# The Curve Number Concept as a Driver for Delineating Hydrological Response Units

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview of Schematization and Parameterization Approaches in Hydrological Modelling

^{2}. It was found that HRUs are a reliable means for regional hydrological watershed modelling, allowing spatial up- and down-scaling [53,55]. Bongartz [56] compared the topographic-based and homogeneous HRUs and reported that, for watersheds with areas less than 200 km

^{2}, homogeneous HRUs provided better representation of the watershed processes.

_{j}, where n

_{j}is the number of classes corresponding to the i-th layer. It is worth mentioning that, in contrast to classical parameterization approaches, HRUs do not represent contiguous geographical areas (while sub-basins are by definition contiguous). Instead, they represent basin partitions with common characteristics, and thus common parameter values. The intersection of the sub-basin and HRU layers represents the minor geographical elements in the modelling procedure, driven by the rainfall and Potential Evapotranspiration (PET) of the corresponding sub-basin and responding according to the parameter values of the corresponding HRU. The shape of this non-contiguous element is of no interest, since at each time step, the runoff generated by HRUs is integrated over sub-basins and propagated to their outlet.

## 3. Curve Number Approach for HRU Delineation

#### 3.1. The Standard CN Approach and Its Shortcomings

#### 3.2. Analytical Method for CN Assessment

#### 3.3. GIS-Based Procedure for Extracting CN Maps

#### 3.4. Validation Based on Observed Flood Events

^{2}), the quite significant extent of highly-permeable geological formations and the steep slopes. The key task was the evaluation of the NRCS-CN method for extracting the effective rainfall, combined with the unit hydrograph theory, and the development of empirical formulas within this procedure to better represent the peculiarities of Mediterranean catchments that are mainly affected by flash floods [72].

#### 3.5. HRU Delineation Approaches Based on CN Classes

#### 3.6. Which Is the Recommended Number of HRUs?

## 4. Case Study

#### 4.1. Modelling Approach

#### 4.2. Study Area and Data

^{2}and an average elevation of 770 m, reaching a maximum elevation of 1715 m and a minimum of 93 m at the Latomeio Baka outlet. Terrain slope ranges from almost flat on the lowland and riverside areas to 76% on the steep mountain slopes, with the mean slope calculated at 22%. Nedontas originates in the western slopes of Taygetos and is mainly formed by three tributaries: its headwaters comprise the Nedousa and Alagonia tributaries, as well as spring flows in their sub-basins; the upper reach of Nedontas is joined by the lower reach of Karveliotis stream emanating from the SE area of the basin. The length of the main river course is about 26 km; the river discharges to the Gulf of Messenia, traversing the city of Kalamata, a regional economic center of SW Peloponnese, with 55,000 inhabitants.

^{3}/s).

#### 4.3. Model Setup and Other Assumptions

^{2}and by setting additional nodes at the three flow station sites, as illustrated in Figure 4. Their main properties are summarized in Table 3. Spatially-averaged precipitation time series of hourly resolution were extracted at the sub-basin scale, using the Thiessen polygon method. For the assignment of PET time series over sub-basins, we employed a parametric radiation-based approach that uses extraterrestrial solar radiation (which is periodic function of latitude and time), temperature and three parameters [86,87]. Areal temperature data were also estimated through the Thiessen polygon method, while the model parameters have been derived by fitting the model against Penman–Monteith data from the neighboring meteorological station of Kalamata. Finally, hourly discharge time series, used within calibrations, were constructed based on raw hydrometric data, i.e., 15-min interval river stage observations and sparse flow measurements were used to construct rating curves at the three stations.

#### 4.4. Preparation of CN Map

#### 4.5. Calibration Experiment 1: Varying the Number of HRUs

#### 4.6. Calibration Experiment 2: Contrasting Alternative HRU Delineation Approaches

#### 4.7. Investigation of Model Results for CN-Based Parameterization

## 5. Summary and Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Brief Description of the HYDROGEIOS Model

**Figure A1.**Representation of modelling components and associated fluxes within basin partitions. Meteorological inputs (Precipitation (PET)) vary across sub-basins, while model parameters, shown in callouts, vary across HRUs.

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**Figure 1.**(

**a**) Layers of geographic information for permeability classes (${i}_{\mathrm{PERM}}$), vegetation density classes (${i}_{\mathrm{VEG}}$) and drainage capacity classes (${i}_{\mathrm{SLOPE}}$); (

**b**) layer overlay; (

**c**) CN parameter map.

**Figure 3.**HRU delineation based on the CN map: (

**a**) CN parameter classes and (

**b**) configuration of two HRUs, using CN = 63 as the threshold to determine the associated CN classes.

**Figure 4.**Digital map of Nedontas River Basin, also showing monitoring stations (meteorological and hydrometric) and the main modelling components (junctions, sub-basins, river segments).

