# Application of the Entropy Method to Select Calibration Sites for Hydrological Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology and Basic Theory

#### 2.1. Entropy Method for Information Measurement

#### 2.2. Genetic Algorithm

#### 2.3. SWAT for Runoff Simulation

## 3. Application and Results

#### 3.1. Study Area

^{2}, and the length of the related river is approximately 280 km. The average altitude of the basin, calculated using a 50 × 50 m

^{2}grid, is 610 m; its maximum altitude is 1560 m; its minimum altitude is 71 m; and its standard deviation is 261 m. We selected five weather-gauging sites (the red circles in Figure 2), which have collected data for five years (2008–2012), from the Korean Meteorological Agency. Table 1 shows the geographic information for the weather stations and the daily data (minimum temperature, maximum temperature, precipitation, relative humidity, wind speed, and solar radiation) from the collection period. There are 21 water-level gauging sites in the basin (the black and pink triangles in Figure 2). However, only eight discharge-gauging sites (the pink triangles in Figure 2) had discharge data for the period from 2008 to 2012, as most gauging stations were either recently installed or have not developed a relationship between water level and discharge.

Stations | Code | Station Name | Latitude (°) | Longitude (°) | Elevation (m) | Period of Record (Year) |
---|---|---|---|---|---|---|

Weather gauging stations | 100 | Daegoanrung | 37.68 | 128.82 | 772.4 | 2008–2012 |

114 | Wonju | 37.34 | 127.95 | 150.7 | 2008–2012 | |

216 | Taebaek | 37.17 | 128.99 | 714.2 | 2008–2012 | |

221 | Jecheon | 37.16 | 128.19 | 263.1 | 2008–2012 | |

272 | Youngju | 36.87 | 128.52 | 210.5 | 2008–2012 | |

Discharge-gauging stations | 1 | Chungju Dam | 37.00 | 128.00 | 80.0 | 2008–2012 |

2 | Youngchun | 37.10 | 128.51 | 190.0 | 2008–2012 | |

3 | Youngwol 1 | 37.18 | 128.48 | 200.0 | 2008–2012 | |

4 | Geowun | 37.23 | 128.51 | 221.0 | 2008–2012 | |

5 | Youngwol 2 | 37.19 | 128.41 | 383.0 | 2008–2012 | |

6 | Panwoon | 37.30 | 128.38 | 722.0 | 2008–2012 | |

7 | Pyeongchang | 37.37 | 128.41 | 762.0 | 2008–2012 | |

8 | Jucheon | 37.27 | 128.27 | 720.0 | 2008–2012 |

#### 3.2. Entropy Estimation

Discharge-Gauging Sites | Discharge-Gauging Sites | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Sum | |

1 | 7.667 | 2.708 | 2.643 | 2.543 | 2.353 | 1.745 | 2.128 | 1.609 | 23.396 |

2 | 2.708 | 7.079 | 2.599 | 2.530 | 2.337 | 1.452 | 2.070 | 1.641 | 22.415 |

3 | 2.643 | 2.599 | 6.783 | 2.505 | 2.771 | 1.867 | 2.354 | 1.857 | 23.378 |

4 | 2.543 | 2.530 | 2.505 | 6.007 | 2.755 | 2.049 | 2.462 | 1.948 | 22.798 |

5 | 2.353 | 2.337 | 2.771 | 2.755 | 6.457 | 1.938 | 2.353 | 1.808 | 22.772 |

6 | 1.745 | 1.452 | 1.867 | 2.049 | 1.938 | 4.288 | 3.075 | 2.474 | 18.888 |

7 | 2.128 | 2.070 | 2.354 | 2.462 | 2.353 | 3.075 | 5.124 | 2.187 | 21.755 |

8 | 1.609 | 1.641 | 1.857 | 1.948 | 1.808 | 2.474 | 2.187 | 4.140 | 17.665 |

Number of Sites | Selected Sites | Total Information | Change of Total Information |
---|---|---|---|

