Enhanced Identification of Snow Melt and Refreeze Events From Passive Microwave Brightness Temperature Using Air Temperature

Abstract

Snow melt and refreeze events are important determinants of spring runoff timing, and snowpack stratigraphy and metamorphism. Previous studies have established the utility of differences between twice-daily passive microwave brightness temperature (T_b) observations, called the diurnal amplitude variation (DAV), for identifying snow melt and refreeze. Liquid water in snow leads to a large increase in microwave emissivity compared to a completely frozen snowpack, so phase changes from nighttime freezing and daytime melting result in high DAV values. However, the physical temperature of the land surface also contributes to brightness temperature, independent of the phase of water. Thus, it is important to account for physical temperature change when using T_b differences to detect snow melt and refreeze. Here, we use near-surface air temperature (T_a) to approximate the physical temperature of the land surface and compare diurnal T_b changes (ΔT_b) from the Advanced Microwave Scanning Radiometer for the Earth Observing System satellite instrument to coincident T_a changes. We find that an approximately linear relationship exists between ΔT_b and ΔT_a for frozen snow and fit this relationship using modal linear regression. Melt and refreeze events are identified as large positive and negative excursions from the regression line, respectively. We demonstrate the method in the Northern Great Plains, USA, and evaluate it using ground-based data from Senator Beck Basin Study Area, Colorado, USA. Melt and refreeze events identified from satellite observations mostly occur after the annual peak snow accumulation and are consistent with snow temperature and snowpack energy balance observations at Senator Beck Basin.

Key Points

• A method is presented to enhance detection of snow melt and refreeze from twice-daily satellite passive microwave brightness temperature
• The method accounts for the influence of physical temperature change on brightness temperature change, using air temperature as a proxy
• Ground observations of snow from Senator Beck Basin, Colorado, are used to evaluate the method, yielding physically reasonable results

1 Introduction

Snow melt is closely linked to a cascade of hydrological and ecological processes. In snow-dominated basins, the runoff from spring snow melt often produces the highest streamflow of the year. This is a crucial resource for many arid regions, but rapid snow melt can also result in flooding (e.g., 1997 spring flood in the Red River of the North; Todhunter, 2001). Midwinter melt events can lead to snowpack densification, snow crystal metamorphism, and formation of ice lenses as well as impact the underlying soil. All of these changes can influence water percolation through the snow and subsequent timing and magnitude of snow melt runoff (Singh et al., 1997). Additionally, ice lens formation can inhibit the ability of animals to forage for food beneath the snow (Grenfell & Putkonen, 2008), and changes in the timing of spring snow disappearance can lead to asynchrony between microbial processes and vegetation phenology (Groffman et al., 2012).

Snow melt also poses a significant challenge for passive microwave remote sensing of snow depth and snow water equivalent (SWE), which are important for water resources management and spring flood forecasting. Microwave radiation that is emitted from the land surface (snow and underlying ground) can be scattered and absorbed by snow and ice crystals (Mätzler, 1987). Snow crystals scatter higher microwave frequencies more strongly than lower frequencies, so the comparison of passive microwave observations at two different wavelengths can provide information on the depth of the snowpack (because deeper snowpacks typically contain more crystals, for a given snow density and crystal size, which leads to more scattering; Chang et al., 1987; Ulaby & Stiles, 1980). However, when liquid water is introduced into the snowpack (e.g., via melting), absorption processes dominate, emissivity increases, and the snow acts almost as a black body (Chang et al., 1976; Mätzler, 1987; Stiles & Ulaby, 1980). Surface scattering dominates, which obscures the volume scattering signal that would be present for a completely frozen (or “dry”) snow (Mätzler, 1987). In this case, there is no differential scattering for different microwave wavelengths. Thus, determination of snow depth and SWE by comparing two different wavelengths becomes difficult, if not impossible.

While the presence of liquid water complicates estimation of snow depth and SWE from passive microwave observations, it is possible to use its impact on the microwave signal as an advantage to determine when snow melting occurs. Early melt detection methods focused on wet snow detection on large ice sheets (e.g., Greenland: Mote et al., 1993; Antarctica: Zwally & Fiegles, 1994; Steffen et al., 1993; Abdalati & Steffen, 1995) using brightness temperature (T_b) from the Special Sensor Microwave Imager (SSM/I) series of satellite instruments and various thresholding techniques. Walker and Goodison (1993) used SSM/I data from the Canadian prairies to determine that a difference of greater than 10 K between the horizontal and vertical polarizations at 37 GHz, along with a difference of 0 K between the 37 and 19 GHz frequencies at vertical polarization, indicates the presence of wet snow. Grenfell and Putkonen (2008) used the normalized gradient ratio between 19- and 37-GHz frequencies (for the same polarization) and the normalized polarization ratio between the horizontal and vertical polarizations (at the same frequency) jointly to differentiate satellite observations of Banks Island, Canada, into clusters of wet snow, dry snow, and dry snow with an ice layer after a rain event.

It is also possible to use the overpass times of some polar-orbiting satellites to identify snow melt events. Passive microwave instruments on polar-orbiting satellites observe most high-latitude locations on Earth at least twice per day, including once during the daytime or late afternoon and once during the nighttime or early morning. This timing coincides with the diurnal cycle of daytime solar insolation and heating, followed by nighttime cooling, which can result in daytime melting of snow followed by nighttime refreeze. Ramage and Isacks (2002) developed a method called the diurnal amplitude variation (DAV) to identify the spring snow melt onset period. The DAV is the absolute value of the running difference between brightness temperature observations from twice-daily satellite overpasses. As described previously, when snow melts, absorption processes dominate, resulting in a higher brightness temperature (T_b) than would be observed for the same snowpack if it were completely frozen. So, when the snow melts in the daytime and refreezes at night, the phase change from ice to liquid water results in a large difference in the amount of emitted radiation and thus a high DAV value calculated from twice-daily satellite T_b.

Ramage and Isacks (2002) used 37-GHz T_b observations from the SSM/I series of instruments to calculate the DAV and identify the annual spring period of diurnal melt and refreeze on glaciers in southeast Alaska and British Columbia from 1988 to 1998. If the DAV value were above a certain threshold, and T_b were above a minimum T_b magnitude threshold, then diurnal melt-refreeze would be indicated. Ramage and Isacks (2003) used the similar methods to extend the analysis over a larger region of southeastern Alaska for the same time period and restricted the analysis to the vertically polarized, 37-GHz T_b observations because it was found to be the frequency most sensitive to moisture variation. The method was used to determine that the snow ablation season (i.e., the period of daytime melt and nighttime refreeze, also later called the “melt onset” or “melt duration” period) increased in length and the start date shifted earlier from 1988 to 1998. If the snow contained liquid water throughout the nighttime, then the DAV method would no longer be triggered, so this method only identifies the transition period of melt-refreeze between completely frozen and persistently wet snow. Subsequent studies used the DAV to relate snow melt-refreeze timing to the timing of river hydrograph peaks (Kopczynski et al., 2008; Ramage et al., 2006) and prevalence of forest fires (Semmens & Ramage, 2012), extended the DAV method to incorporate T_b observations from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) satellite instrument (Apgar et al., 2007), compared melt onset timing of locations with different land surface properties (Ramage et al., 2007), and detected midwinter melt events (Semmens et al., 2013). Most DAV studies have focused on Canada and Alaska, although variations of the method were also used in the Southern Patagonia Icefield (Monahan & Ramage, 2012), Greenland (Tedesco, 2007), and Antarctica (Tedesco et al., 2007). Further studies used melt timing identified from the DAV method and SWE to inform snow melt rates in a simple hydrological model of streamflow (Ramage & Semmens, 2012; Yan et al., 2009).

