Abstract In March 1988 a team from the Radiation Laboratory of the University of Michigan performed field measurements of the backscatter characteristics of snow at millimeter-wave frequencies. This short series of measurements was one of the first operational uses of specialized equipment only recently available to the Radiation Laboratory and served as a practice run for extensive snow experiments planned for the winter of 1988-89.- Several types of measurements were made, including the diurnal experiment described in this report.l 1 Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Contents 1 Introduction 1 2 Previous Observations 1 3 Description of Experiment 2 3.1 Equipment................................ 3 3.2 Experimental Technique........................ 6 3.2.1 Target Preparation....................... 6 3.2.2 Calibration........................... 10 3.2.3 Fading Variations...................... 16 3.2.4 Procedure............................ 19 4 Data Reduction 20 4.1 Calibration and Errors......................... 22 4.2 Illumination Integral and Generation of a~.............. 23 5 Ground Truth 25 5.1 Snow Gravimeteric Liquid Water Content.............. 25 5.1.1 Significance........................... 25 5.1.2 Procedure............................ 25 5.2 Snow Pit Data............................. 31 5.2.1 Surface Profile.......................... 34 5.2.2 Snow Temperature...................... 34 5.2.3 Air Temperature..................... 34 i

5.2.4 Snow Crystal Characterization................. 36 6 Discussion 39 6.1 Diurnal Variations....................... 39 6.2 Surface Variations....................... 41 6.3 Variation of Backscattering Coefficient with Liquid Water Content.41 7 Recommendations for Future Snow Experiments 46 7.1 Data Collection............................. 46 7.2 Ground Truth............................. 48 7.3 Miscellaneous Items........................... 49 References 51 Appendix 53 ii

List of Figures 1 The MMP system mounted on the boom truck............ 3 2 Close view of boom sensors....................... 4 3 Interior of the control shed....................... 5 4 A typical sample from the upper surface of the snowpack...... 7 5 Three snow surfaces..................... 8 6 Preparation of the snow surface.................... 9 7 "Slightly rough" snow surface................... 10 8 Cross sectional photograph of the "slightly rough" snow surface.. 11 9 Undisturbed or "smooth" snow surface................ 12 10 Cross sectional photograph of the undisturbed or "smooth" snow surface................................. 13 11 "Very rough" snow surface....................... 14 12 Cross sectional photograph of the "very rough" snow surface... 15 13 Calibration sphere........................... 16 14 Calibration configuration........................ 17 15 Top view of experiment site...................... 20 16 Nighttime view of experiment site................... 21 17 Collection of a snow sample...................... 27 18 Calorimeter procedure......................... 28 19 Cleaning the calorimeter........................ 29 20 Measured gravimetric liquid water content of the snow....... 31 21 The face of the snow pit........................ 32 iii

22 A technician collects a density sample from the snow pit...... 33 23 Microscope photographic equipment................ 36 24 New snowfall........................... 37 25 Freshly fallen snow crystals...................... 38 26 a~ vs. time for undisturbed snow surface............... 40 27 a~ vs. time for three surfaces at 35 GHz, w-polarization...... 42 28 a~ vs. time for three surfaces at 35 GHz, hv-polarization...... 43 29 Functional fit to measured gravimetric liquid water content of the snow................................... 44 30 ao vs. GLWC for undisturbed snow at 35 GHz, vv-polarization.. 45 31 ao vs. time for slightly rough snow surface............ 54 32 a~ vs. time for very rough snow surface................ 55 33 a~ vs. time for three surfaces at 94 GHz, vv-polarization...... 56 34 aO vs. time for three surfaces at 94 GHz, vh-polarization...... 57 35 a~ vs. time for three surfaces at 94 GHz, hh-polarization...... 58 36 aO vs. GLWC for slightly rough snow at 35 GHz, w-polarization..59 37 a~ vs. GLWC for very rough snow at 35 GHz, vv-polarization.. 59 38 a~ vs. GLWC for undisturbed snow at 35 GHz, hv-polarization.. 60 39 a~ vs. GLWC for slightly rough snow at 35 GHz, hv-polarization..60 40 a~ vs. GLWC for very rough snow at 35 GHz, hv-polarization... 61 41 a~ vs. GLWC for undisturbed snow at 94 GHz, vv-polarization... 61 42 a~ vs. GLWC for slightly rough snow at 94 GHz, w-polarization..62 43 a~ vs. GLWC for very rough snow at 94 GHz, vv-polarization... 62 iv

44 a~ vs. GLWC for undisturbed snow at 94 GHz, vh-polarization.. 63 45 a~ vs. GLWC for slightly rough snow at 94 GHz, vh-polarization.. 63 46 a~ vs. GLWC for very rough snow at 94 GHz, vh-polarization... 64 47 a~ vs. GLWC for undisturbed snow at 94 GHz, hh-polarization... 64 48 a0 vs. GLWC for slightly rough snow at 94 GHz, hh-polarization.. 65 49 r~ vs. GLWC for very rough snow at 94 GHz, hh-polarization... 65 List of Tables 1 Mean and standard deviation of rms roughness of various surface areas.................. 34 2 Snow and air temperatures during diurnal experiment....... 35 3 Coefficients of curve fit to liquid water data........ 47 v

1 Introduction Snow is an important natural resource which is receiving increasing interest in the field of remote sensing. Scientists in hydrology, climatology, agriculture, meteorology, and other disciplines desire increased accuracy in measuring the extent and characteristics of snowpacks on local, regional, and continental scales [1]. Modern developments in remote sensing show much potential in the determination of snow areal extent, snow depth, snow liquid water content, and snowpack structure. The millimeter-wave portion of the spectrum (30-300 GHz) has not yet been extensively utilized in the remote sensing of snow (compared to centimeter wavelengths and optical frequencies). Further study and additional data are necessary to determine which snow parameters are optimally detected at millimeter-wave frequencies. Our study is designed to help alleviate this shortage of data. The experiment described in this report was conducted to study the diurnal variation of the radar backscatter from snow. The effects of surface roughness, liquid water content, and other snow characteristics are also considered. 2 Previous Observations Liquid water content has been found to have a significant effect on the radar backscatter at millimeter-wave frequencies [8,9,10]. In addition, "hysteresis" effects have been observed by Stiles and Ulaby [6], in which the backscatter response leads the liquid water content during the melting stage and lags behind it during the refreezing stage. The sensitivity of radar scattering to liquid water content has been found to decrease with increasing frequency [10], and the radar response saturates 1

