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Wide-Area Soil Moisture Estimation Using the Propagation of Low-Frequency

Electromagnetic Signals

William Scheftic (Graduate Student, Atmospheric Sciences, University of Arizona)

Kenneth L. Cummins and E. Philip Krider (Atmospheric Sciences, University of Arizona)

David Goodrich, Susan Moran, and Russell Scott (USDA Southwest Watershed Research Center)

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Discussion Outline

- Finite soil surface conductivity has a quantifiable effect on surface-wave radio propagation in the 100 kHz to 1 MHz range

- Brief theoretical explanation

- Lightning Based method

- Methodology

- Preliminary results

- Some Limitations

- Radio transmission method

- Overview of summer 2007 field campaign

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1 104

1 105

1 106

1 107

1 103

0.01

0.1

1

3.5

3

2.5

2

1.5

1

0.5

0

Freq [Hz]

Sig

nal

Att

enu

atio

n

Pha

se [

rad]

Conductivity = 10 mS/m; Propagation distance = 100 kmEffect of finite conductivity on surface-wave signal propagation

(propagation model of Norton, 1937):

U2 i

i 0 c2

U U2

R R U2 i2c

R

z

RU

z

RU

F R 1 i4 R

1 R 2exp

4 R

1 R 2

erfc i 4 R

1 R 2

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Variation with Conductivity

• Soil – Low pass filter on propagating fields

• Smaller conductivity or larger distance: lower cutoff-frequency

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Electrical conductivity varies with soil moisture content

Percent soil saturation

Ele

ctric

al C

ondu

ctiv

ity

(mS

/m)

σ=2.

%W=0.34

0 0.063 0.13 0.19 0.25 0.31 0.38 0.44 0.50

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

Archie’s Equation:

WwRAmW

eR%%1

Where σ is the electrical conductivity, Re is the resistivity, %W is the percent water content, and β represents the relevant soil properties. The exponent α is typically in the range of 1.5 and 2.2.

Figure: β = 10, α = 1.5 (blue) and 2.0 (red)

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Lightning Background

2 3 4 – 6 7 - 13 14

17 – 33 ms ... 50 – 83.5 ms … 216 – 233 ms

23:42:47.542 ... No NLDN

Report … 23:42:47.762

Cloud-to-ground lightning electromagnetic fields: (b) First, and (c) Subsequent strokes

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Rise-time determined by the highest frequencies

2 3 4 – 6 7 - 13 14

17 – 33 ms ... 50 – 83.5 ms … 216 – 233 ms

23:42:47.542 ... No NLDN

Report … 23:42:47.762

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Propagation Animation - 75->450 km distanceConductivity = 5 mS/m

55 56 57 58 59 60 61 62 63 64 651

0.83

0.67

0.5

0.33

0.17

0.0

0.858

xf75m

sensor_lpf m

6555m

106

fs

75 km

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55 56 57 58 59 60 61 62 63 64 651

0.83

0.67

0.5

0.33

0.17

0.0

0.858

xf75m

sensor_lpf m

6555m

106

fs

75 km

Propagation Animation - 75->450 km distance

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55 56 57 58 59 60 61 62 63 64 651

0.83

0.67

0.5

0.33

0.17

0.0

0.858

xf150m

sensor_lpf m

6555m

106

fs

150 km

Propagation Animation - 75->450 km distance

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55 56 57 58 59 60 61 62 63 64 651

0.83

0.67

0.5

0.33

0.17

0.0

0.858

xf225m

sensor_lpf m

6555m

106

fs

225 km

Propagation Animation - 75->450 km distance

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55 56 57 58 59 60 61 62 63 64 651

0.83

0.67

0.5

0.33

0.17

0.0

0.858

xf300m

sensor_lpf m

6555m

106

fs

300 km

Propagation Animation - 75->450 km distance

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55 56 57 58 59 60 61 62 63 64 651

0.83

0.67

0.5

0.33

0.17

0.0

0.858

xf375m

sensor_lpf m

6555m

106

fs

375 km

Propagation Animation - 75->450 km distance

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55 56 57 58 59 60 61 62 63 64 651

0.83

0.67

0.5

0.33

0.17

0.0

0.858

xf450m

sensor_lpf m

6555m

106

fs

450 km

Propagation Animation - 75->450 km distance

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Rudimentary LTG Method

200 km LordsburgTucson

Williams

Window Rock

Yuma

• Select desired path for analysis

• Starting at a polygon that defines the lightning-observation region

• Ending at a sensor location (e.g., Lordsburg; Williams)

• Evaluate risetime of lightning waveform measured by the selected sensor.

