Active microwave measurement of soil water content

REMOTE SENSING OF ENVIRONMENT

3, 185-203 (1974)

185

Active Microwave Measurement of Soil Water Content* F. T. ULABY, J. CIHLAR, and R. K. MOORE University of Kansas Center for Research, Inc., Lawrence, Kansas 66045

Measurements of radar backscatter from bare soil at 4.7, 5.9, and 7.1 GHz for incident angles of 0-70° have been analyzed to determine sensitivity to soil moisture. Because the effective depth of penetration of the radar signal is only about one skin depth, the observed signals were correlated with the moisture in a skin depth as characterized by the attenuation coefficient (recipi-ocal of skin depth). Since the attenuation coefficient is a monotonically increasing function of moisture density, it may also be used as a measure of moisture content over the distance involved, which varies with frequency and moisture content. The measurements show an approximately linear increase in scattering with attenuation coefficient of the soil at angles within 10° of vertical and all frequencies. At 4.7 GHz this increase continues relatively large out to 70° incidence, but by 7.1 GHz the sensitivity is much less even at 20° and practically gone at 50° . An inversion technique to determine how well the moisture content can be estimated from the scattered signal indicates good success for near-vertical angles and middle ranges of moisture density, with poorer success at smaller moisture densities and an anomaly in the data at the highest moisture density that must be resolved by further experimentation.

1. I n t r o d u c t i o n The amount of water stored near the terrain surface is of considerable importance from both theoretical and practical viewpoints. Soil moisture enters as a basic component into the hydrological cycle, energy exchanged near the surface, and into modeling of various ecosystem processes. Practically, a knowledge of soil moisture levels is important for flood forecasting, growing crops, wildlife management, etc. The present approach to soil water content estimation is based on an areal extrapolation of point measurements. However, such extrapolation is questionable because both precipitation and soil properties and consequently distribution of soil moisture vary spatially (Dawdy et al., 1969; Huff, 1966; Mason et al., 1967; Mader, 1963; Andrew and Stearns, 1963). An alternative potential approach is to estimate soil moisture by remote sensing methods

which can directly cover large areas within a short time period. The microwave region of the electromagnetic spectrum is especially attractive since the presence of water strongly affects the microwave return and at the same time the return is not directly influenced by the chemical and minerological properties of the soil material (Lundien, 1971; Edgerton et al., 1971). Application of radiometers to soil moisture determination has been investigated in a number of studies (Edgerton et al., 1968, 1971; Poe et al., 1971; Jean et al., 1972; Schmugge et al., 1972). Radar response to soil moisture has been studied only recently (Dickey et al., 1972; King, 1973). In the only systematic investigation of the active microwave response of bare soils reported so far, Ulaby (1974) presented some results and initial analysis of backscatter measurements from two fields. The purpose of this paper is to discuss the active microwave response to soil moisture using a new model based on the skin depth (attenuation) concept.

*This research reported was supported by NASA/JSC under Contract NAS 9-10261.

© American Elsevier Publishing Company, Inc., 1974

186

F.T. ULABY, J. CIHLER, AND R. K. MOORE

This model is particularly relevant for remote soil moisture determination. In addition, vertical transmit-vertical receive (VV) polarization data are 'compared to those for horizontal transmit-horizontal receive (HH) polarization reported by Ulaby (1974). 2. D a t a A c q u i s i t i o n Ulaby (1974) reported results of measurements from two fields: a slightly rough field (in terms of wavelength) where the root-meansquare (rms) height variation was 2.5 cm and a rougher field with a r m s height variation of 5.5

cm. The difference in surface roughnesses was due to management. The rough field was plowed when wet, which resulted in the formation of large clods of soil material; these clods hardened upon drying and thus preserved their shape throughout the period of measurements. In contrast, the slightly rough field was cultivated under a lower moisture content; therefore few clods were formed, and roughness was caused mainly by the cultivation pattern. Since the roughness exhibited by the rough field was considerably higher than that usually encountered in a cultivated area, the present paper deals only with the data on the slightly

FIG. 1. The experimental field used for scattering coefficient measurements. Soil is Pawnee clay loam, rms surface height is 2.5 cm.

SOIL WATER ACTIVE MICROWAVE MEASUREMENTS

rough field. Soil on this field, classified as Pawnee clay l o a m (Dickey and Z i m m e r m a n , in preparation) is a deep, well to m o d e r a t e l y drained soil developed in glacial till (Fig. 1). The field was located on an upland, gently sloping surface. Radar return m e a s u r e m e n t s were made by MAPS (Microwave Active and Passive Spectrom e t e r ; see Ulaby, 1973) over a period o f one m o n t h . Each " s e t " o f data consisted o f returns measured at frequencies 4 GHz-8 GHz and incidence angles 0 ° (nadir)-70 ° (increments o f 0.4 G H z and 10 °, respectively). Radar backscatter data were collected for five different soil moisture conditions. Prior to analysis, the f r e q u e n c y range was divided into three segments, and the backscattering coefficients within each segment were averaged. The central frequencies were 4.7 GHz, 5.9 GHz, and 7.1 GHz.

