02972-1-T SNOW PROBE FOR IN SITU DETERMINATION OF WETNESS AND DENSITY Technical Report U.S. Army Research Office DAAL 03-92-G-0269 John R. Kendra Fawwaz T. Ulaby Kamal Sarabandi Radiation Laboratory Department of Electrical Engineering and Computer Science The University of Michigan June 1993 THE VIEW, OPINIONS, AND/OR FINDINGS CONTAINED IN THIS REPORT ARE THOSE OF THE AUTHOR(S) AND SHOULD NOT BE CONSTRUED AS AN OFFICIAL DEPARTMENT OF THE ARMY POSITON, POLICY, OR DECISION, UNLESS SO DESIGNATED BY OTHER DOCUMENTATION.

Abstract The amount of water present in liquid form in a snowpack exercises a strong influence on the radar and radiometric responses of snow. Conventional techniques for measuring the liquid water content my suffer from various shortcomings, which include poor accuracy, long analysis time, poor spatial resolution, and/or cumbersome and inconvenient procedures. This report describes the development of an improved design of the "Snow Fork", a hand-held electromagnetic sensor that was introduced by Sihvola and Tiuri [1], for quick and easy determination of snow liquid water content and density. The novel design of this sensor affords several important advantages over existing similar sensors. Among these are improved spatial resolution and accuracy, and reduced sensitivity to interference by objects or media outside the sample volume of the sensor. The sensor actually measures the complex dielectric constant of the snow medium, from which the water content and density are obtained through the use of semi-empirical relations. To confirm the validity of these relations, it was necessary to conduct comparisons against reliable and accurate direct techniques. For liquid water determination, two direct procedures were investigated: freezing calorimetry and dilatometry. Of these only the freezing calorimeter was judged suitable. An extensive comparison study was then carried out between it and the snow probe. Through this comparison, the following specifications were established for the snow probe: (1) liquid water content measurement accuracy = +0.66 % in the wetness range from 0 to 10% by volume and (2) wet snow density measurement accuracy = +0.03 g/cm3 in the density range from 0.1 to 0.6 g/cm3. In addition, it was found that the existing semi-empirical expressions relating dielectric constant to the snow physical parameters fail to agree with experimental observations when the snow liquid water content exceeds ~ 3%. Accordingly, the expression was modified to correctly model the observed behavior. i

Contents 1 Introduction 1 2 Snow Dielectric Probe 2.1 Snow Probe Measurement System..... 2.2 Sensor Design............... 2.3 Characterization of Snow Probe...... 2.4 Spatial Resolution / Outside Interference. *......... *......... *......... *......... 3 Liquid Water Content and Density Retrieval 3.1 Procedure....................... 3.2 Results......................... 3.2.1 Liquid Water Content............ 3.2.2 Density.................... 2 2 5 9 12 12 12 15 15 17 22 *.......... *..... * * * * * 4 Conclusion References 25 APPENDIX A: Evaluation of Dilatometer and Freezing ter A.1 Dilatometer Evaluation................. A.2 Freezing Calorimeter Evaluation............ CalorimeA-1.... A-1..... A-2 APPENDIX B: Resonant Cavity Measurements of Dielectric Constant I APPENDIX C: Snow Probe Program Listing C 3-1 — 1 ii

List of Figures 1 Photograph of snow probe system................ 3 2 Schematic of snow probe system................ 4 3 Illustration of Snow Probe..................... 6 4 Photograph of snow probe with cap............... 7 5 Snow probe resonance bandwidth as a function of permittivity. 10 6 Variation in measurement of e" of sugar as a function of sensor proximity to metal plate...................... 13 7 Comparison of snow wetness results obtained via snow probe and freezing calorimetry respectively............... 16 8 Comparison of snow density results obtained via snow probe (with associated relations) and gravimetric measurements... 18 9 Aes versus rnm (experimental observations).......... 19 10 Comparison of snow density results obtained via snow probe (with associated modified relations) and gravimetric measurem ents................................ 21 11 Nomogram giving snow liquid water content (mr) and equivalent dry-snow density (pds) in terms of snow probe parameters f and A f.............................. 24 A.1 Calorimeter accuracy tested at three different levels of water content.............................. A-3 iii

List of Tables 1 3-dB bandwidth of Snow Probe as a function of e, (real part of perm ittivity).......................... 11 iv

1 Introduction In the study of microwave remote sensing of snow, it is necessary to consider the presence of liquid water in the snowpack. The dielectric constant of water is large ( e.g., e, = 88 - j9.8 at 1 GHz [1] ) relative to that of ice ( Ei 3.15 - j0.001 [2]), and therefore even a very small amount of water will cause a substantial change in the overall dielectric properties of the snow medium, particularly with respect to the imaginary part. These changes will, in turn, influence the radar backscatter and microwave emission responses of the snowpack. Among instruments available for measuring the volumetric liquid-water content of snow, rnm, under field conditions, the freezing calorimeter [3, 5, 6] offers the best accuracy ( 1%) and is one of the more widely used in support of quantitative snow-research investigations. In practice, however, the freezing calorimeter technique suffers from a number of drawbacks. First, the time required to perform an individual measurement of rnv is on the order of thirty minutes. Improving the temporal resolution to a shorter interval would require the use of multiple instruments, thereby increasing the cost and necessary manpower. Second, the technique is rather involved, requiring the use of a freezing agent and the careful execution of several steps. Third, the freezing calorimeter actually measures the mass fraction of liquid water in the snow sample, W, not the volumetric water content mv. To convert W to my, a separate measurement of snow density is required. Fourth, because a relatively large snow sample (on the order of 250 cm3) is needed in order to achieve acceptable measurement accuracy, it is difficult to obtain the sample from a thin horizontal layer, thereby rendering the technique impractical for profiling the variation of mr with depth. Yet, the depth profile of mn,, which can exhibit rapid spatial and temporal variations [7, 8], is one of the most important parameters of a snowpack, both in terms of the snowpack hydrology and in terms of the effect that mV has on the microwave emission and scattering behavior of the snow layer. In experimental investigations of the radar response of snow-covered ground, it is essential to measure the depth profile of rn with good spatial resolution ( on the order of 2-3 cm) and adequate temporal resolution (on the order of a few minutes), particularly during the rapid melt and freeze intervals of the diurnal cycle. Examination of available techniques narrowed the list to two potential instruments: (a) the dilatometer, which measures the change in 1

volume that occurs as a sample melts completely, and (b) the "Snow Fork", which is a microwave instrument that was developed in Finland [1]. As discussed in Appendix A of the report, the dilatometer approach was rejected because of poor measurement accuracy and long measurement time (about one hour). In the process of examining the Snow Fork approach, we decided to modify the basic design in order to improve the sensitivity of the instrument to m, and reduce the effective sampled volume of the snow medium, thereby improving the spatial resolution of the sensor. Our modified design, which we shall refer to as the "snow probe" is described in Section 2. The snow probe measures the real and imaginary parts of the relative dielectric constant of the snow medium, from which the liquid water content m, and the snow density p, are calculated through the use of semi-empirical relations that had been established by Hallikainen et al. [2] and by Sihvola and Tiuri [1]. To evaluate the performance of the snow probe, independent measurements of density were performed using a standard tube of known volume, whose weight is measured both empty and when full of snow, and of rm, using a freezing calorimeter. One of the unexpected by-products of this study was the discovery that the semi-empirical relations developed by Hallikainen et al. [2] are not valid over the full ranges of snow wetness and density. Consequently, a modified set of expressions is proposed instead, as discussed in Section 3. 2 Snow Dielectric Probe 2.1 Snow Probe Measurement System Figures 1 and 2 show a photograph of the snow probe measurement system, and a schematic of the same, respectively. The sweep oscillator, under computer control, sweeps (in discrete 10 MHz steps) over a relatively large frequency range. This serves to determine, within ~5 MHz, the frequency at which the detected voltage is a maximum, corresponding to the resonance frequency of the probe. The RF power transmitted thru the snow probe is converted to video by the crystal detector, measured by the voltmeter, which in turn sends the voltage values to the computer. The frequency spectrum is generated in real-time on the monitor of the computer. In the second pass, a much narrower frequency range is centered around the peak location and 2

