Sediment Transport Dynamism in the Conﬂuence Area of Two Rivers Transporting Mainly Suspended Sediment Based on Sentinel-2 Satellite Images

: Downstream of the conﬂuence of rivers, complex hydrological and morphological processes control the ﬂow and sediment transport. This study aimed to analyze the spatio-temporal dynamics of suspended sediment in the conﬂuence area of the Tisza and its main tributary Maros River using Sentinel-2 images and to reveal the correlation between the hydrological parameters and the mixing process through a relatively long period (2015–2021). The surﬁcial suspended sediment dynamism was analyzed by applying K-means unsupervised classiﬁcation algorithm on 143 images. The percentages of the Tisza (TW) and Maros (MW) waters and their mixture (MIX) were calculated and compared with the hydrological parameters in both rivers. The main results revealed that the areal, lateral, and longitudinal extensions of TW and MIX have a better correlation with the hydrological parameters than the MW. The Pearson correlation matrix revealed that the discharge ratio between the rivers controls the mixing process signiﬁcantly. Altogether, 11 mixing patterns were identiﬁed in the conﬂuence area throughout the studied period. The TW usually dominates the conﬂuence in November and January, MW in June and July, and MIX in August and September. Predictive equations for the areal distribution of the three classes were derived to support future water sampling in the conﬂuence area.


Introduction
River confluences are one of the most essential geomorphological spots along rivers, as they control the flow and sediment transport conditions downstream [1]. The confluences can form in various hydro-morphological configurations. The most common is when a smaller tributary joins a mainstream with higher discharge, but two similar streams can also join to form a new river. However, when two side-channels are separated by an island and re-join at the end of the island, this also creates a confluence [2].
The hydrodynamics in the confluence area is complex, and it has a spatio-temporal variability. This complexity arises from the various parameters (e.g., water slope, velocity, discharge, momentum, and geomorphological characteristics) of the joining rivers, controlling the water and sediment transport process [3,4]. The transferred momentum from the tributary and the water circulation in the confluence area increases the probability of scour hole formation, which could alter river morphology [5]. Similarly, the turbulence intensity in the confluence area plays a key role in sediment transport and the mixing of various pollutants, which affects the water quality conditions downstream [4]. Therefore, the sampling process of any water constituents in a confluence should be performed only if the actual mixing situation is identified, as various mixing can highly influence the results. mixing of the waters depends on the actual hydrological parameters of the two joining rivers. The goals of the research were: (1) to map the spatial distribution of surficial suspended sediment in the confluence area; (2) to identify the driving hydrological factors which affect the spatial characteristics of the mixing water; (3) to identify mixing patterns based on their lateral and longitudinal characteristics; (4) to derive predictive equations of the areal and longitudinal distribution and mixing of the waters of the two rivers based on the hydrological parameters; and (5) to identify those zones in the confluence area where within future sampling campaigns low-error burden samples could be collected.

Study Area
The Tisza River discharges the eastern part (area: 157,200 km 2 ; length: 962 km) of the Carpathian Basin in Central Europe, while the Maros/Mures River is its most significant tributary (area: 30,000 km 2 ; length: 750 km [50]). The study area extends 4.2 km downstream of the confluence of the Tisza and Maros Rivers ( Figure 1). Therefore, the general aim of this study is to investigate the multi-year spatio-temporal dynamism of the mixing of two rivers using Sentinel-2 satellite images. The confluence of the Tisza and Maros Rivers (Hungary) was selected as a study area as the two rivers transport a considerable amount of suspended sediment, and they can influence each other significantly during floods by impoundment. Therefore, it was hypothesized, that the mixing of the waters depends on the actual hydrological parameters of the two joining rivers. The goals of the research were: (1) to map the spatial distribution of surficial suspended sediment in the confluence area; (2) to identify the driving hydrological factors which affect the spatial characteristics of the mixing water; (3) to identify mixing patterns based on their lateral and longitudinal characteristics; (4) to derive predictive equations of the areal and longitudinal distribution and mixing of the waters of the two rivers based on the hydrological parameters; and (5) to identify those zones in the confluence area where within future sampling campaigns low-error burden samples could be collected.

Study Area
The Tisza River discharges the eastern part (area: 157,200 km 2 ; length: 962 km) of the Carpathian Basin in Central Europe, while the Maros/Mures River is its most significant tributary (area: 30,000 km 2 ; length: 750 km [50]). The study area extends 4.2 km downstream of the confluence of the Tisza and Maros Rivers (Figure 1).  Both rivers have two floods within a year. The first and largest one occurs in early spring due to snowmelt, while the second flood occurs in early summer due to rainfall [51]. Floods usually inundate the floodplains of the Tisza River for 2-3 months, while they last only for 1-2 weeks on the Maros River. During simultaneous floods they can impound each other, or the Danube can impound them. As the Maros has a higher slope [50], it is impounded just along ca. 25 km long section (up to Makó gauging station). However, the Tisza with a lower slope [52] can be impounded by the Danube up to 330 km (to Szolnok). The Tisza enters the confluence area with a lower flow velocity (mean: 0.54 m/s) than the Maros (mean: 0.66 m/s).
The mean discharge of the Tisza is ca. sixfold of the Maros River (Table 1), though the difference between their maximum discharge is just 1.7 times [50]. The Maros transports three times more bedload, and it has ca. three times higher suspended sediment concentration than the Tisza River. The high sediment load of the Maros can be explained by the highly erodible rocks and steep slopes of its catchment, the steep valley and channel slope, and its rapid water level changes. However, as the result of greater water discharge, the annual suspended load of the Tisza is ca. twice as much as that of the Maros [53].
The confluence of the Maros is located at the 177 fluvial km of the Tisza River (0 fkm is at the confluence of the Tisza and Danube Rivers in Serbia). The confluence angle is 23 • . The lower reach of the Tisza River is wider (bankfull width: 164 m) and deeper (bankfull depth: 14.1 m; recorded in 1999 [54]) than the lower reach of the Maros (width: 126 m; depth: 4.26 m; recorded in 1991 [53]). However, it should be noted that upstream of the confluence both rivers are much narrower (Tisza: 140 m; Maros: 70 m) and deeper (Tisza: 16.8 m; Maros: 4.8 m) as the result of intensive channel regulation works. The studied confluence zone extends 4.2 km downstream of the confluence point ( Figure 1C). Here the channel is 170 m wide on average, and the mean thalweg depth is 13.6 m. However, in the confluence area, significant depth variations occur. The narrowest width (149 m) is associated with the greatest channel depth (18.6 m) at cross section No. S4. Meanwhile, the widest width (200 m) can be observed at S5, with a relatively shallow depth (11.6 m). The channel material is mainly clay. The first channel regulation of the studied confluence dates back to the beginning of the 18th century when salt mining and logging flourished in Transylvania. As their main transport route was the Maros, its channel was cleared from shipping barriers [56]. Meantime, it was also a problem that the Maros joined the Tisza almost in the opposite direction (θ: 97 • ). Thus their floods blocked each other, creating extremely large floods, inundating the city of Szeged. In the 1830s there was a debate on the relocation of the conjunction south of Szeged, but economically and commercially this would have adversely affected the city. According to the other plan, the location of the conjunction would have remained almost at the same place, but a new channel section of the Maros is created, so the confluence angle could have been reduced to ca. 23 • . Finally, this plan was implemented in the mid-1850s [57]. However, the new conjunction was badly designed, thus during floods, the artificial channel section of the Maros was almost totally plugged by sediment, and the channel of the Tisza also became aggraded (depth: ≤1 m); thus, the intensive sand bar formation hindered shipping [56]. Therefore, additional plans were made to solve the problem. During the 1860s, the downstream section of the Maros was almost completely straightened, and stone bank protection was built [58], and the channel of the Tisza was narrowed by groynes.

