Sub-Bankfull Flow Frequency versus Magnitude of Flood Events in Outlining Effective Discharges. Case Study: Trotuș River (Romania)

Effective discharge, which represents the flow, or range of flows, that transport the most sediment over the long-term, was determined based on the mean daily flow discharge and mean daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stations along the Trotuș River. This study proposes an efficient method for the estimation of effective discharge based on observed values of the suspended sediment load. By employing this method the suspended sediment load is no longer either under- or overestimated as in the cases when the assessment is based on sediment rating curves. The assessment on effective discharge was performed at two distinct levels: for the entire data series during the investigated time spans and, subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspended sediment transport characteristics revealed highly multimodal characteristics with many peaks, indicating ample ranges for the effective discharges. The main effective discharge corresponded to large flood events, which are typical for the upper end of the discharge range, whereas the secondary effective discharges corresponded to sub-bankfull flows, which are more frequent. The changes that occurred in the channel bed are reflected by the temporal variations in the effective discharge.


Introduction
Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this 1. Introduction Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this

Introduction
Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this discharge could be used as a reference index for the entire series of discharges characteristic for the respective channel. Such index discharges include flows with a specified return period, including the one-in-two year flood (Q 2 ), the bankfull discharge (Q bf ) and the effective discharge (Q eff ) [6]. Effective discharge is the flow (or narrow range of discharges) which transports the most sediment over time in the stream and, hence, does the most (or greatest proportion of) work in the stream channel [7].

Introduction
Streamflow is probably the most extensively studied hydrogeom fact that the volume of water that flows through the channel, sets the sc The observation that the shape and size of a stream channel in a are the result of a single reference discharge pertains to hydraulic e irrigation channels in India in the late 1800s [3]. They noted that these depending on the magnitude and frequency of the discharge of wate configuration is attained [4]. In time, these observations resulted in equations which were latter applied to natural streams [5]. By expandi channels to natural stream channels, the idea has arisen that a single ref range of discharges maintain the long-term equilibrium shape and size 1. Introduction Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this basin is an upper mesoscale mountainous catchment (i.e., 4350 km 2 ) located in the central-eastern part of the Eastern Carpathians ( Figure 1). Trotu

Introduction
Streamflow is probably the most extensively studied hydrogeomo fact that the volume of water that flows through the channel, sets the sca The observation that the shape and size of a stream channel in a s are the result of a single reference discharge pertains to hydraulic en irrigation channels in India in the late 1800s [3]. They noted that these c depending on the magnitude and frequency of the discharge of water configuration is attained [4]. In time, these observations resulted in equations which were latter applied to natural streams [5]. By expandin channels to natural stream channels, the idea has arisen that a single refe range of discharges maintain the long-term equilibrium shape and size o River is one of the major tributaries of Siret River, which is, in turn, the largest tributary of the Danube within the Romanian territory.
Water 2018, 10, x FOR PEER REVIEW 3 of 23 In this paper, long-term (21 years) water discharge and suspended sediment load transport data from the Trotuș River are used to calculate its effective discharge. The assessment of effective discharge was performed based on several methods established in the literature or methods introduced in this study and described in Section 2.3. To highlight multiple effective discharges, their values were also determined for flows below the bankfull discharge.
In summary, the main objectives of this study focus on (i) developing a calculation model for the effective discharge based on observed suspended sediment data instead of data estimated by sediment rating curves; (ii) calculating the effective discharge for the entire data series and the flows below the bankfull discharge; (iii) computing the effective discharge prior to, and after, the 2005 flood events; and (iv) evaluating the relations between effective discharge and stream power.

Materials and Methods
This study was based on the use of mean daily flow discharge and suspended sediment. These data were provided by the National Administration "Romanian Waters" Siret Water Branch. The use of high temporal resolution data is typically recommended (e.g., 5-, 15-, 30-, and 60-min interval flow values) [6], particularly for small rivers where the differences between the mean and peak daily discharges are relatively large. In the case of the Trotuș River, the average daily values are regarded as optimal for determining the effective discharge.

Study Area
The Trotuș basin is an upper mesoscale mountainous catchment (i.e., 4350 km 2 ) located in the central-eastern part of the Eastern Carpathians ( Figure 1). Trotuș River is one of the major tributaries of Siret River, which is, in turn, the largest tributary of the Danube within the Romanian territory. In terms of lithology, the Carpathian flysch accounts for the largest area of Trotuș drainage basin (~55% of the basin area), ensued by the pericarpathian molasse (~25%), composed of highly erodible rocks such as friable sandstones, clays and marls. The elevation ranges between 73 m above Streamflow is probably the most extensively studied hydrog fact that the volume of water that flows through the channel, sets t The observation that the shape and size of a stream channel are the result of a single reference discharge pertains to hydrau irrigation channels in India in the late 1800s [3]. They noted that th depending on the magnitude and frequency of the discharge of w configuration is attained [4]. In time, these observations resulte equations which were latter applied to natural streams [5]. By expa channels to natural stream channels, the idea has arisen that a singl range of discharges maintain the long-term equilibrium shape and 1. Introduction Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this River is~160 km. The median diameter (D 50 ) of the bed material along the 160 km amounts to an average of 71.3 mm, with extreme values ranging from 130 mm (in the midcourse) to 20 mm (in the lower course) [34,35]. The mean gradient of the channel ranges between 0.17 mm −1 in the upper course (Lunca de Sus) and 0.018 mm −1 in the lower course (just downstream of Vrânceni) [36]. Based on the average suspended sediment yield (263 t/km 2 /year) Trotu 1. Introduction Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this River where long-term records of streamflow discharge and suspended sediment load are available. The location and key attributes of these stations are shown in Figure 1 and Table 1, respectively. Note: DRM-distance to the river mouth (km); A-drainage area (km 2 ); S-slope (m/m); Q avg -mean daily discharge (1994-2014) (m 3 /s); Q min -minimum mean daily discharge (1994-2014) (m 3 /s); Q max -maximum mean daily discharge (1994-2014) (m 3 /s); R ed -ratio of maximum mean daily discharge to minimum mean daily discharge; Qs-mean daily suspended sediment load (1994-2014) (kg/s); Qs max -maximum mean daily suspended sediment load (1994-2014) (kg/s); SSY-suspended sediment yield (t/km 2 /year).

Flow Data Frequency Analysis
Subsequent to the publication of the study by Wolman and Miller [7], a whole array of studies approached the magnitude-frequency analysis (MFA) of flow discharge, which is an essential part of determining the effective discharge [16,39,40]. Although Wolman and Miller [7] suggested that a theoretical probability density function (PDF) can be employed to illustrate the flow regime, it was only after the 1990s that the theoretical MFA approach was perfected [8,19,23,[40][41][42].
Three major approaches were used to determine flow frequency [27,43,44], including (i) employing a fixed number of classes (e.g., 25) of equal width and magnitude [16,17]. This method is employed most often but is likely the most criticized [6,11,32] because it depends, to a large extent, on the number of classes. Studies based on the MFA for assessing effective discharge used either an arithmetic scale for flow or a logarithmic scale for building histograms [45]. The following elements should be considered during the process of producing flow-frequency histograms [11,43,45]: the size of the class interval, the number of flow discharge classes, the time period for averaging the discharge, and the length of the period of record. Yevjevich [46] suggested that the size of the class interval for flow discharge should not be larger than SD/4 (where SD represents the standard deviation of the flow for the considered sample), and the number of classes should range between 10 and 25 depending on the sample size. In regard to the length of the period of record, Biedenharn et al. [43] recommended the use of data series 10 to 20 years in length. The second approach is (ii) representing the observed frequency of flow based on the theoretical flow frequency distribution that approximates it, such as the lognormal distribution. This conceptual approach was introduced by Wolman and Miller [7] and later developed by Nash [19]. The application of this method may create particular problems in the case of bimodal, multimodal, heavy-tailed, or heavily skewed flow frequencies [27,41]. The third approach is (iii) computing the amount of sediment transported for each flow class and determining the effective discharge from the steepest point of the cumulative sediment transport curve [26].

