Improving cold-region streamflow estimation by winter precipitation adjustment using passive microwave snow remote sensing datasets

The RRB flows through two U.S. states and one Canadian province, starting at the border between North Dakota and Minnesota, and ending in Manitoba, Canada. The catchment of this north-flowing river occupies 287 500 km², and springtime ice congestions in the north result in considerable flooding because of the backwater effect of these frozen water bodies [21]. In recent decades, the RRB has experienced regular annual flooding incidents, causing national-level concern [22]. The floods from January to April are primarily driven by fast snowmelt. Significant community efforts have been expended with support from state and federal governments [23] to establish flood prediction and monitoring capabilities for residents throughout the main stem of the RRB. It is critical to establish a monitoring system for spatially distributed SWEs. Satellite passive microwave observations, with revisits twice per day, can be used to determine the daily status of the SWE throughout the basin, thereby allowing observations of the peak amount of SWE.

Figure 1 (left) depicts the location and extent of the RRB headwaters, to which this study was applied, which has an area of 13 476 km². The outlet of the RRB headwaters is located in Fargo, ND and was gauged using the USGS streamflow gauge ID 05054000. The enlarged view of the watershed in figure 1 (center) provides a topographic representation of the RRB; the elevation difference over 130 km of the river was 200 m, with an average slope of only 0.08°. The large area of the basin and the rapid increase in air temperature during the spring season resulted in abrupt flooding in the local municipalities, particularly along river banks in the Fargo metropolitan areas. An abrupt increase in the air temperature, coupled with the flat topography, caused a free water body to form from the meltwater, and small melt ponds enlarged abruptly owing to the poor drainage of the Northern Great Plains. The average maximum winter precipitation, from December to March, is approximately 100 mm SWE, which is sufficient to create a large snow mass. During wet winters, the peak SWE in the large basin can reach up to 200 mm, which is disastrous to many communities when any abrupt melting occurs in the spring. For a general depiction of the climatology of this region, figure S1 (available online at stacks.iop.org/ERL/16/044055/mmedia) demonstrates the monthly snowfall, rainfall, and air temperature averaged from 1995 to 2013 in the headwaters of the RRB.

Zoom In Zoom Out Reset image size

In this study, a semi-distributed macroscale hydrological model known as the VIC model (version 4.0.6) was used [24] in addition to a routing scheme, VIC-ROUT. The VIC model has been widely applied to assess hydrological responses to weather and climate over numerous river basins globally [for example, 25, 26]. The VIC model was used in this study for streamflow calibrations, with emphasis on the snowmelt runoff in the headwaters of the RRB in the Northern Great Plains. Detailed descriptions of the snow scheme are included in pages 6–9 of the supplementary data. Precipitation and temperature observations were provided by weather stations, and the synergraphic mapping system algorithm [27] was employed to generate gridded temperatures spatially interpolated from the point observations [26, 28]. Specifically, the precipitation data were obtained from NOAA cooperative observer (COOP) stations using standard precipitation gauges. Wind speeds were obtained from a reanalysis dataset from the National Centers for Environmental Prediction–National Center for Atmospheric Research [29]. Point measurements were linearly interpolated from approximately 1.9° to 1/8° resolution, which is similar to the grid resolution used in the AMSR-E SWE retrieval.

With the baseflow and runoff from the VIC considering snowmelt with three soil layers, classic streamflow calibration was performed by minimizing the cost function between the observed and simulated streamflows at the outlets of a watershed [30, 31]. Calibrated soil parameters were applied to the validation period to evaluate the accuracy of streamflow prediction. It is beyond the scope of this study to identify the optimal soil parameters to accurately represent the overall peak of the streamflow associated with rainfall and snowmelt.

