Assessment of probability distributions and minimum storage draft- rate analysis in the equatorial region

Assessment of probability distributions and minimum storage draftrate analysis in the equatorial region Hasrul Hazman Hasan, Siti Fatin Mohd Razali, Nur Shazwani Muhammad, Zawawi Samba Mohamed, Firdaus Mohamad Hamzah Department of Civil Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, Bangi, 5 43600, Malaysia Department of Engineering Education, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, Bangi, 43600, Malaysia Correspondence to: Siti Fatin Mohd Razali (fatinrazali@ukm.edu.my)


Introduction
Droughts are long-term natural disaster phenomena resulting from less than average precipitation causing significant damages 20 to a wide variety of sectors and affecting large regions. The rapid development of the world now shows an increase in populations, and climate change lends to increase drought occurrences (Bakanoğullari and Yeşilköy, 2014;Tigkas et al., 2012).
Droughts have considerable economic, societal, and environmental impacts. Drought can typically be classified into four types depending on different kinds of drought impacts in different areas: meteorological, hydrological, agricultural and socioeconomic (Hasan et al., 2019;Tri et al., 2019). Any types of drought are dynamic and defined by various characteristics such 25 as frequency, severity, duration, and magnitude. The main factor involved in hydrological drought is climate change and anthropogenic activities of surface water resources. The assessment of hydrological drought provides a better representation of the hydrological cycle's water surface. Hydrological drought also allows the incorporation of spatial details that impact internal storage and soil, vegetation and terrain characteristics. This study mainly focuses on hydrological drought. The related https://doi.org/10.5194/nhess-2020-105 Preprint. Discussion started: 22 April 2020 c Author(s) 2020. CC BY 4.0 License. economic and streamflow in the watershed (Azadi et al., 2018;Iqbal et al., 2016;Tigkas et al., 2012). The hydrological drought was referred to as the most critical aspect of drought with significantly reduced streamflow and lower water storage in the river 65 system (Hasan et al., 2019). Because of this, in order to ensure that water supply requirements are met, the storage rate for each river should be known to ensure that the minimum storage during low flow and drought in the coming years will be able to accommodate consumers' water demand.
This study concentrates on three significant issues. First, to find the best-fit models for determining the frequency analysis of 70 low flow over return periods. Second, to evaluate the threshold level value for drought analysis, and finally, to estimate the storage-draft rate required at the recurrence interval for the streamflow station in Selangor. This study is essential to understand the concept of low flow, drought characteristics, and the predictive significance of river storage-draft rates in managing sustainable water catchment. The results are useful for developing measures to maintain flow variability and can be used to develop policies for risk management. 75

Methodology
Streamflow data were obtained from the Department of Irrigation and Drainage Malaysia, which covers approximately 40 years (1978 to 2017) of records for all streamflow gauging stations. Precautions were taken to ensure reasonable low flow regimes are captured. The daily streamflow had consistent statistical properties and analysis of streamflow for determining the threshold level values to drought analysis. Lastly, the minimum storage draft rate required for Selangor was determined using 80 a mass curve analysis.

