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The difficulties inherent in ranking global threats are due to them being context-dependent, which result from conditions and the nature of the threats themselves differing among locations, habitats, and taxa (Fig. 1). Current high-risk hotspots from habitat loss and overexploitation are primarily located in the tropics, whereas Europe is documented as a threat hotspot for pollution6. On islands, biological invasions mainly threaten biodiversity in the Pacific and Atlantic Oceans, while islands in the Indian Ocean and near the coasts of Asia are mostly threatened by overexploitation and agriculture3. Climate change affects species more at higher latitudes and altitudes because species are constrained by the physical environment (geographic barriers and mountain tops) to follow their optimal isotherms.Fig. 1: Divergence of global threat rankings across different references and international agencies.IPBES, WWF, and IUCN established global rankings of the five threats responsible for the current biodiversity crisis (B: central, yellow panel). However, the relative importance of each threat depends on the taxon, system, species’ characteristics, time, and/or the metric considered, resulting in divergences. Global biodiversity threats are represented by colors and symbols, given in the top panel. This figure encapsulates results combined from different studies detailed in Supplementary Table 1 with their associated references.Full size imageThe relative importance of threats also depends on the taxon considered. At the global scale, vertebrates are primarily threatened by habitat loss, overexploitation, and then biological invasions. But even within the vertebrates rankings differ — birds and mammals are mainly affected by overexploitation, while amphibians have a higher probability of succumbing to habitat loss6. Because of species-specific traits and adaptations, some species are likely to respond differently to global threats even within a clade. Large-bodied vertebrates are more likely to be threatened by overexploitation, whereas small-bodied vertebrates are more prone to habitat loss or pollution (Fig. 1). Threat ranking also depends on the habitat under consideration. Marine mammals are more threatened by overexploitation and pollution than terrestrial mammals for which habitat loss is the primary threat (Fig. 1). On islands, habitat loss is secondary to the pressures of biological invasions in freshwater systems, but the former is more important for terrestrial vertebrates and plants3. Another source of uncertainty is that most studies examining threats are based on well-studied taxa such as terrestrial vertebrates, which only represent a small subset of the tree of life. For instance, only 0.2% of fungi, 1.7% of invertebrates, and 10% of described plants are assessed in the IUCN update of 20197, potentially underestimating the intensity of some threats and biasing conservation priorities for these groups. Similarly, there is a bias of research effort towards regions with high-income countries, while research from low or middle-income countries is generally underrepresented8. This may give the false impression of absence of threats in some regions of the world.Likewise, period-specific global threat ranks are subject to the vagaries of temporal dynamics (Fig. 1). However, distinguishing past, current, and future threats is essential for current or future conservation interventions. Historically, overexploitation caused most of the Pleistocene megafauna extinctions, likely exacerbated by climate change. As agricultural practices intensified, habitat loss played a major role in extinctions. As humans later colonized islands, biological invasions caused the extinction of hundreds of species worldwide3. In contrast, climate change is only predicted to become major in the near future9. In fact, the effects of recent threats might be masked by delayed species’ responses, especially in under-studied regions, resulting in a large extinction debt. For instance, the severity of biological invasions often causes native species to decline rapidly to local extinction, while other threats such as habitat loss might affect species more slowly. In both cases, the eventual extinctions are ultimately if similar magnitude. More