Effective Discharge Computation
The methods involving the use of the flow frequency distribution and a sediment rating curve for the assessment of effective discharge [7,19,47] are regarded as traditional approaches (or deterministic approaches). Moreover, the methods derived from the methodology presented by Crowder and Knapp [11] are considered mean approaches [6,25]. In other articles, the methods for estimating the effective discharge are ranked as class-based (magnitude-frequency) and model-based (analytical) approaches [48].
The estimated value of the effective discharge is strongly influenced by the size and number of class intervals used in the flow frequency analysis [6,9,11,25,27,32,39,49,50]. To remove some of the subjectivity generated by the empirical choice of the size of class interval (CI) or the number of flow discharge classes (N) [25], four different methods were employed for determining the CI and N.
The first method was introduced by Yevjevich [46]. According to the observations by Ma et al. [25] on streams with large flow amplitudes, the criteria proposed by Yevjevich [46] (CI ≤ SD/4 and N = 10-25), Biedenharn et al. [39] and Crowder and Knapp [11] (each class interval should contain at least one flow event) are difficult to apply. For example, at the Vrânceni gauging station, the minimum discharge is 2.2 m 3 /s, whereas the peak discharge is 2359 m 3 /s (and the second largest discharge is 1468 m 3 /s, which results in a difference of 891 m 3 /s). The SD/4 value is 12.36. Under these circumstances and by considering the previously mentioned recommendations, the number of classes either exceeds 25 or falls below 10 (i.e., four classes, where the effective discharge is placed into the first class, which is also not recommended). To eliminate these drawbacks, Ma et al. [25] proposed to divide flow discharge records into classes by using equal arithmetic intervals corresponding to SD, 0.75 SD, 0.5 SD, and 0.25 SD. Considering the fact that the smaller the size of the class interval is, the more precise the results [9], the class intervals corresponding to 0.25 SD/4, 0.5 SD/4, 0.75 SD/4, and SD/4 were employed for this study.
The second method for determining the CI and N consisted of using kernel density estimation (KDE), which is a non-parametric way to estimate the PDF of a stream flow [23]. The kernel distribution histogram was built using the R statistical software, version 3.5.1. (R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing). In the case of the two approaches (SD and KDE) employed to estimate the effective discharge of suspended sediment transport, several steps were necessary [14]: (i) determining the flow-frequency distribution, (ii) determining the suspended sediment transport rating curve, and (iii) calculating the effective discharge by multiplying the suspended sediment transport rate for a certain discharge class with the frequency of the respective discharge. The discharge class that accounted for the maximum value of the product was defined as the effective discharge [1].
The third method pertaining to the class-based approach used in this study is the one introduced by Sichingabula [32], which is also known in the literature as the event-based class method (EBM). For this method, the discharge class width is equal in magnitude to the number of decimal places in the maximum value of the data series. For instance, for a maximum discharge ranging between 1 and 9.99 m 3 /s, the class width is 0.01 m 3 /s; between 10 and 99.99 m 3 /s, the class width is 0.1 m 3 /s; and above 100 m 3 /s, the class width is 1 m 3 /s [12,27] Abstract: Effective discharge, which represents the flo sediment over the long-term, was determined based daily suspended sediment discharge recorded betw along the Trotuș River. This study proposes an effi discharge based on observed values of the suspende the suspended sediment load is no longer either und assessment is based on sediment rating curves. T performed at two distinct levels: for the entire data s subsequently, for flows less than the bankfull dischar sediment transport characteristics revealed highly m River, the 0.1 and 1 m 3 /s class widths were used, which resulted in a total number of classes on the order of hundreds or thousands. For each discharge class, we determined the average magnitude for the class and subsequently used the sediment transport rating curve to evaluate the sediment transport for that class via the class-averaged discharge. The sediment transport rate for each class was multiplied by the flow frequency corresponding to the respective class. The effective discharge was considered to be either the discharge class with the largest value after multiplying the sediment transport and frequency or the peak in the plot of the frequency of sediment transport versus discharge [12].
The fourth method introduces a new way of estimating the effective discharge based on the utilization of real suspended sediment load data instead of the transport rate, which is determined using the suspended sediment rating curve. In fact, this approach is a mixture of the computational versions proposed by Andrews [1]; Sichingabula [32]; Crowder and Knapp [11]; Ma et al. [25]; Tena et al. [50]; and López-Tarazón and Batalla [9]. The discharge classes were established according to the method introduced by Sichingabula [32]. For simplicity, the representative discharge in each class was considered to be the midpoint of the corresponding interval. While Crowder and Knapp [11] employed the average suspended sediment load for each discharge class, Tena et al. [50] and López-Tarazón and Batalla [9] used the real sediment rate for each flow class. In the study by Ma et al. [25], the total suspended sediment load (SSL) transported by the flow discharge of each class interval was calculated by summing the suspended sediment loads of all sample points that fell within the corresponding class interval. The data processing included the following steps: summing the suspended sediment loads for each flow class from the data series, and dividing the value obtained for each class by the frequency (i.e., number of days) of the respective class to yield SSL/day (kg/s). The metric SSL/day (kg/s) was converted into the suspended sediment flux (SSF) (tons/day) [51] for each class. By multiplying the SSF (tons/day) by the flow frequency characteristic for each class, the total suspended sediment load (TSSL) was obtained for each class. TSSL is equivalent to the product of transport rate for suspended sediments and flow frequency, which was yielded via methods based on the sediment rating curve. A much simpler version yielding the same result would imply converting SSL (kg/s) into SSF (tons/day) and summing all of the values obtained for each class, which would determine the real suspended sediment load (RSSL) corresponding to each flow class. The midpoint of the discharge class that transported the largest amount of suspended sediments was considered the effective discharge.
The assessment of effective discharge using an analytical approach was performed according to the indications provided by Nash [19]; Vogel et al. [8]; Goodwin [41]; Quader and Guo [42]; Klonksy and Vogel [23]; and Sholtes et al. [40]. According to this method, the sediment transport mechanics are represented by a power function: where Qs represents the amount of suspended sediment load (kg/s), Q represents the flow rate (m 3 /s), and a and b are the fitting parameters. If f(Q) represents the frequency distribution function of the flow series, combining f(Q) with Equation (1) results in the transport effectiveness curve, where the peak is taken as the effective discharge for maximum geomorphic work. The function f(Q) was determined by fitting the logarithmic function to the original distribution of the historical discharge data [48]. According to Nash [19], it was assumed that the daily river discharge (Q) follows a two-parameter lognormal (LN2) distribution, such as: where µ and σ represent the mean and standard deviation, respectively, of ln(Q). where Q eff (Wolman and Miller) represents the effective discharge based on the Wolman and Miller [7] approach (Q effWM ) [8]. Vogel et al. [8] questioned the geomorphic significance of effective discharge and preferred instead to use the half-load discharge (Q 1/2 ) (i.e., the discharge above which half of the total load is transported) to summarize the effectiveness of rare floods [12]. Q 1/2 was determined according to the methodology presented by Klonksy and Vogel [23].
The effective discharge was estimated at each gauging station using all the approaches described in this section. At each station the following effective discharges were determined: the effective discharge for the entire investigated time frame (1994)(1995), the effective flow below the bankfull discharge, and the effective flow prior to and after the floods of 2005.

