# Plant water content and temperature of the Amazon forest from satellite microwave radiometry

Jean-Christophe Calvet, J.-P. Wigneron, E. Mougin, Y.H. Kerr, J.L.S. Brito

► To cite this version:

Jean-Christophe Calvet, J.-P. Wigneron, E. Mougin, Y.H. Kerr, J.L.S. Brito. Plant water content and temperature of the Amazon forest from satellite microwave radiometry. IEEE Transactions on Geoscience and Remote Sensing, 1994, 32 (2), pp.397-408. 10.1109/36.295054. meteo-05337498

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# Plant Water Content and Temperature of the Amazon Forest from Satellite Microwave Radiometry

Jean-Christophe Calvet, Jean-Pierre Wigneron, Eric Mougin, Yann H. Kerr, and Jorge L. S. Brito

*Abstract*—In this study, an attempt is made to derive the evolution of the temperature and the water status of the Amazon forest canopy from satellite microwave radiometry. The Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) temperature-corrected tapes data are analyzed for the 6.6, 10.7, 18, and 37 GHz frequencies, at daytime and nighttime, over a zone near Manaus (3°S, 60°W), Brazil. Two periods are investigated: the wet (April-May) and dry (July-August) seasons of 1985. After separating forest- from river-contaminated pixels, atmospheric corrections are performed for water vapor, clouds, and rain, using surface and satellite data. Algorithms are developed to model the microwave thermal emission of vegetation following a continuous approach and a discrete approach. A sensitivity study is performed in order to determine which frequencies are relevant to retrieve land surface parameters. The models are then used along with an optimization procedure so as to carry out the inversion of the canopy structure parameters. The vegetation temperature and water content are retrieved through the continuous model.

## I. INTRODUCTION

THE estimation of evaporation over land surfaces at general circulation models scale, typically 100 × 100 km, is an important issue for climate modeling or for agrometeorological monitoring of the biosphere. Evaporation depends on the energy and hydrological budgets of the surface. The variable driven by the energy budget is surface temperature, which can be estimated through the use of infrared or microwave remote sensing radiometry, provided the emissivities are known [1]. The variable driven by the hydrological budget is surface

moisture. Passive and active microwave remote sensing are likely to gain access to this latter variable [2].

In recent years, several studies have focused on the use of the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) data over land surfaces. In [3], the difference of vertically and horizontally polarized 37 GHz brightness temperatures is considered as a vegetation index and as an indicator of soil moisture. In [4] and [5], the evolution of the normalized polarization difference is simulated over semi-arid areas and the importance of performing atmospheric corrections is emphasized. In the case of a vegetation canopy, the microwave signal may allow us to retrieve structure parameters and micrometeorological variables such as leaf temperature and stomatal resistance. The limitations are: 1) the high number of vegetation parameters liable to influence the signal, and their rapid temporal evolution, 2) the rather strong contribution of soil on the measured signal, and 3) the coarse resolution of the Nimbus-7 SMMR. The Amazon forest is less affected by these limitations than other types of canopy since structure parameters and soil humidity are expected to vary little and since it is a wide, homogeneously vegetated area whose size is compatible with the SMMR resolution. In this study, the radiometric zone is a "terra firme" forest area near Manaus (3°S, 60°W). It covers the Ducke Reserve Forest (DRF) site (2°57'S, 59°57'W).

As opposed to studies over patchy vegetation [4], thorough numerical modeling of the emission of vegetation is necessary over a dense canopy. Two algorithms were developed to model the microwave thermal emission of vegetation: 1) a discrete model, based on the calculation of the scattering and absorbing properties of each bioelement (leaves, branches, and stems) [6]–[8], and 2) a continuous model which uses a statistical description of the dielectric properties of the canopy [9]–[11]. The vegetation structure parameters were first assessed from literature review and calibration for each model. Simulations of the SMMR signal were then performed for the wet season (April-May) and the dry season (July-August) 1985. The inverse problem was solved by using an iterative method. The results were compared with micrometeorological measurements from the Anglo-Brazilian Amazon Region Micrometeorology Experiment (ARME) [12], and from the U.S.-Brazilian Global Tropospheric Experiment (GTE)/Amazon Boundary Layer Experiment (ABLE) 2A mission [13] at the DRF site.

Manuscript received March 26, 1993; revised October 8, 1993. This work was supported by Météo-France, LERTS, the French Foreign Affairs Ministry, and INPE. This work was performed at the Laboratoire d'Etudes et de Recherches en Télédétection Spatiale, Toulouse, France, and at the Instituto Nacional de Pesquisas Espaciais, São José dos Campos, Brazil, in the framework of a French-Brazilian cooperation program.

J.-C. Calvet is with Météo-France/CNRM, 42 Avenue G. Coriolis, 31057 Toulouse Cedex, France.

J.-P. Wigneron is with the Institut National de la Recherche Agronomique (INRA), Bioclimatologie, Domaine St. Paul, BP 91, 84143 Montfavet, France.

E. Mougin is with the Centre d' Etude Spatiale des Rayonnements (CESR), Complexe Aérospatial de Toulouse-Lespinet, BP 4346, 31029 Toulouse Cedex, France.

Y. H. Kerr is with the Laboratoire d' Etudes et de recherches en Télédétection Spatiale (LERTS), 18 Avenue E. Belin, 31055 Toulouse Cedex, France.

J. L. S. Brito is with the Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, CP 515, 12201 São José dos Campos—SP, Brazil.

IEEE Log Number 9214663.
## II. DATA

### A. Surface Data

The micrometeorological measurements of ARME (April-May 1985) and GTE/ABLE 2A (July-August 1985) were used as ground data in this study. Moreover, GTE/ABLE 2A radio soundings were analyzed together with the DRF tower data to perform atmospheric corrections on the microwave signal.

The DRF is a dryland or "terra firme" forest. The average height of the canopy is about 35 m [13]. Biomass and plant density are given in [14] and [15]. The plant density is about 3000 stems/hectare with dominance of low diameter stems [15]. Reference [14] gives a leaf area index (LAI) of 5.2. A description of the atmospheric circulation over the Amazon region can be found in [16].