187

Soil samples were taken f r o m the following depths: 0-2 cm, 2-5 cm, 5-9 cm, 9-15 cm, and 15-25 cm. In addition, ten cores have been collected f r o m the d e p t h 0-35 cm for bulk density determinations. A m o r e detailed description o f data acquisition, reduction, and precision was given by Ulaby (1974). 3.

Backscattering Coefficient vs S o i l M o i s t u r e

In previous investigations o f the microwave response to soil moisture, it was c u s t o m a r y to relate the microwave signal to water c o n t e n t within a soil layer of a constant thickness, determined either prior to the m e a s u r e m e n t s or from the data to be analyzed as the " m o s t representative" thickness. In the above ment i o n e d paper, Ulaby ( 1 9 7 4 ) used a w e i g h t e d average moisture c o n t e n t of the top 5 cm o f

TABLE 1. Skin Depth 8 in cm for the Soil Moisture Profiles of Figure 5. Profile Incidence Angle Number b

Date of Measurement

Moisture Content a

Frequency in GHz

0°

10°

20 °

30 °

40 °

50 °

60 °

70 °

1

8/18/72

4.8

4.7 5.9 7.1

6.2 5.8 5.5

6.2 5.8 5.5

6.2 5.8 5.4

6.2 5.8 5.4

6.2 5.8 5.4

6.2 5.7 5.4

6.2 5.7 5.4

6.2 5.7 5.4

2

8/15/72

15.8

4.7 5.9 7.1

3.3 3.1 2.8

3.3 3.1 2.8

3.3 3.1 2.8

3.3 3.1 2.8

3.3 3.0 2.8

3.3 3.0 2.8

3.3 3.0 2.8

3.3 3.0 2.8

3

8/29/72

24.0

4.7 5.9 7.1

1.4 1.2 1.0

1.4 1.2 1.0

1.4 1.1 1.0

1.4 1.1 1.0

1.4 1.1 1.0

1.4 1.1 0.9

1.4 1.1 0.9

1.4 1.1 0.9

4

9/5/72

30.2

4.7 5.9 7.1

1.1 0.9 0.7

1.1 0.9 0.7

1.1 0.9 0.7

1.1 0.9 0.7

1.1 0.9 0.7

1.1 0.8 0.7

1.0 0.8 0.7

1.0 0.8 0.7

5

8/25/72

36.3

4.7 5.9 7.1

1.1 0.9 0.7

1.1 0.9 0.7

1.1 0.9 0.7

1.1 0.9 0.7

1.1 0.8 0.7

1.1 0.8 0.7

1.0 0.8 0.7

1.0 0.8 0.7

6

c

20.0

4.7 5.9 7.1

1.5 1.2 1.0

1.5 1.2 1.0

1.5 1.2 1.0

1.5 1.2 1.0

1.5 1.2 1.0

1.5 1.2 1.0

1.4 1.2 1.0

1.4 1.1 0.9

aAverage moisture content of the top 5 cm of soil mwe in percent by weight. bMoisture profiles are shown in Fig. 5. CHypothetical case, moisture profile assumed constant with depth.

188

soil as a measure of soil water content. The depth o f 5 cm was a compromise choice made on the basis o f skin depth (defined in Sec. 3.1) calculations. Using dielectric constant data from Wiebe (1971), the skin depth for 5% moisture content by weight is 8 cm at 4.7 GHz. As moisture content and frequency are increased, the skin depth decreases to less than 1 cm (Table 1). For the five moisture conditions under consideration, the average moisture contents over the top 5 cm were calculated to be 4.3, 15.8, 24.0, 30.2, and 36.3%. The radar backscattering coefficient, o °, of a given target is a measure of the backscattering strength (power) of the target relative to an isotropic scatterer having the same crosssectional area. Since o ° can vary over several orders of magnitude as a function of incidence angle or target type, it is usually expressed in decibels (dB) for convenience. The associated polarizations of the transmitter and receiver antennas are indicated in the form of subscripts. Fig. 2 shows aH~t plotted against the soil moisture contents by weight mw. Two main observations were made (Ulaby, 1974). First, the OHH 0 response to moisture appeared linear between approxiamtely 15 and 30% moisture content; the response was low below 15% moisture, and a slope reversal tendency existed for moistures above 30%. Secondly, the moisture range with a linear o ° response increased as the frequency increased from 4.7 to 7.1 GHz. Backscattering coefficients measured for VV polarization (Fig. 3) were similar in shape at all frequencies and incidence angles to those for HH polarization; however, differences existed in the magnitudes of o ° values. The curves for VV polarization closely approximated those for HH polarization at all frequencies and angles o f incidence for moisture contents below 15% but were located below the HH curves for higher moisture contents. In addition, Ovv ° values increased only after moisture content exceeded 20%, and the increase was smaller than for HH polarization.