Study sitesThe sample site Tei Tong Tsai is located within the Island District (112°5’ E, 22°5’ N Hong Kong, China) and connected to Lantau Country Park. The rich woods in Tei Tong Tsai provide a suitable environment for insects to survive, with rich biodiversity. Weather records (Supplement 1) for May 2019 show that the highefst temperature was 27.2 °C, the lowest was 15.7 °C, the average was 21.7 °C; and the annual average rainfall was 297.8 mm. The suitable temperature and rainfall have created a suitable ecological environment and high biodiversity, establishing Tei Tong Tsai as a prime location for studying beetle diversity. In May 2019, a 13 sample sites were selected for beetle collection (Fig. 1). All latitude and longitude formats were converted to degrees, minutes, and seconds.Fig. 1Sampling points for the three passive acquisition methods used in the Tei Tong Tsai sampling site (indicated by red dots).Full size imageExperimental protocolIn this study, three passive collection methods were used for beetle collection. FIT is an efficient collecting method for insects with strong flying abilities and was first developed and used abroad14. MT and PT collect insects that are not strong flyers and live on the surface. A flight interception trap, a malaise trap, and 10 pitfall traps were set up to collect beetles in each sample site. Samples were selected to cover ecological environments at different longitudes, latitudes, altitudes, and distances from water sources. Reasonable sampling distances (depending on the terrain, with an interval between 100 and 200 m) were set up between sample sites to fully cover Tei Tong Tsai’s habitats. Due to the topography, the distance between the 10th and 11th sample points was about 350 m. The distance between two other close sample points were in the range of 100–200 m. All three traps were based on the original device to maximize the advantages and achieve better collection results.Collection devices. The flight interception trap (Fig. 2a) mainly comprises an interceptor screen (plastic net, PVC plastic glass, or plexiglas) and an insect specimen receiver (PVC), which is an efficient collection device for intercepting and collecting insects with strong flight ability. The detailed installation steps include the following: Firstly, punch two holes on the long side of the PVC screen with a hole puncher spaced about 30 cm apart; then, fix the screen to a bamboo pole with silk, install the specimen receiver, fix all three, bolt the rope, and fix it in the air with a thick rope (the sink is about 0.5–1 m from the ground). After installation, relevant drugs were placed inside the specimen receiver to poison the insects. The drugs used depend on the purpose of the study. For morphological studies, saline (5 mmol/L NaCl solution) or water with detergent is used. By contrast, DNA molecular studies use a mixture of 2% SDS (sodium dodecyl sulfate) and EDTA (ethylene diamine tetraacetic acid, 0.1 mol/L, PH = 8) or highly concentrated alcohol, which effectively controls the degradation of DNA. Currently, high-concentration alcohol, SDS and EDTA mixtures are commonly used. The device is widely applicable and can be installed in almost any habitat; however, it is best installed along the insects’ flight paths, including roads, rivers, or creeks between valleys. In this experiment, we improved this device by increasing the size of the water trough considering the actual situation of the sample site. Also, to properly conduct the molecular experiments, the reagents we used were a mixture of SDS and EDTA. Therefore, the improved device was more suitable for diverse habitats, and the insect species collected were abundant, reflecting good collection practices14.Fig. 2Three passive acquisition methods: (a) flight interception trap; (b) malaise trap; (c) pitfall trap.Full size imageMalaise traps (Fig. 2b) are large tent-like structures constructed from thin mesh. They are among the most commonly used static non-attractant insect traps and insect collection devices. Invented by Malaise (1937) and later improved upon by Townes and Sharkey, these traps are important tools for insect collection and monitoring worldwide15. The malaise trap used at the Tei Tong Tsai Country Park was the Townes type, which is generally set up in forest areas with rich habitats and relatively stable ground. The material is usually meshed mosquito netting fabricated into a tent-shaped insect interception field. The insects hit the net vertically, continue to fly upward, and are gradually led into the trap by the tilted top. The drug in the trap is usually anhydrous ethanol, which intercepts beetles with weak flying abilities16,17.The pitfall trap (Fig. 2c) is an effective method for capturing surface beetles; it is simple to use, easy to carry, and a common device for collection in the wild. The PT is created by digging a pit into the ground with the same depth as a wide-mouth plastic cup (20 cm high, 10 cm in diameter); The upper edge of the cup must be flushed with the soil surface, and a mixture of absolute ethanol is poured inside to collect flightless beetles14. About one-quarter of the way from the top, small holes are punched above the