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MODELING THE POTENTIAL EFFECTS OF CLIMATE CHANGE ON WATER TEMPERATURE DOWNSTREAM OF A SHALLOW RESERVOIR, LOWER MADISON RIVER, MT MICHAEL N. GOOSEFF1 , KENNETH STRZEPEK2 and STEVEN C. CHAPRA3 1

Department of Geology and Geological Engineering, Colorado School of Mines, Golden, CO 80401, U.S.A. E-mail: [email protected] 2 Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO U.S.A. 3 Department of Civil and Environmental Engineering, Tufts University, Medford, MA, U.S.A.

Abstract. A numerical stream temperature model that accounts for kinematic wave flow routing, and heat exchange fluxes between stream water and the atmosphere, and stream water and the stream bed is developed and calibrated to a data-set from the Lower Madison River, Montana, USA. Future climate scenarios were applied to the model through changes to the atmospheric input data based on air temperature and solar radiation output from four General Circulation Models (GCM) for the region under atmospheric CO2 concentration doubling. The purpose of this study was to quantify potential climate change impacts on water temperature for the Lower Madison River, and to assess possible impacts to aquatic ecosystems. Because water temperature is a critical component of fish habitat, this information could be of use in future planning operations of current reservoirs. We applied air temperature changes to diurnal temperatures, daytime temperatures only, and nighttime temperatures only, to assess the impacts of variable potential warming trends. The results suggest that, given the potential climatic changes, the aquatic ecosystem downstream of Ennis Lake will experience higher water temperatures, possibly leading to increased stress on fish populations. Daytime warming produced the largest increases in downstream water temperature.

1. Introduction Water temperature is an important water quality parameter in aquatic ecosystems, impacting chemical reaction rates, dissolved oxygen content of water, and aquatic flora and fauna growth rates and mortality. Water temperature in streams depends on both climactic and initial (discharge and temperature) conditions. Modeling stream water temperatures has been accomplished at various levels of model complication, as data availability is generally a limiting factor. At the simplified extreme, numerous studies have related air temperature to water temperature (e.g., Stefan and Preud’homme, 1993; Webb and Nobilis, 1997; Mohseni et al., 1998; Mohseni and Stefan, 1999; Caissie et al., 2001), using either regression analysis (linear and nonlinear) over daily, weekly, or monthly water and air temperature or empirical equations. At the other end of the spectrum, several studies have also approached stream temperature modeling with analytical and numerical methods to Climatic Change (2005) 68: 331–353

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quantify heat fluxes (e.g., Brown, 1969; Vugts, 1974; Brocard and Harleman, 1976; Bowles et al., 1977; Ford and Stefan, 1980; Joss and Resele, 1987; Bravo et al., 1993; Sinokrot and Stefan, 1993; Kim and Chapra, 1997; Webb and Zhang, 1997). Although regression models may reveal relationships between daily, monthly, or annual mean air and water temperatures, extreme water temperature episodes are best studied with deterministic models, which account for the heat fluxes that affect water temperature. Fishes are sensitive to changes in water temperature as their body temperature changes with the change in temperature of their environment. Fish species that thrive in cold water temperatures (≤24.3 ◦ C) (Eaton and Scheller, 1996), generally populate alpine river systems. Elevated water temperature can affect fish in several ways. Firstly, it can affect their mortality rate if immediate water temperatures are too high. It is reported that rainbow trout populations show no growth at water temperatures of 23 ◦ C (EPA, 1995). Secondly, fish species’ food supply may be more susceptible to water temperature fluctuations than the fish themselves (Hogg et al., 1995), which affects the fish population dynamics and feeding habits. Thirdly, fish spawning and egg development may be affected at lower threshold water temperatures than those that affect adult or more mature fish directly. A maximum water temperature of 12.8 ◦ C is recommended for spawning and egg development for trout (non-lake trout) and salmon (Nemerow, 1974). Water temperature also dictates the amount of dissolved oxygen that water can hold. Increased water temperature results in reduced capacity of dissolved oxygen, which can affect an entire aquatic ecosystem. Additionally, the rate of change in water temperature can also adversely change metabolic and other biological process rates in fish, possibly becoming lethal (Logue et al., 1995; Nemerow, 1974). Although it is desirable to avoid large-scale fish kills from elevated water temperatures, it is also important to understand the lower thresholds of other physiological change, rather than just lethal water temperature limits. Sub-lethal thermal injuries include hyper-excitability, loss of equilibrium, and loss of motor activities. It is possible for these injuries to become irreversible, eventually ending in death (Logue et al., 1995). Although elevated temperatures in natural waters may occur from scenarios such as thermal effluent mixing in low flows, or extremely warm atmospheric conditions, there is also cause for concern that global climate change may result in general atmospheric warming, and therefore elevated stream water temperatures (Mohseni et al., 2003). There are several hypotheses regarding the impact of increased global atmospheric carbon dioxide (CO2 ) concentrations and other atmospheric chemistry changes on global climate, air temperatures, and hydrology. The current understanding of global circulation and atmospheric chemistry is not complete enough to precisely predict future conditions, but even with current knowledge, general circulation models (GCMs) have been designed and run under