Multiple studies used the DAV to diagnose climate change trends in high-latitude areas, for example, the Yukon basin (Semmens & Ramage, 2013), northern Canada (Mioduszewski et al., 2014), Arctic sea ice (Markus et al., 2009), and the entire Arctic (Wang et al., 2011). Tedesco et al. (2009) presented a modified version of the DAV method, called the dynamic DAV, where the minimum DAV threshold to indicate snow melt was set to the January-February average DAV plus 10 K, and the T_b threshold was determined by fitting a bimodal Gaussian distribution to T_b and finding the minimum density between the two peaks of the distribution. If both thresholds were exceeded, then melt-refreeze was indicated. The method was applied to the entire Arctic (>60°N) from 1979 to 2008 using Scanning Multichannel Microwave Radiometer and SSM/I observations, and the authors found that the transition from persistently dry to persistently wet snow (or no snow) occurred earlier and faster over time. Foster et al. (2011) incorporated melt onset identified using the DAV from AMSR-E observations into the joint U.S. Air Force Weather Agency/NASA Snow Algorithm blended global snow product. Li et al. (2012) evaluated melt onset identified from AMSR-E using the DAV method against dates derived from the temporal evolution of SWE from snow pillows in the Kern River basin of the Sierra Nevada Mountains, concluding that passive microwave data contain useful information about snow ablation in mountain areas.

In this study, we build on the DAV method of Ramage and Isacks (2002) and others and develop a new methodology that uses diurnal air temperature change (ΔT_a) to enhance identification of snow melt and refreeze events from diurnal brightness temperature change (ΔT_b; hereafter called the ΔT_b-ΔT_a method). Additionally, we use the 12-hr difference between overpasses of a polar-orbiting satellite instrument to differentiate snow melt events from snow refreeze events. We demonstrate the use of this method with data from the Northern Great Plains (NGP), USA. Finally, we evaluate the method using independent ground observations from Senator Beck Basin Study Area in Colorado, USA.

2 Study Area

Data from the NGP and Colorado are used to (1) demonstrate the ΔT_b-ΔT_a method and (2) evaluate the method, respectively. To demonstrate the method, an area located south of Fargo, North Dakota, USA, which encompasses one 25-km-resolution pixel from the AMSR-E satellite instrument (see section 3.1.1 and top right panel of Figure 1) that spans the border between North Dakota and Minnesota, was chosen. The land surface within the pixel is very flat, with land cover dominated by cropland (NALCMS, 2010), which is predominantly bare in the winter months. This flat, bare area allows for unobstructed satellite view of the snow surface during the winter. The general characteristics of the area are shown in Table 1 (and supporting information Figures S1 and S2).

Figure 1

Locations of the sites in this analysis. The bottom right panel displays the locations of the two 25-km-resolution AMSR-E pixels, which are shown in the top right (Northern Great Plains) and bottom left panels (Colorado). Senator Beck Basin Study Area, which is located within the Colorado AMSR-E pixel, is shown in the top left panel, including the Senator Beck and Swamp Angel Study Plots. (Image data: Google, Landsat/Copernicus.) AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System.

Table 1. Characteristics of the Sites Used in This Analysis

	Northern Great Plains AMSR-E pixel	Colorado AMSR-E pixel	Senator Beck Basin Study Areaa
			Swamp Angel Study Plot	Senator Beck Study Plot
Location (center)
Longitude (deg)	46.5180	37.8103	37.906914	37.906883
Latitude (deg)	−96.7098	−107.7056	−107.711322	−107.726265
Area (km^2)	625	625	point	point
Elevation (m)b
Maximum	293	4,232	—	—
Minimum	277	2,662	—	—
Median	283	3,501	3,371	3,714
Mean annual air temperature (°C)c	6.7	−1.1	0.5	−1.2
Mean annual precipitation (m)c	0.72	0.92	1.19	—
Land cover (%)d
Temperate needleleaf forest	0	35.9	100	—
Temperate broadleaf deciduous forest	0.1	1.0	—	—
Temperate shrubland	0	12.8	—	—
Temperate grassland	0	23.7	—	100
Cropland	99.9	<0.1	—	—
Barren land	0	12.0	—	—
Water	0	<0.1	—	—
Snow and ice	0	14.6	—	—

• Note. AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System; NALCMS = North American Land Change Monitoring System.
• ^a Senator Beck Basin Study Area is located within the larger Colorado AMSR-E pixel.
• ^b Elevation statistics are from Landry et al. (2014) for the two Senator Beck Basin sites and were calculated from U.S. Geological Survey (2017) for the AMSR-E pixels.
• ^c Mean annual air temperature and precipitation values are from Landry et al. (2014) for the two Senator Beck Basin sites and were calculated from North American Land Data Assimilation System, version 2 (Xia et al., 2012; see section 3.1.2) for the AMSR-E pixels.
• ^d Land cover statistics for the two AMSR-E pixels were calculated from NALCMS (2010). Note that the NALCMS land cover for Senator Beck Basin Study Area differs slightly from the description in Landry et al. (2014).

Unfortunately, there are no snow measurement sites in the NGP location that could serve to directly evaluate snow melt and refreeze. Instead, we use data from study sites in the Senator Beck Basin Study Area (http://snowstudies.org), a 2.91-km² watershed in the San Juan Mountains of southwest Colorado, USA (top left panel of Figure 1). Senator Beck Basin Study Area contains two study sites that collect in-depth measurements of snow, radiation balance, and meteorological variables: Swamp Angel Study Plot (SASP) and Senator Beck Study Plot (SBSP). SASP is located below the tree line in a sheltered clearing surrounded by subalpine forest, while SBSP is located in a level area above the tree line in alpine tundra (Landry et al., 2014). The general characteristics of each site are shown in Table 1. The average annual peak snow depth at SASP and SBSP is 2.35 and 2.0 m, respectively.

The 25-km-resolution AMSR-E pixel containing the Senator Beck Basin (bottom left panel of Figure 1) is mountainous, with land cover consisting of forest, shrubland, grassland, barren land, and snow and ice (NALCMS, 2010; see Table 1 and Figures S1 and S2). Senator Beck Basin Study Area is fairly representative of this encompassing 25-km-resolution AMSR-E pixel, but the pixel contains some additional lower-elevation, forested areas. With such significant relief and moderate forest cover, this is a challenging location to remotely sense snow properties. However, most in situ snow measurements are collected in mountainous areas (at least in the United States), due to the importance of mountain snow to water supply in many arid regions, so it is worthwhile to evaluate the method in this location.

3 Data and Processing

3.1 Data Used in the ΔT_b-ΔT_a Method

Two types of data are needed for the ΔT_b-ΔT_a method described in section 4: passive microwave brightness temperature observations and physical temperature estimates.

