Journal of

Hydrology ELSEVI E R

Journal of Hydrology 188-189 (1997) 330-360

Feasibility of simultaneous surface temperature-emissivity retrieval using SSM/I measurements from HAPEX-Sahel Xuwu Xiang, Eric A. Smith* Department of Meteorology and Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL 32306-3034, USA

Abstract An algorithm to simultaneously retrieve land surface temperatures and spectral emissivities in the microwave spectrum for applications with SSM/I measurements is developed and tested over the HAPEX-Sahel region. A closed but overspecified system of radiative transfer equations, written in terms of unknown surface temperatures and unpolarized spectral emissivities at 19, 37, and 85 GHz, is solved with a non-linear least-squares optimization technique. Clear-sky multispectral SSM/I brightness temperature measurements at full resolution pixel scale, obtained at least twice during a diurnal cycle (corresponding to the ascending and descending nodes of a DMSP satellite orbit), are used as input over a target area. It is assumed that the spectral emissivities remain constant during the time period under consideration. High-resolution temperature-moisture profiles obtained from the M6t6o France-CNRM balloon-launch station sited at Hamdallay are used to help account for atmospheric effects in the radiative calculations. Retrieved surface temperatures are consistent with ground-based radiometer skin temperature measurements and in situ soil temperature measurements obtained during the 1992 Intensive Observing Period (lOP) at the West-Central supersite for the 8 October golden day case. Qualitative agreement is also found with split window surface temperature estimates retrieved from AVHRR satellite measurements, although this cannot be considered a rigorous verification procedure because of uncertainties in the IR technique and dissimilar overpass times between DMSP and NOAA satellites. The microwave emissivity estimates are consistent with results reported in the published literature. The algorithm is applied over an extended North African region surrounding the HAPEX-Sahel study area for an ensemble of golden days to illustrate its potential for large-scale applications. As an independent test of its utility, output from the algorithm is used over the study area in conjunction with a physically based precipitation retrieval algorithm which requires representative estimates of surface temperature and emissivity in the forward

* Corresponding author. Tel: +904-644-4253; Fax: +904-644-9639; e-mail: [email protected] 0022-1694/97/$17.00 © 1997- Elsevier Science B.V. All rights reserved PII S0022-1694(96)03 165-4

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radiative transfer model calculations. This test is successful in that rain events are correctly identified and their intensity is accurately retrieved in the course of the 1992 IOP, demonstrating the value of a simultaneous temperature-emissivity algorithm in aiding other types of terrestrial remote sensing schemes.

1. Introduction Whereas the radiometric properties of water surfaces are relatively well understood, such properties of land surfaces are only known in general terms and with significant levels of uncertainty. Land surfaces exhibit complex radiometric characteristics which cannot be easily specified according to conventional climatological-geographical factors. Variations in soil moisture, soil composition, vegetation cover, and surface roughness all affect the radiometric temperature of land surfaces, a quantity which can be separated into two distinct physical parts: (1) thermometric temperature; (2) emissivity (which determines reflectivity). Direct satellite-retrieval of these terms is of particular value if the retrieval scheme can avoid having to make assumptions about dielectric properties and other fundamental physical characteristics of the surface. Major progress has been achieved in the retrieval of surface water temperatures using split window IR measurements. This is partly related to the fact that the IR emissivity of a water surface can be determined theoretically to good accuracy (Masuda et al., 1988), unless the water is turbid (Yao et al., 1987), and because water exhibits minor emissivity variation across the window spectrum. Thus, satellite remote sensing of sea surface temperatures (SST) in the IR spectrum has achieved uncertainties on the order of 0.5°C from split window AVHRR measurements (McClain et al., 1985; Barton et al., 1989). For the land case, it is more difficult to address the emissivity problem theoretically, and thus the remote sensing of land surface temperatures by IR means is made difficult by the varying emissivities between different window channels (see Becker (1987) and Prata (1993)). Furthermore, combined retrieval of IR emissivities along with surface temperature using the split window approach is considered a difficult retrieval problem because small errors in differential emissivity lead to large errors in the atmospheric correction term and thus large errors in retrieved surface temperature (Kerr et al., 1992). Nevertheless, progress is being made (Becker and Li, 1990; Li and Becker, 1993; Prata, 1994). In this study, we look to microwave radiometry and physically based inversion principles as an alternative means to collect simultaneous information on surface temperature and emissivity. A recent paper by Calvet et al. (1994) has already attempted to demonstrate the viability of simultaneous retrieval based on physical inversion with satellite passive microwave measurements and radiative transfer models of forest canopies. They sought to retrieve canopy temperature and plant water content at two levels within the Amazonian rain forest using four frequencies from the Scanning Multichannel Microwave Radiometer (SMMR). Neither the temperature or moisture quantities were explicitly validated in that study. Moreover, plant water contents were not reported;

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instead, they were presented in the form of seasonally averaged ratios called MRs, obtained by dividing the difference in retrieved 37 and 6.6 GHz gravimetric moisture quantities (GM37, GMt.6) by their sum. The canopy temperature retrievals were compared with air temperatures and the time-averaged MRs with modeled stomatal resistances. Neither comparison demonstrated significant correlation. Thus, although the algorithms concepts were tenable, questions remain as to the viability of simultaneous retrieval of surface properties using remotely sensed passive microwave measurements in physically based retrieval algorithms. Amongst the published work with primary focus on land surface temperature and emissivity retrieval, virtually all is based on thermal IR radiometry rather than microwave radiometry (see Kahle et al. (1980), Wan and Dozier (1989), Becket and Li (1990), Kerr et al. (1992), Salisbury and D'Aria (1992), Kealy and Hook (1993), and Li and Becker (1993)). Notably, the relatively large IR absorption properties of water droplets and ice crystals in clouds limit the use of IR surface retrieval to nearly clear atmospheric conditions, whereas microwave surface retrieval can be applied for suppressed cloud situations in which the cloud hydrometeors have not become large and thus are not significantly influencing total atmospheric optical depth. This represents one of the key differences between the two spectra in terms of practical applications. Another important difference is that surface emissivity at microwave frequencies generally varies more than in the IR region, for which many natural land surfaces are nearly perfect emitters (generally, IR emissivities are above 0.95). Microwave emissivities range from 0.4 to 0.6 for water surfaces (even higher for foam-covered water), and from 0.7 to 1.0 for land surfaces, mostly depending on the prevailing soil moisture and ground cover conditions. The more variable emissivities in the microwave spectrum are useful for surface identification and become essential inputs for microwave-based atmospheric retrieval schemes in which radiative surface boundary conditions are needed. The latter issue is particularly relevant to physically based precipitation retrieval (see Smith et al. (1994a)). Various previous passive microwave studies whose focus was on the remote sensing of soil moisture, such as those of Schmugge et al. (1974), Njoku and Kong (1977), and Wang and Schmugge (1980), had to consider the nature of surface emissivity but did so with theoretical calculations. These were based on certain highly idealized conditions, such as assuming a smooth bare soil surface and using laboratory-measured dielectric constants obtained for typical soil samples as the physical input. The disadvantage of such approaches is that the approximations often led to considerable uncertainties in the retrievals, and thus become impractical for large-scale applications. In this study, we describe a method to recover land surface temperature and emissivity quantifies simultaneously, based on passive microwave retrieval principles, but avoiding having to specify the surface dielectric properties. The method involves solving a non-linear equation system using multispectral twice-per-day Special Sensor Microwave Imager (SSM/I) brightness temperature measurements as input, along with information on the temperature-moisture profi.42 Tc0 rg0.43 o Tc0 Tw(involves l d ) 0 TD1 1e 1 rg0.3er5ui6 0 TD1T1 1 rg0.48j Tc0 Tw(bltk9 Tc0 Tw5ve 1