The amount of winter precipitation in the model was adjusted with a factor to match with the amount of SWE based on the U.S. AMSR-E SWE product (25 km), compared with the 12.5 km grid cell of the VIC model. A M_factor of winter precipitation was used to scale the winter precipitation in relation to the observed AMSR-E SWE. Despite the well-known microwave saturation that occurs when the SWE exceeds 150 mm [32–34], the AMSR-E SWE offers several advantages, including long temporal coverage (2002–2011), near-daily observations, and global spatial coverage [35]. The National Snow and Ice Data Center (NSIDC) archives the microwave brightness temperature (Tb). The SWE products from the AMSR-E Tb datasets were processed based on a spectral difference between the 18.7 GHz Tb (least affected by snow) and the 36.5 GHz Tb (most affected by snow [36],). The period from 2002 to 2011 was used to encompass the global domain with a 25 km grid using the equal area scalable earth grid (EASE-Grid) format from the NSIDC (later updated to EASE-Grid 2.0 [37]). A spatially averaged ratio was obtained using a solution for linear equations between the AMSR-E based observed and the baseline simulated SWE in all grid cells throughout the hydrologic years from 2003 to 2011. The M_factor was calculated using the following equation:

$$\begin{align} & {\left. {{\text{[SW}}{{\text{E}}_{{\text{VIC - baseline}}}}} \right]_{2003 - 2011}} \cdot {M_{{\text{factor}}}} \nonumber\\ & \quad = {\left. {{\text{[SW}}{{\text{E}}_{{\text{AMSR - E}}}}} \right]_{2003 - 2011}}\end{align} \tag{ 1 }$$

$$\begin{align}{M_{{\text{factor}}}} = {\text{SW}}{{\text{E}}_{{\text{AMSR - E}}}} \cdot {\text{pinv}}\left( {{\text{SW}}{{\text{E}}_{{\text{VIC - baseline}}}}} \right),\end{align} \tag{ 2 }$$

where SWE_AMSR-E is the AMSR-E-retrieved daily SWE (mm), and SWE_VIC-baseline is the VIC-simulated daily SWE (mm) without M_factor adjustment. M_factor is determined by solving a system of linear equations with the assumption that both time series are row vectors of the same size from hydrological years 2003–2011. It is noted that M_factor is determined by considering the entire hydrologic year, and it is specific to the basin where the M_factor method is applied. A classical $A \cdot x = B{\text{ }}$solution for the linear equations is represented by the Moore–Penrose pseudoinverse [38, 39] of SWE_VIC-baseline (A) owing to the non-invertibility of its row vector. Subsequently, ${\text{pinv}}\left( {{\text{SW}}{{\text{E}}_{{\text{VIC - baseline}}}}} \right)$ is multiplied by SWE_AMSR-E (B), which is the left term of the right-hand side in equation (2), to obtain M_factor on the left-hand side. Physically, this system solution of the linear equations only accounts for days when snowfall appears for both the SWE_VIC-baseline and SWE_AMSR-E cases. Specifically, the M_factor for the headwaters of the RRB was 2.53. It is noteworthy that 2.53 was derived by applying equation (1) to the headwaters of RRB; however, its values typically vary from 2 to 3 when applied to the other subwatersheds of the RRB.

Furthermore, the winter precipitation was multiplied by M_factor during the hydrologic modeling period, i.e. 1995–2013, by assuming that the AMSR-E SWE sufficiently captured the underestimated baseline SWE even outside of the period where M_factor was calculated. The National Oceanic and Atmospheric Administration National Climatic Data Center and COOP (hereinafter NOAA COOP) weather stations and SNODAS [40] snow assimilation data can be used to replace the AMSR-E SWE; however, it is only applicable to well-observed watersheds such as the RRB, where the number of observations is abundant. However, snow undercatch problems persist in NOAA COOP stations.

Figure 2 displays three basin-averaged SWE estimates: the baseline VIC simulation, the M_factor-adjusted VIC simulation, and the AMSR-E SWE observations. The spatially averaged ratio from equation (1) during the M_factor calculation period, i.e. 2003–2011, was used as the scaling factor for the winter precipitation at all 70 grid cells in the RRB headwater region and was applied to the longer hydrologic modeling period, i.e. 1995–2013, to demonstrate the validity of M_factor outside the M_factor calculation period. A M_factor-adjusted hydrologic simulation was performed to demonstrate the improved predictability of snowmelt-driven floods. A schematic illustration is shown in a block diagram in the right panel of figure 1 to show the M_factor calculation period from 2003 to 2011. The hydrologic simulation from 1995 to 2013 was independent of M_factor calculation to calibrate the soil parameters and had a wide temporal range. A hydrologic calibration scheme was applied to two cases: a baseline VIC simulation without M_factor and a VIC simulation with M_factor. Streamflow calibrations were conducted by fitting to the observed streamflow for both cases, from January to April, to adjust the soil parameters. The two applications illustrate the degree to which M_factor affects the SWE, followed by the extent to which the winter precipitation adjustment aided by passive microwave observations improved the streamflow prediction during the subsequent months of melt-runoff.

