Contributors: Miriam Kosmale, Kari Luojus, Mikko Moisander, Matias Takala, Pinja Venäläinen (Finnish Meteorological Institute)

Issued by: Finnish Meteorological Institute / Miriam Kosmale, Kari Luojus

Date: 30 Jun 2025 

Ref: C3S2_313d_ENVEO.WP3-DDP-SWE-v1.0_202506_SWE_ATBD

Official reference number service contract: 2024/C3S2_313d_ENVEO/SC1

History of modifications

List of datasets covered by this document

Acronyms

General definitions

Accuracy: is defined as the “closeness of the agreement between a measured quantity value and a true quantity value of the measurand”. The concept “measurement accuracy” is not a quantity and is not given a numerical quantity value. (GCOS-200, p293)

Brightness Temperature is the measurand of passive microwave remote sensing systems (radiometers). Brightness temperature (in degree Kelvin) is a function of kinetic temperature and emissivity. Depending on the depth of a snowback the brightness temperature observed from the satellite and channel varies. The emissivity of a snowpack originates from its snow surface, characteristics of its deeper snow layers and from the ground beneath. Attenuation in emissivity and hence brightness temperature depending on the underlying snow depth is lower at lower frequencies. Means of a brightness temperature gradient between two channels allow for estimating snow characteristics. 

Backscatter is the measurand of active microwave remote sensing systems (radar). As the energy pulses emitted by the radar hit the surface, a scattering effect occurs and part of the energy is reflected back. 

Bias: “Bias is defined as an estimate of the systematic measurement error” (GCOS-200, p293)

Error: “The term error refers to the deviation of a single measurement (estimate) from the true value of the quantity being measured or estimated, which is always unknown” (Gruber et al., 2020)

EASE grid: Equal-Area Scalable Earth (EASE) Grid, which is a system of projections that is used by NASA for distribution of some of the polar orbiting satellite sensors. (ref to EPSG definition: https://epsg.io/6933 and https://epsg.io/6933 and https://nsidc.org/data/user-resources/help-center/guide-ease-grids). EASE grids utilise an equal-area projection which minimises the amount of distortion over the poles, using the Northern and Southern Hemisphere projections, and on other key areas of the globe, using the temperate and global projections.

Freshet: Freshet is used to describe an annual high water event on rivers resulting from snowmelt and river ice melting

GCOS Breakthrough (B): An Essential Climate Variable (ECV) requirement level set by Global Climate Observing System (GCOS) which "[...], if achieved, would result in a significant improvement for the targeted application. The breakthrough value may also indicate the level at which specified uses within climate monitoring become possible. It may be appropriate to have different breakthrough values for different uses." (GCOS-244)  

GCOS Goal (G): An Essential Climate Variable (ECV) requirement level set by Global Climate Observing System (GCOS) which "[...], if achieved, would be an ideal requirement above which further improvements are not necessary." (GCOS-244)  

GCOS Threshold (T): An Essential Climate Variable (ECV) requirement level set by Global Climate Observing System (GCOS) which "[...], if achieved, would be the minimum requirement to be met to ensure that data are useful." (GCOS-244)  

Radiometer: Spaceborne radiometers are satellite-carried sensors that measure energy in the microwave domain emitted by the Earth. The amount of radiation emitted by an object in the microwave domain (~1-20 GHz). The observed quantity is called “brightness temperature” and depends on kinetic temperature of an object and its emissivity. Due to the high emissivity of water compared to dry matter, radiometer measurements of Earth’s surface contain information in the water content in the observed area.

Satellite processing level 0: Raw measured signal at satellite: Reconstructed, unprocessed instrument and payload data at full resolution, with any and all communications artifacts (e.g., synchronization frames, communications headers, duplicate data) removed.

Satellite processing level 1: Level 1A (L1A) data are reconstructed, unprocessed instrument data at full resolution, time-referenced, and annotated with ancillary information. L1C data are L1B data that include new variables to describe the measured spectra. 

Satellite processing level 2: Derived geophysical variables at the same resolution and location as L1 source data. For SWE products derived from PMR satellite observations the projection used is Equal-Area Scalable Earth (EASE) Grid.

Satellite processing level 3: Variables mapped on uniform space-time grid scales; for C3S SWE is a regular 0.1 degree latitude-longitude grid and daily temporal resolution.

SMMR: Scanning Multichannel Microwave Radiometer sensor onboard Nimbus-7 satellites in space between 1979-1987. The passive microwave radiometer data is used to derive Snow Water Equivalent.

SSM/I: Special Sensor Microwave/Imager is a seven-channel, four-frequency, linearly polarized passive microwave radiometer system. It is flown on board the United States Air Force Defense Meteorological Satellite Program running from 1987-2008. The passive microwave radiometer data is used to derive Snow Water Equivalent.

SSMIS: Special Sensor Microwave Imager / Sounder is a 24-channel, 21-frequency, linearly polarized passive microwave radiometer system. The instrument is flown on board the United States Air Force Defense Meteorological Satellite Program F-16, F-17, F-18 and F-19 satellites, which were launched in October 2003, November 2006, October 2009, and April 2014, respectively. It is the successor to the Special Sensor Microwave/Imager (SSM/I). The passive microwave radiometer data is used to derive Snow Water Equivalent.

Snow Water Equivalent retrieval algorithm: The here described snow water equivalent (SWE) retrieval algorithm combines information from satellite-based microwave radiometer and optical spectrometer observations with ground-based weather station snow depth (SD) measurements and produces daily hemispherical scale SWE estimates.

Snow Water Equivalent (SWE): Snow water equivalent (SWE) is a measure indicating the amount of accumulated snow on land surfaces. SWE represents the resulting water column of a snowpack melt in place. SWE is the product of depth and density of a snowpack. => Snow water equivalent (SWE) = snow depth (SD) * snow density (ρ)

Snowpack: An accumulation of precipitated snow at the surface that compresses with time and melts seasonally. Snowpacks are an important water resource for the surrounding area.