Site description
The scope of this study covers the entire streamflow station in the Selangor state. Selangor covers an area of 8,104 km 2 and is located on Peninsular Malaysia's west coast. Selangor's water supply system not only covers the state of Selangor but also supplies water to the Kuala Lumpur and Putrajaya areas (Sakke et al., 2016). Langat River Basin, Klang River Basin, and 85 Selangor River Basin are the main river basins in Selangor. There are also three other river basins in Selangor, Buloh River Basin, Bernam River Basin, and Tengi River Basin. Table 1 shows the locations and characteristics of all streamflow gauging stations involved in this study. Figure 1 shows the seven streamflow gauging stations involved in this study with four streamflow gauging stations located at 90 Langat River Basin at Dengkil, Kajang, Semenyih, and Lui. There are also streamflow gauging stations each at Rantau Panjang for the Selangor River Basin, Tanjung Malim, and JAM SKC for the Bernam River Basin, respectively (Department of Irrigation and Drainage Malaysia, 2011). The headwater of the Langat river basin starts from the northeast of the basin, flows to the southwest, and joins with the Semenyih River. Two dams, the Langat and Semenyih dams, are located at the upper https://doi.org/10.5194/nhess-2020-105 Preprint. Discussion started: 22 April 2020 c Author(s) 2020. CC BY 4.0 License. reaches of the Langat river (Elfithri et al., 2018). Both dams serve to regulate the raw water flowing to treatment plants 95 downstream. The main tributaries of Selangor Rivers are Sembah, Kanching, Kerling, Rawang, and Tinggi River. There are two dams, namely the Selangor and Tinggi dam, in the Selangor river basin. Lastly, the Bernam river basin is located in the southern part of the Perak state with a total area of 3,364 km 2 with the main tributaries rivers of Slim, Daharoi, Erong and Trolak river (Department of Irrigation and Drainage Malaysia, 2011).

Climate characteristics 100
Selangor state is characterised by its geographical position, which lies near the equator climate that is warm and humid over the year with an average annual rainfall of more than 2477 mm (Lassen et al., 2004). The average annual temperature varies between 27-30 °C, and the average annual relative humidity is between 70-90% (Lee et al., 2013). The climatic equatorial regions are influenced by two monsoons, which are the southwest Indian monsoon and the northeast Asian monsoon.

105
Two rainy seasons due to northeast and southwest monsoons contribute a significant amount of storm events resulting in a mean annual rainfall of about 2500 mm (Mamun et al., 2010). Even though Selangor is located in the humid region, it occasionally encounters drought periods. Dry spells, low rainfall, and increased soil impermeability due to population growth are the leading causes of low flow events. The low flow usually refers to a stream regime that indicates the average annual streamflow variability associated with the regional climate's annual cycle. A stream's regime can display one or more 110 low flow events depending on the climate. Two rainy and two dry seasons represent the equatorial climate, and the two streamflow regimes have two corresponding periods of high flow and low flow.

