An evaluation of regionalization and watershed classification schemes for continuous daily streamflow prediction in ungauged watersheds

Figures & data

Figure 1. Location map of selected Ontario watersheds and sample watersheds.

Table 1. Catchment characteristics used in this study and their range of values for the 90 Ontario basins (modified after Samuel et al. 2011).

Catchment attributes			Unit	Range of values	Notes
Location of watershed (centroid)	Latitude		Degrees	44.2–55.3
	Longitude		Degrees	−94.4–−74.6
Morphology of basins	Area		km^2	85.5–91,802
	Mean watershed slope		%	1.5–208.3
	Mean elevation		m	13.5 – 785.6
Percentage of area covered by	Lakes		%	0 – 0.2	Percentage of area covered by lakes
	Forest		%	0–100	Sum of percentage of area covered by coniferous, deciduous and mixed forest
	Rapid drainage class		%	0–100	Sum of percentage of area covered by rapid, well and moderately well drained drainage classes
	Rooting depth deeper than 150 cm		%	0–100	Percentage of area covered by rooting depth deeper than 150 cm
	Surficial geology	Glaciofluvial sediments	%	0–55	Sum of percentage of area covered by glaciofluvial sediments
		Glacio-deposits	%	5–100	Sum of percentage of area covered by till blanket and till veneer
		Rocks	%	0–66	Percentage of area covered by undivided bedrocks

Figure 2. Flowchart of methodology showing the four regionalization techniques – inverse distance weighted (IDW), multi-layer perceptron (MLP), support vector machine (SVM), and counter propagation neural network (CPNN) – used to transfer the parameters of two hydrologic models (McMaster University Hydrologiska Byråns Vattenbalansavdelning [MAC-HBV] and Sacramento Soil Moisture Accounting [SAC-SMA]) from gauged to ungauged watersheds considering two scenarios of classified and unclassified watersheds using non-linear principal component analysis (NLPCA), CNLPCA (compact NLPCA), and self-organizing map (SOM) techniques.

Table 2. Parameters of McMaster University Hydrologiska Byråns Vattenbalansavdelning (MAC-HBV) and Sacramento Soil Moisture Accounting (SAC-SMA) models and optimized ranges (using particle swarm optimization [PSO] algorithm).