**Figure 5.**(

**a**) Water permeability classes; (

**b**) land cover classes; (

**c**) terrain slope (%) classes; (

**d**) CN parameter map of the initial Nedontas River Basin map of 18 CN classes.

**Figure 7.**HRU delineation of Nedontas River Basin: (

**a**) SWAT GIS overlay and threshold definition method, 31 HRUs; (

**b**) HYDROGEIOS union of layers method, four HRUs.

**Figure 8.**Computed vs. observed discharge series at the basin outlet (Latomeio Baka) for HRU delineation with: (

**a**) unique combination; (

**b**) union of layers; (

**c**) CN approach.

**Figure 9.**Computed vs. observed discharge series at Karveliotis monitoring station for HRU delineation with: (

**a**) unique combination; (

**b**) union of layers; (

**c**) CN approach.

**Figure 10.**Computed vs. observed discharge series at Alagonia monitoring station for HRU delineation with: (

**a**) unique combination; (

**b**) union of layers; (

**c**) CN approach.

**Table 1.**Coding of the physiographic characteristics for the estimation of parameter Curve Number (CN) for reference conditions (Antecedent Soil Moisture (AMC) Type II and initial abstraction ratio 20%).

Permeability Class | ${\mathit{i}}_{\mathbf{P}\mathbf{E}\mathbf{R}\mathbf{M}}$ | Vegetation Class | ${\mathit{i}}_{\mathbf{V}\mathbf{E}\mathbf{G}}$ | Drainage Capacity Class | ${\mathit{i}}_{\mathbf{S}\mathbf{L}\mathbf{O}\mathbf{P}\mathbf{E}}$ |
---|---|---|---|---|---|

Very high | 1 | Dense | 1 | Negligible | 1 |

High | 2 | Moderate | 2 | Low | 2 |

Moderate | 3 | Low | 3 | Moderate | 3 |

Low | 4 | Sparse | 4 | High | 4 |

Very low | 5 | Negligible | 5 | Very high | 5 |

Basin | Area (km^{2}) | Examined Events | Average Runoff Coefficient | Average Observed CN (Adjusted) | Reference CN |
---|---|---|---|---|---|

Nedontas | 120.8 | 11 | 0.121 | 53 | 61 |

Karveliotis | 15.3 | 10 | 0.171 | 52 | 65 |

Alagonia | 20.9 | 10 | 0.350 | 74 | 70 |

Lousios | 166.3 | 11 | 0.156 | 70 | 63 |

Sarantapotamos | 144.6 | 12 | 0.059 | 62 | 48 |

Oinoe | 51.2 | 12 | 0.012 | 52 | 45 |

Chalandri stream | 5.2 | 1 | 0.215 | 88 | 62 |

Drafi | 15.7 | 10 | 0.094 | 52 | 54 |

Lykorema | 7.9 | 11 | 0.101 | 78 | 52 |

Peristerona (Cyprus) | 77.1 | 14 | 0.407 | 72 | 71 |

Xeros (Cyprus) | 68.5 | 10 | 0.279 | 70 | 66 |

Sub-Basin | Name | Area (km^{2}) | Mean Elevation (m) | Main Stream Length (m) | Mean Slope (%) |
---|---|---|---|---|---|

W60 | Nedousa | 19.47 | 1008.9 | 4296 | 23.1 |

W180 | Alagonia | 20.72 | 1092.4 | 497 | 18.2 |

W130 | Karveliotis | 14.92 | 1096.5 | 1721 | 21.2 |

W170 | Downstream of Alagonia | 10.91 | 739.4 | 2807 | 20.3 |

W120 | Downstream of Karveliotis | 11.81 | 710.1 | 5755 | 25.9 |

W70 | Downstream of Nedousa | 12.53 | 741.9 | 4589 | 26.0 |

W90 | Latomeio Baka | 28.2 | 654.8 | 5921 | 18.4 |

**Table 4.**Overall model performance, expressed in terms of the composite error function, considering alternative parameterizations, by means of the number of HRUs.

HRUs | CN Classes | HRU Parameters | No. of Trials | Error Measure in Calibration | Error Measure in Validation |
---|---|---|---|---|---|

1 | 29-91 | 7 | 2000 | 2.465 | 3.674 |

2 | 29–61 | 14 | 4000 | 2.072 | 3.043 |

64–91 | |||||

3 | 29–57 | 21 | 6000 | 1.985 | 2.675 |

61–67 | |||||

70–91 | |||||

4 | 29–55 | 28 | 8000 | 2.094 | 3.621 |

58–64 | |||||

67–70 | |||||

73–91 | |||||

5 | 29–49 | 35 | 10,000 | 2.390 | 3.519 |

52–58 | |||||

61–64 | |||||

67–70 | |||||

73–91 |

Hydrometric Station | Calibration Period | Validation Period | ||
---|---|---|---|---|

