Precipitable water vapor from radar and 6.7 �m radiometer 1Accepted for publication by Journal of Atmospheric and Oceanic Technology, June 14, 2000.Comparison of precipitable water vapor observations byspaceborne radar interferometry and Meteosat 6.7 �mradiometryRamon HanssenDelft Institute for Earth-Oriented Space Research, Delft University of Technology, Delft, TheNetherlandsArnout FeijtRoyal Netherlands Meteorological Institute, De Bilt, The NetherlandsRoland KleesDelft Institute for Earth-Oriented Space Research, Delft University of Technology, Delft, TheNetherlandsAbstract. Satellite radar interferometry (InSAR) can be applied to studyvertically integrated atmospheric refractivity variations with a spatial reso-lution of 20 m and an accuracy of 2 mm, irrespective of cloud cover or solarillumination. The data are derived from the di�erence between the radarsignal delay variations within the imaged area during two acquisitions witha temporal separation of one or more days. Hence, they re ect the super-position of the refractivity distribution during these two acquisitions. Onshort spatial scales integrated refractivity variations are dominantly causedby spatial heterogeneities in the water vapor distribution. Validation ofthe radar interferometric results can be di�cult since conventional imagingradiometers do not provide quantitative measures for water vapor contentover the entire tropospheric column and lack in spatial resolution. More-over, comparable quantitative data such as signal delay observed by GlobalPositioning System (GPS) receivers are only available as time series at a�xed position. In this study, the technique of InSAR integrated refractivitymapping is discussed and validated for a speci�c atmospheric situation wherebrightness temperature variations in Meteosat 6.7 �m radiometer data couldbe mapped to precipitable water vapor to validate the InSAR data. Theparameterization of the radiometer data is obtained by using a series of 27hourly GPS signal delay observations at a �xed location and correspondingMeteosat observations at the location of the GPS receiver. Although thismethodology for validating the InSAR results is not generally applicable,the results for this speci�c situation show that the precipitable water vaporobservations in both data sets agree to an accuracy of 1.23 kg m�2, supportingthe interpretation of the InSAR data in terms of water vapor distribution.

1. IntroductionA Synthetic Aperture Radar (SAR) image containsinformation on the path length between the radar an-tenna and the resolution cells on earth. The interfero-metric combination of two radar images with a temporalseparation of 1 day provides a sensitive tool to mea-sure these path length di�erences at a fraction of theradar wavelength, which is 5.66 cm for C-band radarused here. Conventionally, path length di�erences canbe attributed either to topographic height di�erences,depending on the relative positions of the satellites [Ze-bker and Goldstein, 1986], or to surface deformation,depending on the time interval between the two observa-tions [Gabriel et al., 1989;Massonnet et al., 1993, 1995].However, e�ective path length variations are also causedby radar signal delay variability within the imaged area,due to the heterogeneous refractivity distribution in theatmosphere. Signal delay, in seconds, is equivalent to anexcess path length by multiplication with the speed oflight in vacuum. The excess path length can be directlyobtained by integrating over the (dimensionless) refrac-tivity along the line of sight. Over small spatial scales,the variation in the integrated refractivity is mainlydue to the spatial variation of water vapor during thetwo image acquisitions. To a less extent temperature,liquid water, and pressure gradients in uence the delayvariation [Hanssen et al., 1999].Delay measurements observed by space-geodetic tech-niques such as the Global Positioning System (GPS)and radar interferometry (InSAR) can be used to de-rive precipitable water vapor in the atmosphere [Saas-tamoinen, 1972; Hogg et al., 1981]. Precipitable watervapor is the amount of vertically integrated water va-por and can be expressed in [kg m�2] or as the height ofan equivalent column of liquid water in [m]. GPS mea-surements provide temporal variations in precipitablewater vapor at one position, see e.g., Bevis et al. [1992].Using InSAR, the data re ect spatial variations in pre-cipitable water vapor during the two image acquisitions.Figure 1 shows the geometric con�guration of the radaracquisition and the GPS zenith measurement.Although InSAR and GPS have the same sensitivityto tropospheric refractivity variations, the validation ofthe InSAR images using a single GPS receiver at a �xedlocation only holds for one point in the image. Ideally,the validation of the InSAR results is performed usingcomparable image data. Unfortunately, conventionalimaging radiometers do usually not provide quantitativemeasures for water vapor content over the entire tropo-spheric column and lack in spatial resolution [Weldon

