Identifying stream temperature variation by coupling meteorological, hydrological, and water temperature models

Abstract

In this study, we demonstrate a physically based semi-Lagrangian water temperature model known as the River Basin Model (RBM) coupled with the Variable Infiltration Capacity (VIC) hydrological model and Weather Research & Forecasting Model in the Mississippi River Basin (MRB). The results of this coupling compare favorably with observed water temperature data available from six river gages located in the MRB. Further sensitivity analysis indicates that the mean water temperatures may increase by 1.3, 1.5, and 1.8°C in northern, central, and southern MRB zones under a hypothetical uniform air temperature increase of 3.0°C. If air temperatures increase uniformly by 6.0°C in this scenario, then water temperatures are projected to increase by 3.3, 3.5, and 4.0°C. Lastly, downscaled air temperatures from a global climate model are used to drive the coupled VIC and RBM model from 2020 to 2099. Average stream temperatures from 2020 to 2099 increase by 1.0 to 8.0°C above 1950 to 2010 average water temperatures, with non-uniform increases along the river. In some portions of the MRB, stream temperatures could increase above survival thresholds for several native fish species, which are critical components of the stream ecosystem. In addition, increased water temperatures interact with nutrient loadings from sources throughout the MRB, which is expected to exacerbate harmful algal blooms and dead zones in the Gulf of Mexico.

1 |. INTRODUCTION

Stream temperature is an important physical property of rivers. Streamflow and water temperature affect many aspects of water quality, aquatic life, harmful algal blooms, and freshwater ecosystems. In addition, river and water temperature influence the cooling water use, and as a result are key factors for thermoelectric power production.

Stream temperatures are influenced both by the amount of heat exchange at the air/water interface and the temperature of the contributing hydrologic components to the stream reach such as groundwater, surface runoff, and snowmelt inputs (Ficklin et al., 2012; Mohseni & Stefan, 1999; Webb & Nobilis, 1997). Stream temperature responds to solar radiation which tends to be correlated with air temperature for most regions (e.g., Ducharne et al., 2007). However, attempts to extend the air–water temperature relationship to snow-dominated areas has not been robust. Snowmelt in the spring results in runoff that temporarily lowers stream temperatures even though seasonal air temperatures are warming (Brown & Hannah, 2007; Mohseni & Stefan, 1999). Due to the air and stream temperature relationships, increases in air temperature expected from future climatic changes are thought to raise stream temperatures. However, the potential of these future stream temperature increases has, to date, not been systematically explored.

Historically, streams have been warming with increasing air temperatures over the past several decades. For large low elevation European and North American rivers, several studies found an increase in stream temperature of 0.01–0.1°C/year (e.g., Moatar & Gailhard, 2006; Webb & Walling, 1992). Correspondingly, several studies considering mountainous North American streams have reported annual stream temperature increases of 0.03–0.5°C/year (e.g., Hari et al., 2006; Pekarova et al., 2008). A study to estimate future temperatures of the Tigris River (one of the largest rivers in the Middle East) under an increasing air temperature scenario of 2.0°C resulted in a 0.9 and 1.5°C increase in water temperature at Baeji and Baghdad, respectively (Al-Murib et al., 2019). Ren et al. (2020) discovered that water temperature decreased in summer and increased in winter, and there was a time delay in water temperature processes in reservoirs in the Yellow River, China.

Robust estimates of water temperature are important for understanding stream ecology, yet poorly understood. Fish that are sensitive to water temperature changes have experienced substantial declines in the past century. Higher water temperatures reduce native fish productivity and can exceed the maximum temperature tolerance of these species (Tornabene et al., 2020). Warmer freshwater conditions can affect water quality and electric power plant generation efficiency, including the ability to meet stream discharge standards at those power plants (Forster & Lilliestam, 2011). Thus, for effective management of water ecosystems, estimates of water temperature at high temporal and spatial resolution are necessary.

There are stream temperature models that accounts for energy exchanges between air and water, heat exchanges between land and streams (Li et al., 2015). However, to our knowledge, previous studies have not considered the dynamic interactions among the air, land, and water in estimating surface water temperatures. This study is unique because we realistically represent these interactions and maintain internally consistent mass balance among the processes. We then apply this modeling system to estimate water temperature changes in the past (1950–2010) and future (2020–2099) throughout the Mississippi River Basin (MRB) using the coupled Weather Research & Forecasting (WRF) model with the Variable Infiltration Capacity (VIC) model, linked to the River Basin Model (RBM) (Yearsley, 2009).