at lower values of the liquid water content as the frequency is increased [7]. Surface effects are expected to be significant only for the wet snow case and the work of Williams, Gallagher, et al. [8,9,10] supports this. The role of snow crystal size has been investigated with varied results. The snow grain size was found to not be significant for dry snow by Williams et al. [8,9], but earlier studies by Williams et al. [10] found it to be significant, with a~ decreasing as grain size increased. The goal of this investigation is to examine all of these effects. However, due to the difficulty associated with varying crystal size, the primary parameters examined thus far are liquid water content and surface roughness. 3 Description of Experiment A team of four researchers from the University of Michigan Radiation Laboratory traveled to Houghton, Michigan, located on the Keweenaw Peninsula of Michigan's Upper Peninsula, during the week of March 27-April 2, 1988. Snow experiments were conducted on March 29, 30, and 31 at a test site adjacent to the Keweenaw Research Center. The experiments included measurement of the radar backscatter from snow as a function of incidence angle (at several polarizations and two frequencies), in addition to a "diurnal" experiment in which the radar backscatter was measured as a function of time over a complete darkness-daylightdarkness cycle. The diurnal backscatter experiment was conducted on March 31. 2

33.H.-.. = 333333. —.. -. ==r.. =.r r.-. r.: r t3. s.=. m s r. -............................................ r..r- 3 _siii~i~,_~ iiir' ssi~s... t =.si: P = - ii i. -.-: iii -...:.r.. *33333-., —,.-., —,-,-.i:,- r iri,,-ri.i::r.r, I-, irui:;r ji i: irir:iiiiiir iiii ii-.-E-rii i -........ 3 r -. 3 3-. 3 E —.r i iir 3. i-.......... 3 i; nt:-.-8."ts~~~~.................... r....-..: -i..ii.i-i-:ii,:i,- ii, —***....* —-. i,................i.........irr~~r..:..::r..:.:..,.::l..:::::lr:.:.: rrrii~~~~j,...:r: rir i:: r::r:::::rr, ri:r. ~-r ~-~~ r ri Figur 1: The'''' MMP system'''"- is shown mounte on th boom truck (cntr at the Houghton The~~~* Unvrst of Mihia Millimeteri-Wave Poaietr(MP atepi maryinstrum..........e ue inte. experimet.r T..e M P is a s.r..r b. ae scatte —.: —-.rometer antennas are mounted on an extendabe bm on a r truk,, mak~~~~~~~~ing measre nt of a wid vrit of natural trget posil. L — ikei- an....................... —. --- -rir..-r'.''i.......' 1'''................ r —-r-r-r ~~~~~~~~~~~~~~~~~~......................................................................................................................... ------- bandwidth, with.. cente-,r frequen s.-. 35an. 94 Grz. (A 140 G'''' channel,- *: - ^ i rj H................................................. 11 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~...................iiiiir..........i,:,.....,.~11ii il~ti i~i'...'.,.r.'...''r''=- iir:'i''r r~~~~~~~~~~~~r''''' g'' i -''''''i' g'r.''''''''':'':: - - -............................... i E-,. g..,'- rr=__'.iiBE.Ejr.'R:......................................................' r LE E:i......................................... -..................: H i _ _.=z —.g~,,,,,'''''''l''' l''''''''' L"' r'''......................'...'.....',.: s ^:.. irur —*-rr r rj-rr jrj Lj.,.,..H~~~~~~~~............... iii | _ ~ ~ ~ ~ ~~ ~ ~~~~~~~~~~~~~~~~iiiii~iiiii'~tit~ifi....L'ir'..,ii,.==-rri.,,..r3 m _ _ _~~~~~~~~~...............'::nn~~~~~~~r..-.*-.i E~~~~~~~~~~~~r r _ t H _ _ F | s..,.,:rB~~~~~~~~~...........:'''~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i-:fl i:~'.r —=. r~- -i~ Ei,i~j:r — _ _ -:::::': i:s:::.''' -''r~~~~~~~r~~= r~.r.r.'.:..............._.' been-. addedsin e she da te ofthiis:. experiment.) In ddiin rth se...............,~~~~~~~~~~~~~... r=. g *........... r -.-... r......-.. tral rsp the ines-F ct of th Hall ow s, real-tim ti e 3 E~i~l | E!.l |........................... -.'.,'.,.:.::.:.-.,'.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. w.j-iE.:r.:-...............r.............r:.._..... Figutre 1: Ther MMP syast i how mounted on the boom truck (center at thre Houghto expeimnt mesite.so wd ait o aua arespsile ie The Universwity ofte Michigance 3 Mlier-ave94Gz( Poarmee (MMP whas te primary intrmntued inceh dthe exphseriment.nt. The dito MM i a ipan scttrmee bsped o thel HeP 8510 Vheco iNvretwork cAnaiiyo teHalyzr ssown nFgrs 1,2,and 3,e thme scatterometer antennas are mounted on an extendable boom on a large truck,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............... making measurements of a wide variety of natural targets possible. Like- and~~~~~~~~~........................... cross-polarized backscatter are measured at 401 discrete frequencies over a 2 G~~~~~~.......................... bandwidth, with center frequencies of 35 and 94 G~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~z. (A 140 G~~~~~~~~~z channel........has. been added since the date of this experiment.) In addition to displaying the spec-~~~~~~~~~~~~~~~~~~.................. tral response, the inverse-FFT capability of the HP 8510 allows real-time time-~~~~~.................................:::... 3~~~~~~~~~~~~~~~...................

.............. iiii iii i: iiiii~iiiiiiiiiiiiiiiiiiiii~iii1............. ~ I Figure 2: A close view of the sensors mounted on the boom. The radiometers are oil tile left.,~~~~~~~~~~~~~~~............. and the radars are on the right.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...........

