Continuous discharge monitoring of the Mirim-São Gonçalo system by the index velocity rating curve method

SQRC

stage–discharge rating curve

IVRC

index velocity rating curve

ADCPs

acoustic Doppler current profilers

H-ADCP

horizontal acoustic Doppler current profiler

SGC

São Gonçalo Channel

GS1

gauge station 1

GS2

gauge station 2

IVC

integrated velocity cell

MCV

multi-cell velocity

D-ADCP

dynamic acoustic Doppler current profiler

MAE

mean absolute error

V_D-ADCP

cross-section water velocity from the D-ADCP

V_mean

cross-section water velocity from the IVRC model

V_INDEX

x-axis index velocity

Covering approximately 13% of the world's coastal zones, coastal lagoons are characterized by a shallow water body, generally oriented parallel to the coast and separated from the ocean by a land barrier often affected by natural and anthropogenic aspects (Kjerfve 1994). The hydrodynamics in coastal lagoons is complex (Fiandrino et al. 2017), influenced by different forcings such as winds, tides, precipitation, and river discharge. Understanding the physical, chemical, geological, and ecological dynamics of these environments is an important task for the better adoption of coastal management strategies and planning in coastal lagoon areas (Kjerfve 1994).

The Patos-Mirim lagoon system is the largest coastal lagoon system in South America, having a 500 km long coastline (Oliveira et al. 2019). This system is considered complex due to the strong influence of wind action on the water level dynamics (Costi et al. 2018; Oliveira et al. 2019) causing multidirectional and stationary flow, as backwater effects. The northeast wind pushes the water into the southern portion of the Mirim Lagoon and disturbs the patterns of seasonal variability, resulting in water level oscillations (Costi et al. 2018), while the southerly winds push the water toward the north, raising the water level in that direction (Munar et al. 2018). When this region is under southwest wind influences, the Mirim Lagoon flows toward the Patos Lagoon through the São Gonçalo Channel (SGC). Under the northeast wind influence, the SGC mouth's water level rises (Oliveira et al. 2019), causing inversive discharges.

All these reported dynamics directly influence the quality and availability of water, as well as the pollutants’ residence time and navigability conditions in the Patos-Mirim lagoon system (Costi et al. 2018). Therefore, the continuous monitoring of water levels and flow discharges on this environment is relevant from both a social and economic perspective, as well as for the understanding of the hydrodynamic patterns of such a complex system. Among the used methods for continuous monitoring of the flows and consequent discharge estimations, the stage–discharge rating curve (SQRC) is the most common and traditional approach (Muste & Hoitink 2017; Cheng et al. 2019), and it is performed through a graphical and hydraulic analysis (WMO 1980; Dias et al. 2019). However, SQRCs are influenced by a minimum number of observations, and the stage–discharge relationship may vary over time, or even become impossible to determine especially in cases of backwater and inversive flow occurrence (Le Coz et al. 2008). Furthermore, in the SQRC approach, there is no distinction between the different hydrograph phases (rising and falling), since under unstable flow conditions, the hysteresis effects may occur between these two (stage and discharge) variables that are used to construct this relationship (Muste et al. 2020). In order to overcome the limitations imposed by the SQRC, the index velocity rating curve (IVRC) method relates the velocity at a specific point, the cross-section's mean velocity and wetted area to the stage, where the discharge value is the result from multiplying these relations (Chen et al. 2012). Thus, in complex flow situations, such as unstable and non-uniform flows, it is expected that the addition of permanent indexed velocity measurements will improve discharge estimates, due to the inclusion of flow dynamics information (Cheng et al. 2019).

While guidelines for developing SQRC are well known and extensively documented (e.g., WMO 1980; Rantz 1982a), the application of the IVRC has gained greater attention in recent decades, especially with the joint use of acoustic Doppler current profilers (ADCPs) (Levesque & Oberg 2012; Farahmand & Hamilton 2016). Continuous flow velocity measurements became possible since the implementation of horizontal acoustic Doppler current profilers (H-ADCPs), in a riverbank fixed position (Vougioukas et al. 2011). The H-ADCPs monitor the horizontal velocity profile in uniformly discrete intervals (cells) along the x-axis of the main beam (Vougioukas et al. 2011), at a specific flow depth (Kästner et al. 2018). Thus, the IVRC approach requires two models to estimate the discharge, one is the stage–area and the other is the index velocity-mean velocity. One of the main challenges in IVRC modeling is the model exploration and analysis in order to find the optimal regression model predictor(s) and model type (Farahmand & Hamilton 2016).

