International Snow Science Workshop Grenoble – Chamonix Mont-Blanc – 2013

Operational SWE forecasts using a hybrid approach Edward H. Bair 1

1,2*

1

, Robert Davis , Karl Rittger

3,2

4

, and Jeff Dozier ,

US Army Corps of Engineers Cold Regions Research and Engineering Laboratory, Hanover, NH, USA 2 Earth Research Institute, University of California, Santa Barbara, CA, USA 3 California Institute of Technology, Jet Propulsion Laboratory, Pasadena, CA, USA 4 Bren School of Environmental Science & Management, University of California, Santa Barbara, CA, USA

ABSRACT: Accurate spatial measurement of SWE in mountain watersheds is perhaps the most significant problem in snow hydrology. Because of the spatial variability of snow in these areas, operational models can have large errors, particularly in remote regions. We describe how operational needs led us to merge different approaches. Recently, SWE reconstruction has been shown to match well the rank order of snowmelt runoff across the Sierra Nevada, CA USA, especially for very dry and wet years. Ending with a date for peak SWE and starting with the disappearance of snow in a satellite image, reconstruction retrospectively builds the snow cover by calculating the amount of snow melted at each time step in each pixel. Operational experience has demonstrated the need for subjective context and perspective. We place the current water year into a historical perspective graphically by displaying a family of accumulation-depletion curves. Because reconstruction cannot estimate SWE prior to peak, we use an ensemble of normalized products for accumulation. The products in the ensemble depend on whether the study area is sparsely or heavily gauged. For instance, in the Sierra Nevada, a heavily gauged area, we use snow pillow interpolation and the Snow Data Assimilation System (SNODAS) for SWE accumulation. In Afghanistan, a sparsely gauged area, we use satellitederived SWE from passive microwave emission for accumulation. From the normalized accumulation curves, we obtain the predicted rank of a water year prior to peak SWE. From the predicted rank, we find similar water years from the Reconstruction ensemble. This hybrid method provides a user with a series of SWE and depletion possibilities. By providing improved SWE estimates over the current operational model, we hope to improve information available to water managers of snowmeltdominated watersheds. KEYWORDS: SWE, microwave, reconstruction 1

INTRODUCTION

Accurate estimates of snow water equivalent (SWE) in mountain watersheds are a longstanding and unsolved problem. Operational models have high uncertainty, and this uncertainty has high costs for water users. For instance, April to July runoff forecasts for the American River in California’s Sierra Nevada have an 18% error on average, and sometimes exceed 100% (Dozier, 2011). Uncertainty stems from the heterogeneous nature of mountain snow. Spectroscopic techniques using satellite-based imagery in the visible and nIR bands have been successful at mapping snow covered area (SCA) at sub-pixel resolution (e.g., Rosenthal and Dozier, 1996; Painter et al., 2009). Measurements of SCA are combined with a Reconstruction technique (Martinec and Rango, 1981), which has successfully modeled SWE in large basins in the Rocky Mountains (Molotch, 2009) and the *Corresponding author address: Edward H. Bair, Earth Research Institute, University of California, Santa Barbara CA 93106-5131, USA, email: [email protected]

Sierra Nevada (Rittger, 2012). The main advantage of Reconstruction is that it provides spatially resolved SWE estimates without the need for extensive ground based observations. The biggest disadvantage is that reconstruction can only be run retroactively after snow disappears, as we discuss in Section 2.1. We suggest a hybrid approach for large scale SWE estimates over the entire water year. Rather than focus on accurate SWE mapping, we focus on rank order statistics, which may be more useful to water managers who place a premium on information that helps them discern between normal (business as usual) and extreme (very wet/very dry) years. This hybrid approach ranks SWE estimates from several real-time products into a family of accumulation curves. From this family of accumulation curves, the user can select one or more corresponding depletion (i.e. reconstruction) curves, chosen based on rank. Given a sufficient historical catalog that captures the range of variability, we can estimate peak SWE from the corresponding Reconstruction depletion curve. This classification is based on nearest neighbors,

International Snow Science Workshop Grenoble – Chamonix Mont-Blanc – 2013

where ranks are used as the independent variable. 2 2.1

METHODS Reconstruction

Reconstruction uses an energy balance approach. For each pixel, from date of peak SWE through the disappearance of snow in a satellite image, reconstruction retrospectively builds the snow cover by calculating the amount of snow melted at each time step (Molotch, 2009): n