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domain analysis. The MMP is described in more detail by Ulaby et al. [2]. The original experiment plan included the collection of snow emission data concurrently with the backscatter data using three radiometers with center frequencies of 35, 94, and 140 GHz. However, mechanical failures precluded the use of the radiometers. 3.2 Experimental Technique Due to a variety of logistical and technical problems, the MMP system was not available for snow measurements until quite late in the winter, thus narrowing the scope of our experiments. However, by preparing the snow surface in various ways, we were able to maximize our experimental opportunities. 3.2.1 Target Preparation At the date of the experiment (late March), the snow surface was heavily metamorphosed, having gone through numerous melt/freeze cycles. Individual snow crystals were no longer distinguishable, having formed into large icy clumps. A typical sample from the upper surface of the snow is shown in Figure 4. In order to measure the effect of surface roughness on the backscatter from snow, the snow surface to be measured was divided into three sections, as shown in Figure 5. Preparation of the snow surface areas is shown in Figure 6. A garden rake was used to roughen the surface of the first section, resulting in a "slightly rough" area, with a typical rms surface roughness of 0.880 cm (Figures 7 and 8). The second section was left undisturbed and will be referred to as "smooth" snow. Its rms surface roughness was 0.488 cm (Figures 9 and 10). Several people walked 6

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Figure 7: "Slightly rough" snow surface through the third section, which will be designated "very rough" snow. Its typical rms surface roughness was 1.976 cm (Figures 11 and 12). 3.2.2 Calibration A 38.1 cm (15-inch)-diameter aluminum sphere mounted atop a cylindrical styrofoam pedestal was used as a calibration target, as shown in Figures 13 and 14. The calibration was performed in the time domain; i.e., the time-domain response of the sphere was integrated to give the total power returned from the sphere in the 2 GHz bandwidth. The system constant K was determined using this result, the range to the sphere, and the known radar cross section of the sphere. Separate system constants were obtained for each frequency and polarization. The entire 10

va m m - i iii~iiiiiiila. Figure 8: Cross sectional photograph of the "slightly rough" snow surface~~~~~~........ -------- --- M

Figure 9: Undisturbed or "smooth" snow surface 12

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-- -- -- -- - Figure II: Very rough"snow surfMM 14~~~~~~~~~~~~~~~~~~~~~~~~~~~...........

................................................................................ ------- -- ---------................................................................................................................................................................................... OIL..........I.................................................................................................................................................................................................... UZILM - ---------................ -- - ---------........................................................................... - ------- --............................ ----------- - -- ------------..................................... -------..................................... -................................................................................................................................................................................................................................................................................................................................................................................. - ------------..................... I........... ----- - -- ----- --....... Figure 12: Cross sectional photograph of the "very rough" snow surface

Figure 13: A 38.1 cm (15-inch) diameter aluminum sphere mounted atop a cylindrical styrofoam pedestal was used as a calibration target. system was calibrated at regular intervals throughout the experiment. 3.2.3 Fading Variations Fading-caused fluctuations in the backscatter measured from distributed targets are often overlooked. The topic of signal fluctuation statistics for distributed targets is treated in Ulaby et al. [3]. For a snow target, we assume that each target footprint contains a large number of independent scatterers, and that the 16

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individual scatterers are comparable in magnitude; i.e., no single scatterer dominates the returned signal. Using these assumptions and others described in [3], we may assume that the backscattered signal follows a Rayleigh distribution (for square-law detection, which is our case). For such a distribution, the ratio of the standard deviation a to the mean value y of the backscatter is given by 1 0 1 VN(1) where N is the number of independent samples, which can be obtained spatially (Nsp) and/or through frequency averaging (Nf). In each target area, the radar was continuously swept in azimuth in order to increase NSp. Approximately 40 independent samples per measurement were obtained by observing independent target areas. Frequency averaging provided additional independent samples. For both 35 and 94 GHz measurements, a bandwidth of 2 GHz was used, providing more independent samples than a comparable single-frequency measurement. As described in [3], the number of independent samples Nf obtained by frequency averaging is given by 2D Nf = -B (2) C where c is the velocity of light, B is the radar bandwidth (in hertz), and D is the difference in range (in meters) between the least and most distant points in the radar footprint. For our experiment, D was approximately 0.555 m and 0.164 m at 35 and 94 GHz, giving values of 7.41 and 2.19 for Nf at 35 and 94 GHz, respectively. The total number of independent samples N is given by the product of Nf and Np. For our experiment, N(35GHz) = 296, and N(94GHz) = 87.6. Using (1), the 18

expected values of alp/ are 0.058 and 0.107, while our experimental values were 0.083 and 0.086 for 35 and 94 GHz, respectively. 3.2.4 Procedure The experimental layout is shown in Figures 15 and 16. The three snow surfaces were measured in rotation at all frequencies and polarizations, in the following order: 35-vv, 35-hv2, 94-vv, 94-vh, 94-hh. The incidence angle was 40~ from nadir, and the average range to the snow surface was 9.34 m. During a given measurement run, the truck boom was swept in azimuth, moving the radar footprint back-andforth within the boundaries of the surface area. A video camera and monitor allowed the operator to view the radar footprint during the measurement. At night, flashlights were placed at the boundaries of each surface area, allowing the operator to distinguish the boundaries when it was too dark to observe the snow directly on the monitor. As a consequence of the limited area available for scanning, individual measurements of ao were not completely spatially independent; i.e., the footprints (determined by the half-power beamwidth) did overlap. However, in Ulaby [3], we see that the returns from two footprints may be considered independent even if the footprints do overlap, provided that two conditions are satisfied: (1) d > Ld, where d is the distance between the centers of adjacent footprints and Ld, the fading decorrelation distance, is approximately 4y/2, where ty is the antenna width in the azimuth direction, and (2) d > L,, where L, is the spatial correlation length of the random surface. In the diurnal experiment, d > 0.5 m, Ld = 7.62 cm, and 2This report uses a tr convention for the cross-polarized backscattering coefficient; i.e., "vh" denotes transmit v, receive h. 19

footprint \ \] |Smooth, Snow / Slightly Rough / Very Rough Snow' L Snow s. ~,;;~:- I:..~:. S:.n~: —~:.,...... q......., S-.~ ~~~~~Snow | Figure 15' Top view of experiment site L'' < 0.5mforaltre Cont roltom return frmalN fotr 20 r ^^^YY ^Y S j^Y>'Y)'Y>Y)'Y'YY' _x- r YFxV'Y Auxiliary |' > ^.y>.^.y^.y'.y*.:. I IJ^.Ny>6.wy.y.^.^.:y^y^y ^^^^^ I NVII Tru k... >* Gravel Road v Yg _.__jL - Snow Figure 15: Top view of experiment site L, < 0.5 m for all three surfaces. Hence, the returns from all Nsp footprints were independent, giving Nsp independent samples (spatially). 4 Data Reduction All data and supplementary information was recorded on a computer printout during the experiment. Upon returning to Ann Arbor, the data was entered into the university's mainframe computer for reduction. 20

