Hydrology Modeling in Brief
Within Willamette Envision, we model the storage and flux of water from rain or snow, into soils, groundwater, and streams using a sub-model developed for the project called the Willamette Hydrology Model (WHM). WHM is, in part, based on the widely-used rainfall-runoff model called HBV (Bergström and Singh 1995; Bergstrom et al., 2001; Seibert, 1997). For a more detailed explanation of the hydrologic modeling framework concept, refer to Vache et al. (in review).
WHM translates daily values of meteorological input (including precipitation, air temperature, wind speed, and radiation) into a spatially distributed estimate of water storage and release. It is run on a daily timestep over the full 90-year WW2100 modeling timeframe, and results in a dynamic estimate of the response of the hydrology to the evolving landscape. The hydrologic model is comprised of four overall elements describing key features of the system.
The mountain snowpack - Each winter, snow accumulates in the higher elevations of the Willamette River Basin (WRB). This natural reservoir serves to store a proportion of the winter precipitation, releasing into streams (and reservoirs) during the spring. We simulate the seasonal evolution of the mountain snowpack with a hybrid approach that includes the influence of both air temperature and radiation. The temperature- and radiation-driven melt depends directly on vegetation, so that the snowpack changes as forest disturbance and growth occurs over the scenario timeframe.
Watershed runoff - Incoming precipitation and snowmelt are stored within a set of conceptual reservoirs representing soil and groundwater (Fig. 1). WHM defines the spatial distribution of those reservoirs based primarily on a set of approximately 9000 sub-watersheds, defined by the National Hydrography Dataset (NHD). Water is released from the reservoirs based on algorithms developed as part of the HBV model (Bergström and Singh 1995; Bergstrom et al., 2001; Seibert, 1997). Biophysical processes such as evapotranspiration respond to changes in land cover simulated by the forest and human systems models.
Instream routing and reservoir storage - WHM uses a kinematic wave approach to simulate the flow of water within the stream network. The spatial pattern of the network was taken from NHD, and allows the model to estimate stream discharge throughout the watershed. Manmade reservoirs are a key feature of the Willamette river system, and WHM simulates operation of the 13 largest reservoirs – those that are managed by the U.S. Army Corp of Engineers (USACE) as the Willamette Project. Refer to the reservoir operations page for more details about reservoir modeling.
Water Allocation and water use - The use of water by human society is the fourth key feature of the hydrology of the Willamette. WHM models the movement of water through the stream network, while also allowing water to be added or removed at specific points in accordance with Oregon water law. Human water demand is estimated in the WW2100 economic models as the outcome of household and farm demand relationships. Refer to the agricultural land and water use and urban water use pages for more information about these models.
Figure 1. Hydrologic modeling within Willamette Envision involves movement of water through a set of conceptual reservoirs simulating soil and groundwater (diagram by K. Vache).
Willamette Envision models both biophysical and human aspects of water use. The primary biophysical use modeled is evapotranspiration (ET) — water movement from soil and plants into the atmosphere. ET is calculated on a daily basis for all modeling polygons and responds to changes in landcover modeled by the forest and human systems modeling components. ET is modeled as follows:
Forest (~70% of the basin land area in 2010 starting conditions) - For forested lands, WHM models ET using a Penman-Monteith expression that includes both transpiration from vegetation and soil evaporation. The Penman-Monteith expression includes vegetation canopy, represented by leaf area index (LAI), as an independent variable. Thus, forest areas respond to changes in canopy cover simulated by the forest dynamics models. For example, as the forest in a modeling polygon matures, leaf area index (LAI) rises, which leads to a higher ET. When a fire occurs, the LAI decreases to almost zero. Refer to Turner et al. (2016) for more details about modeled vegetation shifts and modeling ET in the Willamette upland forests. Some forest IDUs (about 2% of basin area) were left out of the state-and-transition model due to gaps in the initial condition data. Those forest IDUs are modeled for ET using Penman-Monteith, an LAI of 1, and a canopy height of 10 meters.
Agricultural lands (~22% of the basin land area in 2010) - On agricultural lands, modeling of ET takes into account crop type and growth stage, and augmentation of soil moisture due to irrigation. The sequence for a modeling polygon is as follows. First, the human systems modeling components set the crop type and determine whether the land will be irrigated that year. Next, at a daily timestep, WHM determines crop growth stage and water requirements. The model then estimates actual crop water use (ET) by taking into account the amount of water available in the soil. Soil water can come from natural sources (e.g., precipitation) or it can be supplemented by irrigation if water is available (as determined by the water rights model). Modeling of crop water demand and ET is based on the crop cover approach as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 (Allen, Pereira, Raes, & Smith, 1998) and further developed by Allen and Robison (2007). Refer to Jaeger et al. (in prep) for more details.
Urban and other non-forested, non-agricultural lands (~8% of the basin land area in 2010) - Elsewhere, WHM approximates ET using a Penman-Monteith expression using a LAI of 1.0, and a canopy height of 10 meters, that does not change. In urban areas (~5% of the basin land area in 2010) modeling of ET also takes into account outdoor water use for lawns and gardens. Municipal water use is modeled by the human systems models as a unit for each urban growth area. A fraction of the water diverted for municipal use is added to ET. This fraction varies seasonally so that it is very small in winter and higher in summer when outdoor water use peaks.