F.I. ULABY, J. CIHLAR, AND R. K. MOORE

The tendency for slope reversal at high moisture contents and its frequency dependence was explained as being due to the smoothing effect of rainfall (Ulaby, 1974); this caused the return to decrease at 4.7 GHz but less so at 7.1 GHz where the surface appears rougher. The same explanation probably holds also for VV polarization. The small moisture response of the signal at low moisture contents appears to be due to dielectric properties of the soil/water mixture. Dielectric constant measurements of soils at different water contents have indicated a similar lag (Cihlar and Ulaby, 1974). An explanation advanced by Lundien (1971) and Wiebe (1971) utilized the dielectric constant decrease of water molecules adsorbed at the soil particles. It may be noted that a similar lag of microwave response to low soil moisture contents was observed in passive radiometric data (e.g., Schmugge et al., 1972), which was also plotted against the average moisture content in a constant-width layer. A consideration of dielectric behavior of materials suggests that microwave response to soil moisture as outlined above and in other studies where a constant thickness of the soil was used can be regarded only as a first approximation. The reason is that the thickness of soil actually interacting with the electromagnetic radiation varies with moisture content and incident angle. Therefore, a more realistic picture of active microwave response to soil moisture should include these variations.

3.1. Skin Depth Model Electromagnetic energy incident normally upon the surface o f a homogeneous soil medium is partly reflected and partly transmitted through the medium. If the medium is conductive, the transmitted portion will undergo attenuation at a rate defined by the field (electric or magnetic) attenuation coefficient a. Since the attenuation rate is exponential, at a depth ~ = 1/a the field magnitude will reduce

189

SOIL WATER ACTIVE MICROWAVE MEASUREMENTS 20

/,, o*

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].5.8 24.0 30.2 36.3 40.0 Percent Moisture Content by Weight, m. (a) 221 Frequency 7.1 GHz )P0* Polarization HH Incidence Angle

4.3

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Percent Moisture Content by Weight. m~ (c)

FIG. 2.(a) Scattering coefficient as a function of moisture content in the top 5 cm. Frequency is 4.7 CHz. (b) Scattering coefficient as a function of moisture content in the top 5 cm. Frequency is 5.9 GHz. (c) Scattering coefficient as a function of moisture content in the top 5 cm. Frequency is 7.1 GHz.

190

F . T . ULABY, J. CIHLAR, AND R. K. MOORE

20

Frequency 4.7 GHz Polarization VV Incidence Angle

16

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4.3 1 .8 24.0 .2 36.3 40.0 Percent Mo sture Content by Weight, m,,,

(a) 0. 20 16

12 .E

Frequency 5.9 GHz Polarization VV Incidence Angle o - - - - - . 0. o----.. 1.0. t~-30° z)..-- ~ pOO g 70*

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16

Frequency 7.1 GHz Polarization VV Incidence Angle o.-- ~ . 0.

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15.8 24.0 30.2 3613 4().0 Percent Moisture Content by Weight, rnw

4.'3 ' ' ' 40.0 ' 15.8 24.0 3,().2 36.3 Percent Mt)isture Content by Weight, rn~ (c)

(b) FIG. 3(a) Scattering coefficient as a function of moisture content in the top 5 cm. Frequency is 4.7 CHz. (b) Scattering coefficient as a function of moisture content in the top 5 cm. Frequency is 5.9 CHz. (c) Scattering coefficient as a function of moisture content in the top 5 cm. Frequency is 7.1 CHz.

SOIL WATER ACTIVE MICROWAVE MEASUREMENTS

to 1/e (0.37) of its surface value and the power will reduce to 1/e 2 (0.135) of the power at the surface. 8 is defined as the soil "skin depth." In a nonhomogeneous medium where the soil dielectric parameters vary with depth, an equivalent multilayered model can be employed to calculate the attenuation and the effective reflection coefficient at the surface. In this case, the reflected component of the incident wave has contributions from all the layers due to the vertical nonhomogeneity of the soil medium. The contribution from a layer at a depth 6 will undergo additional attenuation of l/e 2 thereby arriving at the surface with a magnitude 1/e 4 (0.0183) of its original incident value. Hence neglecting contributions from deeper layers represents an omission of less than 2% of the returned power. The attenuation coefficient, a, in nepers/m is defined in terms of the wavelength ~ in meters and the real and imaginary parts of the relative dielectric constant, K~ and K2 respectively as

ot=---~-

2

\--~-1,/

-

1

(1)

At normal incidence the skin depth 6 can then be defined as the depth at which 8

.f" o~z) dz = l,

(2)

o

where z represents depth. The skin depth 8 of a nonhomogeneous medium can be used to define an equivalent homogeneous medium having an effective attenuation coefficient % = 1/8. At a given frequency, values of K1 and K2 are strongly affected by soil moisture content but relatively little by other soil characteristics. Unfortunately, the moisture dependence of the soil dielectric properties has not been well defined so far. A survey of available data (Cihlar and Ulaby, 1974) indicated a wide range of Ka and K2 values obtained by different investigators for similar soils and

