The effect of riparian vegetation on stream temperature has long been understood conceptually. Riparian canopies shade streams to various degrees, reducing incident solar radiation and helping to maintain lower temperatures than would be the case in the absence of vegetation. Riparian vegetation also tends to suppress the diurnal stream temperature range.

Numerous models have been developed to predict stream temperature (see, e.g., Sinokrat and Stefan, 1993, for a brief review). These models fall into two general classes: empirical relationships based on observations of stream temperature and stream properties (such as discharge, channel geometry, and streamside vegetation characteristics) and models that represent the energy balance of the stream, where stream temperature is the controlling state variable. The State of Washington’s Forest Practices Act, and the accompanying Forest Practices Manual (State of Washington Department of Natural Resources, 1995) uses an empirical method to predict annual maximum stream temperatures based on elevation and fractional canopy cover (see Figure 1). This figure is based on data collected for 92 sites from Western Washington streams during July and August 1987.

Although easy to use, empirical methods cannot reflect the effects of a number of factors that affect the energy balance of a stream reach hence its temperature. These factors include:

• Variations in streamflow (Figure 1 is based on data for low flow conditions in one particular year),
• Geometry of the vegetative cover (e.g., vegetation buffer width and height),
• Cumulative effects of upstream disturbances in riparian areas,
• Stream orientation effects on incoming solar radiation,
• Synergistic effects of the above parameters.

The use of physically based models to predict stream temperature once implied a level of complexity considered undesirable for management applications. However, it is now possible to represent the energy balance of a stream, especially the dominant radiative terms, explicitly through use of GIS methods that utilize digital topographic, and streamside vegetation overlays. This paper describes such a model, which consists of two components: a shortwave radiation scheme, which accounts for topography and shading due to near-stream vegetation, and stream energy balance scheme, which predicts stream temperature along a (one-dimensional) reach.

  2.0 MODEL STRUCTURE

2.1 Calculation of Incoming Short Wave Radiation:

Direct and diffuse beam solar radiation are calculated using a modified version of the Solarflux add-on for ARC/INFO (Rich et al., 1995).

Topography:

Topographic influences on incoming radiation are estimated via inputs from the basin’s digital elevation model (DEM), Julian day, latitude and longitude of the stream reach, atmospheric transmissivity and sky view factor. This topographic shading algorithm takes the form of:

(1)

Where I is the direct beam shortwave radiation, S₀ is extra-atmospheric solar constant ~ 1353 W/m², is the fraction of shortwave transmitted through atmosphere, slope = slope of pixel in direction of greatest elevation decrease, j = elevation angle of the sun, q_sun = solar azimuth, aspect = direction in which pixel drains,  is the azimuth angle, and is the sun angle above the horizon. Diffuse beam radiation was calculated according to Rich et. al., 1995. (2)

In the above equation, f is the sky view factor.
 

Forest Effects on Direct Beam Radiation:

To accurately describe the attenuation of light through the vegetative canopy, the light is partitioned into three components based on the fraction of the canopy through which it must travel before reaching the stream (Figure 2). This division allows assessment of buffer width on incoming radiation. The attenuation of each partition is calculated using Beer’s Law (Wigmosta et al., 1994), (3)

where I₀ is the above canopy direct beam radiation (calculated from Eq. 1), k is the coefficient of attenuation and LAI is leaf area index (Montieth & Unsworth, 1992).

 
2.2 Stream Energy Balance

To predict stream temperature, a finite difference, explicit numerical model STRTEMP was developed to solve the stream energy balance. Conservation of energy for the stream in its one–dimensional state (i.e., uni–directional flow) takes the following form: (4)

Where t is time, v is water velocity, x is longitudinal distance, T is water temperature, U is a dispersion coefficient along the direction of flow, m is mass of water, c_p is specific heat of water, A is surface area, and E is energy exchange per unit area with the environment.

Defining the reach as a series of continuous temporal and spatial control volumes (Figure 3) allows for the solution of the energy equation at each cell via the explicit finite difference approximation.

Solving for temperature at time t+1 for node i gives:

(7)

where A_c represents the cross sectional area.

 
Energy Transfer Terms:

The terms associated with the energy (E) flux across the stream boundary are:

• net long and short wave radiation
• latent heat flux (evaporation and condensation)
• sensible heat flux (convection)
• advection (groundwater)
• conduction (streambed heat flux)

The relative magnitudes of these components for the Deschutes River in southwestern Washington are shown in Figure 4. The net short wave radiation is calculated as described above. Net long wave radiation is estimated by: (8)

Where  Stefan Boltzman constant, T_a = air temperature, T_w = water temperature, e_w = emissivity of water, and e_a = emissivity of air.