wide-mouth cup to prevent the loss of specimens from rainwater filling the cups. The 10 sets of traps in this experiment were not evenly distributed, but they were all in suitable habitats.Specimen samplingThe sampling site for this study was Tei Tong Tsai, and the sampling period was from 1st May to 28th May (2019). FIT, and PTs were collected once every two days. Due to the small number of beetles collected by MT, mt was collected only once. All beetles were picked out and arranged separately after collection, added to anhydrous ethanol, preserved, and labeled. The beetles collected by the three passive acquisition methods were picked according to morphological species.Specimen identificationThe taxonomic status for the family level of all samples was determined based on the relevant literature18,19,20,21. Relevant experts completed further identification (Supplement 2).All the specimens collected in this study are currently in the zoological museum of the Institute of Zoology, Chinese Academy of Sciences (Beijing, China).Specimen photographyBeetles were poured from the bottle and arranged separately according to the general species. Firstly, we used tweezers or a brush to place the beetles on unbreakable and unwrinkled paper (as far as possible with the backside upwards to keep them tight and neat, reducing the space left, and considering the label in the photograph). Simultaneously, we captured multiple photos according to the size and species of insect for the large specimens in the tube, adjusted the light near them to brighten the background, placed graph paper next to the beetles as a reference scale, then adjusted our Olympus camera settings to the appropriate photographing parameters. Finally, we inserted the photographed beetles and matching labels back into the tube and added anhydrous ethanol for preservation (Fig. 3). The labels were set in the photos as 2019 DTZ-FIT/MT/PTX-5XX-5XX (-N), in which 2019 represents the collection time, DTZ represents Tei Tong Tsai, FIT/MT/PT signifies the collection method, X represents the number of sampling points, 5XX-5XX represents sampling time, and N represents the photo number. If a sample site had many insects on the same date and required more than one photo, n was used to represent the number of photos. See the Supplement 3 for the complete document.Fig. 3Examples of beetles collected from three passive acquisition methods: overall photos of beetles collected by (a) FIT, (b) PT, and (c) MT. On the bottom right corner shows scale in each photo.Full size imageAfter the morphological data of the samples were collected, their Latin name and collection information were recorded in a table. Each passive acquisition method corresponded to a table, and each table was divided into 13 sheets according to 13 sampling points. The collection time was listed horizontally on each sheet, and the beetles’ species names were listed vertically (were named in the morphological species order as 1, 2, 3, …, N). The number of beetles was recorded in the corresponding position and the Supplement 4 file.Finally, data show the beetles’ biodiversity collected from each sampling site. Firstly, we summarized the data from each sampling point after completing the data statistics. Afterward, we counted the number of beetle individuals collected under the different passive acquisition methods at different points (Fig. 4). In Fig. 4, red, blue, and green represent the number of beetle individuals collected by MT, PT, and FIT, respectively. Fig. 4 shows that MT collected fewer beetles than FIT and PT. Secondly, the data of 13 sampling points in each collecting method were summarized to obtain the total number of families and species collected by each method (Fig. 5). A graph created in Excel 2016 displays the collection method as the horizontal coordinate and the number as the vertical coordinate. In the graph, red represents the number of families, and blue represents the number of species. Fig. 5 shows that FIT collected more beetle species and individuals than PT and MT, and MT collected the least. Thirdly, all data from the 13 sampling points and the three collection methods were summarized. The number of species collected in all families was counted. Families with more than ten species were selected (a total of 11 families) for data presentation (Fig. 6). Finally, a graphic was drawn in Excel 2016. Fig. 6 shows that the number of species in Staphylinidae, Curculionidae, and Chrysomelidae accounted for a large number, and the diversity was relatively high.Fig. 4Data table of numbers of individual beetles collected by different methods at 13 sampling points. The red, blue, and green columns represent the number of beetles collected by MT, PT, and FIT, respectively.Full size imageFig. 5The number of beetles collected by different passive acquisition methods. Horizontal coordinates represent collection methods. The red column and blue column represent the number of beetles collected on the family level and species level, respectively.Full size imageFig. 6Families with more than ten species (a total of 11 families) were selected for presentation. The sample sizes of each groups were also shown.Full size image More

