida State University and other partners in the university community are developing COSMIC (Constellation observing System for Meteorology, Ionosphere and Climate), a follow-on project for weather and climate research, climate monitoring, space weather, and geodetic science. COSMIC plans to launch eight LEO satellites in 2004. Each COSMIC satellite will retrieve about 500 daily profiles of key ionospheric and atmospheric properties from the tracked GPS radio-signals as they are occulted behind the Earth limb. The constellation will provide frequent global snapshots of the atmosphere and ionosphere with about 40000 daily soundings.
This paper discusses some of the applications of COSMIC data for meteorology, including polar meteorology, numerical weather prediction (NWP), and climate. Applications to ionospheric research including space weather and geodesy are described elsewhere in this issue of TAO.
In meteorology COSMIC will provide high vertical resolution temperature, pressure and water vapor information for a variety of atmospheric process studies and improve the forecast accuracy of numerical weather prediction models. The COSMIC data set will allow investigation of the global water vapor distribution and map the atmospheric flow of water vapor that is so crucial for understanding and predicting weather and climate. The data set will provide accurate geopotential heights, enable the detection of gravity waves from the upper troposphere to the stratosphere, reveal the height and shape of the tropopause globally with unprecedented accuracy, support the investigation of fronts and other baroclinic structures, and improve our understanding of tropopause-stratosphere exchange processes. 
COSMIC data will complement other observing systems and improve global weather analyses, particularly over the oceans and polar regions, and NWP forecasts made from these analyses. Through assimilation in numerical models, COSMIC data will improve the resolution and accuracy of the global temperature, pressure and water vapor fields, and through the model’s dynamical and physical adjustment mechanisms, the wind fields as well. These improved analyses and forecasts will provide significant benefits to aviation and other industries. 
For climate research and monitoring COSMIC will provide an accurate global thermometer that will monitor Earth’s atmosphere in all weather with unprecedented long-term stability, resolution, coverage, and accuracy. COSMIC will provide a data set for the detection of climate variability and change, the separation of natural and anthropogenic causes, the calibration of other satellite observing systems and the verification and improve events especially in remote oceanic regions, and it will enable scientists to monitor the response of the global atmosphere to regional events such as Volcanic eruptions, the Kuwait oil fires, or the recent Indonesian and Mexican forest fires. Upper-tropospheric refractivity data from COSMIC may shed new light on the controversy over the role that tropical convection of COSMIC data will provide new insights into the global hydrologic cycle.

detection of gravity waves from the upper troposphere to the stratosphere, reveal the height and shape of the tropopause globally with unprecedented accuracy, support the investigation of fronts and other baroclinic struc tures, and improve our understanding of tropopause-stratosphere exchange processes.
COSMIC data will complement other observing systems and improve global weather analyses, particularly over the oceans and polar regions, and NWP forecasts made from these analyses.Through assimilation in numerical models, COSMIC data will improve the resolution and accuracy of the global temperature, pressure and water vapor fields, and through the modePs dynamical and physical adjustment mechanisms, the wind fields as well.These improved analyses and forecasts will provide significant benefits to aviation and other industries.
For climate research and monitoring COSMIC will provide an accu rate global thermometer that will monitor Earth's atmosphere in all weather with unprecedented long-term stability, resolution, coverage, and accuracy.COSMIC will provide a data set for the detection of climate variability and change, the separation of natural and anthropogenic causes, the calibra tion of other satellite observing systems and the verification and improve ment of climate models.COSMIC will contribute to studies of El Nifio events especially in remote oceanic regions, and it will enable scientists to monitor the response of the global atmosphere to regional events such as volcanic eruptions, the Kuwait oil fires, or the recent Indonesian and Mexi can forest fires.Upper-tropospheric refractivity data from COSMIC may shed new light on the controversy over the role that tropical convection plays in climate feedback.Global water vapor fields derived with the use of COSMIC data will provide new insights into the global hydrologic cycle.

