A numerical study on the contribution of melting layer composed by coated ice spheres to the...

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Journal of Quantitative Spectroscopy &

Radiative Transfer 91 (2005) 437–452

0022-4073/$ -

doi:10.1016/j.

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A numerical study on the contribution of melting layercomposed by coated ice spheres to the upwelling brightnesstemperatures in TMI channels using VDISORT algorithm

Xin Jina,b, Wanbiao Lia,�, Yuanjing Zhua, Bolin Zhaoa

aDepartment of Atmospheric Sciences, School of Physics, Peking University, Beijing, 100871, ChinabDepartment of Environment & Geography, University of Manitoba, Winnipeg, Canada MB R3T 2N2

Received 4 December 2003; accepted 16 July 2004

Abstract

To examine the influence of bright band on the retrieval of precipitation rate, the performance of meltinglayer composed by coated ice precipitable particles on the satellite-based measurement of polarizedmicrowave brightness temperatures is discussed in this article by a vector discrete ordinate radiative transfermodel. After comparing the simulated brightness temperatures in different TMI channels with and withoutthe melting layer, we conclude that: (1) The melting layer composed by liquid-coated ice spheres weakensthe upwelling microwave brightness temperatures because of the absorption/emission effect caused by theliquid coat. This effect is more conspicuous in middle and high frequency channels (19, 37 and 85GHz) but,in 85GHz channel, with the increase of rain rate, the multi-scattering can weaken its effect. (2) In a specificfrequency, the horizontally polarized brightness temperature is more severely weakened by the meltinglayer than the vertically polarized. With the ‘‘cold’’ background (ocean surface, for example), this characteris more conspicuous than that with a warm background. That is to say, the inner structure of a cloudsystem is easier to be detected under a cold background. Only in the 85GHz frequency and when the rainrate is larger than 4mm/h can we find that the vertically polarized brightness temperature is more severelyweakened than the horizontally polarized one. (3) The melting layer with the assumption of coated icespheres can change the difference of brightness temperatures between the vertically and horizontallypolarized channels in the same frequency. In general, the value of such difference with the assumption of

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X. Jin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 91 (2005) 437–452438

melting layer is larger than that without it. With a warm background, this value is negative and only inmiddle frequency (37GHz), it is both stable and conspicuous.r 2004 Elsevier Ltd. All rights reserved.

Keywords: Melting layer; TMI; Microwave radiative transfer

1. Introduction

When we focus on the simulation of the microwave radiative transfer process within aprecipitable cloud system, some issues, such as the distribution spectrum of droplets (DSD), thegeometric shape and thermodynamic phases of particles, even their spatial orientations, are veryimportant. In some specific conditions, such factors are very sensitive to the simulated brightnesstemperatures [1,2]. When we use the so-called ‘‘physical retrieving method’’ to retrieve the rainrate, a precipitable cloud model that is closer to the real conditions can be very important toensure the reliability of the simulated brightness temperatures. For example, the vertical profilesof different precipitation components contained in the level 2 products of Tropical rainfallmeasurement mission (TRMM) microwave imager (TMI) are generated by such physicalretrieving method based on the Goddard cumulus ensemble model [3].The melting layer refers to a special area in a stratiform precipitable cloud system located

from the freezing height to several hundred meters above it. Because of its thermodynamicallymixed status, the microwave radiative characters in this layer are significantly different withthose in other areas. On radar screen, it appears as a conspicuously bright band, representingits strong backscattering ability [4]. With the development of microwave radiative transferalgorithms, the contribution of the melting layer to the brightness temperature gets moreand more recognition. Neglecting the influence of this layer has been taken as one of theimportant sources to cause errors during the simulation of microwave radiative transferprocess. There are many different theories of how the liquid and ice water mix together withinthe melting layer. The direct outcome of these different theories leads to differentcomplex refractive indexes. Bauer et al. [5–7] and Olson et al. [8] developed some sensitiveexperiments to test the radiative characters of different mix theories and concluded thatthe melting layer has conspicuous emissive effect within the microwave spectrum ranging from10 to 90GHz.Barthazy et al. [9] made a series of field experiments to examine the microphysical characters