MADISON RIVER TEMPERATURE AND CLIMATE CHANGE

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various assumptions. Although no two GCMs seem to agree completely with each other, most suggest that air temperatures will increase over the continental US under increased atmospheric CO2 concentrations. The potential for hydrologic changes in response to climate change is evident and has received attention with respect to both hydrologic processes (Gleick, 1986; Gleick, 1987a; Gleick, 1987b; Lettenmaier and Gan, 1990; Stefan et al., 1993; Stefan and Sinokrot, 1993), and aquatic ecology (Magnuson et al., 1990; Matthews and Zimmerman, 1990; Meisner, 1990; Toon, 1990; Hogg et al., 1995; Eaton and Scheller, 1996; Rahel, et al., 1996; Stefan et al., 1996; Farge et al., 1997; Hauer et al., 1997; Reid et al., 1997; Schindler, 1997; Van Winkle et al., 1997). The effects of global warming on freshwater ecosystems are expected to have a negative impact on freshwater ecosystems, and until recently, there has been little quantification of the impact (Rahel et al., 1996). Schindler et al. (1996) found that climate change deepened boreal lake thermoclines, reducing lake trout habitat. Stefan et al. (2001) have quantified potential changes to fish habitat in 209 North American lakes owing to climate warming, and their results suggest that habitat for cold and cool water fishes will become drastically reduced under conditions of atmospheric CO2 concentration doubling. Other studies have attempted to characterize the effects of climate change on fish habitat using distributed geographic information system modeling (Clark et al., 2001; Keleher and Rahel, 1996). Water temperature models have been built and utilized to study several processes: flood hydraulics interaction (Bowles et al., 1977), thermal electric power plant discharge (Morse, 1970), spatial and seasonal variability of heat fluxes (Webb and Zhang, 1997) and the threat of global climate change (Sinokrat and Stefan, 1993; Fagre et al., 1997). Various theoretical methods and numerical models have been applied to the heat budgets of many streams in an effort to better understand and predict water temperature dynamics. But, due to limited data and resources, most previous models worked on a scale of days or more. Most meteorological datasets are limited by data collection frequency. Daily measurements and predictions of daily average water temperatures from limited data are not good indicators of extreme thermal water quality if there are large diel swings in water temperature, which occur on timescales shorter than a day. This study sets out to develop a temperature model for the Lower Madison River, calibrate the model, and then apply GCM output to the meteorological input of the temperature model and analyze potential changes to water temperature, specifically with respect to fish habitat. It is the goal of this paper to roughly quantify the potential impact that global climate change may have on extreme water temperature events in aquatic ecosystems. In doing so, we recognize the limitations of this modeling approach including the uncertainty in GCM output, and uncertainty in our water temperature model. Thus, the results presented here are an indication of the effects of climate change on water temperature changes in the Lower Madison River, and are not intended to be exact predictions.

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Figure 1. Location map of the Lower Madison River. Scale is approximate.

2. Study Area and Methodology 2.1.

SITE DESCRIPTION

The Madison River is a world renowned trout fishery in southern Montana (Figure 1). The headwaters of the Madison River flow from Yellowstone National Park. The Upper Madison River meanders through a wide valley for over 80 km until it reaches Ennis Lake. Ennis Lake is a small reservoir (roughly 56.7 × 106 m3 ) that was constructed in 1906 for power generation. Initially the power was used for the mining industry of Butte, Montana. In the early 1990s, it was run by Montana Power Company (MPC) and used for run-of-the-river power production. Ennis Lake is a small impoundment with a mean depth of only 3.69 m, and an area of approximately 1538 ha. Over an approximate 2-week detention time, the reservoir effectively raises the temperature of the water entering the Lower Madison River. The average water temperature at Valley Garden, a site 4.8 km upstream of Ennis Lake on the Upper Madison River, for July 1994 was 16.5 ◦ C, whereas average water temperature at the dam outlet was 19.5 ◦ C.


