Water and life from snow: A trillion dollar science question
Abstract
Snow provides essential resources/services in the form of water for human use, and climate regulation in the form of enhanced cooling of the Earth. In addition, it supports a thriving winter outdoor recreation industry. To date, the financial evaluation of the importance of snow is incomplete and hence the need for accelerated snow research is not as clear as it could be. With snow cover changing worldwide in several worrisome ways, there is pressing need to determine global, regional, and local rates of snow cover change, and to link these to financial analyses that allow for rational decision making, as risks related to those decisions involve trillions of dollars.
Key Points
- Snow is a critical but often-unappreciated resource used by humans, and it is changing due to global warming in worrisome ways
- Work presented here suggests the valuation across many years of western US snow resources exceeds a trillion dollars
- More research is needed to help society make sound decisions on expensive major climate-driven snow resource changes
Plain Language Summary
Snow is critical in sustaining human life. It provides water and plays a key role in the climate through its unrivaled power to cool the Earth. It is also changing rapidly. To date, a full financial evaluation of the importance of snow in our lives has not been made, but computations here and elsewhere indicate it is on the order of trillions of dollars. Against this value, the current costs of scientific research are trivial. We provide a strong rationale and guidelines for accelerated snow research that will allow society to make major impending decisions related to snow resources on the soundest base and best scientific knowledge.
1 The Importance of Snow
About one sixth of the world's population (1.2 billion people) relies on snowmelt water for agriculture and human consumption [Barnett et al., 2005], while virtually all of the world's population benefits from the climate services provided by snow. Vast areas of the world receive the bulk of their annual precipitation in the form of snow (Figure 1), and even in California, where most of the population lives in a largely snow-free zone near the coast, the water people drink and their electrical power is largely derived from mountain snowmelt [cf. Sibley, 1977; Kahrl, 1979]. The same Sierra snowpack sustains a $47 billion per year California agribusiness [CDFA, 2017].
Annual precipitation falling as snow (%) for the period 2000–2010 computed from ERA-Interim data. The area where 40% or more of the precipitation comes as snow exceeds 15 × 106 km2 in the Northern Hemisphere. At peak, over 57 × 106 km2 of the Northern Hemisphere are usually blanketed with snow. Credit: Drew Slater, NSIDC.
The climate benefits of snow, while harder to quantify or monetize, may actually be worth more. These arise mostly from the superlative reflectance of solar energy by snow [Warren, 1982] and the vast area of the Earth that is snow covered each year (Figure 1). The combination produces an enhanced cooling critical to the Earth's heat budget [Groisman et al., 1994]. For example, late-lying spring snow in northern Canada, Alaska, and Siberia (an area of 19 × 106 km2) sheds about 2 × 1012 GJ of energy per year back to space, an amount that otherwise might have heated our planet (data from Flanner et al. [2011]). This cooling benefit doubles when we add in the effect of snow-covered Arctic sea ice [Curry et al., 1995]. Economic losses from reductions in snow-covered area [Mudryk et al., 2017], and the associated losses of Earth cooling, have been valued at $575 billion [Euskirchen et al., 2013; see also Lutz and Howarth, 2015]. Beyond these essential life services, snow also provides a platform for the multibillion dollar outdoor recreation industry [Burakowski and Magnusson, 2012].
Like the weather that delivers it, snow cover tends to be fickle, exhibiting large year-to-year variations in depth, snow water equivalent (SWE), area coverage, and the speed with which it melts in the spring [e.g., Kohler et al., 2006]. Humans have learned to live with these annual variations, but to aid in doing so, in the U.S., we have developed extensive snow observation networks. These include over 850 SNOTEL sites and a greater number of snow courses run by the USDA-National Resource Conservation Service [NRCS, 2017]. The Department of Commerce, through the National Weather Service and other centers [NOHRSC, 2017], also monitors snowfall and snow cover. In the western U.S., where it is estimated that 70% of the runoff arrives as snow, thousands of dams have been constructed by the U.S. Army Corps of Engineers [USACE, 2017] and the Bureau of Reclamation [USACE, 2017] in order to capture and store snowmelt water in good years to tide us through droughts.