Figure 16: Nighttime view of experiment site 21

4.1 Calibration and Errors The calibration target was a steel sphere with a diameter of 38.1 cm (15 inches). We begin with the point-target form of the radar equation: Pt Gtp Grp A2~P PrT~~ =~ WR^ ~~~(3) r (4ir)3R4 () where Pr = received power Pt = transmitted power Gtp = gain of transmit antenna in direction of sphere Grp gain of receive antenna in direction of sphere A = wavelength ap= radar cross section of sphere Rp = range of sphere from antennas The calibration and measurements were performed using the time-domain option of the HP 8510, providing a real-time display of the ratio of received to transmitted power as a discrete function of range. The return signal from the sphere was clearly visible among the 401 trace points displayed on the screen of the HP 8510 (each corresponding to a particular range). The trace points representing the sphere return are summed to obtain the ratio of the total power reflected from the sphere to the power transmitted according to P~ tE'end Pt i (4) 22

Rewriting the radar equation, we now have p =,,G. O (5) (4ir)3 R4 Let the terms on the left be represented by K: K =G G GA2 (6) (47r)3 Then P=K R (7) and, therefore, R4 K -P (8) o7p which gives a value for K, the system constant. Note that this value is independent of range. 4.2 Illumination Integral and Generation of a~ To obtain values of the backscattering coefficient a~ we use the distributedtarget form of the radar equation, PtA2 (9) Pr= -- GtGr dA (9) (41r)3 Jluminated area R4 where Pr = received power Pt = transmitted power A = wavelength Gt = gain of transmit antenna 23

Gr = gain of receive antenna a~ = backscattering coefficient of distributed target R = range of distributed target Assuming a~ is constant over the pattern and using (4), we have A2010 r GtG, _ = dA. (10) (47r)3 1. area R(10) Let Gt = Gtogt and Gr = Gr,,gr where Gt, and Gro are the maximum values of the transmit and receive antenna gains. We now have -A2GtG oo / g,gtd p A2GtGro~ j t dA (11) (47r)3 area R4 Assume Gto and Gro are the same as Gtp and Grp. From (6), we have P ^= K f rgtdA (12) I1I. area R We define the integral in (12) as the illumination integral I. It is a function of the antenna patterns of the two antennas and the geometry of the measurement. Values of I were calculated for a wide range of antenna heights and incidence angles; interpolation of these results was used to obtain values for our measurements. Solving (12) for the backscattering coefficient, we have =Ii (13) KI where I is the illumination integral, K is the system constant, and P is the ratio of the received to the transmitted power. 24

The value of K used for a particular measurement was that determined by the last preceding calibration. The assumption was that the system response was fairly constant over time. 5 Ground Truth A variety of ground truth data were collected concurrently with the radar measurements. Ground truth data included air temperature, snow temperature profile, snow density, snow crystal characterization, snow surface profile, and snow gravimetric liquid water content. An excellent discussion of various ground-truth measurements of snow is found in Jones [4]. 5.1 Snow Gravimeteric Liquid Water Content 5.1.1 Significance The snow gravimetric liquid water content (GLWC) is perhaps the most important parameter that influences the radar backscatter. This is due to the large difference in the relative dielectric constants of liquid water ( 10 -j20 at 35 GHz) and ice (w 3.15). Thus, even a small amount of liquid water in a snowpack can cause a dramatic change in the backscatter characteristics of the snow. 5.1.2 Procedure The snow gravimetric liquid water content was measured using a freezing calorimeter. This method has been determined to be the most accurate method for field measurements of GLWC [4,5], although the procedure is quite tedious and difficult to perform in the field. 25

A thermos containing a vacuum-sealed insulating bottle was modified for use as a calorimeter by drilling a small hole in the cap and inserting a thermistor (Omega Model ON-401-PP) through the cap. Toluene was used as the freezing agent. After several days of use, the plastic covering of the thermistor was dissolved by the toluene, rendering it unsafe. A Type K thermocouple was provided by the Keweenaw Research Center for use with the freezing calorimeter during most of the diurnal experiment. The procedure is as follows: (1) The mass of the empty thermos is recorded. (2) Approximately 300 ml of toluene, which had been cooled to roughly -40 ~C, is added to the thermos. (3) The mass of the thermos and toluene is recorded. (4) The thermos is closed with the thermistor inserted in the toluene. (5) While agitating the calorimeter gently, the temperature of the toluene is recorded at 15-second intervals. When the rate of temperature change is roughly constant (usually within about 5 minutes), the thermos is considered to be at equilibrium, with a small amount of heat leaking into the thermos at a constant rate. (6) The snow sample is collected, its temperature is noted, and it is added to the toluene in the thermos. (7) The exact time that the snow is added is recorded, and the agitation and 15-second interval temperature recordings are resumed. The temperature is monitored until the rate of temperature change is again constant. At this point, the liquid water in the snow sample has been frozen and the mixture is again in equilibrium, except for the small leakage into the calorimeter. (8) The mass of the thermos, toluene, and snow sample is recorded. (9) The toluene/snow mixture is then discarded, and the thermos is cleaned in preparation for the next 26

Figure 17: A sample is collected from the surface of the snow for the gravimetric liquid water content measurement. measurement. An entire measurement sequence, including cleanup, took 30-40 minutes when performed by a single operator. Various steps in the procedure are illustrated in Figures 17, 18, and 19. Through later experience we learned the importance of vigorous agitation of the calorimeter during the temperature measurements. The gentle agitation recommended in earlier reports [4,5] and used in this experiment may have contributed to experimental errors. We recommend vigorous agitation and inversion of the calorimeter in order to obtain adequate mixing and accurate temperature measurements. The fraction of the snow mass which is in the liquid state is determined by one 27

Figure 18: The calorimeter is gently agitated and the temperature is recorded every 15 seconds. 28

Figure 19: The calorimeter must be thoroughly cleaned after each measurement. 29

of the following two equations. If the snow temperature is greater than the freezing point of water (T, > T,), we have mW (mT + E)CTif(Tf - Ti) - m,Cdzf(Tz - T) (14) rm, m,[L + Cwsz(Ts - Tz)] If the snow temperature is less than the freezing point of water (T. < TZ), we have m, (mT + E)CTif(Tf - Tj) - mCdf(T - Tf) 15 m, m,[L - Cd.sf(T - Tf) + Cdzf (Tz -Tf)] where m, = mass of liquid water in the snow (g) m, = mass of snow (including both liquid and solid components) (g) mT = mass of the toluene (g) E = calorimeter constant (g) Tf = final temperature of the toluene/snow mixture (K) Ti = temperature of the toluene before adding the snow sample (K) T = freezing point of water (= 273.15 K) T = temperature of the snow sample prior to adding to the toluene L = heat of fusion of water (= 79.7 cal/g) CTif = heat capacity of toluene at T = (Ti + Tf)/2 (cal/g * K) Cdzf = heat capacity of ice at T = (T, + Tf)/2 (cal/g * K) CZ, = heat capacity of water at T = (T. + T,)/2 (cal/g * K) Cdf = heat capacity of ice at T = (T, + Tf)/2 (cal/g * K) The results of the liquid water measurements are shown in Figure 20, where 30