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Specifications of the study areaUrmia Lake, as the largest inland lake of Iran, is a national park and one of the largest Ramsar sites of Iran (Ramsar, 1971). The lake is formed in a natural depression within the catchment area in the northwest of Iran. The basin of the lake covers an area of 52,000 km2 and its area is about 5,700 km249. In addition, its maximum length and width are 140 and 50 km, respectively. Further, the lake catchment is a closed inland basin in which all rainwater runoff flows to the central saline lake, and evaporation from the surface of the lake is the only way out. More importantly, it is the largest saltwater lake in Iran and the second largest saltwater lake in the world.The current surface flow system to Urmia Lake consists of 10 main rivers with permanent flow potential, including Zola, Nazlu, Rozeh, Shahrchai, Baranduz, Gadar, Mahabad, Simineh, Zarrineh, and Aji. In terms of the water supply potential of Urmia Lake, Zarrineh, Simineh, Aji, and Nazlu rivers with a flow allocation of 41, 11, 10, and 6% have a key role, respectively.The rivers of this basin are originated from mountains and pass through the heights and enter the agricultural plains. The main usage in plains are for agriculture which cause the changes in natural rivers flow regime. On the other hand, the natural flow regime of the rivers should be considered as the basis for e-flow calculation. So, in the current study the obtained data from the stations situated in the upstream of the rivers and the stations before the agricultural plains are utilized to alleviate the effects of agricultural use on natural flow regime of the rivers. Also, to eliminate the effects of dam rule curve on river flow regime, stations situated in the upstream of the dams are considered as the main scale in the upstream of the dammed rivers like Zarrineh, Mahabad and Zola. Despite all the efforts made to select stations with the least human impact, the two stations related to Aji and Shahar Rivers have been affected by the structures built above them. Therefore, in order to eliminate the effects of the constructed structures at the upstream of the stations, flow naturalization methods were used only for the two stations of Venyar of Aji River and the Band Urmia station of Shahar River. There are several ways to naturalize hydrometric station data. Terrier et al.51 by studying flow naturalization methods in various researches were able to provide a comprehensive study of naturalization methods and selection criteria for each of these methods. According to their studies, the first and the most important prerequisite for stream naturalization is to identify the factors affecting the river and the quality of data in the region, which play a major role in choosing the flow naturalization method. Two factors play a major role in affecting river hydrology. The first factor is the construction of hydraulic structures along the path of rivers and the second factor is the change of land use that has occurred in the rivers basin. In the current study, the purpose of flow naturalization is to eliminate the effects of large dams built on the inlet rivers of the lake, which can affect the hydrology of the river flow. It should be noted that it is not possible to eliminate the effects of land use change due to the gradual nature of the changes, the inability to determine the exact amount and time of the changes and the lack of required data as well. Therefore, in this study, the effects of land use change at the upstream of the stations have been neglected. The most important reason that the Aji River needs to naturalize is the existence of several small dams upstream of Venyar station. To eliminate the effects of dams and flow naturalization at the upstream of this station, the spatial interpolation method introduced by Hughes and Smakhtin52 was used. In this method, Sahzab hydrometric station located at the upstream of the river was used as a base station to naturalize the flow. The next station which needs to be naturalized the flow is the Band Urmia station Shahar River. The main problem for this river has been the construction of a dam upstream of Band Urmia river station since 2004. The drainage area ratio method introduced by Hirsch53 was used to eliminate the effect of this dam on the station data. This method has been used by various researchers to naturalize river flow54,55,56 which is based on the upstream drainage area of the stations. In this method the ratio of the drainage area of the two stations is used to naturalize the flow in the affected station. For this purpose, the data of Bardehsoor station located upstream of the dam was used to naturalize the data of the Band Urmia station. So, anthropogenic effects are at the minimum level in calculations. The utilized stations to calculate the e-flow as upstream stations are illustrated in Fig. 1.Figure 1An overview of the Urmia Lake basin, the rivers, and selected gauging stations. Figure 1 was generated by ArcGIS v10.2 software50 (Environmental Systems Research Institute, Inc., USA, URL http://www.esri.com/).Full size imageAppropriate criteria for allocating the EWR of the Urmia LakeDue to the high salinity of Urmia Lake, only a small number of invertebrates make up the living organisms of this huge water body. Saltwater shrimp or Artemia is a type of aquatic crustacean which can be found in saltwater lakes or coastal lagoons worldwide. Artemia can tolerate salinity less than 10 gl−1 up to 340 gl−1 and adapt to environmental conditions. Artemia Urmiana, the most well-known species of the Urmia Lake, is considered as the main food of migratory birds that spend part of their wintering period on the lake and surrounding wetlands. The presence of this species in the Urmia Lake was first reported by Gunter (1899), and many researchers have confirmed the existence of this bisexual creature in this lake57,58,59,60,61.One of the key factors in estimating the EWR of Urmia Lake is to create an appropriate environmental condition for its dominant species. Abbaspour and Nazari Doost39 identified the EWR of the Urmia Lake by considering the living conditions of Artemia as its dominant species. In this study, Artemia Urmaina was selected as a biological indicator, along with NaCl and elevation above mean sea level (AMSL) as the indicators of water quality and quantity, respectively. The combination of these three indicators forms the ecological basis of Urmia Lake. Therefore, salinity is considered to be equal to 240 gl−1 as the tolerable limit of the biological index. Using long-term statistics in the Urmia Lake and the relationship between quantitative and qualitative water indicators, the water level of 1274.1 m (AMSL) was chosen as the ecological level of the lake so that the balance of these three indicators remained within the allowable range. The study indicated that the calculated environmental water demand of Urmia Lake was equal to 3084 Mm3 per year provided by main rivers entering the lake. Therefore, the proposed new methods should be able to deliver this volume of water to the lake and simultaneously feed the EFR of the river. To supply this water volume, government has programs in order to mitigate the water consumption especially in agriculture. The most important program is 40 percent reduction in agricultural water consumption which is accompanied with the increase of efficiency. Also the government pursues urban wastewater treatment to retrieve some of domestic water to the lake. The mentioned programs are time consuming, however, the new methods presented in this study can be useful for managers in determining the allocation patterns and consumption management. Ordinary method of flow duration curve shifting (FDCS) in estimating e-flowSince the early 1990s, various methods have been developed based on the hydrological indices62 in order to determine the e-flow by taking into account the flow variability and adaptation to the ecological conditions of rivers. One of the intended diagrams in the study of the hydrological characteristics is the flow duration curve (FDC), which is used to assess the fluctuations and variability of water flow from an environmental point of view. Given the importance of the presence of flood currents in the restoration of the river and wetland ecosystems63,64, the FDC is one of the most practical methods to show the full range of river discharge characteristics from water shortage to flood events. This diagram also demonstrates the relationship between the amount and frequency of the flow which can be prepared for daily, annual, and monthly time intervals65. The FDCS is a method in which FDC is employed to estimate the river flow. This method was introduced by Smakhtin and Anputhas66 to evaluate the e-flow in the river system. The method, which is called FDCS, provides a hydrological regime to protect the river in the desired ecological conditions.In the previous research, most of the rivers in the Urmia Lake basin have been compatible with FDCS, and due to the lack of biological data regarding these rivers, it is always one of the top priorities among the methods of estimating the e-flow in rivers leading to the Urmia Lake67,68. It is noteworthy that the characteristics of calculation steps of the ordinary method are provided as follows.This method consists of four main steps:

1.

Assessing the existing hydrological conditions (preparing the FDC for a natural river flow regime),

2.

Selecting the appropriate environmental management class;

3.

Acquiring the environmental FDC;

4.

Generating e-flow time series.

The first step is to prepare the FDC in the desired river range using monthly flow data. In this method, FDC for the natural river flow regime is prepared by 17 fixed percentage points of occurrence probabilities (0.01, 0.1, 1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99, 99.9, 99.99) where P1 = 99.99% and P17 = 0.01% represent the highest and lowest probability of occurrence, respectively. These points ensure that the entire flow range is adequately covered, as well as facilitating the continuation of the next steps.This method, which uses mean monthly flow (MMF) data, considers six environmental management classes (EMC) from A to F. The FDC of EFR (FDC-EFR) for each class in terms of EMC is determined based on the obtained natural river FDC by the MMF. The higher EMC needs more water to maintain the ecosystem. These classes are determined based on empirical relationships between the flow and ecological status of rivers, which currently have no specific criteria for identifying these limits. The selection of the appropriate class individually relies on the expert’s judgment of the river ecosystem condition.After obtaining the natural FDC, the next step is to calculate the FDC-EFR for each EMC using the lateral shifts of FDC to the left along the probabilistic axis. For EMC-A rivers, one lateral shift to the left is applied while two, three, and four lateral shifts are employed for EMC-B, EMC-C, and EMC-D rivers, respectively. It should be noted that the overall hydrological pattern of the flow will be maintained although the flow variation is lost for each shift.In the current study, global e-flow calculation (GEFC) v2.0 software69,70 has been utilized to compute the e-flow by the FDCS method. The long-term data (at least 20 years) of MMF are the required input data for this software.According to the research conducted on the rivers of the Urmia Lake basin, EMC-C is the minimum considered EMC for 10 main rivers of the lake, thus the EMC-C has been considered in this study, and all calculations for classes A, B, C have been performed accordingly.The description of new methods based on ordinary methodThe main purpose of presenting new methods is to combine the EWR of wetlands or lakes and the hydrological method of FDCS, which can be used to calculate the e-flow of rivers and meet the needs of lakes or wetlands in downstream. These methods relies on the FDCS while with the difference that the proposed method includes three fundamental changes compared to the original one.

1.

Applying monthly FDC (FDC for each month separately) instead of annual FDC,

2.

Employing daily flow data instead of MMF,

3.

Considering the downstream EWR in the amount of the lateral shift in the FDCS method.