Zoom In Zoom Out Reset image size

The calibration and validation periods were 1995–2007 and 2008–2013, respectively, and M_factor was applied to both periods. It is noteworthy that the calibration was only applied from January to April when spring snowmelt was the dominant factor determining peak streamflow. The simulated streamflow using the M_factor SWE more accurately replicated the observed streamflow during both the calibration and validation periods, compared with the streamflow from the baseline SWE. The M_factor-driven streamflow during the calibration period achieved an NSE of 0.74 for the snowmelt-runoff season. The VIC baseline streamflow was underestimated against the observed streamflow, even with the annually averaged streamflow, as reflected by the low NSE of 0.38. Additionally, the validation period showed the underestimation of the baseline streamflow simulation, but the degree of underestimation was lower than that for the calibration period. The NSE values were 0.48 and 0.11 for the M_factor and baseline streamflow simulations, respectively. The relatively low NSE during the validation period was attributed to the short validation period of only 6 years, and differences from the streamflow peak were associated with the timing of snowmelt. Furthermore, streamflow calibration was not applied to the periods October–December and May–September when snowmelt was not the main contributor of floods.

It is noteworthy that hydrologic calibration was only applied from January to April in this study. Figure 3 shows the monthly averaged streamflow performance during the hydrologic simulation period, and these results suggest that all the hydrological years contributed to a stable improvement in the streamflow predictions corresponding to January to April. However, as shown by the event-based simulations of streamflow in figure 4, the improvement in the flood prediction was apparent only during the snowmelt season within the shaded areas. Figure 4 (top) shows the baseline, M_factor-driven, and USGS-observed streamflows for the historic 1997 flood in Fargo, ND. The baseline, SWE-adjusted, and USGS-observed streamflows were plotted using the left-hand y-axis. The predicted streamflow was nearly identical to the USGS streamflow in April 1997, with a peak of 500 m³ s⁻¹, which was attributed to the increasingly adjusted SWE shown in the right y-axis, in the reverse direction (also represented in figure S2). The matching of streamflow in the spring of 1997 suggests that the adjusted amount of winter precipitation from the AMSR-E SWE may improve the streamflow prediction of the observed precipitation. This successful identification of the peak streamflow was achieved in 1997 without the availability of AMSR-E SWE. This implies that the M_factor calculated from 2002 to 2011 is also valid in 1997, thereby allowing an accurate capture of peak streamflow.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In the hydrological years of 2010 and 2011, the AMSR-E SWE was available, and the VIC baseline streamflow continued to underestimate the observed streamflow. The M_factor-adjusted winter precipitation resulted in an improved prediction of streamflow that was comparable to the USGS peaks for March 2010 and April 2011. The prediction for 2010 indicated better performances than those for 2011; this is attributable to the difference in the timing of the SWE peaks in 2011 between the AMSR-E (in February) and the baseline (in January), as shown at the bottom of figure 4. Interestingly, the baseline VIC streamflow simulation could not capture the low observed streamflow in June and July. This was because the adjusted soil parameters from January to April promoted runoff and baseflow, which are associated with the spring snowmelt, thereby resulting in increased streamflow; however, it was insufficient to reflect the observed peak in streamflow. The SWE-adjusted M_factor streamflow, however, successfully identified the observed spring peak as well as moderately dry streamflow following snowmelt floods in June and July, which are rainfall-dominated months. In contrast to the baseline, the relatively better performance of M_factor from May to September was associated with the calibrated soil properties from the M_factor simulation from January to April, which was applied equally to the other months. The relatively poor performance of the M_factor streamflow during January and February was caused by a difference between rainfall-runoff and snowmelt-runoff. Snowmelt runoff has a longer lead time than rainfall-runoff, i.e. the released water requires a longer time to arrive at the land surface; therefore, a discrepancy occurs between streamflow predictions in January and February, as well as those in March and April.