6 0.12 -a —-- Snow temp (~C) Mw/Ms O 0.10 o.. / / \0.08 a. E o.o6 0.06 0.02 -4 * 0.00 6 8 10 12 14 16 18 20 22 Time (hr) Figure 20: Measured gravimetric liquid water content of the snow gravimetric liquid water content is plotted along with T,, the snow temperature near the surface. 5.2 Snow Pit Data Most of the other ground truth parameters were measured in the snow pit by various members of the experiment team. The snow pit was dug in an area adjacent to the radar target area, as shown in Figure 15. The snow pit is illustrated in Figures 21 and 22. Care was taken not to disturb the front face of the pit, which was used to characterize the snow at varying depths. Periodically, the pit was extended in the direction of the front face, thus exposing a fresh profile which had been unexposed to air and/or sun. The front face of pit was exposed on the north side; hence it was shaded at all times. 31

HIRUMMIRM-1111HUMU" ~ ~ ~ i.............'".....i.IH'', U. Z:~~ ~ ~.....'....-..: ~.:!iE~~~~~~~~~~~~~~~~~~~~~~~....'..?j....j.....?~,i'- ~ ""'~~ ""'~"" )t —-mm'a~lm ~'mm ~ ~ -— ~'..'L:':i;;l............... ------............................................................................. F......igu r e 2....1.........e of. t si.t...........................................................................0.0.................::::::::: il~~lli~iiiiiiiiiiiiii....................................................................:'i~~~~~f i~~~~~ii'ii~~~~~~~iiiiii~~~~~~~~iiiiiiiiiiiiiiiiiiiiiiiii....................... i:'iiiiiliiiiiiiiiiiiiiiiiiiiiiiiijiiiii~~~~~~~~~~~~~~~....................................................................... llilli~ liiil.............. I..................................fiiill iilli ll II.................... Unii ii i:::,,i~ii ~~iii~i~,,~,,~~,............. UUU iiiii:g:iiii iil i:ip ii.:ii~~~~~~~ii:.:Iiiiliiiiiiiiilli~~~~~~~~~~~~~~~~~~iiiiiUUl _U........::.::::iiiiiiiiriiiiiiiiiiiiiiiiiiiiiiiiii~....................................:iii..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..........:::'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............................... U F ig u r e 2 1: T h..................................im..............

... -........................................... - -....... r —. -H..r.rrfii;= r...................... =............... _r....... = _......-............................ r _E_._........... -..-r. r........ r................. - - r _..................................................................:iiiiili~~~~~~iI~~ii~~~ii"~~~:~~Ei~~:.~~~~~:~.i ~...................................... liiiiiiiiiiiiiiiiiiiiE~liii~i~..:~ii~i _ -r::..r.::: r~: ---—.:.:'.-..:.:..: r...:~.:............. -----......................iiiii~i:~i~~::~:::.:.:i~l~i~:.I:::l~illi:ti~i..........................::::::...i............................. N~ ~ ~ ~ ~ ~ ~ ~ ~~.............~~: ii:ii:::i~ Figure 22: A technician collects a density sample from theiii~i~i~;:-:i~i~ii i snow pi:it.i~...3...3......................................~~~~~88 ~ ~ ~ ~ ~~~" ss~~~~~~~i~:"%' ~li::I: ~~~~~~~~~~~~~~~~~~~~~~~............... ijiifiiiiirii iiii~~~iii~iiii ii................. =:................................................. * t:..........................iiiiiiiiiiiii...........................iiii i i i iiiiiiiiiiiii iii jiiiiiiii..............................................~~ ~~~~~~~~iiiii~r Figure 22: A technician collects a density sample from................................

Surface rms roughness Std. Dev. smooth 0.488 cm 0.161 cm slightly rough 0.880 cm 0.314 cm very rough 1.976 cm 1.130 cm Table 1: Mean and standard deviation of rms roughness of various surface areas 5.2.1 Surface Profile Snow surface profiles were used to estimate the roughness of the snow surface. In each surface area, a flat plate was inserted vertically into the snowpack and the snow on one side was removed, exposing a cross section of the snow surface. The profile of the surface was then photographed with a ruled grid placed in the background for comparison. The resulting surface profiles are shown in Figures 8, 10, and 12. The surface roughnesses are summarized in Table 1. 5.2.2 Snow Temperature A snow temperature profile was obtained by inserting mercury thermometers into the face of the snow pit at varying depths. In addition, a thermometer was inserted almost horizontally into the upper centimeter of the snowpack, giving regular "surface snow" readings. The snow temperatures are summarized in Table 2. 5.2.3 Air Temperature Air temperature was monitored by an alcohol thermometer which was suspended in air in the shade (under the equipment truck, which remained stationary with its engine off throughout the entire experiment). Air temperatures are sum34

Time (hr) Snow temperature (~C) Air temperature (~C) 6.5 -1.50 -1.8~ 7.23 -1.30 -2.0~ 10.05 1.1~ -1.0~ 10.8 1.9~ -0.50 12.03 3.50 0.5~ 13.03 3.00 0.8~ 15.58 4.50 1.1~ 17.7 -0.30 0.0 0 18.78 -1.0~ -1.5~ 19.87 -2.7~ -1.5~ Table 2: Snow and air temperatures during diurnal experiment 35

Figure 23: Snow crystals were photographed using a microscope with 35 mm camera attachment. marized in Table 2. 5.2.4 Snow Crystal Characterization Snow crystal type was recorded using a microscope with a 35 mm camera attachment (Figure 23). As shown in Figure 4, the upper snow surface did not contain many intact snow crystals. The heavily metamorphosed snow was mostly in the form of icy clumps, with occasional abrasions showing. There was a brief period of snowfall on the morning of the experiment, although there was no significant accumulation. Figure 24 shows the fresh snow against a footprint in mud that had been free of snow before the brief snowfall. A sample of the freshly fallen snow crystals is shown in Figure 25. 36