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from the Mttto France-CNRM high-resolution balloon launch system are used to specify atmospheric properties. Verification of the retrieval estimates with ground-based radiometer and in situ soil probe temperature measurements, split window skin temperature retrievals from AVHRR satellite measurements, and emissivity data from the published literature indicate both qualitative and quantitive agreement. The scheme is also applied over a North African region surrounding the HAPEX-Sahel study area for an ensemble of golden days, demonstrating its potential for large-scale applications. Finally, the algorithm is used to provide radiative surface boundary conditions for a physically based precipitation retrieval algorithm which requires relatively accurate characterization of surface emission before rain areas can be properly detected and rainrates accurately estimated. 2. Methods

If we consider a non-scattering plane-parallel atmosphere, the radiative transfer equation (RTE) suitable for the passive microwave spectrum is ~t

dTB i( r, I~) dr = - TBi(r, I~) + T(r)

( 1)

where TBi(r,l~) is the brightness temperature at frequency i, # is the cosine of the zenith angle, 7 is the vertical optical depth coordinate, and T(T) is the environmental temperature at r. Thus, the only source of radiance is due to thermal emission. The solution to Eq. (1) for upwelling top-of-atmosphere (TOA) brightness temperature TB,(0, -/~), incorporating a land surface with surface temperature Ts and emissivity ei, is given by T B i ( 0 , - # ) - ' - [ e i T , + ( l - e i )-T B l i l e x p ( - r ~ / ~ ) +

ji

T(r')exp(-r'/~)dr'/~

(2)

where TBI,~ is the average downwelling brightness temperature at the surface, and ri is the optical depth of the entire atmosphere resulting solely from oxygen and water vapor absorption. The variables T, and e~, as noted, are considered as the unknowns to be found through retrieval. In such a multispectral framework, with i = 1,2 . . . . . N in Eq. (2), the number of unknowns (N + 1), is always one more than the number of equations (N). To obtain an extra equation, various approaches have been adopted for the IR problem, such as assuming that emissivity at a given wavelength region is a known constant (Kahle et al., 1980; Wan and Dozier, 1989), expressing emissivities from the pattern of multispectral radiance measurements using regression formulae based on laboratory analysis o[ rock and soil samples (Kealy and Hook, 1993), or seeking to utilize near-IR measurements as additional information to a thermal IR scheme to close the system (Becker and Li, 1990; Li and Becker, 1993). In this technique, we have adopted an idea of Watson (1992), in which multispectral radiance measurements at different surface temperatures can be used to provide a closed equation system for multiple unknown temperatures and a set of spectral emissivities. Thus for our purposes, we have T B j•i ( O , - I x ) = g j . ~(T~,, el)

j = 1,2; i = 1,2 ..... N

(3)

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X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

where TBj,i represents the model brightness temperature at the ith frequency for the jth surface temperature (denoted by T~), where j = 1,2 for twice-per-day temperatures. The functional transform gj,i is described by Eq. (2). Actual TOA brightness temperature measurements, TBMj, i(O, -/z), for both surface temperatures and at all N frequencies, in conjunction with the RTE-derived TBj,~ values, give rise to the difference function F:

Fj, i(Tj, ei)= TBj, i(O, -I~)- TBMj, i(O, -Iz) j = l , 2 ; i= 1,2 ..... N

(4)

Eq. (4) contains N + 2 unknowns and 2N non-linear equations in which the problem is to determine the surface temperatures and emissivities which minimize the Fj,i. It is an overdetermined system that can be solved as a non-linear least-squares minimization problem using an optimization technique, provided N > 2. For N = 2, it is an exact system. In this study dl rxSM/I 0.48 Tc missivities

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3. Data sets

Various data sets are required for the analysis. The source of the multispectral passive microwave measurements is the SSM/I instrument on the F11 Defense Meteorological Satellite Program (DMSP) satellite. High-resolution radiosonde measurements of temperature and moisture are used for input to the RTE model. Infrared thermometer and soil probe temperature measurements, along with AVHRR-derived skin temperature measurements, are used for direct verification of the algorithm. We have focused on the principal HAPEX-Sahel 'golden days' (mostly clear sky conditions over the study area), during which sufficient radiosonde data were available. Thus, 6 days were selected for the analysis from the 1992 Intensive Observing Period (IOP), consisting of 21 August (Day 234), 6 September (Day 250), 12 September (Day 256), 25 September (Day 269), 3 October (Day 277), and 8 October (Day 282). The verification analysis was confined within the one-degree square HAPEX-Sahel study area (13-14°N, 2-3~E) in Niger (see Goutorbe et al. (1994)). To demonstrate the utility of the algorithm at larger scales, an extended analysis is conducted over a region of North Africa surrounding the study area for the ensemble of golden days. 3.1. SSM/I measurements

Raw SSM/I brightness temperature (TB) measurements for individual DMSP overpasses were selected for analysis if they were situated in a grid extending from the equator to 30°N in latitude and from 20°W to 15°E in longitude. This grid encompasses the onedegree HAPEX-Sahel study area. Only six of the seven SSM/I channels were included in the selection process (19V, 19H, 37V, 37H, 85V, 85H), as the emissivities were calculated as unpolarized quantifies, i.e. (V + H)/2, and 22 GHz is not dual polarized. For each day, there are two overpass times, in the morning (descending node) and evening (ascending node). As DMSP satellites are in Sun-synchronous orbit, the overpass times for a given location are constant with respect to mean solar time and nearly constant for local time (see Hollinger (1989)). The times when the F11 satellite brightness temperature measurements are made over the greater HAPEX-Sahel region are approximately 05:00 h UTC for the descending node orbits and 17:00 h UTC for the ascending node orbits, although the times vary according to which specific orbit passes over a given position. It should be noted that for the HAPEX-Sahel site, UTC time and local standard time (LST) are interchangeable. As the incidence (zenith) angle of the SSM/I radiometer at a point on the spherical Earth is constant at 53.1 °, because of its conical scanning pattern, the retrieved surface emissivities have to be interpreted in terms of that angle. The raw SSM/I swath measurements that were situated within the 30° x 35 ° study area were mapped to standardized 560 x 480 rectangular grids using bi-linear interpolation. This means that each 1° × 1° map element is made up of a 16 x 16 pixel subgrid. The mapping procedure facilitated the retrieval process, which was designed to input sets of brightness temperatures at different frequencies associated with fixed pixel locations. Such an approach only partially overcomes the footprint mismatch owing to the diffraction limited nature of a microwave radiometer, and thus there is a source of inconsistency in the retrievals related to the different channels viewing dissimilar ground areas. We suspect

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from the results that the inconsistency was largely manifested in the 19 GHz emissivities, although this cannot be absolutely ascertained or verified from the results. 3.2. Radiosonde measurements

During the HAPEX-Sahel lOP, the M6t6o France-CNRM team made high-resolution radiosonde measurements at Hamdallay (13°33'N; 02°24'E). On each golden day, 6-10 radiosondes were launched approximately 2 h apart. The measuring levels extend from approximately 240 m, the station height, up to about 26 km. Relevant quantifies are temperature and relative humidity at sequential pressure levels. We assume for purposes of verification analysis that the measurements are representative of atmospheric conditions over the 1° x 1° study area. 3.3. A VHRR skin temperature measurements

Skin temperature estimates obtained from AVHRR satellite measurements of 1.1 km resolution using the split window scheme described by Kerr et al. (1992) have been used for qualitative validation purposes. The temperatures are based on Channels 4 and 5 (10.3-11.3 #m and 11.5-12.5 #m) from the AVHRR instruments on-board the NOAA 11 and 12 spacecraft (the overpass times for these spacecraft are approximately 07:00 and 19:00 h UTC, and 02:00 and 14:00 h UTC, which are dissimilar to the SSM/I overpass times). In the Kerr et al. (1992) algorithm, skin temperatures are obtained as a linear combination of canopy and soil temperatures in which the vegetation and soil emissivities for the two thermal bands are specified a priori and a vegetation index derived from AVHRR Channels 1 and 2 (0.58-0.68 #m and 0.725-1.1 #m) is used to specify fractional vegetation cover. A source of uncertainty in this algorithrn is that the vegetation index calculation (a normalized difference vegetation index), is susceptible to error and misinterpretation in the presence of inhomogeneously reflective bare soil. This is a ubiquitous property of the Sahelian landscape. 3.4. Ground-based temperature measurements

Canopy skin temperature and sub-surface soil temperature data were measured at the West Central supersite (13°32'36"N, 02°30'52"E) by the Agricultural University at Wageningen, Netherlands. On each day, downward pointing IR thermometer measurements and sub-surface soil probe measurements at five depths (3, 5, 10, 25 and 50 cm) for densely and sparsely vegetated areas were measured continuously every 10 min. We use temperatures at the 3 cm depth as most representative of the surface soil temperature, recognizing that this is not the ideal depth for characterizing the near-surface thermometric temperature. For purposes of verification, it is best to consider a single day for which both descending and ascending node SSM/I overpasses cover the HAPEX-Sahel site. The only golden day meeting this condition was 8 October (Day 282), therefore, that day was selected for verifying the algorithm. For purposes of the large-scale analysis, the SSM/I and radiosonde data sets for all golden days have been incorporated.

