Snow mass decrease in the Northern Hemisphere ( 1979 / 80 – 2010 / 11 )

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Introduction
The world's snow cover is concentrated in the Northern Hemisphere and plays a crucial role in climate change and regional water supply (Pardé et al., 2007;Takala et al., 2011;Barnett et al., 2005;Hancock et al., 2013;Immerzeel et al., 2010).Snow cover extent (SCE) shrank over the Northern Hemisphere between the 1970s and 2006 (Karl et al., 1993;Gao et al., 2012;Déry and Brown, 2007;Armstrong and Brodzik, 2001).Snow water equivalent (SWE) is a more comprehensive parameter that takes into account snow extent, density and depth, and represents the corresponding depth of water that would result were the snow to melt in place.The pan-Arctic average trend in peak seasonal SWE was −0.17 cm decade −1 , with maximum and minimum trends of 5.70 and −2.5 cm decade −1 , respectively, for the period 1979-2009 (Liston and Hiemstra, Figures Back Close Full 2011).However, the variation in SWE differed according to location and time.During the period covering the last 30 years and more, three passive microwave radiometers have been used to generate the SWE data.The products that have been used to estimate the SWE at the scale of the Northern Hemisphere consist of: 1. "Global Monthly EASE-Grid Snow Water Equivalent Climatology" product, which covers the period from November 1978 to May 2007 (Armstrong et al., 2007).The passive radiometers used to produce this were the Scanning Multichannel Microwave Radiometer (SMMR) and selected Special Sensor Microwave/Imagers (SSM/I).The AMSR-E L3 Global SWE product, which covers the period June 2002 to October 2011 (Tedesco et al., 2004;Chang et al.,1987;Armstrong and Brodzik, 2001).Both the two products are released by the National Snow and Ice Data Center (NSIDC).
Due to their different inversion algorithms, the three SWE products have different estimated accuracies and no comparison between them, or error analysis for them, has been produced at the scale of the Northern Hemisphere during their period of operation.

Data preprocessing
SMMR and SSM/I are passive radiometers and their brightness temperatures at frequencies of 18(19) and 37 GHz are employed to estimate SWE.In the inversion algorithm, two important approximations have been made: firstly, the snow grain size is assumed to be a constant 0.3 mm; secondly, snow density is set to a constant 0.3 g cm Introduction

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Full  (Tedesco and Narvekar, 2010).This data set is projected on to the Equal Area Scalable Earth Grid (EASE-grid) at the hemisphere scale.Pixels from the 25 km EASE-Grid version of the BU-MODIS Land Cover data that had more than 50 % ice cover were set as permanent ice (ice sheets, ice shelves, and large glaciers) and without SWE inversion values.As any vegetation scatters microwaves in the same way as snow, the presence of vegetation will affect the SWE estimates.Therefore, pixels covered by forest were adjusted using the forest fraction.
The AMSR-E L3 Global SWE is also projected on to a 25 km × 25 km EASE-grid on the hemisphere scale.The algorithm used to produce this product is derived from the spectral difference method and is similar to the Global Monthly SWE Product of SMMR & SSM/I.With the availability of the special X-band channels on AMSR-E at 10.7 GHz, the algorithm's ability to detect deep snow (using the difference between 10.7 and 18.7 GHz) is improved and its dynamic range to help with forest attenuation is enhanced (Tedesco and Narvekar, 2010).Before the SWE values can be retrieved, wet snow pixels have to be excluded.The forest effect is corrected with the IGBP (International Geosphere Biosphere Programme) data obtained from the Boston University.It should be noted that the snow density employed in the AMSR-E L3 product is no longer a constant; instead, its value is obtained from a global snow density map, in which the average snow density values for each of the six seasonal classes (Sturm and Holmgren, 1995) are calculated according to in situ measurements made in Canada (Brown and Braaten, 1998) and the former Soviet Union (Krenke, 2004).In addition, the land cover, ocean, and ice-sheet masks are based on the MOD12Q1 data, re-gridded as a 25 km EASE-Grid version of the land cover data (MOD12Q1 IGBP, collection V004).The method of defining "ice" pixels is the same as for the SMMR & SSM/I Global Monthly SWE product discussed earlier.
The GlobSnow SWE product is retrieved using an assimilation scheme based on a semi-empirical snow emission model from satellite data combined with ground-based weather station measurements and covers all land surface areas except for mountainous regions and Greenland.The data are stored in the EASE-Grid format.The snow Introduction