The use of the structure of new methods lead to a dynamic process that is based on the selected EMC of the river, the amount of the natural flow, and the date of occurrence and can compute the amount of the e-flow of the river on each day of the year.River hydrology greatly varies depending on the type of the basin, the climate of the area, and the relationship between the basin and the river each exhibiting different behaviors during the months of the year. Accordingly, the proposed methods should provide sufficient comprehensiveness in estimating the e-flow by considering different flow characteristics. Due to the type and timing of precipitation in the Urmia Lake basin, the rivers are full of water from March to June and spend extremely less flows during the other times of the year. For example, Fig. 2 shows the distribution of the Nazlu River flows in the west of Urmia Lake throughout the year. According to the data, 74% of the AF crosses the river from March to June, and the highest and lowest river discharges are related to May with 29% and September and August with 2% of the AF, respectively.Figure 2Historical hydrograph at the Tapik Station, Nazlu River: (a) Daily and mean monthly distribution of flows and (b) Magnified hydrograph for a typical year (1993).Full size imageAccording to the flow distribution throughout the year, the annual FDC is an average FDC of each month of the year. However, the flow of a river during the months of the year represents significant changes. Therefore, the monthly FDC is higher than the annual FDC in the high-water months (e.g., May). Additionally, this curve is lower compared to the annual FDC in the low-water months (e.g., September). Accordingly, the use of monthly FDCs provides more details of changes in the hydrological parameters of the flow and can be a better indicator of the hydrological index of river flows.In the conventional FDCS method, the FDC is obtained using the MMF data of each station. The obtained curve represents the monthly average of river flow and does not illustrates the minimum, maximum and the effect of flow fluctuations in the estimation of e-flows (Fig. 2).In the new methods, all FDC diagrams were obtained by daily data. Both annual (EFR-Ann) and monthly (EFR-Mon) methods are separately utilized to compare the calculation of the e-flow and to choose the best method. The annual FDC is a probabilistic chart for the whole year and the monthly FDC includes 12 probability curves for each year. Due to the use of FDC in e-flow estimations, it has been attempted to perform all calculations from this diagram. Therefore, concepts related to the flow volume can be integrated with the FDCS method. Some of the applied concepts for this purpose are as follows.In the FDCS method, the FDC is defined based on 17 probabilistic percentage points. To calculate the mean AF (MAF) volume, the theorem of the mean value for a definite integral is employed in the FDC diagram. Accordingly, considering that FDC is continuous between the first and seventeenth probability points, the mean flow (Fm) is obtained from Eq. (1) as.
$$F_{m} = frac{1}{{P_{1} – P_{17} }}mathop smallint limits_{{P_{17} }}^{{p_{1} }} Fleft( p right)dp$$
(1)
Fm = Mean flow. P1, P17 = Points of FDC probability that P1 = 99.99 and P17 = 0.01.Given that the FDC consists of 17 probability points and the probability function ‘F(P)’ is unavailable for this curve as a mathematical equation, obtaining this equation for each flow curve increases the computational cost. Therefore, numerical integration methods can be used in this regard. The trapezoidal numerical solution method has been utilized for this purpose. By applying the trapezoidal method in solving Eq. (1), Eq. (2) is obtained, which is used to compute the mean flow of the FDC.$$F_{m} = frac{1}{{P_{1} – P_{17} }}mathop sum limits_{i = 1}^{17} frac{{left( {F_{i} + F_{i + 1} } right)}}{2}{*}left[ {P_{i} – P_{i + 1} } right]$$
(2)
Pi = 17 points of FDC probability that P1 = 99.99% and P17 = 0.01%. Fi = The amount of the river flow with the probability of the occurrence of Pi.To calculate the AF volume by monthly and annual FDCs, Eq. (3) can be applied for the AF volume in the EFR-Ann method, as well as employing Eqs. (4) and (5) for the monthly and AF volume in the EFR-Mon method, respectively.$${text{V}}_{{AF_{Ann} }} = frac{365*24*3600}{{P_{1} – P_{17} }}mathop sum limits_{i = 1}^{17} frac{{left( {F_{i} + F_{i + 1} } right)}}{2}{*}left[ {P_{i} – P_{i + 1} } right]$$
(3)
$${text{V}}_{Monthly } = frac{{D_{k} *24*3600}}{{P_{1} – P_{17} }}mathop sum limits_{i = 1}^{17} frac{{left( {F_{i} + F_{i + 1} } right)}}{2}{*}left[ {P_{i} – P_{i + 1} } right]$$
(4)
$${text{V}}_{{AF_{Mon} }} = mathop sum limits_{k = 1}^{12} left[ {{text{V}}_{Monthly } } right]_{k}$$
(5)

VAFAnn = AF volume using annual FDC. VMonthly = Monthly flow volume. VAFMon = AF volume using monthly FDC. Dk = Number of the days of the kth month. k = Number of each month.The required e-flow by wetlands and lakes must have two basic characteristics. The volume of EWR for maintaining their ecological level must be determined and provided by the studies of their ecosystems. In addition, fluctuations must be maintained in water levels in the lake due to hydrological conditions under the basins of the lake supplying rivers given the fact that maintaining the hydrological conditions of the river is one of the major goals of the FDCS method in estimating the e-flow of the river. On the other hand, the rehabilitation of the wetland or lake downstream of rivers requires a certain amount of water, and the new methods must be applied to combine these two goals. In this regard, the AF volume, which can be transferred to the lake (VL Mon or Ann) by these rivers, is calculated by taking into account the natural flow conditions of the rivers in the basin and without considering the consumptions,.$${text{V}}_{{L_{Ann} }} { } = mathop sum limits_{j = 1}^{{text{n}}} left[ {{text{V}}_{{AF_{Ann} }} } right]_{j}$$
(6)
$${text{V}}_{{L _{Mon} }} = mathop sum limits_{j = 1}^{{text{n}}} left[ {{text{V}}_{{AF_{Mon} }} } right]_{j}$$
(7)