3.1.1 Passive Microwave Brightness Temperature

The brightness temperature data used in this study are from the AMSR-E satellite instrument, which is mounted on NASA's Aqua satellite platform. AMSR-E operated from 19 June 2002 until 4 October 2011, at which time the instrument failed. AMSR-E daily coverage is near global, with one descending, nighttime overpass at approximately 1:30 a.m. at the equator and one ascending, daytime overpass of approximately 1:30 p.m. at the equator. At high latitudes (greater than approximately 52° latitude), more than two overpasses may be observed per day, while low latitudes may only receive one overpass on some days. The data used in this study are from the AMSR-E/Aqua Daily EASE-Grid Brightness Temperatures (NSIDC-0301; Knowles et al., 2006) data set available from the National Snow and Ice Data Center (NSIDC; https://nsidc.org/data/docs/daac/nsidc0301_amsre_gridded_tb.gd.html). The brightness temperature data are provided in Northern Hemisphere Equal-Area Scalable Earth Grid (EASE-Grid) (Lambert azimuthal) projection at 25-km resolution (i.e., grid spacing is 25 km, resulting in an areal coverage of 625 km² for each pixel). Only the 36.5-GHz frequency, vertically polarized channel is used because these data were previously found to be sensitive to liquid water in snow (Stiles & Ulaby, 1980), as well as a good estimate of land surface temperature (Holmes et al., 2009), and were also used in previous snow melt studies (e.g., Apgar et al., 2007; Li et al., 2012; Semmens et al., 2013; Yan et al., 2009).

3.1.2 Physical Temperature

In this study, we use air temperature as an approximation of the physical temperature of the land surface observed by the satellite instrument. The air temperature data are from the North American Land Data Assimilation System, version 2 (NLDAS-2; Xia et al., 2012; Mitchell et al., 2004; Cosgrove et al., 2003), which were derived from the National Center for Environmental Prediction North American Regional Reanalysis (NARR; Mesinger et al., 2006). The data have hourly temporal resolution and 1/8° spatial resolution in a geographic coordinate system and were obtained from the NASA Goddard Earth Science Data and Information Services Center (Xia et al., 2009; https://disc.gsfc.nasa.gov/datasets/NLDAS_FORA0125_H_V002/summary). NLDAS data are available from 1979 to present, but only air temperature estimates coincident with the operational period of AMSR-E were used in this study. The air temperature data were spatially averaged to match the larger resolution EASE-Grid projection of the AMSR-E data by weighted averaging, where the fractional area of a given EASE-Grid pixel that fell within each NLDAS pixel was used for weighting. The 2:00 a.m. and 2:00 p.m. air temperature observations were used in the analysis due to their close proximity to the mean overpass times of AMSR-E (~1:30 a.m. and ~1:30 p.m. local time).

3.2 Snow Cover Data

Snow cover data were used to restrict the analysis to only dates when snow was present. Snow cover was determined from the NASA Making Earth System Data Records for Use in Research Environments (MEaSUREs) Northern Hemisphere Terrestrial Snow Cover Extent data set (Robinson et al., 2014; https://nsidc.org/data/NSIDC-0530), which is provided by the NSIDC at daily temporal resolution in a Northern Hemisphere 25-km-resolution EASE-Grid 2.0 projection. The snow cover product contains three independent assessments of snow cover extent: the Interactive Multisensor Snow and Ice Mapping System, Moderate Resolution Imaging Spectroradiometer Cloud Gap Filled Snow Cover, and passive microwave brightness temperatures. For a given EASE-Grid 2.0 pixel, if two or more of the three snow cover products indicated that snow was present, then the pixel was considered to be snow-covered. The EASE-Grid 2.0 pixels were then compared to the given AMSR-E EASE-Grid pixel of interest (for which brightness temperature and air temperature values were calculated). If more than or equal to 50% of the given AMSR-E pixel was covered with snowy MEaSUREs pixels, then the AMSR-E pixel was considered to be snow-covered and the data from that time step were included in the analysis.

3.3 Ground-Based Data From Senator Beck Basin Study Area

Ground-based observations from Senator Beck Basin Study Area in Colorado were used to evaluate the melt and refreeze events identified by the ΔT_b-ΔT_a method. These data were obtained from the Center for Snow and Avalanche Studies (Landry et al., 2014; Center for Snow and Avalanche Studies (CSAS), 2017; https://snowstudies.org/archived-data/) and are listed in Table 2. All data are hourly averages, unless otherwise noted, and include observations from the beginning date listed in Table 2 until 30 September 2016 (i.e., end of the water year 2016). However, only data coincident with the operational period of AMSR-E were used in this study. Snow depth was used in order to restrict the analysis to only dates with snow cover. If snow cover for a given date was observed at either study plot, the date was included in the analysis.

Table 2. Data From Senator Beck Basin Study Area Used in This Analysis

Observation	Swamp Angel Study Plot		Senator Beck Study Plot
	Instrument height (above ground; m)	Begin date of data collection	Instrument height (above ground; m)	Begin date of data collection
Snow depth (m)a	3.2	8 Nov 2003	3.55	20 Jan 2005
Snow temperature (°C)	0, 0.1, 0.2, 0.3, 0.4	8 Nov 2003 (0, 0.2, 0.4 m) and 25 Jan 2005 (0.1, 0.3 m)	0, 0.1, 0.2, 0.3, 0.4	20 Jan 2005
Infrared snow surface temperature (°C)	3.2	9 Mar 2005	3.5	11 Mar 2005
Air temperature, minimum and maximum (°C)b	3.4, 5.95	8 Nov 2003 (lower) and 8 Feb 2006 (upper)	3.8, 8.7	29 Oct 2003 (lower) and 6 Feb 2006 (upper)
Relative humidity (%)a	3.4, 5.95	8 Nov 2003 (lower) and 8 Feb 2006 (upper)	3.8, 8.7	29 Oct 2003 (lower) and 6 Feb 2006
Wind speed (m/s)	3.8, 6.0	8 Nov 2003 (upper) and 29 Jan 2005 (lower)	4.0, 9.6	29 Oct 2003 (upper) and 17 Oct 2004 (lower)
Downwelling shortwave radiation (W/m^2)	5.7	25 Jan 2005	9.4	20 Jan 2005
Upwelling shortwave radiation (W/m^2)	3.1	25 Jan 2005	3.55	20 Jan 2005
Downwelling longwave radiation (W/m^2)	5.7	25 Jan 2005	9.4	20 Jan 2005
Soil heat flux (W/m^2)	−0.03	11 Jul 2005	−0.03	16 Jul 2005
Barometric pressure at sea level (in Hg)a	3.0	8 Nov 2003	—	—
“Height of snow” stake measurementsc	−0.44, −0.04, 0.60, 0.06	2 Nov 2004	−0.26, −0.07, 0.13, 0.22, 0.41, −0.19	3 Nov 2004

• ^a Snow depth, relative humidity, and barometric pressure are instantaneous measurements at the given observation time.
• ^b The air temperature data are maximum and minimum observed in the previous hour.
• ^c The snow stakes were located a few meters away from the main instrument tower in all directions and were used to determine the orientation of the snow surface. Thus, the listed measurement heights are the ground elevation at the base of each given stake.

Mean snow temperature in the bottom 0.4 m of the snowpack was calculated by averaging the snow temperature at all measurement heights. Only sensors that were buried within the snowpack were used for this calculation (e.g., if snow was 25 cm deep, then the 30- and 40-cm temperatures were not included in the average), so the effective height range of the mean snow temperature could vary from 0 m up to 0.4 m, depending on snow depth.