Figure 1: Photograph of snow probe system. 3

/ HP Computer HPIB Interface Crystal Detector HPIB Interface output) V Snowfork (RF output) Figure 2: Schematic of snow probe system. 4

swept over with a finer step size (m 1 MHz). The center frequency and the 3-dB bandwidth around it are found, and from these, first the dielectric constant and then the snow parameters rnm and ps are determined according to procedures described in detail in Section 3 of this report. 2.2 Sensor Design The snow probe is essentially a transmission-type electromagnetic resonator. The resonant structure used in the original design [1] was a twin-pronged fork. This structure behaves as a two wire transmission line shorted on one end and open on the other. It is resonant at the frequency for which the length of the resonant structure is A/4 in the surrounding medium. The RF power is fed in and out of the structure using coupling loops. For our design, we used a coaxial type resonator, as illustrated in Figure 3. The skeleton of the outer conductor is achieved using four prongs. The principle is basically the same: a quarter wavelength cavity, open on one end, shorted on the other, with power delivered in and out through coupling loops. The coaxial design was chosen for purposes of spatial resolution. Being a shielded design, the electric field is confined to the volume contained within the resonant cavity, as opposed to the original design, which used only two prongs. The coaxial design also had a much higher quality factor, (- 120 vs. 40 - 70 for the original design) which, as discussed below, allows for more accurate determination of the complex dielectric constant. A photograph of the snow probe is shown in Figure 4. The real part of the dielectric constant is determined by the resonant frequency of the transmission spectrum, or equivalently, the frequency at which maximum transmission occurs. As mentioned above, this corresponds to the frequency for which the wavelength in the medium is equal to four times the length of the resonator. If the measured resonant frequency is fa in air and f, in snow, then the real part of the dielectric constant is given by e= (f )2 (1) The imaginary part of es is determined from the change in Q, the quality factor of the resonator. The quality factor is defined as follows [9]: w(time-average energy stored in system) (2) energy loss per second in system 5

Coupling Loops Prongs Top VIe Prongs forming Resonant Cavity Coupling Loop (Reinforced with for strength) Handle CoaHial cables (transmit & receiue) run thru hollow handle Perspective View Figure 3: Illustration of Snow Probe. Coaxial transmission lines extend through handle. At the face of the snow probe, the center conductors of the coaxial lines extend beyond and curl over to form coupling loops. 6

-2i*^ 1 - ~ - i s *: -_- - - - - - - - _- _ - --, = Figure 4: Photograph of snow probe with cap. 7 1

and it may be determined by measuring Af, the half-power bandwidth [9]: Q f, (3) fo where fo is the resonant frequency (fa or f,, depending on whether the medium is air or snow). In the case of the snow probe, power losses exist due to radiation, coupling mechanisms (ie. coupling loops), and to dissipation in a lossy dielectric. Thus the measured Q is given by: _ 1 1 = Q- +, (4) where Q,,, is the measured Q when the probe is inserted in the snow medium, QR, is the quality factor describing both the radiation losses and the power losses due to the external coupling mechanisms for the dielectric-filled snow probe, and Qd pertains to the dielectic losses. It has been shown [9] that 1 E" =tan= -. (5) Qd e As can be seen from (4) and (5), in order to calculate c" one must not only measure Qm. and know e', but the value of QR, should be available also. As long as tan 6 is very small, we may assume that QR,, which is related to the power radiated by the snow probe, is a function of the real part of e only. We can therefore define experimentally the functional dependence of QR, on c', and then, for the actual test materials, having found e' from the shift alone in the resonance curve, specify QRE and hence compute e". The details of how the snow probe was characterized are given in the next sub-section. We noted at the beginning of this section that our coaxial design for the snow probe had a considerably higher Q than the original twin-prong design. Why this increases the precision of the dielectric measurements may be understood from an examination of the relations already cited in this section. A high Q means a sharper resonance, and thus greater precision in determining the center frequency f,, and from (1), c'. From equations (4) and (5) it is seen that e" is determined from the contribution of the dielectric power loss to the total power loss. As the radiated power increases ( QR, decreases), the contribution of the dielectric loss becomes an increasingly smaller fraction of the total power loss. Thus a small change in dielectric loss, or equivalently, a small change in - = tan 6 = E"/Ce, becomes more difficult to detect from the measured Q. 8

2.3 Characterization of Snow Probe In order to compute the functional dependence of QR, on e', it was necessary to determine very precisely the complex dielectric constants of a variety of materials. This was achieved using an L-band cavity resonator. The materials used were sand, sugar, coffee, wax, and of course, air. The cavity used was cylindrical in shape with a diameter of 13.9 cm and a height of 6.35 cm. Details of how the dielectric constant of a material is determined using such a cavity are given in Appendix B. We now recall equation (4) which pertains to Q of the snow probe: 1 1 e" Qmn QRe e Once Qm is measured for our calibration materials, exact knowledge of the loss tangent for a given material allows isolation of the quantity QR,. The quantity QR, is equivalent to Qm, for a lossless material having dielectric constant e'. That is, for such a lossless material, 1 1 _ A/fs=o (6) QMn QR, fr The quantity Afs=o is thus the 3-dB bandwidth of the resonance spectrum of the snow probe when immersed in a lossless material having dielectric constant e'. From our measurements of the five calibration materials, the quantity Afs=o was found to be a linear function of the resonant frequency. Information pertaining to the analysis of the calibration materials is given in Table 1, and a plot of Afs=o versus fr is given in Figure 5. Figure 5 also shows (triangles) the 3-dB bandwidths of each of the calibration materials before the effect of the dielectric losses was removed. We rewrite (4) to reflect the linear dependence of Afs=o on fr: 1 Af - mf, + b e" + r, (7) Qm f1 fr + where rn and b are the slope and intercept respectively of the line in Figure 5 relating Afs=o to fr. Invoking (1) allows us to write, f r3 // Af = mf, + b + (8) fa 9

160. I A Direct Measurements 140. - E tans effect removed - / --- = 0.0 N 120. -. / 2 100. - ---- s^=0.02,,,, | 8 0.0 e — /= 0.03 -/ 4 80.0.___. 004 -// iQ 60.0 - ------ - 0 5 00,- ' - 100. -..... ' 0. 0 2 4 0.03.- ' El - - - — ""- - - - - " " 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Frequency (GHz) Figure 5: Snow probe resonance bandwidth as a function of permittivity. Marks (A) represent 3-dB bandwidth of materials (lowest freq. to highest) sand, wax, sugar, and coffee. Squares represent bandwidth of resonances if materials are lossless (e" = 0). materials are lossless (~"-= 0). 10

(GHz) (MHz) Material e fR Qm Af6=o Air 1.0 - O.0 1.715776 125.2 13.700 Sand 2.779 - 3.7e-2 1.036 51.7 6.245 Sugar 1.984 - 7.778e-3 1.22947 89.3 8.947 Coffee 1.497 - 3.32e-2 1.43125 30.4 15.339 Wax 2.26 - 2.9e-4 1.150308 137.0 7.853 Table 1: 3-dB bandwidth of Snow Probe as a function of e, (real part of permittivity). where fa is the resonant frequency of the device in air. We have made use of (8) in Figure 5 to generate curves of Af for particular values of e". It is clear from (7) that, given a measured Qr and resonant frequency fr and given knowledge of the constants rn and b, e" may be directly calculated as follows: -" =(f) — (m + (9) The determination of the function parameters m and b therefore constitutes the "calibration" of the probe. In general, we expect this calibration to be valid as long as nothing occurs which might affect the radiating or power input/output characteristics of the device. However, if we assume that the function of Afs=0 versus fr is always a linear one, re-calibration may be performed at any time by measuring just two materials for which the dielectric constant is known exactly. In practice, we calibrate the device daily when used, by measuring air and heptane (e = 1.925 - 0.8 x 10-4). Generally the calibration coefficients are reproduced quite closely, and the daily calibration is done mainly as a precaution. A typical calibration curve is, Af(MHz) = 8.381 x f(GHz) + 0.7426 (10) The determination of dielectric constant with the snow probe is summarized as follows: parameters m and b are obtained by measuring the Q of two materials of known dielectric constant (air and heptane) and then applying (8); e' is obtained from the shift in resonance relative to air (equation (1)); and finally, c" is computed from (9). 11