SWEn = SWE0 − ∑ M j

(1)

j =1

SWEn and SWE0 are the SWE at time steps n and 0, and Mj is the melted SWE. Knowing the value of n when SWEn=0 (i.e. when SCA=0) allows the back-calculation of the initial SWE0. Melted SWE is the product of the potential melt energy Mp,j and the fractional snowcover fSCA :

Mj = Mp,j × fsca

(2)

The potential melt (on a fully snow covered pixel p at time step j) is estimated with a restricted degree day model (Kustas et al., 1994):

Mp,j = mqRd + BrTd

(3)

The energy balance terms are: mq, an energy to radiation melt factor and Rd, the mean daily net radiation. The degree day terms are: Br, a degree day melt factor, and Td, the average daily air temperature if > 0 ºC; otherwise Td is zero. The reconstruction method is especially suited to areas with little accumulation during the melt season. The main drawback is that it can only be done retrospectively, as the method hinges on knowledge of the date when SCA=0 for each pixel. 2.2

SNODAS and Interpolation

To address this drawback, we use a different approach to estimate SWE prior to the peak. We use an ensemble of products, chosen by the availability of ground-based observations. For the instrumented Sierra Nevada, we use SNODAS (SNOw Data Assimilation System, National Operational Hydrologic Remote Sensing Center, 2004) and snow pillow interpolation (Fassnacht et al., 2003) for accumulation. SNODAS results come directly

from the National Snow and Ice Data Center and are available daily. The snow pillow interpolation is a research product. One of its key inputs, time and spaced smoothed SCA (Dozier et al., 2008), is not yet produced daily for public use. 2.3

Passive Microwave SWE

For regions with austere infrastructure, we cannot use models that rely on ground-based observations. In Afghanistan, we use satellitederived measurements of SWE from passive microwave emission through the snow (Daly et al., 2012). Specifically, these measurements come from the AMSR-E and SSM/I satellites. In this study, we use SWE estimates from the AMSR-E satellite. AMSR-E stopped functioning October 2011, but global SWE products are available from SSM/I and the recently launched Japanese AMSR2. Passive Microwave pixel areas are 2500X larger than those in Reconstruction, Interpolation, and SNODAS (25.0 vs. 0.5 km) and suffer from a variety of complicating factors such as forests, wet snow, and rough terrain (Dong et al., 2005; Vander Jagt et al., 2013). These complicating factors cause noise in the AMSR-E signal, which we smooth in two steps: 1) we find peaks over a 7day interval, and 2) we interpolate between peaks with splines. 2.4

Full Natural Flow

In the Sierra Nevada, we include spring full natural flow (FNF) as an independent measure of water year rank. Full natural flow is the measured streamflow adjusted for reservoir evaporation and withdrawals upstream of the gauge. Spring full natural flow is the summed (April 1 - June 30) flow for 19 gauges in the Sierra Nevada where full natural flow is calculated. These gauges collect runoff from a 2 total area of 54,000 km , or only 43% of the Sierra. We expect the ranks of the FNF data to match the ranks of the SWE estimates because SWE has the most influence over FNF variability. Ideally, the FNF data would be adjusted to remove rainfall. For this study, we find that using the FNF data without adjustment is acceptable, as the April 1-June 30 period in the Sierra is usually quite dry. Precipitation records from the California Data Exchange Center (http://cdec.water.ca.gov) show that this period only accounts for 10-13 cm or 8% to 10% of annual precipitation. Because the Sierra Nevada is well gauged, we focus on results there to validate methods, with the goal to apply our techniques to large watersheds in Afghanistan’s Hindu Kush.

International Snow Science Workshop Grenoble – Chamonix Mont-Blanc – 2013

60

(a) Reconstruction

max 75th 50th 25th min 2007

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(b) SNODAS

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SWE, km3

SWE, km3

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0 Jan 50 45

Feb Mar

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May

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0 Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

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(c) Interpolation

(d) AMSR-E

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SWE, km3

SWE, km3

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20 15

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5 0 Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

0 Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep

Figure 1 (a-d) 2004-2011 SWE Time series for the Sierra Nevada. The driest year, 2007, is shown for comparison. Note the different scales on the y-axes. rank

WY

Recon.

WY

Interp.

