Modeling of peak inflow dates for a snowmelt dominated basin Evan Heisman CVEN 6833: Advanced Data Analysis Fall 2012 Prof. Balaji Rajagopalan
The Dworshak reservoir, a project operated by the Army Corps of Engineers with a number of uses, including flood control. It is located in the Idaho Panhandle, on the north fork of the Clearwater River, a tributary of the Snake River. During the spring, it is operated as a flood control project with space allocated for the system downstream on the Columbia River, and for the local region of the Clearwater River and it s confluence with the Snake River. The basin is snowmelt dominated, with the largest monthly inflows for the entire year occurring from April through June. It is sparsely populated, with the majority of the basin being forested. Inflows to the reservoir are calculated from the storage and outflow at the dam, as there are no currently operating upstream streamflow gauges. As part of the operations during the spring snowmelt, a decision to shift system flood control space to the Grand Coulee Dam is considered each spring. By storing extra water and being able to release it to return to the normal flood control season prior to the refill period, the dam is able to supplement environmental flows for fish migration in the Columbia basin. The impacts of the storage shift on the operations of the Dworshak reservoir are not well understood; thus, a determination of when the shift is appropriate would be of great benefit. To answer this question, it may be of use to be able to predict not just the volume of spring inflow, as is currently done by the Corps with the NWD2005 principal components regression models, but also the size and the temporal characteristics of the spring snowmelt. These factors may better inform the decision to make the storage shift. The timing and shape of the spring snowmelt hydrograph may influence the decision to shift flood control space as some situations may make it difficult to return to the un-shifted state, without violating other criteria, in particular, a high inflow period coinciding while the dam
operators are trying to return to the required lower elevation after the shift may cause the dam to violate limits on the outflow from the reservoir. The NWD2005 model and previous modeling efforts Several statistical or regression based models have been used for predicting basin inflows in the past. Different techniques, all derivative of a linear regression, have been applied, and the models have been recalibrated or changed over time as data collection stations used for predictors become available or are disbanded. The current model, known as NWD2005, and previous models are outlined and compared in the Dworshak Water Supply Forecast report by Randal Wortman, of the Corps Northwestern Division. The NWD2005 principal component regression models are used to predict the total volume of inflow from April through July each year. The model is calibrated on data collected from 1961 through 2004. A separate regression equation is used for the forecast for the first of each month prior to the completion of the snowmelt season, starting in October and going through June. The October model relies only on the Southern Oscillation Index (SOI) for September as a predictor, while November and December take into account accumulated Table 1: NWD2005 forecast model parameters for each lead-time. Forecast Date Predictors Oct Nov Dec 1- Jan 1- Feb 1- Mar 1- Apr 1- May 1- Jun September SOI X Precipitation at HQSI X X SWE Elk Butte, ID X X X X X X SWE Hemlock Lake, ID X X X X X X SWE Hoodoo Basin, MT X X X X X X SWE Peirce RS, ID X X X SWE Shanghai Summit, ID X X SWE Lost Lake, ID X X Inflow January X X X Inflow February X X Inflow March X Inflow April X Inflow May X
precipitation as well. The September SOI was chosen for the NWD2005 model as it had the most correlation with the spring inflow, as shown in Figure 4 of the Corps of Engineer s report on the model (Wortman, 2005). January through June use the September SOI along with the measured snow water equivalence (SWE) at various SNOTEL sites around the basin. The variables used in each basin are summarized in Table 1. A problem with the current model is that it tries to predict the total volume of April through July inflow, yet there are models for May 1 st and June 1 st, which are already into the melt season. While the previous month s runoff is included as a predictor in this model, they know nothing about the change in snowpack from the previous month, only the current conditions. Trying to predict the remaining runoff, rather than trying to predict the runoff that has already occurred could potentially improve the performance of the May and June models. Examination of spring hydrographs for prediction of peaks Understanding and predicting the timing of the spring snowmelt presents a number of challenges: the behavior of the snowmelt does not always follow a single large pulse, and rainon-snow events can confound the prediction of the timing of the peak. Initially an attempt was made to understand how the September SOI impacts the timing of the events, and here the issues with the shapes where encountered. It appears that SOI cannot be used to predict the timing of the peak, as is shown in the following Figures 1 through 3, showing the hydrographs discretized over daily, weekly, and monthly maximum. In Figure 4 and Figure 5 where daily streamflow plots from El Niño and La Niña events are shown. In these plots, it can be seen that behavior of the daily streamflow hydrograph varies between El Niño years and La Niña years, with higher peaks in the La Niña years. La Niña years also appear to have multiple significant peaks and more brief peaks that may suggest a rain-on-
snow event. The daily time series for La Niña years appears to have more day-to-day variability than El Niño years, and by computing lag-1 auto-correlation for each year s daily time series, this effect can be seen in figure 6. There is some potential to use the SOI as a covariate for the autocorrelation while trying to match the behavior of these time-series using an auto-regressive approach. From looking at the composite plots of all maximums by time period, it seemed that a weekly sum of streamflow was plotted with both the November and December precipitation at Headquarters, ID, in an attempt to see if the precipitation impacts the timing as a result of the impact on antecedent moisture in the soil. As only water years from 1997 to 2011 are available for the precipitation dataset, fewer years are considered than for the SOI. These results are shown in Figures 7 and 8. From both looking at the boxplots of maximum inflow dates grouped by both SOI and precipitation in the previous months, there appears to be very little influence on the timing of the peak from either of these variables. Both variables do exhibit an impact on the size of the peak, which is expected as they are used to predict the total spring inflow. As neither variable appears to be a good predictor, no further analysis was conducted. The measured Snow Water Equivalent was not compared to peak inflows. Future directions for hydrograph time-series analysis Several ideas are being considered to further the prediction of when a peak may occur. First, SWE at SNOTEL sites should be considered, which was not done here. It may be possible that since the variables used in this study, SOI, and November and December precipitation, are not independent of the accumulated SWE, SWE may not provide a better prediction of when the peak will occur.
