A New Approach Towards Large Scale Soil Moisture Mapping by Radio Waves

  • Christof Huebner
  • Christoph Kottmeier
  • Alexander Brandelik
Original Paper

Abstract

A new approach for obtaining integrated estimates of soil moisture content over larger regions of typically 10–50 km is described. It is based on a known correlation between propagation characteristics of low frequency radio surface waves and surface soil moisture, and provides valuable new benefits especially for meteorological prognostic models and for soil water estimation in agriculture. The paper consists of (1) a description of the theory of radio wave propagation with an extension of the classical theory of Norton (Proceedings of the Institute of Radio Engineers, Vol. 24, 1936), specifically the exploitation of the phase information, (2) demonstration of a method which guarantees the selection of reliable results from a large measurement data set, (3) a presentation of a new low cost measurement device to detect the amplitude and phase changes, and (4) results from initial measurements providing evidence that theoretical calculations are consistent with the measured change of electromagnetic signal properties due to soil moisture change.

Keywords

Soil moisture Radio wave propagation Surface wave Large scale sensing 

1 Introduction

Large-area integrated soil moisture measurements are required for various applications in the fields of meteorology, surface geology, hydrology, agriculture, and forestry. Advances in theory and measurement methods over the last two decades have resulted in major improvements that enable the sensing of soil moisture both locally and for larger areas. New measurement approaches include local ground based techniques as well as aircraft and satellite technologies. However, there is still a significant gap between small-scale sensors and very large surface airborne and satellite remote sensing systems. The latter provide a very shallow soil penetration, and are not adequate for deriving estimates of water evaporation and retention. Continuous mapping of the surface layer down to 1–2 m on scales between kilometers and hundreds of kilometers has not been achieved so far. This paper deals with new approaches using low frequency radio surface waves, where a correlation between propagation characteristics and surface soil moisture exists. The large scale soil moisture data will provide significant advances, especially for meteorological prognostic models and for soil water estimation in agriculture.

Commonly used in situ sensors measure soil moisture locally in a small measurement volume and exhibit a high spatial variability due to heterogeneity of the soil. Networks of in situ sensors have been established and operated in the frameworks of, for example, the African monsoon multidisciplinary analysis, AMMA, in 2006 [1] and the Convective and Orographically-induced Precipitation Study, COPS, in 2007 [2]. They rely on low-cost soil moisture sensors covering lengths of about 20 cm [3]. Advanced soil moisture sensors with a length of a few tens of meters were developed as well [4]. Additionally, there are satellite based soil moisture sensing systems which cover large areas but usually suffer from coarse temporal availability and shallow penetration depth. Spatial resolution for the satellite systems ranges from tens of meters to tens of kilometers. As an example, the recently launched ESA earth explorer with its microwave imaging radiometer [5] has a temporal resolution of 3 days and a spatial resolution around 50 km. Therefore, there exists a gap between in situ sensors and remote sensing systems.

New approaches have been made at the authors’ institution in recent years by using the influences of soil moisture on electrical properties exerted on transmitted electromagnetic signals. The so-called FreeLineSensing method has been developed for continuous soil moisture monitoring over large distances using wave propagation along high voltage power lines [6, 7]. The propagation of low frequency (30–300 kHz) signals along these power lines depends on the soil electrical parameters below the lines, such as conductivity and permittivity, which are related to soil moisture. The low frequency signal has to be coupled by hardware devices to the high voltage line both at the transmitter and the receiver site. Typical lengths of the sensing lines are between 5 and 50 km. An improvement of the method was made by replacing the hardware connection of the signal generator and receiver with magnetic or capacitive coupling. Though the FreeLineSensing method is a significant improvement towards large scale soil moisture mapping, the installation and measurement activities require the technical and legal permission by the line owner. In addition, this method is limited to sensing the soil properties directly under the line.

Another approach for large area determination of soil moisture is based on electromagnetic waves generated by lightning [8]. The rise time of propagated electromagnetic fields produced by cloud-to-ground lightning is sensitive to changes of the surface conductivity, which is related to soil moisture. The main limitation of this method is the requirement of vertical lightning, so there may be not sufficient data available.

