Development of a Global River Water Temperature Model Considering Fluvial Dynamics and Seasonal Freeze-Thaw Cycle

Abstract

In this study, we developed a global river water temperature model that explicitly represents water and heat budgets. The model considers fluvial dynamics such as floodplain inundation and as well simulates seasonal freeze-thaw cycles for temperate and arctic rivers, and it was found that proposed physically based parameterizations appropriately reproduced in situ observed seasonal variations in 12 global rivers. Theoretically, floodplain inundation has two major effects on water temperature variability: (1) “broadening” of water surfaces, which increases heat exchange with the atmosphere and friction with river bed, and (2) “shallowing” mean water depth, which increases the absorption rate of shortwave radiation per unit volume. In contrast to the broadening which affects both warming and cooling processes, the shallowing causes warming only and has dominant impacts mainly during the ice melting season in Arctic regions and the rainy season in the tropics. Furthermore, it was revealed that lateral mixing between channel and floodplain has a significant impact on determination of river water temperature. Although water temperature plays an important role in water quality and riverine material circulation linking terrestrial and coastal environments, it has not been considered in most Earth system models. The improvements in global-scale river water temperature modeling demonstrated in this study will benefit for future Earth systems research.

Key Points

• A global model was developed to simulate river water temperature considering fluvial and thermodynamics, including floodplain inundation
• Floodplain inundation increases the temperature of the river water mainly due to an increase in the absorption of shortwave radiation
• Refinement of a topographic data and water distribution representation potentially improves understanding of the riverine environment

1 Introduction

The circulation of chemicals, including carbon and nitrogen, within the Earth system cannot be understood without hydrodynamics. Hydrodynamics plays a key role not only on riverine transportation from land to ocean but also on chemical exchange on the interface of water bodies with the atmosphere (Intergovernmental Panel on Climate Change, 2014). River water temperature is one of the major determinants of the numerous processes that such materials undergo in the water. It affects the solubility and reactivity of dissolved materials, as well as ecological activities (Abril et al., 2014; Ozaki et al., 2003; Webb, 1996). It also has an effect on industrial activities, as it can, for example, limit the cooling efficiency for power plants and factories (van Vliet et al., 2016).

Much research has focused on modeling of river water temperature. One of the approaches used is a data-oriented method which estimates, or trains a model to estimate, temperature using existing observed data. The earliest application of this method involved a linear regression of river water temperature with air temperature (Keller, 1967; Smith, 1968). More recent studies have proposed applying logistic regression to these two variables (Mohseni et al., 1998; Mohseni & Stefan, 1999). Since then, the effect of heat capacity change has been considered in this nonlinear model by adding a river discharge term (Webb et al., 2003); this model has also been applied at the global scale (van Vliet et al., 2011).

However, because of the presence of strong autocorrelated characteristics of water temperature, such air-water temperature regression models (statistical models) do not work well when a fine temporal resolution (e.g., daily) is desired (Benyahya et al., 2007). Instead, some types of models divide water temperature changes into long-term and short-term variations (e.g., Caissie et al., 1998). Long-term temperature variations are based on sinusoidal regression of water temperature seasonality (Johnson, 1971), and there are several approaches to estimate the residual variations, such as multiple regression of the residuals of air temperature (Kothandaraman, 1971), second-order Markov (Cluis, 1972), and Box-Jenkins (Box & Jenkins, 1976) modeling. These approaches are called stochastic modeling. In addition to these methods, nonparametric approaches including artificial neural networks (Conrads & Roehl, 1999) and k-nearest neighbors (Benyahya et al., 2008) have been proposed.

Since heat fluxes such as latent heat and friction are difficult to observe directly, deterministic modeling combines the heat conservation law and heat flux calculations with additional meteorological data. Despite the data requirements of the model, previous research (Caissie, 2006) has identified advantages of the deterministic modeling over data-oriented approaches such as those described above. Because it incorporates physical processes, it can represent various temporal scales and can be applied for broader purposes such as future projections and impact assessment related to climate change and human activities.

Earlier studies simplified the heat conservation law. One example is the equilibrium temperature model proposed by Edinger et al. (1968). Another type of early model used additional meteorological data (e.g., air humidity or wind speed) to calculate downstream temperature with the observed upstream temperature as a boundary condition (Brown, 1969). To explicitly consider changes in discharge and water storage volume, a deterministic model requires additional hydrological data such as discharge and velocity (Sinokrot & Stefan, 1993; Theurer et al., 1984). To address this challenge, it has been proposed that the water and heat budgets be solved simultaneously (Kim & Chapra, 1997; Westhoff et al., 2007; Younus et al., 2000). Since recent studies have reported that there are large regional differences in long-term river water temperature trends (e.g., Kaushal et al., 2010), global-scale river water temperatures have received increasing attention in recent years. For example, there is recent research interest in deterministic and global-scale modeling of river water temperature (Beek et al., 2012; van Vliet et al., 2012).