INTRODUCTION AND SUMMARY OF GPS/MET
The Global Positioning System (GPS), established in prototype in the 1970s, and fully operational by the 1990s by the Department of Defense at a cost of approximately 15 billion U.S. dollars, is a satellite-based positioning system developed for navigation and positioning.More recently, civilian organizations from various nations have established the International GPS Service (IGS) network, which includes more than 100 globally distributed tracking sta tions and provides orbit determination with 5-cm accuracy in support of geodetic and geo physical research activities.The GPS today consists of 24 satellites that transmit L-band radio signals (19 and 22 cm wavelengths) to a wide variety of users in navigation, time transfer and relative positioning and to an ever-increasing number of scientists in geodesy, atmospheric sciences, oceanography and hydrology.It is not an exaggeration to say that we are witnessing the beginnings of an explosion of scientific applications and discoveries using GPS for inter disciplinary studies in geosciences.
In atmospheric sciences, there are two primary methods by which GPS is being used to sense the atmosphere (Ware, 1992;Bevis et al., 1992;Businger et al., 1996).In the first method, dual-frequency GPS signals are collected at ground-based receivers and used to ob tain the signal delay and thus the integrated water vapor along the path from the GPS satellites to the receiver ( Rocken et al., 1993( Rocken et al., , 1995;;Businger et al., 1996).In the second method, atmospheric soundings are obtained through the radio occultation technique, in which satel lites in low-Earth orbit (LEO), as they rise and set relative to the GPS satellites, measure the change in frequency of the GPS dual-frequency signals.The Doppler-shifted frequency mea surements are used to compute the bending angles of the radio waves, which are a function of atmospheric refractivity.The refractivity is a function of electron density in the ionosphere and temperature, pressure and water vapor in the neutral atmosphere.Hence the radio occul tation measurement technique provides useful information about the structure of the iono sphere, stratosphere and troposphere.
The radio occultation sounding technique was developed by scientists at Stanford Univer sity and the Jet Propulsion Laboratory (JPL) for the remote sensing of planetary atmospheres (see review by Melbourne et al., 1994).The GPS/MET (GPS/Meteorology) program (Ware et al., 1996) 4 was established by the University Corporation for Atmospheric Research (UCAR) in 1993, joint with the University of Arizona and JPL, to demonstrate active limb sounding of the Earth's neutral atmosphere and ionosphere using the radio occultation technique.The demonstration system observed occulted GPS satellite signals received on a LEO satellite, MicroLab-1 (ML-1), launched April 3, 1995.From raw GPS/MET observations, vertical profiles of ray bending angle and refractivity were retrieved; from which ionospheric electron density, neutral atmospheric density, pressure, temperature, and moisture profiles were com puted.
5 The program has been exceptionally successful, having accomplished nearly all of the "proof of concept" goals, plus a number of additional ones.As a direct result, GPS/MET technology is now widely recognized as a potential candidate for a new, accurate global ob serving system in support of weather prediction, climate change research and space weather.
4rhe GPS/MET Program was sponsored primarily by NSF, with additional funding provided by the Federal Aviation Administration (FAA) and the National Oceanic and Atmospheric Administration (NOAA).In addition, the National Aeronautics and Space Administration (NASA) provided significant "in kind support'' via funding provided directly to JPL for support of GPS/MET.Orbital Sciences Corporation accommodated the GPS/MET payload on its Microlab-1 Satellite and provided a Pe gasus rocket launch.Allen Osborne Associates, Inc. worked with GPS/MET investigators to convert its commercial Turbo Rogue GPS receiver for us in space.
A summary of key GPS/MET results is presented in Table 1.
During and after the GPS/MET experiment, UCAR has made all data and related products freely available to the research community on the web.
The high theoretical accuracy of radio occultation soundings (Melbourne et al., 1994;Kursinski et al., 1997) was demonstrated in the GPS/MET experiment.Rocken et al. (1997) present statistical validation of GPS/MET data by comparing over 1,200 GPS/MET soundings of the troposphere and stratosphere to a variety of correlative data sets.Comparisons were carried out with NCEP (National Centers for Environmental Prediction) and ECMWF (Euro pean Centre for Medium-Range Weather Forecasting) analyses, radiosondes, and satellite data including GOES-8, TOYS (TIROS Operational Vertical Sounder), HALOE (Halogen Occul tation Experiment) and MLS (Microwave Limb Sounder) instruments.Figure 1 summarizes the temperature comparison statistics.
The radio occultation method for obtaining atmospheric soundings is described elsewhere in this issue (Kursinski et al., 2000).Here it suffices to say that from the measured Doppler shift and the resulting bending angle data, vertical profiles of refractivity, N, can be derived.In the neutral atmosphere (stratosphere and troposphere), the bending angle-derived refractiv ity profiles are a function of temperature (T in K) , pressure (P in mb ), and water vapor pressure (e in mb), Table 1.Summary of Results from GPS/MET Experiment. (1) . Ei �E������I �if#�le�t�� �f.: • .
• :1a:;�•����c .ai .A:total of 123 data• us.e agreemeilh w�re isstle(i for access ' tl:iroi.lgh•the GP SIM.ET web site, which still receives about 40 000' ''hits"/itionl:h .i!cbsmtc;' sme' t. ucar.eilw smet The d at a have.been usecl .extefuiYely and : i)ltel1l.atfonally• ;for science 'and plilniling . of rollo'W-on miSsions: Fig_ J _ Summary of temperature comparison statistics from Rocken et al. ( 1997) verification study.The upper six bars compare correlative temperature data and the lower 8 bars compare GPS/MET temperatures with correla tive "dry" temperatures."Dry" temperatures are computed from refrac tivity under the assumption of zero water vapor as discussed in more detail in section 2.2.Colors indicate altitude intervals of the compari sons.Regions where the average temperatures agree within+/-1 Kare indicated in green.Positive average differences greater than 1 K are indi cated in red; negative average differences less than -1 Kare indicated in blue_ The magnitude of the average differences is labeled where it oc curs in degrees K. RMS differences about the mean are not shown here, but they are discussed in Rocken et al. 1997.In the OPS/MET experiment, only setting occultations were observed and only about 10% of the soundings penetrated into the lowest kilometer of the atmosphere.The goal for COSMIC is to track 90% of all rising and setting occultation soundings to within one kilome ter of the Earth's surface.This will be achieved with (a) -10 db higher gain antennae and (b) with "open loop" tracking in the lower part of the troposphere (Meehan et al., 2000, personal communication).
Atmospheric inhomogeneities and multipath are the dominant error sources for profiles of refractivity below 20 km, obtained with the standard Abel inversion technique (Gorbunov and Gurvich, 1998).Resulting errors reach up to 10% near the surface (Kursinski et al., 1997).
One way to avoid the error due to horizontal inhomogeneity, as discussed by Kuo et al. (2000) elsewhere in this journal, is to avoid the Abel inversion, and to assimilate profiles of bending angles into numerical weather models (Eyre, 1994;Zou et al., 19 99).To minimize the errors due to multipath, the bending angles should be calculated after back-propagating of the re ceived complex electromagnetic field closer to the limb, where the multipath effects are smaller (Gorbunov and Gurvich, 1998).
Unlike in-situ observations, a single radio occultation observation represents a fairly com plicated average of atmospheric properties over a volume resembling a horizontal tube with an along-track horizontal scale of approximately 300 km and a radius of approximately 1 km (Fig. 1, Appendix A).Appendix A discusses this important issue of the spatial scales repre sented by radio occultation data, and distinguishes the concept of scale, or representativeness of a single observation, from resolution, which is a measure of the ability of a set of observa tions to define or analyze (resolve) atmospheric features of various horizontal and vertical scales.Appendix A also argues that the spatial scales represented by occultation soundings are ideal for use in global NWP models and for climate studies.
The characteristics of COSMIC data and their relevance to meteorology (including weather prediction) and climate are summarized in Table 2.The set of unique characteristics, includ ing the accuracy and independence from all other observing systems, the fact that the retrieval process does not require a first-guess sounding, the absence of instrument drift and satellite to-satellite bias and the ability to retrieve soundings in all weather (as shown by Solheim et al., 1999, the retrievals are minimally affected by clouds, aerosols or light precipitation), will make the COSMIC data very useful as complements to other observing systems.ESA (1996), Hoeg et al. (1996) and Melbourne et al. (1994) provide excellent discussions of the potential value of radio occultation data for meteorological and climate research and operations.

COSMIC AND METEOROLOGY
The characteristics of COSMIC data summarized above will make them valuable addi tions to the global observing system for a number of meteorological process studies, espe cially over the oceans and polar regions (Hoeg et al., 1996).The lack of accurate and high resolution data over the oceans and polar regions, despite advances in operational satellite based remote sensing capability, contributes much to the uncertainties in the initial state of weather-prediction models, which in turn limits the forecast skill of these models.With a total of 4,000 soundings per day, uniformly distributed around the globe, COSMIC will provide the much-needed additional data over data-sparse areas.The high vertical resolution, accurate, and independent COSMIC data will complement data from geostationary (Menzel et al., 1998) and polar-orbiting satellites, which provide high horizontal but low vertical resolution sound ings.COSMIC represents a factor of four increase in terms of upper-air observations over the existing global radiosonde network, which has a total of -900 stations (Fig. 2).The average horizontal spacing of the 4000 daily soundings shown in"Fig. 2 varies with latitude, and is summarized in Fig. 3.The horizontal spacing is least near the poles (approxi mately 300 km) and greatest at the Equator (approximately 500 km).

