Evaluation of storage–discharge relationships and recession analysis-based distributed hourly runoff simulation in large-scale, mountainous and snow-influenced catchment

Figures & data

Table 1. Major characteristics of the study catchments.

Characteristic (units)	Gaulfoss	Hugdal bru	Eggafoss	Lillebudal bru
Latitude/longitude of streamflow station (°)	63.12/10.25	63.01/10.19	62.93/11.08	62.83/10.48
Catchment area, A (km^2)	3090	549	653	168
Elevation 25 m DEM (m a.m.s.l.)	54–1330	130–1257	285–1286	516–1304
Mean elevation of catchment (m a.m.s.l.)	730.60	651.27	832.33	915.20
Elevation of climate stations	127–885	127–885	127–885	127–885
Catchment averaged annual precipitation (mm)	874.21	863.53	884.06	864.70
Lake percentage (%)	2.05	1.00	2.84	1.14
Forest percentage (%)	36.72	53.59	24.55	21.70
Bare rock/mountain above timberline (%)	35.80	20.69	43.96	65.33
Marsh/bog (%)	14.53	16.70	12.57	8.98
Farmland (%)	2.66	5.99	2.11	0.52

Figure 1. (a) Maps of locations and hypsometric curves for the study catchments; (b) mean annual (from hourly observations) precipitation–elevation relationships; (c) model structure (grid cell) based on Kirchner’s runoff response routine. The snow routine is based on Kolberg and Gottschalk (2006). Q_inst is instantaneous runoff, Q_gi denotes average runoff (over the time step) generated at the grid cells, and Q_sim denotes routed simulated flow.

Figure 2. (a) Flow recession rates and fitted recession plots; (b) ln(−dQ/dt) versus ln(g(Q)) plots showing effects of the lower end of the recession.

Table 2. Parameters and their prior ranges.

No.	Calibrated (free) parameter	Description	Unit	Prior range [Min., Max.]
	Snow
1	TX	Threshold temperature	°C	[−3,2]
2	WS	Snow melt sensitivity to wind speed	–	[1,6]
	Runoff response
3	EvR	Discharge at which AET equals 0.95PET	mm/h	[0.1,Qmax]
4	β0	Regression parameter (constant term)	–	[−4.2,−1]
5	β1	Regression parameter (linear term)	–	[0.2,1.5]
6	β2	Regression parameter (quadratic term)	–	[−0.5,0.5]
	Routing
7	V	Velocity of flow	m/s	[1.9,2.6]
8	D	Dispersion coefficient of flow	m^2/s	[200,1500]

Q_max is maximum streamflow for the calibration period.

Table 3. Estimated and calibrated parameters corresponding to NSE for Gaulfoss.

Cases	TX	WS	EvR	β2	β1	β0	V	D
1	NSE: regression parameters estimated from recession*
	−1.482	5.708	0.273	0.130	0.920	−2.850	2.198	774.215
2	NSE: calibrated parameters (routed)
	−1.482	5.708	0.273	−0.040	0.684	−2.477	2.198	774.215
	NSE: calibrated parameters (unrouted)
3	−0.999	5.895	0.670	−0.127	0.286	−3.234

*Parameters other than the regression parameters are calibrated parameters for the runoff routed case. Bold font indicates regression parameters.

Table 4. Parameter correlation matrix (r), and maximum and minimum values of marginal posterior parameters from calibration (runoff-routed) for Gaulfoss.

Parameter	TX	WS	EvR	β1	β0	β2	V	D
TX	1.00	0.44	0.27	0.03	0.12	−0.07	0.06	0.05
WS		1.00	0.23	0.25	0.27	0.23	−0.28	0.12
EvR			1.00	0.51	0.64	0.40	−0.17	−0.37
β1				1.00	0.91	0.97	−0.28	−0.23
β0					1.00	0.80	−0.36	−0.23
β2						1.00	−0.23	−0.20
V							1.00	−0.08
D								1.00
Max.	−0.73	6.00	0.34	1.49	−1.55	0.10	2.59	1466.24
Min.	−1.41	2.71	0.13	0.27	−3.63	−0.13	1.91	201.11

Bold font indicates |r| > 0.6.

Table 5. Results for maximum values of NSE for parameter estimation from recession segments and calibration for Gaulfoss, and temporal and spatial transferability or validation for “proxy ungauged” internal sub-catchments.

Cases	Max. NSE	Temporal validation (01/09/2010–01/09/2011)	Spatial validation
			Eggafoss	Hugdal bru	Lillebudal bru
1	NSE: regression parameters estimated from recession
	0.77	0.81	0.70	0.80	0.55
2	NSE: calibrated parameters (runoff routed)
	0.82	0.83	0.68	0.75	0.52
3	NSE: calibrated parameters (runoff unrouted)
	0.80	0.82	0.65	0.79	0.51

Figure 3. Hydrographs for Gaulfoss corresponding to the NSE: (a) regression parameters estimated from recession (runoff routed); (b) calibrated parameters (runoff routed); and (c) calibrated parameters (runoff unrouted). Simulation for calibrated or estimated parameters (1 September 2008–1 September 2010) and simulation for temporal validation (1 September 2010–1 September 2011). P represents IDW interpolated and catchment averaged precipitation.

Figure 4. (a) Typical results from diagnostic of the regression for the recession analysis: normality test for Hugdal bru (left), residuals plot for Gaulfoss (middle) and systematic lack of fit due to missing quadratic term for Eggafoss (right); (b) 95% ICL and JCR for regression parameters for Gaulfoss; (c) parameter uncertainty in terms of histograms of marginal posteriors from calibration (runoff-routed) for Gaulfoss.

Figure 5. (a) Precipitation and streamflow duration curves and (b) discharge sensitivity function (g(Q)) and “response time” (τ) for Gaulfoss. The g(Q) and τ were computed based on Equation (4) from the regression parameters estimated or obtained by calibration.

Kolberg, S.A. and Gottschalk, L., 2006. Updating of snow depletion curve with remote sensing data. Hydrological Processes, 20 (11), 2363–2380. doi:10.1002/(ISSN)1099-1085

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