2.4 Spatial Resolution / Outside Interference As mentioned earlier, the partially shielded design of this sensor reduces its sensitivity to permittivity variations outside the sample volume. By sample volume, we refer to the volume inside the cylinder described by the four outside prongs (Figure 3). The coaxial design will tend to produce greater field confinement relative to a twin-prong structure. The effective sample volume was tested in the following way: a cardboard box (30cm x 30cm) was filled with sugar to a depth of m 16 cm. The snow probe was inserted into the sugar at a position in the center of the top surface, and then the dielectric constant was measured. Next, a thin metal plate (, 25 cm square) was inserted into the sugar, parallel to and resting against one side of the box. The dielectric constant was re-measured. The metal plate was incrementally moved closer to the sensor position, with dielectric measurements recorded at each sensor-to-plate distance. The results of the experiment are shown in Figure 6, in which c" is plotted as a function of the sensor-to-plate separation. The plate appears to have a weak influence on the measurement, even at a distance of only 0.6 centimeters. To put this variation into perspective, had the material been snow, and using the relations given in section 3.1, the fluctuation in the estimate of liquid water would have ranged from m, = 0.6% to m, = 0.8%. The real part of the dielectric constant (not shown in Figure 6) stayed within the range 2.00 - 2.01 during the experiment. The results of this experiment, which essentially confirm the expectation that the electric field is confined to the volume enclosed by the four prongs, translate into a vertical resolution on the order of 2 cm when the snow probe is inserted into the snowpack horizontally (the snow probe cross section is l cm x 1cm ). 3 Liquid Water Content and Density Retrieval 3.1 Procedure The volumetric liquid water content, my, and the snow density p, can be calculated from the complex dielectric constant e (and knowledge of the exact frequency at which it was measured) using a set of semi-empirical relation 12

9.0 8.3 7.6 6.9 eN 66.2 5.5 >X 4.8 4.1 3.4 2.7 2.0 0.0 3.0 6.0 9.0 12.0 15.0 Sensor-To-Metal Plate Separation (cm) Figure 6: Variation in measurement of e" of sugar as a function of sensor proximity to metal plate. ( Real part c' stayed in the range 2.00 - 2.01. ) 13

ships [1, 2]. These equations are: /ds = 1+ 1.7pds + 0.7p (11) 0.073ni'31 AE = e - ds = 0.02rn115+ 00 3 (12) Ws Ws ds V + I1 + (f/f1)2,, 0.075(f/fw)m 31) Ws 1 + (f/f )2 ( where: Eds = the real part of the dielectric constant of dry snow, Pd = the "dry density" of snow, which would result if all the volume occupied by water was replaced with air, W' = the real part of wet-snow dielectric constant eds = the real part of dry-snow dielectric constant, n v= the volumetric liquid water content (%), f, = 9.07 GHz (related to relaxation frequency of water at 0~ C), f = frequency (GHz) at which es, is determined. Equation (11), from [1], relates the real part of the dielectric constant of dry snow to its density. Equations (12) and (13), from [2], are semi-empirical Debye-like equations. Upon measuring Ec (by the snow probe), m,, can be calculated directly from (13): m= f{ 0[107 fi+ (f /fw)2] 1.31 rn-I 0,075(//) JS I' (14) Note that (13) basically relates e" to the imaginary part of the dielectric constant of water, E, scaled by its volume fraction in the snow mixture, m,. This follows from the fact that e = 0 for the air constituent and e' of the ice constituent is several orders of magnitude smaller than E' of water. From (11) and (12) we may compute ed as follows: '^ = 's - 0.02m'7701 1 +(f 2 (15) 0ds =' 1015_ 0.073= '31 (fo15) Then from (11) and (15) we can compute pds from the quadratic equation: pds = -1.214 + /1.474-1.428(1 - s), (16) 14

in which only the positive root is considered. The the dry snow density Pd,, and the volumetric liquid water content mv (%) are related to the the wet snow density ps by [4]: Pws = Pds + 1o (17) 3.2 Results Since the physical snow parameters yielded by the snow probe are the results of empirical and semi-empirical equations, it was necessary to see how closely the snow probe reproduced the results obtained from well-established direct techniques. The parameters tested were density and liquid water content. The direct techniques used were a simple gravimetric density measurement and freezing calorimetry for liquid water. It should be noted that the relations used with the snow probe (given in (11),(12), and (13) ) deal with liquid water volume fraction, mr. The freezing calorimeter, however, produces liquid water mass fraction (W ) as its output. In order to compare m, as measured by the snow probe with W as measured by the freezing calorimeter, we need to use the relation, m = 100 x pSW (18) where mr is volumetric liquid water expressed in percent, and ps is the density of the snow. In our tests, we have converted the freezing calorimeter results to volume fractions using the gravimetrically determined density and (18). 3.2.1 Liquid Water Content The results for the liquid water content comparison are shown in Figure 7. The error bars associated with the freezing calorimeter data points show the range of results obtained from typically two separate (and usually simultaneous) determinations. (Data points with no error bars indicate only a single measurement or that only the mean value of a set was available.) The freezing calorimeter is seen to have generally excellent precision. The values for mn obtained from the snow-probe dielectric measurements are computed using equation (13). The data points and error bars shown for the snow probe are based on an average of twelve separate measurements made for each snow sample and the uncertainty of the estimate of the mean 15

II,-' -i 12. 11 10 3 o 7 2 ) 5. I,' 1-,,._ rms error = 0.66 0 1 2 3 4 5 6 7 8 9 10 11 12 mv (Frzg. Clmtr.) Figure 7: Comparison of snow wetness results obtained via snow probe (marks) and freezing calorimetry respectively. Snow probe data points are based on an average of twelve separate measurements. 16

value as represented by the error bars was computed as ~ta /V- where a is the standard deviation of the set of measurements and N is the number of measurements in that set. From the figure, it is seen that the agreement between the two techniques is generally very good and, with the exception of an outlier at the 6% level, the use of the snow probe and (13) give results which are within ~0.5% of the freezing calorimeter results. This result strongly supports the validity of equation (13). 3.2.2 Density The outputs of equations (12) and (11), with dielectric information supplied by our sensor, were compared with the results of gravimetric density measurements. The comparison was conducted over a density range extending between 0.1 and 0.55 g/cm3. The results are shown in Figure 8. It is seen that, with the exception of a single outlier, excellent agreement is obtained for the cases where the snow volumetric wetness level was < 3%. In contrast, density estimates made via (12) and (11) when snow wetness exceeded 3% departed markedly from the gravimetric measurements. The procedure for the retrieval of density, outlined il Section 3, employs a conceptual quantity Ae', (Eq. (12)), which is defined to be a measure of the increase in the real part of the dielectric constant of snow, relative to that for dry snow, which would occur if some of the air in the snow medium was replaced by liquid water. Application of (12) to measured values of E', then allows determination of a theoretical d,, from which, using (16), a theoretical dry-snow density, pd,, may be determined. Wet-snow density, pw,, is then related to pds using (17). The quantity A', is a function of both the resonant frequency fr and nm. Across the frequency range over which the snow probe operates (a 0.9 - 1.7 GHz), (' is approximately constant for both water and ice. Hence, Ae' may be examined as a function of m, alone. This function is plotted in Figure 9. Also included are experimental quantities which were generated by taking the difference between measured values of e', (averages of typically twelve independent snow probe measurements) and calculated values of ds,, determined through the use of (17) and (11). The solid curve drawn through the experimental quantities is seen to diverge from the behavior predicted by (12), for m, > 2.5 %. 17