In recent years, many studies have been carried out in the Patos-Mirim lagoon system aiming to analyze, among other aspects, its environment hydrodynamics (Costi et al. 2018; Munar et al. 2018; Oliveira et al. 2019; Possa et al. 2022), the Mirim Lagoon residence time (Silva et al. 2019), spatial and seasonal water surface temperature variations (Munar et al. 2019), and the Mirim Lagoon bed sediment composition (Vieira et al. 2020). All these mentioned studies had used punctual in situ observed data (water velocity, current direction, discharge, stage) from the main Patos-Mirim lagoon system tributaries and the SGC, and also daily water level time-series from this region in their simulations and analyses. These studies evidence the lack of continuous monitoring programs involving equipment deployments and accurate techniques. Thus, continuous, accurate, and robust information regarding flow velocities, water discharges, and water level variation on a semi-daily scale are timely over this region.

Moreover, given the importance of this environment, both in terms of social and economic development, there is still no research investigating the best approach for IVRC use at the Patos-Mirim lagoon system and the SGC, despite the great potential of this territory, which covers an international transboundary basin shared between Brazil and Uruguay. Hence, this study assessed the performance of the IVRC method from applying velocity measurements provided by H-ADCPs, as a promising approach for continuous monitoring of flow velocities and discharges in a natural channel with typical complex flow characteristics. By analyzing discharge measurements under different flow conditions in two gauge stations along the SGC, on which H-ADCPs continuously monitor both gauges, we intend to answer the following questions:

• Is the rating curve traditional approach suitable for representing these flow conditions?

• Which IVRC development methods are most promising for representing the mean flow velocity at both gauge stations?

The Mirim-São Gonçalo Transboundary Basin (Figure 1) has an area of 62,250 km², of which 29,250 km² is attached to the Brazilian territory, including 21 municipalities and an estimated population of 770,308 inhabitants, where 88.8% of the population lives in the urban area and 11.2% in the country area (SEMA 2021). In the Uruguayan side, the basin has an area of 33,000 km², with a population of 154,699 which corresponds to 5% of the total population of the country, 92% living in urban areas and 8% in country areas (MVOTMA 2017). The main tributaries in the Brazilian territory are the Pelotas stream, the rivers Piratini and Jaguarão, and the SGC (Figure 1). On the Uruguayan side, the main rivers are Cebollati, Tacuari, Sarandi, and San Miguel. The climate of the Mirim-São Gonçalo basin region is characterized as humid subtropical (Cfa in the Köppen classification), with hot summers and well-distributed rainfall throughout the year (Peel et al. 2007). The annual precipitation in this region is 1,400 ± 296 mm, the annual reference evapotranspiration is 1,080 ± 36 mm, and the annual mean temperature is 18.5 ± 0.5 °C (1971–2020).

The MCV itself can look at each of the 10 cells along the cross-section from the two H-ADCP horizontal beams, allowing a more precise and discretized assessment of the x-axis velocity distribution over the horizontal profile. Considering the MCV, each cell from 1 to 10 is a mean value from beams 1 and 2, for example, x-axis velocity into Cell 4 is going to be the mean x-axis velocity from Cell 4 beam 1 and Cell 4 beam 2. The x-axis velocity of Cell 4 on GS2 (see Figure 4) is a 10-m long portion starting 34 m from the H-ADCP (considering blanking distance equals to 4 m + 10 m for each of the Cells 1–3), instead of the IVC which considers a 98 m portion along the cross-section (considering cell start and cell end as 2 m and 100 m, respectively).