Infrared snow surface temperature was used to evaluate the satellite-derived snow melt and refreeze events, both individually and as part of a calculation to determine the net energy exchange of the snow.

All other measurements were used to determine the net energy exchange of the snow (i.e., net energy input rate to the snowpack) on an hourly basis at each Study Plot starting in July 2005. All components of the energy balance, including downwelling and upwelling shortwave and longwave radiation, turbulent heat fluxes (calculated using wind speed, air temperature, and relative humidity at two heights), and ground heat flux, were either measured or estimated from measurements at the site. The downwelling shortwave radiation data were corrected to account for the slope of the snow surface according to Painter et al. (2012) using snow stake measurements and the sun incidence angle. Outgoing longwave radiation was estimated from the snow surface temperature observations, and sensible and latent heat fluxes were estimated from meteorological variables and corrected for atmospheric stability. Using these energy balance components, the net energy input rate into the snowpack was determined. For details about the calculation of net energy exchange, see supporting information.

4 The ΔT_b-ΔT_a Snow Melt and Refreeze Identification Method

The DAV method of Ramage and Isacks (2002) and others has proved useful to identify instances of water phase changes in snow and to determine snow melt onset at high latitudes. However, the DAV considers only the diurnal difference in brightness temperature. The observed brightness temperature of a given region of the Earth is a function of more than simply the phase of water within that region. According to the Rayleigh-Jeans approximation, brightness temperature is approximated as

(1)

In equation 1, ε is emissivity and T_phys is the physical temperature. The emissivity of liquid water is approximately 0.98, while the emissivity of snow ranges from approximately 0.5–1.0, depending on frequency, as well as snow depth, density, microstructure, and stratigraphy (Ulaby & Stiles, 1980). This variability of snow emissivity is the basis for identifying snow phase change using the DAV. However, higher physical temperatures also lead to higher brightness temperatures, so changes in physical temperature from night to day will also result in brightness temperature changes. The ground surface, snow, water bodies, vegetation, and the atmosphere all contribute to the microwave brightness temperature signal based on their temperature. Positive correlation between the DAV and the diurnal amplitude of air temperature was noted by Li et al. (2012) in the Kern River basin of the Sierra Nevada Mountains. Thus, it is potentially important to consider the impact of physical temperature change on the DAV.

The DAV method of Ramage and Isacks (2002; equation 1) yields the absolute value of the difference between two consecutive T_b observations. However, we do not take the absolute value of the brightness temperature change. Satellite T_b data are often provided separately by ascending and descending overpasses, but we combine these data chronologically to create a single 12-hourly time series of T_b, and calculate the running 12-hourly T_b differences (i.e., daytime T_b on day 1 minus nighttime T_b on day 1, then nighttime T_b on day 2 minus daytime T_b on day 1, and so on).

(2)

In equation 2, i is the time step of the 12-hourly (T_b or T_a) data. ΔT_b is equivalent to the DAV, except that the DAV is the absolute value of the difference.

Because brightness temperature differences, rather than brightness temperature values, are used, only the contributions to the microwave signal that change on these time scales will show up in the ΔT_b signal. Thus, any contributions that are relatively unchanged over diurnal time scales (e.g., emission from the ground beneath the snow) will cause little T_b difference. However, aspects of the surface that do change on these time scales (e.g., air temperature, snow surface temperature, and snow emissivity changes) may contribute to ΔT_b.

Similarly, the coincident air temperature differences are

(3)

In equation 3, i is time step of the 12-hourly (T_b or T_a) data.

All 12-hourly brightness temperature change (ΔT_b) observations for a given pixel are plotted against coincident change in air temperature (ΔT_a), so that the two can be compared. An illustration of this is shown in Figure 2 using AMSR-E T_b and NLDAS-2 T_a data for an AMSR-E pixel in the NGP, USA (see section 2). Data were only included in Figure 2 for periods when snow cover was present, as determined from the MEaSUREs snow cover data set (Robinson et al., 2014; see section 3.2). Figure 3 shows an example time series of air temperature, brightness temperature, ΔT_b, and ΔT_a from the same location, with snow cover indicated by the gray bars.

Figure 2

The 12-hourly brightness temperature difference (ΔT_b; x axis) versus 12-hourly air temperature difference (ΔT_a; y axis) during snow-covered periods for a 25-km-resolution AMSR-E pixel in the Northern Great Plains, USA, from fall 2002 to spring 2011. (a) Night-to-day differences (which mostly correspond to increases in T_b and T_a) are plotted as open circles, and day-to-night differences (which mostly correspond to decreases in T_b and T_a) are plotted as open triangles. A simple linear regression fit to the data is shown in the dashed black line, and a modal linear regression fit, which fits a regression line through the mode of the data, is shown in the solid black line. (b) Melt (red) and refreeze (blue) events are defined as ΔT_b deviations beyond a threshold value from the modal linear regression line (in this case, ±10 K). Melt events are positive ΔT_b deviations that also correspond to ΔT_a values above −2 °C, while freeze events are negative ΔT_b deviations that also correspond to ΔT_a values below 2 °C. All other data are shown in gray. AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System.

Figure 3

Example time series from summer 2007 to summer 2009 for the same 25-km-resolution AMSR-E pixel from Figure 2. (top panel) The NLDAS-2 air temperature at the nighttime (descending) and daytime (ascending) overpass times of AMSR-E is shown in the black line and the gray line, respectively. (middle panel) AMSR-E brightness temperature observations from the nighttime (descending) and daytime (ascending) overpasses. (again, nighttime = black line, daytime = gray line). (bottom panel) The 12-hourly brightness temperature difference (ΔT_b) is shown in the black line, and the 12-hourly air temperature difference (ΔT_a) is shown in the orange line. In all three panels, the red points indicate identified melt events, and the blue points indicate identified refreeze events. The gray regions indicate periods of snow cover (according to the NASA MEaSUREs snow cover extent data set; Robinson et al., 2014). Only data within the gray regions (i.e., when snow cover was present) were included in the ΔT_b-ΔT_a method. AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System; NLDAS-2 = North American Land Data Assimilation System, version 2, MEaSUREs = Making Earth System Data Records for Use in Research Environments.

Two characteristics of the data are immediately evident in Figure 2a. First, there is an approximately linear relationship between a majority of the ΔT_b and ΔT_a data, which are plotted with partial transparency to show point density. A change of approximately 2.2 K in air temperature results in a corresponding change of 1 K in brightness temperature (note the difference in the axis limits). The night-to-day transitions (circles) are mostly located in the upper right of Figure 2a, as the surface and near-surface atmosphere heats up (i.e., positive ΔT_a) due to increasing solar insolation during this period, leading to increases in brightness temperature (i.e., positive ΔT_b). The day-to-night transitions (triangles) are located in the lower left of Figure 2a, as cooling due to decreasing solar radiation decreases air temperature (i.e., negative ΔT_a) and leads to decreases in brightness temperature (i.e., negative ΔT_b). If the air temperature can be assumed to be a good approximation of the physical temperature of the region observed in the satellite pixel footprint, then the slope of this linear relationship is determined by the emissivity of the observed region. For this analysis, we restrict the data to only include time periods when snow is present at the ground surface. So, if air temperature is a good proxy for physical temperature, then the slope of the line reflects the emissivity (ε) of the AMSR-E pixel in the NGP when the land surface is snow covered.