Stability may be thought of as the extent to which the uncertainty of measurement remains constant with time. [...] “stability” refer to the maximum acceptable change in systematic error, usually per decade. (GCOS-200, p293)

Uncertainty: Uncertainty (of measurement) non-negative parameter, associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand. (GCOS-200). Satellite retrievals of SWE usually contain considerable systematic errors which, especially for model calibration and refinement, provide better insight when estimated separate from random errors. Therefore, we use the term bias to refer to systematic errors only and the term uncertainty to refer to random errors only, specifically to their standard deviation (or variance).

Executive summary

The Algorithm Theoretical Basis Document (ATBD) is part of the Copernicus Climate Change Service (C3S) C3S2_313d for the cryosphere. The document summarises the Climate Data Record (CDR) and Intermediate Climate Data Record (ICDR) for Snow Water Equivalent (SWE), where the ICDR represent consistent extensions of the CDR. 

This CDR provides daily estimates on Snow Water Equivalent (SWE) with a spatial coverage of the Northern hemisphere. The data is derived from passive microwave radiometer (PMR) measurements onboard polar-orbiting satellites, which have been available since 1979 to present. 

This document describes the physical and mathematical basis of algorithms and systems used to generate SWE, including the scientific justification for the algorithms (i.e. underlying physics) selected to derive the product, an outline of the used approach, as well as a description of the error propagation and identification of major sources of uncertainty, and a listing of the assumptions and limitations of the algorithm. Sections 1 summaries the satellite input data with all sensors and missions used for the long term time-series of snow water equivalent. Section 2 briefly describes the auxiliary data needed for the retrieval algorithm. The retrieval method itself is given in section 3. It contains sufficient detail to be able to serve as a reference document for implementing the production systems, including the choice of the Fundamental Data Record used as baseline reference for L3/L4 products, and ensure full traceability to the source. The document also contains a short description of the data products for SWE and file formats. For a more detailed description on the product also refer to the Snow Water Equivalent (SWE) version 1.0: Product User Guide and Specification (PUGS). Information about the quality control and product validation is given in the Snow Water Equivalent (SWE) version 1.0: Product Quality Assessment Report (PQAR).

Missions and Instruments

The retrieval methodology for the production of Snow Water Equivalent (SWE), combines satellite Passive Microwave Radiometer (PMR) measurements with ground-based synoptic weather stations observations by a Bayesian non-linear iterative assimilation. It is built on the GlobSnow SWE and ESA CCI production systems, which have been further developed by improving various aspects of the processing chain, including time-varying snow density, influence of land cover and implementation of techniques for enhancement of brightness temperature resolution. The daily global time series is based on spaceborne observations from Scanning Multi-channel Microwave Radiometer (SMMR), Special Sensor Microwave Imager (SSM/I) and Special Sensor Microwave Imager/Sounder (SSMIS) data, onboard Defense Meteorological Satellite Program satellite series (DMSP) F-series satellites starting in 1979 to present day (Figure 1). The retrieval uses passive microwave radiometer (PMR) data considering the change of brightness temperature due to different snow depth, snow density, grain size and snow characteristics. 

The advantage of using PMR measurements for Earth observations lies in the fact that at those frequencies the signal is not affected by clouds or does not require sunlight. This combined with the wide swaths of the satellite instruments allow for continuous daily observations of snow without any undue gaps in the time series.

Figure 1: Schedule of satellite Passive Microwave Radiometer (PMR) sensors used for production of C3S SWE (ref.: https://nsidc.org/sites/default/files/documents/technical-reference/smmr-ssmi-ssmis-sensors.pdf)

Passive Microwave Systems

The space borne passive microwave radiometer brightness temperature measurements are derived from the SMMR, SSM/I and SSMIS instruments on board NIMBUS-7 and the DSMP series satellites F8, F11, F13, F17 and F18 respectively. The most important frequencies for snow detection and SWE retrieval are 19 and 37 GHz. Channels close to these frequencies are available from all instruments, although with different native footprint dimensions. These differences in swath level resolution are removed through TB re-sampling to the EASE2-Grid 2.0 as described in Brodzik et al. (2024). The nominal spatial resolutions of the data grids are 3.125 km, 6.25 km and 12.5 km  depending on the frequency.  Some data gaps exist both in time and space within the satellite passive microwave data record. SMMR had a narrower swath width (780 km), compared to the later instruments with more than double of swath widths (SSM/I and SSMIS with ~1400km). Due to the smaller swath width of the older sensor SMMR and due to power constraints this sensor allows only observations bi-daily for the period 1979–1987. 

SMMR was a ten-channel sensor that measured orthogonally polarized antenna temperature data in microwave frequencies from 6.6 to 37.0 GHz. The SSM/I sensor was a seven-channel, four-frequency, orthogonally polarized, passive microwave radiometric system that measured atmospheric, ocean, and terrain microwave brightness temperatures at 19.35, 22.2, 37.0, and 85.5 GHz. SSMIS is a 24-channel, passive microwave radiometer designed to obtain a variety of polarized atmospheric temperature, moisture, and land variables under most weather conditions. Channel frequencies range from 19 GHz to 183 GHz.

Nimbus-7 SMMR (NASA)

Scanning Multi-channel Microwave Radiometer (SMMR) was a ten-channel sensor that measured orthogonally polarized antenna temperature data in following microwave frequencies: 6.6, 10.7, 18.0, 21.0, and 37.0 GHz. Table 1 gives a summary about the technical details of the SMMR sensor. 

Table 1: Summary of satellite sensor SMMR

DMSP-SSM/I (NESDIS NOAA)

The SSM/I is a seven-channel, four frequency, linearly-polarized, passive microwave radiometric system which measures atmospheric, ocean and terrain microwave brightness temperatures at 19.35, 22.235, 37.0 and 85.5 GHz. The data are used to obtain synoptic maps of critical atmospheric, oceanographic and selected land parameters on a global scale. Table 2 summarises the techincal details of the SSM/I sensor. 