The DRF micrometeorological data consisted of 15 mn averaged air temperatures and humidities at four levels in the canopy (1.45, 13.45, 23.25, and 30.51 m above the soil surface), and of hourly averaged incident solar radiation and precipitation rate above the canopy, at the top of the tower (45 m).

### B. Satellite Data

1) Description: The satellite data consisted of SMMR half-degrees temperature-corrected tapes (TCT) maps of antenna temperatures for ten channels (five frequencies, all dual polarized), at 1200 Local Standard Time (LST) and 0000 LST. Each map corresponds to a unique measurement within a six-day period, which is the time required for global coverage [17]. The exact day of measurement was not identified.

In order to discriminate a possible seasonal evolution of the vegetation emission, the 1985 SMMR data were extracted from DoY (Day of Year) 92 to DoY 138 for the wet season and from DoY 182 to DoY 240 for the dry season. These two sets of data correspond to the ARME and GTE/ABLE 2A surface measurements, respectively.

Table I lists the five frequencies with the 3 dB footprint size. In this study, the 21 GHz channels could not be used for one polarization failed during year 1985. Considering the short period covered by the data, no attempts were made to correct for sensor drift.

Fig. 1 shows the wet season TCT raw brightness temperatures images over the Amazon basin for the vertical polarization. For each six-day period, the 37, 18, 10.7, and 6.6 GHz frequencies, daytime and nighttime, are presented from left to right. Fig. 2 shows the polarization ratio for the same frequencies and periods. The polarization ratio PR is expressed as

$$PR = (T_{Bv} - T_{Bh})/(T_{Bv} + T_{Bh}) \quad (1)$$

where $T_{Bv}$ and $T_{Bh}$ are, respectively, the vertical and horizontal polarized raw brightness temperatures. For all the frequencies, the pixels are selected within a 300 × 300 km area covering the site of the DRF. Fig. 3 presents the Amazon basin as well as the pixel selection area. The DRF site being near the Equator, the SMMR swathes do not

<figure><img src="image_2.png" /><figcaption>Fig. 1. Temporal evolution of the SMMR vertical polarization brightness temperature over the Amazon basin (55°W-65°W × 2°N-8°S) for wet season 1985, 1200 and 0000 LST.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. As in Fig. 1, except for polarization ratio.</figcaption></figure>

<table><caption>TABLE I
THE FIVE FREQUENCIES OF THE NIMBUS-7 SMMR AND RESOLUTIONS</caption><thead><tr><th>Frequency (GHz)</th><th>Wavelength (cm)</th><th>Pixel Size at 3 dB Beamwidth (km × km)</th></tr></thead><tbody><tr><td>37.0</td><td>0.8</td><td>27 × 18</td></tr><tr><td>21.0</td><td>1.4</td><td>46 × 30</td></tr><tr><td>18.0</td><td>1.7</td><td>55 × 41</td></tr><tr><td>10.7</td><td>2.7</td><td>91 × 59</td></tr><tr><td>6.6</td><td>4.6</td><td>148 × 95</td></tr></tbody></table>

U-M-I

DUE TO LACK OF CONTRAST, GRAPHS DID NOT REPRODUCE WELL.
GRAPHS FOLLOW SAME SEQUENCE AS LEGEND
<figure><img src="image_4.png" /><figcaption>Fig. 3. Amazon basin (55°W-65°W × 2°N-8°S), Ducke Reserve site, and pixels selection zone location.</figcaption></figure>

overlap, as can be seen in Figs. 1 and 2. It can also be observed that the pixels which include a portion of a river, as well as neighboring ones, show a sharp contrast with forest pixels.

2) SMMR Data Processing: A first step consisted of selecting and averaging the pixels which are not contaminated by the Amazon river contrasting signal. Then atmospheric corrections were performed.

Rivers and flooded land surfaces present high PR values. It was possible to establish a PR threshold of 0.015 for all the frequencies, above which the pixel is considered as contaminated by the river. The number of contaminated pixels is the highest at the 6.6 GHz frequency, which has the lowest resolution and a poor beam efficiency.

Atmospheric corrections take into account the rain rate, the integrated water content of the atmosphere (IWC), the altitude of the lower and upper boundaries, and the liquid water density of the cloud layer. The rain rate was given by the surface measurements. The IWC, base, and top of the cloud layer were evaluated using the GTE/ABLE 2A radio soundings. Determining the presence and altitude of a cloud layer from radiosoundings without sky state observations is not an easy task. In this study, we tried to take advantage on the DRF measurements of the solar incident radiation at the top of the canopy at 1200 LST (RG). A coarse approximation of the thickness (Z) of the cloud layer at 1200 LST is given by a Beer extinction law of the solar radiation as a function of RG:

$$Z = Z_{\max} \frac{\ln(RG/RG_{\max})}{\ln(RG_{\min}/RG_{\max})} \quad (2)$$

where Zmax, RGmax, and RGmin are maximum cloud layer thickness, and maximum and minimum values of RG, respectively,

during the considered season. The values of Z and Zmax can be estimated from radiosoundings as the sum of the thickness of successive layers of the atmosphere where the air humidity profile is close to saturation. These potential cloud layers were determined from available radiosoundings according to saturation criteria defined from mixing ratio (r) and saturated mixing ratio (rw), and from air temperature (T) and dew point (Td). These criteria are (rw - r)/r < S<sub>r</sub> and (T - T<sub>d</sub>) < S<sub>t</sub> below and above the 4 × 10<sup>4</sup> Pa level, respectively. It was shown that the value of S<sub>t</sub> being (arbitrarily) set at 5 K, the value S<sub>r</sub> = 0.21 provides the best agreement between Z determined from (2) and radiosounding Z values (rms difference of 740 m).

The estimated mean altitude of the base of the cloud layer is 1680 m at nighttime, 2000 m at daytime. The maximum cloud layer thickness (Zmax) was estimated as 1850 m at nighttime, 2130 m at daytime.