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Precipitable water vapor from radar and 6.7 �m radiometer 3and Holmes , 1991].For the speci�c atmospheric situation studied here,with relatively transparent air, it is investigated whetheraccurate precipitable water vapor values can be re-trieved fromMeteosat radiometer observations at 6.7 �m(Water Vapor channel) at a local pixel resolution of5�9 km. Corresponding values of precipitable wa-ter vapor derived from a GPS ground station are usedto obtain a parameterization of the relation betweenthe Meteosat WV brightness temperatures and precip-itable water vapor.The objective of this paper is to present the tech-nique of integrated refractivity measurements with In-SAR, introduced by Hanssen et al. [1999], into somemore detail and to discuss the interpretation of a SARinterferogram acquired in March 1996 in terms of pre-cipitable water vapor distribution. Second, it is inves-tigated whether it is possible, for this speci�c situation,to obtain a parameterization of radiometer brightnesstemperatures as a function of precipitable water vapor,using Meteosat observations and GPS time series. Af-ter establishing such a relationship for a single point, itis extended spatially to derive precipitable water vaporwhich can be used for validating the SAR interferogram.In section 2 the basic principles of SAR interferom-etry are addressed, equations needed for the analysisof the signal delay in terms of integrated refractivityare derived, and some basic characteristics of the Me-teosat observations are described. As the applicationand analysis of radiometer observations such as the Me-teosat Water Vapor channel are well understood, theradar techniques are emphasized. Section 3 describesthe methodology to derive precipitable water vaporestimates, and presents the main results of this study.Discussion and conclusions make up section 4.2. Background2.1. SAR interferometryThe SAR of the ERS-1 and ERS-2 satellites pro-vides an amplitude and a phase value for every resolu-tion cell of approximately 4�20 m. Information on thepath length between the radar antenna and a groundresolution cell is contained in the phase measurement.Unfortunately, the phase observation tip of resolutioncell p in a SAR acquisition at ti is a superposition of anumber of contributions: tip = tip;geom + tip;prop + tip;scat; �� � < �; (1)where tip;geom is related to the geometric distance and tip;prop to the signal propagation velocity variations.

Most important, the scattering component, tip;scat, isthe contribution of many arbitrary scatterers in the res-olution cell, which add up to produce a uniform prob-ability density function (pdf) for tip;scat. As a conse-quence, the sum of the pdf's of all components in eq. (1)will have a uniform distribution as well, and no usefulphase information can be obtained.In the interferometric combination two SAR images,acquired at di�erent times, are accurately aligned anddi�erenced, which yields the interferometric phase:�p = t1p � t2p ; �� � � < �; (2)consisting of a di�erenced geometric component �p;geom,propagation component �p;prop, and scattering compo-nent �p;scat. If the second satellite orbit is su�cientlyclose (< 500 m) to the �rst and the physical scatter-ing characteristics remain constant ( t1p;scat � t2p;scat),the scattering component in each interferometric phaseobservation will be eliminated in the di�erencing. Inthat case, useful information may be obtained from theresulting di�erence phase image or interferogram. Theassumption of a stationary scattering component is thelimiting factor for the application of SAR interferome-try. For example, over water or rapidly changing sur-faces it is not possible to obtain coherent phase observa-tions. Over many agricultural areas, as in the test sitein this study, phase noise increases with increasing timeintervals or after anthropogenic activities, see, e.g., Usaiand Klees [1999]. During the ERS-1 and ERS-2 `tan-dem mission', which lasted from August 1995 to April1996, SAR images were acquired with a repeat period of24 hours. This short time interval ensures a su�cientlyhigh correlation between consecutive acquisitions overmost land surfaces.In order to analyze the propagation component of theinterferogram, the in uence of the geometric componentneeds to be eliminated. Geometric phase di�erences arecaused by either a change in satellite position or a coher-ent change in the position of the scatterers on earth, be-tween the two acquisitions. A di�erence in satellite po-sitions will measure topographic height variation in theSAR image. Using a reference elevation model, a syn-thetic topographic interferogram can be constructed,which can be subtracted from the observed interfero-gram, resulting in a so-called `di�erential', topographic-free, interferogram [Massonnet et al., 1993]. Other vari-ations in the geometric component, e.g., due to sur-face deformation, can be safely ignored for these shorttime intervals. Therefore, observed phase gradients inthe di�erential interferogram can only be attributed topropagation delay variability and residual trends due to