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4. Algorithm implementation The algorithm has been tested on the HAPEX-Sahel golden days. For verification we focus on 8 October (Day 282), for which there was contiguous coverage of the study area

30Deg K

Descending Node (Morning)

275

20N

15N

250

225

10N

200.

5N

175Ascending Node (Evening)

30Deg K

20N

275"

15N

250"

225"

ION

200"

5N

175" 20W

10W

0

10E

Fig. I. Morning (05:37 h UTC; top panel) and evening (16:47 h UTC; bottom panel) SSM/I overpasses over North Africa on 8 October 1992. The images are unpolarized 19 GHz brightness temperatures. To improve map appearance, a five-point two-dimensional weighted filter is applied to a transformed version of the original 560 × 480 grid mesh, in which each 16 x 16 map element (representing a I ° x I ° sub-grid mesh) as bi-linearly interpolated onto an 81 x 81 sub-grid mesh. The small boxes indicate the 1° x 1° HAPEX-Sahel study area.

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X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

z

z

z

z

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0 0

o

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".-" ..-

x. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

339

for both the descending and ascending node SSM/I overpasses. Fig. 1 shows morning and evening SSM/I 19 GHz brightness temperature images on this day for a portion of the data sector; these diagrams are presented at the continental scale. The small boxes in the two panels denote the 1° x 1° HAPEX-Sahel study area. The times when the overpasses traverse the HAPEX-Sahel site are 05:37 and 16:47 h UTC (equivalent to LST). Over much of the northwestern portion of the continent, 8 October was relatively cloud free, and, coupled with the fact that at 19 GHz clouds minimally attenuate the surface signal, these images mostly exhibit features purely associated with variable surface conditions. Therefore, the strong brightness temperature gradients are a result of both changing surface temperature and emissivity. The highest brightness temperatures are found in a curved band positioned at approximately 10-12°N at the meridian of the HAPEX-Sahel study area, arcing to the north in both east and west directions. Fig. 2 shows AVHRR 3.7 #m (Channel 3) and 10.8 #m (Channel 4) IR imagery at much higher resolution (1.1 km) and smaller scale (just the 1° x 1° study area), for the morning (07:15 h UTC) NOAA 12 overpass on 8 October and afternoon (14:26 h UTC) NOAA 11 overpass on 10 October (neither the afternoon NOAA 11 nor NOAA 12 overpass on 8 October was acquired). The signature of the Niger river is evident in the southwest sectors of these images running from northwest to southeast, just to the north of the Southern supersite. These images help illustrate the magnitude of temperature variability over the site, including the extent of diurnal variation. The morning image contains the edge of a cloud band in the southwestern corner of the study area (as well as some smaller cloud areas north and west of the central supersites), whereas the afternoon image contains slight penetration of a cloud band in the southeastern corner, plus a few other small cloud fields to the north and southwest of the central supersites. The approach used to specify the input profiles of temperature and moisture for the RTE model has required attention because the algorithm is sensitive to the vertical structures of these parameters. Initially, an analysis of the impact of the actual temperature and moisture variations taking place during the six golden days on the TOA microwave brightness 20

........

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t

85GHz, SuffaceCon~bution=71%

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~ 100

Fig. 3. Surface-atmospherebrightness temperature weighting functions (given in units of percentagecontribution) at 19, 37, and 85 GHz for clear-skyconditions using a goldenday compositetemperature-moistureprofile. The percentage surface contributions are given in the key.

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Table 1 Statistical summary of seven radiosonde profiles flown on 8 October 1992 (Day 282) from Hamdallay (05:00, 07:00, 09:00, 1 I:00, 13:00, 15:00, and 17:00 h UTC); mean values of temperature and relative humidity, along with their standard deviations (aT and OR) at 42 height-pressure levels, are given No.

Height (kin)

Pressure (mbar)

Temperature (K)

aT (K)

RH (%)

aR (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

18.500 18.250 17,750 17.250 16.750 16.250 15.750 15,250 14.750 14.250 13.750 13.250 12.750 12.250 11,750 11.250 10.750 10.250 9.750 9,250 8.750 8.250 7,750 7,250 6,750 6,250 5,750 5,250 4.750 4.250 3,750 3.250 2.776 2.342 1.939 ! ,571 1.232 0.922 0.637 0,375 0.125 0.000

68.82 71.77 78.14 85.12 92.80 I 01.29 110.55 120.57 131.31 142.88 155.33 168.58 182.77 197.79 213.75 230.70 248.63 267.62 287.66 308.83 331.18 354.74 379.59 405.79 433.41 462.55 493.34 525.92 560,23 596.72 635.18 675.39 715.24 753. ! 6 789.58 824.22 856.96 887.85 917.03 944.53 971.53 985. i 8

204.01 203.50 199.21 200.14 196.29 194.37 195.63 198,44 201.64 202.59 206,62 209.89 213.90 217.91 221.78 225.88 230.31 234.28 238.49 242.48 246.53 250.30 254.03 257.62 261.08 263.89 265.75 268.38 271.07 271.45 275.85 280.60 284.99 288.91 292.33 295.43 298.14 300.41 301,73 302,55 303.88 305.37

1.5 1.5 0.8 1,5 0.6 1.1 0.7 0.4 0.6 0.5 0.6 0.5 0.4 0.4 0,3 0.3 0.4 0.3 0.3 0. I 0.2 0.4 0.4 0.3 0.2 0,4 1.4 1.0 1.9 1.1 0.2 0.2 0.1 0.4 0,6 0.9 1.2 1.0 1.8 3.1 4.2 6,6

8.51 9.57 10.51 12.33 11,86 1 t .57 12.29 13.86 16.57 17.29 18.14 21.50 26.40 29.42 30.72 21.57 9.72 3.86 3.57 3.91 3.86 3.29 3.19 3.21 2.43 3.86 9.60 21.71 19.40 45.05 39.83 31.21 25.97 22.39 23.00 23.75 26.30 26.93 33.14 38.42 39.58 43.52

2.1 2.1 2.1 1.9 1.9 2.3 1.9 2.2 2.3 3.1 3.3 2.9 3.3 7.1 3.6 4.2 4.0 0.7 0.8 0.7 0,4 1.0 0.7 0.4 0.5 0.9 5.4 4.2 12.2 15.7 2.1 2.4 1.9 1.4 4.6 10.4 12.3 8.8 9.6 12.7 15.5 19.1

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

341

temperatures was carded out. To interpret these results, it is first important to understand the weighting function properties of the surface and atmosphere in terms of their relative contributions to the TOA brightness temperatures (see Smith and Mugnai (1989) and Mugnai et al. (1993) for a discussion of microwave weighting functions). Based on a

(a)

Water Vapor Mixing Ratio ( g . k g "~) 0 20

4 8 12 16 20 24 28 . . . , . . . , . . . , . . . , . . . , . . . , . . . .~

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Fig. 4. (a) M o r n i n g - e v e n i n g temperature and moisture structure on the 8 October golden day. The mean temperature profile is shown along with the m o r n i n g - e v e n i n g soundings, based on using all seven soundings from that day (plus or minus standard deviation bars are also indicated). The box surrounding the lower portion of the temperature profile is magnified in (b) to illustrate the relationship between the retrieved profiles and the actual profiles. (b) Schematic representation of the relationship between the actual m o r n i n g - e v e n i n g temperature profiles within the boundary layer and their representation in the retrieval algorithm. The algorithm forms the profiles by parabolic interpolation between the lowest two points from the fixed mean temperature profile (starting at 1.2 km A G L ) and the point represented by the retrieved skin temperature.

