# Optimization of Hydrologic Response Units (HRUs) Using Gridded Meteorological Data and Spatially Varying Parameters

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Area of the Study Case

^{2}, but its topography ranges from 780 m.a.s.l. up to 3985 m.a.s.l., with almost half of its area located above 2500 m.a.s.l. In winter and during rainfall, the 0 °C isotherm in Central Chile is typically located at about 2500 m.a.s.l. [19], allowing snow accumulation in most parts of the Andes Mountains. Hence, at the outlet of the basin, there is an important flow between mid-spring and the beginning of summer in the southern hemisphere (from October to January) due to snow melting. Agriculture uses the waters from La Ligua River, but most of the discharge of this river during the dry season comes from upper basins, such as the Alicahue River, where snow accumulation is possible during the cold and wet winter.

^{3}/s for mean annual streamflow, 267 mm for total annual precipitation and 15.1 °C for mean annual temperature.

#### 2.2. Hydrologic Parameters and Meteorological Datasets

#### 2.3. Clustering Processes and HRU Delineation

_{1}, a

_{2}, …a

_{p}are constants, and the variance of Xa is a’Sa, where S is the sample covariance matrix and ‘ denotes transpose. The maximization of variance is solved by using the Lagrange multiplier λ. Simple mathematical calculations prove that

**a**must be a (unit-norm) eigenvector, and λ the corresponding eigenvalue of the sample covariance matrix S [22]). The p × p covariance matrix S has exactly p real eigenvalues λ

_{1}, λ

_{2}, λ

_{p}, and their corresponding eigenvectors can be defined to form an orthonormal set of vectors. Using the Lagrange multiplier approach, the full set of eigenvectors of S are the solutions to the problem of obtaining up to p new linear combinations (principal components) which successively maximize variance, subject to uncorrelatedness with previous linear combinations [23]. Uncorrelatedness results from the fact that the covariance between two linear combinations, Xa

_{k}and Xa

_{k’}, is zero for k ≠ k’ given the orthogonality of the eigenvectors a

_{k}and ak’ of the matrix S.

#### 2.4. Hydrological Model Setup and Simulations

## 3. Results

#### 3.1. PCA and Cluster Analysis

#### 3.2. Hydrological Modeling and HRU Contribution

^{2}.

^{2}). The relative importance of each HRU changes, especially for clusters 2, 5 and 6. As shown in Table 3, the relative contribution to the total discharge of those clusters doubles their area relative to the total area. The hydrologic regime of cluster 2 tends to be closer to the precipitation season (May to August) and it has a high areal production of water due mainly to the concentration of rainfall in that area of the catchment. Cluster 5 presents the higher average of areal production (7.6 l/s/km

^{2}) and even its base value of nearly 5.0 l/s/km

^{2}is also higher than the rest of the base values. Again, this may be explained by the nature of the vegetation covering most of that cluster and by the slow release of water stored in it. The highest peak of 23.9 l/s/km

^{2}in the month of January corresponds to cluster 6 and it is a combination of high rates of precipitation during winter in a relatively small area of the catchment, accumulating a massive volume of snow with the rise of temperatures in summer, producing the highest peak of discharge per unit of area due to snowmelt.

