(None) = RL-2002 MAPPING FREEZE/THAW BOUNDARIES WITH SMMR DATA B. W. Zuerndorfer, A. W. England, M. C. Dobson, and F. T. Ulaby Radiation Laboratory Department of Electrcal Engineering and Computer Science The University of Michigan Ann Arbor, MI 48109-2122

ABSTRACT Nimbus 7 SMMR data are used to map daily freeze/thaw patterns in the upper Midwest for the Fall of 1984. The combination of a low 37 GHz radiobrightness and a negative 10.7, 18, and 37 GHz spectral gradient, -b, appears to be an effective discriminant for classifying soil as frozen af or thawed. The 37 GHz emissivity is less sensitive to soil moisture than are the lower frequency emissivities so that the 37 GHz radiobrightness appears to track soil surface temperature relatively well. The negative gradient for frozen ground is a consequence of volume scatter darkening at shorter microwave wavelengths. This shorter wavelength darkening is not seen in thawed moist soils. INTRODUCTION Soil moisture contributes to the energy exchange between the air and ground through latent heats of fusion and vaporization. Whether as boundary conditions for mesoscale climate modelling, or as inputs to an agricultural productivity model, the amount and state of soil moisture are regional parameters that one would like to estimate through satellite remote sensing. There is a large body of literature that addresses the estimation of soil moisture from remotely sensed radiobrightness (e.g. Burke et al., 1979; Wang et al., 1982; Blanchard and Chang, 1983; Schmugge, 1983; Jackson et al., 1984; Camillo and Schmugge, 1984; Schmugge et al., 1986; and Grody, 1988). We present evidence that moisture state can also be inferred from radiobrightness. Freezing influences the measured radiobrightness temperature of the ground, Tb, through parameters in the approximation (Ulaby et al., 1981), Tb = e To + (l-e) Tsky, where e and To are the emissivity and surface temperature of the ground, respectively, and Tsky is the effective sky brightness. In this approximation, atmospheric transmissivity is ignored. Frozen ground exhibits signatures of (1) lower thermal temperatures, To, (2) higher emissivity, e, and, as we will demonstrate, (3) a decrease in brightness temperatures with microwave frequency, iTb < 0. 3f Signatures (1) and (2) are frequently ambiguous indicators of frozen ground because the changes in radiobrightness that result from freezing may be either positive or negative, depending upon the soil moisture content. Water molecules in frozen plants and soils are not free to align themselves with microwave electric fields. This constraint upon the rotational freedom of water gives rise to an apparent dryness to microwaves. The consequence is a decrease in the real part of the dielectric constant, e', and an increase in frozen soil emissivity. For example, the real part of dielectric constants, e', and corresponding emissivities at nadir, e(0), of two, homogeneous, smooth surfaced, 15% moist soils at 10 GHz are (e' from Hoekstra and Delaney, 1974):

+ 50 C - 50 C Material ~El b 2 e(01 Tb Goodrich Clay 8.2 0.77 221 4.9 0.86 235 Fairbanks Silt 9.6 0.74 214 4.1 0.89 242 Because of increasing emissivity with frequency, a 100 decrease in the clay and silt soil temperatures, from +50 C to -50 C, would cause an increase in Tb of approximately +14 K and +28 K, respectively. The positive direction of change in Tb with soil freezing will cause confusion in discrimination between moist soils which will appear radiometrically warmer when frozen, and dry soils which undergo little molecular change and will appear radiometrically colder. The shift in emissivity with freezing is most pronounced at the lower microwave frequencies. At 37 GHz, the effect is reduced but not absent. We observe that the 37 GHz radiobrightness correlates relatively well with air temperature (Figure 1). Since soil surface temperature should follow the air temperature, the 37 GHz radiobrightness can be expected to provide a reasonably reliable estimate of soil surface temperature. However, discrimination based only on the 37 GHz radiobrightness would misclassify too often. Our data suggest a third signature of frozen soil. Freezing reduces the imaginary part of the dielectric constant, ~", proportionally more than it does the real part, ~'. The loss tangent, tane6=E"E', is a measure of the attenuation per microwave wavelength. Reduced loss tangent, or lower attenuation, means that thermally emitted photons originate deeper within emitting media. That is, the effective depth of emission, ze, (1-e-1 of the emission originates above ze) becomes a larger fraction of the free-space wavelength, Xo (England, 1974, 1975, 1976, and 1977). For example, Goodrich Clay and Fairbanks Silt exhibit an increase of Ze with freezing (dielectric data from Hoekstra and Delaney,1974), + 5 C - 5~ C Material E' tan 6 e | ~ X tan 6 Z Goodrich Clay 8.2 3.5 0.43 0.13 Xo 4.9 1.0 0.20 0.36 X Fairbanks Silt 9.6 5.0 0.52 0.10 Oo 4.1 0.02 0.005 15.7.o The effective emission depth of moist soils is typically 10% of the free-space wavelength. Frozen soils have effective emission depths that may be 30% or more of free-space wavelength. The effective emission depth of frozen sandy soils, like the Fairbanks Silt, can be several wavelengths. In the more transparent emitting media, particularly in frozen sandy soil or dry snow, the greater average thermal photon path lengths have two effects: a greater likelihood that thermal gradients affect spectral gradients, and a greater opportunity for volume scattering of photons. Thermally induced spectral gradients occur because longer wavelength photons tend to originate below the optical surface where thermal temperatures may differ by several degrees from surface temperatures. For the lower loss tangents of frozen soil, this difference in average emitting depth is enough to reflect near surface thermal gradients caused by diurnal heating. That is, a 2