Second, there are large ΔT_b excursions from the central linear relationship in Figure 2a. Because they are not entirely caused by temperature change, these excursions likely reflect emissivity changes due to phase change between frozen and liquid water. As snow melts from night to day, the brightness temperature increases dramatically, leading to a large positive ΔT_b between the daytime and nighttime values. The opposite is true when snow freezes from day to night, leading to large negative ΔT_b values. These large ΔT_b values are the basis of the DAV method of Ramage and Isacks (2002) and others.

The DAV method does not consider the contribution of physical temperature change to ΔT_b, as diurnal temperature changes lead to brightness temperature changes. We account for this contribution by fitting a regression line to the ΔT_b versus ΔT_a data and identifying suspected melt and refreeze events as deviations from this relationship. Unfortunately, fitting a regression line to the ΔT_b versus ΔT_a relationship is not straightforward because there are a large number of systematic, large ΔT_b deviations, due to diurnal emissivity changes. These deviations influence a simple linear regression to result in a lower slope than is observed for the majority of the data (dashed black line in Figure 2a) because simple linear regression models the mean of f(y|x), where f(y|x) is the conditional density function of the response variable (y) given the independent variable (x). However, it is not possible to remove the ΔT_b deviations before the melt-refreeze events have been identified. To solve this problem, we use modal linear regression (Yao & Li, 2014), which models the mode (i.e., “most probable” value) of f(y|x) as a linear function of x. In other words, the regression line is plotted through the region of the ΔT_b versus ΔT_a relationship with the highest density of data points, as shown in the solid black line in Figure 2a. The regression coefficients are found by maximizing a kernel-based objective function using a modal expectation-maximization algorithm. As described in Yao and Li (2014), “modal linear regression is robust to outliers that do not follow the relationship exhibited by the majority of the sample” and is useful when f(y|x) is asymmetric. Most of the data are unaffected by melt-refreeze (because this area of the NGP is characterized by very cold winters), so modal linear regression is minimally affected by the systematic ΔT_b deviations and fits the regression line to the ΔT_b versus ΔT_a relationship for frozen snow.

Using the modal regression line, we identify suspected melt and refreeze events as excursions from the line beyond a certain threshold value. Thus, in our method, melt and refreeze events are only detected if the ΔT_b values are beyond that which would be expected from physical temperature change alone, allowing for some variability in the ΔT_b versus ΔT_a relationship. Melt events (red points) lie in the upper right portion of the plot, which corresponds to increases in air and brightness temperature, while refreeze events (blue points) are located in the lower left portion of the plot, which corresponds to decreases in air and brightness temperature (see Figure 2b). In this case, we choose a threshold of ±10 K from the regression line (dashed black lines on either side of solid black line), based on visual inspection of the data. However, the choice of a threshold value may vary based on the objectives of the user: A larger threshold value will decrease the risk of false positive identification of melt and refreeze events but increase the risk of false negatives, while a smaller threshold value will have the opposite effect. Additionally, we require that the change in air temperature be above −2 K for a melt detection and below +2 K for a refreeze detection. This keeps the detection of melt events consistent with physical reasoning (i.e., the snow must warm in order to melt, and cool in order to freeze), allowing for some leeway due to air temperature errors or delayed melt/freeze. The values of −2 and +2 K were chosen to be similar to the root-mean-square error found for National Center for Environmental Prediction North American Regional Reanalysis (NARR) 2-m air temperature in Mesinger et al. (2006), but these limits could use further evaluation. The few points that do not meet these criteria could be the result of rain-on-snow events, which can add liquid water to the snowpack without increasing snow temperature, or errors in the T_b or T_a data.

The ΔT_b-ΔT_a method is not restricted to any specific type or phase of snow or time of winter. Early-winter events, midwinter events, and events during spring melt onset are detectable using this method. However, the method is based on phase change in the snowpack. Any instance of snow phase change that leads to the appearance or disappearance of liquid water in the snowpack on a diurnal time scale, and that also leads to changes in the microwave emission from the snowpack, can be potentially identified using the ΔT_b-ΔT_a method. Thus, if the snow is continually frozen or continually wet throughout the diurnal cycle, no melt or refreeze events will be detected using this method.

5 Results

In order to evaluate the ΔT_b-ΔT_a method, it is necessary to verify that the events identified by the method are indeed instances of snow melt and refreeze. We do this using (1) timing of identified melt and refreeze events, (2) large-scale air temperature from NLDAS-2, (3) infrared snow surface temperature from field sites in Senator Beck Basin, and (4) calculated snowpack energy balance, also from Senator Beck. All evaluation results use the melt and refreeze events identified using the ΔT_b-ΔT_a method (described in section 4) for the 25-km-resolution AMSR-E pixel that contains Senator Beck Basin (Figure 4). Due to the consistently large diurnal changes in air temperature at this site, the modal linear regression line was fit only to ΔT_b versus ΔT_a data with daytime air temperatures below −10 °C (in order to ensure that the relationship was restricted to frozen snow). These are shown in Figure 4 in a darker shade of gray. Similar to the NGP site, a threshold of >10 K from the regression line was used to identify melt and refreeze events. Every 12-hr period that coincided with a snow depth greater than 5 cm at either of the two Senator Beck study plots, or with greater than 50% snow coverage of the AMSR-E pixel that contains Senator Beck Basin (see section 3.2), was included in the analysis.

Figure 4

Same as Figure 2b, but for the AMSR-E pixel that contains Senator Beck Basin Study Area in Colorado, USA, from fall 2002 to spring 2011. Due to the large diurnal temperature swings at this location, the modal linear regression line used to identify melt (red) and refreeze (blue) events was fit only to time intervals with air temperature less than −10 °C (to ensure frozen snow). These data are shown in the darker shade of gray, while all other points are shown in lighter gray. AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System.

The entire Senator Beck Basin Study Area (2.9 km²), and thus both SBSP and SASP within the Basin, is contained within a single AMSR-E pixel (625 km²). Thus, it is important to note that there is a vast scale discrepancy between the ground-based and satellite data (see Figure 1). However, this limitation is unavoidable given the sparsity of ground-based observations of snow melt properties. We separately used SBSP and SASP to evaluate the snow melt and refreeze events identified at the satellite pixel scale.

5.1 Melt and Refreeze Timing

While assessment of the timing of melt and refreeze events identified using the ΔT_b-ΔT_a method is not strictly validation, it is useful to examine the event timing to see if it makes physical sense based on typical snowpack accumulation and ablation patterns (Dingman, 2015). Figure 5 shows the distribution of identified melt and refreeze events throughout the water year, shown as the fraction of observations with identified events, aggregated into weekly bins. The absolute number of melt events is less important than the relative magnitude, as AMSR-E observations are not available at this site for every 12-hr time interval due to satellite orbital dynamics. For the Colorado AMSR-E pixel, melt (red) and refreeze (blue) events cluster between day of water year (DOWY) 150 and 260 (i.e., between very late February and mid-June). The peak in observed events (approximately from DOWY 200–225, mid-April to mid-May) lags behind the peak in snow depth for SASP (black line; approximately DOWY 180–195, late March to mid-April), but is fairly coincident with the peak in snow depth at SBSP (gray line; approximately DOWY 190–215). The number of melt and refreeze events declines to 0 as the snowpack disappears at the two sites (median of approximately DOWY 248, early June, for Swamp Angel and DOWY 263, late June, for Senator Beck). A second, smaller peak in melt and refreeze events is present in the fall (approximately DOWY 15–55, mid-October to mid-November), as snow begins to accumulate, but air temperatures still often exceed 0 °C during the daytime. In total, the temporal distribution of snow melt and refreeze events identified using the ΔT_b-ΔT_a method is consistent with what we would expect from current understanding of snow processes in the Rocky Mountains.

