The remote sounding, by satellite, of atmospheric temperature and humidity is an important source of data for assimilation into operational weather forecasting routines. For retrievals of these variables near the surface, wavebands with low optical depths are monitored to allow penetration through the overlying atmosphere. Brightness temperatures in these relatively transparent bands are also sensitive to the land surface emissivity and effective temperature. Inadequate understanding of these land surface emissivities is a major issue when assimilating Advanced Microwave Sounding Unit data for the land-covered portion of the globe. One approach for estimating the emissivity of snow-covered surfaces is an empirical model derived from satellite-based and land-based retrievals of emissivity for a variety of snow types. The Met Office’s Hercules C-130 aircraft flew over snow-covered Arctic terrain of northern Finland during the Polar Experiment (POLEX) of March 2001. On these flights, microwave radiometers provided microwave brightness temperatures at 23.8, 50.3, 89.0, 157, and 183 GHz. The work presented here uses these data along with a robust multiparameter optimization routine [Shuffled Complex Evolution Metropolis (SCEM-UA)] coupled to the Atmospheric Radiative Transfer Simulator (ARTS) to retrieve emissivities at the measured frequencies. These results are then used to validate an empirical model. This latter model predicts 23.8–157-GHz emissivities with an RMSE of less than 0.02 and bias of less than 0.01 when compared with data at an incidence angle of 40°. Nonmonotonic behavior in the emissivity spectrum for this campaign, reported in earlier work, is confirmed by the retrievals presented here.
a. Importance of emissivities
Determination of temperature and humidity profiles using satellite-based microwave radiometers is an important source of information for numerical weather forecasting. There have been several microwave instruments mounted on different satellites launched in the past decade that were specifically designed to retrieve temperature and humidity profiles and improved on previous profilers such as the Microwave Sounding Unit (MSU). These instruments provide nearly complete global coverage several times per day and serve the purpose of providing temperature and humidity sounding data over all regions for assimilation into NWP analyses. The four classes of instrument include the following: the Advanced MSU [(AMSU)-A and AMSU-B] instruments, launched as part of the payloads of the National Oceanic and Atmospheric Administration (NOAA)-15, -16, and -17 satellites starting in 1998 (Prigent et al. 2000; Diak et al. 1992); the Special Sensor Microwave Water Vapor Profiler (SSM/T2), first launched in November of 1991, on the Defense Meteorological Satellite Program (DMSP) F series of polar-orbiting satellites (Prigent et al. 2000); the first in a series of Special Sensor Microwave Imager/Sounder (SSMIS) instruments, launched with DMSP on 18 October 2003 (Deblonde and English 2003); and the Microwave Humidity Sounder (MHS), launched on the NOAA-18 satellite on 20 May 2005. These SSMIS, SSM/T2, and MHS instruments have channels that are only slightly different than those of AMSU-B. SSMIS is a conically scanning instrument, whereas the AMSU, SSM/T2, and MHS instruments scan across track. Satellite-based sounding provides the only data for many remote regions of the globe and thus yields very important constraints on NWP model fields. In addition, in the absence of precipitation, data quality is relatively unaffected by cloud, allowing profile retrievals where the higher-resolution infrared sounders [such as the Atmospheric Infrared Sounder (AIRS; Aumann and Miller 1995) and, in the future, the Infrared Atmospheric Sounding Interferometer (IASI; Cayla and Javelle 1995)] may be ineffective. When considered as a unit, AMSU and the High-Resolution Infrared Radiation Sounder (HIRS) were found to reduce errors in forecast sea level pressure by 20% in the Southern Hemisphere and 5% in the Northern Hemisphere, with AMSU providing the majority of the improvement (English et al. 2000).