The rainfall-runoff model within WHM has nine calibration parameters related to snowfall, runoff, and percolation. Calibration of these parameters affects the flux between the conceptual reservoirs shown in Figure 1. We used the Parameter Estimation program, PEST, to identify sets of the 9 parameter values which produce good correlations between modeled and measured datasets. The calibration period was 1980-1994 and we used the following measured data sets in the calibration process: USGS stream gage records, NRNI synthetic flow data, Oregon SNOTEL snow survey records, and measured inflow data for federal reservoirs. We ran the model for the calibration period using meteorological forcings representing simulated historical climate conditions from the MIROC5 global climate model (MACAv1-METDATA).
We divided the WRB into a number of sub-basins for calibration purposes, ultimately using 14 different sets of parameter values in different parts of the WRB. Thirteen of the parameter sets were produced by Oregon Freshwater Simulations in 2016; one parameter set was taken from prior calibration work by Eric Watson and Heejun Chang at Portland State University in 2015. Our use of PEST was an adaptation and refinement of the methods used by Watson and Chang (PSU) in 2015.
The main analysis steps within PEST are as follows: (1) PEST selects a set of parameter values, (2) it runs the WHM model, and (3) it calculates a value representing the divergence of the simulation results from the historical stream gage records. This process is repeated with different sets of parameter values in a systematic exploration of the parameter space. The process terminates when successive adjustments to the parameter values fail to reduce the divergence by a specified amount. The model may exhibit equifinality: different sets of parameter values may produce equally good simulation results.
Accurate simulation of the inflows to the WRB reservoirs is important to the success of the WW2100 model as a whole, so we identified nine reservoir drainages to be individually calibrated using PEST as the first step in our process. Parameter values for the remaining parts of the WRB were selected using a variety of methods in subsequent steps. For a more detailed description of model calibration, refer to Jaeger et al (in prep).
Because our focus in WW2100 was on water scarcity, calibration focused on low flows and reservoir inflows. The model was less able to accurately predict high flows, and users should use caution when making interpretations about flood events and winter peak flows.
As of summer 2016, Willamette Envision does not include a detailed groundwater model and instead relies on the simpler approach of a conceptual groundwater reservoir that is part of HBV, and includes a calibration parameter, which represents groundwater recharge. Because of the simplified groundwater model, we do not model water scarcity for groundwater withdrawals. We simulate water withdrawals from groundwater, but the model does not impose a specific limit on them.
In addition, we do not model potential future changes in groundwater supplied by mountain springs in the High Cascades. Instead, we simulate springflow by adding constant discharge to High Cascades catchments that reflect measured spring flows (Jefferson et al., 2007; Grant & Lewis, 2016). The addition of High Cascades groundwater is held constant throughout the simulations. This assumption is based on measured flows in spring-fed mountain sub-basins.
As of summer 2016, Willamette Envision does not model water quality or water temperature. We are developing an energy balance stream temperature model and hope to incorporate it into future versions of Willamette Envision. WW2100 did include some offline field measurements and modeling of the potential effects of increased water temperature on mainstem fish population. Read about that analysis on the fish and stream temperature section of this website.
Water Budget Calculations
One of our goals for the hydrologic analysis was to determine how the flow of water into and out of the WRB might change in response to changing climate and water demands. WHM allowed us to calculate a water budget for the WRB and estimate how the inputs and outputs to that budget might change over the 21st century. Here we describe the calculations we made to determine the water budget using output from Willamette Envision.
All calculations were performed using daily values that were then averaged over each month of the year. All values were calculated and reported as fluxes (cm3/y per cm2 of the WRB, so cm/y). Most of us are familiar with precipitation as cm/y, but all other inputs, stores, and outputs of water can be reported in the same way. This allowed us to easily compare basinwide precipitation, storage, human diversions of water, and so forth. Monthly, seasonal, and annual fluxes are all reported in the same units of cm/y. Therefore, the annual precipitation can be calculated simply as the sum of the monthly precipitation.
Precipitation is the sum of all rain and snow in the basin divided by the basin area. Evapotranspiration (ET) is all ET in the WRB. The ET related to human uses (municipal and agriculture) is included in the basinwide number and indicates the fraction of total ET based on human uses. Environmental flows are those in the Biological Opinion [U.S. Fish and Wildlife Service, 2008, Appendix B, p. 12, Table 9.2-1] for the Willamette River at Salem. These are the flow objectives for "adequate" and "abundant" water years. We did not include upstream environmental flows because these would be duplicates for the purpose of the water budget. Reservoir storage was calculated as the difference between inflow and outflow each month. Snow was calculated as the difference between snow water equivalent (SWE) on the first of each month and the first of the previous month. Municipal water use was calculated endogenously within Willamette Envision. The ET for municipal uses was calculated as the total water use each month minus the municipal indoor water use, which we estimated each year from Jan. 3 to Feb. 3. Agriculture ET was calculated within Willamette Envision. Storage of water in soil moisture and groundwater was calculated to balance the monthly water budget of the basin. The model does not include evaporation from open water such as reservoirs and lakes.
The seasons “Summer” and “Winter” were chosen to be of the same length of time, six months. No single six-month period uniquely qualifies as “Winter” or “Summer”, but we chose Winter to be defined in the water budget as November 1 through April 30. This aligns approximately with the historical snow storage season. We defined “Summer” as the other six months of the year. This seasonal definition is equivalent to “dry” and “wet” season in the WRB (Chang and Jung, 2010).