Development of a modified two-scale electromagnetic model simulating both active and passive microwave measurements: Comparison to data remotely sensed over the ocean



[1] Spaceborne microwave remote sensing allows the determination of oceanic and atmospheric parameters. Operational payloads such as ERS-1 and ERS-2 and TOPEX/Poseidon as well as missions such as Jason (from NASA–Centre National d'Etudes) or Envisat (from the European Space Agency), have contained or contain paired microwave instruments looking at the nadir direction. This combination consists of microwave radiometers and a radar-altimeter. For the frequencies chosen in oceanographic satellite payloads, the active mode signal is mostly dependent on the surface state through its reflectivity and thus used for the near-surface wind speed retrieval. The active mode can also be attenuated by the atmosphere. On the other hand, the passive mode is related to the surface emissivity and the atmospheric radiation through the radiative transfer equation. Until now, the oceanic and atmospheric parameters have been retrieved separately, the latter being used to correct radar measurements. However, the reflectivity and the emissivity of a target are not independent quantities; hence the synergistic use of these two kinds of microwave measurements should allow one to improve the retrieval quality of the sea and atmosphere parameters. For this purpose, a unified model has been developed for the simulation of both the microwave backscattering coefficient σ° (active measurement) and the microwave emissivity, an important factor for the brightness temperature TB simulation, for every configuration (incidence angles, frequency, polarizations), taking into account the fact that the reflectivity and the emissivity are complementary to unity. The atmospheric absorption is computed following a widely used model from the literature. This paper gives a description and a first attempt of validation of this approach through a comparison with real data. The performance of the model is assessed by comparing the simulations to both brightness temperatures and backscattering coefficients from ERS-1 and TOPEX/Poseidon's instruments during the SEMAPHORE experiment, over a two-month period.

1. Introduction

[2] The surface effects on passive brightness temperatures are far from being negligible [Wilheit and Chang, 1980; Lojou, 1990] and the atmospheric effect on the active backscattering coefficients σ° (especially in Ku band) is well proven now [Walsh et al., 1984; Goldfinger, 1980]. The emissivity, which is necessary for brightness temperature simulation, and the reflectivity are not independent. Therefore, it is appropriate to follow a unified approach in order to calculate the brightness temperatures together with the backscattering coefficients, for any passive and active microwave spaceborne instruments looking at the same scene. An electromagnetic model has been developed at UCL (Université Catholique de Louvain) by Guissard et al. [1992] for the simulation of microwave measurements in any spaceborne configuration (passive radiometers and active scatterometers/altimeters). This model, hereafter called the UCL model, has been improved by introducing recent results in microwave characterization of sea water and atmospheric constituents. The atmospheric water vapor absorption is computed following the Liebe et al. [1993] model. The dielectric constant of salt sea water follows the Guillou et al. [1998] model while the sea surface description is made using both the Lemaire et al. [1999] full-range spectrum and the widely used Bjerkaas and Riedel [1979] spectrum. The foam effect is also included in the UCL model by using the foam coverage model of Monahan and Lu [1990] and the foam emissivity model of Droppleman [1970]. A brief description of the various components of this model is presented in the next section, before an attempt to validate it is undertaken. This is performed by comparing the simulations in passive and active modes to coincident satellite measurements. Comparison with the ERS scatterometer geophysical model functions (GMF) and data has also been undertaken [Lemaire et al., 1999] and is shown here for completeness.

2. Description of the UCL Model

[3] The main advantage of the physical model is that it takes consistently into account the interdependence between passive and active measurements, at the level of electromagnetic quantities. The aim of the direct model is to calculate the brightness temperatures and the backscattering coefficients as they would be measured by a spaceborne radiometer/radar pair. The surface emissivity eP is a quantity that ranges from zero to unity and is a function of surface roughness, polarization P, incidence angle θ, complex dielectric constant, frequency and physical temperature [Peake, 1959]. If the surface has an absolute temperature Ts, the apparent temperature measurable by a radiometer antenna is Tapp = eP × Ts. In general, an object both emits and reflects thermal radiation. Under thermodynamical equilibrium, the emissivity eP and the reflectivity ΓP of an observed target are related by