Resolution of Important Atmospheric Structures
To be valuable for process studies and for NWP, COSMIC data must add additional infor mation (beyond that already contributed by present observing systems) that resolves important features of the atmosphere.They must also contribute to the reduction of errors in the initial conditions of models that contribute most to forecast error growth.Palmer et al. (1998) dis cuss the use of singular vectors to study the sensitivity of models to initial errors .They point out that the vertical vm"iation of the energy spectrum of the typical analysis error field is flatter than that of the analysis itself.Thus, while the energy spectrum of the typical analysis field peaks near the tropopause, or jet-stream level, the energy spectrum of the analysis error field is more nearly constant throughout the tropopause.Similarly, the horizontal energy spectrum of analysis errors shows a flatter peak at smaller scales (e.g., wavenumbers 15-25 , horizontal scales approximately 2,000 km) than does the analysis itself in which the peak is at planetary scales (wavenumbers 4-6, horizontal scales 7 ,000 -10,000 km) .From the structure of present analysis errors we expect COSMIC to be most useful in improving the initial structure of the atmosphere at relatively small (1,000-5,000 km) horizontal scales and from the lower tropo sphere into the lower stratosphere.
As shown in Fig. 3, the horizontal spacing of COSMIC data on a daily basis varies from approximately 300 km near the poles to 500 km in the tropics.In middle latitudes, the pre dominant features of interest are baroclinic waves and the associated cyclones and anticy clones.The horizontal wavelength of these waves varies from roughly 2,000 km for the short est waves to 8,000 km for the long planetary waves.Wavenumbers 5-7 (wavelengths approxi mately 6,000-8,000 km) dominate the observed spectra (Staley and Gall, 1977;Holton, 1979).With an average spacing of approximately 300-400 km poleward of 20° latitude, COSMIC data will resolve these baroclinic waves well, especially when combined with other data.COSMIC data will also contribute to the observation and resolution of incipient baroclinic waves, especially over the oceans, because the wavelength of maximum baroclinic instability for typical conditions of static stability is about 4,000 km (Holton, 1979).
In the tropics, COSMIC data by themselves will not resolve the detailed structure of tropi cal cyclones with scales of typically several hundred kilometers .However, they will contrib ute significantly to the definition of the pressure, temperature and water vapor, and through data assimilation, the wind field in the large-scale environment surrounding the storm.The typical scale of circulation affecting the motion of tropical cyclones is 3,000-5,000 km from the cyclone center (Anthes, 1982;Pielke and Pielke, 1997).With a horizontal spacing of 350-450 km between latitudes 10 ° and 30°, COSMIC soundings will resolve the environment of the tropical storm and thereby contribute to improved tropical storm forecasts.
COSMIC data will resolve vertical scales as small as 0.5 km (Appendix A).This vertical resolution is considerably higher than satellite-based radiometric soundings.The GPS/MET experiment has indicated that the radio occultation soundings are capable of resolving strong temperature inversions associated with upper-level fronts and the tropopause (Kuo et al., 1998) .The high accuracy and vertical resolution of COSMIC data in the upper troposphere and lower stratosphere should improve the analysis of potential vorticity in the vicinity of the jet stream and tropopause, a region known to be important in the accurate initialization of NWP models for predictions of cyclogenesis (Davis and Emanuel, 1991;Fehlmann and Davies, 1997).
Lindzen and Fox-Rabinovitz ( 1989) discuss the importance of having a consistency be tween the horizontal and vertical scales resolved by NWP models and observational systems.They show that most models and observational systems do not meet the consistency criteria over much o f the Earth .Appendix A discusses this issue and shows that the horizont al and vertical scales of radio occultation data are close to meeting the consistency criteria; therefore COSMIC observations are expected to add significant value to the global observing system.
As noted earlier, many of the GPS/MET soundings did not penetrate into the lower 5 km of the atmosphere.This was a limitation of the GPS/MET data because of the importance of the lower troposphere in weather prediction and climate.Not only is most of the atmosphere's water vapor located below 5 km, much of the atmospheric structure which is important in cyclogenesis occurs below 5 km.For example, Gelaro et al. (1998) show through construction of optimal perturbations using singular vector analysis that NWP models are most sensitive to small-scale baroclinic structures that have their maximum amplitude in the lower to middle troposphere.Observing system simulation experiments performed by Kuo et al. (1997) dem onstrated the importance of GPS/MET data in the lower troposphere (below 3 km) for cyclone prediction.To realize the full potential of the radio occultation technique in improving nu merical weather prediction and contributing to weather and climate studies, therefore, requires achieving the COSMIC goal of retrieving reliable soundings to at least within 1 km of the Earth's surface.

Retrieval of Temperature and Water Vapor
Given measurements of refractivity N, the relationship among refractivity, temperature, pressure and water vapor (Eq.I), together with the hydrostatic equation, comprise a system of two equations with three unknowns.Equation ( 1) may be solved for either temperature To r water vapor pressure e given independent estimates of the other variable: and 77.6 P + [ 6022.0P2+14.92x l05eN ]"2 T2N-77.6PT e= ------ 3.73x10 5 (2) (3) Where water vapor is negligible, such as in the stratosphere and upper troposphere, pres sure and temperature may be obtained directly from the refractivity ( e:::: : O in (2)).Tempera tures retrieved with the assumption of zero water vapor are termed "dry temperatures " ( T dr) ; the neglect of water vapor implies that T J ry is always less than or equal to T. Figure 4 shows comparisons of GPS/MET T J ry profiles with radiosonde temperatures in the tropics.There is excellent agreement between T., and the radiosonde temperatures between 10 and 35 km.
urv Below 10 km the presence of water vapors causes T J ry to be less than the radiosonde temperature.
Where water vapor is present in significant amounts, it is impossible, without additional independent data, to separate out the effects of temperature and water vapor.However, in principle it is possible to calculate either water vapor or temperature given refractivity and the independent estimate of the other variable.In practice, it is much more likely that useful estimates of water vapor can be obtained given the refractivity and an independent estimate of temperature than the other way around.This can be seen by the relationship between errors in calculating temperature and water vapor from refractivity given independent estimates of wa ter vapor and temperature.As shown by Ware et al. (1996), the relationship between errors in temperature and water vapor pressure, under the assumption of no errors in N or P, is 6e � (2TN -77.6P)Li T.

125
(4) ( 5 ) The above error equations show that water vapor must be independently known to a very high accuracy if useful estimates of temperature from refractivity are to be obtained.Specifi cally, e would have to be known to within an accuracy of at least 0.23 mb to obtain tempera ture estimates accurate to within 1 K.However, if temperature is known independently to within an accuracy of 2 K, estimates of water vapor pressure can be determined with an accu-racy of about 0.5 mb.This would be a useful estimate in many regions of the lower tropo sphere where water vapor typically varies between 5 and 20 mb and other measurements of water vapor are unavailable.Thus, if a reasonably accurate independent estimate of tempera ture is available (e.g., from a global analysis or a 12-hour forecast), accurate profiles of water vapor can be obtained 6 (Fig. 5).Gorbunov et al. (1996a,b) discuss alternative ways of estimat ing water vapor and temperature from refractivity and show examples of accurate retrievals of water vapor using simulated radio occultation measurements and output from a general circu lation model.

Upper Level Fronts and the Tropopause
As demonstrated by GPS/MET, COSMIC data will provide high-vertical resolution data that can contribute significantly to the observation and analysis of atmospheric fronts and the tropopause.Kuo et al. ( 1998) showed that GPS/MET data accurately resolved an intense upper-level front over China (Fig. 6), and that even though this front occurred in a region of dense radiosonde data, the operational analyses of NCEP and ECMWF resolved this front only in a very smooth way.
6 The situation is somewhat different in the upper troposphere, where the saturation water vapor pre ssure is small, and much more accurate estimates of temperature are necessary to obtain useful es timates of water vapor pressure (Kursinskl et al. 1996).For example, for a standard atmosphere at 300 mb (approximately 7 km).T""' 243K, e, ""'0.5mb,N ""100 and Lie"" 0.07 LiT.Here a 1 K error in T produces an error in e that is a significant fraction of e,.NCEP and ECMWF analyses interpolated to the GPS/MET sounding location at 00:00 UTC October 22, 1995 (Kuo et al., 1998).
An inversion of about 2 K is present at about 7.5 km (approximately 400 mb).The inversion is not present in either the ECMWF or the NCEP analyses.The 400-mb analysis for 12:00 UTC 14 October (Fig. 8) shows a trough centered over Wisconsin with a strong baroclinic zone ahead of the trough.The GPS/MET sounding is located near the leading edge of the baroclinic zone in a region of modest temperature gradient.
A third example of an upper-level front is shown in Fig. 9.This front, located about 750 km west of Los Angeles (31.2°N 135.3°W), was observed at 22:54 UTC 8 February 1997 in advance. of an upper-level trough (not shown).It shows a temperature inversion between 11 and 12 km of approximately 7 K, and again, this inversion is not present in the NCEP and ECMWF analyses.
COSMIC soundings will improve the resolution of the tropopause over the world.Figure 10 illustrates the capability of the radio occultation technique to resolve the tropopause with higher resolution than TOVS data, and also higher than that typically achieved by operational analyses, which depend heavily on TOVS data in regions where radiosondes are not present.Other examples of soundings that resolve the tropopause very well are shown in Fig. 11.

