Geologic Setting

Mount Rainier, which is 14,410 feet (ft) in elevation, is a widely glaciated, active composite volcano on the west slope of the Cascade Range in Washington State. It is primarily composed of andesitic and dacite lava flows built upon a base of altered volcanic and granitic rocks (Fiske and others, 1963). Some of the youngest rocks consist of unconsolidated glacial and glaciofluvial debris, mudflows, and ash and pumice deposits, with the most recent pyroclastic eruptions occurring as recently as 500 years ago (Fiske and others, 1963). There are 26 named glaciers that cover portions of Mount Rainier, and they serve as the headwaters for 5 major rivers: the Cowlitz, Nisqually, Puyallup, Carbon, and White Rivers. The Emmons Glacier, on the northeast flank of the volcano, is at the headwaters of the White River (Pringle, 2008).

The Emmons Glacier and the White River have eroded through Mount Rainier’s volcanic material into the Keechelus andesitic series. However, the distribution of these formations is now hidden by the glacier and its deposits, and by the large areas of talus on the slopes above the lateral moraines (Fahnestock, 1963). Glacial valley fills are mostly covered by volcaniclastic material in the upper White River and West Fork White River valleys, primarily from the Osceola Mudflow that occurred about 5,600 years ago (Crandell, 1971; Crandell and Miller, 1974). The White River valley contains mostly alluvial deposits made up of sand, gravel, and cobbles. Alluvial sediments are relatively consistent down the length of the valley with median grain-size diameters of about 30–50 millimeters (mm; Anderson and Jaeger, 2020).

Climate

Mount Rainier’s location on the west side of the Cascade Range drainage divide and its proximity to the Pacific Ocean significantly affect the area’s climate in both summer and winter (Fahnestock, 1963). The following climate data are derived from the 1991–2020 monthly and annual normals provided by the National Oceanic and Atmospheric Administration (National Oceanic and Atmospheric Administration, 2022) for Rainier Paradise Ranger Station, Washington (station ID USC00456898), which is about 10 mi southwest of Sunrise Visitor Center. Mean annual precipitation was about 116 inches (in.), with November, December, and January each averaging 17–18 in. of monthly precipitation. Summers (June–August) are normally dry, with a mean total precipitation of 6.89 in. Mean monthly temperature is about 27 degrees Fahrenheit (°F) in December and about 54 °F in August. Glacial meltwater from the Emmons Glacier to the White River is generally at its highest when annual temperatures are at their highest in late summer. The rain-snow mixed-precipitation that is typical of the White River basin has contributed to the area’s largest-magnitude floods. These floods occur in fall and winter, associated with atmospheric rivers (Neiman and others, 2011; Konrad and Dettinger, 2017). Smaller floods associated with snowmelt have occurred in the spring.

Stream Discharge Measurements

From September 21 to September 22, 2020, low-flow synoptic stream discharge measurements were made at 14 sites on the White River and its tributaries to determine streamflow gains from or losses to groundwater between sites, hereafter referred to as a “seepage run” (table 1; fig. 2). The period for measurement was selected because the prevailing cool temperatures would minimize glacial melt contributions to stream discharge and was prior to the region’s rainy season, minimizing runoff contributions to stream discharge (National Oceanic and Atmospheric Administration, 2022). During this period, stream discharge was steady and at or near the lowest values of the year, resulting in the best conditions for estimating the rate of transfer of water between groundwater and streams (Rosenberry and LaBaugh, 2008; fig. 2). Cross-sectional areas were measured and velocity was recorded at these locations using a hand-held velocity meter to estimate discharge using the velocity-area method (Rantz and others, 1982). Stream discharge measurements are available from the USGS National Water Information System (NWIS; U.S. Geological Survey, 2022).

