Two Methods for Sounding the Wet RefractivityProfl e by GPSY.C. Cao', Y.M. Bi2, Z.Y. Fang3

'The National Setellitete Meteorological CenterChina Meteorological Administration, caoycgnsmc.cma.gov.cn

46, South Avenue, Zhongguancun, Beijing, 100081, China2The National Setellite Meteorological Center

China Meteorological Administration, biymgnsmc.cma.gov.cn46, South Avenue, Zhongguancun, Beijing, 100081, China

3The National Setellite Meteorological CenterChina Meteorological Administration, Fangzygnsmc.cma.gov.cn

46, South Avenue, Zhongguancun, Beijing, 100081, China

Abstract-The water vapor in the atmosphere plays a very promising for future meteorological use have been developed

important role on the variation of the atmospheric refractivity, recently. . Precipitable water vapor (PWV) can be determined with

which has a great influence on the applications of remote sensing. an accuracy of 1-2 mm [1,2], and it has been used in a number of

During recent years, new techniques have been developed to institutions and weather services [3-5]. The determined PWVs are,

retrieve the water vapor by global positioning systems (GPS). however, not very easy to use in meteorological analysis and weather

This paper uses tomographic and downward looking radio modeling because they cannot describe the vertical structure of water

occultation (RO) methods to retrieve the wet refractivity profile. vapor. Two methods have been introduced to tackle the problem: a

Results from both approaches are compared with the radiosonde. downward-looking radio occultation method using a GPS receiver

It suggests that the RO method can recover the wet refractivity installed on top of a mountain and a tomographic technique to

profile with a much higher vertical resolution, but a smaller construct a water vapor vertical profile with a dense GPS network in

coverage in height, compared with the tomographic method. a region.Profiles from both methods agree well with a similar accuracy of With GPS receivers installed on top of a mountain, a method

5-7 N (refractivity unit) when compared with the observation similar to radio occultation can be used to retrieve the atmosphericfrom the radiosonde. The two approaches complement each refractivity profile. The technique was first proposed by Zuffada et al.

other in water vapor profiling, which gives great potential for the [6] and applied by Mousa [7] in the Mount Fuji Campaign. In the

application to meteorology and remote sensing. case of downward-looking radio occultation, the bending angle is

I. INTRODUCTION* derived as a function of the impact parameter from the excessDoppler shift due to the refrectivity of the atmosphere.

The global positioning system (GPS) is one of the greatest Along with a dense GPS network, the tomographic method can

revolutionary techniques in the 1990's, and GPS meteorology is just estimate the slant wet delay along the ray from the GPS site to theone of the many GPS applications to appear since its advent. To

retrieve water vapor in the atmosphere, a few methods that are very trpshicdlyunguafeqnypaeobrvin.Te

The research is sponsored by the Grant for Research and Development of efc fmlipt a anymtgtdb dpigcoernthe China Meteorological Administration.

1-4244-1057-6/07/$25.00 ©)2007 IEEE. 337

antenna with a clear observation environment for the GPS sites. The

wet delay can be subtracted from the slant tropospheric delay by the

hydrostatic one. The slant wet delay along the ray path was modeled

by mapping the zenith to the slant. With a priori horizontal and lim=/ f

vertical constraints, the observational equations can be solved by a

method similar to CT to recover the atmospheric profiles [8].

In the study we retrieved wet refractivity profiles using both

methods and then compared them with the radiosonde observation.

Results show that both methods can work with considerable Fig. 1. Schematic diagram ( from [7])

accuracies and that they complement each other in the vertical for the mountain-based radio occultation

resolution and coverage. where r is the distance from the origin of symmetry to a point on

II. METHODOLOGY the ray path, S is the angle between the direction of r and the

1. The downward looking radio occultation method tangent to the ray path and n is the refractive index at r .With GPS receivers installed onboard the low earth orbiter (LEO), We can write (2) in other forms in this case as

the radio occultation technique can retrieve the atmospheric

refractivity profile with a very high vertical resolution. When the rr sinfl, = r, sinfl , (3)

GPS signal is propagated through the atmosphere to the LEO, it is

bent, due to vertical gradients in atmospheric refractivity. The where s7t and 0Ar can be solved from (1) and (3). The bending

bending angle of the ray path can be derived from the phase delay of angle acan finally be obtained bythe received GPS signal under the assumption of local spherical

symmetry in the atmosphere [9]. This bending angle can be used in a =Ot + Or + 0 - , (4)the Abel transformation to retrieve the atmospheric refractivity. The

technique can also be applied to a mountain-based GPS receiver where 0 is the angle between rr and rt .

observing the GPS satellite from the negative angle to the positive Equation (2) corresponds to Snell's law in polar coordinates for a

angle. The technique was first proposed by Zuffada et al. and applied spherically symmetric medium known as Bouguer's formula. On thisby Mousa in the Mount Fuji Campaign. basis, a signal traveling in a spherically symmetric medium will bend