When radio soundings were not available, the values of IWC were evaluated using the monthly climatology given by [16]. The altitude of the base of the cloud layer was taken as the mean value, and the thickness (Z) of the cloud layer was inferred from Zmax and from DRF measurements of the solar incident radiation (RG) at 1200 LST. After determining the minimum and maximum values of RG during the considered season, RGmin and RGmax, respectively, Z was estimated from (2). For nighttime, Z was extrapolated from the daytime value using infrared GOES images over Brazil, archived at INPE, Brazil. Cloud coverages [18], C00 and C12, ranging from 0 to 1, were estimated over the Manaus region at, respectively, 0000 LST and 1200 LST. It is shown that 1 - C12 can be used as an estimation of the RG/RGmax term in (2). The rms error is 0.31 for the wet season, 0.22 for the dry season. The nighttime extrapolation consisted of replacing RG/RGmax in (2) by γ

$$\gamma = \left( \frac{1 - C_{00}}{1 - C_{12}} \right) \left( \frac{RG}{RG_{\max}} \right) \quad (3)$$

The liquid water density of clouds was supposed to keep the constant value 0.80 g · m⁻³, which is typical of medium-altitude *Cumulus congestus* [18].

As explained above, the SMMR measurements were acquired on one undetermined day within blocks of six-day periods. Consequently, all the meteorological variables (rain rate included) entering the atmospheric corrections procedure were averaged over each SMMR period, at noon and midnight. If all adequate information had been available, the problem with determining the spatial variation of cloud characteristics within the resolution area of the SMMR should have been addressed. Given the uncertainties on SMMR measurements dating, such nicety was unnecessary.

Once the average atmosphere characteristics are determined, the effective temperature of the canopy can be approximated as a function of the radiometric brightness temperature T<sub>Bp</sub>:

$$T_{Ep} = (T_{Bp} - T_{au})e^{\tau_{au}} \quad (4)$$
where $p = v$ or $h$ denotes the vertical or horizontal polarization, $T_{au}$ is the upwelling atmospheric emission, and $\tau_{au}$ is the upward atmospheric opacity. The detailed description of the computation of these atmospheric radiation components can be found in [19], [20].

### III. MODELS

In the domain of active or passive microwave remote sensing, the modeling of the signal observed on vegetation canopies has been developed in two main directions: discrete and continuous models. Here, an attempt was made to use both discrete and continuous approaches.

Both models are based on the resolution of the radiative transfer equation which can be written, for the vertical polarization [1]:

$$ \mu \frac{dT_{Ev}(\mu, \tau_v)}{d \tau_v} = - T_{Ev}(\mu, \tau_v) + (1 - \omega_v) T(\tau_v) + \int_{-1}^{1} ((v, v') T_{Ev}(\mu', \tau_v) + (v, h') T_{Eh}(\mu', \tau_h)) d \mu' \quad (5) $$

where

$$ \tau_v = \int_0^z k_{ev} dz' \quad (6) $$

is the opacity of the vegetation layer between the soil surface and the altitude $z$,

$$ \omega_v = k_{sv}/k_{ev} \quad (7) $$

is the single scattering albedo, $k_{ev}$ and $k_{sv}$ are, respectively, the vegetation volumetric extinction and scattering coefficients, $\mu$ is the incidence angle cosine, $(v, v')$ and $(v, h')$ are scattering phase functions, and $T(\tau_v)$ is the mean vegetative elements' temperature at altitude $z$.

The absorbing and scattering properties of the canopy are related to the dielectric constant ($\epsilon$) of the vegetative bioelements for both the discrete and the continuous models. Variations of $\epsilon$ depend on constraints on water molecules due to their interaction with solutes and structural elements of the cells [21]. The dielectric constant of a bioelement can therefore be considered as the intermediate variable between the microwave emission properties and the water potential of the bioelement. Up to now, no parameterization of $\epsilon$ as a function of water potential has been proposed. In this study, an empirical parameterization in function of the gravimetric moisture (GM) and the dry matter density proposed by [22] was used.

The same soil emission model is used in both discrete and continuous algorithms. Soil roughness effects are modeled by modified Fresnel reflection coefficients [23]. The soil dielectric constant parameterization can be found in [24].

#### A. Discrete Model

Along with the dielectric properties, the geometrical characteristics (dimensions and orientation) and density

of each bioelement are taken into account in the computation of the extinction and scattering coefficients and scattering phase functions. Branches and stems are modeled as dielectric cylinders [6], and leaves as thin disks [7]. In both cases, the Helmholtz integral equation is used to calculate the scattering amplitudes. In the case of leaves, the scatterer inner field is calculated under the Generalized Rayleigh-Gans (GRG) approximation, valid for scatterers with at least one characteristic dimension ($\epsilon$, here the thickness of the leaves) small with respect to the wavelength ($\lambda$). More precisely, the validity condition for the GRG approximation can be written

$$ \frac{2\pi e}{\lambda} (\epsilon^{1/2} - 1) \ll 1. \quad (8) $$

This validity condition efficiently extends the application of the discrete modeling towards high frequencies [25] (up to 25 GHz [26]). In this study, it was supposed that the GRG approximation can also be applied at 37 GHz.

Two algorithms (DM1 and DM2) were developed. In DM1, the integration of (5) is performed for the leaves only, using a Gauss quadrature method [8]. Vegetation is considered as one layer of homogeneous medium. The use of DM1 is limited by the high computing time it requires to retrieve land surface parameters in inversion problem. In DM2, (5) is simplified according to the $\delta$-Eddington approximation [27]:

$$ \mu \frac{dT_{Ep}(\mu, \tau_p^*)}{d \tau_p^*} = -T_{Ep}(\mu, \tau_p^*) + (1 - \omega_p^*) T(\tau_p^*) \quad (9) $$

and can be analytically integrated. In (9), $\omega_p^*$ and $\tau_p^*$ are equivalent albedo and opacity, respectively, given by

$$ \omega_p^* = (1 - F_p) \omega_p/(1 - F_p \omega_p) \quad (10) $$

$$ \tau_p^* = (1 - F_p \omega_p) \tau_p \quad (11) $$

where $F_p$ is the proportion of forward scattering for polarization $p$. The values of $k_{ep}$ and $k_{sp}$ are calculated for all bioelements and averaged according to their respective concentrations. The $\delta$-Eddington approximation avoids the computation of the scattering phase functions. The computation time is thus significantly reduced, which enables us to take branches and stems into account, as well as vertical heterogeneity. Nevertheless, the computing time of DM2 remains high, especially for branches and stems, and it introduces two additional unknown parameters $F_v$ and $F_h$.