#1 | 1 | 23.4 | |

#2 | 1, 3 | 41.5 | |

#3 | 1, 3, 7 | 54.3 | |

#4 | 1, 2, 5, 7 | 62.4 | |

#5 | 1, 2, 3, 5, 6 | 66.03 | |

#6 | 1, 2, 3, 5, 6, 8 | 64.9 | |

#7 | 1, 2, 3, 4, 5, 6, 8 | 59.1 | |

#8 | 1, 2, 3, 4, 5, 6, 7, 8 | 47.5 |

#### 3.3. Model Setup and Calibration

^{2}Digital Elevation Model (DEM) and a stream network. In addition, a land cover map (Figure 5b) and a soil map (Figure 5c) from the National Water Resources Management Information System (WAMIS; http://www.wamis.go.kr/) were used. The basin was classified into eight different land-use conditions, among which forests (82.2%) and rice paddies (10.3%) accounted for 92.5% of the land use. The soil map, which included classifications of 141 total types of soil, showed that apb (17.8%) and ana (15.5%) were the most prevalent soil types in the area. To build the model used for the study, GIS data were prepared to generate hydrological response units, based on the above data. Terrain analyses were conducted to delineate the channel network using the DEM of the Chungju Dam basin. The basin was divided into ten sub-basins, as shown in Figure 5a. The extract geomorphological characteristics in each sub-basin are shown in Table 4.

**Figure 5.**GIS data as SWAT input. (

**a**) Stream network and sub-basins map; (

**b**) Land use map; (

**c**) Soil type map.

Sub-Basin | Basin | Stream | Remark | ||||||
---|---|---|---|---|---|---|---|---|---|

Area (km^{2}) | Slope (%) | Altitude (El. m) | Upstream Area (km^{2}) | Length (km) | Slope (%) | Min. Alt. (El. m) | Max. Alt. (El. m) | ||

B-1 | 1905.1 | 27.2 | 391.0 | 6631.4 | 101.5 | 10.2 | 71.0 | 174.0 | Site 1 |

B-2 | 553.6 | 35.0 | 487.0 | 4726.2 | 16.4 | 29.3 | 157.0 | 205.0 | Site 2 |

B-3 | 164.6 | 33.7 | 243.0 | 2398.5 | 12.0 | 70.9 | 136.0 | 221.0 | Site 3 |

B-4 | 2233.9 | 32.2 | 667.0 | 2233.9 | 128.9 | 30.2 | 216.0 | 605.0 | Site 4 |

B-5 | 276.9 | 22.6 | 328.0 | 1774.2 | 26.8 | 17.9 | 193.0 | 241.0 | Site 5 |

B-6 | 88.5 | 28.6 | 421.0 | 896.1 | 19.3 | 56.9 | 215.0 | 325.0 | – |

B-7 | 110.1 | 31.1 | 476.0 | 807.5 | 23.7 | 33.0 | 257.0 | 335.0 | Site 6 |

B-8 | 697.4 | 28.5 | 636.0 | 697.4 | 52.4 | 47.0 | 291.0 | 537.0 | Site 7 |

B-9 | 67.3 | 21.1 | 351.0 | 601.2 | 14.0 | 28.5 | 211.0 | 251.0 | – |

B-10 | 533.9 | 26.0 | 548.0 | 533.9 | 43.2 | 44.0 | 251.0 | 441.0 | Site 8 |

Num. | Parameter | Description | Range |
---|---|---|---|

Parameters governing surface water response | |||

1 | CN2 | Curve number 2 | 35–98 |

2 | ESCO | Soil evaporation compensation factor | 0–1 |

3 | SOL_AWC | Available soil water capacity | 0–1 |

Parameters governing subsurface water response | |||

4 | GWQMN | Threshold depth of water in the shallow aquifer for return flow to occur (mm) | 0–5000 |

5 | REVAPMN | Threshold depth of water in the shallow aquifer for reevaporation to occur (mm) | 0–500 |

6 | GW_REVAP | Groundwater reevaporation coefficient | 0.02–0.2 |

7 | ALPHA_BF | Base flow recession constant | 0–1 |

^{3}/s. This shows both the applicability of the GA and its usefulness in solving the problem of complex combinations in this study.

