The Spatial Distribution

UNIVERSITY OF CALIFORNIA

Santa Barbara

A solution to one of mountain hydrology’s principal mysteries: the spatial distribution

of snowfall

A dissertation submitted in partial satisfaction of the requirements for the degree Doc-

tor of Philosophy

in Environmental Science and Management

William Tyler Brandt

Committee in charge:

Professor Jeff Dozier, Chair

Professor Christina (Naomi) Tague

Professor James Frew

Doctor Thomas H. Painter

Doctor Jeffrey S. Deems

September 2019

The dissertation of William Tyler Brandt is approved.

______

Christina (Naomi) Tague

______

James Frew

______

Thomas H. Painter

______

Jeffrey S. Deems

______

Jeff Dozier, Committee Chair

September 2019

A solution to one of mountain hydrology’s principal mysteries: the spatial distribution

of snowfall

William Tyler Brandt

iii

ACKNOWLEDGEMENTS

This was a high alpine expedition on an unexplored route. I would not be here with- out the guides and expedition support who helped along the way.

Principally, I would like to thank my lead guide: Jeff Dozier. You were always there testing the route, and quick to lend a hand if need. You patiently guided me through those high exposure areas, while allowing me to climb and descend on my own—something I will always thank you for.

Naomi Tague—thank you for perspective, balance, your artistic nature and good coffee recommendations. From the very start you have stretched my thinking beyond the realms of snow, and onto the landscape as a whole. Thank you!

James Frew—thank you for your boundless passion for spatial data. Your curiosity is infectious and your enthusiasm helped to keep this expedition on track.

Jeff Deems and Tom Painter—thank you for letting me into the extended Airborne

Snow Observatory (ASO) family. Your data has been the bedrock of this thesis, and our many meetings, phone conservations, g-chats and texts have helped to shape my ideas and perspectives. Thanks for letting me “tag” along at the AGU Chapman Conference in

Hawaii 7 years ago—little did I know, it was the start of something great.

I also need to thank the entire ASO flight and compute teams and also the United

States Department of Agriculture (USDA) Agricultural Research Service (ARS) for data collection, processing and prompt delivery of snow depths, snow water equivalent, and

albedo estimates. In particular, I would like to thank Danny Marks, Mica Johnson, An- drew Hendrick, Scott Havens, and Mckenzie Skiles.

Thank you to my coauthors including Kat Bormann (ASO), Forest Cannon (UCSD), and Ned Bair (ERI). Your constructive criticism, thoughtful insight, and willingness to review my manuscripts has been central to the success of this thesis.

I also would like to thank a number of key faculty that have either taught me, or that

I have TA’d for. Tom Dunne, I cannot thank you enough for the many years of ESM 203

(Earth System Science), coffee and hours in the courtyard. Your steadfast commitment to applied and pure science is inspirational, and your “keep it simple” approach will for- ever underlay my approach to work and life. Thank you Dar Roberts for all the remote sensing classes—they were by far some of the most rigorous classes I have taken and will serve as my benchmark for remarkable teaching. Additional thanks to Bob Wil- kinson for our many office conversations, Derek Booth, Lisa Leombruni, Allison Horst and Bodo Bookhagen.

The staff at both the Bren School and UCSB’s Earth Research Institute (ERI) have also been incredibly supportive and helpful over the past 7 years. At the Bren School— thank you to Dean Steve Gains, Assistant Dean Satie Airamé, Kristine Duarte, Corlei

Prieto, Dee White, Kim Fugate, Doris Bleecher, Casey Hankey, Patti Winans, Aleah

Van Woert, BJ Danetra, David Parker, Kristi Birney, Steve Miley, Brad Hill, Goeff

Jewel, Sage Davis and James Badham. At ERI, I owe a special thank you to Laurel

Neidigh for helping me with my NASA fellowship submission and to the compute team—in particular Michael Collee and Aaron Martin for keeping the Dozier compute systems up, running and problem free.

Thank you to the rest of the Dozier Lab including Timbo Stillinger, Karl Rittger, and Annelen Kahl as well as all those that came before us. I also need to thank the Tague

Lab for partially tolerating this snow scientist in their ever more complex ecohydrologic world. Thank you Chris Heckman, Aubrey Dugger, Kyongho Son, Erin Hanan, Xiaoli

Chen, Elizabeth Garcia, Janet Choate, William Burke, and Rachel Torres.

Thank you both to NASA’s Earth and Space Science Fellowship, and ERI’s Summer

Fellowship. Your generous support made this work possible.

Friends have also served a critical role in this process. For all the coffee, food, surf- ing, biking, skiing and good times—thank you. In particular I would like to thank Chris

Heckman (again), Jess Perkins, Kendra Garner, Kate Voss, Sarah Shivers, Alana Ayasse,

Zachary Tane, Erin Wetherley, Susan Meerdink, Karly Miller, Lili Prahl, Tessa Mon- tini, Marcia Zilli, Dozie Dinobi, Steven Lue, Waseem Kalam, Giles Marsen, David An- drews, Iain Whitaker, Dave and Cara Borchers, Chris and Rachel Beck, Christina Sachs,

Lemice Harding, and Jane Scott. I especially would like to thank Margie and Mel An- drews for allowing me to stay with them in Mammoth and being supportive these long 7 years. Finally, thank you Handlebar coffee (De La Vina Street) for keeping me caffein- ated and tolerating my procrastination.

My family has served as the true expedition support staff for this thesis. I would like to thank my godparents Holly and Tom Westcott and their son Alec Wescott. I also owe a huge debt of gratitude to my aunt and uncle (Dr. Ellen Lehman and Dr. Charles

Kennel). It is due to you that I pursued this path—thank you for supporting me in this goal, reading my drafts, and continuing to help me be curious. To my mum (Jo Baer

Brandt), and my dad (Bill Brandt), and my brother (Peter Brandt)—thank you. This is as much for you, as it is for me. Thank you for never giving up and continuing to light the torch whilst guiding me back to the path.

Finally, last but by no means least, thank you to my wife Allison June Armstrong and all of her family (Hank, Julie, Dana, Carly, Kit, and Sally). Alli, you are the com- panion everyone in life deserves, but rarely finds. Your compassion, care and spirit are truly remarkable and these qualities helped me through the many cruxes along the route and to the mountain top.

Thank you all | we did it.

vii

VITA OF WILLIAM TYLER BRANDT June 2019 EDUCATION Bachelor of Arts in Biology, Whitman College, June 2007 Master of Science in Coastal and Watershed Science and Policy, California State Univer- sity, Monterey Bay, June 2012 Doctor of Philosophy in Environmental Science and Management, University of Califor- nia, Santa Barbara, July 2019 (expected)

PROFESSIONAL EMPLOYMENT 2012-19: Graduate Student Researcher, Department of Environmental Science and Management, University of California, Santa Barbara 2015-2018: Teaching Assistance, Department of Environmental Science and Manage- ment, University of California, Santa Barbara 2011-2012: Graduate Student Researcher, Department of Coastal and Watershed Sci- ence and Policy, California State University, Monterey Bay 2007-2011: Research Technician, Stanford University, Monterey, CA

PUBLICATIONS Brandt, W. T., Bornman K. J., Cannon F., Deems J. S., Painter T. H., & Dozier J. [In Submission]. Quantifying the spatial variability of a snow storm using differential airborne lidar. Water Resources Research. Painter, T. H., Skiles, S. M., Deems, J. S., Brandt, W. T., & Dozier, J. [2018]. Variation in rising limb of Colorado River snowmelt runoff hydrograph controlled by dust radiative forcing in snow. Geophysical Research Letters, 45(2), 797–808. https://doi.org/10.1002/2017GL075826. Klinger, D. H., Dale J. J., Gleiss A. C., Brandt T., Estess, E. E., Gardner L., Machado B., Norton A., Rodriguez L. E., Stiltner J., Farwell C., & Block B. A. [2016]. The effect of temperature on postprandial metabolism of yellowfin tuna (Thunnus alba- cares), Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology, https://doi.org/10.1016/j.cbpa.2016.01.005. Aceves-Bueno, E., Adeleye A. S., Bradley D., Brandt W. T., Callery P., Feraud M., Garner K. L., Gentry R., Huang Y., McCullough I., Pearlman I., Sutherland S. A., Wilkinson W., Yang Y., Zink T., Anderson S. E., & Tague C. [2015]. Citizen science as an approach for overcoming insufficient monitoring and inadequate stake- holder buy-in in adaptive management: criteria and evidence, Ecosystems, 18, 493- 506, https://doi.org/10.1007/s10021-015-9842-4. Jorgensen, S. J., Gleiss A. C., Kanive P. E., Chapple T. K., Anderson S. D., Ezcurra J. M., Brandt W. T., & Block B. A. [2015]. In the belly of the beast: resolving stomach tag data to link temperature, acceleration and feeding in white sharks (Carcharodon viii

carcharias), Animal Biotelemetry, 3, 1-10, https://doi.org/10.1186/s40317-015- 0071-6. Clark, T. D., Brandt W. T., Nogueira J., Rodriguez L. E., Price M., Farwell C. J., & Block B. A. [2010]. Postprandial metabolism of Pacific bluefin tuna (Thunnus orien- talis), Journal of Experimental Biology, 213, 2379-2385, https://doi.org/10.1242/jeb.043455.

AWARDS NASA Earth and Space Science Fellowship [2016, 2017, 2018] UCSB Earth Research Institute Summer Fellowship [2014, 2015]

FIELDS OF STUDY Major Fields: remote sensing, mountain hydrology, water resource management

Abstract

A solution to one of mountain hydrology’s principal mysteries: the spatial distribution

of snowfall

William Tyler Brandt

The dynamic nature in which the atmosphere and land interact can render the spatial distribution of precipitation highly variable. This is particularly the case in mountain environments where the topography is steep and the elevational variability is large. To capture this variability, we presently rely on a network of gauges, and to make these measurements meaningful we utilize statistics or models to “fill the gaps”. However, the “gaps” often include vast areas of topographic variability, making model validation challenging at best. Nonetheless, these data are used in streamflow forecasts and even in some of the most technologically advanced regions in the world these forecasts can have large errors, in some cases exceeding 100% absolute error. A large part of this error is due to an inadequate understanding of the spatial distribution of mountain precipitation. Snow, unlike rain, remains roughly in place post snowfall, and can be measured both from the ground and now from the air. In my first chapter, I take advantage of this by using snow remote sensing from the Airborne Snow Observatory (ASO) to establish a methodology for measuring the spatial distribution of snowfall during a single storm. The second chapter utilizes spatial scaling of the ASO data to parse changes in snow accumulation by the principal

driving force—either precipitation or wind redistribution. The third and final chapter evaluates the Weather Research and Forecasting (WRF) model’s ability to replicate the spatial patterns in yearly snow accumulation as observed by ASO. Importantly, all three chapters lay the groundwork for the increased use of snow remote sensing to both help augment and evaluate existing models for precipitation monitoring and forecasting in mountain environments.

Table of Contents

Introduction ...... 1

Chapter 1 Quantifying the spatial variability of snow storm using differential airborne lidar ...... 7 Abstract ...... 7 1.1 Introduction ...... 8 1.2 Study site ...... 12 1.2.1 California precipitation ...... 12 1.2.2 Upper Tuolumne River Watershed ...... 13 1.2.3 Tuolumne subbasins ...... 14 1.3 Data and models ...... 15 1.3.1 Airborne Snow Observatory ...... 15 1.3.2 Snowfall estimation from ASO data ...... 17 1.3.3 ASO accuracy and precision ...... 18 1.3.4 Surface station measurements ...... 20 1.3.5 Modeled new snow density ...... 24 1.3.6 Regional reanalysis ...... 25 1.3.7 Observed melting levels, precipitable water and wind speeds ...... 25 1.3.8 Landsat imagery ...... 26 1.4 Results and discussion ...... 27 1.4.1 Synoptic analysis of the April 2015 storm ...... 27 1.4.2 In situ data ...... 31 1.4.3 Compaction ...... 33 1.4.4 ASO-estimated snow water equivalent ...... 36 1.4.5 Spatial distribution of precipitation ...... 38 1.5 Conclusions ...... 46

Chapter 2 Using repeat airborne lidar and measurement scale to reveal areas of wind driven snow transport in mountain catchments ...... 48 Abstract ...... 48 2.1 Introduction ...... 49 2.2 Data and Models...... 51 2.2.1 Airborne Snow Observatory and Snowfall Observations ...... 51 2.2.2 Compaction and Snowmelt ...... 52 2.2.3 Digital Elevation Model ...... 54 2.2.4 Snow Process through Scale ...... 55 2.2.5 Meteorological Analysis ...... 59 2.3 Results and Discussion ...... 61 2.3.1 The Storm Periods ...... 61 xii

2.3.2 ASO ∆ �� ...... 62 2.3.3 Snow Process through Scale ...... 64 2.3.4 Recorded and Modeled Wind Speeds and Directions ...... 67 2.4 Conclusions ...... 68 2.5 Chapter 2 Supplementary Material ...... 71

Chapter 3 Assessing WRF’s seasonal winter precipitation in California’s Sierra Nevada using the Airborne Snow Observatory ...... 76 Abstract ...... 76 3.1 Introduction ...... 77 3.2 Study site ...... 83 3.3 Data and models ...... 84 3.3.1 Overview...... 84 3.3.2 Hydrologic surface station measurements ...... 85 3.3.3 Airborne Snow Observatory ...... 88 3.3.4 Digital Elevation Model ...... 89 3.3.5 WRF ...... 90 3.4 Results and discussion ...... 91 3.4.1 Surface Observations ...... 92 3.4.2 ASO Peak SWE ...... 97 3.4.3 West-WRF Precipitation ...... 100 3.4.4 Water Equivalence vs. Elevation ...... 107 3.4.5 Atmospheric Melt Levels ...... 110 3.5 Conclusions ...... 112

REFERENCES ...... 116

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Introduction

Precipitation is arguably the most important flux in mountain hydrology. It is the biggest flux by far, dwarfing evapotranspiration (ET) and runoff, and it supplies the water required for both mountain ecosystems and people alike. Both the spatial variability and phase (water versus ice) are key attributes of this flux—and are critical in determining the quantity and temporal variations in both runoff and even ET. And yet, both these quantities (the spatial variability and the phase) are still somewhat largely unknown.

The principle reason for the unknown is both simple and complex. From a “simple” standpoint, countries have either managed to endure the variabilities in mountain precipitation that generate both floods and famine, or have “gotten by” with the use of good infrastructure and empirically based forecasts with a known, but acceptable error. How- ever, the climate is becoming ever more volatile and our population is increasing. Addi- tionally, more people are demanding a western life style that requires increasingly more water from an already stressed system, while simultaneously also demanding a healthier environment. As a result, either enduring, or “getting by with error” is no longer an option—we need a more accurate and precise accounting of our water, and this starts with improved estimates of precipitation.

From the “complex” standpoint, mountain precipitation is challenging and expensive to observe—i.e. there are good reasons for why we have just gotten by. Highly

variable, topographically complex terrain directly challenges the use of surface measurements to truly represent the landscape. Additionally gauges can suffer from data gaps (in some cases a few days, and in others up to a year) due to harsh weather and electronic failures. The measurements themselves can also have individual nuances. Precipitation gauges largely suffer from undercatch due to wind; this is particularly the case during snowfall. In snow dominated regions, snow depth sensors and snow pillows are better at measuring the accumulated snow. However, snow depth sensors suffer spurious values during snowfall due to reflections off falling snow crystals and snow pillows, whilst more accurate over the long run, are expensive, hard to deploy, and require low sloping terrain in wind sheltered environments (a rare find in mountain environments, and not necessarily representative). These problems withstanding, we use these surface measurements to generate runoff forecasts. However, any inherent bias in the measurements will naturally be carried over into the forecast themselves.

Other ways of directly measuring the spatial distribution of mountain precipitation include ground based radar and satellite active/passive remote sensing. However, ground based radars are usually absent from mountainous terrain as they are expensive to deploy, suffer from beam blocking due to terrain, fail to capture data close to the surface (~100 m), and possess ambiguities associated with the snow-rain transition. If ground based radars are used, precipitation estimates are often tuned using surface measurements, and so any surface station bias also gets incorporated into the radar

estimate. Satellite based estimates of mountain precipitation have improved substantially since their original development. Currently NASA’s Global Precipitation Mission

(GPM) satellite constellation can measure precipitation rates across much of the planet on an hourly basis. However, the spatial resolution can be quite coarse (>5 km), and therefore not always appropriate for the fine scale precipitation observations required for small to medium sized mountain watersheds.

As an alternative to direct measurements, we also model the weather at mesoscale levels to produce precipitation forecasts, as well as in hindcast experiments to try and resolve critical processes driving the flux. A good example of these models is the

Weather Research and Forecasting (WRF) model. WRF uses physics, and in some cases parameters, to physically downscale regional reanalysis datasets. Using the computing power of today, WRF can be run at sub km scales. It is an impressive model with vast amounts of data output both in 3D and 4D matrices. Nonetheless, the model still requires validation, and usually this comes in the form of surface measurements. And while it is tempting to treat WRF as “truth” given its highly sophisticated use of physics, there is still a reasonable amount of uncertainty as to its fidelity of the physical mechanisms driving mountain precipitation.

For these aforementioned reasons, the spatial distribution of precipitation, and its phase, still remain somewhat unknown; so, how do we improve on our current observational efforts? Snow, unlike, rain remains roughly in place post snowfall. As a result,

if the spatial distribution of the snow water equivalent (SWE) can be resolved, a proxy for the spatial distribution of snowfall and other redistribution forces exists. However, no current remote sensing technique can directly resolve SWE (at least at a high enough spatial resolution to be relevant here). Nonetheless, we can utilize airborne lidar to accurately and precisely measure the snow depth, and when combined with modeled estimates of the density (which have far less uncertainty) can be used to estimate SWE.

Since 2013 NASA’s Airborne Snow Observatory (ASO) has used this technique to determine SWE at a 50 m spatial resolution across much of California’s southern and central Sierra Nevada for snowmelt forecasting. The airborne platform has also obtained data in Colorado’s Rocky Mountains, and Washington and Oregon State’s Cascade

Range. While ASO is constrained temporally (i.e. flights do not occur every day and are limited by cloud cover), the platform does provide a spatially complete dataset thereby vastly improving on, for example, individual surface stations.

