# New Analysis Method for Continuous Base-Flow and Availability of Water Resources Based on Parallel Linear Reservoir Models

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Digital Filtering Method

_{t}≤ Q

_{t}. Reference [48] adapted the method for stream flow partitioning, making the assumption that low frequency base-flow could be distinguished from high frequency high flows and proposed Equation (2). References [49,50], with the collaboration of other authors, provide a fruitful trajectory on algorithms based on Digital Filters, with Equations (3) and (4) being two of the most widespread. The base-flow index (BFI) is the ratio of the base-flow volume (calculated from F

_{t}) to the volume of streamflow (Q

_{t}) over a specified period. Reference [51] proposed the general form (Equation (5)) of a digital filter considering a digital filter parameter and BFImax (maximum value of long term BFI over a specified period).

_{t}is the quick-flow response at the tth sampling instant, Q

_{t}is the original streamflow at the tth sampling instant and α is the parameter that enables the shape of the separation to be modified.

_{t}is the base-flow at the tth sampling instant. The filter is generally run through multiple times per dataset. For example, three passes are commonly used—forward, backward and forward.

#### 2.2. Parallel Linear Reservoir Models

_{i}is the discharge of the reservoir I, and S

_{i}is the storage. For a model of two reservoirs, one is the quick-flow and the other is the base-flow.

_{0i}and α

_{i}are parameters of the model that are determined from the recession curves of the hydrographs. The α

_{i}parameter is called a depletion or recession coefficient and is also known as the response factor. Q

_{0i}is the flow for a given instant, being the same instant for all the Q

_{0i}. To be precise, there are nr-1 equations and since we are trying to find nr unknowns, another equation is needed—the mass conservation equation (Equation (8)).

_{0i}and α

_{i}are already known based on the streamflow records (Q

_{t}) of the time series, figuring out the Q

_{i}values of each reservoir through Equations (7) and (8) is needed, thus separating the quick-flow and the base-flow. Therefore, it is possible to propose a unique equation dependent on the discharge of one of the reservoirs (Equation (9)) with a single unknown, Q

_{1}.

_{1}is obtained through the set of Equation (7), the remaining Q

_{i}values can be obtained.

#### 2.3. Calibration of the Parallel Linear Reservoir Models

_{0i}and α

_{i}to the actual recession curves of the time series of total streamflow.

_{0i}and α

_{i}parameters), segments from the recession curve are selected from an actual hydrograph. These segments can be individually or collectively analysed to understand the processes that generate the flow. To obtain a solution for these segments, a graphical approach is traditionally adopted. However, recently analysis has involved the definition of an analytical solution or a mathematical model that can properly fit the recession segments. Reference [39] developed a completely automatic method that is based on adjustment via the least squares method, combining the Reference [12] equation with Equation (7) of this paper.

#### 2.4. Case Study of the Continuous Streamflow Time Series of a Catchment

## 3. Results

#### 3.1. Setting PLR Models

_{0}). In the case of the 3R model, the parameters of the 14 recession curves are aligned. Each model is the best fit for a particular recession curve but it is necessary to establish a generic model applicable to the complete time series. The mean of all the parameters of each model is the result yielding the best fit by the least squares method and approaching the regression line. Table 2 and Table 3 show the parameters for the generic 2R model and the 3R model, respectively. The squared Pearson’s correlation coefficient (R

^{2}), with respect to the linear regression line, is 0.789 for the 2R Model and 0.934 for the 3R model.

#### 3.2. Flow Separation with PLR Models

_{0}y α parameters of the generic models described in Table 2 and Table 3, flow separation in each reservoir for the continuous time series of the stream gauge A033 was performed. The series extends temporarily from 1987 to 2013, with data recorded every 15 min. In Figure 5 and Figure 6, six stretches of the hydrograph of the time series are represented.