The list of U.S. agencies, and the effort entailed in their work, makes it clear that society values snow, but how much? Answering this question is becoming increasingly important as the competition for research funds increases, and there is the real prospect of significant cuts in future funding, particularly climate change research [VERGE, 2017; Washington Post, 2017]. One of the problems is that the value of snow depends on the user, and snow has many uses: winter recreation, a source of water, climate regulation, winter habitat, and even as an aesthetic resource. A second problem is that snow tends to have its most value “downstream,” far away from where the snow itself falls. Generally, the farther downstream from the snowpack one gets, the less clear it is to the general public that snow is providing the resource. For example, while the recent drought may have increased awareness, how many citizens of Los Angeles are aware that the water in their tap, their power, and even much of their food comes from snowmelt runoff?
Researchers understand that snow is important, but not all decision makers, stakeholders, or the general public are aware of that fact. Nor are they aware of the corollary: that snow research can provide valuable, actionable information when making expensive societal decisions. A key step in convincing people outside the research community of these points is to develop a formal and complete monetary valuation of snow. While such an analysis would show that snow is essential to economic well-being, the “killer argument” to the wider public that vigorous snow research is important would come by framing the argument in terms of money, something everyone understands. Time and space preclude such extensive valuation here, but we outline below how such an analysis might be constructed.
2 How is Snow Changing?
Research into snow as a water resource dates to 1906 in the United States, when Dr. James E. Church began his pioneering studies near Reno, Nevada [Church, 1908]. He recognized that the winter snowpack determined the amount of runoff available in spring and summer. His work was funded by the U.S. Department of Agriculture; one reason why today that agency runs the SNOTEL network, a point that highlights how important the winter snowpack is to food security. Since then there has been steady progress, with snow remote sensing being both a priority [NRC, 2007] and perhaps also the most difficult research area [Clifford, 2010; Dietz et al., 2012]. While the problem of tracking snow extent by satellite has largely been surmounted, tracking snow mass or volume (i.e., SWE) remains elusive, with a major NASA field campaign focused on that specific topic having taken place in February, 2017 [DURANGO, 2017].
- The global extent of snow-covered area on land has been declining over the past 30 years [Brown, 2000; Derksen and Brown 2012; Kunkel et al., 2016; Mudryk et al., 2017].
- The mass of this snow (it's SWE) is also declining [Brown, 2000; Mote, 2006; Clow, 2010; Hamlet et al., 2005; Kunkel et al., 2016], a trend also observed on Arctic sea ice [Webster et al., 2014]. This trend appears to be a direct consequence of warming global temperatures [Mote et al., 2005].
- The snow that does fall is melting sooner, producing earlier stream runoff and decreasing the period during which snow covers the ground [Brown, 2000; Laternser and Schneebeli, 2003; Stewart et al., 2005; Clow, 2010; Liston and Hiemstra, 2011; Kunkel et al., 2016].
- In many places, particularly those with a more maritime climate, winter precipitation is arriving increasingly as rain [McCabe et al., 2007; Ye et al., 2008; Cohen et al., 2015], a trend associated with increasing flood risk in snow-covered mountain areas [Allamano et al., 2009]. This trend also appears to be having an adverse impact on wildlife and transportation.
- The number and intensity of winter snowfall events appears to be declining [Lute and Abatzoglou, 2014; Lute et al., 2015]; since these often account for the majority of the winter snow deposited in some locations, the trend is consistent with (2).
- The worldwide reduction in glacier mass balance [Gardner et al., 2013] also implies a loss of snow on glaciers and ice sheets, again a partial confirmation of (2).
All of these trends are consistent with (and feedback to) a warming climate. Currently predicted by climate models [Räisänen, 2008; Dominguez et al., 2012], but yet to be observed, is an increase in winter precipitation due to a warmer atmosphere.
The trends have direct implications for snow resource users. Changes in snowmelt timing [cf. Stewart et al., 2005] impact when water becomes available for agricultural use, potentially creating a mismatch between availability and need. As recognized by Gleick and Chalecki [1999], and clearly stated by Barnett et al. [2005], “…there is not enough reservoir storage capacity… so most of the ‘early water’ will be passed on to the oceans.” The shift to more winter rain produces an overall decrease in stream runoff [Berghuijs et al., 2014; Zhang et al., 2015], and observed reductions in land and ice snow-covered areas have reduced the ability of high-latitude snow to cool the planet by about 0.5 W m−2, or 2 to 15% depending on latitude [Flanner et al., 2011].
