Multi-Satellite and Sensor Derived Trends and Variation of Snow Water Equivalent on the High-Latitudes of the Northern Hemisphere

Utilizing more than 30 years of satellite-microwave sensor derived snow water equivalent data on the high-latitudes of the northern hemisphere we investigate regional trends and variations relative to elevation. On the low-elevation tundra regions encircling the Arctic we find high statistically significant trends of snow water equivalent. Across the high Arctic Siberia and Far East Russia through North America and northern Greenland we find increasing trends of snow water equivalent with local region variations in strength. Yet across the high Arctic of western Russia through Norway we find decreasing trends of snow water equivalent of varying strength. Power density spectra identify significant power at quasi-biennial and associated lunar nodal cycles. These cycles of the upper atmosphere circulation, ENSO and ocean circulation perturbations from tides forms the causative linkage between increasing snow water equivalent on lowelevation tundra landscapes and decreasing coastal sea ice cover as part of the Arctic system energy and mass cycles.


Introduction
The boreal winter snow cover and depth play many roles in the Earth's climate, energy and water cycles.These include albedo, insulation for permafrost and vegetation, ecosystems, and a source of water in spring to lakes, rivers, soil moisture and groundwater [1][2][3][4][5].Snow water equivalent, i.e. the mass of snow is a critical parameter of the Earth [6,7].
The Earth is currently experiencing the latest inter-glacial era of a long period of glaciations that stretch back to the late Tertiary [8].To date our most robust global data records for snow water equivalent are derived by satellite-based microwave sensor systems and retrieval algorithms, which began in late 1978 and continue.Over this period much has been experimented and learned of the microwave characteristics of snow and sensed from an orbital perspective.In addition our abilities to engineer and maintain in precise orbits for artificial satellites has evolved into precise global measurement network systems, which includes the Global Positioning System (GPS).
In our study we investigate snow water equivalent, the water equivalent mass of snow on the northern high latitudes of the Arctic non-glaciated land regions.Our datasets for snow water equivalent derive from satellite microwave sensor systems and retrieval algorithms.These are the Scanning Multi-Channel Microwave Radiometer (SMMR), the Special Sensor Microwave/Imager (SSM/I) and the Advanced Microwave Scanning Radiometer for the NASA Earth Observation System (AMSR-E).
To interrogate the datasets we employ mathematical techniques from Inverse Theory and time series analysis [9][10][11][12].Our objective is to search the datasets for regional trends, variations and significance levels of snow water equivalent.This will serve as aid in assessments of changes in boreal snow water equivalent over the period of measurement from November 1978 through May 2010.The National Snow and Ice Data Center (NSIDC), as part of the NASA Distributed Active Archive Center System distribute the datasets in hierarchical data format and binary files.More background information on algorithms and measurement theory, processing, projection-grids, sa-tellites and sensors can be found at NSIDC (http://nsidc.org).Table 1 provides a brief summary of pertinent sensor specifications.
The signal received at the satellite sensor originates from the surface with contributions from the snow pack and sub-snow pack interface.Microwave channels used are chosen for minimal atmosphere interference.Processing of the raw data takes into account antenna orientation, orbit (including solar and tide effects) and timing [17].Algorithms developed during the SMMR and SSM/I eras were refined as better knowledge of physics regarding atmosphere, snow pack (density, grain size, depth hoar and moisture), terrain (complexity) and vegetation (canopy closure, internal scatters and littoral scatters) became known [15,18,19].The AMSR-E snow water equivalent algorithm was initially based on work published in [14] and updated by work published in [20][21][22].Subsequent improvements have been made to the SSM/I and AMSR-E snow water equivalent algorithms [22][23][24][25][26]. Monthly composite climatology from the sensors is processed from daily passed-retrievals through averaging.
All three sensors are subject to uncertainties of the physical state of snow packs including depth hoar and metamorphism [27,28].Under-estimations can occur on mountains of complex geometry, along marine-coastlines where signals from ocean bodies are partly convolved, and the beginning and ending of the snow season when snow depths are thin and moist [16].Ocean masks are used to help mitigate strong contrasts of land-ocean brightness temperature and emissivity.Noise from transitory atmosphere conditions is removed using a five-day filtering for SSM/I retrievals for instance.Missing retrievals due to swath coverage gaps are interpolated from neighboring swaths.Adjustment for tall and dense vegetation uses vegetation indices derived during the sensor eras with most docs/daac/ae_swe_ease-grids.gd.html).Surface meteorolorecent ones from MODIS [18,29] (http://nsidc.org/data/gical station data over the northern hemisphere were used in calibration and re-calibration of the algorithms [22].
Inter-comparison and validation campaigns on sites over the mid-to-high northern latitudes have been undertaken [15,19,26,30].