Channels 4 (52.8 GHz) and 5 (53.6 GHz) of AMSU are thought to be particularly useful in providing information about the temperature profile in the lower to middle troposphere. Channels 16–20 of AMSU-B at 89, 150, 183.3 ± 1, 183.3 ± 3, and 183.3 ± 7 GHz, respectively, were designed for humidity retrievals. The 183.3-GHz channels have pass bands at 1, 3, and 7 GHz to either side of and all centered on the strong water vapor absorption line. However, all of these channels are, to differing degrees, sensitive to land surface emissivity, which varies with frequency and surface characteristics such as vegetation cover, soil moisture, and open-water fraction. English (1999) studied the impact of poor knowledge of emissivities on the retrieval of atmospheric humidity and temperature. It was found that for cloudy-sky temperature retrievals and clear-sky or cloudy-sky humidity retrievals over land, emissivities must be known to an uncertainty of 0.02 or better to achieve the most significant improvement in such profiles. Hence, modeling these emissivities has been a research objective for the past two decades. Simulation of emissivity of deserts, snow-covered land, sea ice, glaciers, and land areas that have significant water fraction such as wetlands or those containing large lakes and rivers are challenging (Hilton et al. 2005; Prigent et al. 2000; Mätzler 1994). The emissivity of snow-covered surfaces is particularly difficult to model because of the effects of volume scattering that phases in and out with freeze–thaw cycles (Prigent et al. 2003, 2005; Wiesmann et al. 2000). The focus of this work is the retrieval of emissivity for snow-covered land, but there is no reason that the techniques described herein could not be applied to other surface types.
b. Emissivity of snow
For ground-based and low-level airborne microwave measurements, previous analyses of emissivities of snow typically use the following equation:
Here, e is the emissivity, TB⇓ and TB⇑ are the downwelling and upwelling microwave brightness temperatures, respectively, and Teff is the effective radiating temperature of the scene (Mätzler 1994). The Teff is a weighted average of the physical temperature over the penetration depth that is a function of frequency. In addition, Eq. (1) is only valid if TB⇓ and TB⇑ are evaluated at the surface. When TB⇓ and TB⇑ are measured using aircraft from appreciable heights in the atmosphere, an atmospheric radiative transfer model is used to estimate values of TB⇓ and TB⇑ at the surface. For channels for which the atmosphere is highly opaque, TB⇓ approaches the radiating temperature of the scene Teff, leading to large errors in the estimation of emissivity because of the singular nature of Eq. (1).
There is a dearth of airborne microwave emissivity observations of snow at AMSU-B frequencies. Hewison and English (1999) describe measurements of microwave emissivity at 23.8, 50.3, 89.0, and 157 GHz. They observed deep dry snow and dense forest with snow cover (called close forest and snow in the paper) on 15 March 1997 near Sodankylä, Finland, as well as the time evolution of emissivities of wet and refrozen snow on three days in late March/early April of 1995 near Pudasjärvi, Finland. Although classified as dry snow, the snowpack was laid down during relatively warm conditions and may have contained some refrozen snow in the profile (Hewison et al. 2002). Effective temperatures were assumed to be equal to the IR brightness temperature. This approach is taken in many satellite-based retrievals (e.g., Prigent et al. 2005; Jones and Vonder Haar 1997). However, the penetration depth at microwave frequencies is variable, with typical values in dry snow ranging from 120 cm at 37 GHz to 7 cm at 220 GHz (Haggerty and Curry 2001; Ulaby et al. 1986). Because the effective temperature is determined by temperatures over approximately the penetration depth and temperature tends to increase with depth in a dry snowpack, effective radiating temperatures might be expected to decrease with frequency. Wet snow is highly absorbing and has much smaller penetration depths. Thus penetration depth and effective temperature can be indeterminate near the onset of thaw.
Hewison et al. (2002) describe an analysis of the Polar Experiment (POLEX) data that are also analyzed here. This was the first experiment in which low-level airborne measurements were made at the three channels on the 183.3-GHz water vapor line (AMSU channels 18–20). Hewison et al. (2002) find the effective temperature through the minimization of differences between modeled and measured TB⇑ for the 183-GHz channels under the explicit constraint that the emissivity is the same for the channels at 183 ± 1, 183 ± 3, and 183 ± 7 GHz. [This method is described fully in Selbach (2003).] The effective temperature retrieved is then assumed to be valid for all channels in the 23.8–183.3-GHz range. For a snow temperature that increases with depth, as expected for cold subarctic clear-sky conditions, this assumption results in an underestimation of the effective temperature at lower frequencies leading to an overestimation of the corresponding emissivities. It is also probable that the low-frequency microwaves penetrate to depths greater than the depth of the snow, leading to further difficulty in predicting the effective temperature. Assuming that 23.8-GHz microwaves penetrate approximately 1 m more than those at 183 GHz (Haggerty and Curry 2001) and assuming a typical temperature gradient for taiga snow of approximately −0.3°C cm−1 (Sturm et al. 1995), emissivity at 23.8 GHz is overestimated by 0.12. Although this estimate probably has a large uncertainty associated with it [taiga snow depths are generally 30–70 cm (Sturm et al. 1995), implying possible penetration into the ground], this calculation illustrates that the magnitude of the error associated with the assumption that Teff is independent of frequency can be very large.