4 Hanssen and Feijtthe inaccuracy of the satellite position during the acqui-sitions. Finally, the interferometric phase, which is orig-inally `wrapped' to the interval [��; �), is unwrappedusing dedicated phase-unwrapping algorithms, see, e.g.,Goldstein et al. [1988].2.2. Interferometric delay analysisAfter obtaining the di�erential interferogram, the ob-served phase di�erences can be interpreted as (i) thespatial delay variation between the radar antenna andmillions of pixels in the interferogram and (ii) the dif-ference between the two generally uncorrelated statesof the atmosphere during the SAR acquisitions. Dueto satellite orbit errors and the wrapped nature of thephase observations it is only possible to measure thelateral variation of the delay, rather than the total de-lay. The delay variation �p;q = �p � �q between pixelp and q is directly related to the interferometric phasedi�erence �p;q = �p � �q by [Hanssen, 1998]:�p;q = �4��p;q = 28 � �p;q2� [mm]: (3)Mapping the incidented delay variation to zenith valuescan be achieved by�zp;q = �p;q cos �; (4)with look angle � varying between 19 and 23 degrees, seeFig. 1. Such a simple mapping function is su�cientlyaccurate for steep incidence angles [Bean and Dutton,1968].The standard deviation �� is derived from the co-herence , i.e., the amount of correlation between thetwo SAR images, with 0 � � 1, see Just and Bamler[1994]. For � 0:8, as observed in the interferogramused in this study, we �nd �� � 52�. Using eq. (3)and (4), and averaging �ve pixels to obtain 20� 20 mresolution cells yields a formal accuracy of the zenithdelay (vertically integrated refractivity) observations of��z � 2 mm. Additional spatial averaging to a groundresolution of approximately 160� 160 m yields a phasestandard deviation �� � 5� [Joughin and Winebrenner ,1994] and consequently ��z � 0:2 mm.Possible systematic errors in these delay observationsare manifested as long wavelength gradients in the in-terferogram, caused by inaccuracies in the satellite's po-sition during image acquisition. These additional tiltsare removed from the interferogram before analyzingthe delay di�erences. This procedure also removes longwavelength delay gradients caused by pressure and tem-perature gradients or gradients in ionospheric electrondensity.

The technique now reveals incidented delay di�er-ences or integrated refractivity along every path be-tween the antenna position, a, and the resolution cellson earth. The relation between zenith delay observed atresolution cells p and q and the refractivity distributionduring SAR acquisition ti can be written as:�z;tip;q = 2 � 10�6 cos ��Z ap Ndz � Z aq Ndz� ; (5)where N(x; y; z; t) is the dimensionless refractivity. Thezenith delay variation �zp;q observed in the interferogramcan be de�ned as �zp;q = �z;t1p;q � �z;t2p;q : (6)For C-band radar and the location of the test site therefractivity can be written as [Smith and Weintraub,1953; Kursinski , 1997; Hanssen, 1998]:N = k1PT +�k02 eT + k3 eT 2�� 4:03 � 107nef2 + 1:4W;(7)where P is the total atmospheric pressure in hPa, T isthe atmospheric temperature in Kelvin, e is the partialpressure of water vapor in hPa, ne is the electron num-ber density per cubic meter, f is the radar frequency(5:3 GHz), and W is the liquid water content in g/m3.The terms k1 = 77:6, k02 = 23:3 and k3 = 3:75 � 105 areobtained from Smith and Weintraub [1953], but also re-sults from Thayer [1974] are commonly used. The fourterms are referred to as hydrostatic term, wet term,ionospheric term, and liquid term, respectively. Resch[1984] indicated that the �rst two parts are accurate to0.5 percent.It is obvious that the inverse problem, the retrievalof all atmospheric parameters in four dimensions froma nearly vertically integrated measurement, is ill-posed.However, there are several considerations that make areasonable interpretation of the signal delay in terms ofthe wet term (integrated water vapor) likely.� The sensitivity of the delay di�erences tovariationsin the atmospheric parameters. Under standardatmospheric conditions, a change in surface pres-sure of 1 hPa will result in 2.3 mm delay dif-ference, whereas a small variation in moisture of1 g kg�1 (1.2 hPa), at 0�C already produces 6 mmper vertical km. The sensitivity for a change intemperature of 1�C is 4{20 times smaller than achange in moisture of 1 hPa, depending on ambi-ent conditions. The in uence of cloud droplets is

