Influence of depth hoar on microwave emission from snow in northern Alaska

Cold Regions Science and Technology, 13 (1987) 225 -231

225

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

INFLUENCE OF DEPTH HOAR ON MICROWAVE EMISSION FROM SNOW IN NORTHERN A L A S K A Dorothy K. Hall Hydrological Sciences Branch, Code 624, Laboratory for Terrestrial Physics, Goddard Space Flight Center, Greenbelt, MD 20771 (USA) (Received April 16, 1986; accepted in revised form August 18, 1986)

ABSTRACT More than 80% o f the total land area o f Eurasia and North America can be covered by snow during the winter. Snow is highly reflective and the amount o f time that it remains on the ground is important for regional and global energy balance since 90% o f the solar energy available to heat the earth can be reflected away by snow. In previous work, global snow depth maps have been prepared based on Scanning Multichannel Microwave Radiometer (SMMR ) passive microwave satellite data. A two-layer radiative transfer model is used to generate an algorithm by which global snow depth is calculated from the SMMR brightness temperatures (TB). Analysis o f these SMMR snow maps has shown that the snowpack o f the Arctic Coastal Plain o f Alaska displays values o f microwave TB that are lower than wouM be expected for the shallow snow which is known to occur there. In addition, observed values o f TB in northern Alaska decrease as the winter progresses. The snowpack has a structure that consists o f a low density depth hoar (lower) layer and an upper layer which consists o f dense, windpacked snow. In this paper a two layer radiative transfer model is employed to calculate microwave TB for model snowpacks that have a depth hoar layer, in order to simulate snowpack conditions in northern Alaska. The observational data consist o f a time series o f 37 GHz horizontally and vertically polarized SMMR data o f the Arctic Coastal Plain o f Alaska during the period from January through March 1980 and snow depth and air temperature measurements from Umiat, Alaska from the same time period. In the simulations, 0165-232X/87/$03.50

© 1987 Elsevier Science Publishers B.V.

the thickness o f the depth hoar layer was lOcm in early January and increased by 0.50cm per week, throughout a 3 month study period, to simulate a reported increasing thickness o f the depth hoar layer as the winter progresses. When simulated and observed TB were correlated for 15 data points, a coefficient o f correlation o f R = 0.84 was obtained. Results show that the presence and variability o f the depth hoar layer in northern Alaska can have a significant effect on the microwave emission from a snowpack.

INTRODUCTION Snow and ice cover up to 51 million km 2 of the Northern Hemisphere during the winter. This is more than 80% of the total land area of Eurasia and North America. The extent of seasonal snow cover is highly variable as is its duration and depth. Passive microwave satellite remote sensing has been employed to aid in the measurement of snow extent, depth and water equivalent on global and regional scales (Kunzi et al., 1982; Schanda et al., 1983; Matzler, 1985; Chang, 1986). The ability to measure snow depth using microwave radiometry, in part, depends upon knowledge of the effect of snow structure on the microwave emission from snow. In this paper, the effect of snow structure on the microwave emission is modelled for the Arctic Coastal Plain of Alaska for the winter of 1980. Values of simulated brightness temperature (TB) are compared with observed values of TB from the snowpack using data from the 3 7 G H z horizon-

226 tally-polarized sensor on the Scanning Multichannel Microwave Radiometer (SMMR). A two-layer radiative transfer model has been used to develop an algorithm to estimate global snow depth using SMMR data (Chang, 1986). Analysis of the SMMR snow maps has revealed that the Arctic Coastal Plain of northern Alaska can display anomolously low microwave emission. As previous work has mentioned the fact that the presence of depth hoar should decrease microwave emission (Chang et al., 1976; Matzler et al., 1982), the area was studied in terms of both its snow depth and structure. The same two-layer radiative transfer model that was employed to develop the SMMR map algorithm is employed in this study because this model has been shown to be useful for modelling a snowpack that contains a layer of depth hoar (Hall et al., 1986a).