342

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

mean temperature-moisture profile produced from the golden day soundings and a constant surface emissivity of 0.9, weighting functions at 19, 37, and 85 GHz have been calculated, and are shown in Fig. 3. The weighting functions are expressed in the form of percentage contribution extending from the surface up to a vertical level where the percentage falls below 0.01%. The results show that for clear sky conditions, the surface has an overwhelming effect on TOA brightness temperatures, contributing 90% and 88% to the 19 GHz and 37 GHz brightness temperatures, and 71% to the 85 GHz brightness temperatures. The weighting functions of all three frequencies decrease nearly exponentiaUy with increasing altitude (the abscissa of Fig. 3 is logarithmic), indicating that the major source of atmospheric contribution is from the planetary boundary layer. Table 1 shows the means and standard deviations of temperature and relative humidity at 42 height-pressure levels, calculated from the seven soundings obtained on 8 October. It can be seen that relative humidity is generally more variable than temperature (relative to the means), particularly above 1.5 km. Above 1.5 km, the standard deviation of temperature is almost always below l°C, except at the very upper levels where standard deviations increase to approximately 1.5°C. Height-dependent temperature variance statistics calculated separately for each of the other golden days show the same pattern. RTE model sensitivity tests indicate that the maximum changes in the TOA brightness temperatures (ATB values), with respect to the maximum possible variations in the seven atmospheric temperature soundings taken on 8 October above 1.23 km, are 0.03°C, 0.03°C, and 0.07°C for 19 GHz, 37 GHz, and 85 GHz, respectively. These variations are below the noise equivalent temperatures of the SSM/I channels and therefore indicate that diurnal variability of temperature above the boundary layer is inconsequential with respect to the surface retrievals. The corresponding ATB values for moisture variations are 17-20 times larger (0.6, 0.5, and 1.3°C); therefore, diurnal variations of mixing ratio above the boundary layer are much more significant in terms of affecting retrieval. Sensitivity tests with the retrieval algorithm verify that morning-afternoon variations in the upper-level temperatures can be ignored but those of moisture should be considered. Accordingly, we have adopted an approach in which a single mean temperature profile for the golden day is fixed at and above 1.23 km, whereas individual morning and afternoon soundings closest to the times of the descending and ascending node SSM/I overpass are used to obtain the moisture profile input. The schematic diagram in Fig. 4(a) illustrates the situation on 8 October. The morning and evening temperature-moisture profiles closest to the SSM/I overpass times are shown, along with the mean temperature profile of all seven soundings flown that day. Although diurnal variations of temperature above 1.23 km are found to have negligible effect on the retrievals, the sensitivity tests do indicate that the retrievals are sensitive to temperature variations within the boundary layer. As these variations are strongly coupled to skin temperature variations, and skin temperature is a free variable in the retrieval scheme, we have sought a means to relate the temperature profile within the boundary layer to the skin temperature for the two overpass times. This has been done by non-linear interpolation between the skin temperature as it adjusted during the optimizer-controlled iteration process, and the first two temperatures above the 1.23 km level, which is at the base of the fixed portion of the mean temperature profile. The method is a three-point Lagrangian scheme, which provides a parabolic shape to the boundary layer temperature profile. The contents of

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X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

the box surrounding the l o w e r portion o f the temperature profile in Fig. 4(a) has been magnified in Fig. 4(b) to illustrate this process. The temperature profiles from the 05:00 and 17:00 h U T C soundings (thin dashed lines) are s h o w n a l o n g with the typical retrieved temperature profiles at the 05:37 and 16:47 h S S M / I overpass t i m e s (thick dashed lines).

(a) Morning (0537 U T C )

Evening (1647 U T C )

/ 2.1E 23E 2.5E 2.7E 2.9E

298

299

300

301

2.1E 2.3E 2.5E 2.7E 2.9E

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311

312

313

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Degrees K (b)

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,

.

.

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.

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.

.

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- -

.

,

.

.

.

.

,

.

.

.

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v

morning 60

Oct 08,0537 (SSM/I) ~ , P l Oct 04,0700 (NOAA12)

(~ '~ 40

~ Oct 08,071S ( N O A A ~

20

0

t , . , . i .... 285

290

~

Oct 13,1531 (NOAA 1I)

Oct 10,142( (NOAA 11)

i .y, m, 295

Oct 08,1647 (SSM/I)

, i , . 300

305

, 310

315

320

Surface Temperature (K) Fig. 5. (a) Retrieved surface temperature maps of the HAPEX-Sahel study area for morning (left panel) and evening (right panel) overpasses on the 8 October golden day. The same interpolation-filter transform as used to prepare the graphic in Fig. I is also used here. The locations of the supersites are indicated. (b) Histograms of surface temperature based on SSM/I and AVHRR retrievals for morning and evening overpasses. The SSM/I retrievals are on 8 October. The AVHRR retrievals are on 4 and 8 October for the morning case, and on l0 and 13 October for the evening case (an 8 October AVHRR evening overpass was not recorded). The various overpass times are indicated. The average temperatures for the AVHRR retrievals are 298.7 K, 298.4 K, 316.5 K, and 314.2 K on 4, 8, I 0, and 13 October, respectively, and 300.3 K and 312.2 K for the 8 October SSM/I morning and evening retrievals, respectively. The six associated standard deviations are 0.72, 0.70, 1.33, 1.35, 0.63, and 0.38°C, respectively.

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

344

Tests with the temperature interpolation scheme, and use of separate morning and evening moisture profiles, indicate stable convergence of the retrieval algorithm for all of the pixels. Tests with a single mean moisture profile led to instances where the optimizer failed to find a satisfactory solution within the allowed ranges of skin temperature and emissivity. That is, a proper local minimum is not found and the optimizer drifts to the edge of the allowed temperature or emissivity range interval, failing to converge. In essence, any thermodynamic configuration in which the RTE model produces systematic and correlated differences in the frequency-dependent brightness temperatures too unlike those associated with the measured brightness temperatures will lead to unsatisfactory retrievals. If we simply specify the skin temperature, rather than retrieve it, for example, to the lowest level radiosonde value or by extrapolation of the lowest reported level to the surface, the simultaneous least-squares optimization is no longer necessary and the whole retrieval procedure greatly simplifies. However, because of the variable boundary layer temperatures (see Table 1 or column), and hence the highly variable specified skin (a)

19 GHz

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--

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.....

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......... 85 GI-lz(rosen=0.921)

g

0 0.85

0.90

0.95

1.00

SurfaceEmissivity Retrieved surface emissivity maps of the HAPEX-Sahel study area at 19, 37, a n d 85 G H z on the 8 October golden day. The same interpolation-filter transform as used to prepare the graphic in F i g . ! is also used here. The locations of the supersites are indicated. (b) Histograms of retrieved surface emissivity at 19, 37, and 85 G H z on the 8 October golden day for the entire HAPEX-Sahel study area. The site-averaged emissivities are also indicated in parentheses. F i g . 6. (a)

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

345

temperatures, which in turn play a crucial role in the TOA brightness temperatures as shown in Fig. 3, the uncertainty on retrieved surface emissivities becomes substantial. Therefore, the introduction of the simultaneous solution approach is compelling.

