3.1.

Aerial Survey

An aerial survey of the research area was conducted on October 31, 2013, between 12:30 and 3:00 p.m. UTC on behalf of the Federal Institute of Hydrology (BfG). Data of the Rhine River were acquired with two camera systems: a digital camera with RGB and near-IR channels, and a thermal imaging camera measuring the brightness temperature in the 8 to $12\mu \mathrm{m}$ wavelength region. The thermal camera was an extended version of the Image IR 8800 by InfraTec with an mercury cadmium tellurid detector, an absolute accuracy better than 1%, a relative temperature resolution, and accuracy of 0.025 K. This camera system had a focal plane array of $640\times 512$ pixels and a focal length of 13 mm and was deployed on an aircraft that flew at an altitude of $\sim 3000\mathrm{m}$. At the given flight altitude, the resolution of the TIR camera allowed for a ground sampling distance of 4 m and an orthorectified image of $\sim 2800\mathrm{m}\times 2150\mathrm{m}$ covering the whole width of the main stream and larger branches. The RGB and NIR data were acquired with the digital camera UltraCamXp by Vexcel and captured at the same time as the TIR data. Due to a higher pixel resolution, the final RGBNIR image had a spatial resolution of 0.8 m. A classification of the RGBNIR images was performed to eliminate land or mixed pixels and the effects of land surface temperatures as well as to identify clouds and shadows present during the data acquisition. The classification was based on band indices (normalized difference vegetation index based on the NIR and the red bands, normalized difference water index based on the green and NIR bands) and thresholds, derived from training areas/ground control points in the RGBNIR dataset where the surface characteristics were known. With very strict thresholds, mixed pixels capturing a combination of land and water surfaces were identified and with the land pixels omitted from further analysis. Fortunately, no clouds were identified over the water surface.

3.2.

Satellite Data

As mentioned in Sec. 1, river water temperatures can also be provided by satellite data. The accuracy of temperatures from Landsat ETM+ and the possibility to identify dischargers along the Rhine River has been evaluated in a previous study.⁶ In this paper, the capabilities of satellite data will be evaluated based on artificial satellite datasets derived from the aerial survey (see Sec. 4.3).

3.3.

Longitudinal Temperature Profiles

To reduce the amount of data to be processed, longitudinal profiles of the river temperature were created by selecting points evenly distributed every 100 m along the river center line. The temperature from the aerial survey extracted at their coordinates normally represents the water temperature of the main river stream (see Fig. 2). To capture water plumes on either stream side, an additional point raster with 100 m spacing was distributed over the river and related to the closest 100 m profile point for a distributed longitudinal profile. Raster temperature and classification value (water, land, cloud, or shadow) were extracted for each raster point and summary statistics, such as mean and standard deviation of the water temperature, were calculated for each 100 m profile point.

Fig. 2

Example of the RGBNIR (land) and thermal infrared data (water area) from the aerial survey as well as the longitudinal profile with 100 m intervals and the distributed longitudinal profile with 100 m spacing (data source: BfG).

3.4.

In Situ Measurements

The measurements from several water quality measurement stations along the Rhine and its tributaries were used for the comparison of remote sensing temperatures with in situ temperatures (see Fig. 1). The measurement stations are listed in Table 1 with the responsible operators. The measurement stations measure the bulk water temperature at the river shore and, in some cases, also across the river (Worms and Mainz). Independent of the instrumental accuracy, the accuracy of the bulk water measurements can vary from 0.1 to 0.25°C up to 0.5°C,²² depending on the maintenance of the measurement station.

Table 1

Water quality stations and temperature data loggers along the Rhine and its tributaries (operators and data sources: BfG, HLUG: Hessian Agency for the Environment and Geology, LUBW: Agency for the Environment, Measurements and Nature Conservation Baden-Württemberg, LUGW: State Office for the Environment, Water Management and Trade Supervision Rhineland-Palatinate, WSV).

In addition to the water quality measurement stations, temperature data loggers were temporarily deployed with the support of the Federal Waterway and Shipping Administration (WSV) at lateral buoys of the river channel at a depth of 1 m. Their locations were close to some of the regular measurement stations but were also in between to complement the density of the in situ measurement network. The absolute accuracy of the temperature data loggers was $\pm 0.1°\mathrm{C}$ according to the manufacturer’s calibration and the test calibration performed before deployment. Most temporary temperature loggers close to water quality measurement stations confirmed the station measurements within the expected accuracy limits.

