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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)



          University of Arizona   Institute of Atmospheric Physics
                                                                     Page 1
                       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

                University of Arizona   Institute of Atmospheric Physics
                                                                           Page 2
           Effect of finite                                                             Conductivity = 10 mS/m; Propagation distance = 100 km
           conductivity on                                                                                                1                                                                    0

           surface-wave                                                                                                                                                                            0.5
           signal
           propagation                                                                                                                                                                             1




                                                                                                   Signal Attenuation
                                                                                                                         0.1




                                                                                                                                                                                                         Phase [rad]
                                                                                                                                                                                                   1.5


                                                                                                                                                                                                   2

                                                                                                                        0.01
           (propagation model                                                                                                                                                                      2.5

           of Norton, 1937):
                                                                                                                                                                                                   3
                                             i
                 U2    
                                                          2      U     U2   
                                     i    0  c
                                                                                                          1 10
                                                                                                                         3
                                                                                                                                                                                                   3.5
                                                                                                                          1 10                     1 10                1 10             1 10
                                                                                                                                  4                         5                 6                    7
                                                                                     U   
                                                                                z
                             R U2     i
           R                                            R  
                                                                                R

                                                                                     U   
                                    2c                                          z
                                                                                R
                                                                                                                                                                  Freq [Hz]
                       4     R           4    R    erfci 4    R  
F   R   1  i                        exp                                                       
                        1     R   2   1     R   2
                                                                           
                                                                                       1     R   2
                                                                                                             



                                                                           University of Arizona                                      Institute of Atmospheric Physics
                                                                                                                                                                                  Page 3
           Variation with Conductivity
• Soil – Low pass filter on propagating fields
• Smaller conductivity or larger distance: lower cutoff-
frequency




               University of Arizona   Institute of Atmospheric Physics
                                                                          Page 4
                           Electrical conductivity varies with soil moisture
                                               content
                                                                                                  Archie’s Equation:


                                                                                                                       m
                                                                                                              1  %W   %W  
                                                                                                                  Re        A Rw
                                                                 %W=0.34
                           4
Electrical Conductivity




                          3.6                                                                     Where σ is the electrical conductivity, Re is the resistivity,
                          3.2                                                                     %W is the percent water content, and β represents the
                          2.8                                                                     relevant soil properties. The exponent α is typically in the
                          2.4
                                                                                                  range of 1.5 and 2.2.
                           2
                                                                                             σ=2.
                          1.6
                                                                                                  Figure: β = 10, α = 1.5 (blue) and 2.0 (red)
(mS/m)




                          1.2

                          0.8

                          0.4

                           0
                                0   0.063   0.13   0.19   0.25   0.31   0.38   0.44   0.5



                                            Percent soil saturation



                                                             University of Arizona          Institute of Atmospheric Physics
                                                                                                                                        Page 5
                                 Lightning Background




Field #        1             2         3         4–6        7 - 13         14
Interval   0 – 16 ms    17 – 33 ms     ...   50 – 83.5 ms     …       216 – 233 ms
 NLDN
                                              No NLDN
 Time                  23:42:47.542    ...                    …        23:42:47.762
                                               Report
  (UT)
   Cloud-to-ground
   lightning
   electromagnetic
   fields: (b) First, and
   (c) Subsequent
   strokes


                            University of Arizona      Institute of Atmospheric Physics
                                                                                          Page 6
           Rise-time determined by the highest frequencies




Field #         1             2        3         4–6        7 - 13         14
Interval    0 – 16 ms    17 – 33 ms    ...   50 – 83.5 ms     …       216 – 233 ms
 NLDN
                                              No NLDN
 Time                   23:42:47.542   ...                    …        23:42:47.762
                                               Report
  (UT)




                            University of Arizona      Institute of Atmospheric Physics
                                                                                          Page 7
Propagation Animation - 75->450 km distance
          Conductivity = 5 mS/m
                        0
               .0



                     0.17

                                                            75 km
                     0.33


      xf75 m
                      0.5
      sensor_lpf m



                     0.67




                     0.83



          0.858
                       1
                            55   56   57   58    59     60          61   62   63   64        65
                            55                                  6                       65
                                                           10
                                                      m
                                                           fs


                University of Arizona           Institute of Atmospheric Physics
                                                                                              Page 8
Propagation Animation - 75->450 km distance
                       0
              .0



                    0.17

                                                           75 km
                    0.33


     xf75 m
                     0.5
     sensor_lpf m



                    0.67




                    0.83



         0.858
                      1
                           55   56   57   58    59     60          61   62   63   64        65
                           55                                  6                       65
                                                          10
                                                     m
                                                          fs