of melting layer in the Alps area. They found that the meting layer is located between the snowlayer and the rainfall layer and has very complex inner characters, including different geometricshapes, melting degrees and final falling speeds. It is difficult to find a one for all solution togeneralize the radiative characters under different conditions. But, to study the radiativecharacters of each specific object and then combine them together by parameterization is areasonable goal.Dr. Weng [10] developed a new microwave radiative transfer model based on the discrete

ordinate algorithm [11]. In his model, the brightness temperatures in each channel with differentpolarization methods (i.e. vertical and horizontal polarizations) can be simulated. So the model isnamed as vector discrete ordinate radiative transfer model (VDISORT). Weng [12] tested his

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Fig. 1. The sketch map of a melting ice particle (1, 2, 3 represent the ice core, water coat and air, correspondingly).

X. Jin et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 91 (2005) 437–452 439

model by simulating the dual-polarization microwave brightness temperatures in each specialsensor microwave imager (SSMI) frequency with the assumption of independently mixed liquidand ice precipitable particles.In this paper, we use VDISORT to discuss the contribution of melting layer to the upwelling

microwave brightness temperatures in all of TMI polarization channels based on a stratiformcloud system containing melting ice spheres coated by liquid water shells with equal depth inevery direction. The highlight is to examine the influence of melting layer on the differentpolarized channels in each frequency. Fig. 1 is the sketch map of a melting ice sphere with liquidwater coat.

2. The scattering field of single coated ice sphere (CIS)

Bohren and Huffman [13] provided the analytic solution of the scattering field of a coatedice particle. It has the same form with that of the ice and liquid spheric particles based onMie theory. The only difference is about the coefficients al and bl in the equations. Whencoated, they will change with the change of dielectric constant e and permeability m along theradius:

al ¼clðyÞ½c

0lðm2yÞ � Alw0lðm2yÞ� � m2c

0lðyÞ½clðm2yÞ � Alwlðm2yÞ�

xlðyÞ½c0lðm2yÞ � Alw0lðm2yÞ� � m2x

0lðyÞ½clðm2yÞ � Alwlðm2yÞ�

;

bl ¼m2clðyÞ½c

0lðm2yÞ � Blw0lðm2yÞ� � c0

lðyÞ½clðm2yÞ � Blwlðm2yÞ�

m2xlðyÞ½c0lðm2yÞ � Blw0lðm2yÞ� � x0lðyÞ½clðm2yÞ � Blwlðm2yÞ�

: (1)

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Here

Al ¼m2clðm2xÞc

0lðm1xÞ � m1c

0lðm2xÞclðm1xÞ

m2wlðm2xÞc0lðm1xÞ � m1w0lðm2xÞclðm1xÞ

;

Bl ¼m2clðm1xÞc

0lðm2xÞ � m1clðm2xÞc

0lðm1xÞ

m2w0lðm2xÞclðm1xÞ � m1c0lðm1xÞwlðm2xÞ

;

m1;m2 are complex refractive indexes, suffixes 1, 2 represent the ice and water.

3. The microwave radiative properties of precipitation composed by coated ice spheres (CISs)

Here we discuss the microwave radiative properties of a cluster of CISs.Some assumptions for the simulation:

�
Rain rates (RR) (mm/h): 2 and 8, represent light rain and moderate rain, correspondingly. � Frequencies (GHz): 10.7, 19.35, 22.235, 37.0, and 85.5, all of TMI frequencies included. � Temperatures (K): 273K–233K, DT ¼ 2K: � The melting ratio q ðq ¼ OA=OBÞ: It is represented by comparing the radius of the ice core(OA) with that of the whole sphere (OB). It ranges from 0.0 to 1.0 (Fig. 2). In this study, weassume that the densities of ice and water are 0.91 and 1.0 (unit: g=cm3), correspondingly, notchanging with the variation of temperature (Fig. 2).
�
DSD: According to the field experiment result from Barthazy et al. [9], Marshall–Palmer (MP)spectrum (2) is still suitable to delineate the distribution of most precipitable particles within themelting layer.
NðDÞ ¼ N0e�LD: (2)

In case of rainfall, N0 ¼ 0:08 cm�4; L ¼ 4:11I�0:21; I represents rain rate.