positive thermal gradient, aTo/az, where z is depth in the soil, will yield a negative spectral gradient, aTb/lf, where f is microwave frequency. SMMR data are collected at midnight and noon. In the absence of changing weather conditions, midnight thermal gradients will be positive and noon thermal gradients will be negative (Figure 2) so that midnight spectral gradients will be negative, and noon spectral gradients will be positive. An average +0.2 Kelvin/f(GHz) shift in the spectral gradient is observed between midnight and noon for SMMR radiometric brightnesses (Figure 3). We are developing a computer model of these gradient effects. For now, thermally induced spectral gradients are noise to be filtered out. The second consequence of soil freezing is a greater opportunity for volume scattering -- particularly at shorter microwave wavelengths. This occurs because of the greater average photon path lengths in frozen soil, and because plants and soil appear increasingly heterogeneous at shorter wavelengths. This "law of darkening" means that, for an isothermal, volume scattering halfspace, aTb <0 Of (England, 1974). Frozen terrain may also be snow covered. Dry snow is exceedingly transparent to microwaves so that snow exhibits significant of darkening (Figure 4, Edgerton et al., 1971). That is, both frozen soil and snow tend to exhibit negative spectral gradients. While neither a low 37 GHz radiobrightness nor a negative spectral gradient is solely adequate as a classifier of frozen soils, particularly at the relatively coarse resolutions of the Nimbus-7 SMMR, a discriminant based upon a combination of these signatures offers considerable promise. Our objective under NASA Interdisciplinary Research Program Grant NAG5-852 has been to determine whether such a discriminant is feasible. RADIOBRIGHTNESS AND GROUND TEMPERATURES, AND THE CLASSIFICATION DISCRIMINANT Nimbus 7 SMMR (Scanning Multichannel Microwave Radiometer) radiobrightness data at 6.6 GHz, 10.7 GHz, 18 GHz, and 37 GHz were obtained for August 1, 1984, through December 31, 1984, over an area that included North Dakota, about half of each neighboring state, and part of southern Canada (Figures 7-9). We chose this large, relatively uniform area because of the low spatial resolution of the SMMR instruments -- 150 Km at 6.6 GHz, 100 Km at 10.7 GHz, 60 Km at 18 GHz, and 30 Km at 37 GHz, and because of the importance of soil moisture state to this region's hydrologic processes. The data arrived from the National Space Science Data Center (NSSDC) on 21, high density, SMMR Cell Tapes. Such data are referenced to latitude and longitude in a satellite-centered coordinate system. We produced two types of image products: Single-band, radiobrightness images at the intrinsic resolution of each sensor, and (2) composite, multi-band images at a common resolution based upon local area averaging. Each radiobrightness pixel was referenced to latitude-longitude in a Mercator projection by interpolation and resampling the Cell Tape data. We used a bi-cubic approximation of a sinc function (Moik, 1980) for the interpolation. H and V radiobrightnesses were averaged to produce a single brightness for each pixel for each frequency. In addition to large area images, local area spatial averages of radiobrightness were calculated for each radiobrightness channel at 7 meteorologic sites within our test region —Miles 3