Parameter | GA | BSA |
---|---|---|

CN2 | 48 | 48 |

ESCO | 0.73 | 0.8 |

SOL_AWC | 0.32 | 0.3 |

GWQMN | 1694 | 1600 |

REVAPMN | 132 | 150 |

GW_REVAP | 0.08 | 0.1 |

ALPHA_BF | 0.6 | 0.5 |

**Figure 7.**Scatter plot for the relation between observation and simulation. (

**a**) Calibration at one site (Case 1); (

**b**) Calibration at five sites (Case 5).

#### 3.4. Calibration Results and Discussion

Site Number | All Sites | Outlet Site | ||||
---|---|---|---|---|---|---|

CC | RMSE (m^{3}/s) | NSE | CC | RMSE (m^{3}/s) | NSE | |

#0 (Non-C.) | 0.782 | 147.4 | 0.482 | 0.763 | 351.3 | 0.501 |

#1 | 0.800 | 142.8 | 0.516 | 0.784 | 330.4 | 0.554 |

#2 | 0.805 | 141.1 | 0.530 | 0.798 | 325.2 | 0.568 |

#3 | 0.810 | 140.0 | 0.538 | 0.798 | 325.1 | 0.573 |

#4 | 0.812 | 139.7 | 0.539 | 0.799 | 324.0 | 0.575 |

#5 | 0.813 | 138.8 | 0.540 | 0.798 | 325.1 | 0.573 |

#6 | 0.809 | 140.3 | 0.536 | 0.797 | 325.5 | 0.572 |

#7 | 0.809 | 142.1 | 0.524 | 0.794 | 329.0 | 0.562 |

#8 | 0.809 | 142.1 | 0.524 | 0.794 | 329.2 | 0.562 |

**Figure 8.**Calibration results using evaluation functions. (

**a**) Coefficient of correlation; (

**b**) RMSE; (

**c**) NSE; (

**d**) RMSE range in case of all sites.

_{21}C

_{n}= 2,097,151). While this assumption does not consider the importance of the sites, the number of cases for the hydrological model calibration must still be high. If the brute-force search method is considered to select calibration sites in this area, we would waste too much time and effort. Sometimes, a modeling result does not improve any further, although we try to get a good result in model calibration. This study confirmed that the selection of more calibration sites did not lead to improved calibration results from the model. Therefore, the entropy method attempted in this study is expected to provide an excellent guideline to conduct the calibration of the hydrological model. In addition, the application of the theory will further increase when selecting a certain number of sites, depending on the purpose of the application of the model, because the theory also provides information as to which sites need to be selected.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Moriasi, D.N.; Wilson, B.N.; Douglas-Mankin, K.R.; Arnold, J.G.; Gowda, P.H. Hydrologic and water quality models: Use, calibration, and validation. Trans. ASABE
**2012**, 55, 1241–1247. [Google Scholar] [CrossRef] - Beven, K. Changing ideas in hydrology—The case of physically based models. J. Hydrol.
**1989**, 105, 157–172. [Google Scholar] [CrossRef] - Duan, Q.Y.; Sorooshian, S.; Gupta, V. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour. Res.
**1992**, 28, 1015–1031. [Google Scholar] [CrossRef] - Beven, K.J.; Binley, A.M. The future of distributed models: Model calibration and uncertainty prediction. Hydrol. Process.
**1992**, 6, 279–298. [Google Scholar] [CrossRef] - Beven, K. Prophecy, reality, and uncertainty in distributed hydrological modeling. Adv. Water Resour.
**1993**, 16, 41–51. [Google Scholar] [CrossRef] - Oudin, L.; Perrin, C.; Mathevet, T.; Andréassian, V.; Michel, C. Impact of biased and randomly corrupted inputs on the efficiency and the parameters of watershed models. J. Hydrol.
**2006**, 320, 62–83. [Google Scholar] [CrossRef] - Tang, Y.; Reed, P.; van Werkhoven, K.; Wagener, T. Advancing the identification and evaluation of distributed rainfall-runoff models using global sensitivity analysis. Water Resour. Res.
**2007**, 43. [Google Scholar] [CrossRef] - Engel, B.; Storm, D.; White, M.; Arnold, J.; Arabi, M. A hydrologic/water quality model application protocol. J. Am. Water Resour. Assoc.