## 4. Discussion

#### 4.1. Methodology and Data Uncertainties in the Dataset Preparation

#### 4.2. Clustering Method and Results

#### 4.3. Discharge Independence in the Hydrologic Modeling

## 5. Conclusions and Further Developments

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Leavesley, G.; Lichty, R.; Troutman, B.; Saindon, L. Precipitation-Runoff Modeling System; User’s Manual; US Department of the Interior: Washington, DC, USA, 1983. [Google Scholar] [CrossRef] [Green Version]
- Flügel, W.-A. Delineating hydrological response units by geographical information system analyses for regional hydrological modelling using PRMS/MMS in the drainage basin of the River Bröl, Germany. Hydrol. Process.
**1995**, 9, 423–436. [Google Scholar] [CrossRef] - Pilz, T.; Francke, T.; Bronstert, A. lumpR 2.0.0: An R package facilitating landscape discretisation for hillslope-based hydrological models. Geosci. Model Dev.
**2017**, 10, 3001–3023. [Google Scholar] [CrossRef] [Green Version] - Savvidou, E.; Efstratiadis, A.; Koussis, A.D.; Koukouvinos, A.; Skarlatos, D. The Curve Number Concept as a Driver for Delineating Hydrological Response Units. Water
**2018**, 10, 194. [Google Scholar] [CrossRef] [Green Version] - Höge, M.; Wöhling, T.; Nowak, W. A Primer for Model Selection: The Decisive Role of Model Complexity. Water Resour. Res.
**2018**, 54, 1688–1715. [Google Scholar] [CrossRef] - Nijzink, R.C.; Hutton, C.; Pechlivanidis, I.G.; Capell, R.; Arheimer, B.; Freer, J.; Han, D.; Wagener, T.; McGuire, K.; Savenije, H.H.G.; et al. The evolution of root-zone moisture capacities after deforestation: A step towards hydrological predictions under change? Hydrol. Earth Syst. Sci.
**2016**, 20, 4775–4799. [Google Scholar] [CrossRef] [Green Version] - Orth, R.; Dutra, E.; Pappenberger, F. Improving Weather Predictability by Including Land Surface Model Parameter Uncertainty. Mon. Weather. Rev.
**2016**, 144, 1551–1569. [Google Scholar] [CrossRef] - Dehotin, J.; Braud, I. Which spatial discretization for distributed hydrological models? Proposition of a methodology and illustration for medium to large-scale catchments. Hydrol. Earth Syst. Sci.
**2008**, 12, 769–796. [Google Scholar] [CrossRef] [Green Version] - Haghnegahdar, A.; Tolson, B.A.; Craig, J.R.; Paya, K.T. Assessing the performance of a semi-distributed hydrological model under various watershed discretization schemes. Hydrol. Process.
**2015**, 29, 4018–4031. [Google Scholar] [CrossRef] - Han, J.; Huang, G.; Zhang, H.; Li, Z.; Li, Y. Effects of watershed subdivision level on semi-distributed hydrological simulations: Case study of the SLURP model applied to the Xiangxi River watershed, China. Hydrol. Sci. J.
**2013**, 59, 108–125. [Google Scholar] [CrossRef] - Haverkamp, S.; Fohrer, N.; Frede, H.-G. Assessment of the effect of land use patterns on hydrologic landscape functions: A comprehensive GIS-based tool to minimize model uncertainty resulting from spatial aggregation. Hydrol. Process.
**2005**, 19, 715–727. [Google Scholar] [CrossRef] - Young, C.A.; Escobar-Arias, M.I.; Fernandes, M.; Joyce, B.; Kiparsky, M.; Mount, J.F.; Mehta, V.K.; Purkey, D.; Viers, J.H.; Yates, D. Modeling the Hydrology of Climate Change in California’s Sierra Nevada for Subwatershed Scale Adaptation1. JAWRA J. Am. Water Resour. Assoc.
**2009**, 45, 1409–1423. [Google Scholar] [CrossRef] - Yates, D.; Sieber, J.; Purkey, D.; Huber-Lee, A. 21—A Demand-, Priority-, and Preference-Driven Water Planning Model. Part 1: Model Characteristics. Water Int.
**2005**, 30, 487–500. [Google Scholar] [CrossRef] - Bonelli, S.; Vicuna, S.; Meza, F.J.; Gironás, J.; Barton, J.R. Incorporating climate change adaptation strategies in urban water supply planning: The case of central Chile. J. Water Clim. Chang.
**2014**, 5, 357–376. [Google Scholar] [CrossRef] - Vicuña, S.; Garreaud, R.D.; McPhee, J. Climate change impacts on the hydrology of a snowmelt driven basin in semiarid Chile. Clim. Chang.
**2011**, 105, 469–488. [Google Scholar] [CrossRef] - Skamarock, W.C.; Klemp, J.B.; Dudhia, J.; Gill, D.O.; Barker, D.M.; Duda, M.G.; Huang, X.-Y.; Wang, W.; Powers, J.G. A Description of the Advanced Research WRF Version 3. Available online: http://opensky.ucar.edu/islandora/object/technotes%3A500/datastream/PDF/view (accessed on 9 October 2018).
- Tachikawa, T.; Kaku, M.; Iwasaki, A.; Gesch, D.B.; Oimoen, M.J.; Zhang, Z.; Danielson, J.J.; Krieger, T.; Curtis, B.; Haase, J.; et al. ASTER Global Digital Elevation Model Version—Summary of Validaton Results. NASA Land Processes Distributed Active Archive Center. 2011. Available online: http://www.jspacesystems.or.jp/ersdac/GDEM/ver2Validation/Summary_GDEM2_validation_report_final.pdf (accessed on 17 March 2015).