There are disadvantages to the traditional approach to retrieving surface emissivity [Eq. (1)]. It says nothing about how errors in Teff affect the accuracy of the retrieval. Also, errors in the two brightness temperatures and the effective temperature contribute to the error in the emissivity in a complex fashion. Error propagation in Hewison and English (1999) takes into account uncertainty in TIR and ignores the error associated with equating TIR to Teff. This uncertainty in TIR was taken as that resulting from the spatial variability. There is clearly an uncertainty in the determination of emissivity that is a result of errors in the estimation of Teff, TB⇓, and TB⇑. Error propagation may either be done using averages over large regions or on a point-by-point basis. When large-scale averages are of interest, the uncertainty in the brightness temperatures may be estimated by the standard error:
Here, σTB is the standard deviation and n is the number of measurements of TB. In this case the sensitivity to the uncertainty in the effective temperature is more than an order of magnitude greater than that resulting from the uncertainty in brightness temperature. In any case, errors resulting from the uncertainty in Teff are at least of the same order of magnitude as those resulting from uncertainties in TB⇓ and TB⇑, and thus the former should not be neglected. Another disadvantage of the traditional approach is that the calculation of emissivity using Eq. (1) also requires TB⇓, which can be difficult to model—in particular, in cold dry conditions (Hewison 2005). Last, in previous work with this dataset, because Deimos (described in section 2a) did not measure TB⇓ and TB⇑ simultaneously, TB⇓ at 23.8 and 50.3 GHz was obtained using a radiative transfer model, whereas TB⇓ at the AMSU-B frequencies was measured with the Microwave Airborne Radiometer Scanning System (MARSS) instrument. Hewison (2005) compared modeled and measured TB⇓ over a full range of northern latitudes throughout the troposphere. It was found that, under cold dry conditions, modeled TB⇓ underestimated measured values by ≤20 K for measurements near the bottom of profiles. This result emphasizes the value of eliminating determination of TB⇓ from the retrieval process.
c. Outline of current work
In this work, a method is presented that overcomes some of the weaknesses of the traditional approach. The method combines the knowledge of radiative transfer contained in the Atmospheric Radiative Transfer Simulator (ARTS; Buehler et al. 2005a) with the global optimization routine known as the Shuffled Complex Evolution Metropolis (SCEM-UA; Vrugt et al. 2003) routine. Temperature TB⇑ contains contributions from the thermal radiation from the surface, the reflected component of TB⇓, and the thermal radiation from the atmosphere underneath the aircraft. Because TB⇑ is an output and the emissivity e and Teff are input parameters of ARTS, retrieval is accomplished as a search for the e and Teff that best match the model to the measurements of TB⇑. The use of SCEM-UA allows the retrieval of the surface emissivity as well as the uncertainty in the retrieval Δe from a combination of measurement error and the uncertainty in Teff. This procedure eliminates requirements for measured TB⇓, which contains little additional information regarding the surface emissivity.
Central to this study are the measurements, the model, the optimization routine, and the retrieval method, all of which are described below.
a. Aircraft campaign
The measurements used in this study were gathered during the POLEX airborne campaign over Sodankylä between 1040 and 1240 UTC 17 March 2001. A radiosonde was released at 1200 UTC from the Sodankylä airfield, which was centrally located in the flight pattern at 67°23′N, 26°37′E. The Met Office Hercules C-130 aircraft provided the other basic meteorological and radiation data. The profile used in this study was flown from 1246 to 1313 UTC over the study area. Some important instruments on the C-130 included the microwave radiometers MARSS and Deimos, which are described below; a Heimann KT 19.82 infrared radiometer with a fixed downward field of view; navigational equipment that provided information about the position and attitude of the aircraft; a General Eastern chilled-mirror hygrometer; and other in situ instruments that provided, among others, measurements of air temperature, pressure, and humidity content. More information about the aircraft instrumentation may be found in Selbach (2003) and Taylor et al. (2003).