Precipitable water vapor from radar and 6.7 �m radiometer 5maximally a few mm, depending on the dropletsize and cloud height. Ice crystal in uence can beneglected for 5.66 cm radar wavelengths [Hanssenet al., 1999].� The dominant spatial wavelengths of the variations.For example, the in uence of the hydrostatic termdepends on the spatial variation of surface pres-sure within a 100 � 100 km SAR image. Formost meteorological situations, this variation canbe approximated by a single gradient. For theionospheric term, similar reasoning holds in mostcases for latitudes studied here. Moisture varia-tions, however, of 1 g kg�1 are common even on a1-km spatial scale and will have a directly notice-able e�ect in the interferogram [Weckwerth et al.,1997]� Assumptions on vertical strati�cation and topographice�ects. As long as the vertical variation of atmo-spheric parameters is identical for every resolutioncell in the interferogram, these e�ects will not in- uence the interferometric phase. Note that a dif-ferent vertical layering during the two SAR acqui-sitions will, however, in uence the interferogram ifsigni�cant topography is present [Delacourt et al.,1998; Hanssen and Klees , 1999]. The signaturesof these e�ects will have strong correlation withthe topography. For the test site analyzed here,with height variation within a range of 100 m, notopographic induced e�ects are expected or ob-served.2.3. Meteosat Water Vapor channelThe Meteosat WV channel, centered around 6.7 �m,is used in operational meteorology to observe the devel-opment of structures of upper tropospheric water vapor,which carry the signatures of atmospheric conditions.Especially subsidence inversions, i.e., downward verti-cal transport of dry air behind a frontal zone, are clearlyvisible in the WV images. Due to the strong absorptionby water vapor at this wavelength, the observed bright-ness temperatures usually originate from troposphericlayers above 3 km [Weldon and Holmes , 1991]. There-fore, quantitative analysis is restricted to upper tro-pospheric water vapor as described by [Schmetz et al.,1995]. Unfortunately, however, the concentration of wa-ter vapor is highest near the Earth's surface, where rel-atively high pressure and temperature allow the air tocontain more water vapor. Therefore, in general it isnot possible to make one unique parameterization ofWV channel brightness temperatures into precipitable

water vapor. In section 3.2 it is discussed whether GPStropospheric delay time series are suitable for establish-ing a tailor-made parameterization to obtain Meteosatspatial precipitable water vapor values for the specialcase of a subsidence inversion.3. Methodology and Results3.1. SAR interferogram analysisAn interferogram, covering a strip of 100� 200 km,has been formed using SAR acquisitions on 26 and 27March, 1996, 21:41:05 UTC (22:41:05 Local Time). Theorbital separation, parallel to the look direction, is ap-proximately 32 m, which makes the con�guration mod-erately sensitive to topographic height di�erences, seeFigure 1. An a-priori reference elevation model is usedto correct for the topographic phase in the interfero-gram [TDN/MD , 1997]. Some additional corrections fortilts in the length and width direction are applied, andwater surfaces are masked. The resulting di�erential in-terferogram is shown in Figure 2. The phase values areconverted to zenith wet delays, using eqs. (3) and (4),and consecutively to di�erential precipitable water va-por using eq. (10), where we use the term `di�erential'to indicate the di�erence between the two states of theatmosphere during the SAR acquisitions.A strong, large scale, gradient is clearly visible in thesouth of the interferogram, aligned approximately per-pendicular to the radar ight direction. The interpre-tation of this phenomenon is a key topic of this study.Previous studies have shown that phase variation per-pendicular to the ight direction might be caused byoscillator drift errors in the on-board reference clock[Massonnet and Vadon, 1995]. A possible way to ex-amine this possibility would be the calculation of a longswath of connected SAR images, but this is outside thescope of this study. Here it is assumed that the phasevariation is caused by atmospheric water vapor only.The likelihood of this assumption can be tested usingthe combined analysis with Meteosat and GPS.Note that, apart from the gradient in the south of theinterferogram, also wave phenomena can be observed inthe interferogram, see the lower left part of Figure 2.These are possibly due to low level moisture variationsof which the structure seems to indicate the presence ofboundary layer rolls.Wet delay di�erences �zpq can be related to integratedprecipitable water (I) values, the liquid equivalent ofthe integrated water vapor:�zpq = �t1Ts(It1p � It1q )��t2Ts(It2p � It2q ): (8)