MAC-HBV
Parameter	Description	Unit	Initial range	Optimized range
tr	Upper threshold temperature to distinguish between rainfall and snowfall	°C	−1.5–2.5	0–2.5
scf	snowfall correction factor	_	0.4–1.6	0.44–1.55
ddf	Degree day factor	mm/(day °ͦC)	0–5	0.5–5
athorn	A constant for Thornthwaite’s equation	_	0.1–0.3	0.1–0.3
fc	Maximum soil box water content	mm	50–800	111–800
lp	Limit for potential evaporation	mm/mm	0.1*fc–0.9*fc	5–717
beta	A non-linear parameter controlling runoff generation	_	0–10	0.25–10
k0	Flow recession coefficient in an upper soil reservoir (for soil moisture exceeds a threshold lsuz value)	days	1–30	1–30
lsuz	A threshold value used to control response routing on an upper soil reservoir	mm	1–100	1–100
k1	Flow recession coefficient in an upper soil reservoir	days	2.5–100	30–100
cperc	A constant percolation rate parameter	mm/day	0.01–6	0.01–6
k2	Flow recession coefficient in a lower soil reservoir	days	20–1000	100–500
maxbas	A triangle weighting function for modelling a channel routing routine	days	1–20	1–17
rcr	Rainfall correction factor	_	0.5–1.5	0.65–1.5
α1	An exponent in relation between outflow and storage representing non-linearity of storage –discharge relationship of lower reservoir	_	0.5–20	0.6–1.5
SAC-SMA
UZTWM	Upper-zone tension water maximum storage	mm	1–150	1–150
UZFWM	Upper-zone free water maximum storage	mm	1–150	17–145
LZTWM	Lower-zone tension water maximum storage	mm	1–500	1–446
LZFPM	Lower-zone free water primary maximum storage	mm	1–1000	1–996
LZFSM	Lower-zone free water supplemental maximum storage	mm	1–1000	1–1000
ADIMP	Additional impervious area	-	0–0.4	0–0.4
UZK	Upper-zone free water lateral depletion rate	day^−1	0.1–0.5	0.1–0.5
LZPK	Lower-zone primary free water lateral depletion rate	day^−1	0.0001–0.025	0.0001–0.025
LZSK	Lower-zone supplemental free water lateral depletion rate	day^−1	0.01–0.25	0.01–0.25
ZPERC	Maximum percolation rate	-	2.5–100	30–100
REXP	Exponent of the percolation equation	-	0.01–6	0.01–6
PCTIM	Impervious fraction of the watershed area	-	20–1000	100–500
PFREE	Fraction percolating from upper to lower zone free water storage	days	1–20	1–17
Rq	Routing coefficient	_	0.5–1.5	0.65–1.5
ddf	Degree day factor	_	0.5–20	0.6–1.5
scf	Snowfall correction factor	-	0.4–1.6	0.5–1.5
tr	Upper threshold temperature to distinguish between rainfall and snowfall	°C	−1.5–2.5	0–2.5
athorn	A constant for Thornthwaite’s equation	-	0.1–0.3	0.1–0.3
rcr	Rainfall correction factor	-	0.5–1.5	0.7–1.5
Constant numbers
RIVA	Riparian vegetation area	-	0
SIDE	Ratio of the deep recharge to channel baseflow	-	0
RSERV	Fraction of lower zone free water not transferable to tension water	-	0.3

Figure 3. Schematic representation of the Sacramento Soil Moisture Accounting (SAC-SMA) model as used in this study showing the model state parameters used. Abbreviations are presented in Table 2. Arrows indicate fluxes between components and the streamflow at the watershed outlet is shown (adapted from Vrugt et al. 2006).

Figure 4. Box plots of NSE and VE values for simulated daily stream flows for 90 watersheds across Ontario using calibrated model parameters of (a) McMaster University Hydrologiska Byråns Vattenbalansavdelning (MAC-HBV) and (b) Sacramento Soil Moisture Accounting (SAC-SMA). These resulted from the following optimization algorithms: particle swarm optimization (PSO), shuffle complex efficiency (SCE), non-sorted genetic algorithm II (NSGA II), and Monte Carlo simulation for validation period 1986–1994. Nash Sutcliffe efficiency (NSE) values above 0.5 and volume error (VE) values between −0.1 and 0.1 are considered to be models with good performance.

Table 3. Statistics of Nash Sutcliffe efficiency (NSE) values of estimated daily streamflow using McMaster University Hydrologiska Byråns Vattenbalansavdelning (MAC-HBV) and Sacramento Soil Moisture Accounting (SAC-SMA) models coupled with the following regionalization techniques: inverse distance weighted (IDW), multi-layer perceptron (MLP), counter propagation neural network (CPNN) and support vector machine (SVM). These were applied to unclassified watersheds (Unc) and classified watersheds with self-organizing map (SOM), non-linear principal component analysis (NLPCA) and CNPLCA (compact NLPCA) for the validation period from 1986 to 1994.