#### B. Continuous Model

As opposed to discrete models, the vegetation is considered as a whole. The canopy is reduced to a continuous medium which is described in a statistical way through the spatial fluctuation of $\epsilon$ [9]–[11]:

$$ \epsilon(r) = \epsilon_m + \epsilon_f(r) \quad (12) $$

where $r$ indicates the position in space, $\epsilon_m$ is the spatially averaged permittivity, and $\epsilon_f$ is the fluctuating part of $\epsilon$.
The expression of $\epsilon_m$ depends on the dielectric constant of the vegetation elements, on the volume fraction ($V_f$), and the structure of vegetation [1]. In the case of weak fluctuations of $\epsilon$, the $\epsilon_f$ term in (12) is defined by the following autocorrelation functions [9], [10]:

$$ \langle \epsilon_f(r) \cdot \epsilon_f(r') \rangle = \delta \epsilon_m^2 \exp \left( - \frac{|z - z'|}{L_z} - \frac{|x - x'|^2 + |y - y'|^2}{L_r^2} \right) \quad (13) $$

where $\delta$ is the normalized variance of fluctuations. The description of the medium is exponential in the vertical direction and Gaussian in the horizontal direction. The correlation lengths for both directions are $L_z$ and $L_r$, respectively.

In this algorithm (CM), the definition of $\epsilon_f$ is extended to the case of strong fluctuations [10], [11], more appropriate in the case of leafy vegetation. The integration of (5) is performed using a 12-point Gaussian quadrature method [1], [9]. Preliminary tests showed that, with the DRF canopy structure parameters described in Section IV, 12 points are enough to converge to the right final $T_{Ep}$ values. CM is far less computer time-consuming than DM1 since the phase matrix calculation of the continuous random media is much quicker.

### C. Inverse Problem

For a given set of entry variables, the canopy microwave emission models (i.e., DM1, DM2, and CM) enable us to compute the effective temperatures $T_{Ep}$ provided the canopy structure parameters are known. Here, the entry variables are bioclimatic parameters with a possible diurnal and seasonal variation, namely, the gravimetric moisture (GM) and the vertical temperature profile of vegetation. The temperature profile, supposed to be linear, is characterized by the temperature at the soil surface level ($T_1$) and at the top of the canopy ($T_2$).

The retrieval of the entry variables consisted of three steps: evaluating possible values of the structure parameters (literature review and calibration), investigating the sensitivity of $T_{Ep}$ to variations of the entry variables (sensitivity study), and finally, determining the value of GM, $T_1$, and $T_2$ for which the modeled effective temperatures are as close as possible to the measured $T_{Ep}$ (inversion). In this study, calibration and inversion were performed through the minimization of the rms difference between the modeled and measured $T_{Ep}$ by using the Powell's iterative optimization procedure [30].

## IV. STRUCTURE PARAMETERS

Table II lists the vegetation structure parameters for the three models (DM1, DM2, and CM) and the soil parameters. The DM1 vegetation structure parameters are: the height of the canopy (H), the volume fraction of vegetation ($V_f$), the angular distribution (B), diameter (d), thickness (e), and dry matter density ($\rho_L$) of leaves. The

values of H, B, d, e, and $\rho_L$ are the same for DM2. For leaves, DM2 takes the leaf area index (LAI) and the vertical profile of leaf area density (LAD) into account; six classes of branches and stems are defined, and for each of them, the angular distribution, diameter, and height. The forward-scattering proportions $F_v$ and $F_h$ are additional structure parameters for DM2. The CM structure parameters are H, $V_f$, and the correlation lengths ($L_z$ and $L_r$).

Some of these parameters could be inferred from the existing literature: $H = 35$ m in [31], LAI = 5.2 in [14], B was taken as a Beta distribution [32] whose parameters were chosen to satisfy the leaf angle distribution factor condition given by [31] ($\chi_L = 0.1$), and LAD was taken as a triangular profile with a maximum at 28.2 m [31]. Stems and branches biomass for various diameter classes (Tables III and IV, respectively) can be found in [14], [15]. The value of $\rho_L$ is 330 kg · m⁻³ for leaves [22], and $\rho_B$ is 960 kg · m⁻³ for branches and stems [15].

The parameters $V_f$, e, $F_v$, $F_h$, $L_z$, and $L_r$ were calibrated along with GM for the second April-May SMMR period, 1200 LST, for which $T_1$ and $T_2$, modeled from ARME data (DoY 100) [33], were available ($T_1$ = 301.5 K and $T_2$ = 306 K). The values of $V_f$ and e were first calibrated at 6.6 GHz using the DM1 and CM algorithms. DM1 gives $V_f$ = 122 parts per million (ppm) and e = 0.4 mm. The value of $\rho_L$ = 330 kg · m⁻³ was measured for a corn leaf [22]. No estimate of $\rho_L$ for DRF is available. The doubt over this value may affect the calibrated leaf parameters, the thickness in particular. It was possible to test for the consistency of $\rho_L$ with e from fresh leaf biomass ($W_f$) and dry leaf biomass ($W_d$) data from [34]. The value of e can be simply related to $\rho_L$ by $e = \{\rho_0^{-1} W_f + (\rho_L^{-1} - \rho_0^{-1}) W_d\}/\text{LAI}$, where $\rho_0$ = 1000 kg · m⁻³ is the density of water. It was found that, given $\rho_L$ = 330 kg · m⁻³, the mean leaf thickness should be $e = 0.47 \pm 0.09$ mm. Therefore, the calibrated value of e (0.4 mm) seems consistent with $\rho_L$. Nevertheless, the in situ value of $W_f$ is determined with difficulty in practice, especially for a forest canopy. Indeed, $W_f$ is likely to be underestimated. Data from [34] give GM = 0.55. This is a low value, compared with GM = 0.8 determined for agricultural canopies [29].

