1 INTRODUCTION

More than 26% of the global population depends on snowmelt runoff as their main water source (Mankin et al., 2015). Snow-dominated forested headwaters therefore contribute substantially to sustainable water supply; for example, North American forests cover approximately 40% of the snow zone (Klein et al., 1998). However, the snowpack in western North America has declined unprecedently in recent decades and is projected to further decrease at all elevations throughout the 21st century and beyond (Barnett et al., 2008; Mote et al., 2018).

Snow duration is the net result of accumulation and ablation and can be lengthened or diminished, depending on climate and the effects of forest vegetation (Varhola et al., 2010). Snow accumulation and ablation are affected by forest cover acting synergistically with the climate regime (Lundquist et al., 2013). Forests reduce snow accumulation by intercepting precipitation (Hedstrom & Pomeroy, 1998; Huerta et al., 2019) and affect snow ablation by either reducing or increasing melt rates (Essery et al., 2008; Mahat & Tarboton, 2012). Subcanopy snow receives less solar radiation (Musselman et al., 2012; Webster et al., 2016a), but this reduction in energy can be offset or reversed by increased longwave radiation emitted from the canopy and tree boles (Malle et al., 2019; Webster et al., 2016b). Subcanopy snow is also sheltered from wind, which decreases snow redistribution, reduces turbulent fluxes at the snow surface and lowers sublimation rates (Reba et al., 2012).

Warmer climate conditions will affect forest snowpack not only through changes in average temperature and precipitation but also through increased ecosystem stress from changes in the severity of summer droughts (Luce et al., 2016). That is, warmer and drier conditions increase forests' susceptibility to disturbances (Seidl et al., 2017), leading, for example, to spatially larger and more frequent fires that alter vegetation cover and forest structure (Dennison et al., 2014). In addition, earlier spring snowmelt is associated with an earlier onset and longer duration of the wildfire season in certain climates (Westerling et al., 2006). Accelerated fire-mediated vegetation changes, combined with changing temperature, precipitation and snow regimes, could change snowmelt runoff magnitude and timing substantially (Gleason et al., 2019).

Fire is a characteristic ecological process in montane conifer forests of western North America, maintaining a dynamic mosaic of different forest structures and compositions (Agee, 1998). Effects of fire on forest structure and, therefore, on forest snowpack and runoff, depend on fire severity and pre-fire forest structure (Boisramé et al., 2017; Stevens, 2017). Fire severity is defined as the magnitude of the effect that a fire has on the environment, i.e., the degree to which a site has been altered (Lentile et al., 2006). Although high-severity fires can cause stand replacement, low- to moderate-severity fires are commonly associated with substantial tree survival (Sugihara et al., 2006). Fire-induced canopy removal and tree mortality typically lead to reduced snow interception and increased light transmission and wind speeds, modifying the surface energy balance and snow accumulation and ablation rates (Burles & Boon, 2011; Micheletty et al., 2014; Winkler, 2011; Figure 1). In addition, charred woody debris and increased litter fall due to immediate or delayed tree mortality decrease snow albedo and accelerate snow albedo decay (Gleason & Nolin, 2016). These dark-coloured materials absorb solar radiation and release it as longwave radiation into the subcanopy snowpack, increasing ablation rates (Gleason et al., 2013). The amount of litter and debris falling onto the snow surface depends on fire severity and post-fire tree mortality rates, with the effect on snow albedo persisting for up to 15 years after high-severity fire (Gleason et al., 2019).

After high-severity fire, the immediate and short-term effects of canopy removal influence snow accumulation and ablation rates (Figure 1), which can lead to earlier but higher snowmelt runoff in post-fire environments relative to unburned forests. For example, Burles and Boon (2011) found for the southern Canadian Rocky Mountains that 50% more snow water was available for melt in burned compared to unburned forest, but mean daily ablation rates were three to five times higher, which could alter the snow duration and water provision in spring and summer months when water demands increase.

Low- to moderate-severity fire preferentially kills smaller-diameter trees while leaving at least some larger trees alive (Kane et al., 2013; Lutz, Furniss, et al., 2017; Lutz, Matchett, et al., 2017). This may lengthen or diminish snow duration, depending on the presence and spatial distribution of large trees in the post-fire forest. Large-diameter trees are a feature of old-growth forests; their large canopies intercept snow and reduce solar radiation transmission (Lutz et al., 2013, 2018). Therefore, heterogeneity in tree canopies at scales equivalent to canopy radii (between 1 and 10 m) likely contributes to small-scale differences in snow duration, which could moderate fire effects on snowmelt runoff at landscape scales.

Accurate predictions of snow duration depend on understanding the net effects of forested environments on snowpack, which can be inferred from observations on the spatial distribution of subcanopy snow (Dickerson-Lange et al., 2015; Molotch et al., 2009; Roth & Nolin, 2017; Schneider et al., 2019; Teich et al., 2019). Despite the prevalence of fire and its known effects on snow duration, few direct observations exist for snowpack accumulation and ablation in fire-affected forests (Burles & Boon, 2011; Gleason et al., 2013; Harpold et al., 2014; Stevens, 2017; Winkler, 2011). Understanding how post-fire tree mortality and forest structure affect snow accumulation and ablation processes is important for forest and water managers to reliably predict magnitude and timing of snowmelt runoff from burned areas.

