Is It Optimal to Use the Entirety of the Available Flow Records in the Range of Variability Approach?

: Reducing the degree of ﬂow regime alteration is a basic principle for biodiversity conservation in rivers. The range of variability approach (RVA) is the most widely used method to assess ﬂow regime alteration. Generally, researchers tend to put all of the available pre-impact and post-impact ﬂow records into the RVA. However, no research has tested whether it is optimal to use the entirety of the available ﬂow records from the perspective of calculation accuracy for the degree of ﬂow regime alteration. In this research, a series of numerical simulations is conducted, demonstrating that the greatest accuracy for ﬂow regime alteration degree assessed by the RVA is achieved when the length of both the pre- and post-impact ﬂow time series is set equal to multiples of periodicity length, and that, when attempting to put the whole available ﬂow record into the RVA, calculation accuracy may be reduced. On the basis of these ﬁndings, we further propose revising the traditional RVA procedure by assessing the periodicity of the pre- and post-impact ﬂow time series in advance. If the periodicity of the pre- or post-impact ﬂows is detected, the length of the time series should be set equal to its periodicity.


Introduction
The natural flow regime plays a crucial role in preserving the structures and functions of riverine ecosystems [1,2]. It can be defined by five major ecologically relevant characteristics, i.e., magnitude, frequency, duration, timing, and rate of change [3,4]. Alteration of these hydrologic characteristics could have significant ecological consequences [5][6][7]. Maintaining the natural flow regime is a foundational principle for biodiversity conservation in rivers [1,6], but human activities and climate change have seriously altered the natural flow regimes of rivers worldwide, leading to degradation of riverine ecosystems [8][9][10]. Assessing the degree of flow regime alteration is a basic step in river protection and restoration.
Many methods have been developed to assess flow regime alteration. Among them, the range of variation approach (RVA) proposed by Richter et al. [11][12][13] is the most widely used approach and represented a milestone in efforts to assess the degree of hydrologic alteration. It has been cited more than 2400 times in scientific publications by 2020 according to Google Scholar. The RVA is widely used to assess the difference in flow regimes between two time periods [14][15][16] and to optimise the operation of hydraulic facilities [17][18][19][20][21][22][23]. The RVA includes 32 hydrologic indicators, which form a suite of indicators of hydrologic alteration (IHAs). The difference between the proportions of pre-and post-impact values falling within the target range is considered to represent the degree of alteration of the IHAs [12]. If the frequency is the same for the pre-and post-impact time series, flow regime alteration is considered to be negligible. After the establishment of the RVA, many scientists seek to

Methods
In the method section, the traditional RVA was briefly introduced for comparison with the revised RVA. Then, the method to generate flow time series was developed based on the Thomas-Fiering model. Finally, a series of scenarios of flow record lengths was established based on the randomly generated flow time series to explore the influence of flow record length on the RVA.

RVA
In the RVA, 32 IHAs were used to assess the degree of flow regime alteration. On the basis of pre-impact flows, the values of each of the 32 IHAs were divided into three ranges. The target range was defined as extending from the 25th to the 75th percentiles of the pre-impact indicator values. The difference between the proportions of pre-and post-impact values falling within the target range was considered to represent the degree of alteration of the IHA, which was defined by where D m was the alteration degree for the mth IHA; N o,m was the observed number of post-impact years in which the value of the mth IHA fell within its RVA target range; and N e,m was the expected number of post-impact years in which the IHA value fell within the RVA target range. The average degree of alteration of these IHAs was applied to quantify the overall impact on the river, which can be expressed as follows: where D was the overall degree of flow regime alteration [11][12][13].
In the RVA, the first step is to input the pre-impact and post-impact flow data. In this step, users tend to include all of the available pre-impact and post-impact flow records. Improving this step is the key aim of this paper.

Method to Generate Random Daily Flow Time Series
To test the validity of using all of the available pre-impact and post-impact flow records in the RVA, a series of daily flow time series need to be randomly generated. The following steps were used for random flow generation.

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Step 1: Generate annual mean flows The Thomas-Fiering model is widely applied to generate weekly, monthly and annual flow sequences [32][33][34]. A simplified Thomas-Fiering model, shown in Equation (3), is adopted in this research for annual mean flow generation [35]. The parameters in this model include mean annual flow, the coefficient of variation, and the correlation coefficient of the flows, which are denoted as µ, C v , and ρ. Q t is the annual mean flow for year t; δ is a standard normal random number.
According to research on global rivers by McMahon et al. [36], the annual coefficient of variation (C v ) varies between 0.062 and 2.97, and the correlation coefficient (ρ) varies between −0.48 and 0.90. For the generation of each annual mean flow sequence, the parameters C v and ρ were randomly determined within these ranges. The mean annual flow µ was set equal to 1 in this research, and the annual mean flow for the first year Q 1 was also randomly chosen within 0 and 1.