Hydrological Data
Daily water stage (H) and discharge (Q) data were used for the period of January 2015-May 2021 from three gauging stations: the Makó gauging station is located on the Maros 24.5 km upstream of the confluence ( Figure 1B), the Algyő fluviometer is located on the Tisza 14.9 km upstream of it, while the Szeged gauging station is located 3.4 km downstream of the confluence, approximately in the middle part of the study area. The water stage is measured by the local hydrological authority (ATIVIZIG) with a precision of ±0.5 cm. The daily discharge is calculated by the authority applying water level data. However, the discharge rating curves are recalculated monthly based on at-a-site measurements to ensure the quality of the collected data. Daily water level change (∆H) was calculated at the three stations by subtracting the water level at a particular day from its counterpart on the previous day. The differences between daily water level changes between Tisza (Algyő) and Maros (Makó) were calculated by subtracting the daily change in Algyő (∆H Algyő ) from the daily change in Makó (∆H Makó ). The absolute difference in discharge (∆Q) of the two rivers was calculated between Algyő and Makó, while their discharge ratio was calculated between Makó and Szeged stations (Q Makó/ Q Szeged ), which reflect the contribution of the tributary to the main river. In order to calculate the daily slope (S) of the water, the first step was to transform the relative stage data into absolute water levels (m asl.) based on the "0" points of the fluviometers (Makó: 79.50 m, Algyő: 74.00 m and Szeged: 73.70 m asl.). Then the length of the two rivers along their centerlines was measured between gauging stations. Finally, the daily water slope values represent the Tisza slope (S Tisza ) between Algyő and Szeged, and the Maros (S Maros ) between Makó and Szeged were calculated. To calculate the slope difference (∆S) between the Tisza and the Maros Rivers, the daily slope data of the Tisza were extracted from the Maros data.

Remote Sensing Data
Between July 2015 and May 2021, altogether, 143 Sentinel-2 A-B satellite images (free of clouds to ensure the quality of the acquired data) covering the confluence area were downloaded from the Copernicus Open Access Hub [59]. Sentinel-2 captures the Earth with 13 spectral bands ranging from visible-to short-wave infrared [60]. The spatial resolution of the bands ranges between 10 to 60 m; the temporal resolution of the images is five days; however, it reaches three days at mid-latitudes such as the study area at Szeged [61]. The Sentinel-2 products take advantage of ground control points, which resulted in georeferencing accuracy of 12.5 m [62]. Furthermore, the mission's specifications set a limit of 5% radiometric uncertainty and a goal of 3% ideal accuracy [61], which is suitable for this application. The images taken in 2015 and 2016 were available only in level 1C; therefore, they were atmospherically corrected to remove the effects of atmosphere, which differs from time to time, guaranteeing the uniformity of the data and consequently its quality. Meanwhile, the rest of the images (2017-2021) were available in level 2A; thus, they were already atmospherically corrected. The Sen2Cor 2.8 processor, which is integrated with SNAP 8.0 software [59], was applied to perform the atmospheric correction process by converting the top of atmosphere reflectance into the bottom of atmosphere reflectance in three steps (i.e., scene classification for cloud detection, deriving water vapor content and aerosol optical thickness, and finally, converting the top of atmosphere reflectance to the bottom of atmosphere reflectance [63]).
In order to mask the study area, the normalized difference water index (NDWI; developed by McFeeters and Stuart K [64]) was implemented on one image (9 April 2021) to extract water pixels only and to produce a shapefile for the confluence area. The NDWI depends on the reflectance of the near-infrared and visible green bands to enhance the presence of water. It was calculated by the "Band Math" tool in SNAP 8.0 software. Concerning the threshold value, it was identified by trial and error by comparing the output visually, as the authors performed several field campaigns in the study area; thus, they could distinguish the water and non-water pixels. The produced shapefile was used to mask the confluence area on all 143 images.
The high contrast of the reflectance of pixels between the water of the two rivers in the confluence area, which resulted from the difference in their suspended sediment load, was exploited to study the mixing process in the confluence using an unsupervised classification technique. The K-means unsupervised classification algorithm [65] was applied to classify pixels based on their reflectance value to discriminate between the surficial suspended sediment concentrations of both rivers in the confluence area. The general theory of this algorithm is to identify a centroid for every cluster (k), then every point in the data is allocated to each cluster by reducing the sum of the square error to the centroid [65,66]. The number of clusters is identified by the user according to the nature of the data. The algorithm begins the learning process by identifying random centroids; afterwards, it performs repetitive iterations to optimize their positions. The optimization process halts when the centroids stabilize, or when the maximum number of iterations is achieved [65]. In the present study the bands 2, 3 and 4 of Sentinel-2 were chosen for classification, due to their relatively high spatial resolution (10 m), and their sensitivity to suspended sediment concentration [67][68][69][70].
The pixels were classified into three classes, representing the water of the Tisza (TW), which usually has lower suspended sediment concentration; the water of the Maros (MW) with higher suspended sediment concentration; and their mixture (MIX), which has a moderate amount of suspended sediment. The threshold of reflectance of MW in bands 2, 3 and 4 are 0.057, 0.084 and 0.081, respectively, while in the case of MIX, it is 0.055, 0.078, and 0.063, and for TW, it is 0.052, 0.072, and 0.050, respectively. It also demonstrates the reflectance gradient from the lowest values in case of TW to the highest in case of MW. However, these threshold values are an example of one image acquired on 9 April 2021, as they could change temporally because of (1) the dynamism of suspended sediment load transported by the studied rivers, and (2) the changes in chemical and biological processes which affect the water quality of both rivers, and consequently the spectral reflectance of the water surface. Therefore, K-means was applied to accommodate the threshold dynamism, as it automatically selects the threshold of the three bands based on reducing the sum of square error of pixels to the centroid of each class. Despite the algorithm's automated process, every image was analyzed individually to make sure that the actual mixing situation was represented perfectly. In order to avoid misclassification problems which would arise from defining three classes only (due to the existence of shadow developed by trees or bridges), more than three classes were defined, then they were merged to form the TW, MW, and MIX classes. The number of classes was identified by trial and error, comparing the results with the visual overview of the confluence to achieve the most representative classification of the mixing process. The area of the shadow class was extracted from the whole study area. Then the area occupied by the three water types was recalculated and expressed as the proportion of the study area (%).
The areal distribution (%) of the water classes (TW, MIX, and MW) was calculated on all 143 images. The longitudinal mixing was studied by measuring the longitudinal extent (L) of the water of the Maros (MW) into the Tisza as a function of the average width (w) of the Tisza River in the study area (162.2 m). The lateral mixing was also evaluated along five cross sections (S1-5) spaced 1 km apart (ca. 6-times of the width of the Tisza; Figure 1C). Along these cross sections the width of MW, MIX, and TW were measured and divided by the cross-section width to convert it to a percentage, which demonstrates the dominancy of each water type along a cross section.

Correlation between Hydrology and Suspended Sediment Dynamism: Statistical Analysis
The correlation between all measured and calculated hydrological parameters at the three gauging stations (Algyő, Szeged, and Makó) and the spatial and temporal characteristics of the mixing waters (TW, MW, and MIX) were analyzed based on the Pearson correlation matrix. The correlation coefficient (r) was interpreted as very weak 0.0 ≤ r ≤ 0.19, weak: 0.2 ≤ r ≤ 0.39, moderate: 0.4 ≤ r ≤ 0.59, strong: 0.6 ≤ r ≤ 0.79 and very strong: 0.8 ≤ r ≤ 1.0 [71]. Hierarchical cluster analysis (HCA) was applied to classify the images into two groups based on the calculated area (%) of various waters (TW, MW, and MIX) and the hydrological parameters. In this study, Ward's algorithm [72] was used to classify the data, defining the similarity between the clusters based on the summation of squares within the clusters aggregated overall object. Finally, the stepwise multilinear regression technique was applied to produce predictive equations for the areal percentages of various waters (TW, MW, and MIX) in the confluence area and the longitudinal extent of the Maros into the Tisza (L), considering the various hydrological parameters as independent variables. The predictive equations were produced for three cases of data. In Case 1, all data were considered; thus, the resulted equations can be used at any discharge or water stage, and they produce rough predictions, as these models were built based on all measured and calculated data. In Case 2, the data of cluster I were considered, thus the model can be used for predictions with low or medium discharges, while in Case 3, only the cluster II data were dealt with; thus, it is suitable to predict the mixing conditions during high (flood) discharges. All the applied statistical analyses were performed by IBM SPSS software v26.0 [73].