Fig. 2. The assumed relationship between temperature and melting ratio.

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Ta

Th

Fr

RR

0

.1

.2

.3

.4

.5

.6

.7

.8

.85

.9

.95

1.0


Moreover, we assume that the coated ice particles have the same final falling speed as the liquid.According to the conservation of mass, we can get

NðDÞ ¼N0

rmix

e�LD: (3)

Here, rmix is the equivalent density of coated particle and D is not more than 3mm.

rmix ¼ ½ricel3OA þ rwaterðl

3OB � l3OAÞ�=l3OB (4)

rice and rwater are densities of ice core and liquid coat, correspondingly.
� Complex refraction index (CRI): Ray [14] made a detailed analysis about the CRI of ice andwater. Here we use the equations provided in his paper.The extinction coefficient (EC), scattering coefficient (SC), albedo and asymmetric factor (AF)are listed in the Tables 1–4, correspondingly.
Fig. 3 shows the relationships between frequency and some optical characters in cases ofdifferent rain rates and melting ratios. In general, all of them grow when rain rate and frequencyincrease even though such tendency is not very regular especially when the frequency is low. Also,we can find that some radiative characters are very sensitive to the variation of melting ratio q. Inthe following, we discuss such relationships in detail.

�
EC: Pure ice particles (q ¼ 1:0) have the smallest EC in all TMI frequencies with both rain rateassumptions. When the frequency is high ð445GHzÞ; the pure liquid water particles (q ¼ 0:0)have the largest EC, and the EC of CISs is between these two extreme conditions. But, when thefrequency is low ðo45GHzÞ; the ice particles with thick liquid coat (qo0:7) have the largest ECthan that of others.
�
SC: The SC becomes larger with the increase of frequency. When the rain rate is small (2mm/h,for example), the SC of CISs is always smaller than that of pure liquid spheres and larger than
ble 1

e EC (unit: 1/km) of coated ice spheres with different assumptions

eq. 10.7 (GHz) 19.35 (GHz) 22.235 (GHz) 37 (GHz) 85.5 (GHz)

2 8 2 8 2 8 2 8 2 8

0.00753 0.03322 0.02995 0.13551 0.04146 0.18664 0.12994 0.54193 0.45726 1.39728

0.00766 0.03348 0.03019 0.13583 0.04175 0.18714 0.13046 0.54276 0.45489 1.39166

0.00796 0.03413 0.0308 0.13693 0.04251 0.18866 0.1315 0.54425 0.44831 1.37607

0.00836 0.03512 0.03175 0.13929 0.04371 0.19169 0.13285 0.54615 0.43819 1.35235

0.00895 0.03669 0.03329 0.14378 0.04566 0.19756 0.13505 0.55054 0.42405 1.31919

0.00983 0.03919 0.03568 0.1513 0.0487 0.20739 0.13842 0.55818 0.40554 1.27581

0.0112 0.04321 0.03932 0.16296 0.05322 0.22219 0.14238 0.56727 0.38154 1.22202

0.01342 0.04994 0.04467 0.18024 0.05948 0.24264 0.14752 0.59908 0.3473 1.14153

0.0172 0.06158 0.05154 0.20254 0.06624 0.26387 0.13689 0.54857 0.29541 1.01439

0.01993 0.06992 0.05407 0.21032 0.06722 0.26515 0.12087 0.47927 0.26037 0.9276

0.02281 0.07823 0.05228 0.20163 0.06169 0.24083 0.09687 0.39547 0.21721 0.8179

0.0223 0.07424 0.03794 0.14338 0.04171 0.1611 0.05882 0.25727 0.16338 0.67392

0.00008 0.00044 0.00048 0.00326 0.00079 0.00544 0.00498 0.03247 0.07758 0.38873

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Table 2

The SC (unit: 1/km) of coated ice spheres with different assumptions

Freq. 10.7 (GHz) 19.35 (GHz) 22.235 (GHz) 37 (GHz) 85.5 (GHz)