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Full density is treated as a constant with a value of 0.24 g cm −3 , a reasonable "global" value given by the analysis by Sturm (2010).This inversion algorithm is developed further and is fully described in the article by Pulliainen et al. (2006), where considerations of the temporal continuity of the SWE are added.The mountain mask applied is derived from a 2 × 2 grid of ETOP2 data containing global elevation and bathymetry from the National Geophysical Data Center (NGDC).Due to the saturated brightness temperature response, wet snow or temporary thin snow layers are not reliably detected and are masked by observed brightness temperature values using an empirical equation.

Ground station data validation
We selected coarse snow depth measurements from 7388 weather stations (Fig. 1) -each of them with at least 15 days' snow cover -from Global Historical Climatology Network-Daily (GHCN-DAILY) to be used as ground truth data, in order to validate monthly SWE estimate products.Accumulations are displayed in 5 mm steps in Fig. 2, in order to show the trends more clearly.The results of the comparison, used as ground truth for SWE values between 0 and 200 mm (Fig. 2), suggest that in the Northern Hemisphere, for values of SWE over 30 mm, the linear relationship between the estimated GlobSnow SWE and the ground truth SWE is better than for the SWE products released by the NSIDC.For GlobSnow the correlation index is over 0.5, while for the other products the correlation indexes are only 0.22 and 0.12.This is largely because a large number of in situ measurements of snow depth have been introduced into GlobSnow's inversion algorithm and improved its accuracy (Luojus et al., 2010).However, since the microwave upwelling radiation emitted from the ground by scattering no longer decreases with increasing snow depth at higher frequency microwaves (such as 37 GHz), passive microwave SWE retrieval algorithms do not have the ability to detect deep snow.The assimilation retrieval process of GlobSnow is also influenced by this limitation.In previous studies, the observable scattering at higher frequencies saturates for thick snow packs after a certain threshold, often between 120 and 180 mm.Introduction

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Full While SWE values exceed the threshold, the accuracy of all the inversion procedures drops sharply, as the situations shown in Fig. 2. Note that for thin snow -that is for values of SWE less than 30 mm (equivalent to a snow depth of 12 cm for a snow density of 0.24 g cm −3 , and a snow depth of less than 10 cm for a snow density of 0.3 g cm −3 ) -the GlobSnow SWE values are clearly overestimates, which is the same as the result obtained from the accuracy testing experiments for Eurasia (Luojus et al., 2010).

Data merge
According to the results of comparing the three estimated SWE products and the station measurements, it was seen that for SWE > 30 mm, the GlobSnow product is more accurate than products produced by the NSIDC and that for SWE < 30 mm, the situation is reversed.In order to optimize the SWE dataset, we chose pixels that had monthly SWE values continuous above 30 mm in winter (December to March) for the period 1979/80 to 2010/11 from GlobSnow, and the other pixels that had monthly SWE values no more than 30 mm in the same period from the two NSIDC products.However, the period covered by the sets of pixels from the two NSIDC products is different: SMMR & SSM/I end in May 2007, whereas the AMSR-E data cover the period from June 2002 to October 2011.We built linear fitting equations for each pixel in every month during the period of overlap (2002)(2003)(2004)(2005)(2006)(2007) in order to simulate winter SWEs in 2007-2011 using AMSR-E products.For each pixel, where SWE is obtained from NSIDC SWE products derived from SSMR & SMM/I data at location (i , j ) in one of the winter months and SWE is obtained from the NSIDC SWE product derived from AMSR-E data, α and β are linear coefficient.Considering the differences in the algorithms used to produce these products, this kind of forecasting is not effective in all areas.Simulated data was added only for pixels that proved to be Introduction

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Full statistically significant at p = 0.05 under both a t test and an F test.For the remainder, the SWE series from SSMR & SMM/I (ending in 2007) was retained in the pixels and the simulated data is not added, in order to avoid the introduction of errors into the trend analysis.However, in the calculation of the total snow mass, the values of SWE in the non-simulated pixels were still replaced by those from the NSIDC AMSR-E product as the low number of small values has relatively little influence.
In the merged products, the distribution maps of the three different products are shown in Fig. 3.The GlobSnow product accounts for the largest proportion (more than 50 %) in the merged data in all the four months, and it mainly concentrates in high altitude regions.The NSIDC (SMMR & SSM/I and the linear fitted AMSR-E) product accounts for a little larger proportion than the NSIDC (SMMR/SSM/I) product in all the four months except in February, and both of the two products mainly distributed in low altitude regions.