Therefore, we asked how snow duration is affected by post-fire tree neighbourhood characteristics and tree mortality-induced deposition of charred debris and litter at spatial scales between 2.5 and 40 m in an old-growth, mixed-conifer forest in the Sierra Nevada, California, USA. We used annual, spatially explicit data documenting trees and tree mortality, snow depth and snow disappearance collected at the Yosemite Forest Dynamics Plot (YFDP) 3, 4 and 5 years after the YFDP burned at low to moderate severity in the Rim Fire of August 2013.

2 METHODS

2.1 Study site

The Yosemite Forest Dynamics Plot (YFDP) is one of the 71 Smithsonian ForestGEO large, spatially explicit study sites (Davies et al., 2021) and is located in Yosemite National Park, California, USA (37.77°N, 119.92°W), in an old-growth white fir–sugar pine (Abies concolor–Pinus lambertiana) mixed-conifer forest (Figure 2; for details, see Lutz et al., 2012; van Wagtendonk et al., 2020).

The 25.6-ha YFDP was established in 2009 and 2010 on mostly north-facing slopes with a mean inclination of 19.5°. Elevation ranges from 1,774 to 1,911 m. The climate of the YFDP is Mediterranean and characterized by cool, wet winters and warm, dry summers. The modelled mean daily temperature for the period between 1981 and 2010 ranged from −2.7°C to 9.7°C in February and 12.2°C to 26.1°C in July (PRISM Climate Group, 2012); the majority of precipitation falls as snow during the winter months with a mean annual precipitation of 1,061 mm (Lutz et al., 2012). Annual snow accumulation and duration over the study period from 2016 to 2018 were marked by considerable variation. Snow water equivalent (SWE) on 1 April, retrieved from snow courses at the nearby Gin Flat station (CDEC code: GFL), was 597 mm in 2016, which is 74% of the 89-year average of 807 mm. SWE in 2017 was above normal at 940 mm (116% of average), and SWE in 2018 was below normal at 432 mm (53% of average). The study period was also preceded by 4 years of snow drought, including 2015, which had the lowest 1 April SWE of 0 mm (Figure S1).

During plot instalment all trees with a diameter at breast height (dbh) ≥ 1 cm were identified, measured and mapped (38,009 stems). Tree species were A. concolor, which accounted for 46% of the pre-fire basal area, P. lambertiana (45%), Calocedrus decurrens (7%) and Quercus kelloggii (2%) as well as Cornus nuttallii, Prunus spp., Abies magnifica, Salix scouleriana, Pseudotsuga menziesii, Pinus ponderosa and Rhamnus californica with less than 1% each of the total basal area. The dominant and fire-tolerant tree species P. lambertiana and A. concolor (fire intolerant when small) were also the most abundant large trees (69% and 21% of the total number of live trees with dbh ≥ 100 cm), which were spatially clustered over scales between 2 and 38 m (Lutz et al., 2012). Following the initial census, tree mortality was assessed annually, and dbh and height of each newly dead tree were recorded.

The historical (pre-Euro-American settlement) fire regime of the YFDP was characterized by low- to moderate-severity surface fires and a mean fire return interval of 29.5 years, but the area has been largely fire-excluded since 1900, leading to high tree density (Barth et al., 2015). In early-September 2013, the YFDP was burned at low- to moderate-severity (based on the satellite-derived differenced Normalized Burn Ratio [dNBR]; Key & Benson, 2006) in a fire set by Park managers to control the spread of the Rim Fire (Kane et al., 2015; Figure 2b). The fire was unmanaged after ignition, and the patterns of post-fire survival were broadly characteristic of the natural fire regime (Cansler et al., 2019; Lutz, Furniss, et al., 2017). In May 2014, every stem in the YFDP was revisited and, in addition to dbh and height of newly dead trees, bole scorch height and crown volume scorched (CVS) were recorded. The Rim Fire led to immediate mortality of 63.5% of trees (i.e., 24,154 trees had died by May 2014), and 3-year mortality rates of 82% for trees ≥1 cm dbh, 63% for trees ≥50 cm dbh and 28% for trees ≥100 cm dbh. Trees that died immediately (i.e., within 1 year of the fire) had a mean dbh of 7.4 cm while the mean dbh of surviving trees 1 year post fire was 35.1 cm. The mean CVS was 82% for trees ≥1 cm dbh, 19% for trees ≥50 cm dbh and 12% for trees ≥100 cm dbh (Furniss et al., 2019).

2.2 Data

2.2.1 Snow disappearance timing

The YFDP was equipped with Onset (Cape Cod, Massachusetts) HOBO Pendant loggers (hereafter referred to as HOBOs) continuously collecting temperatures at the soil-snow interface during water years (WYs; e.g., WY 2016: 1 October 2015 to 30 September 2016) 2016–2018. Sixty-three HOBOs were installed on a regular grid and at the soil interface throughout the YFDP (Figure 2b). The grid positioned 40 HOBOs within 40 m of the edge of the YFDP and at least 80 m apart from one another. Fourteen additional HOBOs were installed in the northeast corner of the plot and another nine in the northwest corner of the YFDP, which differs from the rest of the plot because of its south-eastern aspect. HOBOs were mapped to surveyed grid corners or trees based on slope-corrected distance and azimuth. HOBO sensors recorded temperature every 3 h during the winter months.