The research presented herein utilizes snow remote sensing to improve our understanding of the spatial distribution of mountain precipitation—specifically snowfall. In

Chapter 1, I develop a methodology to use ASO’s lidar to estimate the spatial distribution of snowfall for a single storm. Two ASO flights are used to bracket a single storm and measure an accumulated depth. The depths are then combined with a modeled estimate of the new snow density to produce a spatial estimate of the water equivalent. The work clearly demonstrates the potential for ASO by augmenting surface observations to

“fill the gaps”, and in helping to improve our understanding of the meteorological mechanisms producing snowfall. Future versions of this work will utilize the methodology to measure snow accumulation in different watersheds/regions and to improve snowfall representation in both weather and climate models.

In Chapter 2, I utilize ASO observations from two storm periods to help identify regions of the basin that are impacted by secondary controls on snow accumulation, i.e. wind redistribution. In the Sierra Nevada, moisture transport within mid-latitude cyclones are modified by orographic processes which drives snow accumulation. How- ever, second-order controls like wind, sloughing, and avalanches often distort this distribution. Because these different processes occur at various measurement scales, spatial measurements of snow can represent these processes explicitly or implicitly. Here I use data from ASO to differentiate between the different controls on snow accumulation using a new method I call Snow Process Through Scale. For each storm, I spatially coarsen the ASO measurements, and use the different pixel sizes to identify areas that are subject to the predominant control (snowfall) versus secondary controls like surface winds.

The method will be useful for modelers trying to identify where wind redistribution mechanisms are operating in mountain landscapes, which might help to improve a model’s spatial representation of the snowpack.

Finally, Chapter 3 directly evaluates WRF’s seasonally accumulated precipitation using snow remote sensing. WRF is currently extensively used in precipitation

forecasting, as well as in hindcast experiments to improve our scientific understanding of precipitation mechanisms; however its ability to properly replicate the spatial distribution and phase of precipitation in mountain environments is still unknown. Chapter 3 presents results from a direct comparison between total winter precipitation from WRF and remotely sensed estimates of the peak SWE from ASO in the Central Sierra Nevada over 4 water years. Overall, WRF tended to underestimate snow accumulation at the highest elevations. Additionally, WRF struggled with its precipitation phase as evidenced by its total precipitation (rain + snow) matching ASO observation and snow pillows better than just snowfall estimates alone. We conclude that in snow dominated watersheds, the use of remotely sensed snow water equivalent will help to significantly improve WRF through either better parametrization schemes for specific regions or more broadly in helping to update the model physics.

Chapter 1 Quantifying the spatial variability of snow storm using differ-

ential airborne lidar

W. Tyler Brandt, Kat J. Bormann, Forest Cannon, Jeffrey S. Deems, Thomas H.

Painter, and Jeff Dozier

Abstract

California depends on snow accumulation in the Sierra Nevada for its water supply.

Snowfall is measured by a combination of rain gauges and snow pillows. However, the paucity of these stations, particularly at high elevations, introduces artifacts into spatial precipitation estimates, and these errors have implications for hydrologic forecasting.

To reduce these errors, we need high-resolution, spatially complete measurements of precipitation across mountainous terrain. Remotely sensed snow depth and snow water equivalent (SWE), with retrievals at time scales that resolve storms, could provide the solution to this problem. Since 2013, NASA’s Airborne Snow Observatory (ASO) has measured snow depth across multiple basins in California’s Sierra Nevada and the Colo- rado’s Rocky Mountains to improve streamflow forecasting through improved SWE estimates. In early April 2015, two flights bracketed a single storm. They provided an opportunity to difference the lidar-observed snow depths and obtain an accumulated snow depth deposited by the storm, and thereby a direct measure of the basin-wide

precipitation. We then combined the accumulated depth with a modeled new snow density to produce a spatial estimate of the water equivalent of the snowfall. The work shows that extension of ASO operations to additional storm events could benefit the understanding of hydrometeorology by delivering observations that are ideal for the evaluation of the spatial distribution of snowfall in weather and climate models.

1.1 Introduction

Snow and rain in the mountains supply critical water resources throughout the world, including the Western U.S. Yet estimates of the total amount of water held in this environment throughout the year are uncertain. A primary challenge in determining the water storage is the limited in situ sampling of the heterogeneous spatiotemporal variability of precipitation.

Specifically, observing winter accumulation presently depends on a sparse network of surface stations, which are mainly absent from high elevations, prone to error, and biased when used to infer precipitation across rugged terrain (McMillan et al., 2012;

Molotch & Bales, 2005; Rittger et al., 2016). To compound the issue, the source of measurements (precipitation gauges, snow depth sensors, or snow pillows) affects both the recorded timing and total precipitation measurement. For example, during snowfall, wind reduces the amount of snow entering precipitation gauges by up to 50%

(Rasmussen et al., 2012; Yang et al., 2005), snow depth sensors can report specious values during snowfall due to reflections off falling snow (Bair et al., 2018b), and snow 8

pillows can falsely indicate the timing of precipitation because of temporal delays caused by snowpack bridging (Johnson & Marks, 2004). While techniques exist to identify and adjust gauge measurements for snowfall measurement (e.g., Kochendorfer et al.,

2017), considerable uncertainty remains.

These problems aside, gauge data are often used to validate precipitation estimates from weather models or are interpolated and extrapolated to generate stand-alone spatial estimates of precipitation. These spatial products are then used as the precipitation forcing for hydrologic models and runoff forecasts. However, the challenge of evaluating the performance of these products remains, as the use of gauge withholding techniques or the use of new networks of surface stations still suffer from high uncertainty and a lack of sampling across all physiographic conditions within a basin (Lundquist et al., 2015; Nelson et al., 2016). As such, precipitation variability within mountainous watersheds is still poorly understood. This spatial uncertainty can have hydrologic consequences. For example, an inadequate representation of the spatial distribution of water inputs into the basin can lead to incorrectly calibrated, or initialized, ecohydrological models and therefore error-prone forecasts of streamflow and estimates of evapotranspiration and soil moisture (Henn et al., 2018; J. W. Kirchner, 2006).

Alternatives to gauge data or models for precipitation measurement include ground- based weather radar and space-based passive microwave radiometers and radars. How- ever, ground-based radar estimates suffer from terrain blocking, beam spreading, and

the ambiguity associated with rain/snow reflection (Austin, 1987). Snowfall algorithms designed for spaced-based radiometers and radars are also still in development

(Skofronick-Jackson et al., 2015) and do not provide the spatial resolution required

(Behrangi et al., 2018). While future technology and algorithms might enable space- based estimates of precipitation at resolutions that are appropriate for frozen and mixed- phase precipitation in small mountain watersheds (National Academies, 2018), at present we still require better ways of estimating the spatial distribution of precipitation. In snow-dominated watersheds, an answer now lies in airborne remote sensing of snow depth and snow water equivalent.

Unlike rain, which can immediately run off or infiltrate, snow generally remains on the landscape after deposition. While both wind and avalanches redistribute snow after deposition, much of the deposited snow remains in place or moves only short distances.

Therefore, in regions where precipitation falls largely as snow, remotely sensed snow accumulation can improve our understanding of the spatial variability of precipitation and can serve as a validation dataset for other precipitation products (Behrangi et al.,

2018; Dozier et al., 2016). NASA’s Airborne Snow Observatory (ASO), a scanning lidar, imaging spectrometer, and distributed modeling system (Painter et al., 2016), has measured snow in numerous river basins in California’s Sierra Nevada, the Olympic

Peninsula in Washington, and the Rocky Mountains in Colorado. The Tuolumne River

Basin (Figure 1) has the most temporally complete record, spanning 2013 to present.

ASO monitors snow depth and snow albedo periodically through the melt season for water supply forecasting, but in early April 2015, two ASO flights bracketed a single storm event, providing an opportunity to characterize the spatial distribution of an individual storm at a fine spatial resolution.

Figure 1. (a) Elevation of the windward HUC 8 basins in the Central Sierra Nevada: Stanislaus, Tu- olumne, and Merced in California, US. The Upper Tuolumne is highlighted in navy blue. “Met” demarcates precipitation gauges used in this study, “SWE” and “SD” mark locations for snow pillows and snow depth sensors. Black triangles symbolize wind sensors. (b) Elevation of the Upper Tuolumne Ba- sin, along with a dividing line separating the northern windward and southern leeside subbasins. The Hetch Hetchy Reservoir lies at the lowest elevations on the western edge of the basin. (c) 3 m ASO snow depths before and after the April 2015 storm, with a mean depth change of +0.41 m between flights.

Our primary objective is to outline the methods by which ASO data can be used to produce distributed estimated water equivalent for snowfall events. ASO has only bracketed one storm in its six years of operation, but ASO measures the distributed accumulated snowfall and provides a gauge-independent dataset that can be used to evaluate precipitation accumulation and phase from numerical weather prediction models and gauge-based interpolations. We also examine the synoptic conditions responsible for the given storm to show how ASO can be used to validate our understanding of the linkages between large-scale atmospheric processes and watershed impacts. Particularly in places where precipitation has large interannual variability, gaining a better understanding of the precipitation distribution and phase is a first step towards improving meteorological and hydrological forecasting.

1.2 Study site

1.2.1 California precipitation

California’s water supply, which supports a diverse array of users, depends on snow accumulation during winter storms in the Sierra Nevada. Extratropical cyclones generate almost all of this water (Catto et al., 2012; Hawcroft et al., 2012). The storms that produce the most precipitation are greatly enhanced by atmospheric rivers, long narrow bands of enhanced water vapor transport (F. M. Ralph et al., 2004). While all heavy snowfall and rainfall events over California require enhanced low-level moisture

transport normal to topography to generate orographic precipitation, considerable event-to-event variability exists in their evolution, magnitude, and precipitation mechanisms (Houze et al., 1976; Katzfey, 1995; Lee, 1984).

In most years, only a dozen or fewer storms build the seasonal California snowpack

(Lundquist et al., 2005; Serreze et al., 2001), with the higher elevations usually accumulating the most snow (Huning & Margulis, 2017). Normally, two thirds of these storms occur from December to February, and the biggest storm can bring as much as a quarter of the total snowfall for a season (Huning & Margulis, 2017). The small number of events and narrow time window in which they occur make California’s water supply vulnerable to shifts in the atmospheric circulation that impede the “normal” storm track

(Swain et al., 2016). Even the loss of a single storm can shift the Sierra Nevada from a wet to a drier than normal year, impacting the State’s ability to deliver water to agriculture, cities, and the environment itself (Dettinger, 2013). Thus, the infrequency of precipitation in California necessitates the need for understanding both the spatial distribution of precipitation and the mechanisms that drive its variability in time and space.

1.2.2 Upper Tuolumne River Watershed

The Upper Tuolumne River watershed above Hetch Hetchy Reservoir (hereafter the

“Tuolumne Basin”) lies in California’s Central Sierra Nevada within the northern bounds of Yosemite National Park (Figure 1). The reservoir lies at 1200 m above sea level, has a contributing catchment area of 1175 km2, and stores 0.442 km3 of water for 2.7 million 13

people living in the greater San Francisco Bay Area. Slopes generally face northwest, southeast and due west. Numerous streams drain the area, and the Watershed Boundary

Dataset 12-digit Hydrologic Unit Code (HUC 12) divides the watershed into 13 subbasins. However, for simplicity, we combine these into two assemblages: the northern and southern subbasins. The reservoir also produces hydrologic power via two down- stream plants and maintains environmental flows in the river reaches below.

1.2.3 Tuolumne subbasins

The northern subbasins can be considered a collection of “windward” basins, into which moisture predominantly advects from the west or southwest. These subbasins collectively act as a large incline for oncoming moisture and their ridge lines form hillslopes that predominantly face northwest and southeast. In contrast, the southern subbasins are topographically more complex and contain slopes that primarily face west and to a lesser extent east. Many of these subbasins comprise both leeside and windward slopes, examples being Cathedral Creek and parts of the Lyell Fork and Dana Fork (dis- cernable on Figure 1b). Finally, the southern subbasins have twice as much area above

3000 m as the northern subbasins (210 km2 versus 102 km2).

While the southern subbasins comprise more area above 3000 m, the northern subbasins have steeper slopes, an important characteristic when considering orographic effects, and snow redistribution by avalanching, sloughing, and wind. Many of these steep slopes are concentrated above Hetch Hetchy Reservoir itself in the form of large granite 14

walls, but many also trace the ridge lines that separate the various northern subbasins.

The southern subbasins possess fewer of these steeper slopes, owing partly to the low relief of the Tuolumne Meadows. Finally, the northern and southern subbasins also differ in their land cover, according to the 2011 National Land Cover Database (Homer et al., 2015). The southern subbasins have taller trees and a denser tree canopy (as observed by airborne lidar), and their fractional coverages of forest (41.5% versus

30.4%), and wetlands (1.3% versus 0.6%) are greater than those of the northern subbasins.

1.3 Data and models

The research herein combines data from: (1) remote sensing; (2) snow modeling;

(3) meteorological and hydrological surface stations; and (4) atmospheric reanalysis. We show how these data can be synthesized to estimate the spatial distribution of precipitation and the elevation of the snow-rain transition, along with an understanding of the weather synoptics that generated the April 2015 storm.

1.3.1 Airborne Snow Observatory

Beginning in 2013, NASA’s Airborne Snow Observatory has acquired regular lidar and spectrometer surveys of the Tuolumne Basin. ASO comprises two primary instruments (Painter et al., 2016): a Riegl Q1560 airborne laser scanner (ALS) and an itres

CASI 1500 imaging spectrometer. The ALS measures the ground’s elevation when

snow-free in the summer and then the snow surface throughout the melt season to provide estimates of snow depth via subtracting the snow-free from snow-on elevations.

The ASO spectrometer measures the reflected radiance across a wavelength range from

380 to 1050 nm at 10 nm nominal spectral resolution, from which snow-covered area, spectral albedo, snow grain size, and radiative forcing by impurities are calculated. The

ASO computing pipeline fuses the snow-covered area with the lidar-derived snow depths to improve positional accuracy in the snow depth measurements.

Obtaining basin snow water equivalent (SWE = depth × density) is the primary goal of ASO. However, because no sensor can yet directly measure SWE in the mountains

(Dozier et al., 2016), ASO combines lidar-derived snow depths with modeled density fields, constrained by available measurements to calculate SWE (Deems et al., 2013;

Painter et al., 2016; Tedesco et al., 2014). Compared to density, snow depth exhibits greater variability in mountain landscapes and is therefore more crucial when trying to constrain estimates of SWE (Bormann et al., 2013; Jonas et al., 2009; Raleigh & Small,

2017; Smyth et al., 2019). This is especially true late into the melt season, when the Si- erra Nevada snowpack is ripe and the snowpack’s density varies less, averaging 400 kg m–3.

The snow density is spatially modeled across the Tuolumne Basin using the iSnobal model (Marks et al., 1999; Painter et al., 2016), which represents the snowpack as a two-layered system and estimates the snow density using a time-sensitive algorithm that

accounts for snow aging, mechanical compaction, liquid water, and new snow deposition. The model has produced reliable results across different landscapes (Garen &

Marks, 2005; Link & Marks, 1999; Marks et al., 2002; Nayak et al., 2012).

1.3.2 Snowfall estimation from ASO data

The raw 3 m snow depth fields are first masked by a basin boundary and water mask to remove pixels within lakes and streams and outside the basin boundary. At this stage the snow depth fields possess a positive-skewed, long-tailed distribution. To reduce the error in the snowfall calculation, we omitted snow depths above a threshold of 6 m. We picked the threshold only after a careful inspection of snow depths in known deeper snow pockets, i.e. within the leeside of cirques in the southern half of the Tuolumne.

This step removed only 0.006% from the 3 April snow depths and 0.05% of the snow depths from the 9 April acquisition. It is possible that the 9 April acquisition had a few more of these “high” snow depths due to snow in the trees.

A single storm’s contribution to snow depth is estimated by differencing the ASO- measured depth at 3 m spatial resolution after and before the storm. The change in snow depth, ∆��, between the two surveys results from snow accumulation, but also from melt, sublimation, wind redistribution, and compaction. For this study, ASO flights on 3 and 9 April 2015 bookended a storm that occurred between 5 and 8 April.

To convert from depth to SWE, we modeled the new snow density at a 50 m spatial

resolution (Section 1.3.5), and multiplied this by ∆�� coarsened to 50 m using a

Gaussian pyramid reduction (Burt & Adelson, 1983).

ASO has bracketed a few other storms, but many of these other events suffered from longer revisit periods between flight acquisitions, multiple storms, or greater likelihood of melt and sublimation between flights. The April 2015 storm provided the shortest lags between storm start to end and the cleanest acquisition due to little melt and lack of strong winds, providing an excellent test case to explore how airborne lidar and snow modeling can combine to generate high-resolution spatial estimates of mountain snowfall.

1.3.3 ASO accuracy and precision

To measure small changes in snow depth via lidar requires high accuracy and precision and an estimate of the error. The error can have both vertical and horizontal com- ponents and can be both systematic (i.e. with bias) and stochastic (i.e. random). Here we briefly review the two types of error, how ASO presently minimizes them, and our estimate of the error for the change in snow depth.

Systematic errors, i.e. boresight errors and co-registration errors, are minimized within the ASO processing stream though both calibration and relative registration.

Boresight errors occur due to the angular offset between the laser scanner and the Iner- tial Measurement Unit (IMU). This type of error can produce systematic errors in both the vertical and the horizontal at centimeter and decimeter scales (Glennie, 2007). To 18

minimize the error, ASO completes a boresight calibration before each flight season, maintains the position of the IMU relative to the laser scanner, and preforms line-to-line registration.

ASO uses elevation differencing to estimate snow depth for any specific flight acquisition, and therefore co-registration errors in the digital elevation models can be another source of systematic bias (Joerg et al., 2012; Nuth & Kääb, 2011). The bias can be minimized using proper co-registration techniques, and ASO completes this step for every collection through relative registration. The ASO relative registration process ensures that areas mapped as snow-free remain at the original snow-free elevations.