In order to overcome this limitation, alternative man-made signal sources, like amplitude modulated radio, navigation or time distribution transmitters operating between some 10 kHz and about 1 MHz are proposed. In this paper we focus on radio waves of the Normal Time Service Germany, which are transmitted continuously from Mainflingen (near Frankfurt am Main, Germany) at a frequency of 77.5 kHz with 50 kW [9, 10]. The physical basis being developed in the following sections can be generally also applied to other time dissemination transmitters, non-directional beacons or broadcast stations operating in the VLF to MF range [ITU Recommendation, NDB handbook, World Radio & TV Handbook]. Figure 1 shows the general idea. The electromagnetic wave from the transmitter TX propagates to receiver RX 1 and receiver RX 2. Amplitude and phase are affected by the soil properties, especially the conductivity. By measuring amplitude and phase variations the average soil properties along transect d1, along transect d2 and between receiver RX 1 and receiver RX 2 are determined.
Fig. 1

Determining soil properties using electromagnetic wave propagation (simplified model)

2 Low Frequency Radio Wave Propagation

The basic idea is demonstrated by a simplified model (Fig. 1). In reality radio waves may propagate in four different ways from a transmitter to a receiver. Usually, the received signals result from multipath propagation. The direct wave travels on the optical path between transmitter and receiver. The second wave is reflected at the ground between transmitter and receiver. The third one is a reflected wave at the ionosphere. The fourth one is the so-called surface wave according to the definition of Sommerfeld [11]. For soil moisture determination only the surface wave, which travels in a limited region at the air/soil interface, is useful. It is very important that the other waves are avoided so that the simplified model with a single surface wave (Fig. 1) is valid. Therefore, transmitter and receiver have to be close to the earth to avoid the ground reflection. Also the direct wave has to be avoided; this can be achieved by keeping a minimum distance of approximately 50 km between transmitter and receiver to make use of the earth’s curvature. The ionosphere reflection can be neglected by choosing a proper measurement time and circumstances. Usually there is strong ionospheric absorption without reflection for the low frequency range during daytime around noon due to the effect of solar radiation.

2.1 Selection of the Surface Wave Only Condition

A method has been developed to identify these favorable conditions for performing the measurement. This has been achieved by installing two kinds of receiver antennas, a ground and a loop antenna respective for the electric and magnetic components of the waves. If the relationships of the two antenna signals are constant in amplitude and phase over time, there is no contribution from other reflections and consequently, only the surface wave is present. This is a requirement for soil moisture determination. Figure 2 shows the amplitude and phase variations with multipath propagation registered during a night field test. Ionospheric propagation path changes lead to varying interference conditions at the receiver. In these situations, the soil moisture determination is impossible. During daytime, Fig. 3, most of the signal directed to the ionosphere is attenuated. Therefore, the stable surface wave dominates the propagation and the received signal remains nearly constant both in amplitude and phase.
Fig. 2

Relative field strength and phase variations of the receiver signal compared to long time mean values with multipath conditions at nighttime

Fig. 3

Relative field strength and phase variations of the receiver signal compared to long time mean values with surface wave only at daytime

3 Surface Wave Theories and Simulation

There is a rich literature on surface wave propagation at low frequencies [e.g., 12, 13]. From the beginning of radio wave transmission experiments, physicists were surprised by the long distance transmission capability of low frequency radio waves in the frequency range from 10 kHz to about 1 MHz. Here we present a short review of the most important works in this field. Zenneck [14] analyzed a solution of Maxwell’s equations that already included a “surface wave” property in 1907. This Zenneck wave is a vertically polarized plane wave at the planar boundary that separates the atmosphere from a half space earth with a finite conductivity. For large conductivity compared to dielectric impedance of the soil surface, such a wave has a Poynting vector that is approximately parallel to the planar boundary. The amplitude of this wave decays exponentially in the directions both parallel and perpendicular to the boundary, each with different decay constants. This analysis helped to explain the long distance propagation ability of the low frequency radio waves. Sommerfeld further improved the theory in 1909 and studied the extension of the field down to the atmosphere/soil interface region. Figure 4 shows the electric field of the Sommerfeld surface wave in the interface region for low soil conductivity. Due to the soil impedance the E-field lines tilt from the vertical direction. This retardation is stronger in the soil and the electromagnetic field penetrates into the soil less than into the air. The solution by Sommerfeld is very complicated and requires advanced mathematical skills. Therefore, Norton developed simplified, easier to use formulas in 1936 [15]. We quote here from his introduction “Since that time (Sommerfeld′s time, inserted by the authors) many other investigators have obtained similar solutions of the problem in various ways. However, very few of these results have been left in a form convenient for engineering use. It is the purpose of this paper (Norton, inserted by the authors) to reduce the complex equations of the Sommerfeld theory to the form of simple formulas and graphs which may readily be used by the engineer and to show their limitations by comparing them to the available experimental data.” Indeed, Norton gave a simple approximation of the Sommerfeld solution, but he restricted his solution to the amplitude decay only. He did not develop a complex solution which would have enabled the calculation of the accompanying phase change as well.
Fig. 4