**2007**, 43, 1223–1236. [Google Scholar] [CrossRef] - Moriasi, D.N.; Arnold, J.G.; van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Harmel, R.D.; Smith, P.K.; Migliaccio, K.L. Modifying goodness-of-fit indicators to incorporate both measurement and model uncertainty in model calibration and validation. Trans. ASABE
**2010**, 53, 55–63. [Google Scholar] [CrossRef] - Pushpalatha, R.; Perrin, C.; le Moine, N.; Mathevet, T.; Andréassian, V. A downward structural sensitivity analysis of hydrological models to improve low-flow simulation. J. Hydrol.
**2011**, 411, 66–76. [Google Scholar] [CrossRef] - Beven, K.; O’Connell, P.E. On the Role of a Physically Based Distributed Modeling in Hydrology; Institute of Hydrology: Wallingford, UK, 1982. [Google Scholar]
- Abbott, M.B.; Bathurst, J.C.; Cunge, J.A.; O’Connell, P.E.; Rasmussen, J. An introduction to the European hydrological system—Systeme hydrologique Europeen, “SHE,” 1: History and philosophy of a physically based, distributed modelling system. J. Hydrol.
**1986**, 87, 45–59. [Google Scholar] [CrossRef] - Refsgaard, J.C.; Storm, B. Construction, Calibration and Validation of Hydrological Models. In Distributed Hydrological Modeling; Kluwer Academic: Dordrecht, The Netherlands, 1996; pp. 41–54. [Google Scholar]
- Lee, H.; McIntyre, N.; Wheater, H.; Young, A. Selection of conceptual models for regionalization of the rainfall-runoff relationship. J. Hydrol.
**2005**, 312, 125–147. [Google Scholar] [CrossRef] - Sahoo, G.B.; Ray, C.; de Carlo, E.H. Calibration and validation of a physically distributed hydrological model, MIKE SHE, to predict streamflow at high frequency in a flashy mountainous Hawaii stream. J. Hydrol.
**2006**, 327, 94–109. [Google Scholar] [CrossRef] - Hu, W.; Shao, M.; Wang, Q.; She, D. Effects of measurement method, scale, and landscape features on variability of saturated hydraulic conductivity. J. Hydrol. Eng.
**2013**, 18, 378–386. [Google Scholar] [CrossRef] - Gholami, V.; Chau, K.W.; Fadaee, F.; Torkaman, J.; Ghaffari, A. Modeling of groundwater level fluctuations using dendrochronology in alluvial aquifers. J. Hydrol.
**2015**, 529, 1060–1069. [Google Scholar] [CrossRef] - Taormina, R.; Chau, K.W. ANN-based interval forecasting of streamflow discharges using the LUBE method and MOFIPS. Eng. Appl. Artif. Intell.
**2015**, 45, 429–440. [Google Scholar] [CrossRef] - Wu, C.L.; Chau, K.W.; Li, Y.S. Methods to improve neural network performance in daily flows prediction. J. Hydrol.
**2009**, 372, 80–93. [Google Scholar] [CrossRef] - Wang, W.C.; Chau, K.W.; Xu, D.M.; Chen, X.Y. Improving forecasting accuracy of annual runoff time series using ARIMA based on EEMD decomposition. Water Resour. Manag.
**2015**, 29, 2655–2675. [Google Scholar] [CrossRef] - Chen, X.Y.; Chau, K.W. A comparative study of population-based optimization algorithms for downstream river flow forecasting by a hybrid neural network model. Eng. Appl. Artif. Intell.
**2015**, 46, 258–268. [Google Scholar] [CrossRef] - Chau, K.W.; Wu, C.L. A hybrid model coupled with singular spectrum analysis for daily rainfall prediction. J. Hydroinform.
**2010**, 12, 458–473. [Google Scholar] [CrossRef] - Park, M.K.; Kim, D.G.; Kwak, J.W.; Kim, H.S. Evaluation of parameter characteristics of the storage function model. J. Hydrol. Eng.
**2014**, 19, 308–318. [Google Scholar] [CrossRef] - Hogue, T.S.; Sorooshian, S.; Gupta, H.V.; Holz, A.; Braatz, D. A multi-step automatic calibration scheme (MACS) for river forecasting models. J. Hydrometeorol.
**2000**, 1, 524–542. [Google Scholar] [CrossRef] - Nelder, J.A.; Mead, R. A simplex method for function minimization. Comput. J.
**1965**, 7, 308–313. [Google Scholar] [CrossRef] - Wang, Q.J. The genetic algorithm and its application to calibrating conceptual rainfall-runoff models. Water Resour. Res.