M P-4 a) a) a) a) 0 0~ F —4 rn 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 / /.. / A/ T, ( a/ / T A/ tE^ | i v<m3% | / 5 mv>3%,/R' /,/11|1 1 1 >1 1 1\ ~.L I~~~~~ I - ~ ~ ~ ~ ~ ~ I~~ ^ t% L U.0U '0....20.....4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 pr (Gravimetric) Figure 8: Comparison of snow density results obtained via snow probe (with associated relations) and gravimetric measurements. Data points represented with squares were from snowpacks having volumetric wetness levels of > 3%; with circles, < 3%. 18

2.5 2.2 kl 11U11 i -------- Modified Debye-like Formula / 2.0 - 9o 2. ~ Measurements 1.7 / 1.4.-," - ^3 01.1 - / 0.9 - 0.6.-, ' " - 0.3 -,," -. -.3 0.0 2.0 4.0 6.0 8.0 10.0 12.0 mv (Volumetric Liquid Water) Figure 9: As' (computed using snow probe-measured e, snow probedetermined rni, and gravimetrically measured pws) versus mn (snow probedetermined). 19

This curve is produced by the following function, which is based on the original formula but which is consistant with the observed behavior: ws = ws eds 0.073m'l31 -0.02rnm.05 + 0.073m ' 1 + (f/fo)2 + [0.155 + 0.0175(mv - 2.5)] {1 + (2/7r) tan-1 [4(mn - 2.5)]} (19) This function accomodates the essential discontinuity which exists in the data in the neighborhood of w 2.5%. Note the data points shown in the figure follow this functional form given in (19) independent of density. As an example, the two data points corresponding to, 4.5% liquid water had densities of 0.19 and 0.55 respectively-yet they still exhibit an incremental Ae' according to (19). Having derived (19) from the measured data, we have produced a formula relating measured dielectric constant and snow density which is valid in the region 0.1 to 1 0.6 g/cm3. The sensor data, re-processed using (19) and (11) is compared against the gravimetric data in Figure 10. It is seen that over the range examined, with the exception of one outlier at p x 0.34, the snow probe method agrees with the gravimetric method to within ~0.03 g/cm3. The concept of dry-snow density pd,, as understood in the above context, is a conceptual quantity which cannot be measured. Its use is motivated by a desire to attach a physical basis to the dielectric behavior of wet snow; that just as e' may be understood in terms of the dispersion behavior of water, so may the behavior of e be understood, as an addition of a quantity based on the dispersion behavior of the real part of the dielectric constant of water, namely equation (12), to ed, for which a reliable empirical model exists. The results from the present investigation indicate that the physical reasoning put forth to explain the behavior of e' is incomplete; that there are important factors in addition to the real part of the dielectric constant of the water itself. That there exists, or should exist, an abrupt transition in the dielectric constant of snow as a function of moisture is an idea which has been cited by previous researchers. Colbeck [13] describes a transition between the pendular regime, wherein "air occupies continuous paths throughout the pore space" 20

1.0 0.9 - / 0.7 E fl / l j oS 0.68 0.5 0.45 mv<3% 0.2- mv>3% 0.1 -,/, rms error = 0.03 0.0:. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p, (Gravimetric) Figure 10: Comparison of snow density results obtained via snow probe (with associated modified relations) and gravimetric measurements. Data points represented with squares were from snowpacks having volumetric wetness levels of > 3%; with circles, < 3%. 21

and the funicular regime, wherein liquid water "occupies continuous paths throughout the pore space". Denoth [14] estimated this transition at 11 to 15% of the pore volume, which would correspond to 7 to 10% of the total volume for an average snow sample have density 0.3 g/cm3. Another description, attributed to Colbeck by Hallikainen ct al. [2], suggests that such a transition occurs when liquid water inclusions in snow transform from being primarily needle-shaped (at low values of liquid water content) to being primarily disk shaped. In [2], snow dielectric constant data in the 3 to 37 GHz range was analyzed using Polder Van Santen mixing models. It was concluded that the shape factors in the models which provided the best fit to the data supported the concept of a needle-to-disk transformation of the water inclusions. The two-phase Polder Van Santen model with the shape factors (or depolarization coefficients) specified in [2] was applied to the current snow probe data. It was found however to give a result very comparable to the Debye-like model (Equ. 12), that is, it predicts no transition. 4 Conclusion This report has described the development and validation of an electromagnetic sensor and associated algorithm for the purpose of rapid (a 20 seconds) and non-destructive determination of snow liquid water content and density. The sensor is similar in principle to an existing device known as a "Snowfork", but offers additional advantages in spatial resolution and accuracy owing to a novel coaxial-cavity design. Direct methods of snow wetness determination were evaluated for their suitability as standards against which the device could be tested. The dilatometer, though simple in principle, was found to give very unfavorable performance. The freezing calorimeter, which has, as a system, been brought to a high degree of sophistication in our lab, was found capable of delivering accuracy better than ~1%, and excellent precision. The snow probe determines the dielectric constant directly. Empirical and semi-empirical models use this information to compute liquid water volume fraction and density. To test the suitability of these models, the snow probe was tested against the freezing calorimeter and gravimetric density determinations. In general, excellent agreement was obtained: liquid water 22

measurement accuracy ~0.66 % in the wetness range from 0 to 10% by volume; wet snow density measurement accuracy ~0.03 g/cm3 in the density range from 0.1 to 0.6 g/cm3. The relations employed to translate measured dielectric constant to snow parameters were those set forth by Hallikainen [2]. The equation relating e" to rn, and frequency was found to be entirely valid. However, the equation predicting Ae in terms of m, and frequency failed to taken into account an abrupt increase in Et which occurs in the range of m, equal to 2.5 to 3%. This failure results in very large errors in the estimate of density. The formula was accordingly modified (equation (19) to correctly model the observed effect. Figure 11 is a nomogram, based on these equations which have been found to be valid in the specified ranges. It consists of contours of constant rn, and pds respectively, in a 2-dimensional representation bounded by the two parameters which are directly obtained by the snow probe: resonant frequency and bandwidth (3-dB) of the resonance spectrum. With the measurement of these two quantities, rn, and Pd, may be uniquely specified. Dry-snow density, pds, is related thru (17) to wet-snow density pws. 23

50 i.s - ^ —r '"^-.. / 4-5,:"!/ Q / I \ 45 - I!" 4 I /0-/ ' ' \ s 25 / A., V >'.... / \% \... '., 3 5 20."?,', 15 5 -L -- -l-sS - - -- -\ — " 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Resonant Frequency (GHz) Figure 11: Nomogram giving snow liquid water content (-n) and equivalent dry-snow density (Pds) in terms of two parameters directly measured by the snow probe: resonance frequency () and resonance (3-dB) bandwidth (Af). 5~~~,-\\ -'m~, O~~~.' snow probe' resonance frequency (f) and resonance (3-dB) bandwidth (A f). 24

