# Hydrogeological Parameter Determination in the Southern Catchments of Taiwan by Flow Recession Method

^{*}

## Abstract

**:**

_{y}), and transmissivity (T). Based on the field test reports of the locations of groundwater observational wells on the Chianan and Pingtung plains, the study area was divided into the Chianan sub-area (Zengwun, Yanshui, and Erren river basins) and the Kaoping sub-area (Kaoping, Donggang, and Linbian river basins). The estimation results of the present study were compared to the field test results. The results showed significant differences in the recession index K between the dry and wet seasons. Slight differences between the estimated hydrogeological parameters and the field test results were also observed for the two sub-areas because of differences in scale. Furthermore, regional differences in the estimation results were found to be consistent with the distribution of geological structures, which indicates a high degree of feasibility in the application of flow recession methods for catchment-scale hydrogeological parameter determination.

## 1. Introduction

## 2. Study Area

^{2}, accounting for approximately 28% of the total area of Taiwan. Because of its tropical monsoonal climate, terrain, and geographical location, the rainy season is influenced by southwestern monsoons and typhoons from May to October. The dry season is influenced by northeastern monsoons from November to April and the leeward side causes less rainfall in this region [26]. The main rivers in the study area are the Bazhang, Zengwun, Yanshui, Erren, Kaoping, Donggang, and Linbian. In the present study, streamflow data from nine gauge stations in the catchments of Southern Taiwan were classified into dry season (November–April) and wet season (May–October) for the estimation of the respective catchment discharge characteristics and hydrogeological parameters during the dry and wet seasons. Table 1 shows information on the gauge stations in the catchments of Southern Taiwan.

## 3. Methodology

#### 3.1. Low-Flow Recession Analysis Method

_{0}was used as the dimensionless discharge in the integration of Equation (1), the obtained recession index was highly correlated with 1/a. Therefore, in many subsequent studies, the recession index K has been applied in the explanation of nonlinear recession behavior. In the present study, the recession index was also investigated.

_{y}is the specific yield (-), k is the hydraulic conductivity (L/T), D is the saturated aquifer depth (L), A is the catchment area (L

^{2}), and B is the distance between the stream and the watershed (L) (B = A/2L, where L is the length of the main stream). However, it is difficult to clearly determine the actual location of the transitional point in the plot of dQ/dt vs. Q. Therefore, in this study, strategies proposed by Mendoza et al. [14] were adopted to locate three possible transition points to determine the range of values of the hydrogeological parameters in the catchment instead of using single values as representations of the respective characteristics. The placement strategies used to identify the transitional points are as follows:

- (1)
- First transition point: The intersection of the lower envelope lines of the short-term flow regime (b = 3) and long-term flow regime (b = 1.5) were defined through the application of the methodology proposed by Brutsaert and Nieber [12]. The envelope lines were placed such that 10% of the data points lay below the lines to reduce the influence of evapotranspiration.
- (2)
- Second transition point: The intersection of the linear regression line on the plot of dQ/dt vs. Q and the lower envelope for b = 3.
- (3)
- Third transition point: The intersection of the upper envelope for b = 1 and the highest log (Q) value among the data points.

#### 3.2. Selection Criteria for Recession Flow Data

- (1)
- Eliminate all data points with positive and zero values of dQ/dt.
- (2)
- Eliminate two data points before dQ/dt becomes positive or zero, and three data points after the last positive and zero dQ/dt.
- (3)
- Eliminate four data points after major events, with major events defined based on the discharge duration curve [36].
- (4)
- Eliminate anomalous points in the data series.
- (5)
- Eliminate data points corresponding to days with daily rainfall >0 and several days after rainfall.

#### 3.3. Recession-Curve-Displacement Method

^{2}) at a given time t, as shown in the following expansion formula:

^{2}/T), h

_{0}is the instantaneous groundwater level rise (L), B is the distance between the stream and the watershed (L), and S is the storage coefficient (-). Assuming that small recharges can be neglected, Equation (3) can be simplified as follows:

^{3}/T) can be determined from the product of the groundwater discharge q on both sides of the stream and the length of the main stream L (L) ($\mathrm{L}=\mathrm{A}/2\mathrm{B}$, where A is the catchment area), as follows:

_{t}is the peak flow of the recharge event and Q

_{0}is the flow at the start of the recharge event.