Figure 24: The brief period of snowfall on the morning of the experiment resulted in negligible accumulation. There was a brief period of snowfall on the morning of the experiment, although there was no significant accumulation. Figure 24 shows the fresh snow against a footprint in mud that had been free of snow before the brief snowfall. A sample of the freshly fallen snow crystals is shown in Figure 25. 6 Discussion In spite of the limited scope of this experiment, the surface preparation and ground truth data allow us to analyze the effects of several variables on the radar backscatter. 37

Figure 25: Freshly fallen snow crystals 38

6 Discussion In spite of the limited scope of this experiment, the surface preparation and ground truth data allow us to analyze the effects of several variables on the radar backscatter. 6.1 Diurnal Variations The diurnal experiment began at 6:37 AM local time on March 31 and concluded at 9:57 PM. Starting before sunrise and ending well after sunset allowed the observation of a complete melt/freeze cycle. A graph of the backscattering coefficient vs. time is shown in Figure 26, which includes data for all five frequency/polarization combinations for the undisturbed or "smooth" snow. Actual data points are shown along with curve fits using Gaussian curves with constant offsets. As expected, backscatter is higher for the cooler periods before sunrise and after sunset. Temperatures during these periods were several degrees below the freezing point of water, resulting in completely dry snow, composed only of ice particles. During the day, the warm temperatures melted some of the surface snow, resulting in decreased backscatter due to the large increase in dielectric constant as ice changes to liquid water. Figure 26 also shows the dependence of a~ on frequency and polarization. The backscattering coefficient is higher at 94 GHz than at 35 GHz due to the increased roughness of the surface compared to a wavelength. The like-polarized return is dominant over the cross-polarized return at both frequencies, as expected. Similar graphs for the slightly rough and very rough cases are shown in Fig39

6..o 4 r- 0 \ V' CD -0 —-- 35wi -2. "', 0 0 -------- 94l - 94hh8... co. -"-6 C) <D ^ --— e 35h -6. 8. 10. 12. 14. 16. 18. 20. 22.35hv Time (hours) Figure 26: Backscatter from undisturbed snow surface as a function of time. Symbols are actual dtponsLiearbetft40tthd CD _ ~ — - 40 -4. o 94vh 4O

ures 31 and 32 in the Appendix. 6.2 Surface Variations The snow target area was divided into three areas to observe the effect of surface roughness. The backscattering coefficients for all three areas are shown in Figure 27 for 35 GHz, vv-polarization, and in Figure 28 for 35 GHz, hv-polarization. As described previously, the undisturbed section was quite smooth, having been blown smooth by the wind. As expected, this surface type had the smallest values of ao at 35 GHz for both like- and cross-polarized returns. Returns from slightly rough and very rough surfaces were mostly 0.5-1.5 dB higher for vv, and 0.7-2.4 dB higher for hv, indicating that the rough snow depolarizes more than the smooth snow. Backscatter at 94 GHz seems less dependent on surface roughness, with smooth, slightly rough, and very rough returns all within 2 dB and often within 1 dB of each other. This is presumably because all three of the surfaces were "rough" compared to the wavelength at 94 GHz (A = 3.2 mm). Indeed, the rms surface roughnesses for the three surfaces are 1.525A, 2.750A, and 6.175A at 94 GHz. Graphs of a~ vs. time for the three surfaces at 94 GHz are shown in Figures 33, 34, and 35 in the Appendix. 6.3 Variation of Backscattering Coefficient with Liquid Water Content Since gravimetric liquid water content (GLWC) seems to be the dominant factor in determining the backscattering coefficient, it was desired to observe this relationship directly. In order to accomplish this, it was first necessary to charac41

6. 4. -o -4. X <S -6.2- --- ) o \ / tO -6' ~|-o- Smooth o -... Slightly Rough - ----- Very Rough -1 O. V 6. 8. 10. 12. 14. 16. 18. 20. 22. Time (hours) Figure 27: Backscatter from three snow surfaces as a function of time at 35 GHz, vv-polarization. 42

4. 2. ~~2. ~ —- Smooth mr --- Slightly Rough 0. o — V4 —- Very Rough a) -2. a) A:0 r O > art,//R's W a) -6. 0- X. [. -10. -12. I. II 6. 8. 10. 12. 14. 16. 18. 20. 22. Time (hours) Figure 28: Backscatter from three snow surfaces as a function of time at 35 GHz, hv-polarization. 43

Snow Wetness E 0.14 i i E / ~ 0.12 0 0.10 ~0 0.08 0.08 S- 0.06'~ 0.04 0.02 \ E Xo 0.00 - I C) 6. 8. 10. 12. 14. 16. 18. 20. 22. Time (hours) Figure 29: Functional fit to measured gravimetric liquid water content of the snow terize the variation of GLWC with time, since the liquid water measurements were not simultaneous with the radar measurements. A Gaussian curve with constant offset was fit to the liquid water data points to provide a usable (though obviously imperfect) approximation to the variation in GLWC. This approximation and the actual data points are shown in Figure 29. Next, values of a~ were plotted against estimated snow GLWC at the time of each radar measurement. The results were somewhat mixed. Although there is a clear decrease in ao with increasing GLWC, the scatter in some of the data sets, especially for the dry snow, leads us to believe that a few of the data points may 44

1.0...,...,..,... a... a.... 1.0 0. CO ~- -3.0I3 -2.0 m. q...,...os...,...,..., ~. ~, ~ ~. -5.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 30: Backscattering coefficient as a function of gravimetric liquid water content for undisturbed snow at 35 GHz, vv-polarization. be questionable. However, most of the data do seem to follow expected trends, at least qualitatively. A much larger collection of data is needed to reduce the fraction of outlying points. In addition, an increase in ground truth data quality and quantity is needed so that other variables may be considered. Since we expect a~ to decrease rapidly with small values of GLWC and then level out somewhat, an exponential function with constant offset was fit to measured data for all fifteen combinations of frequency, polarization, and surface type. The 35 GHz, vv-polarized, smooth surface case is shown in Figure 30. The form of the 45

equation was ai = A + B exp(-Cx) (16) where x = m,/m,, and A, B, and C are arbitrary constants chosen to minimize the X2 error, where N X2 - E(-it)2 (17) i=l The coefficients A, B, and C are given in Table 3, along with the corresponding values of x2. The remainder of the plots of the fitted curves and data points are shown in Figures 36-49 in the Appendix. 7 Recommendations for Future Snow Experiments The diurnal experiment described in this report was one of the first operational uses of the MMP system in a non-laboratory setting and the first full-scale snow experiment performed by the research team. In the long run, the experience gained in performing this experiment will probably outweigh the data that was collected. This section is meant to serve as a guide to those who will be participating in the more extensive snow experiments planned for the winter of 1988-89. 7.1 Data Collection The most obvious recommendation for future experiments is that the quantity of data taken should rise dramatically. Measurement hardware and software should be optimized to increase data rates and facilitate simple operation by the equipment operator. Snow data should be collected on a wide variety of snow types and 46