5. Test and validation of algorithm over HAPEX-Sahel study area

Results from the algorithm on the 8 October golden day are given in Fig. 5 and Fig. 6. Fig. 5(a) shows the surface temperature retrievals over the study area at the SSM/I morning and evening overpass times. There are three features evident in the temperature patterns worthy of note. The first is the basic similarity between the AVHRR-derived and SSM/I-derived morning and afternoon temperature distributions as given in Fig. 2 and Fig. 5(a), regardless of the fact that the sensor resolutions are significantly different and the overpass times not coincident (in the case of the afternoon overpasses, they also occur 2 days apart). The morning similarity is tenuous at best, but both sensors detect higher temperatures in an arc extending from west of the central supersites, around to the north, and then back down along the western side of the study area. The comparison between the afternoon patterns is more coherent, with higher temperatures in the northwest and northeast sectors, and lowest temperatures in the southeast. The second feature of note is seen in the afternoon SSM/I map, involving the amorphous ring of lower temperatures surrounding a broken-up local maximum south of the central supersites. Examination of the cumulative rainfall map obtained during the IOP period from Goutorbe et al. (1994) shows a ring of higher rainfall amounts surrounding the area south of the two supersites. This suggests the retrieved temperature map is physically consistent with soil moisture conditions, in which the moist ring is cooler. The third feature of interest is that the cloudinduced band of lower temperatures in the southwest corner of the morning AVHRR map has no apparent impact on the microwave retrievals because the associated cloud is optically thin. Fig. 5(b)shows the temperature histograms associated with these maps (thick lines) along with similar histograms derived from AVHRR retrievals at their corresponding overpass times. AVHRR results are given for two clear days for the morning case (4 and 8 October) and two additional clear days for the evening case (10 and 13 October) for which an 8 October afternoon overpass was not available. It should be noted that the times of the AVHRR overpasses do not correspond to the times of the SSM/I overpasses. That is why the histograms are not aligned, particularly for the evening case in which the AVHRR overpass times are actually taken in midafternoon, during which time surface heating is rapidly changing. Nevertheless, the temperature peaks of the AVHRR overpasses and SSM/I are physically consistent with the times of the overpasses during the course of the diurnal surface heating cycle. For the morning case on 8 October, the surface cools approximately 1.9°C between 05:37 and 07"15 h UTC (SSM/I average is 300.3 K; AVHRR average is 298.4 K), whereas for the evening case, overlooking the different days, the surface cools steadily from mid-afternoon (316.5 K at 14:26 h UTC) to late-afternoon (312.2 K at 16:47 h UTC), denoting qualitative consistency. The SSM/I morning and evening surface temperature means are 300.3 K and 312.2 K,

346

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

Table 2 Comparison of SSM/I-retrieved surface temperatures, ground-based IR thermometer-derived skin temperatures, and 3 cm measured soil temperatures at the West Central supersite

Latitude (°N) Longitude (°E) Surface temperature (K) Morning (05:37 h UTC) Afternoon (16:47 h UTC)

SSM_/I Retrieval

IR thermometer

3 cm soil

13.531 2.531

13.543 2.514

13.543 2.514

300.8

294.2

311.7

309.7

302.2 299.0 314.5 316.7

(Site (Site (Site (Site

I) II) I) II)

Location and time information is included. For the soil temperatures, Site I is densely vegetated, whereas Site II is sparsely vegetated.

or an approximately 12°C diurnal range. In Table 2, the IR thermometer and soil probe temperature measurements at the West Central supersite are compared with the SSM/I retrievals for the pixels closest to the measuring locations. Soil temperatures are taken at 3 cm for both densely and sparsely vegetated locations. Although the two different ground truth measuring techniques and the satellite retrieval approach are entirely different in terms of both physical detection principles and spatial resolution scales, the intercomparison provides a first-order check on consistency. At the morning overpass time, the SSM/I value (300.8 +_ 0.5 K) falls between the canopy temperature (294.2 K) and Site I soil temperature (302.2 K), tending toward the soil value. As the microwave estimate represents an integrated rendition of both canopy emission and near-surface soil emission, the SSM/I retrieval is physically consistent with ground truth measurements. The same consistency is seen at the afternoon overpass time, except the SSM/I value (311.7 +_ 0.35 K) falls between the canopy (309.7 K) and Site I soil (314.5 K) measurements. The fact that, at both overpass times, the ground truth measurements bracket the SSM/I values lends quantitative assurance that the retrieval scheme is sound. A more comprehensive validation would have to be carried to provide meaningful uncertainty estimates to the retrieval scheme. The emissivity maps at 19, 37, and 85 GHz are shown in Fig. 6(a). There is an emissivity gradient across the study area, with the lowest emissivities to the northwest and the highest in the southeast. The signature of the Niger river is barely apparent at 37 and 85 GHz in the southwestern sector of the map, although the relatively low resolution of the SSM/I data inhibits detailed elucidation of the feature. There is no objective means to establish the validity, or lack thereof, of this gradient pattern, so we turn to bulk statistical properties for establishing credibility of the result. The histograms of the pixel-level values are given in Fig. 6(b). The mean emissivities are 0.933, 0.922, and 0.921 at 19 GHz, 37 GHz, and 85 GHz, respectively. The Standard deviations are all less than 0.01. The magnitudes compare well with measured values of emissivity for dry soil conditions as tabulated by G-rody (1993), who reported values of approximately 0.95 across the 10-85 GHz frequency range for dry land. At lower frequencies, the study of Schmugge et al. (1986) reported 1.4 and 5 G H z emissivities between 0.9 and 0.95 for dry sandy loam soil based on measurements from

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

347

a truck-mounted radiometer; the study of Jackson and Schmugge (1986) reported 1.4 GHz aircraft-derived emissivities for dry rangeland o f approximately 0.93. In contrast, a modeling study by Camillo and Schmugge (1984) for different textured soils indicated dry soil emissivity values at L-band (1.4 GHz) lower than shown by the measurements (0.85-0.9). The result given by Grody (1993) shows little frequency dependence across the 1085 GHz spectral interval. Monotonic increase of emissivity from lower to higher frequency would be expected as the moisture content of the upper soil layer increases. This behavior would be strong for a wet surface (see the theoretical calculations of Wang and Schmugge (1980) for idealized wet bare soil). Soil conditions on 8 October were dry, as the rainy period had ended around mid-September (Prince et al., 1995). Our results show that the site mean emissivities at 37 and 85 GHz are nearly equivalent, with the site mean emissivity at 19 GHz approximately 0.01 larger. The means are consistent with a dry surface. The small difference found at 19 GHz is within the uncertainty limits of the retrieval technique and may be related to the dissimilar fields-of-view of the diffraction limited channels of SSM/I (see Farrar et al. (1994)).

6. Retrieval test at larger scale To demonstrate the applicability of the retrieval algorithm at larger scales, we have used twice-per-day SSM/I overpasses from the six golden days giving extended coverage over the North African region. The algorithm was configured for generating independent retrievals on each day over sectors where the morning and evening overpasses intersected, and merging the resultant emissivity information of the individual intersect sectors, such that whenever two or more retrievals are made at the same pixe ! position, an emissivity average is taken. The vertical structure of temperature-moisture was specified in two ways. In the first case, the daily composite profiles obtained from the Hamdallay soundings for the individual golden days were used to represent conditions throughout the large-scale area (i.e. variable in time but not in space). In the second case, gfidded profiles from the European Centre for Medium Range Weather Forecasting (ECMWF) data assimilation runs were used. These data, which were obtained from the National Center for Atmospheric Research (NCAR) in Boulder, are nominally interpolated to a 2.5 ° × 2.5 ° grid, allowing for both a time-space varying field of temperature-moisture structure within the large-scale SSM/I maps. For reasons discussed in Section 2, depending on the convergence tolerance, the algorithm cannot necessarily find solutions for the surface variables when there are significant deviations between the specified moisture profile from actual environmental conditions. For this reason, the tolerance was kept relatively large (0.01). Before making the retrieval calculations, the SSM/I images were cloud filtered, to prevent making surface temperature-emissivity estimates in regions containing significant amounts of cloud liquid water (and possibly ice). The screening procedure of Ferraro et al. (1994a) has been used (stemming from the study of Grody (1991)), which for a warm semi-add background is based on differentiating the scattering surfaces of exposed soil and cloud by the polarized nature of soil emission at 19 GHz.