City, MT; Bismark, Fargo, and Williston, ND; and Abileen, Huron, and Rapid City, SD. A local area is defined as a 150 Km cell centered on the meteorological site (150 Km is the spatial resolution of the 6.6 GHz channel). Air and ground temperature data for the Fall of 1984 were obtained from NOAA's National Climatic Data Center in Asheville, North Carolina. Air temperature measurements were available for noon and midnight at the meteorologic sites (i.e., simultaneously with the satellite pass), but ground temperature measurements were for 7:00 a.m. and 7:00 p.m. EST, and were not co-located with the meteorologic sites. Ground temperatures are measured at 5 cm depths. Diurnal heating will weakly affect 5 cm temperatures so that there will be some differences for the times of the satellite pass. Local area averages at the meteorologic sites were used to define the preliminary boundaries in our Freeze Indicator discriminant. For example, Figure 1 illustrated the correlation between 37 GHz radiobrightness and reported air temperature. The nominal line in these figures is a single best fit linear regression in the least squares sense of all local area averages. Individual linear fits will differ slightly as shown in Figure l(a). We used the nominal line in our discriminant for simplicity, but a more sophisticated discriminant might use the actual least squares fit for the local area and for the time of day. The discriminant boundaries in Figures l(b) and l(c) are merely estimates based upon the nominal regression and a compromise between midnight and noon air temperatures that would imply frozen soil (the lower boundary) and thawed soil (the upper boundary). Remember that diurnal temperature gradients will generally cause midnight, subsurface soil temperatures to be warmer than air temperatures, and noon, sub-surface soil temperatures to be colder. Similarly, local area averages of spectral gradient versus air temperature were the bases for the spectral gradient decision boundaries shown in Figure 3. Note that the midnight freeze boundary in this example is relatively unambiguous, while a more effective noon freeze boundary would be shifted upwards by 0.2 K/GHz. Again, for simplicity in this preliminary study, we used discriminant boundaries that were time and location independent. Our 2-parameter Freeze Indicator incorporates the single-band, 37 GHz radiobrightness, and a spectral gradient based upon linear regression of 10.7, 18, and 37 GHz radiobrightnesses for each pixel. Based upon the decision boundaries in Figure l(b) and l(c), the likelihood of frozen ground in a 37 GHz pixel, p37, is estimated as 0 Tb(37) > Tbmax P37T - Tb( Tb3 min < Tb(37) <Tbmax Tbmax - Tbmin 1 Tb(37) < Tbmin where Tb (37) is the measured 37 GHz radiobrightness, and the preliminary decision boundaries are Tbmax = 259 K Tbmin = 247 K The likelihood of frozen ground based upon spectral gradient decision boundaries in Figure 3(a) and 3(b) is Psg, and is estimated as 4

Psg = < I 0 aTb f > ~f aT) max aTb af '''TI"' (aT) 'af min aTb af maxT ha max (~) ~max (aTh) max min 1 aTb Of f min where the preliminary decision boundaries are (T) = 0.3 K/GHz v max (aTf = -0.3 K/GHz min These boundaries are preliminary in that they were chosen to yield the fewest misclassifications in plots of the type shown in Figure 5(a) and 5(b). More refined discriminants would incorporate area and time specific decision boundaries. This would be relatively straightforward if there were a higher density of weather stations in the test area. As it is, we believe that diurnal temperature modeling well yield effective time dependent boundaries, and, perhaps, requiring sub-region consistency within a classification will yield improved spatially dependent boundaries. These refinements are to be part of our continuing project. However, it is the basic sparseness and lack of control of air and ground data that should prompt some caution about over-interpreting our results. Our freeze/thaw discriminant, or Freeze Indicator, is the product of p37 and Psg, and is applied at the scale of the 10.7 GHz data. Resolution differences between different frequency channels can produce anomalous composite image results if the data were processed directly at their original scale. To avoid these problems, the resolution of the data from each channel is compensated to the (coarse) resolution of the lowest frequency channel used in estimating spectral gradients (i.e. 10.7 GHz and 100 Km resolution). Under certain constraints upon the classification process, these images can be referenced to the higher resolution, 37 GHz format for better location of freeze/thaw boundaries (Zuerndorfer, et al., 1989). The effort needed to do this would be justified as a part of an improved classification process. Figures 7 through 12 include images of the Freeze Indicator for various times during the test period. Black in these images indicates a high likelihood of frozen ground. 5

OBSERVATIONS Figure 6(a) and 6(b) show normalized brightness temperatures for midnight and noon, respectively, in the northern Great Plains during the Fall of 1984. Normalized brightnesses are the average regional brightness at each microwave frequency divided by the average regional air temperature. Normalized brightness thus has the dimension of emissivity. Note that there is little systematic ordering among the 10.7, 18, and 37 GHz normalized brightnesses during August through most of November. However, during the latter half of November through December, the normalized brightnesses at midnight are uniformly ordered, 10.7 GHz brightnesses are high, 18 GHz brightnesses are middle, and 37 GHz brightnesses are low. That is, they exhibit negative average spectral gradients. The noon normalized brightnesses for December exhibit a similar trend, but with exceptions. These are, we believe, illustrations of the law of darkening for frozen soils. Soils at midnight in December for the northern Great Plains are very likely to be frozen. Performance of the freeze/thaw discriminant is demonstrated in Figures 7-9 where Freeze Indicator (FI) images are compared with ground and air temperature measurements for midnight on 9/20/84, 10/24/84, and 12/9/84. Midnight FI images are shown as better examples of the potential of a freeze discriminant. Noon FI images are generally less consistent with meteorologic reports because of the contribution of the noontime positive diurnal spectral gradient to the negative frozen ground spectral gradient that we discussed in the last section. Areas not covered by the satellite in a particular pass are shown in white. Tables 1-3 are summaries of the meteorologic reports. On the night of September 20 (Fig. 7), air temperatures throughout the region were near 60~ F and had been above freezing for several days. The FI image shows weak, probably false indications of freezing in the prairies of ND, southern Canada, and the rolling glacial terrain east of the Red River Valley in Minnesota. While the dry air of the northern prairies permits nighttime radiation cooling of the ground to temperatures below that of the air, the more likely explanation for the weak freeze indication is short wavelength scattering by the tall prairie grasses in the northern great plains, and by woodland areas in Minnesota. However, there are no strong indications of freezing in the FI image. On the night of October 24 (Fig. 8), air temperatures hovered about freezing throughout the area, but had been below freezing at Williston for several days, and generally above freezing toward the east (see the temperatures for Fargo, Aberdeen, and Huron in Table 2). The FI image shows a strong freeze indication in northwestern ND which is consistent with the temperature patterns. Similarly, the definite thaw indication along the Red River Valley is consistent with the warmer temperatures reported and the generally more moist soil in the Valley. On the night of December 9 (Fig. 9), air temperatures were generally below freezing except at Rapid City, SD, and had been below freezing for several days. There was no more than trace snow on the ground anywhere in the region. The FI image shows strong freeze indications throughout most of the region with weaker indications near Rapid City, and in the Aberdeen-Fargo sub-region (Aberdeen is not shown on the December 9 map because its temperature report was missing for that date). Again, the FI image is consistent with the temperature record. 37 GHz radiobrightness and FI image sequences were produced at midnight and noon for six-day periods in September, October, and December (Figures 10-12). SMMR coverage is based on a 48 hour cycle —midnight (0000 local hours on the date shown), noon (1200 hours on the same date), and then midnight again 36 hours later. However, orbit precession causes gaps in the cycle and variations in the coverage footprint. Within these constraints, our objective was to observe, if possible, weather dynamics reflected in the FI images. 6