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On the Lower Madison River, several fish kills have been reported, two during the 1950’s, and two in the extremely warm summer of 1988 (Jourdonnais et al., 1992). The 1950s fish kill events cannot be decisively linked to elevated water temperatures, but the 1988 fish kills are thought to be related to elevated water temperatures in the Lower Madison River. 2.2.

STREAM WATER TEMPERATURE MODELING

The temperature of a body of water can be calculated by assessing the heat sources and sinks as well as the volumetric changes of the body (Brown, 1969; Chapra, 1997). Water temperature is a function of the amount of heat in a body of water at any one moment and the volume of the water body: Tw =

H ρC V

(1)

where, Tw is the water temperature (◦ C), H is heat (cal), ρ is the density of water (g cm−3 ), C is the specific heat of water (cal g−1 ◦ C−1 ), and V is the volume of water (cm3 ). To facilitate modeling a river, we assume that a one-dimensional, finite difference scheme represents the system. Further, we account for dynamic changes in flow and atmospheric conditions. Kinematic wave theory was utilized to characterize the movement of changing flow downriver: ∂ Q ∂ Ac + =0 ∂x ∂t

(2)

where, Q is the flow rate (m3 s−1 ), and Ac is the cross sectional area of the channel (m2 ). The kinematic wave theory assumes that the gravity force and the friction force acting on the water are in balance. Thus, the water is being kept from gravitationally accelerating by an equal friction force, acting in the opposite direction. Flow and cross sectional area are related by Manning’s equation: 1 Ac So n P 2/3 5/3

Q=

(3)

where, n is the empirical Manning’s coefficient, P is the wetted perimeter (m), and So is the bed slope (m m−1 ) for uniform flow, which we believe is a valid assumption for this river. Bed slope values were obtained from USGS topographic maps and were found to be 0.005 from Ennis dam to Bear Trap Creek, 0.004 from Bear Trap Creek to Greycliff. Rearranging Equation (3) and solving for cross sectional area as a function of flow, Ac = α Q 3/5

(4)

336 where,


n P 2/3 3/5 α= √ (5) So Differentiating Equation (4) for use in Equation (2), ∂ Ac 3 ∂Q 3 = α Q 5 −1 (6) ∂t 5 ∂t so that Equation (2) becomes: ∂Q 3 ∂Q 3 + α Q 5 −1 =0 (7) ∂x 5 ∂t Because this model is solved in an explicit scheme, the Courant condition was satisfied for the model to be stable. This time step was computed for each model simulation, based on the highest discharge of the input hydrograph. Thus, for our spatial discritization (dx) of 100 m, stable time steps were on the order of 40–50 s. The amount of heat in a parcel of water changes over time due to thermodynamic surface fluxes and advection of the water flow. The derivative of heat content with respect to time is made up of two advective heat fluxes and a total surface heat flux component: ∂H Hi−1 Q i−1 Hi Q i = − + (Jtot As ) (8) ∂t Vi−1 Vi where, Jtot is the total surface heat flux (cal cm−2 d−1 ), As is the surface area of the control volume (cm2 ) and i is the control volume index number. Here, we model six thermodynamic heat exchanges occurring on the control volume of water at any one time: Jtot = Jsol + Jan + Jsed − (Jbr + Jcc + Je )

(9)

where, Jsol is the shortwave solar heat flux, Jan is the atmospheric longwave radiation flux, Jsed is the sediment heat flux, Jbr is the longwave back radiation flux from the water, Jcc is the conduction/convection heat flux, and Je is the evaporation/condensation heat flux, all heat fluxes are in units of cal cm−2 d−1 . The shortwave solar radiation (Jsol ) can be directly measured and input into the model. Cloud cover, topographic, and vegetation canopy shading are assumed to be taken into account in the measurement. Atmospheric longwave radiation is a heat flux (Jan ) that is applied to the water from the atmosphere, as a function of air temperature and air vapor pressure, based on the Stefan-Boltzmann law: √ Jan = σ (Tair + 273)4 (A + 0.031 eair )(1 − RL ) (10) where, σ is the Stefan-Boltzmann constant (11.7 × 10−8 cal cm−2 d−1 K−4 ), Tair is the air temperature (◦ C), A is the atmospheric attenuation coefficient (0.5–0.7, Thomann and Mueller, 1987; we assume A = 0.6), eair is the air vapor pressure (mmHg), and RL is the atmosphere reflection coefficient (0.03). The atmo√ spheric attenuation term (A + 0.031 eair ) and the reflection term (1 − RL ) are both


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generally