A process-based recovery indicator for anthropogenically disturbed river system

The present paper utilizes entropy theory and Google earth engine cloud computing technique to investigate system state and river recovery potential in two large sub-basins of the Mahanadi River, India. The cross-sectional intensity entropy (CIE) is computed for the post-monsoon season (October–March) along the selected reaches. Further, a normalized river recovery indicator (NRRI) is formulated to assess the temporal changes in river health. Finally, NRRI is related to a process-based variable-LFE (low flow exceedance) to comprehend the dominating system dynamics and evolutionary adjustments. The results highlight the existence of both threshold-modulated and filter-dominated systems based on CIE and NRRI variabilities. In addition, the gradual decline in CIE and subsequent stabilization of vegetated landforms can develop an ‘event-driven’ state, where floods exceeding the low-flow channel possess a direct impact on the river recovery trajectory. Finally, this study emphasizes the presence of instream vegetation as an additional degree of freedom, which further controls the hierarchy of energy dissipation and morphological continuum in the macrochannel settings.


Study area
The Mahanadi River basin is the fifth largest watershed in India, covering a total geographic area of nearly 4.3% (India-WRIS). The earlier studies on the Mahanadi and its tributaries include understanding of the flowsediment-water quality variability [75][76][77][78] , the morphological characteristics [79][80][81] , and the ecological entities [82][83][84] . The Ong and the Tel are the two largest tributaries of the Mahanadi (India), with a combined catchment area of 27, 946 km 2 and a channel length of 184 km (Fig. 1). These rivers drain along mix red and black soils 85 . During the south-west monsoon (June to September), the river basins have an average annual rainfall of about 1463 mm. The Ong is governed by the Guchhepali dam 86 , and the Tel has a dynamic flow-sediment regime owing to the combined effects of natural and anthropogenic stresses. Two gauging stations, Salebhata and Kantamal, are present at 30 km and 40 km upstream of the Ong-Mahanadi and the Tel-Mahanadi confluences, respectively.
The channel form of the Ong and the Tel is described as macrochannel, in which a smaller low flow channel is inset within a larger channel. At the measured cross-section locations, the macrochannel and inset bankfull widths are close to 0.4 and 0.1 km, respectively. The significant difference between the inset and the macrochannel dimensions offers large space for geomorphic adjustments at multiple inundation surfaces (Fig. 2). The macrochannel bank height is 8 to 10 m, which can accommodate a flow regime of high hydrological variability. Tributary inflow and bank erosion are also absent, and geomorphic units such as benches, chutes and various bar types (vegetated and unvegetated) are effectively confined between the macrochannel bank margins. The instream vegetation covers are normally shrubs, grasses, and twinners plants with soft stems, and flexible bends and have deep roots into the sand. The vegetations like tamarix ericoides, coix lacryma-jobi, hedyotis corymbosa, cyperus rotundus, typha latifolia, polygonum aviculare and polygonum barbatum spread profusely in the fluvial corridor. In particular, an accelerated conversion of the submerged shelf to bar and the exposed shelf to bench with plants like Saccharum spontaneum, Vetiver zizanioides and Ipomoea carnea have developed stable vegetated landforms along the study reaches (Fig. 2). www.nature.com/scientificreports/ reaches. Then, the macrochannel bank lines are digitized based on field-observed floodplain signatures, and subsequent polygon layers are generated. The space between the macrochannel bank lines is selected as the fluvial corridor for instream vegetation cover assessment. The post-monsoon time refers to the low-flow hydrological condition during October-March. In this period, the flow is majorly concentrated in the thalweg (the deepest portion of the river) and therefore, geomorphic units like bar, bench, and instream vegetation cover are effectively captured from the field investigations and satellite imagery. The atmospherically corrected and orthorectified surface reflectance from Landsat 5 ETM, and 7 ETM + sensors are accessible by the GEE. For the given study period, these datasets are used to derive seasonal NDVI time series inside the fluvial corridor. Reflectance images in red and NIR bands of the electromagnetic spectrum from corresponding days of the acquisition are used to compute NDVI. Later, the temporal median of NDVI images is evaluated to derive a single seasonal NDVI representing the most general low-flow hydrological condition in the post-monsoon season. These computations are performed in the cloud platform of GEE, and final NDVI image time-series are exported for instream vegetation cover assessment (Fig. 3).