Table 2: Summary of satellite sensor SSM/I

DMSP-SSMIS (NESDIS NOAA)

Beginning with the launch of the DMSP F-16 satellite on 18 October 2003, the SSMIS marks the commencement of a series of passive microwave conically scanning imagers. SSMIS improves upon the surface and atmospheric retrievals of the Special Sensor Microwave Imager (SSM/I) and the SSMIS imaging and sounding sensors share the same viewing geometry, thereby allowing surface parameters to be retrieved simultaneously. The SSMIS instrument is able to estimate atmospheric temperature, moisture, and surface parameters from data collected at frequencies ranging from 19 to 183 GHz over a swath width of 1707 km. SSMIS is currently carried aboard DMSP-F17, and -F18 satellites. All technical details of the SSMIS sensor are given in Table 3. 

Table 3: Summary of satellite sensor SSMIS

Input and auxiliary data

As described in the section above the retrieval is based on space borne passive microwave radiometer brightness temperature measurements from the SMMR, SSM/I and SSMIS instruments. Beside that the retrieval algorithm is using synoptic Snow Depth (SD) in-situ observations, which are assimilated to the algorithm. 

SD data is available through FMI near real time weather observations database and has been augmented from several archive sources, such as European Centre for Medium-Range Weather Forecasts (ECMWF), NOAA National Climatic Data Center (NCDC), All-Russia Research Institute of Hydrometeorological Information - World Data Centre (RIHMI-WDC) and Meteorological Service of Canada (MSC) archives. The passive microwave radiometer data record has been acquired through NSIDC archives containing the SMMR, SSM/I and SSMIS calibrated brightness temperature data record (Brodzik et al., 2024).

Snow masks

The algorithm deriving Snow Water Equivalent (SWE), described in section 3.3.2, can be used to measure snow packs roughly between 0.05 m and 1.00 m in thickness and only under dry snow conditions. Depth less than 0. 05 m cannot be reliable retrieved because the brightness temperature difference between the two frequencies, falls within 2 K detection precision of the radiometer instruments used. This leads that areas on edges of snow covered areas with relatively low snow depth are difficult to retrieve from PMR measurements. In a post-processing step snowmasks from external datasets are overlaid to the direct SWE retrieval output to account for adequate snow clearance. More details are also described in section 3.3.

CryoClim

SWE products before summer 2018 have a CryoClim-based snowmask added to the SWE. The technical details of this dataset are summarised in Table 4.

The CryoClim fractional snow cover (FSC) product is based on a multi-sensor time-series fusion algorithm combining observations by optical and passive microwave radiometer (PMR) data. The product combines an historical record of AVHRR sensor data with PMR data from the SMMR, SSM/I and SSMIS sensors. CryoClim FSC time series provides daily products for the period 1982 – 2019 and is applied for SWE products until the winter season of 2017/2018. For the early years 1979-1981, where CryoClim was not available a simple snowmask scheme is used, which is based on a simple channel difference of PMR measurements of the same sensors used for the C3S retrieval algorithm. A more detailed description is given in section 3.3.2.1.

Table 4: Summary of auxiliary data CryoClim snowmask

GlobLand SCE cumulative snowmask

SWE products starting from 01.07.2018 have a cumulative snowmask applied, which had been derived from Copernicus Land monitoring service snow cover extend product. In the following the specifics for the applied snowmasks is given. The cumulative snowmask has been created based on Snow Cover Extend (SCE) data from Copernicus Land Monitoring Service CLMS. The table below gives a short summary of the auxilliary data used for the creation of the snowmask. The method is briefly described in section 3.3.2, while some technical details are given in Table 5.

Table 5: Summary of auxiliary data: cumulative snowmask based on CLMS SCE product

Snow depth information from synoptic weather observation for SWE retrieval algorithm

Weather station snow depth (SD) data are acquired from multiple sources. ECMWF dataset for Eurasia, acquired for years from 1979 to 2018, is complemented by RIHMI-WDC data which covers in-situ measurements covering Russia from the years 1979 to 2018 (Bulygina et al., 2011).  Global Historical Climatology Network (GHCN) daily SD data by NOAA from 1979 to 2018 is used as the main dataset for North America. This dataset is enhanced with data from the Meteorological Service of Canada for years 1979 to 2018 and a large set of measurements from across the continental United States for latitudes above 40° for years 1979 to 2009.

Each of the five synoptic SD datasets are filtered for duplicate observations. Observations are considered duplicates if the difference between latitude and longitude of two stations is less than 0.001° in which case the median of the observations is used (in case of 2 duplicates, the average is used). After initial filtering, datasets are combined into Eurasian and North American datasets. The two combined datasets are again median filtered for duplicate observations. This time, observations are considered duplicates if they are in the same (25km x 25km) EASE-grid pixel, which can occur in regions with a relatively dense surface observing network.

The Eurasian and North American synoptic weather station datasets are then filtered for extremely high SD values (observations over 500 cm are removed). After that, stations with at least 20 measurements for at least 5 separate years are kept, so that stations which report only for brief time periods are removed. Stations where the measured SD is zero for more than 95 % of the measurements are also removed. Median filtering is then applied to replace values that differ more than 20 cm from the median value over a 9-day window. Next, stations with unusually deep snow conditions are filtered out if the mean March SWE exceeds 150 cm in at least 50% of the years that the station has had at least 20 measurements. Lastly, all SD observations above 200 cm are filtered out.

The remaining filtering step is conducted for the North American dataset that has a large fraction of 0 cm observations at lower latitudes (the data volume is computationally excessive for the SWE retrieval without this reduction step) . For latitudes from 30° to 45°, a 2° by 2° grid is created and the mean of all (filtered) SD observations in each 2° cell is used. For latitude from 45° to 50°, a 1° by 1° grids are used. Data from latitudes above 50° is not reduced through gridding because observations are sparse. Data reduction to 1° and 2° grids for lower latitudes is not applied for Eurasia (reduction is necessary to make the North American dataset computationally feasible).