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Using the density of liquid water, we �nd that 1 mmintegrated precipitable water is equal to 1 kg m�2 in-tegrated water vapor. The conversion factor �tiTs is ap-proximated using surface temperatures Ts for the imageacquired at ti, de�ned by Askne and Nordius [1987].After �rst models for �tiTs were derived by Davis et al.[1985] and Bevis et al. [1994], a polynomial model wasdeveloped to approximate �tiTs for De Bilt, the referencesite in the Netherlands, using 1461 radiosonde pro�les[Emardson and Derks , 1998]:�tiTs;tD = a0 + a1(Ts � T0) + a2(Ts � T0)2+ a3 sin(2� tD365) + a4 cos(2� tD365); (9)where T0 is the mean annual surface temperature forthe location, and tD is the day number of the year.The used coe�cients are a0 = 6:443, a1 = �1:33 � 10�2,a2 = 0:18 � 10�4, a3 = 3:6 � 10�2, a4 = 3:0 � 10�2, andT0 = 283:80 K. Using surface temperatures provided by18 stations in the area, we �nd 1=�t1 = 0:1513�0:0004and 1=�t2 = 0:1507� 0:0005, for 26 and 27 March re-spectively. Applying one factor for both days, 1=�m =0:1510 � 0:0005 is justi�ed, since the fractional errorin � is one order of magnitude smaller than the frac-tional error in the delay measurement. We can rewriteequation (8) asrIt1;t2pq = (It1p � It1q )� (It2p � It2q ) := ��1m � �zpq ; (10)where we de�ne rIt1;t2pq as the double di�erence of inte-grated precipitable water in space and time. Note thata single, isolated anomaly will have a di�erent sign inthe interferogram, depending on whether it appeared inthe �rst or the second acquisition. In that case, one ofthe single spatial �Itipq di�erences can be regarded asnearly zero, in which case we can interpret the doubledi�erence as a single spatial di�erence during the otheracquisition.3.2. Meteosat WV channel analysisOn 27 March 1996 a strong subsidence inversionpassed the Netherlands from North to South, which wasclearly visible in the WV channel images (Fig. 3). Thesubsidence inversion can be identi�ed by the dark bandin the image, corresponding to relatively high bright-ness temperatures. Because the descending air in thesubsidence inversion is rather dry, the absorption (andemission) of radiation is low and therefore the air is rel-atively transparent. This enables radiation from lower(warmer) layers to contribute to the signal, which re-sults in high apparent brightness temperatures. The

Precipitable water vapor from radar and 6.7 �m radiometer 726 Mar 96. 22:00 UTC

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Figure 3. Meteosat 6:7 �m water vapor images at 26March, 22:00 UTC, 27 March, 10:00, and 22:00 UTC.Brightness temperatures range from �50�C (white) to�10�C (black). The interferogram area is indicated inthe center of the image. The arrow indicates the rangeover which brightness temperatures were used for com-parison with the GPS observations.

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Figure 4. Scatter plot of observed GPS precipitablewater vapor and Meteosat water vapor channel signalintensity, for hourly observations between 26 March,18:00 UTC and 27 March, 20:00 UTC. The derivedpolynomial is indicated by the line. The RMS best leastsquares quadratic is 0.6 kg m�2.center of the subsidence inversion moves in one day fromabout 53� N to 48� N, as apparent from Fig. 3.Assuming that the brightness temperature variationsin the Meteosat WV images re ect the variations ofthe total water vapor column, we use GPS-derived pre-cipitable water vapor observations to parameterize thebrightness temperature. The reference to the WV chan-nel are collocated measurements from GPS ground sta-tion Kootwijk, at [52:17�N,5:80�E], see Fig. 2. Fromthe GPS measurements reliable absolute values for pre-cipitable water vapor are derived, using the standardmethodology described in Bevis et al. [1992, 1994]. Theaccuracy of the GPS-derived precipitable water vaporis approximately 2 mm. For 27 hourly observations ofGPS precipitable water vapor and Meteosat signal in-tensity, shown as scatter plot in Fig. 4, the correlationcan be parameterized asI = 36:7� 0:56� + 0:0022�2; (11)with I in kg m�2 and � the signal intensity of the WVchannel in number of counts. The RMS value of the dif-ference between model and observations is 0.6 kg m�2.In Fig. 5 the change in I over Kootwijk is shownderived from both GPS and Meteosat. We �nd thatthe rms of 0.6 kg m�2 is accurate enough for our analy-sis. The passage of the subsidence inversion from North