Data and methodology
Cross-sectional intensity entropy. Shannon's information entropy theory is applied in this study, which is a measure of uncertainty or variability or disorder associated with the random variable X = X(x 1 , x 1 , x 1 · · · · · · · · · , x n ) 26 . Shannon 87 defined the uncertainty of occurrence of an event x i from the possible events in X as entropy H(X), which is given by here, p(x i ) is the probability of x i , which is based on the empirical frequency of X values. The present study uses the concept of intensity entropy (IE) to investigate the seasonal (post-monsoon) variability associated with the macrochannel cross-sections. The cross-sectional intensity entropy (CIE) can be assessed as follows.
(1)  www.nature.com/scientificreports/ 1. At-a-station hydraulic geometry dataset is obtained from India-WRIS, which consists of multi-decadal records . This dataset is collected with 10 m bin size intervals to understand the geomorphic aggradation (or degradation) associated with the instream geomorphic units. 2. Then, the alteration in channel bed elevation is computed from the reference year (1988), and the macrochannel geometry is further segregated into different zones based on the maximum breaks in slope. 3. The class intervals are carefully selected by examining the hydraulic geometries in post-monsoon seasons and decided based on the upper and lower bounds of the alterations in bed elevation. Therefore, all the possible variations in at-a-station hydraulic geometry and gradual macrochannel adjustments like thalweg shifting, chute development and the conversion of bar to bench are integrated to the analysis. The cross-sectional intensity entropy (CIE) is calculated as  15 suggested various geomorphic adjustments like wide symmetrical channel to macrochannel, bank erosion to bench formation, actively widening to contracted channel, high width-depth ratio braid like low flow channel to well-defined low width-depth ratio thalweg as indicators between the pre-recovery and recovery states.
Normalized river recovery index. Recovery is related to the improvement in geomorphic conditions, normally over the decadal period. It is also associated with the adjustments of the river to the prevailing boundary conditions like flow-sediment alteration, modifications in land-use practices, changes to instream fluvial cover etc. In addition, recovery is associated with the inherent sensitivity of the river, where each reach can be placed in its catchment context. The presence, absence or reconstruction of the assemblage of geomorphic units facilitate key indicators regarding the deterioration and recovery trajectory responses. Further, it is noted that the rate at which geomorphic units emerge provides a sign of the effectiveness of the recovery process. The present study has considered two important attributes of macrochannel rivers, i.e. vegetative measures and geomorphic disorderness, to provide a snapshot of how the system is performing at present. The normalized river recovery index (NRRI) as a system-state response is formulated as www.nature.com/scientificreports/ where VI is vegetation intensity, CIE is cross-sectional intensity entropy, and NORM stands for normalization with maximum and minimum values. The vegetative measures often develop some fluvial landforms that trigger and engineer the river recovery process. In the present study area, instream vegetation growth is closely linked with CIE, where, after the stability of fluvial landforms, seed germination and gradual colonization have initiated. According to Thompson et al. 45 , with-in channel benches becomes more resilient after the vegetation growth and may reduce the disorderness in hydraulic geometry. Moreover, instream vegetation has improved the channel boundary resistance in present macrochannel settings, and the multiple inundation surfaces (bar, bench and macrochannel bank) have approached towards recovery with increased VI and gradual reduction of CIE.
