A newly developed state-of-the-art snow water equivalent (SWE) reanalysis dataset over the Sierra Nevada (United States) based on the assimilation of remotely sensed fractional snow-covered area data over the Landsat 5–8 record (1985–2015) is presented. The method (fully Bayesian), resolution (daily and 90 m), temporal extent (31 years), and accuracy provide a unique dataset for investigating snow processes. The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlation greater than 0.95 compared with in situ SWE observations. The reanalysis dataset was used to characterize the peak SWE climatology to provide a basic accounting of the stored snowpack water in the Sierra Nevada over the last 31 years. The pixel-wise peak SWE volume over the domain was found to be 20.0 km3 on average with a range of 4.0–40.6 km3. The ongoing drought in California contains the two lowest snowpack years (water years 2014 and 2015) and three of the four driest years over the examined record. It was found that the basin-average peak SWE, while underestimating the total water storage in snowpack over the year, accurately captures the interannual variability in stored snowpack water. However, the results showed that the assumption that 1 April SWE is representative of the peak SWE can lead to significant underestimation of basin-average peak SWE both on an average (21% across all basins) and on an interannual basis (up to 98% across all basin years).
1. Introduction and background
Snow-dominated mountain systems are important, with estimates that over 15% of the world’s population derive the majority of their water resources from basins containing seasonally accumulating and melting snowpacks (Barnett et al. 2005). In many semiarid regions, snow water equivalent (SWE) accumulated in the regional mountains acts as a “virtual” seasonal reservoir that provides the primary water supply for urban and agricultural users (e.g., Viviroli et al. 2007). In addition to the water balance, snow plays a key role in the montane energy balance because of its high albedo, and ecological systems and biogeochemical processes are highly sensitive to variability in the montane hydrologic cycle (Bales et al. 2006; Trujillo et al. 2012).
Highly variable spatial and temporal patterns in snow cover are the result of complex montane topography and orographic effects and equally complex atmospheric circulation patterns (e.g., Dettinger et al. 2004; Lundquist et al. 2010) that influence both accumulation and melt spatial variability. Yet, most mountain regions remain undersampled with respect to in situ data. For example, the Sierra Nevada range (United States), which is one of the most densely sampled regions in the world, has a snow pillow network that samples less than 1% of the snow-dominated area (Guan et al. 2013), much of which is concentrated at middle elevations, leaving most high-elevation regions completely unsampled. As a result, it is possible during the later portions of the melt season for the in situ data to show no SWE, despite the fact that higher-elevation areas of the range are still snow covered. This problem is generally exacerbated in dry years when the preponderance of snow may occur at high elevations. Other important mountain regions such as the Andes (Masiokas et al. 2006) and the Hindu Kush–Karakoram–Himalaya (HKKH; Palazzi et al. 2013) have almost no in situ data. Such sparse in situ data networks in mountainous regions make it impossible to accurately and comprehensively understand how snow is distributed spatially and temporally.
Based on the limited in situ data, we argue that significant strides in our understanding of snow processes in montane regions could be made using a regional reanalysis–type approach that merges information from uncertain model estimates and globally available remote sensing measurements to derive spatially and temporally continuous estimates over long periods. Examples of other reanalysis datasets include the North American Regional Reanalysis (NARR; Mesinger et al. 2006), the NCEP–NCAR reanalyses (Kalnay et al. 1996), or Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al. 2011). These multidecade datasets have proven extremely useful for large-scale climatological and meteorological applications, but their coarse spatial resolution and modeling/assimilation approaches are generally insufficient and/or inaccurate for direct application to analysis of snow processes in complex mountainous terrain.
The reanalysis approach we present in this paper is focused specifically on snow and is based on the leveraging of long-term Landsat fractional snow-covered area (fSCA) datasets together with meteorological reanalysis products and snow modeling, merging all information streams within a fully Bayesian data assimilation framework. Many other recent studies have explored estimating SWE via the assimilation of fSCA from MODIS and/or satellite retrievals of snow depth or radiances from passive microwave sensors (e.g., Andreadis and Lettenmaier 2006; Durand and Margulis 2006, 2007; De Lannoy et al. 2012; Kumar et al. 2014; Liu et al. 2015). The primary differences between this previous work and that presented herein include the fact that the previous studies focused heavily on passive microwave data and/or used the ensemble Kalman filter (EnKF) assimilation scheme. Passive microwave–derived snow depths are known to be erroneous in mountainous terrain and therefore generally require a priori bias correction prior to assimilation (e.g., Kumar et al. 2014; Liu et al. 2015). Usage of filtering schemes, such as the EnKF, with fSCA data have also been found to provide limited improvements in SWE estimates (e.g., Andreadis and Lettenmaier 2006; De Lannoy et al. 2012) because of the fact that instantaneous correlation between fSCA and SWE is relatively low, especially in deep snowpacks. The fully Bayesian smoother approach developed in Margulis et al. (2015) and applied here leverages the much higher correlation between fSCA time series over the ablation season and SWE to generate significant improvement in retrospective SWE estimates. Usage of Landsat fSCA data also allows for much higher-resolution estimates than those typically used when assimilating passive microwave data or even MODIS fSCA.
The application described below is for the regionally important Sierra Nevada range, but the methodology is developed to be generally applicable to other domains. The objective of this paper is primarily the presentation of the new reanalysis dataset, its validation, and illustration of its utility in the context of characterizing peak SWE climatology. Methods and data for the current work are presented in section 2 along with a discussion of how the work presented herein compares with other comparable studies covering the Sierra Nevada. The results and a discussion are presented in section 3. Conclusions and implications for future work are presented in section 4.