Seven runs were flown at a speed of approximately 92 m s−1 along lines of constant longitude between 67° and 67°45′N and between 26°30′ and 27°E. Aircraft altitude was maintained at approximately 431 m above mean sea level. Measurements used in this study included air dry-bulb and wet-bulb temperatures, static air pressure, radar measurement of height, upwelling IR, and upwelling and downwelling solar radiation. Deimos and MARSS are the onboard passive microwave radiometers. Deimos provides horizontally and vertically polarized brightness temperatures at 23.8 and 50.3 GHz at downward viewing angles of 0°, 5°, 15°, 25°, and 35° along track with a repeat every 3 s. From the dual-polarization information, mixed polarization brightness temperatures were calculated using
where TBV, TBH, and TBM are the vertically, horizontally, and mixed polarized brightness temperatures, respectively, and θ is the incidence angle. Each view is integrated for 50 ms, and the beamwidth is 10° [full width at half maximum (FWHM)]. MARSS measures mixed polarization brightness temperatures at the AMSU-B frequencies at upward and downward viewing angles of 0°, 10°, 20°, 30°, and 40°, repeating every 3 s. The channels have the same frequencies as AMSU-B, except that the 150-GHz channel 17 of AMSU-B is replaced in MARSS with a 157-GHz channel. Because these channels are both in a window region this difference should not have a dramatic effect on the brightness temperatures. The polarization of the MARSS 89-GHz channel 16 has the same mix with viewing angle as does AMSU-B. The polarization angle of the other channels of MARSS rotates with scan angle from approximately horizontal in the forward view to approximately vertical in the backward view (Hewison 2001). The integration time is 100 ms, and the FWHM beamwidth is 6.2° for the 183-GHz channels, 11° for the 157-GHz channel, and 11.8° for the 89-GHz channel. Both radiometers perform a calibration during each scan using hot and cold blackbody targets. In the analysis that follows, retrievals made at 40° have used the Deimos data observed at 35° and MARSS data at 40°. Further information about these radiometers may be found in Hewison (1995) and McGrath and Hewison (2001). All of the core instrument and radiometric data are quality controlled to remove spikes more than two standard deviations from the mean and to remove data from situations in which instruments have poor performance. For example, when the cold and hot calibration targets in the microwave radiometers have temperatures that are too close to each other, resulting in poor signal-to-noise ratios, such data are removed.
Emissivity retrievals were performed for the average scenes “all,” “open snow,” and “close forest and snow.” These scenes are similar to the surface types used by Hewison et al. (2002) and Hewison and English (1999). However, here averaging is performed before emissivity retrieval whereas in the previous work the averaging was done after retrieval with Eq. (1). The all scene is composed of averages from all data that make it through the quality-control postprocessing routines. The open-snow and close-forest-and-snow scenes are constructed from those data with 0.3–3-μm-wavelength albedo greater than 0.75 and less than 0.25, respectively. These thresholds are the same as those defined in Hewison and English (1999). The mean and the standard deviation of the albedo in the open-snow case were 0.81 and 0.02, respectively; those for the close-forest-and-snow case were 0.23 and 0.01.
For each scene, average values of surface elevation, instrument height (from radar), IR brightness temperature, and the microwave brightness temperatures were calculated. These values are presented in Table 1. It is important to remember that this scene averaging relies on the linearity of contributions of brightness temperature from the thousands of fields of view that make up the scenes. It is felt that this approach more realistically simulates the type of average quantities seen by the AMSU-B instrument’s 16-km resolution than do point calculations using Eq. (1). Note that the total area sampled by the footprint of the microwave radiometers on the aircraft was approximately 6% of the spatial area of an AMSU-B pixel at nadir.
Clear-sky conditions were encountered throughout the entire sortie with the exception of a few very small and scattered cumulus at the south end of the runs that were not in the field of view of any of the radiometers. Table 1 outlines the mean conditions as well as the variability encountered during the flight for the three scenes studied here. It is seen from this table that, although the atmospheric conditions are consistent for the three scenes, the surface elevation and temperature for the open-snow and close-forest-and-snow scenes differ considerably from average (represented by the all scene). The open-snow scene represents higher, colder surfaces, and the close-forest-and-snow scene represents lower, warmer surfaces. This variation in surface temperature between the scenes is partially an artifact of the albedo cutoffs used to define the scenes as well as that resulting from elevation differences in a thermally stratified atmosphere.
ARTS is a readily obtainable, user-friendly, line-by-line radiative transfer scheme developed as a result of a collaboration between the University of Bremen and Chalmers University of Technology (Buehler et al. 2005a; Eriksson et al. 2005). It is applicable over the frequency range from 1 GHz to 1 THz and is highly flexible, allowing the selection of numerous line profiles and data from several spectroscopic databases. It allows the simulation of ground-based or satellite measurement geometries at arbitrary viewing angle. Complete documentation of ARTS can be found in its user’s guide (Buehler et al. 2005b). For this study, the Rosenkranz (1998) water vapor and the Rosenkranz (1993) molecular oxygen and nitrogen absorption models were selected within ARTS. These models represent both the continuum and line absorption at submillimeter wavelengths. Transmissivities for the total column of atmosphere and beneath the aircraft have been calculated using ARTS and the observed profile of temperature and humidity for the three scenes (Table 2).