Trend analysis
Trend analysis covers both detection and attribution for hydrological drought (Zou et al., 2018). Trends in streamflow have consequences for hydraulic models that are often based on the notion of stationarity that many researchers are now debating 115 because of climate change effects within not only local but also regional climate patterns, or perhaps basin and regional scale (Zeng et al., 2015). Despite significant improvements in statistical hydrology for trend evaluations in recent years, researchers are beginning to pay more attention to trend analysis in order to understand better hydro-climatic variables such as precipitation (Nam et al., 2015), temperature (Marx et al., 2018), and streamflow in the context of prevailing uncertainties and changes in climate (Bormann and Pinter, 2017). 120 The function of trend analysis defines the situation of one variable versus the other and determines if a shift occurs within specified limits. Either positive or negative is displayed in the orientation of the shift. Mann-Kendall and Sen's T-tests are the most commonly used non-parametric trend analysis methods (Hisdal et al., 2001). The consistency of the performance of the analysis has a crucial significance in the trend analysis studies, particularly on the discharges of any stream. For this study, the 125 Mann-Kendall test is chosen due to its capability of identifying any trend in a time series. The Mann-Kendall test is also based https://doi.org/10.5194/nhess-2020-105 Preprint. Discussion started: 22 April 2020 c Author(s) 2020. CC BY 4.0 License. on rank order and straightforward to calculate. On the other hand, most studies are using Sen's slope estimation technique that presents the shift quantity (Assefa and Moges, 2018). Sen's slope is a non-parametric method for determining any trend's slope.
It utilises data from a time series that is similarly distributed. The difference in slope is calculated per changed time for each data point. 130 In the streamflow time series data, the trend was analysed using the Mann-Kendall test to evaluate the significance of monotonic trends. The test is as follows; Assuming X1, X2, ...., Xn is a series of data over a time period, the null hypothesis (H0) is tested, and the data comes from a series with identically distributed and independent variables. Over time, the data of the H1, the alternative hypothesis, follows a monotonic trend. Under H0, the Mann-Kendall test statistic is given by Eq. (1): 135 where xj and xi are the data values in years j and i, respectively, with j > i; n is the total number of years; sgn() is the signum function. The alternative hypothesis H1 of a two-sided test is that the distribution of xi and xj are not identical for all i, j ≤ n with i ≠ j. Therefore, the probability associated with S and the sample size, n, is determined to statistically measure of the trend significance. Normalised test statistics Z are expressed as follows by Eq. (2): 140 The null hypothesis of no trend is rejected at 99% significance if |Z| > 2.575; the null hypothesis of no trend is rejected at 95% significance if |Z| > 1.96; and the null hypothesis of no trend is rejected at 95% significance if |Z| > 1.645. In the test statistic, S calculates the sum of the difference between data points and the associations between samples to show the presence or 145 absence of a trend. When the value of Z is positive, it gives a positive trend and a negative trend when Z gives a negative value. In this study, the level of significance of 0.05 or 95% (P-value = 0.05) was used. If their P-value was equal to or less than 0.05 (P-value ≤ 0.05), the trend tests were considered significant, as shown by Eq. (3) (Coch and Mediero, 2016): The Mann-Kendall test is associated with the calculation of Sen's slope. Some patterns may not be considered as being 150 statistically significant while they may be of practical interest and if there are any shifts in streamflow, statistical tests may not detect them at a sufficient level of significance. Then a linear trend analysis is also conducted and the trend magnitude is determined by the Sen's slope method. If a trend is identified in a time series, the slope can be determined using the slope https://doi.org/10.5194/nhess-2020-105 Preprint. Discussion started: 22 April 2020 c Author(s) 2020. CC BY 4.0 License. estimator (β) in Sen's slope test. The estimator β is the median of all slopes between data pairs for the entire data set. A positive β shows an increasing trend, and a negative β a decreasing trend as given by Eq. (4): 155 with n the number of data; i, j are indices with i = 1, 2, …… (n-1) and j = 2, 3, …., n.

Probability distribution of low flow frequency analysis
There are several types of frequency distribution functions that have been successfully applied to hydrologic data. The probabilistic behaviour was analysed using four probability distribution functions (PDFs), widely used in extreme value 160 analysis (Joshi and St-Hilaire, 2013;Zaidman et al., 2003). Then, probability distribution functions were fitted with their parameters estimated using the method of maximum likelihood estimation (Assefa and Moges, 2018). Goodness-of-fit was judged by the Kolmogorov-Smirnov test. Here, a 95% confidence level was accepted to reject or accept a fit, based on Dvalue.

165
The graphical illustration of probability plot is described as the i th -order statistic of the sample, y(i), as a function of a plotting position, which is simply a measure of the non-exceedance probability related to the i th -order statistic from the assumed standardised distribution (Sharma and Panu, 2015). The r th -order statistic is acquired by way of rating the observed sample from the smallest (i = 1) to the greatest (i = n) value, then y(i) equals the i th largest value. According to Koteia et al. (2016), the plotting position of low flow, P can be obtained using the Weibull formula given by Eq.
where, P = The probability of low flow; m = the ranking, from highest to lowest, of mean annual minimum flow; and N = the total number of the mean annual minimum flow.
The selection of probability is according to the shape parameter. This is because the shape parameter can be represented as the skewness parameter. Table 2 shows the probability density functions for each distribution. For this study, the method of 175 maximum likelihood is used for parameter estimation. The likelihood function is defined as Eq. (6): Once the parameters are estimated, the selected distributions will be tested for the assumption that the observed data is actually from the fitted distribution of probability. The Kolmogorov-Smirnov (KS) test has been used to determines the largest discrepancy between the theoretical (Fn(xi)) and empirical (F0(xi)) cumulative distribution functions. The KS test obtains a D-180 statistic; the maximum vertical is given by Eq. (7): https://doi.org/10.5194/nhess-2020-105 Preprint. Discussion started: 22 April 2020 c Author(s) 2020. CC BY 4.0 License.
Where r is the rank of the observation i in ascending order. The smaller D-values imply a better fit of the streamflow series to the selected probability distribution. If D was greater than the critical value (α = 0.05), the distribution was rejected.