It is well beyond the scope of this paper to discuss whether humans can alter snow climate trends, but we can ask what we most need to know about these trends as we move forward. As the next section makes clear, the rate of change matters, for that, combined with financial conditions, govern the value of mitigation and resource replacement strategies. Getting accurate rates of change is not simple: there is a very high natural interannual variability in snow conditions, and we are still developing high-resolution remote sensing products that would allow the determination of these rates throughout the snow-covered world (Figure 1). A strong start has been made in quantifying the rates in the western U.S. [Groisman et al., 1994; Brown, 2000; Hamlet et al., 2005; Mote, 2006; Clow, 2010], where the snow observational network is dense and the records reasonably long. For that region, a clear linkage between declining snow resources and trends in temperature and precipitation has emerged [Luce et al., 2014]. Unfortunately, for most of the world, there are far fewer snow records and the knowledge of trends is poor, while the need to know those rates of change is high.
3 Valuing Snow Resources
There have been studies on the impact of declining snow resources on the winter outdoor recreation industry [Burakowski and Magnusson, 2012] and on agriculture and industry in the American Southwest, a region dependent upon snowmelt from the Colorado River [James et al., 2014]. Estimated losses for the latter range from $1 billion to over $1 trillion dollars, and as reported above, the reduction in global snow-covered area over the next several decades could produce losses in the half-trillion-dollar range [Euskirchen et al., 2013]. These focused valuations are useful, but they examine snow in a piecemeal fashion, and, more importantly, they have not been structured in a way that lends itself to financial-based decision making with respect to replacement or adaptation.
To illustrate how a general valuation might be conducted, we examine snow water lost due to shifting patterns of winter precipitation and runoff. The question we ask is: What is the financial loss as the resource changes? Knowing the loss allows farmers, businesses, and policymakers to make rational decisions as to whether a particular replacement or adaption strategy is worthwhile (i.e., is the replacement cost greater than the loss itself?). The analysis combines (1) the amount and the rate of change of the snow resource (its trajectory) with (2) a present value (PV) analysis to account for the multiyear nature of the problem over time. To compute monetary values, we price snow water using a range of water purchase prices, and, because the current knowledge of the rates of change of most snow metrics is limited, multiple rate of change trajectories.
Consider the western United States (Figure 2, top) where most of the useable water arrives in winter and forms a mountain snowpack that stores the water until spring and summer when it is most needed. The timing of when this water is available is changing [Stewart et al., 2005], in part because many mountain basins are seeing more rain in winter than before. Part of the early runoff flows in dammed basins where some portion may be captured in a reservoir, while part is in undammed basins where most, if not all, may all be lost. We define the total water loss over time as W, a value we can easily adjust to account for any partial recapture. This loss will occur over a period of time before it is fully realized (Figure 2, bottom). To account for this transition period, we define a set of trajectories (N = 5, 10, 15 years, and so on). The water loss starts at zero and increases each year by an amount W/N, until by the end of the trajectory, W is being lost each year. From that point on, W continues to be lost in perpetuity (the rain does not go back to snow).
(top) We examine the mountain snow cover of the western U.S., where both dammed and undammed basins exist and provide water for irrigation. (bottom) In many of these basins, winter precipitation, formerly coming as snow, is now increasingly arriving as rain, which can result in more rapid runoff. The rate of the snow-rain transition is uncertain, so we assume multiple change trajectories (5, 10, 15 years, etc.) during which the snow water loss (W) increases from 0 to 100% of the total, then remains at 100% in perpetuity.
Two well-known financial concepts appear in the analysis: discount rate and present value (PV). Even in a world with no inflation, people would prefer to get $100 today instead of $100 ten years from now, or to use 100 acre-feet of water today rather than get the equivalent in a decade (Water in the Western U.S. is customarily sold and priced in acre-feet. To convert one acre-foot to cubic meters multiply by 1233.48.). This is the concept of time value, and it is why we see positive interest rates. In finance, the traditional way to deal with the diminishing value of money or commodities across time is through the concept of present value (PV), where the discount rate (r) governs how rapidly the value of an item in the future goes down to people valuing it today.