Stochastic errors are more challenging to eliminate as the variations result from random noise in both the vertical and horizontal plane. Flight trajectory accuracy is one of the largest sources of noise as a result of the positional and attitude uncertainties in the aircraft’s position (Glennie, 2007). Another additional source of stochastic error includes two forms of terrain errors. First, in high relief areas, planimetric locational uncertainty can cause a vertical error when the measured elevation is offset horizontally from the target location (Deems et al., 2013). The second type of terrain error is a

“time-walk,” which occurs due to beam spreading on an inclined surface. The spreading of the laser pulse induces a delay in the timing of the return signal, thereby decreasing the relative elevation of the target (Deems et al., 2013). Both types of terrain errors can

be minimized by rigorous flight planning, by increases in pulse repetition rates and point density, and by using a coarser pixel resolution (Deems et al., 2013).

We assess the signal-to-noise ratio for the storm deposition using a reasonable estimate of the bias and random noise. Based on the above discussion, typically reported error measures, and the ASO accuracy results reported by Painter et al. (2016), we con- servatively estimate that the bias for the change in snow depth could be as much as 0.05 m with an additional random error of 0.025 m at a 50 m pixel resolution. To explore the impact of the combined error, we add and subtract 0.05 m with the addition of a normally distributed error between 0 and 0.025 m from the ∆��. If the combined error plus the ∆�� sums to a negative number, we set that pixel’s accumulated snow depth to zero. This process allows us to bound the snowfall measurement with confidence intervals based on estimates of uncertainty and helps us assess whether the ∆�� truly represents an increase in depth or instead a combination of the stochastic and random errors.

1.3.4 Surface station measurements

Throughout the Sierra Nevada, the California Department of Water Resources

(DWR) and other agencies operate more than 100 snow pillows that measure the accumulated SWE. The pillows directly measure pressure changes, thereby integrating snowfall, melt, sublimation, and wind redistribution. The instruments are generally located in low sloping, sheltered forest clearings and report hourly. Data are posted to the 20

California Data Exchange (http://cdec.water.ca.gov/snow/current/snow/index.html) at hourly and daily resolutions. Usually the daily data are used for analysis because they are filtered for outliers and tend to be smoother and also because snow pillows can sometimes require a few hours to adjust and register new snow (Beaumont, 1965;

Johnson & Marks, 2004). These problems aside, this study employed hourly data because the temporal resolution is better suited to estimating the change in SWE from a storm. Changes in pillow SWE result only from changes in mass. Therefore, new snow accumulation or rain on snow that freezes or fails to drain will increase measured SWE.

Decreases in SWE result from melt, sublimation, and scouring from wind.

The suite of instruments at snow pillow sites often also includes sensors for snow depth. The acoustic snow depth sensors are not always located above the snow pillows, so a snow depth measurement does not necessarily correspond to the pillow SWE.

Snow depth can increase because of snowfall or wind redistribution; it can also decline because of snowmelt, sublimation, wind scouring, or compaction. Finally, during snowfall and windy periods, acoustic reflections from airborne snow crystals can cause snow depth data to be noisy (Bair et al., 2018b).

Table 1 summarizes in situ data used in this study. Included are precipitation gauges, wind sensors, snow pillows, and snow depth sensors.

Table 1. Snow pillow, snow depth, precipitation, and wind sensors used in this study, sorted by type of measurement and elevation, data from http://cdec.water.ca.gov/snow/, http://www.snow.ucsb.edu, https://mesowest.utah.edu/, and https://www.esrl.noaa.gov/psd/data/obs/datadisplay/.

Station Name CDEC ID NOAA ID MesoWest ID Latitude Longitude Elevation Yosemite Valley YYVC1 37.750 -119.589 1219 Cherry Valley CEVC1 37.974 -119.916 1457 Hetch Hetchy Met Station HHWC1 37.961 -119.783 1520 Pinecrest 1NNE PNCC1 38.200 -119.983 1707 Leavitt Meadows LVTC1 38.304 -119.551 2194 Tuolumne Meadows TUMC1 37.873 -119.350 2621 Precipitation Deadman Creek DDMC1 38.332 -119.653 2819 Virginia Lakes Ridge VGAC1 38.073 -119.234 2868 Ellery Lake ERYC1 37.935 -119.233 2897 Wild Creek wcc WCCCA 37.800 -120.640 113 Oroville ovl OVLCA 39.532 -121.488 114 Pine Flat pfd PFDCA 36.830 -119.332 184 New Exchequer ner NERCA 37.597 -120.278 259 ONeals onl 37.204 -119.570 684 Smith Peak SEWC1 37.801 -120.101 1180 Crane Flat CNFC1 37.759 -119.821 2022 White Wolf WWRC1 37.859 -119.652 2450

Wind and Precipitationand Wind or SWE Gem Pass GEM 37.780 -119.170 3277 Black Springs BLS 38.375 -120.192 1981 Lower Kibbie Ridge KIB 38.032 -119.877 2042 Lower Relief Valley REL 38.243 -119.758 2469 Gianelli Meadow GNL 38.205 -119.892 2560 Horse Meadow HRS 38.158 -119.662 2560 Tuolumne Meadows TUM 37.873 -119.350 2621 Leavitt Lake LVT 38.282 -119.621 2926

SWE and SnowandDepth SWE CUES* 37.643 -119.029 2940 Dana Meadows DAN 37.897 -119.257 2987 Gem Pass GEM 37.780 -119.170 3277 Slide Canyon SLI 38.092 -119.430 2804 Only Snow Depth Virginia Lakes Ridge VRG 38.077 -119.234 2835 *CRREL/UCSB Energy Site, http://www.snow.ucsb.edu/

We used hourly data from 10 local snow pillows, and 12 local snow depth sensors to assess for the potential of melt, sublimation and compaction between ASO flight

acquisitions (Table 1). Initially both SWE and snow depth were hand cleaned for spurious values. SWE and depth values were then smoothed using a robust discretized spline, which filled the data gaps (5% of the data) but preserved the overall shape of the time series (Garcia, 2010).

The National Weather Service (NWS), Bureau of Land Management (BLM), Na- tional Park Service (NPS), National Resources Conservation Service (NRCS), and

DWR also operate a network of precipitation sensors, often co-located with the snow pillows. Individual gauges have varying configurations, including tipping buckets, accumulation reservoir gauges, and reservoir gauges that contain antifreeze. This study used

11 local precipitation sensors that varied in elevation from 1219 m to 2897 m. Precipi- tation gauge data in combination with temperature data from the same stations were used to spatially model the density of the new snow (Section 1.3.5). In addition to the

“local” precipitation gauges, and comparable to the methods of Dettinger et al. (2004), we also used five precipitation gauges located in the Central Valley to assess the orographic potential of the storm (i.e. the ratio between observed snow accumulation in the basin to the average of the observed precipitation in the Central Valley). Ranging from 113 m to 684 m, these stations included Wild Creek, Oroville, Pine Flat, New

Exchequer, and O’Neals (Table 1). All five stations are part of the NOAA Hydromete- orology Testbed.

Finally, this study also employed a single USGS stream gage above Hetch Hetchy reservoir (USGS Gage Number: 11274790). These data were used to help assess whether the storm produced rain during its many phases within the Tuolumne.

1.3.5 Modeled new snow density

We used the Spatial Modeling for Resources Framework (SMRF), developed by the

USDA Agricultural Research Service (ARS), to estimate the new snow density at a 50 m spatial resolution (Havens et al., 2017). SMRF is part of the iSnobal modeling suite and is used to gather and process input data before ingestion into iSnobal. The SMRF new snow density is modeled using a combination of gauge-interpolated precipitation and temperature (Susong et al., 1999) and accounts for compaction via overburden pressure

(Kojima, 1967) and equilibrium metamorphism (Colbeck, 1998). Gauge data, originally from CDEC but obtained from USDA ARS, included 11 local weather stations (see Fig- ure 1 for station locations, and Table 1 for station names).

We used SMRF to estimate the hourly snow densities for each grid cell at 50 m spatial resolution. We combined the pixel mean with the 50 m ASO ∆�� (Section 0) to estimate the change in snow water equivalent, and we used the standard deviation for each pixel to generate upper and lower bounds for the new snow density and thereby error bounds on the ASO-estimated snow water equivalent.

1.3.6 Regional reanalysis

For meteorological analysis of the ASO April 2015 storm, we used the Climate

Forecast System Reanalysis (CFSR) Version 2 (ds094.0) (Saha et al., 2014) from the

National Centers for Environmental Prediction (NCEP). CFSRv2 begins on 30 March

2011, is a global, third generation reanalysis product, and possesses a coupled atmosphere-ocean-land surface-sea ice system. The model has a spatial resolution of 0.5o and is initialized four times daily (0000, 0600, 1200, and 1800 UTC) with 40 vertical levels.

(F. Ralph et al., 2012) found CFSRv2 to be one of the better performing reanalysis models for studying atmospheric rivers and the large-scale meteorological processes leading to extreme precipitation in the Western U.S.

1.3.7 Observed melting levels, precipitable water and wind speeds

Melting levels for the April 2015 storm, i.e. the rain-snow transition elevation, were measured using snow level radars at Colfax, New Exchequer, and Pine Flat Dam.

All three stations are upwind of the Tuolumne Basin in the Central Valley. The melting level is associated with the Bright Band layer, which is a region of enhanced radar reflectivity caused by the high dielectric function and large particle size of melting snow as it falls through the atmosphere.

To investigate precipitable water amounts for the April 2015 storm, the integrated water vapor (IWV) and integrated vapor transport (IVT) observations were obtained from the atmospheric river observatory (A. B. White et al., 2013) at Bodega Bay. The 25

449-MHz doppler wind profiler collects vertical profiles of horizontal wind velocities from 0.18 to 8 km at roughly 100-m vertical resolution with an accuracy of ±1 m s–1 on the central California coast. The profiler is co-located with a Global Positioning System

(GPS), and the GPS receiver can be used to measure the IWV. Both datasets (wind and

IWV) are combined to estimate the IVT. The IVT is a primary requirement for orographically-forced precipitation (Neiman et al., 2002; Roe, 2005). The observations from Bodega Bay, situated along the coast approximately 300 km due west of the study watershed, are ideal for evaluating the characteristics of the storm prior to modification by terrain.

Surface wind speeds and directions within the study area were analyzed using a transect of five wind sensors from NOAA’s Wild Creek meteorological station at 113 m to

Gem Pass at 3277 m (Figure 1). We used these data to assess the potential for blowing snow during the April 2015 storm, using the average saltation threshold of 7.7 m s-1 established by Li and Pomeroy (1997) and also used by P. B. Kirchner et al. (2014). The other three stations (Table 1) are Smith Peak, Crane Flat, and White Wolf.

1.3.8 Landsat imagery

In addition to the snow level radars, we identified the change in snow-covered area from Landsat 8 false color imagery to assess the elevation of the rain-snow transition in the April 2015 storm. In the period spanning the storm, the satellite passed over the Tu- olumne Basin on 23 March and again on 8 April—before and after the storm. Given the 26

low amounts of snow during water year 2015, the expansion of the snow extent post storm identifies the rain-snow transition.

1.4 Results and discussion

1.4.1 Synoptic analysis of the April 2015 storm

O’Hara et al. (2009) determined that key ingredients for heavy Sierra snowfall events include: (1) the intensity and angle of the moisture transport relative to the Si- erra Nevada; (2) the static stability of the air mass; and (3) the presence of strong upper- level dynamics. While orographic forcing of moisture transport is the primary precipitation mechanism over the West Coast (F. M. Ralph et al., 2013), static stability and dynamical forcing for ascent also contribute to the spatiotemporal distribution of precipitation in any given storm (Cannon et al., 2018; Katzfey, 1995). Because these consider- ations are critical for both a storm’s precipitation magnitude and spatial distribution, we describe the meteorological conditions leading up to and during the April 2015 storm.

Figure 2. (a) Mean sea level pressure, 500 hPa geopotential height, precipitable water (mm), and IVT magnitude for the April 2015 storm at 11:00 am PST on 7 April 2015; (b) schematic of the synoptically driven dynamical forcing which generated the precipitation for the April 2015 storm. The 250 hPa winds serve to keep the surface low pressure active through diver- gence in the upper atmosphere, thereby induc- ing lift at the surface.

Figure 2 illustrates the April 2015 storm’s relevant characteristics. While precipitable water values were relatively low for a California winter storm and did not meet atmospheric river criteria based on the Rutz et al. (2014) catalog, the following conditions appear to have contributed to heavier Sierra Nevada snowfall: (1) moderate strong southwesterly IVT (468 kg m-1 s-1 event maximum over Bodega Bay from 204°) generated by strong low-level winds; (2) weak static stability and relatively cold temperatures in the region of enhanced moisture transport; and (3) co-located dynamical forcing for ascent (Cannon et al., 2018). Putting these conditions into context, the April 2015 storm was notable in the extremely dry water year of 2015 but was not atypical for the

Sierra Nevada. Although the largest Sierra storms occur in association with atmospheric rivers (F. M. Ralph et al., 2016), this event demonstrates that heavy snowfall can also be generated through enhanced dynamical forcing despite comparatively little available moisture. While events of this nature are rarely recorded in the literature, they are known to the forecasting community and are important because they can produce a more uniform spatial distribution of precipitation across the Sierra in comparison to strongly orographically-forced events (Houze, 2012; Katzfey, 1995; Lee, 1984; Oakley et al., 2018). As a result, we would expect the ASO estimated water equivalent to exhibit a much more uniform distribution at the basin scale, rather than the usual enhanced precipitation/elevation relationship more typical of orographically forced ascent.

Snow level radars at Colfax, New Exchequer, and Pine Flat observed average atmospheric melting elevations of 1180 m, 1320 m and 1214 m (Figure 3c). All three snow level radar sites are located on the windward slope of the Sierra Nevada, observing the free atmosphere. Based on theory (Minder et al., 2011), we would expect the atmospheric melting elevation within the Sierra Nevada to be lower than those observed in the Central Valley. Observations from Landsat 8 (Figure 3) put the snowline at ~1200 m, which is 120 m below snow level radar observations from New Exchequer, the site directly upwind of the Tuolumne Basin. The lowering of the melt level is consistent

with observations of melt level declines of 170 m between sites in the Central Valley and the central Sierra Nevada (Minder & Kingsmill, 2013) .

Figure 3. Rain-snow transition line for the April 2015 storm. (a & b) Landsat 8 false color images prior to and following the storm. The turquoise color is snow, white is clouds. The inset maps identify Hetch Hetchy Reservoir, with 500 m elevation contours. The blue outline demarcates the Tuolumne Basin. The post-storm image in (b) shows the large increase in snow-covered area. (c) Snow radar melting elevations for Colfax, New Exchequer (directly upstream of the Tuolumne) and Pine Flat. (d) Streamflow into Hetch Hetchy Reservoir during the ASO measurement period showing only a small rise in streamflow post storm. To put the increase in streamflow into context, (e) shows the streamflow over a three-month period, the grey box marking the ASO measurement period. The rise in streamflow was minimal during the storm, and from the Landsat 8 imagery, we know that the storm was cool enough to produce solid precipitation over most of the elevations in the Tuolumne Basin.

Nonetheless, to thoroughly examine whether the storm, through its many different phases—pre-frontal warm moisture transport, frontal dynamics, and post frontal cold air advection and instability—was cool enough to produce mostly snow throughout the

Tuolumne, we evaluate additional in situ data from the basin.

1.4.2 In situ data

During the April storm, the average air temperature at Cherry Valley (1457 m) was

0.5℃ ± 0.9. Unfortunately, the Hetch Hetchy Meteorological Station (1520 m) failed to collect temperature data on 6 April, nonetheless recorded average temperatures were 4.1℃ ± 4.5. Since air temperature is not always a good indicator of precipitation phase (Marks et al., 2013), we also examined data from the Hetch Hetchy reservoir for any changes to the inflow, outflow or reservoir levels that might indicate the presence of rain rather than snow. Between ASO flights, the reservoir dropped by 0.2 m, equivalent to a decrease in storage of 106 m3, outflow from the dam fluctuated between 14 and

15 m3 s–1, and inflows averaged 8 m3 s–1 (see Figure 3d and 3e for the inflow time series). These data taken together, including data from Landsat and the snow level radars, indicate that snow predominated the precipitation phase throughout the storm. Addi- tionally, onsite records confirmed that snow was present on the mornings of 6 and 8

April (C. Graham, San Francisco Public Utilities Commission, 2019, Personal Commu- nication). We acknowledge that the lowest elevations of the basin, around Hetch

Hetchy, were at the rain-snow transition, and this may have impacted snow depth measurements at these locations.

Figure 4. Snow pillow and snow depth sensor data between ASO acquisition flights (midday on 3 and 9 April). (a) SWE at Lower Kibbie Ridge, Paradise Meadows, Lower Relief Valley and Dana Mead- ows. (b) Snow depth for the same locations; both Lower Kibbie Ridge and Dana Meadows snow depths approach zero towards 9 April. The snow depth sensors measure to 2.5 mm precision and are known to be noisy, which might explain how snow depth could approach zero post storm. However, we are not as interested in absolutes, just the average declines in snow depth. White areas within the graphs delineate times of accumulation. Grey areas mark periods pre- and post-accumulation. Lower Kibbie Ridge, Paradise Meadows, and the Lower Relief Valley pillows are in the northern subbasin, whereas Dana Meadows is in the southern subbasin.

Above the April 2015 rain-snow transition, snow pillows and snow depth sensors either within or close to the Tuolumne recorded average increases in SWE of 41 mm and snow depth of 428 mm (Figure 4). Snow pillows in the northern part of the basin

(Lower Kibbie Ridge, Paradise Meadows, and Lower Relief Valley) recorded two separate accumulation periods on 5 and 7 April, whereas snow pillows in the south, for example Dana Meadows, also recorded increases in SWE but almost entirely on 7 April.

During pre- and post-accumulation periods (grey areas in Figure 4), SWE remains relatively constant (the exception is Dana Meadows, where little SWE was present initially so the pillow responded to air pressure). These data indicate that little to no melt or 32

sublimation occurred before or after the April 2015 storm. While little change in mass occurred at the snow pillows, we observe large decreases in snow depths following accumulation (Figure 4b). Since melt and sublimation were minimal and wind redistribution would have reduced both SWE and depth, the most likely process responsible for the decline in snow depth during this post-storm period is compaction.

1.4.3 Compaction

Substantial declines in snow depth (220 mm) were observed in situ across the Tu- olumne following the April 2015 storm, but losses in SWE were negligible. Conse- quently, compaction must have been responsible for much of the reduction in depth.

