# Comparing the Runoff Decompositions of Small Experimental Catchments: End-Member Mixing Analysis (EMMA) vs. Hydrological Modelling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of Study Objects, Data, and Measurements Methods

^{2}) and Medvezhy (7.6 km

^{2}) creeks) that belong to the Upper-Ussuri Biocenological Experimental Station (45 km

^{2}, 44°02′ N, 134°11′ E). The considered area is characterized by mid-mountainous relief with moderately steep (Table 1), locally very steep, hillslopesof up to 30% [3,35]. The average altitudes are 500–700 m a.s.l, and maximal values reach 1100 m a.s.l. (Figure 1).

^{−1}during high-intensity rainfall caused by tropical cyclone–typhoon activity. The range of maximal daily heavy rain is 100–200 mm, and frequency of such events is assessed as one time per 5–6 years. The stable snowpack usually occurs in November, snow-cover depth reaches 0.5–1 m by the end of March, and the common range of the snow water equivalent is 100–200 mm.

_{3}concentration was taken to be equal to total alkalinity, and estimated in the field laboratory after 2–4 h of sampling by the potentiometric titration method in unfiltered water samples using the standard technique. Water samples for chemical analysis were filtered at the field laboratory through the Durapore filter (Millipore, Burlington, MA, USA) with a pore size of 0.45 μm. To determine the content of cations, about 10 mL of each filtered aliquot was acidified with purified nitric acid and stored in polypropylene bottles at room temperature prior to analysis. Then, filtration samples of water for DOC analysis were stored in 30 mL glass bottles at a temperature of 4–8 °C [38,39,40].

_{3}, SO

_{4}were determined using a Shimadzu LC 10Avp liquid chromatograph. Dissolved Si was determined by spectrophotometry method using blue complex with ammonium molybdate, and DOC by a TOC analyzer—Shimadzu TOC-VCPN.

#### 2.1. EMMA Model

^{T}G* according to the equation

^{T}× (S × S

^{T})

^{−1}× S

_{1}(k × m) extracted from the matrix G

_{1}, which includes only k conservative tracers. Tracer concentrations in EMs were standardized using the mean and standard deviation of each tracer in streamflow samples and projected using the same eigenvectors S

_{1}. Mixing diagrams were plotted in the U-space to screen EMs which contribute to the streamflow. In our study, the first two or three principal components (PCs), or the PCA scores, were used to determine the proportions of the EMs in the runoff composition. Thus, the PCs are considered as the tracers for the mixing model—two tracers for a three-source mixing model or three tracers for a four-sources mixing model.

#### 2.2. ECOMAG Model

#### 2.3. SWAT Model

#### 2.4. HBV Model

^{Beta}. The model first recharges the upper storage and then the lower storage using percolation parameter PERC. Surface flow appears when the upper storage capacity exceeds a certain threshold. Potential evapotranspiration (PET) is input to the model, which can be tuned by the Cet parameter. Actual evaporation is equal to PET when SM/FC is higher than the LP parameter; otherwise, a linear reduction is used. The runoff is calculated as the sum of three linear outflows: surface flow Q0, interflow Q1, and baseflow Q2 with three correspondent recession coefficients K0, K1, and K2. A transformation function with the triangular weighting parameter MAXBAS [53] is used for smoothing the total runoff to obtain the discharge at the outlet.

## 3. Results

#### 3.1. EMMA Results

^{2}< 0.5 (see Table 3).

_{3}, SO

_{4}, Ca, and Mg. The first two PCs explain more than 92% of the total variance of these data (see Table 4). Analysis of PCA-model residuals against measured values for individual solutes at two-dimensional mixing subspaces is shown in Figure 2a. The random pattern for each solute indicates that these six tracers could be considered as conservative and can be used for adopting the mixing model with three EMs.

^{2}assessments by sample (with its true value zero), calculated based on the well-known Fisher’s normalizing z-transform at a significance of 99% [56]. For samples of 69 and 126 members, the critical values of R

^{2}are approximately 0.101 for the Medvezhy and 0.054 for the Elovy, respectively (compared with Figure 2).

^{2}, the inclusion of the tracer can be justified by independent considerations and analysis of the simulation results as a whole. For example, R

^{2}for Ca (see Figure 2a) is essentially non-random. However, there is a group of three outliers in this residual plot, related to samples taken during one week in May 2015. The exclusion of this group from the sample reduces the value of R

^{2}by almost half, which serves as an argument for including this tracer in the model. The use of not completely conservative tracers decreases the accuracy and reliability of estimates in the mixing model. This fact was taken into account when discussing the conclusions below. The example above probably indicates that the existing dataset does not sufficiently account for the seasonal dynamics; hence the mixing models are considered reliable only for the summer-autumn rain-flood season (from June to September for the studied territory).