Freq. Pol. Surface A B C X2 35 GHz vv sm -3.407104 2.860178 207.6808 21.96233 sr -4.030170 5.319317 20.37669 7.871177 vr -1.769970 3.129681 90.59702 1.624946 hv sm -10.44650 4.089747 77.99965 37.64211 sr -9.170826 5.131781 32.54294 15.09465 vr -9.239279 5.271280 21.75925 8.898164 94 GHz vv sm 0.6074919 2.691298 21.86616 5.975779 sr 1.261313 2.358287 11.91724 7.661778 vr 1.007773 1.989005 46.85294 2.489407 vh sm -2.494925 2.899044 180.8764 3.088548 sr -2.069181 2.596421 77.20051 5.467927 vr -2.051307 2.357536 137.0364 2.490696 hh sm 0.2231809 3.389608 44.24685 4.701183 sr -0.2360335 4.196653 12.82903 8.415516 vr 1.266275 2.586488 161.4549 7.175722 Table 3: Coefficients of curve fit to liquid water data 47

surface roughnesses, which may be natural or man-made. Time and temperature variations are also of interest. An extensive preparation period will help insure that all experiments proceed smoothly. Radar and radiometer hardware should be hardened to withstand expected extremes in temperature as well as the other hazards of vibration, power variation, dust, etc. which always accompany experiments in the field. Extensive testing and debugging of all measurement software should avoid many computer problems in the field. Practice measurement sessions will aid in the early detection of potential problems. Since it is obviously impossible to measure snow backscatter and emission as a function of all variables (due to the limited resources of time, personnel, and snow), careful thought needs to be given to select a set of variables which will maximize the return on resources devoted to the snow experiment. Specific theoretical questions need to be selected early in order to avoid unnecessary measurements. 7.2 Ground Truth The increase in the quantity of backscatter and emission data must be accompanied by a corresponding or even more extensive increase in ground truth data. The collection of ground truth data must be regarded as a primary task which is every bit as important as (and often much more difficult than) the collection of radar/radiometer data. Ground truth equipment and procedures should be improved to increase the sampling rate as much as possible. In each experiment, several people should have the responsibility of collecting ground truth data only. These individuals should 48

be thoroughly trained and allowed to practice ground truth techniques before the actual experiment. Standard forms should be created to facilitate the recording and processing of ground truth data. Extensive photographs of the experiment site are necessary for later analysis of experimental data. The determination of the snow liquid water content is the most difficult yet most vital ground truth procedure. A better insulated calorimeter with a more durable temperature probe would increase the accuracy of the GLWC measurements. An alternate freezing agent, such as silicone oil, would be preferable to toluene due to the toxicity and low flash point of toluene. An electronic scale, capable of withstanding cold temperatures, would speed the measurement process. Dry ice should be investigated as a means to cool the freezing agent, rather than the liquid nitrogen which was used in this experiment. Leaving the freezing agent/snow mixture in the calorimeter until just before the next measurement helps keep the calorimeter cool, resulting in shorter times necessary to reach equilibrium. It is especially important that GLWC data be taken often throughout the experiment; this will give a detailed picture of the snow GLWC with time and will reduce the effect of any bad data points. Printed forms for GLWC data or, even better, computerized recording of this data will help speed the process. Two people should be assigned to collect GLWC data alone-perhaps running two calorimeters in rotation. 7.3 Miscellaneous Items Some miscellaneous items that were quite useful or that would have been useful include a snow shovel, several extra thermometers, several containers for snow49

gathering, salt or sand for the work area, and a 40-liter container of water for drinking, washing, cleaning, etc. A separate generator is recommended for the mobile lab to allow more flexibility in location and to decrease the load on the truck generator. 50

References [1] NASA Snowpack Properties Working Group, Plan of Research for Snowpack Properties Remote Sensing - (PRS)2, Goddard Space Flight Center, June 1982. [2] Ulaby, F. T., T. F. Haddock, J. East, and M. Whitt, "A Millimeter-Wave Network Analyzer Based Scatterometer," IEEE Transactions on Geoscience and Remote Sensing, vol. GE-26, no. 1, January 1988, pp. 75-81. [3] Ulaby, F. T., T. F. Haddock, and R. T. Austin, "Fluctuation Statistics of Millimeter-Wave Scattering From Distributed Targets," IEEE Transactions on Geoscience and Remote Sensing, vol. GE-26, no. 3, May 1988, pp. 268-281. [4] Jones, E. B., Snowpack Ground-Truth Manual, NASA Contractor Report 170584, May 1983. [5] Stiles, W. H., and F. T. Ulaby, Microwave Remote Sensing of Snowpacks, NASA Contractor Report 3263, June 1980. [6] Stiles, William H., and Fawwaz T. Ulaby, "The Active and Passive Microwave Response to Snow Parameters: 1. Wetness," Journal of Geophysical Research, vol. 85, no. C2, February 20, 1980, pp. 1037-1044. [7] Ulaby, Fawwaz T., and William H. Stiles, "The Active and Passive Microwave Response to Snow Parameters: 2. Water Equivalent of Dry Snow," Journal of Geophysical Research, vol. 85, no. C2, February 20, 1980, pp. 1045-1049. 51

[8] Williams, Larry D., John G. Gallagher, David E. Sugden, and Richard V. Birnie, "Surface Snow Properties Effects on Millimeter-Wave Backscatter," IEEE Transactions on Geoscience and Remote Sensing, vol. GE-26, no. 3, May 1988, pp. 300-306. [9] Williams, Larry D., and John G. Gallagher, "The Relation of MillimeterWavelength Backscatter to Surface Snow Properties," IEEE Transactions on Geoscience and Remote Sensing, vol. GE-25, no. 2, March 1987, pp. 188-194. [10] Williams, L. D., R. V. Birnie, and J. G. Gallagher, "Millimeter-Wave Backscatter from Snowcover," Proceedings of the 1985 International Geoscience and Remote Sensing Symposium, Amherst, Mass., pp. 842-847. 52