SNOW STRUCTURE ON THE ARCTIC COASTAL PLAIN OF A L A S K A

Local and regional energy balance processes influence the structure of a snowpack. Snowpack structure changes with time as a result of air temperature changes, wind, type and quantity of precipitation and length of time that snow is on the ground. When snow remains on the ground for a substantial portion of the winter and especially when air temperatures are very cold, metamorphism at the base of the snowpack results in the formation of large, loosely-bonded crystals known as depth hoar. In Alaska, some depth hoar crystals can grow 1 0 - 1 5 m m in diameter (Benson et al., 1975). A steep, negative temperature gradient occurs in the snowpack of the Arctic Coastal Plain. Early snow accumulation reduces upward soil heat flux (Santeford, 1979). Even though the winter air temperatures can be lower than --45°C, snow/soil interface temperatures will be much higher due to the insulating properties of the snow. For example, in interior Alaska, there can be a 40°C difference in temperature between the snow/air and snow/soil interfaces because continuous heat flux from the soil maintains the soil/snow interface temperatures between -- 3 and --5°C (Trabant and Benson, 1972). Associated pressure gradients cause water vapour to diffuse from

warmer to colder parts of a snowpack. This leads to a situation in which snow crystal size increases with time as crystals grow from one side of existing snow crystals in a direction that is opposite to the vapour pressure gradient. Faster crystal growth occurs in the warmer (lower) layers of a snowpack. Though soil/ snow interface temperatures may be higher in interior Alaska compared to northern Alaska, there can still be a large temperature gradient in the snowpack in northern Alaska.

PREVIOUS WORK

Previous studies have shown that there is an inverse relationship between snow depth and microwave TB as measured by passive microwave sensors at specified wavelengths in dry snow (Rango et al., 1979; Kunzi et al., 1982; Foster et al., 1984). Matzler (1985) has reported that snow water equivalent (WE) can be mapped using passive microwave data when WE< 30cm. The 37GHz (0.81 cm wavelength) sensor on the Nimbus-7 SMMR has been shown to be particularly useful for analyzing internal properties of snowpacks using both the horizontal and vertical polarizations. In addition, it is possible to discriminate between dry and wet snow, using passive microwave techniques (Schanda, 1983 and Robinson et al., 1984). The intensity of microwave radiation which is emitted by a medium and sensed remotely, is expressed as Ta in degrees Kelvin and follows the Rayleigh-Jeans approximation. This shows that the radiance from a backbody is proportional to its temperature:

TB = eTse-r + T1 + ( 1 - - e ) T 2 e - r + ( 1 - - e) × Tspe-= r

(1)

where e is the emissivity of the surface, Ts is the sensible temperature of the surface, r is the total atmospheric opacity, Tx is the upward emitted radiance contribution of the atmosphere, T2 is the total downward (emitted and reflected) atmospheric brightness temperature, and Tsp is the average temperature of free space (Gloersen and Barath, 1977). Calculations using a microscopic scattering model

227 for snow have shown that the scattering of 37 GHz radiation from a snowpack is dependent strongly upon the grain size of the snow particles (Chang et al., 1976, 1982; Matzler, 1985; Hall et al., 1986a; Hallikainen and Jolma, 1986). Larger grain sizes within the snowpack cause more scattering of microwave radiation as the grain size approaches the size of the wavelength. The intensity of microwave radiation emitted from a snowpack depends on the physical temperature, grain size, density and the underlying surface conditions of the snowpack. The radiation emerging from a snowpack can be calculated by solving the radiative transfer equation which employs the above parameters. This radiative transfer equation can be written

o(x)I(x, la) + u(x){ [1--w(x)]B(x)

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where the radiation intensity is at a depth x and travelling in the direction towards increasing x, making an angle whose cosine is/~ with the normal. The functions and are the extinction per unit length, the single scattering albedo, and the source and phase functions, respectively (Chang et al., 1982). Recently, this two-layer radiative transfer model was employed to study the effect of a depth hoar layer on microwave emission from snow (Hall et al., 1986at. Calculations showed that the microwave TB decreased with increasing depth hoar layer thickness. Thus, an increase in the thickness of the depth hoar layer will cause even more scattering for a given snow depth and will result in a lower overall TB for the snowpack. Calculations show that when the depth hoar layer is first formed, the greatest decrease in T B occurs (Fig. 1). In the present study, the same model is employed to simulate a time series of TB data.