Hydrological Characteristics of the Studied Period
No considerable flood appeared on the studied rivers during the studied period. Five small overbank floods (Algyő: ≥610 cm; Szeged: ≥500 cm) were recorded in the Tisza River at Szeged (Figure 2), whereas just two floods developed on the Maros (Makó: ≥310 cm). These floods created shallow inundations on the floodplains (at Szeged: 6-30 cm; at Algyő: 59-98 cm; at Makó: 18-65 cm). On both rivers, floods developed from February to July; only one of their flood waves coincided (June 2020). The near bankfull stages (at and below bankfull stage by 1.0 m) were more common on both rivers, and they were recorded in the same late winter and spring months. During floods or near-bankfull levels, the Tisza usually had a flood peak simultaneously or slightly later (by 1-2 days) than the Maros (Figures 2 and 3).    Low stages were recorded in the Tisza River, usually between August and January. Similar to floods, the low stages developed on the Tisza simultaneously or slightly later (by 1-4 days) than on the Maros. The lowest water stages in both rivers (Algyő < 60 cm; Makó < −100 cm) were usually measured between August and November. During the studied period, low stages were the dominant stages in both rivers, as their probabilities Low stages were recorded in the Tisza River, usually between August and January. Similar to floods, the low stages developed on the Tisza simultaneously or slightly later (by 1-4 days) than on the Maros. The lowest water stages in both rivers (Algyő < 60 cm; Makó < −100 cm) were usually measured between August and November. During the studied period, low stages were the dominant stages in both rivers, as their probabilities were nearly 80%, and the mean and mode values of annual stages shifted towards low waters (Figures 2 and 3).
In the confluence zone, the mixing of the water of the two rivers might be influenced by the daily stage changes of the two rivers; therefore, it was calculated and analyzed (see Appendix A, Figure A1). Furthermore, the absolute difference in daily water level changes between Algyő and Makó was also calculated ( Figure A1). The data reflect that the Maros had more significant variations in water stages during floods than the Tisza.
In the studied period, during floods, the discharge in the Tisza River varied between 827 and 2087 m 3 /s (Table 2), while the Maros had only 70-731 m 3 /s discharge. In non-flood periods the Tisza had 128-1045 m 3 /s discharge, while the Maros had just 30-393 m 3 /s. However, the ratio between discharges is more informative (Figure 3). The ratio between the discharge measured at Makó and Szeged refers to the contribution of the Maros to the discharge of the Tisza downstream of the confluence (at Szeged). It can be observed that the highest numbers (greater contribution of the Maros) appeared during low stages in both rivers, usually in the winter months or during summer or early autumn. In these cases, the discharge ratio was 0.37-0.57; thus, the Maros contributed by 37-57% to the discharge of the Tisza. The lowest discharge ratios (0.06-0.10) were recorded usually in the winter months, when the Maros increased the amount of transported water of the Tisza just by less than 10%. In the studied period, usually, the Maros had a ninefold greater slope than the Tisza (Table 2, Figure 4). The Maros had greater variations in slope, as it had a range of 16.9 cm/km (min: 2.7 cm/km; max: 19.6 cm/km), while it was only 5.5 cm/km for the Tisza, respectively (min: 0.0 cm/km; max: 5.5 cm/km). Usually, during floods, the slope of the Tisza ranged between 1.3 and 5.5 cm/km, while the Maros had a 2.7-19 cm/km gradient. However, during non-flood periods the slope of the Tisza dropped considerably (0.0-3.4 cm/km), whereas the Maros kept the high slope values (8.4-19.6 cm/km). The temporal change of slope conditions of the Tisza River opposes its counterpart of the Maros River (Figure 4), thus when the slope of the Tisza increased (following the same pattern as the stage and discharge), usually the slope of the Maros decreased, referring to impoundment.  The difference in slope conditions was also analyzed, as it can fundamentally influence the mixing of the waters of the two rivers. The slope differences between the Tisza and Maros showed significant temporal variations, as the difference could be as high as 20.8 cm/km (min: −18.8 cm/km, max: 2 cm/km). The Tisza and the Maros had very similar slope conditions; only when the slope of the Maros declined (due to impoundment), and the Tisza had a high slope during a flood wave, the difference between their slope values get close to 0 cm/km or above it. Such cases were observed in late winter and early summer. On the contrary, the negative values (<−17 cm/km) refer to the high slope on the Maros due to its small flood wave and a simultaneous low stage of the Tisza, when the Törökbecse Lock impounded it. This situation was observed in the summer months (June-July), when the Maros had a greater slope than the Tisza by 17.4-18.2 cm/km. The difference in slope conditions was also analyzed, as it can fundamentally influence the mixing of the waters of the two rivers. The slope differences between the Tisza and Maros showed significant temporal variations, as the difference could be as high as 20.8 cm/km (min: −18.8 cm/km, max: 2 cm/km). The Tisza and the Maros had very similar slope conditions; only when the slope of the Maros declined (due to impoundment), and the Tisza had a high slope during a flood wave, the difference between their slope values get close to 0 cm/km or above it. Such cases were observed in late winter and early summer. On the contrary, the negative values (<−17 cm/km) refer to the high slope on the Maros due to its small flood wave and a simultaneous low stage of the Tisza, when the Törökbecse Lock impounded it. This situation was observed in the summer months (June-July), when the Maros had a greater slope than the Tisza by 17.4-18.2 cm/km.