RR 2 8 2 8 2 8 2 8 2 8

0 0.00027 0.00216 0.00308 0.02428 0.00541 0.04099 0.03394 0.1912 0.18142 0.6166

.1 0.00027 0.00216 0.00307 0.02422 0.00539 0.04087 0.03368 0.18981 0.17921 0.61043

.2 0.00026 0.00215 0.00304 0.02402 0.00534 0.04048 0.03295 0.18617 0.17385 0.59579

.3 0.00026 0.00213 0.003 0.02371 0.00525 0.03983 0.0318 0.18063 0.16639 0.57626

.4 0.00026 0.00211 0.00294 0.0233 0.00512 0.03896 0.03023 0.17343 0.15638 0.55056

.5 0.00026 0.00207 0.00287 0.02282 0.00496 0.03795 0.02823 0.16453 0.144 0.51893

.6 0.00025 0.00203 0.00277 0.02222 0.00475 0.03673 0.02573 0.15349 0.13063 0.4896

.7 0.00024 0.00196 0.0026 0.02128 0.00441 0.03484 0.02497 0.16197 0.11484 0.44868

.8 0.00022 0.00181 0.00228 0.01936 0.00377 0.03106 0.01828 0.12293 0.09711 0.39767

.85 0.0002 0.00166 0.00198 0.01743 0.0032 0.02745 0.01438 0.10042 0.08895 0.37614

.9 0.00017 0.00141 0.0015 0.01401 0.00235 0.02166 0.01076 0.08035 0.0817 0.35752

.95 0.00011 0.00093 0.00083 0.00829 0.00132 0.0142 0.00702 0.05617 0.07664 0.3468

1.0 0.00004 0.00028 0.00039 0.00298 0.00069 0.00511 0.0047 0.03149 0.07595 0.3825

Table 3

The albedo of coated ice spheres with different assumptions


RR 2 8 2 8 2 8 2 8 2 8

0 0.03527 0.06511 0.10271 0.17916 0.13053 0.21963 0.26121 0.35281 0.39675 0.44129

.1 0.03465 0.06448 0.10164 0.17828 0.12919 0.21838 0.25818 0.34971 0.39397 0.43863

.2 0.03324 0.06293 0.0988 0.17544 0.12558 0.21456 0.25054 0.34207 0.38778 0.43297

.3 0.03146 0.06067 0.09449 0.17019 0.12002 0.20777 0.23937 0.33074 0.37972 0.42611

.4 0.02914 0.05742 0.0884 0.16203 0.11209 0.19719 0.22382 0.31502 0.36876 0.41735

.5 0.02618 0.05294 0.08037 0.15081 0.10179 0.18301 0.20397 0.29475 0.35509 0.40674

.6 0.0225 0.04695 0.07032 0.13637 0.08917 0.1653 0.18068 0.27057 0.34238 0.40065

.7 0.01804 0.03915 0.05821 0.11807 0.07419 0.14357 0.16925 0.27037 0.33066 0.39306

.8 0.01288 0.02935 0.04419 0.09558 0.05696 0.1177 0.13355 0.2241 0.32875 0.39203

.85 0.01011 0.02378 0.03659 0.08287 0.04761 0.10351 0.11898 0.20952 0.34162 0.40549

.9 0.00732 0.01798 0.02873 0.06947 0.0381 0.08995 0.11105 0.20318 0.37614 0.43711

.95 0.00479 0.01248 0.02182 0.0578 0.03176 0.08812 0.11927 0.21833 0.46909 0.5146

1.0 0.44288 0.65324 0.81981 0.91255 0.87181 0.93867 0.94314 0.97008 0.97898 0.98397


that of pure ice spheres. However, when the rain rate gets larger, the increasing tendency ofspheres with large qð40:9Þ is larger than that of other spheres in high frequency channels, i.e.thinner the depth of the liquid coat, more sensitive the spheres to the increase of frequency andrain rate.