_{2}is the theoretical groundwater discharge at a critical time T

_{c}after the peak value of the recharge event, which is extrapolated from the post-event streamflow recession (L

^{3}/T); Q

_{1}is the theoretical groundwater discharge at T

_{c}extrapolated from the streamflow recession of the previous event (L

^{3}/T); K is the recession index of each log cycle (T) (also the characteristic drainage timescale); and T

_{c}is the time from the peak to the end of infiltration recharge (i.e., linear recession) (T). Rorabaugh and Simons [38] defined the relationship between T

_{c}and K as T

_{c}= 0.2144K. From Equations (5) and (6), the formula for the estimated transmissivity of T can be obtained as follows:

_{0}, Q

_{1}, Q

_{2}, and Q

_{t}in Equation (9) (refer to Figure 3). After obtaining the estimated transmissivity from further calculations, the transmissivity was directly proportional to the product of the hydraulic conductivity and the aquifer depth was used in combination with the equations for hydrogeological parameter estimation (Equation (2)) in the low-flow recession analysis method. This formed three equations with three unknowns, which could then be directly solved for the estimation of catchment-scale hydrogeological parameters.

## 4. Results and Discussion

#### 4.1. Low-Flow Recession Analysis

#### 4.2. Estimation of Hydrogeological Parameters

_{y}, and hydraulic conductivity k, and the recession-curve-displacement method, which was used to estimate the transmissivity T. Based on the fact that transmissivity is directly proportional to the product of hydraulic conductivity and effective aquifer depth, direct calculations could be performed to obtain estimates of transmissivity, hydraulic conductivity, and specific yield. This approach effectively eliminated the subjectivity involved in the determination of the proportionality constant for the initial estimation of effective aquifer depth. To evaluate hydrogeological parameters, the three transition points were determined by a regression line and envelopes in the graph of Q vs. –dQ/dt to calculate the placement with the dimensionless transition points. Figure 4 and Figure 5 show the transition points of dry and wet seasons determined by the low-flow recession method in each catchment. Lastly, the estimation results were compared to those of field tests.