Mixing of Waters in the Confluence Area-General Characteristics
In the study area, the Tisza (TW) and Maros waters (MW) and their mixing (MIX) showed characteristic spatio-temporal variations throughout the studied period ( Figure 5). Usually, the water of the Tisza dominated the confluence area (mean areal proportion: 48.7%), while the Maros water occupied a much smaller area (mean: 12.4%), but their mixed water also occupied high proportions (mean: 38.9%). When there was a flood on the Tisza, the incoming Tisza water was even more dominant, as it occupied 60-100% of the confluence area. In some cases, the Maros water covered as much as 10-25; however, during a flood (June 2020), it covered 55.5% of the confluence due to its high water level. On the other hand, the mixed water of both rivers changed within a wide range (0-52%). The areal changes of the water of the Tisza (TW) compared to the variations of hydrological parameters can help to understand the mixing process. For instance, during simultaneous bankfull or over bankfull (flood) events (e.g., January 2016, December 2017, and March 2018), the dominancy of TW was found in the confluence area, as the Tisza water covered 98-99.5% of the area.
On the other hand, in the confluence zone, the Maros water (MW) had more complex temporal changes ( Figure 5), as it had minimal coverage when the Tisza had bankfull/over bankfull stages and also during simultaneous low stages. However, the highest coverage of the Maros was achieved when both rivers had near-bankfull stages. Thus, the high stage of the Maros resulted in elevated momentum values, which enabled the river to interact more with the Tisza. Therefore, the MW seemed to negatively correlate with the stages greater than bankfull level in both rivers; however, it had a positive correlation with the stages below that level.
The proportion of mixed waters of the two rivers (MIX) was in closer correlation to the areal percentage of TW than to the MW ( Figure 5). The highest MIX percentages were observed during low stages in both rivers, whereas the lowest mixing occurred during flood periods in both rivers.
The spatial distribution of the three water types was studied along cross sections (S1-S5), to reveal characteristic patterns ( Figure 6). The areal changes of the water of the Tisza (TW) compared to the variations of hydrological parameters can help to understand the mixing process. For instance, during simultaneous bankfull or over bankfull (flood) events (e.g., January 2016, December 2017, and March 2018), the dominancy of TW was found in the confluence area, as the Tisza water covered 98-99.5% of the area.
On the other hand, in the confluence zone, the Maros water (MW) had more complex temporal changes ( Figure 5), as it had minimal coverage when the Tisza had bankfull/over bankfull stages and also during simultaneous low stages. However, the highest coverage of the Maros was achieved when both rivers had near-bankfull stages. Thus, the high stage of the Maros resulted in elevated momentum values, which enabled the river to interact more with the Tisza. Therefore, the MW seemed to negatively correlate with the stages greater than bankfull level in both rivers; however, it had a positive correlation with the stages below that level.
The proportion of mixed waters of the two rivers (MIX) was in closer correlation to the areal percentage of TW than to the MW ( Figure 5). The highest MIX percentages were observed during low stages in both rivers, whereas the lowest mixing occurred during flood periods in both rivers.
The spatial distribution of the three water types was studied along cross sections (S1-S5), to reveal characteristic patterns ( Figure 6). In general, the TW and MW had a decreasing trend from S1 towards S5, while the mixed water increased. The TW proportion slightly increased between S1 and S2 (from 58% to 61%), then it dropped gradually until S4 (32%), and finally, it was almost stabilized between S4 and S5. However, during floods, the TW had almost full lateral coverage along all cross sections (see the heat map in the Appendix A, Figure A2). On the contrary, the proportion of the MW decreased suddenly between S1 (36%) and S2 (11%), and then it remained the same; however, it decreased substantially again by the last cross section (S5: 5%). However, when the Maros had near bankfull level, and the water stages in the Tisza were relatively low, the MW was represented in all cross sections with an average lateral percentage of 35% (Appendix A Figure A2). The gradual areal decrease of the waters of the two rivers and the simultaneous increase of the mixed water reflected the gradual mixing of the waters towards downstream. The MIX water usually did not have any coverage at the first cross section as the joining waters just interacted (Appendix A Figure  A2), furthermore, it was only slightly represented during floods, as the study area was already covered by the Tisza or the Maros water. However, the MIX had significant coverage during low stages in both rivers (summer and autumn) when it appeared between the S2 and S5 cross sections.
The distance (L) of the last downstream Maros water pixel was measured from the conjunction point to reveal the longitudinal dimension of the mixing (Figure 7). The longitudinal extent of MW into the Tisza River was 1.3 km on average, thus 7.8 times of the Tisza's channel width (w). However, it had significant variations throughout the studied period, as it varied from 650 m to kilometers (4-26 w). It can be noticed that the temporal changes of the longitudinal extent of MW corresponded to the temporal pattern of the areal percentage of MW; thus, it reached its peaks at near bankfull stages mostly at summer times and had the shortest extent during late summer or autumn low stages, or at near bankfull stages in late winter or early spring. In general, the TW and MW had a decreasing trend from S1 towards S5, while the mixed water increased. The TW proportion slightly increased between S1 and S2 (from 58% to 61%), then it dropped gradually until S4 (32%), and finally, it was almost stabilized between S4 and S5. However, during floods, the TW had almost full lateral coverage along all cross sections (see the heat map in the Appendix A, Figure A2). On the contrary, the proportion of the MW decreased suddenly between S1 (36%) and S2 (11%), and then it remained the same; however, it decreased substantially again by the last cross section (S5: 5%). However, when the Maros had near bankfull level, and the water stages in the Tisza were relatively low, the MW was represented in all cross sections with an average lateral percentage of 35% (Appendix A Figure A2). The gradual areal decrease of the waters of the two rivers and the simultaneous increase of the mixed water reflected the gradual mixing of the waters towards downstream. The MIX water usually did not have any coverage at the first cross section as the joining waters just interacted (Appendix A Figure A2), furthermore, it was only slightly represented during floods, as the study area was already covered by the Tisza or the Maros water. However, the MIX had significant coverage during low stages in both rivers (summer and autumn) when it appeared between the S2 and S5 cross sections.
The distance (L) of the last downstream Maros water pixel was measured from the conjunction point to reveal the longitudinal dimension of the mixing (Figure 7). The longitudinal extent of MW into the Tisza River was 1.3 km on average, thus 7.8 times of the Tisza's channel width (w). However, it had significant variations throughout the studied period, as it varied from 650 m to kilometers (4-26 w). It can be noticed that the temporal changes of the longitudinal extent of MW corresponded to the temporal pattern of the areal percentage of MW; thus, it reached its peaks at near bankfull stages mostly at summer times and had the shortest extent during late summer or autumn low stages, or at near bankfull stages in late winter or early spring.

Hydrological Parameters and Mixing
The relationship between TW, MW, and MIX and the various hydrological param ters of the joining rivers were analyzed in detail, as probably the dominance of one another water reflects the weight of rivers from the point of view of their hydrologic parameters (see Appendix A, Figure A3). The discharge ratio was in the closest relatio ship to water types (especially TW and MIX) at any water stage; however, the slope an discharge differences between the rivers showed a weaker correlation with the area waters with various origins. However, the slope and discharge differences between bo rivers suggest that it must be considered whether it was a period with low slope durin low stages or impoundment, or a high slope period during flood waves. This was al confirmed by the HCA analyses as it classified the data into two clusters. Those mixin patterns belonged to Cluster I, which developed at low and medium discharges (QTisza 747 m 3 /s and QMaros ≤ 150 m 3 /s), while Cluster II contained mixing patterns developing high discharges.
To support these statements, a correlation matrix was created between (1) the are percentage of waters (TW, MW, and MIX) and the longitudinal extent of MW in the co fluence area, and (2) the various measured and calculated hydrological parameters (Tab 3). Based on the Pearson correlation matrix, there was a moderate to strong correlatio between the areal percentages of water pixels (TW, MW, and MIX) and water level, slop slope difference, discharge, discharge ratio, and discharge difference; and very weak co relation with the daily change of water level (ΔH) and the difference between the tw river's daily stage changes. The areal distribution of the main river's water (TW) showe a strong positive correlation with ΔS

Hydrological Parameters and Mixing
The relationship between TW, MW, and MIX and the various hydrological parameters of the joining rivers were analyzed in detail, as probably the dominance of one or another water reflects the weight of rivers from the point of view of their hydrological parameters (see Appendix A, Figure A3). The discharge ratio was in the closest relationship to water types (especially TW and MIX) at any water stage; however, the slope and discharge differences between the rivers showed a weaker correlation with the area of waters with various origins. However, the slope and discharge differences between both rivers suggest that it must be considered whether it was a period with low slope during low stages or impoundment, or a high slope period during flood waves. This was also confirmed by the HCA analyses as it classified the data into two clusters. Those mixing patterns belonged to Cluster I, which developed at low and medium discharges (Q Tisza ≤ 747 m 3 /s and Q Maros ≤ 150 m 3 /s), while Cluster II contained mixing patterns developing at high discharges.
To support these statements, a correlation matrix was created between (1) the areal percentage of waters (TW, MW, and MIX) and the longitudinal extent of MW in the confluence area, and (2) the various measured and calculated hydrological parameters (Table 3). Based on the Pearson correlation matrix, there was a moderate to strong correlation between the areal percentages of water pixels (TW, MW, and MIX) and water level, slope, slope difference, discharge, discharge ratio, and discharge difference; and very weak correlation with the daily change of water level (∆H) and the difference between the two river's daily stage changes. The areal distribution of the main river's water (TW) showed a strong positive correlation with ∆S  The longitudinal extent of MW into the Tisza showed very similar correlations to the areal percentage of MW, as it had the highest correlation with H Makó and Q Makó (r = 0.5 and 0.5 respectively). Thus, the TW and MIX showed their highest correlations with discharge ratio between the two rivers, slope and their slope difference, while the MW showed less sensitivity to discharge ratio and water slopes, and higher sensitivity to discharge and water level measured at Makó gauging station. Thus, it can be concluded that the areal distribution of TW and MIX waters in the confluence area were highly correlated to each other and most of the hydrological parameters of both rivers, whereas the areal distribution of MW was mainly dependent just on the hydrology of the Maros.
In order to understand the mixing processes, some events were selected, when the Tisza and the Maros had very different (low versus high stage) or very similar hydrological situations (i.e., both rivers had floods or low stages). During the studied period, simultaneous floods on both rivers occurred just once, on 30 June 2020, when both rivers reached a peak, the Tisza stage was 585 cm (Szeged) and Maros had 324 cm (Makó). It must be noted that it was a very small flood, as the recorded highest flood was ca. 500 cm higher at both gauging stations. During this event, the mixing was very limited, as the TW and MW had high areal coverage (TW: 38.8%, MW: 55.6%), while the MIX had a very low area (5.6%). The lowest stages in both rivers were recorded on 19 October 2019 (the Tisza at Szeged: 72 cm; Maros at Makó: −96 cm). In this hydrological situation, the MIX dominated the confluence area (67.7%), while the TW and MW areas were limited (24.2% and 8.0%, respectively). In this hydrological situation, the Tisza appeared (upwelled) at the downstream half of the confluence area (S3-S5). Those hydrological situations when the water stages in both rivers were in an adverse condition (high vs. low) were analyzed as well: on March 18th 2016, the greatest difference between the water stages (Tisza (Szeged): 491 cm; Maros (Makó: 33 cm) occurred throughout the studied period. On this day, the Tisza covered almost the whole study area (TW: 89.3%, MW: 6.4%, and MIX 4.4%) without any upwelling, and the water of the Maros was detected along the first three sections (S1-3). In an adverse situation, on 14 July 2018, the Maros had a relatively high stage (Makó: 150 cm), and the Tisza had a low stage (Szeged: 193 cm). At this time, the MW was dominant in the confluence zone (TW: 12.1%, MW: 79.3%, and MIX: 8.5%), and no upwelling occurred.