#### 3.3. Flow Separation with Mathematical Digital Filter

#### 3.4. Efficiency Analysis

^{2}), the root mean square error (RMS, RMSE or EMC), the ratio of absolute error of peak flow (RAE), the Nash–Sutcliffe efficiency coefficient with logarithmic values (lnNSE), the Relative efficiency criteria of the Nash–Sutcliffe coefficient (NSErel), the Relative efficiency criteria of the index of agreement (IOArel), the weighted coefficient of determination (wR

^{2}) and the percent bias (pBIAS). The meaning of these parameters and their equations can be found in Reference [39] and for pBIAS in Reference [54].

## 4. Discussion

_{0i}and α

_{i}), thus they are parsimonious models, which fit the recession curves of the real hydrographs of the streamflow time series. Figure 5 and Figure 6 show the flow separation results for the 2R and 3R models and Figure 7 describes the results for the filter model of Reference [49].

#### 4.1. Flow Duration Curves

#### 4.2. Contribution of Each Flow Component to the Total Streamflow

^{3}/year, of which 8 hm

^{3}circulate through the quick reservoir, 33 hm

^{3}circulate through the intermediate reservoir and 76 hm

^{3}flow through the base flow reservoir.

^{3}—which represents 65% of the total streamflow, while the second aspect refers to the capacity of regulation of the water resource available in the basin and distributed during most of the time, which for 350 days/year represents the main contribution to surface water.

#### 4.3. Availability of Water Resources in the Catchment and Residence Time

^{3}, with a distribution of 7.1, 7.3 and 8.7 hm

^{3}respectively for quick, middle and slow reservoirs, respectively.

_{i}) of each reservoir.

^{3}for reservoirs 1, 2 and 3, respectively, which again indicates that the main water guarantee comes from the slow reservoir.

^{3}and the maximum value of mean discharge for the slow reservoir of the 2R model being 3.05 m

^{3}/s.

## 5. Conclusions

- −
- Calibration of model parameters, based on actual recession curves recorded in the hydrographs of gauging stations. The proposed formulation allows adjustment of the parameters of the models with a single optimal solution, derived from a least squares adjustment, unlike other techniques in which it is necessary to manually intervene in the adjustment. This makes the results of the PLR models conform to the real hydrographs, especially in the recession stretches, as demonstrated in the study of actual episodes carried out in Reference [39].
- −
- Models with more than two flow components can be established. In the example proposed for the Alcanadre River in Spain, three components better reflect the actual response of the basin, in the upper zone of which a large karst system is developed. In this area, the main recharge of fracturing aquifers developed in the carbonate formations (ages between the upper Cretaceous and the Eocene) that outcrop in the more elevated parts of the catchment takes place.
- −
- In addition to the separation between the different flow components, the PLR models with the proposed formulation allow the investigation and evaluation of the dynamic relations between the different components and also the drawing of conclusions about their state in each moment, the volumes stored in each reservoir, the discharges over time, the water reserves in each reservoir and the entire basin, the detractions of the aquifer flow and its recharge, the average residence time of the water volume, the volume of contribution of each type of reservoir, and so forth.

^{3}of capacity.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

_{1}. In order to simplify the equation, the terms with constant values are grouped:

## References

- Fekete, B.M.; Looser, U.; Pietroniro, A.; Robarts, R.D. Rationale for Monitoring Discharge on the Ground. J. Hydrometeorol.
**2012**, 13, 1977–1983. [Google Scholar] [CrossRef] - Mateo-Lázaro, J.; Sánchez-Navarro, J.A.; García-Gil, A.; Edo-Romero, V. Flood Frequency Analysis (FFA) in Spanish catchments. J. Hydrol.
**2016**, 538, 598–608. [Google Scholar] [CrossRef] - Lacasta, A.; Morales-Hernández, M.; Murillo, J.; García-Navarro, P. GPU implementation of the 2D shallow water equations for the simulation of rainfall/runoff events. Environ. Earth Sci.
**2015**. [Google Scholar] [CrossRef] - Guo, W.; Wang, C.; Zeng, X.; Ma, T.; Yang, H. Quantifying the spatial variability of rainfall and flow routing on flood response across scales. Environ. Earth Sci.
**2015**, 74. [Google Scholar] [CrossRef] - Beskow, S.; de Mello, C.R.; Vargas, M.M.; De Lima-Correa, L.; Caldeira, T.L.; Duraes, M.; Sanchonete-Aguilar, M. Artificial intelligence techniques coupled with seasonality measures for hydrological regionalization of Q90 under Brazilian conditions. J. Hydrol.
**2016**, 541. [Google Scholar] [CrossRef] - Rahmati, O.; Haghizadeh, A.; Stefanidis, S. Assessing the Accuracy of GIS-Based Analytical Hierarchy Process for Watershed Prioritization; Gorganrood River Basin, Iran. Water Resour. Manag.
**2016**, 30, 1131–1150. [Google Scholar] [CrossRef] - Barberá, J.A.; Andreo, B. River-spring connectivity and hydrogeochemical interactions in a shallow fractured rock formation. The case study of Fuensanta river valley (Southern Spain). J. Hydrol.
**2017**, 547, 253–268. [Google Scholar] [CrossRef] - Moore, R.D. Storage-outflow modelling of streamflow recessions, with application to a shallow-soil forested catchment. J. Hydrol.
**1997**, 98, 260–270. [Google Scholar] [CrossRef] - Griffiths, G.A.; Clausen, B. Streamflow recession in basins with multiple water storages. J. Hydrol.
**1997**, 190, 60–74. [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] - Boussinesq, J. Essai Sur la Theories des Eaux Courantes; Memoires presentes par divers savants a l’Academic des Sciences de l’Institut National de France: Paris, France, 1877. [Google Scholar]
- Maillet, E. Essais D’hydraulique Souterraine et Fluviale; Librairie Science Hermann Paris: Paris, France, 1905. [Google Scholar]
- Thomas, M.P.; Cervione, M.A. A proposed streamflow data program for Connecticut. Conn. Water Resour. Bull.
**1970**, 23. [Google Scholar] - Tasker, G.D. Estimating low flow characteristics of streams in southeastern Massachusets from maps of groundwater availability. US Geol. Surv. Prof. Pap.
**1972**, 800, 217–220. [Google Scholar] - Parker, G.W. Methods for Determining Selected Flow Characteristics for Streams in Maine; US Geological Survey Open-File Reports; USGS: Reston, VA, USA, 1977; pp. 78–871.
- Vogel, R.M.; Kroll, C.N. Regional geohydrologic-geomorphic relationships for the estimation of low-flow statistics. Water Resour. Res.
**1992**, 28, 2451–2458. [Google Scholar] [CrossRef] - Woods, R. The relative roles of climate, soil, vegetation and topography in determining seasonal and long-term catchment dynamics. Adv. Water Resour.
**2003**, 26, 295–309. [Google Scholar] [CrossRef] - Mijatovic, B. Détermination de la transmissivité et du coefficient d’emmagasinement par la courbe de tarissement dans les aquifêres karstiques. Int. Assoc. Hydrogeol.
**1974**, 10, 225–230. [Google Scholar] - Brutsaert, W.; Nieber, J.L. Regionalized drought flow hydrographs from a mature glaciated plateau. Water Resour. Res.