The initial combined Eurasian dataset has 26 739 497 observations. The final Eurasian dataset after the described filtering steps contains 12 106 721 observations. Initial combined North American dataset has 162 689 571 observations. After the filtering and data reduction steps, the final North American dataset contains 9 638 050 observations, which are consistently available for the various seasons and over different decades.

Algorithm description

The CDR and ICDR provide information on Snow Water Equivalent (SWE) derived by satellite measurements. The products cover the Northern hemisphere from passive microwave radiometer measurements onboard on polar-orbiting satellites since 1979 to present. The algorithm to derive SWE is based on the latest research developments within European Space Agency (ESA) Climate Change Initiative (CCI) Snow Water Equivalent production with latest improvements in the algorithm applied for the product of C3S. 

The SWE retrieval algorithm combines information from satellite-based microwave radiometer and optical spectrometer observations with ground-based weather station snow depth (SD) measurements and produces daily hemispherical scale SWE estimates. In the following section the retrieval scheme is described, which consists of the full processing chain from Level-1 PMR satellite K- and Ka-band (19 GHz and 37 GHz respectively) measurements over Level-2 native satellite EASE-Grid projection to the final Level-3 processing stage. 

SWE baseline retrieval algorithm

Retrieval evolution and outline

The basis of the SWE processing system is presented by Pulliainen (2006), Takala et al. (2011) and Luojus et al (2021). As applied here, estimates of SWE (snow depth) based on emission model inversion of two frequencies, 19.35 and 37.0 GHz, are first calibrated over EASE grid cells with weather station measurements of SD available. Snow grain size is used in the model as a scalable model input parameter (being determined from the input radiometer and weather station data). These values of grain size are used to construct a Kriging interpolated background map of the effective grain size, including an estimate of the effective grain size error. The map is then used as an input in model inversion over the span of available radiometer observations, providing an estimate of SWE. In the inversion process, the effective grain size in each grid cell is weighed with its respective error estimate. The weather station observations of SD are further interpolated to provide a first guess estimate of SD (or SWE). The SWE estimate map and SD map from weather station observations are combined using a Bayesian spatial assimilation approach to provide the final SWE estimates, with the interpolated SD field constraining radiometer retrievals. A snow density value is applied to each grid cell to connect depth to SWE. Areas of wet snow are masked according to observed brightness temperature values using empirical thresholds, as model inversion of SD/SWE over areas of wet snow is not feasible due to the saturated brightness temperature response.

The snow emission model applied is the semi-empirical Helsinki University of Technology (HUT) snow emission model (Pulliainen et al., 1999). The model calculates the brightness temperature from a single layer homogeneous snowpack covering frozen ground in the frequency range of 11 to 94 GHz. Input parameters of the model include snowpack depth, density, effective grain size, snow volumetric moisture and temperature. Separate modules account for ground emission and the effect of vegetation and the atmosphere.

Basic underlying assumptions

The underlying principle in passive microwave retrieval of SWE is based on observing the attenuating effect of snow cover on the naturally emitted brightness temperature from the ground surface. The ground brightness temperature is scattered and absorbed by the overlying snow medium, resulting typically in a decreasing brightness temperature with increasing (dry) snow mass. The scattering intensity increases as the wavelength approaches the size of the scattering particles. Considering that individual snow particles are measured in millimetres, high microwave frequencies (short wavelengths) will be scattered more than low frequencies (long wavelengths). The intensity of absorption can be related to the dielectric properties of snow, with snow density largely defining the permittivity for dry snow. Absorption at microwave frequencies increases dramatically with the inclusion of free water (moisture) in snow, resulting in distinct differences of microwave signatures from dry and wet snowpacks.

Initial investigations by e.g. Ulaby and Stiles (1980) pointed out the sensitivity of microwave emission from snowpacks to the total water equivalent. This led to the development of various retrieval approaches of SWE from passive microwave instruments in space (e.g. Rango et al., 1979; Künzi et al., 1982). From the available set of observed frequencies, most algorithms for retrieval of SWE employ a 36-37 GHz (l » 8.1 mm) and a 18-19 GHz (l » 15.8 mm) channel in combination. The scattering of a 18-19 GHz signal in snow is considered smaller when compared to 36-37 GHz, while the emissivity of frozen soil and snow is estimated to be largely similar at both frequencies. Observing the brightness temperature difference of the two channels allows to establish a relation with the detected signal and snow depth (or SWE), with the additional benefit that the effect of variations in physical temperature on the measured brightness temperature are reduced. Similarly, observing a channel difference reduces or even cancels out systematic errors of the observation, provided that the errors in the two observations are similar (e.g. due to using common calibration targets on a space-borne sensor). Typically, the vertically polarized channel is preferred due to the inherent decreased sensitivity to snow layering (e.g. Rees et al., 2010).

Forward model

The HUT snow emission model (Pulliainen et al., 1999) is a radiative transfer-based, semi-empirical model which calculates the emission from a single homogenous snowpack. The model assumes that most scattering of radiation propagating in a snowpack is concentrated in the forward direction (of propagation). Based on this assumption, the HUT model applies the delta-Eddington approximation to the radiative transfer equation, applying an empirical constant to determine the forward scattered intensity of snow. The radiative transfer equation essentially assumes only the forward propagating flux; however, the propagation of emission is considered in both up- and downward directions in snow (see e.g., Pan et al., 2015). The forest transmissivity model by Kruopis et al. (1999) is used to calculate forest transmissivity. Correction for atmospheric transmissivity and emission is provided by a statistical approach based on the 55% fractile of atmospheric conditions in northern latitudes (Pulliainen et al., 1993).