^{2}values (0.75–0.98).

#### 3.2. Results of Hydrological Simulations

^{2}, Nash and Sutcliffe efficiency (NSE) [57], and relative bias (BIAS, %) against the measured discharge at catchment outlets (see Table 6). NSE is categorized as “very good” when its value > 0.75 and “unsatisfactory” when its value < 0.5, interim ranges (0.75 > NSE > 0.65 and 0.65 > NSE > 0.5) are defined as “good” and “satisfactory”, respectively. According to BIAS values, simulation results are assumed to be unacceptable if |BIAS| > 25%, “satisfactory” if |BIAS| > 15% and < 25%, “good” for if |BIAS| < 15% < and > 10%, and “very good” if |BIAS| < 10% [58]. According to these criteria, more complex and sophisticated models provide better results for both catchments, and ECOMAG outperforms SWAT in most cases. HBV provides good results for the period of high flow but demonstrates poor performance for low flow (0.01–1.0 mm d

^{−1}) periods.

## 4. Discussion of Hydrograph Separations

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

^{2}. In the model, soil and groundwater flow was described by the Darcy equation, and surface flow was described by the kinematic wave equation. In conditions of high soil moisture, the actual evaporation was equal to the potential, and then, it decreased linearly to zero as the soil moisture decreased to the wilting point. Potential evaporation was estimated according to the Dalton method. The snowmelt rate is calculated using the degree-day method. Initial parameter values were assigned from available measurements and databases. During calibration, the ratio between the initial and optimized parameter values is fixed [64]. The values of the main calibrated parameters are presented in Table A1.

Parameter | Short Name | Medvezhy | Elovy |
---|---|---|---|

Coef. of vertical saturated hydraulic conductivity | GFB | 8.3 | 6.5 |

Coef. of horizontal saturated hydraulic conductivity | GFA | 1 | 10 |

Soil evaporation coefficient | EK | 0.75 | 0.8 |

Baseflow constant, mm day^{−1} | GROUND | 0.009 | 0.0001 |

Coef. of snowmelt intensity, mm day^{−1} °C | ALF | 0.28 | 0.45 |

Critical air temperature snow/rain, °C | TCR | 0.5 | 0.5 |

Snowmelt air temperature, °C | TSN | 0.1 | 0.1 |

Air temperature gradient, °C 100 m^{−1} | TGR | −0.6 | −0.6 |

Precipitation gradient, mm 100 m^{−1} | PGR | 0 | 0 |

Coef. of vertical saturated hydraulic conductivity | GFB | 8.3 | 6.5 |

Coef. of horizontal saturated hydraulic conductivity | GFA | 1 | 10 |

## Appendix B

^{2}. Potential evaporation was computed by the Penman–Monteith method. Channel routing was simulated by variable travel time method. A set of calibrated parameters and their values are presented in Table A2. Values of CN2 (runoff curve number) of both basins correspond to group “A” of high infiltration capacity soils [66]. Calibrated values of the evaporation compensation factor (ESCO) from soil profile allow the roots of trees to extract water from all soil layers for evapotranspiration. Parameters for groundwater simulation (DEP_IMP, ALPHA_BF, GW_DELAY and GWQMIN) were specified during model calibration.

^{−1}).