The 37 GHz sequence beginning on September 16 (Figure 10 and Table 1) shows the moist area associated with the Missouri River, Sakakawea and Devils Lakes in ND, and the Missouri River and Lake Oahe in SD. Rain during the night of September 21 appears as a regional darkening of the 37 GHz image for midnight on the 22nd. Note that the rain is not picked up in the Fl image. The October sequence (Figure 11) is dominated by a cold front passing through the area from the northwest with rain and snow beginning on October 19. The region is warmer and drier by the 26th. The moisture pattern dominates the 37 GHz image, but only the apparent freeze pattern, which generally lags the cold front, is shown in the FI image. Note that strong freeze indications follow the cold front but weaken in the south with warming on the 26th. The December sequence (Figure 12) is characterized by cold temperatures and snow from December 2 through December 5, followed by daytime warming into the 40's (and even 58~ at Rapid City, SD) by the 9th. The FI images reflect this general coldness, but also show daytime thawing toward the end of the period. CONCLUSIONS Freeze Indicator images based upon a preliminary, 2-parameter discriminant —37 GHz radiobrightness and 10.7, 18, and 37 GHz spectral gradient —show relatively good correlation with the expected state of moisture in northern Great Plains soils during the Fall of 1984. The discriminant is preliminary in the sense that both theoretical and experimental work needs to be done to fully exploit the diurnal radiobrightness signatures of frozen soils. The concept underlying the preliminary discriminant is that frozen soil will exhibit volume scatter darkening at shorter microwave wavelengths much like the effect observed in dry snow. Few other. phenomena cause negative microwave spectral gradients. However, one such phenomenon is diurnal insolation which should cause negative spectral gradients at midnight, but positive spectral gradients at noon. We are in the process of tayloring our discriminant to allow for these diurnal gradients. Freeze Indicator images based upon SMMR data effectively map temporal variations in the freeze/thaw pattern for the northern Great Plains at the time scale of days. These patterns are synchronized with weather patterns, but are not identical. We intend to expand our test data set to include several complete seasons. The product would be, in essence, a movie of freeze/thaw patterns as weather fronts sweep through the Great Plains throughout several seasons. The development of these data from SMMR archives should provide one aspect of a meso-scale climatic baseline for the region. 7