Calculation of brightness temperature for a satellite scene

For a satellite scene consisting of a mixture of non-forested terrain, forests, and ice (and snow) covered lakes, the Beneath-of-Atmosphere brightness temperature is calculated so that

Eq. 1

Where FF is the forest fraction and LF the lake fraction of a given grid cell. T_B,snow,T_B,forest, and T_{B, lake} are the brightness temperatures emitted from non-forested terrain (ground/snow), forested terrain and over lake ice. Land cover fractions FF and LF are determined from ESA GlobCover data resampled to the 12.5 km EASE2 grid).

Brightness temperature from snow-covered ground

The brightness temperature T_B,snow for snow-covered, non-forested terrain is calculated using the Helsinki University of Technology (HUT) snow emission model (Pulliainen et al., 1999). The model is a radiative transfer-based, semi-empirical model which calculates the emission from a single homogenous snowpack.

The absorption coefficient in the HUT model is determined from the complex dielectric constant of dry snow, applying the Polder-van Santen mixing model for the imaginary part (Hallikainen et al., 1986). The calculation of the real part of the dielectric constant for dry snow is presented by Mätzler (1987). Snow wetness and salinity content can be simulated if required; the modified dielectric constants for wet or saline snow are described through empirical formulae.  Emission from the snow layer is considered as both up-and down-welling emission. These are, in turn, reflected from interfaces between layers (air-snow, snow-ground). The transmission and multiple reflections between layers interfaces are calculated using the incoherent power transfer approach.

Applying the delta-Eddington approximation to the radiative transfer equation, the HUT model assumes that most of the scattered radiation in a snowpack is concentrated in the forward direction (of propagation) due to multiple scattering within the snow media. This assumption is based on previous studies by Hallikainen et al. (1987). The emission of the snow medium (up- or downwelling) with thickness  just before the medium boundary can then be obtained from (Pulliainen et al., 1999)

Eq. 2

Where  T_snow is the physical snow temperature, κ_a the absorption coefficient,  κ_s the scattering coefficient, κ_e=κ_a + κ_s the extinction coefficient, q an empirical parameter determining the portion of forward scattered radiation,  d₀ the depth of the snow layer, and  θ the angle of propagation. An empirical equation is used to relate the snow extinction coefficient to frequency and snow grain size D_obs (Hallikainen et al., 1987). For frequencies 1 to 60 GHz;

Eq. 3

where f is the frequency in GHz and D_obs is the observed scattering particle (snow grain) diameter in millimetres. The empirical parameter q in Eq .2 has been defined for snow by fitting the HUT model to experimental snow slab emission data (Pulliainen et al., 1999). A common value of q=0.96 was found to be applicable for all frequencies in this range.

It should be noted that the parameter q=0.96 includes effects from multiple scattering in the snowpack and is as such relatively high compared to a case of singular scattering following e.g. the Rayleigh scattering approximation. As pointed out by Hallikainen et al. (1987), in snow the losses due to scattering are approximately equal to generation of incoherent intensity by scattering. However, Pan et al. (2015) noted that the omission of the backward scattering component (which in the case of HUT would be (1-q) = 0.04) will lead to underestimation of brightness temperature for deep snowpacks.

Ground reflectivity

The rough bare soil reflectivity model by Wegmüller and Mätzler (1999) is applied to simulate the upwelling brightness temperature T_{B, gnd} of the soil medium. The model is semi-empirical and is based on measurements of soil samples on 1–100 GHz. The behaviour of reflectivity on V polarization is based on results from H polarization due to more problematic modelling of reflectivity at V polarization. The equations for rough bare soil reflectivity are:

Eq. 4

Eq. 5

where   r_h,Fresnel is the Fresnel reflectivity on H polarization, k is the wave number,  h_gnd is the standard deviation of surface height and   θ is the incidence angle. The Fresnel reflectivity is dependent on permittivities of snow (calculated by HUT snow model) and soil. The relative dielectric constant of frozen soil is assumed to be constant ε_i,soil  on all frequencies based on work by Hallikainen et al. (1985).

Forest vegetation

The brightness temperature over forested portions of the grid cell T_{B, forest} is derived from  T_B,snow using a simple zeroth-order approach so that

Eq. 6

Where t_veg is the (one-way transmissivity of the forest vegetation layer, T_veg the physical temperature of the vegetation (considered to be equal to air, snow and ground temperatures, Tveg = Tair = Tsnow = Tgnd = -5°C ) and e_snow the emissivity of the snow covered ground system. One-way forest transmissivity  is obtained from a study by Cohen et al. (2015) so that

Eq. 7

Where κ_e is the forest vegetation extinction coefficient, and SV the forest stem volume (biomass). Based on an airborne survey, Cohen et al. (2015) determined κ_e for 10.65, 18.7 and 36.5 GHz; Figure 2 shows the obtained model fits to observed airborne brightness temperatures, as well as comparisons to transmissivity models by Kruopis et al. (1999) and Langlois et al. (2011). The model by Kruopis et al. (1999) applied in GlobSnow products (1.0 and 2.0); had a distinct problem of the model is saturation for even model stem volumes (50 m3 ha^-1 at 18.7 GHz and 100 m3 ha^-1 at 36.5 GHz), which contradicts observational data. In fact, the earlier GlobSnow products applied a constant stem volume of 80 m3 ha^-1 for the entire Northern Hemisphere, due to lack of a reliable stem volume dataset at the time of development of those products.

Snow Water Equivalent (SWE) version 1.0: Algorithm Theoretical Basis Document (ATBD)#Eq. 3 and the derived extinction coefficients of  κ_e= 0.007 at 18.7 GHz and  κ_e= 0.011 at 36.5 GHz (for V-polarization) derived by Cohen et al. (2015) are applied to replace the transmissivity model by Kruopis et al. (1999). The ESA BIOMASAR (Santoro et al., 2011; Santoro et al., 2015) stem volume estimates are applied to calculate spatially variable transmissivity, replacing the constant stem volume applied in earlier versions.