2. Methods and data
a. Application domain
The domain examined in this study consists of the key snow-dominated watersheds in the Sierra Nevada range spanning California and Nevada in the western United States (Fig. 1). It is representative of a large regional mountain range responsible for a majority of the water supply of California. Specifically, the watersheds on the western slope (i.e., from Upper Sacramento in the north to Kern in the south) along with the Owens and Mono basins on the eastern slope, supply water to California. The remaining watersheds on the eastern slope (i.e., from Truckee in the north to Walker in the south) generally drain to lakes, including Lake Tahoe and others in the Great Basin. The watersheds in the Sierra Nevada span elevations from a few hundred meters above mean sea level to 4421 m. The reanalysis dataset presented herein covers 20 watersheds and is applied to elevations above 1500 m, which represents the nominal snow line (Bales et al. 2006; Guan et al. 2013) and covers 49 409 km2. The range-wide and basin-wise distribution of elevation, land cover, and fractional forest cover are illustrated in Fig. 1 and in Table 1. The highest elevations occur in the southern Sierra Nevada, while the most highly forested areas tend to be in the mid- to lower elevations of the west-draining basins (Fig. 1). In general, the eastern basins are significantly steeper and are less vegetated than those on the western slopes because of a strong rain-shadow effect.
b. Reanalysis (data assimilation) methodology
The reanalysis method applied in this study consists of a particle batch smoother (PBS) approach developed and validated in Margulis et al. (2015), which generates an ensemble posterior SWE estimate, based on a prior estimate from a land surface model (LSM) with a snow depletion curve (SDC), and remotely sensed fSCA observations that are used to condition (update) the prior estimate. The prior estimate leverages high-resolution elevation and land-cover data as static inputs, and downscaled meteorological forcing (Girotto et al. 2014b; Margulis et al. 2015) as dynamic inputs, to generate high-resolution ensemble SWE and fSCA estimates over the full water year (WY; from 1 October to 30 September). Modules were developed and applied to account for the uncertainty in key model inputs, including the downscaled meteorological forcings (Girotto et al. 2014a,b; Margulis et al. 2015). The data assimilation step consists of using the measurement–model fSCA misfit and the fSCA measurement error covariance to derive the posterior ensemble estimate via a likelihood function (Margulis et al. 2015). The approach is a fully probabilistic Bayesian method that provides daily SWE estimates at 90-m resolution. The probabilistic approach characterizes not only the first-order moments of SWE (e.g., mean and median), but also the higher-order moments (e.g., variance and interquartile range) that result from the propagation of input uncertainties through the forward model and measurements errors inherent in the fSCA observations. It is the Bayesian nature of the methodology that makes the approach a generalization of other approaches that rely on deterministic forward modeling alone and/or SWE reconstruction approaches (e.g., Rice et al. 2011; Molotch and Margulis 2008) that are restricted to ablation season estimates and include semiempirical models and/or simplifying assumptions on the error characteristics of inputs (e.g., assuming no precipitation during ablation season, no measurement error in fSCA). A more detailed description of the methodology is provided in Margulis et al. (2015).
c. Datasets used
1) Forward model input data
Static model inputs for the prior modeling system used in this study [i.e., the Simplified Simple Biosphere (SSiB; Xue et al. 2003) LSM coupled to the Liston (2004) SDC model] consisted of 30-m resolution elevation and land-cover information from the ASTER database (http://asterweb.jpl.nasa.gov/) and National Land Cover Database (Homer et al. 2007). These inputs were aggregated to 90-m resolution for use in the reanalysis. The spatial resolution was chosen based on literature values of typical correlation length scales seen in montane SWE (e.g., Blöschl 1999) and estimates of modeling resolution of ~100 m needed in order to resolve key spatial features (Winstral et al. 2014). The aggregation from the raw 30-m data was also done to reduce noise in the data and computational expense. The hourly meteorological inputs used were taken from the ⅛° resolution phase 2 of the North American Land Data Assimilation System (NLDAS-2) dataset (Xia et al. 2012) and were downscaled probabilistically to 90 m based on topographic corrections and uncertainty models using the methods outlined in Girotto et al. (2014a,b) and Margulis et al. (2015).
2) Remotely sensed fSCA data
The retrieved fSCA estimates used for assimilation in this study were derived from Landsat 5 Thematic Mapper (TM), Landsat 7 Enhanced Thematic Mapper (ETM+), and Landsat 8 Operational Land Imager (OLI) reflectance data using a spectral end-member unmixing approach based on Painter et al. (2003) and Cortés et al. (2014) and as previously applied in Girotto et al. (2014a) and Margulis et al. (2015). Landsat 1–3 Multispectral Scanner (MSS) data were not considered for this study primarily because of a lack of data availability. Even if available, the limited number of spectral bands would limit the effectiveness of the spectral unmixing algorithm used to retrieve fSCA data. Based on data availability, only Landsat 5 is used from WY 1985 to 1998, Landsat 5 and 7 are used from WY 1999 to 2011, Landsat 7 is used solely in WY 2012, and Landsat 7 and 8 are used in WY 2013–15. Note that the Landsat 7 ETM+ data from 2003 to present include missing data in each scene because of the scan line corrector (SLC) malfunction, and hence WY 2012, where only Landsat 7 data were available, generally has less fSCA data than other years. That said, Girotto et al. (2014b) showed that a reanalysis data assimilation approach is more robust to missing fSCA estimates compared to an SWE reconstruction approach.