WY

AMSR-E

WY

SNODAS

WY

FNF

1 2 3 4 5 6 7

2005 2011 2006 2010 2008 2004 2009

50.2 48.6 41.5 35.0 29.7 29.5 29.0

2011 2005 2006 2008 2010 2004 2009

50.6 40.9 40.6 34.7 34.0 30.3 24.3

2011 2008 2005 2010 2009 2006 2004

9.4 9.2 8.7 8.0 7.1 6.5 6.2

2011 2006 2010 2005 2008 2009 2004

42.2 29.2 28.8 27.7 26.9 21.8 19.0

2006 2011 2005 2010 2009 2008 2004

24.8 22.1 19.0 14.9 10.8 8.2 7.7

8 2007 22.8 2007 15.0 2007 4.8 2007 11.1 2007 5.1 3 Table 1 2004-2011 Ranks and maximum SWE, in km , (pixel-by-pixel) for each method and spring full natural flow (FNF). Pixel-by-pixel maximum SWE is the sum of maximum SWE for each pixel of the four models and spring full natural flow.

International Snow Science Workshop Grenoble – Chamonix Mont-Blanc – 2013

Full natural flow

SNODAS

AMSR-E

Interpolation

Reconstruction

Spearman

Reconstruction 1.00 Interpolation

0.95 1.00

AMSR-E

0.67 0.76

1.00

SNODAS

0.83 0.86

0.67 1.00

Full natural flow 0.83 0.81

0.50 0.93 1.00

Table 2 Matrix of Spearman rank correlation coefficients for maximum SWE. 3

RESULTS

The models produce vastly different amount of SWE (Figure 1 and Table 1). Reconstruction estimates the most, while AMSR-E estimates the least SWE. AMSR-E also produces more SWE in the early season. Although the models produce different amounts of SWE, they rank water years similarly for extremes. All models rank 2007 as the driest year, which also corresponds to the lowest FNF. All models rank the wettest year, except 2011 as Reconstruction, which ranks 2005 as the wettest year and 2011 as the second wettest. The FNF data show 2011 as the second wettest year, like Reconstruction, but 2006 as the wettest. In almost all years, there is more FNF than AMSR-E SWE, affirming that AMSR-E underestimates SWE. Low SWE values probably owe to large pixels and attenuation issues with wet or deep snow. Clearly, the high-resolution models perform better than AMSR-E. Looking at the Spearman rank correlation coefficients (Table 2), we see that AMSR-E consistently has the lowest correlation with full natural flow (0.50). SNODAS has high correlation with full natural flow (0.93), as does Reconstruction (0.83), and Interpolation (0.81). The Spearman correlation coefficients represent correlation of ranks only, not in SWE volumes. For SWE volumes, Reconstruction is probably the most accurate; it is the only method that consistently produces enough SWE to exceed FNF for many individual basins (Rittger, 2012). Given that AMSR-E was able to correctly pick out the driest year, 2007, we show an example of how the AMSR-E and Reconstruction data could be normalized to produce a hybrid product (Figure 2). From the hybrid product, one can see how AMSR-E could be used to accurately rank 2007 and to pick out

a corresponding ablation Reconstruction (Figure 1a). 4

curve

from

DISCUSSION

Out of all the products, passive microwave is the only global daily SWE product. For mountain regions like the Hindu Kush, where there are virtually no ground-based sensors, PM is the only option for real-time SWE measurements (Vuyovich and Jacobs, 2011). Given that AMSR-E does a reasonable job of estimating rank (mean Spearman = 0.65) and it ranked the driest year on record with the other models, we suggest that PM is an acceptable method to estimate SWE in regions of austere infrastructure. Moreover, the large watersheds 2 in Afghanistan (some more than 200,000 km ) are better suited to the coarse PM resolution than many watersheds in the US. For comparison, the entire Sierra Nevada covers 3 about 125,000 km . 5

CONCLUSION

Reconstruction is a promising method for spatial estimates of SWE, but it can only be performed retroactively after snow has disappeared from a pixel. Also, Reconstruction can only produce a depletion curve. To address this shortcoming, we use other methods during the accumulation season to rank the current water year. In the well instrumented Sierra Nevada, we use two highresolution methods: SNODAS and Interpolation.

Figure 2 Normalized SWE curves. AMSR-E is shown as the dotted lines (Oct 1-Mar 31), Reconstruction is shown as the solid lines (Apr 1-Sep 30). The max, min, and mean are from 2004-2011 and the driest year, 2007, is shown for reference.