3.5.

Additional Data

For the atmospheric correction, the atmospheric conditions were derived from a combination of weather data at ground level and predefined standard atmospheric profiles from the atmospheric band model (see Sec. 4.2). Temperature, relative humidity and station pressure at weather stations in the research area were accessed from the German Meteorological Service (DWD)²⁵ and linearly interpolated in space and time to obtain representative input parameters for each image that was corrected (see Ref. 26).

4.1.

Comparison with In Situ Measurements

The ability to estimate bulk water temperatures with the remote sensing datasets was assessed by a comparison with in situ measurements at the acquisition time. The temperature is extracted from the remote sensing data at the location of the measurement station or its water outtake, respectively. For the characterization of the dataset, the mean and standard deviation of the temperature difference were calculated. Additionally, the RGBNIR classification was consulted to determine whether the remote sensing sensor actually acquired water temperature at that location.

4.2.

Calibration and Atmospheric Correction of the Aerial Survey

When evaluating the local effect of the water temperature on the river ecosystem, it is necessary to obtain absolute bulk temperature values and their error estimates. The TIR camera sensor, however, acquires the brightness temperature of the observed surface ($T_B$), including all radiances emitted into the line of sight of the camera. As water is a good, but not a perfect, absorber, it has an emissivity ($\epsilon$) between 0.96 and 0.99 in the 8 to $14\mu \mathrm{m}$ region.²⁷ Thus, a correction for the emissivity of the observed surface and the influence of the atmosphere is mandatory for calculation of kinetic surface temperatures ($T_{\text{surface}}$). Based on the wavelength range of the TIR sensor, the low suspension load of the Rhine River, and only few waves with foam during the acquisition, an emissivity value of $ϵ=0.99$ was chosen. After the correction for emissivity, two different approaches for correcting the datasets were tested with the aim of evaluating the efforts necessary for their calculation in relation to the quality of the results: As retrieval schemes for the river water temperature with regression between in situ and brightness temperatures was employed as well as straightforward atmospheric correction based on the physical parameters and modeling of the atmosphere.

When a sufficient number of in situ measurements is available for a dataset and the variability of the bias between remote sensing and in situ temperatures is low, a linear regression of the remotely sensed $T_{\text{surface}}$ based on in situ measurements is a possible option. This is a well-established method for the calibration of sea surface temperatures (SST) acquired by various satellite sensors. The SST or $T_{\text{surface}}$ is compared to in situ measurements ($T_{\text{insitu}}$), the coefficients ${\alpha }_0$ and ${\alpha }_1$ for a linear relationship between $T_{\text{surface}}$ and $T_{\text{insitu}}$ are fitted using the least squares approach, and $T_{\text{surface}}$ is directly calibrated to the bulk temperature of the sea water.

For the aerial survey, this was accomplished by randomly selecting half of the in situ measurements for calibration and calculating the coefficients for a linear regression between the aerial dataset and the in situ measurements. The surface temperatures from the aerial survey were then calibrated based on the discovered relationship and validated with the remaining in situ measurements. For SST products, using the linear relationship between $T_{\text{surface}}$ and bulk temperature is simple and effective, but it has been disputed and more advanced calibration algorithms have been developed.^28–30 They take into account the water vapor content and vertical structure of the atmosphere or the state of the water surface and consider nonlinear errors due to the nonlinear relationships among brightness temperatures, water surface temperatures, and the state of the atmosphere. The nonlinear nature of these relationships, however, is more relevant on larger spatial scales ($>5\mathrm{deg}$) than the scale of the aerial survey,³⁰ where a calibration based on linear regression seemed suitable.