Gravity Waves and Stratospheric Dynamics
As summarized in the planning document for the SPARC (Stratospheric Processes and their Role in Climate) Program (WCRP, 1998), the stratosphere plays an important role in weather and climate.COSMIC data will contribute strongly to the SPARC goals of under standing stratosphere-troposphere exchange and the structure and climatology of stratospheric gravity waves and their parameterization in NWP and climate models (BSA, 1996).Hocke (1997) describes the use of GPS/MET data for the study of gravity waves in the middle and upper atmosphere.For example, Kursinski et al. (1996) show a OPS/MET tem perature sounding with oscillations in the stratosphere of vertical wavelengths around 3 km; these waves were in excellent agreement with waves resolved by a nearby radiosonde.The vertical oscillations shown in Fig. 4 above about 35 km and in Fig. 12 above 40 km are likely due to gravity waves.Tsuda et al. (2000) have used the temperature variance of individual OPS/MET profiles, which is assumed to be caused by gravity waves, to compute the potential energy Ep.They found that OPS/MET derived Ep around Japan shows a seasonal variation with enhancement in the winter months, which is consistent with several years of radar observations.They also generated a global map of Ep from winter (Nov 96-Feb 97) OPS/MET soundings.These results are shown in Fig. 13, and they strongly suggest that atmospheric gravity waves are and temperature (dashed lines, contour interval 2 K) from NCEP analysis at 12:00 UTC October 14, 1995.The symbol x just north of Lake Huron marks the location of the GPS/MET sounding.
generated by convection in tropical regions, particularly over the Indonesia archipelago, the Indian Ocean, Africa and the eastern Atlantic and South America.COSMIC promises to detect gravity wave activity globally with much better temporal and spatial resolution, thus allowing studies of how gravity waves relate to wind shear, thunderstorms, cyclones and other meteorological phenomena.,

Polar Meteorology
COSMIC will greatly increase the amount of atmospheric soundings in the polar regions where operational analyses often show large errors (e.g., Fig. 11).Figure 14 shows the ex pected soundings from 8 satellites in one day.These data will contribute to polar science in a variety of ways.Duck et al. (1998) report observations of annual late December warming of the upper stratosphere in the Arctic polar vortex.This warming, which extended into the lower strato sphere and which was accompanied by increased gravity wave activity, is important to under standing ozone depletion.Ozone depletion is sensitive to temperatures within the arctic vor tex (Schoeberl and Hartmann, 1991).Dense and accurate temperature and gravity wave ob servations from COSMIC will help to reach an improved understanding of detailed processes controlling intra-vortex stratospheric temperatures, and will lead to improvements in Global Circulation Models (GCMs).Such improvements may enable GCMs to produce reliable pre dictions of the future state of the ozone layer (Duck et al., 1998).We attribute these differences to analysis errors.COSMIC data can help improve analyses of surface air pres su res in regions of low atmo spheric water vapor.This is important to the GRACE (Gravity Recovery and Climate Experi ment) mission_ GRACE can detect the gravitational change due to changing ice sheets, if the Fig. 14.Proj ected COSMIC soundings near the poles every 24 hours (green).
Radiosonde sites are shown in red.
gravitational "noise" due to changing surface pressure (weight of the total column of air) is calibrated (Gurvich and Sokolovskiy, 1985).The data from COSMIC promise to improve this calibration and therefore the "ice signal" of GRACE.Additional studies, such as assimilatio n of simulated COS MIC re fractivity observ ations into numerical weather models, are needed before we can state by how much pre ssure , temperature and moi sture are improved near the surface.COSMIC data will also aid monitoring of atmospheric water vapor in the polar re gions, an important parameter for mass balance st udie s of the ice sheets.
Weather analysis and forecasting in the polar reg ions are likely to be sig nificantly en hanced by COSMIC and will have important applications in areas such as the aviation indus try and in the execution of various scie ntific and commercial missions in these remote re gio ns.To summarize some examples where COS MIC can be useful to polar meteorology: • Improved meteorological analyses and forecast s • Surface pressure corrections for ice balance studies with GRACE • Vertical temperature profiles for ozone depletion studies • Polar water vapor studies (assuming temperat ures are known, or available through model assimilation of refractivity) • Inve stigation of su dden strato spheric warming events during the polar spring • Improved aviation weather analysis and prediction over the polar regions

COSMIC AND NUMERICAL WEATHER PREDICTION
COSMIC will generate meteorological products within three hours of observation for tests in operational weather prediction.This sectio n expands upon the di scussion of Anthes et al. ( l 997a) and argues that COSMIC data, if assimilated effectively in NWP models, will improve global analyses and forecasts.This conclusion is supported by previous independent st udies (Hoeg et al., 1996)

Effect on Analysis
Although the global coverage of data from the GPS/MET experiment was inadequate to make a differe nce operationally, the GPS/MET data did provide evidence that COSMIC data will have a significant positive impact on global operational analyses.For a new data set such as COSMIC to make a positive difference in an operatio nal analysis and subsequent forecast, the data must add useful information by contributing differ ences to the analysis that make the analysis more accura te, especially in regions of the at mosphere that are sensitive to initial errors (Palmer et al., 1998).Leroy (1997) compared time-averaged analyses of geopote ntial heights computed from GPS/MET data with oper ational analyses over the same period from ECMWF and found large differe nces over data-spar se regio ns such as the South Pacific ocean.Since the differe nces were small over data-rich reg ions, this study suggests that COSMIC data will make a positive difference to operational analyses even at large scales over the oceans.Similarly, Rocken et al. ( 1997) fo und a significantly greater difference between GPS/MET refractivities and derived temperatures from NCEP analyses over data-poor regio ns versus data-rich regions (Fig. 15).
The four GPS/MET soundings shown in Fig .
L l, taken during January and February 1997, show large differe nces in stratospheric temperatures obser ved by GPS/MET and the NCEP operational analyses.Since the soundi ngs agree well in the lower troposphere, these system atic differences in the str atosphere suggest that the NCEP stratospheric analyses are biased toward temperatures that are too high and that COSMIC data will have a significant positive impact in the st ratospheric analyses.
Further evidence that COSMIC data will significantly modify operational analyses is pre se nted in Fig .16, which shows comparisons for GPS/MET 100 mb temperatures over a 53day period (January 6-February 27 , 1997) with the NCEP/NCAR reanalysis (16a) and the ECMWF operational analysis (16b ).Differences in GPS/MET temperatures and NCEP/NCAR temperatures range from -5.8 K to + 3.4 K while the corresponding differences from the ECMWF analysis range from -3.3 to + 3.9 K. [Note that the color shading reflects an objective analysis of the temperature differe nces, which were calculated at the GPS/MET sounding sites (indicated in the figure by black dots).Temperature differences for individual soundings be tween GPS/MET and NCEP/NCAR temperature can be as large as 8 K. ] The NCEP/NCAR temperatures show a systematic warm bias in the latitude band +/-30 degrees from the Equa tor.This systematic warm bias is not present in the ECMWF analysis.Figure 16c shows the comparison of the ECMWF and NCEP/NCAR analyses over this period.The NCEP tempera tures are higher than the ECMWF temperature over the Equator a nd lower between about 30°N and 60°N.The differe nces shown here are consistent with the temperature differences shown in the example in Fig. l 0. These comparisons show that significant differences, and ther efore uncertainties, exist betwee n obj ective analyses from leading world meteorological center s.Hence COSMIC data can be expected to make a significant I mpact on operational analyses and re-analyses.Similar global comparisons will be conducted with COSMIC real-time data and provided to operational centers as a tool for quality control and evaluation.
On smaller scales and over data-rich regions, it is difficult to estimate in advance what the impact of COSMIC data will be.However, the improved vertical resolution of upper-level fronts by GPS/MET soundings compared to the operational weather analyses, as illustrated in Figs. 6, 7 and 9, provide evidence that COSMIC data may have a positive impact on analyses even over data-rich regions.It is possible that the impact will be small on many days and large on a few significant days.Given the theoretical accuracy and high vertical resolution of COS MIC data, which have been confirmed by the GPS/MET experiment, and the data assimilation studies conducted so far (Kuo et al., 1997;2000), we can reasonably expect a signifi cant positive impact of COSMIC data on operational analyses.