References [1] Sihvola, A., M. Tiuri, "Snow Fork for Field Determination of the Density and Wetness Profiles of a Snow Pack", IEEE Trans. Geosci. Remote Sensing, vol. Ge-24, pp. 717-721, 1986. [2] Hallikainen, M., F. T. Ulaby, M. Abdelrazik, "Dielectric Properties of Snow in the 3 to 37 GHz Range", IEEE Trans. Antennas Propagat., vol. AP-34, pp. 1329-1339, 1986. [3] Jones, E. B., A. Rango, S. M. Howell, "Snowpack Liquid Water Determinations Using Freezing Calorimetry", Nordic Hydrol., 14, pp. 113-126, 1983. [4] Tiuri, M. E., A. H. Sihvola, E. G. Nyfors, and M. T. Hallikainen,"The Complex Dielectric Constant of Snow at Microwave Frequencies",IEEE J. Oceanic Engr., vol. OE-9, pp. 377-382, 1984 [5] Stiles, W. H., F. T. Ulaby, Microwave Remote Sensing of Snowpacks, NASA Contractor Report 3263, June 1980. [6] Austin, R. T., Determination of the Liquid Water Content of Snow by Freezing Calorimetry, Univ. of Michigan Radiation Lab Report 022872 -2, Jan. 1990. [7] Ellerbruch, D. A., and H. S. Boyne, "Snow Stratigraphy and Water Equivalence Measured with an Active Microwave System", J. Glaciol., vol. 26, pp. 225-233, 1980. [8] Colbeck, S. C., "The Layered Character of Snow Covers", Revs. of Geophys., 29, pp. 81-96, 1991. [9] Collin, R. E., Foundations for Microwave Engineering, New York: McGraw-Hill, 1966. [10] Nyfors, E. and Vainikainen, P., Industrial Microwave Sensors, Norwood, MA: Artech House, 1989. [11] Altschuler, H. M., "Dielectric Constant", Handbook of Microwave Measurements, vol. II, 3rd ed., Polytechnic Press, 1963. 25

[12] Leino, M. A. H., P. Pihkala, and E. Spring, "A Device for Practical Determination of the Free Water Content of Snow", Acta Polytechnica Scandinavica, Applied Physics Series No. 135, 1982. [13] Colbeck, S.C, "An Overview of Seasonal Snow Metamorphism", Rev. Geophys. Space Phys, vol. 20, pp. 45-61, 1982. [14] Denoth, A., "The Pendular-Funicular Transition in Snow", J. Glaciol., 25(91), pp. 93-97, 1980 26

APPENDIX A: Evaluation of Dilatometer and Freezing Calorimeter A.1 Dilatometer Evaluation Attracted by the simplicity of the concept, apparatus, and procedure, we expended considerable effort in evaluating the dilatometer technique. As we ultimately rejected it as a result of its poor performance in determining liquid water content, we will not go into the details of the apparatus itself; a complete description is provided in [12] for those interested. Instead, we will just briefly describe the method and then present some of the drawbacks that led us to reject the method. In the method, a weighed snow sample is placed in a cooled ( 0~C) jar, and then the jar is completely filled with 0~C water. A lid with a graduated tube is fixed onto the jar, and the tube itself is filled with freezing water and the level noted. The jar is placed in a warm water bath to melt the snow and then the entire system is returned to a temperature very close to 0~C. The change in the volume is related to the mass of ice present, and subtracting this from the original snow mass gives the mass of water in the snow sample. The principal drawbacks we found were the following: * Lack of accuracy due to non-ideal behavior of the materials. We tried the following experiment: we filled the apparatus entirely up with 0~0( water (no snow or ice) and cycled the temperature up and then back down as described above. In each of several trials, the volume of the water (which should have returned to its original value, about 1 liter) was found to have increased by about 0.1%, enough to cause a very significant error in an actual trial. In quantitative terms, if a 75 gram sample of snow having 5% water mass fraction was analyzed, it would appear that the sample had 20% water mass fraction. We believe this volume expansion effect may be caused by gases that are liberated when the cold water is warmed. Additional slight but critical volume changes may be caused by expansion or contraction of any of the parts of the dilatometer apparatus. * Long analysis time. The snow, once added, can be melted relatively quickly by warming the system. However, to return back to 0~C (which A-1

is absolutely critical to avoid unwanted volume changes in the system) the wait required is on the order of one hour. The reason is that, unlike the warming case, for the cooling there is a relatively small temperature gradient. The bath can be no less then 0~C; so when the temperature gets down to 5 or 6~C, there is very little gradient to drive it down further. A.2 Freezing Calorimeter Evaluation As noted earlier, the theoretical background and the procedural details of the freezing calorimeter method are thoroughly discussed in a previous Radiation Lab report [6]. Since that report was written, there have been several major improvements made in the freezing calorimeter system: * A second calorimeter was constructed, identical to the first, to allow for duplicate measurements to be done in parallel. * A motorized tripod-mounted mechanical shaker was constructed which is capable of shaking both calorimeters simultaneously. * The system has been made PC-based. Software was written which handles two calorimeter channels independent of one another. Data from each channel is collected, displayed, and reduced automatically by the computer. The method, with these improvements, was tested for precision and accuracy. To our knowledge, it is the first time a systematic test of the method precision and accuracy has been performed. The accuracy of the method was tested at three different levels of wetness. We prepared a sample of snow with zero wetness by placing it in a freezer at -20~C for several hours. Four separated analyses were performed on the snow from this batch. To test at two other wetness levels, at the point in the procedure where the lid is removed from the calorimeter and snow added, we added-in addition to the zero-wetness snow from above-a precisely measured volume of water at exactly 0~C. In this way, we "spiked" dry snow samples at levels corresponding to 5% and 11% liquid water mass fraction. Each case was analyzed in duplicate. The results of the accuracy tests performed at these three levels are shown in Figure A.1. Shown is A-2

5.00: ~ (suspect) i~ 3.00 (suspect) c. D. 1.00 ^ * 0 A. c,I 0 o 0% Level o. [a 5% Level *. -3.00 A 11% Level tQ~2}C ------ Ref. Level -5.00 0.00 Figure A. 1: Calorimeter accuracy tested at three different levels of water content. Data is normalized so all results are compared to what actual level was calculated to be in each case. The two points marked "suspect" correspond to analyses noted at the time of execution as problematic. A-3

the degree to which the experimental results deviated from the known mass fractions. Two results, one at the 0% level and one at the 11% level, come from analyses which were noted as problematic at the time of analysis, and are marked as "suspect". From these tests, it appears that the method is accurate to a level somewhat better than ~1%. The precision of the method was clearly observed since all analyses were done in duplicate. From the results shown in Figure A.1 and the results which will be seen in the next section wherein the calorimeter is compared to the snow probe, it seems that the precision is on the order of ~0.5%. A-4

APPENDIX B: Resonant Cavity Measurements of Dielectric Constant The L-band cavity used for the present study was a cylindrical, transmissiontype resonator, with diameter 13.9 cm and depth 6.35 cm. The TMojo mode is resonant at 1.64618 GHz and the loaded (measured) Q for the air-filled cavity was. 3750. To insure reliable, reproducible performance, the cover of the resonator was always fixed on using a torque wrench (60 ft-lbs) and following a prescribed pattern in tightening the screws. In the most general case, the quality factor of a resonant system is given as follows: 1 1 1 -- = -+ (B.1) Q QAu Qext where, Q1 is the loaded Q, Qu is the unloaded Q, and Qext the external Q. The unloaded Q is the "real" Q of the resonator but it is possible to measure it directly. The coupling devices (loops, probes) used to couple power in and out of the resonator also contribute to power leakage out (represented by Qext) which is a source of loss not inherently related to the resonator itself or its contents. The reciprocal of Qu may be written as the sum: 1 1 1 1 -Q = Q + + (B.2) Qu QR Qd Q(B2 where QR is, as before, related to the radiated losses, Qd to the dielectric losses, and Qm to the losses associated with the metal walls of the resonator having a finite conductivity. For a closed resonator, as ours is, the radiated losses are zero and we need not consider QR. Also, for the empty (air-filled) resonator, Qd is not considered. Furthermore, it can be demonstrated [10] that for a resonator filled with a dielectric e, 1 _ Qm7= Q10^ (B.3) Q11m Qmo where Qm is associated with the metal losses in the dielectric-filled cavity, and Qo with the metal losses il the air-filled cavity. From (5) the loss tangent tan 6 may be found from Qd which may in turn be obtained if Qu as given in (B.2) may be found and (B.3) is also used. The problem then becomes how, B-1