The remotely sensed data used in the assimilation include both estimates of fSCA and fractional vegetation cover fveg at each overpass time, both of which are aggregated to the 90-m model resolution. The pixel-wise fSCA values were screened to include only reliable (cloud free) measurements during the assimilation window, and the concurrent fveg data were used in the measurement model to account for forest that obscures snow-covered ground (Margulis et al. 2015). One primary trade-off with the high spatial resolution of Landsat data is the lower temporal availability (i.e., every 16 days). Other sensors, for example, MODIS, provide higher temporal frequency (approximately daily) but at the expense of spatial resolution (500 m) and temporal extent (from 2000 to present). As shown in previous work (Girotto et al. 2014a; Margulis et al. 2015) and below, the Bayesian smoother framework implicitly interpolates across measurements in a way that is consistent with inherent uncertainties in model estimates and fSCA measurements and leads to reliable SWE estimates when used with Landsat data. The high spatial resolution and long temporal extent of Landsat makes it more desirable than other data sources.
3) Verification data
The data used for verification in this study are in situ SWE data taken from 108 snow pillow and 202 snow course sites scattered across the Sierra Nevada. The quality-controlled data are available from the Department of Water Resources California Data Exchange Center (CDEC; CDEC 2016). Snow pillows provide daily measurements, while snow courses provide monthly measurements near the first of each month from January through May. Many of the snow courses are collocated with snow pillows. The spatial distribution and basin-specific number of verification sites in the Sierra Nevada are shown in Fig. 1 and Table 1. The in situ data generally span the intermediate elevations of the Sierra Nevada between 1500 and 3500 m. Specifically, approximately 50% of the stations are at elevations between 1500 and 2500 m and 90% of the stations are at elevations below 3250 m. Most of the snow pillow sites date back to the 1980s or earlier, while the snow courses date back much further.
Representativeness is a significant issue with in situ snow measurements (e.g., Meromy et al. 2013), as evidenced by the fact that collocated snow pillow and course sites typically show some discrepancies (Rice et al. 2011; Margulis et al. 2015). This is expected as they are typically measuring different characteristics of the underlying SWE fields. Snow pillows measure the point-scale (i.e., typically 3 m × 3 m) SWE at the pillow location. Snow course measurements are the average of SWE measurements across a ~200-m transect. Since they are measuring SWE over different spatial footprints, it is expected that the data will be different even at collocated sites unless the SWE is uniformly distributed over the spatial footprint of both measurements (generally not the case). Moreover, snow pillow/course location coordinates are generally only known to within ~100 m. While the in situ data provide point-scale measurements and sample only a small fraction of the domain, they generally provide the most direct way of assessing the precision/accuracy of the reanalysis dataset. It is important to note that the reanalysis method provided here does not assimilate any of this in situ data and can therefore use it as an independent verification dataset.
d. Qualitative comparison with other studies aimed at characterizing spatially/temporally distributed SWE in the Sierra Nevada
Previous efforts aimed at providing spatially and temporally continuous estimates of SWE over the full Sierra Nevada range include forward modeling approaches (e.g., Knowles and Cayan 2004), those falling under the “SWE reconstruction” approach (e.g., Rittger 2012; Guan et al. 2013), and those based on assimilation schemes designed to minimize misfit between model predictions and ground-based/airborne/satellite data [e.g., Snow Data Assimilation System (SNODAS); http://nsidc.org/data/docs/noaa/g02158_snodas_snow_cover_model/]. These deterministic datasets differ from each other and the work presented herein in several important ways. Table 2 attempts to summarize some of these key differences.
Offline forward modeling approaches are generally limited by availability and uncertainty in meteorological forcing data (which is often sparse and uncertain in mountainous regions) and subject to direct propagation of errors in those forcings and model errors, both of which impact the modeled SWE estimates. Knowles and Cayan (2004) provided one example of such an approach through development of a historical control run (at 4-km resolution) over the full Sierra Nevada for 23 years (1965–87) that was used as a baseline to examine a climate change scenario. SWE reconstruction approaches use temporally interpolated fSCA data to constrain SWE estimates based on cumulative modeled ablation season melt fluxes. They are applied only over the ablation period to get an estimate of SWE from a predefined peak SWE date through melt-out (and therefore provide no SWE estimates during the accumulation season). Rittger (2012) and Guan et al. (2013) both used a similar SWE reconstruction approach over 2000–11 and 2000–12, respectively. Rittger (2012) applied the reconstruction at 100-m resolution and used a simple downscaling of the 500-m MODIS fSCA data, while Guan et al. (2013) generated SWE estimates at the native MODIS resolution of 500 m. Guan et al. (2013) additionally showed that errors in the SWE reconstruction estimates could be reduced by blending those estimates with in situ snow pillow data. SNODAS provides the most operational snow dataset at large scales (over the period from 2003 to present). The method uses a forward modeling approach (applied at 1-km resolution over the contiguous United States) to provide a first guess that is then updated via nudging from a variety of remote sensing and in situ data (Barrett 2003). Guan et al. (2013) examined SNODAS over the Sierra Nevada for 2003–12.