Process linkage. The recovery trajectory is enhanced or constrained by limiting factors and pressures. These limiting factors operate internally in the system and generally incorporate the changes to sediment supply, flow regime and instream vegetation cover. The pressures are the external agents and are integrated with environmental management policies and climate change etc. In the present study reach, it is well-established that effective discharge shapes the inset channel to carry a maximum portion of sediment load in the long term 26 . Further, the excess energy above the effective sediment transport level re-organises the chutes and diagonal bars close to the inset channel. Hence, a new process indicator-Low Flow Exceedance (LFE) is proposed to understand the impacts on the hierarchy of energy dissipation and river recovery processes in the morphological continuum zone of the macrochannels Ong and Tel. LFE signifies the number (N) of moderate-to-high flows exceeding the inset channel and submerging the instream vegetation zones at different platform levels. The LFE is proposed as where N is number of days, Q is flow (in m 3 /s) and Q L is carrying capacity of the inset channel (in m 3 /s).

Results and discussion
Longitudinal variation of instream vegetation cover. No extensive changes to macrochannel position have occurred through bank erosion in the Ong and the Tel Rivers. The macrochannel bank is highly stable by riparian vegetation and the internal resistance of substrate lithology (Fig. 4a,b). The major changes are in terms of within-macrochannel adjustments like chute and floodways formations, bar and bench establishments and the gradual emergence of vegetated landforms. The decadal average vegetation cover is close to 14% and 4% along the Ong and the Tel, respectively. It should be noted that no wholesale change to vegetated landforms has occurred in the Tel river and periodic destruction, survival, and succession continued in the 2010s. In contrast, the Ong has experienced a drastic change in instream vegetation cover in the 2015-2020 time slice and increased the area from 19% to more than 30%. The instream vegetation type, structure, density and position affect the process, form and dynamics of alluvial rivers at micro and macro scales [88][89][90][91] . In particular, the macrochannel river settings display multiple surfaces of varying inundation frequency and sediment trapping potential 39 . In the Ong, major vegetated landform zones and biomass density are observed on the bench surface and close to the low-flow channel (Fig. 4i). Furthermore, similar to the findings of Gurnell et al. 92 , the Ong river has experienced aggradation of the submerged shelf to lateral bars and the exposed shelf to a bench. These linear benches are natural repositories of seed germination and allow vegetation like S. spontaneum, V. zizanioides and I. carnea to colonize in the post-monsoon season.
A schematic representation of the distribution of soil moisture and fluvial disturbance suggests that vegetation patches have the support of perennially flowing water even at the lowest discharges. Therefore, the Ong River is affected by the development of vegetated patches close to the thalweg. Further, the periodic bio-geomorphological interactions have helped these vegetation patches to retain the upstream sediment, form deeper and narrower low-flow channels and eventually develop self-organized landforms. In contrast, the Tel resembles a confined channel with stable macrochannel banks, where high fluvial disturbances dominate the bio-geomorphological interactions (Fig. 4j). In this process, small-rooted plants have grown until they are destroyed by excessive fluvial erosion, leaving the small patches of deeper rooted plants to colonize the bare sediment of linear benches.
Hydrological data analysis and variability in CIE and NRRI. The oscillation of the south-west monsoon rainfall regime generates unimodal wet (June-September) and dry (October-May) seasons along the Ong and Tel Rivers (Fig. 5). The wet flows (floods and extreme events) are periodic, and a significant variation in discharge and stage (with respect to mean sea level-MSL) are observed along the study reaches. The transition between wet and low flows is characterized by moderate flows that provide a significant contribution to the bio-morphological activities. The time-averaged flow and stage along the Ong River are close to 130.80 m and  (Fig. 5a). The Tel River observes a notable hydrological variability with time-averaged and maximum stages as 119.02 m and 132.7 m, respectively. The maximum observed discharge is 20,000 m 3 /s, which is considerably greater than a time-averaged value of 384 m 3 /s. Such extreme flow and water level variability highlight the ample in-channel space of macrochannel configuration, which can capture both high floods and extreme events (Fig. 5b). www.nature.com/scientificreports/ Figure 6 shows the temporal variability of CIE along the Ong and Tel Rivers. It is observed that both river systems demonstrate continued hydraulic geometry adjustments via thalweg shifting, bar formation-sculptingerosion and bench growth-destruction. In the Ong River, the temporal average of CIE is close to 2.05, whereas the Tel river has a slightly decreased CIE of 1.88. The maximum CIE in the Ong and Tel are close to 2.34 and 2.15, respectively. The Ong has a distinct minima of CIE variability in the early 2000s. Moreover, the Ong has displayed a continuous decreasing trend of CIE between 1997 and 2002 and after the extreme floods of 2003 and 2004, an increased CIE is noted in the late 2000s. In contrast, the Tel has no significant trend in CIE variability, and periodic fluctuations are noted over the entire study period.