               University of Arizona           Institute of Atmospheric Physics
                                                                                             Page 9
Propagation Animation - 75->450 km distance
                       0
               .0



                    0.17

                                                           150 km
                    0.33


     xf150 m
                     0.5
     sensor_lpf m



                    0.67




                    0.83



         0.858
                      1
                           55   56   57   58    59     60          61   62   63   64        65
                           55                                  6                       65
                                                          10
                                                     m
                                                          fs


                University of Arizona          Institute of Atmospheric Physics
                                                                                             Page 10
Propagation Animation - 75->450 km distance
                       0
               .0



                    0.17

                                                           225 km
                    0.33


     xf225 m
                     0.5
     sensor_lpf m



                    0.67




                    0.83



         0.858
                      1
                           55   56   57   58    59     60          61   62   63   64        65
                           55                                  6                       65
                                                          10
                                                     m
                                                          fs


                University of Arizona          Institute of Atmospheric Physics
                                                                                             Page 11
Propagation Animation - 75->450 km distance
                       0
               .0



                    0.17

                                                           300 km
                    0.33


     xf300 m
                     0.5
     sensor_lpf m



                    0.67




                    0.83



         0.858
                      1
                           55   56   57   58    59     60          61   62   63   64        65
                           55                                  6                       65
                                                          10
                                                     m
                                                          fs


                University of Arizona          Institute of Atmospheric Physics
                                                                                             Page 12
Propagation Animation - 75->450 km distance
                       0
               .0



                    0.17

                                                           375 km
                    0.33


     xf375 m
                     0.5
     sensor_lpf m



                    0.67




                    0.83



         0.858
                      1
                           55   56   57   58    59     60          61   62   63   64        65
                           55                                  6                       65
                                                          10
                                                     m
                                                          fs


                University of Arizona          Institute of Atmospheric Physics
                                                                                             Page 13
Propagation Animation - 75->450 km distance
                       0
               .0



                    0.17

                                                           450 km
                    0.33


     xf450 m
                     0.5
     sensor_lpf m



                    0.67




                    0.83



         0.858
                      1
                           55   56   57   58    59     60          61   62   63   64        65
                           55                                  6                       65
                                                          10
                                                     m
                                                          fs


                University of Arizona          Institute of Atmospheric Physics
                                                                                             Page 14
    Rudimentary LTG Method
• Select desired path for analysis                                                             Window
                                                                                               Rock
    • Starting at a polygon that
    defines the lightning-                                      Williams
    observation region
    • Ending at a sensor location
    (e.g., Lordsburg; Williams)
• Evaluate risetime of lightning
waveform measured by the                       Yuma          Polygon
                                                                          Tucson
selected sensor.                                      200 km                                   Lordsburg

• Convert risetime to apparent                                                                    Sensor
electrical conductivity                                                            Path
• Convert apparent conductivity to
soil moisture
• Used North American Regional
Reanalysis (NARR) as validation

                       University of Arizona   Institute of Atmospheric Physics
                                                                                     Page 15
Average Risetime over U.S.




          University of Arizona   Institute of Atmospheric Physics
                                                                     Page 16
Distribution of Risetime And Soil Moisture

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

                      0.35                                                                                                                                               16
                       0.3                                                                                                                                               14
                                                                                                                                                                         12
    Vol Soil. Moist




                      0.25




                                                                                                                                                                              Risetime [μs]
      [fraction]




                                                                                                                                                                         10
                       0.2
                                                                                                                                                                         8
                      0.15
                                                                                                                                                                         6
                       0.1                                                                                                                                               4
                      0.05                                                                                                                                               2
                        0                                                                                                                                                0
                             6/22


                                       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)




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

    1.00
    0.90
    0.80
    0.70                                                                                                                                                           7-7 to 7-21
    0.60                                                                                                                                                           7-22 to 7-27
    0.50                                                                                                                                                           7-29 to 8-5
    0.40                                                                                                                                                           8-6 to 8-23
    0.30                                                                                                                                                           9-5 to 9-11
    0.20
    0.10
    0.00
              2.5                      3             3.5           4             4.5               5                5.5             6                 6.5
                                                                          Risetim e [μs]


                                                    University of Arizona                Institute of Atmospheric Physics
                                                                                                                                                      Page 17
Soil Moisture vs. Conductivity
(loose criteria)

                                                                                                          condc       soil0_10

                                              26
                                                                                                                                                                             0.27
                                              24
          (100/RT) [100/μs]


                                                                                                                                                                             0.25




                                                                                                                                                                                     Vol. Soil Moist.
                                              22                                                                                                                             0.23