191

frequencies. The spread in reported data may be explained by differences in experimental techniques and the difficulties involved in sample preparation and handling during the measurements but it presents problems in the choice of representative dielectric constant values. Fig. 4 shows results of several measurements of the soil dielectric constant obtained near 10 GHz. Average curves were drawn through the data points and extrapolated for higher soil moisture contents using dielectric constant values of water at 20°C and 9.3 GHz (Paris, 1969). These data were selected as the closest available approximation to the frequency range 4.7 to 7.1 GHz and were considered representative for Pawnee clay loam. It may be noted that frequency dependence of the dielectric properties of a moist soil is due to that of the water component only (Cihlar and Ulaby, 1974). To calculate skin depths for the five moisture profiles, measurements from different depths were approximated with a step function at 1-cm increments (Fig. 5). Subsequently, skin depths for normal incidence were computed by considering cumulative attenuation of soil layers 0.1-cm thick. At other look angles, the skin depth was calculated using Snell's law of refraction, the depth being measured vertically (Table 1). It is noteworthy that the skin depth calculated for the five profiles was almost independent of incidence angle (Table 1). This behavior occurred because in all profiles the moisture increased with depth (Fig. 5) and so did K~ and K2 values. Consequently, the angle of refraction approached zero. If soil moisture decreased with depth, the angle of refraction would approach 90 ° instead. At the intermediate point, i.e., when soil moisture does not change vertically, skin depth decreases in proortion to the cosine of the angle of refraction in the medium, which in turn is related to the incidence angle and index of refraction by Snell's law. These trends are confirmed in

192

F . T . ULABY, J. CIHLAR, AND R. K. MOORE

REALPART ] ABILENECLAYLOAM, 10.6 GHz (WlEBE. 19711 [ o AMARILLOFINESANDYLOAM.10.6GHz(WIEBE,1971)I 70 o RICHFIELD SILTLOAM, 9.4 GHz (LUNDIEN0 1966) [ V LOAM, 9.5 GHz (LESCHANSKII et al., 1971) ! • WATER,9.3 GHz, 20° C (PARIS, 1969) ]

60 .

/

SO

// //

/

/ o/

~

IMAGINARY PART I ~BILENECLAY LOAN, / ~ 1 0 . 6 GHz (WIEBE, 1971)I I• AMARILLO FINE SANDY [ [ L O A M , 10.6 GHz [ {WIEBE, 1971) • WATER,9.3 GHz, 20°C PAR S, i%9) |

II

I

30

H

LOSS

K~ ~ , /

TANGENT,~ / 20

\.i. /

9

REALPART,K I ~ A G I N A R Y PART,K~

//

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/

I 50

//

!0.4 '0.3~

ID.2

10

!0.1 ~ 10

20 30 40 50 60 70 80 90 SOl L MOI STURE(PERCENTBY WEI GHT)

Io.o 100

FIG. 4. Measured dielectric constant data of loamy soil as a function of moisture content b y weight around 10 GHz. Solid curves were drawn t o fit the data points and the broken curves were extrapolated.

fi

Moisture Contentin Percentby Weight

° o.

io

3o

2o

~

4o

,

7- 10

15

20L

1

FIG. 5. Vertical soil moisture profiles for Pawnee clay loam measured at the following dates: 1(8/18), 2(8/15), 3(8/29), 4(9/5), and 5(8/25).

SOIL WATER ACTIVE MICROWAVEMEASUREMENTS

Table 1 where a hypothetical profile (profile six) was assumed to contain a constant 20% moisture. Under field conditions, moisture content usually increases with depth in the near-surface layer, except shortly after rain when it does not change, or decreases as the depth increases. This behavior suggests that the depth of penetration should be approximately equal at all incidence angles under most field conditions for each frequency considered in this paper. For large depths of penetration, vertical moisture gradients will introduce differences in penetration depths between incidence angles. Measured backscatter coefficent o ° is plotted against skin depth 6 and the corresponding effective attenuation coefficient ae in Fig. 6(a-f). The graphs show several systematic trends. First, o ° increases almost linearly at all frequencies, incidence angles, and both polarizations as the attenuation increases. The exception occurred at small and large incidence angles for the highest moisture case (moisture profile five) where o ° deviated from the linear trend. The differences occurred at 4.7 GHz [Fig. 6(a) and (d)] and to some extent at 5.9 GHz [Fig. 6(b) and (e)]. Ulaby (1973b) suggested that these deviations were due to changes in surface roughness due to rain and his explanation is also applicable here. There is some uncertainty as to the accuracy of the moisture measurements but even if very high moisture contents were assumed, the large increase in the scattering coefficient at low incidence angles between moisture profiles four and five could not be accounted for on the basis of dielectric properties alone. For example, reflection coefficient increases less than 4.0 dB when moisture content increases from 20% to 40% (Ulaby, 1973b). Thus the roughness effect is evident. It is worth noting, however, that the roughness change resulting in the interference with o ° response to soil moisture was only temporary and directly associated with the rainfall. Other data points, taken both before and after the rain (Table 1)

193

conformed to the general trend of a linear increase in scattering coefficient with increasing attenuation. At a given frequency, the slope of o ° - v s attentuation curves decreases with increasing incidence angle; this trend was most apparent at 7.1 GHz (both polarizations) and almost absent at 4.7 GHz (HH polarization). Furthermore, at the near-vertical angles, the slope was higher for 7.1 GHz than for 4.7 GHz. Thus the high frequency exhibited a more extreme response to soil moisture at different incidence angles than the low frequency. The vertical spacing of curves in Fig. 6(a-f) shows that the decrease in scattering coefficient was considerable between 0 and 30°-40 ° incident angle but smaller for higher angles. Most of the above discussed trends in the o ° - v s - a t t e n u a t i o n relationship were better exhibited for HH polarization than for VV. The values of OHH° were higher than Ovv ° for almost all frequency and incidence angle combinations; this behavior might have been in part due to the roughness effect as the preferred orientation of the roughness pattern was parallel to the range direction (Fig. 1). These results suggest that complex target roughness/soil moisture content/radar signal interactions took place during the measurements. For example, the anomalous behavior of 5.9 GHz measurements [600-70 °; Fig. 6(b) and (e)] could be explained by the relationship between radar frequency and surface roughness spectrum. The above noted rms height of 2.5 cm was based only on the large roughness elements. However, soil particles (individual and aggregates) probably ranged in size from 10-2 cm to 10 cm. Thus, depending on the frequency used, radar return could be affected by a particular range of roughness element sizes. If such an explantion is valid, a more precise understanding of radar response to soil moisture will depend on the knowledge of soil properties and processes leading to formation and breakdown of soil aggregates.