Two metrics were calculated from the HOBO temperature data: (1) at the plot scale, variability in snow disappearance timing and fractional snow-covered area (fSCA), and (2) at each HOBO location, the snow disappearance date (SDD). Diurnal fluctuations in surface ground temperature (T_g) are damped or absent when snow is present and insulates the ground due to its low thermal conductivity (Lundquist & Lott, 2008; Tyler et al., 2008). Therefore, daily snow presence can be inferred during periods with a reduced diurnal cycle in T_g (Dickerson-Lange et al., 2015; Schmid et al., 2012).

We converted T_g time series of 3-h intervals to daily time series of binary snow presence (i.e., 0 = snow-free, 1 = snow) at each sensor following the methods of Raleigh et al. (2013); i.e., snow on the ground was detected when the diurnal range in T_g was no greater than 1°C, indicating dampened temperatures associated with thermal insulation due to snow cover. Snow cover mapping also required T_g to not exceed 2.75°C (e.g., to account for potential sensor bias) and a minimum of 48 h with minimal changes (1°C) in T_g between 3-h timesteps. These thresholds were based upon inspection of histograms of the diurnal T_g range and 3-h values of T_g and matched values used by Raleigh et al. (2013). A final constraint was imposed by requiring a three-day minimum precipitation accumulation of 10 mm for new snow cover to be detected from previously snow-free conditions. This was done to reduce false positives in snow cover during extended cold and cloudy but dry conditions prior to establishment of persistent snow cover. We used precipitation time-series data from the daily 4-km PRISM (Daly et al., 1994) product to calculate three-day precipitation totals.

Using all HOBOs each year, daily time series of fSCA were derived to represent snow cover dynamics at the plot scale. For each day, the number of sensors reporting snow presence was summed and divided by the total number of active sensors to calculate fSCA. Using the daily snow presence time series from each HOBO sensor during each year, we calculated SDD. First, the day of the WY where snow disappeared following the final snow event was identified (SDD_final). Second, the longest period of continuous snow cover was found, and SDD_cont was calculated as the day of the WY when snow disappeared in that period. If the longest period of continuous snow cover occurred twice in a WY (e.g., a 10-day period in December and a 10-day period in March), then the later period in that WY (e.g., March in the prior example) was selected for determining SDD_cont. We then standardized SDD_final and SDD_cont for each HOBO location and year to account for year-to-year variations in snow fall (Equation 1):

$${\mathit{\text{sSDD}}}_i=\frac{\left({\mathit{SDD}}_i-\mu \right)}{\sigma },$$ (1)

where SDD_i is the snow disappearance date at the ith HOBO location, μ is the mean SDD in each year and σ is the standard deviation in SDD across all sensors in that year.

2.2.2 Snow depth distribution

On 13–15 March 2017, during a period of snow ablation, we sampled snow depth (HS) along one 798-m, east-to-west transect (Transect 1) and a parallel 342-m, east-to-west transect (Transect 2) that spanned areas of all burn severities in the YFDP (Figure 2b). Snow depth was measured with 1-cm graduated avalanche probes every 3 m along each transect. A compass and a detailed stem map were used to find the sampling point locations with an estimated horizontal accuracy of ±50 cm. On 25–27 March 2018, we repeated HS measurements along the same two transects (expanding Transect 2 to 699 m) and at the same locations as in 2017, but after a snowfall event, i.e., during a period of snow accumulation rather than ablation. Sampling points were omitted if their location coincided with a tree bole or a stream.

To study patterns of spatial correlation and to define focal points for further analysis of tree neighbourhood-snowpack interactions, we used experimental and modelled semivariograms (hereafter referred to as variograms) following the approach recommended in Oliver and Webster (2014). First, one experimental variogram was estimated for each year from our snow depth measurements by (Equation 2):

$$\widehat{\gamma }\left(\mathrm{h}\right)=\frac{1}{2m\left(\mathrm{h}\right)}\sum _{i=1}^{m\left(\mathrm{h}\right)}{\left\{z\left({\mathrm{x}}_i\right)-z\left({\mathrm{x}}_i+\mathrm{h}\right)\right\}}^2,$$ (2)

where z denotes snow depth measurement pairs at locations x, i = 1, 2, … separated by the lag distance h, and m(h) is the number of paired comparisons at lag distance h.

By incrementing the lag distance (h) in 3-m steps as given by one interval of our equally spaced snow depth measurements, we obtained and plotted an ordered set of values for each year (i.e., two experimental variograms). We then fit spherical and exponential models by weighted least squares (Cressie, 1985) and plotted the fitted models on the graph of the experimental variogram. Lastly, we assessed the fit of each model, calculated the (weighted) sum of squared errors (SSE) and chose the model with the smallest SSE (Figure S2).

Sill (variance approached at large lag distances, i.e., the variance of the random process) and range (the lag distance at which the model variogram reaches 95% of the sill variance, i.e., the limit of the spatial correlation) were calculated from the best-fit modelled variogram for each year. Since HS observations that are closer to one another than the range are autocorrelated and those farther apart are independent, we used the range, which was 9.5 in 2017 and 8.5 in 2018, to define the distances between focal points along our transects. That is, we randomly selected a snow depth sampling point along each transect and, starting from that point, selected snow depth sampling points in East and West directions spaced by 9 m. These focal points represent independent HS observations (124 in 2017 and 166 in 2018), and their UTM coordinates were then used to calculate tree neighbourhood metrics to study the influence of tree neighbourhood structure on snow depth distribution. Analysis of spatial correlation was conducted in R version 4.1.1 using the gstat package version 2.0–8 (Gräler et al., 2016; Pebesma, 2004; R Core Team, 2021).