- Martínez, E.; Flores, J.; Retamal, M.; Ahumada, I.; Brito, S. Informe Técnico Final Monitoreo de Cambios, Corrección Cartográfica y Actualización del Catastro de Bosque Nativo en las Regiones de Valparaíso, Metropolitana y Libertador Bernardo O’Higgins.; Centro de Información de Recursos Naturales (CIREN): Santiago, Chile, 2013. [Google Scholar]
- Garreaud, R. Impact of the Variability of Snowline in Winter Discharge Peaks in Basins of Mixed Regime in Central Chile; Sociedad Chilena de Ingeniería Hidráulica: Santiago, Chile, 1992. (In Spanish) [Google Scholar]
- Purkey, D.R.; Joyce, B.; Vicuña, S.; Hanemann, M.W.; Dale, L.L.; Yates, D.; Dracup, J.A. Robust analysis of future climate change impacts on water for agriculture and other sectors: A case study in the Sacramento Valley. Clim. Chang.
**2007**, 87, 109–122. [Google Scholar] [CrossRef] - Hijmans, R.J. Geosphere: Spherical Trigonometry; Version 1.5-7; R Package. Available online: https://CRAN.R-project.org/package=geosphere (accessed on 11 May 2017).
- Jolliffe, I.T.; Cadima, J. Principal component analysis: A review and recent developments. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
**2016**, 374, 20150202. [Google Scholar] [CrossRef] - Jolliffe, I.T. Principal Components as a Small Number of Interpretable Variables: Some Examples; Springer: New York, NY, USA, 1986; pp. 50–63. [Google Scholar] [CrossRef]
- Zuśka, Z.; Kopcińska, J.; Dacewicz, E.; Skowera, B.; Wojkowski, J.; Ziernicka-Wojtaszek, A. Application of the principal component analysis (PCA) method to assess the impact of meteorological elements on concentrations of particulate matter (PM10): A case study of the mountain valley (the Sacz Basin, Poland). Sustainability
**2019**, 11, 6740. [Google Scholar] [CrossRef] [Green Version] - Jolliffe, I.T. Principal Component Analysis, 2nd ed.; Springer: Verlag, NY, USA, 2002; Volume 98, p. 487. [Google Scholar] [CrossRef]
- Lê, S.; Josse, J.; Husson, F. FactoMineR: An R Package for Multivariate Analysis. J. Stat. Softw.
**2008**, 25, 1–8. [Google Scholar] - Team, R.C. A Language and Environment for Statistical Computing. 2019. Available online: https://www.r-project.org/ (accessed on 15 September 2019).
- Husson, F.; Julie, J.; Jérôme, P. Technical Report—Agrocampus Principal component methods -hierarchical clustering—Partitional clustering: Why would we need to choose for visualizing data? Appl. Math. Dep. Agrocampus.
**2010**, 1, 1–17. [Google Scholar] - Fouedjio, F. A hierarchical clustering method for multivariate geostatistical data. Spat. Stat.
**2016**, 18, 333–351. [Google Scholar] [CrossRef] - Kalnay, E.; Kanamitsu, M.; Kistler, R.; Collins, W.; Deaven, D.; Gandin, L.; Iredell, M.; Saha, S.; White, G.; Woollen, J.; et al. The NCEP/NCAR 40-Year Reanalysis Project. Bull. Am. Meteorol. Soc.
**1996**, 77, 437–471. [Google Scholar] [CrossRef] [Green Version] - Alvarez-Garreton, C.; Mendoza, P.A.; Boisier, J.P.; Addor, N.; Galleguillos, M.; Zambrano-Bigiarini, M.; Lara, A.; Puelma, C.; Cortes, G.; Garreaud, R.D.; et al. The CAMELS-CL dataset: Catchment attributes and meteorology for large sample studies—Chile dataset. Hydrol. Earth Syst. Sci.
**2018**, 22, 5817–5846. [Google Scholar] [CrossRef] [Green Version] - DGA: Actualización del Balance Hídrico Nacional, SIT N° 417. Santiago. 2017. Available online: http://documentos.dga.cl/REH5796v1.pdf (accessed on 1 August 2019).
- Kolmogorov, A. Curves in a Hilbert space that are invariant under the one-parameter group of motions. Dokl. Akad. Nauk SSSR.
**1940**, 26, 6–9. [Google Scholar] - Hurst, H.E. Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civil Eng.
**1951**, 116, 770–799. [Google Scholar] - Koutsoyiannis, D. Hurst-Kolmogorov Dynamics and Uncertainty1. JAWRA J. Am. Water Resour. Assoc.
**2011**, 47, 481–495. [Google Scholar] [CrossRef] - Dimitriadis, P.; Koutsoyiannis, D. Stochastic synthesis approximating any process dependence and distribution. Stoch. Environ. Res. Risk Assess.
**2018**, 32, 1493–1515. [Google Scholar] [CrossRef]

