Estimating near-surface soil water content from...

Bydrological Sciences—Journal—des Sciences Hydrologiques, 43(4) August 1998 Special issue: Monitoring and Modelling of Soil Moisture: Integration over Time and Space 521

Estimating near-surface soil water content from passive microwave remote sensing—an application of MICRO-SWEAT

L. P. SIMMONDS Department of Soil Science, The University of Reading, Whiteknights, Reading RG6 6DW, UK

E. J. BURKE Institute of Hydrology, Crowmarsh Gifford, Wallingford, Oxfordshire 0X10 8BB, UK

Abstract The emissivity of soil surfaces at microwave frequencies depends strongly on the near-surface water content. However this relationship varies between soils. Use is made of a model (MICRO-SWEAT) which couples water, heat and microwave radiation transfers through soils to show that the main cause of soil variation in the relationship between apparent emissivity at 1.4 GHz (eapp) and the average water content of the upper 2 cm of the profile (90„2) are differences in the dielectric properties. A simple semi-empirical model is proposed, based on the effect of soil particle size distribution on bound/free water partitioning, which provides a calibration between em and 0O_2. Although, in principle, the detailed shape of the water content distribution close to the surface will influence the eapp/90_2 relationship, such effects are only significant during short periods ( < 1 h) following the onset of rainfall which produces steep wetting fronts close to the soil surface.

Estimation par télédétection du contenu en eau du sol près de sa surface à l'aide d'un détecteur passif de microondes—une application de MICRO-SWEAT Résumé L'émissivité de la surface du sol dans la gamme de fréquence des microondes dépend énormément du contenu en eau du sol près de sa surface. Cette dépendance dépend du type de sol. L'utilisation d'un modèle (MICRO-SWEAT) qui couple le contenu en eau, la conduction de la chaleur et la transmission des microondes à travers le sol montre que la variation selon les différents types de sols de la relation entre l'émissivité apparente à 1.4 GHz (<?app) et la quantité moyenne d'eau dans les deux premiers centimètres du sol (60.2), résulte essentiellement des différences de leurs propriétés diélectriques. Nous proposons un modèle semi-empirique simple, fondé sur les effets de la distribution des tailles des particules du sol sur la répartition de l'eau en eau libre et en eau liée, qui conduit à une relation entre eapp et 90_2. Bien qu'en principe la répartition des formes de l'eau près de la surface du sol influence la relation entre eapp et 90_2, de tel effets ne sont significatifs que pendant de courtes périodes ( < 1 h) suivant le début de précipitations produisant un front d'humidité près de la surface du sol.

INTRODUCTION

Water has a strong influence on the soil dielectric properties (and hence the soil emissivity) at microwave frequencies. Much work has been done to explore possibilities for inferring the water content close to the soil surface from measurement of passive microwave emission, given that the emissivity of wet soil

Open for discussion until I February 1999

522 L. P. Simmonds & E. J. Burke

(typically around 0.6) is so much lower than for dry soil where the emissivity can exceed 0.9 (Jackson & Schmugge, 1989; Schmugge et al, 1986).

Empirical relationships have been established between the apparent emissivity of the land surface and the near-surface water content (e.g. Schmugge & Jackson, 1994). The apparent emissivity, <?app, is usually expressed in terms of the ratio of the measured microwave brightness temperature, TB, to the effective physical temperature, Teff, of the segment of the soil profile from which the microwave radiation is emitted. A number of ways have been suggested for estimating Tef{

(Choudhury & Schmugge, 1982; Chanzy et al., 1997). The choice of the depth of soil over which to average the "near-surface water content" is rather arbitrary (usually 0-2 or 0-5 cm in the case of L band), though there is significant contribution from greater depths. For example, Simmonds & Burke (in press) found that the thermal sampling depth at L band varied between 8 and 20 cm, depending on the soil water content. The longest (hence most deeply-penetrating) wavelength generally used for remote sensing of soil water is L band (1.4 GHz, 21 cm wavelength), though shorter wavelengths (e.g. C and S band, 5 and 2.65 GHz respectively) are also used. The longer wavelengths are preferable in the context of remote sensing of soil water because the emission is less influenced by surface roughness, penetrates a greater thickness of soil, and there is less interference from overlying material (e.g. vegetation canopy or crop residues).