Advection is heat transfer from groundwater, calculated by: (9)

Where  is the density of water, C_p = specific heat of water, Q_g = ground water flow, and T_g is the groundwater temperature.

Latent heat is calculated by: (10)

The variable definitions are as follows: is saturated vapor pressure at water surface temperature,  is vapor pressure of air at height z,  is the latent heat of vaporization of water, f(W) is a wind function of wind velocity at two meters (m/s). The function as defined by Ryan and Harleman and modified by Gulliver and Stefan for a sheltered stream is:

                                          (11)
where  is the virtual temperature difference. The sensible heat exchange between the air water surface is modeled after Bowen (1926): (12)

where f(W) is the same wind function described previously.

Streambed heat transfer was approximated based on Adams and Sullivan (1990) as: S_b = h_eff(T_avg-2-T_w) (13)

Where T_avg is the daily average air temperature and h_eff is the effective heat transfer coefficient.
 

Data Requirements:

The inputs required for the model are:

• hourly net short wave radiation
• hourly air temperature and mean annual air temperature,
• hourly wind speed,
• atmospheric pressure,
• average depth, width, length of the reach,
• average flow velocity,
• discharge at the top and bottom of the reach,
• water temperature at the upstream reach boundary.

  3.0 MODEL APPLICATION:

3.1 Study Sites:

Two reaches within the Deschutes River catchment in southwestern Washington were selected as study sites (Figure 5) . Meteorological, hydrologic, channel geometry, and vegetation data were taken from State of Washington Department of Natural Resources (1990). Terrain data were taken from USGS 3 arcsecond digital topography.

Table 1. Site description for model runs.

3.2 Model Runs:

The model runs consist of sensitivity tests of:

• vegetation removal effects on incident short wave radiation and stream temperatures,
• flow effects on stream temperatures ,
• sensitivity tests for effects of upstream reach temperature and reach length on predicted reach outflow temperatures,
• and comparison of predicted observed August, 1988 stream temperatures.

    4.0 RESULTS AND DISCUSSION  
4.1 Short-wave Model Experiments:

Effects of varying forest vegetation width along the stream (i.e. buffer width) on incoming short-wave radiation are shown in Figure 6a and Figure 6b for August 25^th, 1988. At the Road 1000 site, the reach orientation is predominately east - west. For the hours from 10 am until 2 pm, streamside vegetation provided substantial shade, resulting in total incoming radiation below 300 W/m² for large buffer widths. For the 3350 Road site the short wave inputs are higher even though the stream is narrower and the vegetation is taller, because the stream flows northward.

The results show that for these two sites:

• Buffer widths greater than 10 to 15 meters are generally sufficient to maintain the equivalent shading as uncut riparian vegetation.

• However, the results may be reflective of relatively short canopy heights. Streams shaded by larger trees are likely to have fewer branches on the lower trunk, and may require a wider buffer width to maintain the same shading as continuous streamside vegetation.

• Results for the 2pm run at 3350 Road suggests lower solar angles require wider buffers to block a maximum amount of solar radiation (Figure 6b). However, solar radiation at low sun angles generally does not control peak stream temperatures.

 
The direction of stream flow can have a large impact on the timing and total delivery of solar radiation. The reach at 3350 Road receives a large amount of sunlight in the midday because it flows northward and riparian vegetation does little to reduce incoming shortwave. In order to quantify this effect, total daily insolation was calculated for a series of stream orientations for the site at 1000 Road (Figure 7a).

The stream receives maximum solar radiation when oriented east west, due to sunlight entering the stream without attenuation by vegetation early in the morning and late in the day. During the middle of the day, the sun is at its highest elevation, sunlight still reaches the stream because the ratio of stream width to tree height is relatively large. Increasing the tree height to 28 meters (Figure 7b) gives less variation in the amount of solar radiation reaching the stream. However, the highest daily insolations are recorded for stream angles, which are nearly north-south. Thus the time of day the stream receives sunlight without vegetative interference drives the daily insolation cycle.
 

4.2 STRTEMP Model Runs:

Stream temperature at the upstream reach boundary was not available and therefore two different boundary conditions were used. The first holds the upstream temperature constant over the model run time. If the reach is of sufficient length, the "memory" of this condition should not be present at the reach end. If the outflow temperature is dependent on the initial boundary condition, it reflects the importance of measuring water temperatures at the beginning of the reach and the cumulative effects of temperature increases in successive reaches.

Figure 8 demonstrates the dependence of outflow temperature on inflow temperatures along a reach. As the reach length increases this dependence decreases. However, even the 1800-meter reach is not long enough to eliminate the influence of the upstream boundary condition. Figure 8 has several important implications.