Main Patterns of Mixing Waters
The previously illustrated spatio-temporal changes of the mixing waters in the confluence area had characteristic patterns. Considering the areal dominancy of each water type, three main mixing patterns were identified: TW dominant, MW dominant, and MIX dominant (Table 4, Figure 8). Within the TW and MIX classes, further subclasses were identified considering the spatiality of the mixing, and the appearance of one of the waters at the end of the study area ("upwelling pattern"). Within the MW dominant class, no upwelling from any other waters was observed, so this class has no subclasses.
In the patterns of the first class, the TW dominated most of the confluence area (Table 4, Figure 8). Sometimes, at the end of the study area, the sudden appearance (upwelling) of one of the rivers was visible (TW4 pattern: Tisza; TW5 pattern: Maros). In other cases, the upwelling was not obvious (TW1-TW3).
In the case of TW1, minor mixing could be observed (Table 4, Figure 8): the TW dominated the confluence area (S1-S5: 70-100%), with a very limited extent of MW (just at S1: 0-30%) and no real mixing of the two water types. This pattern appeared in the winter months, usually in January and November when the discharge of the tributary was very low compared to the Tisza (mean Q Makó /Q Szeged : 0.16; mean ∆Q: 618 m 3 /s), the stage of the Tisza fluctuated more (mean ∆H Algyő -∆H Makó : 1.9 cm), and it had a slightly higher slope; thus, the slope difference of the two rivers was less characteristic (mean ∆S: −9.6 cm/km). This pattern had the highest occurrence frequency (18.9%).
In the subsequent subclasses (TW2 and TW3), considerable mixing was apparent (Table 4, Figure 8); the difference between them was the appearance of MW. In the TW2 subclass, the MW was identified along most of the confluence zone (S1-4), and the MIX was characteristic at all cross sections. This pattern was characteristic in February and March when the Maros had increased discharge compared to TW1 (mean Q Makó /Q Szeged : 0.19; mean ∆Q: 788 m 3 /s), and the Maros had greater changes in stage (mean ∆H Algyő -∆H Makó : −5.6 cm), but the slope changes were similar to the TW1 pattern (mean ∆S: −8.2 cm/km).
In the case of TW3, the MW appeared just at the beginning of the confluence zone (S1), while the MIX appeared in the second half (S3-5) of the confluence zone (Table 4, Figure 8), but its extent could reach 100% at particular sections. This subclass appeared in December when the difference between the discharge of the two rivers was smaller than in case of the TW1 or TW2 (mean Q Makó /Q Szeged : mean: 0.22; mean ∆Q: 476 m 3 /s); however, a tiny flood wave appeared on the Tisza (mean ∆H Algyő -∆H Makó : 3.9 cm), though the slope of the Maros was still higher (mean ∆S: −11.6 cm/km).
The upwelling of the Tisza was observed in case of the dominancy of TW (Table 4, Figure 8). The characteristic feature of the TW4 pattern was the disappearance of TW at the confluence area (within S1) and afterwards it reappeared at the downstream of the confluence (between S3 and S5), as the TW seemed to be blocked by the MIX due to the stratification of MIX water above the TW. Though the MIX extended between S1 and S5 and had high lateral coverage, which could reach to 100% at some cross sections, the TW had the greatest areal percentage; therefore, the TW4 pattern was grouped into TW dominant condition. On the other hand, the MW could be identified along the study area too, but with limited lateral extent (5-35%). The TW4 usually appeared in October and November, when both rivers had low stages, and the discharge difference between the Tisza and Maros decreased (mean ∆Q: 323 m 3 /s), and the slope of the Maros increased (mean ∆S: −12.9 cm/km). However, the discharge ratio and the daily water change difference did not change significantly (mean Q Makó /Q Szeged : 0.2; mean ∆H Algyő -∆H Makó : −4.4 cm).  Figure 8). Within the TW and MIX classes, further subclasses we identified considering the spatiality of the mixing, and the appearance of one of the wate at the end of the study area ("upwelling pattern"). Within the MW dominant class, upwelling from any other waters was observed, so this class has no subclasses. In the patterns of the first class, the TW dominated most of the confluence area (Tab 4, Figure 8). Sometimes, at the end of the study area, the sudden appearance (upwellin of one of the rivers was visible (TW4 pattern: Tisza; TW5 pattern: Maros). In other cas the upwelling was not obvious (TW1-TW3). In the case of the TW5 pattern, the upwelling of the Maros was observed during the dominancy of TW (Figure 8). The characteristic feature of the TW5 pattern was the disappearance of MW at the confluence area (within S1) and its reappearance between S3 and S5 cross sections. It seemed that the lower density TW stratified above the MW, probably because the TW had lower suspended sediment concentration. In this pattern, the TW was dominant (55-95%) but just at the upstream half of the study area (S1-S3), and at the downstream half, the MW had great lateral extent (up to 95%). The MIX appeared in all cross sections, but with limited lateral extent (10-80%; mean: 25%). Due to the low occurrence probability of this pattern (2.1%), it did not have a characteristic occurrence period; however, it had very similar hydrological parameters to the TW4 pattern (mean Q Makó /Q Szeged : 0.2; mean ∆Q: 363 m 3 /; mean ∆H Algyő -∆H Makó : 4.7 cm; mean ∆S: −12.1 cm/km).
The pattern MW6 represented the case when the MW was dominant in the entire confluence zone (Table 4, Figure 8), covering a wide area (30-80%). The TW was also identifiable (S1-S4: 10-75%), as well as the MIX (S1-S5: 10-60%); however, their lateral coverage was smaller than, for example, in subclass TW2. The MW6 pattern usually appeared in June and July when the discharge of the Maros was high compared to the Tisza (mean Q Makó /Q Szeged : 0.34; mean ∆Q: 454 m 3 /s) and when they had a low slope difference (mean ∆S: −13.7 cm/km). This pattern had no further subclasses, and its occurrence frequency was 4.9%.
Concerning the MIX dominant class, five subclasses were identified, similarly to the TW class (Table 4, Figure 8). In the case of MIX7-MIX9 subclasses, the mixed water appeared at every cross section (S1-S5), and the contribution of the mixed water was 5-100%; additionally, none of the waters reappeared (no upwelling) at the downstream end of the confluence area. The specialty of the MIX7 subclass was that the MIX appeared in the entire study area (S1-S5). Nevertheless, TW was detectable along most of the confluence zone (S1-S4: 10-60%), but the MW appeared just on a short section (S1-S2)in a wide strip (5-85%). This mixing pattern usually appeared in August and October.