The alteration in instream vegetation coverage and CIE have resulted in variable responses along the river recovery trajectory. In the regulated Ong, the temporal average of NRRI is close to 0.13, and it shows an inclining trend in the initial study period (1991)(1992) due to the combined effect of decreased bar disorderness and slight reduction of instream vegetation cover on the bench surface (Fig. 6a). After the 1994 catastrophic flood, the morphological responses (in terms of CIE) has continued to decrease for the next 10 years. At the same time, the instream vegetation cover has increased from 10.76% (in 1992) to 21.06% (in 2001), and therefore, NRRI has increased from − 0.56 to 0.70. In contrast to the 1994-peak flood's morphological and vegetation cover responses, the Ong has reacted in a different fashion to the 2003 and 2004 peak floods. A decrease in vegetation cover from 21.06 to 14.46% along with an increment in CIE from 1.91 to 2.27 has altered the NRRI from 0.7 to − 0.51. From this period onwards (2008-2011), the Ong river has accelerated the instream vegetation growth from 14.46 to 23.14% and gradually transformed into a macrochannel dominated by well-vegetated geomorphic units. In addition, CIE has followed a declining trend due to the occurrence of bench and transition to a depositional form of adjustments. The temporal average of NRRI in the Tel is close to − 0.06. The overall CIE  www.nature.com/scientificreports/ trajectory establishes an initial increment of 51%, followed by a declining trend up to 1996, and finally, periodic fluctuations in the remaining years of the study period (Fig. 6b). The instream vegetation cover shows sporadic patterns of emergence, succession and decay and establishes an aerial coverage between 5 to 10%. Therefore, NRRI has observed a noticeable reduction (1.0 to − 0.1) between 1989 and 1994. After the 1994 extreme flood, diagonal bars have gradually transformed into vegetated landforms, and uniform aggradation of channel bed has improved the geomorphic condition, and therefore, NRRI was increased from − 0.24 to 0.01. The last time slice (2003-2011) is punctuated by two major floods in 2003 and 2004, and erosional form of adjustments like chute formation, channel straightening, sculpting of diagonal bars, and degradation of bench have continued for the next 3-4 years. In addition, the removal of smaller vegetated landforms and further succession in the subsequent years have helped the river to improve its geomorphic health and thus, NRRI has increased from − 1.0 to 0.05. This analysis establishes that the Tel river (unlike the Ong) in the Mahanadi catchment has not undergone the wholesale river change but has been adjusting within its behavioural regime. The synthesis of literature pertinent to the form, process and evolution of macrochannel systems suggests that the channel-in-channel physiography provides sufficient space for both erosional activities (removal of a geomorphic unit, channel widening, bank mass failure, bend extension, the occurrence of chute channels, scour, and incision) and depositional processes (formation of new geomorphic units and accretion of sediment on multiple platform levels) 24,26,27,29,31,39,45,93 . The present study reaches along the Ong and the Tel are predominantly macrochannel, where geomorphic activities are limited to re-organisation of materials at different inundation surfaces. As per Phillips and Dyke 64 , a system state consists of a morphological structure held together by interwoven form-process relationships. Therefore, in this study, CIE as a system state is concentrated on addressing the geomorphic adjustments at sub-bankfull stages. In the Ong, the linear bench gets partially eroded, washed away or accreted by floods which are discrete geomorphic disturbing events. The seldom realigning thalweg and bench evolution by sediment deposition and vegetation colonisation altered the system state of the Ong River. Furthermore, the post-disturbance states show a vegetated configuration that did not exist earlier. Thus, the gradual emergence of vegetated landforms and the declining trend of CIE can be referred to as a 'state space expansion event' , coined by Phillips and Dyke 64 . However, in the Tel River, the fixed controls (macrochannel resistant banks) dominate over flux disturbances (floods) and result in a resilience system. The system state (CIE) and vegetation density oscillate about a mean structure, where the post-disturbance system state is either close to the pre-disturbance configuration or undergoes some minor adjustments.