X. Xiang, E.A. Smith~Journalof Hydrology 188-189 (1997)330-360

348 (a)

Aug 21,1992 (234)

Sep 6,1992 (250)

Sep 12, 1992 (256)

ION 51',,I ON

Sep 25, 1992 (269)

Oct 3, 1992 (277)

f ~~ I I I1 f I I I I [~L 20W 15W 10W 5W

0

SE

20W 15W 10W SW

0

$'E

Oct 8, 1992 (282)

20W 15W 10W 5W

0

SE

(b)

(c)

"il LU g

Fig. 7. (a) Depiction of morning-evening intersect coverage (indicated with black cutouts) on six golden days (Days 234, 250, 256, 269, 277, and 282). White patches within cutouts identify cloud-obscured areas. The HAPEX-Sahel study area is indicated by a square. (b) Emissivity map of north African region at 19 GHz based on ensemble of retrievals from six golden days identified in (a). In these calculations, the composite soundings from Hamdallay within the ItAPEX-Sahel study area (indicated by a square) are used to specify the vertical temperature-moisture structure over the entire large-scale area. No smoothing has been applied to the composite map. (c) Same as (b) except for three golden days after the end of the wet season (Days 256, 269, and 282) and using time-space-dependent ECMWF temperature-moisture profiles as input for retrievals.

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

349

Fig. 7(a) shows a set of six maps for the individual golden days highlighting the regions where retrievals were possible. In these maps, the black cutouts identify the sectors where the morning and evening overpasses intersected. The white patches within the black cutouts identify the regions where clouds were detected by the screening procedure. Fig. 7(b) illustrates the retrieved 19 GHz emissivity composite map in which all six intersect regions are merged by averaging within cells containing more than one result. The two white triangular cutouts are the areas where no SSM/I day-night intersect coverage was available on any of the six golden days. A few patches remain within the data coverage areas, representing instances where there was intersect coverage but no cloudfree pixels were found. The Fig. 7(b) result is for the case in which the time-varying but space-fixed composite Hamdallay soundings were used. Fig. 7(c) provides the result in which the ECMWF soundings were used. In the last diagram, only the results for 3 days after the commencement of the dry period were merged (Days 256, 269, and 282), for purposes of clarity in the following discussion. It is evident the emissivity distribution is generally consistent with the 19 GHz brightness temperature distribution given in Fig. 1, i.e. an arcing band of higher emissivities with the band apex situated at 10-12°N, just south of the HAPEXSahel study area. These are not duplicate patterns, as the brightness temperature pattern in Fig. 1 is brought about by a combination of variable surface temperature and emissivity fields. The distinction in the patterns is most evident to the west of the study area, where a band of large emissivities extends approximately 3 ° further north than the bright band of 19 GHz brightness temperatures seen in the top panel of Fig. 1. Of additional note are the patches of blank (white) pixels in the ECMWF-based retrieval, largely confined to the northeast, but not representing cloud-covered areas as shown in Fig. 7(a). These pixels are where the retrieval algorithm failed to converge, and can be attributed to using temperature-moisture profiles too unlike actual atmospheric conditions that bring about the convergence problem discussed at the end of Section 4. Evidently, the optimal interpolation results produced by the ECMWF initial analyses were less representative for this region of Africa than the soundings obtained at Hamdallay. Using the HamdaUay composite soundings, the algorithm produces a 19GHz emissivity distribution over the large-scale study area ranging from 0.80 to 0.97, with mean of 0.92 and standard deviation of 0.014 (i.e. from the Fig. 7(b) distribution). If the three dry period days based on the ECMWF analysis are considered separately (Fig. 7(c)), the 19GHz emissivity range is 0.85-0.96, with the same mean and standard deviation values from the 6 day analysis. These variations are consistent with soil moistures ranging from intermediate to trace levels. Because we have no current means to reliably confirm actual soil moisture conditions outside the study area, this larger-scale retrieval cannot be quantitatively validated at this time. However, such calculations highlight the potential for global applications given composited sets of cloud filtered SSM/I measurements and adequately spaced profiles of temperaturemoisture. As discussed in the next section, we find the algorithm is sufficiently reliable in retrieving surface emissivities over the HAPEX-Sahel study area for purposes of providing radiative boundary condition information to a physically based precipitation retrieval algorithm.

350

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

7. Using retrieved surface parameters as input to precipitation algorithm As an independent test of the validity of the temperature-emissivity estimates, we use them as input to a physically based precipitation retrieval algorithm which requires specification of the radiometric properties of the underlying surface. Such boundary conditions are needed by the forward radiative transfer model used in the algorithm for inversion of rain profiles. As the surface temperature-emissivity factors determine both its emitted and reflected contributions to the upwelling radiation field, the accuracies of the modeled top-of-atmosphere upwelling brightness temperatures, which the inversion procedure depends on for matching to the associated measured brightness temperatures, are partly a function of how accurately the surface boundary conditions are specified. This is a particularly important issue for light rainfall conditions, when the microwave transmission of the rain column is significantly non-zero.

7.1. Description of precipitation algorithm The algorithm used for rain retrievals is a physically based profile-inversion scheme developed at Florida State University (FSU) (see Smith et al. (1994c, 1995)). It is being used for applications with measurements from multispectral passive microwave radiometers, including the spaceborne SSM/I radiometers and the Advanced Microwave Precipitation Radiometer (AMPR), which is flown on NASA's high-flying ER-2 aircraft (see Spencer et al. (1994) and Smith et al. (1994b)). The theoretical foundations for the algorithm have been given by Smith et al. (1992) and Mugnai et al. (1993). The design and validation of the algorithm are described in the studies of Smith et al. (1994c, 1995)). A general overview of profile algorithms has been given by Smith et al. (1994a). The conceptual design is based on using a cloud model to guide an inversion procedure. The algorithm uses microphysical structure information acquired from cloud model simulations, in conjunction with a forward radiative transfer model, in which an optimizer is used to perturb first-guess microphysical structure information extracted from a cloudradiation database until the RTE-generated top-of-atmosphere upwelling brightness temperatures at a selection of frequencies are optimally matched to the measured brightness temperatures. For SSM/I applications, 19, 37, and 85 GHz are the relevant frequencies most strongly responding to precipitation microphysics (Mugnai et al., 1990). The use of a selection of frequencies at various windows in the millimeter-centimeter spectrum allows depth probing into a raining cloud column because the frequency-dependent weighting functions exhibit peak responses at different vertical levels in the column owing to differential scattering across the frequency range (see Smith and Mugnai (1989) and Mugnai et al. (1993) for discussion of the theory and application of emission-scattering weighting functions relevant to the microwave spectrum). The microphysical structures are obtained from two- and three-dimensional limitedarea prediction models containing explicit or parameterized cloud-microphysical process models and configured for cloud-scale simulations. To date we have used four such models: (1) a two-dimensional version of the mesoscale model of Clark (1977) using the explicit cloud microphysics package of Hall (1980); (2) a predecessor model to the