2.2.3 Tree neighbourhood and mortality metrics

Using tree locations and mortality data, we first calculated a suite of tree neighbourhood and mortality metrics to describe the vegetation surrounding two types of focal points: (1) the 63 HOBO locations (see Section 2.2.1) and (2) the focal point locations along the snow depth transects (see Section 2.2.2). For each HOBO location and snow depth transect focal point, we computed nine neighbourhood metrics for 2013 through 2018 within radii of 2.5, 5 and 10 m (Table 1; Figure 3). Three of the nine metrics (density of live trees [D_tree], density of snags [D_snag] and mortality rate [Mort]) were calculated specific to five dbh classes (dbh <10, 10–30, 30–60, 60–100 and >100 cm).

TABLE 1. Tree neighbourhood and mortality metrics calculated within radii of 2.5, 5 and 10 m of focal points for each year from 2013 to 2018 using tree and tree mortality data from the Yosemite Forest Dynamics Plot

Tree neighbourhood metrics	Symbol	Unit
Density of live trees by diameter classa	Dtree(<10, 10–30, …)	Stems ha−1
Density of snags by diameter classa	Dsnag(<10, 10–30, …)	Stems ha−1
Density of deadwood in each year	Dlog	Stems ha−1
Mortality rate by diameter classa,b	Mort(<10, 10–30, …)	—
Basal area of live trees	BAtree	m2 ha−1
Basal area of snags	BAsnag	m2 ha−1
Basal area of deadwood	BAlog	m2 ha−1
Mean scorch height	SHmean	m
Crown volume dead	CVD	m2 ha−1

• ^a dbh < 10, 10–30, 30–60, 60–100, >100 cm.
• ^b Number of new mortalities in the current year ÷ number of live trees in the previous year.

Mean bole scorch height (SH_mean) in 2016, 2017 and 2018 was calculated for standing trees and snags, using the 2014 bole scorch height records. Trees and snags that fell in 2016–2018 were not included in the calculation of SH_mean after they had fallen.

To represent the volume of dead tree crowns in the neighbourhood in 2016, 2017 and 2018, we multiplied the percent CVS of each live tree by its basal area and added these values to the basal area of trees in the neighbourhood that died in or after the fire. We refer to this metric as crown volume dead (CVD, or dead crown basal area [m² ha⁻¹]). This metric is a proxy in units of basal area for the volume of dead needles in the canopy, which influences canopy transmittance.

In addition to the neighbourhood metrics calculated within radii of 2.5, 5 and 10 m, we computed a shading metric, S_tree, as the density of live trees inside a 180° half-ring on the south side of each HOBO (see Figure S3 and Table S1 for details). To avoid redundancy with the other neighbourhood metrics that extend to a 10 m radius, the S_tree metric was calculated for inner and outer radii of 10 and 40 m, respectively, for dbh-classes 10–30, 30–60, 60–100 and >100 cm. We selected 40 m as the maximum distance because HOBOs were placed at least 40 m within the YFDP boundary. The S_tree metric accounts for the effects of shading on snow disappearance by trees that are 10–40 m from the HOBO locations.

2.2.4 Litter density

Adjacent to each of the 63 HOBO locations, litter deposition measurement sites were installed in July 2015 (Figure 2b). Each litter deposition measurement site contained two 0.544 m × 0.544 m litter traps collecting litter and debris in an interception area of 0.296 m² (Figure 2c). During installation, the existing litter was cleared away, and the frame was secured to the ground with two stainless steel bolts that were hammered through holes drilled in two sides of the frame. The centre of each litter trap was mapped to surveyed grid corners based on slope-corrected distance and azimuth. The slope of each litter trap was measured with a digital inclinometer so that the area of litter deposition could be slope corrected. Litter and woody debris that fell onto the snow surface over the winter accumulated in the snowpack and were deposited in the litter traps after snow melt. The litter traps were emptied in May 2016, 2017 and 2018. Litter pieces that extended over the wooden frame of the litter trap were clipped at the inner edge of the wooden frame. Only litter that landed directly over the interior mesh of the trap was collected.

The litter and 1-h fuels (<0.6 cm) were dried and weighed; cones were not included. We calculated litter density (D_litter) in kg m⁻² for WYs 2016–2018 based on litter weight at the two litter deposition traps and total slope-corrected area of the two trap interiors (Figure S4). We tested for correlation between D_litter and tree mortality (Mort₁₀) and found no relationship between them. We further used the Kruskal–Wallis test to examine differences in D_litter and tree mortality rates in 2016–2018. No significant differences were found in D_litter among the 3 years (χ²[2] = 0.71, p = 0.97), but tree mortality rates differed significantly (χ²[2] = 12.12, p = 0.002).