Flooding has been found to affect water temperature and other qualities by reducing the spatial heterogeneity within a river channel and a surrounding floodplain, which is called the flood pulse concept (Arscott et al., 2001; Junk et al., 1989; Tockner et al., 2000; Ward et al., 2001). In the field of hydrodynamical modeling, it has been reported that floodplain inundation plays a significant role on river flow within global- and/or continental-scale water cycles (e.g., Coe et al., 2002), because floodplain inundation mitigates the seasonal variations in water depth and river discharge. Despite having this knowledge, the global models of river water temperature have not been considering the effect of flooding on temperature.

Here we describe a global river water temperature model, Heat Exchange and AdvecTion with fLood and Ice NumeriKs (HEAT-LINK), coupled with a global river flow model, to consider the effects of fluvial dynamics including flooding and inundation. We report on the effect of flooding, as well as on a comparison of model results with observed data in several continental rivers.

2 Model Description

HEAT-LINK solves three governing equations (described in the following section), and it calculates water distribution in both a river channel and a floodplain. HEAT-LINK calculates heat advection, energy fluxes (e.g., the absorption of shortwave radiation and evaporation), and changes in mass and energy of water and ice using these variables and the atmospheric conditions. Ice affects the hydrodynamics due to changes in the wetted perimeter, roughness, and head of the water slope. Please note that the model does conserve mass and energy throughout the calculation processes.

The river routing model is driven by runoff from a land surface model, Minimal Advanced Treatments of Surface Interaction and RunOff (MATSIRO) (Takata et al., 2003), which solves for mass and heat budgets over the surface layers of the land. Since it also calculates the runoff temperature, these variables can be input into HEAT-LINK. Thus, the input data to HEAT-LINK are the atmospheric forcing data and the outputs of the land surface model MATSIRO, which is also driven by the same atmospheric forcing.

2.1 Governing Equations

The governing equations in HEAT-LINK are the one-dimensional mass conservation law (equation 1), the Saint-Venant equation for momentum conservation (equation 2), and the conservation law of energy (equation 3)

(1)

(2)

(3)

where A is the cross-sectional area, t is time, Q is the discharge, x is the distance along the river, q_L is the runoff per unit length, g is acceleration due to gravity (= 9.8 m/s²), h is the flow depth, z is the bed elevation, n is Manning's friction coefficient, R is the hydraulic radius, c_w is the heat capacity of water, ρ_w is the density of water, T is the water temperature, T_L is the runoff temperature, B is the width of the cross section, and ϕ is the source term of energy per area. In this study, the water was assumed to be in a well-mixed condition, and therefore, we did not consider the temperature distribution over river channel and floodplain separately; instead, a single water temperature (T) was applied. Another simplification used in this study was ignoring a diffusion term in the energy conservation law, as done previously by researchers (e.g., Sinokrot & Stefan, 1993).

2.2 Fluvial Dynamics Modeling

Fluvial dynamics, including floodplain inundation, were calculated using a physically based river routing model, CaMa-Flood (Yamazaki et al., 2013, 2011). It solves the momentum equation (equation 2) by approximating it with a local inertial flow equation by neglecting the advection term (the second term in the left hand side) to achieve a high-efficiency flow computation (Bates et al., 2010). The model still considers advection terms in mass and energy conservation laws. The equations are discretized explicitly using a forward-time central-space scheme to simulate the time evolution of the state variables.

CaMa-Flood calculates the discharges in a river channel and floodplain as prognostic variables and the shape of the cross sections (e.g., water depth and surface area) as diagnostic variables. In order to represent the cross section based on high-resolution topographic data instead of conceptual reservoirs (Decharme et al., 2008), it divides the land surface into “unit catchments” (or subbasins) and extracts topographic parameters of each unit catchment from the elevation distribution in it. These procedures allow objective representation of the cross section. However, CaMa-Flood assumes that water depths are equal within a river channel and floodplain in the same unit catchment, so it does not fully consider water exchange between them or the in-grid distribution of water depth.

2.3 Heat Flux

The heat source term ϕ includes the following heat fluxes:

(4)

where ϕ_SW↓ is the contribution of downward shortwave radiation, ϕ_LW↓ is that of downward longwave radiation, ϕ_LW↑ is that of upward longwave radiation, ϕ_H is that of sensible heat transport, ϕ_lE is that of latent heat transport, and ϕ_friction is that of friction on the river bed. We assumed that the conduction heat flux from the riverbed was negligible, as per Hondzo and Stefan (1994). Figure 1 shows a conceptual diagram of this model. Since the calculation methods for ϕ_LW↓, ϕ_LW↑, and ϕ_friction are identical to Webb and Zhang (1997), we do not describe them herein. The calculations for the remaining terms are described as follows.

Figure 1

(a) Conceptual diagram of the heat exchange and AdvecTion with fLood and Ice NumeriKs model. (b) Method to calculate the ratio at which radiation reaches the river bed in the river channel and floodplain. (c) Parameterization of river ice shape.

2.3.1 Downward Shortwave Radiation

The contribution of downward shortwave radiation was calculated as follows (Webb & Zhang, 1997):

(5)

where α is the albedo of water (= 0.1), p is the rate at which shortwave radiation passes through the water body and is absorbed by the river bed, R_SW↓ is shortwave radiation that reaches the water surface, r is the rate at which radiation is absorbed by the water surface (= 0.6), b is the rate at which radiation is reflected at the river bed, D is the ratio at which radiation reaches the river bed, and λ is the attenuation rate of water (= 0.05/m). In this study, shading by the adjacent canopy was ignored because the target was a continental-scale large river basin, in which the river width is much greater than the shaded area.