Initialization of NWP Models Using COSMIC Data
COSMIC data will be available for testing in real-time in operational NWP models.It is likely that the data will be assimilated into the models using three-dimensional or four-dimen sional variational techniques (3DV AR or 4DV AR).Either of these data assimilation tech niques may, in principle, assimilate bending angles, refractivities, or derived temperature and water vapor data.Eyre ( 1994) suggests that the most powerful use of COSMIC neutral atmo sphere data is to assimilate the refractivity or bending angle profiles directly into numerical models.In this way, which is analogous to assimilating satellite-observed radiances in models and the standard error of the mean differences (green envelope around red line).The blue line is the number of soundings at each level.(Rocken et al., 1997).
rather than soundings derived from these radiances (Derber and Wu, 1998), a minimum num ber of assumptions are made.Numerical experiments have shown that assimilation of refrac tivity and bending angles directly into numerical models causes the model's temperature, wa ter vapor, and wind fields to adjust toward actual atmospheric values (Zou et al., 1995;Kuo et al., 1997, Zou et al ., 1999).How this mutual adjustment occurs is investigated in the fol low ing sections.

Adjustment of Models to COSMIC Mass Field Data as Predicted by Geostrophic
Adjustment Theory COSMIC data will provide information on the temperature, pressure and water vapor fields of the atmosphere.These variables constitute the mass field of the atmosphere.For large scales of motion, the mass field is in near balance with the wind field, meaning that the gps_nmcrs_temp_ 1 00mb_9 7 .006-058(a) •Ii.BO -4.00 -3.96 -3.04 -2.12 -t20 -0.28 064 1.liB 2.48 3_40 Delta Temperature (C)  net accelerations of the wind are small compared to the accelerations associated with the Co riolis force and pressure gradient force individually.Under these conditions, accurate specifi cation of either the three-dimensional mass field or the three-dimensional wind field deter mines the other through rather simple diagnostic relationships.
The type of balance between the mass and wind fields varies de pending on the horizontal and vertical scales of motion of the atmospheric feature, the latitude, and whether or not sig nific ant acceleration effects are present.The important acceleration effects are associated with curved atmospheric flow, friction, and diab atic heating.The simplest balance is given by the geostrophic relationship in which the wind speed and direction are directly re lated to the horizontal pressure gradient force.Simple geostrophic balance is most valid for large-scale, straight flow in high latitudes in the absence of frictional or di abatic heating effects.Addition of curvature in the flow modifies the geostrophic wind re lationship by accounting for centrip etal acceleration effects; the result is the gradient wind relationship, which takes into account the ra dius of curvature of the trajectory.A further generalization for horizontal flow that takes in to account nonlinear effects in the equation of motion results in the balance equation (Holton, 1979, p. 179).
In fact, the atmosphere is never in complete balance; it is continuously adjusting to small imbalance s between the mass and the wind fields through the generation and propagation of inertial gravity waves.
For motion at small scales, low latitudes, or when friction or diabatic heating are present, the atmosphere often shows large de partures from the balances described above and ageostrophic motions can be large.Under these conditions there are no simple diagnostic equations re lating the wind and mass fields .However, through the data assimilation process, if one assimilates accurate observations of either the mass or the wind field into the model, the other fiel d will adjust through the model's equations to an appropriate balance, even in the presence of these ageostrophic effects.Herein lies one of the great advantages of continuous data assimilation.
An important question is how will COSMIC data impro ve the initial conditions in NWP models and thereby im prove the subsequent forecasts.COSMIC data provide independent and accurate information about the atmosphere' s mass field.How will assimilation of these data affect the model 's wind field?To help answer these questions, we consider geostro phic adjustment theory (see Haltiner and Williams, 1980, p.47 for an introduction to this theory).
Although, in principle, either mass or wind observations may be assimilated in models and the other field will adjust appropriately (Atlas et al., 1985), the efficiency of the adjust ment process varies depending on the vari able being assimilated, the horizontal and vertical scale of the phenomenon, the latitude, the static stability, and the nearness to the surface of the Earth.The relative efficiency of assimilating mass or wind observations may be investigated through geostrophic adjustment theory.In geostrophic adj ustment theory, we assume that the atmosphere is in a quasi-balanced state but that small imbalances exist between the mass and the wind field.Since both the wind and the mass fields contain small errors, to assess the impact of COSMIC data on models, we ask how the model atmosphere will adjust to an in put of accurate mass field data (data with an accuracy significantly above the accuracy of the model's mass field data).
To consider the relative importance of mass and wind observations in a model, consider a linearized shallow fluid model on a resting basic state (Haltiner and Williams, 1980, p.48).
This system consists of a steady state solution in geostrophic equilibrium and three wave solutions: two inertial gravity waves and a Rossby wave.If an imbalance between the mass and wind fields exists in the initial conditions, the system adjusts to the steady state geo strophic solution through the propagation of the inertial gravity waves away from the system.
The final balanced state, denoted by subscript "s," is related to the initial unbalanced state, denoted by subscript "o," is given by the solution (Haltiner and Williams, 1980, p. 5 1) where Vs (V0) and hs (h0 ) represent the adjusted steady state (initial) wind and mass fields respectively, L is the wavelength of the perturbation, g is the acceleration of gravity, f is the Coriolis parameter, i = H and L R is the Rossby radius of deformation given by where H is the mean depth of the fluid.Now, we assume that the Coriolis force and the pressure gradient force have the same order of magnitude, which means that V0 and g h 0 have the same order of magnitude.We get f L two very different final states depending on the scale of the disturbance.First consider the case where L2 << L2 R , in which case and In this case, which is favored for small-scale horizontal disturbances with significant depth and low latitudes, the final wind is equal to the initial wind, and the final mass field is related geostrophically to the initial wind field.In this case the mass field has adjusted to the wind field, which means that accurate initial wind data would be more effective than accurate initial mass field data.Thus COSMIC data under these conditions would be relatively ineffective in causing the model wind field to adjust to the correct mass field data.The information in the COSMIC data will tend to radiate away as inertial gravity waves.
In the case where L 2 >> L 2 R , a much different result is obtained.In this case ( 6) and ( 7) reduce to and Therefore, for large horizontal and shallow phenomena and high latitudes, the initial mass field determines the final state.Under these conditions, COSMIC data would be effective in causing the model's wind fields, as well as the mass fields, to adjust toward more accurate values.
As verified by more complex theories and by numerical experiments with non-linear models (0kland, 1970;Anthes, 1974;Hoke and Anthes, 1976;Hoke and Anthes, 1977), the above results are surprisingly general, applying to a two-dimensional barotropic atmosphere and to stably stratified baroclinic atmospheres.For the latter, the results apply if L R = c g If where cg is the phase speed of internal gravity waves where 8 is potential temperature and L, is the vertical scale of the phenomenon .Thus, in a stably stratified atmosphere, COSMIC observations will be most useful when the static stabil ity is relatively low.
Table 3 shows values of the Rossby radius of deformation for some representative values of latitude, static stabilities and vertical scales of disturbance.This indicates that for the hori zontal and vertical scales of motion resolved by the COSMIC data ( L ;::: 300 km and Lz ;::: 2 km ), the wind field will tend to adjust to the mass field, and COSMIC data will be effective in causing the model's wind fields to adjust.The situation where COSMIC data are least likely to be effective in this regard are for deep motions near the Equator under very stable conditions.

