Abstract
Estimating the streamflow corresponding to a particular probability is of great importance in many hydrological studies, such as determining hydroelectric water potential, assessing water quality, and investigating sedimentation and drought. This paper aims to effectively estimate low-flow quantiles since hydrologic droughts motivate the study. The study illustrates a methodology, where droughts are characterized by the lower part of the flow–duration curve (FDC), and offers a perspective estimating low-flow quantiles related to the basin characteristics. Low-flow quantiles are derived both from traditional FDCs curves and median annual FDCs (AFDCs). As an innovation, the concept of areal scale factor, which represents a scaling ratio between the basin area and flow quantiles, was introduced. Unlike many other parametric approaches, this study models the streamflow quantiles depending on the basin characteristics instead of the parameters in the analytical equation of FDCs. The methodology was evaluated for the Western and Southwestern Anatolia regions in Turkey. The outcomes were compared for two types of FDCs in two regions. The approach gave similar results for both study regions. AFDCs provided a distinct advantage over traditional FDCs, especially for low-flow quantiles, due to the superiority of AFDCs in estimating streamflow quantiles of intermittent streams.
HIGHLIGHTS
This research study offers a practical solution in terms of low-flow estimation.
It uses median annual flow–duration curves (AFDCs) instead of traditional FDCs, which were frequently used in the literature.
Instead of FDC used in many studies, it models the streamflow quantiles.
It proposes the areal scale factor, which describes the ratio between flow quantiles and basin area, as an innovation.
INTRODUCTION
Hydrological studies can employ a range of methodologies to assess flow variability, taking into account elements such as droughts, low flows, high flows or floods, annual flows, and the seasonal flux of these flows. The variability of the flow in a basin and/or a stream is related to many climatic and hydrological factors (precipitation, evapotranspiration, infiltration, surface storage, land slope, vegetation, and soil type), and one of the most common tools used in hydrology and environmental sciences in examining this variability is the flow–duration curve (FDC). Flow period is also an important factor that significantly affects flow variability. The FDC graphs the relationship between a certain flow magnitude and a time period at which the flow magnitude is equalized or exceeded (Vogel & Fennessey 1995). Introduced by Clemens Herschel in 1880, FDCs have gained widespread acceptance and are used in environmental and hydrological studies around the globe.
There are two distinct types of FDCs mentioned in the literature with respect to their production. The first and the traditional one represents a long-term demonstration of the flow regime using all the long-term flow records and is reported in the literature as a period-of-record FDC (Vogel & Fennessey 1994). The second one is based on the annual interpretation of FDCs (LeBoutillier & Waylen 1993; Vogel & Fennessey 1994) and considers FDCs for separate years (annual FDCs, AFDCs); each one is constructed similar to the FDC, using only annual hydrometric information (Castellarin et al. 2013). A conjunctive evaluation of AFDCs provides a perspective of the interannual variability of the FDCs, which allows the estimation of the median of the AFDCs. The median AFDC is a hypothetical FDC representing the annual flow regime for a typical hydrological year and is not affected by the observations of abnormally wet or dry periods during the period of record (Vogel & Fennessey 1994; Castellarin et al. 2004a). The use of a traditional period-of-record FDC for regionalization limits the representation of the flow regime to the specific record period for which the FDC is constructed (Copestake & Young 2008; Taye & Willems 2011; Mendicino & Senatore 2013). AFDCs are presented to be less sensitive to the period-of-record than traditional FDCs, specifically in the region of low flows (Vogel & Fennessey 1994; Castellarin et al. 2013).
For similar reasons, Niadas (2005) suggested that for regional analysis involving multiple sites, AFDCs represent regional conditions better compared to traditional FDCs for which concurrent data are more important.
The estimation methods of regional FDCs are usually categorized into three groups (Castellarin et al. 2004b; Shu & Ouarda 2012):
- (i)
Statistical methods, which assign a regional parent frequency distribution by estimating regional FDCs at ungauged sites (Fennessey & Vogel 1990; Leboutillier & Waylen 1993; Yu & Yang 2000; Singh et al. 2001; Yu et al. 2002; Croker et al. 2003; Claps et al. 2005; Burgan & Aksoy 2018)
- (ii)
Parametric methods, in which the FDCs of the study area are represented by analytical equations (Castellarin et al. 2004b; Mohamoud 2008; Viola et al. 2011; Müller et al. 2014; Pugliese et al. 2016; Ridolfi et al. 2018; Longobardi & Villani 2020; Gaviria & Carvajal-Serna 2022)
- (iii)
Graphical methods, which construct regional dimensionless FDCs standardized by an index flow (Smakhtin et al. 1997)
Parametric methods have widely been used in various forms for basins in several parts of the world to derive FDCs in unmeasured or partially measured basins. Castellarin et al. (2004b) compared three different parametric approaches of the literature (Quimpo et al. 1983; Mimikou & Kaemaki 1985; Franchini & Suppo 1996). The approach of Franchini & Suppo (1996) outperformed all other parametric approaches due to the regionalization of flow quantiles (Q30, Q70, Q90, and Q95) instead of parameters and therefore inspired this study.
This study aimed to estimate the low-flow quantiles effectively. For this purpose, the FDC model of Franchini & Suppo (1996), based on an empirical regression equation between the streamflow quantiles and the basin characteristics, was improved here by also taking into account the median AFDCs. The relationship between the hydrological, geographical, and meteorological characteristics of the basin and the low-flow quantiles was examined. Low-flow quantiles are derived from the lower part of both traditional and median annual FDCs obtained from daily flow records. The findings revealed that the basin area is the most important basin characteristic to represent low-flow quantiles (Q30, Q40, Q50, Q60, Q70, Q80, Q90, Q95, and Q99). The relationship between low-flow quantiles and the basin area is defined by a ratio parameter called the areal scale factor (ASF). It is pointed out that low flows can be successfully estimated by using ASFs, which is presented as an innovation in this study. A case study for Western and Southwestern Anatolia regions in Turkey was implemented to show its applicability. Ungauged sub-basins are expected to benefit from the developed model.