Our hypothesis was that the dependency on water depth has a major role in determining water temperature. Because ϕ_SW↓ (incoming energy per surface area) is absorbed by a water column of which the depth is h, the increase in its temperature, ∆T_SW↓, is determined as per equation 6. Also shown is the changing rate of it over water depth (equation 7).

(6)

(7)

When we consider a function f(h) = kλ · h exp (−λh) + k exp (−λh) − 1 and its derivative, we obtain

(8)

This means that shallower water is warmed up more by the shortwave radiation than is deeper water (this result is reasonable because water near the riverbed absorbs only the radiation which has not been absorbed by water above it). In particular, flooding reduces the water depth in a river channel and redistributes shallower water in the floodplain, which leads to an increase in water temperature.

2.3.2 Sensible and Latent Heat Transport

The fluxes of sensible and latent heat were calculated based on a corrected bulk method, as per Kondo (1992)

(9)

(10)

where c_p is the specific heat at constant air pressure, ρ_a is the density of air, C_HD and C_ED are the corrected bulk coefficients for the water surface, V is the wind velocity, T_a is the air temperature, T_s is the temperature of the water surface, l is the latent heat of water, β is the evaporation efficiency at the water surface (= 1.02), q_sat is the saturated specific humidity at the water surface temperature, and q_a is the specific humidity of air. The model does not distinguish the temperature of the water body, T, from that of the water surface, T_s; that is, T_s = T.

C_HD and C_ED are corrected by variables s and s₀, which indicate atmospheric stability

(11)

(12)

where z_obs is the observation height of the wind. If T_S ≤ T_a (stable atmosphere), then

(13)

Otherwise (unstable atmosphere, T_S > T_a)

(14)

where C_H and C_E are the bulk coefficients for stable air (C_H = C_E = 1.2 × 10⁻³).

While we consider the evaporative energy flux, we assumed at this moment that water depletion by evaporation would be negligible compared with river channel and floodplain storage.

2.4 Consideration of Varying Surface Water Extents

The effects of floodplain inundation can be divided into two components. The first is broadening of the water surface, which accelerates heat exchange at the interface with the atmosphere and due to friction. The heat exchange can be either positive or negative, depending on atmospheric conditions. CaMa-Flood calculates the water surface area including the floodplain, and we used this to calculate the amount of heat exchange.

The other effect is a reduction in the water depth in a river channel (and floodplain), which increases the absorption of shortwave radiation per volume, as mentioned previously. We can calculate that effect by integrating ϕ_SW↓ or D for the inundated floodplain. Current HEAT-LINK ignores the floodplain bed gradient change and calculates the flooded area gradient i_f as h_f/w_f (h_f and w_f are the water depth and width of the floodplain, respectively, as shown in Figure 1b). The mean absorption rate in the floodplain, , is calculated under this simplification as follows:

(15)

where z is the water depth at a point which is a distance y from the edge of the floodplain.

Therefore, the total mean absorption rate of a river channel and floodplain, , is given by

(16)

where D_c(= exp (−λh_c)) is the absorption rate of the river channel and h_c and w_c are the water depth and width of the river channel, respectively. If flooding occurs in a grid, we would replace the D in equation 5 with this to calculate the absorption of shortwave radiation.

2.5 Minimum Water Treatment

To stabilize the calculation, the model defines a minimum depth of water (h_min). CaMa-Flood assumes a rectangular cross section in a river channel. Under this assumption, numerical instability occurs when river water depth becomes very shallow, because heat exchange becomes too large compared with the water storage. If a calculated water depth is shallower than h_min, the depth h and width B of the river channel are updated as

(17)

where S is the storage of water. In this study, h_min was set as 1 cm. The temperature of the water body was not changed, and this correction conserves mass and energy.

2.6 River Ice Processes

Rivers at high latitudes can remain frozen for more than 6 months per year (Beltaos, 2000). There are previous studies related to numerical modeling of the detailed processes of river ice, including border, frazil, and anchoring ice, as well as ice jams and breakup (Shen, 2010; Shen et al., 1995). However, since the spatial resolution of the state-of-the-art global model was insufficient to represent these phenomena, we solved the mass and heat budgets for surface ice using a method similar to the existing global river temperature model (Beek et al., 2012).

To represent the changes in surface ice mass, the heat budget at the ice surface is first solved by calculating the heat fluxes, including contributions by shortwave radiation, longwave radiation, sensible heat flux to the atmosphere, and conductive heat from the water body. If ice melts, it is presumed to add to the liquid water. If the heat budget of the ice is negative, additional water beneath the ice is assumed to freeze. The total heat flux into the water are calculated by weighting the fluxes at the interface of the water with the river ice and with the atmosphere. Finally, the heat budget for the water body is solved, and if the water temperature drops below the melting point, the mass of the surface ice is increased. In this study, we assumed a simple parameterization for the fraction and shape of surface ice (Figure 1c). This allowed us to diagnostically calculate the ice area and thickness from the whole water surface area and ice volume, respectively.