2.2.5 Incoming solar radiation

To represent variations in snowmelt energy across the YFDP, we modelled hourly incoming solar radiation over WYs 2016–2018 across a digital elevation model (DEM) at a 1 m spatial resolution (derived from aerial LiDAR data acquired in 2010 by Watershed Sciences Inc., Corvallis, Oregon; Lutz et al., 2012). The modelled solar radiation was produced with ALPINE3D, a detailed distributed model for representing surface processes in mountains (Lehning et al., 2006). Because nearby surface observations of solar radiation were unavailable, the source solar radiation data were taken from the NLDAS-2 hourly reanalysis at a 1/8° resolution (Xia et al., 2012). The NLDAS-2 grid nearest to the YFDP was identified and treated as a surface station. At each hourly time step, ALPINE3D split the global radiation data from the NLDAS-2 grid cell into direct and diffuse components to account for variations in atmospheric state and cloudiness (Erbs et al., 1982; Iqbal, 1983). ALPINE3D then distributed these across the 1 m YFDP model domain while accounting for solar geometry, surface slopes and aspects, and topographic shading (Meeus, 1998), which were recombined to a single incoming solar radiation value at each hour and location. The ALPINE3D simulations were conducted using a bare-earth DEM (i.e., no vegetation) because canopy effects were accounted for with tree neighbourhood and mortality metrics. In each of the three study years, we computed the average incoming solar radiation Rad (W m⁻²) at each 1 m grid location over two periods: mid-winter (1 December to 28 February; Rad_winter) and spring (1 March to 31 May; Rad_spring; Figure S5). These summarized solar radiation metrics were then extracted at each HOBO location for the linear mixed models analyses of snow disappearance timing.

3 RESULTS

3.1 Snow disappearance timing

Daily fSCA values were either <0.1 or >0.9 approximately 90% of the time, with intermediate values observed during melt events (Figure 4). The drier WY 2018 had four short periods of snow cover, while the relatively wetter WYs 2016 and 2017 had fewer but longer periods of snow cover.

On average, snow disappeared earlier in 2016 compared to 2017 and 2018, which showed a longer lasting snowpack until the beginning of May for both SDD measures (Table 2); however, variation in the disappearance of continuous snow cover (SDD_cont) was higher among HOBO locations in 2017 and 2016 than in 2018. The day of the WY when snow disappeared after the final snow event (SDD_final) varied only slightly between HOBO locations in all WYs.

TABLE 2. Summary of snow disappearance date (SDD) calculated from surface ground temperature measurements (HOBO) following the longest period of continuous snow cover (SDD_cont) and the final snow event (SDD_final) in a water year (WY) at the Yosemite Forest Dynamics Plot

	WY
	2016		2017		2018
Summary statistics	SDDcont	SDDfinal	SDDcont	SDDfinal	SDDcont	SDDfinal
Number of data points (HOBOs)	60	60	63	63	63	63
Earliest (DOWY)	132	134	131	162	175	175
Latest (DOWY)	191	191	209	211	204	204
Mean (DOWY)	146	169	182	199	190	202
Median (DOWY)	147	170	184	199	190	203
Standard deviation (DOWY)	10.8	7.7	17.7	6.1	5.2	4.2
Coefficient of variation	7.40	4.51	9.73	3.05	2.71	2.10

• Abbreviations: DOWY, day of water year; WY, 1 October to 30 September.

Our best-fit LMM suggests that variation in the day of the WY when snow disappeared after the longest period of continuous snow cover (response variable sSDD_cont) was best explained by the fixed effects PC2_SDD(5), PC1_SDD(5), D_litter and Rad_winter (Table 3). These combined fixed effects explained approximately 27% of the observed variance (R²_m = 0.27). PC2_SDD(5) and PC1_SDD(5) were the most important predictors followed by the amount of litter that fell throughout the year and accumulated in the snowpack (D_litter) and simulated incoming winter solar radiation (Rad_winter). The tree neighbourhood metrics associated with the second and first PCs within a 5-m radius around each HOBO location were associated with earlier snow disappearance. In contrast, tree neighbourhood metrics calculated within a closer distance (r = 2.5 m) or a further distance (r = 10 m) to HOBO locations had no significant effect on sSDD_cont. The R²_c, which is interpreted as the variance explained by the entire model, is 0.57.

TABLE 3. Fixed effects estimates and analysis of deviance table (Type II Wald χ² test), where values represent the effect of predictor variables on the day of the water year when snow disappeared after the longest period of continuous snow cover (sSDD_cont)

	Direction of PC loadings ≥∣0.40∣	Estimate	SE	χ2	p	Summed Akaike weights for variable importance
PC2SDD(5)	+BAtree +Dtree(>100)	−0.17	0.06	9.33	0.002	0.93
PC1SDD(5)	−BAsnag −Dsnag(>100) −CVD	−0.17	0.05	11.81	<0.001	0.87
Dlitter		−0.23	0.09	6.25	0.012	0.86
Radwinter		−0.01	<0.00	11.33	<0.001	0.68

• Note: Variable importance weights are based on a global model fit containing N = 524,288 models. See Table 4 for principal component (PC) loadings.
• Abbreviation: SE, standard error.

The loadings of PC2_SDD(5) and PC1_SDD(5) quantify the contribution of each forest neighbourhood metric to each principal component (Table 4). PC2_SDD(5) is a measure of BA_tree and D_tree(>100). PC1_SDD(5) is a measure of BA_snag, D_snag(>100) and CVD which are all negatively related to PC1_SDD(5). Early snow disappearance was therefore associated with a high density of trees with dbh > 100 cm, increasing basal area of live trees, a low density of large snags and decreasing dead crown volume, in combination with increasing litter density and higher simulated incoming solar winter radiation.