Streamflow gain from or loss to groundwater (seepage gain or loss) was calculated for seven sections of the White River between sites (reaches), using the Williams (2011) equation below:

Each site on the White River was upstream from a tributary confluence except for sites 2 and 5. Site 2 was the most upstream on the White River and site 5 is where Sunrise Road crosses the White River, the location of a historical USGS stream gage (12096600). Stream discharge measurement stations are shown in figure 2, and the corresponding zones and reach numbers are shown below in table 2.

Soil-Water Balance Model

The soil-water-balance (SWB) model v. 1.2 (Westenbroek and others, 2010) provided gridded estimates for groundwater recharge (fig. 3). The SWB calculates water-balance components at daily time steps for each model cell using a modified Thornthwaite Mather soil-water-balance approach. Seven spatially distributed (gridded) input datasets were used to drive SWB recharge simulations: daily climate data (precipitation, maximum and minimum air temperature), land cover, flow direction, and soil properties (hydrologic soil group and available soil-water capacity). All input and output datasets for the SWB were resampled to a uniform cell size of 10 meters (m) for the 35 m² study area. The model run was set up for January 1999–December 2020, with the year 1999 being used as the initialization period. Results were reported for January 2000–December 2020. The SWB model and output used in this study are available in Headman (2022).

Daily climate input datasets included precipitation (inches) and maximum and minimum temperature (Fahrenheit). Daily climate data were obtained from the Daymet dataset available from Oak Ridge National Laboratory (Thornton and others, 2022). The Daymet climate data were computed through interpolation from spatially referenced observation stations and available in 2-degree areas at a spatial resolution of 1 kilometer (km) for all of North America. Daily Daymet climate data were obtained for the study area for the period from January 1999 through December 2020.

The 2016 National Land Cover Database (Wickham and others, 2021) was used to characterize land cover. The NLCD is produced by the Multi-Resolution Land Characteristics consortium to describe land-cover characteristics across the United States using a 16-class classification schema at a resolution of 100 ft. The NLCD was obtained from https://www.mrlc.gov/data/nlcd-2016-land-cover-conus (Wickham and others, 2021). The NLCD data were resampled to the 10 m cell size of the SWB model using a majority sampling technique in ArcGIS (ESRI, 2021). A comparison of the resampled and original gridded datasets indicated that the spatial pattern for the principal land-cover classes in the study area were similar.

The flow direction grid was generated from light detection and ranging (lidar) elevation data at 6 ft resolution (Watershed Sciences, 2009) accessed via the Washington Lidar Portland D8 flow-routing convention of Lehner and others (2008). D8 Flow Routing is a hydrological modeling method used to simulate the movement of water through a digital elevation model (DEM) in eight flow directions. In this approach, each grid cell is assigned a flow direction based on the steepest descent, and flow is directed toward one of the eight neighboring cells.

Individual lidar files were combined and resampled to the 10 m cell size of the SWB model using a mean sampling technique in ArcGIS. The resulting elevation grid was processed to smooth over small sinks that were artifacts of data processing and the D8 flow-direction grid was then generated with the ArcGIS “flow direction” tool.

Two gridded datasets of soil properties, hydrologic soil group (HSG), and available water capacity (AWC) were compiled by the U.S. Department of Agriculture Natural Resources Conservation Service (NRCS) for the United States. The NRCS classified HSGs in four groups (A, B, C, and D) on a continuum from high infiltration capacity with low runoff potential to low infiltration capacity with high runoff potential. The AWC is the amount of water a particular soil column can hold at various depths; the AWC for the top meter of soil was used by the SWB model. Data for HSG and AWC were obtained from the NRCS Gridded Soil Survey Geographic (gSSURGO) database (National Resources Conservation Service, 2021). The HSG and AWC grids were resampled using ArcGIS raster resampling tool to 10 m cells using the majority technique for HSG data and the mean sampling technique for AWC data.