The surface ice model used calculates ice discharge based on an existing river ice model (Lal & Shen, 1991; Shen et al., 1995), which assumes that surface ice flows at the same velocity as water. As discussed in those papers, the velocity can vary spatially due to the complicated distribution of the ice. In this study, it was assumed that ice is stationary when the entire water surface is covered with ice.

The effects of river ice on water flow were represented in virtually the same way as in the existing model (Beek et al., 2012). River ice causes a change in Manning's roughness coefficient and results in a wetted perimeter. Since we consider the ice discharge, the model calculates those effects only when the entire water surface is covered with ice. In addition to these changes, the weight of river ice was added to the water head in calculating water discharge in the current study.

2.7 Boundary Conditions

A boundary condition at the river mouth is necessary when backflow occurs, because river water and seawater mix. In the model used, the temperature and ice concentration of seawater were assumed to be equal to that of the river mouth. The model also ignores the salinity effect on the heat budget and ice formation. Since the land surface model calculates runoff temperature, the temperature of headwater is not required as an upstream boundary condition.

2.8 Calculation Order

The calculation order is shown in Figures 2 and 3. First, the model updates input data, including meteorological forcing data and outputs from the land surface model. Next, a hydrodynamics module calculates discharges in the river channel and floodplain considering the effect of river ice and diagnostically calculates the shape of the cross section, including the inundated area. Heat advection and ice transport are then calculated from these discharges. Runoff water is added to the water body after the calculation. The model mixes water in the river channel and floodplain and the runoff, and updates the water temperature. The model then solves the mass and heat budgets for the surface ice and the water body.

Figure 2

Flow chart of input and output data and models used in this study.

Figure 3

Flow chart of calculation processes for each time step.

3 Configuration of Numerical Experiment

3.1 Input Data

The input data and other models used in the simulation are shown in Figure 2. We used a global meteorological forcing data set (Kim, 2017a, 2017b), which consisted of reanalysis data corrected using observational data. Runoff amounts and temperatures were calculated from an off-line land surface simulation using MATSIRO (Takata et al., 2003), forced by identical meteorological data.

The spatial resolution of the forcing data and the land surface model output was 1° × 1° and that of the river flow model and river water temperature model was 0.25° × 0.25° (Table 1). Variables in the coarse resolution (e.g., runoff and air temperature) were interpolated using weighting by the fraction of overlapped unit catchment area.

Table 1. Spatial and Time Resolution of the Data and Models Used in This Study

Data/model	Product name	Resolution		Reference
		Space (degree)	Time (hr)
Meteorological forcing data	JRA55_ELSE	1	6	Kim (2017a, 2017b)
Land surface model	MATSIRO	1	24	Takata et al. (2003)
River flow model	CaMa-Flood	0.25	24	Yamazaki et al. (2011, 2013)
River temperature model	HEAT-LINK	0.25	24	This study

• Note. The river flow model and river temperature model were coupled. Meteorological forcing data and outputs of the land surface model were spatially interpolated. MATSIRO = Minimal Advanced Treatments of Surface Interaction and RunOff; HEAT-LINK = Heat Exchange and AdvecTion with fLood and Ice NumeriKs.

The temporal resolution of the model output was 24 hr. However, the river routing model automatically adjusts width of calculation time step to satisfy the Courant-Friedrichs-Lewy condition. As a result, the time step in the model was approximately 7–10 min.

3.2 Target Period

The target period of this calculation was set to 10 years (1990–1999). The spin-up period of the land surface model was 10 years and that of the river flow and temperature models was 1 year. The initial condition for the river water temperature was the air temperature on the first day of 1990.

3.3 Experimental Design

As previously mentioned, we hypothesized that the role of the floodplains on river water temperature can be divided into two components: water depth reduction and broadening of the water surface area. In order to distinguish these impacts, we performed two additional experiments (described below), and the results were compared with the original model configuration (control experiment, hereafter CTL).

1. No floodplain experiment (NoFLD): This model configuration turns off floodplain dynamics. It assumes that water is stored only in river channels, and not in floodplains, and causes changes in river water depth and discharge. This experiment can be regarded as a river water temperature model combined with a river flow model which does not represent floodplain inundation.
2. Separation of river channel and floodplain (SEP): The NoFLD experiment modified not only the heat budget of the water body but also the heat capacity due to changes in water discharge and storage. On the other hand, the SEP experiment defines the temperatures of a river channel and floodplain separately, and it calculates advection and heat budget for each storage area. Since the distribution of water in the SEP experiment is identical to that in the CTL experiment, except for ice mass change due to its heat budget, comparing the two allowed us to extract the effect of heat budget solely on the floodplain.

While the original model (CTL) assumes that water in river channels and floodplains is well mixed, this modified model is used to focus only the heat budget effect of floodplains. Since the river flow model used in this research assumes that the water surface elevations in river channels and floodplains are the same and does not represent water exchange between them, we assumed that heat is transported only by net water exchange between river channels and floodplains under the same assumptions used in the river flow model mentioned above.