The MRB covers more than 40% of the United States (U.S.) and its waters drain into the Gulf of Mexico (GoM) which is inhabited by 100 globally important aquatic species. The GoM experiences annual dead zones in the late summer and early fall, in part due to water temperature increases. Increased water temperatures accelerate the growth of algae, which strip oxygen from the water creating zones that are uninhabitable by many of the native aquatic species (Malone & Newton, 2020). Many changes in the MRB indicate this basin is undergoing a system-wide response to climate change, land-cover change, and human activities (Bjoernsson, 2011).

As the largest basin in nation, the MRB spans a wide range of climatic regions with snow-dominated, transitional, and rain-dominated regions. This study examines the effect of climate change across this large watershed and its differing environments.

The questions that motivate this research are as follows: (1) How well does the coupled air–land–water system simulate water temperature in the MRB? (2) How does the water temperature vary with regions, and which region of the MRB shows the greatest changes in water temperature from 1950 to 2010? (3) What is the sensitivity of surface water temperatures to air temperatures and how do the temperatures differ across the MRB regions? (4) How will future climate change impact water temperatures spatially and temporally in the MRB?

This study demonstrates the use of a multimedia coupled modeling system in skillfully simulating water temperatures for historical and future time periods. This is the first time a linked multi-media modeling system (WRF, VIC, and RBM) is applied to MRB, the nation’s largest water basin, at as high as 1/16° spatial resolution. This assessment of climate change impacts on water temperatures will inform the Environmental Protection Agency’s (EPA) Gulf Hypoxia task force, and is broadly applicable to water management, nutrient load investigation, power plant production, and the protection of natural ecosystems.

2 |. STUDY AREA

The MRB (Figure 1) encompasses the Mississippi River, which is the third longest river in the world, flowing 2340 miles (3770 km) from its source in Lake Itasca in northwestern Minnesota to the GoM. The MRB spans a wide range of climatic regions with snow-dominated, transitional, and rain-dominated regions. Published air–water temperature associations are not applicable to the more complex temperature regimes of the snow-dominated sub-basins within the MRB (Brown & Hannah, 2007; Mohseni & Stefan, 1999). To represent different climate zones, the MRB was divided into three sub-basins based on latitude (Figure 1b): northern area (snow-dominant zone with a latitude higher than 42°), central area (transition zone with a latitude from 37.5° to 42°), and southern area (rain-dominant zone with a latitude less than 37.5°).

FIGURE 1.

Study area –Mississippi River Basin (MRB) (a), with the six calibration United States Geological Survey (USGS) gage stations and the three sub-basins (upper, lower, and Missouri Basins), and the three climate zones (b).

3 |. METHODS AND EXPERIMENTAL DESIGN

In this study, the VIC model was coupled with the WRF model, and then coupled with the RBM to model daily water temperatures throughout the MRB. In this study, “coupled” describes the approach of using the output from one model to drive another model “offline” on a daily timestep. In this case, variables from the WRF model were used to run the VIC model, and output from the VIC model was used to run the RBM. The coupled modeling system was run to simulate a 61-year historical period (1950–2010) and an 80-year future period (2020–2099). Thirty years of available U.S. Geological Survey (USGS) water gage measurements (1950–1979) was used for calibrating the models, and a subsequent 31 years of gage measurements (1980–2010) was used for model evaluation.

3.1 |. The VIC model

Consistent, long-term hydrological observations are not available for the MRB. Thus, the VIC (version 4.6) model was utilized to simulate streamflow for a daily timestep at a spatial resolution of 1/16° (about 6.5 km) for the period from 1950 to 2010. The methods used to calibrate the model are reported in more detail in Tang and Piechota (2009).

The VIC model is a macroscale, grid-based water and energy balance model, which has been successfully applied to many large river basins with plausible results (Clark et al., 2015; Liang et al., 1994; Maurer et al., 2001; Mishra & Cherkauer, 2011; Tang & Dennis, 2014). Distinguishing features of the VIC model include the sub-grid variability of soil moisture, land surface vegetation, precipitation, and topography in use of different elevation bands. The elevation bands inside grid cell are used to improve the model’s performance in areas with different topography, especially mountainous regions, where the effects of elevation on land cover might be lost. The VIC model, in general, simulates robust daily and monthly streamflow.

