Hydrologie Applications of Space Technology (Proceedings of the Cocoa Beach Workshop, Florida, August 1985). IAHS Publ. no. 160, 1986. Snow fork for field determination of the density and wetness profiles of a snow pack MARTTI TIURI & ARI SIHVOLA Helsinki University of Technology, Radio Laboratory, SF-02150 Espoo, Finland Abstract A radiowave sensor (a snow fork) for determining the density and wetness profiles of a snow pack with a single measurement has been developed. The snow fork is based on the measurement of the dielectric properties (real and imaginary part) of snow around 1 GHz. Due to the open structure of the resonator the measurement is non-destructive. Automatic measuring equipment guarantees instantaneous measurement results that can be recorded in the field. Introduction In snow studies and in remote sensing applications it is important to know the dependence between the dielectric properties of snow and its density and wetness. Instruments for measuring the dielectric properties of snow in the field have been developed after Ambach /l/ first suggested a method to measure the wetness of snow through its dielectric properties. With these methods, the real part of the permittivity of wet snow must be measured and, by weighing, the density of snow. From these the wetness of snow can be calculated. In this paper an instrument for field studies of snow packs will be presented which measures non-destructively both the real part and the imaginary part of the complex permittivity of snow at the same time. From these two values both the density and wetness of snow can be determined. This eliminates the need of a separate density measurement. Previous field measurement systems The snow sensors developed in Austria HI operate at relatively low frequencies (f < 100 MHz). They use air gap condensers as dielectric sensors and alternating current bridges (a Twin-T-bridge or a Wien-Robinson-bridge) as sensor electronics. The condensers consist of 7 stainless-steel plates, 10 x 10 cm, 1.5 mm in thickness, and a spacing of 2.1 cm. The sensor electronics have been optimized for different operating frequencies, and, after completed tuning, the dielectric constant can be calculated through a simple formula /2/. The Swiss snow research group has developed two snow sensors appropriate to usage in the field, namely a quarter-wavelength coaxial resonator and a "saw" resonator /2/, /3/, /4/. The coaxial resonator penetrates partly in the snow the penetration depth being adjustable. The sensor therefore only measures the properties of the uppermost layer of the snow cover. The desired dielectric properties result as a solution of a transcendental equation. The saw resonator is specially suitable for hard materials. It is a parallel-wire resonator and the wire line consists of the real saw blade and its mirror image. Both sensors operate at the 1 GHz region. The dependence between the dielectric properties and the density and the wetness The present snow sensor is based on the simultaneous measurement of both the real part and the imaginary part of the dielectric constant of snow. 225
226 Martti Tiuri S Ari Sihvola Latest studies of the dielectric properties of snow show that the knowledge of these allows both the density and the wetness to be determined /5/, /6/. The imaginary part of the dielectric constant is directly related to the wetness and the real part is dependent on the density and wetness. From the reported results and from the additional measurements made by the Finnish snow research group the following formulas explaining the dielectric properties of snow have been discovered /5/: e d ' Ae s ' = 1 + l,7 Pd + 0,7 Pd z e d ' = (0,10 W + 0,80 VT)e w ' (1! (2! e s " = (0,10 W + 0,80 W Z )e w " (31 where d Pd Ps W Pd e w is the real part of the permittivity of dry snow is the real part of the permittivity of snow is the imaginary part of the permittivity of snow of water is (the the density "dry density" of snow of when snow all relative liquid to water the in density is replaced by air) is the density of wet snow relative to the density of water is the wetness by volume = Ps " W = e w ' - je w " is the complex permittivity of water U w = 88 - j9,8 at 1 GHz) The effect of liquid water on the complex permittivity of wet snow is equal for both the real part and the imaginary part. The formulas (1), (2), and (3) are frequency-independent (i.e. Ae s ' and e s " follow the frequencydependence of water) in the microwave range where ice is dispersionless. Figure 1 illustrates the dielectric properties of.snow as a function of s =1 + 1.7pd+0.7pd+8.7Wv + 70Wv 2 FIG.l Nomograph for determining the wetness and density of snow from its complex dielectric constant at 1 GHz.