Compaction caused by densification can be driven by overburden pressure of new snow

(Kojima, 1967) and snow grain sintering. The post-storm ASO survey on 9 April occurred after compaction of the newly accumulated snow. Therefore, to invert the ASO snow depths for an estimate of the storm’s total accumulation, we applied a compaction correction to account for the declines in snow depth during the period between the end of the storm and the post-storm ASO survey.

The rate of compaction this soon after snowfall is generally nonlinear (Kojima,

1967). To investigate the compaction rate for this storm, we calculated the post-storm compaction rate at 48 snow study plots (which included the 12 snow study sites listed in

Table 1) throughout the central and southern Sierra Nevada (data not shown). We ex- panded our study area for this part of the investigation to enable a more robust 33

examination of compaction versus a few potential physical drivers. These included: (1) elevation; (2) latitude, (3) distance to the Sierra Nevada Crest; (4) accumulated snow depth; (5) mean temperature during the storm; and (6) mean temperature post storm.

For each snow study site, we isolated the snow depths from the time of peak snow depth to the snow depth at the time of the second ASO flight. We then filled the data gaps in the snow depth record using a monotonically declining spline. A lognormal distribution was then fit to the distribution of the smoothed snow depths, and the measure of central tendency of the lognormal distribution (�), was then used to characterize the nonlinear rate of compaction. �, the measure of dispersion of the values, was used as a measure of fit. The compaction rate, as determined by the value of �, was then re- gressed against the variables to identify the key drivers for the decline in depth. The scatter plot between accumulated snow depth and � produced the best correlation with an R2 of 0.58 and a p value of 0.00. The result is consistent with conceptual theory: the larger the accumulated snow depth, the greater the gravitational settlement. We were surprised by the lack of correlation between compaction and the temperature-based metrics, but this may have been due to the relatively short temporal scale, as temperature-based compaction (i.e. snow metamorphism) might have needed longer time periods to become evident.

In general, a nonlinear process over short time periods can be represented linearly by the first term in a Taylor series expansion. Because only 36 hr elapsed between the

peak snow depth and the second ASO flight, we argue that compaction could also be modeled using this simple approach. Average linear compaction rates between the point of peak snow depth and the second ASO flight are 113 mm d–1. This compaction rate is consistent with values from McClung and Schaerer (2006), who state that settling rates can vary from 100 mm d–1 for newly fallen snow to 0.01 mm d–1 for dense snow. While wind speed also accelerates compaction, only 7 stations in the Sierra Nevada recorded

SWE, snow depth, and wind speed simultaneously, so empirical results would be inap- propriate.

Figure 5. Snow depth at 9 regional snow pillows between ASO flight acquisitions. Sharp declines in snow depth following the April 2015 storm result from snow compaction. The various markers showcase two methods to account for compaction post-storm and back-calculate the peak snow depth from the snow depth at the time of the second ASO flight. “Linear” uses the average of the slope of the linear fits over the snow depth decline. “Delta SD” uses the average loss in snow depth due to compaction post-accumulation.

To obtain a compaction correction factor to reconstruct the peak snow depth, we investigated two methods (Figure 5): We used the slope of the linear compaction rate, and we averaged the measured loss in snow depth at the snow pillow sites. In both cases, these efforts produced consistent estimates of the peak snow depth across 12 local snow depth sensor locations. As a result, a blanket compaction value of 220 mm, based on the second method above, was added to the ASO ∆�� to compensate for compaction across the basin between the end of the storm on 7 April and the ASO flight on 9

April.

1.4.4 ASO-estimated snow water equivalent

Estimates of the storm’s snow water equivalent using airborne lidar for the April

2015 storm were obtained by: (1) differencing the lidar surveyed elevations from before and after the storm to derive a ∆�� ; (2) correcting the ∆�� for compaction; and then

(3) modeling a new snow density and multiplying this by the ∆��.

The ∆�� between lidar surveys was estimated by subtracting the snow-on elevations (at 3 m spatial resolution) on 3 April from those on 9 April. The resulting changes can be negative because of random and systematic errors (Section 0), false positives from snow in trees, or wind redistribution. Accordingly, if the ∆�� was positive, then a compaction factor was added (220 mm). If, on the other hand, the ∆�� was negative or zero, the compaction factor was ignored. Finally, the ∆�� were coarsened to 50 m

using a Gaussian pyramid reduction (Burt & Adelson, 1983); the average ∆�� is 0.41 m.

To convert the ∆�� to a water equivalent, we estimated a new snow density using

SMRF (Havens et al., 2017) and validated the data using manually observed new snow densities from Mammoth Mountain, California. The average new snow density from

SMRF, across both space and time, was 71 kg m–3. The mean of the maximum new snow density was 95 kg m–3, and the mean of the minimum was 61 kg m–3.

Mammoth Mountain Ski Patrol manually records new snow density at the Sesame

Snow Study Plot at Mammoth Mountain, CA (Bair et al., 2018b). While the site lies on the leeside of high topography, and therefore prone to differing microphysical processes related to snow crystal growth, we include these data for three reasons: (1) Mammoth is only 25 km southwest of the southernmost point of the Tuolumne. (2) Given the large-scale dynamical forcing mechanisms at work, the Mammoth data inform the other methods of estimating density. (3) Systematic manual measurements of new snow density are rare and Mammoth documents the measurement (Bair et al., 2018b). During the April 2015 storm, the Ski Patrol logged two new snow densities of 70 and 80 kg m–

3. The modeled SMRF mean new snow density lies between these observations, and therefore gives us confidence in SMRF’s ability to replicate the new snow density for this storm.

1.4.5 Spatial distribution of precipitation

Driven by the April 2015 storm’s meteorology, the precipitation was more evenly distributed throughout the Tuolumne than would have been anticipated based on previous climatological values for orographic precipitation enhancement (Figure 6 in

Dettinger et al., 2004). The mean ASO-estimated water equivalent for the April 2015 storm was 28.3 mm, and much of the precipitation fell between 2500 m and 3000 m.

Local snow pillows quantitatively confirmed the magnitude of the event (Figure 6c), and the result also suggests that the new snow density estimates are reasonable. Finally, estimates of the bounds in the water equivalent, i.e. the sensitivity test, are not widely different from the measurements (Figure 6d), and the various fitted curves (dashed black) exhibit similar shapes to the measurements (solid red)—albeit with a slightly shifted peak water equivalent.

Figure 6. ASO-estimated water equivalent (50 m spatial resolution)) for the April 2015 storm. (a) Spatially distributed water equivalent accumulation using the compaction corrected ASO changes in snow depth with the SMRF density of new snow. The red borders mark the northern and southern subbasins. (b) The spatial distribution of the estimated water equivalent equal to or above the 75th percentile (cream), which emphasizes the uniformity in the spatial distribution of the greatest accumulations. (c) a scatter density plot of the precipitation/elevation gradient exhibiting a somewhat uniform distribution. Most of the accumulated SWE at the snow pillows lie within the measured bounds of the ASO-estimated water equivalent. Grey pixels are where the scatter density is close to zero (d) Sensi- tivity test to explore how systematic and stochastic errors in both the lidar-estimated snow depth and density affect the result. While bias and stochastic errors in the snow depths and stochastic errors in the new snow density affect the estimated water equivalent, their overall impact on the precipitation/elevation signal is not large.

Binned and summed according to elevation and aspect, 52.5% of the ASO-estimated water equivalent was deposited between 2000 m and 3000 m, with 35.6% on west-facing slopes (Figure 7a and 7c). Most basin elevations lie between 2000 m and 3000 m,

and west-facing slopes dominate the overall basin aspect. North-facing slopes in comparison represent a smaller fraction of the basin and therefore had the lowest total water equivalent. These data can also be normalized by area to generate a water depth for each elevation band and aspect subset. Figure 8b demonstrates that elevations between 2000 m and 3000 m possessed the deepest snow accumulations, not unexpected given that this elevation also had the greatest total volume of snow. However, the depths appear to be relatively insensitive to aspect as demonstrated by the similarities across all four aspect medians (30.9 mm (N), 26.3 mm (E), 29.0 mm (W), and 23.0 mm (S)) (Figure

7d). These results corroborate the meteorological analysis which suggested that weak upslope IVT along with strong upper level dynamics would have substantially lowered orographic enhancement and therefore the storms’ sensitivity to both elevation and aspect.

Figure 7. Distribution of the ASO-estimated water equivalent across all elevations and aspects within the basin as a summed total and a depth. (a) Summed ASO-estimated water equivalent binned by elevation. (b) Box plot of the estimated water equivalent binned by elevation. (c) Water equivalent binned and summed by aspect. (d) Box plot of the estimated water equivalent binned by aspect.

The storm-total precipitation was not strongly orographically-enhanced given the measured distribution of water equivalent; however, as additional proof we also calculated the average orographic ratio. A measure of the precipitation accumulation enhancement due to topography (Dettinger et al., 2004), the orographic ratio was calculated by averaging the ASO-estimated water equivalent divided by the mean precipitation total observed at five Central Valley meteorological stations (identified in Table 1):

Wild Creek (17 mm of precipitation), Oroville (30 mm), Pine Flat (8 mm), New Ex- chequer (14 mm), and ONeals (18 mm). The orographic ratio for this storm was 1.6.

The value is below those observed by Dettinger et al. (2004), who establish an average

orographic ratio of 3.3 using three sets of stations in the central Sierra Nevada over a similar elevation gradient between 1954 and 1999. In this case, the smaller orographic ratio for the April 2015 storm owed to the storm being strongly influenced by synoptic forcing for ascent (Cannon et al., 2018), rather than producing precipitation strictly by orographic forcing. Additionally, the April 2015 storm was also colder and drier than many of the storms that Dettinger et al. (2004) analyzed.

The difference between the two subbasin’s estimated water equivalent is also small, which we would expect given the strong dynamical forcing for precipitation during the given storm (Figure 8). Slightly more precipitation fell in the northern subbasins than in the southern subbasins, with mean water equivalents (± one standard deviation) of

28.4±15 mm and 26.9±10 mm (Figure 8). While the means are statistically different using a two-sample t-test, these differences are hardly meaningful from a physical perspective. Had the storm been strongly orographically forced, we would have expected larger differences between the two subbasins. Specifically, the spatial pattern would have mimicked the Precipitation-elevation Regressions on Independent Slopes (PRISM)

April Normal climatology (Daly et al., 2008; Daly et al., 1994), with the more windward northerly subbasins collecting more orographically enhanced precipitation than the southern subbasins, which lie in a rain shadow behind the Merced River drainage (Fig- ure 1).

Figure 8. ASO measured distribution of water equivalent in the northern (a) and southern subbasins (b). Beneath are the corresponding scatter density plots for the precipitation/elevation relationship for the (a) northern and (b) southern subbasins that include a fitted spline representing the mean water equivalent at every elevation as well as the “high” and “low” estimate based off the error estimate.

In both subbasin precipitation/elevation plots (Figure 8), as well as the overall basin precipitation/elevation plot (Figure 7b), a decline in snow accumulation coincides with the highest elevations. The observed trend with elevation is neither unique to this storm

(Huning & Margulis, 2018) nor this part of the world (Bookhagen & Strecker, 2008;

Grünewald et al., 2014). Conceptual explanations of the decline in snow accumulation with elevation include: (1) moisture depletion within the storm itself (Houze, 2012; P.

B. Kirchner et al., 2014; Roe, 2005); (2) steep headwalls, which encourage sloughing and avalanching (Elder et al., 1991; Grünewald et al., 2014); and (3) wind

redistribution, which scours the snow and usually moves it downslope (Winstral et al.,

2002). All three explanations could be at play during the April 2015 storm.

We briefly explore each for their relevance, beginning with wind. Li and Pomeroy

(1997) established that the transport of fresh snow required a mean wind speed of 7.7 m s–1 at 10 m above the surface. NOAA’s Wild Creek station, directly upwind of the Tu- olumne and unsheltered, measures wind speed and direction at 1-minute intervals (Fig- ure 9b). During the April 2015 storm, the station measured maximum wind speeds of

13 m s-1 with an average of 2.5 m s-1 (data presented in the figure are hourly, hence the maximum is less than the 1-minute maximum). Wind speeds broke the 7.7 m s-1 threshold for a total of 5 hours (3% of the total time period), mostly on 7 April and almost exclusively from the southwest. Other wind station sites along the elevation gradient (Fig- ure 1) including Smith Peak (Figure 9c), Crane Flat (Figure 9d), White Wolf (Figure

9e) and Gem Pass (Figure 9f) all exhibited similar wind speeds. Wind direction during periods of maximum wind speed were almost exclusively from the south varying between the southeast and southwest depending on station location (Gem Pass excluded).

At the higher elevation sites, wind speeds were well below the 7.7 m s-1 threshold.

These data indicate that the April 2015 storm did not produce the sustained wind speeds to induce substantial blowing snow at the surface. Large-scale wind redistribution, as would be required to remove snow from the top third of basin, was probably not the cause of the decline in accumulation with elevation above 2500 m.

Figure 9. Data from a transect of wind sensors along an elevation gradient. (a) Wind speed for all stations along the elevation gradient including Wild Creek (83 m), Smith Peak (1179 m), Crane Flat (2022 m), White Wolf (2450 m), and Gem Pass (3276 m). (b) through (f) each wind stations’ hourly wind rose representing speed and direction. In general, the lower elevation stations (Wild Creek, Smith Peak and Crane Flat) recorded higher wind speeds. Evidence of significant wind redistribution during this storm is not apparent.

To elucidate whether slope, land class (rocks vs vegetation), and canopy density contributed to the decline in SWE with elevation, we identified 12 transects, 6 each in the northern and southern subbasins. The transects were picked to ensure a consistent aspect and to cover various land cover classes and elevation. In all cases, transects failed to yield a clean correlation between elevation, slope, land cover type, and the ASO- estimated water equivalent. Therefore, consistent with behavior of orographically lifted air, we conclude that moisture depletion was the primarily cause in the decline in the observed snowfall post peak accumulation. Snow pillow observations (Figure 7c) and

lidar observations along an elevation transect (P. B. Kirchner et al., 2014) support this interpretation.

1.5 Conclusions

The spatial distribution of precipitation in mountain watersheds is one of the greatest sources of uncertainty in hydrology, especially in snow-dominated watersheds. The problem arises from the use of sparse surface station networks to quantify relatively in- frequent processes that are dynamic and chaotic over fine spatial scales.

In snow-dominated watersheds, the remote sensing of snow properties can provide the spatial context to measure a storm across the entirely of a landscape and fill the gaps between stations. Additionally, the data yield an independent validation data set for both gauge-interpolated and extrapolated precipitation products and dynamically downscaled precipitation models—something that presently is lacking and greatly needed.

This study examines a cold late season storm that generated widespread precipitation via strong upper level and frontal dynamics rather than orographic enhancement.

ASO acquisitions bracketed the storm, and these data were used to derive a spatially explicit accumulated water equivalent. We found the distribution of the water equivalent to be somewhat uniform across many of the basin elevations and aspects. These data supported the general pattern of precipitation and snow accumulation suggested by the synoptic setup and provided a good demonstration of the potential for ASO and 46

snowfall monitoring. Going forward, a source of uncertainty will be in the density estimates of new snow. To improve these, direct measurements of the density during and over the course of several storms and across climatic, topographic and vegetation gradients would provide a data source for comparison with models.

This study is intended as demonstration paper and outlines the method that can be used to leverage ASO surveys for snowfall monitoring. While the April 2015 storm does not represent the majority of the big snowfall events in the Sierra Nevada, which are frequently associated with atmospheric rivers and larger orographic influences, the analysis of this storm demonstrates that lidar observations for snowfall monitoring can span the spectrum of convective through stable systems. By directly observing the snowfall distribution, ASO data provide high-quality validation of the hydrometeorology across a whole basin or mountain region. Research that utilizes the technology to investigate multiple storms, spanning a variety of snow climates, would help to enhance our understanding of precipitation mechanisms and thereby improve how statistical methods, weather models, and even climate models represent mountain precipitation.

Chapter 2 Using repeat airborne lidar and measurement scale to reveal

areas of wind driven snow transport in mountain catchments

W. Tyler Brandt, Edward H. Bair, Kat J. Bormann, Forest Cannon, Jeffrey S. Deems,

Thomas H. Painter, and Jeff Dozier

Abstract

In the Sierra Nevada, the spatial distribution of snow accumulation is primarily driven by orographic forcing of moisture transport in mid-latitude cyclones. However, second- order controls like surface winds, sloughing, and avalanches distort this distribution. Be- cause these different processes occur at various measurement scales, spatial measurements of snow can represent these processes explicitly or implicitly. We use data from

NASA’s Airborne Snow Observatory, which bracketed two winter storms in the Tu- olumne River Basin of the Central Sierra Nevada, to differentiate the various controls on snow accumulation using a new method we call Snow Process Through Scale. For each storm, we spatially coarsen lidar snow depth, and use the various pixel sizes to identify areas that are subject to the predominant control (snowfall) versus secondary controls like surface winds. The method will be useful for modelers trying to identity where redistribution mechanisms are operating in mountain landscapes, which might help to improve a model’s spatial representation of the snowpack.

2.1 Introduction

In snow-dominated mountain regions around the world, the heterogeneity of snow accumulation drives the spatial and temporal availability of water for ecosystems and people. Snow accumulation results from the complex interaction of the atmospheric boundary layer with topography. At the basin scale, snowfall generally increases with elevation due to orographic effects, but sometimes decreases at higher altitudes due to moisture depletion and topographic forcings (Grünewald et al., 2014; Huning &

Margulis, 2017, 2018; P. B. Kirchner et al., 2014). Locally, secondary controls such as wind, avalanches, and sloughing add to the spatiotemporal heterogeneity (Deems et al.,

2006; Elder et al., 1991; Winstral et al., 2009). While avalanches and sloughing depend on slope and are in many cases very localized (i.e. hill slope scale and smaller), wind influences are highly spatially variable and dynamic, making the process a critical control on snow distribution but challenging to observe and model (Mott et al., 2018).