Soil parameters for the DRF site are given by [35]. The biomass value obtained with CM is $V_f$ = 173 ppm. For all the frequencies, Table V summarizes the value of GM, $L_z$, and $L_r$ for CM, $F_v$, and $F_h$ for DM2. In the case of CM, the values of GM are representative of all vegetation material (leaves and wood). The high values of $L_z$ obtained at low frequencies may denote a higher influence of vertical structures (stems). In DM2, the gravimetric moisture of branches and stems has the constant value $GM_b$ = 0.31, as calculated from [14]. In order to limit the number of entry variables to a value compatible with the number of SMMR available channels, GM, common to all frequencies for DM2, is only representative of the leaves. The assumption that $GM_b$ is constant may be erroneous, which may explain why the inversion of DM2 does not give physically possible values at 6.6 and 10.7
<table><caption>TABLE II
PARAMETERS OF THE VEGETATION STRUCTURE AND SOIL CHARACTERISTICS NECESSARY TO MODEL THE MICROWAVE EMISSION OF THE "TERRA FIRME" AMAZON FOREST CANOPY</caption><thead><tr><th>Symbol</th><th>Definition</th><th>Value</th><th>Source</th></tr></thead><tbody><tr><td colspan="4">(a) Structure parameters of the discrete model (DM1)</td></tr><tr><td>H</td><td>Height of the canopy</td><td>35 m</td><td>[31]</td></tr><tr><td>V<sub>f</sub></td><td>Volume fraction of vegetation</td><td>122 ppm</td><td>calibration</td></tr><tr><td>B(ν, μ)</td><td>Beta angular distribution<br>of leaves [28]</td><td>ν = 2.4<br>μ = 1.6</td><td>satisfies<br>x<sub>L</sub> = 0.1 [31]</td></tr><tr><td>d</td><td>Diameter of leaves</td><td>5 cm</td><td>arbitrary</td></tr><tr><td>e</td><td>Thickness of leaves</td><td>0.4 mm</td><td>calibration</td></tr><tr><td>ρ<sub>L</sub></td><td>Dry matter density of leaves</td><td>330 kg · m<sup>-3</sup></td><td>[22]</td></tr><tr><td colspan="4">(b) Structure parameters of the δ-Eddington discrete model (DM2)</td></tr><tr><td>H<sub>s</sub></td><td>As for DM1</td><td></td><td></td></tr><tr><td>B(ν, μ)</td><td></td><td></td><td></td></tr><tr><td>d, e, ρ<sub>L</sub></td><td>Leaf area index</td><td>5.2</td><td>[14]</td></tr><tr><td>LAI</td><td>Height of maximum LAD<br>(leaf area density)</td><td>28.2 m</td><td>[31]</td></tr><tr><td>F<sub>ν</sub>, F<sub>h</sub></td><td>Forward-scattering ratios</td><td>see Table V<br>see Tables III and IV</td><td>calibration<br>[14], [15]</td></tr><tr><td>Stems and branches biomass<br>and geometric properties</td><td></td><td></td><td></td></tr><tr><td>ρ<sub>B</sub></td><td>Dry matter density of stems<br>and branches</td><td>960 kg · m<sup>-3</sup></td><td>[15]</td></tr><tr><td colspan="4">(c) Structure parameters of the continuous model (CM)</td></tr><tr><td>H</td><td>As for DM1</td><td></td><td></td></tr><tr><td>V<sub>f</sub></td><td>Volume fraction of vegetation</td><td>173 ppm</td><td>calibration</td></tr><tr><td>L<sub>z</sub>, L<sub>r</sub></td><td>Correlation lengths</td><td>see Table V</td><td>calibration</td></tr><tr><td colspan="4">(d) Soil parameters (10 cm surface layer) at DRF</td></tr><tr><td>Clay</td><td>Proportion of clay</td><td>78%</td><td>[35]</td></tr><tr><td>Sand</td><td>Proportion of sand at DRF</td><td>10%</td><td>[35]</td></tr><tr><td>Silt</td><td>Proportion of silt</td><td>12%</td><td>[35]</td></tr><tr><td>ρ<sub>L</sub></td><td>Bulk density</td><td>0.9 g · cm<sup>-3</sup></td><td>[35]</td></tr><tr><td>M<sub>s</sub></td><td>Volumetric moisture</td><td>0.4</td><td>[35]</td></tr><tr><td>h</td><td>Electromagnetic roughness</td><td>0.1</td><td>arbitrary</td></tr></tbody></table>

<table><caption>TABLE III
THE THREE CLASSES OF STEMS OF THE "TERRA FIRME" AMAZON FOREST WITH ASSOCIATED DENSITIES AND DIMENSIONS</caption><thead><tr><th>DBH*<br>Class<br>(cm)</th><th>Equivalent<br>DBH<br>(cm)</th><th>Equivalent<br>Height<br>(m)</th><th>Layers</th><th>Density<br>(No ha<sup>-1</sup>)</th><th>Biomass<br>(kg · m<sup>-2</sup>)</th></tr></thead><tbody><tr><td>3.5-10</td><td>4.0</td><td>6.5</td><td>1</td><td>2400</td><td>1.3</td></tr><tr><td>10-30</td><td>16.5</td><td>16.8</td><td>1-2</td><td>540</td><td>13.0</td></tr><tr><td>30 and +</td><td>38.4</td><td>23.8</td><td>1-2-3</td><td>60</td><td>11.0</td></tr><tr><td>Sum</td><td>...</td><td>...</td><td>...</td><td>3000</td><td>25.3</td></tr></tbody></table>