(1)
(2)
(top) Present value factors for 1, 3, and 6% discount rates. (bottom) The PV cost multiplier for a range of climate change trajectories (5, 10, 15 years, etc.) and a 3% discount rate. The PV cost multiplier for a 15 year trajectory, for T = 40 years (dotted lines) is 17.1 and increases to 24.2 at 80 years. These factors continue to increase for larger values of T, but evermore slowly.
), that can be easily applied to water prices and amounts in computing present values. We assume that the full annual water loss, W, will be realized after some number of years determined by the climate trajectory (Figure 2, bottom). The loss in any given year on the runup to that full realization is given by Wt = FtW, where Ft is the fraction lost in year t. Noting that W is a constant, we can write (2) as:
(3)
(4)
(5)
) times the steady state water loss (W) times the price of the water (P). Equation 5 can now be applied to any price and water loss amount. Present value cost multipliers (equation 4 and Appendix Appendix A) have been computed and are plotted in Figure 3 (bottom). An example shows how they can be used: at a 3% discount rate on a 15 year trajectory, over a 40 year period (T = 40) the present value cost multiplier is 17.1X, meaning the present value of the loss is 17.1 times the annual loss. This increases to 24.2X for the same trajectory at T = 80 years, and when projected to infinity (Figure 4, top) reaches a value of 27X. We have summarized the results for different trajectories and discount rates for long periods of time in Figure 4 (top).
(top) PV cost multipliers for snow water lost due to climate change, western U.S. computed over the next millennium. (middle and bottom) Water loss costs (in $trillion) for the same area and period (@ $200 and $900/acre foot replacement cost). A more complete description of the model appears in Appendices A and B. In computing actual $values, we omit 6% discount rate because it is fairly extreme and unlikely to be correct in a water-stressed future world.
A salient point is that it is the interaction of the trajectory (the climate rate of change) and the discount rate that determines value, and therefore, whether something is worth replacement. At a 1% discount rate, the present value today of all the lost water (including the steep part of the trajectory at the beginning) from now in perpetuity for a 15-year trajectory is 93X, but at a 3% discount rate, it is 27X, a huge difference, particularly (see next) when billions of dollars are involved.
We can make these results even more graphic if we use real numbers and dollars (Figure 4, middle and bottom). Approximately 162 million acre feet (MAF) of snow is deposited in the western mountains each winter (see Gergel et al. [2017] and Appendix Appendix B). A reasonable estimate is that half of this might come as rain in the future, and of that half, as much as two thirds might runoff to the ocean without utilization (Appendix Appendix B). That is a loss of 53.9 MAF each year, which at $200–$900 per acre foot results in cumulative replacement costs (in PV) of 0.12–4.76 trillion dollars, depending on our assumptions of climate trajectory and discount rate.
4 Implications of the Valuation
The sheer magnitude of the potential losses (measured in PV) is astounding. The losses are measured in trillions, not billions, of dollars. For reference, the U.S. Gross Domestic Product, which is the total value of all goods and services produced in the U.S., was $18.6 trillion in 2016 [Bureau of Economic Analysis, 2017], and the entire U.S. government budget was $3.8 trillion for fiscal year 2016 [Frentz et al., 2016]. A key point is that these costs cannot be computed or estimated without merging snow science with financial analysis, because it is the interplay between the two that determines the amount, and therefore the likelihood, of any replacement or mitigation effort.
A practical outcome from the analysis is that it produces actionable information. For example, if the cost of building a dam to recover lost water is computed to have a present value cost multiplier (in water units or dollars) of 75X, it is unlikely that backers would take on such a project at a 3% discount rate, but they might at a 1% discount rate (Figure 4, top). Similarly, the results highlight just how important the climate-driven rate of change is in deciding future actions and investments. For example, at a 3% discount rate, the difference in the present value cost multiplier for a 10 versus 75 year trajectory is a factor of two (29X versus 14X), which could easily mean the difference between a go- and no-go decision on a replacement or mitigation project.