REFERENCES Blanchard, B.J., and A.T.C. Chang, 1983, Estimation of soil moisture from Seasat SAR data, Water Res. Bull. 19, p. 803-810. Burke, W.J., T. Schmugge, and J.F. Paris, 1979, Comparison of 2.8- and 21-cm microwave radiometer observations over soils with emission model calculations, JGR 84, p. 287-294. Camillo, P.J., and T.J. Schmugge, 1984, Correlating rainfall with remotely sensed microwave radiation using physically based models, IEEE Trans. on Geosc. and Rem. Sens. GE-22, p. 415-423. Edgerton, A.T., A. Stogryn, and G. Poe, 1971, Microwave Radiometric Investigations of Snowpacks. Final Rept. 1285R-4 of Contract 14-08-001-11828 between Aerojet-General Corp., El Monte, CA, and the U.S. Geological Survey. England, A.W., 1974, The effect upon microwave emissivity of volume scattering in snow, in ice, and in frozen soil, Proc. URSI Spec Mtg on Microwave Scattering and Emission from the Earth, Berne, Switzerland, 23-26 Sept., 1974. England, A.W., 1975, Thermal microwave emission from a scattering layer, JGR 80, p. 4484 -4496. England, A.W., 1976, Relative influence upon microwave emissivity of fine-scale stratigraphy, internal scattering, and dielectric properties, Pageoph 114, p. 287-299. England, A.W., 1977, Microwave brightness spectra of layered media, Geophysics 42, p. 514 -521. Grody, N.C., 1988, Surface identification using satellite microwave radiometers, IEEE Transactions on Geoscience and Remote Sensing, V. 26, p. 850-859. Hoekstra, P., and A. Delaney, 1974, Dielectric properties of soils at UHF and microwave frequencies, JGR 79, pp.1699-1708. Moik, J., 1980, Digital Processing of Remotely Sensed Images, NASA SP-431. Schmugge, T.J., 1983, Remote sensing of soil moisture: Recent advances, IEEE Trans. on Geosc. and Rem. Sens. GE-21, p. 336-344. Schmugge, T.J., 1987, Remote sensing applications in hydrology, Rev. Geophvs. 25, p. 148 -152. Schmugge, T.J., P.E. O'Neill, and J.R. Wang, 1986, Passive microwave soil moisture research, IEEE Trans. on Geosc. and Rem. Sens. GE-24, p. 12-22. Ulaby, F.T., R.K. Moore, and A.K. Fung, 1981, Microwave Remote Sensing. Active and Passive, Addison-Wesley, p. 186-255. Wang, J.R., T.J. Schmugge, W.I. Gould, W.S. Glazar, and J.E. Fuchs, 1982, A multifrequency radiometric measurement of soil moisture content over bare and vegetated fields, Geophys. Res. Let. 9, p. 416-419. 8

Watson, K., L.C. Rowan, and T.W. Offield, 1983, Application of thermal modeling in the geologic interpretation of IR images, Remote Sensing, SEG Reprint Series, no. 3, p. 345-369. Zuemdorfer, B., A.W. England, and G.H. Wakefield, 1989, terrain, Proc. of IGARSS '89, Vancouver, B.C., July 10-14, The radiobrightness of freezing in press. 9

TABLE 1 Year 1984 9/15 9/16 Air Temp (o 9Q 12 Site Aberdeen Bismark Fargo Huron Miles City Rapid City Williston Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 9/17 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 9/18 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 40 39 46 44 50 44 48 46 53 47 50 58 52 55 57 56 57 58 61 64 56 64 57 64 62 60 63 67 59 55 65 68 67 60 57 62 58 54 62 63 59 54 59 58 59 60 66 60 57 61 52 72 66 46 45 45 63 64 63 64 65 63 60 65 67 69 64 74 70 68 71 83 73 73 80 84 74 81 80 81 84 80 90 73 84 86 90 90 76 90 72 65 63 62 71 72 67 51 82 81 77 83 56 83 54 65 60 66 66 52 60 44 2 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 2 8 Cloud Cover (x/101 ga 12 2 3 0 0 8 0 0 3 2 2 4 2 6 0 1 3 0 2 0 0 5 10 0 3 3 6 0 3 8 1 3 3 0 0 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 9 9 6 2 2 6 9 O 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O Snow Pack Precid. (in.) fiin.) QQ 12 2i h Ram 2h 0 0 0 0 0 0 0 0 0 0 T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9/19 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 9/20 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 0 0 0 0 o 0 0 0 0 0 0 0 o O 0 0 0 0 0 0 0 1 0 0 0 T 0.01 0.15 (R) 9/21 9/22 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 2 2 8 7 10 9 0 0 10 10 2 1 10 10 8 2 3 1 9 0 10 2 4 6 3 4 10 9 0 0 0.1 0 0 0.3 (R) 0 0 0 0 0 0 - 0.18 (R) 0 0 0.07 (R).02.01 0.3 (R) T 0 T 0 0 0 T 0 0.02.05 0.011(R) 0 0 0 0 0 0 0 O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0