DATA AND METHODS
Study area and dataset
Although the two regions in the study show similar climatic features, they differ geologically. In Western Anatolia, 85% of topographic surfaces are composed of metamorphic and volcanic rocks, whereas in Southwestern Anatolia, 80% of the surface is composed of sedimentary rocks (limestone). The majority of groundwater resources in Southwestern Anatolia are due to the existence of complexes characterized by high infiltration. The geological formation of the region clearly highlights the significance of the outcropping of limestone complexes in relation to the infiltration and circulation of rainwater. In such basins, finding a direct relationship between the area and the amount of water flowing into the basin outlet is difficult (Franchini & Suppo 1996). Therefore, the effect of limestone complexes on the drainage mechanism and low-flow characteristics is significant and differs considerably to that within the non-karstic regions in Western Anatolia.
Daily streamflow data were provided for the study by State Water Works of Turkey. Only unregulated river basins with a minimum of 10 years of data were considered. In the study, 30 flow gauging stations in Western Anatolia and 21 in Southwestern Anatolia were used. The average daily flows of the basins range from 0.43 to 39.64 m3/s in Western Anatolia and from 0.08 to 27.47 m3/s in Southwestern Anatolia. A substantial number of the rivers in southwestern Anatolia are fed by groundwater. The minimum record length is 10 years, the maximum record length is 54 years, and the mean sample size is approximately 20 years in both regions. The basin areas range from 32 to 15,848 km2 in Western Anatolia and from 8 to 2,448 km2 in Southwestern Anatolia. The average annual rainfall varies between 556 and 658 mm in Western Anatolia and between 526 and 729 mm in Southwestern Anatolia. The main hydrological and geographical characteristics of the basins and flow gauging stations are given in Tables 1 and 2 for Western and Southwestern Anatolia, respectively.
Basin characteristics in Western Anatolia
. | Basin . | Drainage area (km2) . | Mean flow (m3/s) . | Annual rainfall (mm) . | Altitude (m) . | Basin yield (mm/year) . |
---|---|---|---|---|---|---|
1 | Orhaneli Creek at Kucukilet | 1,622 | 5.14 | 631 | 795 | 100 |
2 | Atnos Creek at Balikli | 1,384 | 7.67 | 601 | 94 | 175 |
3 | Emet Creek at Dereli | 1,126 | 4.61 | 579 | 557 | 129 |
4 | Kille Creek at Buyukbostanci | 544 | 2.66 | 609 | 105 | 154 |
5 | Simav Creek at Osmanlar | 1,254 | 7.74 | 571 | 271 | 195 |
6 | Dursunbey Creek at Sinderler | 975 | 5.86 | 622 | 294 | 190 |
7 | Zeytinli Creek at Zeytinli | 123 | 3.18 | 572 | 35 | 814 |
8 | Manastir Creek at Kavaklar | 32 | 1.02 | 576 | 55 | 1,003 |
9 | Inonu Creek at Inonu | 73 | 0.86 | 580 | 65 | 371 |
10 | Cumalidere Creek at Cumali | 85 | 0.21 | 562 | 115 | 79 |
11 | Yagcili Creek at Yagcili | 86 | 0.63 | 564 | 210 | 230 |
12 | Medar Creek at Kayalioglu | 902 | 3.34 | 561 | 77 | 117 |
13 | Kum Creek at Killik | 3,189 | 7.94 | 562 | 54 | 78 |
14 | Selendi Creek at Derekoy | 690 | 2.38 | 598 | 345 | 109 |
15 | Deliinis Creek at Topuzdamlari | 735 | 3.29 | 596 | 381 | 141 |
16 | Murat Creek at Sazkoy | 176 | 1.66 | 585 | 790 | 297 |
17 | Yigitler Creek at Yigitler | 64 | 0.72 | 579 | 158 | 357 |
18 | Tabak Creek at Caltili | 81 | 1.09 | 600 | 137 | 425 |
19 | Gediz River at Muradiye Bridge | 15,848 | 39.64 | 556 | 17 | 79 |
20 | Ahmetli Creek at Derekoy | 95 | 0.74 | 590 | 125 | 245 |
21 | Uladi Creek at Yakapinar | 69 | 0.43 | 572 | 120 | 198 |
22 | Cine Creek at Kayirli | 948 | 4.79 | 636 | 262 | 159 |
23 | Büyük Menderes River at Burhaniye | 12,799 | 21.40 | 630 | 120 | 53 |
24 | Büyük Menderes River at Citak Bridge | 3,946 | 6.88 | 598 | 802 | 55 |
25 | Yenidere Creek at Calikoy | 669 | 1.14 | 647 | 855 | 54 |
26 | Akcay Creek at Degirmenalani | 855 | 7.66 | 653 | 397 | 283 |
27 | Sarhos Creek at Goktepe | 236 | 1.16 | 648 | 390 | 156 |
28 | Büyük Menderes at Cogasli | 4,664 | 7.28 | 610 | 617 | 49 |
29 | Mortuma Creek at Yemisendere | 170 | 1.63 | 658 | 478 | 302 |
30 | Banaz Creek at Ulubey | 2,286 | 4.85 | 605 | 531 | 67 |
. | Basin . | Drainage area (km2) . | Mean flow (m3/s) . | Annual rainfall (mm) . | Altitude (m) . | Basin yield (mm/year) . |
---|---|---|---|---|---|---|
1 | Orhaneli Creek at Kucukilet | 1,622 | 5.14 | 631 | 795 | 100 |
2 | Atnos Creek at Balikli | 1,384 | 7.67 | 601 | 94 | 175 |
3 | Emet Creek at Dereli | 1,126 | 4.61 | 579 | 557 | 129 |
4 | Kille Creek at Buyukbostanci | 544 | 2.66 | 609 | 105 | 154 |
5 | Simav Creek at Osmanlar | 1,254 | 7.74 | 571 | 271 | 195 |
6 | Dursunbey Creek at Sinderler | 975 | 5.86 | 622 | 294 | 190 |
7 | Zeytinli Creek at Zeytinli | 123 | 3.18 | 572 | 35 | 814 |
8 | Manastir Creek at Kavaklar | 32 | 1.02 | 576 | 55 | 1,003 |
9 | Inonu Creek at Inonu | 73 | 0.86 | 580 | 65 | 371 |
10 | Cumalidere Creek at Cumali | 85 | 0.21 | 562 | 115 | 79 |
11 | Yagcili Creek at Yagcili | 86 | 0.63 | 564 | 210 | 230 |
12 | Medar Creek at Kayalioglu | 902 | 3.34 | 561 | 77 | 117 |
13 | Kum Creek at Killik | 3,189 | 7.94 | 562 | 54 | 78 |
14 | Selendi Creek at Derekoy | 690 | 2.38 | 598 | 345 | 109 |
15 | Deliinis Creek at Topuzdamlari | 735 | 3.29 | 596 | 381 | 141 |
16 | Murat Creek at Sazkoy | 176 | 1.66 | 585 | 790 | 297 |
17 | Yigitler Creek at Yigitler | 64 | 0.72 | 579 | 158 | 357 |
18 | Tabak Creek at Caltili | 81 | 1.09 | 600 | 137 | 425 |
19 | Gediz River at Muradiye Bridge | 15,848 | 39.64 | 556 | 17 | 79 |
20 | Ahmetli Creek at Derekoy | 95 | 0.74 | 590 | 125 | 245 |
21 | Uladi Creek at Yakapinar | 69 | 0.43 | 572 | 120 | 198 |
22 | Cine Creek at Kayirli | 948 | 4.79 | 636 | 262 | 159 |
23 | Büyük Menderes River at Burhaniye | 12,799 | 21.40 | 630 | 120 | 53 |
24 | Büyük Menderes River at Citak Bridge | 3,946 | 6.88 | 598 | 802 | 55 |
25 | Yenidere Creek at Calikoy | 669 | 1.14 | 647 | 855 | 54 |
26 | Akcay Creek at Degirmenalani | 855 | 7.66 | 653 | 397 | 283 |
27 | Sarhos Creek at Goktepe | 236 | 1.16 | 648 | 390 | 156 |
28 | Büyük Menderes at Cogasli | 4,664 | 7.28 | 610 | 617 | 49 |
29 | Mortuma Creek at Yemisendere | 170 | 1.63 | 658 | 478 | 302 |
30 | Banaz Creek at Ulubey | 2,286 | 4.85 | 605 | 531 | 67 |
The basins used for the validation are in bold.