Regionalization technique		IDW				MLP				CPNN				SVR
Classification technique		Unc	SOM	NLPCA	CNLPCA	Unc	SOM	NLPCA	CNLPCA	Unc	SOM	NLPCA	CNLPCA	Unc	SOM	NLPCA	CNLPCA
MAC-HBV	Minimum	−0.75	−0.48	−0.63	−0.14	−2.20	−0.02	−0.25	−0.28	−1.21	−0.47	−0.13	−1.11	−0.82	−0.95	−2.80	−0.89
	Mean	0.44	0.45	0.45	0.47	0.35	0.47	0.43	0.41	0.26	0.41	0.43	0.42	0.29	0.31	0.34	0.33
	Median	0.49	0.48	0.51	0.50	0.43	0.51	0.47	0.45	0.32	0.44	0.46	0.47	0.33	0.36	0.44	0.43
	Maximum	0.68	0.73	0.69	0.69	0.64	0.68	0.69	0.68	0.72	0.69	0.70	0.70	0.66	0.64	0.68	0.70
SAC-SMA	Min	−1.50	−1.28	−0.41	−0.38	−0.68	−1.07	−0.53	−1.97	−2.52	−1.03	−1.66	−0.70	−3.05	−1.07	−2.85	−0.91
	Mean	0.40	0.45	0.45	0.48	0.40	0.44	0.43	0.45	0.26	0.38	0.39	0.42	0.29	0.34	0.31	0.36
	Median	0.52	0.53	0.53	0.53	0.47	0.52	0.50	0.50	0.40	0.48	0.48	0.49	0.41	0.46	0.46	0.47
	Maximum	0.70	0.71	0.72	0.71	0.70	0.68	0.70	0.68	0.71	0.69	0.70	0.69	0.68	0.66	0.69	0.67

Table 4. Nash Sutcliffe efficiency (NSE) values of estimated daily baseflow using McMaster University Hydrologiska Byråns Vattenbalansavdelning (MAC-HBV) and Sacramento Soil Moisture Accounting (SAC-SMA) models coupled with the following regionalization techniques: inverse distance weighted (IDW), multi-layer perceptron (MLP), counter propagation neural network, (CPNN) and support vector machine (SVM). These are applied to unclassified watersheds (Unc) and classified watersheds with self-organizing map (SOM), non-linear principal component analysis (NLPCA) and CNPLCA (compact NLPCA) for the validation period from 1986 to 1994.

Regionalization technique		IDW				MLP				CPNN				SVR
Classification technique		Unc	SOM	NLPCA	CNLPCA	Unc	SOM	NLPCA	CNLPCA	Unc	SOM	NLPCA	CNLPCA	Unc	SOM	NLPCA	CNLPCA
MAC-HBV	Minimum	−0.31	−0.43	−0.65	−0.44	−0.73	−0.32	−0.80	−0.29	−1.15	−0.66	−0.40	−0.68	−0.69	−0.55	−1.09	−0.69
	Mean	0.48	0.48	0.48	0.50	0.37	0.50	0.45	0.44	0.27	0.44	0.46	0.47	0.32	0.36	0.38	0.40
	Median	0.51	0.52	0.54	0.54	0.47	0.52	0.51	0.49	0.33	0.47	0.51	0.53	0.36	0.43	0.49	0.49
	Maximum	0.60	0.73	0.72	0.70	0.66	0.71	0.74	0.70	0.73	0.72	0.72	0.73	0.67	0.67	0.70	0.71
SAC-SMA	Minimum	−0.91	−0.37	−0.92	−0.36	−1.26	−1.33	−1.41	−1.20	−1.89	−1.32	−0.83	−0.98	−1.37	−0.96	−1.69	−0.80
	Mean	0.46	0.50	0.39	0.52	0.42	0.47	0.45	0.48	0.33	0.42	0.44	0.45	0.34	0.40	0.39	0.41
	Median	0.57	0.58	0.53	0.58	0.52	0.57	0.54	0.52	0.51	0.51	0.53	0.56	0.43	0.50	0.50	0.51
	Maxiimum	0.75	0.76	0.78	0.76	0.71	0.72	0.72	0.71	0.73	0.72	0.73	0.72	0.71	0.68	0.70	0.70

Table 5. Percentage of basins with deterioration more than −20% and improvement greater than 20% in (a) root mean square error (RMSE) of daily streamflow, (b) volume error (VE) of daily baseflow, (c) VE of daily peak flow, using the following classification techniques: non-linear principal component analysis (NLPCA), CNLPCA (compact NLPCA), and self-organizing map (SOM), applied prior to the following regionalization techniques: inverse distance weighted (IDW), multi-layer perceptron (MLP), counter propagation neural network (CPNN) and support vector machine (SVM), and on hydrologic models McMaster University Hydrologiska Byråns Vattenbalansavdelning (MAC-HBV) and Sacramento Soil Moisture Accounting (SAC-SMA).

