# Exercise 5: Parameter Uncertainty

HBV-light allows many model runs to be carried out easily with randomly generated parameter sets by using the tool “Monte Carlo Runs”. In this exercise you are asked to perform both sensitivity studies (allowing one or two parameter values to vary) and parameter uncertainty estimations (allowing all (many) parameters to vary). Use the catchments HBVland or Vattholma (exercises 1 or 2) for this exercise.

**Parameter sensitivity, one parameter:**

- In the Monte Carlo tool, set the minimum and maximum for all parameters to the optimal values from the previous exercises and save the parameters (“save settings”).
- Change the limits for one parameter (e.g., CFMAX, FC, K1...) based on the values in the table below and let the software do many (~100–1000) model runs.
- Open the file results\multi.txt in MATLAB or Excel and plot the model efficiency (Reff) against the parameter value that you allowed to vary.
- Go to 2 and repeat the same for other parameters. Discuss the sensitivity of the different parameters. It might also be interesting to look at the sensitivity with regard to the log-transformed efficiency (logReff) and volume error (meandiff).

**Parameter sensitivity, two parameters: **

Perform the same steps as above, but allow two parameters to vary simultaneously now (e.g., TT and CFMAX, BETA and LP, K2 and PERC, ...). For visualization you now need to use 3-D or contour line plots.

**Monte Carlo runs:**

- In the Monte Carlo tool, set the minimum and maximum for all parameters according to the feasible limits given in the table below (you might want to save these values with “save settings” to avoid putting the numbers in more than once).
- Choose “save only if Reff >0.6” (to avoid large files) and let the software do a large number of runs (depending on available time, 10 000–1 000 000, you may go for a coffee or lunch in the meantime).
- Produce so-called “dotty-plots” by plotting individual parameter values against model efficiency (Reff).
- Discuss which parameters are less/more constrained. Compare these results with your conclusions from the sensitivity analysis.

Parameter |
Explanation |
Min. |
Max. |
Unit |
---|---|---|---|---|

Snow routine |
||||

TT |
Threshold temperature |
-1.5 |
2.5 |
°C |

CFMAX |
Degree-day factor |
1 |
10 |
mm °C-1 d-1 |

SCF |
Snowfall correction factor |
0.4 |
1 |
- |

CWH |
Water holding capacity |
0 |
0.2 |
- |

CFR |
Refreezing coefficient |
0 |
0.1 |
- |

Soil routine |
||||

FC |
Maximum of SM (storage in soil box) |
50 |
500 |
mm |

LP |
Threshold for reduction of evaporation (SM/FC) |
0.3 |
1 |
- |

BETA |
Shape coefficient |
1 |
6 |
- |

CET |
Correction factor for potential evaporation |
0 |
0.3 |
°C-1 |

Response routine |
||||

K1 |
Recession coefficient (upper box) |
0.01 |
0.4 |
d-1 |

K2 |
Recession coefficient (lower box) |
0.001 |
0.15 |
d-1 |

PERC |
Maximal flow from upper to lower box |
0 |
3 |
mm d-1 |

MAXBAS |
Routing, length of weighting function |
1 |
7 |
d |