Empirical relationships between em and near-surface water content inevitably have considerable scatter, and the relationships vary with soil type. There are a number of reasons why there is not a unique relationship between eapp and near-surface water content, including: (a) soils differ in their relationship between soil dielectric properties and soil water

content, as a consequence of differences in particle size distribution affecting the partitioning between bound and free water; and

(b) soils can have very different distributions of soil water content for a given value of the average near-surface water content. This paper uses an established model (MICRO-SWEAT—Burke et al, 1997,

1998; Burke, 1997) which links microwave emission and transfer through soil to a model of simultaneous heat and water flow in the soil profile in order to examine the relative importance of these two factors on the relationship between em and the average water content of the upper 2 cm of the soil profile.

FIELD MEASUREMENTS

Results are presented from a field experiment carried out in 1985 by USD A/NASA Goddard Space Flight Center personnel at the USDA Beltsville Agricultural Research Center. Adjacent plots (10 m X 10 m) containing soils of different textures were created by importing soils with a range of texture into beds 25 cm deep overlying the native loamy sand soil. The soils were the native soil (loamy sand, 75% sand, 5% clay) and the imported loam (45% sand, 22% clay) and sandy loam soils (65% sand, 10% clay). The soil surfaces were smoothed, and half of each plot was used to grow

Estimating near-surface soil water content from passive microwave remote sensing 523

soybeans, though this paper only considers results from the bare soil areas. Microwave emission was measured several times each day during the experimental periods using dual-polarized L- and C-band radiometers that were mounted 6 m above the soil surface on a track boom, with a measurement angle of 10° off nadir. The experiment was carried out during the summer when rainfall was infrequent, and the progress of microwave emission was monitored during several drydown periods following heavy irrigations (approximately 100 mm irrigation applied each time). The footprint of the radiometer was approximately 1 m2. At each time of measurement of microwave brightness temperature (TB), measurements were made of the gravimetric water content of the 0-2 cm soil layer (three replicates, each of about 50 g soil taken just outside the radiometer field of view). Half-hourly measurements of windspeed, air temperature and humidity, and net radiation were available as inputs to MICRO-SWEAT, together with twice daily measurements of rainfall. Further details are given by Burke (1997).

MICRO-SWEAT

MICRO-SWEAT is based on a model coupling heat flow (Fourier equation) and water flow (Richards equation) though a soil profile (SWEAT—Daamen & Simmonds, 1996). The soil surface is linked to the atmosphere via the surface energy balance and aerodynamic equations describing the exchanges of sensible and latent heat between the soil surface and the reference height at which the meteorological variables (air temperature and humidity, windspeed and either net or downwelling solar radiation) are measured.

The water retention and conductivity characteristics of the soil are represented by the following equations:

I

and (1) , 2+3/h

where 0 is the volumetric water content, \\i and \\ie are the matric and air entry potentials, K and Ksll are the unsaturated and saturated hydraulic conductivity, b is a "shape" parameter, and 9sat is the saturated water content, estimated from the bulk density. Though not used in the context of this paper, MICRO-SWEAT has the facility to model layered soils, and also includes routines for plant water extraction.

The model of simultaneous heat and water flow through the soil profile enables simulations of the dynamics of soil water content and temperature in each layer, which are then used as inputs into the microwave emission and transfer component of MICRO-SWEAT. The first step of the microwave transfer sub-model is the estimation of the dielectric constant for each soil layer. An important aspect of this paper is