An alternative to the calibration with in situ measurements is the correction for atmospheric influences during the acquisition. The surface temperature can be underestimated by up to 5 to 10°C if the influence of the atmosphere is not corrected.²⁶ During the aerial survey, the difference was smaller, but could not be ignored (see Sec. 5.2). The temperature measured by the camera sensor is calibrated under laboratory conditions, but in reality, measured radiance and brightness temperature are affected by downwelling $L_a^{\text{down}}$ and upwelling $L_a^{\text{up}}$ atmospheric radiances as well as the transmissivity $\tau$ of the atmosphere [Eq. (2)]. The temperature measured during the aerial survey has to be converted to radiance $L_{\text{meas}}$ with Planck’s radiation law and corrected for the emissivity ($ϵ$) of the surface and the atmosphere between surface and sensor altitude ($L_a^{\text{up}}$, $L_a^{\text{down}}$, $\tau$) (Refs. 31 and 32, references to the wavelength are omitted).

The atmospheric parameters in Eq. (2) were modeled based on radiative transfer equations by the software MODTRAN^®5.3.2. It is widely used to correct single-band thermal data acquired by satellite and airplane; for some datasets, predefined input parameters and weather data are available (e.g., in the AtmCorr Calculator,³² ATCOR).

Individual atmospheric parameters were calculated for each image of the aerial survey; weather data (air temperature, station pressure, and relative humidity) from a DWD meteorological station was linearly interpolated for the acquisition time and center point of each temperature raster and combined with a standard atmospheric profile (U.S. Standard) as input for MODTRAN^®5.3.2. When computing $L_a^{\text{down}}$ and $L_a^{\text{up}}$, the radiances were integrated over the wavelength and the response function of the sensor as suggested by McCarville et al.³³ The temperature raster was then corrected based on Eq. (2) and compared to in situ measurements where available.

The atmospheric correction does not take into account other processes at the water surface that can influence the acquired brightness temperatures. These are the difference between the skin temperature at the water surface measured by the TIR sensor and the subsurface bulk water temperature represented by the in situ measurements, the possible stratification of the water, or the effects of viewing angle, wind, waves, and foam on the emissivity.

4.3.

Artificial Satellite Datasets

One aim of this study was to test the methods for the detection of inflows for datasets with different resolutions and noise levels, but thermal images from satellites were not available at the same point of time as the aerial survey. Hence, several artificial datasets that resemble actual datasets provided by the Landsat missions were created by degrading or upscaling³⁴ the TIR and RGBNIR raster data of the aerial survey. For the upscaling of thermal raster data, a spatial filter designed to simulate the sensor response should be applied,^35,36 but block averaging is commonly used and gives satisfactory results.^36–38 The brightness temperatures acquired by the aerial survey were used as input, as the effect of the exponential term in the Planck’s radiation law to convert between radiance and temperature should be small and there is no obvious difference between the scaling of temperature and radiance.³⁸ It was implemented by using the functions measure.block_reduce from the skimage package³⁹ and the module gdal from the osgeo package⁴⁰ in python.⁴¹ Subsequently, a random noise mask with a normal distribution, with zero as mean value and a standard deviation equal to the desired noise equivalent differential temperature ($\mathrm{NE}\mathrm{\Delta }T$) was created and added to the degraded raster data with the new, lower resolution. Of the final datasets, one dataset was created with the $\mathrm{NE}\mathrm{\Delta }T$ and acquired resolution of Landsat ETM+ thermal data.^42,43 The other two datasets received the spatial resolution of the new Landsat TIRS sensor (100 m), with two different $\mathrm{NE}\mathrm{\Delta }T$: 0.4°C, required during the planning phase of the satellite mission,⁴⁴ and the actually evaluated 0.1°C.⁴⁵ Table 2 assembles the characteristics of the original survey data and the three artificial satellite datasets. While the mean temperature remained almost the same, the block averaging reduced the temperature range of the dataset and the standard deviation decreased with increasing pixel size rather than with increasing $\mathrm{NE}\mathrm{\Delta }T$ (see Ref. 38).

Table 2

Overview of the evaluated remote sensing datasets with their spatial resolution and sensor noise.

4.4.

Inflow Detection

For the detection of inflows along the Rhine River, the mean and the standard deviation of the water temperature for every 100 m were calculated from the distributed longitudinal profile (see Fig. 3). For every 100 m of the longitudinal profile, the temperature from evenly spaced points across the whole river was collected and summary statistics (mean ${\mu }_{100\mathrm{m}}$ and standard deviation ${\sigma }_{100\mathrm{m}}$) were calculated to represent the characteristics of the river temperature and further analyzed.