Basin characteristics in Southwestern Anatolia
. | Basin . | Drainage area (km2) . | Mean flow (m3/s) . | Annual rainfall (mm) . | Altitude (m) . | Basin yield (mm/year) . |
---|---|---|---|---|---|---|
1 | Yenice Creek at Zindan Bogazi | 62 | 3.068 | 561 | 1,250 | 1,568 |
2 | Dim Creek Irrigation Channel | 195 | 0.967 | 580 | 38 | 156 |
3 | Korkuteli Creek at Salamur Bogazi | 131 | 0.974 | 595 | 1,190 | 235 |
4 | Kucukaksu Creek at Gebiz | 239 | 4.36 | 587 | 62 | 576 |
5 | Aglasun Creek at Aglasun | 49 | 0.566 | 582 | 1,100 | 367 |
6 | Duden Creek at Weir | 1,782 | 16.587 | 685 | 96 | 294 |
7 | Sücüllü Creek at Dam Inlet | 103 | 0.594 | 526 | 1,198 | 181 |
8 | Karpuz Creek at Uzunlar | 303 | 4.192 | 576 | 100 | 436 |
9 | Kargi Creek at Turkler | 336 | 6.801 | 567 | 16 | 638 |
10 | Oba Creek at Kadipinari | 46 | 2.071 | 580 | 91 | 1,420 |
11 | Aksu River at Belence | 349 | 4.88 | 584 | 1,000 | 441 |
12 | Degirmendere River at Sutculer | 131 | 1.453 | 591 | 750 | 350 |
13 | Çandir Creek at Yemisli Pinar | 164 | 1.788 | 700 | 160 | 344 |
14 | Basak River at Yanikkoy | 223 | 3.315 | 584 | 1,085 | 469 |
15 | Doyran River at Doyran | 106 | 0.773 | 700 | 145 | 230 |
16 | Esen Creek at Kinik | 2,448 | 27.471 | 609 | 8 | 354 |
17 | Ballik River at Ballik | 126.2 | 0.757 | 641 | 1,091 | 189 |
18 | Basgoz Creek at Gokbuk | 222.2 | 3.47 | 554 | 208 | 492 |
19 | Akcay Creek at Gombe | 114.5 | 1.243 | 602 | 80 | 342 |
20 | Cataloyuk River at Karaculha | 8 | 0.075 | 637 | 1,340 | 296 |
21 | Geyik Creek at Nif | 8.2 | 0.233 | 729 | 1,035 | 896 |
. | Basin . | Drainage area (km2) . | Mean flow (m3/s) . | Annual rainfall (mm) . | Altitude (m) . | Basin yield (mm/year) . |
---|---|---|---|---|---|---|
1 | Yenice Creek at Zindan Bogazi | 62 | 3.068 | 561 | 1,250 | 1,568 |
2 | Dim Creek Irrigation Channel | 195 | 0.967 | 580 | 38 | 156 |
3 | Korkuteli Creek at Salamur Bogazi | 131 | 0.974 | 595 | 1,190 | 235 |
4 | Kucukaksu Creek at Gebiz | 239 | 4.36 | 587 | 62 | 576 |
5 | Aglasun Creek at Aglasun | 49 | 0.566 | 582 | 1,100 | 367 |
6 | Duden Creek at Weir | 1,782 | 16.587 | 685 | 96 | 294 |
7 | Sücüllü Creek at Dam Inlet | 103 | 0.594 | 526 | 1,198 | 181 |
8 | Karpuz Creek at Uzunlar | 303 | 4.192 | 576 | 100 | 436 |
9 | Kargi Creek at Turkler | 336 | 6.801 | 567 | 16 | 638 |
10 | Oba Creek at Kadipinari | 46 | 2.071 | 580 | 91 | 1,420 |
11 | Aksu River at Belence | 349 | 4.88 | 584 | 1,000 | 441 |
12 | Degirmendere River at Sutculer | 131 | 1.453 | 591 | 750 | 350 |
13 | Çandir Creek at Yemisli Pinar | 164 | 1.788 | 700 | 160 | 344 |
14 | Basak River at Yanikkoy | 223 | 3.315 | 584 | 1,085 | 469 |
15 | Doyran River at Doyran | 106 | 0.773 | 700 | 145 | 230 |
16 | Esen Creek at Kinik | 2,448 | 27.471 | 609 | 8 | 354 |
17 | Ballik River at Ballik | 126.2 | 0.757 | 641 | 1,091 | 189 |
18 | Basgoz Creek at Gokbuk | 222.2 | 3.47 | 554 | 208 | 492 |
19 | Akcay Creek at Gombe | 114.5 | 1.243 | 602 | 80 | 342 |
20 | Cataloyuk River at Karaculha | 8 | 0.075 | 637 | 1,340 | 296 |
21 | Geyik Creek at Nif | 8.2 | 0.233 | 729 | 1,035 | 896 |
The basins used for the validation are in bold.