IABLE 2 I Year 1984 Sit 10/19 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 10/20 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 10/21 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 10/22 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 10/23 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 10/24 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 10/25 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston 10/26 Aberdeen Bismark Fargo Huron Miles City Rapid City Williston Air Temp (OF1 QQ 12 37 44 36 40 40 38 38 45 28 39 26 42 27 34 36 44 35 38 37 42 35 41 31 33 26 43 33 33 37 41 36 37 38 39 35 44 29 32 33 38 32 33 34 41 33 39 36 38 31 42 25 38 24 43 27 32 35 46 36 43 34 39 32 46 23 37 29 42 27 40 31 54 33 48 33 49 36 57 35 44 36 57 30 42 Cloud Cover (x/10Q 9Q 2 10 8 10 10 10 10 10 7 7 4 2 7 2 10 - 10 9 10 10 10 0 10 10 10 0 0 10 10 - 10 10 10 10 9 2 6 8 9 10 10 10 9 7 8 10 8 10 10 0 3 0 7 3 8 7 10 10 4 10 3 10 10 3 5 1 0 0 0 10 0 0 4 0 7 0 8 0 1 5 10 0 3 5 7 Snow Pack Preci. (in. (in.l QQ 12 2zh Rsm 24h.01 0.1 (R) 0 0 0.04(S) 0.07 0.2.77 (R) 0 0.1 0.01 0 - T 0 0 T T T - -.1 (S) 0 0 0 T T.01.1 (R) T.01.12(R) 0 0 T.01 (S) 0 0 T (S).02 0.08(S) 0 0 T 0 0.03(S) 0 T.07 (R) 0 0 T T T 0 T (S).01 0 T (S) 0 0 T 0 0 0 T 0 T 0 0 0 0 0 0 0 0 T T 0 0 0 0 0 0 0 0 0 0 0 0 ' - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 " 0 0 0 0 0 0 T 0 0 0 0 0 0 0 0 0 0 0 0 - T 0 0 0 T 0 T 0 0 0 0 0 0 0 0 0 0 0 0 - - T 0 0 0 0 0 T O 0 0 0 0 0 0 T 0 0 0 0 T T T T T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (S) 38 37 10 10 34 39 10 10 38 42 10 10 43 40 8 10 33 44 10 10 34 54 1 1 30 42 10 10 0 0 0 0 0 0 0 O 46 56 41 57 43 53 46 61 44 52 53 65 39 50 0 4 3 10 0 7 0 0 0 10 0 5 6 10 0 0 0 0 0 0 0 O (R) (R 0 N

TABLE 3 Cloud Snow Cloud Snow Air Temp Cover Pack Y(~Q (,1 (x/10) Preci. (inl.) (in. 1984 0i QQ 12 0QQ.12 QQ 12 2 m 24h 12/2 Aberdeen 17 10 10 4 T 0 T (S) 2 Bismark 14 19 10 10 T T.01(S) 1 Fargo 8 3 10 10 T T T (S) T Huron 19 14 10 1.01 T.07(S) 6 Miles City 13 11 10 9 - -.01(S) 4 Rapid City 19 19 4 4 0 0 T (S) T Williston 11 8 10 8 T 0 T (S) 1 12/3 Aberdeen 4 17 0 4 0 0 T (S) 2 Bismark 15 15 10 7 T T T (S) 1 Fargo 0 10 0 0 0 T 0.1 T Huron 5 14 0 0 0 0 T(S) 6 Miles City -3 -2 10 1 - - 0 4 Rapid City 11 27 0 1 0 0 0 T Williston 9 9 10 8 T T T (S) 1 12/4 Aberdeen 13 10 10 0 0 0 0.02(S) 2 Bismark 8 15 10 1 T 0 T 1 Fargo 9 15 10 0 0 0 0 T Huron 5 12 6 2 T 0 T (S) 5 Miles City -1 7 0 10 - - 4 Rapid City 15 24 2 0 0 0 0 T Williston -5 10 0 10 0 0 0 1 12/5 Aberdeen 14 7 3 5 T 0 T (S) 2 Bismark 19 -1 4 0 0 0 T (S) 1 Fargo 11 -1 10 10 0 0 T (S) T Huron 15 15 4 7 0 T T 4 Miles City 24 13 10 10 - - T (S) 3 Rapid City 26 19 8 7 0 T T (S) T Williston 8 -5 3 3 T 0 T (S) 1 12/6 Aberdeen -14 3 0 0 0 0 0 2 Bismark -11 20 0 8 0 0 T 1 Fargo -8 8 0 3 0 0 0 T Huron -6 11 0 4 0 0 0 4 Miles City 9 23 0 9 - - 0 3 Rapid City 6 44 1 1 0 0 0 T Williston -7 24 0 9 0 0 T 1 12/7 Aberdeen 18 42 7 4 0 0 0 2 Bismark 30 43 9 8 0 0 0 1 Fargo 12 43 7 9 0 0 0 T Huron 19 42 3 0 0 0 0 3 Miles City 35 44 4 0 - 0 2 Rapid City 43 61 10 0 0 0 0 0 Williston 34 43 3 6 0 0 0 1 12/8 Aberdeen 30 36 2 3 0 0 0 T Bismark 31 42 7 2 0 0 0 T Fargo 30 43 2 5 0 0 0 0 Huron 31 42 0 4 0 0 0 1 Miles City 29 33 3 3 - 0 1 Rapid City 33 51 0 10 0 0 0 0 Williston 31 37 7 8 0 0 0 T 12/9 Aberdeen - 46 7 0 0 0 T Bismark 31 43 2 3 0 0 0 T Fargo 29 40 0 9 0 0 0 0 Huron 35 39 7 7 0 0 0 T Miles City 26 35 5 4 - - 1 Rapid City 43 58 6 0 0 0 0 0 _Williston 28 37 0 2 0 0 0 0