Results
The distribution map of the average optimized SWE product for the 32 years is presented in Fig. 4. In December, snow cover is mainly located between 55 and 70 • N in Eurasia and between 60-70 • N in North America.Snow cover extends to mid-latitude regions near 50 • N in January in Eurasia and North America, and there is little differ- According to the SWE change map (Fig. 5), in December, there was a significant change in central Siberia (60-70 • N, 110-130 • E) of about −1 cm decade −1 .Over the West Siberian Plain and parts of the Eurasian continent near 60 • N there was a slight increase, but the most significant rise was concentrated around 66 • N, 90 • E -the rate of increase here was over 1 cm decade −1 .In January, the area where there was a significant decrease in SWE increases several fold, and is not only concentrated in the same regions as December but also extends to Baffin Island and northern Europe.In February, the rate of SWE decrease in Siberia accelerates, reaching over −2 cm decade −1 ; the areas where there is a decrease also grows further to include most of the Hudson Bay coastline.Meanwhile, the rising trend around 60 • N in Siberia weakens, with the maximum rate being 0.7 cm decade −1 .In March, the significant reduction in SWE in North America is still obvious even though the pattern is variable with some small areas where there is an increase.In Northern Europe, there is a reduction in the area where there is a significant decrease, whereas there is a clear expansion in areas where there is an increase and this area of increase extends to the Eastern European Plain.
Overall, then, significant drops in SWE are concentrated at high latitudes of around 65 • N in Siberia and in North America; areas where there was a rise are mainly scattered around 60 • N in Eurasia.In Eurasia there was a significant decline in SWE in northern areas but an increasing trend in areas towards the south of the snow-covered areas, except for the "edges" of the snow-covered area below approximately 58 • N.
In North America the overall SWE declined and significant changes are concentrated along the coast of Hudson Bay and parts of Alaska in January and February.
From the temporal view, although the monthly total snow mass fluctuates from year to year, there is a declining trend in the Northern Hemisphere for all winter months in the period 1979/80-2010/11 (Fig. 6).The monthly total snow mass is calculated by summing the total mass of snow in all pixels.The most serious snow mass change occurred in January and February, at rates of −16.45 ± 6.68 and −13.55 ± 7.80 Gt year −1 , respectively, corresponding to −0.67 and −0.45 % per year, whereas the rate in March was −12.58 ± 6.88 Gt year There is high confidence in these monthly total snow mass changes (significance level p < 0.01).From the perspective of monthly differences, at less than 2000 Gt the total snow mass in December is the lowest for the four winter months; the value increases to about 2500 Gt in January, and reaches a peak of about 3000 Gt in February, with this value lasting into March.
Focusing on the more recent 15 years from 1996/97 to 2010/11, we found that the rate of decrease in the SWE slows down for the four months studied except in March, and the trend becomes less significant.During this period, the changing rate was −9.08 ± 6.90 Gt year −1 in December, −13.15 ± 8.74 Gt year −1 in January and −10.87 ± 10.56 Gt year −1 in February (p < 0.1).It should be noted that the February results are not statistically significant.In March the rate accelerated to −13.16 ± 6.6 Gt year −1 (p < 0.1).
To validate the results of this work, the results of the merged data are compared with the SWE changes in North America (Gan et al., 2013) which uses the SSMR and SSM/I data only, as shown in Fig. 7.Both Gan et al.'s (2013) and our results use the Mann-Kendall trend analysis method, which guarantees the differences are caused by the data source only.In the comparison, both the two data sets show decreasing trend in the studied four months, but in different decreasing rate.Compared to the results of Gan et al., the decreasing rate acquired from the merged data is faster in December and January, but slower in February and March.