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Figure 5. Comparison of hourly precipitable watervapor over Kootwijk derived from Meteosat brightnesstemperature, using eq. (11), and derived from GPSzenith delays.to South is clearly visible. Values range from 1 to 7kg m�2.Using the parameterization in eq. (11), precipitablewater vapor can be derived from the Meteosat WVchannel image. The parameterization yields accuratevalues for the area near Kootwijk (location indicated inFig.2), but with increasing distance the accuracy willprobably decrease.For the comparison with the SAR interferograman elongated area is selected (indicated by the ar-row in Fig.3), which ranges from [51.38�N, 5.93�E] to[52.72�N,5.43�E]. The area includes the GPS stationKootwijk to optimize the validity of our parameteriza-tion, and is parallel to the ground track of ERS. Thesubsidence inversion band is nearly perpendicular to thepro�le and moves approximately parallel to it. As aresult the analyzed precipitable water vapor signal isdominated by only one atmospheric process|the sub-sidence inversion. Therefore, the parameterization isassumed to be su�ciently accurate for the selected pro-�le.All pixels which contain high altitude clouds (tem-perature below �20�C) are excluded from the analysis,to increase the reliability of the parameterization. In acloud the fraction of total water that is clustered in par-ticles is generally small, but the absorption of radiationby these particles is much larger than the absorptionby the water vapor in the cloud. Therefore, the corre-lation between the Meteosat WV channel observationsand the correct amount of precipitable water vapor willdeteriorate if clouds are present.To obtain similar quantities as in the interferogramthe extracted pro�les corresponding with 26 March,22:00 UTC, and 27 March, 22:00 UTC are di�erenced.The resulting values are indicated by the triangles in

Fig. 7, where the position of the pixels along the pro-�le is expressed by their latitude. From the MeteosatWV images in Fig. 3 it appears that at 26 March,22:00 UTC, the selected area was in the front part ofthe subsidence inversion, which results in a decreasingamount of precipitable water vapor with latitude. At27 March, 22:00 UTC, the selected area was in theback part, resulting in an increasing amount of pre-cipitable water vapor with latitude. As a consequenceof these opposite trends the quantities in Fig. 7|whichare formed by subtracting the values at 27 March fromthe values at 26 March|have an ampli�ed North-Southgradient. In the next section these results will be com-pared with the results from SAR interferometry.3.3. IntercomparisonThe evaluation of the water vapor observations fromthe Meteosat WV channel and the radar interferogramis subject to �ve degrees of freedom.1. The interferogram shows relative delay di�erences.Therefore the analyzed pro�le has an arbitrarybias when compared with the absolute values ofthe Meteosat pro�le.2. Due to the oblique viewing geometry of the radar(23 degrees from zenith) the pro�le will be shiftedsome kilometers parallel to the West, see Fig. 6.As the atmospheric situation during the two ac-quisitions was nearly symmetric (i.e., perpendic-ular to the pro�le) the e�ect of this lateral shiftis negligible.3. The inaccuracy in the satellite orbits might lead toa small tilt in the pro�le. Here we assume that thistilt is su�ciently eliminated by using a number ofreference points during preprocessing.4. The Meteosat positioning accuracy is approxi-mately 0.5 pixel, corresponding to a 4.5 km un-certainty in north-south direction.5. Due to the geostationary position over the equa-tor, there is an additional shift D in north-southdirection when the majority of the water vaporis at a height h, see Figure 6. In that case, theinformation will appear northward shifted in theimage. For the location analyzed here, this shiftis approximately D = 1:7�h. Note that the timedi�erence between the SAR acquisition and theMeteosat scan of the latitudes of the Netherlands(13 minutes) might also account for a slight addi-tional shift.

Precipitable water vapor from radar and 6.7 �m radiometer 9PSfrag replacements a bDD hh ��North South EastWest

Figure 6. Sketch of the horizontal shift of the position of water vapor due to the oblique viewing geometry ofMeteosat (a) and ERS (b). For latitude 52�N, the elevation angles � are 30:5� for Meteosat and 69� for ERS.Estimates of the a-priori standard deviation of both theMeteosat and InSAR precipitable water vapor estimatesare needed to evaluate the correlation between the twopro�les. For the Meteosat observations, �I;msat is as-sumed to be uncorrelated and equal for every observa-tion. In section 3.2, an rms-value of 0.6 kg m�2 was de-rived from a comparison with GPS observations. Theanalyzed pro�le values are di�erences between corre-sponding observations for two consecutive days. As-suming zero covariance between the two days, stan-dard error propagation yields the a-priori value for��I;msat = 0:85 kg m�2.The expected variance for the InSAR observationsis assumed to be uncorrelated between adjacent valuesand equal for every observation. In section 2.2, thedelay standard deviation ��z = 0:2 mm (or kg m�2) wasderived. Using equation (10), simple error propagationyields an a-priori value for the integrated water vaporobservations of �I;sar = 0:08 kg m�2.A goodness-of-�t parameter between the InSAR andthe Meteosat observations can be optimized by adjust-ing the �ve degrees of freedom mentioned above, or byadjusting the a-priori variances of both observations.Here a combination of both approaches is suggested.Parameters 2{4 are assumed to be su�ciently well ap-proximated. A northward shift of the Meteosat obser-vations (parameter 5) of 5 km is used as a �rst orderapproximation, derived from an average height of thedominant water vapor signal in the WV channel. Theadditional Meteosat pro�le shift, the bias of the In-SAR pro�le (parameter 1), and the scaling factor forthe variances are now estimated by deriving the mini-mal reduced chi-square value, �2� , of the two pro�les asa function of the bias of the InSAR pro�le [Bevington

