Modelling surface water dynamics in an Amazonian sub-basin: impacts of hydraulic geometry refinement

Figures & data

Figure 1. Purus river basin

Table 1. Bankfull width (W) and depth (D) obtained for the cross-sections of river gauge stations located in the Purus River basin

Gauge station	Name	River	Lat	Long	A (km^2)	W (m)	D (m)
13180000	Manoel Urbano	Purus	−8.89	−69.28	32,714	214.6	7.5
13300000	Seringal São José	Iaco	−9.37	−68.72	11,264	170.1	6.7
13410000	Seringal da Caridade	Purus	−9.04	−68.59	63,108	261.1	12.9
13450000	Assis Brasil	Acre	−10.95	−69.56	3,722	86.7	4.7
13470000	Brasiléia	Acre	−11.01	−68.75	7,035	106.7	6.6
13580000	Fazenda Santo Afonso	Branco	−10.09	−67.90	6,400	80.5	6.2
13600002	Rio Branco	Acre	−9.98	−67.80	23,484	130.3	10.5
13650000	Floriano Peixoto	Acre	−9.07	−67.40	34,699	210.7	9.7
13,710,001	Valparaíso-Montante	Purus	−8.65	−67.38	105,476	350.4	12.2
13740000	Fazenda Borangaba	Pauini	−7.54	−67.48	23,957	146.4	9.9
13750000	Seringal Fortaleza	Purus	−7.72	−67.00	154,242	379.5	16.0
13870000	Lábrea	Purus	−7.26	−64.80	226,939	471.0	16.7
13880000	Canutama	Purus	−6.54	−64.38	236,373	478.6	17.7
13885000	Cristo	Mucuim	−7.43	−64.24	5,789	171.1	5.6
13886000	Bacaba	Tapaua	−6.31	−64.89	38,228	292.8	5.9
13962000	Arumã-Jusante	Purus	−4.73	−62.14	366,384	726.1	24.0

where Lat is the latitude; Long is the longitude; A is the drainage area; W is the bankfull width; and D is the bankfull depth.

Table 2. Efficiency metrics used in this study

Metric	Abbreviation	Assessment	Equation	Range	Optimal Value
Coefficient of Determination	r^2	Linear correlation		0.0 to 1.0	1.0
Root Mean Square Error	RMSE	Deviation of predicted values	$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}\right)}^2}$	0.0 to ∞	0.0
Mean Absolute Error	MAE	Deviation of predicted values	$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}\right|$	0.0 to ∞	0.0
Mean Bias Error	MBE	Deviation of predicted values	$\mathrm{M}\mathrm{B}\mathrm{E}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}}\right)$	-∞ to ∞	0.0
Nash-Sutcliffe efficiency	NSE	Agreement for high values	$\mathrm{N}\mathrm{S}\mathrm{E}=1-\frac{{\sum }_{\mathrm{i}=\mathrm{i}}^{\mathrm{n}}{\left({\mathrm{O}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}}\right)}^2}{{\sum }_{\mathrm{i}=\mathrm{i}}^{\mathrm{n}}{\left({\mathrm{O}}_{\mathrm{i}}-\bar{\mathrm{O}}\right)}^2}$	-∞ to 1.0	1.0
Log-transformed Nash-Sutcliffe efficiency	NSElog	Agreement for low values	$\mathrm{N}\mathrm{S}{\mathrm{E}}_{\mathrm{l}\mathrm{o}\mathrm{g}}=1-\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left(\mathrm{l}\mathrm{o}\mathrm{g}{\mathrm{O}}_{\mathrm{i}}-\mathrm{l}\mathrm{o}\mathrm{g}{\mathrm{P}}_{\mathrm{i}}\right)}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left(\mathrm{l}\mathrm{o}\mathrm{g}{\mathrm{O}}_{\mathrm{i}}-\mathrm{l}\mathrm{o}\mathrm{g}\bar{\mathrm{O}}\right)}^2}$	-∞ to 1.0	1.0
Overall BIAS (%)	BIAS	Under- and overestimation	$\mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}=\left(\frac{{\sum }_{\mathrm{i}=\mathrm{i}}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{i}}-{\sum }_{\mathrm{i}=\mathrm{i}}^{\mathrm{n}}{\mathrm{O}}_{\mathrm{i}}}{{\sum }_{\mathrm{i}=\mathrm{i}}^{\mathrm{n}}{\mathrm{O}}_{\mathrm{i}}}\right)\times 100$	-∞ to ∞	0.0
Kling-Gupta efficiency	KGE	Overall performance	$\mathrm{K}\mathrm{G}\mathrm{E}=1-\sqrt{{\left(\mathrm{r}-1\right)}^2+{\left(\frac{{\sigma }_{\mathrm{p}}}{{\sigma }_{\mathrm{o}}}-1\right)}^2+{\left(\frac{\bar{\mathrm{P}}}{\bar{\mathrm{O}}-1}\right)}^2}$	-∞ to 1.0	1.0
BIAS in standard deviation (%)	σBIAS	Under- and overestimation	$\sigma \mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}=\left(\frac{{\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{o}}}{{\sigma }_{\mathrm{o}}}\right)\times 100$	-∞ to ∞	0.0