**1977**, 34, 233–240. [Google Scholar] [CrossRef] - Troch, P.; De Troch, F.; Brusaert, W. Effective water table depth to describe initial conditions prior to storm rainfall in humid regions. Water Resour. Res.
**1993**, 29, 427–434. [Google Scholar] [CrossRef] - Szilagy, J.; Parlange, M.B.; Albertson, J.D. Recession flow analysis for aquifer parameter determination. Water Resour. Res.
**1998**, 37, 1851–1857. [Google Scholar] [CrossRef] - Wittenberg, H. Baseflow recession and recharge as nonlinear storage processes. Hydrol. Process.
**1999**, 13, 715–726. [Google Scholar] [CrossRef] - Rupp, D.E.; Selker, J.S. Information, artifacts, and noise in dQ/dt—Q recession analysis. Adv. Water Resour.
**2006**, 29, 154–160. [Google Scholar] [CrossRef] - Sujono, J.; Shikasho, S.; Hiramatsu, K. A comparison of techniques for hydrograph recession analysis. Hydrol. Process.
**2004**, 18, 403–413. [Google Scholar] [CrossRef] - Zoch, R.T. On the relation between rainfall and streamflow. Mon. Weather Rev.
**1934**, 62, 315–322. [Google Scholar] [CrossRef] - Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology; McGraw-Hill: New York, NY, USA, 1988. [Google Scholar]
- Nash, J.E. The form of the instantaneous unit hydrograph. IASH Publ.
**1957**, 45, 114–121. [Google Scholar] - Dooge, J.C.I. A general theory of the unit hydrograph. J. Geophys. Res.
**1959**, 64, 241–256. [Google Scholar] [CrossRef] - Wang, G.T.; Chen, S. A linear spatially distributed model for a surface rainfall–runoff system. J. Hydrol.
**1996**, 185, 183–198. [Google Scholar] [CrossRef] - Jeng, R.I.; Coon, G.C. True form instantaneous unit hydrograph of linear reservoirs. J. Irrig. Drain. Eng. ASCE
**2003**, 129, 11–17. [Google Scholar] - McCuen, R.H. Hydrologic Analysis and Design; Prentice Hall: Upper Saddle River, NJ, USA, 1989; pp. 355–360. [Google Scholar]
- Arnold, J.G.; Allen, P.M. Validation of automated methods for estimating baseflow and groundwater recharge from stream flow records. J. Am. Water Resour. Assoc.
**1999**, 35, 411–424. [Google Scholar] [CrossRef] - Kovács, A.; Perrochet, P. A quantitative approach to spring hydrograph decomposition. J. Hydrol.
**2008**, 352, 16–29. [Google Scholar] [CrossRef] - Birk, S.; Hergarten, S. Early recession behaviour of spring hydrographs. J. Hydrol.
**2010**, 387, 24–32. [Google Scholar] [CrossRef] - Geyer, T.; Birk, S.; Liedl, R.; Sauter, M. Quantification of temporal distribution of recharge in karst systems from spring hydrographs. J. Hydrol.
**2008**, 348, 452–463. [Google Scholar] [CrossRef] - Biswal, B.; Marani, M. ‘Universal’ recession curves and their geomorphological interpretation. Adv. Water Resour.
**2014**, 65, 34–42. [Google Scholar] [CrossRef] - Biswal, B.; Kumar, N. Estimation of ‘drainable’ storage—A geomorphological approach. Adv. Water Resour.
**2015**, 77, 37–43. [Google Scholar] [CrossRef] - Stewart, M.K. Promising new baseflow separation and recession analysis methods applied to streamflow at Glendhu Catchment, New Zealand. Hydrol. Earth Syst. Sci.
**2015**, 19, 2587–2603. [Google Scholar] [CrossRef] - Mateo-Lázaro, J.; Sánchez-Navarro, J.A.; García-Gil, A.; Edo-Romero, V. A new adaptation of linear reservoir models in parallel sets to assess actual hydrological events. J. Hydrol.
**2015**, 524, 507–521. [Google Scholar] [CrossRef] - Mateo-Lázaro, J.; Sánchez-Navarro, J.A.; García-Gil, A.; Edo-Romero, V. Developing and programming a watershed traversal algorithm (WTA) in GRID-DEM and adapting it to hydrological processes. Comput. Geosci.