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METHODOLOGY

Values of TB were calculated at the 37 GHz frequency horizontal polarization using the radiative transfer model described above for the winter of

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BOTTOM LAYER THICKNESS (cm) Fig. 1 Calculated 37 GHz (horizontal polarization) brightness temperatures for dry snow cover over frozen ground showing the effect of changing the thickness of the depth hoar layei (from Hall et al., 1986A).

1980 (January through March). The meteorological data used were obtained from the Umiat, Alaska (69°22'N, 152°08'W) National Weather Service station. The horizontally-polarized 37 GHz data were used in the correlations instead of the vertically-polarized 37 GHz data because when the horizontally-polarized data were correlated with snow depth and 37GHz TB, over a four year period, the correlations were generally better than when vertically-polarized data were used as seen in Table 1. This is often true when a time series of data are analyzed. (The horizontallypolarized data are not always preferred, for example,

228 TABLE 1 Correlations (R), coefficient of determinations (R ~), standard errors (SE), significance level ( S L ) and number of points (n) for 37 GHz horizontally-polarized data and snow depth and vertically-polarized data and snow depth for October through May in 1979-1983. Snow depths are from Barrow, AK 37V

1979-80 1980-81 1981-82 1982-83

37H

R

R 2

SE

SL

R

R ~

SE

SL

n

-0.72 -0.44 -0.84 -0.57

0.52 0.20 0.71 0.33

6.814 11.478 6.973 4.674

99% 98% 99% 99%

-0.76 -0.52 -0.84 -0.61

0.58 0.27 0.71 0.37

8.040 12.313 9.486 4.812

99% 98% 99% 99%

39 39 40 40

Hallikainen and Jolma (1986) have found better correlations in Finland study areas using the verticallypolarized data.) To calculate the TB using the radiative transfer model, the air temperature as measured at Umiat, Alaska (NOAA, 1980) is used as a guide to infer relative snow temperature changes through time. The actual snow temperature is not known because there were no simultaneous field measurements. Air temperature is an adequate indicator of relative temperature changes but a poor indicator of absolute snow temperature. This is to be expected since the average snow temperature is much warmer than the air temperature in northern Alaska. Snow depth reported at Umiat was also used in the model. The snow crystal diameters of the upper and lower layers of the model snowpack were 0.50 mm and 1.40 mm respectively as estimated in previous work (Hall et al., 1986a). The density of the upper and lower layers was 0.40 and 0.25 g cm -3 respectively, in the model snowpack. These values were selected based upon densities found by Benson et al. (1975) during field work in 1972 in northern Alaska. The ground beneath the snow was assumed to be frozen. The assigned diameters of the depth hoar crystals in the model are considerably smaller than the actual sizes as they occur in the snowpack. As mentioned previously, depth hoar crystals may grow 1 0 - 1 5 mm in diameter in Alaska and they are hollow and angular. However, assumptions in the model are that the crystals in the snowpack are spherical and solid. Solid, spherical crystals are more effective scatterers of the microwave radiation than are irregularlyshaped, hollow crystals. Thus, the size of the crystals

in the model in the lower layer was adjusted downward relative to the actual crystal size as it occurs in nature. In addition, the average size of the crystals in the depth hoar layer would be far less than the maximum size (1 O - 15 ram) reported. RESULTS