Data Assimilation and Geostrophic Adjustment
The classic theory of geostrophic adjustment as discussed above applies to the adjustment of a model atmosphere that is perturbed instantaneously by wind or mass field data.In a data assimilation cycle as practiced in modern operational centers, data are inserted into the model atmosphere more than once during an assimilation cycle; for example, data every six hours, or even every one hour, may be used in an assimilation cycle.For data derived from continuous observing systems such as satellites, the assimilation of data may occur nearly continuously over a 24-hour cycle.In this case, simple application of the geostrophic adjustment theory to interpret how the atmosphere adjusts to mass or wind data may be misleading.For example, consider a disturbance of a horizontal and vertical scale at a latitude in a model atmosphere with static stability such that for a given mass-field perturbation, half of the impulsive mass perturbation remains in the steady state adjusted wind field with the other half radiating away as inertial gravity waves.A second impulse of mass data a short time later would result in more than half of the mass field data being retained in the model's final wind field.And a continuous assimilation of accurate mass data would force the model's wind field to adjust to a value much closer to balance with the "final" mass field than would a single application of mass data.
The above argument suggests that even for short waves in tropical regions where geo-strophic adj ustment theory indicates that mass data will have less impact on the wind field, a continuous assimilation of mass data will have a much greater effect on the winds than simple geostrophic adjustment theory indicates.And in fact, data assimilation studies by Charney et al. (1969); Jastrow andHalem (1970, 1973), Williamson and Kasahara (197 1), Kasahara (1972), Gordon et al. (1972) and others have shown that if any one of the three primary meteorological variables (wind, pressure or temperature) is assimilated over time in a model, the other two variables will adjust to the correct values (Atlas et al., 1985).Fig. 17 illustrates this fact by showing the reduction in wind error over time given the assimilation every 12 hours of tem perature data with varying errors superimposed.In middle latitudes ( 49° in this example, 17 a) the reduction in wind error is relatively rapid.At the Equator, the adjustment of the wind to the temperature data is slower in accordance with geostrophic adjustment theory, but even directly on the Equator there is a positive impact of assimilating accurate temperature data.In another example, numerical experiments with a primitive equation model of a tropical cyclone indicate that continuous assimilation of accurate temperature data has almost as much positive effect on the model cyclone as does the continuous assimilation of both temperature and wind data (Fig. 18).Near the Earth 's surface, assimilation of temperature and pressure data has an advantage over assimilation of wind data.Small temperature changes in the free atmosphere as a result of insertion of accurate wind data occur through adiabatic cooling or warming associated with vertical motions resulting from imbalances between the adjusted wind field and the original mass field.Near the surface vertical motions are suppressed, and no amount of accurate wind data can correct an erroneous temperature field.Therefore, COSMIC data, which provide information on the temperature and pressure fields, will be particularly important in the lower kilometer or so of the atmosphere, and it is extremely important that a large fraction of COS MIC sounding reach to within one kilometer of the surface as planned.
In summary, we agree with the conclusions from the analysis of the value of GPS/MET soundings by Hoeg et al. (1996): "Atmospheric profiling using the radio occultation tech nique offer a major potential for improving the products from operational numerical weather Table 3. Rossby Radius of Deformation (LR) for Vertical Scales of Phenomena Equal to 2 km and 5 km at Low, Middle and High Latitudes, and for Relatively Unstable and Stable Conditions.
L, = 2km L, =5km : =ll)lkm : = s ry km : =ll)lkm �-5 1){ prediction models.The observations from the technique will be one of the most economical ways of improving the observational data base for the NWP models.The good global data coverage will correct the forecast models by preserving the horizontal gradients in the atmo spheric parameters."