The novelty of the reanalysis dataset presented herein lies in the fully probabilistic Bayesian assimilation method used and the long temporal extent and high spatial resolution afforded by using the Landsat record. The appropriate leveraging of the strengths (and weaknesses) of both fSCA remote sensing data and modeling frameworks to generate estimates of complex snow states and their corresponding uncertainty is best done using Bayesian smoothing methods. The new dataset is the longest existing snow reanalysis dataset of such spatial and temporal extent at high spatial and temporal resolution. The application and characterization described below is meant to be illustrative of potential future applications over even larger domains.
e. Characterization of peak SWE climatology
In addition to the presentation and verification of the new dataset, the primary focus of this study was to use the SWE reanalysis dataset to characterize the 31-yr climatology of peak SWE in terms of its mean and interannual variability. Basic questions about how much water accumulates in the Sierra Nevada snowpack and how the water is distributed in space and time remain relatively poorly characterized based on the sparse in situ network. The peak SWE can be characterized in different ways. We focused primarily on characterizing the climatology of the “pixel wise” peak SWE, which represents the maximum value of SWE at each 90-m pixel across the domain in a given WY. The pixel-wise peak SWE represents the maximum water available for partitioning into snowmelt, evaporation, and soil water storage, and has a corresponding spatially varying pixel-wise day of peak (DOP) at which the peak SWE occurs. The pixel-wise peak SWE provides a more complete characterization of the total maximum available water integrated over the full melt season since it takes into account the variability of accumulation and melt timing across the domain. Secondarily, we focused on characterizing the basin-average peak SWE for each basin in the Sierra Nevada range. These estimates correspond to a particular day of the water year (DOWY) where the basin-average SWE is at its maximum. This latter metric was compared to the pixel-wise peak SWE and the 1 April SWE, which is also often used as an index for use in water supply forecasts.
3. Results and discussion
a. Verification using in situ SWE data
For verification, the SWE reanalysis estimates were compared to all snow pillow and snow course sites (Fig. 1) using the same approach outlined in Girotto et al. (2014a) and Margulis et al. (2015). For snow pillow data, the verification was performed on the peak SWE values. For the snow course data, the verification was performed for all data (typically at the beginning of the month between January and May). The comparison method attempts to mitigate geolocation and representativeness errors by comparing the in situ data values to those from the nine neighboring 90-m pixels and computing error statistics based on the pixel with the smallest prior or posterior errors (which is assumed to be the most representative pixel). This is reasonable since the snow pillow and course locations are only given to the nearest 0.001° (~100 m) and the snow courses cover about a 100–200-m transect. The comparison performed includes over 9000 station years of data.
Verification statistics for the prior and posterior (ensemble median) SWE estimates are shown for each basin in Table 3 (snow pillows) and Table 4 (snow courses). The posterior SWE estimates are generally significantly improved over the prior estimates in terms of mean error (ME), root-mean-square error (RMSE), and correlation coefficient when compared to the in situ data. The prior ME values for snow pillows (Table 3) range across the basins from −6 to 52 cm (30 cm across all sites), while the posterior values range from −12 to 1 cm (−1 cm across all sites). In general, the prior values are positively biased, while the posterior estimates are relatively unbiased. The prior RMSE values for snow pillows (Table 3) range from 19 to 67 cm (48 cm across all sites), while the posterior values range from 5 to 18 cm (11 cm across all sites). The prior correlation coefficient values for snow pillows (Table 3) range from 0.75 to 0.94 (0.85 across all sites), while the posterior values range from 0.91 to 0.99 (0.97 across all sites). The results are qualitatively similar for snow courses (Table 4), with uniform and significant improvement in all metrics across all basins (with posterior ME, RMSE, and correlation coefficient across all sites of −3 cm, 13 cm, and 0.95 respectively). Scatterplots showing the comparison of posterior estimates to observations are shown in Fig. 2 and visually confirm the general agreement between the posterior estimates and observations. It should be reiterated that the comparison to snow pillow and course data has weaknesses in that the sites generally undersample sloped and forested conditions and are thus potentially nonrepresentative of grid-averaged estimates.
The accuracy of the SWE reanalysis estimates does not vary significantly across watersheds, despite forest fraction ranging nearly an order of magnitude, from 7.3% to 71.1% (see Table 1). As shown in Fig. 3, forest fraction has at most a marginal impact on the overall accuracy at the watershed scale; the coefficient of determination R2 of the relationship between RMSE and forest fraction is 0.13 and 0.18 for the snow pillows and the snow courses, respectively. The slope of the linear regression between forest cover and RMSE is not statistically different than zero for either the snow pillows (p = 0.123) or the snow courses (p = 0.069). These findings are consistent with Durand et al. (2008), where forest cover had to exceed 90% to significantly degrade a similar SWE reanalysis in the context of a numerical experiment; they are also consistent with Margulis et al. (2015), where the SWE reanalysis errors evaluated for the American River watershed were found to be relatively insensitive across three pixels with forest fraction ranging from 14% to 76%. Additional analysis (not shown) indicated that the posterior errors did not vary significantly with mean elevation or seasonally for either the snow pillows or courses.