The final point, and a key one, is the critical importance of knowing the rate of change of the snow resources, an area in which there is a lot of scope for improvement. For the western U.S., the difference in replacement costs (3% discount; $900/acre ft.) between a 10 and 50 year trajectory pencil out at $560 billion, 70 times the annual budget of the National Science Foundation. Even small refinements in our scientific knowledge of climate change trajectories through snow research could save billions. Given the magnitude of the impact and possible mitigation costs, we need to be making these decisions on the soundest and best scientific facts and knowledge possible.
5 Wisely Into the Future
There are in fact two things, science and opinion; the former begets knowledge, the later ignorance.
Hippocrates
- Continue and accelerate its efforts to improve snow measurement tools, including snow remote sensing. These needed tools will help delineate trajectories of changes at scales relevant to users and at regional and global scales.
- Focus on quantifying snow change trajectories more accurately. The snow community should continue to forge strong collaborations with climate modelers and paleoclimatologists in order to extend snow records both backward and forward in time.
- Entice more economists and financial experts into our ranks. Since research and ultimately mitigation will cost money, the findings and the value of the findings of research need to be explained in money as well. Economists can help clarify the value of needed research to key decision makers by using terms they will understand, and they can help scientists tailor their efforts so that they are easily acted upon.
Acknowledgments
Jessica Lundquist and Stephen Burges tutored and guided us through the complex topic of western water and dams. Chris Derksen and Henry Huntington provided key references on very short notice. Martyn Clark, Charlie Luce, and an anonymous reviewer made substantial and useful improvements in the paper through their review comments. Data supporting the analysis and conclusions presented in the work can be found in the references as cited. No original measurements were made as part of this work. M.S. and C.P. have been supported to do snow research on two grants from the NASA Terrestrial Hydrology Program.
Appendix A: A Snow Valuation Model
Notation
PV Present Value (standard notation)
V0 Present value at date 0 (today)
Present value at date 0 (today) of a value in year t
Ct cost of replacing the fraction of water lost in year t (
Dt Discount factor in year t where r is the discount rate (r = 1, 3, or 6%)
Ft fraction of W that is lost of the total snowpack in year t (Wt = FtW)
L Loss fraction (L = 1/N)
N Length (in years) of the climate trajectory
Pt Price of the water in year t. For simplicity we assume this is constant, so Pt = P
t denotes the year (starting with now=0)
W total amount of water lost due to transition snow to rain once steady state is reached
Wt amount of water that will be lost in year t (where t is measured from now =0) into the future
Z Initial period (in years) of an infinitely long period; used for computational purposes
(A1)The valuation process is done in real terms (i.e., in 2017 dollars) so that it includes any time-varying inflation. Since the water losses occur over a number of years, we need to account for the time value of the commodity. We do this using the concept of present value. This concept is rooted in basic human behavior: people would rather get something today than the same thing 10 years from now. For example, even in a world with no inflation, people prefer to get $100 today instead of $100 ten years out. This is why interest rates are positive. While the time value concept is generally applied to money, money is merely an indicator of value, and the concept can be applied directly to the consumption of goods and services (like water) as well. To assess the value of future losses in today's water amounts or dollars, we use the concept of present value (PV).
(A2)
(A3)
(A4)
(A5)
, where the subscript w denotes the value priced in water:
(A6)
(A7)
) for all water needing to be replaced is simply:
(A8)
(A9)This is a handy equation that states that the present value (in $) of the lost water is simply the water price times the water amount times the present value cost multiplier (
).
(A10)
(A11)
(A12)Factors can then be applied to any price P and any amount of water W. To illustrate, in Table A1 we show the present values for the entire time, the first 100 years, and the period after the first 100 years for different transition periods of length N and for r = 1, 3, and 6%.