**2013**, 51, 418–429. [Google Scholar] [CrossRef] - Mateo-Lázaro, J.; Sánchez-Navarro, J.A.; García-Gil, A.; Edo-Romero, V. Sensitivity analysis of main variables present on flash flood processes. Application in two Spanish catchments: Arás and Aguilón. Environ. Earth Sci.
**2014**, 71, 2925–2939. [Google Scholar] [CrossRef] - Mateo-Lázaro, J.; Sánchez-Navarro, J.A.; García-Gil, A.; Edo-Romero, V. 3D-geological structures with digital elevation models using GPU programming. Comput. Geosci.
**2014**, 70, 147–153. [Google Scholar] [CrossRef] - Mateo-Lázaro, J.; Sánchez-Navarro, J.A.; García-Gil, A.; Edo-Romero, V.; Castillo-Mateo, J. Modelling and layout of drainage-levee devices in river sections. Eng. Geol.
**2016**, 214, 11–19. [Google Scholar] [CrossRef] - García-Gil, A.; Vázquez-Suñé, E.; Sánchez-Navarro, J.A.; Mateo-Lázaro, J. Recovery of energetically overexploited urban aquifers using Surface water. J. Hydrol.
**2015**, 531, 602–611. [Google Scholar] [CrossRef] - García-Gil, A.; Vázquez-Suñé, E.; Sánchez-Navarro, J.A.; Mateo-Lázaro, J.; Alcaraz, M. The propagation of complex flood-induced head wavefronts through a heterogeneous alluvial aquifer and its applicability in groundwater flood risk management. J. Hydrol.
**2015**, 527, 402–419. [Google Scholar] [CrossRef] - García-Gil, A.; Epting, J.; Garrido, E.; Vázquez-Suñé, E.; Mateo-Lázaro, J.; Sánchez Navarro, J.A.; Huggenberger, P.; Marazuela Calvo, M.A. A city scale study on the effects of intensive groundwater heat pump systems on heavy metal contents in groundwater. Sci. Total Environ.
**2016**, 572, 1047–1058. [Google Scholar] [CrossRef] [PubMed] - Lyne, V.D.; Hollick, M. Stochastic Time-Variable Rainfall-Runoff Modeling. In Proceedings of the Hydrology and Water Resources Symposium, Perth, Australia, 10–12 September 1979; pp. 89–92. [Google Scholar]
- Nathan, R.J.; McMahon, T.A. Evaluation of Automated Techniques for Baseflow and Recession Analysis. Water Resour. Res.
**1990**, 26, 1465–1473. [Google Scholar] [CrossRef] - Chapman, T.G. Comment on “Evaluation of automated techniques for base-flow and recession analyses” by R. J. Nathan and T. A. McMahon. Water Resour. Res.
**1991**, 27, 1783–1784. [Google Scholar] [CrossRef] - Chapman, T.G.; Maxwell, A. Baseflow Separation—Comparison of Numerical Methods with Tracer Experiments. In Proceedings of the 23rd Hydrology and Water Resources Symposium, Hobart, Australia, 21–24 May 1996; pp. 539–545. [Google Scholar]
- Eckhardt, K. How to construct recursive digital filters for base flow separation. Hydrol. Process.
**2005**, 19, 507–515. [Google Scholar] [CrossRef] - Sánchez, J.A.; Martínez, F.J.; De Miguel, J.L.; San Román, J. Los acuíferos carbonatados del macizo de Guara, análisis e interpretación de la curvas de recesión de caudales de los ríos que drenan. Rev. Acad. Cienc. Zaragoza
**1988**, 213–222. [Google Scholar] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models. Part I: A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Gupta, H.V.; Sorooshian, S.; Yapo, P.O. Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration. J. Hydrol. Eng.
**1999**, 4, 135–143. [Google Scholar] [CrossRef] - Partington, D.; Brunner, P.; Simmons, C.T.; Werner, A.D.; Therrien, R.; Maier, H.R.; Dandy, G.C. Evaluation of outputs from automated baseflow separation methods against simulated baseflow from a physically based, surface water-groundwater flow model. J. Hydrol.
**2012**, 458–459, 28–39. [Google Scholar] [CrossRef]