Comparison of the posterior reanalysis results presented herein with the previous studies mentioned in section 2d is instructive but imperfect because of differences in spatial resolution, time period, and verification data and methods used. The most comparable previous study over the Sierra Nevada is the SWE reconstruction performed by Rittger (2012), who used the same verification method and data and reconstructed SWE at 100-m resolution (while using 500-m resolution MODIS data). Over the 2000–12 analysis period they found peak SWE snow pillow ME and RMSE values (averaged across all sites) equal to 2.5 and 19 cm, respectively. Snow course SWE ME and RMSE values were 7.2 and 23 cm, respectively. For the same period, the reanalysis results presented herein (i.e., subsampled for 2000–12) showed ME values of −2.6 and −3.8 cm and RMSE values of 11.0 and 9.9 cm for snow pillows and courses, respectively. Hence, the errors from previous work represent ME values that are comparable for pillows and ~90% larger in magnitude for courses than the posterior reanalysis estimates presented herein. Similarly, these RMSE values are ~70%–130% larger than the posterior reanalysis pillow and course RMSE. These larger errors are qualitatively consistent with the results presented in Girotto et al. (2014b), which illustrated the improved performance of a data assimilation method over a deterministic SWE reconstruction method.
Guan et al. (2013) compared their SWE reconstruction estimates (aggregated to 1 km) and SNODAS estimates to 17 independent intensive snow surveys scattered across the Sierra Nevada near peak SWE accumulation and found SWE ME (RMSE) values of −19 cm (25 cm) and −18 cm (25 cm), respectively. While using a different verification dataset at a different scale, these results show generally higher ME (i.e., larger in magnitude) and RMSE values than the posterior reanalysis estimates presented herein. Guan et al. (2013) also compared their near-peak (1 April) SWE reconstruction estimates to snow pillow data and found site-averaged ME values ranging between ~−40 and 0 cm and RMSE values ranging between ~20 and 50 cm across the 13 years. To reduce the biases in their reconstruction estimates, Guan et al. (2013) proposed a blended product that incorporated the in situ data directly. In doing so, a cross-validation comparison showed an effectively unbiased estimate with an RMSE value of ~20 cm. In summary, while this comparison to previous work is not definitive, based on the differences in verification data/methods and spatial resolution noted above, it generally indicates a level of accuracy in the posterior reanalysis results that compares favorably to other studies.
b. Pixel-wise peak SWE climatology
1) 31-yr average pixel-wise peak SWE maps
Figures 4a and 4b show the climatological (31-yr average) maps of pixel-wise peak SWE and DOP. The climatological map of 1 April SWE (Fig. 4c) is also shown for reference since it is often cited as representative of peak SWE (Montoya et al. 2014). The 1 April date is also important historically because it is the nominal date where the emphasis of water management switches from flood management to water supply. The pixel-wise peak SWE generally shows the highest values at high elevations and on the windward (western) side of the range. The pixel-wise DOP shows that at lower elevations, SWE peaks significantly (i.e., 30 days or more) before 1 April, while at higher elevations, most notably in the southern Sierra Nevada, the DOP is 30 or more days after 1 April. The 31-yr average integrated pixel-wise peak SWE volume over the full Sierra Nevada range is 20.0 km3. The pixel-wise peak SWE is an important metric in that it represents the maximum available water across the season rather than just a snapshot of the SWE at a specified time. This is not only relevant to water resources, but vegetation in water-limited regimes will generally be sensitive to the locally available amount of water from snowmelt (Trujillo et al. 2012), which is a strong function of elevation (Fig. 4).
The 31-yr average 1 April SWE (Fig. 4c), with an integrated volume of 15.7 km3, shows a reduced amount of SWE, with some areas (e.g., lower elevations in eastern basins) showing no snow on 1 April. Based on these results, on average 4.3 km3 (~22%) of the pixel-wise peak SWE melts prior to 1 April. The spatially distributed patterns of melt are illustrated in Fig. 4d, which maps the percent difference between pixel-wise peak and 1 April SWE. Significant (lower elevation) fractions of upper Sacramento, Truckee, Walker, Mono, Owens, and Kern show a near 100% reduction between pixel-wise peak and 1 April SWE. The difference between integrated pixel-wise peak and 1 April SWE highlights how 1 April SWE (or any estimate of SWE at a specified time) is an imperfect metric of the total (spatially distributed) available water over the WY.
2) Elevational and basin-wise distribution of 31-yr average pixel-wise peak SWE
The elevational distribution of the 31-yr average pixel-wise peak SWE is shown in Fig. 5 (black line) in terms of both SWE volume and depth. The largest volume of pixel-wise peak SWE [Fig. 5 (left), black line] is generally stored in the elevation band near 2000 m, with less SWE volume stored at lower and higher elevations. To a large degree this is a function of larger contributing areas in this elevation range (Fig. 1, bottom) since orographic effects on the SWE distribution [Fig. 5 (right)] indicate the largest pixel-wise peak SWE depths (black line) occur at higher elevations (around 3500 m). Specifically, the climatological pixel-wise peak SWE depth increases nearly monotonically from ~0.2 m at 1500 m up to ~0.8 m at 3600 m. Above 3600 m the SWE actually decreases. The decrease in orographic effect at high elevations is seen in other work (e.g., Kirchner et al. 2014) and is likely related to a combination of 1) a lack of atmospheric moisture for precipitation at high altitudes on the windward side of the range (after orographic precipitation at lower elevations), 2) the presence of high-elevation pixels on the leeward side of the range (e.g., Walker, Mono, and Owens, where rain-shadow effects are apparent), and 3) a correlation between high elevations and steep slopes leading to potential gravitational and wind redistribution of SWE. There are also fewer pixels contributing to the mean at the highest elevations, leading to a noisier signal.