Accuracy analysis
Due to different data sources and different processing procedures, the existing three SWE products may differ greatly in different regions (Liu et al., 2014).The accuracy of the three existing SWE products is tested with ground station data in the Northern

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Full Hemisphere, and the 30 mm threshold is acquired.Theoretically, the fusion of the Glob-Snow products thicker than 30 mm and the NSIDC products thinner than 30 mm is the best choice.However, it should be noted that, the conclusion is based on about 30 years ground station validation in the whole Northern Hemisphere, so it is only a statistical result.The merged product is superior in the Northern Hemisphere for the past 30 years, and it is more suitable for total SWE or average SWE calculation in the whole Northern Hemisphere, but it is not necessary the most accurate choice for a certain region or a certain time.

Relation to climate changes
As a feature that is responsive to climate change, SWE is affected by changes in air temperature and also by changes in precipitation timing and seasonality (Immerzeel et al., 2010).To find out the relation between changes in the value of SWE and climate change, we collected the global monthly gridded datasets of air temperature and precipitation, and analyzed the trends in these data for the past 32 years.Snowfall and rainfall cannot be separated in the precipitation records; however, the study areas used in this work are mostly at latitudes higher than 50 • N and so all the precipitation in the four months being considered was treated as snow.
The average winter temperature and precipitation changes in the snow-covered areas found using the TFPW-MK method are shown in Fig. 8.In the past 32 years, the temperature has increased at a rate of 0.17 • C decade −1 and the precipitation increased at a rate of 0.4 mm decade −1 .
On a global scale, most climate data and models agree that there is a near-surface warming trend due to the rising levels of greenhouse gases in the atmosphere (Barnett et al., 2005).According to the fifth IPCC report (IPCC, 2013), the global warming rate over the past 15 years (1998-2012) has been 0.05 (−0.05 to +0.15) • C decade −1 and for the period since 1951  the rate is calculated as 0.12 (0.08 to 0.14) • C decade −1 .In a warmer world, the melting and sublimating of winter snow Introduction

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Full accelerates (Cox et al., 2000).Even though the precipitation is also increasing, the total snow mass on the ground decreased.The decrease in SWE directly reduces water supply in the spring (Barnett et al., 2005;Diffenbaugh et al., 2012) and also influences vegetation growth (Wahrent et al., 2005;Wang et al., 2013).In addition, it has a complex influence on the ground climate.
On the one hand, the snowpack insulates soil from cold air so the thinning of the snow weakens the insulating effect and cools the soil (Zhang et al., 2005) in winter; on the other hand, thinning of the snow is positively related with snow-season shortening and soil without snow cover absorbs more solar energy and warms up in spring (Lawrence et al., 2010).

Conclusions
Three SWE products, NSIDC (SSMR & SSMI), NSIDC (AMSR-E L3) and GlobSnow are verified using global weather station data.The results show that for values of SWE less than 30 mm, the NSIDC product has the best correlation with the ground truth data; when the SWE is between 30 and 200 mm, the GlobSnow product shows the best Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ence between January, February and March in these areas.Large areas in central and western Siberia have the biggest and deepest snow accumulations of snow in all four months.Using the optimized SWE product (1979/80-2010/11), and the trend-free prewhitening Mann-Kendall (TFPW-MK) (Yue et al., 2002) method, which has been widely used for hydro-meteorological trend assessments (Gao et al., 2012), we analyzed the SWE changes in the past 32 years in the Northern Hemisphere for different regions and different months, as shown in Fig. 5Discussion Paper | Discussion Paper | Discussion Paper | −1 , or nearly −0.42 % per year.The smallest change was in Discussion Paper | Discussion Paper | Discussion Paper | December -only −10.70 ± 5.62 Gt year −1 , taking up to a change rate of −0.64 % per year.
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Figure 1 .
Figure1.Ground station distribution.The crosses stand for 29 814 stations that provide snow depth measurements for 1979-2010.The points stand for 7388 selected stations -at each of these, there were at least 15 days of snow cover in the month studied and the stations used in the assimilation algorithm of the GlobSnow product were eliminated.