## 5. Conclusions

_{y}for the dry and wet seasons were compared to the results of field tests. The comparison results indicated small differences between the estimation results for the dry and wet seasons as well as slight differences in the local-scale and catchment-scale hydrogeological parameters. The graphs of hydraulic conductivity vs. specific yield showed significant regional differences and consistency with the distribution of geological structures. They demonstrated the applicability and representativeness of the low-flow recession analysis method in the estimation of hydrogeological parameters. The present study differs from costly field tests, which merely produce local-scale results for the estimation of hydrogeological parameters, because hydrological data that could be readily acquired and were representative of catchment discharge behavior were used. A combination of two flow recession analysis methods was employed to eliminate subjectivity in the initial estimation of one parameter, a problem that has frequently been encountered in previous studies. The estimated catchment-scale hydrogeological parameters demonstrated that flow recession analysis can provide a rapid, low-cost, and effective means of estimating hydrogeological parameters, which can facilitate the construction of future hydrological models and a better understanding of the role of groundwater in various catchments or basins of Taiwan in the hydrological cycle. They can also serve as a reference for decisions regarding groundwater resource management under conditions of climate change.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Alley, W.; Healy, R.; LaBaugh, J.; Reilly, T. Hydrology—Flow and storage in groundwater systems. Science
**2002**, 296, 1985–1990. [Google Scholar] [CrossRef] [PubMed] - Xu, C.Y.; Singh, V.P. Review on regional water resources assessment models under stationary and changing climate. Water Resour. Manag.
**2004**, 18, 591–612. [Google Scholar] [CrossRef] - Conama, D. Estudio de la Variabilidad Climática en Chile Para el Siglo XXI; Departamento de Geofısica, Universidad de Chile: Santiago, Chile, 2006. [Google Scholar]
- Berghuijs, W.R.; Hartmann, A.; Woods, R.A. Streamflow sensitivity to water storage changes across Europe. Geophys. Res. Lett.
**2016**, 43, 1980–1987. [Google Scholar] [CrossRef] - Staudinger, M.; Stoelzle, M.; Seeger, S.; Seibert, J.; Weiler, M.; Stahl, K. Catchment water storage variation with elevation. Hydrol. Process.
**2017**, 31, 2000–2015. [Google Scholar] [CrossRef] - Lin, K.T.; Yeh, H.F. Baseflow recession characterization and groundwater storage trends in northern Taiwan. Hydrol. Res.
**2017**. [Google Scholar] [CrossRef] - Oyarzún, R.; Godoy, R.; Núñez, J.; Fairley, J.P.; Oyarzún, J.; Maturana, H.; Freixas, G. Recession flow analysis as a suitable tool for hydrogeological parameter determination in steep, arid basins. J. Arid Environ.
**2014**, 105, 1–11. [Google Scholar] [CrossRef] - Vannier, O.; Braud, I.; Anquetin, S. Regional estimation of catchment—Scale soil properties by means of streamflow recession analysis for use in distributed hydrological models. Hydrol. Process.
**2014**, 28, 6276–6291. [Google Scholar] [CrossRef] - Arumí, J.L.; Maureira, H.; Souvignet, M.; Pérez, C.; Rivera, D.; Oyarzún, R. Where does the water go? Understanding geohydrological behaviour of Andean catchments in south-central Chile. Hydrol. Sci. J.
**2016**, 61, 844–855. [Google Scholar] [CrossRef] - Senkondo, W.; Tuwa, J.; Koutsouris, A.; Lyon, S.W. Estimating Aquifer Transmissivity Using the Recession-Curve-Displacement Method in Tanzania’s Kilombero Valley. Water
**2017**, 9, 948. [Google Scholar] [CrossRef] - Smakhtin, V.U. Low flow hydrology: A review. J. Hydrol.
**2001**, 240, 147–186. [Google Scholar] [CrossRef] - Brutsaert, W.; Nieber, J.L. Regionalized drought flow hydrographs from a mature glaciated plateau. Water Resour. Res.
**1977**, 13, 637–643. [Google Scholar] [CrossRef] - Roques, C.; Rupp, D.E.; Selker, J.S. Improved streamflow recession parameter estimation with attention to calculation of −dQ/dt. Adv. Water Resour.
**2017**, 108, 29–43. [Google Scholar] [CrossRef] - Mendoza, G.F.; Steenhuis, T.S.; Walter, M.T.; Parlange, J.Y. Estimating basin-wide hydraulic parameters of a semi-arid mountainous watershed by recession-flow analysis. J. Hydrol.
**2003**, 279, 57–69. [Google Scholar] [CrossRef] - Dewandel, B.; Lachassagne, P.; Bakalowicz, M.; Weng, P.H.; Al-Malki, A. Evaluation of aquifer thickness by analysing recession hydrographs. Application to the Oman ophiolite hard-rock aquifer. J. Hydrol.
**2003**, 274, 248–269. [Google Scholar] [CrossRef] - Brutsaert, W. Long-term groundwater storage trends estimated from streamflow records: Climatic perspective. Water Resour. Res.
**2008**, 44, W02409. [Google Scholar] [CrossRef] - Sawaske, S.R.; Freyberg, D.L. An analysis of trends in baseflow recession and low-flows in rain-dominated coastal streams of the pacific coast. J. Hydrol.
**2014**, 519, 599–610. [Google Scholar] [CrossRef] - Stoelzle, M.; Stahl, K.; Weiler, M. As simple as possible? Drought recognition based on streamflow recession. In Proceedings of the 10th International Conference on Hydroinformatics, Hamburg, Germany, 14–18 July 2012; pp. 1–8. [Google Scholar]
- Stoelzle, M.; Stahl, K.; Morhard, A.; Weiler, M. Streamflow sensitivity to drought scenarios in catchments with different geology. Geophys. Res. Lett.