Flow Frequency
The empirical distribution functions of the discharge time series at all gauging stations along the Trotu Abstract: Effective discharge, which represents the flow, or range of flows, that transport the most sediment over the long-term, was determined based on the mean daily flow discharge and mean daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stations along the Trotuș River. This study proposes an efficient method for the estimation of effective discharge based on observed values of the suspended sediment load. By employing this method the suspended sediment load is no longer either under-or overestimated as in the cases when the assessment is based on sediment rating curves. The assessment on effective discharge was performed at two distinct levels: for the entire data series during the investigated time spans and, subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspended sediment transport characteristics revealed highly multimodal characteristics with many peaks, indicating ample ranges for the effective discharges. The main effective discharge corresponded to large flood events, which are typical for the upper end of the discharge range, whereas the secondary effective discharges corresponded to sub-bankfull flows, which are more frequent. The changes that occurred in the channel bed are reflected by the temporal variations in the effective discharge.
Keywords: effective discharge; suspended sediment load; magnitude-frequency analysis; sub-bankfull flow; temporal variation; geomorphic threshold Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this River are heavy-tailed ( Figure 2 and Table 2). The heavy-tail properties of the data are characterized by skewness and kurtosis [52].
where Qeff (Wolman and Miller) represents the effective discharge based on the Wolman and Miller [7] approach (QeffWM) [8]. Vogel et al. [8] questioned the geomorphic significance of effective discharge and preferred instead to use the half-load discharge (Q1/2) (i.e., the discharge above which half of the total load is transported) to summarize the effectiveness of rare floods [12]. Q1/2 was determined according to the methodology presented by Klonksy and Vogel [23].
The effective discharge was estimated at each gauging station using all the approaches described in this section. At each station the following effective discharges were determined: the effective discharge for the entire investigated time frame (1994)(1995), the effective flow below the bankfull discharge, and the effective flow prior to and after the floods of 2005.

Flow Frequency
The empirical distribution functions of the discharge time series at all gauging stations along the Trotuș River are heavy-tailed ( Figure 2 and Table 2). The heavy-tail properties of the data are characterized by skewness and kurtosis [52].  The kurtosis of the empirical distribution function in a time series provides a quantitative measure of the flow regime variability. While kurtosis values below 3 indicate a normal distribution, values above 3 indicate a type of flow variability where low flows are prevalent. Positive skewness implies that the probability density function is right skewed. Vogel et al. [8] and Klonsky and Vogel [23] showed that in the case of asymmetric (skewed) distributions, much of the total sediment transported may be moved by rare events.

Suspended Sediment Transport Rating Relations
A statistically significant positive relation between discharge and the SSL (  Abstract: Effective discharge, which represents the flow, or range of flows, that transport the most sediment over the long-term, was determined based on the mean daily flow discharge and mean daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stations along the Trotuș River. This study proposes an efficient method for the estimation of effective discharge based on observed values of the suspended sediment load. By employing this method the suspended sediment load is no longer either under-or overestimated as in the cases when the assessment is based on sediment rating curves. The assessment on effective discharge was performed at two distinct levels: for the entire data series during the investigated time spans and, subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspended sediment transport characteristics revealed highly multimodal characteristics with many peaks, indicating ample ranges for the effective discharges. The main effective discharge corresponded to large flood events, which are typical for the upper end of the discharge range, whereas the secondary effective discharges corresponded to sub-bankfull flows, which are more frequent. The changes that occurred in the channel bed are reflected by the temporal variations in the effective discharge.
Keywords: effective discharge; suspended sediment load; magnitude-frequency analysis; sub-bankfull flow; temporal variation; geomorphic threshold 1. Introduction Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size  Abstract: Effective discharge, which represents the flow, sediment over the long-term, was determined based on t daily suspended sediment discharge recorded between along the Trotuș River. This study proposes an efficien discharge based on observed values of the suspended se the suspended sediment load is no longer either under-o assessment is based on sediment rating curves. The performed at two distinct levels: for the entire data series subsequently, for flows less than the bankfull discharge. T sediment transport characteristics revealed highly mult indicating ample ranges for the effective discharges. The large flood events, which are typical for the upper en secondary effective discharges corresponded to sub-bank changes that occurred in the channel bed are reflected b discharge.
Keywords: effective discharge; suspended sediment sub-bankfull flow; temporal variation; geomorphic thresh Streamflow is probably the most extensively studied fact that the volume of water that flows through the chann The observation that the shape and size of a stream c are the result of a single reference discharge pertains to River. The kurtosis of the empirical distribution function in a time series provides a quantitative measure of the flow regime variability. While kurtosis values below 3 indicate a normal distribution, values above 3 indicate a type of flow variability where low flows are prevalent. Positive skewness implies that the probability density function is right skewed. Vogel et al. [8] and Klonsky and Vogel [23] showed that in the case of asymmetric (skewed) distributions, much of the total sediment transported may be moved by rare events. Abstract: Effective discharge, which represents the flow, or range of flows, that transport t sediment over the long-term, was determined based on the mean daily flow discharge an daily suspended sediment discharge recorded between 1994 and 2014 at four gauging along the Trotuș River. This study proposes an efficient method for the estimation of e discharge based on observed values of the suspended sediment load. By employing this the suspended sediment load is no longer either under-or overestimated as in the cases w assessment is based on sediment rating curves. The assessment on effective dischar performed at two distinct levels: for the entire data series during the investigated time spa subsequently, for flows less than the bankfull discharge. The effectiveness curves of the sus sediment transport characteristics revealed highly multimodal characteristics with many indicating ample ranges for the effective discharges. The main effective discharge correspo large flood events, which are typical for the upper end of the discharge range, wher secondary effective discharges corresponded to sub-bankfull flows, which are more freque changes that occurred in the channel bed are reflected by the temporal variations in the e River. The values of the b exponent are greater than 1 in all instances (with values ranging between 2.19 and 2.62), which reflects the amount of bed material (i.e., gravel-bed channel) and the fact that discharge must reach a certain threshold to displace the transported alluvium.

Suspended Sediment Transport Rating Relations
Water 2018, 10, x FOR PEER REVIEW 8 of 23 material (i.e., gravel-bed channel) and the fact that discharge must reach a certain threshold to displace the transported alluvium. In general, the suspended sediment rating curves tend to underestimate high and overestimate low suspended sediment concentrations [51]. In other instances, it was observed that using a simple transport method developed with a single power function commonly overestimates concentrations with high flow rates, which leads to significant errors when calculating annual loads and the effective discharge [14]. Such differences between the suspended sediment load values and estimated values were also documented in the case of the Trotuș River ( Figure 4). By employing the method described by Horowitz [51], the difference percentages were calculated: −37.8% at Lunca de Sus, −32.7% at Goioasa, +49.1% at Târgu Ocna, and −57.1% at Vrânceni. A minus sign indicates an underprediction, whereas a positive sign indicates an overprediction relative to the measured value.
Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this River (1994River ( -2014.
In general, the suspended sediment rating curves tend to underestimate high and overestimate low suspended sediment concentrations [51]. In other instances, it was observed that using a simple transport method developed with a single power function commonly overestimates concentrations with high flow rates, which leads to significant errors when calculating annual loads and the effective discharge [14]. Such differences between the suspended sediment load values and estimated values were also documented in the case of the Trotu Abstract: Effective discharge, which represents the flow, or range of flows, that transport th sediment over the long-term, was determined based on the mean daily flow discharge and daily suspended sediment discharge recorded between 1994 and 2014 at four gauging s along the Trotuș River. This study proposes an efficient method for the estimation of ef discharge based on observed values of the suspended sediment load. By employing this m the suspended sediment load is no longer either under-or overestimated as in the cases wh assessment is based on sediment rating curves. The assessment on effective discharg performed at two distinct levels: for the entire data series during the investigated time span subsequently, for flows less than the bankfull discharge. The effectiveness curves of the susp sediment transport characteristics revealed highly multimodal characteristics with many indicating ample ranges for the effective discharges. The main effective discharge correspon large flood events, which are typical for the upper end of the discharge range, where secondary effective discharges corresponded to sub-bankfull flows, which are more frequen changes that occurred in the channel bed are reflected by the temporal variations in the ef discharge.
Keywords: effective discharge; suspended sediment load; magnitude-frequency an sub-bankfull flow; temporal variation; geomorphic threshold Streamflow is probably the most extensively studied hydrogeomorphic process [1] due fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equil are the result of a single reference discharge pertains to hydraulic engineers who were bu irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust the depending on the magnitude and frequency of the discharge of water and sediment until a configuration is attained [4]. In time, these observations resulted in the development of r equations which were latter applied to natural streams [5]. By expanding this concept from ar channels to natural stream channels, the idea has arisen that a single reference discharge or a n range of discharges maintain the long-term equilibrium shape and size of the channel, therefo River ( Figure 4).
Water 2018, 10, x FOR PEER REVIEW 8 of 23 material (i.e., gravel-bed channel) and the fact that discharge must reach a certain threshold to displace the transported alluvium. In general, the suspended sediment rating curves tend to underestimate high and overestimate low suspended sediment concentrations [51]. In other instances, it was observed that using a simple transport method developed with a single power function commonly overestimates concentrations with high flow rates, which leads to significant errors when calculating annual loads and the effective discharge [14]. Such differences between the suspended sediment load values and estimated values were also documented in the case of the Trotuș River (Figure 4). By employing the method described by Horowitz [51], the difference percentages were calculated: −37.8% at Lunca de Sus, −32.7% at Goioasa, +49.1% at Târgu Ocna, and −57.1% at Vrânceni. A minus sign indicates an underprediction, whereas a positive sign indicates an overprediction relative to the measured value.