International Snow Science Workshop Grenoble – Chamonix Mont-Blanc – 2013

In Afghanistan, a sparsely-gauged region, we rely on PM SWE estimates. These methods all produce different SWE volumes, but similar ranks. Thus, we normalize by maximum SWE in order to compare accumulation products with Reconstruction. From the predicted rank of the current water year, we estimate peak SWE based on the corresponding Reconstruction curve. Also, a water manager could use the predicted rank to look up inflow records from the closest year to the current year. This hybrid method has potential to provide a user with a series of SWE and depletion possibilities. By providing improved SWE estimates over the current operational model, we hope to improve information available to water managers of snowmelt-dominated watersheds. 6

REFERENCES

Daly, S.F., Vuyovich, C.M., Deeb, E.J., Newman, S.D., Baldwin, T.B. and Gagnon, J.J., 2012. Assessment of the snow conditions in the major watersheds of Afghanistan using multispectral and passive microwave remote sensing. Hydrological Processes, 26(17): 2631-2642, doi: 10.1002/hyp.9367. Dong, J., Walker, J.P. and Houser, P.R., 2005. Factors affecting remotely sensed snow water equivalent uncertainty. Remote Sensing of Environment, 97(1): 68-82, doi: 10.1016/j.rse.2005.04.010. Dozier, J., 2011. Mountain hydrology, snow color, and the fourth paradigm. Eos, Transactions American Geophysical Union, 92(43): 373-374, doi: 10.1029/2011eo430001. Dozier, J., Painter, T.H., Rittger, K. and Frew, J., 2008. Time-space continuity of daily maps of fractional snow cover and albedo from MODIS. Advances in Water Resources, 31(11): 15151526, doi: 10.1016/j.advwatres.2008.08.011. Fassnacht, S.R., Dressler, K.A. and Bales, R.C., 2003. Snow water equivalent interpolation for the Colorado River Basin from snow telemetry (SNOTEL) data. Water Resources Research, 39, doi: 10.1029/2002wr001512. Kustas, W.P., Rango, A. and Uijlenhoet, R., 1994. A simple energy budget algorithm for the snowmelt runoff model. Water Resources Research, 30(5): 1515-1527, doi: 10.1029/94wr00152. Martinec, J. and Rango, A., 1981. Areal distribution of snow water equivalent evaluated by snow cover monitoring. Water Resources Research, 17(5): 1480-1488, doi: 10.1029/WR017i005p01480. Molotch, N.P., 2009. Reconstructing snow water equivalent in the Rio Grande headwaters using remotely sensed snow cover data and a spatially distributed snowmelt model. Hydrological Processes, 23(7): 1076-1089, doi: 10.1002/hyp.7206. National Operational Hydrologic Remote Sensing Center, 2004. Snow Data Assimilation System (SNODAS) Data Products at NSIDC. National Snow and Ice Data Center, Boulder, CO USA.

Painter, T.H., Rittger, K., McKenzie, C., Davis, R.E. and Dozier, J., 2009. Retrieval of subpixel snowcovered area, grain size, and albedo from MODIS. Remote Sensing of Environment, 113: 868–879, doi: 10.1016/j.rse.2009.01.001. Rittger, K., 2012. Spatial estimates of snow water equivalent in the Sierra Nevada. Ph.D. Thesis, Unversity of California, Santa Barbara, Santa Barbara, 225 pp. Rosenthal, W. and Dozier, J., 1996. Automated mapping of montane snow cover at subpixel resolution from the Landsat Thematic Mapper. Water Resources Research, 32(1): 115-130, doi: 10.1029/95WR02718. Vander Jagt, B.J., Durand, M.T., Margulis, S.A., Kim, E.J. and Molotch, N.P., 2013. The effect of spatial variability on the sensitivity of passive microwave measurements to snow water equivalent. Remote Sensing of Environment, 136(0): 163-179, doi: 10.1016/j.rse.2013.05.002. Vuyovich, C. and Jacobs, J.M., 2011. Snowpack and runoff generation using AMSR-E passive microwave observations in the Upper Helmand Watershed, Afghanistan. Remote Sensing of Environment, 115(12): 3313-3321, doi: http://dx.doi.org/10.1016/j.rse.2011.07.014.