In many instances, the vegetation succession and macrochannel evolution adhere to a linear, sequential logic 94 . Binary models have also gathered recent attention, which suggest oscillation of systems between two stable states 95,96 . The present study suggests that CIE and NRRI have followed fixed sequences of developmental stages in the study reaches unless extreme events are absent as disturbing agents. After the floods, the channel evolution is non-linear and follows complex relaxation paths. The catastrophic floods have accelerated the planform adjustments signaling a slow relaxation, less resilient and threshold-modulated system where CIE and riverine health is governed by extreme events in the Ong. In contrast, the Tel River has probably fast relaxation time and a filter-dominated system, where recurring impacts of catastrophic floods are quickly absorbed, and finally, a dynamically stable system is developed. Figure 7 shows the relationship between process (N(Q ≥ Q L )) and recovery state (NRRI) along the study reaches. In the Ong, N(Q ≥ Q L ) varies between 0 (Q ≥ Q L ~ 40) to 1 (Q ≥ Q L ~ 130) for the daily discharge hydrographs. The temporal variability of LFE indicates that the 1990s is punctuated by a distinct major flood in 1994, which has increased the LFE up to 0. 91 As suggested by Pradhan et al. 26 , most of the geomorphic adjustments occur below the macrochannel bankfull level, and the river goes through a transition to accommodate the effective discharge in the inset channel. In addition, excess energy above the effective sediment transport re-organises chutes and diagonal bars close to the low-flow channel. The present research finding is pertinent to rivers with transitional channel patterns, where the river fluctuates the planform state between sinuous and weakly braided. This study highlights the hierarchy associated with the (re)organisation process in the macrochannel river system and its contribution to the river recovery state (Fig. 7b,d). For example, the inter-comparison of LFE and NRRI trends showed that two distinct time periods are observed on the basis of low-flow exceedance number variability in the Ong River (Fig. 7a). In period 1 (1991-1998), LFE and NRRI are less related to each other and in period 2 (1999-2011), both parameters are well-correlated. In period 1, the Ong has high fluctuations in small-moderate flood magnitudes, and CIE has initial variability due to the bar disorderness, followed by an initiation of the decreasing trend. This morphological activity is combined with the erratic instream vegetation growth pattern and has generated a 'lagged system' , where LFE and NRRI are not correlated. However, in period 2, both parameters have followed a similar trend attributed to the gradual alteration in CIE and subsequent stabilisation of vegetated landforms. Hence, the macrochannel system may have switched to an 'event-driven' state, where floods exceeding the low-flow channel possess a direct impact on the river recovery trajectory. In the Tel river, the vegetation cover is significantly www.nature.com/scientificreports/ low (5-10%), and this large macrochannel system has witnessed extreme flow variability (20-20,000 m 3 /s) in the 1990s. Such drastic changes to the flow regime have triggered morphological adjustments and have kept the channel perpetually in transition between sinuous and weakly braided states. Therefore, for such large channelin-channel physiography, the relationship between LFE and NRRI is challenging to establish and may entail the integration of additional process variables. The geomorphic threshold is one of the fundamental concepts related to the existence of discrete planform states (straight-meandering-braided) [97][98][99][100] . However, the presence of intermediate, transitional channel patterns within the behavioural regime suggests the presence of a continuum in the macrochannel systems 26 . Fluvial controls like flow strength index, bank erodibility and sediment supply are related to the morphological continuum 101,102 . In our river systems, amplifiers (AS) (both low-flow and extreme events) and effective sediment transport (ES) constitute the hierarchy of energy dissipation. Furthermore, the zone of the morphological continuum lies just above the effective sediment transport stage level (Fig. 7b,d), which incorporates the major form of geomorphological adjustments. As per Gurnell et al. 103 , the 