Appendix 53

6. 0 A -— ~ om ~ A A 0 -' 4. ~ --- Q % A & ~, s__ 2 —. A 4. 0'' a -2 ------— * 35hv X o 20..-..94w o --— \ —.. —.. — 35w0 4-4. M c \ — a — 94vh m) -4. -,".'.' r - - v - - 94vh ('.)' — 0 —. 94hh. 6 \' -6. ___-_,, 0' %, E " CZ -8. -10. -12..,,, I i, I. I. I ~ 6. 8. 10. 12. 14. 16. 18. 20. 22. Time (hours) Figure 31: Backscatter from slightly rough snow surface as a function of time. 54

64 l r l * i * l * l * l p l * l. 4. ~e o2 ^"^0' - < A- A o A' o 0 -o —- 35w 0A -._)-^<_^ - — a(3_ — 35hv- 94w i) 64. - X" q-"B..^.. 94vh CZ -8. 3, -12... 6.. 0. 12. 14. 16. 18. 20. 22. Time (hours) Figure 32: Backscatter from very rough snow surface as a function of time 55 55

6.. 4. ~m L.r | -- e - lg...tl Ro ghl- - -e 2 a -- B- — o —- o -40.'U 3 -62. 0) -0. 0) 6. 8. 10. 12. 14. 16. 18. 20. 22.oth Cu.. —-—. Slightly Rough —.s~ — Very Rough 6. 8. 10. 12. 14. 16. 18. 20. 22. Time (hours) Figure 33: Backscatter from three snow surfaces as a function of time at 94 GHz, vv-polarization 56

6. 4. -o 2. m^ L~r-A"B-> at | —-—'-R.~ 0. r^^^ ^'^ —^ 041 o -2. A. CD -- 4. Cu 0 CI) — 6. -o~ -6. -o-~e Smooth -—. Slightly Rough. ----- Very Rough -10. I. I. 6. 8. 10. 12. 14. 16. 18. 20. 22. Time (hours) Figure 34: Backscatter from three snow surfaces as a function of time at 94 GHz, vh-polarization 57

6. I. I.. | IE] 40 -2 ". - -4. o. 0 0 O 0 2>. A.,''Smooh co 00 iC m t | -— e —- Slightly Rough -fj -. 0) -8.~ | —A —- Very Rough -10.. I, I, I, I. I. I, I 6. 8. 10. 12. 14. 16. 18. 20. 22. Time (hours) Figure 35: Backscatter from three snow surfaces as a function of time at 94 GHz, hh-polarization 58

2.0 00.0 a) -2.0 - a -3.0 -4.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 36: Backscattering coefficient as a function of gravimetric liquid water content for slightly rough snow at 35 GHz, vv-polarization 2.0 - - D 1.0 8 o 0.0 c -1.0 o 0 0 -2.0 -3.0 -3.0 - - - I-, -..' -.-' ---.' - - 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/m, Figure 37: Backscattering coefficient as a function of gravimetric liquid water content for very rough snow at 35 GHz, vv-polarization 59

-3.0., i -4.0 019 0^ -5.0 _ o _o -7.0.=. -8.0.0 -8.0 7 X -o-9.0 \o -10.0 0 -11.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 38: Backscattering coefficient as a function of gravimetric liquid water content for undisturbed snow at 35 GHz, hv-polarization -2.0..... 0 c -3.0 -4.0 G.2 -5.0 ~ -6.0 *,i.-7.0 -8.0 - -9.0 -10.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 39: Backscattering coefficient as a function of gravimetric liquid water content for slightly rough snow at 35 GHz, hv-polarization 60

-2.0.....,. -o3 -3.0 013 -4.0 O -5.0 \o 0 7 ~~ -6.0 > *' - -7.0 -8.0 -9.0 -10.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 40: Backscattering coefficient as a function of gravimetric liquid water content for very rough snow at 35 GHz, hv-polarization 5.0 - -....,....,..,.,. - 5.0 -% 4.0C._ 3.0 8 0 0) 2.0 1.0 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/m8 Figure 41: Backscattering coefficient as a function of gravimetric liquid water content for undisturbed snow at 94 GHz, vv-polarization 61

5.0 %~ 4.0 c a). 0 o 0 0 iE 3.0. 2.0 - _ 0D 0 1.0 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 42: Backscattering coefficient as a function of gravimetric liquid water content for slightly rough snow at 94 GHz, vv-polarization 4.0 -,,. -. m 3.0.' o 2.0 o) 1.0 0.0...,. 0. 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/m, Figure 43: Backscattering coefficient as a function of gravimetric liquid water content for very rough snow at 94 GHz, vv-polarization 62

1.0' "I''''"'... i,. i...I... i... i... I... j. 1.0 O 0.0.C -1.0 c -2.0 -3.0 0 0 -4.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 44: Backscattering coefficient as a function of gravimetric liquid water content for undisturbed snow at 94 GHz, vh-polarization 2.0 OoC 1.01.0 o 00.0 C 0 0 -1.0 ~ -2.0r -3.0 - -4.0 I,, 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 45: Backscattering coefficient as a function of gravimetric liquid water content for slightly rough snow at 94 GHz, vh-polarization 63

1.0 0.0 o -1.0 i -2.0 -3.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 46: Backscattering coefficient as a function of gravimetric liquid water content for very rough snow at 94 GHz, vh-polarization 5.0,, 4.0 r oI 3.0 o 2.0 CC, -1.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 47: Backscattering coefficient as a function of gravimetric liquid water content for undisturbed snow at 94 GHz, hh-polarization 64

UNIVERSITY OF MICHIGAN II 1IIII II1IIII 1IIIIL l1111 1II 1 11 NIIII 3 9015 02493 8295 5.0.. m ~'0 o 4.0 *~ 3.0 o 2.0 0| _0.0- 1.0 10.0... 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 48: Backscattering coefficient as a function of gravimetric liquid water content for slightly rough snow at 94 GHz, hh-polarization 5.0..'','''.,''',''',.' i'-' - 5.0 I %0 4.0 0 0 C 32.0 1.0 - 0 o o 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 gravimetric liquid water content mw/ms Figure 49: Backscattering coefficient as a function of gravimetric liquid water content for very rough snow at 94 GHz, hh-polarization 65