**2014**, 41, 6174–6183. [Google Scholar] [CrossRef] [Green Version] - Van Dijk, A.I.J.M. Climate and terrain factors explaining streamflow response and recession in Australian catchments. Hydrol. Earth Syst. Sci.
**2010**, 14, 159–169. [Google Scholar] [CrossRef] - Beck, H.E.; Dijk, A.I.; Miralles, D.G.; Jeu, R.A.; McVicar, T.R.; Schellekens, J. Global patterns in base flow index and recession based on streamflow observations from 3394 catchments. Water Resour. Res.
**2013**, 49, 7843–7863. [Google Scholar] [CrossRef] [Green Version] - Rorabough, M.I. Estimating changes in bank storage and grounwater contribution to streamflow. Int. Assoc. Sci. Hydrol. Publ.
**1964**, 63, 432–441. [Google Scholar] - Abo, R.K.; Merkel, B.J. Investigation of the potential surface–groundwater relationship using automated base-flow separation techniques and recession curve analysis in Al Zerba region of Aleppo, Syria. Arab. J. Geosci.
**2015**, 8, 10543–10563. [Google Scholar] [CrossRef] - Rutledge, A.T. Computer Programs for Describing the Recession of Ground-Water Discharge and for Estimating mean Ground-Water Recharge and Discharge from Streamflow Record; U.S. Geological Survey, U.S.G.S. Earth Science Information Center, Open-File Reports Section: Reston, VA, USA, 1993.
- Zhang, L.; Brutsaert, W.; Crosbie, R.; Potter, N. Long-term annual groundwater storage trends in Australian catchments. Adv. Water Resour.
**2014**, 74, 156–165. [Google Scholar] [CrossRef] - Water Resources Agency. Hydrological Year Book; Water Resources Agency: Taipei, Taiwan, 2017. (In Chinese) [Google Scholar]
- Water Resources Agency. The Third Stage Management Project of Climate Change Impacts and Adaptation on Water Environment (3/5); Water Resources Agency: Taipei, Taiwan, 2016. (In Chinese) [Google Scholar]
- Water Resources Agency. Assessment of Groundwater Potential Exploiting Zones and Groundwater Yields in Kaoping and Chianan Watersheds (2/2); Water Resources Agency: Taipei, Taiwan, 2017. (In Chinese) [Google Scholar]
- Central Geological Survey. Hydrogeology Investigation and Groundwater Resource Assessment for Taiwan-Groundwater Recharge Estimation amd Model Simulation Pingtung Plain; Central Geological Survey: Taipei, Taiwan, 2012. (In Chinese) [Google Scholar]
- Boussinesq, J. Essai sur la théorie des eaux courantes. Imprimerie Nationale: Paris, France, 1877.
- Bogaart, P.W.; Van Der Velde, Y.; Lyon, S.W.; Dekker, S.C. Streamflow recession patterns can help unravel the role of climate and humans in landscape co-evolution. Hydrol. Earth Syst. Sci.
**2016**, 20, 1413–1432. [Google Scholar] [CrossRef] [Green Version] - Rupp, D.E.; Selker, J.S. On the use of the Boussinesq equation for interpreting recession hydrographs from sloping aquifers. Water Resour. Res.
**2006**, 42, W12421. [Google Scholar] [CrossRef] - Zhang, L.; Chen, Y.D.; Hickel, K.; Shao, Q. Analysis of low-flow characteristics for catchments in Dongjiang Basin, China. Hydrogeol. J.
**2009**, 17, 631–640. [Google Scholar] [CrossRef] - Szilagyi, J. Vadose zone influences on aquifer parameter estimates of saturated-zone hydraulic theory. J. Hydrol.
**2004**, 286, 78–86. [Google Scholar] [CrossRef] [Green Version] - Parlange, J.Y.; Stagnitti, F.; Heilig, A.; Szilagyi, J.; Parlange, M.B.; Steenhuis, T.S.; Hogarth, W.L.; Barry, D.A.; Li, L. Sudden drawdown and drainage of a horizontal aquifer. Water Resour. Res.
**2001**, 37, 2097–2101. [Google Scholar] [CrossRef] [Green Version] - Kingsford, R.T.; Thomas, R.F. Environmental Flows on the Paroo and Warrego Rivers; National Parks & Wildlife Service: New South Wales, Australia, 2000. [Google Scholar]
- Troch, P.A.; Mancini, M.; Paniconi, C.; Wood, E.F. Evaluation of a distributed catchment scale water balance model. Water Resour. Res.
**1993**, 29, 1805–1817. [Google Scholar] [CrossRef] [Green Version] - Rorabaugh, M.I.; Simons, W.D. Exploration of Methods of Relating Ground Water to Surface Water, Columbia River Basin-Second Phase: U.S. Geol. Survey (USGS) Open-File Report; US Geological Survey: Reston, VA, USA, 1966. [Google Scholar]
- Bevans, H.E. Estimating Stream-Aquifer Interactions in Coal Areas of Eastern Kansas by Using Streamflow Records; US Geological Survey Water Supply Paper; US Geological Survey: Reston, VA, USA, 1986; pp. 51–64.
- Barnes, B.S. The structure of discharge-recession curves. Eos Trans. Am. Geophys. Union
**1939**, 20, 721–725. [Google Scholar] [CrossRef] - Anderson, M.G.; Burt, T.P. Interpretation of recession flow. J. Hydrol.
**1980**, 46, 89–101. [Google Scholar] [CrossRef] - Lyon, S.W.; Koutsouris, A.; Scheibler, F.; Jarsjö, J.; Mbanguka, R.; Tumbo, M.; Robert, K.K.; Sharma, A.N.; van der Velde, Y. Interpreting characteristic drainage timescale variability across Kilombero Valley, Tanzania. Hydrol. Process.
**2015**, 29, 1912–1924. [Google Scholar] [CrossRef] - Shaw, S.B.; McHardy, T.M.; Riha, S.J. Evaluating the influence of watershed moisture storage on variations in base flow recession rates during prolonged rain-free periods in medium-sized catchments in New York and Illinois, USA. Water Resour. Res.
**2013**, 49, 6022–6028. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Spatial distribution of gauge stations and geological map of Southern Taiwan. C—Chianan sub-area; K—Kaoping sub-area.