<table><caption>TABLE IV
AS IN TABLE III EXCEPT FOR BRANCHES</caption><thead><tr><th>Diameter<br>Class<br>(cm)</th><th>Equivalent<br>Diameter<br>(cm)</th><th>Equivalent<br>Height<br>(m)</th><th>Layers</th><th>Density<br>(No ha<sup>-1</sup>)</th><th>Biomass<br>(kg · m<sup>-2</sup>)</th></tr></thead><tbody><tr><td>1-5</td><td>3.7</td><td>1.8</td><td>1-2-3-4</td><td>7290</td><td>1.0</td></tr><tr><td>5-10</td><td>9.1</td><td>4.5</td><td>2-3-4</td><td>780</td><td>1.5</td></tr><tr><td>10-30</td><td>20.2</td><td>10.0</td><td>3-4</td><td>180</td><td>3.8</td></tr><tr><td>Sum</td><td>...</td><td>...</td><td>...</td><td>8250</td><td>6.3</td></tr></tbody></table>

<table><caption>TABLE V
CALIBRATED GRAVIMETRIC MOISTURE AND STRUCTURE PARAMETERS OF THE "TERRA FIRME" AMAZON FOREST VEGETATION FOR CONTINUOUS AND DISCRETE MICROWAVE EMISSION MODELS (Wet Season SMMR-period 2)</caption><thead><tr><th rowspan="2">Frequency<br>(GHz)</th><th colspan="3">Continuous Model</th><th colspan="3">Discrete Model 2</th></tr><tr><th>GM</th><th>L<sub>z</sub> (mm)</th><th>L<sub>r</sub> (mm)</th><th>GM</th><th>F<sub>ν</sub></th><th>F<sub>H</sub></th></tr></thead><tbody><tr><td>37.0</td><td>0.44</td><td>0.964</td><td>1.000</td><td>0.83</td><td>0.974</td><td>0.974</td></tr><tr><td>18.0</td><td>0.56</td><td>1.551</td><td>1.035</td><td>0.83</td><td>0.958</td><td>0.964</td></tr><tr><td>10.7</td><td>0.63</td><td>3.620</td><td>1.017</td><td>—</td><td>—</td><td>—</td></tr><tr><td>6.6</td><td>0.63</td><td>9.246</td><td>1.668</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

GHz, for which the influence of stems of higher. The study must therefore be restricted to the highest frequencies for DM2.

Tables VI and VII present the obtained vegetation volumetric scattering and extinction coefficients for CM and DM2, respectively. Again, the greater albedos and extinction coefficients observed for vertical polarization at low frequencies (Table VI) can be attributed to vertical structures.

The SMMR-TCT data may be uncorrectly calibrated. A study over Finland [36] showed that a strong bias exists

<footnote>*DBH is the diameter at breast height.</footnote>
<table><caption>TABLE VI
SCALED EXTINCTION AND SCATTERING COEFFICIENTS (m · m⁻¹) AND SINGLE SCATTERING ALBEDO OBTAINED WITH THE CONTINUOUS MODEL WITH CALIBRATED GRAVIMETRIC MOISTURE AND STRUCTURE PARAMETERS OF TABLE V</caption><thead><tr><th rowspan="2">Frequency<br>(GHz)</th><th colspan="3">Vertical Polarization</th><th colspan="3">Horizontal Polarization</th></tr><tr><th>H × k<sub>ev</sub></th><th>H × k<sub>sv</sub></th><th>ω<sub>ν</sub></th><th>H × k<sub>eh</sub></th><th>H × k<sub>sh</sub></th><th>ω<sub>h</sub></th></tr></thead><tbody><tr><td>37.0</td><td>3.60</td><td>1.89</td><td>52.5%</td><td>3.63</td><td>1.92</td><td>52.9%</td></tr><tr><td>18.0</td><td>1.05</td><td>0.40</td><td>37.8%</td><td>0.92</td><td>0.26</td><td>28.7%</td></tr><tr><td>10.7</td><td>0.91</td><td>0.27</td><td>30.1%</td><td>0.69</td><td>0.06</td><td>8.3%</td></tr><tr><td>6.6</td><td>0.92</td><td>0.37</td><td>40.0%</td><td>0.60</td><td>0.04</td><td>7.3%</td></tr></tbody></table>

<table><caption>TABLE VII
SCALED EXTINCTION AND SCATTERING COEFFICIENTS (m · m⁻¹) OBTAINED WITH THE DISCRETE MODEL DM2: AVERAGE VALUE FOR STEMS, BRANCHES, AND LEAVES (with the Gravimetric Moistures 0.31, 0.31, and 0.83, Respectively). EQUIVALENT CANOPY ALBEDO AND OPACITY FROM F<sub>p</sub> VALUES GIVEN IN TABLE V. SYMBOLS *l* AND *e* STAND FOR STEM OR BRANCH DIAMETER AND LEAF THICKNESS, RESPECTIVELY.</caption><thead><tr><th rowspan="2">Channel</th><th colspan="2">Stems</th><th colspan="2">Branches</th><th colspan="2">Leaves</th><th colspan="2">Canopy</th></tr><tr><th>l × k<sub>e</sub></th><th>l × k<sub>s</sub></th><th>l × k<sub>e</sub></th><th>l × k<sub>s</sub></th><th>e × k<sub>e</sub></th><th>e × k<sub>s</sub></th><th>τ*</th><th>ω*</th></tr></thead><tbody><tr><td>37 GHz V</td><td>1.70</td><td>0.31</td><td>2.11</td><td>0.42</td><td>9.66</td><td>8.11</td><td>1.73</td><td>9.1%</td></tr><tr><td>18 GHz V</td><td>2.16</td><td>0.61</td><td>2.16</td><td>0.64</td><td>4.00</td><td>3.13</td><td>1.39</td><td>8.1%</td></tr><tr><td>37 GHz H</td><td>1.69</td><td>0.29</td><td>2.11</td><td>0.42</td><td>10.5</td><td>8.82</td><td>1.81</td><td>9.2%</td></tr><tr><td>18 GHz H</td><td>2.06</td><td>0.55</td><td>2.18</td><td>0.64</td><td>4.22</td><td>3.31</td><td>1.42</td><td>7.2%</td></tr></tbody></table>

for some SMMR channels. However, this conclusion cannot be easily extrapolated to equatorial regions since such bias may depend on the Nimbus-7 position on its orbit. These uncertainties in the SMMR calibration can affect the physical realism of the derived parameters. The calibrated model structure parameters may be particularly concerned by an SMMR-TCT bias (if any) over the Amazon region.