4 Results

4.1 Model Validation

4.1.1 Target Variables and Validation Data Sets

We validated three variables: discharge, inundated area, and water temperature. Discharge and temperature were compared with site-observed data collected by the Global Runoff Data Centre and the Global Environmental Monitoring System. For river water temperature in the Amazon River, we used observed data from the Hydrology and Geochemistry of the Amazon basin observatory. The temporal resolution of the Global Runoff Data Centre discharge data is 1 day and that of the Global Environmental Monitoring System and Hydrology and Geochemistry of the Amazon basin temperature data is 1 month. Although the temperature data are monthly instantaneous values, we compared the monthly mean value of simulated temperature with them. We validated the simulated inundated area with Global Inundation Extent from Multi-Satellites data set, which was derived from microwave remote sensing (Papa et al., 2010). We determined a rectangular-shaped target area in each basin and compared the inundated area within it. This data set is monthly averaged, and the spatial resolution is 0.25° longitude and latitude.

We evaluated bias (BIAS), root-mean-square error (RMSE), correlation coefficient (CORR), and Nash-Sutcliffe efficiency (Nash & Sutcliffe, 1970) as statistical indices. BIAS and RMSE were standardized by the mean observed value and converted into unitless indices (hereafter pBIAS and pRMSE) for river discharge and inundated area, respectively.

We selected four major rivers from each of Arctic, temperate, and tropical regions for evaluation. Table 2 shows the basin area, the stations used to validate discharge and temperature data, and the target domain for the inundated area in each basin. Figures 4-6 show the validation results in these regions, and the results of statistical evaluation are provided in Tables 3 and 4.

Table 2. Target Basins and Stations Used for Model Validation

River	Basin area [(10^6 km^2)	Discharge station	Temperature station	Target domain for inundated areaa
(a) Arctic
Lena	2.47	Stolb	Kusur	(70°N, 120°E) (60°N, 130°E)
Mackenzie	1.77	Arctic Red River	Liard	(67^oN, 120^oW) (60^oN, 108^oW)
Ob	2.47	Salekhard	Salekhard	(67°N, 62°E) (57°N, 82°E)
Yenisei	2.51	Igarka	Selenga	(69^oN, 86°E) (66^oN, 90°E)
(b) Temperate
Danube	0.787	Ceatalizmail	Budapest	(46^oN, 27°E) (45^oN, 29°E)
Mississippi	3.18	Hermann, MO	Hermann, MO	(40^oN, 94^oW) (30^oN, 88^oW)
Yangtze	1.91	Zhimenda	Yangtze	(34^oN, 100°E) (28^oN, 118°E)
Yellow	0.652	Tanglaiqu	Lijin	(37^oN, 112°E) (34^oN, 117°E)
(c) Tropics
Amazon	5.89	Obidos	Obidos	(0°S, 72°W) (8°S, 54°W)
Brahmaputra	1.57	Bahadurabad	Padha	(30°N, 80°E) (24°N, 95°E)
la Plata	2.59	Portodo Alegre	Corrientes	(16°S, 63°W) (32°S, 55°W)
Mekong	0.772	Khong Chiam	Khong Chiam	(15°N, 104°E) (10°N, 107°E)

• ^a We set a rectangular-shaped target domain for validation of the inundated area, and this column shows the (north, west) and (south, east) boundaries.

Figure 4

Comparison of the time series of discharge (m³/s), inundated area (km²), and temperature (^oC) in the high latitudes. Black lines or dots show observations, while, blue (or red) lines show the results of a simulation considering (or ignoring) floodplain inundation. The dashed line in the bottom figure indicates the air temperature at each observation station.

Figure 5

Comparison of the time series of discharge (m³/s), inundated area (km²), and temperature (^oC) in the middle latitudes. Black lines or dots show observations, while blue (or red) lines show the results of a simulation considering (or ignoring) floodplain inundation. The dashed line in the bottom figure indicates the air temperature at each observation station.

Figure 6

Comparison of the time series of discharge (m³/s), inundated area (km²), and temperature (^oC) in the low latitudes. Black lines or dots show observations, while blue (or red) lines show the results of a simulation considering (or ignoring) floodplain inundation. The dashed line in the bottom figure indicates the air temperature at each observation station.

Table 3. Statistical Indices for Discharge and Inundated Areas

River	Discharge (CTL)				Discharge (NoFLD)				Inundated area (CTL)
	pBIAS	pRMSE	CORR	NSE	pBIAS	pRMSE	CORR	NSE	pBIAS	pRMSE	CORR	NSE
Yenisei	−0.182	1.43	0.343	−0.888	−0.170	0.636	0.961	0.626	1.41	2.00	0.783	−0.184
Ob	0.659	2.59	0.156	−10.5	0.674	2.12	0.793	−6.71	1.51	1.69	0.904	−0.605
Lena	−0.161	1.54	0.480	−0.439	−0.164	0.935	0.892	0.467	1.21	2.08	0.855	−0.674
Mackenzie	−0.0154	0.775	0.805	−0.111	0.0253	1.89	0.420	−5.63	2.05	2.29	0.708	−1.87
Mississippi	0.231	0.414	0.737	−0.565	0.233	1.20	−0.0230	−12.2	0.529	0.742	0.832	−1.17
Yangtze	6.89	7.90	0.789	−84.8	6.12	7.35	0.878	−73.3	−0.439	0.584	0.427	−0.929
Danube	−0.0400	0.302	0.323	−0.976	−0.00660	0.696	0.218	−9.51	7.26	7.31	0.303	−93.1
Yellow	−0.406	0.497	0.886	0.280	−0.450	0.787	0.336	−0.807	4.00	4.22	−0.632	−12.0
Amazon	−0.411	0.417	0.970	−1.26	−0.412	0.441	0.870	−1.52	0.843	1.17	0.944	−40.5
la Plata	—	—	—	—	—	—	—	—	−0.640	0.667	0.841	−4.28
Ganges	−0.234	0.336	0.962	0.765	−0.234	0.448	0.901	0.583	−0.591	0.753	0.903	0.131
Mekong	−0.388	0.483	0.957	0.717	−0.388	0.458	0.967	0.746	0.730	1.00	0.727	−2.37