Wind redistribution can be separated into two categories (Mott et al., 2018;

Winstral et al., 2013): (1) pre-depositional, also known as preferential deposition

(Lehning et al., 2008), which occurs during snowfall due to the modification of the surface flow field and leads to reduced snowfall on windward slopes, and increased snowfall on leeward slopes; and (2) post-depositional, which includes creep, suspension and saltation of snow particles (Filhol & Sturm, 2015). Both categories are impactful, as they can either shift snow from one slope to the adjacent or excavate snow further

downslope (Winstral et al., 2009, 2013). The shift in the spatial distribution modifies the snowmelt dynamics, producing less or more water at specific elevations and aspects thereby impacting runoff timing (Hartman et al., 1999; Hunsaker et al., 2012).

Here we introduce a new method called “Snow Process Through Scale” that is designed to help identify areas of a basin that are impacted by wind redistribution processes—both pre-depositional and post-depositional. Snow Process through Scale ex- ploits the measurement scale differences between primary (i.e. snowfall—as shown here, or melt) and secondary (i.e. wind) controls on the distribution of snow. The method can be used either over the course of individual storms, or to assess the cumula- tive impacts of seasonal wind redistribution using peak snow water equivalent (SWE)— arguably a simpler application.

To showcase the new method we measure the changes in snow depth (∆ ��) for two end of season storms using bracketing flights by NASA’s Airborne Snow Observa- tory (ASO) across the Upper Tuolumne River Basin in California’s Sierra Nevada (from here on referred to as the Tuolumne; Figure 1a). We then reconstruct the storm’s actual accumulation using estimates of melt and compaction, and isolate regions of inter- est (ROIs) where secondary controls dominate the snow’s spatial distribution using

Snow Process Through Scale. Even though the two storms produced similar accumulation amounts, we find that Snow Process Through Scale identifies ROIs on opposite aspects due to post-depositional versus pre-depositional wind redistribution. Results are

consistent with measured and modeled wind speeds and directions from surface observations and reanalysis data.

2.2 Data and Models

We base our analyses on two storms, which occurred from 25 April 2014 to 26

April 2014 and from 6 April 2015 to 8 April 2015. The bracketing ASO flights acquired data on 20 April 2014, 28 April 2014, 3 April 2015, and 9 April 2015.

2.2.1 Airborne Snow Observatory and Snowfall Observations

A Riegl Q1560 airborne laser scanner (ALS) and an itres CASI 1500 imaging spectrometer comprise ASO’s instrument package (Painter et al., 2016). The lidar measures the snow depth at 3-m pixel resolution by subtracting a summer snow-free digital elevation model (DEM) from a snow-on DEM, and the spectrometer measures the snow’s spectral reflectivity to determine snow grain size and the broadband albedo. In addition to snow depth, ASO’s lidar also produces a measure of tree height, and canopy density—both used in this study.

We use the lidar to measure snow accumulation by differencing the ASO-measured depths from before and after the storms, hereafter referred to as the measurement period. The ∆ �� primarily results from snowfall. However, to consider the reduction of snow depth from compaction and melt (section 2.2), we modeled both processes and added the declines to the ∆ ��. Future efforts will also include a sublimation estimate.

To reduce the random error in the lidar measured ∆ ��, we coarsened the 3 m

∆ �� to a 10 m grid using a Gaussian pyramid reduction (Burt & Adelson, 1983). The

Gaussian pyramid reduction was selected, over averaging for example, because of its computational efficiency and its ability to maintain the target pattern integrity while reducing noise. Finally, a brief literature review determined that a 10 m grid size was coarse enough to reduce the random error for the lidar but still sufficient to explicitly resolve wind impacts (Clemenzi et al., 2018; Deems et al., 2006; Painter et al., 2016;

Trujillo et al., 2007; Winstral et al., 2009, 2013).

2.2.2 Compaction and Snowmelt

To determine the contribution of compaction to the ASO measured ∆ ��, we collected data from 11 snow depth sensors and 11 local snow pillows (see Table S1). Snow pillows were included in the compaction analysis to ensure that declines in snow depth were attributable to compaction and not melt. The raw snow depths and SWE were first hand-cleaned and then smoothed using a robust discretized spline (Garcia, 2010).

For both the 2014 and 2015 storms, snow depth declined after the storm but SWE did not. The observation is highly suggestive of compaction, and to account for this, we averaged the change in snow depth at each depth sensor between peak accumulation and the time of the post-storm flight acquisition. The average decline in snow depth, i.e. the

compaction correction factor, was then added to the ∆ �� so long as the ∆ �� was positive.

While snow pillows did not register a loss in SWE after the storms, pillows did measure a loss in SWE in 2014 between the pre-storm ASO flight and the beginning of the storm. To account for this loss, we spatially modeled the melt across the Tuolumne at 500 m spatial resolution using the ParBal energy balance model (Bair et al., 2016).

Since the analysis herein uses snow depth, rather than SWE, the ParBal-estimated melt was converted from a mass to a length using an estimated snow density. During melt, snow densities in the Sierra Nevada average ~400 kg m-3 (DeWalle & Rango, 2008;

Lundquist & Dettinger, 2005), and by combining the density with the estimated melt, we computed a spatial loss in snow depth. The loss in snow depth was then re-gridded to 10 m and added to the ASO ∆ �� and compaction correction to generate a best estimate of the accumulated snowfall for the 2014 and 2015 storms (Figure 1b and c).

Figure 2. (a) Elevation of windward HUC 8 basins in the Central Sierra Nevada: Stanislaus, Tu- olumne (red), and Merced. The Upper Tuolumne and the northern and southern subbasins are highlighted in blue and green. “SWE/SD” demarcates snow pillows and snow depth sensors, “Met” demarcates precipitation gauges used in this study, circles with crosses symbolize wind sensors which measure the average hourly wind speed and in most, but not all cases, the hourly peak wind speed. (b) a slightly oblique and three-dimensional view using a digital elevation model of the ASO measured and corrected ∆ �� from a storm in 2014. Northern and southern subbasins are demarcated by blue and green polygons (c) ASO ∆ �� from a storm in 2015.

2.2.3 Digital Elevation Model

Elevation data were obtained from the USGS’s National Map (https://viewer.nationalmap.gov/basic/) as a seamless 1/3 arc-second (~10 m) digital elevation model

(DEM). We used the DEM to estimate the snowfall/elevation relationship for each storm and to calculate a few landscape characteristics including: slope, aspect, the topographic position index (TPI: Revuelto et al., 2014; Weiss, 2001) using a 21 m search radius, and what we call ‘terrain’, the product of the sine of the slope and the cosine of the aspect (see Figure S1). The search radius for TPI was selected after a few iterations and a brief literature review. The index was included based on the findings of Revuelto et al. (2014) who established it as a primary explanatory variable in the distribution of snow in high alpine watersheds. The terrain metric was included to help separate ROIs on sloped northern versus southern aspects.

2.2.4 Snow Process through Scale

To account for differing snowfall/elevation relationships owing to topography and local orographic effects, we first subsetted the ∆ �� into two subbasin assemblages: the northern and southern subbasins (Figure 1a). Pixels were then filtered using an ASO- generated canopy density to exclude pixels in dense tree stands (only 4% of the basin area was removed from the analysis). We then systematically coarsened the ∆ �� and

DEM to 50 m, 100 m, 200 m, 300 m, 400 m, 500 m, 750 m, 1 km, and 2 km. For every grid size, we plotted the ∆ ��/elevation relationship to identify the spatial resolution at which the snowfall/elevation signal dominated and became explicit, i.e. the secondary controls became implicit—in essence, averaged out.

For both storms, we found that a 200 m grid produced a well-defined snowfall/elevation relationship (Figure 2). This pixel resolution is somewhat subjective; good cases could be made for using 300 m or 400 m. Nonetheless, too coarse a resolution and the averaging process renders little snow at the highest elevations; too fine a resolution causes the secondary snow processes to confound the snowfall/elevation relationship.

The upper and lower bounds of the ∆ ��/elevation relationship (200 m resolution) were then modeled using a robust discretized spline (Figure 2; red lines). This step ap- proximated the variability in the snowfall/elevation relationship. The bounds were then used to classify the ∆ �� at the 10 m resolution as “within,” “above,” or “below” the expected snowfall/elevation relationship. If the 10 m pixel was above or below, we calculated the distance between the ∆ �� and the expected relationship. Positive pixels exhibited more snow accumulation than expected (given snowfall), and negative pixels exhibited less accumulation than expected. These differences can be attributed to secondary controls, i.e. wind redistribution, avalanches, or sloughing.

The newly identified 10 m pixels from the subbasins were then reassembled into the basin as a whole, and snow-covered regions smaller than 5 contiguous pixels and pixels with slopes greater than 50° were removed from the analysis. Steeper slopes should exhibit greater sloughing and therefore be less dependent on wind (Blöschl et al., 1991;

Sommer et al., 2015). Finally, we examined the pixels within the “above” and “below”

ROIs as a function of ASO-derived tree height and landscape characteristics including

slope, aspect, TPI, and terrain. Tree height was included in the analysis based on the work by Hiemstra et al. (2006).

Figure 2. The ∆ ��/elevation relationship at 10 m and 200 m spatial resolution for the 2014 and 2015 storms across the northern and southern subbasins of the Tuolumne (a, c, e, and g). The upper and lower bounds of the snowfall/elevation relationship, in red, were delineated using the 200 m data. Snow depth observations are demarcated by orange squares and match accumulation measured by ASO at the 200 m spatial resolution. Figures b, d, f, and h are the density scatter plots for the 10 m data. During the 2014 storm, 22% and 20% of 10 m pixels are located above/below the upper/lower bounds (red lines) for the northern and southern subbasins. During the 2015 storm, 13% of pixels are located above/below the upper/lower bounds for both the northern and southern subbasins.

2.2.5 Meteorological Analysis

To evaluate the ambient environment of the two storms, and identify time periods in which wind redistribution was possible we performed a simple meteorological analysis that included wind data from surface stations and reanalysis as well as atmospheric melt level elevations. We recognize that the meteorological processes driving snow redistribution during the two storms is not resolved using the assembled data sources, but a full meteorological analysis using a model like the Weather Research and Forecasting model run at a spatial resolution << 1 km is beyond the scope of this study.

2.2.5.1 Surface Station Winds

To investigate the potential for wind redistribution (both pre-depositional and post- depositional), we obtained hourly peak wind speed and directions from 27 wind stations, and average hourly wind speed and direction from 33 stations within the San

Joaquin and South Lahontian hydrologic areas (Figure 1a and Table S2). Sensors ranged in elevation from 69 m to 3277 m with a median elevation of 1504 m. Not all sensors collected data during both storms. Generally, wind speeds above ~ 10 m s-1 have been found to be required for large amounts of post-depositional redistribution (Filhol &

Sturm, 2015). Here we use a wind guest threshold of 7.7 m s-1 established by Li and

Pomeroy (1997) and recently utilized by P. B. Kirchner et al. (2014) to indicate time periods in which wind redistribution (both pre and post depositional) was likely.

2.2.5.2 Spatially Distributed 700 mb Wind Speeds

Since wind data from surface stations can be highly variable due to localized surface flow fields and few of the wind sensors are actually located within the Tuolumne, we also evaluated wind speeds and directions at the 700 mb elevation using the Climate

Forecast System Reanalysis (CFSR) Version 2 (ds094.0) (Saha et al., 2014) from the

National Centers for Environmental Prediction (NCEP). Temporal wind speeds and directions were extracted over pixels centered over the Tuolumne and in the foothills of the Sierra Nevada directly west of the Tuolumne for a “free” atmosphere evaluation.

CFSR was also used to qualitatively assess the synoptic evolution and ambient environment during both storms.

2.2.5.3 Atmospheric Melt Levels

Snow level radars at Colfax, New Exchequer, and Pine Flat were used to measure the atmospheric melt level of each storm. Data between the two flight acquisitions were averaged to generate a single elevation of the freezing elevation for each station and averaged across all three stations to compare the two storm events.

2.3 Results and Discussion

2.3.1 The Storm Periods

The storms were remarkably similar in precipitation amounts, as measured by surface stations, and in their respective synoptic structure and evolution (assessed using

CFSR). Accumulated snow depths at surface stations for the April 2014 and 2015 storms were 387 mm and 440 mm respectively, and gains in SWE amounted to 38 mm and 41 mm. Precipitation gauges also recorded similar accumulation amounts of 32 mm and 30 mm water equivalent. The two storms also arrived at the end of the accumulation period and were driven more by synoptic lift and frontal dynamics rather than orographic effects—not necessarily typical for Sierra Nevada winter storms (Dettinger et al., 2004).

The two storms did differ in their atmospheric melt elevations. Snow level radars at

Colfax, New Exchequer and Pine Flat recorded a station average melt elevation of 1680 m during the 2014 storm, and a station average of 1238 m during the 2015 storms. The elevational difference between the two storms was 400 m, and the ASO data reflect this difference with a visibly higher snowline for the 2014 storm (see Figure 1b and 1c).

Greater compaction amounts during the first storm (267 mm versus 220 mm) could be explained by the first storm’s warmer temperatures. Snow falling through a warmer atmosphere, would naturally generate higher new snow density due to riming.

In addition to more compaction, the April 2014 measurement period also experienced snowmelt/sublimation losses. 9 of the 11 snow pillows (data from 2 pillows were not reliable) observed average declines in SWE of 41 mm over a 5-day period, a notable amount as the storm itself only deposited 38 mm. The spatially explicit ParBal energy balance model only averaged losses in SWE of 18 mm with a maximum loss of 86 mm; losses were nonlinearly related to elevation. The difference between snow pillow observations and ParBal could be due to sublimation losses, which we did not model. None- theless, when the ParBal melt was converted to a snow depth, the average loss in snow depth amounted to 47 mm, with a maximum of 214 mm. During the 2015 storm both snow pillows and ParBal recorded little to no mass loss, i.e. no melt and/or sublimation.

2.3.2 ASO ∆ ��

The mean ASO ∆ �� in the northern subbasins for the April 2014 and 2015 storms was 170 mm and 400 mm. In the southern subbasins the mean ∆ �� was 250 mm and

420 mm. While the 2014 ∆ ��′� are well below snow depth sensor observations and roughly half of the observed accumulation observed during the 2015 storm, the ASO values incorporate large losses in snow depth (see Figure 2). When these losses are dis- counted, the 2014 ∆ �� are a much better match for snow depth sensor observations,

and exhibit similar totals recorded during the 2015 storm—thus reinforcing the notion that the two storms were similar from an accumulation stand point.

The ∆ ��/elevation profile can also be used to compare ASO observation with local snow depth sensors and for the intra storm comparison. Figure 2a, c, e, and g not only confirm that the coarsened, and “corrected” ASO ∆ �� (black points in Figure 2a, c, e and g) match snow depth observations well (orange points in Figure 2a, c, e and g), but also that the two storms exhibited strong similarities across their respective ∆ ��/elevation relationships.

Given the similarities in storm deposition, why are there striking differences between the two storm’s spatial distributions of ∆ �� (Figure 1b and c)? ∆ �� is not only a function of the storm’s snowfall, but also other controls, specifically wind redistribution. During the 2014 measurement period, there are clear signs of snow erosion on windward ridges and obvious signs of snow deposition on adjacent slopes—this is particularly the case in the northern subbasins which possess strong northwest/southeast ridging (Figure S1). Additionally, there is more deposition in the southern subbasins than in the northern subbasins, and predominantly in forested regions. During the 2015 measurement period, the deposition appears to be more uniform at the basin scale, but ridge lines exhibit lower than expected ∆ ��—particularly on southeastern exposures.

To further map these ROIs we employ Snow Process through Scale.

2.3.3 Snow Process through Scale

Apparent in Figure 2, numerous 10 m pixels were outliers based on the ∆ ��/elevation relationship defined by the maxima and minima of the 200 m ∆ ��. These outliers represent a ∆ �� in which some process (other than snowfall) drove the distribution of snow. If these outlier pixels are filtered, such that only contiguous ROIs larger than 5 pixels are retained, then in 2014 18% of the total snow-covered 10 m pixels are outliers, and in 2015 10% are outliers.

Figure 3 shows the spatial distribution of the ROIs from both storms; red ROIs indicate places were snow was primarily lost (i.e. “below” what was expected given snowfall), and blue ROIs mark regions were snow was primarily gained (i.e. “above” what was expected given snowfall). The ROIs have also been subsetted to exclude pixels whose slope is above 50° (these pixels appear in green in Figure 3). Slopes above 50° would be subjected to sloughing, and not exclusively wind affected.

Spatially, the two measurement periods produced different distributions of ROIs

(Figure 3a and f). Nonetheless, some of the ROIs appear to be the inverse between the two measurement periods, i.e. a “below” ROI during storm 2014 appears as an “above” for storm 2015. This is particularly evident in the polar histograms of the aspects of snow covered pixels within each ROI (Figure 3b and g).

Figure 3. The spatial distribution of the various ROIs for the two storms generated from the Process from Scale method (a and f). Polar histograms of the aspect of ROI pixels (b and g), aspect rose of hourly peak wind speeds above 7.7 m s-1 (c and h), and probability histograms of slope (d and i) and tree height (e and j) for each pixel within an ROI.

To further investigate the topographic position of the ROIs, we generated probability histograms of a few landscape characteristics for each pixel as function of whether the ROI was “above” or “below” the ∆ ��/elevation gradient. Landscape characteristics for the probability histograms included the cosine of the aspect (1 representing due north, -1 due south; Figure S2), slope (Figure 3d and i), terrain (cosine of the aspect multiplied by the sine of the slope; Figure S2), TPI (Figure S2), and tree height (Figure

3e and j).

During the 2014 measurement period, aspect and tree height exhibited the greatest separation between “above” and “below” ROIs. This was particularly the case for aspect

(Figure 3b and g), whereby the majority of “below” ROIs were found on northwest-facing slopes and “above” ROIs were generally located on southeast and northwest-facing slopes (albeit on lower slopes) and in the company of larger trees. “Below” ROIs were also found at higher elevations, but generally in and around smaller trees. The distribution is highly suggestive of post depositional wind redistribution which is further supported by wind observations (see Section 3.4). During the 2015 measurement period, aspect and tree height also exhibited the greatest separation between “above” and “below” ROIs. However, the trend from the 2014 measurement period, whereby “below”

ROIs were found on northwest facing slopes and “above” ROIs were found on southeast

facing slopes, was reversed. Additionally, and like the 2014 measurement period,

“above” ROIs were associated with large trees, and “below” ROIs were found in and around smaller trees. Finally, for both the 2014 and 2015 storms, TPI did not exhibit large differences between “above” and “below” ROIs. The result was consistent across several different kernel sizes.