The elevational distribution of pixel-wise peak SWE is further disaggregated by grouping basins into those in the northwest (NW), southwest (SW), northeast (NE), and southeast (SE) regions of the Sierra Nevada range (as labeled in Fig. 1 and Table 1). Additionally, the individual basin-wise SWE volumes are shown in Table 5. Figure 5 (left) illustrates that the NW and SW basins have the highest volumes of SWE, with the NW basins peaking at lower elevations compared to the SW basins (i.e., ~1800 vs ~2800 m). The integrated percent of total pixel-wise peak SWE in the NW and SW basins is 41.5% and 40.7%, respectively (Table 5). The NE and SE basins store significantly less SWE volume, with the peak SWE volume stored at ~2500 and ~3100 m, respectively. The integrated percent of total pixel-wise peak SWE in the NE and SE basins is 7.9% and 9.5%, respectively (Table 5). As illustrated in Fig. 5 (right), the northern basins get more precipitation and therefore larger accumulated SWE depth than the southern basins. The comparable SWE volumes from north to south (Fig. 5, left) are due to the larger areal coverage in the southern basins. In general, there are strong SWE gradients from west to east because of the windward–leeward contrast, leading to rain-shadow effects, and from north to south because of the gradients in precipitation. Based on the results shown in Table 5, about 56% of the total pixel-wise peak SWE volume is stored in six of the 20 basins (Feather, upper Sacramento, San Joaquin, Kings, Tuolumne, and American), and about 77% is stored in nine of the 20 basins (adding Kern, Owens, Yuba, and Stanislaus).
3) Interannual variability in pixel-wise peak SWE
The spatiotemporal patterns in interannual variability in pixel-wise peak SWE are illustrated in Fig. 6, where the absolute anomalies relative to the 31-yr climatology are mapped for all WYs between 1985 and 2015. Many years have either uniformly positive or negative anomalies over the full Sierra Nevada range, indicating the effects of large-scale atmospheric phenomena. Specifically, the large-scale dry years were WYs 1987, 1988, 1990, 1994, 2007, and 2012–15, while the large-scale wet years were 1993, 1995, 1998, and 2011. Other years show spatial variance in SWE anomalies across the range, which may be indicative of more local-scale processes (e.g., orographic processes and anomalous temperatures) and/or shifts in the storm track that lead to variations in local precipitation and snow accumulation. Many of these mixed-anomaly WYs are simply near average (with small negative/positive anomalies), while others show subregions with significant dry (2001) or wet (1986, 2005, and 2006) anomalies. Some WYs show strong elevational gradients in SWE anomalies, for example, WY 1986, which has above-average SWE at high elevations and below-average SWE at low elevations (due to the large storms being warm in that year). WYs 1985 and 1989 show negative anomalies in the central basins of the domain with positive anomalies to the north and south. WY 1999 exhibits a relatively uniform south–north gradient with negative anomalies in the southern basins, minimal anomalies in the central basins, and positive anomalies in the northern basins. In general, the largest absolute anomalies tend to be at high elevations where the mean climatology has the largest SWE values (Fig. 4); that is, regions with large average peak SWE values can more easily have large depth anomalies. If mapped as a percentage anomaly (not shown), the lower elevations tend to show the higher percent anomalies from year to year since the climatological values are lower in those regions (i.e., it is easier to have significant percentage departures from the mean when the mean is low). A more detailed investigation into the drivers of these heterogeneities will be the subject of future work.
The interannual results indicate a range of pixel-wise peak SWE volume from 4.0 (2015) to 40.6 km3 (1993) over the 31-yr record (Fig. 6). This represents a percent difference range from −80% to over +100% relative to the 31-yr mean. At least some of this interannual variability is likely due to variations in the number of atmospheric river (AR) and Pineapple Express (PE) events that occurred in a given year. In particular, the number of annual November–March AR/PE events cataloged in Dettinger et al. (2011) for WYs 1998–2008 explain the above-average WYs of 1998, 2005, and 2006 and the below-average WY of 2001. However, other above-average (e.g., 2003) and below-average (e.g., 2008) WYs do not correspond to an above- or below-average number of AR/PE events. The recent drought in California is evident in the last four years of the record, where the two lowest SWE volumes occurred (2014 and 2015). In fact, the 2014 and 2015 peak SWE values were ~57% and ~38% of the next lowest year (2007), which had 10.7 km3. Compared to the 31-yr average, these two years were ~31% and ~20% of the average, respectively.
The time series of pixel-wise peak Sierra Nevada–wide percent anomalies is shown in Fig. 7 (black line) to highlight large-scale dry versus wet years. It is often the case (e.g., by the California Department of Water Resources) that the anomaly of SWE is used (i.e., relative to long-term average 1 April SWE) as an index for water supply forecasting. The results presented here are an attempt to quantify how anomalies in the various metrics for peak SWE anomalies differ and therefore how an error in the 1 April anomaly could erroneously propagate to a forecast of runoff. The record shows that 17 of the 31 years are below average, with 11 years at least 20% below average. The persistent periods of below-average SWE are 1987–92 (with four of the six years more than 20% below average), 2000–03 (with only one year more than 20% below average), and 2012–15 (with all four years more than 20% below average, including the two lowest values on record). The wet years tend to have larger positive anomalies. The record shows four years with positive anomalies greater than 60% above the mean, while only two such negative anomalies exist. That said, the wet years tend to be more intermittent than dry years. For years with anomalies of more than 20% above average, the only period with two consecutive years was 2005–06. The longest above-average period is 1995–98, which had two very wet years bracketing two years of near-average SWE.