'critical zone' for physical ecosystem engineering exists within the area of the river corridor that is perennially inundated. The adjacent areas are subjected to frequent inundation and significant shear stresses and erosion-deposition of sediment. Therefore, in the present study, the zone of morphological continuum and critical areas of plant-hydrogeomorphology interactions overlap within the sub-macrochannel bankfull level (Fig. 7). This bio-geomorphological interaction can also affect the changes in river planform type and future directions 104,105 . Our findings suggest that the instream vegetation growth close to the inset channel affects (or controls) the morphological activities in terms of crosssectional disorderness. Hence, within the continuum zone, the vegetation patches can grow, self-organise (SO) and expand to form enlarged vegetated landforms or become smaller and widely spaced under the influence of fluvial disturbances (FD). If SO starts to dominate over FD, the vegetation growth reduces the CIE variability, stabilizes the low-flow channels and increases NRRI (Fig. 7b). In contrast, if chutes and bar disorderness dictate SO through frequent fluvial disturbances, the rate of planform fluctuations increases between the end-points of the morphological continuum (sinuous and weakly braided states) (Fig. 7d). The channel evolution models are also associated with channel adjustments along the four degrees of freedom (cross-section, planform, bed and slope) 106 . The present paper emphasizes the presence of instream vegetation as an additional degree of freedom, www.nature.com/scientificreports/ which further controls the hierarchy of energy dissipation and morphological continuum in the macrochannel settings.

River recovery and process linkage.
In the era of big data and cloud computing, assessment of system state indicator-CIE and process-based indicator-NRRI will certainly help to comprehend the fluvial trajectory and develop recovery enhancement approaches. Further, this framework will be helpful for planning and prioritizing recovery indicators which can reduce the cross-sectional disorderness and promote improvements in river health. However, many fluvial systems in developing countries are poorly gauged, and assessing CIE and system disorderness with the continuous hydraulic and hydrological dataset is challenging. Therefore, the delicate balance between big data and remote sensing-based tools with archival benchmark information, 'place-based understanding' and 'reading the landscape' frameworks   107 will be key to capture and inform process-form relationships of fine-scale geomorphic units.

Conclusion
The present study has developed a process-based river recovery indicator for anthropogenically disturbed macrochannel river systems. The major conclusions of this study are as follows: • The disorderness in bed-elevation at sub-bankfull stages is effectively captured by a system state indicator-CIE. The temporal variation of CIE has further addressed the existence of both threshold-modulated and filter-dominated systems in macrochannel settings. • Vegetation density and CIE integrated recovery indicator (NRRI) symbolize river health for channel-inchannel fluvial systems. The present study suggests that CIE and NRRI have followed fixed linear sequences of developmental stages unless extreme events are absent as disturbing agents. • A gradual decline in CIE and subsequent stabilization of vegetated landforms can develop an 'event-driven' state, where floods exceeding the low-flow channel (LFE) possess a direct impact on the river recovery trajectory. • Finally, the dominance between self-organization of vegetated landforms and fluvial disturbances develops an additional degree of freedom and further decides the recovery state of macrochannel and planform fluctuations between the end-points of the morphological continuum (sinuous and weakly braided states).
Natural rivers are gradually subjected to altered flow-sediment conditions through various natural and anthropogenic stressors. Therefore, predicting the trajectory of recovery potential is crucial in river restoration programs. The present study presented a novel approach to predict the system state and recovery potential in anthropogenically disturbed macrochannels. This work can be further extended to rivers with different morphological settings and channel pattern types to better understand the fluvial dynamics.