• Note. RMSE = root-mean-square error; NSE = Nash-Sutcliffe efficiency.

Table 4. Statistical Indices for Temperature

River	Temperature (CTL)				Temperature (NoFLD)				Temperature (Tair)
	BIAS	RMSE	CORR	NSE	BIAS	RMSE	CORR	NSE	BIAS	RMSE	CORR	NSE
Lena	0.108	1.97	0.936	0.848	−1.07	3.21	0.800	0.595	−14.0	17.8	0.801	−11.4
Mackenzie	−0.272	1.44	0.971	0.928	−0.772	1.58	0.968	0.912	−6.41	8.11	0.955	−1.30
Ob	−3.12	5.80	0.687	0.246	−3.85	6.57	0.668	0.0339	−9.64	11.4	0.897	−1.93
Yenisei	−0.601	1.23	0.990	0.975	−1.06	1.83	0.982	0.945	−4.51	5.77	0.958	0.445
Danube	−0.693	3.00	0.987	0.793	−2.18	2.80	0.984	0.820	−0.407	1.84	0.991	0.922
Mississippi	−1.10	2.53	0.993	0.918	−1.96	3.27	0.983	0.863	−0.861	1.49	0.991	0.971
Yangtze	0.473	2.53	0.984	0.862	−1.08	1.74	0.985	0.935	−0.329	2.07	0.975	0.908
Yellow	0.0826	3.19	0.978	0.871	−1.39	3.04	0.974	0.883	0.222	2.08	0.976	0.945
Amazon	1.20	1.21	0.983	−1.59	−0.0777	0.754	0.982	−0.00379	−3.53	3.56	0.900	−21.3
Brahmaputra	−0.178	2.90	0.714	0.361	−2.10	3.96	0.518	−0.198	−0.552	2.70	0.697	0.446
la Plata	0.776	1.97	0.946	0.748	0.334	1.71	0.947	0.811	−1.59	2.12	0.938	0.710
Mekong	−0.115	0.870	0.935	0.831	−0.597	1.30	0.871	0.625	−1.74	2.10	0.871	0.0142

• Note. The “Temperature (Tair)” column shows the evaluation of air temperature at each observatory. RMSE = root-mean-square error; NSE = Nash-Sutcliffe efficiency.

4.1.2 Rivers in Arctic Regions

In high-latitude areas, rivers are covered with ice during winter, and the model produced a good match to the general seasonal variations observed in water temperature. However, the rises in discharge and temperature simulated by the model were delayed compared with observed data. It is possible that the representation of river ice processes in the model is too simple and requires improvements. Runoff increases at the start of the ice melting season, and it causes the ice to be pushed up and break (ice breakup). The ice pieces flow downstream, and ice jams are formed when some of these pieces pile up, for example, in narrow sections. Ice jams usually cause flooding. The model ignores such processes and instead considers the removal of surface ice in mechanisms related only to heat budget.

This explanation is consistent with the results of the NoFLD experiment. NoFLD underestimated the effect of river ice on flow. River ice slows down the discharge, and the underestimation of this effect resulted in reproducing the observed discharge peak better than the CTL experiment did. However, the NoFLD experiment underestimated the water temperature after ice melt, which suggests that ignoring the inundated floodplain underestimates the heat exchange of ice-free water.

4.1.3 Rivers in Temperate Regions

We observed that including floodplain inundation in the model suppressed the discharge variation and led to better reproduction of the seasonal patterns, which was in accordance with Yamazaki et al. (2011). River water temperature was well correlated with air temperature in temperate areas, as shown in Table 4. The simulated temperatures from the CTL experiment were higher than those of the NoFLD experiment in most seasons. As mentioned above, floodplain inundation could either increase or decrease the water temperature, and we observed a dominant warming effect in temperate regions. In the Yellow River, although a larger inundated area was simulated during the winter, the difference in temperature between the two experiments was much smaller than that during the summer.