and Robinson, 1992]:�2� = 1n� 1 nXi=1( ri�i )2: (12)The number of measurements is denoted by n, ri are thedi�erences between the Meteosat and the INSAR pro�levalues, and �i are the a-priori standard deviations ofthe di�erences, i.e., �2i = �2I;sar;i + �2�I;msat;i. Here we�nd �i = 0:85 kg m�2 for all i 2 [1 : : : n]. Note thatthe contribution of ��I;msat;i is one order of magnitudelarger than �I;sar;i.The �2� values are expressed as a function of the In-SAR pro�le bias and the horizontal shift of the Meteosatpro�le. The search window of the bias has been con�nedbetween �3 and 3 kg m�2, whereas the horizontal shiftis con�ned between �1:1 and 1:1 km. The minimumvalue, �2� = 2:1 is found for a bias of 1 kg m�2 and ahorizontal shift of �1:1 km. Figure 7 shows the originalposition of the InSAR pro�le, indicated by the thin lineand the new position, indicated by the bold line. Theoriginal position of the Meteosat pro�le values is indi-cated by the triangles, the new positions are indicatedby the squares. A 95% con�dence interval for the dif-ference of the two data sources is indicated by the innererror bars. Note that the error bars are drawn at theMeteosat positions, although they also include a smallcomponent of the InSAR pro�le.From this evaluation it is clear that the adjustmentof the free parameters is not su�cient to reach a sat-isfying comparison. The estimated variance �̂2 can beapproximated by [Bevington and Robinson, 1992]�̂2 = �2��2i ; (13)if all variances �2i are equal. If both pro�les describe thesame physical process, the estimated variance should

10 Hanssen and Feijt

50.8 51 51.2 51.4 51.6 51.8 52 52.2 52.4 52.6 52.8−8

−6

−4

−2

0

2

4

Latitude

Pre

cipi

tabl

e W

V [k

g/m

2 ]

Original SAR profile

Shifted SAR profile

Original Meteosat pos.

Shifted Meteosat pos.(a−priori/a−posteriori)

Figure 7. Goodness of �t analysis, based on best �2�value. The error bars express the scaled 2� (95%) con-�dence interval based on the combined variance of theMeteosat and INSAR pro�le. The original (arbitrary)values of the INSAR pro�le are shown as the thin line,the best-�t values by the bold line. The original Me-teosat positions are indicated by the triangles and theslightly shifted best-�t values by the squares. The best�2� value is obtained by scaling the a-priori variances(bold inner error bars) with factor 1.44, resulting in thethin outer error bars.

agree well with the a-priori variance and the value ofthe reduced chi-squared should be approximately unity.In order to reach this situation, the a priori standarddeviations of the di�erence need to be scaled by a factorp�2� = 1:44. This implies that the a-priori standarddeviation of the di�erence has been too optimistic. Ana-posteriori standard deviation of 1.23 mm is found,indicated in Figure 7 by the outer error bars.4. ConclusionsSatellite radar interferometry can be applied to studyvertically integrated atmospheric refractivity variationswith a spatial resolution of 20 m and an accuracy of2 mm, irrespective of cloud cover or solar illumina-tion. Although satellite repeat-acquisitions are still farto sparse for operational meteorology, the techniquecan currently be used for studying meso-scale atmo-spheric dynamics and provides new insights, particu-larly in mapping the small-scale water vapor distribu-tion. This study elaborates on the main principles andlimitations.For a speci�c atmospheric situation in March 1996,precipitable water vapor obtained from SAR interfer-ometry is validated by GPS time delay analyses com-bined with Meteosat 6.7 �m WV channel observations.The interferometric phase observations are convertedto relative signal delay observations and consecutivelyprocessed to precipitable water vapor. For a point lo-cation, Meteosat brightness temperature time series areconverted to precipitable water vapor using a param-eterization obtained from GPS wet signal delay obser-vations. Applying this parameterization spatially for apro�le of brightness temperatures in two WV channelimages, acquired at nearly the same time as the twoSAR images, enables a direct comparison between thetwo sources.The results show that the phase gradient observed inthe SAR interferogram is fully accounted for by a sub-sidence inversion which moved over the interferogramarea during the two SAR acquisitions. The subsidenceinversion resulted in temporal precipitable water va-por variations over a range of approximately 6 kg m�2,as observed by GPS and Meteosat. Accounting for therelative character of the InSAR observations, and thepositioning uncertainty of the Meteosat images, bothdata sets describe the same phenomenon in a mini-mal reduced chi-squared sense with 1.23 kg m�2 stan-dard deviation. As the range of the signal encompassesapproximately 6 kg m�2, signal to noise ratio valuesare su�cient to identify the same signal in both data