TABLE 4. Loadings of variables (tree neighbourhood metrics) for the principal components (PCs, cutoff = 0.1) that were part of the best-fit LMMs to predict the day of the water year when snow disappeared after the longest period of continuous snow cover (sSDD_cont; PC2_SDD(5), PC1_SDD(5)) and the final day of snow disappearance (sSDD_final; PC2_SDD(5), PC2_SDD(10), PC1_SDD(5))

Variable	Principal component
	PC2SDD(10)	PC1SDD(5)	PC2SDD(5)
Dtree(<10)	−0.362	0.167	−0.161
Dtree(10–30)	−0.277	0.221	−0.101
Dtree(30–60)	0.216		0.271
Dtree(60–100)	0.409		0.372
Dtree(>100)		0.120	0.440
Dsnag(<10)	−0.361	0.195	−0.209
Dsnag(10–30)	0.125	−0.104
Dsnag(30–60)	0.358	−0.277
Dsnag(60–100)	0.215	−0.226	0.193
Dsnag(>100)	−0.288	−0.459	−0.146
Dlog	−0.293	0.138	−0.250
BAtree	0.273		0.606
BAsnag	−0.086	−0.556
BAlog
CVD		−0.434

• Note: Principal component analyses were performed separately for circles of radii 10 m (PC_SDD(10)), 5 m (PC_SDD(5)), and 2.5 m (PC_SDD(2.5)) surrounding HOBO locations. Loadings in bold (≥∣0.40∣) are considered most important for each PC. See Table 1 for explanations of variable symbols.

The influence of Rad_winter was higher on south-facing slopes and led to an earlier disappearance of continuous snow cover (Figures 5a and S5). Mean densities of live trees with dbh > 100 cm within circles of radius 5 m were always higher (between 30 and 32 stems ha⁻¹) at HOBOs with a negative, and therefore earlier, sSDD_cont than they were at HOBOs with a positive, and therefore later, sSDD_cont (4 to 8 stems ha⁻¹). The presence or absence of large-diameter snags (dbh > 100 cm) within 5 m of a HOBO location had the opposite effect with mean values of 11–17 stems ha⁻¹ linked to earlier SDD_cont and 23–25 stems ha⁻¹ related to later SDD_cont (Figure 5b). Mean densities of large-diameter trees (between 10 and 18 stems ha⁻¹) within a 10-m radius of HOBO locations were similar at HOBOs with earlier and later disappearance of continuous snow cover; their potential shading effect was not significant in our best-fit LMM predicting sSDD_cont (Table 3).

Similar to sSDD_cont, the variation in the final day of snow disappearance (sSDD_final) was best explained by PC1_SDD(5) and PC2_SDD(5), but sSDD_final was also best explained by PC2_SDD(10) and simulated incoming solar spring radiation (Rad_spring) instead of Rad_winter (Table 5). These fixed effects explained about 19% of the observed variance (R²_m = 0.19); 58% of the observed variance was explained by the entire model (R²_c = 0.58). In contrast to sSDD_cont, D_litter had no significant effect on the final snow disappearance date. In addition to the simulated incoming solar spring radiation, and basal area and number of large trees and snags present within 5 m of a HOBO location (PC2_SDD(5) and PC1_SDD(5)), sSDD_final was also influenced by the number of larger trees (60 cm < dbh < 100 cm) that were present within a distance of 10 m. PC2_SDD(10) is a measure of D_{tree(60–100)} (Table 4), distinguishing tree neighbourhoods with a high number of larger trees (positive loadings) from tree neighbourhoods with high numbers of small-diameter trees (D_tree[<10]) and snags (D_snag[<10]). Both best-fit LMMs showed that HOBO locations that were surrounded by a higher number of large-diameter trees within 5 m melted out earlier (Figures 5 and 6). However, a higher density of larger trees within 10 m (D_{tree(60–100)}), which was the tree neighbourhood metric that dominated the second most important predictor variable PC2_SDD(10), had the opposite effect on final snow disappearance, showing that large-diameter trees also prolong the duration of the spring snow cover by shading.

TABLE 5. Fixed effects estimates and analysis of deviance table (Type II Wald χ² test), where values represent the effect of predictor variables on the final day of snow disappearance (sSDD_final)

	Direction of PC loadings ≥∣0.40∣	Estimate	SE	χ2	p	Summed Akaike weights for variable importance
PC2SDD(5)	+BAtree +Dtree(>100)	−0.25	0.07	11.56	<0.001	0.90
PC2SDD(10)	+Dtree(60–100)	0.16	0.08	4.23	0.040	0.65
Radspring		−0.02	0.01	6.67	0.010	0.62
PC1SDD(5)	−BAsnag −Dsnag(>100) −CVD	−0.11	0.06	3.99	0.046	0.52

• Note: Variable importance weights are based on global model fit containing N = 524,288 models. See Table 4 for principal component (PC) loadings.
• Abbreviation: SE, standard error.

The tree neighbourhood metrics S_tree, which we included to account for shading effects from trees that are located outside of the 10-m radius circle, and mean bole scorch height (SH_mean) were not significant predictors in either of the two LMMs.

4 DISCUSSION

Snow is a key resource for fresh water supply and ecosystem function in California's water-stressed Mediterranean climate (Fayad et al., 2017; Kittredge, 1953). Snow duration determines the water availability in spring and summer months and is the net result of snow accumulation and ablation, which are both affected by the presence of trees (Lundquist et al., 2013). Forests shield the snowpack from solar radiation and can prolong snow duration, extending water availability into the summer months (Schneider et al., 2019). In warmer Mediterranean climates, snow interception and longwave radiation emitted from the canopy and tree boles dominate accumulation and ablation processes, usually leading to less snow under the canopy compared to open areas and highly variable daily fractional snow-covered area values (Figure 4). However, fire changes the number and pattern of trees and the canopy structure, altering the effect of the forest on snow duration (Safa et al., 2021; Stevens, 2017).