4.1.4 Rivers in Tropical Regions

The model reproduced seasonal variations in simulated discharge and inundated area well for tropical regions, regardless of some bias, as shown in Table 3. Temperature patterns in these rivers have unique characteristics compared with those in other regions. One of the observed characteristics of tropical river temperatures was smaller correlation with air temperatures. The exception to this was La Plata River, in which air and water temperature were well correlated. In high- and middle-latitude areas, air and water temperature were generally well correlated, except during periods of the existence of ice cover. River temperature was consistently higher than air temperature in the Amazon River. As CORR was high (>0.98) in this basin, the seasonal variation of water temperature was reproduced well by the model, although simulated temperatures were constantly higher than observed. While discharge was underestimated, the inundated area was overestimated over long time periods. From these results, it is speculated that improvement of the hydrodynamics representation and topographic data set in the model may reduce the bias in the simulated temperature in Amazon River.

Another unique characteristic observed for tropical rivers was a bimodal pattern of water temperature seasonality in the Brahmaputra and Mekong Rivers, with one temperature peak during the dry season (from November to May) and another during rainy season (from June to October), though air temperature was highest during the dry season. The simulated temperatures in the CTL experiment reproduced both peaks. This result suggests that considering floodplain inundation improves the reproduction of the seasonal pattern of river water temperature.

4.2 Seasonal Changes in Global River Water Temperature

In Figure 7 (i), we present global comparisons of the difference between river and air temperatures. In general, the trends shown and described below are in accordance with Beek et al. (2012). In high-latitude regions, river ice formation leads to a larger discrepancy between water and air temperatures during the winter. There was a strong meridional gradient of the temperature difference during melting (March-April-May, MAM) and freezing (September-October-November) seasons. River water temperature was lower than air temperature in middle latitudes, in particular during MAM. The Previous research showed that water temperature is lower than air temperature even during June-July-August season in rivers in northeastern part of Eurasia continent (e.g., Yenisei and Lena Rivers); the proposed model in this study did not reproduce this pattern. It could be inferred that the difference was caused by considering floodplain inundation and its effect on the heat budget, according to Figure 4.

Figure 7

Global comparison of temperature (°C). (i) Simulated river water temperature considering floodplain inundation and air temperature. Red indicates that river water temperature is higher than that of air. (ii) Simulated river water temperature considering and ignoring floodplain inundation. Red indicates that the inclusion of floodplain inundation in the model increases river water temperature. Values are climatology means for 1990–1999. Values are plotted only where mean calculated discharge exceeded 500 m³/s. DJF, MAM, JJA, and SON mean December-January-February, March-April-May, June-July-August, and September-October-November, respectively.

Figure 7 (ii) shows the difference in calculated temperature with and without floodplain inundation (CTL and NoFLD). In most regions and seasons, considering the floodplain resulted in an increased river water temperature. While it had little impact under ice covered conditions, the impact was considerable during ice-free seasons at high latitudes. In middle-latitude areas, including the Danube and Mississippi Rivers, the temperature difference was largest during MAM, followed by June-July-August because of the maximum incoming shortwave radiation during this period, as shown in Figure 5. Regardless of the larger incoming solar radiation at the surface during the summer period, the temperature did not increase considerably because the flooded water surface was not expanded. In the upper stream area of Mississippi and Amazon Rivers, the temperature simulated in the CTL is lower than that in the NoFLD experiment. Broadening water surface increases negative heat budget of the water body in these cases. While the temperature difference became greater in the downstream area in the Brahmaputra River, the Amazon River showed the opposite tendency. Such results suggest that the water temperature is not only governed by local heat balance, but it is also closely related to surface water dynamics in the entire watershed.

4.3 Sensitivity to Mixing Between a River Channel and Floodplain

The SEP experiment enabled analysis of the detailed effects of floodplain inundation on water temperature. Figure 8 shows scatter plots of the temperatures simulated in the SEP experiment. In the Mississippi, Mackenzie, Brahmaputra, and Mekong Rivers, flooded water tends to have a higher temperature than water in the river channel, which is in accordance with the results of the previous sections in which the temperatures in the CTL experiment were higher than those in the NoFLD experiment. However, the opposite trend was observed in the Ob and Lena Rivers throughout a year and for a part of a year in the Amazon River.

Figure 8

Comparison of simulated river water temperatures.

The gap between these results can be explained using another scatter plot comparing the river temperature in the NoFLD and SEP experiments (Figure 8). All rivers showed similar trends, with the exception of a few outliers, in which the river temperature in the SEP experiment was higher than that in the NoFLD experiment. This reflects the dependency of shortwave radiation absorption on water depth, as mentioned previously. Ignoring the floodplain leads to overestimating the water depth and underestimating the river water temperature as a result. The temperature increase with flooding in Figures 4-6 was a result of mixing between the warmer river water and the flooded water.

4.4 Sensitivity to Meteorological Conditions

In order to observe the dependency of the results on meteorological conditions, we conducted a sensitivity analysis by inputting other forcing data sets. We compared GSWP3 (Kim, 2017a, 2017b) and Prcp_GPCCLW90 (Kim et al., 2009) with JRA55_ELSE, which was used in the previous experiments. Figure 9 shows scatter plots comparing the CTL and NoFLD experiments using those data sets. In general, we observed a similar pattern in which considering floodplain inundation increased the water temperature. Even in middle latitudes, floodplain inundation had a large effect on warming the water using the GSWP3 and Prcp_GPCCLW90 data sets.

Figure 9

Comparison of results of different meteorological forcing data sets: JRA55_ELSE, GSWP3, and Prcp_GPCCLW90.

