# Can Remotely Sensed Snow Disappearance Explain Seasonal Water Supply?

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}over the western U.S. This, paired with the cost and difficulty of repairs, limits the widespread availability of SNOTEL data. Additionally, sparse spatial coverage implies that predictions based on SNOTEL must implicitly assume a stationary relationship between snow observed at those points relative to basin-wide SWE volume. This assumption has varying utility dependence on the path of winter storm tracks and a non-stationary climate [11]. Conversely, satellites can monitor the presence of snow nearly continuously over the entire landscape. Despite its limitations, SNOTEL data has been vital in the initialization of many models used to predict seasonal water supply. Previous studies have shown a strong relationship exists between peak SWE and flow volume, with lower peak values of SWE corresponding with less runoff in the snow ablation season [12]. In the Sierra Nevada, a 10% decrease in peak SWE led to larger decreases (9% to 22% reduction) in summer minimum streamflow [13], with minimum downstream flows occurring 3–7 days earlier than average annually with each 10% decrease in SWE. A relationship has also been found between the timing of peak SWE and the volume of AMJJ runoff; earlier peak SWE leads to below average AMJJ runoff [14,15]. When considering the response of annual streamflow volume to changing future snow conditions, the expected outcomes may partially depend on which ablation mechanisms dominate; e.g., changes in aridity, water-inputs, or energy-inputs. There is limited consensus on changes in streamflow volume, but greater consensus on how warming-driven changes in snow ablation will drive earlier peak hydrograph timing [16].

## 2. Materials and Methods

#### 2.1. Data Description

^{2}, with at least one SNOTEL station within the basin boundary or less than 10 km from the basin boundary, with a full record of SNOTEL [31] and USGS-gaged streamflow observations [32] available between water-years 2001 and 2019 [33]. The selected date range was chosen to overlap with snow timing data from Heldmyer et al., 2021, which motivated this work. The resulting basins fell within snow-dominated ecoregions and were also identified as having minimal anthropogenic influence on streamflow as part of metadata from the GAGESII dataset [34]. Following procedures outlined in Heldmyer et al., 2021, DSD values greater than 275 (day of year) were discarded under the assumption that these pixels are permanently snow-covered.

_{valid}) during a one-year period. The pixelwise means for all locations within the basin were then averaged to obtain the annual basin-wide mean DSD. From the same pixelwise data, we further calculated the daily snow free fraction, (SFF) or the fraction of a given basin for which snow has ablated by a specific date. This value was calculated with Equation (1), by determining the fraction of pixels which had DSD values less than or equal to the forecast date (n

_{DSD}≤ day) with respect to n

_{valid}. The dates chosen for this analysis began on 1 April and were evaluated biweekly (on 15 April, 1 May, 15 May), ending on 1 June.

#### 2.2. Evaluation of the Relationship between DSD and Seasonal Water Supply

^{2}and p-value of the regression were reported. The null hypothesis for the regression was that the slope of the regression line is equal to zero, or that there is no observable relationship between the two datasets. To better understand the interannual variability in each source of data and how this may affect model skill, the quartile coefficient of dispersion (QCD) was calculated for each basin. Equation (2) shows the calculation of the QCD for a single data source, where Q1 is equal to the 25th percentile of the data, and Q3 is equal to the 75th percentile of the data. This nonparametric metric is a more robust alternative to the coefficient of variation, which is sensitive to outliers.

#### 2.3. Analysis of Predictive Skill

_{AMJJ}is the total AMJJ streamflow volume, or seasonal water supply, β

_{1–3}are model coefficients corresponding to mean DSD, SFF, and SNOTEL SWE terms, and β

_{0}is the model error.

#### 2.4. Model Evaluation

_{AMJJ}, y is the predicted value of V

_{AMJJ}for a given model, and n is equal to the number of predicted values.

## 3. Results

#### 3.1. Evaluating the Relationship between Satellite Variables and Seasonal Water Supply

^{2}values expected to be larger later in the season, as the DSD information for each year has captured more snow disappearance. Other variables, such as the SFF or SNOTEL SWE, may increase the R2 values within these basins. By discussing the relative predictive skill of each model, the following Sections (Section 3.2 and Section 3.3) discuss how this relationship develops over time and with respect to different predictor variables. The addition of other meteorological predictors—including total precipitation—may improve R

^{2}further but were not considered in this study.

#### 3.2. Evaluation of Forecast Skill of Linear Models Only Using Satellite Data

#### 3.3. Evaluation of Skill of Linear Models Combining Satellite and In Situ Data

## 4. Discussion

#### 4.1. Insights and Implications

#### 4.2. Limitations

#### 4.3. Future Research Directions

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The 15 study basins spread across eight western states. Correlation values between DSD mean and yearly seasonal water supply are calculated at basin-wide level, marked at the outlet location for each basin.