524 L. P. Simmonds & E. J, Burke

consideration of the influence on microwave emission of differences between soils in their dielectric properties. At low water contents there is a curvilinear relationship between the dielectric constant of soil and water content until a transitional water content is reached (0,) above which the relationship is linear. The transitional water content is that above which there is no further increase in bound water content, and so is well correlated with the water retained at the permanent wilting point. MICRO-SWEAT uses the empirical approach adopted by Wang & Schmugge (1980), though other, more physically-based approaches, have been used by other workers (e.g. Dobson et al, 1985). Wang & Schmugge (1980) provide a regression equation to estimate 8, from the mass fractions of sand (msand ) and clay (mclay):

0, = 0.1983 - 0.03136/Ksand + 0.2342mclay (2)

Following Wang & Schmugge (1980), MICRO-SWEAT estimates the soil dielectric constant, s, from the relative fractions of the soil volume occupied by solids, water and air, as follows:

e = > 0

s , + ( e w - e ; ) — y + (P-Q)ea+(1-P)e, for0<0, (3)

e = e / [6 ,+(6w -8 / )y] + ( 9 - e / ) e w + ( P - e ) 6 a + ( l - / > ) s , for0>0, (4)

where sa, s„ EW and er are the dielectric constants of air, ice (= bound water), free water and soil solids, respectively; P is the porosity; and y is a constant involved in the partitioning between free and bound water, and depends on the soil texture as follows:

y = 0.442 + 0.0365«sand - 0.272mclay (5)

With knowledge of the distributions of temperature and of dielectric properties through the soil profile, the Wilheit (1978) model is used by MICRO-SWEAT to describe the propagation of electromagnetic radiation through the soil layers. The microwave energy flux at the soil surface, expressed in terms of the brightness temperature, is calculated as:

TB =Xf,Ti+rsarfTsky (6)

where 7j is the physical temperature of the zth soil layer, ft is a fraction determining the contribution of the ith layer to the microwave emergent at the soil surface (Wilheit, 1978), rsurf is the surface reflectance (which depends on the dielectric propertiesof the surface layer) and Tsky is the radiometric sky temperature. The distribution of f-t through the soil layers is also used to determine the effective physical temperature of the soil, with respect to microwave emission (jTefr):

T./X

TeK is used in this paper to normalize TB in order to calculate the apparent emissivity of the soil surface.


RESULTS AND ANALYSIS

Verification of MICRO-SWEAT

Figure 1 shows for the sandy loam soil the measured courses of microwave brightness temperature (TB) in both the C and L bands during one of the drydown periods following irrigation, and also those predicted using MICRO-SWEAT following the procedure of Burke et al. (1997). Irrigating the dry soil on day 252 caused TB to fall by 75K, which was followed by a drying period during which the brightness temperature increased. Diurnal fluctuation in TB driven by fluctuation in the physical soil temperature, and by diurnal oscillation in the near surface soil water content caused by fluctuating evaporative demand. The increase in the C band TB during the drydown was faster than in the L band, reflecting the shallower depth of penetration at the shorter wavelength. The predicted courses of TB using MICRO-SWEAT were remarkably close to the observed brightness temperatures, with the root mean square error in TB

being less than 3K. Similar goodness of fit was obtained with the other soils, and during other dry downs, and has been achieved in other experiments (Burke et al, 1997', 1998). The only exception has been when attempting to model microwave emission from vertisols (Simmonds et al, in press), the most likely explanation of which is that the Wang & Schmugge (1980) mixing model for soil dielectric constant is inappropriate for vertisols, as found by others (Sabbing et al., 1997).

The relationship between apparent emissivity and near surface water content

The purpose of the paper is to examine the robustness of the relation between em and 90_2, and how (and why) this relationship varies between soils of different texture.

- measured C band modelled C band

A measured L band

modelled L band

250 252 254 256 258 260 262 264 Time (DOY)

Fig. 1 The time courses of measured and modelled microwave brightness temperatures in the L and C bands (horizontal polarization) over the sandy loam soil.

275

g | 250 C3

<D

a* B 9^5 3 d j l 200 (5

175

V aiU -ft > / X /

!•- .^

150


0.95

0.9

0.85

% 0.8 H

H* 0.75

0.7

0.65

0.6

5 10 15 20 25 30

Volumetric water content of 0 - 2 cm soil layer (%)

Fig. 2 The relationship between the apparent emissivity (L band) and the average water content of the upper 2 cm of the profile for the loam and the loamy sand (data are from the same period as Fig. 1).