The cross-sectional discharge at the gauge stations was also measured by a Dynamic Acoustic Doppler Current Profiler (D-ADCP). At GS1, there were 27 surveys between October 2015 and June 2019, and at GS2 there were 22 surveys between March 2019 and November 2019 (Table 2; Supplementary information, Tables S1 and S2). These D-ADCP data are only used on the IVRC development step which needs cross-section mean velocity (V_D-ADCP) punctual data. The discharge measurements were carried out with a D-ADCP designed using a Sontek™/YSI RiverSurveyor™ M9 model, built-in with nine transducers, 4 × 3 MHz and 4 × 1 MHz both responsible for measuring the velocity and flow direction with 0.002 m s⁻¹ accuracy, and 1 × 0.5 MHz transducer for bathymetry purposes. In addition, the D-ADCP has a temperature sensor applied for acoustic pulse velocity instantaneous correction, as well as an internal compass. To ensure data consistency, the measurements were post-processed by QRev™ software (Mueller 2016), which allows us to analyze deeply the collected velocity profiles. The D-ADCP collected data used bottom tracking as the reference for position. Following the recommendation by Mueller et al. (2013), each measurement was made by at least two pairs of reciprocal transects. Moreover, stationary moving-bed tests were performed on GS1 and GS2, under different flow conditions. On both sites no moving-bed characteristics were detected considering the discharge measurements performed, following criteria pointed out by Mueller et al. (2013).

According to Rantz (1982b), the IVRC approach separates the cross-section area and the mean velocity; the cross-section area is obtained from observing the stage through a linear regression between these two; the flow velocity (V_mean) is obtained from the relationship between the cross-section mean velocity (V_D-ADCP) and the indexed velocity (it can be a random point at the cross-section, usually the x-axis velocity, perpendicular to the flow). While considering H-ADCPs, the indexed velocity (V_INDEX) applied to the IVRC development may be the beam integrated velocity from cell begin to cell end (IVC), and it may also be the discretized average velocity registered by a single cell or multiple cells (MCV), as illustrated in Figure 4. In turn, the V_D-ADCP and V_INDEX relationship is inherent for each studied cross-section, and it can consider the use of the IVC, the MCV, or MCV + IVC on the development of the IVRC.

The IVRC quality is dependent on the number of V_D-ADCP measurements performed and the variability of the hydraulic conditions observed, that is, the greater the number of measurements and the greater the variability observed (measurements in dry and flood season period, high stage, low flow velocity, high flow velocity, inverse flows, backwater, and bi-directional flows occurrence, etc.), the greater the capacity of the IVRC models to represent real flow conditions on the channel.

The assessment of the IVRC models was based on the mean absolute error (MAE) and the coefficient of determination (r²). Also, MAE and r² were considered for the MCV cell selection at each gauge station. Further statistical performances from the best IVRC models developed are detailed in Supplementary Information, Table S3.

From the use of H-ADCP and D-ADCP, the necessary hydraulic variables for IVRC modeling, on both GS1 and GS2, were obtained. The V_D-ADCP from the D-ADCP measurements are only used for IVRC models development. The V_INDEX from the H-ADCP, even the MCV and IVC on the x-axis, is used for IVRC model developments and then for further V_mean estimations. The topobathymetric survey is only used for the stage × area relationship and it was developed using the software AreaComp 1 – Version 1.13 (Lant & Mueller 2012) widely used from the United States Geological Survey (USGS) at their monitored stations, following good practices mentioned on Levesque & Oberg (2012). The stage is monitored by the H-ADCP (obtained from the pressure sensor/vertical beam) and further applied to estimate the cross-section wetted area (Figure 5).

From the 27 D-ADCP surveys performed at GS1 and 22 performed at GS2, the maximum/minimum observed for discharge and V_D-ADCP are shown in Table 2.

These results show the D-ADCP discharge measurements were capable of covering a decent amplitude of data over the year. At GS2 some moments with negative flow and/or with stationary flow (4 and 0.0042 m s⁻¹) were identified. Over the year, for both gauge stations, the flood period was identified between September and January, and the drought period between March and June.

The detailed information from each discharge measurement is in the Supplementary Information.

From the GS1 models (Figure 7), it seems the linear regression using stage (Figure 7(a)) as a predictor variable has shown the worst performance when compared to the others, resulting in an MAE of 0.194 m·s⁻¹ and r² of 0.534. However, the IVC and MCV models (Figures 7(b) and 7(c)) both presented similar results with small error (MAE of 0.032 and 0.017 m·s⁻¹, respectively) and r² of 0.986 and 0.996, respectively. However, the best fit model was obtained when considering MVC + IVC (Cell 2 and Cell 6, Figure 7(d)) in a multiple linear regression model, with r² of 0.998 and an MAE of 0.012 m s⁻¹. Comparing the MCV + IVC model, it represents an MAE of 90% less than the SQRC approach, MAE 60% less than the IVC model, and MAE 30% less than the MCV model itself.