**Figure 2.**Study area with the water divide of the catchment, altimetry shade with Ski View Factor algorithm, geological synthesis and drainage network.

**Figure 5.**Calibration Flow separation for the six stretches selected of the time series with the 2R model.

**Figure 8.**Flow duration curves (FDCs) for two reservoir (2R), three reservoir (3R) and Filter model; (

**A**) flow duration curves for two reservoirs model; (

**B**) flow duration curves for three reservoirs model; (

**C**) flow duration curves for Chapmann Filter model; (

**D**) the cut-off points for the 3R model in detail.

**Figure 9.**Storage duration curves (SDCs) for the 2R and 3R models. The storage represents the availability of water resources in the catchment; (

**A**) storage in two reservoirs model; (

**B**) storage in three reservoirs model.

Characteristic | Value | Unit |
---|---|---|

Area | 765 | km^{2} |

Main channel length | 69 | km |

Main channel slope | 1.96 | % |

Mean slope of the catchment | 16.84 | % |

Mean slope of the network of DEM | 20.26 | % |

SCS-Curve Number | 73 |

Curve | α1 | α2 | Q_{01} | Q_{02} |
---|---|---|---|---|

1 | 1.96 × 10^{−5} | 1.78 × 10^{−6} | 3.015 × 10^{−7} | 5.553 × 10^{−8} |

2 | 1.52 × 10^{−5} | 1.42 × 10^{−6} | 9.965 × 10^{−8} | 1.564 × 10^{−8} |

3 | 2.17 × 10^{−5} | 1.83 × 10^{−6} | 1.092 × 10^{−7} | 2.498 × 10^{−8} |

4 | 3.53 × 10^{−5} | 3.31 × 10^{−6} | 2.724 × 10^{−7} | 4.573 × 10^{−8} |

5 | 2.52 × 10^{−5} | 1.67 × 10^{−6} | 2.157 × 10^{−7} | 3.935 × 10^{−8} |

6 | 2.34 × 10^{−5} | 1.39 × 10^{−6} | 8.807 × 10^{−8} | 2.301 × 10^{−8} |

7 | 1.32 × 10^{−5} | 1.69 × 10^{−6} | 3.598 × 10^{−8} | 2.761 × 10^{−8} |

8 | 2.12 × 10^{−5} | 2.16 × 10^{−6} | 1.390 × 10^{−7} | 4.126 × 10^{−8} |

9 | 1.53 × 10^{−5} | 1.44 × 10^{−6} | 9.079 × 10^{−8} | 1.925 × 10^{−8} |

10 | 2.06 × 10^{−5} | 1.20 × 10^{−6} | 1.128 × 10^{−7} | 2.556 × 10^{−8} |

11 | 4.51 × 10^{−5} | 2.96 × 10^{−6} | 1.147 × 10^{−7} | 2.132 × 10^{−8} |

12 | 1.51 × 10^{−5} | 1.16 × 10^{−6} | 6.363 × 10^{−8} | 9.694 × 10^{−9} |

13 | 2.70 × 10^{−5} | 1.89 × 10^{−6} | 1.228 × 10^{−7} | 2.243 × 10^{−8} |

14 | 2.73 × 10^{−5} | 1.45 × 10^{−6} | 1.098 × 10^{−7} | 2.811 × 10^{−8} |

Mean | 2.323 × 10^{−5} | 1.812 × 10^{−6} | 1.340 × 10^{−7} | 2.853 × 10^{−8} |

Curve | α1 | α2 | α3 | Q_{01} | Q_{02} | Q_{03} |
---|---|---|---|---|---|---|

1 | 2.87 × 10^{−5} | 5.14 × 10^{−6} | 4.35 × 10^{−7} | 2.55 × 10^{−7} | 1.07 × 10^{−7} | 1.29 × 10^{−8} |

2 | 2.62 × 10^{−5} | 6.48 × 10^{−6} | 7.06 × 10^{−7} | 7.04 × 10^{−8} | 4.50 × 10^{−8} | 6.90 × 10^{−9} |

3 | 4.36 × 10^{−5} | 6.70 × 10^{−6} | 7.08 × 10^{−7} | 8.62 × 10^{−8} | 5.32 × 10^{−8} | 8.44 × 10^{−9} |

4 | 5.29 × 10^{−5} | 1.05 × 10^{−5} | 1.08 × 10^{−6} | 2.23 × 10^{−7} | 9.93 × 10^{−8} | 1.22 × 10^{−8} |