Methods
Construction of FDCs and AFDCs
This study uses both traditional FDCs and AFDCs to estimate streamflow quantiles. The traditional method represents a long-term demonstration of the flow regime using all the long-term flow records obtained by sorting all records in descending order and plotting them against their exceedance probabilities. AFDCs, on the other hand, describe FDCs with a time span of one year, as advocated by Vogel & Fennessey (1994). Obtaining the median AFDCs consists of a few simple steps described below:
- (a)
sorting daily observed flows Qi for each year from largest to smallest to produce an ordered series (i= 1,2, … , 365),
- (b)
repeating the sorting procedure in the previous step for N observation years, and thus N number of AFDCs are obtained,
- (c)
- (d)
generating the typical median AFDC of a stream (or a basin) by calculating the median of N AFDCs for each percentile.
In particular, the methodology addresses the analysis of the lower part of the FDC that refers to low flows as hydrological droughts are the motivation for this paper. Therefore, the range of P= 0.30–0.99 of the probability of exceedance is considered. For similar reasons, Fennessey & Vogel (1990), Franchini & Suppo (1996), and Castellarin et al. (2004b) suggested describing the lower part of the FDCs (i.e., P ≥ 0.5 or P ≥ 0.3) for studying hydroelectric engineering, water quality assessment, sedimentation, low-flow analysis, or drought.
ASF-based regionalization
Furthermore, it has been shown that the p-quantiles of the flows are proportional to the drainage area, that is, . If A is not too large, the characteristic power β is often close to 1. It tends theoretically to 1 as the drainage area is less than a few km2.



Parametric approach for modeling streamflow quantiles using regression relationship

Validation



Performance criteria categorizations
Performance . | NSE . | RSR . |
---|---|---|
Very good | 0.75 < NSE ≤ 1.00 | 0.00 ≤ RSR ≤ 0.50 |
Good | 0.65 < NSE ≤ 0.75 | 0.50 < RSR ≤ 0.60 |
Adequate | 0.50 < NSE ≤ 0.65 | 0.60 < RSR ≤ 0.70 |
Inadequate | NSE ≤ 0.50 | RSR > 0.70 |
Performance . | NSE . | RSR . |
---|---|---|
Very good | 0.75 < NSE ≤ 1.00 | 0.00 ≤ RSR ≤ 0.50 |
Good | 0.65 < NSE ≤ 0.75 | 0.50 < RSR ≤ 0.60 |
Adequate | 0.50 < NSE ≤ 0.65 | 0.60 < RSR ≤ 0.70 |
Inadequate | NSE ≤ 0.50 | RSR > 0.70 |
RESULTS AND DISCUSSION
Traditional FDCs and median AFDCs
There is greater variability between the traditional FDCs than the median AFDCs, because median AFDCs are less affected by long dry/wet periods.
Modeling low-flow quantiles
Daily streamflow observations of 30 Western Anatolia basins and 21 Southwestern Anatolia basins, with observation lengths varying between 10 and 54 years, are compiled to prepare FDCs. The low-flow quantiles (Q30, Q40, … ,Q99) of each basin are calculated using the lower part of both traditional and median annual FDCs.
P-values of the variables in multiple linear regression in Western Anatolia for streamflow quantiles calculated from traditional FDCs
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.995 . | R2= 0.993 . | R2= 0.986 . | R2= 0.983 . | R2= 0.976 . | R2= 0.959 . | R2= 0.899 . | R2= 0.863 . | R2= 0.598 . | |
p-values . | |||||||||
A | 1.4 × 10−9 | 6.8 × 10−9 | 6.8 × 10−8 | 1.75 × 10−7 | 4.55 × 10−8 | 1.59 × 10−8 | 1.21 × 10−7 | 6.37 × 10−7 | 3.29 × 10−3 |
Q0 | 2.2 × 10−10 | 1.5 × 10−8 | 2.0 × 10−5 | 4.04 × 10−3 | 0.38 | 0.05 | 3.77 × 10−4 | 4.58 × 10−4 | 0.03 |
MAP | 0.36 | 0.21 | 0.24 | 0.13 | 0.03 | 0.01 | 0.01 | 0.01 | 0.13 |
h | 0.82 | 0.16 | 0.15 | 0.48 | 0.91 | 0.14 | 0.03 | 0.05 | 0.44 |
Lat | 0.34 | 0.35 | 0.34 | 0.21 | 0.07 | 0.03 | 0.03 | 0.02 | 0.02 |
Long | 0.94 | 0.07 | 0.08 | 0.22 | 0.52 | 0.45 | 0.08 | 0.10 | 0.11 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.995 . | R2= 0.993 . | R2= 0.986 . | R2= 0.983 . | R2= 0.976 . | R2= 0.959 . | R2= 0.899 . | R2= 0.863 . | R2= 0.598 . | |
p-values . | |||||||||
A | 1.4 × 10−9 | 6.8 × 10−9 | 6.8 × 10−8 | 1.75 × 10−7 | 4.55 × 10−8 | 1.59 × 10−8 | 1.21 × 10−7 | 6.37 × 10−7 | 3.29 × 10−3 |
Q0 | 2.2 × 10−10 | 1.5 × 10−8 | 2.0 × 10−5 | 4.04 × 10−3 | 0.38 | 0.05 | 3.77 × 10−4 | 4.58 × 10−4 | 0.03 |
MAP | 0.36 | 0.21 | 0.24 | 0.13 | 0.03 | 0.01 | 0.01 | 0.01 | 0.13 |
h | 0.82 | 0.16 | 0.15 | 0.48 | 0.91 | 0.14 | 0.03 | 0.05 | 0.44 |
Lat | 0.34 | 0.35 | 0.34 | 0.21 | 0.07 | 0.03 | 0.03 | 0.02 | 0.02 |
Long | 0.94 | 0.07 | 0.08 | 0.22 | 0.52 | 0.45 | 0.08 | 0.10 | 0.11 |
Significant variables for = 0.05 are in bold.