## V. SENSITIVITY STUDY

A sensitivity study was carried out for CM and DM2 [37] over the biomass (i.e., LAI for DM2, $V_f$ for CM), GM, the temperature gradient ($\Gamma = (T_2 - T_1)/H$) for a given value of $T_1$, and $T_1$ for a given value of $\Gamma$. The sensitivity ($\Psi$) of the variable $X$ to the parameter $p$ can be written

$$ \Psi(X, p) = \frac{p}{X} \frac{dX}{dp}. \qquad (14) $$

The sensitivity of the effective temperature (vertical polarization) and the polarization ratio to $V_f$, GM, $\Gamma$, and $T_1$ is presented for the continuous model in Figs. 4-7, respectively. The reference values of GM are given in Table V; the values of $T_1$ and $T_2$ are 301.5 and 306 K, respectively, as modeled by [35] for day 100. As shown by Fig. 4, the biomass effect on both the intensity of the signal ($T_{E\nu}$) and the polarization difference (represented by PR) are better discriminated at low frequencies (6.6, 10.7, and 18 GHz), except for very low values of $V_f$. Low frequencies are also more informational as far as the temperature effect on PR is concerned. On the other hand, the 37 GHz channels are more useful to discriminate the temperature

effect on $T_{E\nu}$ (Figs. 6 and 7). For vegetation humidity, the 37 and 6.6 GHz channels are liable to carry more information than the other frequencies, whose $\Psi$(PR, GM) can be zero [Fig. 5(b)]. At 37 and 18 GHz, the sensitivity study which was carried out for DM2 gives similar results.

## VI. TEMPERATURE AND HUMIDITY RETRIEVAL

Using the continuous model, the inversion of the vegetation temperature and humidity was performed for both the wet and dry season, 1200 LST and 0000 LST. Once the structure parameters were determined, they were supposed constant over the studied periods. As shown in Section V, both the temperature and water content of vegetation have a strong influence on the signal. The optimization procedure [30] was applied over the three entry variables $T_1$, $T_2$, and GM.

### A. Humidity

Vegetation humidity is expected to be related to the stoma-matal regulation of the transpiration of leaves. The stoma-matal resistance (SR) was calculated from a statistical model [38] for *Piptadenia suaveolens*, which is the highest species at the DRF site. The SR model uses the DRF incident solar radiation and air humidity deficit data [12], [13]. To take into account the complementary information of 37 and 6.6 GHz channels, as seen in the sensitivity study, the moisture ratio (MR) was defined as

$$ \text{MR} = 2 (\text{GM}_{37} - \text{GM}_{6.6})/(\text{GM}_{37} + \text{GM}_{6.6}) \quad (15) $$

where $\text{GM}_{37}$ and $\text{GM}_{6.6}$ are the retrieved gravimetric moistures at, respectively, 37 and 6.6 GHz. It must be
<figure><img src="image_5.png" /><figcaption>Fig. 4. Sensitivity to the vegetation volume fraction of (a) the vertical polarization effective temperature, and (b) the polarization ratio through the continuous model.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. As in Fig. 4, except for gravimetric moisture.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. As in Fig. 4, except for temperature gradient.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 7. As in Fig. 4, except for ground temperature.</figcaption></figure>

<figure><img src="image_9.png" /></figure>

noted that MR is representative of the vertical gradient of humidity within the vegetation, and therefore should give some information on the water status of the plants. Fig. 8 shows that, once the heavy rains periods are excluded, linear relationships can be established between MR and SR (expressed in s · m⁻¹):

$$SR = 282.6 - 223 MR \quad (16)$$

for the wet season and

$$SR = 192.0 - 453 MR \quad (17)$$

for the dry season. The surface resistances in Fig. 8 correspond to averages of noon values over the six-day SMMR periods. The difference in regression lines of wet and dry seasons may be explained by a seasonal evolution of the branches and stems water content. The particular SMMR signal of heavy rains periods, which presents the highest values of MR (MR > 0.15), may be due to the presence of intercepted water on the upper leaves of the canopy or fog.

## B. Temperature

Fig. 9 presents the evolution of the measured air temperatures ($T_a$) at the DRF and of the continuous-model-retrieved temperature of the vegetation ($T_v$) as two altitudes above the soil (1.45 and 30.51 m), along with noon and daily precipitation rates. The evolution of $T_v$ at noon and midnight is in good agreement with the behavior of $T_a$.

The midday values of $T_v$ [Fig. 9(a) and (c)] are 2-6° higher than $T_a$ at the top of the canopy. On the other hand, $T_v$ can be lower than $T_a$ at the bottom of the canopy, and the difference never exceeds 2°. This is consistent with the temperature cycle decoupling between the base of the canopy and higher levels due to the interception of the

<figure><img src="image_10.png" /><figcaption>Fig. 8. Continuous model moisture ratio versus the *Piptadenia suaveolens* stomatal resistance at DRF site [32] for the wet (filled squares) and dry season (asterisks) and regression lines.</figcaption></figure>

solar radiation in the upper portion of the DRF canopy [39]. From Fig. 9(a) and (b), it is observed that there is a clear correspondence between the heavy rains of the wet season fifth SMMR period and a sharp drop in $T_v$ at the top of the canopy. This event is coincident with a reduction in noon SR averages (331 and 281 s · m⁻¹ for periods 4 and 5, respectively) and an increase of MR (-0.16 and 0.01 for periods 4 and 5, respectively). The SMMR periods 2, 3, and 4 present the highest values of $T_v$ and SR at the top of the canopy. During these relatively dry periods, the stomatal regulation tends to limit the transpiration rate (high values of SR), and thus the cooling due to evaporation. This may explain the high values of $T_v$ at the top of the canopy. The heavy rains of SMMR period 5 end this process.