upon measuring Qi (see equation (B.1)), may Q, be determined? For the most general case of the input and output coupling networks being different, Altschuler ([11]) describes a general impedance method for determining Qu, from Qi. If it is assumed that the input and output coupling networks are equivalent, then Q, can be directly calculated [10] from measurements of Qi and the insertion loss ar at the resonant frequency as follows: QU - 1. (B.4) 1 V ra-r For our L-band cavity, it was found that the simple method above gave very comparable results to the general impedance method in all cases. It is noted that the general impedance method detailed in [11] is considerably more involved than that given by (B.4). Based on the above discussion, the procedure for determining dielectric constants with a resonant cavity is summarized as follows: * Real part of dielectric is found in the same way as given in equation (1), using the resonant frequencies of the dielectric-filled and air-filled cavity. * Imaginary part of dielectric requires determination of Qu. Then for the case of equivalent input and output coupling factors, equations (5),(B.3), and (B.4) lead to, e" =e' [l1- ] (B.5) IQ Q,, o where 1 = [1_- 1 _ 1 (B.6) Qm7Lo Qlo Qlo Qexto where the "o" in the subscripts refers to quantities associated with the air-filled cavity. B-2

APPENDIX C: Snow Probe Program Listing This appendix contains the computer program used in conjunction with the snow probe. It is written in HP Basic. See Section 3.4 for additional details of the snow probe system. 2! Program SHOWFORKB! 3 OPTION BASE 1 4 COM /Flag/ Qflag,Calflag 5 COM /Values/ Fstart,Pwrl,Detmax 6 COM /Addr/ QSvp,QDvm 7 COM /Cal.vals/ Mslope,B_cept,Fair 8 COM /Fileinfo/ Fflag,Stars$[15],Fname$[12],QPathl,Dumm 9 COM /Line.loss/ Pstep,Pfrac,Pflag 10 MASS STORAGE IS "SNOWFORK/:CS80, 700, 0" 12 INITIALIZE ":,0",9!CREATE MEMORY VOLUME TO HOLD FILE. 13 STORE KEY "KEYDEFS:,0"!STORE KEY DEFN'S IN FILE "KEYDEFS" 14 DIM A$(23)[1] 15 SET KEY 0,A$(*)!REDEFINE ALL KEYS TO UNDEFINED. 16 CLEAR SCREEN 17 ON KEY 0 LABEL "TAKEDATA" CALL Takedata 18 ON KEY 1 LABEL "CALIBRATE" CALL Calibrate 19 ON KEY 9 LABEL "QUIT" CALL Quit 20 ON KEY 3 LABEL "CREATE.FILE" CALL Create.file 21 ON KEY 4 LABEL "CLOSE.FILE" CALL Close.file 22 ON KEY 5 LABEL "PWR.LVL" CALL Pwrlvl 23 ON KEY 6 LABEL "START.FREQ" CALL Startfreq 24!ON KEY 8 LABEL "SAMPLE.RATE" CALL Rate 26!ON KEY 8 LABEL "CALLINE.LOSS" CALL Calline 27 KEY LABELS ON 28 ON ERROR RECOVER Getfree 30 PLOTTER IS CRT,"INTERNAL" 31 Pflag=O 32 Pstep=2.09*.01 33 Dumm=10 34 Fstart=.95 35 Pwrl=O 36 Mslope=4.53 37 Bcept=5.36 38 Fair=1.663 39 PRINT "CURRENTLY, Mslope = ";Mslope;" B.cept = ";B.cept 40 PRINT "AND, F.air = ";F_air 41 Fflag=O! Denotes no file opened yet. 42 Calflag=O! Denotes Cal not in progress. 43 Stars$="***************" Dividers between file entries. 44 Qflag=O C-1

45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Choose:! INPUT "WHICH DETECTOR (1,2,OR 3)?",Detect SELECT Detect CASE 1 Det_max=.00500 CASE 2 Detmax=.00089 CASE 3 Detmax=.00056 CASE ELSE BEEP PRINT "INVALID CHOICE" GOTO Choose END SELECT ASSIGN QDvm TO 702 ASSIGN eSwp TO 719 OUTPUT QSwp;"IP" WHILE Qflag<>l END WHILE LOAD KEY "KEYDEFS:,0"! RELOAD OLD KE INITIALIZE ":,0",0! RECLAIM MEMORY V Getfree:! IF Fflag=l THEN ASSIGN QPathl TO * PRINT "Program Exited" END!:Y DEFN'S. OLUME STORAGE. SUB Takedata REAL B(1:250) DIN Comment$ [200] CON /Line.loss/ Pstep,Pfrac,Pflag CON /Addr/ QSwp,QDvm CON /Values/ Fstart,Pwrl,Detmax CON /Results/ E1,E11,FO,Q,Mv,Pws CON /Calvals/ Mslope,B.cept,Fair CON /Fileinfo/ Fflag,Stars$,F.name$,QPathl,Dumm CON /Flag/ Qflag,Cal.flag CON /Samprate/ Srate$[2] Comment$=" IF Calflag=l THEN GOTO Jumpl IF Fflag=l THEN PRINT "Current comment is:" PRINT Comment$ INPUT "Enter comment or description if desired:",Comment$ PRINT "Press continue to take data:" PAUSE END IF Jump:! GINIT GRAPHICS ON GCLEAR CLEAR SCREEN N=80 FOR I=1 TO 250 B(I)=O C-2

101 NEXT I 102!Pstep=INT(.209*.01/.006)*.006 103!INPUT "ENTER POWER STEP:",Pstep 104 Pstep=.067 105 OUTPUT eSwp;"PL";Pwrl;"DM CW";Fstart;"GZ SFlOMZ" 106! Instrument preset: power 0 dBm,start Q fstart GHz, 107! step size = 10 MHz. 109 OUTPUT QDvm;"T1 F1 R-2 N3 ZO D3"!Int. trig., DC volts, 110! 30 mV DC, 3.5 digits, autozero off, display off. 111! 112! DIFFERENT CMD FOR FLUKE 8842A METER: 113 OUTPUT @Dvm;"* TO F1 R8 S2 DO"!Int. trig., DC volts, 114 20mV DC, fast aqu., display off. 115! 116 VIEWPORT 10,120,25,75 117 FRAME 118!WINDOW 1,84,-9.E-3,1.2E-2 119 WINDOW 1,84,-.5*Det_max,1.5*Det_max 120 FOR I=1 TO 84 121 ENTER eDvm;Dum 122 B(I)=-Dum 123!OUTPUT QSwp;"PL UP CW UP" 124 OUTPUT eSwp;"UP" 125 PLOT I,B(I) 126!PRINT B(I) 127 NEXT I 128 Bmax=MAX(B(*)) 129!PRINT "Max value:",Bmax 130!GOTO Jump3 131 134 Delt=B(84)/Bmax!FRACTION OF ATTN. 135 Fdelt=.84!gHZ 136 Pfrac=Delt/Fdelt 137 IF Pflag=l THEN 138 SUBEXIT 139 END IF 140 K=1 141 WHILE B(K)<>Bmax 142 K=K+1 143 END WHILE 144 Freq=Fstart+(K-1)*.010 145 Fl=Freq-.06 146 Ss=.120/N 147!Pstep2=Pstep*.0015/.01 148 OUTPUT QSwp;"PL";Pwrl; "D CW";F1;"GZ SF";Ss;"GZ" 149 150 FOR I=1 TO 250 151 B(I)=O 153 NEXT I 154! OUTPUT QDvm;Srate$ 155 FOR I=1 TO N/2 156 ENTER QDvm;Dum 157 B(I)=-Dum+(I-1)*.001*1.117E-2 158 B(I)=-Dum 159 OUTPUT eSwp;"UP" C-3