Snow fork for field determination- 227 its dry density and wetness at 1 GHz according to the formulas above. The permittivity at other frequencies in the frequency range 1 MHz... 4 GHz can be accurately calculated knowing that the real part is constant and the loss tangent increases linearly with frequency /5/. Snow fork Mechanical design The snow sensor developed at the Radio Laboratory, Helsinki University of Technology, consists of a resonator that can be pushed into snow or any other porous, granular, or liquid material which is to be measured. The resonator is a parallel-wire transmission-line resonator that is opencircuited at the one end and short-circuited at the other one according to Figure 2. The purpose of the resonator is to find out the complex permittivity of the material under measurement. This is achieved by measuring the change in the resonance curve of the resonator when it is pushed into snow. When the sensor is put into snow the real part of the permittivity of snow lowers the resonant frequency and the imaginary part broadens the resonance curve also increasing the attenuation at the resonant frequency. The length of the wires of the resonator is about a quarter of the wavelength in the resonance. A resonant frequency in air around 1 GHz makes the dimensions of the resonator suitable. High-frequency power is fed in and out through rigid coaxial cables and coupling loops. The cables are coated and supported by a glass fiber pipe which forms a solid stock. The coupling loops are protected by epoxy plastic. FIG. 2 The snow fork. \ cm The wires are made of stainless steel and they are sharpened at the end which makes the structure easy to push into snowpack even through a possible crust. However, the wires are thin enough so that the measurement operation does not deform snow and change the density considerably. This property, the absence of destructiveness, means a great advantage compared to other measurement systems. Electrical design If the resonant frequency of the resonator in air is f a and f s when put in snow the real part of the permittivity of snow is e s ) 2 T s
228 Martti Tiuri & Ari Sihvola The calculation of the imaginary part e s " or the loss factor tan6 s = e s "/e s ' is more complicated. Owing to the open structure the resonator has radiation losses which broaden the resonance curve and lower the quality factor. Unloaded Q-values of sensors described in this paper are between 40 and 70. The smaller the separation between the wires is, the higher is the Q-value. When Af a is the 3-dB bandwidth of the resonance curve in air, the inverse of the loaded quality factor is 1 ^ When the resonator is pushed in to snow the dielectric losses of snow broaden the resonance curve. If in the snow the loaded quality factor is Qi and the 3 db bandwidth is Af s (5) 1 Qu Afc 1 1 where Q _ is the loaded quality factor of the resonator in a lossless material with the same real part of the permittivity as the snow and Q s is the dielectric quality factor of the snow (1/Q S = tan6 s, loss factor of the snow). The loaded quality factor QL depends on the frequency. It has to be calibrated by measuring 1/Q[_ = e Af e /f e when the sensor os surrounded by different lossless materials e (or such materials whose losses are precisely known). Hence when the loaded quality factor in snow is measured the loss factor of snow can be calculated: es e s = tans s = Af s 1 Afc - Af c (7) Figure 3 shows the relation between the values of e s ' and s s " and the values of f s and Af s for a sensor that has a resonant frequency of 844 MHz in air. Afs/MHz 50-40- 30-20- / ^ /\ y> // / / ).15 (.12 0.1C 0.09,0.08 0.07,0.06 'A / /, 0.05 0.04 0.03 0.02 0.01 E;'=0 10-2 A 12 2.0 1.8 1.6 1.5 U 1.3 1.2 1.1 e;= 1.0 600 700 800 fs/mhz FIG.3 The permittivity curves of a fork with air resonance at 844 MHz. The complete measuring system In order to have real-time results of the permittivity of snow the measure-
( Snow fork for field determination 229 ment is automatized. The system consists of a voltage controlled oscillator and electronics for calculating the resonant frequency, the attenuation, the 3-dB bandwidth, and the real part of the permittivity. These values and information about the depth of the sensor in the snowpack are recorded on the tape in the field using a lightweight instrumentation recorder. The whole system is portable weighing around 2 kg. Figure 4 shows a measured density and wetness profile. 1985-03-22 11.00 1985-03-28 09.00 1985-03-28 12.00 cm 6Q0 0.2 0.4 0 12 3 4 5% 50 40 30 20 10 0. \ ) 50 - \ 40 40 ) 30 30 I it 20 20 10 10 ( 0! 0 FIG.4 A measured density and wetness profile of 'a Spring snowpack. cm 50 - ~7~ Accuracy of the measurement One source of error in measuring compressible materials with the fork is that the spikes, though thin, press the material to be measured and increase the density of the material in the neighbourhood of the spikes. However, the magnitude of this error can be estimated by solving the potential problem of the parallel-wire TEM-line. The relative error in measuring the real part of the dielectric constant can be shown to be 1,5-3 % depending on its absolute value. In measuring dielectric materials with the snow fork the accuracy for the resonant frequency can be approximated to be ± 5 MHz, that for the bandwidth of the resonance peak ± 5 percent, and that for the attenuation ± 1 db. This leads to 1.5% - error in e s ' for snow with the relative density 0.5, and 3% - error in the density estimation calculated through the dielectric measurement. The relative accuracy in wetness determination will be about 10 percent when the wetness is around 0.01 and less than 5 percent when the wetness is 0.05 or more. The method assumes that the snow to be measured is relatively clean (has a ph-value close to seven). If the snow is dirty its losses increase and the measurement gives too high values for the wetness. A correction can be made if the ph-value is known /5/. References 1. W.Ambach, W.Bitter!ich, F.Howorka: Ein Gerat zur Bestimmung des freien Wassergehaltes in der Schneedecke durch dielektrische Messung. Acta Physica Austriaca, Band XX, Heft 1-4, 1965. 2. A.Denoth, A.Foglar, P.Weiland, Ch.Matzler, H.Aebischer, M.Tiuri, A.Sihvola: A comparative study of instruments for measuring the liquid water content of snow. Journal of Applied Physics, Vol. 56, No. 7, p. 2154-2160, 1984.
230 Martti Tiuri S Ari Sihvola 3. H.Aebischer: Methoden zur Messung der Schneefeuchtigkeit mit Hilfe von Mikrowellen. Lizentiatarbeit, Universitât Bern, Institut fiir Angewandte Physik, 1983. 4. H.Aebisher, Ch.Matzler: A microwave sensor for the measurement of the liquid water content on the surface of the snow cover. 13th European Microwave Conference, Nurnberg, Microwave Exhibitions and Publishers Ltd, Kent, England, 1983. 5. M. Tiuri, A. Sihvola, E. Nyfors, M. Hallikainen: The complex dielectric constant of snow at microwave frequencies. IEEE Journal of Oceanic Engineering, Vol OE-9, No 5, p. 377-382, 1984. 6. M.Tiuri, A.Sihvola, E.Nyfors: Microwave sensor for snowpack wetness and density profile measurement. 12th European Microwave Conference, Helsinki, Microwave Exhibitions and Publishers Ltd, Kent, England, 1982.