At the GS2, the IVRC model considering stage (Figure 8(a)) as a predictor variable performed worst, showing asymmetric error distribution and hysteresis effects, as well an MAE of 0.113 m s⁻¹ and r² of 0.815. However, the GS2 IVRC models result considering the IVC (Figure 8(b)), MCV (Figure 8(c)), and MCV + IVC (Cell 4 - Figure 8(d)) presented better results compared to the stage approach (Figure 8(a)). For GS2, the best fit was the IVRC model performed from multiple linear regression with two predictor variables (MCV + IVC considering the Cell 4), which presented an MAE 80% less than the SQRC approach, MAE 37% less than the IVC model, and MAE 5% less than the MCV model itself.

More details from each of the developed models for GS1 and GS2 are presented in the Supplementary Information.

The H-ADCP estimated discharge time-series for GS1 (Figure 9(d)) had fitted in the min/max D-ADCP discharge measurements for almost the entire period, suggesting the SGC variations were covered almost totally.

The results suggest that, for GS1, the IVRC model had performed significantly. The minimum and maximum discharge estimations from the MCV + IVC model (Figure 9(d) – red line) were 43.211 and 1,980.017 m³ s⁻¹, respectively, and the minimum and maximum discharge estimations from the IVC model (Figure 9(d) – black line) were 78.881 and 1,967.831 m³ s⁻¹, respectively. In both situations no periods of inversive flow were registered.

At GS2, the H-ADCP discharge estimations (Figure 10(d)) had fitted in the min/max D-ADCP discharge measurements for almost the entire period, even though the D-ADCP data are concentrated in the first half of the analyzed period. The results of the time-series suggest that the SGC variations were covered totally.

The results herein found for GS2 clearly suggest that the IVRC model had performed significantly with minimum and maximum discharge estimations from the MCV + IVC model (Figure 10(d) – red line) as −270.675 and 1,570.650 m³ s⁻¹, respectively, as well as the minimum and maximum discharge estimations from the IVC model (Figure 10(d) – black line) as −296.727 and 1,590.758 m³ s⁻¹, respectively.

At GS2, the results pointed out four main moments with negative discharge estimation values, with the minimum framed as (i) −122.9 m³ s⁻¹, (ii) −22 m³ s⁻¹, (iii) −270.7 m³ s⁻¹ (the maximum inversive flux registered in this study), (iv) −147.2 m³ s⁻¹ (Figure 10(d)). At none of the four inversive flow moments did the stage variable register negative values.

The results of residuals from the relationship between observed and estimated discharges at GS1 (Figure 11) had shown homogeneous residual distribution for low and high flow discharges, with an MAE of 16.864 m³·s⁻¹ (1.71% of the mean, 0.90% of the maximum, and 10.33% of the minimum estimated discharges for observed moments), with 43.211 m³·s⁻¹ as the minimum estimated in this study by the MCV + IVC model at GS1.

At GS2, the residual (Figure 11) from the relationship between observed and estimated discharges showed a homogeneous distribution with an MAE of 23.414 m³·s⁻¹ (5.60% of the mean, 1.69% of the maximum, and 8.64% of the minimum estimated discharges for observed moments), with −270.675 m³·s⁻¹ as the minimum estimated in this study by the MCV + IVC model at GS2.

The D-ADCP surveys performed to obtain in situ discharge measurements were conducted in both monitored gauge stations during the period of November 2015–2019, comprising a total of 49 campaigns (Table 1, SP1 and SP2) and covering most of the hydraulic situations that occur at the SGC, as flood/drought moments and bi-directional/stationary flows. The amplitude of discharge measurements helps improve the performance of the IVRC models, for example, on the development of the GS2 IVRC models which considered negative D-ADCP discharge measurements (−41.761, −269.83, and −120.938 m³ s⁻¹), registering the occurrence of inversive flows, typical from complex flow channels.