Parameter | Short Name | Medvezhy | Elovy |
---|---|---|---|

SCS runoff curve number for moisture condition II | CN2 | 35.0 | 35.0 |

Roughness coefficient for overland flow | OV_N | 30.0 | 0.01 |

Evaporation compensation from soil | ESCO | 0.1 | 0.46 |

Travel time of lateral flow, days | LAT_TTIME | 3.5 | 7.7 |

Depth of the impervious layer, m | DEP_IMP | 4.25 | 5.1 |

Baseflow recession constant | ALPHA_BF | 0.25 | 0.13 |

Time to reach the groundwater, days | GW_DELAY | 1.5 | 1.55 |

Recharge of deep aquifer coefficient | RCHRG_DP | 0.55 | 0.24 |

Threshold for return flow to occur, mm | GWQMN | 50 | 0.0 |

Capillary rise coefficient | GW_REVAP | 0.2 | 0.2 |

Threshold for GW_REVAP to occur, mm | REVAPMN | 25 | 0 |

Slope length for lateral subsurface flow, m | SLSOIL | 48 | 59 |

## Appendix C

Parameter | Short Name | Medvezhy | Elovy |
---|---|---|---|

Max. soil storage content, mm | FC | 350 | 150 |

PET limit | LP | 0.2 | 0.58 |

Recharge parameter | Beta | 1.7 | 2.7 |

Max. percolation rate, mm day^{−1} | PERC | 2.6 | 1.6 |

Upper zone limit, mm | HL | 28 | 45 |

Recession coef. | K0 | 0.99 | 0.16 |

Recession coef. | K1 | 0.40 | 0.03 |

Recession coef. | K2 | 0.13 | 0.0001 |

Length of triangular weighting function, days | MAXBAS | 1.8 | 2.9 |

PET correction factor, 1 °C^{−1} | Cet | 0 | 0.03 |

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**Figure 1.**The experimental catchments’ topography (vertical distance between iso-level lines is 100 m), localization of observational sites, and soil cover: 1—Dystric Cambisols Humic and Nechic, 2—Dystric Skeletic Leptosols (Humic), 3—Dystric Fluvisols and Sapric Histosols, 4—Dystric Cambisols Gleyic and Stagnic, 5—Dystric Fluvic Cambisols, 6—catchments’ boundary, 7—weather stations, 8—stream gauges, 9—soil lysimeters, 10—river network.

**Figure 2.**The residual plots for two-dimensional mixing subspace: (

**a**) Medvezhy catchment; (

**b**) Elovy catchment.

**Figure 3.**Mixing diagrams in the U-space for: (

**a**) Medvezhy catchment; (

**b**) Elovy catchment. RW—rainwater, GW—groundwater, SW1, SW2—soil water.

**Figure 4.**Comparison of modelled and measured series of streamwater sample tracer concentrations: (

**a**) Medvezhy catchment; (

**b**) Elovy catchment.

**Figure 5.**Streamflow constituents’ rating curves: (

**a**) Medvezhy catchment; (

**b**) Elovy catchment; GW—orange dots, SW1—yellow triangles, and SW1 + SW2—red squares.

**Figure 6.**Dynamics of precipitation (1), calculated (2—ECOMAG, 3—SWAT, 4—HBV) and observed (5) runoff for the whole period of hydrological simulation ((

**a**)—Medvezhy creek, (

**b**)—Elovy creek) and examples of flood events ((

**c**)—Medvezhy creek, (

**d**)—Elovy creek).

**Figure 7.**Examples of calculated absolute (mm) and relative (%) fraction of daily runoff constituents for Medvezhy catchment (

**left panel**) and Elovy catchment (

**right panel**).

**Figure 8.**Comparison of calculated monthly absolute (mm) and relative (%) proportions of runoff constituents: (

**a**)—Medvezhy catchment, (

**b**)—Elovy catchment.

**Figure 9.**Comparison of calculated pentad absolute (mm) and relative (%) proportions of runoff constituents: (

**a**)—Medvezhy catchment, (

**b**)—Elovy catchment.

Characteristics | Elovy | Medvezhy |
---|---|---|

Area, km^{2} | 3.5 | 7.6 |

Avg. height, m | 722 | 704 |

Max. height, m | 962 | 869 |

Avg. slope, % | 13.5 | 13.8 |

Max. slope, % | 28.7 | 31.5 |

Mean annual precipitation, mm ^{1} | 780 | 830 |

Mean annual temperature, °C ^{1} | 3.0 | 3.2 |

Avg. discharge, mm day^{−1 1} | 0.65 | 0.75 |

^{1}based on observations for the period: 01.01.11–31.12.14 for Elovy creek and the period 01.01.14–31.12.17 for Medvezhy creek.

Characteristics | ECOMAG | SWAT | HBV |
---|---|---|---|

Spatial discretization | HRU | HRU | Lumped |

Temporal discretization | Daily | Daily | Daily |

Number of calibrated parameters | 11 | 12 | 10 |

Snow component basis | Degree-day | Degree-day | Degree-day |

Potential evapotranspiration | Dalton method | Penman–Monteith | Penman–Monteith |

Actual evapotranspiration | Linear reduction in PET by soil storage content | Reduction in PET by soil water content | Linear reduction in PET by soil storage content |

Surface flow | Kinematic wave | SCS curve number | Linear storage |

Soil flow | Darcy’s law | Kinematic storage model | Linear storage |

Groundwater flow | Darcy’s law | Linear storage | Linear storage |

Routing method | Kinematic wave | Variable travel time | Triangular weighted |

**Table 3.**Pairwise correlations of the concentrations of solutes, ranked by R

^{2}(n is the number of samples).