equation image

This relationship defines the link that exists between radar and radiometric measurements. Indeed, this appears in the model through a common quantity needed to calculate both kinds of measurements. This common quantity is the bistatic scattering coefficient equation image that yields the scattered energy from an incident direction along equation image in polarization P toward the scattered direction equation image in polarization Q [Sobieski et al., 1991]. For an altimeter configuration as for any monostatic radar, the measurement yields the backscattering coefficient σPQ°, where the incidence and the scattering angle are identical. Since the polarizations are also taken identical in nonpolarimetric radars, σ° is then a particular case of the bistatic scattering coefficient computation. For radiometric configurations, the brightness temperature TBP measured by a spaceborne radiometer is given by the radiative transfer equation [Guissard and Sobieski, 1987, 1994]. The integration of equation image over the upper hemisphere of the incident directions equation image yields ΓP in the scattering direction equation image by

equation image


equation image

and P and Q correspond to orthogonal polarizations (generally vertical V and horizontal H linear polarizations). The radiative transfer equation yields, in absence of scattering,

equation image

where equation image is the contribution of the atmosphere along the upwelling-path, equation image is the contribution of the sea surface, Ts its temperature and equation image its emissivity toward direction equation image. equation image represents the integrated scattering of the downwelling atmospheric temperatures equation image by the sea surface toward direction equation image. equation image is the transmittance of the atmosphere along the scattering direction equation image. The emissivity eP is computed using equations (2) and (1). For radar measurements, the total attenuation of the atmosphere is calculated in order to take into account the two way path attenuation of the backscattering coefficients.

2.1. Surface Model

[4] The surface model uses the bistatic scattering coefficients to compute both the backscattering coefficients and the emissivity. A two-scale model is used for the scattering by the large and small features of the foam-free ocean surface. This two-scale model is subject to several corrections proposed in the literature because the large-scale structure (gravity waves) and the small-scale one (capillary waves) are not totally independent. For a foam-free surface:

equation image

The zero-order term is the scattering coefficient for the large-scale surface, based on the Kirchhoff solution. It is proportional to the local reflection coefficient and to the wave slope probability density function (p.d.f.) TSF [Sobieski et al., 1991]. This term is weighted first by a shadowing function accounting for the probability that a point of the surface is both illuminated and visible. Then, it is corrected by multiplying the Fresnel reflection coefficient by a factor less than unity that takes into account the presence of ripples on the large-scale waves [Guissard et al., 1992]. A second correction for the zero-order term is given by the same authors to account for multiple scattering effects. This correction applied to the dielectric rough sea surface, is based on evaluating the reflectivity ΓP for a perfectly conducting surface using equation (2) that should be equal to unity. The first order term has the form of the convolution of two quantities; its expression is

equation image

where ⊗ denotes the convolution operator. The first of these quantities is the small-scale part of the surface vertical displacement spectrum γ(Kx,Ky), where Kx and Ky are the rectangular components of the surface wave vector equation image. The second quantity is the product of a field function |HPQ|2 depending on the geometry and on the electrical properties of the underlying medium through the permittivity ϵ, the large-scale slopes pdf TSF and the shadowing function P1. The quantities vx, vy, vz are the components of the vector equation image, where k is the electromagnetic wavenumber. α′ = − Kx/vz, β′ = − Ky/vz and the convolution must be evaluated at Kx = vx, Ky = vy. The complete equation (6) simply expresses that a whole range of short waves can be correctly oriented on the tilting large waves, to produce a constructive interference at the Bragg wavelength. Explicit expressions for this calculation are given by Guissard and Sobieski [1987]. The choice of the sea surface wave spectrum equation image is quite important for the simulation of brightness temperatures and backscattering coefficients. Two surface spectra have been tested in this study. The first one is the Bjerkaas and Riedel [1979] composite spectrum, widely used in radar techniques and based on a combination of various spectral models available in the literature. This spectrum is assumed valid for fully developed seas only. It depends only on the sea surface wind speed input. In the next section, we perform comparisons between the simulations based on this spectrum and two months of field and satellite data during the Semaphore experiment. Such a long period obviously includes different sea states. Therefore, a second spectrum developed by Lemaire et al. [1999] for both fully and not fully developed sea cases has been tested. This spectrum depends for the gravity part on the fetch x (or wind action distance) and the significant slope SS, defined as the ratio of the height standard deviation to the wavelength of the dominant waves. For the small capillary-gravity waves and capillary waves, this spectrum depends only on the wind stress friction, which could be related to the wind speed at a reference altitude by a logarithmic law. Finally, the dielectric permittivity ϵ of the sea water is taken following the Guillou et al. [1998] model, based on recent laboratory measurements in the microwave range.