| Transition Period (N Years) | ||||||||
|---|---|---|---|---|---|---|---|---|
| 5 | 10 | 15 | 20 | 25 | 50 | 75 | 100 | |
| 1% Discount Rate | ||||||||
| PV snowpack today | 98.0 | 95.7 | 93.4 | 91.1 | 89.0 | 79.2 | 70.8 | 63.7 |
| PV of first 100 years | 61.1 | 58.7 | 56.4 | 54.2 | 52.0 | 42.2 | 33.8 | 26.7 |
| PV of 101 to infinity | 37.0 | 37.0 | 37.0 | 37.0 | 37.0 | 37.0 | 37.0 | 37.0 |
| 3% Discount Rate | ||||||||
| PV snowpack today | 31.4 | 29.3 | 27.3 | 25.5 | 23.9 | 17.7 | 13.6 | 10.8 |
| PV of first 100 years | 29.7 | 27.6 | 25.6 | 23.8 | 22.2 | 15.9 | 11.9 | 9.1 |
| PV of 101 to infinity | 1.7 | 1.7 | 1.7 | 1.7 | 1.7 | 1.7 | 1.7 | 1.7 |
| 6% Discount Rate | ||||||||
| PV snowpack today | 14.9 | 13.0 | 11.4 | 10.1 | 9.0 | 5.6 | 3.9 | 2.9 |
| PV of first 100 years | 14.8 | 13.0 | 11.4 | 10.1 | 9.0 | 5.5 | 3.8 | 2.9 |
| PV of 101 to infinity | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
Appendix B: Computing the Cost of Western Water Lost When Snow Comes as Rain
The western U.S. hosts a wide range of hydrologic systems with complex water-usage patterns, some with dams, some without. A full accounting of how much water from snowmelt is available, how much runs into reservoirs before it is used, and how much currently flows to the ocean, is beyond the scope of this study. For the amount of snow water, we use the results of Gergel et al. [2017]. They estimate from historical SNOTEL observations that 200 km3 (=162 million acre feet (MAF)) of SWE are distributed across the Rockies, Sierra Nevada, and Cascades. We have checked this value using daily snowfall amounts from the Global Snow Laboratory at Rutgers University (http://climate.rutgers.edu/snowcover/ and Kluver et al. [2016]) and concur.
As the climate warms, the transition from snow to rain will follow complex patterns, with the fraction turning to rain in “warm” snow regions like California and Oregon exceeding that in colder places like the Northern Rockies. For simplicity, and to be conservative, we assume that by the end of each of the trajectories used in our model one half (0.5) of all current snowfall will come as rain. In an extensive climate study done for the State of California, Hayhoe et al. [2004], using eight different climate change model scenarios, found that over the next 10–100 years the snow-to-rain transition will reduce snowmelt runoff by 20%–90%. Not only are these percentage changes consistent with our model assumptions, but also the periods of time over which the Hayhoe simulations were run match the time trajectories we applied in our model.
Of the half of the snow that we now assume arrives as rain, some amount will be captured in existing reservoirs (cf. Vogel et al. [2007]). Again, it is beyond the scope of this paper to make a detailed assessment of that fraction. We do note that Barnett et al. [2005] suggested that most of this water will flow unused to the ocean. Additionally, virtually every report we have found on the heavily dammed water systems of the West suggests that reservoir capacity (except when immediately following drought) is maxed out. We therefore assume that two third of the snowmelt runoff reduction amount is lost across all the water systems. Therefore, of the original 162 MAF of Western snow that is received today, 54 MAF will be lost by the end of each climate change trajectories we use.
Pricing water is yet another complex issue [Brown, 2006]. In some urban water markets, like those fronting the east side of the Rockies, the acre-foot price of water has at times exceeds $26,000 (http://www.waterexchange.com/water-market-insider-westwater-research-announces-2014-water-rights-price-index-results/). In contrast, a USDA Farm and Ranch Irrigation Survey [2008] found that across the Great Plains per acre foot prices varied from $7 to $65, but these turn out to be highly subsidized values. For more natural values, we looked at water costs in the Central Valley of California. In a recent study [Sturm et al., 2016] water in the Valley was priced at $0.73/m3, or $900/acre foot. Other sources list the cost at about $250/acre foot prior to the drought, and during the drought as much as $850/acre foot (see https://www.bloomberg.com/news/articles/2014-07-24/california-water-prices-soar-for-farmers-as-drought-grows). Given the dramatic fluctuations in the price of water, we choose two reasonable prices to monetize and bound the loss of water due to the shift from snow to rain: $200/acre foot and $900/acre foot.
Using these data and the computations listed above, we suggest that the snow-to-rain transition will lead to an annual loss of $10.8–$48.6 billion, and we believe our estimation is a conservative figure because for many of the alpine areas we included, more than half of the snow will likely be rain in the next five decades, and as that transition occurs, water prices are likely to rise dramatically.