• Convert risetime to apparent electrical conductivity

• Convert apparent conductivity to soil moisture

• Used North American Regional Reanalysis (NARR) as validation

Polygon

PathSensor

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Average Risetime over U.S.

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Normalized Cumulative Frequency Distribution of Risetime for Different Time Periods in 2005

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

2.5 3 3.5 4 4.5 5 5.5 6 6.5

Risetime [μs]

7-7 to 7-21

7-22 to 7-27

7-29 to 8-5

8-6 to 8-23

9-5 to 9-11

Risetime for All Negative First Strokes in Tucson Area (Recorded at Lordsburg Sensor)NARR Soil Moisture for 5 Periods During the 2005 Season

0

0.05

0.1

0.15

0.2

0.25

0.3

0.356/

22

6/27 7/2

7/7

7/12

7/17

7/22

7/27 8/1

8/6

8/11

8/16

8/21

8/26

8/31 9/5

9/10

Date (2005)

Vo

l So

il. M

ois

t [f

ract

ion

]

0

2

4

6

8

10

12

14

16

Ris

etim

e [μ

s]

Distribution of Risetime And Soil Moisture

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14

16

18

20

22

24

26

06/27 07/07 07/17 07/27 08/06 08/16 08/26 09/05 09/15

Date (2005)

(100

/RT

) [1

00/μ

s]

0.13

0.15

0.17

0.19

0.21

0.23

0.25

0.27

Vo

l. S

oil

Mo

ist.

[f

ract

ion

]

condc soil0_10

Soil Moisture vs. Conductivity(loose criteria)

y = 0.0126x - 0.0441R2 = 0.1846

0.13

0.15

0.17

0.19

0.21

0.23

0.25

0.27

14 16 18 20 22 24 26

100 / Risetime [100/μs]

Vo

l. S

oil

Mo

ist.

[fr

acti

on

]

>20 w gt. count >35 w gt. count

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17

18

19

20

21

22

23

07/07 07/17 07/27 08/06 08/16 08/26 09/05 09/15

Date (2005)

(100

/RT

) [1

00/μ

s]

0.13

0.15

0.17

0.19

0.21

0.23

0.25

0.27

Vo

l. S

oil

Mo

ist.

[f

ract

ion

]

condc soil0_10

y = 0.0247x - 0.2907R2 = 0.5754

0.13

0.15

0.17

0.19

0.21

0.23

0.25

0.27

17 18 19 20 21 22 23

100 / Risetime [100/μs]

Vo

l. S

oil

Mo

ist.

[fr

acti

on

]

Soil Moisture vs. Conductivity(weighted count > 35)

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Limitations

• Other factors affect conductivity changes

• Soil temperature, soil salinity, conductivity gradient over a several-meter depth

• No perfect set of wide-area data for validation

• NARR can miss precipitation events as occurred for at least one of the 2005 lightning events.

• The size of the lightning region being analyzed determines how similar lightning to sensor paths really are.

• Must have lightning!!

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An alternate signal source is man-made narrow-band radio signals

(LORAN, NDB, AM radio stations)

Sa

Sc

Sb

Tx

dc

da

dab

Longitude

Latitude

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The effect can be seen as changes in magnitude and phase for narrow-band radio signals

φ

μSec

E

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RadioTX Field Campaign ‘07

• June->October Field Campaign in San Pedro Basin

• Three broadband sensors

• Remote control from PAS

• Measure mag/phase vs. fq.

• Derive conductivity

• Correlate with WG and San Pedro in-situ measurements, and NARR

Note: 18 AM transmitter within 100km of Tombstone

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420 kHz NDB

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790 kHz AM station

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Questions?

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Supporting Material

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Wide-area Validation:North American Regional Reanalysis

Specifications• 32 km resolution, every 3

hours

• Available from Jan 1979 through Feb 2007

• Adequate representation of hydrologic balance

• Uses NOAH LSM ver. 2.6

• 4 soil depth layers

• Uses hourly rain gauge data and PRISM technique to assimilate precipitation

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Comparison of Daily Soil Moisture from NARR Dataset (0 to 10 cm) and ARS In-situ Measurements (5cm)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

06/15 06/25 07/05 07/15 07/25 08/04 08/14 08/24 09/03 09/13 09/23

Date (2005)

Re

lativ

e S

atu

ratio

n [(

fra

ctio

n-m

in)/

(ma

x-m

in)]

ARS (Charleston, AZ) NARR (31.66N 110.18W)

Soil Moisture: NARR Vs. ARS In-Situ

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