[5] The sea surface emissivity model could not be complete without including the foam effect. The foam has been modeled by Droppleman [1970] as a porous dielectric layer. Two quantities are necessary for its characterization: the foam coverage and the foam emissivity. Several authors have studied these surface features and various expressions are proposed in the literature [Smith, 1988; Droppleman, 1970; Stogryn, 1972; Monahan and Lu, 1990; Williams, 1971; Monahan and O'Muircheartaigh, 1986]. Monahan and Lu's model is the only one which makes the difference between the active and the passive effects of the foam, which is appropriate in the case of our study since we are developing a synergistic model for active and passive modes. Experimental results showed indeed that the effect of the different wind-induced foam (whitecaps, foam, etc.) is different if you sense with active or passive instruments. The paper by Monahan and Lu [1990] reflects this difference by two foam coverage formulas, one for passive and the other for active instruments. The effect of the foam on active measurements is in general very low, compared to the uncertainty of the measurement itself. In the passive mode, we need a much more accurate measure. In this case, the foam could impact significantly the brightness temperature. Regarding the foam emissivity models, one has to note that Stogryn's model is purely empirical and could be strongly dependent on the database used for its development. It is valid only by extrapolation to 50 GHz. Droppleman's model has the advantage of being physical and consistent with the statistical measurements. Since we are developing a physical model, we have therefore preferred to use Droppleman's model for the foam emissivity. To include the foam contribution, the surface is separated into a foam-free part and a completely foam-covered part with uniform distribution. The bistatic scattering coefficient is then expressed as

equation image

where P denotes horizontal H or vertical V polarization. (σP°)0 and (σP°)1 are the scattering coefficients due to large-scale and small-scale structures, respectively. (σP°)F is the scattering coefficient of 100% foam-covered sea surface. F is the effective fractional foam coverage (considered between zero and unity). (σP°)F is calculated using the same method as used for the zero-order term in which the reflectivity of the water has been replaced by the foam reflectivity [Ulaby et al., 1981].

2.2. Atmospheric Absorption Model

[6] Many features of the atmosphere affect microwave propagation: attenuation of the signal, phase shift, thermal noise and, in some cases, backscattering from atmospheric particles. These effects depend on the components of the atmosphere: water vapor, liquid water and other hydrometeors such as rain, snow, etc. In the UCL model, oxygen and water vapor absorption spectra include a number of distinct lines, following the results of Liebe et al. [1993]. The scattering by rain or snow is not modeled in the UCL model. In the following sections, we eliminate the cloudy points from the comparison data set.

3. Description of the Instruments

[7] The purpose of the European Remote Sensing (ERS) program is to study the earth environment (sea, atmosphere, etc.). It is composed of two satellites: ERS-1, launched on July 16 of 1991, and ERS-2, launched on April 21 of 1995. These two satellites are similar except for some upgrades on ERS-2 instruments and the new GOME instrument, dedicated to the ozone layer study. In particular, the two microwave radiometers MWR1 and MWR2 are exactly the same with two channels for the near nadir viewing at 23.8 GHz and 36.5 GHz (vertical polarization), a complete description of the ERS-1 radiometer is given by Bernard et al. [1993]. They have been designed to determine the altimeter path delay, due to the tropospheric humidity (for better accuracy in determining the sea surface topography). The calibration of the brightness temperatures of the ERS-1 radiometer (MWR1) and the validation of its geophysical products were performed by Eymard et al. [1996]. ERS-1 and ERS-2 contain also a nadir looking radar (altimeter) operating at frequency 13.8 GHz.