Estimation of low flow based on the return period 185
After the probability calculations, P and subsequent returns period the low flow, T, the low flow rate variation will be plotted against the return period, T on the semi-log graph. With this graph, the specific magnitude of a specified period can be determined (Erfen et al., 2015;Gottschalk et al., 2013). The return period describes the probability of occurring extreme events.

Flow duration curve (FDC)
Flow Duration Curve (FDC) describes the ratio of a specified percentage of time with discharge is equal to or surpassed (Croker 190 et al., 2003;Mohamoud, 2008;Vogel and Fennessey, 1994), which reflects the relationship between streamflow magnitude and length of time that relates to the average percentage of time a specific flow is exceeded (Sung and Chung, 2014). The FDC was developed by arranging streamflow values in decreasing magnitude order and assigning rank numbers to each streamflow value with the largest flow ranked as one and the smallest n, where n is the complete record quantity and calculating the percentage of time a given flow was equal to or exceeded (probability of excess) using the relationship in Eq. (8) (Awass, 195 2009;Koteia et al., 2016;Yahiaoui, 2019): While FDCs have a long history in hydrology, they are often criticised because their interpretation historically depends on the specific period in records. A period-of-record of FDC (POR FDC) represents the probability of streamflow exceedance over a long period. This definition can be beneficial as long as the period of record was used to create the FDC is long enough to 205 provide a limiting streamflow distribution, or whether the period of record corresponds to particular planning or design life.
Nevertheless, in many nations, records are shorter than this prescribed time for a large part of the gauged catchments.
Regardless of the following limitations, engineers are still preferring to use FDC compared to POR FDC. For individual years, they considered FDCs and viewed certain annual FDCs like a sequence of maximum or minimum annual flow. Engineers also want to estimate daily streamflow quantiles for hydrological design and planning. FDCs' annual concept requires FDCs to 210 grant confidence intervals and return dates. FDCs can be built to generalise hydrological frequency analysis using average recurrence intervals.

Threshold level method
The low flow value was obtained from the flow duration curve at 90 th percentiles. The magnitude of drought characteristics 215 was determined by the threshold value and value difference between the time series. As the daily data series are used, the existence of minor drought events and mutually dependable drought events can be detected (Van Loon and Van Lanen, 2013).
According to the study by Sakke et al. (2017), to eliminate the minor drought events, the events that occur for less than 15 days will be excluded while the mutually dependable events were also eliminated by the pooling procedure (Sakke et al., 2017).
In this paper, the 7-day moving average was applied as a pooling procedure to obtain smooth data. Through these methods, 220 the mutually dependent drought events will combine into individual and independent drought events (Fleig et al., 2006). The minor drought events will be eliminated or combined with individual drought events automatically (Yahiaoui et al., 2009).

Minimum storage-draft rate method
The minimum storage draft rate was determined by using the mass curve of low flow at a monthly interval (Bharali, 2015).
Although specific evaluation of storage requirements is essential for design, reconnaissance planning can frequently be 225 facilitated by using draft-storage curves based on low-flow frequency analysis. Alrayess et al. (2017) determined the capacity of river storage by the mass curve method. The mass curve has many useful applications in the design of storage capacities, such as to determine the reservoir storage capacity and flood routing (Gao et al., 2017). The procedure for the mass curve method has the following steps; first, construct a mass curve of the historical streamflow (monthly streamflow); determine the slope of the cumulative draft line for the graphical scales; next, superimpose the cumulative draft line on the mass curve; lastly, 230 measure the largest intercept between the cumulative draft line and the mass curve.