SCEM-UA is an efficient global optimization routine that also evaluates the uncertainty in parameter estimates. The routine requires an estimation of the physically determined bounds on the parameters, an estimate of the measurement error, and a set of observed values to be matched by the routine. When coupled to a physical model such as ARTS, SCEM-UA searches within the parameter limits for parameter sets that produce model outputs that match the observations within the estimate of measurement error. It has been found to reduce significantly the number of such trial parameter sets before convergence through complex shuffling, competitive evolution, controlled random search, and the Metropolis algorithm. In addition, histograms of retrieved parameter values give measures of the parameter uncertainty (Vrugt et al. 2003).
d. Retrieval method
In this study, the profile of atmospheric temperature and humidity measured at the end of the flight was used as the lower part of the input profiles used in ARTS. The portion of the profile needed above the highest flight level (24 400 ft or 7440 m) was constructed from the 1200 UTC (1400 LT) radiosonde ascent at Sodankylä and, above the highest level of the radiosonde ascent, the subarctic winter scenario provided with the ARTS installation. The humidity profiles were measured using a General Eastern 1011B thermoelectric hygrometer (GE) and the total water content (TWC) probe. The main problem with the GE is its slow response, but it is generally considered to be accurate to 0.25 K for the dewpoint. This slow response is overcome by calibrating the fast-response TWC to it during straight and level runs. Time series of 183.3 ± 1 GHz downwelling MARSS brightness temperatures, air temperatures, and dewpoint temperatures measured during the straight and level runs were examined visually for trends. No such trends were detected, indicating that the atmosphere changed little during these runs. It was thus assumed that the profile temperature and humidity taken at the end of the runs is representative of the state of the atmosphere during the previous 2 h.
ARTS was coupled to SCEM-UA, allowing the retrieval of (mixed polarization) e and Teff through the minimization of the difference between the modeled and the measured TB⇑. Each such retrieval was obtained using 10 000 function evaluations for each of the seven frequency bands. SCEM-UA requires an estimate of the uncertainty in the measurements. Because the measurements used to drive the retrievals are averages over nonoverlapping scenes, an appropriate error estimate is the standard error of estimation, which accounts for the scene variability and the noise error of the instrument, calculated using Eq. (2). The number of measurements n varied by scene between 30 for close forest and snow and 1000 for all. Typical values of measurement error ΔTB were found to be less than or approximately equal to 1 K. More specific information about the upwelling brightness temperatures measured in this campaign is presented in the bottom half of Table 1.
For each scene, input for ARTS includes the average IR brightness temperature, average radar height, and temperature and humidity profiles. The average TB⇑ are used as the observations that SCEM-UA needs to match in its search over the (e, Teff) parameter space. The intervals for this search are e ∈ [0, 1] and Teff ∈ [TIR, 273.15 K]. The bounds on the effective temperature are the result of a conservative estimate on the extremes in the snow temperature profile that the radiometer sees. In Arctic winter in general and in the Sodankylä area in particular the air–snow interface is the coolest part of the snowpack because of longwave radiative cooling caused by high solar zenith angles and stable atmospheric conditions (Koivusalo et al. 2001; Sturm et al. 1995). During the Land–Surface–Atmosphere Interactions in a Wintertime Boreal Landscape experiment (WINTEX) of 1997, above-freezing temperatures in the top 1.5 m of soil or in the snow did not occur until mid-May. Prior to this time, the temperature increased with depth until the onset of thaw in the top of the snowpack. In the layers undergoing thaw, the temperature was a nearly constant 273.15 K with depth [author’s plot of the soil temperature data of Heikinheimo et al. (2001)]. Thus, the effective temperature is nearly always between TIR and 273.15 K for Arctic snowpacks in the absence of melt ponds. It is expected that, with ground measurements of the density, particle size distribution, and moisture and temperature profiles of the snowpack, numerical models such as the Snow Thermal Model (SNTHERM—a one-dimensional mass- and energy-balance model of snow physics; Jordan 1991) and the Microwave Emission Model of Layered Snowpacks (MEMLS; Wiesmann et al. 2000; Wiesmann and Mätzler 1999) could be used to reduce this range in effective temperature.