The equations used by the SWB model to calculate recharge do not have an input for contribution from glacial melt. The recharge input from glaciated areas was limited to precipitation that occurred during the model simulation. To adjust for this limitation, recharge from snow and (or) ice in areas covered by glaciers in the SWB model area was calculated using a snowmelt rate of 1.5 mm per day (as snow-water equivalent) per average degree Celsius where the daily maximum air temperature (T_max) is above the freezing point (Westenbroek and others, 2010). The landcover for perennial snow and ice, using a runoff curve number of 40 and a root zone depth of 0, is used by SWB for areas with glacial cover. Daily evapotranspiration was computed using the method of Hargreaves and Samani (1985).

Additional non-gridded inputs were required for SWB model for each combination of HSG and land cover type. These data were provided as a table and included runoff curve numbers, vegetation routing depths, maximum infiltration rates, and maximum daily recharge rates used by Gendaszek and Welch (2018), Tillman (2015), and Westenbroek and others (2010).

Stream Discharge Correction for Glaciated Areas

In glaciated areas, streamflow can fluctuate on a diurnal cycle with higher flows during the warmer hours of the day when glacier melting rates are high, and lower flows during the cooler hours of the night when glacier melting rates are low. Stream discharge measurements made during the seepage run were taken at various times over 2 consecutive days. Given the diurnal nature of glacial melting, the amount of glacial melt water contributing to stream discharge varied with the timing of measurement. Two methods were evaluated to estimate and exclude the glacial meltwater contribution from stream discharge measurements using available stream discharge data.

One method evaluated the use of continuous discharge records from a downstream stream gage to estimate the diurnal changes in glacial melt contributions to White River discharge. The nearest gage, upper White River basin (USGS gage 12097000), is about 21 river miles downstream from the park entrance. After review, this method was not useful because additional tributary inflow and travel time over the 21 river miles downstream introduced too much variability to estimate glacier meltwater contributions to base flow in the study area.

A second method evaluated stream discharge measurements collected during the seepage run to estimate the diurnal changes in glacial melt contributions to White River discharge. Site 5 was measured twice during the seepage run: at 1910 hours on September 21 and at 0854 hours on September 22. The change in discharge that occurred during the length of time between the morning and evening measurement was used to estimate the diurnal change in discharge due to glacial melt.

The rate of change in discharge throughout the day is assumed to be a linear increase with respect to time, typical of the rising limb on a simplified hydrograph showing a diurnal response to glacial melt (Singh and Singh, 2001). The relationship between the amount of time between measurements and the change in discharge at site 5 was therefore used to estimate the increase in discharge in ft³/s due to glacial melt for measurements at other sites on the White River based on the time of measurement. This method was used to adjust the discharge by the amount of time that had lapsed from the first station 5 measurement to reduce each station’s measured discharge by its approximate contribution from increased glacial melt (table 3). These discharge values were determined using the following equation:

The consistent air temperatures during the 2 days where measurements were collected allowed for the assumption that the minimum and maximum discharge was the same during these days. The measurements were then treated as having been collected in the same day for the sake of relating this elapsed time with discharge. The length of time between the morning measurement and the time each measurement was taken was used to correct the measured discharge and estimate an “adjusted” discharge (table 3).

Streamflow Gain or Loss and Base-Flow Calculations

The adjusted discharge measurements from White River sites and discharge measurements from the tributary sites were used to calculate streamflow gain and loss (see the equation in “Methods” section) and base-flow contribution to the White River for each reach (table 4).

Upon analysis of the results from the seepage run, three of the reaches were found to be gaining reaches: M2–3, C3–5, and G8–11 (table 4). Analysis of the remaining four segments showed losing reaches.