ș
Streamflow is probably the most extensively studied hydrogeomorphic p fact that the volume of water that flows through the channel, sets the scale of th The observation that the shape and size of a stream channel in a state of d are the result of a single reference discharge pertains to hydraulic engineers irrigation channels in India in the late 1800s [3]. They noted that these channels depending on the magnitude and frequency of the discharge of water and sed configuration is attained [4]. In time, these observations resulted in the dev equations which were latter applied to natural streams [5]. By expanding this co channels to natural stream channels, the idea has arisen that a single reference d range of discharges maintain the long-term equilibrium shape and size of the ch River highlights the highly multimodal characteristics, with many peaks indicating a wide range of effective discharges. With the exception of two instances (i.e., the effective discharges at Lunca de Sus estimated using the SD/4 and KDE methods; Figure 5a), the main effective discharge coincides with large flood events, which typically characterize the upper end of the discharge range. Almost exclusively, the largest measured flood coincides with the effective discharge (see the note in Table 3). Abstract: Effective discharge, which represents the flow, or range o sediment over the long-term, was determined based on the mean daily suspended sediment discharge recorded between 1994 and along the Trotuș River. This study proposes an efficient method discharge based on observed values of the suspended sediment lo the suspended sediment load is no longer either under-or overest assessment is based on sediment rating curves. The assessme performed at two distinct levels: for the entire data series during t subsequently, for flows less than the bankfull discharge. The effecti sediment transport characteristics revealed highly multimodal ch indicating ample ranges for the effective discharges. The main effec large flood events, which are typical for the upper end of the secondary effective discharges corresponded to sub-bankfull flows changes that occurred in the channel bed are reflected by the tem discharge.
Keywords: effective discharge; suspended sediment load; m sub-bankfull flow; temporal variation; geomorphic threshold Streamflow is probably the most extensively studied hydrogeo fact that the volume of water that flows through the channel, sets the The observation that the shape and size of a stream channel in are the result of a single reference discharge pertains to hydraulic irrigation channels in India in the late 1800s [3]. They noted that the depending on the magnitude and frequency of the discharge of wa configuration is attained [4]. In time, these observations resulted equations which were latter applied to natural streams [5]. By expan channels to natural stream channels, the idea has arisen that a single range of discharges maintain the long-term equilibrium shape and si River using traditional and mean approaches.   Abstract: Effective discharge, which repr sediment over the long-term, was determ daily suspended sediment discharge re along the Trotuș River. This study prop discharge based on observed values of t the suspended sediment load is no longe assessment is based on sediment ratin performed at two distinct levels: for the subsequently, for flows less than the ban sediment transport characteristics revea indicating ample ranges for the effective large flood events, which are typical f secondary effective discharges correspon changes that occurred in the channel be discharge.

Station
Keywords: effective discharge; suspe sub-bankfull flow; temporal variation; ge Streamflow is probably the most ext River using analytical approaches.  The large amounts of suspended sediments transported during these flood events decrease significantly compared to those transported at moderate flows, such that the latter appears (at first glance) to be almost negligible (Figure 5d). If these peaks indicating large flood events were removed, the presence of several peaks corresponding to moderate flow events would become noticeable. A similar behavior was described by Ma et al. [25] for a group of rivers in a loess region. Biedenharn et al. [39] recommended that isolated peaks in individual classes at the high end of the range for observed discharges are eradicated by reducing the number of classes. By following this recommendation, in the case of the Trotuș River, the number of classes could be as small as 2-4 classes. To eliminate this drawback, an assessment on the effective discharge was performed at two distinct levels: first, for the entire 1994-2014 data series; second, for the flows below bankfull discharge. The bankfull discharge data at the four gauging stations were extracted from Dumitriu [36].

Station
Both categories of effective discharges are important for the evolution of river channels [12,53]. This topic will be resumed later in the paper. The large amounts of suspended sediments transported during these flood events decrease significantly compared to those transported at moderate flows, such that the latter appears (at first glance) to be almost negligible (Figure 5d). If these peaks indicating large flood events were removed, the presence of several peaks corresponding to moderate flow events would become noticeable. A similar behavior was described by Ma et al. [25] for a group of rivers in a loess region. Biedenharn et al. [39] recommended that isolated peaks in individual classes at the high end of the range for observed discharges are eradicated by reducing the number of classes. By following this recommendation, in the case of the Trotu Abstract: Effective discharge, which represents the flow, or range of flows, that transport the m sediment over the long-term, was determined based on the mean daily flow discharge and m daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stati along the Trotuș River. This study proposes an efficient method for the estimation of effec discharge based on observed values of the suspended sediment load. By employing this met the suspended sediment load is no longer either under-or overestimated as in the cases when assessment is based on sediment rating curves. The assessment on effective discharge performed at two distinct levels: for the entire data series during the investigated time spans a subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspen sediment transport characteristics revealed highly multimodal characteristics with many pe indicating ample ranges for the effective discharges. The main effective discharge corresponde large flood events, which are typical for the upper end of the discharge range, whereas secondary effective discharges corresponded to sub-bankfull flows, which are more frequent. changes that occurred in the channel bed are reflected by the temporal variations in the effec discharge.
Keywords: effective discharge; suspended sediment load; magnitude-frequency analy sub-bankfull flow; temporal variation; geomorphic threshold River, the number of classes could be as small as 2-4 classes. To eliminate this drawback, an assessment on the effective discharge was performed at two distinct levels: first, for the entire 1994-2014 data series; second, for the flows below bankfull discharge. The bankfull discharge data at the four gauging stations were extracted from Dumitriu [36].
Both categories of effective discharges are important for the evolution of river channels [12,53]. This topic will be resumed later in the paper.
The effective discharge estimated for the entire data series (Q effT ) varies depending on significant flood events and is less sensitive to the selected method of computation. In turn, the values of the effective discharge for sub-bankfull flows (Q eff<bf ) indicate small differences depending on the method selected for determination, although these are more evident downstream, where flow variability is higher. Overall, however, the differences are negligible and result mostly from the fact that the effective discharge value is considered to be the midpoint of the corresponding interval whereas, at upstream stations (Lunca de Sus and Goioasa), the differences between the Q eff<bf values estimated using the class-based approaches typically range between ±0.1 and 1 m 3 /s, ±0.4 and 2.6 m 3 /s at midstream stations (Târgu Ocna) (with one exception), and ±0.2 and as high as 16 m 3 /s at downstream stations (Vrânceni). At the Vrânceni station, the lowest values were observed for the SD/4 and KDE methods, which is likely because using an optimal kernel density or bin size may mask some information on event frequencies or magnitudes that could be preserved by a slightly less optimal but event-based grouping scheme [27]. The exception mentioned in the case of the Târgu Ocna gauging station refers to the Q eff<bf determined for the 2005-2014 period using the RSSL method, which is lower by nearly 10 m 3 /s compared to the value estimated using alternative methods. The explanation could reside in the fact that for the 29-30 m 3 /s flow class, the average suspended solid load was approximately 45 kg/s, whereas in May-July 2006, it amounted to as high as 420 kg/s. Since the three other estimation methods use the sediment rating curve to determine the transport rate, the 29-30 m 3 /s class was underestimated with respect to the other classes (approximately 40 m 3 /s).
For the 1994-2005 period, Q effT is represented by the flood event of 12-13 July 2005 ( Figure 6). The discharges recorded during this time frame are historical peaks, which had an outstanding effect on the river-channel morphology. The peak discharge of 2845 m 3 /s recorded at Vrânceni station (with a recurrence interval of 625 years) was ranked as the most significant event documented throughout the entire measurement period in the Trotu