The infrared emissivity used to retrieve surface temperature from infrared brightness temperatures was determined from a dataset supplied by Z. Wan (1996, personal communication). The mean emissivity found over the acceptance window of the Heimann KT 19.82 radiometer was 0.983 ± 0.001.
3. Results and discussion
a. Comparison with models and previous method
Figure 1 shows examples of retrieved emissivity histograms for the scene labeled as all. The root-mean-square error (RMSE) between the measured and modeled microwave brightness temperatures for the ARTS run with mean values of these retrieved emissivities was 0.07 K, indicating that SCEM-UA converged to solutions with, on average, low model error. Note that each of the retrieved emissivity points depicted in Fig. 1 and each of the effective temperature points in Fig. 2 are from converged optimization runs in ARTS/SCEM-UA for the average brightness temperatures and other meteorological conditions that define the all scene as discussed in the previous section. The retrieved emissivities are basically normally distributed with standard deviations of approximately 0.02 for the window channels at 23.8, 50.3, 89.0, and 157 GHz. The distributions are much broader for the 183.3-GHz humidity sounding channels with the uncertainty of emissivity increasing with increasing opacity or proximity to the 183.3-GHz line center. This is as expected because the signals in these channels are less sensitive to the surface and more sensitive to the underlying atmosphere as seen by the smaller values of the relevant transmissivities in Table 2. Figure 1h shows the emissivity spectrum to be nonmonotonic with the minimum observed emissivity at 157 GHz. Note also that the emissivities in the bands at 183.3 ± 7 and 183.3 ± 3 GHz are within one standard deviation of each other. The mean of the channel at 183.3 ± 3 GHz is within the standard deviation of the channel at 183.3 ± 1 GHz, but the reciprocal is not true. This result could be due to sampling error in the water vapor profile because this profile was only measured down to 50 ft (∼15 m) above the surface at one time. Extrapolation of this profile in space and time is an important source of possible error, and is particularly important for retrieval using the channel at 183.3 ± 1 GHz. At this channel, the transmissivity of the atmospheric layer below the aircraft is 0.78, indicating that the accuracy of the measured profile and the model is crucial here.
Figure 2 shows the corresponding retrieval of effective temperature. Note that parameter interaction in ARTS allows emissivity to adjust inversely with effective temperature, which means that a low value of effective temperature is compensated for by a high value of emissivity such that the optimization routine cannot differentiate between many (e, Teff) parameter sets. Thus, the effective temperature fills its original uncertainty bounds, indicating that determination of effective temperature must be obtained by other means. The uncertainties in the emissivities shown in Fig. 1 are mostly due to these fundamental uncertainties in the corresponding effective temperatures. However, the range of retrieved emissivities is much smaller than the initial range, indicating that much is learned about the emissivity in the retrieval process.
The relationship between these uncertainties in e and Teff can be studied by varying the upper and lower bounds on effective temperature and noting the change in the uncertainty in emissivity Δe. Figure 3 shows the results of such a numerical experiment. Here retrievals are performed at 23.8 GHz for Teff ∈ [TIR, Tmax], where Tmax takes the values TIR + 1 K, TIR + 2 K, TIR + 3 K, . . . , 273.15 K. The mean retrieved emissivity and standard deviations (as error bars) are plotted as a function of Tmax in Fig. 3a. The histograms of retrieved emissivity for the smallest and largest ranges in Teff are depicted in Fig. 3b. Note that as Tmax decreases—decreasing the range in and mean of Teff—the mean emissivity increases and Δe decreases. This decrease is nearly linear with some hint of quadratic curvature as the range in Teff approaches small values as seen in Fig. 3c. The Teff ∈ [TIR, TIR + 1 K] case—that with the smallest uncertainty in effective temperature—depicts the kind of emissivity retrieval one would expect if all uncertainty in the retrieval were due only to the measurement errors in TB⇑ and TIR. The only way to achieve this kind of accuracy in the effective temperature estimate is through more complete observations and modeling of the snow and soil underneath. Measurements of snow density, temperature, moisture content, and particle size distribution as well as how these parameters vary in the vertical are necessary for a full treatment of the radiative transfer in the snowpack. The retrieved emissivities and their standard deviations for nadir and 40° incidence are displayed in the bottom half of Table 3.