�
Albedo: The albedo always increases and tends to a saturated value when the frequency getshigher. Larger the rain rate, easier the albedo to get saturated. The albedo of pure ice spheresðq ¼ 1Þ is always the largest and much easier to get saturated in any conditions and in general,when the liquid coat is thick ð0oqo0:7Þ; the albedo decreases ðo0:5Þ with the increase of q. But

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Table 4

The AF of coated ice spheres with different assumptions


RR 2 8 2 8 2 8 2 8 2 8

0 �0.03321 �0.03373 �0.03994 �0.04901 �0.0395 �0.04339 �0.00182 0.02467 0.2000 0.27594

.1 �0.03428 �0.03451 �0.03971 �0.04788 �0.03882 �0.04181 0.00008 0.02707 0.2029 0.27918

.2 �0.03632 �0.0359 �0.03914 �0.04549 �0.03738 �0.03851 0.00412 0.03261 0.20918 0.2863

.3 �0.03816 �0.03686 �0.03816 �0.04253 �0.03549 �0.03462 0.00885 0.03902 0.21719 0.29546

.4 �0.03969 �0.03709 �0.03642 �0.03861 �0.03263 �0.02949 0.01484 0.0466 0.22795 0.3076

.5 �0.04096 �0.03662 �0.03383 �0.03346 �0.02858 �0.02285 0.02193 0.05471 0.24169 0.32279

.6 �0.04227 �0.03601 �0.03078 �0.02746 �0.02369 �0.01495 0.03105 0.06564 0.2569 0.33659

.7 �0.04435 �0.03639 �0.02819 �0.02156 �0.01887 �0.00667 0.07817 0.12426 0.27299 0.35171

.8 �0.04857 �0.03931 �0.02782 �0.01722 �0.01692 �0.00185 0.07119 0.11916 0.28929 0.37272

.85 �0.05251 �0.04256 �0.02963 �0.0162 �0.0176 0.00018 0.0365 0.08127 0.29454 0.38018

.9 �0.0597 �0.04849 �0.03429 �0.01461 �0.0187 0.0083 0.03265 0.08874 0.29907 0.38862

.95 �0.07882 �0.06416 �0.05479 �0.02188 �0.03951 0.01111 0.01305 0.09144 0.30743 0.40288

1.0 �0.15921 �0.14945 �0.13213 �0.10227 �0.11845 �0.0806 �0.04925 0.04483 0.3334 0.45601


when q40:8; the albedo increases with the increase of q and larger the values of q andfrequency, more conspicuous this increasing tendency.

�
AF: The AF increases with the increase of frequency and such increasing tendency gets largerwith the increase of the value of q.
Next, we will merge this kind of melting layer into a stratiform precipitable cloud system andexamine its contribution to the upwelling microwave radiative transfer by VDISORT algorithm.

4. The influence of melting layer on the upwelling microwave radiative transfer

Usually, the microwave radiative transfer process can be written in this format [15]:

cos yd

dzIðy;f; zÞ ¼ �keðyÞIðy;f; zÞ þ I eðy;fÞ þ

ZdO0Pðy;f; y0;f0

Þ � Iðy0;f0; zÞ: (5)

Here, Iðy;f; zÞ is the radiation, y;f; z are three basic parameters in a column coordinate system.The variables with superscript ‘‘0’’ indicate the incident process, keðyÞ is the extinction coefficient,Ieðy;fÞ is the heat source. Land surface and ocean are both heat sources when we study theupwelling microwave radiative transfer. The third item on the right side of Eq. (5) describes themulti-scattering process.To study the radiative characters of the melting layer, a stratiform cloud model is necessary. Liu

[16] analyzed the vertical precipitation profiles provided by TRMM Precipitation Radar in acertain middle latitude area during the summer season in 2000 and concluded that in most cases,the near surface rain rate of stratiform cloud system is less than 10mm/h. Here, we assume nineprecipitation profiles corresponding to nine different near surface rain rate ranging from 1 to9mm/h in a stratiform precipitable cloud system. It includes two parts: pure liquid water that

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Fig. 3. The relationships between frequency and some radiative characters (the numbers in the legend are the values of

q).


