Snow water equivalent (SWE) is an important variable in
describing global seasonal snow cover. Traditionally, SWE has been measured
manually at snow transects or using observations from weather stations.
However, these measurements have a poor spatial coverage, and a good
alternative to in situ measurements is to use spaceborne passive microwave
observations, which can provide global coverage at daily timescales. The
reliability and accuracy of SWE estimates made using spaceborne microwave
radiometer data can be improved by assimilating radiometer observations with
weather station snow depth observations as done in the GlobSnow SWE
retrieval methodology. However, one possible source of uncertainty in the
GlobSnow SWE retrieval approach is the constant snow density used in
modelling emission of snow. In this paper, three versions of spatially and
temporally varying snow density fields were implemented using snow transect
data from Eurasia and Canada and automated snow observations from the United States. Snow
density fields were used to post-process the baseline GlobSnow v.3.0 SWE
product. Decadal snow density information, i.e. fields where snow density
for each day of the year was taken as the mean calculated for the
corresponding day over 10 years, was found to produce the best results.
Overall, post-processing GlobSnow SWE retrieval with dynamic snow density
information improved overestimation of small SWE values and underestimation
of large SWE values, though underestimation of SWE values larger than 175 mm
was still significant.
Introduction
Snow water equivalent (SWE) is an important property of the seasonal snow
cover, and estimates of SWE are required in many hydrological and
climatological applications, including climate model evaluation (Mudryk et
al., 2018) and forecasting freshwater availability. Maximum SWE before the
start of spring snowmelt is one of the most important snow characteristics
for run-off and river discharge forecasts (Barnett et al., 2005; Barry,
2002).
Snow depth or SWE can be estimated by interpolating surface snow depth (Dyer
and Mote, 2006) or snowfall measurements (Broxton et al., 2016). However,
the limited spatial and temporal coverages of the ground-based measurements,
especially in northern and alpine regions, limit the quality of estimates
(Broxton et al., 2016; Mortimer et al., 2020). An alternative approach for
estimating SWE is to use satellite measurements as they can provide global
spatial coverage and good temporal resolution.
Spaceborne passive microwave radiometer (for example Chang and Foster,
1987; Kelly et al., 2003; Pulliainen, 2006) or active radar (for example
Lievens et al., 2019; Rott et al., 2010) observations can be used for
retrieving SWE information. Passive microwave observations are commonly used
as these provide frequent repeat coverage, and the influence of atmospheric
conditions on the observation is limited. Furthermore, passive microwave
radiometer data are also available from 1978 onwards, which allows the
analysis of long time series. Many passive microwave radiometer-based
approaches for estimating SWE are adopted from an algorithm proposed by
Chang and Foster (1987) for estimating snow depth from horizontally
polarized Scanning Multichannel Microwave Radiometer (SMMR) measurements.
The algorithm is based on the difference in measured brightness temperatures
at a frequency insensitive to dry snow, around 19 GHz, and at a frequency
sensitive to dry snow, around 37 GHz. The uncertainty of SWE retrievals
based on the radiometer measurements alone can be quite high (Mudryk et al.,
2015). Retrieval algorithms that use only radiometer data tend to
underestimate SWE in deep snow conditions (Derksen et al., 2005), and the
performance of these algorithms is even more limited in wet snow conditions
(Armstrong and Brodzik, 2001).
To overcome the problems connected to stand-alone passive microwave SWE
retrievals, ground-based observations and satellite radiometer data can be
combined as done in the assimilation approach for SWE retrieval introduced
by Pulliainen (2006) and complemented by Takala et al. (2011). This
assimilation-based approach was used as the baseline method for the Global
Snow Monitoring for Climate Research (GlobSnow) initiative of the European
Space Agency (ESA). The GlobSnow method has been shown to produce good
results when compared to typical stand-alone radiometer algorithms (Mortimer
et al., 2020). The GlobSnow version 3.0 (GSv3.0) climate data record with
spatial bias correction was used for accurate reconstruction of the Northern
Hemisphere snow mass and its trends for period of 1979–2018 (Pulliainen
et al., 2020). Improving the GlobSnow SWE retrieval methodology will help to
further enhance our understanding of the Northern Hemisphere snow conditions
and their changes.