5 | 4.08 × 10^{−5} | 6.33 × 10^{−6} | 7.17 × 10^{−7} | 1.85 × 10^{−7} | 7.44 × 10^{−8} | 1.46 × 10^{−8} |

6 | 4.72 × 10^{−5} | 5.90 × 10^{−6} | 6.82 × 10^{−7} | 7.54 × 10^{−8} | 3.80 × 10^{−8} | 1.05 × 10^{−8} |

7 | 2.55 × 10^{−5} | 3.97 × 10^{−6} | 4.23 × 10^{−7} | 2.40 × 10^{−8} | 3.44 × 10^{−8} | 8.09 × 10^{−9} |

8 | 7.46 × 10^{−5} | 1.18 × 10^{−5} | 1.58 × 10^{−6} | 7.63 × 10^{−8} | 1.00 × 10^{−7} | 2.75 × 10^{−8} |

9 | 4.71 × 10^{−5} | 7.65 × 10^{−6} | 7.90 × 10^{−7} | 4.84 × 10^{−8} | 6.14 × 10^{−8} | 9.65 × 10^{−9} |

10 | 9.57 × 10^{−5} | 1.41 × 10^{−5} | 1.03 × 10^{−6} | 5.54 × 10^{−8} | 8.38 × 10^{−8} | 2.19 × 10^{−8} |

11 | 7.80 × 10^{−5} | 1.06 × 10^{−5} | 9.12 × 10^{−7} | 9.90 × 10^{−8} | 4.29 × 10^{−8} | 6.15 × 10^{−9} |

12 | 2.44 × 10^{−5} | 5.53 × 10^{−6} | 5.18 × 10^{−7} | 4.90 × 10^{−8} | 2.45 × 10^{−8} | 4.27 × 10^{−9} |

13 | 4.08 × 10^{−5} | 8.26 × 10^{−6} | 1.02 × 10^{−6} | 1.01 × 10^{−7} | 4.07 × 10^{−8} | 1.11 × 10^{−8} |

14 | 5.96 × 10^{−5} | 8.39 × 10^{−6} | 9.57 × 10^{−7} | 9.10 × 10^{−8} | 4.69 × 10^{−8} | 1.75 × 10^{−8} |

Mean | 4.893 × 10^{−5} | 7.956 × 10^{−6} | 8.249 × 10^{−7} | 1.029 × 10^{−7} | 6.086 × 10^{−8} | 1.226 × 10^{−8} |

Stretch | NSE | IOA | R | R^{2} | EMC | RAE | lnNSE | NSErel | IOArel | wR^{2} | pBIAS |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0.344 | 0.595 | 0.775 | 0.601 | 14.066 | 76.463 | 0.792 | 0.960 | 0.975 | 0.240 | 25.527 |

2 | 0.817 | 0.940 | 0.913 | 0.834 | 3.005 | 44.609 | 0.952 | 0.959 | 0.986 | 0.715 | 2.218 |

3 | 0.860 | 0.960 | 0.929 | 0.863 | 2.379 | 25.054 | 0.945 | 0.861 | 0.960 | 0.827 | −3.252 |

4 | 0.888 | 0.968 | 0.944 | 0.891 | 2.042 | 20.441 | 0.941 | 0.753 | 0.929 | 0.841 | −1.258 |

5 | 0.774 | 0.917 | 0.917 | 0.841 | 4.178 | 43.834 | 0.942 | 0.947 | 0.981 | 0.627 | 8.879 |

6 | 0.884 | 0.967 | 0.942 | 0.888 | 1.890 | 26.906 | 0.965 | 0.953 | 0.987 | 0.849 | −5.155 |