COSMIC AND CLIMATE
Observing changes and variability in the global climate is one of the most important chal lenges in atmospheric sciences.Because of the many difficulties associated with making long-term in-situ measurements (for example calibration, representativeness, costs, difficulty in making temporally-continuous measurements over remote areas and throughout the entire troposphere and stratosphere), remote sensing from space is, in principle, the most desirable way to observe the global atmosphere over long periods of time.However, difficulties in obtaining reliable climate records from satellites include changes in instruments, platforms, Equator crossing times and algorithms (Hurrell andTrenberth, 1997, 1998;Salby and Callaghan, 1997;Waliser and Zhou, 1997).Calibration problems, instrument drift and lack of high verti cal resolution add to the difficulties of observing small changes in climate or climate variabil ity.The long-standing controversy associated with the Microwave Sounding Unit (MSU) is a case in point, as discussed by Hurrell and Trenberth (1998).The MSU tropospheric tempera ture record shows a slight global cooling (-0.05 K/decade) since 1979, whereas surface tem perature records show a significant global warming (0.13 Kl decade) over this same period.As noted by Hurrell and Trenberth, this discrepancy has been loudly touted by a few individuals as casting serious doubt on whether or not global warming is, in fact, occurring.The question about whether the global climate has warmed over the past several decades and by how much has thus become not only an important scientific question, but a political one as well.
The European Space Agency (ESA, 1996) describes many of the advantages and poten tial contributions of radio occultation data to climate studies.The recent National Research Council (NRC, 1998) assessment of the U.S. Global Change Research Program (USGCRP) emphasizes the importance of obtaining a long-term record of global temperature change that is accurate and stable.According to this report, " .. an essential requirement of the observa tional strategy is to establish long-term, scientifically valid, consistent records for global change studies."(NRC, 1998, p. 11).The NRC report also states (p.26): "The importance of accu racy, continuity, calibration, documentation, and technological innovation in observations for long-term trend analysis of global change cannot be overemphasized."The characteristics of the innovative radio occultation technique in general and COSMIC in particular include accu racy, long-term stability, no calibration, no instrument drift, unaffected by clouds, precipita tion and aerosols and its high vertical resolution, all at relatively low cost.The technique is in many ways the ideal "global thermometer", meeting many of the key objectives of the USGCRP as stated by the NRC and discussed recently by Goody et al. (1998).
The COSMIC mission will deliver data products that are unique and important for climate research.The special nature of GPS occultation data with regard to calibration is very crucial for detecting small variations and trends in climate, since data taken in different intervals by different research groups and from different countries can be compared without concern for 0 10 Eq uator 0 10 Anthes et al.
instrument degradation or calibration.COSMIC will deliver 4,000 soundings/day with ran dom measurement errors of about +/-1 K.For climate studies space-time averages of COSMIC observations can be formed to reduce the random error.A one-month average over each 1 % area of the Earth's surface ( -1,200 soundings) will reduce the random 1 K error to 0.03°C.This is adequate to follow trends of 0. 1 K decade, which is typical of greenhouse gas or other forced climate responses.COSMIC data will provide seamless soundings from orbit altitude to near the surface.It has been shown (North and Stevens, 1998;Stevens, 1999;Leroy, 1998) that stratospheric-tropospheric temperature profile information enhances the sig nal-to-noise ratio of climate data significantly over surface-only observations.For example, Stevens ( 1998) showed that for a transient simulation of the doubling of carbon dioxide in the atmosphere, the signal-to-noise ratio for climate signal detection is increased by a factor of 2.3 when temperature data from the tropical upper troposphere and stratosphere are used, com pared with using only the tropical surface temperature data.Over much of the Earth the green house-warming signal in models is strongest in the upper troposphere and lower stratosphere (Fig. 19), where the accuracy of COSMIC data will be the highest.
The unique capability of COSMIC data in estimating the geopotential heights of constant pressure surfaces independent of surface pressure or temperature data can be used to monitor global or regional scale layer mean virtual temperature, which is a sensitive measure of global change.The mean virtual temperature Tv in an atmospheric layer from the surface ( Z, ) to the geopotential height of a constant pressure surface Pt is given by where P, is the surface pressure and R is the gas constant for dry air.Unlike other observing systems, COSMIC soundings can be used to calculate Z1 above the onset of water vapor independent of any data below this height by integrating the hydrostatic equation downward from great heights to any pressure level.Changes over time of Zt are thus proportional to the changes in mean virtual temperature in the atmospheric layer from Z1 to the Earth's surface, and thus provide an integral measure of global change through deep layers of the atmosphere.
According to model studies, and suggested by observations over the past 25 years (IPCC, 1996) the lower tropospheric vapor concentrations will increase with increasing surface tem perature (the water-vapor feedback effect).The situation is not so clear in the upper tropo sphere, where small amounts of water vapor are important for radiative heat transfer.Lindzen (1990) argues that increased surface temperature and resulting stronger tropical convection will result in increased tropical precipitation and a decrease of tropical/subtropical tropospheric moisture above 6 km.This is in contrast to model predictions of water vapor increases of 20% per degree of surface warming.Clearly it is important to resolve the differing theories and to test the performance of climate models in simulating upper troposphere water vapor.This, however, may be difficult with current observing systems as Rind (1998) points out.Radio sondes are not suitable for detecting long-term global trends, and down-looking radiometers lack the required vertical resolution.COSMIC data will help the situation.Assuming that temperature is known at the 500 mb level from models to within 1-2 degrees, individual COSMIC profiles will measure the water vapor pressure at that height to about 0.2 mb, or, assuming all errors are random, averaged over a 1 % I-month 1,200-sounding "climate box", to 0.006 mb.Water vapor pressure at 500-mb height varies between 0 -6 mb and a several percent change, especially in the tropics, should be detectable by COSMIC data with high vertical resolution.At 300 mb GPS/MET observed water vapor in the range 0-0.7 mb.Fol lowing the same arguments as above, water vapor at that altitude can be measured to -0. 12 mb, or to a climatological average of 0.004 mb.
Figure 20 shows GPS/MET derived water vapor (using ECMWF temperatures) at 300 and 500 mb for two different time windows.These results have not been validated with cor relative data but look generally reasonable with the highest amounts over regions of deep convection.The East Asian monsoon shows up clearly during the June-July period, and we see the high water vapor values over Africa and South America, presumably caused by con vection.(Meehl et al., 2000).
While each panel in Fig. 20 represents 15 or 22 days of data, COSMIC will provide a similar view of the global atmosphere (there are about 1000 occultation soundings in each panel) every six hours.Thus COSMIC will contribute to our understanding of the global hy drologic cycle, which is the goal of GEWEX (Global Energy and Water Cycle Experiment) GVaP (GEWEX Water Vapor Project) (Chahine, 1997;Anthes et al., 1997b).
Because of its insensitivity to smoke and aerosols, COSMIC data will also be useful in studying the effect of volcanoes or large fires on climate and related global change studies .The Mt. Pinatubo eruption in 1991 caused significant changes in the global climate with warming in the stratosphere of up to 1 K and cooling in the troposphere of more than 1 K in certain regions (Fiacco et al., 1996).Both the stratospheric warming and tropospheric cooling pat terns showed large variations in space-patterns that could be resolved with COSMIC data.Christopher et al. (1998) show that the biomass burning in South America significantly per turbs the regional climate.The Kuwait oil fires of 1991 (Husain, 1995) perturbed the weather and short-term climates of this region significantly.Accurate, high-resolution global mea surements over a long period of time are usually difficult to obtain because the events often occur in remote regions, and the environment is hostile to making in-situ measurements.COSMIC can contribute to studies of perturbations to climate by similar episodic events.

SUMMARY
This paper has reviewed the characteristics of the COSMIC data set and some of the ways that they can be used in meteorological research and operational weather prediction and cli mate monitoring and research.COSMIC data offer a number of unique advantages that comple ment existing research and operational observing systems and, together with these systems, offer the potential to improve understanding of global and regional atmospheric processes and to improve weather forecasts and climate projections into the future.Table 4 summarizes the most important scientific contributions to atmospheric science, including meteorolog y and climate, that COSMIC will provide.
The characteristics and wide range of applications as summarized in Table 4 and in this paper will contribute significantly to a number of national and international programs.These include, for example, the U.S.   • Provide 4000 accurate soundings per day globally and in all weather with high vertical resolution of bending .angle,refractivity and derived products such as temperature and water vapor in stratosphere and troposphere.
• Calculate temperature directly where water vapor is negligible (e.g.stratosphere, upper troposphere).
• Calculate water vapor directly where temperature is f�iriy well known independently.
• Estimation of winds .throughgeostrophic or gradient wind relationsh ips in high latitudes or through assimilation of data in models. •