Values for the apparent emissivity (eapp) were obtained by normalizing TB (L band) with respect to the effective soil temperature (Tef{), where Teff was calculated using equation (7). Simmonds & Burke (in press) showed that this method effectively removes scatter in the relationship that is attributable to differences in the shape of the temperature profile close to the soil surface.

The relationships between eapp and 00.2 for the two soils with most contrasting texture (the native loamy sand and the imported loam, Fig. 2) were different, with the loam tending to have the higher apparent emissivity at a given near-surface soil water content. The predictions of the relationship between em and 80_2 generated by the half-hourly time steps of MICRO-SWEAT (open symbols, Fig. 2) agreed well with the values obtained by direct measurement (close symbols), though were rather less scattered because, presumably, the gravimetric measurements had an element of error attributable to spatial variability in soil water content.

The finding that MICRO-SWEAT successfully predicted both the time courses of rs(e.g. Fig. 1) and the differences between soils in the relation between em and 90_2

(e.g. Fig. 2) implies that the sub-models used to predict the soil dielectric properties and the propagation of microwave radiation were sufficiently accurate (except for the vertisol case) to justify using MICRO-SWEAT to investigate further the causes of

Table 1 The water retention and conductivity characteristics of the hypothetical soils.

Sand Clay b \|/e pb Km

(%) (%) (J kg1) (kg m 3 ) (kg s m'3)

Clay 14.9 55.2 11.7 -3.86 1420 0.000124 Loam 40.0 19.7 6.1 -2.59 1480 0.000432 Sand 92.7 2.9 3.3 -0.48 1660 0.002554

*F°i*&£t>o S-

D loamy sand modelled

o loam modelled

• loamy sand measured

• loam measured


W 270 -

250 -

230

£ 210

> 190

••5 170

150 250 252 254 262 264 266 256 258 260

Time (DOY) Fig. 3 The simulated time courses of brightness temperature for the three hypothetical soils detailed in Table 1, using the same weather parameters as Fig. 1.

0 10 20 30 40 50

Volumetric water content of 0 - 2 cm soil layer (%) Fig. 4 The simulated relationships between apparent emissivity and the average water content of the upper 2 cm of the soil profile, derived from the simulations in Fig. 3.

variation between soils in the relation between em and 90_2. This was done in a modelling study of three "hypothetical" soils with very contrasting texture, the water retention and hydraulic conductivity characteristics of which are given in Table 1. Figure 3 shows the differences between these soils in the predicted course of TB

(L band, horizontal polarization) assuming the same boundary conditions as Fig. 1. It


was predicted that the sandy soil dried more rapidly than the loam or clay following irrigation, causing TB to increase more quickly. Figure 4, based on the same set of simulations, shows clear differences between the soils in the relationship between eapp

and 6̂ 2 in that, like Fig. 2, the finer textured soils tended to have much larger emissivity at a given near surface water content.

One reason for the differences between the soils evident in Figs 2 and 4 is that soils with higher clay content have a greater proportion of "bound" water at a given soil water content, and therefore have a lower dielectric constant (and hence a higher emissivity). Alternatively, it is likely that the soils differed markedly in the shape of the distribution of water content with depth, leading to systematic differences between the soils in the correlation between the 90„2 and the effective average soil water content weighted according to the contributions of each soil layer to the emission of microwave radiation.

MICRO-SWEAT provides a means of distinguishing between these separate effects of soil type. Figure 5 shows the relationship between eapp and 80 2 for the same three soils (and the same model boundary conditions) as Fig. 4, the only difference being that the soil texture parameters in the soil dielectric model (6, and y in equations (3) and (4)) were set equal to the average values for the three soils. The soil properties used in the water and heat flow components of MICRO-SWEAT were kept as before (i.e. soil specific), so the simulations would have resulted in the same soil water content and temperature profiles as were predicted in the simulations used to produce Fig. 4. The finding that the curves for the three soils in Fig. 5 coalesced implies that it was differences between the soils in their dielectric properties that were responsible primarily for the differences in their relations between eapp and 6M.