R^{2} | Medvezhy Catchment, n = 69 | Elovy Catchment, n = 126 |
---|---|---|

>0.71 | TDS—HCO_{3}, SO_{4}—Mg, HCO_{3}—Mg, TDS—Mg | – |

0.7–0.61 | DOC—SO_{4}, HCO_{3}—SO_{4}, SO_{4}—Ca, HCO_{3}—Ca, TDS—Ca, Ca—Mg | – |

0.6–0.51 | TDS—SO_{4}, DOC—Mg | – |

0.5–0.41 | – | HCO_{3}—Mg, HCO_{3}—TDS, SO_{4}—NO_{3} |

0.4–0.3 | – | NO_{3}—HCO_{3}, NO_{3}—Na, HCO_{3}—Na, Na—TDS |

Catchment | Tracers | U1 * | U2 | U3 | U4 | U5 | U6 |
---|---|---|---|---|---|---|---|

Medvezhy | TDS, DOC, HCO_{3}, SO_{4}, Ca, Mg | 83.6 | 8.6 (92.2) | 4.4 (96.7) | 2.1 (98.7) | 0.9 (99.6) | 0.4 (100) |

Elovy | HCO_{3}, Mg, NO_{3}, Na | 64.8 | 20.2 (85.0) | 9.7 (94.7) | 5.3 (100) | - | - |

**Table 5.**Chemical composition of end-members. n—number of samples, range of concentrations is in the numerator, average values are in the denominator.

Tracer, mg/L | Medvezhy Catchment | Elovy Catchment | |||||
---|---|---|---|---|---|---|---|

End-Members | |||||||

Rainwater (n = 36) | Groundwater (n = 15) | Soilwater (n = 12) | Rainwater (n = 36) | Groundwater (n = 5) | Soil Water 1 (n = 13) | Soil Water 2 (n = 7) | |

HCO_{3} | <0.1–2.30 | 75.6–90.3 | 14.6–24.3 | <0.1–2.30 | 14.2–19.2 | 10.4–18.0 | 6.71–9.76 |

0.37 | 84.3 | 19.4 | 0.37 | 16.4 | 13.7 | 8.11 | |

Mg | <0.02–0.13 | 1.66–5.18 | 3.25–5.36 | <0.02–0.1 | 0.85–1.04 | 0.34–0.61 | 0.39–0.55 |