Figure 2:  Forest transmissivity using fit of zeroth order model to airborne brightness temperature observations over Sodankylä, Finland. Cohen et al., 2015. Comparison to model predictions of Kruopis et al. (1999) and Langlois et al. (2011). Images show comparisons for different frequencies and polarisation

Lake scenes

Earlier versions of the algorithm used in GlobSnow considered the brightness temperature over within-pixel lakes equal to that of snow-covered ground. T_{B, lake} is calculated separately using the multiple-layer version of the HUT snow emission model (Lemmetyinen et al., 2010), considering frozen lakes as a stacked system of water, ice and snow. While introducing the cumulative effect of multiple reflections in a system of stacked layers, the original formulation of radiation scattering and absorption in individual snow layers was not altered. The mathematical solution is presented by Lemmetyinen et al. (2010) and the practical application for lake ice by Lemmetyinen et al. (2011).

Brightness temperature of ice layers

For a layer consisting of pure ice, the HUT model considers scattering to be negligible. Therefore, it is assumed that the proportion of scattering is completely directed in the forward direction (q=1). In other words, the extinction in an ice layer depends on the absorption

Eq. 8

Layers which can be considered to be pure ice and therefore applicable to Eq. 8 are present in nature mainly in the form of lake and sea ice. Even with these, snow-ice induced by flooding events and bubble formation by upwelling gases may induce scattering effects in ice which are not considered in the above equation.

For calculating T_{B, lake} in the SWE retrieval iterative process, the depth of the snow layer on ice is considered to be always half of the equivalent snowpack on land. Snow density and grain size are considered to be identical. The depth (thickness) of the ice layer is considered to be a constant 50 cm. The physical temperature of ice is considered to be equal to snow temperature (T_ice = T_snow = -5°C), while the temperature of the underlying water layer is considered to be T_water = 0°C.

Effect of ice surface roughness

Emission from the medium under the stacked snow (or ice) layers is calculated based on the estimated dielectric constant of the medium and the roughness of the interface. The original model applied an empirical model for rough soil surfaces, derived by Wegmüller and Mätzler (1999). This is not directly applicable to the ice/water interface, so the empirical modifications to Fresnel reflection coefficients proposed by Wegmüller and Mätzler (1999) are replaced by a simple consideration of modifying the coherent reflectivity component. Following Choudhury et al. (1979), the reflectivity of the ice/water and ice/snow interfaces are given by

Eq. 9

here r_{p, Fresnel} is the Fresnel reflection coefficient for polarization p, k is the wave number, h the standard deviation of height variations of the rough surface and θ the incidence angle. This approach is applicable when surface roughness variations are small compared to the wavelength, i.e. incoherent effects from large scale variations in surface height do not arise. The parameter h can be considered an empirical fitting parameter; based on Lemmetyinen et al., (2011), a constant value of h = 1 mm is applied across all frequencies. Due to the semi-empirical nature of the approach, the consideration of roughness is applied only for the ice/water interface, where the contrast of permittivity (between ice and water) carries the largest effect.

Atmosphere

The top-of-atmosphere brightness temperature is calculated from  T_{B, BO}A so that

Eq. 10

Where t_atm is the transmissivity of the atmosphere, TB,ATM↑(↓) the up-(down)welling atmospheric brightness temperature,  e_gnd the emissivity of the observed scene (snow, forest, lakes etc.)  and 2.7 K the cosmic background contribution.  is given by

Eq. 11

where   α_↑(↓) is the approximate atmospheric profile factor (Aschbacher, 1989) and   T_air is the air temperature (K). Transmissivity   t_atm for different frequencies and t is derived from statistical studies (Pulliainen et al., 1993; Salonen et al., 1990) representing 55 percentile conditions in the Northern Hemisphere. Since the statistical model assumes average conditions, there are always some clouds included.

Summary of ancillary model parameters

The forward model to turn detected brighness temperature to snow water equivalent contains many variables for which extensive measurements are not available, either spatially, temporally or both. This version of the algorithm has dynamic, spatially and temporally changing snow density field based on 10 years averages. Rest of the values are best guess estimates and are treated as constants (see Pulliainen 1999 for details). Should such measurements or modelled data thereafter become available, the accuracy of the retrieval could potentially be increased quite a bit. Table 6 lists constant values used for these variables in this version of the algorithm.

Table 6: Summary of ancillary parameters used for SWE retrieval.

Methodology

The algorithm for estimating SWE assimilating in situ snow depth observations and space borne SWE estimates is presented in detail in Pulliainen (2006), Takala et al. (2011) and Luojus et al. (2021). The processing chain is shown in Figure 3. A summary with clarifications relevant for C3S SWE product is given in the following.

Figure 3: SWE retrieval processing chain.

Step 1: The mountain mask, water mask and dry snow masks are applied to brightness temperature data. The mountain mask criterion removes all observations that fall within EASE2-grid cells with a height standard deviation above 143 m within the grid cell. The water mask removes grid cells with over 50 % water.

Step 2: Synoptic snow depth (SD) observations and observed brightness temperatures (T_B) over reference station locations are applied in numerical inversion of the one-layer HUT snow emission model (Pulliainen et al., 1999) to retrieve values of effective grain size d₀, which matches model predictions to observations. The model is fit to space-borne observed T_B values at the locations of weather stations by optimizing the value of snow grain size d₀. The fitting procedure is:

Eq. 12

where the known snow depth is SD_ref, T_B^19Vand T_B^37V denote the vertically polarized brightness temperature at approximately 19 and 37 GHz with indices mod and obs referring to modelled and observed values, respectively. Vertical polarization is used because it correlates best with SWE in the boreal forest zone (Hallikainen and Jolma, 1992; Pulliainen et al., 1999; Pulliainen and Hallikainen, 2001). Snow density is a temporally and spatially changing value based on climatological snow density fields). At each synoptic station location, the final estimate of d_0,ref (and its standard deviation λ) is obtained by averaging values obtained for the ensemble of the nearest stations, so that

Eq. 13

Eq. 14

where M is the number of stations (default 6).