P-values of the variables in multiple linear regression in Western Anatolia for streamflow quantiles calculated from median AFDCs
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.989 . | R2= 0.995 . | R2= 0.988 . | R2= 0.982 . | R2= 0.980 . | R2= 0.975 . | R2= 0.972 . | R2= 0.968 . | R2= 0.961 . | |
p-values . | |||||||||
A | 3.4 × 10−6 | 7.3 × 10−11 | 1.8 × 10−7 | 1.10 × 10−6 | 9.71 × 10−9 | 1.05 × 10−8 | 5.81 × 10−8 | 1.96 × 10−7 | 6.71 × 10−6 |
Q0 | 8.1 × 10−7 | 3.1 × 10−9 | 2.3 × 10−5 | 7.48 × 10−4 | 0.26 | 0.97 | 0.71 | 0.68 | 0.22 |
MAP | 0.88 | 0.73 | 0.36 | 0.32 | 0.09 | 0.05 | 0.10 | 0.12 | 0.29 |
h | 0.24 | 0.38 | 0.15 | 0.14 | 0.42 | 0.77 | 0.35 | 0.27 | 0.16 |
Lat | 0.63 | 0.11 | 0.38 | 0.39 | 0.10 | 0.05 | 0.06 | 0.03 | 0.08 |
Long | 0.05 | 0.88 | 0.08 | 0.07 | 0.27 | 0.43 | 0.28 | 0.40 | 0.27 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.989 . | R2= 0.995 . | R2= 0.988 . | R2= 0.982 . | R2= 0.980 . | R2= 0.975 . | R2= 0.972 . | R2= 0.968 . | R2= 0.961 . | |
p-values . | |||||||||
A | 3.4 × 10−6 | 7.3 × 10−11 | 1.8 × 10−7 | 1.10 × 10−6 | 9.71 × 10−9 | 1.05 × 10−8 | 5.81 × 10−8 | 1.96 × 10−7 | 6.71 × 10−6 |
Q0 | 8.1 × 10−7 | 3.1 × 10−9 | 2.3 × 10−5 | 7.48 × 10−4 | 0.26 | 0.97 | 0.71 | 0.68 | 0.22 |
MAP | 0.88 | 0.73 | 0.36 | 0.32 | 0.09 | 0.05 | 0.10 | 0.12 | 0.29 |
h | 0.24 | 0.38 | 0.15 | 0.14 | 0.42 | 0.77 | 0.35 | 0.27 | 0.16 |
Lat | 0.63 | 0.11 | 0.38 | 0.39 | 0.10 | 0.05 | 0.06 | 0.03 | 0.08 |
Long | 0.05 | 0.88 | 0.08 | 0.07 | 0.27 | 0.43 | 0.28 | 0.40 | 0.27 |
Significant variables for = 0.05 are in bold.
P-values of the variables in multiple linear regression in Southwestern Anatolia for streamflow quantiles calculated from traditional FDCs
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.994 . | R2= 0.988 . | R2= 0.983 . | R2= 0.979 . | R2= 0.976 . | R2= 0.966 . | R2= 0.634 . | R2= 0.618 . | R2= 0.640 . | |
p-values . | |||||||||
A | 0.05 | 3.8 × 10−3 | 1.8 × 10−3 | 1.06 × 10−3 | 3.97 × 10−4 | 4.87 × 10−4 | 2.45 × 10−2 | 2.61 × 10−2 | 2.47 × 10−2 |
Q0 | 3.7 × 10−5 | 0.04 | 0.35 | 0.82 | 0.60 | 0.29 | 0.09 | 0.09 | 0.09 |
MAP | 0.55 | 0.68 | 0.74 | 0.81 | 0.93 | 0.58 | 0.26 | 0.24 | 0.16 |
h | 0.74 | 0.57 | 0.49 | 0.43 | 0.46 | 0.57 | 0.89 | 0.89 | 0.82 |
Lat | 0.67 | 0.65 | 0.66 | 0.67 | 0.76 | 0.95 | 0.76 | 0.74 | 0.68 |
Long | 0.33 | 0.49 | 0.47 | 0.50 | 0.73 | 0.88 | 0.18 | 0.17 | 0.12 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.994 . | R2= 0.988 . | R2= 0.983 . | R2= 0.979 . | R2= 0.976 . | R2= 0.966 . | R2= 0.634 . | R2= 0.618 . | R2= 0.640 . | |
p-values . | |||||||||
A | 0.05 | 3.8 × 10−3 | 1.8 × 10−3 | 1.06 × 10−3 | 3.97 × 10−4 | 4.87 × 10−4 | 2.45 × 10−2 | 2.61 × 10−2 | 2.47 × 10−2 |
Q0 | 3.7 × 10−5 | 0.04 | 0.35 | 0.82 | 0.60 | 0.29 | 0.09 | 0.09 | 0.09 |
MAP | 0.55 | 0.68 | 0.74 | 0.81 | 0.93 | 0.58 | 0.26 | 0.24 | 0.16 |
h | 0.74 | 0.57 | 0.49 | 0.43 | 0.46 | 0.57 | 0.89 | 0.89 | 0.82 |
Lat | 0.67 | 0.65 | 0.66 | 0.67 | 0.76 | 0.95 | 0.76 | 0.74 | 0.68 |
Long | 0.33 | 0.49 | 0.47 | 0.50 | 0.73 | 0.88 | 0.18 | 0.17 | 0.12 |
Significant variables for = 0.05 are in bold.