On the other hand, with these two data sets, the cooling effect was dominant in the low temperature range in la Plata River and rivers in the temperate region. This suggests that the effect of considering floodplain inundation depends on meteorological conditions. Ignoring floodplain inundation underestimates the width of the seasonal variation, and its inclusion improves the reproducibility by both of the flooding effects.

5 Discussion

Many prior works have developed one-dimensional river water temperature models, which solve the heat budget of the water surface or body. This study considered the effects of floodplain inundation, which redistributes water out of a river channel. It was based on topographic data and feature extraction techniques in hydrological modeling. However, those representations use the assumption that river water and flooded water are well mixed. While the SEP experiment, defining river and flooded water temperatures, assumed a simple mixing, its results suggest that the determinants of river water temperature include not only heat flux and advection but also factors affecting fluvial dynamics such as floodplain inundation and lateral connectivity between the river channel and adjacent floodplain. As reviewed in the introduction, some studies have reported spatial heterogeneity between the river channel and floodplain (e.g., Junk et al., 1989); this has also been examined in other research fields, such as water quality or sediment transportation (e.g., Zeug & Winemiller, 2008). The recent development of satellite imaging products has made it possible to observe a wide range of water bodies simultaneously. For example, Moderate Resolution Imaging Spectroradiometer products have revealed the distribution of suspended sediments in floodplains and oxbow lakes and their flow patterns in Amazon River (Park & Latrubesse, 2014). The simple assumption of a well-mixed condition is not necessarily inconsistent with those studies, but its applicability has to be validated further. It could be effective to simulate other water quality variables, for example, sediment concentration, which have large spatial heterogeneity.

There are several directions that could be taken to examine this assumption. The simplest one is to make the spatial resolution of the model finer. The use of a finer model and topographic data set would define additional river channels and floodplains within a coarser one. However, it cannot represent an isolated water pond such as an oxbow lake. In such areas, a much longer residence time forms a totally different ecosystem, including chemical reactions and ecological activity. In future studies, an objective representation or parameterization based on an improved topographic data set should be developed in order to reproduce the lateral connectivity. In addition to the field of river water temperature, these attempts will contribute to related sciences such as sediment transportation or carbon emissions from floodplains (Pangala et al., 2017).

As the heat budget of land and the runoff temperature were calculated in a land surface model, there were few arbitrary parameters or tuned parameters. On the other hand, we did not consider the effects of salinity or sediments in water, which can affect albedo and the attenuation rate of shortwave radiation. If these variables were to be included in the model, those effects could be represented.

Related to the problem of mixing, the proposed model in this study has ignored the effects of riparian vegetation. Vegetation reduces incoming solar radiation and dampens radiative fluxes controlling the microclimate at the reach scale. Since the width of river channels in the target basins is much larger than this, we have assumed that the shading area of adjacent trees is negligible. However, it is possible that they do affect the heat budget of water in floodplains. As pointed out in Langhans et al. (2006), there is also spatial heterogeneity in the vegetation. Vegetation becomes scarce in flood-prone area, but on the other hand, it is abundant far from a river channel. These dynamics should be included in the future, and they could improve upon the overestimation of water temperature in regions with lush vegetation and in upstream areas in which a river channel is not as wide.

6 Conclusion

In this study, we developed a global model to simulate river water temperature considering fluvial dynamics (e.g., floodplain inundation) and river ice. Although this model simplified some processes, including distribution of water temperature in a cross section, the proposed model successfully reproduced the seasonal pattern of river water temperature in all rivers studied. The results highlighted the impact of including floodplain inundation on river water temperature, as well as the reproducibility of discharge, inundated area, and river water temperatures. According to the heat flux calculation method (Webb & Zhang, 1997), the impact of floodplain inundation can be divided into two aspects: first, the decrease in water depth causes an increase in the absorption of shortwave radiation per unit volume, and second, the broadening of the water surface leads to accelerated heat exchange at the interface with the atmosphere. Even though the latter effect can be positive or negative depending on atmospheric conditions, the results indicate that floodplain inundation generally increases the water temperature. On the other hand, flooded water is cooler than river water in some rivers, which suggests that the removal of river water has a major role in temperature formation.

Recently, the floodplain has been considered to play key roles in sediment transportation (Park & Latrubesse, 2014) and carbon emissions (Pangala et al., 2017). However, its role on water temperature has not been examined at a global scale. From the view point of energy budget of the Earth system, river and flooded water redistribute incoming energy from land surfaces to oceans. For example, the rivers in high latitudes flow warmer water in lower latitudes to high latitudes in the downstream. The present study shows that fluvial dynamics affect river and flooded water temperatures and provides a new tool to investigate the role of rivers in the combined scope of energy and water cycles in the Earth system.

Acknowledgments

The first author is supported by the University of Tokyo via SEUT-RA. Part of this work was funded by the Japan Society for Promotion of Science (JSPS) via 16H0691. We gratefully acknowledge the United Nations Environment Programme Global Environment Monitoring System (GEMS) for providing us with monthly observed data of river water temperature, and the Global Runoff Data Centre (GRDC) for the daily observed discharge data.