Step 3: The effective grain size and variance values are further interpolated over the selected grid of brightness temperature observations using Kriging interpolation, obtaining a spatially continuous field of effective grain size and its variance.

Step 4: SD observations are interpolated to the selected grid of brightness temperature observations using Kriging interpolation (from 35° N to 85° N in latitude and from 180° W to 180° E with resolution of 0.10° x 0.10°). As a modification to the algorithm by Takala et al. (2011), the variance λ_D² assigned to individual SD observations is set at 150 cm² for open areas and 400 cm² for forested areas. This differs from the earlier versions of the algorithm where a constant value of 150 cm² was used. As an output, a spatially distributed estimate of SD and its variance are obtained.

Step 5: a dry snow mask is applied to brightness temperature data to identify areas where snow is not possible, and areas indicating wet snow cover. Snow status retrieval is based on snow depth algorithm presented by Rees (2005):

Eq. 15

where certain threshold values need to be met, for snow to be considered dry. Based on tests performed in the EUMETSAT HSAF project (Pulliainen et. al. 2010), these values have been modified for the C3S Cryosphere to offer better sensitivity to shallow snow, reducing bias during accumulation season (Zschenderlein et. al., 2023). Table 7 presents how the thresholds have been adjusted from the original. 

Table 7: Threshold values for dry snow classification from Rees (2005), and the adapted values used for the dry snow classification in the C3S Cryosphere retrieval.

Step 6: Observed brightness temperatures over the whole area of interest are applied together with the effective grain size and effective grain size variance in numerical inversion of the one-layer HUT snow emission model to retrieve SWE. Similar to the retrieval of effective grain size, an iterative cost function is applied. HUT snow emission model estimates are matched to observations numerically by fluctuating the SWE value. The background field of SD_t is applied to constrain the retrieval. A dynamic  snow density value is applied to calculate SWE_t from SD_t. The cost function constrains the grain size value according to the predicted background grain size and the estimated variance produced in Step 3. Thus, assimilation adaptively weighs the space-borne brightness temperature observations and the background SD_t field (produced in Step 3) to estimate a final SWE and a measure of statistical uncertainty (in the form of a variance estimate) on a grid cell by grid cell basis:

Eq. 16

where

• SD_{ref, t} is the snow depth estimate from the kriging interpolation for the day under consideration, t.
•  λ_{SD, ref, t} is the estimate of standard deviation from the kriging interpolation, and
• SD_t is the snow depth for which  Eq. 16 is minimized (note that SWE =  SD_t * ρ_snow).

The variance of T_B, σ_t², is estimated by approximating T_B as function of snow depth and grain size in a Taylor series:

Eq. 17

Eq. 18

In practice, the variance σ_t² adjusts the weight of brightness temperature data with respect to the weight of the SD background field (parameter λ_D,ref). A basic feature of the algorithm is that if the sensitivity of space-borne radiometer observations to SWE is assessed to be close to zero by formulas Eq. 17 and Eq. 18, the weight of radiometer data on the final SWE product approaches zero (this is the case e.g. if the magnitude of SWE is very high). The higher is the estimated sensitivity of T_B to SWE, the higher is the weight given to the radiometer data. Thus, the weight of the radiometer data varies both temporally and spatially in order to provide a maximum likelihood estimate of SWE.

Post-processing

Re-projection from EASE to regular latitude-longitude grid

For distribution the generated SWE product is re-projected from the original satellite EASE grid projection to a to a regular geographic latitude / longitude grid using bi-liner interpolation. The grid for the final C3S SWE product is a 0.1° x 0.1° latitude-longitude global array of points, based on the World Geodetic System 1984 (WGS 84) reference system. Its dimension is 3600x1800, where the first dimension, latitude is incremental from South (-90°) to North (90°), and the second dimension, longitude is incremental from West (-180°) to East (180°). Grid edges are at multiple of quarter-degree values (e.g. -89.95, -89.85, -89.75, -89.65…), representing the grid centres. An exact definition on the grid and projection is given in the metadata of the netCDF file. More detailed information is also given in the Product User Guide (PUG) related to this dataset (ref.: Snow Water Equivalent (SWE) version 1.0: Product User Guide and Specification (PUGS))

Snow masks

The algorithm can be used to measure snow packs roughly between 0.05 m and 1.00 m in thickness and only under dry snow conditions. Depth less than 0. 05 m cannot be reliable retrieved because the brightness temperature difference between the two frequencies, falls within 2 K detection precision of the radiometer instruments used. This leads that areas on edges of snow covered areas with relatively low snow depth are difficult to retrieve from PMR measurements. In a post-processing step snowmasks from external datasets are overlaid to the direct SWE retrieval output to account for that. Products before summer 2018 have a Cryoclim-based snowmask added to the SWE. Products starting from 01.07.2018 have a cumulative snowmask applied, which had been derived from Copernicus Land monitoring service snow cover extend product. The following chapter briefly describe the specific snowmask used for that post-processing step. Figure 4. shows as example one particular date with maps of both snowmasks and their slight differences, which are used for this post-processing step.

Figure 4: Example date 21.03.2020, where both snowmasks CryoClim and CLMS SCE-based are available, to visualise the slight differences between the two masks

CryoClim

SWE products before summer 2018 have a CryoClim-based snowmask added to the SWE. 

The CryoClim Fractional Snow Cover (FSC) product is based on a multi-sensor time-series fusion algorithm combining observations by optical and passive microwave radiometer (PMR) data. The product combines an historical record of AVHRR sensor data with PMR data from the SMMR, SSM/I and SSMIS sensors. The overall aim of the CryoClim FSC climate data record is to provide one of the longest snow cover extent time series available with global coverage and without hindrance from clouds and polar night (Solberg et al. 2023). The CryoClim FSC time series provides daily products for the period 1982 – 2019 and is available at a 0.05 degree latitude-longitude grid. For the early years 1979-1981, where CryoClim is not available a simple snowmask scheme is used, which is based on a simple channel difference of PMR measurements of the same sensors used for the C3S retrieval algorithm. The description of this method, which also discuss an algorithm to estimate the snowmelt is given in Takala et al. 2009. 