One major objective of this work is to evaluate the validity of Weng and Yan’s snow emissivity scheme (Weng and Yan 2003; B. Yan et al. 2006, personal communication) through comparison with the retrievals using ARTS/SCEM-UA. Weng and Yan’s model (WYM) uses the data documented in Mätzler (1994) and taken with ground-based microwave radiometers at 4.9, 10.4, 21, 35, and 94 GHz in Switzerland. An AMSU snow emissivity database is used to fill in the spectral resolution in the 24–89-GHz frequency range and extend the spectra out to 150 GHz (Yan and Weng 2003). From this database of combined AMSU and ground-based emissivities, polynomial fits to 16 snow types are determined. Of particular interest to this study, the 183.3-GHz emissivity is taken as being equal to that at 150 GHz, which one can see from Fig. 1 is not supported by the data in this study. However, the model uses AMSU measurements in the five window channels at 23.8, 31.4, 50.3, 89.0, and 150 GHz as well as TIR to identify the snow type to use in a specific pixel. This model is precisely the type of emissivity model needed in data assimilation because it is fast and uses relevant data about the surface that is derived directly from AMSU measurements.
Figure 4 shows comparisons of the Weng and Yan emissivities and those retrieved using ARTS/SCEM-UA for each of the scenes described above. The mean and standard deviations of the ARTS/SCEM-UA-retrieved emissivities as well as the RMSE and bias (WYM minus ARTS/SCEM-UA) in emissivity for each of the scenes are presented in Table 3 for nadir and 40° incidence. The RMSE and bias in Table 3 are calculated both using all five channels plotted (23.8, 50.1, 89.0, 157, and 183.3 ± 7 GHz) and without the channel at 183.3 ± 7 GHz. Examination of Table 3 and Fig. 4 indicates that WYM works best when the channel at 183.3 ± 7 GHz is disregarded in the statistics because it underestimates 183-GHz emissivities for all three scenes. This result is not too surprising because 183.3-GHz emissivities are obtained in WYM by equating them to the values at 150 GHz and are not based on data. In general, the RMSE taken without the data at 183.3 ± 7 GHz is less than 0.02 and is smaller for the 40°-incidence-angle data. Thus, the model is accurate to within the uncertainty in the retrieval method for the frequencies studied here up to 150 GHz.
In Fig. 4 retrieved nadir emissivities are also shown from Hewison and English (1999) and Hewison et al. (2002) for comparison with the ARTS/SCEM-UA retrievals. Neither of these investigations recorded an average emissivity retrieval equivalent to the all scene discussed here. However, Fig. 4a shows for comparison the Hewison and English (1999) retrievals, labeled as H99, and those of Hewison et al. (2002), labeled as H02. The dataset used for the H99 analysis has not been used for ARTS/SCEM-UA retrievals but is included for comparison. It is seen that the ARTS/SCEM-UA retrieval for the all scene appears to mimic the average behavior of the surface types identified in the earlier works. To get more specific, in Figs. 4b and 4c retrievals for open snow and for close forest and snow are shown for the two previous investigations alongside the current retrievals. Although there are substantial differences in the retrieval methods, including whether averages are performed before or after the retrieval process, the ARTS/SCEM-UA retrievals fall well within the error bars of the H02 retrievals for open snow and close forest and snow except for the 183.3-GHz result. Note that the difference may be partly due to the use by H02 of a radiative transfer model to determine TB⇓ for use in Eq. (1). This 183.3-GHz result may also be different because H02 lumps the three 183.3-GHz channels together in a complex manner that gives equal weight to the brightness temperatures in the three 183.3-GHz channels. The channel at 183.3 ± 7 GHz might have been given greater weight because it is most sensitive to the parameter of interest, the emissivity. In this work, the three emissivities for the 183.3-GHz channels are retrieved independently, allowing the discussion in section 3b below. The H02 and the ARTS/SCEM-UA emissivities for close forest and snow are slightly more offset than the open-snow results, but there is still remarkably close correspondence. This small offset may be partly due to small differences in the data quality control and data analysis of the profile as well as the modeling of atmospheric radiative transfer.