The GlobSnow SWE retrieval utilizes a fixed density of 240 kg m-3
throughout the retrieval regardless of the snow depth, location, or time of
the year (Takala et al., 2011), which is a known source of uncertainty in
the retrieval. The density of snow changes with time and place, and it is
greatly affected by surrounding weather conditions. For example, wind breaks
down snow crystals, both on the ground and falling from the sky, which
allows snow crystals to pack together tightly and increases the density of
snow (Jordan et al., 1999). The age of the snow cover also affects its
density as the snow on the ground is constantly undergoing metamorphism
(Maurice and Harold, 1981).
One approach considered for GlobSnow SWE retrieval methodology for
estimating temporally and spatially varying snow densities was to use a
statistical snow density model presented by Sturm et al. (2010), which
predicts density of snow as a function of the snow depth, day of the year,
and snow class (Luojus et al., 2013b). However, applying densities obtained
using this approach did not improve retrieval skill notably (Luojus et al.,
2013a). A different approach for obtaining varying snow density information
is to use available snow density data to create snow density fields by
applying temporal and spatial interpolation.
In this study, dynamic snow density information obtained from ground
measurements using interpolation is used to post-process the GSv3.0 SWE
climate data record. Three different versions of the snow densities are
implemented for Eurasia for the years 2000 to 2009. Additionally, one
version of the dynamic snow densities is also implemented for the whole
Northern Hemisphere for the whole period of GSv3.0 SWE data record,
1979–2018.
Data and methodsSnow density and SWE dataEurasia
In situ snow density and SWE measurements were used to obtain dynamic snow
density fields and validate the results of SWE retrievals. SWE and density
datasets for Eurasia were obtained from Russia (Bulygina et al., 2011) and
Finland (Haberkorn, 2019). These datasets contain snow transect data. Snow
transects consist of manual gravimetric snow measurements made at multiple
locations along a pre-defined transect several hundreds of metres to several
kilometres in length which are averaged together to obtain a single
representative (in regard to the spatial resolution of utilized passive
microwave radiometers) SWE value for a given transect on a given date.
Russian data, from a substantial network of snow transects, has been made
available via the All-Russia Research Institute of Hydrometeorological
Information-World Data Centre (RIHMI-WDC) website. This Russian snow survey
dataset contains data from routine snow surveys operated at 515
meteorological station locations, and data are available from 1966 to 2020
(Bulygina et al., 2011); data from 1979 to 2018 are used in this study.
Routine snow surveys are run through the cold season every 10 d or every
5 d during the intense snowmelt season. The Finnish Environment
Institute (SYKE) has a network of about 160 snow survey courses that have
been operated from the beginning of the 20th century (Haberkorn, 2019).
These 2 to 4 km long snow survey courses that go through different
landscapes are visited monthly, and 80 snow depth measurements are made
along the snow course through varying landscapes about 50 m apart. Eight
snow density and SWE measurements are made along each snow course. An
aggregate of the SWE measurements is applied to describe the SWE conditions
for the snow course for the given sampling date.
The Russian snow transect dataset was divided into two parts. The division
of data was done by finding the nearest neighbours and separating them into
different datasets. The first part of the data were used for implementing the
dynamic snow density maps, and the second part, together with snow transect
data from Finland, was used for validating snow density and SWE results. The
implementation dataset contains 257 locations, and the validation data are
formed from data from 625 locations. Implementation and validation snow
transect locations are shown in Fig. 1. Figure 2 shows histograms of the
implementation and validation snow density values.
Locations of Eurasian snow courses divided into two sets:
implementation (red) and validation (blue).
Histogram of the implementation and validation densities
for Eurasia for 2000–2009.