F. T. ULABY, J. CIHLAR, AND R. K. MOORE

194 Frequency 4. 7 GHz Polarization HH Incidence Angle • --__.

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20

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FIG. 6. Scattering coefficient as a function of attenuation and skin depth (calculated for moisture profiles of Fig. 5). (a) 4.7 GHz. HH Polarization, (b) 5.9 GHz, HH Polarization, (c) 7.1 GHz, HH Polarization.

20

Frequency 4. 7 GHz Polarization VV Incidence Angle

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-160 0

I

i

J 1.0 Attenuation (x in Nepers per cm

•

1.5

0.5

e

I

I

8.0 4.0

I

I

I

2.0

1.0

0.7

Skin Depth (S in cm (d) 20

Frequency 5.9 GHz Polarization VV ncidence Angle

16

• __--.

A~,

00 100 20° 30 ° 40 °

A l - -

50 °

o--..

.____ 12

.E

o---

! ...... V- -

8

0 >

/

4

/

16

Frequency 7.1 GHz Polarization VV Incidence Angle e----00

12

o--.. i---o ---

100 20° 30°

A--.

40°

00 /

•

/ '/ / /o /

./

.I/ 0

./

100

~

/

/ i"

0

/."

...i'

o

~---500 ! ...... 6O°

8

.E

V

o

/"

/

el/"e

30

o

6O° 700

6> ~c;

20

/

70°

t, 4

I/i

.~ i

/.

20*

..... ~

/

./

/

./

30°

/

/.

/ i

_....------

.~.~

-8

=12

-12

1160

•

0

L 0.5

, 1.0

Attenuation %in Nepers per cm I

I

8.0 4.0

[

l

2.0

1.0

Skin Depth ~ in cm (e) FIG. 6 ( c o n t i n u e d ) . Polarization.

I 1.5 I

.16 b.

100

.t

•

•

.I

~

o 30°

)

_p_ . . . . . . . _4o0

I

i

I

0.5

1.0

1.5

Attenuation %in Nepers per cm

l I

0.7

•

/ ../

..i O

i'

.......

5e'

-8

0°

, ~-.

./

/

i'O

/

....- ---"

/

/

i

o/' •

/

/

/

I

8.0 4.0

I

I

2.0

1.0

Of7

Skin Depth (~ in cm (f)

(d) 4.7 GHz, V V P o l a r i z a t i o n , (e) 5.9 GHz, V V P o l a r i z a t i o n , a n d (f) 7.1 GHz, V V

196

F.T. ULABY, J. CIHLAR, AND R. K. MOORE

3.2. Soil Water Content Determination from Radar Return The ability of radar to respond to changes in soil moisture content, enhanced by its characteristics as a remote sensor, gives it a unique potential for soil moisture determinations over large areas. It is important to know the actual amount of water retained within a certain thickness of the soil. The previously used methodology of developing the o ° v s moisture content relationship, based on percent (by weight) of moisture, does not represent a realistic approach to determining the amounts of water involved for two reasons. First, the amount of water in a unit volume of soil rnv depends on the bulk density of soil (Hillel, 1971): rnv = 0.01 ( m w ) ( d b )

(g/cm3),

(3)

where m w is moisture content in percent by weight (see Figs. 2 and 3), and db is soil bulk density in grams per c m 3. Second, the total thickness (volume) of soil involved cannot be determined from curves like those in Figs. 2 and 3. In contrast, the total amount of water can in principle be determined using the skin-depth concept, which was first used by Poe et al. (1971) in their analysis of microwave radiometric measurements. Their model consisted of the following sequence: (a) measured radiometric temperature was converted to effective emissivity through knowledge of the system parameters and soil temperature, (b)using a plane surface model, emissivity is related to water content per unit volume nay based on dielectric constant and bulk density, and (c) for m y the skin depth 6 was determined at tile microwave frequency used. The total amount of wate? within a soil volume 1 M 1 X 8 (cm 3) was determined by multiplying rn v and 6. By taking measurements at several Ire-