Relation of Groundwater Recharge to Groundwater Discharge to Streams

Recharge zones A–M were delineated for drainage areas that corresponded to reaches on the White River and its tributaries (fig. 2). Delineation for these zones was achieved by drawing flow lines perpendicular to topographic contours, generally starting with locations that marked the ends and beginnings of each of the reaches, to the point where the drawn flow lines met a ridge. Recharge values were determined for each zone by averaging the SWB simulated recharge grid cell values contained in each zone and converting the recharge value to ft³/s (fig. 3). Recharge from these zones was then used to estimate the groundwater discharge to each of the reaches. Zones M, C, D, L, G, J, and K corresponded to reaches on the White River and were the focus of the comparison of zone recharge and streamflow gains or losses within each zone (table 2; fig. 2). To interpret the results of this comparison, a simple flow model was applied, which is described in the section “Flow Model and Assumptions.”

Flow Model and Assumptions

For this analysis, each zone is treated as a system in which recharge is the input, or forcing. An increase in the forcing results in an increase in the water table, steepening the hydraulic gradient toward the stream, which results in an increase in groundwater flow into the stream. Conceptually, this is illustrated in figure 4A, which shows an increase in springtime recharge resulting from combined snowmelt and precipitation, followed by recharge recession during summer. The response in streamflow gain is simplified and represented by a rising limb and falling limb, each linear, which results in a simple triangle. The peak in streamflow gain lags behind the recharge forcing and is spread out temporally because of the groundwater storage capacity. Storage in groundwater is the reason that streamflow gains can occur throughout summer when recharge becomes nearly zero. The peak in streamflow gain occurs as a lagged response to the peak in recharge, which is hereafter referred to as “peak-to-peak lag time” (fig. 4A). The lag time does not represent a travel time of water molecules; rather, this is the response time corresponding to the transfer of pressure through the groundwater system. Mathematically, this process is well described by convolution, the basis of unit-hydrograph theory (Singh, 1988; Long and Mahler, 2013).

To illustrate how the concept shown in figure 4A applies to this study, a dot along the falling limb of the triangle represents a hypothetical measurement of the streamflow gain during late summer. Because this streamflow gain measurement is the only one available, the peak response time and magnitude cannot be known; however, a minimum and maximum range of the peak-to-peak lag time can be estimated, where the minimum would be concurrent with the recharge peak (peak-to-peak lag=0). It was assumed that the falling limb could not be steeper than the rising limb, an assumption that is consistent with unit-hydrograph theory (Singh, 1988; Long and Mahler, 2013), and therefore, the latest peak response in streamflow gain would be determined by an isosceles triangle that passes through the data point representing the measured streamflow gain (fig. 4). Additional assumptions:

1. the start of the rising limb is concurrent with the initial rise in the recharge rate;

2. for conservation of mass, the volume under the recharge curve is equal to the volume under the response curve; and

3. the base of the recharge curve for computing this volume is defined by a straight line from initial rise in recharge to the base of the recharge curve when it has fallen to zero (fig. 4B). Figure 4 and associated assumptions describe a simple flow model that was applied to each zone in this study to better understand and quantify how recharge-discharge relations differ for the different zones.

Flow Model Applied to Each Zone

A 4-week moving average was applied to the estimated daily recharge rate for each zone to account for the dispersive mixing of recharge water in the unsaturated zone and near the water table. This moving average was used as the recharge forcing function for this analysis. The recharge that began in late February 2020 was assumed to be the primary source of the streamflow gain in the White River during the September 2020 measurement.

The flow model was applied to three zones that correspond to gaining reaches on the White River (reaches M2–3, C3–5, and G8–11, zones M, C, and G, respectively; fig. 2). The discharge measurement, streamflow gain estimate, and corresponding zone recharge estimate from the model for each reach are shown in figure 5. The zone recharge was considered as a 4-week moving average, represented in the figures at the date that falls in the middle of the 4-week time window. The streamflow gain estimate in each of these figures shows the streamflow gain curve with its peak occurring at the maximum time from its initial rise, equal to the time for the streamflow gain rate to return to zero from its peak. This allows for comparison of peak-to-peak lag time between each of the zones.