**Figure 2.**The dimensionless recession curve and dimensionless transition point are translated to the recession curve and transition point with data. Horizontal placement (H) and vertical placement (V) are also identified above.

**Figure 3.**A schematic diagram of the displacement-curve-displacement method with the definition of (

**a**) Q

_{0}, Q

_{t}, Q

_{1}, and Q

_{2}and (

**b**) h

_{0}(h

_{i}and h

_{p}are the streamflow water level corresponding to Q

_{0}and Q

_{t}respectively).

**Figure 4.**The relationship between Q and –dQ/dt for each catchment in dry seasons. Three transition points are indicated with the regression line and envelopes and showed as circles with number. (

**a**) Chu-Kou, (

**b**) Chang-Pan Bridge, (

**c**) Tso-Chen, (

**d**) Hsin-Shih, (

**e**) Chung-Te Bridge, (

**f**) Lao-Nung, (

**g**) San-Ti-Men, (

**h**) Chao-Chou, and (

**i**) Hsin-Pei.

**Figure 5.**The relationship between Q and –dQ/dt for each catchment in wet seasons. Three transition points are indicated with the regression line and envelopes and showed as circles with number. (

**a**) Chu-Kou, (

**b**) Chang-Pan Bridge, (

**c**) Tso-Chen, (

**d**) Hsin-Shih, (

**e**) Chung-Te Bridge, (

**f**) Lao-Nung, (

**g**) San-Ti-Men, (

**h**) Chao-Chou, and (

**i**) Hsin-Pei.

**Figure 6.**Hydraulic conductivity k vs. specific yield S

_{y}at different transition points in Southern Taiwan. The shapes of symbols represent each station, and transition points 1, 2 and 3 are green, blue and orange symbols, respectively. (