quencies, Poe etal. (1971) showed that soil profile moisture distribution could be predicted from radiometric measurements. In the present study, the above concept was modified for active microwave data. From measured backscattering coefficients at a given frequency, incidence angle and polarization, the skin depth is determined from curves in Fig. 6. Next, the amount of water within the skin depth is estimated. This estimation can be done by using skin depth versus water content (in grams per cm a) curves and then multiplying skin depth by water content (Poe et al., 1971). Fig. 7 shows such curves for three frequencies, calculated using dielectric constant data from Fig. 4. Soil water content values in Fig. 7 were calculated from Eq. (3) by assuming constant rn w values with depth and using bulk densities from Fig. 8; since moisture contents calculated in this manner may for practical purposes be considered equivalent to variable profile distributions of moisture with identical skin depths, they are designated as "effective" moisture contents, nave. As the attenuation increases, a banding effect is shown to appear in Fig. 7, which is due to the fact that the attenuation coefficient a is a complex function of two parameters K~ and K2, each of which exhibits a nonlinear dependence on the moisture content naw. Hence, there exists a band of effective moisture contents nave corresponding to a given skin depth. Alternatively, the skin depth water content can be estimated directly using curves relating skin depth and "cumulative" water content My expressed in grams per cm 2 as is shown in Fig. 9 where the total water within a column 1 cm = in cross-section and one skin depth high is calculated (by multiplying rn pe by the skin depth in Fig. 7) as a function of skin depth. Again an uncertainty range develops at high moistures due to the banding effect. This range of uncertainty is less than 0.015 g/cm = for wet soil and is negligible when the moisture contents are low. The slopes of curves in Fig. 9

197

SOIL WATER ACTIVE MICROWAVE MEASUREMENTS Frequency: • 4. 7 GHz "- ..... 5. g GHz • - - - - I. I GHz Calculated for Constant Moistu re Content with Depth (in % by Weight, Indicated by Numbers / Next to thePointsK f f ~

0.4 %

t.} 0.3

~34 ~/"'/'34/~M ;,/

/

D/ ;""SO / / ./

/ /'30

" /~,

E ~o.2

y" / ,

g

,,4

lo\/.-~j xo,c'.V-,I- j r ~ j ~ " 10

O.1

/,,/ 4

0.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Attenuation c( in Nepers per cm e

lz.~-"io 41o

io

Skin Depth8 in cm

llo

o.'7

FIG. 7. Effective moisture content mve as a function of attenuation and skin depth. Values were calculated from dielectric constant data (Fig. 4) and bulk density

profile (Fig. 8). Bulk Density in Grams per 0L 0

1.2

I.I

1 5

L

1.3

Cm 3

1.4

1.5

l_ 1

E "-~ 10

}

"[ 2O

FIG. 8. Measured bulk density profile for Pawnee clay loam.

198

F.T. ULABY, J. CIHLAR, AND R. K. MOORE

0.7

Frequency: •

4. 76Hz

. . . . . . 5.9 GHz ~-7.1GHz Calculated for Constant Moisture Content with Depth (in % by Weight, Indicated by Numbers Next to the Points).

~0.6 4~

\ \ ~.

~o.5 g ¢.)

*~0.4 z~

\ ~,

~0.3

20

10 \,~:,;.,

......

0.2 0.0

0.2

0.4

0.6

., i30

,,,,~'!" f J u

0.8

1.0

1.2

1.4

Attenuation aein Nepersper cm

12.5/8.04.0

2.0 1.0 Skin DepthS in cm

0.7

FIG. 9. Cumulative moisture content M v as a function of attenuation and skin depth. Values were calculated from Fig. 7. reflect variations in loss tangent (1); for example, the minima of the curves at approximately 15-25% moisture by weight correspond to maximum loss tangents K2/K~ (see Fig. 4). To illustrate how cumulative water content can be determined from backscatter measurements, consider the following example. Given OHH° equal to 8.0 dB measured at 4.7 GHz and 0o incidence angle. From Fig. 6(a) the corresponding attenuation is equal to 0.68 nepers/ cm and from Fig. 9 the cumulative water content is 0.325 g/cm 2 + 0.103 g/cm 2 distributed over a skin depth of 1.5 cm. Due to a considerable variability of surface roughness under field conditions, it may not be feasible to prepare a single set of o ° versus skin depth curves for practical purposes. Rather, the effect of roughness might be eliminated by

taking measurements (Stiles, 1973).

at

several frequencies

3.3. Soil Moisture Sensitivity Radar soil moisture sensitivity may be defined as the rate of change of radar backscattering coefficient with soil moisture content by weight or by volume: S w = &o° /ZXmwe or Sv = lXo° / A m v e respectively , where it is understood that rowe (in %) and rove (in grams per cm 3) are the effective moisture contents o f the soil within the skin depth. Thus by combining the measured o ° versus attenuation (or skin depth) data shown in Fig. 6 with calculated values of skin depth as a function of m ve shown in Fig. 7, o ° can be related to rnve d i r e c t l y a s shown in

199

SOIL WATER ACTIVE MICROWAVE MEASUREMENTS

Frequency 4.7 GHz

20

....

Incidence Angle 0o •

o---.

10°

~----

50 °

•----

20°

! ......

° - - -

30°

V

60: 70°

Polarization HH

/

/

16

/

12

/

.E 8

°7(

/

c-

4

Polarization VV 20

•

16

/

/

f

/

8 /

4

o

/

/

:7

• ~;~'..~41

--" 30!'.-. - ~

v/-

y m/

."

./ /

~'-4

/~o

12

o

o/:

L-

40°

.