SMMR-SSM/I
Snow water equivalent estimates in units of millimeters were derived using the horizontally polarized difference algorithm for the 19 and 37 GHz channels from daily orbit swath acquisitions [14,15,31].Nominal spatial resolution for SMMR is about 55 by 41 km (18 GHz) and 37 by 28 km (37 GHz).Nominal spatial resolution for SSM/-I is about 37 by 28 km (37 GHz) and 15 by 13 km (85.5 GHz).SMMR operated in and orbit that allowed for global coverage within 48-hours (every-other day acquisition).SSM/I operates in a faster orbit to allow global same-day day-nighttime acquisitions.Figure 1 shows an example of SSM/I ascending mode brightness temperatures (Kelvin) 19 GHz (A) and 37 GHz (B) during 10 March 2006.

AMSR-E
Based on SMMR-SSM/I algorithms the AMSR-E estimates snow water equivalent in units of millimeters using the horizontally polarized difference algorithm for the 7, 37 and 89 GHz channels [21,22,32,33].Nominal spatial resolution varies from about 6 by 4 km in the 89 GHz channel up to 74 by 43 km in the 7 GHz channel.
Global coverage from NASA-Aqua (EOS-PM) allows for same-day daytime and nighttime acquisitions.

Grid
The processed data were gridded in the equal-area scalable Earth (EASE) projection system at 25-km grid intervals [31,33].For our purposes we project the data into the World Geodetic System (WGS) with WGS-84 ellipsoid and Earth Geopotential Model 1996, consistent with the International Terrestrial Reference Frame 2005 epoch [34][35][36].For co-location with the Digital Elevation Model data we employ bi-linear least squares interpolation to a 5 km grid.We employ a planetocentric graticule with positive East, 0˚ to 360˚ longitudes.This removes the E-W (±180˚) ambiguity.

Digital Elevation Model Data
Our source for land elevation data is the ESA funded Altimetry Corrected Elevation version 2 Digital Elevation Model (DEM) [37].This model is derived from the Shuttle Radar Topography Mission DEM (finished) and ESA multi-mission satellite radar altimetry (ESA ERS-1&2 and Envisat) [38].We use the 15-degree tiles, 3-arc second posting, reference in the EGM96 WGS84 system, consistent with the International Terrestrial Reference Frame 2005.For co-location matching with the snow water equivalent data we employ bi-linear least squares interpolation (up-sampling) to a 5 km grid.

Methodology
Our methodology utilizes mathematical techniques from Inverse Theory through the investigation of time series [9][10][11][12].These we employ to derive least squares trends, analysis of variations, significance levels and error.It has long been known that topography plays important physical roles in influencing the magnitude of precipitation, i.e. the orographic lift by terrain elevation.It has also long been known that our satellite microwave sensors perform with less accuracy on regions of complex terrain due to slope-aspect and the limitations from the instantaneous field of view of the sensors.
For these reasons we apply position co-location of the snow water equivalent data with the DEM.Since our datasets are processed to have matching earth-centered grids sorting and identifying same-location elevation with snow water equivalent can be done efficiently with Linux/UNIX tools and shell scripting for batch processing.Figure 2 shows the DEM (A) and an example of snow water equivalent with same grid and geolocations over the Arctic.The snow water equivalent data are for 3 March 2006.
With co-located elevation-snow water equivalent we then extract the data filling the region beginning at 65˚N latitude.From these we derive the 65˚N region monthly means, standard deviations and standard errors.At this point we then derive calibration factors of the regionalized monthly time series SMMR, SSM/I and AMSR-E snow water equivalents using least squares techniques to mitigate bias offsets of the data groups.We then apply the calibration factors back to the 65˚N datasets using seasonal sinusoids to proportion the calibrations by month.
Having mitigated bias offsets of the data groups we now have a calibrated and consistent dataset covering the non-glaciated land region from 65˚N and higher.To investigate the regional trends and variations we develop extraction regions of interest.averaging from SS/I through AMSR-E given the different instantaneous fields of view of the sensors.