The VIC model is driven by meteorological data (e.g., temperature, precipitation, and wind speed), land cover, and soil parameters. When these input datasets are accurate, the model closely produces daily surface flow, baseflow, soil moisture, and snow accumulation (Clark et al., 2015; Maurer et al., 2001). The water accumulated and transported downstream is simulated using a routing model (Route 1.0) that generates streamflow and finally reaches river systems in the current study. To be specific, surface runoff and baseflow are routed along the stream network to the basin outlet using the unit hydrograph principle within the grid cells. The accumulated waterflows travel through the stream channel by using linearized St. Venant’s equations. Detailed description of the routing model can be found in Lohmann et al. (1998).

3.1.1 |. VIC model calibration and evaluation

The VIC model was calibrated at six USGS gage stations (Figure 1) for which streamflow observations were available from 1950 to 2010. These stations were chosen for availability of long period of both streamflow and water temperature (Section 3.2.1). The VIC model calibration includes six parameters: (a) the infiltration parameter which controls the partitioning of rainfall (or snowmelt) into infiltration and direct runoff; (b) the second and third soil layer thicknesses, which affects the water available for transpiration and baseflow, respectively; and (c) $D{\mathrm{s}}_{\text{max}},D\mathrm{s}$, and $W\mathrm{s}$ are used to estimate baseflow. $D{\mathrm{s}}_{\text{max}}$ is the maximum baseflow velocity, $D\mathrm{s}$ is the fraction of maximum baseflow velocity, and $W\mathrm{s}$ is the fraction of maximum soil moisture content of the third soil layer at which nonlinear baseflow occurs. These three baseflow parameters determine how quickly the water stored in the third soil layer is evacuated as baseflow (Liang et al., 1994).

A 30-year period (1950–1979) of the 61-year record was utilized for the calibration process. This 30-year period encompassed a range of extreme climate conditions (e.g., flood and drought), and normal years for testing the model’s performance. A separate 31-year period (1980–2010) was used for model validation. That period also encompassed a range of climatic conditions under which we evaluated the model’s performance. Two standard statistical techniques, the root mean square error (RMSE) and the coefficient of determination ($R^2$), were used to test and evaluate the accuracy of the model simulations:

$$\text{RMSE}=\sqrt{\frac{\sum _{i=1}^n{\left(x_{i-}{y}_i\right)}^2}{n}},$$ (1)

$$R^2=1-\frac{\sum _{i=1}^n{\left(x_i-y_i\right)}^2}{\sum _{i=1}^n{\left(x_i-\frac{\sum _{i-1}^n{x}_i}{n}\right)}^2},$$ (2)

where $n$ is the total sample size, $x_i$ and $y_i$ are the instantaneous observed and simulated values (streamflow/water temperature here), respectively.

3.2 |. Water temperature model

Figure 2 shows an overview of the RBM used for simulating water temperatures in the MRB. The RBM is a process-based one-dimensional stream temperature model that solves the 1D-heat advection equation using the semi-Lagrangian (mixed Eulerian–Lagrangian) approach (Yearsley, 2009). The RBM was initially developed for sub-basins of the Columbia River (Yearsley, 2012). The RBM was applied to entire MRB for the first time at a 1/16° (~6.5 km) spatial resolution in this study. Modifications were made because the MRB is characterized by different thermal and hydrological regimes and anthropogenic impacts. Effects of anthropogenic heat discharges on simulated water temperatures were incorporated using global gridded thermoelectric water use datasets and representing thermal discharges as point sources into the heat advection equation. This results in the following 1D-heat advection equation:

$$\rho C_p\frac{\partial \left(T_{\mathit{nom}}{A}_x\right)}{\partial t}=\partial C_p\frac{\partial }{\partial \xi \xi }\left(K_L{A}_x\frac{\partial T_{\mathit{nom}}}{\partial \xi \xi }\right)+S+\mathrm{\Phi },$$ (3)

where $\rho$ is the density of water, $C_{\mathrm{p}}$ is the specific heat capacity of water; $T$ is the water temperature, $A_{\mathrm{x}}$ is the cross-sectional area of the stream or river channel, $K_{\mathrm{L}}$ is the longitudinal dispersion coefficient, $S$ is a source term, $\mathrm{\Phi }$ is advected energy from tributaries or groundwater, and $\xi$ is the Lagrangian coordinate given by:

$$\xi =x-x_0-{\int }_{t_0}^{t}udt,$$ (4)

where $x$ is the Eulerian coordinate, $x_0$ is the position of the flow cell at time, $t_0$, and $u$ is the cross-sectionally average speed. $\mathrm{\Phi }$ is calculated by:

$$\mathrm{\Phi }=\frac{\rho C_{\mathrm{p}}{Q}_{\mathrm{t}\mathrm{r}\mathrm{b}}{T}_{\mathrm{t}\mathrm{r}\mathrm{b}}}{D},$$ (5)

where $Q_{\text{trb}}=\mathrm{a}\mathrm{d}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}$ from tributaries or groundwater (m³/s), $T_{\text{trb}}=\mathrm{a}\mathrm{d}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{d}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}$ from tributaries or ground water (°C), and $D$ is the average water depth in a cross-section of the channel. $S$ is given by:

$$S=H_{\mathrm{a}\mathrm{i}\mathrm{r}–\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}},$$ (6)

where $H_{\mathrm{a}\mathrm{i}\mathrm{r}–\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$ is the net exchange of thermal energy across the air–water interface (J/s/m²), and includes shortwave radiation, longwave radiation reflection, evaporation heat flux, and conductive heat flux, which can be computed using meteorological data, such as barometric pressure, cloud cover, wind speed, air temperature, and relative humidity.

FIGURE 2.

Framework of the stream temperature model (Yearsley, 2012). Hcond, conductive or convective heat flux (J/m²/s) (the flux resulting from temperature differences between the atmosphere and river); Hevap, evaporative heat flux (J/m²/s); HnL, longwave atmospheric radiation (J/m²/s); HnS, shortwave solar radiation (J/m²/s); $Q_{\text{effl}}=\mathrm{a}\mathrm{d}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}$ from heat dumps of thermoelectric power plants (m³/s); $Q_{\text{sub}}$, flow from the subsurface; $Q_{\text{trb}}$, advected flow from tributaries (m³/s); RBM, River Basin Model; $T_{\text{sub}}$, the advected temperature from the subsurface; $T_{\text{trb}}$, advected temperature from tributaries or subsurface; $T{\mathrm{w}}_{\text{effl}}$, the advected temperature from heat dumps of thermoelectric power plants (°C).

3.2.1 |. Water temperature model calibration and evaluation

The RBM model was calibrated at the same six USGS gaging stations (Figure 1) for which streamflow observations were available from 1950 to 2010. The observed water temperature data were obtained from the National Weather Service of the National Oceanic and Atmospheric Administration. RBM was set up using the output from the VIC model simulation as input. The RBM calibration was performed using an optimization routine to find the correct Mohseni parameter derived from historic stream temperature, and Leopold parameters derived from streamflow (Yearsley, 2009).

3.3 |. WRF Model

The WRF model is a weather prediction system designed to serve climate forecasting and atmospheric research needs (Skamarock, 2004). The model simulates the variables used for the physics-based calculations in VIC and the RBM such as radiation, the land-surface parameter, and cloud microphysics. WRF uniquely bridges the gap in traditional mesoscale numerical weather prediction and micro-scale modeling over a wide range of temporal scales (Skamarock, 2004). In the study, WRF3.5 was utilized to generate the meteorological data for the VIC model.

3.4 |. Coupled model system

The VIC model was first run using observed meteorological data and calibrated to obtain a good match between the simulated streamflow and the observed streamflow obtained from USGS stream gage measurements. The six calibration parameters (Section 3.1.1) were finalized and used in the following VIC coupling with WRF runs. A contiguous set of WRF simulations were used to create the forcing data sets for the VIC model and RBM models. Subsequently, an offline linkage of WRF and VIC was performed with VIC maintaining the calibrated parameters established above. The output (surface runoff and baseflow) from the VIC model was then provided to an offline routing model to simulate channel flow, depth, width, and flow velocity for the Mississippi River. The routing outputs were the inputs for the RBM models. Figure 3 shows the frame of the coupling system. The channel output parameters with climate forcing, including air temperature, shortwave and longwave radiation, and wind speed, were used to drive the RBM.

FIGURE 3.

Framework of the coupling WRF, VIC, and RBM models.

3.5 |. Experimental design

The coupled WRF with VIC and RBM models were run from 1950 to 2010 at a daily timestep and 1/16° spatial resolution over the 70,000 grid cells in the MRB. Due to the topographic variability, the model used up to five equal-area elevation bands with a vertical interval of approximately 400 m. Three different model scenarios were made:

1. Base scenario: precipitation and temperature data from the WRF model were used as the forcing data from 1950 to 2010.

2. Fixed precipitation scenario: The precipitation forcing data were fixed, but daily temperature was uniformly increased by 3.0 and 6.0°C.

3. Future climate change scenario: Downscaled climate data from a global climate model (GCM) from 2020 to 2099 are used to drive the coupled VIC and RBM.