Precipitable water vapor from radar and 6.7 �m radiometer 11sources. This supports the statement that radar inter-ferometry can be used to derive the spatial variationsin precipitable water vapor.Although the parameterization used in eq. 11 ap-pears to be su�cient to explain the observations, itneeds to be stressed that the use of this method is fea-sible only for a limited area around the GPS receiver.Moreover, in situations with severe cloud cover, the con-version from brightness temperatures to precipitablewater vapor is not likely to succeed, due to insu�cientpenetration caused by absorption. Future applicationsof the technique need to be focussed on consecutive ac-quisitions of SAR images to obtain `cascade' series ofinterferograms. Such approaches can result in resolvingthe ambiguity between the atmospheric states duringthe two acquisitions.Acknowledgments. The European Space Agency isgratefully acknowledged for providing the ERS SAR data.H. Derks and A. van der Hoeven provided valuable help inthe GPS data processing.ReferencesAskne, J., and H. Nordius, Estimation of tropospheric delayfor microwaves from surface weather data, Radio Science,22 , 379{386, 1987.Bean, B. R., and E. J. Dutton, Radio Meteorology , Dover,New York, 1968.Bevington, P. R., and D. K. Robinson, Data reduction andanalysis for the physical sciences, 2nd ed., McGraw-Hill,Boston, 1992.Bevis, M., S. Businger, T. A. Herring, C. Rocken, R. A. An-thes, and R. H. Ware, GPS meteorology: Remote sensingof atmospheric water vapor using the Global Position-ing System, Journal of Geophysical Research, 97 , 15,787{15,801, 1992.Bevis, M., S. Businger, T. A. Herring, R. A. Anthes,C. Rocken, and R. H. Ware, GPS meteorology: map-ping zenith wet delays onto precipitable water, Journalof Applied Meteorology , 33 , 1994.Davis, J. L., T. A. Herring, I. I. Shapiro, A. E. E. Rogers,and G. Elgered, Geodesy by radio interferometry: E�ectsof atmospheric modelling errors on estimates of baselinelength, Radio Science, 20 , 1593{1607, 1985.Delacourt, C., P. Briole, and J. Achache, Tropospheric cor-rections of SAR interferograms with strong topography.application to Etna, Geophysical Research Letters, 25 ,2849{2852, 1998.Emardson, T. R., and H. J. P. Derks, On the relation be-tween the wet delay and the integrated precipitable watervapour in the European atmosphere, Submitted to Mete-orological Applications, 1998.Gabriel, A. K., R. M. Goldstein, and H. A. Zebker, Map-ping small elevation changes over large areas, di�erential

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12 Hanssen and FeijtTDN/MD, TopHoogteMD digital elevation model, To-pogra�sche Dienst Nederland and Meetkundige DienstRijkswaterstaat, 1997.Thayer, G. D., An improved equation for the radio refractiveindex of air, Radio Science, 9 , 803{807, 1974.Usai, S., and R. Klees, SAR interferometry on very longtime scale: A study of the interferometric characteristicsof man-made features, IEEE Trans. on Geoscience andRemote Sensing , 37 , 2118{2123, 1999.Weckwerth, T. M., J. W. Wilson, R. M. Wakimoto, andN. A. Crook, Horizontal convective rolls: Determiningthe environmental conditions supporting their existenceand characteristics, Monthly Weather Review , 125 , 505{526, 1997.Weldon, R. B., and S. J. Holmes, Water vapor imagery inter-pretation and applications to weather analysis and fore-

casting., Tech. Rep. NESDIS 57 , NOAA, 1991.Zebker, H. A., and R. M. Goldstein, Topographic mappingfrom interferometric synthetic aperture radar observa-tions, Journal of Geophysical Research, 91 , 4993{4999,1986.R.F. Hanssen, DEOS, Delft University of Technology,Thijsseweg 11, 2629 JA, Delft, The Netherlands. (e-mail: hanssen@geo.tudelft.nl)A. Feijt, KNMI, Postbus 201, 3730 AE de Bilt, TheNetherlands. (e-mail: feijt@knmi.nl)January 6, 2000; accepted June 14, 2000.This preprint was prepared with AGU's LATEX macros v4.File paper formatted August 16, 2000.