6-:3 0 E Io co I0 c Co <0) 0 0 0) -C ao c.0) 0 a 0 it 0 C 0-.-c In 290 - - ------- -. 2B0 - -~ - - - - - - - Nominal 270 --- —--------------- --------— __ -- 270h IActuall — -- 250 - - -- - 240 --- —----------------- 240 --- —-------------------- Nominal,i (a) Midnight. A linear regression of the Bismark data is shown ("Actual" curve), with a regression line for data collected throughout North Dakota and the surrounding region ("Nominal" curve). Ib) Midnight. Shown with 270 7 the Bismark data is a linear a..;,regression for data collected 260 - - --- - --- I- — throughout North Dakota and eDiscriminant the surrounding region - ("Nominal" curve). Also mscriminanl shown are brightness temperature decision thresholds for a 240, -. - -...- -- --- frozen or thawed surface. I 230 [ 1 - i 230 r-'l /r - - - - ~ - I~ r - -I rarn ^ I T Z.l:~J. 280 270 260 250 240 230 I 7 1 C -- ---------------------------— 0 - i 0 __ _ _ __i..... -----------------— jscrimina ------------------------- ---- (c) Noon. Shown with the Bismark data is a linear regression for data collected throughout North Dakota and the surrounding region ("Nominal" curve). Also shown are brightness temperature decision thresholds for a frozen or thawed surface. 0I --- --- ---------------------------- ----,,, t~ I 1 uiscrinminani P r n I _,. zL.u I I i I I I 1 I I I I I 1 240 250 260 270 20 290 300 310 320 245 255 265 275 285 295 305 315 Ar Terrp (K) Figure 1. 37 GHz SMMR brightness temperature versus measured surface air temperature, Bismark, North Dakota. Data were collected from 8/1/84 to 12/31/84.

In D -J LrU LJ LU LJ Ci. L-' LU H 70 So 30 ZO 0 -o10 LOCAL SOLAR TIME (HRS) Figure 2. Diurnal surface temperature variation for different seasons at 300 N (from Watson, et al., 1983). Subsurface temperatures will exhibit a reduced amplitude and a phase lag with respect to the surface temperature. That is, midnight thermal gradients will be negative, and noon thermal gradients will be positive.

N -' O (U 'D 5) Qn8 r - 0.8 Orq --- —-----— ' 0.6.I 0.24 ---....' ', --- —— j-^ --- —-----------------------— 4 ~sfiigi 0. - - - - - - - - - - - - - - - O - - -Dscriminanti - - - 240 250 260 270 280 290 300 310 320 245 255 265 275 285 295 305 315 Ar Temp (K) 0.5 -- --- ---------- 0. --- —-— 4 --------------— I Discriminant -0.v z — - - - - o --- ---- ---— ^ --- —-— ^ -0~2. - - - - - - - - - - - - -- -0.2 --- —-------------— IDiscriminanti -0.6 I I I "I.i I 1 ' i i1 240 250 260 270 280 290 300 310 320 245 255 265 275 285 295 305 315 Ar Temp (K) (a) Midnight N I c U).-, O (b) Noon Figure 3. Frequency gradient versus measured surface air temperature, Bismark, North Dakota. Data were collected from 8/1/84 to 12/31/84. The frequency gradient is the frequency regression slope for simultaneous SMMR brightness temperatures at 37GHz, 18 GHz, and 10.7 GHz. Shown with the Bismark data are frequency gradient decision thresholds for a frozen or thawed surface.

e - 45~ IL = Wavelength H = Horizontal Polarization V = Vertical Polarization ASS PERV N AR (g,- -2) MASS PER UNIT AREA (9M cm-2 e. Bghesstemperaturvrusequivalent dry snow, Crater Lake, Oregon, 22 March 1970 (Edgerton et al., 197 1). Note the short wavelengthdarningevidnt fo snowpacks.

0.8 -.-.7..... -; *i 0.4h - ^ Irm0L --- —--------- C x (_.iscriminan. L — -—. — I - -. -, - (a) Midnight 220 230 240 250 260 270 280 290 225 235 245 255 265 275 285 'Bres Ta'np (K).- IDiscrimin I (5 --.i C (' Discrimin 0.-8r 0.6t~ ------------ ---------- -—.-.-, x x 0.4-.. --- —--------- o 1 n tx ---- - 0.2 0 5<a<-B --- —-' --- —' 02.4 - - - - - - __ J 220 230 240 250 260 270 280 290 225 235 245 255 265 275 285 Bigess Temp (k) Figure 5. Frequency gradient versus SMMR 37 GHz brightness temperature, Bismark, North Dakota. Data were collected from 8/1/84 to 12/31/84. Shown with the Bismark data are clustering decision thresholds for a frozen, mixed, or thawed surface. Based upon ground truth, the solid boxes are frozen, open boxes are thawed, and x s are mixed pixels.

y -.. y,,e - Lo cx Q{ E 0 0 N E 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 37 GHz 18 GHz. ---.- - 10.7 GHz (a) Midnight Measurement Day L.. QE I — N - E O o 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 37 GHz - 18GHz -—.... 10.7 GHz (b) Noon Aug Sept Oct Nov Dec Measurement Day Figure 6. 37 GHz, 18 GHz, and 10.7 GHz SMMR normalized brightness temperatures versus calender day. Measurements were made at irregular intervals from 8/1/84 to 12/31/84. The normalized brightness temperature of a single SMMR frequency channel is the average brightness divided by the average surface air temperature, averages are calculated over North Dakota and the surrounding region.