From the IVRC-developed models (shown in Figures 7 and 8), the MCV + IVC approach showed better performance compared to the IVC approach, noticed in GS1 and GS2. The SQRC showed the worst performance compared to MCV + IVC and IVC models at GS1 and GS2. Thus, the results clearly suggest that the use of SQRC models is not ideal for the SGC characteristics and its complex flow conditions, despite prior studies (Oliveira et al. 2015; Jung et al. 2020), due to the inability of the SQRC approach in estimating good discharges in moments with bi-directional/inversive flow, which occurs in SGC.

Still from the IVRC models, in addition to the small error presented from the IVC and/or MCV + IVC approaches (Figures 7 and 8), its distribution is quite symmetrical for low and high flow velocities, and it is corroborated by the relationship between observed and estimated discharge values and its residues (Figure 11), which has shown a homogeneous residual distribution with an MAE of 16.864 m³ s⁻¹ for GS1 and 23.414 m³ s⁻¹ for GS2. This fact demonstrates the efficiency of applying the three approaches for the IVRC model development to estimate the V_mean and then estimate discharges in both gauge stations.

From the time-series results, the discharge estimations applying IVRC models on both gauge stations presented reasonable performance. The time-series was capable of estimating discharges under the whole amplitude of SGC hydraulic conditions and in situ observed discharge data. The similarity of model performances when considering the IVC and MCV + IVC approaches allows the user to choose between these while guaranteeing a high degree of certainty (Figures 9(d) and 10(d)), even when out of observed data moments.

What was found here makes it clear that the GS2 discharge estimation time-series from the analyzed period can represent more comprehensive flow conditions compared to the other studies carried out in the SGC, with registered negative flows at GS2, that is, flow direction from Patos toward Mirim, as highlighted in Figure 10(d). According to a study done by Oliveira et al. (2015), these authors performed discharge measurements at GS2 and found positive discharges from 98.54 up to 1,503 m³ s⁻¹ during the period between January 2009 and December 2011. In another study, Oliveira et al. (2019) had found a flow discharge range from 300 up to 2,250 m³ s⁻¹ analyzing in the year 2002, but nonetheless its results are obtained from modeling in the SGC. Despite the maximum values described in prior studies, we have found no conclusive evidence that these discharge magnitudes really occur at SGC, either from the D-ADCP measurements or the H-ADCP registered data.

From the developed models, a time-series for predicted discharges for the two gauge stations in SGC was generated with a high degree of certainty. They are based on the IVRC principles and applied to estimate mean flow velocity, using the hydraulic variables monitored from an H-ADCP. The IVRC models considered the V_INDEX as ICV in the horizontal beam (IVC approach), and the V_INDEX as discretized MCV (MCV approach), both on x-axis direction, through linear and multiple linear regression models. The rating curve traditional approach, which is based only on stage to predict the discharge, is not representative for the SGC, and is therefore not applicable under these conditions.

All three IVRC development methods presented good performances in estimating mean flow velocity at both gauge stations. We highlight the better performance from the combined use of IVC and MCV for developing IVRC multiple linear regression models. In these IVRC models, we have found smaller errors, in addition to a symmetrical distribution of errors, both for low and high flow velocities. Based on these assumptions, for the reproducibility of this work, we suggest that other authors take note if there is no interference at any point of the beams such as contact with the river/channel bed and/or water surface, which may invalidate the use of some cells; as well as trying all the valid cells combinations to find a better IVRC performance.

For the analyzed period, it was possible to register moments with inversive flows, even during D-ADCP discharge measurements and during H-ADCP discharge monitoring (after applying the best fit IVRC model for discharge estimations), evidencing the better performance of the IVRC approach over the SQRC approach and the SGC complex characteristics.

Due to the results, we strongly suggest keeping the hydraulic variables monitored at the SGC. Primarily, to better understand its complex water behavior, and better develop IVRC understanding from natural and complex channels, which is only possible with long-term monitoring of flow characteristics.

We thank NEPE-HidroSedi at the Federal University of Pelotas (UFPel) for field surveys using the D-ADCP and providing the time-series obtained with the H-ADCP. We thank the Mirim-São Gonçalo Basin Development Agency for proposing the study theme that is so important for better understanding the complex hydrodynamics of the SGC. L.S.L. received support from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.