Pilot-point based multi-objective calibration in a surface–subsurface distributed hydrological model

Figures & data

Fig. 1 Location and land use of the Buriti Vermelho basin.

Fig. 2 Location of sensors within the Buriti Vermelho catchment.

Table 1 Hydrological properties, symbols used and dimensions included in the calibration exercise

System	Parameter	Symbol	Units	Spatially variable
Subsurface	Porosity	Φ	m^3 m^−3	Yes
	Soil retention parameter	α	m^−1	Yes
	Soil retention parameter	β	−	Yes
	Saturated horizontal hydraulic conductivity	K sat	mh^−1	Yes
Surface	Leakance	K G	h^−1	Yes
	Manning's n	n	hm^−1/3	Yes
Channel	Channel leakance	K c	h^−1	No
	Channel Manning's n	Ch_n	hm^−1/3	No

Fig. 3 Location and identification number of the pilot points.

Table 2  Estimated value of the parameters at each pilot point after the calibration. The subscript after the parameter identifies the associated pilot point

Param	Value	Param	Value	Param	Value	Param	Value	Param	Value	Param	Value
Ch_n	0.003
K c	0.412
K sat1	0.019	Φ1	0.35	n 1	9.03E-05	K G1	0.052	α1	0.45	β1	1.5
K sat2	0.005	Φ2	0.414	n 2	5.48E-05	K G2	0.098	α2	0.272	β2	4.18
K sat3	2.59E-04	Φ3	0.414	n 3	1.66E-04	K G3	0.006	α3	0.093	β3	1.5
K sat4	0.003	Φ4	0.362	n 4	4.82E-04	K G4	0.023	α4	0.184	β4	3.785
K sat5	4.69E-05	Φ5	0.379	n 5	1.15E-04	K G5	0.022	α5	0.333	β5	6
K sat6	1.15E-05	Φ6	0.65	n 6	2.82E-04	K G6	0.04	α6	0.592	β6	3.243
K sat7	0.006	Φ7	0.481	n 7	2.71E-04	K G7	0.056	α7	0.135	β7	4.529
K sat8	4.29E-04	Φ8	0.624	n 8	2.35E-05	K G8	0.043	α8	0.47	β8	1.971
K sat9	0.103	Φ9	0.557	n 9	4.02E-04	K G9	0.094	α9	0.306	β9	2.82
K sat10	1.00E-05	Φ10	0.389	n 10	4.37E-05	K G10	0.057	α10	0.368	β10	4.219
K sat11	0.075	Φ11	0.367	n 11	2.06E-05	K G11	0.032	α11	0.512	β11	1.5
K sat12	0.001	Φ12	0.35	n 12	6.43E-05	K G12	0.068	α12	1.992	β12	3.308

Table 3  Comparison of statistics between some estimated hydrological properties and a limited number (n = 9) of laboratory measurements done on random soil cores taken within the BV basin. All average differences are statistically significant

		Φ	α	β	K sat
Measured	Average	0.61	0.06	1.35	0.10
	SD	0.02	0.03	0.12	0.07
Estimated	Average	0.44	0.48	3.21	0.02
	SD	0.11	0.50	1.42	0.03

Fig. 4 Parameter fields estimated at the end of the calibration process: (a) overland hydraulic roughness; (b) leakance coefficient at the surface; (c) porosity; (d) horizontal saturated hydraulic conductivity; (e) van Genuchten parameter α; (f) van Genuchten parameter β.

Fig. 5 Measured versus simulated channel flow at the basin outlet (bias = 1.022, mean absolute error = 45.57 m³ h⁻¹, R² = 0.61); bias is defined as the ratio of simulated average discharge to the observed average discharge (Vivoni et al. 2009). An unbiased simulation has a bias = 1.

Fig. 6 Measured versus simulated hydraulic heads at Piezometer #2 (bias = 1.29, mean absolute error = 0.196 m, R² = 0.73); bias is defined as the ratio of simulated average head to the observed average head (Vivoni et al. 2009). An unbiased simulation has a bias = 1. Bias has been calculated setting the reference datum at 910 m. Shaded area is an estimation of the spatial uncertainty of pressure total head (one standard deviation calculated using adjacent cells).

Fig. 7 Measured versus simulated soil moisture content at locations: (a) SMP_D (bias = 0.95, mean absolute error = 0.026, R² = 0.55), and (b) SMP F (bias = 1.04, mean absolute error = 0.017, R² = 0.77). Bias is defined as the ratio of simulated average soil moisture to the observed average soil moisture (Vivoni et al. 2009). An unbiased simulation has a bias = 1. Shaded area is an estimation of the spatial uncertainty of soil moisture (one standard deviation calculated using adjacent cells).

Fig. 8 Composite scaled sensitivity (css) at each pilot point for parameters: (a) Manning's n, (b) leakance, (c) porosity, (d) hydraulic conductivity (log₁₀ of sensitivities), (e) retention curve parameter α and (f) retention curve parameter β. The size of the circle is proportional to the css of the parameter. Square symbol indicates the location of the piezometer; cross symbols indicate the location of soil moisture probes.

Fig. 9 DFBETA influence graph. Each black dot in the graphs indicates that the associated parameter at the location of the pilot point is influenced by the discharge observation in the bottom graph. A parameter is influenced by an observation when the DFBETA statistic is larger than 2/(ND + NPR)^0.5 (see Section 3.7).

Fig. 11 DFBETA influence graph. Each black dot in the graphs indicates that the associated parameter at the location of the pilot point is influenced by the soil moisture observation in the bottom graph. A parameter is influenced by an observation when the DFBETA statistic is larger than 2/(ND + NPR)^0.5 (see Section 3.7).

Fig. 10 DFBETA influence graph. Each black dot in the graphs indicates that the associated parameter at the location of the pilot point is influenced by the piezometric observation in the bottom graph. A parameter is influenced by an observation when the DFBETA statistic is larger than 2/(ND + NPR)^0.5 (see Section 3.7).