Figure 5 implies that any differences between the soils in the detailed shape of

0.9 T

0.85 -

0.8 -

0.75 -

0.65 -

0.6 -

0.55 -

0.5 —

0 10 20 30 40 50

Volumetric water content of 0 - 2 cm soil layer (%) Fig. 5 The simulated relationships between eapp and 90.2 with MICRO-SWEAT parameterized to give the soils identical dielectric properties.

X

-A

clay

sand

loam

•linear fit


the water content profile had relatively minor influence on the apparent emissivity associated with a given value of 90̂ 2, despite the soils being very different in this respect. For example, Fig. 6 shows some of the profiles of water content that were obtained at various stages during the simulated dry downs in Fig. 3. The data sets shown have been selected to enable comparisons between the soil types in situations where the values of 90_2 were virtually identical. Care was taken to select data sets at times when the soils were subject to the same half-hourly potential evaporation rate, to avoid any confounding influence of differences in evaporative demand on the near-surface gradients in soil water content.

Volumetric water content (%) 15 20

mean 0-2 cm water content = 24.5

potential evaporation = 0.12 mm/h Fig. 6 Examples of comparisons between soils of different texture in the shape of their soil water content profiles at times of identical average water content in the upper 2 cm of the profile. In all cases, the soil surface was subject to the same hourly potential evaporation rate (0.12 mm h"1).

A simple semi-empirical model of the effect of soil texture on apparent emissivity

Despite the large differences between soils in the detailed distribution of water within the upper few centimetres of the soil profiles, the coalescence of the curves for the very different soils in Fig. 5 suggests the possibility of a simple calibration between near-surface water content and apparent emissivity that takes account only of differences between soils in the partitioning between bound and free water. A linear regression equation was fitted to the data in Fig. 5, which can be regarded as the calibration for a "standard" soil with dielectric properties that have been set, in this case, to those generated using equations (3) and (4) based on values of 9, and y (cf. equations (2) and (5)) that were the averages for the three "hypothetical" soils detailed in Table 1 (i.e. 9,av = 9.1475 and y2V = 0.3969). The regression equation was:

0.952 - 9.98 le„ (8)


where 602av is the average water content between 0 and 2 cm depth for the "standard" soil with average dielectric properties.

For soils with different texture, the value of 80.2av predicted from eapp using equation (8) has then to be adjusted to take account of the difference in partitioning between bound and free water. To do this, it is assumed the dielectric constant of the soil at the actual average water content in the upper 2 cm (60_2) would be the same as that of the "standard" soil at 80„2av. Assuming the Wang & Schmugge (1980) mixing model is valid, then in the case where the soil water content is less than, or equal to, the transition water content in the dielectric function, the effective dielectric constant of the "standard" soil is obtained by substitution of appropriate parameter values into equation (3):

Ssoil ~ W0-2,av . u0-2,av

+ ( />-e o _ 2 i a v )e f l +( l -P)s r (9)

which should be equal to the effective dielectric constant of the actual soil, calculated similarly as:

'soil "0 -2

8 , / \ 0-2 + ( P - e 0 _ 2 ) s f l + ( l - P ) 6 r (10)

Equations (9) and (10) are then solved for the unknown average water content in the upper 2 cm for the soil in question (90.2)- Where 6„_2iav > 8 /av a similar procedure is adopted based on equation (4). This gives rise to the following equations to compute 0O_2 from the apparent emissivity, given knowledge 8,av, yav, and the values of 8, and y for the soil in question which can be estimated from the sand and clay content (equations (2) and (5)):

9 0 - 2 = 6 , , a v [ s , + ( s , - e , ) Y a v ] + S w ( 0 O - 2 , a v - e , , a v ) ^ 6 , ( S , + ( e w - E , ) y ) + e , E w ( 1 1 )

for 0O-2,av > 6 , , av

or else

-e.. ±Js, - 4(e,--eJ y ( e f - 6 w )