n = Number of input rivers to the lake. VLAnn = AF volume, which can be transferred to the lake using annual FDC. VLMon = AF volume, which can be transferred to the lake using monthly FDC.The ratio of the EWR of the lake or wetland to the average annual volume of the basin should be determined at this stage.$$b = frac{{{text{V}}_{EWR} }}{{{text{V}}_{{L_{Ann} }} or {text{V}}_{{L _{Mon} }} }}$$
(8)
b = The ratio of the EWR of the lake or wetland to the average annual volume of the basin. VEWR = Volume of environmental water requirement of the lake or wetland.In the conventional FDCS method, which is determined using GEFC v2.0 software70 (It is then called the GEFC method), depending on the type of the river EMC, the allocation curve is obtained with one or more shifts of the FDC. Each EMC includes a certain ratio of the MAF volume of the river, and changing the flow EMC facilitates changing the flow volume. It is impossible to supply a specific and predetermined downstream water volume of the river. Therefore, in the new methods, a new process must be used to calculate the amount of the FDC shift in order to provide a certain volume of water in the shifting of the FDC. First, a new definition of the EMC was developed for the new methods. In this definition, instead of using a specific shift of the FDC, the range between the two classes was characterized as an EMC. For example, the region between the curve of EMC-A and the natural flow and the region between the EMC-A and EMC-B curves are defined as EMC-A and EMC-B areas, respectively. These regions can be defined for all EMCs (Fig. 3).Figure 3Comparison of the EFR allocated to each of the environmental management classes from this new approach (on the left) with the conventional FDCS methods (on the right).Full size imageBased on the new definition of the range of EMC, the FDC can be shifted as much as needed according to the volume of downstream EWR. The EWR can be defined as the annual percentage river flow respecting the shift of EMCs or a percentage between two specific classes. If the required flow volume is between two specific classes, Eq. (9) can be used to shift the FDC. In fact, with the new definition, any required probable shift can be applied to the FDC ِdiagram to reach a certain volume. In this case, new probable points are determined using Eq. (9), followed by performing the FDC shift similar to the FDCS method in the next step.$$P_{{i_{new} }} = P_{i} + a{*}left( {P_{i – 1} – P_{i} } right)quad i = t, ldots ,16$$
(9)
Pinew = New shifted probability point. Pi = 17 points of FDC probability that P1 = 99.99% and P17 = 0.01%. a = Coefficient of shift which defined between 0 and 1. t = Number of shifts performed on the FDC diagram numbered 1–6 for the areas of EMC A, B, C, D, E, F, respectively.The concept of numerical integration and Eqs. (9) and (3) were utilized to calculate the annual volume of different EMCs for each river, and Eqs. (10) and (12) were obtained for the new annual and monthly methods, respectively.$$begin{aligned} & {text{V}}_{{AF class_{t} Ann }} = frac{1}{{P_{1} – left[ {P_{17} + a*left( {P_{16} – P_{17} } right)} right]}} \ & quad quad quad quad quad *left[ {F_{1} *left[ {P_{1} – left[ {P_{t + 1} + a*left( {P_{t} – P_{t + 1} } right)} right]} right] + mathop sum limits_{{i = {text{t}} + 1}}^{16} frac{{left( {F_{i – t} + F_{i – t + 1} } right)}}{2}{*}left[ {P_{i} – P_{i + 1} + a{*}left( {P_{i – 1} – 2P_{i} + P_{i + 1} } right)} right]} right]*365*24*3600 \ end{aligned}$$
(10)
$$begin{aligned}&{text{V}}_{{ class_{t} Mon }} = frac{{D_{k} *24*3600}}{{P_{1} – left[ {P_{17} + a*left( {P_{16} – P_{17} } right)} right]}} \ & quad quad quad quad quad *left[ {F_{1} *left[ {P_{1} – left[ {P_{t + 1} + a*left( {P_{t} – P_{t + 1} } right)} right]} right] + mathop sum limits_{{i = {text{t}} + 1}}^{16} frac{{left( {F_{i – t} + F_{i – t + 1} } right)}}{2}{*}left[ {P_{i} – P_{i + 1} + a{*}left( {P_{i – 1} – 2P_{i} + P_{i + 1} } right)} right]} right] end{aligned}$$
(11)
$${text{V}}_{{AF class_{t} Mon}} = mathop sum limits_{K = 1}^{12} left[ {{text{V}}_{{ class_{t} Mon}} } right]_{k}$$
(12)