Initially, each simulated data point was calculated by changing only the snow temperature and total snow depth (as determined from the meteorological data) keeping the thickness of the depth hoar layer constant at 10cm. The resulting correlation between observed and calculated TB for the January through March study period was poor (R = 0.30). When the initial thickness of the lower layer in the model was 10cm and increased by 0.5 cm for each 6 day period, the pattern of TB variability corresponded quite well to the observed patterns. The solid line in Fig. 2 shows a plot of the SMMR (observed) TB for all night time satellite overpasses between January and April 1980 (total = 15). Also shown is a plot of simulated TB (dashed line) where snow depth and air temperature varied with the meteorological data, but the thickness of the depth hoar (lower) layer in the model remained at 10cm during the study period (Case A), and a plot of simulated TB (dotted line) where snow depth and air temperature varied as before, but where the thickness of the depth hoar layer increased 0.5 cm per 6 day period while not altering the total snow depth(Case B). The" pattern of TB variability in Case B corresponds quite well to the pattern of observed TB values. The resulting coefficient of correlation between the

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Fig. 2. Observed and simulated 37 GHz horizontally-polarized Tl3s for the snowpack on the Arctic Coastal Plain of Alaska January through March 1980. The heavy, solid line is the observed TB (from the SMMR); the dashed line (Case A) represents simulated TBS for which the depth hoar layer

remained at 10 cm during the study period; the dotted line (Case B) represents simulated TBs for which the thickness of the depth hoar increased 0.5 cm per 6 day period during the study period.

observed and simulated (Case B) data points is R = 0.84 as shown in Fig. 3. The simulated 37 GHz TB values (Case B) are up to 27 °K lower than the observed values using the SMMR data (Fig. 2). This difference can be explained largely by the fact that the average snow temperature is considerably warmer than the air temperature due to the insulating properties of the snow. Thus the use of air temperature as an indicator of snow temperature is the major drawback of this method of modeling TB and it would be desirable to have in-situ snow temperatures available to use in the modeling.

correlated for northern Alaska that cannot be explained by snow depth and/or air temperature (Hall et al., 1986b). Other factors that contribute to this variability are: atmospheric effects, variability in snow depth within a SMMR grid cell and snow structure variability. Snow structure variability is probably the major factor that influences the T B / snow depth relationships using a time series of data in northern Alaska. The correlation is quite good (R = 0.84) between simulated and observed TB when the influence of increasing depth hoar layer thickness is included in the modelling; this exemplifies the fact that the grain size and depth hoar layer thickness are dominant effects and that the pattern of TB decrease through time in northern Alaska appears to be due, in part, to increasing depth hoar layer thickness. Other factors

DISCUSSION

AND

CONCLUSION

There is a substantial portion of the TB variability when snow depth and passive microwave TB are

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such as changing layer density and small changes in snow depth are less important than is the grain size. It has been reported that the thickness of a depth hoar layer will increase through time as long as a negative temperature gradient is maintained in the snowpack (Giddings and La Chapelle, 1962; Trabant and Benson, 1972). In addition, the crystal size can increase through time. Trabant and Benson (1972) have shown that, by the end of the winter, depth hoar can comprise almost the entire snowpack in central Alaska. In order to understand a time series of SMMR data of the Arctic Coastal Plain snowpack, increasing depth hoar thickness must be considered. When the thickness of the depth hoar layer

was 10cm in early January and increased by 0.5 cm per 6 day period in the model, the simulated data points matched the observed data points dramatically better than when the thickness of the depth hoar layer remained constant (10 cm in thickness) throughout the three month study period in the winter of 1980. Since the microwave TB is actually influenced by the temperature throughout the snowpack, and not just the snow surface temperature, the use of a snow energy balance model to calculate the temperature profile of a snowpack could further improve the modelling of the TB in future work (Hall et al., 1986b). The next step is to invert the algorithms that have

231 been developed to m o d e l microwave emission in order to calculate snow d e p t h in specific regions from the microwave TB. This appears to be possible in areas for which the relevant properties o f the snowpack are well established.

ACKNOWLEDGEMENTS I w o u l d like to thank Dr. A1 Chang, N A S A / G o d d a r d Space Flight Center, for discussions concerning the radiative transfer modelling and Dr. R o b e r t G u r n e y and James Foster, N A S A / G o d d a r d Space Flight Center for reviewing the paper.