Results
The streamflow data from the seven streamflow gauging stations will be analysed in three aspects, which are mean annual low flow and the probability of occurrence, drought characteristics using the threshold level and the estimation of storage draft rate of the river. Statistical characteristics were calculated from the observed 40 years daily streamflow time series: the mean, 235 minimum, and maximum of 14,610 values data; standard deviation, skewness, and kurtosis for each station (Table 3).

Trend analysis
Annual series trend analysis presents the overall view of the shift in systems of streamflow (Assefa and Moges, 2018). The Mann-Kendall test and Sen's slope results are displayed in Table 4. The results of this analysis indicated that five selected stations (S01, S02, S04, S05, and S07) are increasing trends of streamflow. Two of the stations, S03 and S06, have indicated 240 a decreasing trend with the negative change of streamflow.
In the S03 and S06 stations there could be several factors for decreasing streamflow. Some of this involves modifications in the catchment of physical characteristics such as changes in land cover in river basins (Hisdal et al., 2001). Another five stations indicated an increase in trends of streamflow due to climate change for the increasing temperature and soil water 245 evaporation (Siwar et al., 2013;Taye et al., 2011). Simple linear regression is often conducted to evaluate the interaction between interest variables and to obtain a change in hydro-climatological variables over time. A positive slope demonstrates an upward trend, while a negative slope indicates a downward trend. Another benefit for this method is that it offers a significance indicator dependent on the slope hypothesis test and also delivers the degree of alteration magnitude. The total difference can be obtained by multiplying the slope by the number of years during the time under observation. 250

Low flow frequency analysis
Frequency analysis has focused on fitting a theoretical probability distribution function to the observed data, and providing low flow estimates for any given return period. For each station, annual minimum streamflow was plotted using all the distributions. The goodness of fit was performed using Kolmogorov-Smirnov. All the PDFs were ranked for streamflow at each station. Ranks, according to these three goodness of fit, showed a significant variation. In the case of annual minimum 255 streamflow, various distributions were found the best fit for different stations. Best fit distributions were Gamma, Gumbel, Lognormal 2P and Pearson type-3. Figure 2 shows the example probability of mean annual minimum flow for station 1. The estimated parameters were determined and shown in table 5.
The primary purpose of this study is to determine the best-fitted distribution of probability for each station for low flow 260 frequency analysis. Such projections could provide valuable input for policy and decision-making purposes. The information about the return period of extreme can be used in determining the risk management by extreme events such as hydrological drought, while the geographical station location and the surrounding environmental factors for the variation of streamflow. Table 6 shows the best-fit results of the K-S test and P-value results with their ranking.

265
The primary aim of the probability distribution fitting is to represent the low flow probability most accurately. Among all the stations, it was found that among all distributions, the Lognormal 2P yielded the most cases of best-fit distributions, while the Gumbel and Gamma yielded the second and third amount of best-fits respectively. Comparatively, it is proposed that 2P Lognormal distributions predict low-flow discharges for all the rivers under analysis, which can be used in water quality and quantity management at gauged and ungauged areas. When the best fit probability distribution of the low flow series of the D-270 day has been determined, the low flow discharge of the D-day can be estimated according to any given return period. It should be noted that the research is station dependent on this analysis. The low flow-duration-frequency curves were therefore obtained at the base of gauging station. The low flow-duration-frequency curves are powerful tools for many applications, but particularly for engineering practice. An engineer may get any discharge of the low flow-duration-frequency curves from any https://doi.org/10.5194/nhess-2020-105 Preprint. Discussion started: 22 April 2020 c Author(s) 2020. CC BY 4.0 License. low flow model. The fraction of non-zero flows in this river basin is always 100 per cent allowing one to measure up to 100-275 year return cycle D-day low flow discharges. Table 7 shows the return period of low flow at all streamflow stations.
A catchment with a slow or quick response to rainfall intensity that usually has long or rapid recession actions depends entirely on the catchment's physical characteristics. Low flow in catchments that respond quickly is lower than in those that respond slowly. Low flow in catchments that respond slowly is more persistent than in catchments that respond quickly. These 280 differences demonstrate the significant effect on low-flow events of hydrological processes and storages. The boxplot graph displays the full range of variation, which is from minimum to maximum data set in each station. The 285 largest range for low flow per area is in S06 while the smallest range is in S01. The boxplot graph provides information about the shape of a data set. S01, S02, and S04 are skewed right, S03, S05, and S06 are symmetric shape data, and S07 is skewed left. From the discussions above, it is clear that the natural elements that affect a variety of factors of the river's low flow regime consist of distribution and hydraulic components, climate, and topography.