Figure 5

Distribution of snow melt and refreeze events throughout the year. The median snow depth (left axis) from winter 2005 to spring 2016 for the Senator Beck Basin Study Area sites is shown in the black line (for SBSA) and the gray line (for SBSP), plotted against day of water year (DOWY; where DOWY 1 is October 1). The melt events are aggregated into weekly bins (summed across all years in the 9-year study period, fall 2002 to spring 2011), and the fraction of observations with melt events (i.e., the number of events divided by the total number of 12-hourly time intervals with satellite observations) is shown in the red region (and on the right axis). The fraction of observations with refreeze events is similarly tabulated and shown in the blue region (and on the right axis). Melt and refreeze events are concentrated between DOWY 150 and 260 (very late February and mid-June), which is consistent with the spring melt onset following the peak in snowpack accumulation. A smaller peak is present at the start of the snow accumulation period in the fall (DOWY 15–55, mid-October to mid-November).

5.2 Air Temperature

The ΔT_b-ΔT_a method accounts for change in air temperature when identifying snow melt and refreeze events. This temporal difference information is an approximate derivative of air temperature with respect to time and thus largely independent of the magnitude of air temperature. Therefore, we can examine whether the identified melt and refreeze events occur when the air temperature is near the melt/freeze point (0 ° C). Because the surface of the snowpack is in contact with the ambient air, and the effective depth of 37-GHz brightness temperature is on the order of 1 m for dry snow (Chang et al., 1976; Hofer & Mätzler, 1980), it is reasonable to expect that melt and refreeze events detected with the ΔT_b-ΔT_a method should correspond fairly well with air temperature.

Figure 6 shows the NLDAS-2 air temperature for the AMSR-E pixel that contains Senator Beck Basin Study Area at a given AMSR-E overpass time (T_aⁱ) plotted against the NLDAS-2 air temperature at the time of the previous AMSR-E overpass (T_a^i-1; i.e., concurrent with the 12-hourly data used in the ΔT_b-ΔT_a method). From Figure 6, it is evident that nearly all of the identified melt events (red points) occurred when air temperature increased (i.e., the value on the x axis is greater than the value on the y axis). For a large majority of these events the air temperature was initially below 0 °C (y axis) and then rose above 0 °C (x axis). Conversely, nearly all of the refreeze events (blue points) occurred when air temperature decreased (i.e., the value on the y axis is greater than the value on the x axis), and a majority of these events also coincided with a decrease in air temperature from above 0 °C (y axis) to below 0 °C (x axis). Not all melt and refreeze events correspond with a crossing of the 0 °C threshold, which may be related to solar radiation effects (i.e., melting at air temperatures below 0 °C), spatial variability in snow melt within the AMSR-E pixel, or error in the NLDAS-2 air temperature data. However, while these data are not direct measurements of snow melt and refreeze, they suggest that the events identified by the ΔT_b-ΔT_a method make physical sense.

Figure 6

NLDAS-2 air temperature at a given AMSR-E overpass time (T_aⁱ) plotted against the air temperature at the time of the previous AMSR-E overpass (T_a^i-1; i.e., concurrent with the 12-hourly data used in the ΔT_b-ΔT_a method) for the AMSR-E pixel that contains Senator Beck Basin Study Area from fall 2002 to spring 2011. Melt events identified using the ΔT_b-ΔT_a method are shown in red points, while refreeze events are shown in blue points. All other data, where neither melt nor refreeze events were detected, are plotted as gray points. AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System; NLDAS-2 = North American Land Data Assimilation System, version 2.

5.3 Infrared Snow Surface Temperature

Measurements of snow melt are scarce. However, a small number of field sites collect remotely sensed snow surface temperature observations using infrared thermometers. While still an indirect measurement, this is one of the most definitive indications of snow melt, as liquid water cannot exist at the snow surface unless the snow reaches 0 °C. Snow surface temperature is collected at two locations in Senator Beck Basin Study Area using AlpuG SnowSurf infrared thermometers: SBSP and SASP (Landry et al., 2014).

Figure 7 shows the infrared snow surface temperature in Senator Beck Study Basin at a given AMSR-E overpass time (T_IRⁱ) plotted against the infrared snow surface temperature at the time of the previous AMSR-E overpass (T_IR^i-1; i.e., concurrent with the 12-hourly data used in the ΔT_b-ΔT_a method). The melt events identified using AMSR-E T_b and NLDAS-2 T_a via the ΔT_b-ΔT_a method (red points) cluster in negative values on the y axis, and near a snow surface temperature of 0 °C on the x axis, indicating that the snow surface began below freezing at the previous AMSR-E overpass and warmed to the melting point by the time of the subsequent AMSR-E overpass (approximately 12 hr later). The refreeze events (blue points) cluster near 0 °C on the y axis and in negative values on the x axis, indicating that the snow began near the melting point and then fell to freezing temperature. These results show that the snow melt and refreeze events identified from satellite data are consistent with conditions necessary for snow melt and refreeze, respectively, detected using independent ground measurements.

Figure 7

Ground-based infrared snow surface temperature at a given AMSR-E overpass time (T_IRⁱ) plotted against the air temperature at the time of the previous AMSR-E overpass (T_IR^i-1; i.e., concurrent with the 12-hourly data used in the ΔT_b-ΔT_a method) from spring 2005 to spring 2011. Data are shown for the two sites in Senator Beck Basin Study Area: Swamp Angel Study Plot (left panel) and Senator Beck Study Plot (right panel). Melt events identified using the ΔT_b-ΔT_a method are shown in red points, while refreeze events are shown in blue points. All other data, where neither melt nor refreeze events were detected, are plotted as gray points. The snow temperature changes observed for the melt and refreeze events identified using the ΔT_b-ΔT_a method are consistent with the necessary conditions for snow melt and refreeze, respectively (i.e., snow temperature below 0 °C followed by an increase to near 0 °C for melt events and snow temperature near 0 °C followed by a decrease below 0 °C for refreeze events). AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System.