For future climate changes, the future time period was divided to three different periods, 2020–2049 (P2), 2050–2079 (P3), and 2080–2099 (P4). The projected climate model was Hadley Centre Coupled Model (HadCM3) (Collins et al., 2001), which is a coupled atmosphere–ocean model, developed at the Hadley Centre in the United Kingdom. The HadCM3 was one of the major models used in the Intergovernmental Panel on Climate Change Third and Fourth Assessment Report, and also contributes to the Fifth Assessment. Many GCMs require flux adjustment when simulating the climate, whereby often large fluxes of heat and salinity are introduced at the interface between the ocean and the atmosphere components of the model, and such adjustments are clearly unphysical. However, the HadCM3 requires no flux adjustments, and has a stable and realistic present-day mean climate (Collins et al., 2001). That is why the HadCM3 was chosen for this study. The A1 emission which describes a future world of very rapid economic growth with global population that peaks in mid-century and declines thereafter, was used in the Hadley model. The downscaled HadCM3 climate datasets were obtained from Maurer’s lab (Maurer et al., 2007).

4 |. RESULTS AND DISCUSSION

4.1 |. Calibration results

4.1.1 |. VIC model calibration results

The results of the calibration are presented in Table 1, which compares the monthly VIC modeled streamflow with the observed streamflow at Wolf Point, Saint Paul, Pierre, Bonneville, Memphis, and New Orleans stream gage stations. The results for Bonneville, MO are shown in Figure 4. The comparisons of the two streamflow datasets demonstrated similar results which revealed that the seasonal cycles in streamflow were well captured for the six stations. For the Pierre station, the VIC model overestimates peak streamflow at the peak, which can be explained by irrigation withdrawals. The model also overestimates the flows in 1950, which could possibly be due to the initialization of the model. Streamflow was slightly underestimated for the Memphis station. The maximum error between simulated and observed data sets is less than 8%. The $R^2$ are as high as 0.95 and 0.92 at Memphis and New Orleans stations, and the values range from 0.88 to 0.96 across the stations (Table 1). Overall, the monthly hydrographs closely match the observations, with model simulations capturing the time of the peak flows, which indicates that the VIC model is suitable for simulating daily streamflow in the MRB.

TABLE 1.

Coefficient of determination (R²) and the root mean square error (RMSE) between simulated and observed water temperature and streamflow in the MRB.

Station locations	Year (water temperature/streamflow)	R2 (streamflow%a/water temperature)	RMSE
Wolf Point, MT	1950–1980	0.85/0.88	7.63%/3.50
Saint Paul, MN	1950–1980	0.92/0.95	5.32%/2.86
Pierre, SD	1950–1980	0.87/0.93	3.25%/3.33
Bonneville, MO	1950–1980	0.95/0.96	2.15%/2.12
Memphis, TN	1950–1980	0.93/0.95	1.55%/1.51
New Orleans, LA	1950–1980	0.92/0.92	1.68%/2.73

^aWe calculated the percentage of the RMSE for streamflow due to the wide range of values of streamflow as $\text{RMSE\%}=\sqrt{\frac{\sum _{i=1}^n{\left(x_{i-}{y}_i\right)}^2}{n}}$.

FIGURE 4.

Calibration results of streamflow at Bonneville, MO from the VIC model (a, c) and water temperature (b, c) from RBM.

4.1.2 |. RBM model calibration results

After calibration of the VIC model was completed, the RBM was calibrated by comparing the observed and simulated water temperatures (Table 1). The RMSE values between observed and simulated daily stream temperatures ranged from 1.51 to 3.50°C for the majority of the observation stations, indicating the usefulness of the RMB model. The lowest (1.51°C) RMSE is at Memphis station, and highest (3.50°C) is at Wolf Point station, which is mainly because of the dominant influence of snowmelt in the station at the location. Errors are largest during the summer months of July through September. Lowest RMSE values were present during December and February.

Water temperature was simulated realistically during the snowmelt period at Saint Paul and Wolf Point stations even though the stations are strongly affected by snow. The RBM slightly overestimated the water temperature during spring but, overall the magnitude is within a reasonable range. Good agreement was achieved between simulated and observed water temperatures for most of the time in Pierre, Bonneville, and Memphis, stations. The modeled water temperature for the Memphis station is slightly underestimated during the summer and autumn and overestimated during spring. In Wolf Point, the peak summer water temperature was not as well simulated as in other years, especially in July and August. In general, the model tends to overestimate the water temperature early in the Summer season, especially in May, but overall good agreement was also observed in New Orleans station for most seasons.