where n is the number of observations; P_i is the simulated variable; O_i is the observed variable; is the mean of the simulated variable; is the mean of the observed variable; σ_p is the standard deviation of the simulated variable; and σ_o is the standard deviation of the observed variable.

Table 3. Hydraulic geometry relationships obtained for the Purus River basin

Entire basin
	No. of stations	Depth (D)	r^2	Width (W)	r^2
Purus river basin	16	D = 0.2643⋅A^0.3430	0.91	W = 1.5996⋅A^0.4676	0.93
Hydrologically homogeneous regions
HHR 1	12	D = 0.5147⋅A^0.2830	0.92	W = 2.405⋅A^0.4404	0.97
HHR 2	4	D = 0.0362⋅A^0.5044	0.96	W = 5.7287⋅A^0.3708	0.93

Figure 2. Hydrologically homogeneous regions (HHR) obtained for the Purus River basin

Table 4. Efficiency metrics for the comparison between width and depth data obtained by different methods and observed data from gauge stations in the Purus River basin

	RMSE	MAE	MBE	NSE	NSElog
Width
GRWD	150.65	129.93	127.86	0.22	0.44
HG relationship for the entire basin	43.69	34.97	−3.44	0.93	0.87
HG relationships for the HHRs	33.42	24.58	−1.22	0.96	0.95
Depth
GRWD	5.62	4.86	−4.84	−0.13	−0.76
HG relationship for the entire basin	1.63	1.28	−0.06	0.91	0.86
HG relationships for the HHRs	1.24	1.01	−0.07	0.95	0.82

Figure 3. Dispersion diagrams between observed and estimated bankfull widths and depths

Figure 4. Difference between the performances of MGB SA for streamflow metrics using GRWD data and using HG relationships for HHRs for the Purus River basin

Table 5. Streamflow metrics using GRWD data and using HG relationships for HHRs for the Purus River basin

Gauge station	Name	Hydraulic geometries	NSE	NSElog	KGE	BIAS (%)
13880000	Canutama	GRWD	0.45	0.58	0.66	26.50
		HG relationships	0.53	0.79	0.56	28.30
13870000	Lábrea	GRWD	0.50	0.69	0.59	33.90
		HG relationships	0.48	0.79	0.50	35.30
13886000	Bacaba	GRWD	0.55	0.15	0.65	−0.50
		HG relationships	0.74	0.70	0.87	−1.00
13885000	Cristo	GRWD	0.43	0.25	0.37	−4.30
		HG relationships	0.71	0.79	0.63	−3.90

Figure 5. Comparison between streamflow simulated using geomorphological data from GRWD and from HG relationships with streamflow observed in the gauge stations in the Purus River basin

Figure 6. Difference between MGB SA performance for water level metrics (anomaly) using GRWD data and HG relationships for HHRs of the Purus River basin

Figure 7. Comparison between anomalies simulated using GRWD data and HG relationships with observed anomalies from Purus River basin gauge stations

Data availability statement

Some or all data, models, or codes that support the findings of this study are available from the corresponding authors upon reasonable request.