Tilt of the electric field of the Sommerfeld surface wave at the atmosphere/soil boundary

During the time of Sommerfeld and Norton, research focused only on amplitude decay to predict radio range for communication applications. The most comprehensive work on radio wave propagation at low frequencies was presented by Wait [16]. He studied several assumptions such as the earth’s curvature, stratified models and reflections for propagation calculations. In his review paper, he summarized his life work on groundwave propagation. Wait clarified some difficult problem areas, cleared up some confusion on definitions, and listed 123 important papers as references in this field. A recent publication of Green shows further refinement of the theory [17].

We focus our efforts on the soil moisture determination by surface waves in the sense of Sommerfeld and Wait. Therefore, a complex solution for the low frequency surface wave propagation was developed based on the work of Norton [12], and simulations were performed for various electrical soil parameter variations and combinations. The complex propagation coefficient A of the surface wave is given by the following equation instead of the classical Norton-formula with its absolute values only.
$$ A = 1 + j\,e^{ - p} E\,\sqrt {\pi \,p\,} $$
(1)
using
$$ p = {\frac{{\pi \cdot D \cdot e^{jb} }}{X \cdot \lambda }} $$
(2)
$$ b = \arctan \left( {{\frac{{\varepsilon_{r} + 1}}{X}}} \right) $$
(3)
$$ X = {\frac{\sigma }{{\varepsilon_{0} \cdot 2\pi f}}} $$
(4)
and the series expansion of the complex complementary error function E:
$$ E = 1 - {\frac{2}{\sqrt \pi }} \cdot \sum\limits_{n} {{\frac{{\left( { - 1} \right)^{n} \cdot \left( { - j\,\sqrt { - p} } \right)^{2n + 1} }}{{\left( {2n + 1} \right) \cdot n!}}}} $$
(5)
The following abbreviations are used:
D

distance between transmitter and receiver

f

frequency

λ

wavelength

σ

soil conductivity

εr

relative soil permittivity

ε0

free space permittivity

Figure 5 shows the decrease of field strength versus frequency using the formulas above for a 100 km distance between transmitter and receiver, and for selected conductivity values. In all simulations a soil permittivity of 15 is assumed. As expected, higher conductivity is associated with less attenuation.
Fig. 5

Relative receiver field strength compared to long time mean value versus frequency for a 100 km distance between transmitter and receiver with varying surface conductivity σ in S/m

The phase shown in Fig. 6 increases with frequency and conductivity. It can be concluded that higher frequencies exhibit larger phase change but suffer from higher attenuation. Figure 5 indicates that the relative amplitude change at 100 kHz transmitter frequency and 100 km distance is nominally 20% or less, which may not be a sufficient dynamic range in a noisy environment. For these conditions, the exploitation of the phase change, which is nominally greater than 20%, is a better candidate for estimation of average conductivity over the transmission distance and hence correlation to soil moisture.
Fig. 6

Phase versus frequency for a 100 km distance between transmitter and receiver with varying surface conductivity σ in S/m

Figure 7 shows the field strength decrease versus distance for 77.5 kHz, which is used in Germany for time distribution. The phase variation is presented in Fig. 8 for the same conditions. For this range of conductivities and distances between 10 and 100 km, the phase changes are sufficiently large to detect changes in the electrical conductivity of the soil.
Fig. 7

Relative field strength versus distance between transmitter and receiver for f = 77.5 kHz and varying surface conductivity σ in S/m

Fig. 8

Phase versus distance between transmitter and receiver for f = 77.5 kHz and varying surface conductivity σ in S/m

4 Experiment

In order to get an initial estimate of sufficiently large, detectable and soil-moisture-consistent changes of signal amplitude and phase, field experiments were performed using the German 77.5 kHz time distribution transmitter (DCF77) near Frankfurt. The receiver was placed about 100 km south of the transmitter in Karlsruhe. The block diagram of the receiver station is shown in Fig. 9. The receiver station consists of
Fig. 9

Block diagram of the receiver station

  • a loop antenna for the magnetic component of the transmitted wave (oriented transversal to the line of sight to the transmitter for maximal signal reception),

  • a 20 m long ground antenna with metal electrodes pointing in the direction of the DCF77 transmitter which measures the voltage in the soil (line length chosen for a sufficient signal amplitude),

  • a GPS receiver and

  • a storage oscilloscope for data recording.