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Step 2: Generate daily flows based on the annual mean flows generated above In previous research on flow generation, it is generally assumed that flows have a certain distribution type. Normal, log-normal, Gumbel, Weibull, and Pearson type 3 (gamma) are commonly used probability distribution types [37]. The normal and log-normal distributions generally fit the annual flow generation [38]. Gumbel and Weibull distributions are used for extreme values of flows [39,40]. Pearson type 3 (gamma) distribution has the advantage of having only positive values, which is consistent with the characteristics of flows, and is commonly used in daily flow analysis [41]. In China, Pearson type 3 distribution is recommended for water resources planning and management [42]. As a result, Pearson type 3 distribution was also adopted in this research for daily flow generation.
The mean, variance, and skewness coefficient of daily flows are key parameters in Pearson type 3 distribution of daily flows [43]. The mean flow for each year adopts the values of annual mean flow generated above. To date, no studies have given ranges for the skewness coefficient and the coefficient of variation for global daily flows. Here, the skewness coefficient range was set between −3 and 3 [42]. The range of variation coefficient simply adopted the range for global annual flows, i.e., from 0.062 to 2.97 [36]. In the process of daily flow generation, the two parameters were randomly chosen within these ranges.

Results
To reduce the arbitrary nature of N selection (N represents the periodicity length in pre-impact and post-impact flows), N was set between 25 and 40 with an increment of 1 (i.e., 16 scenarios) in this research. Following the methods established above, random daily flows were generated, and the RVA was performed under each length scenario for the pre-and post-impact flow time series. The RVA values were clearly influenced by the length of the pre-impact flow time series under all 10 post-impact flow scenarios. Theoretically, the hydrologic alteration degree is expected to be constant at zero because no human or climatic impacts are imposed on the post-impact flows, and the pre-impact and post-impact flow regimes are the same. The anomalous measurements of flow regime alteration degree by the RVA resulted from uncertainty related to the operation date of the gauging stations and the attempt to include all of the available flow records in the RVA. Figure 2 showed the variation of RVA values with changes in length of the post-impact flow time series. These RVA values were also clearly influenced by the length of the post-impact flow time series. Theoretically, the hydrologic alteration degree should also be constant at zero, due to a lack of human or climatic influence, although the RVA does not exhibit this behavior. The anomalous measurements of flow regime alteration degree also related to uncertainty around the operation date of the gauging stations and the attempt to include all of the available flow records in the RVA.
Water 2020, 12, x FOR PEER REVIEW 5 of 26 of N are shown in the Appendix A for the sake of brevity (the results were similar under all the 16 scenarios of N). The RVA values were clearly influenced by the length of the pre-impact flow time series under all 10 post-impact flow scenarios. Theoretically, the hydrologic alteration degree is expected to be constant at zero because no human or climatic impacts are imposed on the post-impact flows, and the pre-impact and post-impact flow regimes are the same. The anomalous measurements of flow regime alteration degree by the RVA resulted from uncertainty related to the operation date of the gauging stations and the attempt to include all of the available flow records in the RVA. Figure  2 showed the variation of RVA values with changes in length of the post-impact flow time series.
These RVA values were also clearly influenced by the length of the post-impact flow time series. Theoretically, the hydrologic alteration degree should also be constant at zero, due to a lack of human or climatic influence, although the RVA does not exhibit this behavior. The anomalous measurements of flow regime alteration degree also related to uncertainty around the operation date of the gauging stations and the attempt to include all of the available flow records in the RVA.   values measured by the RVA had minimum values when the pre-/post-impact flow time series length was 30 years or 60 years under different post-/pre-impact flow time series lengths, although the alteration degree was not equal to zero. (Figures A1-A32 in Appendix A also showed that minimum RVA values occurred when the pre-/post-impact flow time series length was equal to multiples of periodicity length.) Lesser degrees of flow regime alteration measured by the RVA indicated higher accuracy of the RVA. Thus, if periodicity can be detected in the pre-/post-impact flows, the optimal pre-/post-impact flow record length in the RVA should be multiples of periodicity length.    Figure 2c,j showed that the degree of flow regime alteration was equal to zero when the length of both the pre-and post-impact flow time series was 30 or 60 years, i.e., multiples of periodicity length. The degree of flow regime alteration should be zero. Thus, the optimal flow record length should be multiples of periodicity length for both the pre-and post-impact flow time series.
In addition, the other sub-figures in Figures 1 and 2 showed that the flow regime alteration values measured by the RVA had minimum values when the pre-/post-impact flow time series length was 30 years or 60 years under different post-/pre-impact flow time series lengths, although the alteration degree was not equal to zero. (Figures A1-A32 in Appendix A also showed that minimum RVA values occurred when the pre-/post-impact flow time series length was equal to multiples of periodicity length.) Lesser degrees of flow regime alteration measured by the RVA indicated higher accuracy of the RVA. Thus, if periodicity can be detected in the pre-/post-impact flows, the optimal pre-/post-impact flow record length in the RVA should be multiples of periodicity length. The horizontal dotted line in each sub-figure showed the mean degree of flow regime alteration. The mean alteration degree under post-impact flow lengths of 30 and 60 years in Figure 1 was equal to 0.12, while the mean alteration degree under other lengths was always no less than 0.16. Similarly, the mean alteration degree under the pre-impact flow lengths of 30 and 60 years was equal to 0.11 in Figure 2, while the mean alteration degree under other lengths was always no less than 0.13. These results further demonstrate that if periodicity could be detected in the pre-/post-impact flows, the optimal pre-/post-impact flow record length in the RVA should be multiples of periodicity length.  Many methods, such as the maximum entropy spectrum analysis [44] and wavelet analysis [45], have been developed for periodicity determination. Using these methods, we can determine whether the pre-and post-impact flow time series have periodicity. If periodicity is seen, the length of the periodicity can be further determined. The periodicity length values determined by these methods will not show obvious difference. Any periodicity determination method could be adopted. (3) Apply the RVA to determine the flow regime alteration degree.
If the time series are long enough to cover several periodicities, one flow records of one periodicity length had better be adopted. When the flow time series have periodicity, the starting point of the flow record under a record length of one periodicity will not obviously influence the results of the RVA. Here, we simply use the latest pre-/post-impact flow records of one periodicity length in the RVA. Using the pre-and post-impact flow time series determined above, the RVA is applied to determine the degree of flow regime alteration. This step of the revised RVA is the same as the traditional RVA.

