Parameter Uncertainty of a Snowmelt Runoff Model and Its Impact on Future Projections of Snowmelt Runoff in a Data-Scarce Deglaciating River Basin
Abstract
:1. Introduction
2. Study Area and Data
2.1. Study Area
2.2. Data
3. Methods
3.1. SRM Modeling
3.2. SRM Calibration Methods
3.3. Bias Correction of GCM Outputs
- The LOCI method was used to correct the precipitation occurrence, which ensures that the frequency of the precipitation occurrence simulated by GCMs at the reference period equals that of the observed data for a specific month. A threshold for precipitation occurrence determined at the historical period was then applied to the future period.
- The DT method was used to correct the empirical distribution of GCM-simulated precipitation and temperature magnitudes in terms of 100 quantiles from 0.01 to 1 with an interval of 0.01.
3.4. Future Snow Covered Area Projection
3.5. GLUE Method for Uncertainty Estimates
- 100,000 Monte Carlo sampling points of and were implemented from a feasible parameter space (0–1) with uniform distribution;
- The likelihood values were calculated for all 100,000 model runs;
- The likelihood functions (NSE and VE) and the threshold values (0.55 and ±10%, respectively) were specified as behavioral parameter sets; and
- Posterior parameter sets were extracted depending on the threshold of the likelihood functions.
4. Results
4.1. Parameter Uncertainty
4.2. Confidence Interval of Discharge
4.3. Projected Future Temperature, Precipitation, and SCA
4.4. Uncertainty in the Discharge Projections
5. Discussion
6. Conclusions
- The strategy with a division of 1 or 2 sub-period(s) in a hydrological year is appropriate for SRM modeling when considering the balance between simulation performance and the overfitting problem/uncertainty. In addition, the multi-year calibration approach is more stable than the yearly calibration for SRM hydrological simulation and projection, as the latter presents a lower validation performance combined with higher future projection uncertainty.
- The future runoff projection contains large uncertainties, among which parameter uncertainty plays a significant role. The projection results indicate that the onset of snowmelt runoff is likely to shift earlier, and the discharge of the snowmelt season is projected to increase for the 2041–2050 period.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. SRM Modelling
- = the average daily discharge (m3/s)
- /= the runoff coefficient expressing the losses as a ration of runoff to precipitation, with referring to snowmelt and referring to rainfall
- = the degree-day factor (cm/°C/day)
- = the number of degree-days (°C day)
- = the adjustment by temperature lapse rate when extrapolating the temperature from the station to the mean elevation of the zone (°C day)
- = the ratio of the snow covered area to the total area (%)
- = the precipitation contributing to runoff (cm), which is determined by a preselected threshold temperature, , to be rainfall or snowfall. The contribution of rainfall is immediate while snowfall will be kept on storage until melting conditions occur.
- = the area elevation zone (km2)
- = 10,000/86,400, the coefficient converting data from a runoff depth (cm×km2/day) to discharge (m3/s)
- = the recession coefficient,
- = the day number
Appendix A.1.1. Input Variables
Appendix A.1.2. Parameters
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Zone | Elevation Range (m) | Mean Elevation (m) | Area (km2) | Area (%) |
---|---|---|---|---|
A | 1280–2700 | 2230 | 1324 | 9.07 |
B | 2701–3700 | 3190 | 2248 | 15.40 |
C | 3701–4700 | 4250 | 2170 | 14.86 |
D | 4701–5200 | 4975 | 2485 | 17.02 |
E | 5201–5700 | 5440 | 3238 | 22.18 |
F | 5701–6780 | 6020 | 3135 | 21.47 |
Total | 1280–6780 | 4470 | 14600 | 100 |
Model Name | Institute/Country | Horizontal Resolution (lon×lat) |
---|---|---|
MPI-ESM-MR | Max Planck Institute for Meteorology, Germany | 192 × 96 |
MPI-ESM-LR | Max Planck Institute for Meteorology, Germany | 192 × 96 |
IPSL-CM5A-LR | Institute Pierre-Simon Laplace, France | 96 × 96 |
GFDL-CM3 | USA | 144 × 90 |
NorESM1-M | Norwegian Climate Centre, Norway | 144 × 96 |
MIROC5 | MIROC, Japan | 256 × 128 |
MIROC-ESM | MIROC, Japan | 128 × 64 |
Model Parameters | Values |
---|---|
Degree Day Factor (cm/°C/day) | 0.3 |
Lapse Rate (°C/100 m) | 0.65 |
Threshold Temperature, | 1 (June–August); 3 (September–May) |
Rainfall Contributing Area, RCA | 1 (May–September); 0 (October–April) |
Recession Coefficient, K, which is Determined by: | ; |
Sub-Period(s) | Yearly Calibration | Multi-Year Calibration | ||||
---|---|---|---|---|---|---|
ARIL | PCI | PUCI | ARIL | PCI | PUCI | |
1 | 0.454 | 0.204 | 0.559 | 0.440 | 0.178 | 0.517 |
2 | 1.009 | 0.430 | 0.475 | 0.848 | 0.376 | 0.501 |
4 | 1.287 | 0.500 | 0.427 | 1.192 | 0.470 | 0.436 |
5 | 1.531 | 0.586 | 0.416 | 1.361 | 0.538 | 0.432 |
6 | 1.546 | 0.596 | 0.418 | 1.356 | 0.556 | 0.447 |
7 | 1.548 | 0.606 | 0.424 | 1.396 | 0.570 | 0.444 |
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Xiang, Y.; Li, L.; Chen, J.; Xu, C.-Y.; Xia, J.; Chen, H.; Liu, J. Parameter Uncertainty of a Snowmelt Runoff Model and Its Impact on Future Projections of Snowmelt Runoff in a Data-Scarce Deglaciating River Basin. Water 2019, 11, 2417. https://doi.org/10.3390/w11112417
Xiang Y, Li L, Chen J, Xu C-Y, Xia J, Chen H, Liu J. Parameter Uncertainty of a Snowmelt Runoff Model and Its Impact on Future Projections of Snowmelt Runoff in a Data-Scarce Deglaciating River Basin. Water. 2019; 11(11):2417. https://doi.org/10.3390/w11112417
Chicago/Turabian StyleXiang, Yiheng, Lu Li, Jie Chen, Chong-Yu Xu, Jun Xia, Hua Chen, and Jie Liu. 2019. "Parameter Uncertainty of a Snowmelt Runoff Model and Its Impact on Future Projections of Snowmelt Runoff in a Data-Scarce Deglaciating River Basin" Water 11, no. 11: 2417. https://doi.org/10.3390/w11112417