We divided the Eurasian snow density implementation dataset into three
distinct ways to create three different versions of dynamic snow density
maps. For the first version, called the multi-decadal version, all data
between 1979 and 2018 were used. The second version, called the decadal
version, uses data from 2000 to 2009. The third version, called the annual
version, uses data from 2000 to 2009 and produces daily density maps for
each year using only data from the year under investigation.
A day-of-the-winter (DOW) value was added to each snow density measurement.
DOW values are a modification of the day-of-the-year (DOY) values. DOW
values start from 1 September and then continue to grow from there until the
last day of August. This means that 1 January has a DOW value of 123, and
30 August has a value of 365 or 366. They are used because the Northern
Hemisphere winter season spans from September until June over the new year.
The Eurasian snow survey data were filtered to remove all negative density
observations and all observations larger than 1000 kg m-3. These
measurements are most likely erroneous as snow densities typically range
between 50 and 550 kg m-3 (Fierz et al., 2009). After filtering,
average snow density values were calculated for each DOW that had at least
one measurement.
Most density measurements have been done systematically on the same DOW from
year to year, with few exceptions. This difference in measurement days may
cause average densities to fluctuate from one day to another as some density
values are not averages but measurements from one specific year. To avoid
these fluctuations in multi-decadal and decadal versions, if two consecutive
DOWs had measurements, the average density is calculated using data from
both days, and this density was assigned the DOW value of the first day.
Outlier data points were removed from multi-decadal and decadal datasets
after averaged densities were calculated. Outliers were determined to be
data points that differ from two previous and two following points by more
than 50 kg m-3. Figure 3 shows how average densities calculated for
each DOW and non-consecutive DOWs differ for one snow transect location for
the multi-decadal dataset. The depicted snow transect is located in western
Russia. Figure 3 also shows the 40-year average SWE for each DOW for the
same station.
Average snow density and SWE versus DOW for snow transect
in western Russia with latitude 59.4∘ N and longitude
33.1∘ E using multi-decadal data. Blue asterisks show average
density calculated for each DOW separately. Red square markers show average
densities calculated using data for two consecutive days if available. The
red dashed line shows averaged SWE for the same location.
North America
The North American dataset consists of data from Canada and the United States. The
Canadian snow course network is sampled twice per month (around the first
and 15th) during the snow season, and the dataset extends from 1981–2016
(Brown et al., 2019). The Canadian dataset was complemented with snow
observations from 443 SNOTEL stations located in Alaska and the
north-western United States (Serreze et al., 1999). Data from southern
states are not included as most of the snow in these areas is in mountains
which are excluded from the retrieval. The SNOTEL dataset differs from the
Canadian and Eurasian datasets, as it consists of automated daily
measurements instead of manual snow transect measurements. SNOTEL stations
collect data on snowpack SWE, snow depth, precipitation, and air
temperature. SWE is measured by a snow pillow filled with an antifreeze
solution. Hourly data are available from the snow pillows, but daily
measurements were used as they are more robust as hourly data are easily
affected by wind and sensor issues.
A small part of North American data were separated to be used for validation
of results. The implementation set contains 1455 locations, and the
validation set is made from 242 locations. The locations that form the
validation and implementation datasets are shown in Fig. 4.
Locations of North American snow measurements divided
into two sets: implementation (red) and validation (blue).
Baseline SWE retrieval
The European Space Agency (ESA) GlobSnow and succeeding projects have
produced a family of daily satellite-based SWE climate data records spanning
over 40 years. The most recent GSv3.0 data record is based on methodology
introduced in Pulliainen (2006) and Takala et al. (2011), and the latest
version is presented in detail in Luojus et al. (2021). The retrieval
algorithm combines satellite-based passive microwave measurements with
ground-based synoptic weather station snow depth observations by Bayesian
non-linear iterative assimilation.