P-values of the variables in multiple linear regression in Southwestern Anatolia for streamflow quantiles calculated from median AFDCs
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.992 . | R2= 0.988 . | R2= 0.983 . | R2= 0.979 . | R2= 0.976 . | R2= 0.969 . | R2= 0.972 . | R2= 0.974 . | R2= 0.977 . | |
p-values . | |||||||||
A | 0.03 | 0.01 | 3.7 × 10−3 | 1.37 × 10−3 | 4.14 × 10−4 | 5.01 × 10−4 | 3.06 × 10−4 | 3.33 × 10−4 | 6.74 × 10−4 |
Q0 | 3.0 × 10−5 | 0.01 | 0.18 | 0.77 | 0.57 | 0.35 | 0.31 | 0.38 | 0.79 |
MAP | 0.59 | 0.65 | 0.52 | 0.67 | 0.82 | 0.91 | 0.95 | 0.92 | 0.57 |
h | 0.65 | 0.42 | 0.43 | 0.43 | 0.48 | 0.53 | 0.54 | 0.56 | 0.51 |
Lat | 0.48 | 0.48 | 0.49 | 0.63 | 0.66 | 0.76 | 0.72 | 0.68 | 0.54 |
Long | 0.44 | 0.47 | 0.33 | 0.41 | 0.53 | 0.82 | 0.69 | 0.52 | 0.20 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.992 . | R2= 0.988 . | R2= 0.983 . | R2= 0.979 . | R2= 0.976 . | R2= 0.969 . | R2= 0.972 . | R2= 0.974 . | R2= 0.977 . | |
p-values . | |||||||||
A | 0.03 | 0.01 | 3.7 × 10−3 | 1.37 × 10−3 | 4.14 × 10−4 | 5.01 × 10−4 | 3.06 × 10−4 | 3.33 × 10−4 | 6.74 × 10−4 |
Q0 | 3.0 × 10−5 | 0.01 | 0.18 | 0.77 | 0.57 | 0.35 | 0.31 | 0.38 | 0.79 |
MAP | 0.59 | 0.65 | 0.52 | 0.67 | 0.82 | 0.91 | 0.95 | 0.92 | 0.57 |
h | 0.65 | 0.42 | 0.43 | 0.43 | 0.48 | 0.53 | 0.54 | 0.56 | 0.51 |
Lat | 0.48 | 0.48 | 0.49 | 0.63 | 0.66 | 0.76 | 0.72 | 0.68 | 0.54 |
Long | 0.44 | 0.47 | 0.33 | 0.41 | 0.53 | 0.82 | 0.69 | 0.52 | 0.20 |
Significant variables for = 0.05 are in bold.
When Tables 4–7 are examined, it is noteworthy that most of the stream flow quantiles were successfully described by multiple linear regression relationships for both regions. In Western Anatolia, the determination coefficients (R2) of the multiple linear regression for the flow quantities Q90, Q95, and Q99 calculated from the traditional FDC were 0.899, 0.863, and 0.598, while the coefficients of determination calculated for the quantiles obtained from the median AFDC were 0.972, 0.968, and 0.961, respectively. Similarly, the determination coefficients of the multiple linear regression for the streamflow quantiles Q90, Q95, and Q99 calculated from the traditional FDC in Southwestern Anatolia were 0.634, 0.618, and 0.640, while the coefficients of determination calculated from quantiles obtained from the median AFDC were 0.972, 0.974, and 0.977, respectively. It is noteworthy that the streamflow quantiles obtained from median AFDCs have stronger regression relationships than the quantiles obtained from FDCs, especially for the quantiles of higher probabilities (P > 80%). Only one (A, basin area) of the six basin characteristics has a significant effect on the regression relationship for each of the nine quantiles. This result raises the question of whether streamflow quantiles can be determined solely in terms of basin area.
Areal scale factor
To answer the question ‘Can streamflow quantiles be determined solely in terms of basin area?’ the relationship between streamflow quantiles QP and basin area A is examined.
As explained in Subsection 2.2.2, s defining the relationship between flow quantiles and basin areas were calculated for corresponding probabilities P (0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, and 0.99) using Equation (4). The
s of each quantile and the results of the regression are given in Tables 8–11 in Western Anatolia and Southwestern Anatolia for streamflow quantiles calculated from traditional FDCs and median AFDCs.
and P-values of regression relationship for streamflow quantiles calculated from traditional FDCs in Western Anatolia
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.971 . | R2= 0.974 . | R2= 0.975 . | R2= 0.975 . | R2= 0.973 . | R2= 0.945 . | R2= 0.801 . | R2= 0.734 . | R2= 0.358 . | |
P-values | 7.35 × 10–24 | 1.84 × 10–24 | 7.07 × 10–25 | 8.48 × 10–25 | 2.62 × 10–24 | 7.90 × 10–20 | 1.08 × 10–11 | 7.65 × 10–10 | 3.78 × 10–4 |
ASFP | 0.00225 | 0.00178 | 0.00148 | 0.00122 | 0.00100 | 0.00074 | 0.00043 | 0.00028 | 0.00007 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.971 . | R2= 0.974 . | R2= 0.975 . | R2= 0.975 . | R2= 0.973 . | R2= 0.945 . | R2= 0.801 . | R2= 0.734 . | R2= 0.358 . | |
P-values | 7.35 × 10–24 | 1.84 × 10–24 | 7.07 × 10–25 | 8.48 × 10–25 | 2.62 × 10–24 | 7.90 × 10–20 | 1.08 × 10–11 | 7.65 × 10–10 | 3.78 × 10–4 |
ASFP | 0.00225 | 0.00178 | 0.00148 | 0.00122 | 0.00100 | 0.00074 | 0.00043 | 0.00028 | 0.00007 |
and P-values of regression relationship for streamflow quantiles calculated from median AFDCs in Western Anatolia
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.960 . | R2= 0.977 . | R2= 0.974 . | R2= 0.970 . | R2= 0.979 . | R2= 0.972 . | R2= 0.969 . | R2= 0.965 . | R2= 0.956 . | |
P-values | 7.12 × 10–22 | 2.97 × 10–25 | 1.81 × 10–24 | 1.44 × 10–23 | 8.86 × 10–26 | 3.76 × 10–24 | 2.06 × 10–23 | 9.65 × 10–23 | 2.89 × 10–21 |
![]() | 0.00219 | 0.00172 | 0.00152 | 0.00134 | 0.00114 | 0.00095 | 0.00078 | 0.00060 | 0.00054 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.960 . | R2= 0.977 . | R2= 0.974 . | R2= 0.970 . | R2= 0.979 . | R2= 0.972 . | R2= 0.969 . | R2= 0.965 . | R2= 0.956 . | |
P-values | 7.12 × 10–22 | 2.97 × 10–25 | 1.81 × 10–24 | 1.44 × 10–23 | 8.86 × 10–26 | 3.76 × 10–24 | 2.06 × 10–23 | 9.65 × 10–23 | 2.89 × 10–21 |
![]() | 0.00219 | 0.00172 | 0.00152 | 0.00134 | 0.00114 | 0.00095 | 0.00078 | 0.00060 | 0.00054 |
and P-values of regression relationship for streamflow quantiles calculated from traditional FDCs in Southwestern Anatolia
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.979 . | R2= 0.984 . | R2= 0.989 . | R2= 0.985 . | R2= 0.983 . | R2= 0.976 . | R2= 0.688 . | R2= 0.658 . | R2= 0.645 . | |
P-values | 2.40 × 10–18 | 1.64 × 10–19 | 3.67 × 10–18 | 7.15 × 10–17 | 3.73 × 10–16 | 1.10 × 10–14 | 4.07 × 10–4 | 8.76 × 10–4 | 1.18 × 10–3 |