VAF classt Ann = AF volume for the related class of selected t for annual method. Vclasst Mon = Monthly flow volume for the related class of selected t for monthly method. VAF classt Mon = AF volume for the related class of selected t for monthly method.where t is the number of shifts performed on the FDC diagram numbered 1–6 for the areas of EMC A, B, C, D, E, F, respectively. To find the exact value of a in these equations, the scope of the EMC must be determined based on the required volume by downstream. Therefore, assuming a = 0 in these equations, the AF volume at the boundary of each class is obtained for both EFR-Mon (Eq. (10)) and EFR-Ann (Eq. (12)) methods. The nearest calculated annual volume is selected as the appropriate EMC which is smaller than the volume of downstream. Further, the corresponding t-class is used to solve the equations, representing the range of the selected EMC.At this stage, the value of the obtained ‘a’ from the FDC shift diagram equals the required volume of downstream. For this purpose, Eqs. (13) and (14) for the EFR-Ann and EFR-Mon methods are obtained from Eqs. (10) and (12), respectively.$$b{text{*V}}_{{AF_{Ann} }} = V_{{AF class_{t } Ann }}$$
(13)
$$b{text{*V}}_{{AF_{Mon} }} = V_{{AF class_{t} Mon }}$$
(14)

By solving Eqs. (13) and (14), the obtained value of a represents the annual and monthly methods, and the obtained shifted FDC stands for the required annual volume downstream.After determining the appropriate FDC, it is used to calculate the daily e-flow needs of the river using the spatial interpolation algorithm52, which is also employed in the FDCS method. To this end, the probability of the river flow occurrence from the annual or monthly FDCs (according to the selected method) is determined and then the required river flow in the specified probability of occurrence is obtained using the e-flow curve.The range of variability approach (RVA)71,72 is a complex method based on the use of e-flow for achieving the goals of river ecosystem management. This method is applied to compare the methods and select the best one based on the least hydrological change compared to the natural flow of the river. Furthermore, it is based on the importance of the hydrological feature impact of the river on the life, biodiversity of native aquatic species, and the natural ecosystem of the river and aims to provide complete statistical characteristics of the flow regime.In the RVA method, the indicators of hydrologic alteration (IHA) parameters related to the natural river flow are considered as a basis, and changes in the IHA parameters of different EMCs are evaluated accordingly. Richter et al.72 suggested that the distribution of the annual values of IHA parameters for maintaining river environmental conditions must be kept as close as possible to natural flow condition parameters. In several studies, this method was used to investigate changes in the hydrological parameters of a river over time37.Moreover, the total data related to the natural flow of the river for each IHA parameter are classified into three categories in the RVA method. In this study, this classification is based on Default software, and the 17% distance from the median is introduced as the boundary of the classes. By this definition, three classes of the same size are created, in which the middle category is between 34 and 67, and the lower and higher ranges are called the lowest and highest categories, respectively.Using the current change factor obtained from Eq. (15), the RVA method can quantify the change amount in the values of the 33 IHA parameters compared to the natural flow conditions.$$HA = left( {O_{f} – E_{f} } right)/E_{f}$$
(15)
HA = Hydrological alteration index. Of = Number of flows occurring within a certain category of the IHA parameter under changed flow conditions. Ef = Number of flows occurring in the same category specified by the parameter under natural flow conditions.In this case, for each IHA parameter, three HA factors are obtained, which can be separately examined for river flows in these three categories. In the analysis of parameters, the positive HA means that the number of occurrences of the phenomenon has increased in a certain IHA category compared to the natural conditions of the river flow. Negative values imply a decrease in the number of occurrences of the same phenomenon. To compare the number of changes in IHA parameters, the HA factor of the RVA method and IHA software (Version 7.1)73 was employed to allocate e-flows in different methods. The obtained results using RVA method calculates and represents HA of each 33 parameters. However, making decision to choose the best method, all parameters need to be assessed and presented as a total index. Due to calculate total HA index based on studies of Xue et al.74 Eq. (16) can be used.$$HA_{o} = sqrt {frac{{mathop sum nolimits_{i = 1}^{33} HA_{i}^{2} }}{33}} *100$$
(16)
HAo = Total hydrological alteration index. HAi = Hydrological alteration of each of 33 parameters.Determination of EFR for different EMCs for all methodsInitially, the MMF for each available statistical month was obtained by daily data from stations located in the upstream of the basin rivers of Urmia Lake (Fig. 1). The FDC for the natural flow and various EMCs were obtained using MMF values and GEFC software. Next, to perform the calculations in the EFR-Ann method, the FDC of a natural flow and different EMCs during the year were plotted by daily data. Finally, for the EFR-Mon method, the daily data of each month of the year were examined and the FDC of the natural flow and EMCs were separately plotted for each month.Based on the presented method in this research, Fig. 4 illustrates a step-by-step diagram for determining the e-flows of rivers in the Urmia Lake basin.Figure 4Step-by-step flowchart for determining the environmental flows of rivers in the Urmia Lake basin.Full size image More

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