A principle feature of older forests is their heterogenous structure, including large-diameter trees with large canopies––the very trees that often survive low- to moderate-severity fires (Furniss, Kane, et al., 2020; Kane et al., 2013). These large-diameter trees contribute considerably to ecosystem function in general (Lutz et al., 2018), and their presence has important yet complex implications for snow retention after fire. Supporting our first hypothesis, we found that the presence of trees >60 cm dbh within 10 m of measurement points (PC2_SDD(10)) resulted in longer lasting spring snowpack (sSDD_final). We attribute this to the larger crown area of large-diameter trees, which shields the snowpack, lowering melt rates compared to areas with smaller trees (Figure 6). However, a greater density of nearby (≤5 m) large-diameter stems resulted in earlier snow disappearance (PC2_SDD(5)) and lower snow depths (PC2_HS(5)) and was more important in our model predicting sSDD_final based on the magnitude of the estimate and the sum of Akaike weights for variable importance (Table 5). These findings support our expectation that large crowns would reduce snow accumulation due to interception but then delay snow melt via shading.

The relationships we found between dead crown volume (CVD) and snowpack also have implications for our first hypothesis. Lower CVDs within 5 m of a HOBO location were associated with earlier snow disappearance, potentially due to moderate interception from dead crowns followed by reduced shade and litter deposition (Hypothesis 3). The relationship between higher CVD within a 10 m radius of a snow depth sampling point and deeper snowpack in 2017, during a period of ablation, likely resulted from similar processes. The metric CVD is a measure for dead crown basal area but does not account for the three-dimensional positioning of the dead crown within the canopy. Large-diameter trees often experience partial canopy scorch in their lower canopy strata. Because the basal area of these surviving trees is large, even their partial canopy scorch would increase our CVD value considerably. However, the live upper canopies of these trees still intercept snow and provide shade. Therefore, higher CVD within 10 m could lead to deeper snowpack during a period of ablation due to shading from large-diameter surviving trees that experienced partial crown scorch.

The negative effect of large-diameter trees on snow duration, as indicated by PC2_SDD(5), partially supports our second hypothesis. Shortened snow duration can reflect the formation of tree wells (the area around the tree bole that has a shallower snowpack), which result from both larger interception capacity of large-diameter tree canopies and increased melt rates caused by longwave radiation emitted from large-diameter boles (Musselman et al., 2008). Tree wells in forests of California's Sierra Nevada were described in a recent study by Zheng et al. (2019), which showed that the gradient of the tree well (steepness of the snow surface from the tree bole to the drip edge) was correlated with tree crown area and that the snowpack was 2 cm deeper for every 1 m away from the tree bole. Tree well formation and increased melt rates around tree trunks likely explain why the presence of large-diameter tree boles within 5 m of HOBO sensors led to earlier snow disappearance in our study. Large-diameter trees within 2.5 m of HOBO sensors should carry out the same processes. In support of our second hypothesis, mean large-diameter tree density within the 2.5-m circles was lower at sites with later snow disappearance and higher at sites with earlier snow disappearance (Figures 5 and 6). This is consistent with the idea that longwave radiation from boles and other factors associated with tree well formation led to earlier snow disappearance. However, large-diameter tree density within 2.5 m did not significantly predict snow disappearance in our models (Tables 3 and 5). The 5-m circles may have emerged as better predictors of snow disappearance in the model selection process because the larger area circles included the information within the 2.5-m circles and because longwave radiation and canopy effects within distances of 5 m were additionally influential.

In our model of snow duration, the shading effect of PC2_SDD(10) (i.e., presence of trees 60–100 cm dbh within 10 m) was less important numerically than the longwave radiation effect of PC2_SDD(5) (i.e., presence of trees >100 cm dbh within 5 m; Table 5). This appears to suggest that our second hypothesis has stronger support than our first. However, we point out that the relative importance of these variables in the model does not reflect their relative contribution to the processes that influence snow duration when spatial scale is considered. PC2_SDD(10) represents an area of the forest that is four times larger than the area represented by PC2_SDD(5). Therefore, the area of the forest that is impacted by shading from large-diameter trees is substantially larger than the area that is impacted by longwave radiation from their boles. Weaker shading effects at 10-m scales may counteract stronger longwave radiation effects at <5- m scales.

A second reason shading effects from large-diameter trees may be more influential than they appear in our model is that the tree neighbourhood metrics were calculated using circles of increasing radius. Thus, within the 10-m circles, the effect of shading from large trees positioned 5 to 10 m away from the HOBO sensor would be undermined by the effect of local, longwave radiation in instances where the site has a high basal area of trees within 5 m. This contrasting effect is supported by Figure 6, which shows that prolonged snow duration occurs when densities of large-diameter trees are higher or equal in the 10-m circle (2 out of 3 years) and are lower in the 5-m circle (all 3 years) compared with the large-diameter tree densities associated with earlier snow melt. However, the shading metric, S_tree, that was calculated for a 180° half-ring on the south side of each HOBO, had no significant effect on snow disappearance timing.