The MIX8 mixing pattern was similar to MIX7; however, the MW in MIX8 had a longer appearance (S1-S4), though with a narrower lateral extent (30-40%). Although the MW had a significant coverage in MIX8, which was similar to TW2 and MW6 patterns, the MIX had the largest percentage; therefore, it was grouped into the "MIX dominant" condition. This pattern was typical in the summer months (July and August).
In the subclass MIX9, the MW has the lowest contribution, as it appeared just at the beginning of the study area (S1), and here, its width was only 5-30% of the section. Meanwhile, the TW had a shorter longitudinal extent (S1-3) than in subclasses MIX7 and MIX8, though its proportion was higher (5-95%). On the other hand, the MIX also showed very high coverage (S1-5; 5-100%), similarly to the MIX7and MIX8 patterns. The MIX9 mixing pattern was typical in late summer (August and September), with a high occurrence frequency (16.1%).
These mixing patterns (MIX7-9) appeared at similar discharge conditions, when the Maros contributed by ca. 20-50% to the discharge of the Tisza (mean Q Makó /Q Szeged : 0.31), and the slope difference between the two rivers was low (mean ∆S: −13.9 cm/km). The highest discharge ratio (mean Q Makó /Q Szeged : 0.35), the lowest discharge difference (mean ∆Q: 170 m 3 /s), and the smallest slope difference (mean ∆S: −14.9 cm/km) occurred within the MIX9 pattern, referring to the fact that the high contribution from the Maros not only translated to a dominancy of MW but also the MIX's.
Within the class of dominance of MIX, the water of the Tisza or Maros could upwell forming the patterns MIX10 and MIX11 (Figure 8). In the case of the MIX10 pattern, the Tisza upwelled, similarly to the TW4 pattern: the TW was observed at S1, then it disappeared, and afterward, it reappeared between S2 and S4. However, the characteristic feature of MIX10 was that the TW seemed to be blocked by the MW, and not by the MIX, which was the case in the TW4 pattern. While the MW extended only between S1 and S2, it had a significant lateral extent (35-100%). Due to the upwelling of the Tisza water, the MIX could be observed between S2 and between S3 and S4, then it reappeared at the downstream end of the studied area (between S4 and S5), with a lateral extent range between 10 and 100%. The MIX10 pattern usually appeared during the summer (July and August), when the Maros had a higher contribution than the TW4 pattern, as the discharge ratio in MIX10 (mean Q Makó /Q Szeged : 0.25) was greater than its counterpart in TW4 (mean Q Makó /Q Szeged : 0.2); furthermore, the discharge, daily change and slope differences in MIX10 were lower (mean ∆Q: 223 m 3 /s; mean ∆H Algyő -∆H Makó : −2.5 cm; mean ∆S: −13.7 cm/km) than their counterpart in TW4 (mean ∆Q: mean: 323 m 3 /s; mean ∆H Algyő -∆H Makó : 4.4 cm; mean ∆S:−12.9 cm/km). The pattern MIX10 had greater frequency (12.6%) than the pattern TW4 (5.6%).
The MIX11 pattern represents (Table 4, Figure 8) the upwelling of the Maros with the dominancy of MIX; however, it was very unusual (frequency: 1.4%). This pattern was similar to the TW5 pattern in terms of the disappearance of MIX at the upstream part of the study area (S1-S2) and then reappearance downstream (MIX11: S3-S4; TW5: S3-S5). However, in MIX11, it interfered with the MIX water, not with the TW like TW5. Furthermore, it had less lateral extent (15-35%) than the TW5 (20-95%). The decrease of the areal coverage of MW in MIX11 was substituted by MIX, as the MIX covered greater area than in case of TW5 (S1-S5: 5-100%). The TW had a similar extent in both patterns, as it extended between S1 and S3 with an average lateral percentage of 60%. The MIX11 was observed in April and August, when the discharge ratio (mean Q Makó /Q Szeged : 0.25) was 1.25 times higher than TW5 (mean Q Makó /Q Szeged : 0.2). Moreover, the daily change and slope differences showed lower values in MIX11 (mean ∆H Algyő -∆H Makó : −1.0 cm; mean ∆S: −13.0 cm/km) than in TW5 (mean ∆H Algyő -∆H Makó : 4.7 cm; mean ∆S: −12.1 cm/km), which supported the high contribution of the Maros.
Comparing the mixing patterns with the hydrological parameters of the two rivers (Table 4, Figure 8), it could be noticed that usually, the TW dominated. The TW1-5 patterns developed when the Tisza had high stages and discharges, whereas the Maros had low stages and discharges, as the lowest average discharge ratio (Q Makó /Q Szeged : 0.16) existed within this pattern. Thus, the Tisza impounded the low-discharge Maros. On the other hand, the dominancy of the Maros (pattern MW6) usually occurred during high stages in both rivers, when the discharge ratio was very high (mean Q Makó /Q Szeged : 0.34); thus, the Maros supplied almost one-third of the water of the Tisza. Therefore, the Maros could penetrate the confluence zone deeper; however, due to the high stage of the Tisza, the MW could not extend laterally, but instead, it extended downstream until the end of the study area with a considerable areal coverage. The most common mixed pattern (MIX9) appeared in the confluence zone in late summer (August and September), when both rivers had low stages, and their discharge ratio was high (mean Q Makó /Q Szeged : 0.35), thus the Maros contributed considerably to the discharge of the Tisza, but the MW disappeared quickly due to the mixing process and converted into MIX with a significant area. The appearance of the waters of one of the rivers at the end of the study area (upwelling patterns: TW4-5 and MIX10-11) was not frequent. The upwelling of the Tisza (TW4 and MIX10) usually occurred in August, when both rives had low stages. Probably in these exceptional events, the Maros water stratified over the low velocity Tisza water because of its higher temperature, thus the MW covered almost the whole area at the point of the confluence (S1-2: 35-100%); however, afterward, the Tisza water reappeared downstream (S2-4). The upwelling of the Maros (TW5 and MIX11) had the lowest probability; it usually occurred when the Tisza had high stages, and the Maros had low stages but with a high suspended load. As a result, the Tisza water stratified over the water of the Maros between S1 and S3, however the MW reappeared at the downstream part of the confluence (S3-S5).