2.3.4 Recorded and Modeled Wind Speeds and Directions

Over the course of the 2014 storm measurement period, Snow Process Through

Scale identified large losses and gains of snow along ridge lines likely owing to wind redistribution. Peak (Figure 3c and h) and averaged (Figure S3) hourly wind speeds for the

2014 storm, as measured by surface stations, are supportive of the distribution with wind speeds that exceeded the wind redistribution threshold of 7.7 m s–1 10.0% and

3.8% of the time, respectively. Peak wind speeds were also predominantly from the northwest, and to a lesser extent the south, matching slope aspects for ROI losses. Av- eraged hourly winds speeds were found to be predominantly from the southwest—most likely occurring during storm passage itself. CFSR confirmed surface station measurements, with reported wind speeds at 700 mb exceeding the wind threshold 53% of the time (Figure S4). Winds occurred during and after the storm and switched between southerly and northerly flows. Wind speeds were the strongest and most consistent during post-frontal flow during April 27 and 28, and were almost exclusively out of the northwest. Again, results match the observed ASO ∆�� well and help to explain some 67

of the variability in the ROI distribution, i.e. that not all pixels that were “above” were on north facing slopes—in fact a number were also on south facing slopes as well. These results are broadly supportive of post-depositional wind redistribution both by the observed wind speeds, directions and timing.

During the 2015 storm, surface stations observed peak and averaged hourly wind speeds that exceeded the 7.7 m s-1 threshold 12.3% and 4.4% of the time. Peak wind speeds mainly occurred out of the southwest, however averaged hourly wind speeds were predominantly out of the southeast (Figure S3). In this case, the averaged hourly wind speeds are a better match for the distribution of ROIs from Snow Process Through

Scale. Once again, CFSR confirmed surface station observations with wind speeds that broke the wind threshold 48% of the time (Figure S4). High winds occurred during the storm itself rather than during the postfrontal stage as in the 2014 storm, and were almost exclusively from the south. Again, the spatial distribution of ROIs along with surface station observations and CFSR are broadly supportive of wind redistribution, but in this case pre-depositional rather than post-depositional, i.e. preferential deposition was likely taking place.

2.4 Conclusions

Snow accumulation is driven by mechanisms that range in scale from regional to local. In the Sierra Nevada, mid-latitude cyclones modified by orographic processes primarily drive accumulation, with snow usually increasing with elevation. However, 68

second order controls like wind, sloughing, and avalanches can distort this distribution.

To improve ecohydrolgoical understanding, for example through the spatial distribution of dry-season soil moisture, we need ways of identifying areas of a basin regularly impacted by these secondary controls.

Because these secondary controls occur at different measurement scales, spatial measurements of snow can either represent these processes explicitly or implicitly. We take advantage of this by using NASA’s Airborne Snow Observatory, which bracketed two storms in the Tuolumne, to identify ROIs that had snow above or below the modeled snowfall/elevation relationship in a new method we call Snow Process Through

Scale. The ROIs were found to be mostly contiguous and grouped along ridge lines indicative of wind redistribution. Wind speeds and directions both from surface station and reanalysis are supportive of the ROI distribution, and show that the model is capable of capturing wind redistribution that occurs as a result of different mechanisms, specifically preferential deposition versus post depositional.

Snow Process through Scale is a simple, computationally efficient, effective method for identifying ROIs within a basin where secondary processes control accumulation.

The method considers catchment-specific snowfall/elevation relationships that will vary storm by storm. While we have used Snow Process through Scale to identify wind-affected snow during storm periods—arguably the most complex use of the method, one could also use the method on a seasonal basis. Seasonally, results might be more useful

for modelers trying to refine snow redistribution mechanisms in specific regions of a catchment.

2.5 Chapter 2 Supplementary Material

Table S1. The various surface station types, locations, and elevations used for snowfall monitoring.

Station Name CDEC ID NOAA ID MesoWest ID Latitude Longitude Elevation Storm 2014 Storm 2015 Yosemite Valley YYVC1 37.750 -119.589 1219 1 1 Cherry Valley CEVC1 37.974 -119.916 1457 1 1 Hetch Hetchy Met Station HHWC1 37.961 -119.783 1520 1 1 Pinecrest 1NNE PNCC1 38.200 -119.983 1707 1 1 Leavitt Meadows LVTC1 38.304 -119.551 2194 1 1 Tuolumne Meadows TUMC1 37.873 -119.350 2621 1 1 Precipitation Deadman Creek DDMC1 38.332 -119.653 2819 1 1 Virginia Lakes Ridge VGAC1 38.073 -119.234 2868 1 1 Ellery Lake ERYC1 37.935 -119.233 2897 1 1 Wild Creek wcc WCCCA 37.800 -120.640 113 1 1 Oroville ovl OVLCA 39.532 -121.488 114 1 1 Pine Flat pfd PFDCA 36.830 -119.332 184 1 1

SWE New Exchequer ner NERCA 37.597 -120.278 259 1 1 ONeals onl 37.204 -119.570 684 1 1 Precipitation or Precipitation Gem Pass GEM 37.780 -119.170 3277 1 1 Black Springs BLS 38.375 -120.192 1981 1 1 Lower Kibbie Ridge KIB 38.032 -119.877 2042 1 1 Paradise Meadows PDS 38.047 -119.670 2331 0 1 Lower Relief Valley REL 38.243 -119.758 2469 1 1 Gianelli Meadow GNL 38.205 -119.892 2560 1 1 Horse Meadow HRS 38.158 -119.662 2560 1 1 Tuolumne Meadows TUM 37.873 -119.350 2621 1 1 Leavitt Lake LVT 38.282 -119.621 2926 1 1 SWE andSWE Snow Depth CUES* 37.643 -119.029 2940 1 0 Dana Meadows DAN 37.897 -119.257 2987 1 1 Gem Pass GEM 37.780 -119.170 3277 1 1 Slide Canyon SLI 38.092 -119.430 2804 1 0 Only Snow Depth Depth Virginia Lakes Ridge VRG 38.077 -119.234 2835 1 0 *CRREL/UCSB Energy Site, http://www.snow.ucsb.edu/

Table S2. Surface locations, and elevations used for average hourly wind speed (WS) and peak hourly wind speed.

Station Name CDEC ID Latitude Longitude Elevation Average WS Peak WS Crabtree Weather Station CWS 37.725 -120.601 69 1 1 Green Springs GRN 37.833 -120.500 311 1 0 Cathey's Valley CVR 37.380 -120.077 366 1 1 El Portal EPW 37.675 -119.788 632 1 1 Mariposa Ranger Station MRP 37.504 -119.987 686 1 1 North Fork R S NFR 37.233 -119.500 802 1 1 Tuolumne STF 2 Portable RAWS POU 37.949 -120.271 853 1 1 Mt. Zion MTZ 38.390 -120.653 905 1 0 Dudleys (McDiarmid Fire Station) DDL 37.721 -120.096 914 1 1 Batterson BTT 37.383 -119.617 963 1 1 Metcalf Gap MCF 37.410 -119.765 1006 1 1 Smith Peak RAWS SEW 37.801 -120.101 1180 1 1 Jerseydale JSD 37.542 -119.840 1189 1 1 Jawbone Lava Flat RAWS JFR 37.887 -120.048 1225 1 1 Wawona RAWS WWN 37.534 -119.645 1311 1 1 Mount Elizabeth MTE 38.057 -120.241 1504 1 1 Pinecrest 2 RAWS near Pinecrest 1SW PNW 38.186 -120.011 1707 1 1 Big Sandy BSN 37.468 -119.586 1755 1 0 Crane Flat Lookout CFL 37.750 -119.800 1816 1 1 Mariposa Grove MPG 37.500 -119.600 1951 1 1 Gin Flat GIN 37.767 -119.773 2149 1 1 Fresno Dome FRS 37.464 -119.536 2177 1 0 Devils Postpile DPO 37.629 -119.085 2307 1 1 Crestview CVW 37.745 -118.983 2316 1 1 White Wolf WHW 37.860 -119.652 2408 1 1 Ostrander Lake STR 37.637 -119.550 2499 1 1 June Mountain Weather Plot JMW 37.754 -119.078 2810 1 0 Deadman Creek DDM 38.332 -119.654 2819 1 1 Ellery Lake ERY 37.935 -119.232 2940 1 1 Dana Meadows DAN 37.897 -119.257 2987 1 1 Tioga Pass Entry Station TES 37.911 -119.258 3031 1 1 June Mountain Summit JMS 37.740 -119.073 3095 1 0 Gem Pass GEM 37.780 -119.170 3277 1 1

Figure S3. Maps of the Tuolumne’s elevation, aspect, slope, topographic position index (TPI), and tree height. Also included is a polar histogram of the aspects. Slopes mainly face northwest and southeast.

Figure S4. Probability histograms for the cosine of the aspect, slope, terrain, and TPI.

Figure S5. Aspect rose of hourly average wind speeds.

Figure S6. Wind speeds and directions as modeled by CFSR at 700 mb height during storm 1 (a and b), and storm 2 (b and c) for pixels centered on Wild Creek surface station—just west of the Tu- olumne in the Central Valley, and over the Tuolumne basin. During the 2014 storm measurement period, winds gradually increased over time becoming more northerly. During the 2015 storm measurement period, winds were maximized during the storm itself, and generally consisted of winds from the south and southwest. Importantly, during both measurement periods, winds speeds were above the wind speed threshold of 7.7 m s-1, but wind directions readily switched from south to north and vice versa which would explain at least some of the ambiguity in the ROI landscape characteristics. 75

Chapter 3 Assessing WRF’s seasonal winter precipitation in California’s

Sierra Nevada using the Airborne Snow Observatory

W. Tyler Brandt, Forest Cannon, and Jeff Dozier

Abstract

Moisture transport within a dozen or fewer winter mid-latitude cyclones annually build much of the Sierra Nevada snowpack. These storms produce snowfall on encountering the topography of the Sierra Nevada, and snowfall usually increases with elevation.

However, physical processes and forcings cause snowfall to vary. The mesoscale modeling of these storms in mountain environments has relied on surface stations for validation. However, surface stations cannot cover the entire spectrum of physiographic variability, so while weather models may perform well when compared directly to surface stations, their overall accuracy and precision remain elusive. Snow remote sensing— particularly at peak snow water equivalent—effectively integrates a season’s storms and provides a spatial measurement of the fine scale heterogeneity. Here we present results from a direct comparison between total winter precipitation from the weather research and forecasting (WRF) model and remotely sensed estimates of the peak snow water equivalent from the Airborne Snow Observatory (ASO) in the Central Sierra Nevada over 4 water years. Overall, WRF performed well but tended to underestimate snow

accumulation at the highest elevations. WRF also struggled with its precipitation phase as evidenced by its total precipitation (rain + snow) matching ASO observation and snow pillows better than just its snowfall estimates. We conclude that in snow-dominated watersheds, remotely sensed snow water equivalent could help tune WRF’s parametrization schemes for specific regions or more broadly in updating the model physics.

3.1 Introduction

Mountain hydrology’s largest unknown is the spatial distribution of precipitation.

Direct observations of the flux are challenging, particularly where snow dominates the hydrology and climate of a region. However, two billion people worldwide rely on water resources derived from snow and ice, much from mountain environments (Mankin et al., 2015). This necessitates the need for good forecasting skill, both now and into the future. However, even in well-gauged regions, like California’s Sierra Nevada, streamflow forecasts are error-prone, and in some cases largely so with median absolute errors of ~20%, and on occasion, errors of 100% (Dozier, 2011). Principally the errors are the result of poorly constrained estimates of the spatial distribution of precipitation (Dozier, 2011), which in turn can lead to poorly calibrated hydrology models that break when conditions stretch beyond the normal (J. W. Kirchner, 2006; Milly et al.,

2008). With increasing precipitation volatility predicted in the 21st Century, good forecasting skill will become even more central to supporting the world’s peoples and ecosystems alike (Swain et al., 2018). 77

At watershed scales, orographic effects dominate the spatial distribution of mountain precipitation. Mountains force the ascent of moist air, and on reaching the condensation level, assuming the presence of condensation nuclei, the air produces precipitation. The higher and faster an air parcel is lifted, the more moisture can be wrung out. Nonethe- less, there is an elevational limit to the precipitation increase and this occurs as a result of the exponential decrease in saturation vapor pressure with temperature (Houze,

2012; Roe, 2005). The result is a decrease in precipitation in and around mountain crests (Houze, 2012).

At subbasin scales, the spatial distribution of mountain precipitation is extraordinar- ily complex. This is due to host of interacting linear and nonlinear physical processes that range from large scale synoptic weather patterns to microphysical properties at the mm scale. In California, for example, extratropical cyclones, can be regionally and orographically enhanced by the presence of atmospheric rivers—long narrow bands (~50 km across) of heightened moisture transport ahead of the cold front (Huning et al.,

2017; F. M. Ralph et al., 2004). More locally, the presence of barrier jets (Lundquist et al., 2010), and synoptic forced ascent can nullify the impacts of orographic enhancement by forcing ascent prior to the barrier itself (Cannon et al., 2018; Katzfey, 1995).

More locally still, warm and cold front dynamics (Catto et al., 2012; Houze et al.,

1976), and the direction and speed of overall moisture advection relative to the size and shape of the topographic barrier can both enhance or diminish precipitation totals (Mott

et al., 2018; Picard & Mass, 2017). And finally, microphysical processes at the micro scale strongly govern the precipitation type (snow versus rain) and intensity, and a hydrometer’s speed and path to the surface (Creamean et al., 2013; Sawyer, 1956;

Stoelinga et al., 2013).

To capture the spectrum of theses spatially and temporally variable processes, we presently rely on a network of surface stations including precipitation gauges, snow depth sensors, and snow pillows. Each sensor has its strengths and weaknesses. Precipi- tation gauges suffer from large amounts of under catch, particularly during snowfall due to wind (Rasmussen et al., 2012); snow depth sensors exhibit spurious values during snowfall due to reflections off falling snow (Bair et al., 2018a); and snow pillows, while good at integrating snowfall amounts during the storm itself, suffer from snowpack bridging, delaying or reducing the accumulated snow water equivalent (SWE) (Johnson

& Marks, 2004). Irrespective, gauge data are usually interpolated and extrapolated to generate spatial estimates of precipitation as gridded products, e.g. Daymet (Thornton et al., 1997) and PRISM (Daly et al., 2008). However, gauge type problems aside, these spatial products all suffer from the same pervasive problems: first, large spatial gaps between gauges lead to uncertainty; second, gauges often do not occupy the complete elevation range, and their paucity at the highest elevations misses significant precipitation; third, validation of these spatial products relies on either gauge withholding

or an alternate network of gauges. Under some circumstances, biases in the gridded products integrated over a drainage basin exceed 20% (Lundquist et al., 2015).

Weather models provide good alternatives to precipitation gauge products. Still, observation driven weather reanalysis tend to be temporally and spatially coarse and therefore not always appropriate for small to medium scale watershed studies. Nonetheless, these datasets can be downscaled using models like the Weather Research and Forecast- ing (WRF) model, which dynamically downscales reanalysis data using model physics and parametrizations. In mountain environments, WRF serves both as a precipitation forecasting tool and in hindcast experiments to examine precipitation forcing mechanisms. With computational capacity increasing and statistical downscaling an option, we are currently pushing the capabilities of WRF. For example, Gerber et al. (2019) established that a WRF spatial resolution of 50 m or finer was required to accurately simulate snow deposition along ridge lines. Nonetheless, even if we could run WRF at 50 m scales across entire basins, doing so assumes we comprehend the fine scale dynamics at play, which is not always the case (Gerber et al., 2017). Thus, we return to the principal problem at hand: what is the spatial distribution of mountain precipitation, and more importantly how do we evaluate our understanding?

Snow, unlike rain, remains on the landscape, and while it can be redistributed by wind and avalanches, remains mostly in place (Mott et al., 2018). Therefore, observed spatial patterns in snow accumulation should theoretically approximate snowfall—

particularly at coarser spatial scales (~ 1 km). As a result, in snow dominated environments, we should be able to use snow remote sensing to improve our understanding of the spatial variability of snowfall. The data would “fill” the gaps between surface stations and help to validate both regional climate models like WRF and even gauge interpolated precipitation products like PRISM.

To date numerous studies have attempted to evaluate the various precipitation gauge interpolations; however, few have attempted to fully assess WRF. Therefore the pur- pose of this paper is to use “new”, spatially explicit snow remote sensing estimate of basin peak SWE (the total seasonally accumulated snow) from the Airborne Snow Obser- vatory (ASO) to assess WRF seasonal accumulation over a high elevation watershed in

California’s Sierra Nevada. We do this over the course of four water years (WY) beginning in October 2015 and finishing in April 2019 and also draw on numerous surface based observations to bolster the analysis and compare and contrast the four water years.

While cross-barrier flow, and preferential deposition (Mott et al., 2018) might challenge the direct comparison between ASO basin peak SWE and WRF seasonal accumulation due to hydrometer advection (Hobbs et al., 1973), the analysis is still informative for three key reasons. First, the Sierra Nevada is a maritime climate, and snow tends to fall “fast” due to riming and the scarcity of cloud condensation nuclei. Second, we take advantage of a relativity coarse spatial resolution (3 km) for our WRF simulation to

limit the explicit impacts of hydrometer advection and other snow redistribution processes between pixels. Third, other studies have already directly evaluated WRF’s land surface representation in the Sierra Nevada; specifically Pavelsky et al. (2011) who compared WRF estimates of SWE with those from snow pillows during both accumulation and melt, and a more recent study by Wrzesien et al. (2015), who used satellite estimates of the snow-covered area to evaluate WRF at a 3 km spatial resolution. So, while a direct spatial comparison of WRF’s land surface model estimate of SWE and ASO basin peak SWE during melt would be the most comparable (ASO flights mostly encom- pass the melt period), we believe that a direct evaluation of WRF’s seasonal accumulation with ASO and additional surface observations has more scientific merit and chances for scientific advancement. Finally, snowmelt (turbulent fluxes aside), is a fairly well constrained process (Bair et al., 2016), whereas snow accumulation and the processes that drive the distribution are still somewhat largely unknown.

Figure 7. A map of the Tuolumne watershed, the upper Tuolumne (outlined in red and the focus of this study), and surface observation sites. ASO Peak SWE is also depicted across the four water years in the study.