Overall, the $R^2$ ranged from as high as 0.92 and 0.93 for the New Orleans and Memphis stations, to as low as 0.85 and 0.87 for the Wolf Point and Pierre stations. The main differences between the simulated and observed water temperatures occurred during winter when the model simulations tend to overestimate the water temperature, which may be explained by the model assumptions of constant inflow groundwater temperature (12.0°C) (Yearsley, 2012). Furthermore, the RBM tends to underestimate the temperatures in October and November, which corresponds to more extreme (and harder to predict) conditions, cold air temperatures, and high-water flows. Even though there is bias in some time periods, it is still clear that the model successfully captures the stream temperature at the spatial and temporal variations over the MRB as demonstrated by the high $R^2$. This indicates that the model captures the temporal and spatial variability over the monthly time scale. In general, the simulation water temperature corresponds closely with the observed water temperature for the stations along the river.

4.2 |. Simulated stream temperature

The daily stream temperature was simulated for the 60-year simulation period, and monthly and annual stream temperatures were calculated from these daily stream temperatures. Figure 5 shows the daily water temperatures for the Water Point and Baton Rouge stations over the study period because the two stations represent two most different geographic locations and climate regimes. Regardless of the variation, the ability of the model to capture the annual cycle of water temperatures stands out. The extreme daily water temperatures in 1968 and 2008 are captured by the model for both stations. Similarly, monthly water temperatures for 1970 and 2010 were captured for both stations as well (Figure 5).

FIGURE 5.

Results of water temperature at Water Point, MT, and Baton Rouge, LA. (a, b) Daily temperatures from 1950 to 2010 (red dashed line is average across all years). (c–f) Daily water temperatures for 1968 and 2008; (g–j) monthly averages for 1970 and 2010 for Water Point and Baron Rouge, respectively.

The freezing water temperatures (0°C) at Water Point during January and February were captured by the model, and even the low air temperatures (reaching −20°C) that were influenced by the high turbulence of the flowing water and surface ice cover were captured by the model. The water temperatures peaked in July 1968 and 1970, and in August 2008 and 2010. The low water temperatures in June were due to heavy precipitation during that period. The annual cycle of water temperatures at Water Point station are characterized by freezing in January and February, warming in March reaching a high in July, and then dropping through December. The average water temperature was about 1.5°C higher in 2010 than in 1970.

At Baton Rouge station, daily water temperatures were between 0 and 5°C during January and February. The air temperatures reached a high during July, and as expected, the water temperature peaked within 7 days to 2 weeks later. The highest water temperatures were seen in August 1968, 1970, 2008, and 2010. The water temperature increased as it flowed south to its outlet at the GoM, with the highest average water temperature in the Southern MRB.

The simulated annual mean water temperatures over the 60-year historical time period for the three climate areas (northern, central, and southern) are shown in Figure 6. Figure 6a shows the annual water temperatures from 1950 to 2010, and Figure 6b shows the monthly average water temperatures from 1950 to 2010. Water temperatures in the southern area are much higher than in the other regions. For the southern area, water temperatures are over 20°C from May to October, and average between 22 and 25°C. However, the average water temperature varies between 8.0 and 15°C for the central areas.

FIGURE 6.

Simulated water temperatures for the MRB from 1950 to 2010. (a) Annual averaged water temperatures for northern, central, and southern MRB regions, (b) monthly average (all years) of water temperatures for the three regions.

We mapped water temperatures across all years for the historical (1950–2010) and future (2020–2099) time periods for each 1/16° grid cell along the Mississippi river (Figure 11). The map suggests that the magnitude of the water temperature is highly variable spatially. As expected, the minimum water temperatures can be seen at the headwaters of the river, while the maximum water temperatures are seen at the outlet of the river, increasing by about 3.0°C in the downstream direction.

FIGURE 11.

Comparison of historical (1950–2010) and future (2020–2069) water temperatures in the MRB.

4.3 |. Sensitivity of water temperature to changes in air temperature

Water temperatures are expected to increase as air temperatures increase. To quantify water temperature increases resulting from air temperature increases, the coupled modeling system was run with air temperatures increased uniformly across all grid cells by 3.0°C (T3) and 6.0°C (T6). All other parameter values were kept the same.