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (I997) 330-360

351

Colorado State University three-dimensional Regional Atmospheric Modeling System (RAMS--see Pielke et al. (1992)), originally described by Tripoli and Cotton (1982) and Tripoli (1989), using the microphysical parameterization described by Cotton et al. (1982, 1986); (3) the three-dimensional Nonhydrostatic Modeling System developed at the University of Wisconsin (UW-NMS) by Tripoli (1992a) using the microphysical parameterization described by Flatau et al. (1989) and Tripoli (1992b); (4) another three-dimensional non-hydrostatic mesoscale model incorporating parameterized cloud microphysics from the University of Wisconsin developed by Straka (1989) and applied by Johnson et al. (1993, 1994) for a supercell storm simulation (results provided by Pao Wang (personal communication, 1994)). A cloud-radiation database is created by using the RTE model in a forward mode to precalculate brightness temperatures associated with a large set of cloud microphysical profiles (made up of suspended and precipitating hydrometeors of liquid and ice). This set of profile-brightness temperature pairings forms what is called the cloud-radiation database, and constitutes the underlying brightness temperature-rainrate relationship needed by the algorithm. Specifically, a pairing consists of a group of six vertically distributed hydrometeor profiles, representing a single realization of cloud drops, rain drops, ice crystals, snow flakes, ice aggregates, and graupel particles all specified in equivalent liquid water or ice water contents (LWCs or IWCs), to a three-element brightness temperature vector (19, 37, and 85 GHz). By creating many of these pairings, a database is established which can

man

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

352

Table 3 Retrieved rainrate errors and relative errors from FSU profile algorithm for seven reference rainrates as a function of six imposed surface emissivity errors Ae~

1 2 3 4 5 6

+ 0.05 + 0.03 + 0.01 - 0.01 - 0.03 - 0.05

Referencerainrate (mm h -~) 0.5

1

3

5

0.91180 0.61120 0.1/20 0.3/60 0.5/100 0.81160

2.11210 2.01200 1.3/130 0.9•90 1.6/160 2.1/210

8.71290 4.1/82 4.9/163 0.7/14 3.7/123 1.1/22 1.2/40 - 0.61 - 12 2.1/70 0.1/2 4.7/157 2.5/50

10

20

11.4/114 7.7/77 4.4/44 2.9129 3.4/34 6.1/61

- 0.9/0.0/0 - 1.9/- 0.71 - 3.31 - 2.1/-

30 4 9 3 16 10

-

2.4/1.8/1.9/4.3/6.81 4.7/-

8 6 6 14 23 16

For the control run, the reference surface emissivity is 0.92 at 19, 37, and 85 GHz, whereas the surface temperature is set constant at 300 K. A climatological temperature-moisture profile is used to define atmospheric conditions. For a table entry, the absolute error (in mm h -~) is given first, with the relative error (in %) following the slash. relationship, the next a , - , + relationship, and so on. All profile pairings in the cloudradiation database are first m o n o t o n i c a l l y ordered from smallest to largest according to the r.m.s, differences b e t w e e n database brightness temperature vectors and the given measured brightness temperature vector, so that the first guess s c a n n i n g process is guaranteed to identify profiles that are most consistent with the m e a s u r e m e n t in a radiative sense. Rainrates are obtained b y associating M a r s h a l l - P a l m e r drop size distributions to the retrieved rain L W C and graupel I W C profiles, and then p e r f o r m i n g r a i n - g r a u p e l fallout calculations to form vertical profiles o f l i q u i d - i c e precipitation rates and latent heating.

7.2. Sensitivity o f rainrate retrievals to surface emissivity error Table 3 shows how errors in retrieved rainrate are related to errors in surface emissivity (~es), based on a sensitivity analysis which makes use o f the precipitation retrieval algorithm to establish the error relationships. In these calculations, a climatological temperat u r e - m o i s t u r e profile is used for representing atmospheric conditions; the surface temperature is fixed at 300 K. T h e results in the table represent differences b e t w e e n rainrates retrieved by the algorithm for a set o f six emissivity errors (ranging from 0.05 to 0.05) incorporated into the m o d e l e d brightness temperatures at 19, 37, and 85 GHz, relative to a set o f seven reference rainrates r a n g i n g from light (0.5 m m h -1) to heavy (30 m m h-l). The reference brightness t e m p e r a t u r e - r a i n r a t e relationships are created in the a l g o r i t h m ' s cloud-radiation database for a reference emissivity of 0.92 (consistent with the H A P E X - S a h e l results g i v e n in Fig. 6). Therefore the Aes errors lead to an absolute emissivity range from 0.87 to 0.97. Each i m p o s e d emissivity error leads to a separate cloud-radiation database, and therefore a separate brightness t e m p e r a t u r e - r a i n r a t e relationship. Thus, rainrate errors can be defined w h e n brightness temperatures for a given brightness temperature v e c t o r - r a i n r a t e pairing taken from a database produced for an emissivity v a l u e u n l i k e that used in the reference calculations are associated with rainrates in the reference database. It is evident in Table 3 that for light rainrates, e v e n small emissivity errors of 0.01 produce relative rainrate errors over 50%. The larger

353

X. Xiang, E.A. Smith~Journalof Hydrology 188-189 (1997) 330-360

emissivity errors of 0.5 generate enormous errors at light rainrates, almost reaching 300%. As rainrate increases, retrieved rainrate errors diminish, even for larger emissivity errors, as the optical depths of the rain columns start to cut off contributions by the surface to the top-of-atmosphere upwelling brightness temperatures. At rainrates of 2 0 - 3 0 m m h -I, errors are reduced to magnitudes of 10%.

7.3. Comparison of satellite retrievals with EPSAT-Niger raingage data When the mean study-area temperatures and emissivities obtained from the large-scale calculations are used with the algorithm for precipitation estimates over the lOP, the retrievals are consistent with ground measurements obtained from the high-density HAPEX-Sahel raingage network (see Lebel et al. (1992, 1997), for a discussion of the 107 gage EPSAT-Niger raingage system). Fig. 8(a) and Fig. 8(b) illustrate the lOP time series, broken up into eight weekly panels, giving hourly rainfall accumulations from the gage network superimposed with arrows and times corresponding to when SSM/I overpasses covered the 1° x 1° study area. It should be noted that the satellite overpasses did not provide adequate sampling of the lOP rain events, mostly in the course of the wet period up to 15 September. The undersampling is particularly serious for the six major rain events occurring on 22, 28, and 30 August (morning and evening), and 12 and 14 September. The

(a) t4o 4

First W e e k

Second W e e k

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1.

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Aug 17 .....

18 • ....

19 ,

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21

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Aug 24

A u g 23

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26

27

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4

-

.

5

i. Sep 6

1

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t__LLLI Sel> 7

8

9

-'.

i ........i 10

11

12

Sep 13

Fig. 8. (a) First 4 weeks of hourly rainfall accumulation (cm) for HAPEX-Sahel lOP based on the 107 gage EPSAT-Nigerraingage network. Arrowsindicate the times of the SSM/Ioverpasses;the exact UTC times are also indicated. (b) Same as (a) except for last 4 weeks of IOP.

354

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

only major events that were observed by SSM/I were the 22 August case and the first 30 August case. In both these cases, the overpasses occurred when the rainfall was subsiding. However, seven coincident rain events did occur on 22, 29, and 30 (twice) August, and 14, 15, and 29 September. The associated rainrates are summarized in Table 4. In these results, site averages for the gages are taken with respect to the 5 min intervals closest to the SSM/I overpass times. The site-averaged SSM/I rainrates are also given, along with the averaged rainrates for the rain-only pixels, and the maximum individual pixel rainrates for each of the events. In actuality, the 29 August event indicates no site-averaged rain for either the gage network or the SSM/I retrieval, although the satellite indicates a few raining pixels. Moreover, the 15 September event indicates a very small site-averaged rainrate, whereas the satellite result indicates no rain. In the case of the 29 September event, although the site-averaged SSM/I value is zero relative to the non-zero siteaveraged gage quantity, the rain-only SSM/I pixel average is non-zero. Only the 22 August and first 30 August events exhibit generally intense rainrates; all other events are light rain with only a few satellite pixels indicating moderate or heavy rain. The most salient point in this intercomparison is that, with the exception of the 15 September event, in which the site-averaged gage average is nearly zero, the satellite detects rain only on days in which the gage network indicates rain. The second key result is that the site-averaged gage and satellite results are numerically consistent in

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Fig. 8. Continued.