The GlobSnow approach uses two vertically polarized brightness temperature
observations at 19 and 37 GHz and a scene brightness temperature model (the
HUT snow emission model; Pulliainen et al., 1999). First, an effective snow
grain size is estimated for grid cells that coincide with weather station
snow depth observations. The snow grain sizes are used to construct a
kriging interpolated background map of the effective grain size, including
an estimate of the effective grain size error. This spatially continuous map
of grain size is then used as an input for HUT model inversion to provide an
estimate of SWE. The daily weather station snow depth measurements are also
used to form a continuous background field of snow depth independently from
passive microwave measurements. The interpolated snow depth field is fused
with space-borne brightness temperature observations, using the scene
brightness temperature model in a Bayesian approach that weights all
information sources with their estimated variances, to provide the final SWE
estimates. A constant value of snow density is used (240 kg m-3).
The retrieval method does not produce SWE estimates for mountainous areas,
glaciers, or Greenland. The data record is based on data from the SMMR
aboard NIMBUS-7, SSM/I and SSMIS sensors on board DMSP 5D F-series
satellites, and synoptic weather station snow depth data from the Northern
Hemisphere.
Creation of snow density fields
Two main steps for generating snow density fields are temporal and spatial
interpolation. Snow density measurements are made usually every 10 or 15 d, and thus, there are many days without snow density observations. Simple
linear interpolation was used to obtain estimates of snow density values for
the days lacking observations.
The length of the snow season depends on the year and place, but to get
similar series for each station, and for each version, the average of three
first existing densities was added to DOW 30 if a station did not have
measurements from DOW 30 or before this day. Similarly, if the station did
not have any measurement after DOW 280, the average of the last three
densities was calculated and added as the density for DOW 280. After this
procedure, all stations have density values from DOW 30 to DOW 280, and
interpolation could be performed for this period. Figure 5 shows the results
of interpolation for all three versions for one snow transect location. The
interpolation of the multi-decadal dataset produces the smoothest results, and
yearly data show the most fluctuation.
Temporally interpolated densities for snow transects in north
central Russia for multi-decadal and decadal versions. The figure also shows
results of interpolation for 2 years of annual interpolation, 2004 and
2008.
We used ordinary kriging interpolation for interpolating snow density values
for areas without observations. Kriging interpolation is a spatial
interpolation method that predicts values for the location with no
measurements based on the spatial autocorrelation of measured values
(Goovaerts, 1997). This means that two closely located points are more
likely to have similar values than two points further afield. The main
advantages of kriging interpolation compared to nongeostatistical
interpolation methods are that kriging interpolation provides variance of
predicted values and that the spatial smoothing is defined through the
variogram. The model of spatial variability can be expressed as (Høst,
1999)
Zs=μs+ϵs,
where Zs denotes the predicted value at some location, μs is the deterministic function describing the trend
component of Zs, and ϵs is the
stochastic locally varying but spatially dependent residuals.
The spatial autocorrelation is modelled with a semivariogram (Goovaerts,
1997):
2γd=VarZsi-Zsi+d,
with the assumption of intrinsic stationarity (variance on the right-hand side
is only dependent on the vector difference d) and the assumption that the
process is isotropic (the autocorrelation is only dependent on the distance
between observations). The empirical semivariogram can be estimated from the
observations as follows (O'Sullivan and Unwin, 2010):
γ^d̃j=12Nd∑i=1NdEZsi-Zsi+d,∀d∈d̃j,
where Zsi and Zsi+d are sampled
data pairs at distance d, and d̃j is the distance between
observations. In this study, an exponential function is used for the variogram:
γd=c1⋅expd⋅c2+c0.
Snow density values were predicted for each pixel in 25 km Equal Area
Scalable Grid (EASE-Grid version1, to match GSv3 processor grid) between
latitudes from 42 to 80∘ N and for longitudes from
20 to 180∘ E. The snow density values were estimated
using coordinates for centres of each pixel. Density maps were made for all
three versions of snow densities for each day starting from DOW 30 and
ending at DOW 280. Pixels that are not on land are assigned a value of -1,
and land areas outside the area of interpolation are designated a constant
density of 240 kg m-3 (effectively retaining the original retrieval
methodology for those regions where snow density could not be reliably
established).