**Figure 1.**Area of study. Relative location in South America and Weather Research and Forecasting (WRF) domains (left), topography of the area of study indicating the limits of Alicahue and La Ligua River Basins (red and purple polygons, respectively) and the location of the weather stations (streamflow station co-located with Alicahue Hacienda weather station).

**Figure 2.**Parameter map covering the Alicahue River Basin for: (

**top left**) Runoff Resistance Factor (RRF), (

**top right**) Preferred Flow Direction (f), (

**bottom left**) Soil Water Capacity (Sw) and (

**bottom right**) Root Zone Hydraulic Conductivity (Ks). Sw and Ks are plotted on a log scale.

**Figure 3.**Maps covering the Alicahue River Basin for: (

**left**) Mean annual precipitation, (

**right**) mean temperature.

**Figure 5.**Elevations bands every 550 m (

**left**), as used in the traditional methodology, and hydrological response unit (HRU) delimitations (

**right**) for the simulation with six HRUs by the PCA/HCPC methodology.

**Figure 6.**Boxplots per cluster in the simulation HRU_06 for: (

**a**) Mean annual precipitation, (

**b**) mean temperature, (

**c**) RRF, (

**d**) f, (

**e**) Sw and (

**f**) Ks. Red circles represent the mean value of each cluster. Sw and Ks are plotted on a log scale. Means are shown as red dots.

**Figure 7.**Hydrograph of observed and modeled streamflow in “Rio Alicahue en Colliguay” station for the simulation HRU_06. Observed discharge is shown as dots and the simulated discharge as a continuous line.

**Figure 8.**Mean monthly discharge of each HRU contributing to total streamflow at the outlet, for the six HRUs scenario. (

**Left**) mean annual discharge, (

**right**) mean annual discharge production by area.

**Table 1.**Summary from the principal component analysis (PCA) results for the first five dimensions or eigenvectors. The upper part shows the total variance explained by each dimension and the lower, the contribution of each variable to that dimension.