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Sep 27

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

355

Table 4 Summary of EPSAT-Niger raingage rainrates and SSM/I retrieved rainrates for seven IOP days in which either the gages or the satellite overpasses indicated rain

I 2 3 4 5 6 7

Event

Raingage site average

SSM/I site average

SSM/I rain-only pixels average

SSM/I maximum individual pixel

22 August 29 August 30 August- I September 30 August-2 September 14 September 15 September 29 September

1.36 0.0 1.63 0.27 0.03 0. I I 0.03

0.74 0.0 2.71 0.16 0.02 0.0 0.0

3.72 0.0 6.55 2.87 0.12 0.0 0.15

19.92 2.34 41.41 5.86 24.61 0.0 2.73

The raingage quantities represent site averages for the 5 min intervals closest to the satellite overpass times. Three satellite quantities are shown: (I) site average; (2) rain-only pixels average; (3) individual pixel maximum rainrate. (All rainrates are given in mm h-I.)

the sense that when the gage value is relatively low, the SSM/I value is also relatively low, and vice versa. The last major point is that the sum of the seven site-averaged gage values (3.43 m m h -1) is within 6% of the same sum of SSM/I values (3.63 mm h-I). Thus, in conjunction with the site-integrated rainfall for the satellite overpass times, the satellite result is in remarkably good agreement with the high-density gage result. As discussed above, this depends on an accurate specification of surface radiative boundary conditions. As a final point concerning how well the satellite measurements can ultimately represent the cumulative wet season rainfall in light of sampling limitations, it is worth noting that the average rainrate from the gages for all rain events over the entire lOP is 60

50

40

No. EstimaWs. 1296 M e a n . 0.0 Median . 27.771 M o d e . 71.16 Standard Deviation - 80.889

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20

10

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240

320

400

Fig. 9. Histogram of relative errors generating by considering 1296 satellite overpass configurations in conjunction with the EPSAT-Niger site-averaged raingage time series. A relative error is obtained by the ratio of the difference of the entire gage rainrate record from that obtained at the satellite overpass times, to the former quantity, multiplied by 100. It should be noted that such relative errors are tantamount to assuming that the satellite is making perfect measurements with respect to the raingage measurements. Thus the relative error histogram is the best possible error representation produced by infrequent sampling.

356

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

0.16 mm h -I, whereas the associated gage average considering only the coincident satellite times is 0.09 mm h -I. This is a relative error of approximately 45%. If the ensemble of satellite overpass times are shifted to all other possible time positions with the gage record (all hourly lags), which leads to 1296 realizations, and all 1296 gage averages are taken with respect to the adjusted coincident overpass times, a histogram of 1296 relative differences can be generated. The associated histogram, shown in Fig. 9, reflects the relative error probability distribution for accumulated rainfall owing to incomplete SSM/I sampling. By definition, the mean of this distribution is 0.0, which for a normal distribution would not be problematic. However, the histogram is significantly non-Gaussian, with a median of 27.8% and a mode of 71.2%. Thus, the probability that SSM/I sampling will yield near-zero relative error given perfect measurements is small, whereas the probability of the sampling interval giving rise to a significant error (greater than 20%) is large. Thus, even though the retrievals at the instantaneous satellite times can be calculated accurately based on retrieval of surface radiative boundary conditions, this does not overcome the basic underlying problem with Sun-synchronous satellites in which infrequent sampling of a largely stochastic process leads to errors much greater than those associated with the retrievals themselves.

8. Discussion and conclusions This study demonstrates the feasibility of simultaneous retrieval of surface temperature and emissivity information at multiple microwave frequencies using SSM/I measurements and radiosonde profiles of temperature and moisture as the necessary input data. The algorithm does not require information on the dielectric properties of the soil, and thus is appealing for large-scale applications, for which we have provided one example with reasonable success. To account for the 'missing equation' that would naturally arise if the method were attempted at a single overpass time, the algorithm requires multispectral measurements for a target area taken for at least two times, with enough separation to allow the land surface to evolve to different temperature states but over a short enough period that the surface emissivities will remain essentially constant. For example, the SSM/I descending and ascending node overpass times for a given day satisfy this requirement. The algorithm represents an alternative means to collect land surface temperatures over the prevailing IR techniques, although the ultimate emphasis is on emissivity, not skin temperature. In this vein, a combined split window IR-passive microwave measuring system could be used very effectively for deriving skin temperatures and microwave emissivities with more accuracy and precision than available from either the IR or microwave measurements alone. The great value of such retrievals, besides their own intrinsic definition of surface properties, is that there are various other physically based passivemicrowave retrieval problems over land surfaces (such as water vapor, cloud liquid water, and precipitation), in which radiometric boundary conditions at the surface are essential input to the inversions. In this regard, we use temperature-emissivity retrievals as input to a physically based precipitation retrieval algorithm to evaluate their utility for alternative applications. The

X. Xiang, E.A. Smith~Journal of Hydrology 188-189 (1997) 330-360

357

retrievals over the complete IOP compare very well with a set of verification measurements obtained from the dense EPSAT-Niger raingage network deployed over the experimental study area. This is a promising result, because physical retrieval over a continental background is very sensitive to the specification of radiative surface boundary conditions, particularly in light rain situations when the contrast produced by cloud scattering at 85 GHz is weak and the surface is relatively dry. Five of seven rainfall events that occurred during SSM/I overpasses throughout the HAPEX-Sahel wet period were light rain, thus this result represents an indirect validation of the combined temperature-emissivity retrieval technique. This bodes well for purely physically based rainfall retrieval methods, even though serious problems remain in conjunction with the inadequate sampling capabilities of Sun-synchronous satellites. The atmospheric profiles of moisture need to be specified reasonably accurately' associated with the SSM/I observation times, or the temperature-emissivity algorithm cannot be guaranteed to always converge to a solution for a given set of brightness temperature measurements, depending on how the convergence criterion has been defined. This was emphasized in conjunction with the retrievals which used ECMWF gridded profile data as input, in which convergence failed repeatedly over a sector of the large-scale study area. This could be a practical drawback for applying the algorithm in areas devoid of highquality moisture data, but is not a completely intractable problem, as the convergence criteria can be made less stringent for less representative moisture information (e.g. climatological profiles). The algorithm is less sensitive to the accuracy of the temperature profile input above the boundary layer, and therefore is admissible to the use of climatological information in data sparse areas. Such compromises increase the uncertainties in the resultant retrievals, but that is not inconsistent with what can be ascertained about a data sparse region. Tests we have conducted over the HAPEX-Sahel study area indicate that the use of climatological temperature data alters the temperature and emissivity retrievals by approximately 1%. The distribution of retrieved emissivities over the HAPEX-Sahel study area, and their spectrally uniform properties, based on a selection of golden days occurring towards the end and after the end of the Sahelian rainy season, are consistent with measurements reported in the literature for dry to intermediate soil moistures. The retrieved emissivities cannot be validated directly, as ground emissivity measurements at the SSM/I frequencies were not obtained during the HAPEX-Sahel experiment. However, both the qualitative and quantitative temperature validation tests on the 8 October golden day, as well as the success of the rainfall retrieval algorithm using the temperature-emissivity retrievals as input for surface boundary conditions, suggest indirectly that the retrievals are reliable. This motivates a more rigorous future validation study and the application of the algorithm to global scales.

Acknowledgements The authors wish to express their appreciation to Pierre Bessemoulin for providing the Hamdallay sounding data, to Yann Kerr and Thierry Valero for the AVHRR satellite measurements, to Pavel Kabat and Jan Elbers for the radiometric and in situ temperature

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measurements from the West-Central Supersite, and to an anonymous reviewer for pointing out an inconsistency in our initial analysis pertaining to the radiosonde data. This research has been supported by National Aeronautics and Space Administration Grants NAGW-3109 and NAGW-3970. A portion of the computing resources has been provided by the Supercomputer Computation Research Institute at The Florida State University under US Department of Energy Contract DOE-FC05-85ER250000.

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