Ot

/

¢

/

/

,,/°¸

/ >• I

,

s

20.o-

o

/

-4

-8 -12

-12

-16 0.

. 0.1

.

. 0.2

. 0.3

-16 0.4 0.0

f-170 ° . . 0.1

.

. 012

0.3

0.4

Effective Moisture Content mve in Grams per cm 3 FIG. 10. Scattering coefficient as a function of effective moisture content. Frequency is 4.7 GHz.

Figs. 10-12 for the three microwave frequencies under consideration. Since the accuracy of moisture contents for skin depth smaller than 1 cm. is uncertain, such data points were joined using a thinner line. For the most part, the response appears linear at all incidence angles and frequencies except for the highest moisture case. Comparison of the results shown in Figs. 10-12 using the skin depth model with the earlier results shown in Fig. 2 and 3 using the average moisture content in the top 5 cm of the soil as the soil moisture parameter, clearly indicates the improvement in the response over the low moisture region. Thus the application

of a more realistic model for estimating soil moisture content yields better agreement with theoretical and experimental considerations of dielectric behavior of soils as a function of their moisture contents. The apparent "anomaly" exhibited by the highest moisture content data in the form of sharp increases in 0 and 10 ° and slope reversal at the higher angles for all frequency and polarization cases shown in Figs. 10-12 is attributed to the surface smoothing effect caused by the rain just prior to recording the data set. The radar sensitivity to soil moisture content

200

F . T . ULABY, J. CIHLAR, AND R. K. MOORE

Frequency 5.9 OHz Incidence Angle 0o ,.

....

o .... o

24

.. 10o 20° - 30° •

Polarization HH

40°

z x - - - - 50° ! . . . . . . . 60° ~ 70o Polarization VV 20 I

16l

16~

12~

o/

i

./%'

/

/

i~

.E 8~ E

.//o/

~oL

"r-

~-4

•/4 /

,4

y./"

/o7

...

/

8

F.//o

o

o/o 2 e ~- . / :~ " ;.'~e. I£6o°

/,

l

12

A

o¢ /

o

4t

./

./4

,~0'? "

.X" /...

/ 'Ty

/~

L •

~.<""

69/

~%o

"

-12 -161 O.

~-I6L .

0'1

0.'2

0.'3

0.4 0.0

.

0.1

.

.

0.2

0.3

0.4

Effective Moisture Content mve in Grams per cm 3 FIG. 11, Scattering coefficient as a function of effective moisture content. Frequency is 5.9 GHz.

b y volume Sv was calculated for each anglefrequency combination in Figs. 10-12 (slopes of the linear portion of the soil moisture response curves) and then plotted in Fig. 13 as a function of incidence angle. In general, the sensitivity is highest at 0 ° incidence angle, decreases rapidly to about 40 ° and levels off for higher angles. The highest sensitivity at 0 ° was for 7.1 GHz (both polarization), while at large angles, HH polarization (4.7, 5.9 GHz) indica'ted a considerably better response than the other combinati6ns. At 20 °, the sensitivity to moisture showed the least dependence on frequency and polarization.

4. C o n c l u s i o n s Reasonable correlation has been shown between the radar backscatter from bare soil and the moisture content expressed in terms of the mean attenuation coefficient over a distance of one skin depth below the surface. A method for evaluating the moisture density in the top layer of soil has been compared with experimental data and shown under some conditions to be reasonably successful, but far from perfect. The observations were made at three frequencies: 4.7, 5.9, and 7.1 GHz and at angles of incidence between vertical and 70 ° from verti-

SOIL WATER ACTIVE MICROWAVE MEASUREMENTS

201

Frequency 7. 1 OHz Incidence Angle 0° •

....

o

--10 °

.... o

24

,oI

20°

- 30°

I

! ......

50° 60°

~

700 Polarization VV

Polarization HH

/

16i

40"

~----

20

.

16

/

/

//o

07" o

!

12

• 12 ~ I

/ 8

.E 8 1

// //

c

-

4

/

~"'~

•

.y/:

,~/ /-" ~'3o0~;

//

i

/

°I

-4

~-4

cz3

-8

[;~>~00 ' -12

-t2 r 'I -16t O. 0

1

. O.I

.

. 0.2

. 0.3

-16 . . 0.4 0.0 0. i

.

. 0.2

. 0~3

0.4

Effective Moisture Content mve in Grams per cm 3

FIG. 12. Scattering coefficient as a function of effective moisture content. Frequency is 7.1 GHz. cal. Within 10 ° of vertical, a strong and essentially linear relation was observed at all frequencies between scattering coefficient and effective attenuation coefficient; but at larger angles the sensitivity to changes in attenuation coefficient, and consequently in moisture content, was considerably greater at the lower frequency. An apparent anomaly for the data run involving the largest moisture content m a y be explained by changes in the surface roughness caused by the rain that created the very wet condition in the soft. Additional observations at high moisture contents will be required to establish whether this explanation is correct.