c. Basin-average peak SWE climatology
Figure 8 illustrates the annual cycle in basin-average SWE for all basins over the 31-yr record. To highlight differences between dry, average, and wet years, the individual time series are color-coded based on basin-average peak SWE as red, gray, and blue for the lower, middle, and upper terciles over the 31 years. The results clearly show the large variations in both the peak SWE and the timing of peak SWE over the 31-yr record. For example, the Feather basin (which has the largest climatological SWE contribution) varies from less than 0.5 km3 to more than 5 km3, with peak dates as early as December and as late as mid-April. The DOP is not a strong function of peak SWE, with many examples of average or wet years peaking earliest (Kaweah, Kern, Mono, Owens, Truckee, Walker, and Yuba) and of average or dry years peaking latest (American, Carson, Kaweah, Kings, Merced, Mokelumne, Owens, San Joaquin, Stanislaus, Tahoe, Tuolumne, Walker, and Yuba) over the 31-yr record.
From the time series it is evident that Sierra Nevada snow accumulation is often driven by a handful of storm events in a given year so that the peak SWE and DOP are determined by the presence/absence, magnitude, and timing of the storms. For example, the largest peak SWE over the 31-yr record for most of the basins is the result of a succession of storm events from late December through mid-January (in WY 1993) that took what was an average to slightly above-average year prior to that point and made it an extreme year (highlighted by thick blue line near top of distribution in Fig. 8). For Feather, these events added more than 3 km3 of SWE (Fig. 8). In another example, in WY 1991 most of the basins experienced what was the driest year on record up to the end of February (a point in time where for many years the basin-average peak had already occurred). In late February, a succession of storms over a 3-week period occurred, which made the WY fall into either the average (American, Carson, Kings, Mokelumne, Mono, Stanislaus, Tahoe, Truckee, Tuolumne, Walker, and Yuba; see thick black line in Fig. 8) or wet (Cosumnes, Kaweah, Kern, Kings, Merced, Mono, San Joaquin, Owens, and Tule; see thick blue line near middle of distribution in Fig. 8) tercile for most basins. The extreme drought year of WY 2015 (shown by the thick red line in Fig. 8) is also highlighted. This year was not only characterized by a low peak value, but generally a very early peak (in December–February for most basins).
The mean and standard deviation of the basin-average peak SWE and DOP for each basin are shown in Table 6. The relative distribution of 31-yr mean values for each basin are, as expected, similar to the pixel-wise peak values shown in Table 5, with the basin-average peak values being less than the pixel-wise peak because of melt-out by some pixels by the date of basin-average peak SWE. The standard deviation of the peak SWE values are large, with coefficients of variation (standard deviation as a fraction of the mean) greater than 0.41 in all cases. The largest coefficients of variation in peak SWE occur in Owens and Cosumnes with values of 0.58 and 0.56, respectively. Owens stands out as one of the larger contributing basins (the eighth-most SWE by volume) with one of the highest interannual coefficients of variation. The smallest coefficients of variation in peak SWE correspond to Stanislaus (0.41), Mokelumne (0.41), and Yuba (0.42), with Yuba standing out as one of the larger contributing basins (the ninth-most SWE by volume) with one of the lowest interannual coefficients of variation.
The average DOP values across the basins range from DOWY 152 to 173 (17–22 March) with a basin-wise average of DOWY 164 (13 March) compared to 1 April (DOWY 182). Hence, on average over the 31 years examined, all basins peak prior to 1 April on average. Tule, Mono, Owens, and Feather have the earliest average peak dates. The Feather basin stands out as the largest contributing basin with one of the earliest average peak dates (DOWY 156, 5 March). San Joaquin, Kings, Merced, and Yuba have the latest peak dates. The interannual standard deviation of DOP values is large, with mean values for each basin ranging from 19 (Tahoe and Carson) to 31 (Cosumnes) days.
d. Comparison of 1 April SWE to pixel-wise and basin-average peak SWE
The SWE on 1 April is often invoked as a nominal measure of peak SWE (Montoya et al. 2014), or at the very least as an index to be used for forecasting interannual variations in runoff for water supply forecasting. Given its use as a metric for basin-average peak SWE, and the fact that all basins show an earlier average peak date, it is useful to compare 1 April SWE to pixel-wise and basin-average peak SWE and to characterize the potential error associated with such an assumption.
Focusing on the integrated Sierra Nevada–wide comparison, Fig. 7 includes interannual anomalies in basin-average peak SWE (dark dashed gray line) and 1 April SWE (light gray dotted line). For the most part, the basin-average peak SWE anomalies and pixel-wise peak SWE anomalies are indistinguishable over the 31-yr record, with WY 2003 showing the largest discrepancy. In terms of error relative to pixel-wise peak SWE, the basin-average anomalies have an RMSE of 3.8% and a correlation coefficient of 0.996. Hence, while these two metrics for peak SWE have different meanings and values, the usage of basin-average peak SWE as an index for integrated pixel-wise peak SWE is very accurate. The 1 April anomalies, however, show much larger discrepancies. The 1 April anomalies have an RMSE of 15.2% and a correlation coefficient of 0.97 relative to the pixel-wise peak SWE anomalies. Among the individual WY errors, the 1 April anomalies tend to overestimate wet years (1993, 1995, and 2011) and underestimate dry years (1988, 1990, 1994, 2007, 2013, and 2015).