Fig. 3

The mean temperature and standard deviation of the temperature along the distributed longitudinal profile of the Rhine River, extracted from the original aerial survey acquired on October 31, 2013 (data source: BfG). The changes of mean temperature and standard deviation show the effect of inflows with differing water temperatures on the river temperature.

The change point analysis is a suitable method to identify the points where the statistical properties within the dataset change.⁴⁶ The applied pruned exact linear time method offers exact segmentation of datasets to identify several change points with computational costs linear to the number of data points.⁴⁶ The change point package⁴⁷ of the statistical program R (Ref. 48) was then used to apply the change point analysis of the mean river temperature and to test whether this method could identify inflows even without prior knowledge of them. A standardized method was implemented to set the threshold for the change detection so that the change detection of different datasets could be compared: different threshold values were tested and the threshold was reached when the number of change points converges asymptotically to a stable value. Compared to other methods to define the penalty value, this approach proved to detect the position of the known inflows the best and was the least affected by the variance of the dataset. The change point analysis of the mean was conducted for the ${\mu }_{100\mathrm{m}}$ of all original and artificial datasets (see Sec. 4.3). The locations of known potential inflows²¹ served as validation data and counted as detected if a change point was found within 5 km of a known potential inflow. The change point analysis of the mean and variance proved to result in too many change points as the variance could also change long after the inflow based on the distribution of the water plume.

Additionally, the simple standard deviation of the water temperature for each 100 m section (${\sigma }_{100\mathrm{m}}$) could be used to evaluate the mixing processes of water bodies. After an inflow, the lateral flow of the main stream and the plume of the inflow are indicated by the increasing variability of the water temperatures. Ideally, a certain distance after the outlet, the water bodies have mixed and the stream exhibits a nearly uniform temperature with a low standard deviation in the distributed longitudinal profile (see also Fig. 3). Thus, the standard deviation of the water temperature across the river can serve as an indicator for the existence of plumes or uniform streams. As a threshold for uniform river sections, the mean plus the standard deviation of all ${\sigma }_{100\mathrm{m}}$ of the longitudinal profile was chosen.

5.1.

Characteristics of the Dataset

Throughout the original aerial survey, a systematical error in the form of a temperature decrease could be observed toward the border area of the single scenes. The range was $-0.1$ to $-0.2°\mathrm{C}$ compared to the temperature in the center area of the overlapping neighboring scene. This phenomenon could be observed due to the constant emissivity and only slowly changing temperature of the river water in contrast to the changing emissivities and $T_B$ of the varying land surfaces. The spatial allocation of the pixels was not necessarily accurate as the spatial accuracy was only $\sim 15\mathrm{m}$, but even after applying a $3\text{pixel}\times 3\text{pixel}$ averaging filter, the systematical error was visible. Possible causes for this error include the influence of varying observation angles on the atmospheric parameters (up- and downwelling atmospheric radiances and transmissivity) and emissivity or sensor degradation toward the border areas. The correction of one test scene with MODTRAN^®5.3.2 and different observation angles showed that the look angle off-nadir at the border of the scene (20 deg) caused no changes in transmissivity, but a slightly higher upwelling radiance. This should actually cause higher brightness temperature at the border ($+0.4°\mathrm{C}$). On the other hand, water shows a decrease of emissivity with increasing viewing angle,⁴⁹ which could cause decreasing brightness temperatures. This effect has been calculated to be only around $-0.1$ to $-0.2°\mathrm{C}$. The observation could also be caused by natural vignetting that is more prominent for short focal lengths and wide angle lens as used for the acquisition of the TIR images. Based on these estimations that have an equally large uncertainty, the observed systematic error remains partly unexplained and a sensor error cannot be eliminated.

5.2.