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Fig. 3. (Continued)


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distributes from the surface to the freezing height, a mixture of liquid and ice from the freezingheight to the cloud top (8.9 km). It does not contain a pure ice crystal cover. In the height between3.7 to 4.5 km above the surface, the cloud is composed by CISs. However, in the same range, alayer in which water and ice are independently mixed is also prepared as a control. In otherheights, ice and liquid water are mixed independently. All of the particles obey the MPdistribution. The vertical temperature-decreasing rate is 6:5 C=km: The ice and liquid water existin the range from 3.8 km above the surface to the cloud top. The mixture ratio of ice to liquidincreases with the increase of height and follows such experimental equations:

IWC ¼ ½ðz � 3:8Þ=ð9:323:8Þ�TWC 0o ¼ zo3:8km;

LWC ¼ ½ð9:3� zÞ=ð9:323:8Þ�TWC 3:8kmo ¼ zo8:9 km: (6)

Here, IWC, LWC, TWC represent ice water content, liquid water content and total water content(unit: g=m3), correspondingly, and z is the height (unit: km). Based on the assumption of MPdistribution, the relationship between TWC and rain rate (RR) is

TWC ¼ 1:28� 10�10 � pð450 �RR0:21=3:67Þ4 (7)

Fig. 4 is the sketch map of the stratiform cloud system.When we process the simulation by VDISORT, some assumptions are necessary:

�

Fig

sep

ran

Incidence angle: 52:76 (the same as that of TMI).
� Land surface is Lambertian with an emissivity of 0.9, and the ocean is mirror surface. � The temperature of background is 301K. � Neglect the influence of all of other absorption ingredients (such as the water vapor andoxygen) in order to amplify the performance of melting layer.
. 4. The precipitable cloud model (the solid and dashed lines represent the liquid and ice water vertical profiles

arately, and the belt area is the melting layer; from left to right, each line represents a specific surface rain rate

ging from 1 to 9mm/h).

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Tables 5 and 7 list the simulated upwelling brightness temperatures in TMI channels under the
assumption of CISs with land and ocean backgrounds, correspondingly. Tables 6 and 8 arecontrol groups under the assumption of independently mixed water and ice particles.Fig. 5 shows the simulated 9-channel TMI brightness temperatures with both ocean (left) and
land (right) backgrounds under different assumptions, i.e. without and with CISs, above andbelow, respectively.Fig. 6 shows some derivative information from the simulated brightness temperatures. Fig. 6(a)

and (b) demonstrate the differences between the brightness temperatures with and without thecontribution of CISs in all of TMI channels with the background of ocean and land,correspondingly, and can be written as T c–T s (the subscripts c and s represent the coated andseparated conditions, correspondingly). Fig. 6(c) and (d) delineate the differences between thevertically and horizontally polarized microwave radiative information in the same frequency withthe background of ocean and land, correspondingly, and can be written in form of Tv–Th: In21.3GHz, there is only a vertical polarized channel in TMI. So Tv–Th in this frequency isneglected.

Table 6

The simulated TMI brightness temperatures without CISs (unit: K; the background is land surface)

Rain rate (mm/h) Tv10 Th10 Tv19 Th19 Tv21.3 Tv37 Th37 Tv85 Th85

1.00 271.2 271.3 274.0 274.0 272.1 266.1 267.3 243.9 246.5

2.00 272.0 272.1 275.7 275.8 275.9 262.9 264.7 235.2 238.0

3.00 272.8 272.8 276.7 276.9 277.2 260.2 262.4 231.9 234.0

4.00 273.3 273.4 277.4 277.7 277.4 258.1 260.4 225.7 228.5

5.00 273.8 273.8 277.8 278.1 277.6 256.3 258.7 222.5 225.3

6.00 274.2 274.2 277.1 277.9 277.6 254.9 257.3 220.6 223.3

7.00 274.6 274.6 278.1 278.5 277.5 253.6 256.0 217.6 220.5

8.00 274.6 274.8 278.1 278.5 277.3 252.5 254.9 216.7 219.3

9.00 275.3 275.3 278.0 278.5 277.0 251.5 254.0 214.1 217.0

Table 5

The simulated TMI brightness temperatures with CISs (unit: K; the background is land surface)