One feature that is noticeable in this figure, especially for SBSP, is that the infrared measurements do not always indicate that the snow surface temperature reached 0 °C during melt events or began at 0 °C before freeze events. This is potentially due to the temperature estimation method of the infrared instrument, which assumes a snow emissivity of 0.98. If the snow emissivity falls below this value, the snow surface temperature measurements will have a low bias and thus fall below 0 °C for the identified snow melt and refreeze events. Another possibility is obstruction of the instrument window due to blowing snow, which is likely more common at the open, alpine Senator Beck site than at the sheltered, subalpine Swamp Angel site, or ice growth on the instrument aperture. Finally, the lower-altitude Swamp Angel site may be more representative of the broader AMSR-E pixel (from which melt and refreeze events were identified), while the snow at the higher altitude Senator Beck site may remain frozen during the period when most of the lower-altitude surrounding area experiences melt events. This is a possibility, because the snow disappears approximately 2 weeks later at the Senator Beck site compared to the Swamp Angel site (see Figure 5), suggesting a lag in melt timing at higher altitude. Using the Microwave Emissions Model for Layered Snowpacks, Vuyovich et al. (2017) found that the aerial extent of wet snow within a satellite pixel is approximately proportional to the magnitude of the response in observed 36.5-GHz brightness temperature. So, if most of the pixel contains wet snow, but snow remains frozen at high altitudes, this could trigger a melt or refreeze detection in the ΔT_b-ΔT_a method that would not compare well with snow surface temperature at SBSP.

5.4 Snowpack Energy Balance

The energy balance was calculated on an hourly basis at each of the two Study Plots of Senator Beck Basin Study Area starting in July 2005 (see supporting information for details). Concurrent estimates of the mean snow temperature in the bottom 40 cm of the snowpack were calculated by averaging the observations that were within the snowpack (see section 3.3). In order to melt snow, the snow temperature must be 0 °C. Therefore, as snow temperature decreases, the cold content increases so that more energy is needed to reach the melting point. While it is not realistic to expect that the entire snowpack will always be isothermal (i.e., same temperature at the base and surface of the snow), the temperature of the bottom 40 cm of the snowpack is a reasonable indicator of how much energy is necessary to approach conditions conducive to melting.

Figure 8 shows the temperature in the bottom 40 cm of the snowpack at a given AMSR-E overpass time (T_Snowⁱ) versus the difference in the rate of energy input into the snowpack over the previous 12 hr (i.e., the energy input at the given AMSR-E overpass time minus the energy input at the previous AMSR-E overpass time; E_nⁱ − E_n^i-1). From this plot, we can see that melt (red points) occurs when there is an increase in energy input into the snowpack, and refreeze (blue points) occurs when there is a decrease in energy input. Additionally, melt and refreeze are much more likely to occur when the temperature in the bottom 40 cm of the snowpack is near 0 °C. Both of these characteristics make physical sense.

Figure 8

Mean temperature in the bottom 40 cm of the snowpack at a given AMSR-E overpass time (T_Snowⁱ) plotted against the difference in energy input rate into the snowpack between the times of the current and previous AMSR-E overpasses (E_nⁱ − E_n^i-1) for the two sites in Senator Beck Basin Study Area from winter 2006 to spring 2011. Melt events identified using the ΔT_b-ΔT_a method are shown in red points, refreeze events are shown in blue points, and all other data are plotted as gray points. Melt events occur predominantly when there is an increase in energy input into to the snow and when the snowpack is near to the melting point (0 °C). Refreeze events also occur when the snowpack is near 0 °C but when there is a decrease in energy input. AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System.

There are a handful of points that do not follow this pattern for the Swamp Angel site (i.e., melt indicated with negative difference in energy input, and vice versa). This can occur if, for example, the net energy input to the snowpack was positive for two consecutive time steps (i-1 and i), but the snowpack did not become isothermal in the previous 12-hourly period. If positive net energy input continues, then melt can be produced even if the energy input rate decreases.

Additionally, not all melt events occur when the bottom 40 cm of the snowpack is at 0 °C, especially at SBSP. This could mean that melt sometimes occurs at the snow surface before the snow has become isothermal. The alpine SBSP also receives higher mean and peak global solar irradiance than the subalpine SASP (Painter et al., 2012), which could potentially explain the prevalence of this effect at the former site. Alternately, the subalpine Swamp Angel site may be more representative of the broader AMSR-E pixel (from which melt and refreeze events were identified), as discussed in section 5.3.

6 Discussion

6.1 Comparison With the DAV Method

The ΔT_b-ΔT_a method presented above refines the melt detection capabilities of the DAV of Ramage and Isacks (2002) and other similar methods (Tedesco et al., 2009) by accounting for the effect of diurnal air temperature changes (a proxy for physical temperature change) on observed brightness temperature changes. The physical temperature contribution to the brightness temperature signal is removed, isolating the contribution from changes in emissivity (i.e., water phase changes). However, there are limited data available to precisely validate individual melt events at large scales and thus to determine whether the ΔT_b-ΔT_a method is more accurate than previous DAV methods. The potential improvement is also mainly limited to melt events with weak ΔT_b. This is illustrated in Figure 9, where the 18-K DAV threshold for AMSR-E from Apgar et al. (2007) has been added to the ΔT_b and ΔT_a data from Figures 2 and 4, respectively. (Note that in Figure 9, the threshold is ±18-K.) Events where the ΔT_b-ΔT_a method and the DAV method (including a minimum T_b threshold of 252 K) agree are shown in solid circles. Events triggered by the ΔT_b-ΔT_a method but not by the DAV method are shown as open circles, while events identified by the DAV method but not by the ΔT_b-ΔT_a method are shown with black outlines.

Figure 9

(left panel) Same as Figure 2 (Northern Great Plains AMSR-E pixel) and (right panel) same as Figure 4 (AMSR-E pixel containing Senator Beck Basin, Colorado), but instead comparing the melt and refreeze events identified by the ΔT_b-ΔT_a method to those identified by the DAV method (Apgar et al., 2007). The dashed black lines show the minimum DAV threshold of ±18 K, while the solid black line shows the modal linear regression fit to the data (from Figures 2 and 4, respectively). The solid red points are instances when both methods indicated melt events, and the solid blue points show agreement for refreeze events. The open red (blue) points are melt (refreeze) events identified by the ΔT_b-ΔT_a method that were not indicated by the DAV method. The open circles beyond the 18-K threshold are points that did not meet the minimum 252-K T_b threshold of the DAV method. The red circles with black outlines are melt events that were identified by the DAV method but not by the ΔT_b-ΔT_a method. AMSR-E = Advanced Microwave Scanning Radiometer for the Earth Observing System.

In the case of the NGP (left panel), the 18-K threshold for the DAV method seems to be too high. This is entirely possible, as the 18-K threshold was developed in the Yukon River basin, Canada, and the optimal DAV threshold may change with land cover type and snow properties (e.g., Tedesco et al., 2009). Some open circles are also present for T_b deviations beyond the ±18-K threshold in Figure 9. These are points that meet the >18-K DAV criterion but do not meet the >252-K T_b requirement. The ΔT_b-ΔT_a method does not currently include a minimum T_b requirement for melt and refreeze indication. For the AMSR-E pixel containing Senator Beck Basin, the 18-K DAV threshold is more appropriate, but it still identifies fewer melt and refreeze events than the ΔT_b-ΔT_a method. There were three melt events at the Senator Beck pixel that were indicated by the DAV method but not by the ΔT_b-ΔT_a method (red points with black outlines), while none of these instances occurred for the NGP pixel.