(a) RMSE of daily streamflow
Regionalization	IDW			MLP			CPNN			SVM
Classification	NLPCA	CNLPCA	SOM	NLPCA	CNLPCA	SOM	NLPCA	CNLPCA	SOM	NLPCA	CNLPCA	SOM
MAC-HBV
< −20%	8	3	9	3	17	17	7	43	12	13	14	11
> 20%	4	3	3	16	20	20	39	10	37	16	23	18
SAC-SMA
< −20%	12	1	3	7	7	9	8	10	14	11	9	18
>20%	2	11	8	4	10	6	13	17	19	10	9	12
(b) VE of daily baseflow
MAC- HBV
< −20%	34	16	17	32	38	36	33	44	36	33	34	38
> 20%	41	23	16	53	47	56	56	41	54	51	49	41
SAC-SMA
< −20%	51	26	23	34	38	35	33	44	44	31	37	42
> 20%	11	24	23	48	50	41	49	36	48	46	49	46
(c) VE of daily peak flow < −20% or > 20%
MAC-HBV
< −20%	26	11	12	41	30	22	26	39	20	19	21	29
> 20%	31	19	16	31	43	47	61	36	52	47	47	36
SAC-SMA
< −20%	32	14	17	26	29	18	27	29	44	31	37	42
> 20%	14	12	11	39	29	42	37	37	48	46	49	46

Figure 5. Schematic maps of the spatial distribution of improvements in Root Mean Square Error (RMSE) and Volume Error (VE) of daily streamflow, low flow and peak flow regionalization using the counter propagation neural network (CPNN) technique on the McMaster University Hydrologiska Byråns Vattenbalansavdelning (MAC-HBV) model after (a) non-linear principal component analysis (NLPCA) and (b) self-organizing map (SOM) classification techniques. Small circles identify the basins with a consistent improvement of > 20% in daily mean, low and peak flow regionalization after watershed classification.

Figure 6. Schematic maps of the spatial distribution of improvements of Root Mean Square Error (RMSE) and Volume Error (VE) in daily streamflow, low flow and peak flow regionalization, using the counter propagation neural network (CPNN) regionalization technique on the Sacramento Soil Moisture Accounting (SAC-SMA) model after (a) non-linear principal component analysis (NLPCA) and (b) self-organizing map (SOM) classification techniques. Small circles identify the basins with a consistent improvement of > 20% in daily mean, low and peak flow regionalization after watershed classification.

Figure 7. Observed and simulated streamflow using the following hydrologic models: (a) McMaster University Hydrologiska Byråns Vattenbalansavdelning (MAC-HBV) and (b) Sacramento Soil Moisture Accounting (SAC-SMA) models coupled with counter propagation neural network (CPNN) technique on unclassified (CPN-Unc) and classified watersheds using non-linear principal component analysis (NLPCA) (CPN-NLPCA) on three sample watersheds specified in Figure 1.

Figure 8. The hydrograph of mean monthly flow in northern, central and southern watersheds of Ontario.

Figure 9. Spatial variability of percentage of land covered by: forest, lake, rapid drainage class, glacio-deposit, and glaciofluvial sediments and slope of FDC (Flow Duration Curve) in selected Ontario watersheds.

Samuel, J., P. Coulibaly, and R. A. Metcalfe. 2011. Estimation of continuous streamflow in Ontario ungauged basins: Comparison of regionalization methods. Journal of Hydrologic Engineering 16 (5): 447–459.10.1061/(ASCE)HE.1943-5584.0000338

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