Cumulative snowmask derived from CLMS snow cover extend 

C3S SWE datasets starting from winter 2018/2019 have a cumulative snowmask applied. This snowmask is derived from the Copernicus Land Monitoring Service snow cover extent (SCE) product, available at a 1km resolution. This dataset provides daily maps for the Northern Hemisphere with fraction of snow cover on ground (including forested areas) per pixel in percentage (0% – 100%). The data is available in near real time with a pixel spacing of about 1 km and with the temporal extent from January 2018 to present. This product is derived from the VIIRS satellite sensor, which observes and collects global satellite observations that span the visible and infrared wavelengths across land, ocean, and atmosphere. Measurements in the microwave spectral range, like PMR, are not affected by clouds. On the contrary satellite observation with sensors measuring in the visible channels as they are used to derive SCE from VIIRS has gaps due to cloudy pixels. The high reflectance of clouds in those visible channels does not allow for information of snow within the underlying pixels. To fill the cloud gaps with time a cumulative process builds the snowmask.  Starting from summer months the snowmasking code is cumulatively flagging pixels as snow-covered, as soon as SCE provides a value with at least 25% snow cover extent within the grid. With this method gaps due to clouds as well as polar night can be significantly reduced. Over the winter period this derived snowmask is continuously filled. During melting periods this kind of cumulative snowmask can eventually flag pixels falsely as snow-covered, in case the SCE product could not yet derive actual pixel values due to clouds. Snow melting might be recognised a little delayed with this method.

SWE is only provided for pixels where the cumulative snowmask flag pixels as snow-covered. In a post-process step SWE products after summer 2018 have the cumulative SCE-based snowmask added to the SWE. 

Overlay of static masks

Because of known limitations with such high snow depths for alpine terrain, a complex-terrain mask is applied. Additionally the native satellite pixel size of approximate 25km is not able to resolve such small-scale features in elevation change. A high-resolution digital elevation model excludes therefor mountain pixels for the retrieval. 

Following topography mask and Land-Water mask are used:

• LC2000 (used also in Snow_CCI): The surface classification for the year 2000 from the ESA CCI Land Cover (LC) project is used as auxiliary layer for the processing chain in the second year of snow_cci. Water bodies aggregated to the pixel spacing of the SWE product and, providing percentage (0-100%) of water within pixel, with 50% threshold used for this version of the product. 
• ETOPO1 (Amante et al., 2009) based mountain mask for the Northern Hemisphere, first produced for needs of ESA_GlobSnow project and re-projected to 0.125 deg grid for needs of snow_cci as well as C3S. An EASE2-Grid cell is considered as mountainous if the standard deviation of the elevation within a grid cell is above 143m for 12500m resolution.

C3S SWE data product and file formatting

The C3S SWE product is provided on a daily basis in a NetCDF CF format for the period 1988 to 2023. For years 1979 to 1987 satellite measurements are only available bi-daily due to the data storage capacities and data receiving processes in those early years of satellite remote sensing and satellite -based earth observations. To ensure a continuous daily product the missing days are estimated through the mean between consecutive days of measurements. The product follows the C3S data standards and products are generated with 0.10 degrees pixel spacing. Details of the product format is given in the Product User Guide and Specificatios document (PUGS).

The SWE product file includes two data fields:

• The SWE estimate [mm]
• The statistical standard deviation [mm] representing the pixel-level uncertainty of the SWE estimate

netCDF output format

The file format used for storing the data is NetCDF-4 classic. All NetCDF files follow the NetCDF Climate and Forecast (CF) Metadata Conventions version 1.8. The NetCDF data files are stored in folders for each year with one file per day. The following file naming convention is applied:

C3S_SWE_<YYYYMMDD>_v<VERSIONNUMBER>.nc

Typical netCDF software tools are able to extract and manipulate the datasets. With command-line utility ncdump it is possible print the netCDF data to human-readable text form (e.g. "ncdump -h filename.nc" or "ncdump -v swe filename.nc"). Additionally all kind of netCDF data viewers like Panoply are able to print and visualise the data product.

Table 8 gives an overview on the specifications on the Snow Water Equivalent product file and format specification.

Table 8: SWE Product and format specification

Example visualisation of key variables

All product files are available as netCDF files. NetCDF4-classic files are following the CF1.8 convention. Data are readable by any software tool able to open and read netCDF file format. There are several open source and commercial software tools for reading, displaying and working with netCDF files online available.

For example all datasets can be visualised with standard graphic software tools like Panoply: https://www.giss.nasa.gov/tools/panoply/ 

The data standard allows easy implementation into data manipulation tools, such as CDO and GDAL, in order to manipulate and implement the dataset to new applications. Gdal can be embedded as module into existing python-scripts too.

Figure 5 gives an example plot for SWE observation of the daily C3S product, including flagged pixels for mountain, glacier areas and water bodies. A detailed description on the SWE product including flagged values is given in the Snow Water Equivalent (SWE) version 1.0: Product User Guide and Specification (PUGS)

Figure 5: Example plot for SWE observation of date 01.01.2023. 

Access and download of C3S SWE through Climate Data Store

The Copernicus Climate Change Service provides data storage infrastructure and make ECV data products available through the CDS. The store provides not only consistent estimates of ECVs, but also climate indicators, and other relevant information about the past, present, and future evolution of the coupled climate system, on global, continental, and regional scales. It supports users with data dissemination and visualisation tools¹. C3S satellite snow water equivalent CDRs and ICDRs are available via the CDS. 

¹Source: https://climate.copernicus.eu/climate-data-store. 

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