**1991**, 27, 2467–2471. [Google Scholar] [CrossRef] - Ajami, N.K.; Gupta, H.; Wagener, T.; Sorooshian, S. Calibration of a semidistributed hydrologic model for streamflow estimation along a river system. J. Hydrol.
**2004**, 298, 112–135. [Google Scholar] [CrossRef] - Merz, R; Blöschl, G. Regionalisation of catchment model parameters. J. Hydrol.
**2004**, 287, 95–123. [Google Scholar] [CrossRef] - Young, A. Streamflow simulation within UK ungauged catchments using a daily rainfall-runoff model. J. Hydrol.
**2006**, 320, 155–172. [Google Scholar] [CrossRef] - Choi, Y.S.; Choi, C.K.; Kim, H.S.; Kim, K.T.; Kim, S. Multi-site calibration using a grid-based event rainfall-runoff model: A case study of the upstream areas of the Nakdong River basin in Korea. Hydrol. Process.
**2015**, 29, 2089–2099. [Google Scholar] [CrossRef] - Zhang, X.; Srinivasan, R.; van Liew, M. Multi-site calibration of the SWAT model for hydrologic modeling. Trans. ASABE
**2008**, 51, 2039–2049. [Google Scholar] [CrossRef] - Shannon, C.E.; Weaver, W. The Mathematical Theory of Communication; University of Illinois Press: Urbana, IL, USA, 1949. [Google Scholar]
- Yang, Y.; Burn, D.H. An entropy approach to data collection network design. J. Hydrol.
**1994**, 157, 307–324. [Google Scholar] [CrossRef] - Amorocho, J.; Espildora, B. Entropy in the assessment of uncertainty in hydrologic systems and models. Water Resour. Res.
**1973**, 9, 1511–1522. [Google Scholar] [CrossRef] - Chapman, T.G. Entropy as a measure of hydrologic data uncertainty and model performance. J. Hydrol.
**1986**, 85, 111–126. [Google Scholar] [CrossRef] - Husain, T. Hydrologic uncertainty measure and network design. Water Resour. Bull.
**1989**, 25, 527–534. [Google Scholar] [CrossRef] - Al-Zahrani, M.; Husain, T. An algorithm for designing a precipitation network in the southwestern region of Saudi Arabia. J. Hydrol.
**1998**, 205, 205–216. [Google Scholar] [CrossRef] - Holland, J.H. Adaptation in Natural and Artificial Systems; University of Michigan Press: Ann Arbor, MI, USA, 1975. [Google Scholar]
- Ragab, R.; Austin, B.; Moidinis, D. The HYDROMED model and its application to semi-arid Mediterranean catchments with hill reservoirs 1: The rainfall-runoff model using a genetic algorithm for optimisation. Hydrol. Earth Syst. Sci.
**2001**, 5, 543–553. [Google Scholar] - Bhattacharjya, R.K. Optimal design of unit hydrographs using probability distribution and genetic algorithms. SADHANA Acad. Proc. Eng. Sci.
**2004**, 29, 499–508. [Google Scholar] [CrossRef] - Chang, C.L.; Lo, S.L.; Yu, S.L. The parameter optimization in the inverse distance method by genetic algorithm for estimating precipitation. Environ. Monit. Assess.
**2006**, 117, 145–155. [Google Scholar] [CrossRef] [PubMed] - Refsgaard, J.C.; Storm, B. MIKE SHE. In Computer Models of Watershed Hydrology; Singh, V.P., Ed.; Water Resources Publications: Highland Ranch, CO, USA, 1995; pp. 809–846. [Google Scholar]
- Leavesley, G.H.; Stannard, L.G. The Precipitation Runoff Modeling System—PRMS. In Computer Models of Watershed Hydrology; Singh, V.P., Ed.; Water Resources Publications: Highland Ranch, CO, USA, 1995; pp. 281–310. [Google Scholar]
- Kite, G.W. The SLURP Model. In Computer Models of Watershed Hydrology; Singh, V.P., Ed.; Water Resources Publications: Highland Ranch, CO, USA, 1995; pp. 521–562. [Google Scholar]
- Arnold, J.G.; Srinivasan, R.; Muttiah, R.S.; Williams, J.R. Large area hydrologic modeling and assessment: Part I. model development. J. Am. Water Resour. Assoc.
**1998**, 34, 73–89. [Google Scholar] [CrossRef] - Kim, N.W.; Chung, I.M.; Kim, C.; Lee, J.; Lee, J.E. Development and applications of SWAT-K (Korea). In Soil and Water Assessment Tool (SWAT) Global Applications; World Association of Soil and Water Conservation: Bangkok, Thailand, 2009. [Google Scholar]
- Jaynes, E.K. Information theory and statistical mechanics. Phys. Rev.