Cut Points | 2R Model | 3R Model | |||
---|---|---|---|---|---|

R1/R2 | R1/R2 | R1/R3 | R2/R3 | ||

Exceedence Probability | % | 0.88 | 0.13 | 0.48 | 3.94 |

days/year | 3.23 | 0.46 | 1.74 | 14.39 | |

Discharge | m^{3}/s | 19.15 | 42.03 | 9.04 | 7.79 |

Model | Discharge Volume (hm^{3}/year) | Ratio (%) | ||||||
---|---|---|---|---|---|---|---|---|

Streamflow | Cell 1 | Cell 2 | Cell 3 | Streamflow | Cell 1 | Cell 2 | Cell 3 | |

2R | 117 | 20 | 96 | 100% | 17% | 83% | ||

3R | 117 | 8 | 33 | 76 | 100% | 7% | 28% | 65% |

Filter | 117 | 31 | 85 | 100% | 27% | 73% |

Model | Value | Discharge (m^{3}/s) | Storage (hm^{3}) | ||||||
---|---|---|---|---|---|---|---|---|---|

Reservoir 1 | Reservoir 2 | Reservoir 3 | ∑ | Reservoir 1 | Reservoir 2 | Reservoir 3 | ∑ | ||

2R | Max | 393.16 | 24.24 | 417.40 | 16.92 | 13.38 | 30.30 | ||

Min | 0.00 | 0.11 | 0.11 | 0.00 | 0.06 | 0.06 | |||

Mean | 0.64 | 3.05 | 3.69 | 0.03 | 1.68 | 1.71 | |||

DS | 16.90 | 11.69 | 28.59 | ||||||

3R | Max | 348.49 | 59.29 | 9.61 | 417.40 | 7.12 | 7.45 | 11.65 | 26.23 |

Min | 0.00 | 0.00 | 0.11 | 0.11 | 0.00 | 0.00 | 0.13 | 0.13 | |

Mean | 0.25 | 1.04 | 2.40 | 3.69 | 0.01 | 0.13 | 2.91 | 3.05 | |

DS | 7.12 | 7.32 | 8.74 | 23.18 |

Model | Cut Point | Discharge (m^{3}/s) | Storage (hm^{3}) | ||||||
---|---|---|---|---|---|---|---|---|---|

Reservoir 1 | Reservoir 2 | Reservoir 3 | ∑ | Reservoir 1 | Reservoir 2 | Reservoir 3 | ∑ | ||

2R | R1/R2 | 19.15 | 19.15 | 38.29 | 0.82 | 10.57 | 11.39 | ||

3R | R1/R2 | 42.03 | 42.03 | 9.28 | 93.34 | 0.86 | 5.28 | 11.25 | 17.39 |

R1/R3 | 9.04 | 32.74 | 9.04 | 50.82 | 0.18 | 4.12 | 10.96 | 15.26 | |

R2/R3 | 0.00 | 7.79 | 7.79 | 15.58 | 0.00 | 0.98 | 9.44 | 10.42 |

© 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**

Mateo-Lázaro, J.; Castillo-Mateo, J.; Sánchez-Navarro, J.Á.; Fuertes-Rodríguez, V.; García-Gil, A.; Edo-Romero, V.
New Analysis Method for Continuous Base-Flow and Availability of Water Resources Based on Parallel Linear Reservoir Models. *Water* **2018**, *10*, 465.
https://doi.org/10.3390/w10040465

**AMA Style**

Mateo-Lázaro J, Castillo-Mateo J, Sánchez-Navarro JÁ, Fuertes-Rodríguez V, García-Gil A, Edo-Romero V.
New Analysis Method for Continuous Base-Flow and Availability of Water Resources Based on Parallel Linear Reservoir Models. *Water*. 2018; 10(4):465.
https://doi.org/10.3390/w10040465

**Chicago/Turabian Style**

Mateo-Lázaro, Jesús, Jorge Castillo-Mateo, José Ángel Sánchez-Navarro, Víctor Fuertes-Rodríguez, Alejandro García-Gil, and Vanesa Edo-Romero.
2018. "New Analysis Method for Continuous Base-Flow and Availability of Water Resources Based on Parallel Linear Reservoir Models" *Water* 10, no. 4: 465.
https://doi.org/10.3390/w10040465