• • •
• Direct assimilation of bending angle or refractivity in numerical models to recover temperature, water vapor and winds.
• Improve global analyses in realtime and.research mode (e.g.teanalysiS) to obtain improved estimates of temperature, water vapor and winds,.parth;ularly over oceans and polar regions.
• Improve.vertical resolution cif upper-level • fronts and associated jet streams and trop opause, supporting process studies such as tro p ospherfo�stratospheric exchange.
• Investigation of effects oflarg: e fires anq volcanoes on weather and climate.
• Resolve the diurnal cycle of temperature globally • Monitor gl<ibal and regional temperature change with unprecedented • accu.racy, .vertical resolution and stability in troposphere and stratosphere for climate and global change st udies.• • Resolve discrepancies in temperatur¢ records from various sources (e,g.the Mic.rowave Sounder Unit inferred temperature record compared.t9surra ce tepipetature record measilred by iii-situ instruments).
• Moiµtor global distribution of ge<ipotentiaf heights fo r climate arid global change studies.
• Iill prcive giobal :and regionaLnUfililrical ��ath\'.l'predi2ti9n:Sand operaticinaiforecasts. .• •. comp'iemi;i nt .existing observillg systeiris .:, anct' ptovi<;l.eirideperidetit data 'for deye!opment of improved analysis systems using !ll ergeq.cibservatio�s. . .tions such as radiosonde data), but in reality contains contributions from the atmosphere en closed by the tubular volume surrounding that point.Thus the scale may also be interpreted as the scale of the smearing of the true point-value observational variable.Fig. 2 shows a typical along-track weighting fu nction that quantifies the relative contributions to the observation value, defined at x=O, from the atmosphere at distances away from x=O.More precisely, we may define the vertical scale Z as the vertical distance perpendicular to the ray tangent that defines the layer of depth Z that contributes some fraction (e.g.50%) to the value of the observation.Similarly, the horizontal scale of an occultation sounding may be defined as the horizontal distance along the track of the ray (along-track scale) or normal to the track (cross-track scale) that contributes 50% of the information to the derived refractivity.According to this definition, the horizontal scale associated with the weighting function graphed in Fig. 2 is approximately 300 km.
In contrast to horizontal or vertical scale associated with a single observation, the hori zontal data density is defined as the average spacing between soundings obtained in a fixed period of time (e.g. a day).The horizontal data density is determined by the number and distribution of global soundings for the period.The vertical data density is defined as the average vertical distance between individual data points in the sounding and is determined by the measurement sampling interval.For a sampling frequency of 50 Hz, the vertical data density of a radio occultation is approximately 25 m.
From the discussions of "vertical resolution" associated with a single ray by Melbourne et al. (1994) and Kursinski et al. (1997), we may infer that the vertical scale Z of a single sound ing depends on the first Fresnel zone of the GPS signals, which yields a diffraction-limited scale of approximately 0.2 km to 1.5 km in the troposphere and lower stratosphere.Although .Gorbunov et al. (1996) and Gorbunov and Gurvich ( 1998) describe a "diffraction correction" technique, which reduces the size of the Fresnel zone and can improve (reduce) this scale, for the discussion here, we assume a nominal vertical scale of 1 km.This is also the order of the cross-track horizontal scale (Melbourne et al., 1994, p.90) and thus corresponds to the dia meter of the tube depicted in Fig. 1.
The along-track horizontal scale L of an observation, which represents a weighted aver age of atmospheric properties along the path of the ray as depicted in Fig. 2, varies with the vertical scale H of the atmospheric feature (perturbation) being sampled (Gurvich and Sokolovskiy, 1985).H may range from a minimum limited by the vertical scale Z as defined above to the depth of the troposphere (8 km).From the geometry of the occultation sounding, L may be related to the vertical scale of the perturbation by where R is the radius of the atmosphere at the ray tangent point (Gurvich and Sokolovskiy, 1985).For tropospheric applications R may be approximated by the mean radius of the Earth (6370 km) and (1) becomes L"" 225Hu2 (2) Thus for a shallow perturbation with vertical scale Ho f 1 km, the horizontal scale of the observation is of order 225 km.For a structure extending throughout the troposphere (H :::: 8 which ranges from about 225 for Z:;::: l km to about 80 for Z:;::: 8 km.Hence the ratios of horizon tal to vertical scales of radio occultation soundings are fortuitously close to the ideal ratio for resolving synoptic and sub-synoptic-scales atmospheric features of interest.In contrast, Lindzen and Fox-Rabinovitz showed that for most NWP models and for satellite radiance data, tbe vertical resolution was far too low for consistency.With respect to observing systems, they note "Clearly , if observing systems with fine scale horizontal resolution are not accompanied by sufficient vertical resolution then phenomenon with fine horizontal scales will be incor rectly observed, and the observations will provide incorrect initial conditions for models." This latter condition appears to apply to present radiometric soundings from satellites, which have high horizontal resolution but relatively low vertical resolution.The addition of a global network of radio occultation soundings from COSMIC will therefore be highly complemen tary to the present satellite sounding system and the combined system will provide accurate  To LEO 0 500 km Earth Fig. 2. Typical along-track w�ighting fu nction for a single radio occultation measurement (from Melbourne et al, 1994).Most of the information is contributed by a mesoscale atmospheric volume centered at the ray tan gent point.

Fig. 2 .
Fig. 2. Typical daily COSMIC soundings are shown in green, location of radio sonde sites in red.

Fig. 3 .
Fig. 3. Average spacing (km) between COSMIC soundings made over one day by l 0-degree latitude bands.

Fig. 8 .
Fig. 8. Geopotential heights (solid lines, contour interval 160 m)and temperature (dashed lines, contour interval 2 K) from NCEP analysis at 12:00 UTC October 14, 1995.The symbol x just north of Lake Huron marks the location of the GPS/MET sounding.

FigFig. 11 .
Fig. JO.Comparison of GPS/MET temperature sounding at 17:24 UTC October 21, 1995 and 47.0°S, 59.3°E with NCEP and ECMWF 00:00 UTC Octo ber 22, 1995 analysis temperatures interpolated to the GPS/MET l o ca tion.Also shown is a nearby TOYS sounding.
Fig. 1 2. Comparison of temperature pro files between OPS/MET data (dashed lines) at 15:41 UTC February 5, 1997 at 35.7°N, 137-3°E and Rayleigh lidar data (dotted line) between 15:08 and 16:26 UTC at 36.l 0N, 140.1°E.The lidar data smoothed with a low-pass fi lter with a cutoff at 3 km is also plotted as a solid line (Professor Toshitaka Tsuda, Kyoto Universi ty, per sonal communication)_

Fig. 15 .
Fig. 15.GPS/MET minus NCEP refractivity profiles for data rich (left panel)and data poor (right panel) regions.Shown are the ensemble mean dif ferences (red line), the standard deviation of the differences (black line), and the standard error of the mean differences (green envelope around red line).The blue line is the number of soundings at each level.(Rocken et al., 1997).

Fig. 16 .
Fig. 16.GPS/MET minus analysis temperatures at 100 mb for (a) NCEP/NCARreanalysis(Kalnay et al, 1996) and ECMWF(b).Note the difference in scale, and in the systematic differences in the equatorial regions between GPS/MET and NCEP.NCEP is significantly warmer than GPS/MET in the equatorial regions and somewhat cooler in middle latitudes.The sys tematic bias in the ECMWF analysis is much smaller.The difference map between the ECMWF and NCEP/NCAR temperatures at 100 mb shown in (c) indicate that significant differences, and hence uncertain ties, exist even on large scales and over long time periods.

Fig. 17 .
Fig. 17.Root-Mean-Square (RMS) error in the zonal wind (mis) at 400 mb at (a)49° latitude and (b) the Equator in cases where temperatures with ran dom error perturbations of 0, 0.25, 0.5 and 1.0°C are inserted every 12 hours at all grid points.(Charney et al., 1969).

Fig. 18 .
Fig. 18.Errors remaining in wind field and mini mum pressure in a model tropical cy clone after 12 h of assimilating various combinations of wind (V) ,temperature (T), and specific humidity (q) data(Anthes, 1974).

Fig. 19 .
Fig. 19.Vertical cross sections of zonally-averaged model temperature changes averaged over 20 years (years 60-79) in NCAR Climate System Model in which carbon dioxide alone is increased by 1 % per year(Meehl et al., 2000).
Ke y scientific contributions of COSMIC to climate research are listed below.• Provide a global self-calibrating data set for climate monitoring and climate model testing •Monitor water vapor distribution, especially in the tropics • Study troposphere/stratosphere exchange • Study the effects of volcanic eruptions and large fires on climate • Stimulate development of new climate change parameters (i.e.profiles of bending angles) • Stimulate new climate statistics and correlation studies
and high-resolution global observations with excellent and consistent representation of the important horizontal and vertical scales of motion in the atmosphere .

Fig. I .
Fig. I. Schematic depiction of tubular volume over which atmosphere contrib utes information to a single occultation phase (ray) measurement.The intensity of shading in the tube represents the relative weighting of atmo spheric properties that contribute to the value retrieved at the center of the tube.For typical atmospheric structures, L and Z are approximately 300 and 1 km respectively.

Table 2 .
Characteristics of COSMIC Data and Relevance to Meteorology and Global Change Research Program, the U.S. Weather Research Program, the World Weather Research Program, the Atmospheric Radiation Measurements (ARM) program, and the World Climate Research Programme and its projects (GEWEX),

Table 4 .
Applications of COSMIC data to atmospheric sciences, including weather and climate research and operational weather prediction.