Evaluation of Original, Calibrated, and Corrected Aerial Survey Data

For the evaluation of the usefulness of the remote sensing temperatures and the correction methods, $T_B$ acquired by the aerial survey and corrected $T_{\text{surface}}$ were compared to the water temperatures measured in situ. $T_B$ and $T_{\text{surface}}$ actually represent the skin temperature of the water surface, while the in situ stations and temperature loggers measure the subsurface (bulk) water temperature at 1 to 2 m depths. All datasets were preprocessed as described in Sec. 4.2, and the difference between the temperatures acquired by the aerial survey, $T_{\text{aerial}}$, and the in situ measurements from 19 stations at the time of acquisition was calculated ($\mathrm{\Delta }T$). The mean difference ($\mu$) between the uncorrected original dataset from the aerial survey and the in situ temperature measurements was $-1.23°\mathrm{C}$ with a standard deviation ($\sigma$) of 0.54°C. The aerial data underestimated the real water temperature quite uniformly over the survey area. The in situ measurement stations where $\mathrm{\Delta }T$ was outside $\mu \pm \sigma$ were investigated more closely. Of these stations, two temperature measurement stations located at Rheinhausen and Worms had to be omitted as it is unclear which water body they represent. Both river sections are characterized by a parallel flow of inflow plumes and river water, and the in situ measurements are situated at the boundary layer between the two water bodies. The authors believe that the underwater measurements at the two locations do not represent the surface water temperature as the vertical mixing of the water layers at this location is incomplete. Without the measurements in question, the variance of $\mathrm{\Delta }T$ was reduced (see Fig. 4) and they were omitted for the remaining evaluation of the aerial dataset. A correction for the emissivity improved the mean $\mathrm{\Delta }T$ to $-0.85°\mathrm{C}$, while the standard deviation, as expected, remained almost the same at 0.15°C.

Fig. 4

Boxplot of the temperature differences between aerial survey and in situ measurements ($\mathrm{\Delta }T=T_{\text{aerial}}-T_{\mathrm{insitu}}$), showing the effects of the correction steps on $\mathrm{\Delta }T$ (black line: median, bottom and top of the box: first and third quartiles, whiskers: $\pm 1.58$ interquartile range, roughly a 95% confidence interval).

The remaining $\mathrm{\Delta }T$ could be due to the atmospheric influence and a difference between surface and bulk temperature. At mean runoff, vertical mixing takes place in the Rhine River and prevents a stratification of water bodies: even when low sun angles occurred and hard shadows were visible in the RGBNIR data on the water surface, no temperature differences were detectable in the TIR data at the shadow border. Based on this assumption of vertical mixing, differences between subsurface and bulk water temperature were neglected. However, differences between the subsurface and the cooler skin temperature (skin effect) can occur in the dimension of 0.1°C (daytime) to 0.5°C (nighttime),⁵⁰ but could not be investigated in the absence of additional in situ measurements of the skin temperature.

The correction of the aerial survey based on a linear regression between half of the in situ measurements and the corresponding TIR temperatures should also correct for the skin effect and was quite successful: After the correction for emissivity and the calibration with ${\alpha }_0=1.81$ and ${\alpha }_1=0.93$, the mean $\mathrm{\Delta }T$ between the aerial survey and the second half of the in situ temperatures selected for the validation was $0.04\pm 0.21°\mathrm{C}$ (see also Fig. 5). On the other hand, the atmospheric correction slightly overestimates the atmospheric influence ($\mathrm{\Delta }T=0.14\pm 0.33°\mathrm{C}$). With a subsequent calibration based on linear regression between the temperatures corrected for the atmosphere and in situ measurements (${\alpha }_0=4.81$, ${\alpha }_1=0.64$), mean $\mathrm{\Delta }T$ was reduced to $-0.10\pm 0.21°\mathrm{C}$ when comparing the corrected and calibrated temperatures to the validation in situ data. As the atmospheric correction of the raster temperature images was calculated individually, the values of $\mathrm{\Delta }T$ did not change uniformly (see also the increased standard deviation of $\mathrm{\Delta }T$ for the atmospheric correction in Fig. 4). Hence, mean $\mathrm{\Delta }T$ is not the same as for the calibration only. The resulting mean differences were similar to other studies,^12,13 but with a lower variance of the differences. The authors conclude that the relationship between remote sensing and in situ temperatures is similar for all measurement stations and temperature loggers in this analysis, except the stations excluded before (see beginning of Sec. 5.2).