Results and Discussion
Figure 4 shows the 65˚N regionalized mean snow water equivalent monthly time series and trend.The least squares trend indicates snow water equivalent is increasing by 0.20 ± 0.07 mm/yr with a p-value of 1.72E-09 (100% significance level) from November 1978 through May 2010.
Physics controlling snow cover and snow water equivalent, i.e. precipitation and processes of climate are nonstationary [39,40].A factor in nonstationarity is telecomnection processes at the global scale such as the El Niño/Southern Oscillation (ENSO) [41,42].
In Figure 4 we highlight two ENSO events.Winter 1993 experienced a strong La Niña (cool ENSO phase) shown by the blue circle, and winter 1998 experienced a strong El Niño (warm ENSO phase) shown by the red circle.Our calibrated time series captures this physical teleconnection of equatorial ocean surface temperature and extratropical precipitation in the northern high latitudes.Winter northern hemisphere atmosphere circulation and variability can be described as the coupled Arctic and North Atlantic Oscillation [43].Together with the Pacific North America Oscillation these circulation and energy patterns control the advection of energy and mass and linked surface processes that influence precipitation, storminess and surface temperature on decadal, interannual, seasonal, monthly and less timescales [44].The quasi-biennial persistence of the patterns stems from coupling of tropical and extratropical sea surface temperatures and external forcing from in particular Eurasian snow cover [45].Figure 6 shows 22 sub-region regionalized mean snow water equivalent monthly time series and trends (Table 2) on the northern hemisphere distributed clock-wise from 10˚E through 10˚W (Figure 2(c)).The time series vertical axis is the same for all the plots.Northwest Europe and Russia (Figure 6 and Table 2 A through E) have decreasing trends of snow water equivalent.Northern Siberia, Far East Russia and North America and Greenland (Figure 6 and Table 2 F through V) all show increasing trends.All have very low P-Values indicating high significance over the period of measurement.
Figure 6(J), the Arctic Coastal Plain of Alaska shows mean snow water equivalent values during winter 1989 were exceptionally large.Precipitation records for 1989 at Barrow, Alaska corroborate this result [48].
The mean snow water equivalent varies over all the regions.Interestingly the largest magnitudes of regional mean snow water equivalent occur across northern Siberia.Contrasting to this the smallest magnitudes of regional mean snow water equivalent occur across eastern North America and Greenland.
Our regionalized trends show statistically significant increasing snow water equivalent on low-elevation tundra landscapes from northern Eurasia through North Ame-rica and Greenland.On low-elevation tundra landscapes from northern Norway through northwest Russia there are statistically significant decreasing snow water equivalent.These indicate a likely influence from the Atlantic inflow and perturbation by the North Atlantic Oscillation on the regional snow water equivalent trends [46].
Our analysis of the power density spectra has identified significant power at quasi-biennial and associated lunar nodal cycles.The quasi-biennial (upper atmosphere circulation and ENSO) and lunar nodal cycles (ocean circulation perturbations from tides) forms the causative linkage between increasing snow water equivalent on lowelevation tundra landscapes and decreasing coastal sea ice cover as a subsystem of the Arctic system energy and mass cycles.

Conclusions
We investigate the more than 30-year record of multi-satellite and multi-microwave sensors derived snow water equivalent on the high-latitudes of the northern hemisphere land regions.We accomplish this through application of Inverse Theory.This includes least squares calibration of the sensor snow water equivalent retrievals.We Copyright © 2012 SciRes.IJG  Then we derive hemispheric wide and regionalized snow water equivalent trends and significance levels on non-glaciated lands in the elevation range of 0 up to 100 m.These correspond to low-elevation tundra landscapes.Our results indicate significantly increasing trends of snow water equivalent from northern Siberia through North America and northern Greenland of varying magnitude.Across northern Norway through northwest Russia there are significantly decreasing trends of snow water equivalent.Power density spectra identify significant power at quasi-biennial and associated lunar nodal cycles.These cycles of the upper atmosphere circulation, ENSO and ocean circulation perturbations from tides forms the causative linkage between increasing snow water equivalent on low-elevation tundra landscapes and decreasing coastal sea ice cover as a subsystem of the Arctic system energy and mass cycles.