Introduction
Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this drainage basin [36].
The effective discharge estimated for the entire data series (QeffT) varies depending on significant flood events and is less sensitive to the selected method of computation. In turn, the values of the effective discharge for sub-bankfull flows (Qeff<bf) indicate small differences depending on the method selected for determination, although these are more evident downstream, where flow variability is higher. Overall, however, the differences are negligible and result mostly from the fact that the effective discharge value is considered to be the midpoint of the corresponding interval whereas, at upstream stations (Lunca de Sus and Goioasa), the differences between the Qeff<bf values estimated using the class-based approaches typically range between ±0.1 and 1 m 3 /s, ±0.4 and 2.6 m 3 /s at midstream stations (Târgu Ocna) (with one exception), and ±0.2 and as high as 16 m 3 /s at downstream stations (Vrânceni). At the Vrânceni station, the lowest values were observed for the SD/4 and KDE methods, which is likely because using an optimal kernel density or bin size may mask some information on event frequencies or magnitudes that could be preserved by a slightly less optimal but event-based grouping scheme [27]. The exception mentioned in the case of the Târgu Ocna gauging station refers to the Qeff<bf determined for the 2005-2014 period using the RSSL method, which is lower by nearly 10 m 3 /s compared to the value estimated using alternative methods. The explanation could reside in the fact that for the 29-30 m 3 /s flow class, the average suspended solid load was approximately 45 kg/s, whereas in May-July 2006, it amounted to as high as 420 kg/s. Since the three other estimation methods use the sediment rating curve to determine the transport rate, the 29-30 m 3 /s class was underestimated with respect to the other classes (approximately 40 m 3 /s).
For the 1994-2005 period, QeffT is represented by the flood event of 12-13 July 2005 ( Figure 6). The discharges recorded during this time frame are historical peaks, which had an outstanding effect on the river-channel morphology. The peak discharge of 2845 m 3 /s recorded at Vrânceni station (with a recurrence interval of 625 years) was ranked as the most significant event documented throughout the entire measurement period in the Trotuș drainage basin [36]. The values of Qeff<bf were lower from 2005 to 2014 compared with those during the pre-flood event period, which is possibly due to a change in the sediment supply-sediment transport balance [48]. The values of Q eff<bf were lower from 2005 to 2014 compared with those during the pre-flood event period, which is possibly due to a change in the sediment supply-sediment transport balance [48].
The half-load discharge displays higher values compared to the effective discharge, whereas the Q 1/2 /Q eff<bf ratio ranges between 0.9 and 4. Thus, it can be stated that Q effT > Q 1/2 > Q eff<bf > Q effWM .

Influence of Class Interval Assignments
The number of class intervals considered for the assessment of effective discharge can influence, to a significant extent, the effective discharge values and load histograms [11]. In some situations, it has been noted that the effective discharge generally increases with the number of classes [25]. However, this finding cannot be accepted as a general rule because in the majority of cases, the effective discharge does not continuously increase [6,11] or decrease [9,32] with the number of class intervals. In the case of the Trotu Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this River between 1994 and 2014, an increase (albeit insignificant) in the effective discharge with the number of classes was observed only at Lunca de Sus and Goioasa. At Lunca de Sus, the increase was from 1.9 m 3 /s (78 class intervals) to 2.1 m 3 /s (175 class intervals), and at Goioasa, the increase was from 9.8 m 3 /s (101 class intervals) to 10.5 m 3 /s (206 class intervals). Since the estimated values of the effective discharge show no significant variations with varying class intervals, the average value was used for comparison (Table 3). Considering the fact that the class midpoint is arbitrarily chosen to represent the effective discharge of that class, and the effectiveness curve is rather irregular, it is more appropriate to use a flow class for the effective discharge [6]. Therefore, the following effective discharge classes were obtained: Lunca de Sus, 1.5-2.5 m 3 /s; Goioasa, 9.5-10.5 m 3 /s; Târgu Ocna, 40-45 m 3 /s; and Vrânceni, 50-65 m 3 /s. Some differences, depending on the number of classes, have also been observed in suspended solid load histograms. As the number of classes increases, certain variations, in terms of shape ( Figure 7) and the total amount of transported sediment, became evident. For instance, at the Lunca de Sus, Goioasa and Târgu Ocna gauging stations, the amounts of suspended sediment estimated using the SD/4, KDE, and EBM methods (with an increasing number of classes) were ca. 1.4 to 1.6 lower compared to the real amounts of suspended sediment transported between 1994 and 2014. At the Vrânceni station, the difference was even higher, with estimated values of 2.2 to 2.4 times lower. Therefore, as the number of classes increases, the total amount of sediment carried throughout the section is underestimated. Contrary to what Biedenharn et al. [39] stated regarding the fact that a large number of classes would yield abnormal results, in this case, the opposite situation was noted, which corresponded to the observations of López-Tarazón and Batalla [9], who stated that the resulting accuracy increases Abstract: Effective discharge, which represents the flow, or range of flows, that transport the most sediment over the long-term, was determined based on the mean daily flow discharge and mean daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stations along the Trotuș River. This study proposes an efficient method for the estimation of effective discharge based on observed values of the suspended sediment load. By employing this method the suspended sediment load is no longer either under-or overestimated as in the cases when the assessment is based on sediment rating curves. The assessment on effective discharge was performed at two distinct levels: for the entire data series during the investigated time spans and, subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspended sediment transport characteristics revealed highly multimodal characteristics with many peaks,

Introduction
Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this River are within the ranges presented by Ashmore and Day [18], Sichingabula [32], Ma et al. [25], and Roy and Sinha [48]; however, the durations are higher compared to the values obtained by Wolman and Miller [7], Pickup and Warner [17], Andrews [1], and lower than the values determined by López-Tarazón and Batalla [9]. Table 5. Average flow duration of Q eff<bf (effective discharges are shown in Table 3). The estimated values of Q effT (1994-2014) had recorded percentages for time equaling or exceeding 0.06% at Lunca de Sus, 0.045% at Goioasa, 0.046% at Târgu Ocna, and 0.08% at Vrânceni. In regard to the times equalling or exceeding Q eff<bf , the values range between 12% and 42% (Figure 8). In general, the values are close to those presented by Klonsky and Vogel [23] for the 15 sites chosen to be representative of all types of rivers throughout the United States.

Station
The estimated values of QeffT (1994-2014) had recorded percentages for time equaling or exceeding 0.06% at Lunca de Sus, 0.045% at Goioasa, 0.046% at Târgu Ocna, and 0.08% at Vrânceni. In regard to the times equalling or exceeding Qeff<bf, the values range between 12% and 42% ( Figure  8). In general, the values are close to those presented by Klonsky and Vogel [23] for the 15 sites chosen to be representative of all types of rivers throughout the United States. The recurrence interval (RI) of effective discharge typically falls within the limits mentioned in the literature [11,14,19,20,26,54]: between 1.0 and 1.6 years during the 1994-2014 period, 1.0 to 1.7 years during the 1994-2005 period, and 1.0 to 1.5 years during the 2005-2014 period.