Usage of snow density information and validation
The derived snow density information is used to post-process the baseline
GSv3.0 SWE retrieval. Post processing of SWE retrieval means that SWE values
obtained are scaled with the ratio of dynamic and constant snow density:
SWEnew=SWE⋅ρdynamicρconstant,
where ρconstant has values of 240 kg m-3. Scaling is performed
for each pixel within the area for which dynamic densities are available.
For the regions outside dynamic snow density information, the constant
density consideration is retained.
The obtained snow densities and post-processed SWE datasets were validated
using independent validation data. Validation locations were separated from
the data used for generating snow density fields to ensure independent
cross-validation. Root-mean-squared error (RMSE), bias, correlation
coefficients, and mean absolute error (MAE) are the four statistical measures
used for assessing the performance.
ResultsEurasia 2000–2009Snow density
Annual, decadal, and multi-decadal versions of snow density fields were
produced for Eurasia for the years 2000–2009. These three versions of
dynamic snow densities were compared to validation snow density data from
Eurasia over the same 10-year period. A summary of the validation is shown
in Table 1. Figure 6 shows the comparison of estimated and observed
densities at validation sites for multi-decadal, decadal, and annual snow
densities. As Fig. 2 shows, most snow density values range between 150 and 350 kg m-3, which can explain the departure from 1:1 fit
for small and large snow density values seen in Fig. 6.
Summary of calculated validation parameters for three snow
density sets for the years 2000–2009.
Comparison of multi-decadal, decadal, and annual density estimates.
As can be observed, annual densities perform best for small and large
density values.
Multi-decadal and decadal versions of snow densities exhibit similar
behaviour, with the multi-decadal version having slightly smaller RMSE and
larger correlation coefficient but larger bias than the decadal version. MAE
is equal for these two versions. The annual version differs from the other
two versions more, and it estimates snow densities below 200 and
above 300 kg m-3 better than the other versions. The multi-decadal and
decadal versions of snow densities are produced from data that are averaged
from a large number of measurements. This averaging means that the highest
and lowest measurements have a diminished effect on estimated snow
densities. Annual densities have a wider range of densities present in the
data used for deriving these dynamic densities compared to the range of
densities used for deriving the other two sets of the density maps. Annual
densities also have a negative bias, while the other two versions have
positive biases.
Post-processed SWE
The three different density sets were used to post-process the baseline
GSv3.0 SWE data between 2000 and 2009. Obtained SWE values were compared to
validation SWE measurements of the Eurasian dataset. Two validations were
performed: the first validation took into account SWE values up to 500 mm,
and the second validation considered SWE values only up to 150 mm, as the
bulk of the observations are below this value. Table 2 summarizes the
results of the SWE validation (for different snow density realizations).
Figure 7 shows mean errors for the baseline, multi-decadal, decadal, and
annual versions.
Results of validation for different Eurasian datasets for the
years 2000–2009; left values are for SWE < 500 mm and bold
values are for SWE < 150 mm.
The mean error for the baseline, multi-decadal, decadal,
and annual SWE estimates, 2000–2009 Eurasia.
Post-processing the baseline product with any of the three density sets improves
the baseline product. For SWE values up 130 mm, all three post-processed
datasets show similar behaviour, and as Fig. 7 shows, the overestimation
of SWE values between 0 and 100 mm present in the baseline retrieval has
been mitigated with post-processing. Post-processing also improves the
underestimation of large values present in the baseline retrieval, though
the improvements are smaller than the improvements for small SWE values.