                                                                                                                                                                                        [fraction]
                                                                                                                                                                             0.21
                                              20
                                                                                                                                                                             0.19
                                                    18
                                                                                                                                                                             0.17
                                                    16
                                                                                                                                                                             0.15

                                                    14                                                                                                                       0.13
                                                    06/ 27       07/ 07        07/ 17            07/ 27           08/ 06              08/ 16           08/ 26   09/ 05   09/ 15

                                                                                                            Date (2005)




                                                                                                      >20 w gt. count           >35 w gt. count
                      Vol. Soil Moist. [fraction]




                                                     0.27                 y = 0.0126x - 0.0441
                                                     0.25                     R 2 = 0.1846
                                                     0.23

                                                     0.21

                                                     0.19

                                                     0.17

                                                     0.15

                                                     0.13
                                                            14            16                     18                        20                     22             24                 26

                                                                                                          100 / Risetim e [100/μs]




                                                                 University of Arizona                        Institute of Atmospheric Physics
                                                                                                                                                                           Page 18
Soil Moisture vs. Conductivity
(weighted count > 35)

                                                                                         condc    soil0_10

                                        23
                                                                                                                                              0.27
                                        22
                                                                                                                                              0.25
             (100/RT) [100/μs]




                                                                                                                                                     Vol. Soil Moist.
                                        21                                                                                                    0.23




                                                                                                                                                        [fraction]
                                                                                                                                              0.21
                                        20
                                                                                                                                              0.19
                                        19
                                                                                                                                              0.17
                                        18                                                                                                    0.15

                                         17                                                                                                   0.13
                                          07/07            07/17          07/27        08/06          08/16         08/26    09/05        09/15

                                                                                           Date (2005)




                                       0.27
         Vol. Soil Moist. [fraction]




                                                   y = 0.0247x - 0.2907
                                       0.25
                                                        R2 = 0.5754
                                       0.23

                                       0.21

                                       0.19

                                       0.17

                                       0.15

                                       0.13
                                              17                   18             19                 20                 21           22                         23

                                                                                         100 / Risetim e [100/μs]




                                                        University of Arizona                  Institute of Atmospheric Physics
                                                                                                                                            Page 19
                              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!!



                University of Arizona   Institute of Atmospheric Physics
                                                                           Page 20
An alternate signal source is man-made
       narrow-band radio signals
   (LORAN, NDB, AM radio stations)

                                         dab
                                                    Sb

                         da         Sa
                Tx
                                               Sc




    Longitude                  dc




            University of Arizona        Institute of Atmospheric Physics
                                                                            Page 21
The effect can be seen as changes in magnitude
   and phase for narrow-band radio signals


    E




                                                                     μSec


                           φ


          University of Arizona   Institute of Atmospheric Physics
                                                                      Page 22
                     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

                      University of Arizona   Institute of Atmospheric Physics
                                                                                 Page 23
University of Arizona   Institute of Atmospheric Physics
                                                           Page 24
                               420 kHz NDB




University of Arizona   Institute of Atmospheric Physics
                                                           Page 25
790 kHz AM
station




       University of Arizona   Institute of Atmospheric Physics
                                                                  Page 26
       Questions?




University of Arizona   Institute of Atmospheric Physics
                                                           Page 27
Supporting Material




University of Arizona   Institute of Atmospheric Physics
                                                           Page 28
             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




                   University of Arizona   Institute of Atmospheric Physics
                                                                              Page 29
Soil Moisture: NARR Vs. ARS In-Situ



                                                           Com parison of Daily Soil Moisture from NARR Dataset (0 to 10 cm ) and ARS In-situ Measurem ents (5cm )


                                                 1.0
     Relative Saturation [(fraction-min)/(max-




                                                 0.9
                                                 0.8
                                                 0.7
                                                 0.6
                       min)]




                                                 0.5
                                                 0.4
                                                 0.3
                                                 0.2
                                                 0.1
                                                 0.0
                                                   06/15       06/25      07/05      07/15      07/25      08/04      08/14      08/24        09/03    09/13         09/23
                                                                                                             Date (2005)

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




                                                                       University of Arizona               Institute of Atmospheric Physics
                                                                                                                                                               Page 30
University of Arizona   Institute of Atmospheric Physics
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University of Arizona   Institute of Atmospheric Physics
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University of Arizona   Institute of Atmospheric Physics
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University of Arizona   Institute of Atmospheric Physics
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University of Arizona   Institute of Atmospheric Physics
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University of Arizona   Institute of Atmospheric Physics
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