Predictive Models
Predictive equations were produced for three groups of data: (1) all data considered; (2) cluster I (low and medium discharges) data considered; (3) cluster II (high discharges) data considered. Table 5 shows the produced equations for the three cases and the R 2 (coefficient of determination) for each model. The produced equations show the highest accuracy on the prediction of the areal distribution of TW (R 2 : 0.6-0.63) and MW (R 2 : 0.61-0.7), whereas the lowest accuracy can be observed with MIX (R 2 : 0.4-0.55). The prediction of the longitudinal extent (L) of MW in the confluence area is the most reliable if it is based on the areal distribution (%) of MW (R 2 : 0.64-0.82). Table 5. Predictive equations for the areal distribution of the mixing waters (TW, MW, and MIX) and the longitudinal extent (L) of MW in the study area for the three groups of data.

Discussion
The mixing process in the confluence area of the Tisza and its tributary (the Maros) and its correlation with the hydrological parameters of both rivers were analyzed in detail based on 143 Sentinel-2 satellite images taken between July 2015 and May 2021.

Hydrological Background of the Mixing
Based on the calculated daily water stage changes, the Maros River demonstrated the greatest daily rising and falling stages throughout the studied period, which refers to a flashy regime with rapid flood waves (below or above bankfull level) and short inundation periods. However, within the studied 7 years, only two tiny floods were recorded. This result is in line with the long-term hydrological analysis [74], which revealed that on the Maros there is a dramatic decrease in floods. Between 1876 and 2011, it decreased from 22.1 days/year to 14.7 days/year, while within the studied period (2015-2021) only two floods appeared for 1-5 days/year. From the point of mixing, it is also important, that usually the Maros floods usually precede the Tisza's by 1-2 days, whereas the lowest stages of the Maros are followed by 1-4 days of the Tiszas. During flood waves, both rivers carry a considerable amount of water; however, the highest discharge ratios were recorded during low stages: at these occasions, the Maros contributed to 24-35% of the discharge of the Tisza, as the main river had a significant drop in discharge and slope values. The Maros usually has a much higher slope (max: 13-16.5 cm/km) than the Tisza (max: 4-5 cm/km). However, during floods on the Tisza River, the Maros might be impounded; therefore, the water slope of the Maros decreases. Thus, our study could be applied for rivers which have characteristically different regimes; the tributary has a higher slope, more diverse stage, and discharge values. However, the main river can influence the mixing processes by its higher discharge and impoundment.

Temporal Changes in the Area of Waters with Various Origin
The areal distributions of TW and MIX are highly correlated (r = −0.91); moreover, they are closely related to water stages and discharges of both rivers. The proportion of TW increases during flood-waves on the Tisza, whereas the mixing water is dominant at low stages. The areal coverage of Maros water shows less sensitivity to water stages and discharges, as it shows low coverage both during low and very high stages; however, its highest area is observed at near bankfull stages. This behavior may be interpreted as the impoundment of the tributary by the main river during high stages, as the momentum of the main river overweighs its counterpart's; thus, it prevents the tributary from spreading in the confluence area. One exceptional event was recorded throughout the studied period when the tributary water (MW) showed a significant spread in the confluence area at over bankfull stages of both rivers (June 2020). At this time, the tributary was able to interact effectively with the main river due to its very high momentum, as the tributary had the highest water stage and discharge recorded within the studied period.
The study revealed that the discharge ratio of the two rivers has the greatest influence on the area of the various water types (TW, MW, and MIX). It is especially valid for the water of the main river (TW) and the mixed water (MIX), which have a strong correlation with the discharge ratio (r: −0.73 and r: 0.67, respectively). This result is in line with the findings of Best and Reid [11], who proved a strong positive correlation between the areal coverage of the separation zone and the discharge ratio between the tributary and the mainstream. Furthermore, the discharge difference between the main river (the Tisza at Algyő) and the tributary (Maros at Makó) and their slope difference show moderate to strong correlation with the areal distribution (%) of the water types. However, a better correlation was achieved when the data were separated into two groups, though the mixing characteristics remained similar, which was also confirmed by the HCA cluster analysis.
The Pearson correlation matrix revealed that, while the water of the main river (TW) and the mixed water (MIX) has high sensitivity to the hydrological situations in both rivers, the water of the tributary (MW) shows lower sensitivity to these parameters, as it is much more dependent just on the hydrological parameters of the tributary itself. This behavior is reflected by the mixing process too, as it seems in most cases the tributary with its high concentration of suspended sediment rapidly disappears in the confluence area, and it can keep its high suspended sediment concentration just in rare cases. On the other side, there is a robust variation in the hydrological conditions in the rivers, which does not match with the temporal variation of the water of the tributary (MW).

Mixing Patterns
Based on the lateral and longitudinal extensions of the three identified water classes (TW, MW, and MIX), 11 mixing patterns were identified, which depend on the hydrological characteristics and momentum of both rivers. The characteristic periods of each mixing pattern were revealed, similarly to the analysis of the confluence of the Solimões and Negro Rivers [48,49].
The water of the main river (TW1 pattern) usually dominates during its high stages and simultaneous low stages in the tributary (usually in early winter and early spring). However, it could also dominate during high stages in both rivers (TW2 pattern: high coverage of the tributary's water) and very less common during low stages in both rivers (TW3 pattern: high coverage of the mixed water). The tributary water usually dominates during high stages in both rivers (MW6 pattern), or high stages in the tributary and low stages in the main river during spring and the summer months. In these cases, the higher slope of the tributary creates favorable conditions for the appearance of the tributary's water without considerable mixing with the main river. The considerable mixing of the waters (MIX7-9 pattern) usually is the most common during low stages in both rivers (usually late summer and early autumn), or during high stages in both rivers, or medium stages in the tributary and low stages in the main river, thus in cases when the flow conditions of the joining rivers are similar. The fact that in the confluence area of the Tisza and Maros Rivers, the mixing water can dominate during low stages and that the lowest coverage of MIX water was observed during a flood contradict the results of Park and Latrubesse [49], who concluded that high water mixture usually occurs during floods. The differences between the studies could be explained by (1) the low slope of the Tisza and Maros rivers even during floods and (2) the relatively high confluence angle. These can result in the impoundment; thus, the impounded river is almost blocked by the dominant river. Thus, limited mixing can happen.
There are some exceptional events when the water of the Tisza (TW4 and MIX10) or the Maros (TW5 and MIX11) upwells; thus, their water appears in the downstream end of the confluence area. It could be explained by the different densities of the joining waters, related to the considerable difference between their suspended sediment concentration or their water temperature. These upwelling patterns usually occur during summer or autumn low stages, when the temperature conditions of the joining rivers are very different. As the Maros is very shallow (3.5-5.5 m), at the beginning or the end of summer, its water can be much warmer or colder than the deep Tisza's (10-20 m). As a result, the water of one of the rivers stratifies above the other; thus, due to the spiral flow, the other water appears (upwells) just at the downstream end of the confluence area.

Support for Future Sediment Sampling
The mixing pattern should be known if someone plans a sampling campaign (i.e., for sediment, pollutant, microplastic, phytoplankton) in a confluence area. The analysis based on the collected samples without knowing the mixing pattern might lead to misinterpretations and wrong conclusions, as the joining waters might have very different sediment characteristics, and their mixing is dependent on various parameters. Therefore, predictive equations for the areal distribution of the mixing waters and their longitudinal extent in the confluence area can be helpful when planning a sediment sampling. In our case, by applying the created equations, anyone can predict the areal distribution (%) of the waters in the confluence (TW, MW, MIX) and the longitudinal extent (L) of the tributary's water based on the actual hydrological parameters measured at the three neighboring gauging stations (Algyő, Szeged, and Makó). Thus, the near-future mixing could be predicted, and the sampling campaign could be carefully planned.
The accuracy of the derived equations could be rated as moderate to good. No better accuracy was achieved because of the complexity of the mixing process: it is not only dependent on the hydrological parameters, but also other driving factors, such as the morphological characteristics of the channels, temporal dynamism of the sandy channel, temporal change of the transported suspended sediment load, and water temperature conditions of both rivers.

The Applicability of the Unsupervised Classification Method
The K-means unsupervised classification algorithm proved its ability as a good tool to study the mixing process in confluences. Its application supported the identification of pixels representing the water of the main river, the tributary, and their mixture. The reason behind this is that there are significant differences between the suspended sediment concentrations between the joining rivers [2,7,20,22,38,41], which contrasted the watercolor considerably; and in turn, the reflectance values for the three classes were clearly separated by the unsupervised technique. Fortunately, most confluences have the same feature of watercolor difference; thus, we recommend this technique during the analysis of the mixing process in confluences. It is especially a useful method, as it is often difficult to collect water samples to calibrate satellite images for supervised classification.