[8] The TOPEX/Poseidon satellite, launched in August of 1992, includes a three channel nadir viewing radiometer called TMR, operating at frequencies 18, 21 and 37 GHz in vertical polarization. It is also designed to correct the water vapor-induced path delay of the altimeter signal. The calibration of the brightness temperatures was done by Ruf et al. [1994].

[9] The US-French mission TOPEX/Poseidon, carry on also two altimeters, functioning in the C and Ku bands. The dual-frequency altimeter TOPEX operates at 5.3 GHz (C-band) and 13.8 GHz (Ku band) while Poseidon operates at 13.8 GHz only.

4. Comparison With Satellite Data

[10] The validation of the previously described model is attempted by comparing spaceborne microwave active and passive measurements to the simulations. The data set for the comparison includes satellite data and the calculations produced by the models described here above. These need geophysical parameters as inputs that will be considered as the ground truth. For this analysis, we rely on data produced by meteorological models and databases managed by the ECMWF Archive Center. We have chosen to perform our comparisons with the ECMWF model re-analyses corresponding to the SEMAPHORE experiment's period and region. By taking re-analyses from the ECMWF model in a region and a period where intensive ground measurements have been considered, we provide more confidence in the meteorological analyses. The SEMAPHORE experiment was conducted in 1993, between June and November, southeast of the Azores islands in the North Atlantic Ocean (30W to 15W, 30N to 40N). The ground measurements acquired during this period have been assimilated into the ECMWF re-analyses. The ground measurements consist of ship based data, drifting buoys data, moorings, aircraft data and floats data. The ECMWF re-analyses used in this study were taken between October 8 and November 15, 1993, which corresponds to the intensive observation period (IOP) of SEMAPHORE. The ground measured parameters are the sea surface temperature, the sea surface wind speed and the radiative fluxes from both aircraft and drifting buoys and atmospheric profiles from both aircraft and shipborne instruments. Besides the ground measurements used in the ECMWF model assimilation, several spaceborne data were also used, including SSM/I for the water vapor. A more complete description of the SEMAPHORE experiment is given in several papers, among them Eymard [1998]. All the meteorological data from ships (frequent over the North Atlantic area) are also assimilated into the ECMWF analyses. The grid size of the ECMWF analyses is large (1.125°) but this is compensated by an averaging of the satellite retrieved data within the grid. The North Atlantic ECMWF analyses have already been used successfully in the past to calibrate/validate operational algorithms for the ERS microwave radiometers series [Eymard et al., 1996]. In this paper, it was shown that the ECMWF moisture profiles were in average correct and suitable for this type of studies. We adopted the following criteria for the collocation between the satellite data and the meteorological analyses: ± one hour in time and ±0.5° in space. Four meteorological analyses per day (at 00, 06, 12 and 18 UTC) have been extracted from the ECMWF archives over the North Atlantic. A total of 240 analyses have been extracted. These analyses contain a set of surface parameters such as wind speed and surface temperature as well as atmospheric profiles of temperature and humidity. The atmospheric absorption based on Liebe et al.'s [1993] model is driven by the atmospheric profiles distributed over 31 vertical layers. The surface emission and scattering are calculated by the UCL model. The description of the surface is made using (1) Bjerkaas and Riedel [1979] and (2) Lemaire et al. [1999] full-range spectrum denoted BJKR and DL on the following figures, respectively. The simulations obtained over these analyses are compared to coincident spaceborne measurements. Altimeter and radiometer data from both TOPEX/Poseidon and ERS-1 satellites are used for this purpose. The comparisons between measurements and the predictions of the UCL model are summarized in scatter plot format. The comparisons in both active and passive modes between the simulations using BJKR surface spectrum and spaceborne measurements are shown for TOPEX/Poseidon (Figure 1) and ERS (Figures 2 and 3). The σ°Ku residual error is also plotted versus the wind speed in ERS and TOPEX cases. Both figures show that large errors occur at low wind speeds (<3 m/s) as expected from the BJKR model, which is valid only for fully developed seas. This conclusion is consistent with other observations indicating that for average conditions radar derived high winds are underestimated with respect to ground truth meteorological data. Moreover radar backscattering coefficients at very low wind conditions are strongly perturbed by swell and waves not directly related with the local wind. In passive mode, the simulations fit the measurements quite well for the 21 GHz channel of TMR and the 23.8 GHz channel of MWR1. This is due to the fact that in these channels, the brightness temperatures are mostly dependent on the water vapor absorption, which is well modeled by Liebe et al.'s [1993] model. The surface effect is not the primary one in those channels.