Hydrological drought characteristics 290
The threshold level value per Q percentile obtained from the flow duration curve is shown in Table 8. In this study, only Q90 was used as a threshold level in the determination of drought events. Several days and percentage where the streamflow rate was below the average level are recorded to show the severity of droughts events at each station.

Hydrological drought events and deficits
The growing perception of hydrological drought improvement on a global scale has some necessary implications for water 295 management. It is recognised, for example, that the duration and the volume of the deficit of the drought are associated (Fleig et al., 2006). Table 9 shows the summary of the drought series below the threshold level (Q90), without removing minor drought for each station in the Selangor region.  (1) year. The total number of days of the occurrence of this drought is 1,460 days, which is 9.99% of the total daily flow data. The overall deficit of 28 drought events was 673.54 m 3 /s. The lowest total deficit was recorded in 1983 as much as 7 m 3 /s, while the highest deficit was recorded in 2004 with 131.27 m 3 /s. The average amount of total deficit was 24.06 m 3 /s. 325 Station S05 has been categorised as the most critical station with the highest number of days of droughts events. The longest annual drought event was recorded in 1998 with 217 days, and for individual drought events, this occurred in 1999 with a period of 111 days. Using the threshold level at Q90 = 21.52 m 3 /s, 1,236 days (10%) of the total are below the threshold level categorised as drought. Repeat drought events recorded in 1978, 1979, 1986, 1987, 1990, 1998, 2000 and 2002 1978, 1983, 1985, 1987, 1990, 1991, 1992, 1998, 1999, 2001, 2002, 2005 and 2016. The most prolonged drought period was recorded in 2005 with a period of only 99 days, while the shortest period was in 1971, 1987, 2000, and 2016 with a period of 15 days. The most prolonged period of individual drought events with 205 days occurred in the same year in 2005. The total drought days at this station was 1,614 days, which was 11.05% of the total days. S07 recorded a deficit of 21,740 m 3 /s during the drought episode, and this percentage is the highest percentage recorded compared to other streamflow stations. This stream records a high deficit amount with fewer drought days. The highest deficit reached 1,445 m 3 /s recorded in the drought events in 1990, while the lowest deficit was in 1983 with a total of 161.32 m 3 /s. 345 From the results, S01 exhibits the highest number of drought events, which is 39 episodes, with the mean deficit is 264.10 m 3 /s. This station is located downstream of the Langat basin. It indicates the downstream watershed catchment has more drought episodes compared to the upstream catchment. Magnitudes differ significantly between catchments since there were also varied specific hydrological characteristics, such as station spatial distribution, precipitation and temperature magnitudes, 350 and frequency of extreme events like drought.
To prevent a future catastrophe in the region, it is crucial to properly understand the temporal characteristics of drought in this transboundary river basin with water deficit. Hydrological drought investigation is provided from streamflow records, and very frequently, the lack of recorded long-term streamflow data hinders a reliable analysis of drought and previous 355 understanding of the phenomenon. Hydrological drought management involves determining a possible level of thresholds.
Threshold levels of low exceedance probability are considered to be appropriate for the area of study, unlike the higher exceedance probabilities typically used in a temperate climate.