"/,avY av ' S , e 0 - 2 , a v

2 ( e , . - E j y

(12)

for 60-2,av ^ e / ,av

and 0o_2av is obtained from the measured apparent emissivity using equation (8). It was assumed that the porosity was the same for both soils (differences in

porosity have negligible effect on the calculation of water content), and that there was no difference between the soils in the dielectric constants for the air and solid phases. It was also assumed that the values of 0Oj and 80.2>av were both on the same side of their respective transition water contents.


0.9 -

0.85 -

0.8 -

0.75 -

- 0.7 -H

0.65 -

0.6 -

0.55 -

0.5 0 10 20 30 40 50

Volumetric water content of 0 - 2 cm soil layer (%)

Fig. 7 The simulated relationships between eapp and B0„2 with solid lines showing also the relationships between eapp and QQ„2 predicted using the semi-empirical texture-based model given in equations (11) and (12).

Figure 7 represents the data shown in Fig. 4, but includes also the relationships between the apparent emissivity and 90„2 that were predicted for the three hypothetical soils using equations (11) and (12). Discontinuities occur around the transition water content, and are an artefact of the assumption that both 90_2av and 9M would be on the same side of their respective transition water contents. The good agreement between the two approaches implies that the assumptions made in deriving equations (11) and (12) were reasonable.

A more stringent test of the ability of equations (11) and (12) to predict 90_2 from knowledge of em would be to assess their performance under a much wider range of meteorological conditions involving a range of evaporative demand and a variety of frequencies and amounts of rainfall. Ideally the performance should be verified against direct measurements of eapp and 90.2, but there are no suitable data sets available. Instead, comparison was made with simulations using MICRO-SWEAT for two contrasting hypothetical soils (clay and sand; Table 1), using two very different meteorological data sets (Davis, California, April-September 1995: 20 minute data; Wallingford, UK, January-December 1996: 60 minute data).

The data points in Fig. 8 show the simulated values of em and 90„2, at each time step during the simulation period, where the time steps were set to the meteorological data time steps, but reduced by a factor of 6 during rainfall events). The solid lines show the linear regressions of em against 90,2 that were fitted to the data for the corresponding soil in Fig. 4 (which were well described by equations (11) and (12)). For both soils in both locations the great majority of points were clustered very close to the line obtained from the simulation of the single drydown at Beltsville. Despite there being a wide range of shapes of profiles of water content, it appears that, on


ST > £ ci U Q

00 . u

'"in i™ O ^ w m o


most occasions, such variation had little impact on the predicted relation between eapp

and 60„2. There were outliers, particularly in the mid-range of 90.2, where the apparent

emissivity was substantially less (but never substantially greater) than would have been predicted from the Beltsville drydown. This was particularly marked in the case of the sand, and was more evident in the Californian simulation. These outliers all occurred during rain events, or within 1 h following the cessation of rain, and were most dramatic when rain fell on very dry soil (as was common in the Californian simulation). It is possible that these outliers arise from problems of model stability during periods of rainfall where there are very rapid changes, and very steep gradients in soil water content. However, it is likely that these outliers are real, and that under such circumstances, the linkage, such as it is, between the water contents in the top centimetre or so and the soil below is effectively decoupled, until the wetting front disperses as the water redistributes. Such an effect would be expected to be more marked in sandy soils because of the more sharply defined wetting front. However, to put these outliers into context, it should be noted that each point represents a time step of a few minutes. Hence, in the case of the Californian sand simulation, the 60 or so outliers associated with shallow wetting fronts penetrating dry soil represented only a few hours out of the six months of simulation.