As discussed in Hewison et al. (2002), the H99 emissivities have a different spectral behavior than those of H02. It is believed that this may be due to the evolution of differing snowpack structures at the different sites and times of the two campaigns. Some of the differences between the resulting emissivity spectra are due to the different methods used to retrieve Teff. In H02, Teff was retrieved from the 183.3-GHz channels, whereas H99 used TIR instead of Teff in Eq. (1). There was typically an 18-K difference between TIR and Teff as reported in Hewison et al. (2002).
b. Behavior at 183.3 GHz
Common to H02 retrievals and those using ARTS/SCEM-UA is the nonmonotonic behavior of the emissivity spectrum with an increase in emissivity between 157 and 183.3 GHz. This behavior occurs for all of the scenes presented in this work as well as the following surface types in H02: glacier, first-year ice, and multiyear ice. An increase in emissivity with frequency for sea ice between 150 and 220 GHz was also observed by Haggerty and Curry (2001). As discussed in Hewison et al. (2002), this behavior cannot be represented using the Fast Emissivity (FASTEM) model presented in section II of Hewison and English (1999). FASTEM assumes Debye relaxation of the permittivity with frequency and specular reflectivity given by the Fresnel formulas. The model then treats large-scale roughness by mixing polarizations as in Wang and Choudhury (1981) and small-scale roughness by using the frequency dependent factor of Choudhury et al. (1979).
In the current study, the author has attempted to reproduce this emissivity spectrum using MEMLS with one, two, and three layers by coupling it to SCEM-UA. MEMLS has the following parameters for each layer: density, temperature, liquid water content, correlation length, and thickness. The correlation length is taken as being proportional to snow particle diameter in Wiesmann et al. (2000), and the actual procedure for its calculation from thin sections is described in Wiesmann et al. (1998). Because there are no snow-profile or depth data available during the campaign, all five parameters in each of the one–three layers were searched in 30 000 function evaluations in SCEM-UA. Although it was believed that there was not enough information in the five observations of emissivity to allow optimization of these 15 parameters, the simulations were carried out to see whether MEMLS could reproduce the spectrum with anywhere from one to three layers and 5 degrees of freedom (parameters) per layer with which to play. In none of these optimization runs was the upturn between 157 and 183.3 GHz well represented at the same time that the emissivities at lower frequencies were matched. The inability of MEMLS to simulate this spectrum is to some extent unsurprising because this model was developed with radiometric measurements in the 1–100-GHz portion of the microwave spectrum. The inability of MEMLS to represent the retrieved emissivity spectrum points to the need to extend the radiometric measurements to include the 100–200-GHz portion of the spectrum, allowing an extension of models such as MEMLS to these higher frequencies.
A retrieval method has been developed that combines the current understanding of microwave atmospheric radiative transfer as embodied in ARTS with the robust global optimization routine SCEM-UA. This method uses an estimate of the mean and uncertainty of effective temperature to retrieve distributions of emissivity for use in satellite-based microwave sounding of the atmosphere. The retrieved uncertainty is a measure of the combined effects of measurement error and uncertainty in effective temperature as opposed to scene variability used in previous studies. In the data studied here, the dominant uncertainty is due to the effective temperature, but the method can easily be applied to datasets with tighter constraints on the radiating temperature, allowing the measurement error to contribute a greater fraction of the uncertainty. The technique explicitly takes the absorption and emission of the underlying atmosphere into account in the retrieval of emissivity.
The technique is applied to three snow-covered scenes derived from the airborne data acquired during the POLEX campaign over Sodankylä in March of 2001. The retrieved emissivities are compared with retrievals using the same data but different techniques (Hewison et al. 2002) as well as the empirically based model of Weng and Yan (2003). The latter is poor at predicting the 183.3-GHz emissivities but predicts those for 23.8–157 GHz to an RMSE of 0.014 and a bias of 0.001 for the mixed scene, which most closely approximates that which is seen in the 16-km footprint of AMSU. Retrieved 183.3-GHz emissivities for both ARTS/SCEM-UA and Hewison et al. (2002) are higher than the 157-GHz emissivities, whereas the rest of the spectrum is monotonically decreasing with increasing frequency. More work is necessary to determine the conditions for which this concavity in the spectrum occurs and to extend current snow emissivity models to the 100–200-GHz range.
The author especially thanks Jonathan P. Taylor for his editorial and scientific advice. The experiment was partly funded under the Framework Programme V—Improving the Human Research Potential and Socio Economic Knowledge Base under the Transnational Access to Major Research Infrastructures from the CAATER programme, Contract NPRI-CT-1999-00095. The author thanks the staff of the Norwegian Meteorological Institute (DNMI) for their support and hospitality in Tromsø. The author acknowledges the dedication and support of the aircraft’s ground and air crew and the scientists and technicians of the Meteorological Research Flight.
Corresponding author address: R. Chawn Harlow, Met Office, FitzRoy Road, Exeter EX1 3PB, United Kingdom. Email: email@example.com