The skin depth for the highest moisture contents at the top frequency is only of the order of a centimeter. This means two things: Measurements under these conditions are less valuable for determining moisture content to significant depths, and the validity of the "ground-truth" measurements is somewhat questionable because the significant moisture region is so thin that it is rather difficult to define for a rough surface. These results indicate that radar techniques for determining soil moisture have promise but are far from proven. Lower frequencies for which skin depths are much greater seem necessary if total moisture content over soil

202

F.T. ULABY, I. CIHLAR, AND R. K. MOORE

ot 0.8

'\ \'\\

,,,., O. E

\\

~o.t

I_. - ------

• o • o •

Frequency 4.7GHz 4.7 GHz 5.9 GHz 5.9 GHz 1.1 GHz

Polarization HH VV HH VV HH

----

6

7.1GHz

VV

\-\

~._cO . ~

•~" 0.4 ~0.3 ..... . . . J

o

~0.2

.

O.l

L

o.o o

1'o

1

3'o

4'0

I

60

1

70

Incidence Angle in Degrees

FIG. 13. Moisture sensitivity Sv as a function of incidence angle.

t h i c k n e s s e s i m p o r t a n t t o users is to be measured d i r e c t l y r a t h e r t h a n i n f e r r e d f r o m t h e m o i s t u r e in very t h i n surface layers.

References Andrew, L. E., and F. W. Stearns (1963), Physical characteristics of four Mississippi soils, Soil Sci. Soc. Amer. Proc. 27, 693-697. Cihlar, J., and F. T. Ulaby (1974), Dielectric properties of soils as a function of moisture content, CRES Technical Report 177-47, University of Kansas Center for Research, Inc., Lawrence, Kansas. Dawdy, D. R., and J. M. Bergmann (1969), Effect of rainfall variability on streamflow simulation, Water Resources Res. 5,958-966. Dickey, H., and J. L. Zimmerman, Douglas County Soil Survey Report, in preparation. Di~key, F., C. King, J. Holtzman, and R. K. Moore (1972), Moisture. dependency of radar backscatter from irrigated and non-irrigated fields at 400 MHz and 13.3 GHz, CRES Technical Memorandum

177-33, University of Kansas Center for Research, Inc., Lawrence, Kansas. Edgerton, A. T., R. M. Mandl, G. A. Poe, J. E. Jenkins F. Soltis, and S. Sakamoto (1968). Passive microwave measurements of snow, soils, and snow-icewater systems, Technical R e p o r t No. 4, Aerojet General Corporation, El Monte, California. Edgerton, A. T., F. Ruskey, D. Williams, A. Stogryn, G. Poe, D. Meeks, and O. Russel (1971), Microwave emmission characteristics of natural materials and the environment, Final Technical Report 9016R-8, Aerojet General Corporation, E1 Monte, California. Hillel, D. (1971), Soil and Water: Physical Principles and Processes, Academic Press, New York. Huff, I. A. (1966), The effect of natural rainfall variability in verification of rain modification experiments, Water Resources Res. 2, 791-801. Jean, B. R., C. L. Kroll, J. A. Richerson, J. W. Rouse, Jr., T. G. Sibley and M. L. Wiebe (1972), Microwave radiometer measurements of soil moisture, Technical Report RSE-32, Remote Sensing Center, Texas A&M University, College Station, Texas. King, C. (1973), A survey of terrain radar backscatter coefficient measurement program, CRES Technical

SOIL WATER ACTIVE MICROWAVE MEASUREMENTS

Memorandum 243-1, University of Kansas Center for Research, Inc., Lawrence, Kansas. Lundien, J. R. (1966), Terrain analysis by electromagnetic means, Technical Report No. 3-693, Report 2, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi. Lundien, J. R. (1971), Terrain analysis by electromagnetic means, Technical Report No. 3-393, Report 5, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi. Mader, D. L. (1963), Soil variability-A serious problem in soil-site studies in the northeast, Soil Sck Soc. Amer. Proc. 27,707-709. Mason, D. D., J. F. Lutz, and R. G. Petersen (1957), Hydraulic conductivity as related to certain soil properties in a number of great soil groups-Sampling errors involved, Soil ScL Soc. Amer. Proc. 21, 554-560. Paris, J. F. (1969), Microwave radiometry and its application to marine meteorology and oceanography, Texas A&M University, College Station, Texas.

203

Poe, G., A. Stogryn, and A. T. Edgerton (t971), Determination of soil moisture content using microwave radiometry, Final Technical Report 1684R-1, Aerojet General Corporation, E1 Monte, California. Schmugge, T., P. Gloersen, and T. Wilheit (1972), Remote sensing of soil moisture with microwave radiometers, Goddard Space Flight Center, NASA, Greenbelt, Maryland. Stiles, W. H. (1973), The effect of surface roughness on the microwave measurement of soil moisture content, M.S. Thesis, University of Arkansas, Fayetteville, Arkansas. Ulaby, F. T. (1973), 4-8 GHz Microwave Active and Passive Spectrometer (MAPS), CRES Technical Report 177-34, University of Kansas Center for Research, Inc., Lawrence, Kansas. Ulaby, F. T. (1974), Radar measurement of soil moisture content, IEEE Trans. Antennas Propaga. tion AP22 (2) 257-265, March, 1974. Wiebe, M. L. (1971), Laboratory measurement of the complex dielectric constant, Technical Report RSE23, Texas A&M University, College Station, Texas.

Received May 20, 1974; revised July 22, 1974.