![]() | 0.01182 | 0.01004 | 0.00881 | 0.00756 | 0.00639 | 0.00518 | 0.00214 | 0.00154 | 0.00098 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.979 . | R2= 0.984 . | R2= 0.989 . | R2= 0.985 . | R2= 0.983 . | R2= 0.976 . | R2= 0.688 . | R2= 0.658 . | R2= 0.645 . | |
P-values | 2.40 × 10–18 | 1.64 × 10–19 | 3.67 × 10–18 | 7.15 × 10–17 | 3.73 × 10–16 | 1.10 × 10–14 | 4.07 × 10–4 | 8.76 × 10–4 | 1.18 × 10–3 |
![]() | 0.01182 | 0.01004 | 0.00881 | 0.00756 | 0.00639 | 0.00518 | 0.00214 | 0.00154 | 0.00098 |
and P-values of regression relationship for streamflow quantiles calculated from median AFDCs in Southwestern Anatolia
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.972 . | R2= 0.980 . | R2= 0.976 . | R2= 0.970 . | R2= 0.965 . | R2= 0.957 . | R2= 0.955 . | R2= 0.954 . | R2= 0.953 . | |
P-values | 4.71 × 10–17 | 1.46 × 10–18 | 1.02 × 10–17 | 9.51 × 10–17 | 5.03 × 10–16 | 3.65 × 10–15 | 6.38 × 10–15 | 7.17 × 10–15 | 8.98 × 10–15 |
![]() | 0.01156 | 0.01010 | 0.00894 | 0.00780 | 0.00667 | 0.00568 | 0.00510 | 0.00482 | 0.00425 |
. | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|
R2= 0.972 . | R2= 0.980 . | R2= 0.976 . | R2= 0.970 . | R2= 0.965 . | R2= 0.957 . | R2= 0.955 . | R2= 0.954 . | R2= 0.953 . | |
P-values | 4.71 × 10–17 | 1.46 × 10–18 | 1.02 × 10–17 | 9.51 × 10–17 | 5.03 × 10–16 | 3.65 × 10–15 | 6.38 × 10–15 | 7.17 × 10–15 | 8.98 × 10–15 |
![]() | 0.01156 | 0.01010 | 0.00894 | 0.00780 | 0.00667 | 0.00568 | 0.00510 | 0.00482 | 0.00425 |
(a) The traditional FDC and (b) the median AFDC of Esen Creek at Kinik station.
In Figure 4(a), a sudden jump is observed in the low-flow region corresponding to high probabilities of traditional FDC. This is caused by the long dry periods and/or zero flows in the observation series. On the other hand, the shape of AFDC in Figure 4(b) indicates a relatively stable slope. This confirms the regression results in Tables 8–11 and makes the median AFDC more reliable against the traditional FDC.
It is also observed that ASFs are at higher levels in Southwestern Anatolia than in Western Anatolia. This is caused by the fact that basin yield in Southwestern Anatolia is on average twice as large as in Western Anatolia (Tables 1 and 2), which is due to the contribution of groundwater to the streams in the karstic region. The reason why the significance of ASFs in Western Anatolia is higher than the significance of ASFs in Southwestern Anatolia is that ‘the flow quantile-basin area’ relationship can be constructed more successfully in the region where there is no groundwater effect.
Validation
To test the significance of the proposed model, 10 of the 30 basins in Western Anatolia and seven of the 21 basins in Southwestern Anatolia are initially retained for validation. In Tables 1 and 2, these stations are in bold. The success of the developed model is tested for 10 validation basins in Western Anatolia and seven validation basins in Southwestern Anatolia for streamflow quantiles estimated using traditional FDCs and median AFDCs. Tables 12 and 13 show the validation results of the proposed model. NSE and RSR values indicating the success of the model performance as ‘very good’ are given in bold.
Model performance criteria of streamflow quantiles calculated from traditional FDCs and median AFDCs in Western Anatolia
. | . | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|---|
Traditional FDC | NSE | 0.974 | 0.978 | 0.975 | 0.968 | 0.966 | 0.938 | 0.503 | 0.187 | 0.119 |
RSR | 0.161 | 0.148 | 0.159 | 0.180 | 0.184 | 0.249 | 0.705 | 0.902 | 0.960 | |
MPD (%) | 8 | 7 | 6 | 6 | 6 | 8 | 15 | 18 | 22 | |
Median AFDC | NSE | 0.952 | 0.977 | 0.975 | 0.964 | 0.967 | 0.963 | 0.959 | 0.961 | 0.951 |
RSR | 0.220 | 0.151 | 0.157 | 0.189 | 0.183 | 0.193 | 0.204 | 0.197 | 0.221 | |
MPD (%) | 9 | 8 | 7 | 6 | 6 | 8 | 9 | 9 | 10 |
. | . | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|---|
Traditional FDC | NSE | 0.974 | 0.978 | 0.975 | 0.968 | 0.966 | 0.938 | 0.503 | 0.187 | 0.119 |
RSR | 0.161 | 0.148 | 0.159 | 0.180 | 0.184 | 0.249 | 0.705 | 0.902 | 0.960 | |
MPD (%) | 8 | 7 | 6 | 6 | 6 | 8 | 15 | 18 | 22 | |
Median AFDC | NSE | 0.952 | 0.977 | 0.975 | 0.964 | 0.967 | 0.963 | 0.959 | 0.961 | 0.951 |
RSR | 0.220 | 0.151 | 0.157 | 0.189 | 0.183 | 0.193 | 0.204 | 0.197 | 0.221 | |
MPD (%) | 9 | 8 | 7 | 6 | 6 | 8 | 9 | 9 | 10 |
Model performance criteria of streamflow quantiles calculated from traditional FDCs and median AFDCs in Southwestern Anatolia
. | . | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|---|
Traditional FDC | NSE | 0.951 | 0.987 | 0.985 | 0.975 | 0.963 | 0.939 | 0.555 | 0.529 | 0.527 |
RSR | 0.220 | 0.115 | 0.123 | 0.158 | 0.193 | 0.247 | 0.667 | 0.686 | 0.688 | |
MPD (%) | 6 | 6 | 8 | 9 | 11 | 12 | 15 | 16 | 20 | |
Median AFDC | NSE | 0.917 | 0.974 | 0.977 | 0.974 | 0.961 | 0.947 | 0.946 | 0.949 | 0.951 |
RSR | 0.289 | 0.163 | 0.152 | 0.162 | 0.197 | 0.230 | 0.232 | 0.226 | 0.222 | |
MPD (%) | 8 | 8 | 9 | 9 | 10 | 11 | 11 | 11 | 10 |
. | . | Q30 . | Q40 . | Q50 . | Q60 . | Q70 . | Q80 . | Q90 . | Q95 . | Q99 . |
---|---|---|---|---|---|---|---|---|---|---|
Traditional FDC | NSE | 0.951 | 0.987 | 0.985 | 0.975 | 0.963 | 0.939 | 0.555 | 0.529 | 0.527 |
RSR | 0.220 | 0.115 | 0.123 | 0.158 | 0.193 | 0.247 | 0.667 | 0.686 | 0.688 | |
MPD (%) | 6 | 6 | 8 | 9 | 11 | 12 | 15 | 16 | 20 | |
Median AFDC | NSE | 0.917 | 0.974 | 0.977 | 0.974 | 0.961 | 0.947 | 0.946 | 0.949 | 0.951 |
RSR | 0.289 | 0.163 | 0.152 | 0.162 | 0.197 | 0.230 | 0.232 | 0.226 | 0.222 | |
MPD (%) | 8 | 8 | 9 | 9 | 10 | 11 | 11 | 11 | 10 |