CONCLUSIONS

This paper has shown that soils differ in the relationships between near-surface water content and apparent emissivity at L band. Such differences between soils were explained using a simple model (MICRO-SWEAT) based on a semi-empirical model of soil dielectric properties and the Wilheit (1978) model of radiative transfer through stratified medium. It was concluded that differences between soils in the apparent emissivity associated with a given near-surface water content were attributable primarily to differences in the soil dielectric properties/water content relationship, rather than to the substantial differences between soils in the detailed shapes of the distribution of soil water close to the surface. For a given soil, the relationship between apparent emissivity and near-surface water content was found to be remarkably stable over a wide range of prevailing atmospheric conditions and wetting history. However, the relationship appeared to become unstable very shortly after the onset of rain falling on to dry soil, probably because of the presence of sharp wetting fronts close to the soil surface.

Acknowledgements The authors gratefully acknowledge the assistance of Peggy O'Neill (NASA Goddard Space Flight Center) in making the data from the 1985 experiment available. This project was part of work funded by the UK Natural Environment Research Council (projects GST/02/603 and GR3/11203). Jon Finch (Institute of Hydrology) and Marc Parlange (John Hopkins University) provided the meteorological data from Wallingford and Davis.


REFERENCES

Burke, E. J. (1997) Using a modelling approach to predict soil hydraulic parameters from passive microwave measurements for both bare and cropped soils. PhD Thesis, University of Reading, Reading, UK.

Burke, E. J., Gumey, R. J., Simmonds, L. P. & Jackson, T. J. (1997) Calibrating a soil water and energy budget model with remotely sensed data to obtain quantitative information about the soil. Wat. Resour. Res. 33, 1689-1697.

Burke, E. J., Gurney, R., Simmonds, L. P. & O'Neill, P. E. (1998) Using a modelling approach to predict soil hydraulic properties from passive microwave measurements. IEEE Trans. Geosci. Remote Sens. 36(2), 454-462.

Chanzy, A., Raju, R. J. & Wigneron, J. P. (1997) Estimation of soil microwave effective temperature at L and C bands. IEEE Trans. Geosci. Remote Sens. 35, 570-580.

Choudhury, B. J. & Schmugge, T. J. (1982) A parameterisation of effective soil temperature for microwave emission. /. Geophys. Res. 84, 287-294.

Daamen, C. C. & Simmonds, L. P. (1996) Measurement of evaporation from bare soil and its estimation using surface-resistance. Wat. Resour. Res. 32, 1393-1402.

Dobson, M. C , Ulaby, F. T., Hallikainen, M. T. & El Rayes, M. A. (1985) Microwave dielectric behaviour of wet soil: 2. dielectric mixing models. IEEE Trans. Geosci. Remote Sens. GE-23, 35-46.

Jackson, T. J. & Schmugge, T. J. (1989) Passive microwave remote sensing system for soil moisture, some supporting research. IEEE Trans. Geosci. Remote Sens. GE-27, 225-235.

Sabbing, J., Ball, J. A. R & Hancock, N. H. (1997) Dielectric behaviour of moist swelling clay soils at microwave frequencies. IEEE Trans. Geosci. Remote Sens. 35, 784-787.

Schmugge, T. J., O'Neill, P. E. & Wang, J. R. (1986) Passive soil moisture research. IEEE Trans. Geosci. Remote Sens. GE-24, 12-22.

Schmugge, T. J. & Jackson, T. J. (1994) Mapping surface soil moisture with microwave radiometers. Meteorol. Atmos. Phys. 54, 213-223.

Simmonds, L. P. & Burke, E. J. (in press) Application of a coupled microwave, energy and water transfer model to relate passive microwave emission from bare soils to near-surface water content and evaporation. Hydro! Earth System Sci.

Simmonds, L. P., Burke, E. J. & Gurney, R. (in press) Modelling microwave emission from soils, and it's application in remote sensing of soil moisture. Proc. Int. Soil Sci. Soc..

Wang, J. R. & Schmugge, T. J. (1980) An empirical model for the complex dielectric permittivity of soils as a function of water content. IEEE Trans. Geosci. Remote Sens. GE-18, 288-295.

Wilheit, T. T. (1978) Radiative transfer in a plane stratified dielectric. IEEE Trans. Geosci. Electronics 16, 138-143.

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