160 OUTPUT eSwp;"UP" 161 NEXT I 162 163 164 Bmax=NAX(B(*)) 165! Adjust power level for optimum snr: 166 167! P.level=10((Pwrl)/10) 168 P.level=10 ((Pwrl-10)/10) 169 Pwrl=P.level*(Det_ max/Bmax) 170 Pwrl=10*LGT(Pwrl) 171 Pwrl=INT(Pwrl/.004)*.004+10 172 OUTPUT QSwp;"pl";Pwrl;"DM CW";F1; "GZ" 173! OUTPUT QDvm;Srate$ 174 FOR 1=1 TO N 175 ENTER eDvm;Dum 176!B(I)=-DUM+(I-1)*.001*1.117E-2 177 B(I)=-Dum 178 OUTPUT QSwp;"UP" 179 NEXT I 180 Pwrl=3 182 OUTPUT QSwp;"PL";Pwrl;"DM" 184 Bmax=MAX(B(*)) 185 Half=Bmax/2 186 K=1 187 Btest=B(1) 188 IF (Btest>Half) THEN 189 PRINT "Leading edge of peak not in bracketed region." 190 PRINT "Press Continue to proceed." 191 PAUSE 192 CLEAR SCREEN 193 GCLEAR 194 GOTO Jump3 195 END IF 196 WHILE Btest<Half 197 K=K+1 198 Btest=B(K) 199 END WHILE 200 IF Btest=Half THEN 201 F3db=Fl+(K-1)*Ss 202 ELSE 203 Delts=(Half-B(K-1))/(B(K)-B(K-1)) 204 F3db=Fl+(K-2+Delts)*Ss 205 END IF 206 Khalf=(F3db-F1)/Ss 207 WHILE B(K)<>Bmax 208 K=K+1 209 END WHILE 210 211! Find out if there are duplicate max pts., if so, choose 212! center one. 213 214 K1=K 215 WHILE B(K1)=Bmax 216 K1=K1+1 C-4

217 END WHILE 218 K=INT((K+K1)/2) 219 FO=Fl+(K-1)*Ss 220 Kk=K 221 Btest2=B(Kk) 222 WHILE Btest2>Half 223 Kk=Kk+l 224 Btest2=B(Kk) 225 IF (Kk=N+1) THEN 226 PRINT "Trailing edge of peak not in bracketed region." 227 PRINT "Press Continue to proceed." 228 PAUSE 229 CLEAR SCREEN 230 GCLEAR 231 GOTO Jump3 232 END IF 233 END WHILE 234 IF Btest2=Half THEN 235 F3db2=Fl+(Kk-l)*Ss 236 ELSE 237 Delts=(Half-B(Kk-1))/(B(Kk)-B(Kk-1)) 238 F3db2=Fl+(Kk-2+Delts)*Ss 239 END IF 240 Khalf=(F3db-F1)/Ss 241 Khalf=Khalf+1 242 Khalf2=(F3db2-F1)/Ss 243 Khalf2=Khalf2+1 244! COMPUTE Q: 245 Fdelt=ABS(F3db-F3db2) 246 Q=FO/Fdelt 247 248! CALCULATE COMPLEX DIELECTRIC CONSTANT, 249! AND COMPUTE SNOW MOISTURE AND DENSITY. 250 251 El=(Fair/FO)'2 252 Bw=Mslope*FO+Bcept 253 Ell=El*((l/Q)-Bw/(FO*1000)) 254 IF E11<0 THEN E11=0 255 256 COMPUTE LIQUID WATER VOL. FRAC & DENSITY. 257 258 A1=FO/9.07 259 Mv=(Ell*(l+Al'2)/(.075*A1))-(1./1.31) 260 Eds=El-.02*Mv'1.015-.073*Mv^1.31/(l+Ali2) 261 Neweds=El-.25*SQRT(Mv)-.25*(A1)*Mv-1.8/(l+Al12) 262 Newpds=-1.214+(1.474-1.428*(1-Neweds))-(1/2) 263 Newpws=Mv/100+Newpds 264 Pds=-1.214+(1.474-1.428*(1-Eds))^(1/2) 265 Pws=Mv/100+Pds 266 GCLEAR 267 VIEWPORT 10,120,25,75 268 FRAME 269 WINDOW 1,N,O,l.l*Bmax 270 FOR I=1 TO N 271 PLOT I,B(I) C-5

272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 NEXT I LORG 5 MOVE K,Bmax LABEL "+" MOVE Khalf,Half LABEL "x" MOVE Khalf2,Half LABEL "x" PRINT "Center Freq. =:",FO PRINT "Q =:",Q PRINT "Dielectric Constant:",E1,"-j",Ell PRINT "mv =:",Mv PRINT "Wet snow density =:",Pws," Bmax = ",Bmax PRINT "OR (revised) density =:",Newpws MOVE O,-Bmax IF Cal_flag=l THEN GOTO Jump3 IF Fflag=l THEN INPUT "Store this data (Y/N)?",Answ$ IF (Answ$="Y" OR Answ$="y") THEN CLEAR SCREEN GCLEAR 293 OUTPUT @Pathl;FNPr$(Dumm+l)&TIME$(TIMEDATE) 294 OUTPUT @Pathl;FNPr$(Dumm+2)t"Comment: "tComment$ 295 OUTPUT ePathl;FNPr$(Dumm+3)t"Res. Freq.: "&VAL$(FO) 296 OUTPUT @Pathl;FNPr$(Dumm+4)t"Q: "&VAL$(Q) 297 OUTPUT ePathl;FNPr$(Dumm+5)k"Dielectric const.: "VAL$(E1)k" - j"&VAL$(Ell) 298 OUTPUT @Pathl;FNPr$(Dumm+6)&"mv: "&VAL$(Mv) 299 OUTPUT ePathl;FNPr$(Dumm+7)t"Wet density: "&VAL$(Pws) " (REVISED) "VAL$ (ewpws) 300 OUTPUT ePathl;FNPr$(Dumm+8)t"DET_MAX: "&VAL$(Det_max)t" and Bmax = "&VAL$(Bmax) 301 OUTPUT @Path1;FNPr$(Dumm+9) Stars$ 302 Dunmm=Dunm+9 303 END IF 304 END IF 305 Jump3: 306 SUBEND 307 308 309 SUB Quit 310 CON /Flag/ Qflag,Calflag 311 Qflag=l 312 GCLEAR 313 SUBEND 314 315 316 SUB Calibrate 317 COM /Avgs/ Fs,Qs,Fa,Qa,Caltype 318 COM /Calvals/ Mslope,Bcept,Fair 319 COM /Flag/ Qflag,Cal.flag 320 CON /Fileinfo/ Fflag,Stars$,F.name$,ePathl,Dinnm 321 PRINT "May read in most recent cal parameters or re-calibrate." 322 INPUT "Do you wish you read in old values (y/n)?",Answ$ 323 IF (Answ$="y" OR Answ$="Y") THEN C-6