The observed low-flow quantiles and the low-flow quantile estimates of the parametric model are compared for the validation basins. Validation results show that the estimates of median AFDCs performed ‘very good’ for all streamflow quantiles, but quantiles obtained from traditional FDCs led to ‘inadequate’ model performance for high probabilities (P > 0.8). The validation results confirm the conclusion that ‘median AFDCs are more stable than traditional FDCs especially for intermittent streams’ as explained in the previous section.
In addition, MPDs between the observed low-flow quantiles and the low-flow quantile estimates of the parametric model are calculated. While the percentage differences of median AFDC model predictions generally are less than 10%, model predictions of traditional FDCs showed percentage differences of 15% and above, especially for higher probabilities (P > 0.8).
Regionalization of ASFs
Regional curve of ASFs related to the exceedance probabilities in Western Anatolia.
Regional curve of ASFs related to the exceedance probabilities in Western Anatolia.
Regional curve of ASFs related to the exceedance probabilities in Southwestern Anatolia.
Regional curve of ASFs related to the exceedance probabilities in Southwestern Anatolia.
CONCLUSION
The main purpose of this paper is to reveal the regional relationships that enable effective estimations of low-flow quantiles. While most parametric approaches in the literature involve the regionalization of the parameters that define the FDCs, this study deals with the regional modeling of the streamflow quantiles. Most previous studies on the estimation of streamflow quantiles used traditional FDCs, which are undesirably affected by long dry periods or zero flows causing negative jumps on the FDC (Figure 4(a) and 4(b)).
This study proposes to use median AFDCs in addition to the classical FDC curves encountered in the literature for modeling streamflow quantiles. The performance of the proposed model is compared for two different types of FDCs in two different regions in Turkey. As the study takes low flows into account, streamflow estimations are made for nine fixed percentage points (30, 40, 50, 60, 70, 80, 90, 95, and 99%) of FDCs and median AFDCs. The relationship between low-flow quantiles and the basin characteristics is examined. Among the basin characteristics, the most significant contribution to the statistical definition of flow quantiles was determined to be the basin area, A. This result, as expected, confirms the relationship described in Section 2.2.2. A strong linear relationship was determined between the low-flow quantiles estimated from median AFDCs and the basin area for all fixed percentage points.
Based on the strong relationship between low-flow quantiles and the basin area, ASFs explaining this relationship were obtained. In addition, regional curves have been generated that effectively represent the relationship between ASFs and the exceedance probabilities for both study regions.
Although the two regions in the study have similar meteorological characteristics, they are of completely different types geologically. Two different regions with dissimilar geological structure, drainage mechanism, and low-flow characteristics are selected. Thus, the proposed parametric model is tested in terms of adapting to different geohydrological conditions.
The main results of our paper can be summarized as follows:
- 1.
The relationship between the low-flow quantiles and the hydrological and geographical characteristics of the basins is examined, and it was demonstrated that the low-flow quantiles are successfully represented depending on the basin area.
- 2.
As a novelty of the study, ASF ratios that describe low-flow quantiles related to the basin area are proposed.
- 3.
It has been expressed for both study regions that median AFDCs successfully represent streamflow quantiles for all percentage points compared to traditional FDCs.
- 4.
Regional curves describing the relationship between ASFs and exceedance probabilities allow efficient estimations of ASFs.
- 5.
The low-flow quantile, which is a crucial design criterion for a water resources project, can be estimated simply and practically depending on project basin area A, when the ASF curve is determined for a region.
Thus, the successful representation of the model for these two geologically different regions is promising in terms of the robustness of the model and its use in future studies. However, further examination in different geographical areas of dissimilar meteorological characteristics is needed to generalize the results of the study. Another limitation of the study is that basin characteristics such as evapotranspiration, vegetation cover, and soil type are not included in the model.
The ability to estimate low-flow quantities in a practical way, depending only on the basin area, emerges as important information in many topics of hydrology, such as the design of hydroelectric power plants, calculations of irrigation projects, studies on river pollution, and management of water resources.
ACKNOWLEDGEMENTS
The authors are grateful to the Editor in chief and four anonymous reviewers for their valuable comments and suggestions, and to Prof. Dr. E. Benzeden for support in the revision process.
AUTHOR CONTRIBUTIONS
Both authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by TN and OLA. The first draft of the manuscript was written by OLA, and both authors commented on the manuscript. Both authors reviewed the results and approved the final version of the manuscript.
FUNDING
The authors declare that no fund, grants, or other support were received during the preparation of this manuscript.
DATA AVAILABILITY STATEMENT
All relevant data are available from an online repository or repositories: https://www.dsi.gov.tr/Sayfa/Detay/744.
CONFLICT OF INTEREST
The authors declare there is no conflict.