The Upper Citarum River Basin geographical location is 107° 15' 46.27”-107° 57' 1.99” East Longitude and 6° 43' 8.65”-7° 14' 32.09” South Latitude. The UCRB has a total watershed area of 1,810 km² consisting of six main sub-basins, including the Cikapundung, Cikeruh, Citarik, Cirasea, Cisangkuy, and Ciwidey sub-basin [21] (Fig. 1). The rainfall-runoff modeling was conducted using data from 16 rainfall recording stations within the watershed, and the Thiessen method was used to calculate the rainfall area as in Fig. (1). The recording discharge data was taken from the Citarum-Nanjung Station because it covers the entire UCRB.

Fig. (1). Upper citarum river Basin.

A conceptual rainfall-runoff model was carried out apart from making a hydrological analysis for environmental flow from the discharge recording data. Modeling was performed using Sacramento methods, and the results were compared to those from observation data analysis to identify the significance of differences in low flow on the model and the observed data. The observational discharge data, rainfall data, and climatology for modeling had the same evaluation period from 2008-2019. Regional rainfall was calculated using the Thiessen method to compare areas, as presented in Table 1.

Results obtained from Nanjung gauge stations (the simulated discharge) were validated using observation data. Nanjung gauge station was chosen because it was considered to represent UCRB, and it is located downstream from Cikapundung, Cikeruh, Citarik, Cirasea, Cisangkuy, and Ciwidey sub-basin. The parameters used in the Sacramento modeling are described in Fig. (2).

Fig. (2). The schematic diagram of Sacramento [22].

Model calibration was conducted by comparing the modeling results with the observed data. According to Nash-Sutcliffe [23], the method for determining the model calibration criteria on the field observations results was as follows:

(1)

Where EI = efficiency index; Q₀ = Discharge measurement (observation); Qs = Simulation discharge; and Qa = Average measurement discharge. The EI value, according to the Nash method, is divided into 3 categories, namely:

(a) Very satisfactory/good category, if EI > 0.75

(b) The category is quite satisfactory/good enough, if 0.36 < EI < 0.75

(c) Unsatisfactory category, if EI < 0.36

The Gumbel_min distribution was applied, even though not constantly, as an extremal distribution for modeling annual minima of drought-related variables, including the Q7, the lowest mean discharge of 7 consecutive days in a provided year [21]. The cumulative distribution function for the Gumbel_min was:

(2)

where α symbolizes the scale parameter and β the location parameter. Analogously to the Gumbel_max, β is, actually, the Z mode. The possibility density function of the Gumbel_min distribution was performed by:

(3)

The mean, variance, and skewness coefficient of a Gumbel_min variate were respectively performed as:

(4)

(5)

(6)

The Gumbel_min distribution was skewed to the left with a set coefficient of γ= -1.1396. The Gumbel_min and _max possibility density functions, both with identical parameters, were symmetrical to a vertical line crossing the abscissa axis at the common-mode β [24].

The Gumbel_min quantile function was expressed as:

(7)

T denoted the return period in years, and F represented the annual non-exceedance possibility [24]. For annual minimal, the return period was the reciprocal of F or T=1/PZ≤z =1/F zz. Notably, according to the numerical values of the distribution parameters and the return period goal, the estimation of Gumbel_min quantiles could produce negative numbers. This was a major disadvantage of the Gumbel_min distribution, which had limited its spread application as a model for low-flow frequency analysis [25].

The Extreme-Value type III (EV3) distribution for minima was also related to Weibull_min. Since low flows were surely defined by zero in almost severe cases, its distribution was a normal candidate to model hydrologic minima [24-26]. If low-flows were lower-bounded by zero, the EV3 distribution tended to the two-parameter Weibull_min. Meanwhile, if low-flows were lower-bounded by some value ξ, the EV3 distribution tended to the three-parameter Weibull_min [24].

The cumulative distribution function for the two-parameter Weibull_min was presented by:

(8)

where β and α were scale and shape parameters, respectively. If α ¼ 1, the Weibull_min became the one-parameter exponential distribution with scale parameter β. The possibility density function of the two-parameter Weibull_min distribution was represented as Continuous Random Variables: Probability Distribution [24].

(9)

The mean and variance of a two-parameter Weibull_min variate were, respectively, given by:

(10)

and

(11)

The variation and skewness coefficients of a two-parameter Weibull_min variate were, respectively:

(12)

and

(13)

Estimation of parameters and possibilities for the two-parameter Weibull_min distribution was accomplished by first solving Eq. (14) for α, either through a numerical iterations' procedure comparable to the one applied to measure the GEV shape parameter or by tabulating (or regressing) potential values of α and the auxiliary function Aα=Γ1+1/α against CVZ [24]. The dependence analysis of αα and A(α) on the coefficient of variation CVZ led to the following correlative relations:

(14)

(15)

which provide good approximations to the numerical solution of Eq. (15). Once α and A(α) have been identified, parameter β can be estimated from Eq. (16), or:

(16)

With both parameters identified, the two-parameter Weibull_min quantiles are determined at:

(17)

Another familiar hydrology-based methodology used universally in its usual form is the FDCA method [17]. In this research, the FDCA was used to investigate the probability distribution of recorded data where it (data) was ranked and its corresponding probability calculated by using the following equation:

P= mn+1100% (7)

Smakhtin (2001) characterized that the design low-flow range of an FDC was between 70 and 99% (Symbolized as Q70 and Q99%, respectively). The Q90 and Q95% were usually applied as indicators of low-flow, which has broadly applied to get the smallest EFs [18-20].

Sacramento method proved to provide the best results compared to data acquired from observation, as demonstrated in Fig. (3).

This refers to model testing results with observational discharge data using the Nash-Sutcliffe Efficiency (NSE) method, where the NSE value is close to the Sacramento modeling (Table 2).

The final parameter optimization results can be a reference model for the engineers and modelers at UCRB, as shown in Table 3.

Fig. (3). Comparation Daily Discharge.

Fig. (4). UCRB flow duration curve (2008-2017).

The 7Q10 and Sacramento debit calculation results were carried out using the Gumbel minima and Weibulll minima methods, both from the Nanjung daily recording data and the results of the Sacramento calculation, as presented in Table 4. The results of the Gumbel minima method were negative; thus, it could not be associated with the low discharge in the river. This is in accordance with the hypothesis the estimation of Gumbel_min quantiles could produce negative numbers, which stated that the Gumbel minima method had limitations in the 7Q10 calculation [24].

The value of Q95 for Nanjung AWLR was 7.17 m³/s, while the result for modeling rainfall-runoff was 7.06 m³/s. While Q99 for AWLR Nanjung was 2.48 m³/s and Sacramento modeling for UCRB was 5.35 m³/s (Table 4). The value of 7Q10 showed that the results are significantly smaller than Q95 and also smaller than Q99 (Table 4), thus, the research established that Q95 was widely used in Indonesia to determine EF.

Considering the Weibull minima method, the 7Q10 results for Sacramento modeling are 2.18 m³/s, while the Nanjung AWLR was 1.24 m³/s. The result was used as a reference when comparing UCRB EF and the FDCA method, as illustrated in Fig. (4).