**1957**, 106, 620–630. [Google Scholar] [CrossRef] - Molgedey, L.; Ebeling, W. Local order, entropy and predictability of financial time series. Eur. Phys. J. B
**2000**, 15, 733–737. [Google Scholar] [CrossRef] - Ulaniwicz, R.E. Information theory in ecology. Comput. Chem.
**2001**, 25, 393–399. [Google Scholar] [CrossRef] - Moramarco, T.; Saltalippi, C.; Singh, V.P. Estimation of mean velocity in natural channels based on Chiu’s velocity distribution equation. J. Hydrol. Eng.
**2004**, 9, 42–50. [Google Scholar] [CrossRef] - Mogheir, Y.; de Lima, J.L.M.P.; Singh, V.P. Characterizing the spatial variability of groundwater quality using the entropy theory: І. synthetic data. Hydrol. Process.
**2004**, 18, 2165–2178. [Google Scholar] [CrossRef] - Singh, V.P. The use of entropy in hydrology and water resources. Hydrol. Process.
**1997**, 11, 587–626. [Google Scholar] [CrossRef] - Singh, V.P. The entropy theory as a tool for modeling and decision making in environmental and water resources. Water SA
**2000**, 26, 1–12. [Google Scholar] - Yoo, C.; Jung, K.; Lee, J. Evaluation of rain gauge network using entropy theory: Comparison of mixed and continuous distribution function applications. J. Hydrol. Eng.
**2008**, 13, 226–235. [Google Scholar] [CrossRef] - Monteith, J.L. Evaporation and the environment. In the state and movement of water in living organisms. In 19th Symposia of the Society for Experimental Biology; Cambridge University Press: London, UK, 1965; pp. 205–234. [Google Scholar]
- Van Liew, M.W.; Veith, T.L.; Bosch, D.D.; Arnold, J.G. Suitability of SWAT for the conservation effects assessment project: A comparison on USDA-ARS watersheds. J. Hydrol. Eng.
**2007**, 12, 173–189. [Google Scholar] [CrossRef] - Neitsch, S.L.; Arnold, A.G.; Kiniry, J.R.; Srinivasan, J.R.; Williams, J.R. Soil and Water Assessment Tool User’s Manual; Texas Water Resources Institute: College Station, TX, USA, 2005. [Google Scholar]
- Van Griensven, A.; Meixner, T.; Grunwald, S.; Bishop, T.; Diluzio, M.; Srinivasan, R. A global sensitivity analysis tool for the parameters of multi-variable catchment models. J. Hydrol.
**2006**, 324, 10–23. [Google Scholar] [CrossRef] - White, L.K.; Chaubey, I. Sensitivity analysis, calibration, and validations for a multisite and multivariable SWAT model. J. Am. Water Resour. Assoc.
**2005**, 41, 1077–1089. [Google Scholar] [CrossRef] - Malagò, A.; Pagliero, L.; Bouraoui, F.; Franchini, M. Comparing calibrated parameter sets of the SWAT model for the Scandinavian and Iberian peninsulas. Hydrol. Sci. J.
**2015**, 60, 949–967. [Google Scholar] [CrossRef] - Reca, J.; Martinez, J. Genetic algorithms for the design of looped irrigation water distribution networks. Water Resour. Res.
**2006**, 42. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models Part I—A discussion of principles. J. Hydrol.
**1970**, 10, 283–290. [Google Scholar] [CrossRef]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, S.; Kim, Y.; Kang, N.; Kim, H.S.
Application of the Entropy Method to Select Calibration Sites for Hydrological Modeling. *Water* **2015**, *7*, 6719-6735.
https://doi.org/10.3390/w7126652

**AMA Style**

Kim S, Kim Y, Kang N, Kim HS.
Application of the Entropy Method to Select Calibration Sites for Hydrological Modeling. *Water*. 2015; 7(12):6719-6735.
https://doi.org/10.3390/w7126652

**Chicago/Turabian Style**

Kim, Soojun, Yonsoo Kim, Narae Kang, and Hung Soo Kim.
2015. "Application of the Entropy Method to Select Calibration Sites for Hydrological Modeling" *Water* 7, no. 12: 6719-6735.
https://doi.org/10.3390/w7126652