Estimation of minimum storage draft-rate 360
The estimation of the storage draft rate in this study will determine the minimum storage of a river to sustain the water supply during low flows and droughts. The mass curve of the monthly low flow rate is used in this analysis to obtain the minimum storage rate of the river. The mass curve analysis of low flow for the duration of January to December plotted against duration for recurrence interval of 10-year. The cumulative draw off corresponds to a constant draft rate of 50% of the mean annual flow. Figure 4 shows the flow mass curve for the determination of the minimum storage-draft rate of each station. Table 10  365 shows the monthly minimum storage draft rate value for each station that needs to be maintained at a draft rate of 50% of the mean annual flow during low flows to sustain the water supply.
The minimum storage required for maintaining a draft rate required for S01 is 21.51 m 3 /s in October, S02 is 13.37 m 3 /s in December, S03 is 4.79 in December. The minimum storage required for S04 is 2.32 m 3 /s in October for 40 years' duration 370 period; S05 is 15.00 m 3 /s in September. While, the minimum storage required to maintain the draft rate for S06 is 10.90 m 3 /s in October, and lastly, for S07 is 6.17 m 3 /s in September.

Discussion
The results of the analysis demonstrate the spatial and temporal variability of the hydrological drought using streamflow data.
This section discusses the advantages and limitations of the implications of these findings. 375

Streamflow trend
For the annual average streamflow at the gauging stations, five stations indicated an upward trend, and two stations indicated a downward trend for 40 years' data. The interpretations of trend analysis for relatively partial streamflow records may only reflect a short-term condition and may not be representative of an actual long-term change in the streamflow data. This issue is valid for relatively short-term records that begin or end in a historically low flow condition. One of the influential aims of 380 the time series trend is to define the nature characteristic represented by the sequence of observations and predicted future values of the time series variable. The analysis of observed data for changes and trends of streamflow data can be used to assess the impact of climate change. The streamflow trend can estimate future water availability to maintain and sustain ecosystem functions. Moreover, streamflow trend analysis can also be used to predict any change in river flows for making water withdrawal decisions, which indirectly can improve drought management response. 385

Hydrological drought
The hydrological drought effects will happen slowly but last longer. Hydrological drought can lead to consequences for water supply, agriculture, water quality, and electricity production, which leads to both economic and ecological loss. Low flow statistics are often used in characterizing hydrological drought. There are several ways to define low flows. Low flow rates are generally smaller than the median flow of a river. Different low flows can be used to investigate different ecosystem functions 390 of a river and can be used to indicate when a river is in a drought situation.
This study used a hydrological drought index called threshold level methods to identify drought characteristics. This method uses fixed or moving thresholds to identify at what flow a river is considered to be in a drought and easily determine its duration, severity, and frequency. Commonly, the thresholds level is taken from flow duration curves (FDC) of streamflow 395 data. Flow duration curves show the interaction of frequency and magnitude in streamflow using a graphical method. FDC can be developed for different periods such as daily, monthly, and annually based on objectives study. Multiple low flow indices can be obtained from FDC, such as Flows with 70-99% exceedance, Q20/Q90, Q50/Q90, Q90/Q50, 7 days 10-year flow, and 7 days 2-year flow that describe low flow regime of a river (Blum et al., 2016). Calculating frequency and return period of mean annual minimum n-discharge are a standard index. It uses the mean minimum flow of a certain amount of days (n) ranging 400 from 1-30 for every year of record (Sarailidis et al., 2019b). The limitation of FDC is they do not provide any information about the intensity and duration of low flow events in streamflow time series.
When the streamflow falls under a certain threshold level from a streamflow hydrograph, a series of hydrological drought events can be derived. Therefore, it is possible to obtain the drought characteristics, including duration of drought, deficit 405 volume and interval of drought. The value of the threshold level is subjective, but it is necessary as it influences the number of events, the period of drought, and the volume of a deficit. Thresholds may be flow minima that are either ecologically substantiated or are derived from the water resources management requirements, reservoir operation, and navigation (Sarailidis et al., 2019a). Threshold levels between the 70 th percentile and 95 th percentile flow from the flow duration curve (FDC) are recommended for perennial streams such as the Selangor river catchment (Heudorfer and Stahl, 2017). The 90 th percentile 410 flow is used in this study to characterise hydrological droughts from streamflow series.
Several indices could be used to provide a more accurate representation of hydrological drought. Which indices one chooses to use is going to affect the result directly. One of the problems in the use of an annual Q90 threshold is the drought events may not be entirely accurate. It is important to note that the Q90 threshold merely identifies low flows accounted for catchments 415 regular flow. Therefore, the Q90 threshold does not necessarily imply a situation where functions in nature are affected. The threshold level can reflect a specific requirement, such as for water supply or minimum environmental flow, or a normal low flow condition of the river can be represented. For a bigger picture and understanding of the broad spectrum of hydrological drought, more indices need to be put together in an index. Different methods will allow different characteristics of hydrological droughts. The threshold level method should be used for more detailed deficits and in-depth study. Complex indices would be 420 most useful to verify results in regional studies.