Dim.1 | Dim.2 | Dim.3 | Dim.4 | Dim.5 | |
---|---|---|---|---|---|

Explained Variance (%) | 50.7 | 16.1 | 11.9 | 5.9 | 5.0 |

Variables | Contribution to each dimension (%) | ||||

Temp | 28.2 | 0.1 | 0.7 | 0.2 | 5.1 |

Albedo | 11.5 | 1.1 | 5.6 | 1.6 | 10.0 |

Wind Speed | 10.8 | 1.3 | 0.6 | 0.0 | 8.5 |

Precipitation | 10.7 | 41.5 | 22.6 | 0.0 | 0.6 |

Evapotranspiration | 10.2 | 2.2 | 1.5 | 0.5 | 12.3 |

Net Radiation | 9.7 | 3.5 | 9.6 | 1.4 | 10.7 |

Relative Humidity | 9.5 | 5.6 | 1.4 | 1.0 | 0.0 |

Runoff Resistance Coefficient | 4.9 | 13.9 | 10.5 | 12.1 | 2.5 |

Soil Water Capacity | 4.1 | 20.3 | 6.4 | 4.4 | 9.7 |

Preferred Flow Direction | 0.3 | 4.7 | 32.1 | 0.4 | 35.6 |

Root Zone Hydraulic Conductivity | 0.0 | 5.7 | 9.0 | 78.3 | 5.0 |

**Table 2.**Performance of WEAP model in the 10 scenarios using the new methodology. NSE stands for Nash–Sutcliffe efficiency coefficient and RMSE for root mean square error.

Scenario | NSE | RMSE |
---|---|---|

HRU_01 | 0.58 | 4.1% |

HRU_02 | 0.71 | 4.3% |

HRU_03 | 0.72 | 3.6% |

HRU_04 | 0.77 | 3.5% |

HRU_05 | 0.78 | 3.2% |

HRU_06 | 0.79 | 3.1% |

HRU_07 | 0.78 | 3.1% |

HRU_08 | 0.77 | 3.1% |

HRU_09 | 0.76 | 3.2% |

HRU_10 | 0.74 | 3.2% |

Goal | 1.00 | 0.0% |

**Table 3.**Summary of mean annual variables for the six clusters used in the hydrological simulation. The values correspond to the mean values for the simulation period of 1984–2016.

Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 | Cluster 5 | Cluster 6 | |
---|---|---|---|---|---|---|

Area (km^{2}) | 34.0 | 22.1 | 125.2 | 121.7 | 10.9 | 41.5 |

% over total area | 9.6% | 6.2% | 35.2% | 34.2% | 3.1% | 11.7% |

Elevation (m.a.s.l.) | 1483 | 1460 | 2063 | 2080 | 2837 | 2951 |

Precipitation (mm) | 204 | 413 | 175 | 269 | 287 | 357 |

Evapotranspiration (mm) | 126 | 203 | 110 | 154 | 50 | 161 |

Evapotranspiration/Precipitation (–) | 0.62 | 0.49 | 0.63 | 0.57 | 0.17 | 0.45 |

Discharge | ||||||

Mean (m^{3}/s) | 0.09 | 0.15 | 0.26 | 0.45 | 0.08 | 0.26 |

% over total discharge | 7% | 12% | 20% | 35% | 6% | 20% |

Standard deviation (m3/s) | 0.03 | 0.11 | 0.30 | 0.77 | 0.08 | 0.47 |

Coefficient of variation | 0.34 | 0.76 | 1.16 | 1.72 | 0.99 | 1.79 |

Hydrograph centroid (month index) | 9.65 | 9.85 | 9.79 | 10.57 | 10.35 | 11.49 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 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**

Poblete, D.; Arevalo, J.; Nicolis, O.; Figueroa, F.
Optimization of Hydrologic Response Units (HRUs) Using Gridded Meteorological Data and Spatially Varying Parameters. *Water* **2020**, *12*, 3558.
https://doi.org/10.3390/w12123558

**AMA Style**

Poblete D, Arevalo J, Nicolis O, Figueroa F.
Optimization of Hydrologic Response Units (HRUs) Using Gridded Meteorological Data and Spatially Varying Parameters. *Water*. 2020; 12(12):3558.
https://doi.org/10.3390/w12123558

**Chicago/Turabian Style**

Poblete, David, Jorge Arevalo, Orietta Nicolis, and Felipe Figueroa.
2020. "Optimization of Hydrologic Response Units (HRUs) Using Gridded Meteorological Data and Spatially Varying Parameters" *Water* 12, no. 12: 3558.
https://doi.org/10.3390/w12123558