0.05 | 3.47 | 4.56 | 0.05 | 0.98 | 0.4 | 0.48 | |

TDS | 0.05–14.9 | 121–163 | 30.5–100 | - | - | - | - |

5.32 | 146 | 63.8 | |||||

DOC | 0.18–5.60 | 2.50–4.76 | 4.10–42.9 | - | - | - | - |

1.77 | 3.56 | 18.1 | |||||

SO_{4} | <0.32–5.75 | 16.2–29.0 | 4.07–9.09 | - | - | - | - |

1.42 | 23.9 | 6.71 | |||||

Ca | <0.1–6.78 | 17.8–38.9 | 6.96–22.7 | - | - | - | - |

0.65 | 27.8 | 15.4 | |||||

NO_{3} | - | - | - | <0.2–5.1 | <0.2–0.72 | <0.2–0.15 | 2.13–7.45 |

1.17 | 0.39 | 0.05 | 4.66 | ||||

Na | - | - | - | 0.04–1.0 | 2.82–2.99 | 4.72–7.80 | 2.00–2.66 |

0.14 | 2.91 | 5.79 | 2.41 |

Model | Medvezhy | Elovy | ||||||
---|---|---|---|---|---|---|---|---|

Year | R^{2} | NSE | BIAS, % | Year | R^{2} | NSE | BIAS, % | |

ECOMAG | 2015 | 0.92 | 0.91 | −5 | 2012 | 0.93 | 0.91 | −0.3 |

2016 | 0.92 | 0.90 | 8 | 2013 | 0.87 | 0.80 | 13 | |

2017 | 0.91 | 0.87 | −6 | 2014 | 0.84 | 0.83 | 4 | |

2015–2017 | 0.92 | 0.90 | 4 | 2012–2014 | 0.90 | 0.89 | 10 | |

SWAT | 2015 | 0.94 | 0.88 | −20 | 2012 | 0.90 | 0.90 | −4 |

2016 | 0.89 | 0.85 | 6 | 2013 | 0.82 | 0.81 | −1 | |

2017 | 0.69 | 0.67 | −12 | 2014 | 0.93 | 0.88 | −13 | |

2015–2017 | 0.90 | 0.86 | −1 | 2012–2014 | 0.86 | 0.86 | −6 | |

HBV | 2015 | 0.35 | 0.35 | −8 | 2012 | 0.96 | 0.96 | 1 |

2016 | 0.92 | 0.91 | 18 | 2013 | 0.83 | 0.83 | −6 | |

2017 | 0.56 | 0.53 | −3 | 2014 | 0.64 | 0.62 | 4 | |

2015–2017 | 0.91 | 0.91 | 12 | 2012–2014 | 0.88 | 0.88 | −0.3 |

**Table 7.**Seasonal runoff constituents obtained from rainfall–runoff models and hydrograph separation by EMMA.

Source | Medvezhy | Elovy ^{1} | ||||||
---|---|---|---|---|---|---|---|---|

SWAT | HBV | ECOMAG | EMMA | SWAT | HBV | ECOMAG | EMMA | |

2015 | 2012 | |||||||

Surface, % | 0.0 | 0.0 | 43.5 | 25.6 | 0.0 | 22.1 | 7.7 | 15.1 |

Soil, % | 97.8 | 2.8 | 29.9 | 14.6 | 35.3 | 72.3 | 89.3 | 75.5 |

Ground, % | 2.2 | 97.2 | 26.6 | 59.8 | 64.7 | 5.6 | 3.0 | 9.4 |

Total, mm | 26.9 | 43.9 | 34.6 | 37.2 | 64.6 | 74.1 | 78 | 74.1 |

2016 | 2013 | |||||||

Surface, % | 57 | 7.8 | 32.1 | 34.4 | 0.0 | 5.0 | 3.5 | 24.4 |

Soil, % | 33.3 | 43.7 | 63.0 | 33 | 36.2 | 85.9 | 94.2 | 66.3 |

Ground, % | 9.7 | 48.5 | 4.9 | 32.6 | 63.8 | 9.1 | 2.3 | 9.3 |

Total, mm | 211.3 | 233.4 | 213.3 | 195.2 | 62.2 | 76.6 | 100.3 | 85.6 |

2017 | 2014 | |||||||

Surface, % | 0.7 | 0.0 | 58.3 | 27.3 | 0.1 | 1.0 | 3.8 | 23.8 |

Soil, % | 99.3 | 13.3 | 22.9 | 18.3 | 45.4 | 86.2 | 92.8 | 63.2 |

Ground, % | 0 | 86.7 | 18.8 | 54.4 | 54.5 | 12.8 | 3.3 | 12.9 |

Total, mm | 35 | 38.1 | 37 | 38.7 | 49.4 | 73.7 | 71.0 | 66.6 |

2015–2017 | 2012–2013 | |||||||

Surface, % | 44.1 | 5.7 | 35.8 | 32.1 | 0.0 | 9.3 | 4.9 | 21.2 |

Soil, % | 47.8 | 34.4 | 54.8 | 28.4 | 38.4 | 81.5 | 92.3 | 68.4 |

Ground, % | 8.1 | 59.9 | 9.4 | 39.5 | 61.6 | 9.2 | 2.8 | 10.4 |

Total, mm | 273.1 | 315.5 | 284.9 | 271.2 | 176.2 | 224.3 | 249.3 | 226.3 |

^{1}Soil flow proportion for Elovy catchment obtained by EMMA is the sum of the SW1 (soil organic) and SW2 (soil mineral) parts; see Section 3 for details.

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© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bugaets, A.; Gartsman, B.; Gubareva, T.; Lupakov, S.; Kalugin, A.; Shamov, V.; Gonchukov, L.
Comparing the Runoff Decompositions of Small Experimental Catchments: End-Member Mixing Analysis (EMMA) vs. Hydrological Modelling. *Water* **2023**, *15*, 752.
https://doi.org/10.3390/w15040752

**AMA Style**

Bugaets A, Gartsman B, Gubareva T, Lupakov S, Kalugin A, Shamov V, Gonchukov L.
Comparing the Runoff Decompositions of Small Experimental Catchments: End-Member Mixing Analysis (EMMA) vs. Hydrological Modelling. *Water*. 2023; 15(4):752.
https://doi.org/10.3390/w15040752

**Chicago/Turabian Style**

Bugaets, Andrey, Boris Gartsman, Tatiana Gubareva, Sergei Lupakov, Andrey Kalugin, Vladimir Shamov, and Leonid Gonchukov.
2023. "Comparing the Runoff Decompositions of Small Experimental Catchments: End-Member Mixing Analysis (EMMA) vs. Hydrological Modelling" *Water* 15, no. 4: 752.
https://doi.org/10.3390/w15040752