3.2 Study site

Hetch Hetchy Reservoir collects water from the Tuolumne River headwaters. The man made reservoir was generated after the construction of the O’Shaughnessy Dam in

1923, and lies in a natural granite U-shaped valley. The study area comprises the

watershed above this natural pour point and hereafter is referred to as the Tuolumne

Basin (Figure 1). At 1200 m above sea level, the reservoir roughly coincides with the average elevation of the snow-rain transition during winter storms. Thus, snow dominates the majority of the basin’s precipitation. Snowmelt-fed streams drain the1175 km2 watershed, and the reservoir seasonally gathers 0.42 km3 of water for 2.7 million people living in the greater San Francisco Bay Area. The reservoir also produces hydro- power, generates environmental flows in the spring, and provides water for irrigation in

California’s Central Valley. Like other Sierra Nevada reservoirs, these oft-competing demands require a balance between outflows and inflows that necessitates the need for good knowledge of the snowpack dynamics and meteorological forecasting.

3.3 Data and models

3.3.1 Overview

This study compares and contrasts WRF estimates of seasonal accumulation with

ASO estimates of basin peak SWE during four WYs. To both substantiate and augment our understanding of the four WYs we also utilize a number of surface station observations including: SWE (from snow pillows), precipitation (from rain gauges), temperature, dew point temperature, streamflow and atmospheric melt elevations (from snow level radars). For each WY (1 October through 30 September the following year), we completed the following tasks:

(1) Examined the precipitation accumulation rate as observed by snow pillows and precipitation gauges;

(2) Validated the accumulation rate as modeled by WRF over the Tuolumne with local snow pillows and precipitation gauges;

(3) Evaluated WRF’s ability to duplicate the observed spatial patterns of basin peak

SWE as estimated by ASO.

3.3.2 Hydrologic surface station measurements

The California Department of Water Resources (DWR) consolidates data from 124 snow pillows, ranging in elevation from 1981 m to 3277 m throughout the Sierra Ne- vada. Snow pillows measure the SWE by weighing the snow above. The instruments in- tegrate snowfall, melt, sublimation and wind redistribution; and the DWR posts hourly and daily data to the California Data Exchange (http://cdec.water.ca.gov/snow/current/snow/index.html). For this study we utilized the daily “revised” data. The revised daily data suffer less from errors, but we manually cleaned them to remove spurious values and smoothed them using a robust discretized spline (Garcia, 2010). The spline also filled the data gaps, but it preserved the overall shape of the data with respect to accumulation and melt.

Various government agencies operate a network of precipitation gauges throughout the Sierra Nevada. Gauges are designed and made by different manufactures and so have different specifications and thereby “behave” differently, e.g. some use tipping 85

bucket sensors that regularly fill and tip, while others are weighing gauges that fill over the course of a season recording the total accumulation. Additionally, some precipitation gauges have wind shelters to reduce wind effects, and a few have anti-freeze to keep the gauges from freezing. This study used 11 precipitation gauges that varied in elevation from 1219 m to 2897 m—a similar elevation range to that of the snow pillows.

For all 11 gauges, we obtained data from MesoWest (https://mesowest.utah.edu/). In some cases, precipitation gauge sites are also accompanied by other sensors including snow pillows, snow depth sensors, air temperature, relative humidity and the dew point temperature. We utilized the dew point temperature from three stations (Hetch

Hetchy, Pinecrest, and Ellery Lake), as a proxy for the snow-rain transition based on the findings of Marks et al. (2013).

For each water year we also investigated the melting levels for the seasons’ storms using NOAA’s frequency modulation continuous wave profiling (FMCW) radar, also known as the snow level radar. The radar measures the altitude of the snow-rain transition. Station locations from north to south included Colfax, New Exchequer and Pine

Flat Dam. New Exchequer is the closest to the Tuolumne, due west of Hetch Hetchy

Reservoir and directly upwind of any arriving winter air masses. The snow-rain transition is directly associated with the Bright Band Layer, a region of enhanced radar reflectivity caused by a shift in the dielectric function and a rise in the fall velocity as a hydrometer transforms from snow to rain (Allen B. White et al., 2002).

Finally, this study also used streamflow data from a USGS streamflow gauge

(1127490), which is situated at the inflow to Hetch Hetchy Reservoir on the Tuolumne

River. The data can be obtained from the USGS (https://wa- terdata.usgs.gov/ca/nwis/rt). Table 1 summarizes all the in situ data used in this study.

Included are snow pillows, precipitation gauges, and the snow level radar stations.

Table 1. Snow pillow, precipitation, and snow level radars used in this study, sorted by type of measurement and elevation.

Station Name CDEC ID NOAA ID MesoWest ID Latitude Longitude Elevation [m] Black Springs BLS 38.375 -120.192 1981 Lower Kibbie Ridge KIB 38.032 -119.877 2042 Gin Flat GIN 37.767 -119.773 2145 Paradise Meadows PDS 38.047 -119.67 2332 Lower Relief Valley REL 38.243 -119.758 2469 Tenaya Lake TNY 37.838 -119.448 2484 Gianelli Meadow GNL 38.205 -119.892 2560

SWE Horse Meadow HRS 38.158 -119.662 2560 Tuolumne Meadows TUM 37.873 -119.350 2621 Slide Canyon SLI 38.092 -119.430 2804 Virginia Lakes Ridge VRG 38.077 -119.234 2835 Leavitt Lake LVT 38.282 -119.621 2926 Dana Meadows DAN 37.897 -119.257 2987 Gem Pass GEM 37.780 -119.170 3277 Yosemite Valley YYVC1 37.750 -119.589 1219 Cherry Valley CEVC1 37.974 -119.916 1457 Hetch Hetchy Met Station* HHWC1 37.961 -119.783 1520 Pinecrest 1NNE* PNCC1 38.200 -119.983 1707 Leavitt Meadows LVTC1 38.304 -119.551 2194

Precipitation Deadman Creek DDMC1 38.332 -119.653 2819 Virginia Lakes Ridge VGAC1 38.073 -119.234 2868 Ellery Lake* ERYC1 37.935 -119.233 2897 Pine Flat pfd 36.830 -119.332 184 New Exchequer ner 37.597 -120.278 259 Snow Level Radar Colfax cff 39.080 -120.938 644 * Dew Point Temperature Sensors

3.3.3 Airborne Snow Observatory

NASA’s Airborne Snow Observatory comprises two primary instruments (Painter et al., 2016): a Rigel Q1560 airborne laser scanner (lidar) and an itres CASI 1500 imaging spectrometer. The platform first flew the Tuolumne Basin in early April 2013, and has since acquired regular surveys of the basin from peak SWE (~April 1st), through the melt period.

To obtain basin SWE, ASO combines lidar measurements of the snow depth with modeled estimates of spatially distributed snow density. Snow depth is measured at a 3 m spatial resolution, determined by subtracting a snow-on digital elevation model

(DEM) from a snow-free DEM. Spectrometer measurements of snow covered area

(SCA) constrain the snow depth estimates, but snow depths of 0 m are also snapped to the snow-free DEM to minimize bias. The snow depths are then aggregated to 50 m and combined with a snow density estimate from a 2 layered physically based snowpack model (iSNOBAL: Marks et al., 1999). The spatially explicit estimate of SWE is then constrained using local snow pillows as well as manual observations form snow pits. At

50 m, reported SWE errors are less than 1 cm with zero mean bias (Painter et al.,

2016). For this study we use both the 50 m ASO SWE and a re-gridded 3 km product for direct comparison with WRF. The re-gridding used a gaussian pyramid reduction

(Burt & Adelson, 1983) and makes explicit snow redistribution processes (i.e. wind

redistribution, avalanches and sloughing) at a 50 m resolution, implicit within the 3 km pixel.

While the process by which ASO estimates SWE is complicated, no sensor available can currently directly measure mountain SWE (Dozier et al., 2016). ASO does have uncertainty, and this occurs both in the snow depth measurement as well as in the modeled snow density. Recent advances in airborne lidar mean that depth can now be measured with considerable accuracy and precision with ASO reported depth errors of < 2 cm at a 3 m spatial resolution (Painter et al., 2016). Of course, pixel coarsening only serves to reduce the uncertainty. Snow density remains a source of uncertainty, and the uncertainty increases with a snow depth of 60 cm or more due to snow layer variations

(Painter et al., 2016; Raleigh & Small, 2017; Smyth et al., 2019). Nonetheless, Painter et al. (2016) found that modeled density errors were between 3 and 8%, which equates to 12-30 kg m-3. The error is further reduced by a post processing step that involves correcting for an elevation bias.

3.3.4 Digital Elevation Model

We obtained a seamless 1/3 arc-second (~10 m) digital elevation model (DEM) from the USGS’s National Map (https://viewer.nationalmap.gov/basic/). The data were coarsened to 50 m and 3 km using a gaussian pyramid reduction (Burt & Adelson,

1983), and used to estimate the relationship between water equivalence and elevation for both ASO (at 50 m and 3km) and WRF (3 km). 89

3.3.5 WRF

The Center for Western Weather and Water Extremes (CW3E) provided WRF precipitation from the near real time operational model West-WRF. Martin et al.

(2018) describes the model in detail. Since the paper’s publication, the parametrized physics have been objectively optimized to ensure maximum fidelity for extreme precipitation events in California—specifically over coastal watersheds in Mendocino

County. Nonetheless, the parameter choices are still identical to those used in Martin et al. (2018), and should be broadly applicable for the Sierra Nevada. Model specifications are briefly discussed below.

The National Centers for Environmental Prediction (NCEP) Global Forecast Sys- tem (GFS) analysis (Hamill et al., 2013) provided boundary conditions for West-WRF.

The GFS is produced using the Global Ensemble Forecast System version 9.0.1 which runs at 28 km spatial resolution. West-WRF dynamically downscales the GFS for each water year beginning 1 October and ending 1 April with a 12 hr spin up, and usses the open source WRF-ARW model (Skamarock & Coauthors, 2008). The model uses two domains with horizontal resolutions of 9 and 3 km, an adaptive time step of 45 s and 15 s, with 60 vertical levels. A USGS land-use database was used for static land surface information, and the following physics options were used: the Grell 3D cumulus model (9 km domain only), the Noah land surface model, the Thompson new cloud microphysics scheme, the Yonsei University planetary boundary layer, the Monin-Obukhov surface

layer scheme, the GSFC shortwave radiation model, and the RRTM longwave radiation model. Topographic wind was used for the 3 km inner domain only.

The key outputs from West-WRF included the 3 km non-cumulus total accumulated precipitation (Rain NC) and the non-cumulus accumulated snow and ice (Snow

NC)—both are a direct product of the new Thompson Microphysics scheme

(Thompson et al., 2008). Since Rain NC represents the total accumulated precipitation, it includes both liquid (rain) and frozen (snow) precipitation. Therefore, rain (i.e. liquid only) can be found by subtracting the Snow NC from Rain NC. Observations by

Garvert et al. (2007), Rasmussen et al. (2011), and Pavelsky et al. (2011) show that the

3 km spatial resolution for both Rain NC and Snow NC should be high enough to effectively simulate snowfall over the study area.

3.4 Results and discussion

The primary goal of this paper is to assess West-WRF accumulated winter precipitation with both ASO estimates of basin peak SWE and to buttress conclusions with additional surface observations. The secondary goal is to discuss key differences between the various WYs to aid in the comparison between West-WRF and ASO. However, it is important to note that West-WRF is only run from 1 October through 1 April. When

ASO flies before 1 April, we can directly compare ASO with West-WRF by summing accumulation from 1 October through the flight date. In 3 of the 4 years this was the case, but in WY 2018, ASO first flew on 23 April 2018, creating a potential discrepancy 91

through late season storms (which West-WRF failed to model) and possible additional snowmelt/sublimation (which could render the ASO estimate lower than the actual basin peak SWE).

3.4.1 Surface Observations

3.4.1.1 Determining Peak SWE

We used surface observations to: (1) approximate the timing of basin peak SWE and to assess how well ASO estimates of basin peak SWE matched these observations; and

(2) to validate West-WRF’s precipitation phase and precipitation accumulation rate.

The timing of basin SWE is a critical period for a watershed as it represents the transition from accumulation to ablation. However defining basin peak SWE—necessary for helping to identify whether an ASO flight date properly represents the quantity—is complicated and gets more nuanced the larger the elevation range within a basin. Snow pillow peak SWE, in comparison, is easily defined as it is a point measurement and represents the maximum net accumulated snow at an individual snow pillow (Figure 2a). In locations where melt is absent during accumulation, pillow peak SWE should approximate total snowfall in that location, recognizing that losses due to sublimation and cold season melt should produce an underestimate.

Figure 2a perfectly illustrates the challenge in determining a basin peak SWE across a relatively large elevational gradient. In general, snow pillows at higher elevations reach peak SWE later due to enhanced snowfall and cooler temperatures, whereas lower 92

elevation pillows reach peak SWE sooner due to warmer temperatures both during precipitation (which shifts snow to rain during the seasonal transitions) and more generally during the year. However, there is a large amount of elevational inconsistency, both within years and between years with, for example, some higher pillows achieving peak

SWE earlier in the season. Nonetheless, flight dates for ASO basin peak SWE (the calculation of which is discussed later in Section 3.2) are demarcated in Figure 2 using a black dashed line. In general, the flight date for ASO basin peak SWE appears to represent, qualitatively speaking, the date of pillow peak SWE quite well. ASO basin peak SWE is often positioned between lower elevation pillows—which are transitioning to the ablation period, and higher elevation pillows—which are still accumulating. WY 2018 is the exception, in which the date of pillow peak SWE and ASO basin peak SWE are almost exactly aligned due to a few late season storms.

Figure 2. (a) Snow pillow, and (b) precipitation gauge data for water years 2016 through 2019 colored by elevation (green to brown). The black dashed vertical line marks the flight date of ASO closest to the date of basin peak SWE. (c) snow pillow (grey) and precipitation gauges (blue) displayed super- imposed.

3.4.1.2 Rain versus snow

The date of pillow peak SWE and the date of peak precipitation from precipitation gauges will not produce unanimous dates for basin peak SWE (Figure 2b and c). Precipi- tation gauges can measure both rain and snow, and in many cases will therefore continue to accumulate long into the melt season (in this case precipitation gauge data were capped on 30 April for each WY).

However, precipitation gauges in conjunction with snow pillows can help to reveal the phase of precipitation. In stark contrast to the snow pillow data, precipitation gauges exhibit a negative correlation between accumulated precipitation and elevation, i.e. the higher in elevation, the less precipitation is accumulated. To be clear, this observation

does not imply that higher elevations received less precipitation (over the given elevation range), but rather is a reflection of the gauges’ poor capacity to catch snow in windy conditions (Rasmussen et al., 2012; Thériault et al., 2012). Give this rationale, the strong reversal of the elevational gradient in the accumulated precipitation (i.e. from high elevations to low) during WY 2016, WY 2017, and WY 2019 is heavily suggestive of the presence of rain.

To help resolve whether some WYs experienced rain prior to peak accumulation we also investigated the seasonal patterns in runoff and dew point temperatures (Figure 3).

A steadily increasing streamflow from January through April is indicative of snowmelt, i.e. during WY 2016. However, a “flashy” streamflow record accompanied by dew point temperatures above 0°C is suggestive of rain, i.e. during WY 2017. WY 2017 and

2019 lacked strong snowmelt signals, but high dew point temperatures accompanied with large streamflow pulses is suggestive of rain. However, if rain occurred, it was probably short lived and spatially limited given the rapid rise and fall in the hydrographs.

Streamflow observations in WY 2018 exhibited few rainfall pulses, with the exception of one strong pulse on 7 April (where rain did occur), which is more indicative of a

“cooler” year with mostly snowfall.

Figure 3. Streamflow, incremental precipitation and dew point temperatures for each of the four WYs at Hetch Hetchy reservoir. During WY 2016 streamflow during the ASO measurement period (1-Oct through ASO flight date) amounted to 27% of the total annual water year flow. For WY 2017, WY 2018 and WY 2019 the percent of total annual flow during the ASO measurement period were: 24%, 40% (22% if the 7 April storm was not included), and 12% (using a water year ending on July 11).

3.4.1.3 Surface Observation WY overview

Based on the presented surface observations, we know that both WY 2017 and WY

2019 were “wet years” and that both WY 2016 and WY 2018 were “dry years” (by sheer magnitude alone). We also know that WY 2017 experienced at least some rainfall from a few warm storms (Osborne et al., 2017) and that WY 2018 was mostly dominated by snowfall with the exception of a single large warm storm that arrived on 7

April. WY 2016 appears to have been a relatively warm year, with some snowmelt at lower elevations, and finally WY 2019 was a cold year, but streamflow observations indicate a few rain events did occur.

3.4.2 ASO Peak SWE

ASO peak SWE can be calculated in two ways: (1) basin peak SWE—the date on which the summed total basin SWE reaches its maximum; and (2) pixel peak SWE—the dates at which each pixel’s SWE reaches its maximum. Good arguments could be made for using either, but we elected to use basin peak SWE. While pixel peak SWE would have been a better dataset for the ASO-WRF comparison as it removes the elevational issues discussed earlier, in some years ASO lacked the temporal resolution and temporal extent that would have been required for a good estimate of the pixel peak SWE. Help- fully, pixel peak SWE tended to mostly match basin peak SWE with minor exceptions in WY 2017 and WY 2019. In WY 2017, ASO pixel peak SWE reached its maximum on 3 March (36% of the total basin area), but was closely followed by the 1 April acquisition (35% of total basin area). Basin peak SWE occurred on 1 April owing to a single storm, and given that West-WRF simulations terminate on 1 April, we elected to use the later ASO acquisition. WY 2019 was also an exception, but for a different reason.

Basin peak SWE reached its maximum on 17 April, and pixel peak SWE was almost identical across both the 24 March and 17 April flight dates (50.4% versus 49.6% of basin area). However, we elected to use the 24 March 2019 flight acquisition because of

West-WRF’s termination date on 1 April. While we may have varied our methodology for picking the ASO basin peak SWE estimate, qualitatively these decisions appear well founded when compared to snow pillow observations in Figure 2. Given this, basin peak

SWE from WY 2016 through WY 2019—as measured by ASO at a 50 m spatial resolution— amounted to water equivalent volumes of 0.82 km3 on 26 March 2016, 1.50 km3 on 1 April 2017, 0.49 km3 on 23 April 2018, and 1.24 km3 on the 23 March 2019.