Post-processing with the annual densities produces worse results than the
other two post-processed versions when SWE values up to 500 mm are
considered. The worse behaviour of the annual densities for larger SWE
values can be caused by the annual density dataset having a larger range of
densities than the other two density datasets. If SWE estimation has been
close to correct, but the density used in the retrieval is far from the
estimated density, post-processing causes SWE estimation to change
significantly. A wider range of densities causes more significant changes in
the post-processing. Annual and multi-decadal density sets had higher
estimates for large densities than decadal densities, which explains the
positive mean error for SWE estimates higher than 150 mm.
Results of validation for the whole Northern Hemisphere, Eurasia, and
North America for the whole winter, February, April, and December for 1979–2018.
Left values are for SWE < 500 mm and bold values are for SWE < 150 mm.
Based on the results obtained for the years 2000–2009, the decadal version
of snow densities was extended to cover the whole Northern Hemisphere and
the whole period of the baseline retrieval. Four separate sets of density
maps were made, each covering 1 decade starting from the 1980s and ending
in the 2010s. The decadal density maps were calculated using static 10-year
periods not running 10-year averages because these two methods were found
to produce very similar results, and producing four set of maps is
considerably simpler than producing separate maps for every year using
moving 10-year averages. The density maps were made using the methods
explained in Sect. 2, with a few exceptions: (1) the spatial interpolation
was performed for latitudes from 35 to 80∘ N and for
longitudes from 180∘ W to 180∘ E to cover the same area
as the baseline retrieval, and (2) the North American dataset was filtered
before adding DOW values. Filtering consisted of two steps. First, locations
that were within the same EASE grid cell were combined, and the average value
of measurements was calculated for each day. Then a mountain mask was
applied to remove locations in mountainous areas. After these filtering
steps, the North American implementation set contained 869 locations, and
the validation set was made from 201 locations.
These new decadal snow density maps were used to post-process the whole
GSv3.0 baseline dataset and the results obtained were compared to validation
datasets from Eurasia and North America. Again, SWE values up to 500 and
150 mm were validated separately. Validation was performed for the whole
winter (September to June) and separately for February, April, and December.
Table 3 summarizes the results of this evaluation. Table 3 shows results for
the whole Northern Hemisphere and separately for Eurasia and North America.
Density scatterplots of GSv3.0 baseline and
post-processed retrieval accuracy for 1979–2018 for the whole Northern
Hemisphere, Eurasia, and North America.
The RMSE was 43.5 and 42.5 mm for the baseline retrieval and retrieval
post-processed with decadal densities, respectively. Figure 8 shows scatter
plots for the whole Northern Hemisphere for the baseline (Fig. 8a) and the
post-processed datasets (Fig. 8b), and as expected, post-processing reduces
overestimation of SWE values between 10 and 100 mm. Figure 8 also shows
density scatter plots for the baseline and the post-processed datasets for
Eurasia (Fig. 8c, d) and North America (Fig. 8e, f). The post-processed
Eurasian dataset shows similar improvements as the overall Northern
Hemisphere dataset; overestimation of SWE values between 10 and 100 mm has
been mitigated. For Eurasia, post-processing improves estimations every
month when SWE values up to 500 mm are considered, and the biggest
improvement in RMSE happens in December (over 5 mm). When SWE values only up
to 150 mm are considered, we see similar big improvement in December, but in
April baseline retrieval produces better results than the post-processed
dataset.
North American datasets also show some improvements but not as clearly as
the Eurasian dataset. For North America SWE values are improved for December
and April when SWE values up to 500 mm are considered. When SWE values up to
150 mm are considered, improvements are seen only in December. Figure 9,
which shows the mean retrieval error and standard deviation of the error for
baseline and post-processed retrievals for the Northern Hemisphere, Eurasia,
and North America, agrees with these findings. Mean errors for North America
are similar for SWE values below 100 mm for the baseline and post-processed
retrievals, but for larger values, the mean errors of the post-processed
dataset are smaller than the errors of the baseline set. For Eurasia and the
Northern Hemisphere, the mean error is systematically smaller for the
post-processed dataset than for the baseline dataset. Figure 10 shows SWE
maps for 6 February 2011, for the baseline and post-processed retrievals.