Efficiency | High Flow Efficiency | Efficiency | High Flow Efficiency | |

One HRU | ||||

Basin outlet: Latomeio Baka | 0.524 | 0.297 | 0.591 | −0.521 |

Karveliotis | 0.672 | −0.166 | 0.687 | 0.218 |

Alagonia | 0.662 | 0.054 | 0.708 | 0.416 |

Two URHs | ||||

Basin outlet: Latomeio Baka | 0.798 | 0.810 | 0.560 | −0.793 |

Karveliotis | 0.887 | 0.676 | 0.712 | 0.259 |

Alagonia | 0.674 | 0.083 | 0.722 | 0.496 |

Three HRUs | ||||

Basin outlet: Latomeio Baka | 0.672 | 0.722 | 0.706 | −0.067 |

Karveliotis | 0.892 | 0.761 | 0.809 | 0.571 |

Alagonia | 0.721 | 0.248 | 0.736 | 0.571 |

Four HRUs | ||||

Basin outlet: Latomeio Baka | 0.773 | 0.814 | 0.643 | −0.407 |

Karveliotis | 0.869 | 0.631 | 0.738 | 0.285 |

Alagonia | 0.673 | 0.145 | 0.724 | 0.513 |

Five HRUs | ||||

Basin outlet: Latomeio Baka | 0.716 | 0.762 | 0.567 | −0.563 |

Karveliotis | 0.819 | 0.521 | 0.793 | 0.622 |

Alagonia | 0.737 | 0.160 | 0.672 | 0.495 |

Unique Combination | Union of Layers | CN Approach | |
---|---|---|---|

No. of HRUs | 31 | 4 | 3 |

No. of HRU parameters | 217 | 28 | 21 |

Total No. of parameters | 233 | 44 | 37 |

Relative effort within hybrid calibration * | ~3 | ~1.5 | 1 |

**Table 7.**Optimal values of efficiency, high flow efficiency and average bias for three HRU delineation approaches.

Hourly Runoff | Calibration Period | Validation Period | ||
---|---|---|---|---|

Efficiency | High Flow Eff. | Efficiency | High Flow Eff. | |

HRU delineation | Unique combination | |||

Basin outlet: Latomeio Baka | 0.768 | 0.809 | 0.719 | 0.068 |

Karveliotis | 0.908 | 0.663 | 0.813 | 0.580 |

Alagonia | 0.754 | 0.253 | 0.680 | 0.141 |

HRU delineation | Union of layers | |||

Basin outlet: Latomeio Baka | 0.801 | 0.757 | 0.771 | 0.195 |

Karveliotis | 0.655 | 0.693 | 0.762 | 0.368 |

Alagonia | 0.658 | 0.090 | 0.726 | 0.411 |

HRU delineation | CN based | |||

Basin outlet: Latomeio Baka | 0.814 | 0.816 | 0.802 | 0.241 |

Monitoring station: Karveliotis | 0.892 | 0.789 | 0.837 | 0.579 |

Monitoring station: Alagonia | 0.797 | 0.300 | 0.753 | 0.440 |

HRU | CN 29–59 | CN 61–69 | CN 73–91 |
---|---|---|---|

Total Area (km^{2}) | 40.2 | 54.8 | 22.9 |

Max. infiltration ratio (mm/h) | 80.0 | 61.3 | 39.4 |

Interception capacity (mm) | 50.0 | 39.4 | 5.0 |

Soil capacity up to spill (mm) | 393.5 | 377.0 | 50.0 |

Perc. of infiltration to the lower zone (%) | 78.8 | 54.083 | 5.292 |

Soil capacity up to interflow (mm) | 500.0 | 428.4 | 110.6 |

Recession rate for interflow (%) | 0.426 | 0.231 | 2.571 |

Recession rate for percolation (%) | 0.187 | 0.116 | 0.055 |

Variable | Equivalent Depths (mm) | Volumes (hm^{3}) | |
---|---|---|---|

Precipitation | 1690.3 | 200.1 | |

Evapotranspiration | 623.0 | 73.8 | |

Percolation | 607.1 | 71.9 | |

Surface runoff | 385.5 | 45.6 | |

Spring runoff | 249.6 | 29.6 | |

Underground losses | 343.7 | 49.9 | |

Soil storage change | 183.6 | 21.7 | |

Groundwater storage change | 29.3 | 3.5 | |

Outlet runoff | 557.2 | 66.0 | |

(a) | |||

Overall Water Balance | |||

Output Variable | Percentage of Precipitation (%) | ||

Evapotranspiration | 34.3 | ||

River outflow | 30.7 | ||

Underground losses | 23.2 | ||

Storage change | 11.7 | ||

(b) |

© 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**

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.
https://doi.org/10.3390/w10020194

**AMA Style**

Savvidou E, Efstratiadis A, Koussis AD, Koukouvinos A, Skarlatos D.
The Curve Number Concept as a Driver for Delineating Hydrological Response Units. *Water*. 2018; 10(2):194.
https://doi.org/10.3390/w10020194

**Chicago/Turabian Style**

Savvidou, Eleni, Andreas Efstratiadis, Antonis D. Koussis, Antonis Koukouvinos, and Dimitrios Skarlatos.
2018. "The Curve Number Concept as a Driver for Delineating Hydrological Response Units" *Water* 10, no. 2: 194.
https://doi.org/10.3390/w10020194