Figure 1.

Validation of the UCL model in active (a, b) and passive (c, d, e) modes, Bjerkaas and Riedel [1979] spectrum, TOPEX nadir viewing configuration. Simulated data versus measured ones. Panel (f) is the difference between the simulations and the measurements in the altimeter channel 13.8 GHz, versus wind speed: wind dependent discrepancy.

Figure 2.

(a and b) Validation of the UCL model in passive mode, Bjerkaas and Riedel [1979] spectrum, ERS-1 nadir viewing configuration. Simulations versus coincident measurements.

Figure 3.

(a and b) Same as Figure 2, but for active mode. Figure 3b is the difference between the simulations and the measurements at the altimeter channel 13.8 GHz, versus the wind speed.

[11] Quite large discrepancies exist however in the 18 GHz, 37 GHz (TMR) and 36.5 GHz (ERS) channels. These are essentially due to clouds contamination as will be shown later. Figures 4 and 5 present similar investigations with Lemaire et al. [1999] sea surface spectrum for TOPEX/Poseidon configuration.

Figure 4.

(a, b, and c) Validation of the UCL model in passive mode, using the Lemaire et al. [1999] spectrum for TOPEX configuration.

Figure 5.

(a and b) Same as Figure 4, but for active mode.

[12] Figures 4a and 4b show that the σ0 as simulated by the UCL model and the measured σ0 differ in the C-band by a shift of almost 3 dB, the bias is small in the Ku band. In Figures 1a and 1b, the shape of the scatterplots shows clearly that the difference between the measured and the simulated data depends on the σ0 value (and thus on the wind speed). The differences between the UCL simulations (using the Lemaire et al. [1999] spectrum) and the real data have a correctable shape: by applying a linear correction to the sigma naughts, we can reach a good agreement between the simulations and the data.

[13] This consistency would be necessary in case a unified retrieval using both active and passive measurements is to be undertaken using UCL physical model.

[14] This matching between the simulations and the real data is aimed at eliminating the discrepancies found between the two quantities before any retrieval is performed. These differences are likely to be due to calibration errors on the instrument part and to tuning issues in the physical model.

[15] In passive mode, the brightness temperatures in the water vapor absorption line channels, fit quite well the measurements, while the comparisons in all the other channels are affected by high differences due to cloud contamination. Indeed, the ground truth data we use as inputs for the simulations do not contain information about the cloud liquid water and rain. Their effects are not taken into account when simulating the brightness temperatures. The real data are however affected by the presence of atmospheric hydrometeors. It is therefore important to remove the cloudy points from the comparison data set. To verify this point we applied a retrieval algorithm specifically designed for liquid water content LW [Eymard et al., 1996] and discarded data with LW greater than 0.001 kg/m2. In this case, the large discrepancies disappear as can be seen on Figure 6. The 18 GHz and 37 GHz channels are sensitive to both atmosphere and surface effects. If the surface model was performing poorly, it would show up clearly in these channels.

Figure 6.

(a, b, and c) Validation of the UCL model, Lemaire et al. [1999] spectrum, TOPEX nadir viewing configuration. Points with liquid water content greater than 0.001kg/m2 have been eliminated.

[16] The statistical performance of these comparisons is summarized in Tables 1 and 2 for TOPEX/Poseidon and ERS-1, respectively. They contain the correlation factor, the bias and the slope between the simulations and the real data, computed before and after applying the cloud filter and linearly adjusting the data.

Table 1. Statistical Performance of the UCL Model With Respect to the TOPEX/Poseidon Microwave Data, Before and After Calibration Corrections and Cloud Filteringa
TOPEX18 GHz21 GHz37 GHzσKu
  • a

    Statistical performance: correlation factor (C.F.), bias, and regression slope.