In the case of downward looking occultation, Fig. 1 is a schematic by angle a,diagram for the geometric relationship between the GPS satellite and

the receiver installed on the top of a mountain. Using geometry, we a=-2af dn dr (5)have the following expression: a n(n2r 2 _ a2 ) dr

fd =f0C1 (Vt' cosot -Vt sint), (1) If the concentric stratus atmosphere is composed ofm layers with

m=m,+m, +mC, where m, is the number of negative angle

where fo is the carrier frequency, C is the velocity of light in observation layers, mp, is the number of positive layers, and mc, is thenumber of higher altitude layers, whose refractivities are taken from

the vacuum, 5t is the zenith angle of the signal and VJr andVc a climatological model above the receiver and used as constraints,and assuming that the refractive index decreases exponentially with

are the tangent and the normal component of the satellite. the height, we have the following expression:In geometric optics approximation, a ray passing through the

atmosphere behaves according to Fermat's principle of least time. N(r) ANnorm exp(- r- })J exp( Ai , (6)

The ray travels along a curve defined by: Hj j= H1

nrsin 75=a , (2) where ]?j is the jth layer of the surface, A\ and H, are the density

338

i of the tomographic domain. Then the total delay for ray k isand the height of the ii layer, Nnorm is the refractivity of the

referenced layer and d equals to t for layers under the referenced E CikXi = Sk (9)

layer and -1 for layers above. The value of Hi can be obtained

where C k is a coefficient. The above equation can be rewritten infrom an a priori model. A least-squares ray tracing method can then

be applied to recover the atmospheric refractivity profile. a matrix form as

The model is constrained such that the refractivity is continuous T (

across the boundaries of different layers. The inversion is to find the k k 9

optimal set of scale heights and the overall normalized refractivity where x is an unknown vector of wet refractivity for all voxels and

that best fits the measured bending angles and a priori constraints, CkT is the transposition of ck, Ck- (clk, C2k, Cnk). If there are m

weighted by their respective measurement uncertainty. The wet rays in the area of study, they can be expressed as

refractivity profile can be obtained from the total refractivity CX = 1, (10)

subtracted from the dry refractivity, calculated from the temperature where I is the vector of all SWDs (quasi observations) and C is the

and pressure of the radiosonde data. matrix of coefficients with dimension m X n. In general, the rank

2. The tomographic method of C is smaller than n and the tomographic equations cannot be

In the GPS double-difference method, the slant wet delay can directly solved. This is because there are not enough GPS receivers

finally be expressed as: in the region. Additional information is needed to obtain the solution.

S(A, 0) = Z mw (0) + N(6, A) +e (7) The main idea is to impose a Gaussian constraint in the horizontaldirection and a constraint of an a priori profile in the vertical

where A and 0 are the azimuth and elevation angles of a GPS direction of the observation (10) [12]. We have:

satellite, respectively, Z is the zenith wet delay, N is the c l

non-isotropic delay caused by the gradient, mw(0) is the wet H X=, (11)

mapping function, and £ is the one-way residual which can be V ) 0obtained from double differences of the residuals by imposing two where His the horizontal constraint matrix and Vthe vertical. The

assumptions [10]. Moreover, N can be expressed as [11]: wet refractivity profile can then be solved from (11).

N = mg (0) - (Gns cos A + Gew Sin A), (8) 111. RESULTS

In August 2006, the National Satellite Meteorological Centerwith Gns and Gew being the gradients along the north-south and (China), joined by the Beijing Institute of Applied Meteorology, the

Institute of Space Technology and the Chinese Space Science andeast-west directions, respectively, mg (6) being the mapping Research Center, conducted an experiment on mountain-based

function for the gradients, which can be written as atmospheric profiling by GPS on the top of Mount Wuling (40°36N,117°29E, 2118 m), Hebei Province. A receiver with a sampling rate

mg (6) = 1 /(sin 6. tg6 + C) and C = 0.003. of 50Hz was installed, with its antenna facing south. Five other GPS

Once the GPS data have been analyzed to determine SWD from receivers were also set up at Xinglong, Zunhua, Yutian, Donglingand Jixian, surrounding the mountain for the refractivity tomography,each station to each visible satellite, the tomography technique can '

J

be used to recover the 3D water vapor field. We can divide the with a sampling rate of 30 seconds. Radiosonde data were gathered.. at Xingalonga (about 20 km distance from Mount Wulinga) foratmosphere into voxels; the signal delay of each ray segment within a igog(bu 0k itnefo on uig o

validation purposes.each voxel can be calculated. Let X,: be the wet refr-activity at voxel Using the two methods, we received wet refractivity profiles from

the tomography and total refractivity profiles from the downward

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looking radio occultation method. In order to compare the two ACKNOWLEDGMENT

profiles, we subtracted the total refractivity from the mountain-based We would like to thank Professor Li Huang for his work on the

method by the interpolated dry refractivity, calculated from the radiosonde data, Professor Fu Yang and Hu Xiong for their data

radiosonde data. A case on August 25, 2006, showed that the processing of the downward looking radio occultation.

mountain-based radio occultation can recover the atmospheric profile REFERENCES

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