REFERENCES Benson, C.S., Holmgren, B., Timmer, R., Weller, G., and Parrish, S. (1975). Observations on the seasonal snow cover and radiation climate at Prudhoe Bay, Alaska, during 1972. In: J. Brown (Ed.), Ecological Investigations of the Tundra Biome in the Prudhoe Bay Region, Alaska, Biological Papers at the University of Alaska Special Report Number 2, p. 13-50. Chang, A.T.C., (1986). Nimbus-7 SMMR snow cover data, Proc. of the Snowwatch 1985 Workshop on CO2/Snow Interaction, October, 1985, College Park, MD, pp. 181187. Chang, A.T.C., Gloersen, P., Schmugge, T., Wilheit, T.T. and Zwally, H.J. (1976). Microwave emission from snow and glacier ice. J. Glaciology, 16: 23-39. Chang, A.T.C., Foster, J.L., Hall, D.K., Rango, A. and Hartline, B.K. (1982). Snow water equivalent estimation by microwave radiometry. Cold Regions Science and Technology, 5 : 259-267. Foster, J.L., Hall, D.K., and Chang, A.T.C. (1984). An overview of passive microwave snow research and results. Rev. Geophys. Space Phys. 22: 195-208. Giddings, J.C. and LaChapeUe, E. (1962). The formation rate of depth hoar. J. Geophys. Res. 67:2377-2383. Gloersen, P. and Barath, F. (1977). A scanning multichannel microwave radiometer for Nimbus-G and Seasat-A. IEEE J. Ocean. Eng. OE-2: 172-178. Hall, D.K., Chang, A.T.C. and Foster, J.L (1986a). Detection of the depth hoar layer in the snowpack of the arctic

coastal plain of Alaska using satellite data. J. Glaciol. 32: 87-94. Hall, D.K., Chang, A.T.C. and Foster, J.L. (1986b). Seasonal and interannual observations and modeling of the snowpack on the Arctic Coastal Plain of Alaska using satellite data, Proceedings of the Cold Regions Hydrology Symposium, AWRA, 22-25 July, 1986, Fairbanks, AK. Hallikainen, M. and Jolma, P. (1986). Development of algorithms to retrieve the water equivalent of snow cover from satellite microwave radiometer data. Proceedings of the IGARSS '86 Symposium, 8-11 September, 1986, Irchel, Switzerland. Kunzi, K.F., Patil, S. and Rott, H. (1982). Snow-cover parameters retrieval from Nimbus-7 scanning multichannel microwave radiometer (SMMR) data. IEEE Trans. Geoscience Remote Sensing, GE-20(4): 452-467. Matzler, C., Schanda, E. and Good, W. (1982). Towards the definition of optimum sensor specifications for microwave remote sensing of snow, IEEE Trans. Geoscience Remote Sensing, GE-20: 57-66. Matzler, C. (1985). Can microwave signatures be used to retrieve water equivalent of a dry snowpack? Proc. of the 3rd Colloquium on Spectral Signatures of Objects in Remote Sensing, 16-20 December 1985, Les Arcs, France. NOAA, Climatological Data of Alaska (1980). National Oceanic and Atmospheric Administration, National Climatic Data Center, Asheville, NC. Rango, A., Chang, A.T.C. and Foster, J.L. (1979). The utilization of spaceborne microwave radiometers for monitoring snowpack properties. Nordic Hydrology, 10: 25 -40. Robinson, D., Kunzi, K. Kukla, G. and Rott, H. (1984). Comparative utility of microwave and shortwave satellite data for all-weather charting of snow cover. Nature, 312: 434-435. Santeford, H.S. (1979). Snow soil interactions in interior Alaska. In: S.C. Colbeck and M. Ray (Eds.). Proc. of the Workshop on Modeling of Snow Cover Runoff, 26-28 September 1978, Hanover, NH, p. 311 318. Schanda, E. (1983). Selection of microwave bands for global snow detection. Adv. Space Res., 3: 303-308. Schanda, E., Matzler, C. and Kunzi, K. 0983). Microwave remote sensing of snow cover. Int. J. Remote Sensing, 4: 149-158. Trabant, D. and Benson, C.S. (1972). Field experiments on the development of depth hoar. Geological Society of America Memoir 135, p. 309-322.