Fig. 5

Uncorrected and corrected temperatures from the aerial survey versus in situ measurements. The data points of the original survey show that a correction is necessary, but the bias is fairly uniform and the results of calibration and atmospheric correction lie very close to the line through the origin.

The artificial degraded datasets corrected for emissivity were also compared to in situ measurements (see Fig. 6). The degrading of both the spatial resolution and the sensor noise lead to a decreasing remote sensing temperature that underestimates the actual water temperature at the in situ measurement stations. This may be due to mixed pixels of water and land surface at the river shore, which had a lower $T_B$ at acquisition time, and the measurement stations that were mostly located close to the river shore. The standard deviation of the difference between remote sensing temperatures and in situ measurement increased with the pixel size in this comparison (see Fig. 6), but it is still lower than the standard deviation of the original Landsat ETM+ scenes for the Rhine River ($\sigma =1.3°\mathrm{C}$) from a previous study,⁶ which are additionally affected by the atmosphere and sensor characteristics.

Fig. 6

Boxplot of the temperature differences between the in situ measurements and the four different remote sensing dataset corrected for emissivity ($\mathrm{\Delta }T=T_{\text{dataset}}-T_{\text{insitu}}$) (black line: median, bottom and top of the box: first and third quartiles, whiskers: $\pm 1.58$ interquartile range, roughly a 95% confidence interval).

5.3.

Inflow Detection

The majority of the 20 known inflows could be detected by the change point analysis of the mean: the sensitivity of the change point analysis to the changes of the mean temperature from the distributed longitudinal profile seems to be sufficient as the mean includes any temperature changes across the river caused by inflows and dischargers (e.g., Fig. 7 and Table 3). The change point analysis also detects false positive change points. If one inflow does not mix well with the main river stream and causes several $T_{\text{mean}}$ changes depending on the distribution of the plume of the inflow, several change points are detected by this method (for example, downstream of the power plant in Philippsburg in Fig. 7). This also shows that an inflow plume can change its apparent size and persist over a long distance after the inflow source. On the other hand, when several inflows with a similar effect on the river water temperature are located close to each other, only one change point is detected and the inflows cannot be identified separately (for example, in Karlsruhe and Mannheim/Ludwigshafen).

Table 3

Results of the change point analysis of the mean river temperature from the different remote sensing datasets: mainly the increasing noise level of the datasets caused an increasing number of missed inflows and false positive change points.

Fig. 7

Change point analysis of the mean water temperature from the original aerial survey. 80% of the inflows were successfully detected (marked by green dashed lines) by change points (red dashed lines).

The degrading of the raster datasets (sensor noise and spatial resolution) seemed to have different effects on the ability to detect inflows (see Table 3). With the chosen threshold method, a higher $\mathrm{NE}\mathrm{\Delta }T$ leads to a larger number of false positive change points, when nonexistent inflows are instead caused by sensor noise and mixed pixels. Their influence seems to override the effect of the spatial resolution that should reduce the variance by averaging the temperature values.

In the dataset with the higher resolution, i.e., the original aerial dataset, the effects of the inflows could be detected in the standard deviation of every 100 m part (see power plant Philippsburg, Neckar River at Mannheim, Main River, in Fig. 8): only after a certain distance, the mixing of the main stream and the inflow is completed and the standard deviation of the distributed longitudinal profile falls below the threshold (defined in Sec. 4.4). Especially, the river part 70 km downstream of the power plant in Phillipsburg and the river part from Mainz and the Main River inflow until the Middle Rhine Valley around Rh-km 550 are characterized by inflows with persistent plumes and with a large impact on the variance of the river temperature. The temperature plumes of the inflows prevail until the next inflow and overlay each other. With a lower spatial resolution and more sensor noise, the ability to detect plumes abated as they could not be differentiated from the variance inherent to the dataset.

Fig. 8

The standard deviation of the temperature along the distributed longitudinal profile of the Rhine River and the identified inflow plumes for the dataset with a spatial resolution of $5\mathrm{m}\times 5\mathrm{m}$ (data source: BfG). In the first river section, $\sigma$ is relatively low and the temperature distribution across the river uniform except shortly after the inflows in Karlsruhe. However, from Philippsburg on, temperature differences across the river are prevalent and until 20 km after the Nahe inflow, the river is thoroughly mixed only for short passages.