Second, it would be helpful to consider more variables that will need to be measured during the runoff season, such basin temperatures, in the form of the number of nights above freezing, the previous month s SOI, or month-to-month change in snowpack. These variables may not help improve the predictions required to make a decision on the flood control shift, but may provide for more warning during the season if the shift is no longer appropriate. It may be helpful to run an operational model of the basin, in both a shifted and an unshifted mode, from which information about which years cause the violation of operational policies can be used to find specific attributes of the spring inflow that need to be studied. One candidate that could improve decision-making is to trying to predict the inflow for each month using a principal components analysis, with the data field being the set of monthly inflows during the snowmelt season. This temporal disaggregation approach could provide more information about the timing without specifically trying to predict the timing of the peak inflow. Conclusions From this brief exploration of the data, it has been found that daily streamflow is an inappropriate temporal scale for trying to model when the peak spring inflow will occur due to spurious noise. It has also been found that pre-season indicators, such as the Southern Oscillation Index and the precipitation during November and December will not work for attempting to predict the timing of the peak. Using the weekly time-scale appears that it will provide a good balance between smoothing the data and not aggregating maximums into too few locations for predictions.
150 200 250 300 Daily Spring Inflows to DWR Blue points = positive SOI; Red points = negative SOI Days (MAR to AUG) 150 200 250 300 El Niño Neutral La Niña 25 30 35 40 45 0 100 200 300 400 500 600 Weekly Spring Inflows to DWR Blue points = positive SOI; Red points = negative SOI Days (MAR to AUG) Inflow (kaf) 25 30 35 40 45 0 100 200 300 400 500 600 El Niño Neutral La Niña Figure 1: Daily streamflow hydrographs with ENSO events highlighted by colored lines through maximum points. Figure 2: Weekly streamflow hydrographs with ENSO events highlighted by colored lines through maximum points.
3 4 5 6 7 8 0 500 1000 1500 2000 Monthly Spring Inflows to DWR Months (MAR to AUG) Inflow (kaf) 3 4 5 6 7 8 0 500 1000 1500 2000 El Niño Neutral La Niña Figure 3: Monthly streamflow hydrographs with ENSO events highlighted by colored points
Plot with WY 1974 highlighted. Plot with WY 1975 highlighted. Sept. SOI: 1.2 Sept. SOI: 1.1 Plot with WY 1976 highlighted. Plot with WY 1989 highlighted. Sept. SOI: 2.1 Sept. SOI: 1.8 Plot with WY 2009 highlighted. Plot with WY 2011 highlighted. Sept. SOI: 1.2 Sept. SOI: 2.2 Figure 4: La Niña year hydrographs - Note multiple peaks and high variability in time series.
Plot with WY 1977 highlighted. Plot with WY 1983 highlighted. Sept. SOI: 1.1 Sept. SOI: 1.7 Plot with WY 1992 highlighted. Plot with WY 1995 highlighted. Sept. SOI: 1.5 Sept. SOI: 1.6 Plot with WY 1998 highlighted. Sept. SOI: 1.4 Figure 5: La Niño year hydrographs plotted, exhibiting less variability and less distinct peaks.
Lag 1 Relationship lag 1 covariance 20 40 60 80 100 120 140 El Niño Neutral La Niña 1 0 1 2 SOI Figure 6: Lag-1 autocorrelation with El Niño and La Niña years highlighted.
Weekly Spring Inflows to DWR (vs. Nov. Precip) Inflow (kaf) 0 100 200 300 400 500 600 dry normal wet 25 30 35 40 45 Weeks (MAR to AUG) Blue points = wet; Red points = dry Figure 7: Weekly hydrographs plotted with peaks highlighted by tercile of precipitation in previous November. Weekly Spring Inflows to DWR (vs. Dec. Precip) Inflow (kaf) 0 100 200 300 400 500 600 dry normal wet 25 30 35 40 45 Weeks (MAR to AUG) Blue points = wet; Red points = dry nflow Figure provided 8: Weekly the hydrographs best filter plotted to find with significant peaks highlighted streamflow by tercile peaks. of precipitation As such, in previous the weekly December. data
Bibliography Pagano, Thomas C. The Role of Climate Variability in Operational Water Supply Forecasting for the Western United States. Dissertation, University of Arizona. Ann Arbor: ProQuest/UMI, 2005. (Publication No. AAT 3162815.) Wortman, Randall T. Dworshak Water Supply Forecast: 2005 Update to Statistical Forecast Equations. U.S. Army Corps of Engineers: Northwestern Division, Columbia Basin Water Management Division (2005). Web 15 Oct. 2011.