In order to synchronize the receiver with the transmitter, the GPS timing pulse was used. The DCF77 signal is phase synchronized with the GPS signal. The timing jitter of the GPS receiver is about 40 ns which introduces about 1.1° uncertainty in the phase measurement at 77.5 kHz. The 77.5 kHz receiver uses a narrow band crystal filter. Phase stability of the receiver itself has been verified. The receiver station is shown in Fig. 10, the loop antenna in Fig. 11 and the ground antenna in Fig. 12.
Fig. 10

Receiver station

Fig. 11

Loop antenna

Fig. 12

One end of the ground antenna

5 Experimental Results

The experiment was carried out from May 17 until September 20 2008 with fixed receiver setup and antenna position. Situations with multipath propagation were identified and only measurements with single surface wave propagation were stored and further analyzed. Figure 13 shows the change of the phase and relative field strength by the change of the soil impedance (related to the change in the soil moisture) as a function of time. It was not practically possible to measure the mean soil moisture content along the transmission path for a correlation to the measured phase and amplitude (more than 500 soil samples are required as a rough estimate). As a result, a simplified correlation with the mean precipitation along the 100 km propagation path is shown using the data from six meteorological stations. Even if the task is simplified, it provides a method for an indirect correlation.
Fig. 13

Phase and field strength for the field experiment together with the integrated precipitation along the propagation path (start of the measurements on May 17, 2008)

Dry weather was present for more than 2 months long before the field test period. The initial phase and field strength were used as a reference for dry soil and later changes are considered in relation to these. A rain event on day 3 is associated with marked drops of the amplitude and a phase change of −5°. During a subsequent dry spell of 9 days, the amplitude recovered close to its initial value, which can be attributed to drying soil conditions. The phase angle, however, turns by about −10° which is not easily explainable. In the subsequent 16 days, there are a number of significant rainfalls. The amplitude changes by about −15% and the phase signal consistently changes by approximately an additional −10°. Because of the dry start, we could assume a mean soil conductivity of about 0.005 S/m which changed to about 0.015 S/m between the driest and wettest conditions. Based on the authors’ expertise in this area, and on the experimental results of Grosskopf and Vogt [18], both conductivities appear reasonable. During the following dry period of almost 3 weeks, phase and amplitude data are mostly missing, but the changes within another rainy period show some correlation. The simple but low cost setup of measurement devices (about EURO 500 excluding storage oscilloscope) is not yet ideal. The rain data representing convective precipitation from only six stations must be considered as a poor proxy of average soil moisture over the 100 km long propagation distance. Nevertheless, the data indicate a basic response of the signal properties to dry and moist surface conditions, which can only be assessed quantitatively by much larger experimental efforts which are planned for the future.

6 Conclusions

Based on theoretical calculations, it is shown that low-frequency radio waves may have the potential for large area monitoring of soil moisture which is needed for meteorological modeling and for agricultural applications. The surface wave propagation depends on the soil properties and varies both in amplitude and phase. Using existing man-made, low frequency transmitters and low-cost GPS synchronized receivers placed on a 2D grid, soil moisture estimates with resolution between 10 and 100 km can be achieved. A method has been developed to guarantee favorable conditions for reliable measurement results. Initial results from a simplified experimental setup show some correlation between phase and precipitation. Further experiments, including detailed soil moisture measurements on the transect between transmitter and receiver have to be performed. Other factors which affect the measurement have to be investigated as well, especially soil temperature influence [19, 20], conductivity gradients, penetration depth of the radio wave and disturbances of urban areas. For example, penetration depth can be estimated for a given frequency and a nominal soil conductivity on the basis of a skin depth calculation for homogeneous soils. More realistic cases with stratified soils require more sophisticated models.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Christof Huebner
    • 1
  • Christoph Kottmeier
    • 2
  • Alexander Brandelik
    • 2
  1. 1.Institute for Industrial Data Processing and CommunicationUniversity of Applied Sciences MannheimMannheimGermany
  2. 2.Institute for Meteorology and Climate ResearchKarlsruhe Institute of TechnologyKarlsruheGermany

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