Comparison of Results from the Traditional and Revised RVA
The Roanoke River in the United States was used as a case study to compare the results from the traditional and revised RVA, because Richter et al. [11][12][13] used this case study to illustrate the IHA software and the RVA method (the USGS streamflow gauging station 02080500). Dam impacts on the Roanoke River system began with the completion of Philpott Lake on the Smith River (in the upper watershed) in 1950. In the same year, the Kerr Reservoir was constructed for the purpose of flood control. In 1955, Roanoke Rapids Lake was built downstream of the Kerr Reservoir, which was used for hydropower generation. After that, another reservoir, Lake Gaston, was built between Roanoke Rapids Lake and the Kerr Reservoir. Daily flow data for the Roanoke River have been collected by the U.S. Geological Survey (USGS) since 1913. The pre-impact period was defined as 1912-1949, and the post-impact period covers 1956-2004 [11,13].
The periodicity of the pre-and post-impact flow time series was assessed by the wavelet analysis method, using the continuous Morlet wavelet [46][47][48]. The confidence level of the significance test was set to 90%. The pre-impact stage had significant periodicity, and the average period was approximately 20 years. The post-impact stage also had significant periodicity, with a period of approximately 18 years. Because both of the stages had periodicity, with the data matched the first periodicity situation. Flow regime alterations were assessed by the revised and traditional RVA. The alteration degrees of the majority of IHAs (28 of 32) were different under the traditional and improved RVA. However, the alteration categories (low alteration, moderate alteration, high alteration) for most IHAs (21 of 32) did not change. Among the 32 IHAs, the values for the 18 indicators under the improved RVA were greater than those under the traditional RVA. In addition, the overall flow regime alteration degree under the improved RVA was 0.64, greater than the value (0.56) measured by the traditional RVA.
The results indicate that although the two RVA values belong to the category of moderate change, the alteration degree of the Roanoke River was higher than previously thought.

Conclusions
Assessing the degree of flow regime alteration in rivers is a basic principle for sustainable water resources management. The RVA is the most widely used method to assess flow regime alteration. In this research, we test the suitable length of flow record that should be put into the RVA. The following conclusions are drawn:

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The greatest accuracy for flow regime alteration degree assessed by the RVA is achieved when the length of both the pre-and post-impact flow time series is set equal to multiples of periodicity length.

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Due to the drawbacks in using all of the available flow data in the traditional RVA, we propose revising the traditional RVA procedure by assessing the periodicity of the pre-and post-impact flow time series in advance. If the periodicity of the pre-or post-impact flows is detected, the length of the time series should be set equal to its periodicity.