Air and Ground Temp Night 9/20/84 AIR TEMP Thaw Mixed Freeze 0 0 GND TEMP Thaw - Mixed 0 Freeze e Figure 7. A comparison of reported air and ground temperatures with the Freeze Indicator for midnight, September 20, 1984.

Air and Ground Temp Night 10/24/84 AIR TEMP Thaw Mixed Freeze 0 0 GND TEMP Thaw 1 Mixed t9 Freeze e Figure 8. A comparison of reported air and ground temperatures with the Freeze Indicator for midnight, October 24, 1984.

Air and Ground Temp Night 12/9/84 AIR TEMP Thaw O Mixed 0 Freeze * GND TEMP Thaw E Mixed 3 Freeze | Figure 9. A comparison of reported air and ground temperatures with the Freeze Indicator for midnight, December 9, 1984.

37 GHZ RADIOBRIGHTNESS MIDNIGHT FREEZE INDICATOR (9/16/84) AN047S5 (9/18/84) AN047FG (9/20/84) AN051 S5 "AN051FG ANO51 FG (9/22/84) - AN053S5 AN053FG Figure 10(a). Midnight 37 GHz and Freeze Indicator image sequences for a 6 day period in September.

37 GHZ RADIOBRIGHTNESS NOON FREEZE INDICATOR..... ~. (9/1 6/84) AD047S5 I AD047FG - - (9/1 8/84). AD049S5 (9/20/84) AD049FG... (9/22/84) AD053S5 AD053FG Figure 10(b). Noon 37 September. GHz and Freeze Indicator image sequences for a 6 day period in

37 GHZ RADIOBRIGHTNESS MIDNIGHT FREEZE INDICATOR, -I (10/20/84). AN081 S5 (10/22/84) AN081 FG (10124/84) AN088S5 l AN08SFG (10/26/84) AN087S5 AN087FG Figure 11 (a). Midnight 37 GHz and Freeze Indicator image sequences for a 6 day period in October.

Jo M n UI k; OnIU -1 I Hn t NOON FREEZE INDICATOR f (10/20/84) AD081S5 AD081FG ADO81 FG 10/22/84) AD083S5 (10/24/84) AD083FG:~X~:"".'~'~ ~,.::::;~.~.:~:~X~:~:~:~::I:::: ~ ~:~:~'~:5~:..~.~..~.~..~~ " ' ~''~ ~r.:':5 "' " ' ''''' '''" '''' ''''''' '''''''' ' ''' ''' ~~...-.-..-.-. .~~~...~.~.~..~.~.~ ~.~. ~~~~~~ ~~.~. ~~~.-~~~-. ~~~~~ ~~~~ ~~~~~~ ~~~~:~:~; ''' ''' ~'~' '~:~: ~2.~: ':::~:~:5~:; ''" '~'~:::::: ~~~~ ~~~~~ ~~~ ~~~~ ~~ ~~~ ~~~~~ ~~~~ ~~ ~~~~ ~~~ ~...,.~;~ ~~~:~:~:~ ~~~~ ~;~t, ~.~.,~ "". '''''' ""' ~.. ~.~.~z.~.:::i:::X '''"' -g:~~s:I ~:~: ~.~.~.~;~.~. I:laiiiiiiiiri ''''' '''''.X;;~:~.~ ''' ;~.~ ~~rsC '''~'''' ''''''''''''''' 1 0/26/84).;.;. - AD087S5 AD087FG Figure 1l(b). Noon 37 GHz and Freeze Indicator image sequences for a 6 day period in October.

37 UHL HALUIUHIGHTNESS FEZ NiAO ril I DI 1"li H T FREEZE INDiCATOR (1 2/3/8 4) A N 125 S5 ANil 25FG AN 127FG.4 (12/7/84) ANi 29S5 AN 129FG (1 2/9/84) AN 1 31 55 AN 131 FG Figure 12(a). Midnigaht 37 GHz and Freeze Indicator image sequences for a 6 day period in December.

37 GHZ RADiiOBRIGHTNESS NOON FREEZE INDICATOR, (1 2/3/84 -— _ (12/5/84) AD127S5 AD127FG (12/7/84).., AD129S5 AD129FG ADi 29FG (12/9/84) AD1 31S5 AD131FG Figure 12(b). Noon 37 GHz and Freeze Indicator image sequences for a 6 day period in December. The jagged white lines in the Noon, 12/5/84 image are caused by missing data.