Suspended Sediment Transport Rates at Effective and Half-Load Discharges
The relation among suspended sediment transport, water flow and the time required to carry out the transport is illustrated by the cumulative curve in Figure 9. The analysis of these curves shows that all of the suspended sediment can be moved with a relatively small portion of annual The recurrence interval (RI) of effective discharge typically falls within the limits mentioned in the literature [11,14,19,20,26,54]: between 1.0 and 1.6 years during the 1994-2014 period, 1.0 to 1.7 years during the 1994-2005 period, and 1.0 to 1.5 years during the 2005-2014 period.

Suspended Sediment Transport Rates at Effective and Half-Load Discharges
The relation among suspended sediment transport, water flow and the time required to carry out the transport is illustrated by the cumulative curve in Figure 9. The analysis of these curves shows that all of the suspended sediment can be moved with a relatively small portion of annual water yielded during a small part of the year. For example, at the Lunca de Sus gauging station for approximately 7% of the time, Q eff<bf is responsible for the transport of 47% of the total suspended sediment, and it uses 25% of the water flow. At Goioasa, the Q eff<bf requires greater amounts of time (14%) and water (40%) to transport 30% of the total suspended sediment. The respective values are somewhat similar: during an interval ranging between 5% and 9% of the time, Q eff<bf transports 35% and 30% of the total suspended sediment using 27% and 38% of the water discharge, respectively. Therefore, less than 40% of the flow is responsible for effective suspended sediment transport in the Trotu Abstract: Effective discharge, which represents the flow sediment over the long-term, was determined based on daily suspended sediment discharge recorded betwee along the Trotuș River. This study proposes an effici discharge based on observed values of the suspended the suspended sediment load is no longer either under assessment is based on sediment rating curves. Th performed at two distinct levels: for the entire data seri subsequently, for flows less than the bankfull discharge sediment transport characteristics revealed highly mu indicating ample ranges for the effective discharges. Th large flood events, which are typical for the upper secondary effective discharges corresponded to sub-ba changes that occurred in the channel bed are reflected discharge.

Sub-Bankfull Flow Frequency Flood Events in Outlining Effe
Keywords: effective discharge; suspended sedime sub-bankfull flow; temporal variation; geomorphic thre

River.
Water 2018, 10, x FOR PEER REVIEW 15 of 23 water yielded during a small part of the year. For example, at the Lunca de Sus gauging station for approximately 7% of the time, Qeff<bf is responsible for the transport of 47% of the total suspended sediment, and it uses 25% of the water flow. At Goioasa, the Qeff<bf requires greater amounts of time (14%) and water (40%) to transport 30% of the total suspended sediment. The respective values are somewhat similar: during an interval ranging between 5% and 9% of the time, Qeff<bf transports 35% and 30% of the total suspended sediment using 27% and 38% of the water discharge, respectively. Therefore, less than 40% of the flow is responsible for effective suspended sediment transport in the Trotuș River. The percentages of discharge that were needed to transport 10%, 50%, and 90% of the suspended sediments were calculated and are shown in Table 6 and Figure 10. From 1994 to 2014, 10% of the suspended sediment load for all stations was moved by 0.9-2.2% of the total discharge ( Figure 10a) and within 0.01-0.025% of the total time (Figure 10b and Table 6). This situation highlights the fact that suspended sediment transport is controlled by flood events. From 2000 to 2014, the percentage of total suspended sediment transported during flood events amounted to 40% at Lunca de Sus, 51% at Goioasa, 38% at Târgu Ocna, and 44% at Vrânceni. Over the course of the The percentages of discharge that were needed to transport 10%, 50%, and 90% of the suspended sediments were calculated and are shown in Table 6 and Figure 10. From 1994 to 2014, 10% of the suspended sediment load for all stations was moved by 0.9-2.2% of the total discharge ( Figure 10a) and within 0.01-0.025% of the total time (Figure 10b and Table 6). This situation highlights the fact that suspended sediment transport is controlled by flood events. From 2000 to 2014, the percentage of total suspended sediment transported during flood events amounted to 40% at Lunca de Sus, 51% at Goioasa, 38% at Târgu Ocna, and 44% at Vrânceni. Over the course of the same time frame, several years were recorded when the amount of suspended sediment transported during flood events was greater than 80% of the total suspended sediment: Lunca de Sus (2000), Goioasa (2002Goioasa ( , 2004Goioasa ( , 2005, and 2010), Târgu Ocna (2007) and Vrânceni (2004,2005,2007, and 2014) [36]. These events determined the main peak of the effective discharge (Q effT ). Half of the total suspended sediment load (the 50th percentile for the total cumulative suspended load) was transported by 10-27% of the total discharge during a time interval ranging between 0.14% and 0.85% of the total time.  In a study carried out in the drainage basin for the Ganga River, Roy and Sinha [48] concluded that in rivers with normal sediment transport capacities, ~90% of the sediment load is transported by 35-60% of the total discharge. At the gauging stations along the Trotuș River two distinct situations were observed. At Goioasa and Vrânceni, 90% of the total suspended sediment load was carried by flows below 50% of the total discharge. At Lunca de Sus and Târgu Ocna, the same percentage of sediment was transported by flows exceeding 60% of the total discharge, thus revealing that the transport capacity varies depending on the hydro-geomorphological traits of the river reach. The results determined for the Trotuș River are partially similar to those reported in the literature. For example, Wolman and Miller [7] showed that in the case of the Colorado River, 50% of the total load is carried by flows equating to 8.5% of the time, while in Rio Puerco, 31% of the total load is transported in just 2.75% of the time. These time percentages correspond to a share of 90% of the total suspended sediment load transported into the Trotuș River. Some of the results published by Roy and Sinha [48] for the transport of 50% of the total suspended sediment load are similar to the results yielded by our study but solely in terms of the percentage of discharge (10-27%) and not in terms of the time percentage (which was 20 to 100 times higher in the case of Ganga River). Typically, in small basins, a large percentage of the total sediment load is moved during rare flood events; therefore, the relation between time and load becomes steeper [6,9,50]. Values close to those recorded at gauging stations along the Trotuș River were reported by Meade and Parker [55] and by López-Tarazón and Batalla [9].
The suspended sediment load corresponding to Q1/2 depends primarily on the surface and particularities of the investigated drainage basin and the runoff characteristics of the study period. In a study carried out in the drainage basin for the Ganga River, Roy and Sinha [48] concluded that in rivers with normal sediment transport capacities,~90% of the sediment load is transported by 35-60% of the total discharge. At the gauging stations along the Trotu Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2].
The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this River were reported by Meade and Parker [55] and by López-Tarazón and Batalla [9].
The suspended sediment load corresponding to Q 1/2 depends primarily on the surface and particularities of the investigated drainage basin and the runoff characteristics of the study period. Therefore, a variation along the longitudinal profile of the suspended sediment load transported by Q 1/2 has been documented, such that from 1994 to 2014, Q 1/2 was responsible for the discharge of 155 t × 10 3 at Lunca de Sus, 1717 t × 10 3 at Goioasa, 8152 t × 10 3 at Târgu Ocna, and 13,014 t × 10 3 at Vrânceni. Similar to the effective discharge, it varies from among streams and longitudinally along a given stream. During the 1994-2005 time frame, Q 1/2 had higher values at all stations (with the exception of Goioasa) compared to that during the 2005-2014 period.