1.00 271.2 271.3 273.7 273.7 273.8 262.9 263.8 230.1 231.9

2.00 272.0 272.0 275.2 275.3 275.2 257.5 258.8 217.8 220.0

3.00 272.7 272.8 276.1 276.2 276.2 253.3 254.9 210.8 213.3

4.00 273.2 273.2 276.6 276.8 276.2 250.0 251.7 210.0 212.9

5.00 273.7 273.7 276.9 277.1 276.2 247.4 249.2 208.8 211.9

6.00 274.1 274.1 276.0 276.7 276.0 245.4 247.2 208.8 212.0

7.00 274.4 274.5 276.9 277.2 275.7 243.8 245.7 207.5 210.9

8.00 274.5 274.6 276.8 277.1 275.3 242.5 244.5 207.2 210.2

9.00 275.1 275.1 276.6 277.0 274.9 241.5 243.6 206.6 210.1

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Table 7

The simulated TMI brightness temperatures with CISs (unit: K; the background is ocean surface)


1.00 180.4 84.6 204.9 126.6 136.4 234.3 198.9 224.3 221.7

2.00 184.6 92.9 219.2 155.9 169.1 243.6 230.5 216.3 218.4

3.00 188.5 100.1 229.6 177.7 192.7 245.8 241.4 210.4 213.0

4.00 191.8 106.6 237.7 194.7 209.5 245.7 245.0 209.9 212.8

5.00 195.0 112.6 244.1 208.3 222.7 244.8 245.7 208.7 211.9

6.00 197.9 118.2 248.4 218.9 232.8 243.8 245.4 208.8 212.0

7.00 200.6 123.4 253.3 228.2 240.6 242.8 244.7 207.5 210.9

8.00 203.0 128.3 256.6 235.5 246.6 241.9 243.9 207.2 210.2

9.00 205.7 133.1 259.2 241.5 251.4 241.1 243.3 206.6 210.1

Table 8

The simulated TMI brightness temperatures without CISs (unit: K; the background is ocean surface)


1.00 180.5 84.8 205.4 127.5 134.0 237.6 203.3 238.1 237.1

2.00 184.8 93.1 220.0 157.2 170.7 249.1 237.3 233.8 236.7

3.00 188.7 100.4 230.7 179.3 194.7 252.9 249.8 231.5 233.8

4.00 192.1 107.0 239.0 196.6 211.9 254.0 254.3 225.6 228.5

5.00 195.3 113.1 245.5 210.4 225.2 253.9 255.6 222.5 225.3

6.00 198.2 118.8 249.9 221.1 235.5 253.4 255.7 220.6 223.4

7.00 201.0 124.1 254.9 230.6 243.4 252.6 255.2 217.6 220.5

8.00 203.4 129.0 258.3 238.0 249.6 251.9 254.5 216.7 219.4

9.00 206.1 133.9 261.0 244.0 254.4 251.1 253.7 214.1 217.0

Note: Tv represents vertically polarized brightness temperature and Th horizontally.


Here, we can get some conclusions about the contribution of CISs on the upwelling brightnesstemperatures in different channels from the above figure.

4.1. The influence on ðT c2T sÞ

�
The melting layer composed by CISs weakens the upwelling microwave radiation in all TMIchannels with both the ocean and the land backgrounds and in general, the radiation inhorizontally polarized channels is more severely influenced than that in vertically polarizedchannels.
�
The sensitivities of different backgrounds to the contribution of the melting layer composed byCISs are different and the ocean background is more sensitive than the land surface. FromFig. 6(a) and (b), we can see that the absolute value of (T c–T s) with ocean background is largerthan that with land background when the frequency, the polarized mode and the rain rate aresame. That is to say, the information of melting layer composed by CISs is easier to bedistinguished from the ‘‘cold’’ background.