**Figure 2.**Absolute correlation between V

_{AMJJ}and DSD for the years of 2001–2019 spatially illustrated for the example basins of the East R. at Almont, CO, (

**a**) and the Bruneau R. at Rowland, NV, (

**b**) at the native MODIS resolution of 500 m. The location of the USGS gage and SNOTEL station are denoted by a yellow star and orange triangle, respectively. Contour lines range from yellow (lowest) to orange (highest) elevations.

**Figure 3.**The median relative RMSE, correlation, R, and percent bias, PBIAS, error statistics for three different satellite-based water supply forecasts in the East R. basin, with interquartile range (25/75 percentiles) shaded. Vertical dotted lines denote the days chosen for forecasting—1 April, 15 April, 1 May, 15 May, and 1 June.

**Figure 4.**The median percent bias, PBIAS, statistics for three different satellite-based water supply forecasts with interquartile range (25/75 percentiles) shaded, for all 15 study basins. Vertical dotted lines denote the days chosen for forecasting—1 April, 15 April, 1 May, 15 May, and 1 June.

**Figure 5.**The median relative RMSE, rRMSE, correlation, R, and PBIAS statistics for three different satellite and in-situ-based water supply forecasts in the East R. basin with interquartile range (25/75 percentiles) shaded. Vertical dotted lines denote the days chosen for forecasting—1 April, 15 April, 1 May, 15 May, and 1 June.

**Figure 6.**The median percent bias statistics for three different satellite and in-situ-based water supply forecasts with interquartile range shaded, for all 15 study basins. Vertical dotted lines denote the days chosen for forecasting—1 April, 15 April, 1 May, 15 May, and 1 June.

**Figure 7.**The differences between the QCD for DSD mean and SNOTEL SWE data through time. Negative values indicate that the spread of data relative to its first and third quartile is higher for SNOTEL SWE. Blank values indicate that the Q1 value is equal to zero, or there is no remaining SWE measured at the basin’s SNOTEL site by this date in at least 25% of the study years.

**Figure 8.**A comparison of model skill among satellite and in-situ-based models over time. The satellite model with lowest median PBIAS at a given date was selected for comparison with the Phys_SWE model.

**Table 1.**Description of study basins and relevant attributes. SWE/P is defined as the average ratio of 1 April SWE to cumulative precipitation, as recorded at each SNOTEL station, for the water years 1985–2020. The USGS gage names have been abbreviated for clarity.

Basin Name | USGS Gage Name | USGS ID | Gage Location | Gage Elevation (m) | Basin Area (km^{2}) | SNOTEL Station | SNOTEL Elevation (m) | SWE/P Ratio |
---|---|---|---|---|---|---|---|---|

Walker R. | W Walker River near Coleville, CA | 10,296,000 | 38.38, −119.45 | 2008 | 471 | 575 | 2191 | 0.84 |

Carson R. | E F Carson River near Markleeville, CA | 10,308,200 | 38.71, −119.76 | 1646 | 718 | 697 | 2358 | 0.82 |

East R. | East River at Almont, CO | 9,112,500 | 38.66, −106.85 | 2440 | 750 | 380 | 3109 | 0.92 |

Crystal R. | Crystal River near Redstone, CO | 9,081,600 | 39.23, −107.23 | 2105 | 434 | 618 | 2674 | 0.82 |

San Juan R. | San Juan River at Pagosa Springs, CO | 9,342,500 | 37.27, −107.01 | 2148 | 727 | 840 | 3091 | 0.80 |

Little Wood R. | Little Wood River near Carey, ID | 13,147,900 | 43.49, −114.06 | 1621 | 655 | 805 | 2329 | 0.75 |

Swan R. | Swan River near Bigfork, MT | 12,370,000 | 48.02, −113.98 | 933 | 1753 | 562 | 1448 | 0.76 |

Bruneau R. | Bruneau River at Rowland, NV | 13,161,500 | 41.93, −115.67 | 1372 | 988 | 746 | 2240 | 0.68 |

Sandy R. | Sandy River near Marmot, OR | 14,137,000 | 45.40, −112.14 | 0 | 711 | 655 | 1241 | 0.41 |

Santiam R. | North Santiam River near Detroit, OR | 14,178,000 | 44.71, −122.10 | 485 | 553 | 614 | 789 | 0.24 |

Blacksmith Fork | Blacksmith Fork near Hyrum, UT | 10,113,500 | 41.62, −111.74 | 1530 | 681 | 634 | 2722 | 0.98 |

Sevier R. | Sevier River at Hatch, UT | 10,174,500 | 37.65, −113.43 | 2094 | 864 | 390 | 2928 | 0.74 |

Lamar R. | Lamar River near Tower Falls Ranger Station, YNP | 6,188,000 | 44.93, −110.39 | 1829 | 1741 | 683 | 2865 | 0.96 |

Pacific Cr. | Pacific Creek at Moran, WY | 13,011,500 | 43.85, −110.52 | 2048 | 407 | 314 | 2152 | 0.96 |

Stehekin R. | Stehekin River at Stehekin, WA | 12,451,000 | 48.33, −120.69 | 335 | 839 | 681 | 1402 | 0.86 |

**Table 2.**Description of model inputs, units, and naming scheme. ‘Sat’ describes satellite-based measurements of snow, whereas ‘Phys’ refers to physical, in situ measurements.