Relation between Effective Discharge and Other Parameters
The mean values of the effective discharge calculated at the sub-bankfull flow (Q eff<bfAvg ) were compared to the values of the bankfull discharge (Q bf ), mean annual flood (MAF) (the values were taken from Dumitriu [36]), half-load discharge (Q 1/2 ) and mean annual discharge (Q mad ) ( Table 7). The values of the Q bf /Q eff<bfAvg ratio range between 3.97 and 6.35 and appear to correlate with the tendencies of degradation, which are more pronounced in the mid-and downstream regions [36]. A series of empirical investigations show that in certain dynamically stable rivers, the effective discharge is relatively close to the bankfull discharge (Q eff ≈ Q bf ) [1,26]. However, this situation cannot be generalized [56]. Thus, numerous observations have shown that the relation Q eff ≈ Q bf is valid, particularly for channels in a state of dynamic equilibrium [57]. Q eff < Q bf could offer an indication that the channel is degrading, whereas Q eff > Q bf could point towards aggradation [41]. Values less than 10 for the Q bf /Q eff ratio are not uncommon, as they show an increase in Q bf compared to Q eff due to channel degradation [48].
The value of the Q eff<bfAvg /MAF ratio is less than 1, as the effective discharge is, on average, 50% of the mean annual flood. Wolman and Miller [7] showed that the effective discharge corresponds to the approximate mean annual flood.
At all gauging stations along the Trotu Abstract: Effective discharge, which represents the flow, or range of flows, that transport the m sediment over the long-term, was determined based on the mean daily flow discharge and m daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stat along the Trotuș River. This study proposes an efficient method for the estimation of effe discharge based on observed values of the suspended sediment load. By employing this me the suspended sediment load is no longer either under-or overestimated as in the cases when assessment is based on sediment rating curves. The assessment on effective discharge performed at two distinct levels: for the entire data series during the investigated time spans subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspen sediment transport characteristics revealed highly multimodal characteristics with many pe indicating ample ranges for the effective discharges. The main effective discharge corresponde large flood events, which are typical for the upper end of the discharge range, whereas secondary effective discharges corresponded to sub-bankfull flows, which are more frequent. changes that occurred in the channel bed are reflected by the temporal variations in the effe discharge.

ş
River, Q 1/2 > Q eff<bfAvg , as the values of the ratio range from 0.24 (Vrânceni) to 0.94 (Târgu Ocna). The half-load discharge is typically associated with a higher magnitude and longer return period flow compared to those for the effective discharge [8,23]. In general, Q 1/2 is much more frequent and lower than Q bf but less frequent and higher compared to Qmad. Considering the model proposed by Wolman and Miller [7], where Q eff ≈ MAF, it would be expected that Q 1/2 ≈ Q eff ; however, for strongly skewed effectiveness distributions, Q 1/2 and Q eff combined are descriptive of the skew. For Q 1/2 > Q eff the effectiveness relation is positively skewed (as documented in the case of the Trotu Abstract: Effective discharge, which represents the flow, or range of flows, that transport the most sediment over the long-term, was determined based on the mean daily flow discharge and mean daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stations along the Trotuș River. This study proposes an efficient method for the estimation of effective discharge based on observed values of the suspended sediment load. By employing this method the suspended sediment load is no longer either under-or overestimated as in the cases when the assessment is based on sediment rating curves. The assessment on effective discharge was performed at two distinct levels: for the entire data series during the investigated time spans and, subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspended sediment transport characteristics revealed highly multimodal characteristics with many peaks, indicating ample ranges for the effective discharges. The main effective discharge corresponded to large flood events, which are typical for the upper end of the discharge range, whereas the secondary effective discharges corresponded to sub-bankfull flows, which are more frequent. The changes that occurred in the channel bed are reflected by the temporal variations in the effective discharge. River), and for Q 1/2 < Q eff , the relation is negatively skewed [27]. The Q eff /Q mad ratio describes the relative magnitude of the effective discharge. Abstract: Effective discharge, which sediment over the long-term, was d daily suspended sediment dischar along the Trotuș River. This study discharge based on observed value the suspended sediment load is no assessment is based on sediment performed at two distinct levels: fo subsequently, for flows less than the sediment transport characteristics indicating ample ranges for the effe large flood events, which are typ secondary effective discharges corr changes that occurred in the chann discharge.
River, the values of this ratio vary between 1.49 and 2.46. A strong inverse relation between the relative magnitude and frequency of exceedance for effective discharge [27] can also be observed in our study area ( Figure 11).
(as documented in the case of the Trotuș River), and for Q1/2 < Qeff, the relation is negatively skewed [27].
The Qeff/Qmad ratio describes the relative magnitude of the effective discharge. For the Trotuș River, the values of this ratio vary between 1.49 and 2.46. A strong inverse relation between the relative magnitude and frequency of exceedance for effective discharge [27] can also be observed in our study area ( Figure 11). Figure 11. Relation between frequency of effective discharge and relative magnitude of effective discharge.

Temporal Variations in Effective Discharge
The data presented in Table 3 show differences between the effective discharges determined for the two analyzed time frames (1994-2005 and 2005-2014). The Qeff<bf between 2005 and 2014 was 1.2 to 1.7 lower than that in the previous period at three stations (Goioasa, Târgu Ocna, and Vrânceni). At Lunca de Sus, an increase in the Qeff<bf value of 1 m 3 /s was determined. The decreasing values documented along the mid-and downstream regions can be due to the channel changes that occurred after the flood events of 2005 and 2010. Upstream (Lunca de Sus), channel aggradation became the dominant process, and strong channel degradation was observed in the remaining sectors. In some downstream reaches, the transition from a gravel-bed to gravel bed-bedrock Figure 11.
Relation between frequency of effective discharge and relative magnitude of effective discharge.