An analysis similar to the one done for the zones on the White River was done for the zones representing each of the tributaries (zones A, B, E, F, GH, I, and K) to provide a comparison of the alluvial areas in each of the tributary streams in these zones. For these zones, the amount of gain in the tributary stream is measured by treating the headwater of the stream as having zero discharge, representing the O_U term from the equation in the “Methods” section. Therefore, the streamflow gain for the adjacent reach in each of these zones is equal to the discharge measured at the station at the downstream end of the zone. Glaciers are present in zones A, B, and F. Streamflow gain curves were estimated for these zones but due the limited ability of SWB to estimate recharge in areas with glacial cover, the results were not expected to be accurate. The zones with glacial presence in the published SWB model were slightly truncated from the full basin delineation, most notably in zone B. The same analysis performed for the main stem recharge zones, where response rates were estimated using the two areas on each side of the stream and their respective distances to the stream, was also completed for the tributary zones. This is shown in figure 6. For zone B (fig. 6B), recharge was less than the measured streamflow gain, which is further discussed later in this section.

Table 5.    

Summary of recharge calculations in zones adjacent to gaining reaches.

[Abbreviations: ft³/s, cubic feet per second; d, days; –, no data given]

Table 5.    Summary of recharge calculations in zones adjacent to gaining reaches.

Zone	Recharge peak (days from initial rise)	Recharge peak (ft3/s)	Area (d×ft3/s)	Peak-to-peak (days)
Tributary zones
A1	84	26.5	1,750	–
B1	49	21.1	873	–
E	56	25.5	1,310	48.0
F1	49	47.3	2,690	–
GH2	28	14.2	360	–
I	49	36.8	1,960	61.2
K	42	1.22	33.3	82.1
White River zones
C	49	29.6	1,580	60.1
M	63	10	528	99.4
All3	49	198	3,440	74.4

¹

Glaciers are present in zones A, B, and F.

²

Zones G and H were combined as zone GH.

³

Excludes zones A, B, and F due to glacial presence.

Reach G8–11 showed the largest gain of any of the reaches, 10.2 ft³/s (table 4). Further analysis of reach G8–11 revealed that the tributary stream in zone H enters the White River Valley alluvium at the base of the steeply sloping valley wall, where it parallels the White River for a length of about 1,500 ft prior to exiting zone H and entering the White River (fig. 2). The proximity of this tributary parallel to the White River, its location within the White River alluvium, and the large increase in base flow within reach G8–11 indicate that zone H likely discharges much of its recharge as base flow directly to the White River within reach G8–11. Therefore, the recharge for zone H was combined with that of zone G, and these two zones were analyzed together as a single zone (zone GH) associated with reach G8–11 (fig. 6E). The error associated with the streamflow gain analysis for zones G and H (92.3 and 96.7 percent, respectfully) was reduced by combining the two zones, as the error with the zone GH analysis was 82.8 percent.

Streamflow gain for zone B was more than three times larger than the peak recharge rate (fig. 6B). Discharge from the toe of the glacier was not measured, and most of the discharge at station 1 is assumed to be provided by glacier melt. Because recharge was estimated for the area downslope of the glacier, discharge at the toe of the glacier would be needed for this analysis to be applicable. Zones A and F also include glaciers that are smaller and occupy smaller proportions of the zones than zone B. This analysis was applied to those zones, while accepting that the glaciers in these zones may introduce error.

Flow Model Application to Combined Zones

To perform the same analysis for the upper White River basin as a single zone that was done for each of the individual zones within the basin, the cumulative estimated recharge for all non-glacial zones (zones C, E, GH, I, K, M) were plotted with the total gain measured between the most upstream and most downstream stream discharge measurement locations (locations 1 and 14, respectively), 28.8 ft³/s (fig. 7). Zones A, B, and F were excluded from this analysis due to the large glacial presence in the zones and the associated lack of accuracy with its SWB-modeled recharge estimate. The peak-to-peak for this area was 74.4 days, which was comparable to the peak-to-peak distance found in the analyses done for individual zones (see row “All,” table 5; fig. 7).