Conclusion
Low flow analysis is an essential and widely studied design and management of hydrology and water resources. Varying and complex natural processes may produce low flows in a river on a catchment scale. The flow duration curve is one of the primarily used tools for assessing low flow and the river regime. This method was selected because it is one of the most 425 informative ways to display streamflow characteristics throughout the discharge range, regardless of the occurrence sequence.
The first aim of this work was to determine the characteristics of low flow by using frequency analysis. Based on the results of the low flow frequency analysis, Gumbel distribution methods were used to predict the magnitude of low flow. Gumbel distribution provides a good fit to annual minimum flow data at each station, and the Kolmogorov-Smirnov test was conducted as an indicator of performance. From the result, the range means the low flow of rivers in Selangor is between 0.75 to 19.47 430 m 3 /s.
Drought is a phenomenon of water shortage when the water supply is below the average level. This study developed a useful principle of using threshold level methods to describe the characteristics of streamflow droughts. From this study, we can make the following conclusions: 1) The threshold level using the Q percentile based on the flow duration curve was used as an average level to separate the occurrence of droughts events or otherwise. The number of days and duration of droughts for a station can show the severity of the drought that occurs.
2) The drought characteristics were analysed from time-series below a threshold level (Q90) without removing the minor drought. The magnitude and duration of drought characteristics were determined by the value difference between the 440 time series and the threshold level value.
3) The highest drought events are 39 episodes with a mean volume of the deficit is 557.46 m 3 /s while the lowest events of drought are ten (10) episodes with the mean volume of the deficit is 127.71 m 3 /s. The rate of low flow at the recurrence interval of 10-year was used to ensure the minimum storage-draft rate required to sustain 445 the water demand during low flow periods. The restructure of the minimum storage draft rate must be done by hydrologist at a particular return period to ensure the streamflow gauging station has enough water to be supplied to the user during the low flow and drought periods. Based on the analysis of the study, the estimated minimum storage-draft rates for each station cannot meet the water demand during low flow at specific return periods, which is 10-year recurrence interval for this research.

450
This research is essential to water resources management. Low flow analysis and water availability enable water resource management to make more realistic decisions on water restrictions and provisions for cities and populations. Understanding the concept of low flow and the predictive significance of river storage-rates can also help in managing sustainable water catchment. This study also helps in emphasising the natural flow of water to provide a water supply for continuous use during low flow. Additionally, through this research, the concept of low flow analysis and the predictive significance of minimum 455 storage draft rate can be developed to produce more efficient water resource management systems during the dry season in Selangor, Malaysia.