• To predict outflow temperature, inflow temperature must be known.

• Influences of upstream reach temperature affected by vegetation removal will be transmitted considerably more than 300 meters downstream.

• If upstream temperatures are unknown, longer reaches are needed to predict downstream temperatures.

Figure 8 suggests that if the reach were long enough, the outlet temperature would converge to its equilibrium temperature (for the example in Figure 8, ~18C) for any inlet temperature. Alternatively, if the specified inlet temperature is close to the equilibrium temperature, the water will converge to this temperature somewhere along the reach. Figure 9 gives the time series of maximum possible temperature change at the Rd 1000 site given the climatic forcings for three reach lengths. Therefore, to accurately predict outflow temperatures, the boundary condition inlet temperature must be within this delta. Thus the second upstream boundary condition specifies the inlet temperature in equilibrium with the environment over the run time. This allows the inflow temperature to be close to the reach equilibrium temperature. This boundary condition and a reach length of 1800 meters reduce the dependence of inflow temperatures and allow prediction of outflow temperature.

Figure 10 shows the total canopy removal effects at the Road 1000 site for an 1800-meter reach.

Figure 11 demonstrates the importance of flow conditions on peak temperatures. Flow conditions of 0.5m³/s (approximately equivalent to 7Q10 for this reach), increases peak temperatures equivalent to the effect of total canopy removal.

Comparison of predicted versus observed stream temperature is shown in Figure 12. The model predicts daily peak temperatures above 16^oC quite well (within 1.25 ^oC). The inclusion of a streambed conduction term could improve the low temperature prediction.   5.0 CONCLUSIONS

• Removing the riparian canopy along the Road 1000 reach would results in a daily peak temperature increase of about 3^oC as compared with mature canopy vegetation.

• Differences between predicted temperatures for the observed August 1988 flows and 7Q10 were about as large as predicted temperature difference for vegetation removal given 1988 flows.

• The effect of consecutively harvested reach riparian areas is reflected by the dependence of outflow temperatures on inflow temperatures within the 300-meter reach. In addition, measuring reach inflow temperature is crucial for predicting the absolute reach outflow temperature for 300-meter reach lengths.

• The impact of stream orientation and buffer widths is an important determinant in the dominant energy factor affecting stream temperature, short-wave solar radiation.

• The STRTEMP model was found to predict daily maximum stream temperature within 1.5 ^oC of the measured temperature for the faster velocity and higher discharge reach on the Deschutes River (Rd 1000).

   6.0 REFERENCES

Adams, T.N., K. Sullivan "The Physics of Forest Stream Heating: A Simple Model" Weyerhauser Research Report, Project # 044-5002/89/1  

Bowen, I.S., "The ratio of heat losses by conduction and by evaporation from any water surface, Phys. Rev., Ser. 2, 27, 779-787, 1926

Chapra, S.C. and Canale, R.P., Numerical Methods for Engineers, McGraw-Hill Inc, 1988. pp812  

Dubayah, R., J. Dozier, and F. W. Davis, 1990. Topographic distribution of clear-sky radiation over the Konza Prairie,
Kansas, Water Resources Research, 26, 1190, 679-690.

Gulliver, J.S., and H.G. Stefan, "Wind function for a sheltered stream", J. Environ. Eng., 112(2), 1-14, 1986.  

Monteith, J.L. and Unsworth, M.H., 1990. Principles of Environmental Physics, Edward Arnold, 291 pp.

Penman, H.L., 1948. "Natural Evaporation from Open Water, Bare Soil and Grass," Proc. R. Soc. London, vol. A193, pp. 120-145.

Raphael, J.M., 1962. "Prediction of Temperature in Rivers and Reservoirs," Journal of the Power Division, Proceedings of the American Society of Civil Engineers, July.
 
Rich, P.M., W.A. Hetrick, S.C. Saving, "Modeling Topographic Influences on Solar Radiation: A Manual for the SOLARFLUX Model", Los Alamos National Laboratory, Manual LA-12989-M
 
Sinokrat, B.A., and H.G. Stefan, 1993. "Stream temperature dynamics: Measurements and modeling", Water Resources Research, July.
 
State of Washington Department of Natural Resources, Washington Forest Practices Board, 1995. "Standard methodology for conducting watershed analysis", Washington Forest Practice Act Board Manual, Version 3.0.
 
State of Washington Department of Natural Resources, 1990. "Evaluation of prediction models and characterization of stream temperature regimes in Washington", Timber, Fish and Wildlife Project Temperature Work Group, Report TFW-WQ3-90-006.