Figure 10 also shows the difference between these two SWE maps (baseline minus
post-processed). Maps show how SWE values are lower in the post-processed
maps, and the map of differences reveals that post-processing causes bigger
changes in Eurasia than in North America.
Comparisons of the mean error and standard deviations between
baseline and post-processed SWE datasets.
Discussion
GlobSnow 3.0 SWE retrieval accuracy is affected by the overestimation of
small SWE values and underestimation of large SWE values. Passive microwave
SWE retrievals tend to systematically underestimate SWE under deep snow
conditions as the snowpack changes from scattering medium to a source of
emission, which becomes significant for SWE retrievals over about 150 mm.
While the GlobSnow retrieval estimates large SWE values better than
stand-alone passive microwave SWE retrieval, errors are still evident for
deep snow. The underestimation of SWE in GlobSnow retrieval under deep snow
conditions is additionally driven by the constant density that relates snow
depth and SWE. The constant density tends to decrease SWE estimates for late
winter when the snowpacks are usually denser than the constant density
applied. Post-processing with dynamic densities improves the overall deep
snow retrieval performance as the SWE values are scaled up with larger
dynamic snow density. Similarly, the post-processing helps to improve the
overestimation of small SWE values. The constant snow density used in the
retrieval tends to be too large in the early winter when the snow is fresh,
and the density is at its lowest.
SWE maps for baseline GSv3.0 retrieval (a),
post-processed retrieval (b), and difference between GSv3.0 and
post-processed retrieval (post-processed subtracted from the baseline) for
6 February 2011. The post-processed SWE values are lower as overestimation
of small SWE values is reduced.
Comparisons of the mean error and standard deviations
between baseline and datasets post-processed with decadal snow densities and
densities based on fixed snow classes according to Sturm et al. (2010).
Even though the improvements obtained by post-processing for the whole
winter are not large (RMSE reduced by about 1 mm), significant improvements
are still gained. The small changes in the whole dataset are expected, as most
of the validation data are from areas where there are no large mistakes in
the baseline product and snow density is close to the constant snow density
of 240 km m-3 in mid-winter. However, the monthly analyses (Table 3)
show that the improvements in overestimation of SWE values in early winter
(December) are significant: the RMSE is reduced by about 5 (7) mm for SWE
values up to 500 (150) mm, and bias is reduced by 15 mm for both versions of
validation. Figure 7 also shows that significant improvements (5–10 mm
smaller mean error) are obtained with post-processing for SWE < 100 mm and SWE > 170 mm.
Improvements produced by post-processing are more significant for
Eurasia than for North America. The North American reference
measurements consist of both snow transect and point measurements, which may
affect the results. The measurement frequency of the daily SNOTEL data
also differs from the Eurasian and Canadian data, which have measurements from
every 10 to 15 d. However, when SNOTEL data were resampled to 10 d intervals and validation parameters were recalculated, no significant
differences were detected. Another possible source of error in the SNOTEL data
is the location of snow depth sensor. In some locations, snow depth is not
measured on top of the snow pillow but next to the pillow, and this may
affect the accuracy of the snow density values. However, it should be noted
that the GlobSnow retrieval is known to have worse performance in Canada,
and this is partly due to higher average SWE compared to Eurasia (Mortimer
et al., 2020).
As shown by the results, post-processing with dynamic snow densities can be
used to improve existing datasets, and the post-processing procedure is
straightforward to perform. However, implementing dynamic snow densities
directly into the retrieval could possibly produce even more notable
improvements and is a key research topic to be studied in the future. Snow
density is one of the input parameters of the HUT snow emission model,
determining the absorption coefficient in snow, refraction, and
transmissivity at the air–snow interface and transmissivity at the
snow–ground interface through modelled permittivity of the snow layer
(Pulliainen et al., 1999). The HUT model is used for determining effective
snow grain size over weather station locations as well as for obtaining the
final SWE estimates using numeric model inversion (Takala et al., 2011). The
final snow grain size (and its variance) at each location is the average
grain size of the six nearest stations. If the true snow density between
stations significantly changes, the variance of the estimated snow grain
sizes increases. This in turn potentially reduces the weight of radiometer
measurements on the final SWE estimation, as well as the accuracy of the
individual grain size estimates. Similarly, applying a wrong density value
in the final retrieval step potentially deteriorates the accuracy of the HUT
model and thus retrieval skill.