For individual basins, Table 6 shows the 31-yr mean value for 1 April SWE and Fig. 9 shows the comparison of 31-yr mean values of pixel-wise peak SWE, basin-average peak SWE, and 1 April SWE for each basin. By definition, the pixel-wise peak SWE is the upper limit to basin-average peak SWE as it accounts for pixels that may have melted out prior to the basin-average peak SWE date. The differences between mean pixel-wise peak SWE and basin-average peak SWE are generally relatively small, with mean values between −2% and −12% across all basins. This indicates that using the basin-average peak SWE will generally underestimate the total available water from snowmelt (i.e., the pixel-wise peak SWE for the basin). The difference between basin-average peak SWE and 1 April SWE is in many cases much larger (Fig. 9). As shown in Table 6, the smallest average difference is −11.2% with differences up to −30.8%. Of note is that two of the highest-average errors are for Feather (−23.4%) and upper Sacramento (−22.9%), which have the two largest average SWE amounts by volume. This indicates that, on average, 1 April SWE provides a significant underestimate of the actual basin-average peak SWE (with an even larger underestimate with respect to pixel-wise peak SWE).
It is important to note that this underestimation is only the average case and is not due solely to the fact that the basin-average peak SWE dates tend to be prior to 1 April. Figure 10 (top) shows the full range of basin-average peak SWE dates across the full 31-yr record. While most basins and years have peak dates prior to 1 April, there are several instances of peak dates near 1 April (e.g., many basins in WYs 1985, 1991, 2002, and 2011) and many later than 1 April (e.g., many basins in WYs 1998, 1999, 2003, 2006, and 2010). Based on these results, 17% of the basin years had peaks within ±5 days of 1 April and 33% had peaks within ±10 days. By construct, for those cases where the basin-average peak is near 1 April, the percent error in SWE approaches zero. However, underestimation occurs for all other cases and reaches as large as 98% for individual basins in some years. The basins with the largest SWE errors across each year tend to be Tule, Cosumnes, and Feather, and the years with the largest errors were WYs 1988, 2001, and 2015. The key point is that 1 April SWE is an imperfect metric for peak SWE and generally yields a significant underestimate, both on average and year to year. Hence, any analysis focused on peak SWE, especially those involving trend detection, should avoid using 1 April SWE as the metric for peak SWE.
4. Conclusions and implications for future work
This paper presents a newly developed state-of-the-art snow reanalysis dataset over the Sierra Nevada based on the assimilation of remotely sensed fSCA over the Landsat 5–8 record (WYs 1985–2015). The new dataset provides a unique capability for investigating snow processes at a resolution (daily and 90 m), temporal extent (31 years), and accuracy not available from other existing datasets. Results presented herein provide the first accounting of average annual SWE storage and interannual variability over a large regional mountain range using an advanced (Bayesian) reanalysis (smoothing) approach.
Results found that the pixel-wise peak SWE (which is the most appropriate metric for maximum available water across the full season) is on average 20.0 km3 with significant interannual variability (ranging from a low of 4.0 up to 40.6 km3). The two lowest values in the record (WYs 2014 and 2015) have occurred within the recent and ongoing drought in California. The spatial variability in interannual anomalies in pixel-wise peak SWE is complex in some years with mixed positive and negative anomalies across elevational and spatial gradients. Dry years are more common over the 31-yr record, with wet years being generally more intermittent compared to dry years. It was found that, for a given basin, the basin-average peak SWE is typically only slightly less than the pixel-wise peak (from −2% to −12% different), but that 1 April SWE is generally a poor metric for peak SWE, with 31-yr average errors ranging from −11.2% to −30.8%. Individual basin years led to even larger underestimation (up to −98%).
In this paper, the SWE reanalysis dataset has only been examined with respect to the characterization of peak SWE climatology to provide a basic accounting of the stored snowpack water in the Sierra Nevada over the last 31 years. Follow-on efforts should be aimed at gaining additional insight by examining, among other things, the relationship between peak SWE and underlying physiographic and meteorological variables, relationships between SWE distribution and runoff measurements, trends in SWE, connections between biophysical variables (e.g., NDVI) and SWE, orographic gradients and their connection to hydrometeorological phenomena, and the relationships between interannual variability and large-scale atmospheric processes and teleconnections (e.g., ENSO and PDO). Such insight could be used to build improved models for snow prediction and ultimately runoff. Additional future work could also include an intercomparison with other products (SNODAS, NARR, MERRA, etc.) or model-based estimates (e.g., from regional climate models). Interested users of the dataset should contact the corresponding author until the dataset is readily available on a public website.
Finally, the SWE reanalysis framework is designed to be general and could therefore be applied to other domains (e.g., the broader western United States, the Andes, the Alps, and the HKKH), some of which have sparse to nonexistent in situ networks and could therefore significantly benefit from new insight gained through such a snow reanalysis dataset. Such snow reanalyses would provide a major advance in our understanding of these important montane systems.
This work was based in part upon work supported by a NASA NEWS project (Grant NNX15AD16G), a NASA Earth System Science Fellowship (Grant NNX11AL58H), and the National Science Foundation (Grant EAR-1246473). The NLDAS-2 data used in this study were acquired as part of the mission of NASA’s Earth Science Division and were archived and distributed by the Goddard Earth Sciences (GES) Data and Information Services Center (DISC). The raw Landsat data were obtained from the USGS Earth Explorer Landsat archive (http://earthexplorer.usgs.gov/).