324 ASSIGN @Path_2 TO "CALVALS" 325 ENTER QPath_2;Mslope,Bcept,Fair 326 ASSIGN @Path.2 TO * 327 PRINT "New values of mslope,bcept, and fair are:" 328 PRINT Mslope,Bcept,Fair 329 END IF 330 OFF KEY 331 ON KEY 1 LABEL "HEPTANE",3 CALL Sugar 332 ON KEY 2 LABEL "AIR",3 CALL Air 333 ON KEY 3 LABEL "ESCAPE",3 CALL Quit 334 ON KEY 4 LABEL "COMPUTE",3 CALL Compute 335 WHILE Qflag<>l 336 END WHILE 337! RESET QFLAG. 338 Qflag=O 339 IF Fflag=l THEN 340 INPUT "Store cal data to file (Y/N)?",Answ$ 341 IF (Answ$="Y" OR Answ$="y") THEN 342 OUTPUT @Pathl;FNPr$(Dumm+l)tTIME$(TIMEDATE) 343 OUTPUT @Pathl;FNPr$(Dumm+2)&"HEPTANE: "&VAL$(Fs)&", "&VAL$(Qs) 344 OUTPUT @Path1;FNPr$(Dumm+3)&"Air: "&VAL$(Fa)&","&VAL$(Qa) 345 OUTPUT @Pathl;FNPr$(Dumm+4)&"BW = "&VAL$(Mslope)&" x f + "&VAL$(Bcept) 346 OUTPUT @Pathl;FNPr$(Dumm+5)kStars$ 347 Dumm=Dumm+5 348 END IF 349 END IF 350 SUBEND 351 352! 353 SUB Compute 354 COM /Avgs, 355 COM /Cal_3 356 Bws=Fs*10( 357 Bwa=Fa*10( 358 Mslope=(Bi 359 Fair=Fa 360 Bcept=Bw: 361 362 STORE 363 PURGE "CA] 364 CREATE BDl 365 ASSIGN @Pa 366 OUTPUT @Pa 367 ASSIGN @Pc 368 ASSIGN @Pa 369 370 CLEAR SCRI 371 GCLEAR 372 PRINT "Bw 373 SUBEND 374 375 376 SUB Calmain / Fs,Qs,Fa,Qa,Caltype vals/ Mslope,Bcept,Fair )0*(1/Qs-8 OOE-5/1.925) )0/Qa va-Bws) / (Fa-Fs) s-Hslope*Fs CAL VALUES IN FILE FOR RETRIEVAL. LVALS" AT "CALVALS", ath_2 TO "CALVALS" ath_2; slope,Bcept,Fair ath_2 TO * ath_2 TO "CALVALS" EEN = ";Mslope;" x f + ";Bcept C1-7

377 CON /Avgs/ Fs,Qs,Fa,Qa,Caltype 378 COM /Calarrays/ F(10),Q2(10),N 379 CON /Flag/ Qflag,Calflag 380 N=O 381 Fsum=O 382 Qsum=O 383 OFF KEY 384 ON KEY 1 LABEL "GETDATA",5 CALL Getdata 385 ON KEY 2 LABEL "DONE",5 CALL Quit 386 WHILE Qflag<>l 387 END WHILE 388 IF N=O THEN GOTO Jump 389 FOR I=1 TO N 390 Fsum=Fsum+F(I) 391 Qsum=Qsum+Q2(I) 392 NEXT I 393 IF Caltype=1 THEN 394 Fs=Fsum/N 395 QQs=Qsum/ 396 ELSE 397 Fa=Fsum/N 398 Qa=Qsum/N 399 END IF 400 Jump: 401 Qflag=O 402 SUBEND 403 404 405 SUB Getdata 406 CON /Calarrays/ F(*),Q2(*),N 407 CON /Results/ El,E11,FO,Q,Mv,Pws 408 CON /Flag/ Qflag,Calflag 409 Calflag=l 410 N=N+1 411 PRINT "Insert snow sensor and hit continue." 412 PAUSE 413 CALL Takedata 414 Calflag=O 415 INPUT "Use this one in calibration (Y/N)?",Answ$ 416 IF (Answ$<>"Y" AND Answ$<>"y") THEN 417 N=N-1 418 ELSE 419 F(N)=FO 420 Q2(N)=Q 421 END IF 422 CLEAR SCREEN 423 GCLEAR 424 PRINT "VALUES SO FAR..." 425 FOR I=1 TO N 426 PRINT "F =:",F(I),"Q =:",Q2(I) 427 NEXT I 428 SUBEND 429 430 431 SUB Sugar C-8

432 COM /Avgs/ Fs,Qs,Fa,Qa,Caltype 433 Caltype=l 434 CALL Cal.main 435 SUBEND 436 437 438 SUB Air 439 COM /Avgs/ Fs,Qs,Fa,Qa,Caltype 440 Caltype=2 441 CALL Cal.main 442 SUBEND 443! 444! 445 SUB Start.freq 446 COM /Values/ Fstart,Pwrl,Det_max 447 CLEAR SCREEN 448 GCLEAR 449 PRINT "PRESENTLY, STARTING FREQ. IS ";Fstart;" GHz." 450 INPUT "ENTER DESIRED STARTING FREQ. IN GHz:",Fstart 451 SUBEND 452 453! 454 SUB Pwrlvl 455 COM /Values/ Fstart,Pwrl,Detmax 456 CLEAR SCREEN 457 GCLEAR 458 PRINT "PRESENTLY, POWER LEVEL IS ";Pwrl;" dBm." 459 PRINT "ALLOWED RANGE IS 0 TO 15 dBm." 460 INPUT "ENTER DESIRED POWER LEVEL:",Pwrl 461 SUBEND 462 463 464 SUB Create.file 465 DIN String3$[200] 466 COM /Fileinfo/ Fflag,Stars$,Fname$,@Pathl,Dumm 467 468 GCLEAR 469 CLEAR SCREEN 470 Strl$=DATE$(TIMEDATE) 471 Str2$=TIME$(TIMEDATE) 472 F.name$=Strl$[1,2] Strl$[4,5] Str2$[1,2]kStr2$[4,5] 473 PRINT "Default filename is ";Fname$ 474 INPUT "Use this name (Y/N)?",Answ$ 475 IF (Answ$="N" OR Answ$="n") THEN 476 INPUT "Enter filename of choice (max. 10):",Fname$ 477 END IF 478 CREATE ASCII Fname$,100 479 ASSIGN QPathl TO F_name$ 480 PRINT "FILE ";F_name$;" CREATED." 481 INPUT "Add a comment to top of file (Y/N)?",Answ$ 482 IF (Answ$="Y" OR Answ$="y") THEN 483 LINPUT "Type in message now:",String3$ 484 OUTPUT @Path1;FNPr$(Dumm+l)&"Comment: "&String3$ 485 OUTPUT ePathl;FNPr$(Dumm+2)kStars$ 486 Dumm=Dnmm+2 C-9

487 END IF 488 String3$=" 489 Fflag=l 490 SUBEND 491! 492! 493 SUB Closefile 494 CON /Fileinfo/ F_flag,Stars$,Fname$,QPathl,Dumm 495 ASSIGN QPathl TO * 496 Fflag=O 497 GCLEAR 498 CLEAR SCREEN 499 PRINT "File ",Fname$," closed." 500 SUBEND 501 502 503 DEF FNPr$(Dumm) 504 String$=" " 505 String$=VAL$(Dumm) "! 506 RETURN String$ 507 FNEND 508! 509 SUB Cal.line 510 COM /Line.loss/ Pstep,Pfrac,Pflag 511 COM /Values/ Fstart,Pwrl,Detmax 512 Pstep=O. 513 Pflag=l 514 PRINT "CONNECT TRANSMIT t RECEIVE CABLES TOGETHER W/O PROBE" 515! SET POWER LEVEL TO -5 DBM 516 Dum=Pwrl 517 Pvrl=-5 518 PRINT "THEN PRESS CONTINUE" 519 PAUSE 520 CALL Takedata 521 Dum2=l-Pfrac 522 Dbs=-10*LGT(Dum2) 523 Pstep=.01*Dbs 524!Pstep=INT(Pstep/.006)*.006 525 PRINT "pstep",Pstep 526 Pflag=O 527 Pwrl=Dum 528 PRINT "SYSTEM IS NOW CALIBRATED FOR LINE ATTN." 529 SUBEND 530! 531! 532 SUB Rate 533 COM /Samp.rate/ Srate$[2] 534 INPUT "Select sampling mode (1=med, 2=fast):",Dum 535 SELECT Dum 536 CASE 1 537 Srate$="S1" 538 CASE 2 539 Srate$="S2" 540 CASE ELSE 541 BEEP C-10

542 PRINT "Invalid Choice" 543 GOTO Choose2 544 END SELECT 545 SUBEND C-11

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