Although better results might be achieved with implementing dynamic
densities into the retrieval, post-processing is justified as it can be used
to study different implementations of the snow densities with relative ease,
and the results obtained with post-processing are similar to results
obtained with implementing dynamic densities in retrieval. Running the full
retrieval algorithm is very time consuming and as such not well suited for
testing small changes in methodology. Post-processing can be used to study
which densities and methodologies produce the best results, and these
densities can then be implemented into a final retrieval product. Also, as
some areas have more snow density information available than others, the
introduced post-processing methods provide feasible tools to improve the
accuracy of the global GlobSnow-data-based SWE estimates for regional
hydrological applications in such areas where snow density information is
available.
Different approaches for varying snow density for satellite-based SWE
retrievals have been used. The AMSR-E v1.0 product (Kelly, 2009) uses
spatially varying but temporally static snow density maps based on snow
classes suggested in Sturm et al. (1995). However, evaluation of this
product by Tedesco and Narvekar (2010) pointed out the need to also have
temporal variability in the snow density. The AMSR-E SWE v2.0 product uses
spatially and temporally varying snow density maps based on Sturm et al. (2010) for converting snow depth to SWE (Tedesco and Jeyaratnam, 2016). However, the
densities based Sturm et al. (2010) cause large overestimation of small SWE
values when used for post-processing the GlobSnow product as seen in Fig. 11,
which shows the mean retrieval error for GSv3.0 SWE values post-processed
with densities based on the Sturm et al. (2010) method for Eurasia for
2000–2009.
In this research, linear interpolation was used for temporal interpolation
to obtain density measurements for days without any measurements. However,
snow density measurements may contain some errors, and these errors can
influence the results of the linear interpolation. Thus, alternative
interpolation methods for determining behaviour of snow density throughout
the snow season, such as higher-degree polynomial interpolation of averaged
values or yearly values, could be evaluated in future investigations.
Conclusions
In this study spatially and temporally changing snow density fields were
implemented using snow density measurements from Eurasia and North America. The development of dynamic snow density for GlobSnow retrieval was implemented as part of the European Space Agency Climate Change Initiative – Snow (Snow CCI) project and will be implemented in future SWE retrievals.
The dynamic snow density fields were used to post-process GlobSnow version
3.0 SWE retrievals. Post-processing was found to improve overestimation of
small SWE values between 10–100 mm and underestimation of large SWE values.
This indicates that the constant density used in the baseline retrieval is
too large for early winter and too small for late winter. The overall
results indicate a clear path forward to improve the overall GlobSnow SWE
retrieval methodology by application of dynamic snow density in the
post-processing scheme.
Code and data availability
The GlobSnow code is available at
http://www.globsnow.info/swe/archive_v3.0/source_codes/ (Luojus et al., 2020a), and the GlobSnow v3.0 data are available at
https://www.globsnow.info/swe/archive_v3.0/L3A_daily_SWE/ (Luojus et al., 2020b). The snow density processing code is available
upon request from the corresponding author.
Author contributions
PV, KL, JL, and JP conceived the concept
of the study. PV performed the analyses, data processing, and computing and
produced the first draft of the manuscript, which was subsequently edited by
KL, JL, and JP. MT and MM contributed to the analytical tools and
methods.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Financial support
This research has been supported by the ESA CCI+ Snow project (grant no. 4000124098/18/I-NB).
Review statement
This paper was edited by Carrie Vuyovich and reviewed by two anonymous referees.
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