Table 2. Same as Table 1, But for ERS-1
ERS-123.8 GHz36.5 GHzσKu

[17] Another comparison was performed using scatterometer data from ERS-1 as well as empirical geophysical model functions (GMF). Figure 7 compares the present model with CMOD3 [Long, 1995], CMOD4 [Runefach, 1995] and CMOD-IFR2 [Quilfen and Bentamy, 1996] algorithms, in C band, VV polarization. Figure 8 shows the comparison between the simulations performed using this model and the ERS-1 scatterometer data, measured during the same period as the previous comparisons. The wind speed values are those of the ECMWF fields. The simulations are done using four different values of the significant slope. The azimuthal angle (with respect to the wind direction) from the ERS-1 data is selected at 135° ± 2°. The incidence angle is selected at θ = 20° ± 1°. Figure 7 shows that a good agreement is obtained over the whole incidence angle and wind speed ranges.

Figure 7.

Simulation for C band scatterometer configuration. The dashed, dotted and dot-dashed lines represent CMOD3, CMOD4 and CMOD-IFR2 models, respectively. The continuous line represents simulations for SS = 0.70%.

Figure 8.

Simulation for C band scatterometer configuration, 20° incidence angle. Dots are ERS-1 SCATT data for θ = 20° ± 1° and ϕ = 135° ± 2° collocated with ECMWF wind fields assumed correct.

5. Discussion and Limitations

[18] In the comparison presented in this paper, a number of points have been discarded because of contamination by clouds. Although the cloud has mainly an absorbing effect on the measurements in this range of frequencies, it could also cause scattering in case of precipitating clouds. We do not model atmospheric multiple scattering in our radiative transfer model. This is a limitation that prevents us from using our model at higher frequencies. Introducing multiple scattering capabilities will extend the potential use of this model for higher frequencies and for other geophysical situations (in presence of cirrus ice clouds for instance).

[19] When comparing the model simulations to the ERS-1 GMF and for an incidence angle of 60°, one can notice that for low winds, the model simulations are higher than those predicted by ERS GMF. On the other hand, the model simulations are lower for high winds. Although this is not clearly apparent when comparing the model simulations with real altimeter sigma naughts, this may suggest that some tuning of the wind speed dependence of the model is still necessary in order to fit perfectly the data. The ultimate goal of this study is to allow a consistent approach for the retrieval of atmospheric and surface parameters using passive and active measurements. The inversion in this case would need both the backscatter measurements and the brightness temperature. In order to perform such an inversion, we need to have (1) a physical model that has the ability to simulate both active and passive measurements and (2) consistently calibrated data, in both modes. The two types of measurements have been calibrated independently, without taking into account electromagnetic relationships that could exist between active and passive signals. Therefore, a recalibration is likely to be needed to make the measurements consistent with the model.

6. Conclusion

[20] A unified approach has been proposed in order to simulate the passive brightness temperatures and the active backscattering coefficients as measured by spaceborne instruments above the ocean. The developed model takes into account the fact that these two kinds of measurements are not independent. This study describes this model and shows a first validation of the model by comparing its results to spaceborne measured data from different sensors. Two sea surface spectra have been tested. The Bjerkaas and Riedel [1979] spectrum is found to be valid only for fully developed sea state. The Lemaire et al. [1999] spectrum gives consistent results in the two microwave modes except for the altimetric C-band. This last channel is however not absolutely calibrated. Moreover, the C-band data differ from the simulations simply by a shift of 2.8 dB. This result is consistent with conclusions obtained by Lemaire et al. [1999], who suggested a correction of 2.6 dB on the balance between K and C band channels.

[21] The model simulations have also been compared successfully to empirical algorithms dedicated the ERS-1 scatterometer. From this comparison, it is also likely that the surface spectrum model and the scattering theory should be improved. The surface spectrum might have been distorted to compensate for the possible deficiency of the scattering model. The validation also pointed out that the initial calibration of the active and passive instruments has been done separately and no consistency was ensured between them. Slight corrections are then necessary in order to make the spaceborne measurements compatible in both active and passive modes, with the simulations. The main conclusion of this study is simply that simultaneous inversion of active and passive data in a synergistic way is possible.