Model Classifier | Input Variables | Units |
---|---|---|

Sat_DSD | Day of Snow Disappearance (DSD) | Day of year |

Sat_SFF | Snow free fraction (SFF) | Percentage (%) |

Sat_combo | DSD and SFF | Day of year; percentage (%) |

Phys_SWE | SNOTEL snow water equivalent (SWE) | mm |

SatPhys_combo | DSD, SFF, and SNOTEL SWE | Day of year; percentage (%); mm |

**Table 3.**Relationships between mean DSD, center of water supply volume, and V

_{AMJJ}for the 15 selected study basins. R

^{2}and p-value from OLS model fit statistics using all years of available spatially aggregated DSD and USGS stream gage data. Basins are sorted from highest to lowest elevation at their USGS stream gage.

Basin | Mean DSD | Center of Water Supply Volume | DSD-V_{AMJJ} R^{2} | p-Value |
---|---|---|---|---|

East R. | 130 | 152 | 0.82 | 8.30 × 10^{−8} |

San Juan R. | 114 | 143 | 0.80 | 2.20 × 10^{−7} |

Crystal R. | 136 | 157 | 0.80 | 2.50 × 10^{−7} |

Sevier R. | 95 | 143 | 0.57 | 1.80 × 10^{−4} |

Pacific Cr. | 141 | 147 | 0.60 | 1.10 × 10^{−4} |

Walker R. | 135 | 150 | 0.79 | 4.50 × 10^{−7} |

Lamar R. | 140 | 152 | 0.46 | 1.50 × 10^{−3} |

Carson R. | 119 | 141 | 0.74 | 2.10 × 10^{−6} |

Little Wood R. | 107 | 142 | 0.41 | 3.00 × 10^{−3} |

Blacksmith Fork | 105 | 139 | 0.48 | 1.00 × 10^{−3} |

Bruneau R. | 83 | 130 | 0.38 | 4.80 × 10^{−3} |

Swan R. | 111 | 153 | 0.39 | 4.00 × 10^{−3} |

Santiam R. | 102 | 135 | 0.79 | 4.50 × 10^{−7} |

Stehekin R. | 150 | 153 | 0.60 | 9.30 × 10^{−5} |

Sandy R. | 75 | 132 | 0.52 | 4.90 × 10^{−4} |

**Table 4.**Correlation between SWE/P ratio and median PBIAS values for all basins calculated for each model and each forecast date. Values with a significant relationship (p-value < 0.05) are marked with an asterisk.

1 April | 15 April | 1 May | 15 May | 1 June | Mean | Median | |

Sat_DSD | −0.07 | −0.28 | −0.15 | −0.03 | 0.03 | −0.10 | −0.07 |

Sat_SFF | −0.21 | −0.29 | −0.16 | −0.35 | 0.27 | −0.15 | −0.21 |

Sat_combo | −0.11 | −0.20 | 0.22 | −0.26 | 0.33 | 0.00 | −0.11 |

Phys_SWE | −0.17 | −0.26 | −0.57 * | −0.64 * | 0.11 | −0.31 | −0.26 |

SatPhys_Combo | −0.28 | −0.23 | −0.09 | −0.19 | 0.24 | −0.11 | −0.19 |

Mean | −0.17 | −0.25 | −0.15 | −0.29 | 0.20 | ||

Median | −0.17 | −0.26 | −0.15 | −0.26 | 0.24 |

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**MDPI and ACS Style**

Bishay, K.; Bjarke, N.R.; Modi, P.; Pflug, J.M.; Livneh, B.
Can Remotely Sensed Snow Disappearance Explain Seasonal Water Supply? *Water* **2023**, *15*, 1147.
https://doi.org/10.3390/w15061147

**AMA Style**

Bishay K, Bjarke NR, Modi P, Pflug JM, Livneh B.
Can Remotely Sensed Snow Disappearance Explain Seasonal Water Supply? *Water*. 2023; 15(6):1147.
https://doi.org/10.3390/w15061147

**Chicago/Turabian Style**

Bishay, Kaitlyn, Nels R. Bjarke, Parthkumar Modi, Justin M. Pflug, and Ben Livneh.
2023. "Can Remotely Sensed Snow Disappearance Explain Seasonal Water Supply?" *Water* 15, no. 6: 1147.
https://doi.org/10.3390/w15061147