Conclusions
River confluences are considered as turning spots along streams, as they affect not only the water flowing downstream but also the sediment and pollutant concentrations. The mixing process in the confluence area is very complex, as it is influenced by many factors related to the morphological characteristics, hydrological and sediment transport conditions of the joining rivers. The mixing process is even more complex if one considers that the above-mentioned parameters can change in time and are relative to each other at the two joining rivers.
The impacts of the various hydrological parameters on the spatio-temporal dynamism of mixing in the Tisza and Maros Rivers confluence were investigated using Sentinel-2 satellite images, applying K-means unsupervised classification technique. The mixing pattern was analyzed based on 143 images covering the period between July 2015 and May 2021. The areal distribution of the water originated from the Tisza (TW), the joining Maros (MW), and their mixture (MIX) were compared with the hydrological parameters of the joining rivers.
It was concluded that the water areas of the main river (TW) and the mixed water (MIX) are highly correlated to the water stage in both rivers. However, the area of the water of the tributary (MW) showed a weaker relationship, as it showed a negative correlation with the stages above the bankfull level and a positive correlation with the stages below this level, which could happen due to the impoundment of the tributary by the main river during floods. The lateral extents of the three water types followed also the same temporal change as the areal coverage. Despite the complexity of the mixing process in the confluence area due to the various driving factors, it can be concluded that the hydrological parameters have a significant impact on the mixing process; therefore, they could be used to predict the mixing pattern in the confluence area. The discharge ratio between both rivers gives the best representation of the mixing process, especially for the areal percentages of the water of the main river and the mixed water.
Based on the large number of Sentinel-2 satellite images altogether, 11 mixing patterns were identified. Usually, the water of the main river (TW) dominates the confluence area. It has almost complete coverage in January and November (TW1 pattern) when the main river has high stages, and the tributary has low waters. The water of the tributary (MW) can dominate just in June or July when the water stages in both rivers are high, but the tributary has a much greater slope. The mixing of the two rivers is considerable when they have similar hydrological conditions, and none of them dominates over the other. The upwelling of one of the waters at the downstream end of the confluence area is not rare, and it is in connection with the considerably different density conditions of the joining streams.
The identified mixing patterns appear in distinct periods. Therefore, collecting water samples just from one point in the confluence area can lead to errors, as at a given point, the water has a different origin in the various months. Therefore, in the confluence area, sampling from several points is suggested. However, it also must be noted that various mixing patterns (upwelling, from no-mixing to almost total mixing) alternate within a year, and even at the most downstream cross section of the study area, thus in 26 times of the Tisza's channel width (w) no complete mixing was achieved. It may take 15-150 km for complete mixing according to the assumption of Jirka [21]. Therefore, we suggest to avoid the confluence area during sampling; or carefully analyze the mixing pattern during sampling to evade misinterpretations.

Acknowledgments:
The authors would like to thank the Lower Tisza Hydrological Directorate (ATIVIZIG) for providing the hydrological data.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The Figures A1-A3 and their descriptions are included in the Appendix A. Figure A1: The maximum rising (145 cm/day) and falling (−151 cm/day) rates were recorded on the Maros at Makó during February 2017 flood. On the other hand, the fastest rising on the Tisza was only 113 cm/day (at Algyő) and 94 cm/day (at Szeged) during the flood in January 2016. The rapidest falling stage (−81 cm/day at Algyő and −74 cm/day at Szeged) was detected during the end of the flood in June 2019. The greatest differences in the daily change of water stage between the Tisza and Maros rivers (>80 cm) were observed during floods (November 2015, January 2016, and February 2017); however, apart from these periods, the differences between the two rivers fluctuated steadily. Figure A2: Heat maps were created based on the lateral percentages of Tisza water (TW), Maros water (MW), and their mixture (MIX) at the five studied cross sections. The water of the main river (TW) usually dominated the confluence area. In most cases (75%) in the first (S1) cross section (just 110 m downstream of the confluence), the Tisza water occupied 15-68% of the cross section. In some cases (2%), the mixing was a minor process, thus along all 5 cross sections the TW dominated ( Figure A2A). It happened in the late autumn and winter months (e.g., from November 2015 until January 2016). An almost similar situation evolved (in 13% of the cases) when the TW dominated four cross sections (S2-5), and only in the first (S1) cross section was its proportion below 90%. In the rest of the cases (10%) high contribution of the TW was detected just at the downstream cross sections (S3-5) as if the TW was "upwelling" 2.3-4.1 km far from the confluence. This could happen at any time of the year, but it was common in summer and late autumn.
The Maros water (MW) showed fewer spatio-temporal variations between the five cross sections ( Figure A2B). Almost in every case (99%), the proportion of MW was the highest (10-61%) at the upstream S1 cross section. Additionally, at this cross section, about 5% of cases the Maros water occupied a greater proportion of the channel (38-61%) than the TW (15-47%), despite the fact that the Tisza channel is 103 m wide at the confluence, while the Maros is only 70 m. In most (92%) cases, the MW quickly disappeared, so in the downstream cross sections (S2-5), its average proportion was 30%. In the last case (3%), the MW was detectable even at the S4-S5 cross sections with high areal coverage, as sometimes the "upwelling" MW had a higher proportion (30-100%) than at the upstream cross sections. This case was common from April to mid-August, and for example, this situation dominated the summer in 2016. The measured lateral percentages of MW at the five cross sections and the calculated areal percentages of MW in the entire confluence had similar temporal patterns throughout the studied period.  The mixed water (MIX) of the two rivers showed high spatio-temporal variations between the five cross sections ( Figure A2C). Almost in all cases (99%), the MIX had a very low proportion (2-28%) in the first cross section (S1), as its proportion increased gradually from S1 towards S5. Considering all studied dates, in 17% of cases, no mixing was observed along the five cross sections due to the dominancy of water from one of the joining rivers (usually the Tisza). This case usually occurred in the late autumn and winter months (e.g., from November until January). In 34% of cases, the MIX had very high coverage (>85%) between S4 and S5; however, the significant coverage of MIX between S2 and S5 was observed only in 3% of cases. This significant coverage between S2 and S5 usually occurred in spring and summer (e.g., April and August). In the last case (11%), the MIX almost disappeared or was recorded with very low coverage (0-15%) at S4; however, it appeared again after this section with a significant coverage (>80%) at S5. This case was related to the upwelling of the Tisza or Maros water at the downstream part of the study area (between S4 and S5). This case was observed in early summer (May) or late autumn (September-November). The mixed water (MIX) of the two rivers showed high spatio-temporal variations between the five cross sections ( Figure A2C). Almost in all cases (99%), the MIX had a very low proportion (2-28%) in the first cross section (S1), as its proportion increased gradually from S1 towards S5. Considering all studied dates, in 17% of cases, no mixing was observed along the five cross sections due to the dominancy of water from one of the joining rivers (usually the Tisza). This case usually occurred in the late autumn and winter months (e.g., from November until January). In 34% of cases, the MIX had very high coverage (>85%) between S4 and S5; however, the significant coverage of MIX between S2 and S5 was observed only in 3% of cases. This significant coverage between S2 and S5 usually occurred in spring and summer (e.g., April and August). In the last case (11%), the MIX almost disappeared or was recorded with very low coverage (0-15%) at S4; however, it appeared again after this section with a significant coverage (>80%) at S5. This case was related to the upwelling of the Tisza or Maros water at the downstream part of the study area (between S4 and S5). This case was observed in early summer (May) or late autumn (September-November).   Figure A3: The areal distributions of the various waters and the actual hydrological parameters were compared ( Figure A3) to understand the driving factors of the mixing. The discharge ratio of the two rivers gives the best representation of the areal percentages of TW, MW, and MIX, as it correlated positively with the areal percentage of MW, and MIX, and negatively with the TW percentage ( Figure A3A). The discharge and slope differences showed good correlations as well, but less than the discharge difference ( Figure A3B,C). In contrast, the differences in daily stage change showed no correlation with the areal percentages of water types ( Figure A3D); therefore, this parameter had the lowest impact on the mixing of water with various origins.
Water 2021, 13, 3132 27 of 30 Figure A3: The areal distributions of the various waters and the actual hydrological parameters were compared ( Figure A3) to understand the driving factors of the mixing. The discharge ratio of the two rivers gives the best representation of the areal percentages of TW, MW, and MIX, as it correlated positively with the areal percentage of MW, and MIX, and negatively with the TW percentage ( Figure A3A). The discharge and slope differences showed good correlations as well, but less than the discharge difference ( Figure A3B,C). In contrast, the differences in daily stage change showed no correlation with the areal percentages of water types ( Figure A3D); therefore, this parameter had the lowest impact on the mixing of water with various origins.