Temporal Variations in Effective Discharge
The data presented in Table 3 show differences between the effective discharges determined for the two analyzed time frames (1994-2005 and 2005-2014). The Q eff<bf between 2005 and 2014 was 1.2 to 1.7 lower than that in the previous period at three stations (Goioasa, Târgu Ocna, and Vrânceni). At Lunca de Sus, an increase in the Q eff<bf value of 1 m 3 /s was determined. The decreasing values documented along the mid-and downstream regions can be due to the channel changes that occurred after the flood events of 2005 and 2010. Upstream (Lunca de Sus), channel aggradation became the dominant process, and strong channel degradation was observed in the remaining sectors. In some downstream reaches, the transition from a gravel-bed to gravel bed-bedrock channel occurred as a result of the removal of the armor layer. According to data from the Vrânceni gauging station from 2005 to 2012, the channel bed deepened by 0.85 m [36]. Channel degradation is a major characteristic for most rivers of the Eastern Carpathians [58]. The flood events of 2005 and 2010 transported impressive amounts of suspended sediments, a large part of which was deposited onto the channel bed. On the other hand, suspended sediment availability was strongly dependent upon the stability of the coarse surface layer of the channel bed; when this armor is removed, a significant amount of fine sediments from the subsurface layer becomes accessible to the flow [59,60]. This resulted in an increase in the sources of fine sediments from the channel bed. Such a boost in the sediment supply, particularly the supply of fine sediments, can lead to a decrease in the effective discharge because the channel discharge becomes less capable of transporting excess sediments [48]. This availability of fine sediments is also revealed by higher or sensibly equal amounts of suspended sediments transported at lower Q 1/2 values compared to the previous period. For example, at the Târgu Ocna gauging station between 1994 and 2005, Q 1/2 was 57.5 m 3 /s and moved 2704 t × 10 3 of suspended sediment, whereas from 2005 to 2014, Q 1/2 was 36.0 m 3 /s and transported 4764 t × 10 3 of suspended sediment (i.e., nearly 1.8 times more than the former period).
In the same context of the temporal variation in effective discharge, an inverse relation was observed between its value and the skewness in the mean daily flow. The Goioasa, Târgu Ocna, and Vrâceni gauging stations experienced increases in the skewness values of the mean daily flow during the 2005-2014 period (from 4.5 to 6.3 on average), which was complemented by a decrease in the effective discharge value. Conversely, at Lunca de Sus, where the skewness in the mean daily flow diminished from 4.1 to 3.8, an increase in effective discharge was documented between 2005 and 2014.
A comparison between the results yielded by our study and the data published by Rădoane and Ichim [61] (i.e., the first and only study to date regarding the effective discharge of a Romanian river-namely, the Trotu Streamflow is probably the most extensively studied hydrogeomorphic process [1] due to the fact that the volume of water that flows through the channel, sets the scale of the channel [2]. The observation that the shape and size of a stream channel in a state of dynamic equilibrium are the result of a single reference discharge pertains to hydraulic engineers who were building irrigation channels in India in the late 1800s [3]. They noted that these channels can adjust their size depending on the magnitude and frequency of the discharge of water and sediment until a stable configuration is attained [4]. In time, these observations resulted in the development of regime equations which were latter applied to natural streams [5]. By expanding this concept from artificial channels to natural stream channels, the idea has arisen that a single reference discharge or a narrow range of discharges maintain the long-term equilibrium shape and size of the channel, therefore, this drainage basin, the contribution of the suspended sediment fraction to the total sediment load ranges from 75 to 90% [62]; nevertheless, the transport of suspended sediments in mountain streams is typically considered to be of secondary geomorphic importance. The data regarding the bed load are rather scarce. Quantification in the field is difficult in many respects, while estimations based on empirical bed-load transport equations yield results that differ by several orders of magnitude depending on the equations used [11]. To compensate (to a certain degree) for the lack of bed load data that would support the delimitation of two types of geomorphically-relevant discharges (i.e., channel-maintaining and channel-changing), a surrogate method was applied. This approach is based on the suggestions made by Crowder and Knapp [11] and Phillips [63] for using stream power to determine the potential thresholds for geomorphic flow. Considering that the thresholds for the transport of various particle sizes or the erosion of various channel materials may be expressed in terms of stream power, in this study, the following specified thresholds were used: (i) critical stream power [64] (regarded as the threshold for D 50 incipient motion-D 50 TIM); (ii) the Brookes threshold (BT) or stability point (35 W/m 2 ), below which the major phase of erosion becomes negligible [65]; and (iii) the Magilligan threshold (MT) (300 W/m 2 ), which is considered the threshold for major morphological adjustments in alluvial channels [66] (Figure 12). Stream power and critical stream power values were taken from Dumitriu [36]. Discharges ranging between the BT and MT can result (under certain conditions) in possible channel changes (PCCs) with a short period of recovery, whereas those exceeding the MT value can generate possible major geomorphic changes (PMGCs) with very long periods of recovery. In this context, discharges above the BT value were considered to be channel-changing discharges (CCD), and those below the BT were included in the channel-maintaining category (CMD). The word "possible" was used because this threshold approach, although attractive, should be used with caution given the complexity of fluvial geomorphic processes.
The discharges corresponding to D 50 TIM and BT are very close to Q eff<bf in upstream and midstream regions (Figure 12a-c) (at Târgu Ocna, D 50 TIM and BT correspond to the same discharge (35 m 3 /s), which is slightly less than Q eff<bf (43 m 3 /s)). At these stations, Q eff<bf acts similar to a channel-maintaining discharge. Instead, the interval for manifested flows exceeds that of the MT, which could lead to significant channel changes that increase downstream. This finding, along with the peak values of stream power, are in agreement with the field observations made after the flood events of 2005 and 2010 when important channel changes were detected in the mid-and downstream regions [36].
(35 m 3 /s), which is slightly less than Qeff<bf (43 m 3 /s)). At these stations, Qeff<bf acts similar to a channel-maintaining discharge. Instead, the interval for manifested flows exceeds that of the MT, which could lead to significant channel changes that increase downstream. This finding, along with the peak values of stream power, are in agreement with the field observations made after the flood events of 2005 and 2010 when important channel changes were detected in the mid-and downstream regions [36]. The geomorphic effect of high-magnitude floods has been described in a vast number of papers [67]. These studies discussed the controls of channel responses during flood events. The vast majority of these papers focused mainly on the role of hydraulic variables (e.g., unit stream power and flow duration) [68], whereas others showed that hydraulic variables were insufficient when explaining these changes [69], or their effects differed among streams [70,71]. For example, during the floods generated by Tropical Storm Irene, the minimum threshold of 300 W/m 2 was surpassed for 99% of the 60-km Saxons River under study, but the channel widened along considerably smaller reaches [70]. Investigations on streams from the northern Colorado Front Range [71] showed that in channel beds with slope gradients <3% (as is the case with the region upstream of Lunca de Sus), there is the credible potential for substantial channel widening to occur at values >230 W/m 2 , while at values >700 W/m 2 , major geomorphic changes can occur. The authors suggest that these thresholds can be utilized for assessing geomorphic hazard potentials via hydraulic modelling. In the case of streams with slopes ≥3% (i.e., most of the length of the Trotuș River), hydraulic variables alone are seldom good predictors of geomorphic change due to variations in bedforms and bed armor, which induce a certain resistance to flow [69,71]. However, the high values of stream power The geomorphic effect of high-magnitude floods has been described in a vast number of papers [67]. These studies discussed the controls of channel responses during flood events. The vast majority of these papers focused mainly on the role of hydraulic variables (e.g., unit stream power and flow duration) [68], whereas others showed that hydraulic variables were insufficient when explaining these changes [69], or their effects differed among streams [70,71]. For example, during the floods generated by Tropical Storm Irene, the minimum threshold of 300 W/m 2 was surpassed for 99% of the 60-km Saxons River under study, but the channel widened along considerably smaller reaches [70]. Investigations on streams from the northern Colorado Front Range [71] showed that in channel beds with slope gradients <3% (as is the case with the region upstream of Lunca de Sus), there is the credible potential for substantial channel widening to occur at values >230 W/m 2 , while at values >700 W/m 2 , major geomorphic changes can occur. The authors suggest that these thresholds can be utilized for assessing geomorphic hazard potentials via hydraulic modelling. In the case of streams with slopes ≥3% (i.e., most of the length of the Trotu River), hydraulic variables alone are seldom good predictors of geomorphic change due to variations in bedforms and bed armor, which induce a certain resistance to flow [69,71]. However, the high values of stream power recorded during the 2005 flood event in the mid-and downstream regions (from 830 to 1550 W/m 2 ) were correlated with the field observations, which supported inclusion by comparing these values with Q effT in the channel-forming discharge category. Therefore, depending on the channel characteristics, it is possible that more than one discharge class is responsible for a major part of geomorphic or landform changes [48].
The duration of a flood event can often compensate for the poor predictability of hydraulic variables. In many cases, a better correlation was determined between the magnitude of the channel changes and the flood duration compared to the correlation with hydraulic variables [67]. Thus, in the case of the Trotu Abstract: Effective discharge, which represents the flow, or range of flows, that transport the most sediment over the long-term, was determined based on the mean daily flow discharge and mean daily suspended sediment discharge recorded between 1994 and 2014 at four gauging stations along the Trotuș River. This study proposes an efficient method for the estimation of effective discharge based on observed values of the suspended sediment load. By employing this method the suspended sediment load is no longer either under-or overestimated as in the cases when the assessment is based on sediment rating curves. The assessment on effective discharge was performed at two distinct levels: for the entire data series during the investigated time spans and, subsequently, for flows less than the bankfull discharge. The effectiveness curves of the suspended sediment transport characteristics revealed highly multimodal characteristics with many peaks, indicating ample ranges for the effective discharges. The main effective discharge corresponded to large flood events, which are typical for the upper end of the discharge range, whereas the secondary effective discharges corresponded to sub-bankfull flows, which are more frequent. The changes that occurred in the channel bed are reflected by the temporal variations in the effective discharge.
Keywords: effective discharge; suspended sediment load; magnitude-frequency analysis; River, it was noted that the flood event of 2010 (lower in magnitude but considerably longer compared to the flood of 2005) generated, in some reaches, many more visible changes than the previous event (2005) when the stream power reached its peak value [36].

Conclusions
The relation between flow frequency and magnitude, in terms of outlining effective discharge, is a hot spot in fluvial geomorphology. To reduce the degree of subjectivity generated by the choice of certain flow-class intervals as much as possible, we opted to employ several class-based approaches and