The water temperature response to the air temperature increase was compared at daily, monthly, and annual scales from 1950 to 2010 (Figures 7–9). Figure 7 shows the mean monthly water temperature for the northern and southern areas, black lines are the base scenarios and dashed red lines are the T3 scenarios. To see the details, the differences are also plotted in Figure 7 for the years of 1960 and 1990. The averaged changes are 2.3°C for the northern area, and 2.7°C for the southern area. A moving, 2-year window of average annual water temperature was also applied across the 60-year sample to account for short-term fluctuations and highlight long-term variables. The 2-year moving averages change by 1.6 and 2.2°C for the northern and southern areas, respectively. Similarly, Figure 8 shows the water temperature response when the air temperature is uniformly increased 6.0°C. The 2-year moving water temperature averages are around 3.7 and 4.6°C for the northern and southern areas, respectively. Average monthly water temperature with air temperature increases 3.0 and 6.0°C in the northern (Figure 9a), central (Figure 9b), and southern area (Figure 9c) are shown in Figure 9. The least sensitive water temperature response happened in the winter of northern area and summer in the southern area.

FIGURE 7.

Results of water temperature with air temperature increase 3.0°C in the northern and southern area. (a, b) Daily water temperature for the northern and southern areas under Base and $T$ scenarios. (c–f) Monthly water temperature in 1960 and 1990 for northern/southern area. $T_{\mathrm{w}},T_{\mathrm{a}}$, water temperature under base scenario; $T_{\mathrm{w}},$ $T_{a+3}$, water temperature when air temperature increases 3.0°C.

FIGURE 9.

Results of water temperature with air temperature increase 3.0 and 6.0°C in the northern (a), central (b), and southern area (c). $T_{\mathrm{w}},$ $T_{\mathrm{a}}$, water temperature under base scenario; $T_{\mathrm{w}},$ $T_{a+3}$, water temperature when air temperature increases 3.0°C; $T_{\mathrm{w}},$ $T_{a+6}$, water temperature when air temperature increases 6.0°C.

FIGURE 8.

Results of water temperature with air temperature increase of 6.0°C in the (a) northern and (b) southern area. (c, d) Daily, (e, f) monthly water temperature for the northern and southern areas under base and T6 scenarios in 1960 and 1990. $T_{\mathrm{w}},T_{\mathrm{a}}$, water temperature under base scenario. $T_{\mathrm{w}},$ $T_{a+6}$, water temperature when air temperature increases 6.0°C.

The water temperature differences are very minor between the Base and T3 scenarios because air temperatures are still below zero even though they increased by 3.0°C in 1960. Water temperatures increased as high as 4.8°C in 1990 because the winter of the year is one of the warmest winters for the past 50 years. In comparison, the least sensitive water temperature response happened in the summer in the southern area. During the summer, the heat exchange between the air-water interface stops when air temperatures reach as high as 30°C due to significant increased evaporation from water surface. This, along with increases in intense precipitation events, lowers the water temperature.

Water temperatures for the 2 years of 1960 and 1990 are summarized in Figures 6 and 7. Overall, the basin mean annual water temperatures were most sensitive to air temperatures in the southern area, with the highest increases in water temperatures of 2.6 and 5.1°C occurring in this area when air temperatures were increased by 3.0 and 6.0°C, respectively. The lowest water temperature increases of 0.8 and 1.9°C occurred in the northern area when air temperatures were increased by 3.0 and 6.0°C, respectively.

To gain insight on the spatial variability of water temperatures in the MRB, we plotted the mean monthly water temperatures for the base, fixed precipitation (only temperature is increased by 3.0 and 6.0°C), and future climate change scenarios for the northern, central, and southern areas (Figure 10). It is interesting to note that the patterns for the northern and central areas are similar with higher water temperature sensitivity to air temperature changes happening in the summer, whereas water temperature sensitivity is greatest in the winter for the southern area.

FIGURE 10.

Comparison of monthly average water temperatures for P1 (1950–2010), P2 (2020–2049), P3 (2040–2079), and P4 (2080–2099).

Overall, water temperature increases were climate zone dependent, with the largest water temperature increase in the southern area, and the lowest water temperature increases in the northern area. In some high elevation zones in the northern area, water temperatures remain below freezing despite that air temperatures are increased by 3.0°C/6.0°C. Thus, the water temperatures are more resilient to air temperature increases at the headwaters of the Mississippi River.

4.4 |. Sensitivity of simulated temperature to projected future air temperature

The impacts of future climate change on stream temperature were evaluated by comparing historical (1950–2010) (P1) with future simulations (2020–2099). To address the sensitivity of water temperature to climate change, the statistical downscaled projected climate data were used to simulate future water temperature changes for 2020–2049 (P2), 2050–2079 (P3), and 2080–2099 (P4).