For small diurnal air temperature changes, the ΔT_b-ΔT_a method is similar to the DAV of Ramage and Isacks (2002; which does not consider air temperature) but may detect more or less melt events depending on the DAV threshold value. Air temperature change makes a larger contribution to the DAV as the diurnal change in air temperature increases (i.e., the solid, sloped line gets closer to the vertical, dashed lines in Figure 9 when ΔT_a is very high or low). Thus, when large diurnal changes in air temperature occur, the DAV method likely becomes more sensitive to weak melt and refreeze events than the ΔT_b-ΔT_a method. However, additional observations are needed to fully understand the additional value of the ΔTb-ΔTa method.

6.2 Limitations of the ΔT_b-ΔT_a Method

The ΔT_b-ΔT_a method is not without limitations. The method is dependent on the accuracy of the brightness temperature data. For instance, microwave radiation emitted from snow at higher microwave frequencies (e.g., 36.5 GHz) can be blocked by vegetation (Burke & Schmugge, 1982; Pampaloni & Paloscia, 1985) and may be subject to loss of information due to atmospheric attenuation (Wang & Tedesco, 2007). Additionally, it is important that the air temperature data used in the ΔT_b-ΔT_a method is accurate and representative of near-surface air temperature of the given area. It does not matter if the air temperature data are mean biased, as these data are only used to calculate diurnal differences, but the air temperature must be consistent in its relation to the actual temperature of the given area over time. Air temperature bias on a diurnal time scale could potentially alter the slope of the ΔT_b-ΔT_a relationship. Random error in the air temperature data will increase the variability around the linear ΔT_b-ΔT_a relationship (e.g., Figures 2 and 4), compared to air temperature with less error. Thus, added error will necessitate the selection of a larger threshold value for selection of melt/refreeze and thereby make identification of melt events more difficult and less effective. Moreover, we use air temperature change as a proxy for physical temperature change (because we do not precisely know the physical temperature of the region observed by the satellite). While correlated, these two quantities may not always be representative of each other. This is a source of uncertainty in our method that could also contribute to the scatter around the linear ΔT_b-ΔT_a relationship, and thereby make it more difficult to accurately identify melt and refreeze events. The snow cover fraction may also influence the amount of error around the ΔT_b-ΔT_a relationship or its slope, as snow may be less sensitive to air temperature changes than bare ground. However, the impact of snow cover fraction needs further evaluation.

Additionally, rain-on-snow events are not considered for this analysis. In T_b data alone, rain is indistinguishable from snow melt because they both result in emissivity changes by introducing liquid water to the snowpack. The ΔT_b-ΔT_a method is designed to identify diurnal snow phase changes by removing the effect of physical temperature changes, but it does not discriminate melt events from rain events. It is possible that rain events could explain some of the identified melt and refreeze events at below freezing temperatures in Figures 6-8, but this has not been investigated. Additional conditions could be added to the method to exclude rain on snow, such as use of precipitation phase information or air temperature thresholds.

The ΔT_b-ΔT_a method is also limited by the orbit and swath geometry of the satellite instrument used to observe brightness temperature. For AMSR-E, complete twice-daily coverage only occurs at above approximately 52° latitude. At lower latitudes, data may occasionally (or frequently) be missing for some 12-hourly observation times. The ΔT_b-ΔT_a method requires consecutive 12-hourly observations, so a single missing T_b observation will result in missing ΔT_b data for two consecutive time steps. This does not reduce the effectiveness of the method in identifying melt and refreeze events when data are available, but events may be missed due to missing data at lower latitudes.

The use of the ΔT_b-ΔT_a method depends on fitting a modal regression line to ΔT_b and ΔT_a data for frozen snow. Therefore, this method will only be effective if the given location experiences enough days with below freezing temperatures (where the snow remains frozen) to confidently fit the regression line. Therefore, it will not be viable in consistently warm, wet snowpacks.

As mentioned in section 4, the selection of the threshold for identifying melt and refreeze events (as a deviation from the modal linear regression fit to the ΔT_b-ΔT_a data) is somewhat subjective. A threshold deviation of about 10 K from the regression line was chosen for the NGP and Colorado locations in this study because it separated the variability around the linear ΔT_b-ΔT_a relationship from the large ΔT_b deviations, based on visual inspection. However, this threshold may change according to the properties of the land surface (e.g., vegetation, topography, presence of water bodies, and mean snow depth) and will be limited by the accuracy of the air temperature and brightness temperature data, as well as how closely the air temperature represents the physical temperature of the area observed by the satellite. Users should consider whether minimizing false positives (i.e., identifying a melt or refreeze event when in reality there was none) or false negatives (i.e., failing to identify a melt or refreeze event) is more important for their chosen application.

7 Conclusions

This study presented a new method to enhance detection of melt and refreeze events using passive microwave satellite observations, which builds on the DAV of Ramage and Isacks (2002) and others. The method is based on an observed relationship between diurnal air temperature change and concurrent brightness temperature change at an approximately 12-hourly time step. Melt and refreeze events are identified as large deviations from a modal linear regression fit to the ΔT_b-ΔT_a relationship (hence the “ΔT_b-ΔT_a method”). This method refines the DAV by removing the influence of diurnal air temperature changes on concurrent brightness temperature changes, allowing for isolation of snow phase changes. Additionally, the calculation of 12-hourly differences permits differentiation between snow melt events and snow refreeze events, which are lumped together in the DAV.

The ΔT_b-ΔT_a method can be calculated for any passive microwave instrument with Ka-band observations and approximately 12-hourly overpasses (i.e., at two different times of the day), such as the Scanning Multichannel Microwave Radiometer (SMMR), SSM/I & SSMIS, AMSR-E, and AMSR2. The overpass timing must be fairly consistent and regular, so satellite instruments with other orbital periods, such as those on the Global Precipitation Measurement (GPM) Core Observatory satellite, would not work with this method without significant alterations. The ΔT_b-ΔT_a method is likely most effective for 12-hourly overpass times with the largest diurnal differences in temperature (i.e., close to the overnight low and daily high air temperature), because this would lead to the largest range of ΔT_b and ΔT_a values. However, the method has not yet been tested with T_b observations from platforms other than AMSR-E.

Most studies that utilized the DAV focused on the spring melt onset period (i.e., the period of daily snow melt and refreeze that marks the transition between persistently frozen snow in the winter and persistently wet [or absent] snow in the spring), due to the importance of snow melt timing for spring streamflow, vegetation green-up, and other ecological and biochemical processes. However, identification of individual melt and refreeze events throughout the winter can provide additional information about snow properties. For instance, snow stratigraphy is important for remote sensing of SWE, so the melt and refreeze events from the ΔT_b-ΔT_a method may be useful to inform or evaluate models of snow morphology. Further studies will apply the method at the continental scale and over a longer time period in order to assess the spatiotemporal distribution and trends of melt and refreeze events.

Acknowledgments

The authors gratefully acknowledge support from NASA Applied Sciences grant NNX15AC47G. Thank you to the three anonymous reviewers for their comments on this manuscript. The AMSR-E brightness temperature and MEaSUREs snow cover data used in this research are freely available from the NSIDC (https://nsidc.org/data/nsidc-0301 and https://nsidc.org/data/NSIDC-0530, respectively). The NLDAS-2 air temperature data are freely available from the NASA GES DISC (https://disc.sci.gsfc.nasa.gov/datasets/NLDAS_FORA0125_H_V002/summary). The data from Senator Beck Basin Study Area are freely available from the Center for Snow and Avalanche Studies website (https://snowstudies.org/archived-data/).