Using these totals, it is clear that WY 2017 and WY 2019 are “wet”, and WY 2016 and

WY 2018 are “dry” which is in agreement with surface station data.

A different, and in some ways more interesting way to group the WYs, is based on the spatial distribution of SWE. In Figure 4 we present the spatial distribution of ASO basin peak SWE as equal to or above the 50th, 75th, and 90th percentile. WYs 2016,

2017 and 2018 were notably similar: the higher values in basin peak SWE occurred at the highest elevations of the basin, and generally in the northern subbasins. These three

WYs alone would suggest that the spatial distribution of basin peak SWE varies little between years, and that the only differences lie in the magnitude of SWE. For example,

WY 2017 had the same spatial distribution as WY 2016, just more snow—a useful observation if trying to create a spatial representation of the precipitation for streamflow forecasting.

However, WY 2019’s ASO basin peak SWE was distinctive. Much of the SWE occurred at lower elevations and was more evenly distributed between the northern and southern subbasins (see 50th percentile). Finally, the highest amounts of SWE were found along the very northern edge of the northern subbasins, not at the highest elevations. In short, WY 2019 exhibited a shift in the SWE vs. elevation profile with more

snow at lower elevations than in the other WYs. The pattern is suggestive of different precipitation generating mechanisms than in the previous three WYs.

Figure 4. The spatial distribution of peak SWE equal to, or above the 50th, 75th and 90th percentiles.

We also explored the regional snowline elevation for each WY. The snowline is a rough measure of the atmospheric snow-rain transition, thereby useful in comparing the variability between WYs. Nonetheless, using the measure needs some care, as condensation-driven snowmelt from warm, moist air can cause snowlines to retreat quickly, thereby not truly reflecting the snow-rain transition. The snowlines for the 4 WYs were as follows: 1987 m, 1887 m, 2173 m and 1657 m based on a regional snowline elevation algorithm from Krajčí et al. (2014). The snowline elevations suggest that WY 2016

and WY 2018 were relatively warmer years when compared to WY 2017 and WY

2019, which is somewhat consistent with surface observations. For example, mean temperatures at Hetch Hetchy Reservoir for each WY from 1 Oct through 1 April were

6.8°C, 5.8°C, 6.8°C, and 5.6°C, which match the rank order of snowline elevations— the higher the mean temperature, the higher the snowline.

3.4.3 West-WRF Precipitation

The ASO snowline elevations demonstrate that for the most part the Tuolumne Ba- sin is a snow-dominated watershed. However, snowline presence at the lowest elevations of the basin does not guarantee the absence of rain. Modeled estimates of the precipitation phase from West-WRF determined that rain can occur and has substantial year to year variability within the Tuolumne (Figure 5a). According to West-WRF, the lowest elevations of the basin regularly observe rainfall, and surface observations support this result. For example, the regular, rapid rises in streamflow following precipitation events in Figure 4 are a clear sign of rainfall. West-WRF captures this result, showing reduced snowfall (Figure 5) around the reservoir itself.

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Figure 5. (a) Spatial distribution of percent snowfall relative to total precipitation for the Tuolumne Basin in WY 2016 through WY 2019. (b) dew point temperatures for three surface stations (HHWC1, PNCC1, and ERYC1) across all four WYs along with a smoothed estimate and the accumulated precipitation at HHWC1.

West-WRF also exhibits strong spatial and elevational gradients in the precipitation phase (Figure 5a). For example, in WY 2018 and WY 2019, much larger fractions of precipitation fell as rain rather than snow, and these pixels were located almost exclusively in the northern subbasins. However, the presence of rain itself does not imply hydrologic significance. For example, in WY 2018, even though much of the basin experienced rain, the amount relative to snowfall was small (Figure 5). A full analysis of West-

WRF’s ability to accurately and precisely replicate precipitation phase is beyond the scope of this paper. However, we continue to explore the validity of West-WRF’s precipitation phase using a few lines of evidence. For example, dew point temperatures are 101

a good indication of the precipitation phase (Marks et al., 2013), and Figure 5b exhibits the temporal and elevational changes in dew point temperatures. Across all four WYs, precipitation did occur at Hetch Hetchy (HHWC1) while above dew point temperatures of 0°C, indicating rain. However, stations at increasingly higher elevations confirm dew point temperatures quickly dipped below the 0°C threshold indicating that snow should have occurred. Thus, while West-WRF correctly suggests that rain occurred within the basin, its spatial extent might, in some years, be exaggerated according to dew point temperatures along the elevational transect.

To further explore West-WRF’s phase but more as a function of accumulation rather than spatial extent, we directly compared the temporal evolution of snow pillow accumulation with that of West-WRF’s total precipitation (Rain NC; top row), and snowfall (Snow NC; middle row). From these results, West-WRF’s total precipitation

(Rain NC), rather than snowfall (Snow NC), is clearly a better match for snow pillow accumulation. In most cases, the median and maximum Snow NC underpredicts the accumulated snow, particularly during WY 2019 when even some of the lower elevation snow pillows register more snow than the median water equivalence produced by

West-WRF Snow NC. Again, West-WRF’s shift from rain to snow occurs too high within the basin, and needs to be lowered to more accurately reflect surface observations.

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Figure 6. Temporal evolution of the snow accumulation from both snow pillows and West-WRF. Liquid and frozen precipitation (Rain NC) and frozen precipitation (Snow NC) have been included separately to identify West-WRF’s ability to accurately capture the phase of the precipitation. Simula- tions for West-WRF terminate on 1 April for each WY, and light blue and grey regions establish the maxima and minima for total precipitation (Rain NC), and snowfall (Snow NC) respectively, for any given day. The solid blue and black lines represent the median water equivalent as predicted by West- WRF for each day.

Temporally, West-WRF produces too much rain, but overall, the total accumulation rate (rain+snow) seems to be consistent with snow pillow observations. However, how well do seasonal totals spatially compare with ASO estimates of peak SWE? Figure

7a shows a pixel by pixel subtraction of West-WRF’s Rain NC and Snow NC and ASO basin peak SWE (now coarsened to 3 km resolution). Consistently, West-WRF ob- serves more water equivalence at the lowest elevations, which is to be expected as ASO measures snow only. However, at the middle and higher elevations, the difference

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between West-WRF and ASO is more variable within and across years. West-WRF’s

WY 2019 Rain and Snow NC appears as an outlier across the four WYs—vastly under- estimating the water equivalent at the higher elevations of the basin. WY 2016 exhibits the same spatial pattern, albeit to lesser extent. Additionally, West-WRF’s WY 2017 and WY 2018 Snow NC lacks the necessary accumulation at the higher basin elevations.

However, during those same WY’s, West-WRF’s Rain NC produced ample accumulation throughout the basin that in most cases matched or surpassed ASO’s peak SWE.

Figure 7b and c exhibits the histograms of the differences between West-WRF Rain and

Snow NC and ASO basin peak SWE. While Rain NC exhibits a positive skew due to rain in the lower elevations of the basin, Snow NC varies between a positive and negative bias depending on the WY.

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Figure 7. (a) a pixel by pixel comparison of WRF Rain NC vs ASO, and WRF Snow NC versus ASO. (b) and (c) are the histograms for maps in (a). (d) is a scatter plot of WRF Rain NC versus ASO (dia- monds), and WRF Snow NC versus ASO (filled circles) across all four water years. (e) shows the same result as in (d), but colored by elevation.

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Figure 7d and e display the same data as in Figure 7a, but in a 1:1 scatter plot. Snow

NC regularly exhibits a low bias across higher estimates of ASO basin peak SWE (Figure

7d), and this is particularly the case at higher elevations (Figure 7e). The result would be problematic for melt forecasting—as higher elevation snow tends to be a critical component of late season runoff. As is, West-WRF WY 2016 and WY 2019 would have underestimated late season runoff. WRF’s Snow NC also exhibits a high bias across the lower elevations. The high bias due to either West-WRF producing too much precipitation at the lower elevations, or due to melt and sublimation rendering the ASO result lower than expected. An ASO pixel peak SWE, versus basin peak SWE, and sublimation estimates might help to resolve the issue but are beyond the scope of this paper.

Interestingly, WRF’s Rain NC lacks the low bias of Snow NC at the highest elevations, and in doing so exhibits a linear slope closer to that of the 1:1 line (Table 2). This is a positive result, as it suggests that West-WRF is capable of producing enough moisture at the crest of the watershed. However, because this is the Rain NC output—rather than Snow NC output—means that West-WRF is precipitating rain rather than snow. This is a possibility, particularly given atmospheric melt elevations from snow level radars (see Figure 9), but unlikely given the dew point temperatures presented earlier.

The Rain NC data also exhibits a reduction in the correlation coefficient when compared to the Snow NC output, and a high bias across all elevations (Table 2). The higher

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error and scatter are particularly evident during WY 2017—in which rain is the most likely explanation for the large errors. WY 2018 also possesses large amounts of error and a low correlation. While West-WRF suggests that rain did occur, the hydrograph exhibits only a couple of “flashy” streamflow peaks (with the exception of the large hydrograph peak in streamflow on 7 April—which happened post West-WRF termination on 1 April). Another plausible explanation, and possibly more likely, could be due to early season snowmelt and sublimation—which ASO fails to account for given the late

April flight. A much higher snow level elevation than the other four WYs (presented in

Section 3.2) supports this hypothesis.

Table 2. The mean absolute error (MAE), correlation coefficient (Corr) and slope between WRF Rain NC/Snow NC and ASO estimates of basin peak SWE. The means across all four WYs have also been provided.

Water Year MAE (mm) Corr Slope WY 2016 198 0.5695 1.1315 WY 2017 512 0.717 1.2689

ASO WY 2018 362 0.4236 0.8952

Rain NC + WY 2019 201 0.6988 1.2285 Mean 318 0.6022 1.1310 WY 2016 157 0.8835 1.5811 WY 2017 246 0.9428 1.3349

ASO WY 2018 161 0.9098 1.9056

Snow NC + WY 2019 299 0.8645 1.9199 Mean 216 0.9002 1.6854

3.4.4 Water Equivalence vs. Elevation

Hydrologic models often utilize precipitation lapse rates to scale precipitation measurements across a basin, and year to year variability indicates different precipitation regimes. Here we used ASO to establish the snow accumulation lapse rate for the four

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WYs (Figure 8; density scatter plots). We used a spline to “average” the lapse rate, and found that ASO basin peak SWE was maximized at elevations of 3172 m, 3212 m, 3148 m, and 2849 m for WY 2016 through WY 2019, respectively. While the elevations are at a glance similar, even a 100 m elevation difference can be substantial when considering the horizontal distances with which a 100 m elevation gain can occur. However, based on the shape of the splines, as well the density scatter plots themselves, the four

WYs can be separated into two distinct clusters. WY 2017 and WY 2018 had largely enhanced high elevation amounts of SWE, whereas WY 2016 and WY 2019 both exhibited a distinctly lower elevation snowpack. The difference between these two clusters

(WY 2017 and WY 2018 versus WY 2016 and WY 2019) has interesting ramifications for the hydrology of the basin—in short, and assuming similar snow albedos and temperature regimes, WY 2016 and WY 2019 might have been expected to produce more melt, and sooner, leaving the end of season drier. WY 2017 and WY 2018, in stark comparison, would have produced much of the melt towards the end of the spring and well into the summer months leading to a “wetter” end of summer.

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Figure 8. Water equivalent/elevation plots of the four WYs. (a) compares ASO peak SWE (50 m scatter density plot), with West-WRF Rain NC and snow pillow observations from the 1 April. (b) compares ASO peak SWE, with West-WRF Snow NC and snow pillow observations from 1 April. The red curves in each plot represent the average ASO peak SWE as a function of elevation. Note that West-WRF products will not span the entire ASO elevation range as the West-WRF products use a 3 km grid–thus reducing the elevational range.

Compared with ASO, West-WRF Rain NC and Snow NC produced reasonable estimates of the precipitation lapse rate (Figure 8; red lines). As Figure 8 shows, West-

WRF’s Rain NC produces more precipitation than ASO at the lowest elevations— which is to be expected as ASO cannot measure rain. West-WRF’s Snow NC, because it only produces solid precipitation, naturally does a better job matching ASO across the

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lower elevations of the basin. However, Snow NC does appear to underestimate the magnitude of the lapse rate in both WYs 2016 and 2019, which is interesting given that both years lacked strong orographic enhancement. In WY 2019, the Rain NC produces a better fit of the ASO lapse rate, but in WY 2016 WRF still produced an underestimate. Given these results, West-WRF reproduces a reasonable estimate of the accumulated precipitation across the elevational gradient, but once again the precipitation phase

(based on the differences between Rain NC and Snow NC) appears to be the biggest im- pediment to matching ASO. This is particularly the case at the mid to higher elevations of the basin. Finally, snow pillows in WY 2017 and WY 2019 produced similar lapse rates. Yet ASO identified these two WYs as fairly distinct. For these WYs, the spatial variability in the snowpack is clearly not captured by snow pillow placement. These results are consistent with the findings of Molotch and Bales (2005).

3.4.5 Atmospheric Melt Levels

From the work presented so far, the precipitation phase appears to be a key issue for West-WRF. To exhaust the various ways in which to measure the rain-snow transition, we obtained snow level radar observations for the atmospheric melting elevation from three stations in the foothills of the Sierra Nevada, i.e. directly upstream of the

Tuolumne given the usual flow for incoming precipitating air masses. Figure 9 displays the histograms of the snow-rain elevations separated by station and each WY (note

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snow-rain elevations are only collected during storm activity). New Exchequer is the closest station to the Tuolumne, with Colfax due north, and Pine Flat due south.

The distributions for the elevations of the snow-rain transition for each year are skewed and in a few examples bimodal. That withstanding, the median snow level radar elevations for the 4 WYs at New Exchequer were 1935 m, 2183 m, 2042 m, and 1699 m. Theory states that the atmospheric melting elevation should be higher than the observed snow lines due to the downward bending of the atmospheric melt level (Minder et al., 2011). However, only WY 2017 and 2019 had snowlines lower than the median atmospheric melt level at New Exchequer.

Nevertheless, all four WYs exhibited large amounts of variability in the snow-rain transition elevations. This is to be expected given all storms exhibit some form of warm to cold front passage. Importantly however, the snow level radar observations demonstrate that rain in the Tuolumne is a possibility, and across all years—although not prob- able at the highest elevations of the basin.

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Figure 9. Histograms of the snow-rain transition elevation from 3 snow level radars located upstream of the Tuolumne in California’s Central Valley.

3.5 Conclusions

We compared the spatial distributions of ASO estimates of basin peak SWE and

West-WRF total accumulated precipitation in the Tuolumne basin in California’s central Sierra Nevada during WYs 2015 through 2019. We utilized surface observations to improve our understanding of how the four WYs were distinct and explained discrepan- cies between ASO and West-WRF.

Generally, West-WRF struggled with the snow-rain transition as evidenced by the differences between the Rain NC (rain+snow) and Snow NC (snow only) output. For example, across all four WY’s West-WRF’s Rain NC output matched the temporal

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magnitude of snow pillow accumulation better than Snow NC. Additionally, Rain NC produced better results in the comparison with ASO across all four WYs, albeit with a lower correlation coefficient and higher mean absolute errors due to rain and snowmelt

(which ASO cannot measure). Interestingly, West-WRF performed better in WYs 2017 and 2018 versus WYs 2016 and 2019. The distinction between the WYs is not purely due to “wetter” versus “drier” WYs. In fact WY 2017 and 2019 were “wet” years, and

WY 2016 and WY 2018 were “dry” years. Rather the discrepancy could be due to whether some years experienced more orographic enhancement, or not.

Using ASO, we found that WY 2016 and WY 2019 exhibited accumulated SWE that was predominantly located in the mid elevations of the basin, i.e. minimal orographic enhancement (Figure 8). In these years, it is possible that storms were dominated by precipitation mechanisms that distributed precipitation more evenly, either in- volving synoptic forced ascent and frontal dynamics and/or the presence of the Sierra

Nevada Barrier Jet. In contrast, WY 2017 and WY 2018 both had orographically enhanced snow accumulation, with SWE increasing across almost the entire elevation range. It is noteworthy that WY 2017 produced the 2nd-largest snowpack in the record since 1970, partly caused by a few large atmospheric rivers (Behrangi et al., 2018;

Osborne et al., 2017). As such, it is entirely possible that WRF’s model physics are better equipped to model and forecast storms with strong orographic enhancement rather than storms with a much more even distribution of precipitation.

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While using ASO to “validate” WRF possess large benefits due to its spatially explicit nature, ASO has a number of limitations. First, ASO cannot measure rain, and while rain can sometimes be incorporated into a snowpack—which can be modeled and therefore incorporated into ASO’s density estimates, rain can also just as easily drain through or runoff. Additionally, ASO will always be an underestimate of total snowfall due to losses in sublimation and cold season melt. Sublimation and cold season melt can be modeled, but the estimates require good estimates of the turbulent fluxes (which is still a challenge in mountain environments), and the snow albedo (which ASO presently measures). Additionally, we used basin peak SWE instead of pixel peak SWE for the

West-WRF comparison. As noted in Section 3.2—pixel peak SWE would have been a better comparison product. However, this assumes that ASO flights occur before low elevations transition from accumulation to ablation, which does not always occur due to

ASO’s current focus on the ablation season.

This study takes advantage of two operational programs, the Airborne Snow Obser- vatory and the Center for Western Weather and Water Extremes (CW3E) operational weather model West-WRF. ASO typically collects data from peak SWE through the end of the melt season, so comparison opportunities between ASO and WRF during the accumulation period are limited. The increased frequency of ASO acquisitions during the accumulation phase could help to improve West-WRF, particularly during years with less orographically enhanced storm systems. Follow-on studies from this work

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might: (1) investigate the regional and local meteorological differences in the storms during WYs 2016 and 2019 (less orographically enhanced) and WYs 2017 and WY

2018 (more orographically enhanced); (2) investigate whether different parametrization schemes could yield higher accuracies during WYs that observe less orographic enhancement; and (3) apply the same study in different watersheds, to address whether West-

WRF’s parametrizations might be more, or less appropriate, for different regions.

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