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Fig. 5. The simulated TMI brightness temperatures with both ocean (left) and land (right) backgrounds under different

assumptions, i.e. without and with coated ice particles, above and below, respectively.


�
The sensitivities to the melting layer are related with the frequency. According to Fig. 6(a) and(b), we can conclude that in general, higher the frequency, the more sensitive it is. When the rainrate is small and the frequency is low (for example, 10 and 19GHz), the (T c–T s) is between 0and �3K with both the warm and cold backgrounds. Furthermore, the maximum absolutevalue of (T c–T s) in 10GHz channel is less than 1K and almost impossible to distinguish.

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Fig. 6. The comparison of the contribution of melting layer with and without CISs in TMI channels with different

backgrounds. (a and c: ocean background; b and d: land background).


However, when the frequency is high (37 and 85GHz), the (T c–T s) gets more and moreconspicuous ðo� 5KÞ:

�
The rain rate can also influence the contribution of melting layer to the upwelling brightnesstemperatures. In those middle and low frequencies ðo ¼ 37GHzÞ; the absolute value of(T c–T s) gets larger when the rain rate increases. But this tendency decreases with the increase ofrain rate. This can be explained as the integrated contributions of different mechanisms. The

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melting layer weakens then upwelling radiation but the multi-scattering compensates it. In85.5GHz channel, the later mechanism plays more and more important effect when the rainrate is larger than 3mm/h.

4.2. The influence on (Tv–Th)

�
With the ocean background, we can get such conclusions: The (Tv–Th) decreases when both thefrequency and rain rate increase. When the frequency and rain rate are given, the (Tv–Th) withthe assumption of CISs is slightly larger than that without it (then only exception appears in85.5GHz channel when rain rate is higher than 4mm/h).
�
When focuses on the (Tv–Th) with land surface background, we can get the conclusions similarwith those with the ocean background except that, in this condition, the (Tv–Th) has a negativevalue. In general, the absolute value of (Tv–Th) with the assumption of CISs is smaller thanthat without it. But in 85GHz frequency, when the rain rate is larger than 2.5mm/h, we can getthe opposite conclusion. That is to say, in the high frequency, the attenuation effect of meltinglayer to the upwelling brightness temperature is compensated by the effect of multi-scattering.Another conclusion is that the absolute value of (Tv–Th) is very small ðo1KÞ in lowfrequencies (10 and 19GHz) with and without the assumptions of CISs, while in other middleand high frequencies, it gets large ð41KÞ: Only in middle frequency (37GHz) channel, theinfluence of melting layer on the (Tv–Th) is both stable and conspicuous.
5. Conclusions

In this study, we analyze the microwave radiative transfer characters of melting layer composedby ice spheres coated with liquid water and then examine its contribution to the upwellingradiative brightness temperatures in TMI channels with different polarization methods using theVDISORT model. Comparing with the simulated upwelling brightness temperatures without thecontribution of such a melting layer, we can conclude that:

(1)
The melting layer composed by liquid-coated ice spheres weakens the upwelling microwavebrightness temperatures because of the absorption/emission effect caused by the liquid coat.This effect is more conspicuous in middle and high frequency channels (19, 37 and 85GHz)but, in 85GHz channel, with the increase of rain rate, the multi-scattering can weaken itseffect.
(2)
In a specific frequency, the horizontally polarized brightness temperature is more severelyweakened by the melting layer than the vertically polarized. With the ‘‘cold’’ background(ocean surface, for example), this character is more conspicuous than that with a warmbackground. That is to say, the inner structure of a cloud system is easier to be detected undera cold background. Only in the 85GHz frequency and when the rain rate is larger than 4mm/hcan we find that the vertically polarized brightness temperature is more severely weakenedthan the horizontally polarized one.
(3)
The melting layer with the assumption of coated ice spheres can change the difference ofbrightness temperatures between the vertically and horizontally polarized channels in the same

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frequency. In general, the value of such difference with the assumption of melting layer islarger than that without it. With a warm background, this value is negative and only in middlefrequency (37GHz), it is both stable and conspicuous.

Acknowledgements

This work is supported by National Natural Science Foundation of China (No. 49794030).

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