**a**) Dry season; (

**b**) wet season.

Basin | Station | Area (km^{2}) | X-Coordinate (TWD67 ^{a}) | Y-Coordinate (TWD67 ^{a}) | Record Years |
---|---|---|---|---|---|

Bazhang River | Chu-Kou | 83.1 | 209,775.8 | 2,592,901.4 | 1967–2017 |

Chang-Pan Bridge | 101.1 | 193,794.3 | 2,591,889.4 | 1970–2017 | |

Zengwen River | Tso-Chen | 121.3 | 186,554.1 | 2,551,818.6 | 1971–2017 |

Yanshui River | Hsin-Shih | 146.5 | 175,903.5 | 2,550,924.6 | 1973–2017 |

Erren River | Chung-Te Bridge | 139.6 | 183,217.2 | 2,531,714.6 | 1982–2017 |

Kaoping River | Lao-Nung | 812.0 | 216,098.8 | 2,549,698.6 | 1959–2008 |

San-Ti-Men | 408.5 | 213,804.4 | 2,512,457.7 | 1964–2017 | |

Donggang River | Chao-Chou | 175.3 | 203,071.1 | 2,496,579.8 | 1965–2017 |

Linbian River | Hsin-Pei | 309.9 | 203,708 | 2,484,782.9 | 1962–2013 |

^{a}is Taiwan’s Triangulation Point Coordinates.

Station | K | |
---|---|---|

Dry Season | Wet Season | |

Chu-Kou | 117.65 | 57.80 |

Chang-Pan Bridge | 50 | 30.30 |

Tso-Chen | 51.81 | 31.45 |

Hsin-Shih | 39.53 | 37.45 |

Chung-Te Bridge | 29.94 | 31.25 |

Lao-Nung | 70.42 | 55.56 |

San-Ti-Men | 93.76 | 29.85 |

Chao-Chou | 131.58 | 58.82 |

Hsin-Pei | 40.16 | 34.97 |

Chu-Kou | 69.43 | 40.83 |

**Table 3.**Hydrogeological parameters of pumping test and estimates using the flow recession method in the Chianan and Kaoping sub-areas.

Chianan Sub-Area | |||

Hydrogeological Parameters | Pumping Test | Dry Season | Wet Season |

T (m^{2}/min) | 2.63 × 10^{−1}–4.40 × 10^{−3} | 10^{0}–10^{−2} | 10^{0}–10^{−2} |

k (m/s) | 10^{−4}–10^{−6} | 10^{−3}–10^{−5} | 10^{−4}–10^{−6} |

S_{y} (-) | 10^{−2} | 10^{−2}–10^{−4} | 10^{−1}–10^{−5} |

Kaoping Sub-Area | |||

Hydrogeological Parameters | Pumping Test | Dry Season | Wet Season |

T (m/min) | 3.00 × 10^{−5}–1.51 × 10^{1} | 10^{0}–10^{1} | 10^{0} |

k (m/s) | 10^{−3}–10^{−5} | 10^{−2}–10^{−3} | 10^{−2}–10^{−3} |

S_{y} (-) | 10^{−1}–10^{−5} | 10^{−2}–10^{−3} | 10^{−2} |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huang, C.-C.; Yeh, H.-F.
Hydrogeological Parameter Determination in the Southern Catchments of Taiwan by Flow Recession Method. *Water* **2019**, *11*, 7.
https://doi.org/10.3390/w11010007

**AMA Style**

Huang C-C, Yeh H-F.
Hydrogeological Parameter Determination in the Southern Catchments of Taiwan by Flow Recession Method. *Water*. 2019; 11(1):7.
https://doi.org/10.3390/w11010007

**Chicago/Turabian Style**

Huang, Chia-Chi, and Hsin-Fu Yeh.
2019. "Hydrogeological Parameter Determination in the Southern Catchments of Taiwan by Flow Recession Method" *Water* 11, no. 1: 7.
https://doi.org/10.3390/w11010007