For 0000 LST [Fig. 9(b) and (d)], $T_v$ is 1-4° lower than $T_a$ near the soil. At the top of the canopy, $T_v$ is only 1-2° lower than $T_a$ during the dry season. On the other hand,
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 9. Measured air temperature and inversed vegetation temperature (continuous model) at 30.51 and 1.45 m. Daily and 1200 LST hourly precipitation rates at DRF site. (a), (b) Wet season. (c), (d) Dry season. (a), (c) 1200 LST. (b), (d) 0000 LST.</figcaption></figure>

during the wet season, $T_v$ is 1-2° higher than $T_a$, except for the SMMR period 2 where $T_v \approx T_a$. At nighttime, the SMMR-derived temperatures at the bottom of the canopy are systematically lower than the top canopy temperatures. The difference is about 5° during the wet season and 2° during the dry season. This latter feature is consistent with micrometeorological measurements described in [39]. Indeed, as shown by [40], the vertical structure of the Amazonian forest favors a significant storage of heat in the upper part of the canopy. The particular seasonal cycle of the midnight top $T_v$ may be due to the higher IWC and cloud coverage which are observed during the wet season. The increased downward long-wave emission of the atmosphere during the wet season may significantly affect the components of the nighttime radiative budget of the upper part of the canopy. The reduction of this effect may explain the lower value of the difference between $T_v$ and $T_a$ at the top of the canopy during the wet season SMMR period 2, which is cloudless.

## VII. CONCLUSIONS

Thanks to surface measurements, it was possible to perform atmospheric corrections of the Nimbus-7 SMMR brightness temperatures and to retrieve the vegetation temperature and humidity by using radiative transfer modeling. Three models of the thermal microwave emission of the canopy were tested. The continuous model can be more efficiently inversed than discrete models as it is far less computer time-consuming and, for a given frequency, only four parameters are needed to model the vegetation structure. A vegetation humidity index, the moisture ratio, combining the information of both 37 and 6.6 GHz channels, has proved to be sensitive to variations of stomatal resistance. There is some doubt about SMMR data calibration. However, given the realism of simulated temperatures and the encouraging correlation between moisture ratio and stomatal conductance, it can be assumed that the model-calibration step over structure parameters enabled us to take the (possible) instrument-cal-
ibration errors into account. The inversed surface parameters, vegetation vertical temperature profile, and stomatal resistance may be used as entry variables of one-dimensional models of the energy budget of the vegetation, and thus lead to the estimation of the canopy evapotranspiration.

## ACKNOWLEDGMENT

The authors thank Dr. A. O. Manzi and Dr. J. M. dos Santos (INPE, Brazil), Dr. A. D. O. Marques Filho (INPA, Brazil), and Dr. W. J. Shuttleworth (IH, U.K.), who provided the ground data as well as many helpful comments. They also thank D. S. Han and NSSDC, USA, for providing the SMMR half-degree TCT tapes.

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<figure><img src="image_15.png" /></figure>

Jean-Christophe Calvet received the engineering degree from the Institut National Agronomique Paris-Grignon, Paris, France, in agronomy, a second engineering degree from the École Nationale de la Météorologie, Toulouse, France, in meteorology, and the Ms.Sc. degree from the Université Paul Sabatier, Toulouse, also in meterology.

In 1990 he joined the Centre National de Recherches Météorologiques, Toulouse. From September 1990 to March 1991 he was on leave of absence to work at the Laboratoire d'Etudes et de

Recherches en Télédétection Spatiale, Toulouse, and from April 1991 to July 1992 at the Instituto Nacional de Pesquisas Espaciais, São José dos Campos, Brazil. His applications interests are in the use of remote sensing over land surfaces for meterology.

<figure><img src="image_16.png" /></figure>

Jean-Pierre Wigneron received the engineering degree from the Ecole Nationale Supérieure de l'Aéronautique et de l'Espace, Toulouse, France, in signal processing and radar.

In 1990 he joined the Institut National de Recherches Agronomiques, Station de Bioclimatologie, Avignon, France. He received the Ph.D. degree from the Université Paul Sabatier, Toulouse, France, in 1993. His research interests include passive microwave remote sensing applied to vegetation and microwave modeling.

Eric Mougin received the engineering degree in agronomy from the Ecole Nationale Supérieure d'Agronomie, Nancy, France, in 1981, and the Ph.D. degree from the Institut National Polytechnique, Toulouse, in 1989.

Since 1985 he has been with the Centre d'Etude Spatiale des Rayonnements, Toulouse, working on microwave remote sensing applied to vegetation studies. His current research interests include the coupling of multispectral data to ecosystem models, in particular forest models.

<figure><img src="image_17.png" /></figure>

Yann H. Kerr (M'88) received the engineering degree from the Ecole Nationale Supérieure de l'Aéronautique et de l'Espace, Toulouse, France, in radar and telecommunications, and the Ms.Sc. degree from Glasgow University, Glasgow, Scotland, in electronics and electrical engineering and a Ph.D. from the Université Paul Sabatier, Toulouse, France.

From 1980 to 1985 he was employed by the Centre National d'Etudes Spatiales, Toulouse, France. In 1985 he joined the Laboratoire d'Etudes et de Recherches en Télédétection Spatiale as a Research Scientist where, from May 1987 to December 1988, he was on leave of absence to work at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena. His field of interest are in the theory and techniques for microwave and thermal infrared remote sensing of the Earth, with emphasis on hydrology and vegetation monitoring.

<figure><img src="image_18.png" /></figure>

Jorge L. S. Brito received the engineering degree from the Universidade Federal de Viçosa, Viçosa, Brazil, in land surveying in 1988, and the Ms.Sc. degree from the Instituto Nacional de Pesquisas Espaciais, INPE São José dos Campos, Brazil, in remote sensing in 1992.

In 1988 he worked in irrigation management. During the period 1989-1990 he worked as an Engineer in forest mapping and environment monitoring. From January to May 1992 he worked in the Projecto de Mapeamento de Deforestamento da Amazônia at INPE. Since then, he has been with the Universidade Federal de Uberlândia MG, Brazil. His field of interest is environment management, specifically hydrological modeling with the use of remote sensing techniques.