The mean monthly water temperature difference between P3 and P1, and P4 and P1 is plotted in Figure 10. The results show water temperature increases by 4.2°C on average for P3, and 6.1°C for P4. By contrast, the 2-year average of simulated water temperature increases by 2.3°C for P3, and 5.8°C for P4. The maximum increase in the water temperature is as high as 11 and 15°C for P3 and P4, respectively. The larger snowmelt and lower streamflow contribute to most of the water temperature increases under the future climate change scenarios.

The monthly average water temperatures for P1, P2, P3, and P4 are shown in Figure 11. As expected, the largest differences are chronological (differences between P4 and P1 are largest, followed by P4 and P2, etc.). In general, the months of April and May experience the largest water temperature increases with less of an increase in winter. The water temperatures are more resilient to air temperature increases in the summer because more evaporation occurs at higher air temperatures, which lowers the water temperatures. Water temperatures increase as much as 6.0 and 8.0°C for P3 and P4, respectively. By contrast, average summer stream temperatures increased by 2.5°C during P3, and 4.5°C during P4, which can lead to harmful algal blooms and other negative impacts to aquatic life.

Spatial maps of water temperatures for the historical and future projections are shown in Figure 11. The past and the future water temperatures vary spatially. The central area experiences the greatest seasonal changes in water temperature in response to air temperature increases (warming). Water temperatures show greater spatial differences between the climate areas, with the largest warming occurring in the southern area, where snowmelt is no longer part of the hydrological cycle. Mean annual water temperatures are projected to increase the least (1.3°C) in the northern area, and the most (5°C) in the southern area (Figure 11).

5 |. CONCLUSION AND DISCUSSION

In this study, we couple a meteorology model (WRF) with a land and stream routing model (VIC) to provide the input data needed to run a water temperature model (RBM). The RBM was modified to apply it to the larger MRB at finer spatial and temporal resolutions. This coupled/linked modeling system was used to evaluate the sensitivity of stream temperatures to air temperature increases that could result from future climate change at a high spatial resolution (1/16°). This study addresses the need for mass and hydrologically consistent, physically based estimates of water temperature changes for use in the GoM Hypoxia analyses and temperature-related discharge and wastewater treatment applications. The main contributions of this study are as follows:

1. Possible first-time simulated water temperatures at long term, high resolution for the entire MRB that are plausible as compared to observations.

2. Sensitivity analysis indicating that increasing air temperatures have a strong impact on water temperatures, both spatially and temporally.

3. Water temperature projections in the MRB due to a future climate change scenario.

The MRB was divided into three latitudinal bands and a sensitivity analysis was performed in which the air temperatures were increased uniformly across all grids and regions by 3.0°C (6.0°C). Mean water temperatures increased by 1.3°C (3.3°C), 1.5°C (3.5°C), and 1.8°C (4.0°C) in northern, central, and southern MRB zones, respectively. The coupled model results indicate that the mean average water temperature may experience non-uniform increases along the river by as much as 8°C for the scenario used in the study.

The estimates of water temperature are significant for stream ecology, in particular for fish. Fish species have minimum and maximum temperature tolerance thresholds. In some portions of the MRB, stream temperatures increase above survival thresholds for several native fish species during summer, which could change fish habitat. Increased water temperature accelerates the growth of harmful algal blooms which could result in a larger dead zone in the GoM. Overall, these warmer water conditions could affect water quality, ecosystem health, marine life, and electric power plant generation efficiency.

This linked model approach should provide more scientifically robust estimates of water temperatures in the MRB for use by Federal Agencies (e.g., USEPA), Regions, States and local governments, and industries. Results from this study will be used to investigate the impact of water temperature on the nutrient loads in the MRB. The linkage provides a more physically based water temperature estimate than is currently available from the One-Biosphere modeling system. It will also facilitate the inclusion of a highly parameterized and calibrated nutrient load model, such as the regionalized, monthly Nutrient Export from Watersheds Dissolved Inorganic Nitrogen (NEWS2-DIN) model in future climate applications by providing consistent, physically based hydrologic and water temperature time series.

Follow-on research will include changes in future climate-driven streamflow as well as water temperature using updated downscaled climate change scenarios. Coupling with a water quality model (e.g., NEWS) will also be pursued in the future.

Research Impact Statement.

Coupling meteorological (WRF), hydrological (VIC), and water temperature (RBM) models provides a mass consistent, physically based estimate of water temperatures.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.