Figure 1 .
Figure 1.SSM/I 19 GHz (a) and 37 GHz (b) brightness temperature (Kelvin) measured on 10 March 2006 (ascending mode) used in the algorithm for snow water equivalent retrieval.

Figure 2 (
c) shows our extraction region on the Arctic and the underlying DEM with elevations in the range from 0 to 100 m.These cover the Arctic Coastal Plain of Alaska and the lower Lena watershed for instance.

Figure 2 (
d) gives an example of the calibrated and co-located snow water equivalent data in the elevation range from 0 to 100 m, 3 March 2006.From these we derive the mean, standard deviation and standard error of snow water equivalent and then derive the least squares trends, p-values and significance levels.

Figure 3
shows the regionalized mean snow water equivalent time series in the elevation range from 0 to 100 m, non-calibrated (a) and calibrated (b).In Figure3(a) we denote the satellite-era sensors by color: Red diamonds denote SMMR, Blue squares denote SMM/I and Green triangles denote AMSR-E.The very obvious bias offsets of all three are evident.This we can understand is mostly a function of averaging: mostly temporal averaging from the differing orbits from SMMR to SSM/I and spatial

Figure 2 .Figure 3 .
Figure 2. 65˚N region of interest for snow water equivalent (SWE) investigation.(a) ESA funded Altimetry Corrected Elevation Digital Elevation Model version 2; (b) SSM/I snow water equivalent on 3 March 2006; (c) Elevations in the range of 0 to 100 m and sub-regions referenced in Table 2 and Figure 6; (d) Elevation co-located SWE on 3 March 2006.Grey color corresponds to no data.

Figure 4 .
Figure 4. Calibrated regionalized 65˚N mean snow water equivalent time series.Light-blue squares denote January-February-March months used for least squared derived trend (Black-line).Blue-circle identifies strong La Niña cold-phase ENSO during winter 1993 and red-circle identifies strong El Niño warm-phase ENSO during winter 1998.

Figures 5 (
a) and (b) show the discrete power density spectra of the detrended monthly series, and Figures 5(c) and (d) show the discrete power density spectra of the variance of detrended monthly series.Figures 5(a) and (c) use 256 samples from the series beginning and Figures 5(b) and (d) use 256 samples from the series ending.We use these overlapping short sample lengths to satisfy the 2 N criterion of the Discrete Fast Fourier algorithm and to avoid zero padding and windowing that will reduce power and pose convolution of window artifacts.The red continuous lines are significance levels, 95% lower and 99% upper based on a reference red-noise chi-squared distribution using deviations and variances from the monthly series.Figures 5(a) and (b) show significant power at the frequencies corresponding to the 12-month, 6-month, 4-month, 3-month and quasi-2-month cycles.At low frequencies significant power is at 1.2 and 10.75-year cycles in Figure 5(a) and at 2-, 10.75-, and 21.5-year cycles in Figure 5(b).The power density spectra of the variance series show significant low frequency power at 19.85-year cycles in Figures 5(c) and (d).The 19.85year cycle is a likely alias of the 18.61-year lunar nodal cycle [46,47].

Figure 5 .
Figure 5. Power density spectra (dB) of the calibrated regionalized 65˚N mean snow water equivalent and variance time series.(a-b) Power density spectra of 256 samples from series beginning, (a) and series ending, (b) are shown with reference red-noise spectra at 95% significance (lower red line) and 99% significance (upper red line).(c) and (d) Power density spectra of 256 samples from the variance series beginning, (c) and variance series ending, (d) are show with reference red-noise spectra at 95% significance (lower red line) and 99% significance (upper red line).

Figure 6 .
Figure 6.Regionalized sub-region mean snow water equivalent series and least squares trends.Refer to Table 2 for sub-region trend, p-value and significance level.Longitude in the legend refers to planetocentric, positive East, coordinate graticule.