The formation of tree wells and increased ablation rates close to tree boles are typical features of snow–tree interactions (Hardy & Albert, 1995). However, tree boles scorched by fire also shed charred woody debris, which collects on the snow surface and lowers snow albedo, additionally accelerating snow melt after fire (Gleason et al., 2019). In our analysis, we used bole scorch height as a surrogate for radiation-absorbing impurities that may be directly shed from charred boles onto the snow surface but found that it had no significant effect on snow disappearance timing. In contrast, larger amounts of litter and charred woody debris collected in litter traps adjacent to our snow disappearance sampling locations did decrease snow duration of the winter snowpack (sSDD_cont) but were not a significant predictor of the disappearance of the spring snowpack (sSDD_final). We assume that this is because more litter and charred debris accumulated on the snow over longer periods in the winter than during the shorter period between late spring storms and the final melt event. Although this supports our third hypothesis, mean litter fall did not decrease over the 3 years studied and did not correlate with the mortality rate (Figure S4). To detect the effects of post-fire delayed tree mortality on snow duration, longer study periods starting the winter season following a fire event are necessary (Gleason et al., 2019).

Although live tree density did not change dramatically during our study period (most smaller diameter trees died shortly after the fire; Figure 3), density of smaller snags (1 cm < dbh < 30 cm) decreased, and the associated deadwood density increased from 2016 to 2018 (3–5 years post-fire). High levels of post-fire deadwood may affect snow duration in competing ways by forming local, fine-scale depressions, which collect snow that disappears later (Ford et al., 2013; Lutz et al., 2020), and by increasing melt rates due to increased outgoing longwave radiation reemitted from exposed deadwood (Malle et al., 2019). The results of our multiple regression models that were built to predict snow depth as a function of post-fire vegetation structure did reveal a positive relationship between snow depth and log density within a radius of 10 m of a snow depth sampling point (PC3_HS(10); Equations 5 and 6). To better quantify these relationships, future studies should include all logs on the forest floor as predictors of snow disappearance, as opposed to just logs that fell during a selected time period (i.e., 2011–2018 in this study).

Decreasing numbers of smaller-diameter (10 cm < dbh < 30 cm) and large-diameter snags (dbh > 100 cm; in 2017) as well as larger snag basal areas (in 2017 during an ablation period) were associated with greater snow depths. Areas with decreasing density of smaller-diameter snags that fell in combination with larger snag basal areas could have experienced local high-severity fire followed by substantial canopy loss, which would reduce snow interception and lead to greater snow accumulation (Burles & Boon, 2011); however, the exposure of the snowpack to solar radiation often increases winter ablation rates, reducing the availability of this water for spring runoff (Biederman et al., 2014; Harpold et al., 2014; Hotovy & Jenicek, 2020).

Canopy cover has a large effect on snow accumulation and ablation, influencing snow interception and net radiation balances and patterns on the snow surface (Helbig et al., 2020). We represented these variables by using stem density within diameter classes, partitioning between live and dead trees and simulating incoming solar radiation with ALPINE3D (Lehning et al., 2006). We assert that using these surrogates to represent the effects of post-fire forest, together with measured litter density and bole scorch height, was suitable for predicting snow disappearance timing and snow depth. The remaining variance in snow disappearance timing and snow depth distribution, which cannot be explained by our best-fit LMMs and multiple linear regression models, could be attributed to differences in microclimate and local topography that influence snow accumulation and ablation, such as small knolls, edges or depressions (Ford et al., 2013).

Climate change and the effect of a century of fire suppression will continue to increase the total burned area in the western United States (Littell et al., 2009; Marlon et al., 2012; Westerling et al., 2011). In this region, over 80% of forest fires between 2000 and 2012 occurred in the seasonal snow zone and were 4.4 times larger than fires outside the seasonal snow zone (Gleason et al., 2013). Identifying the effects of post-fire tree mortality on snow duration is key to predicting future water supply and to understanding the long-term effects of fire on vegetation, soil moisture, ecosystem function and forest resilience (Boisramé et al., 2017; Ebel et al., 2012). Forest and wildfire management based on knowledge of the relationships between forest condition and hydrology can mitigate the effects of increasingly warm, dry winters with below average snowpack and more frequent, severe fires in mountain regions across the western US (Miller et al., 2009; Rakhmatulina et al., 2021).

Understanding the effects of widely spaced, large-diameter trees on snow retention is important because these trees promote other benefits (Lutz et al., 2009). Large-diameter trees are more resistant to moderate-severity fire and drought due to their thick bark, lower density and ability to access and store water (Furniss, Larson, et al., 2020). Leaving large-diameter trees in place could help to meet several forest conservation objectives, such as increasing water yield, reducing soil erosion and encouraging post-disturbance forest recovery, which depends on growing-season soil moisture from snowmelt (Goeking & Tarboton, 2020).

5 CONCLUSIONS

Large-diameter trees are important ecosystem components that have both positive and negative effects on snow duration in post-fire, old-growth mixed-conifer forests. We recommend conserving big trees in old-growth forest ecosystems where fire is part of the ecological cycle. Low- to moderate-severity fire primarily kills smaller trees, which decreases snow interception but increases solar radiation transmission. Widely spaced, large-diameter single trees in post-fire environments intercept snow and emit longwave radiation but also shield the snowpack from solar radiation. Although longwave radiation from the boles of large-diameter trees accelerates snow melt locally, shading from their canopies may prolong snow duration over a larger area. Our results expand understanding of how large-diameter trees influence snow dynamics in post-fire, old-growth forests and underscore the importance of large, spatially explicit forest plots to examine ecological processes, such as snow–tree interactions, that resolve at larger spatial scales (Lutz, 2015).