mHM Optimizers

[StephanThober]

Hi all,

which optimization algorithms are contained in the mHM model?

Thanks,
Stephan

[MuellerSeb]

Hi there,

thanks for using mHM. The provided optimization methods are:

• 0 Markov chain Monte Carlo (MCMC)
• 1 Dynamically Dimensioned Search (DDS)
• 2 Simulated Annealing (SA)
• 3 Shuffled Complex Evolution algorith (SCE)

they can be selected by the opti_method variable in mhm.nml.

The target function for optimization can be selected by opti_function. See the documentation from mhm.nml:

• 1 SO: Q: 1.0 - NSE
• 2 SO: Q: 1.0 - lnNSE
• 3 SO: Q: 1.0 - 0.5*(NSE+lnNSE)
• 4 SO: Q: -1.0 * loglikelihood with trend removed from absolute errors and then lag(1)-autocorrelation removed
• 5 SO: Q: ((1-NSE)**6+(1-lnNSE)6)(1/6)
• 6 SO: Q: SSE
• 7 SO: Q: -1.0 * loglikelihood with trend removed from absolute errors
• 8 SO: Q: -1.0 * loglikelihood with trend removed from the relative errors and then lag(1)-autocorrelation removed
• 9 SO: Q: 1.0 - KGE (Kling-Gupta efficiency measure)
• 10 SO: SM: 1.0 - KGE of catchment average soilmoisture
• 11 SO: SM: 1.0 - Pattern dissimilarity (PD) of spatially distributed soil moisture
• 12 SO: SM: Sum of squared errors (SSE) of spatially distributed standard score (normalization) of soil moisture
• 13 SO: SM: 1.0 - average temporal correlation of spatially distributed soil moisture
• 14 SO: Q: sum[((1.0-KGE_i)/ nGauges)6](1/6) > combination of KGE of every gauging station based on a power-6 norm
• 15 SO: Q + domain_avg_TWS: [1.0-KGE(Q)]*RMSE(domain_avg_TWS) - objective function using Q and domain average (standard score) TWS
• `16) (reserved) please use the next number when implementing a new one
  MO: Q: 1st objective: (1) = 1.0 - NSE
  Q: 2nd objective: (2) = 1.0 - lnNSE
• 17 SO: N: 1.0 - KGE of spatio-temporal neutron data, catchment-average
• 18 (reserved) please use the next number when implementing a new one
  MO: Q: 1st objective: 1.0 - lnNSE(Q_highflow) (95% percentile)
  Q: 2nd objective: 1.0 - lnNSE(Q_lowflow) (5% of data range)
• 19 (reserved) please use the next number when implementing a new one
  MO: Q: 1st objective: 1.0 - lnNSE(Q_highflow) (non-low flow)
  Q: 2nd objective: 1.0 - lnNSE(Q_lowflow) (5% of data range)
• 20 (reserved) please use the next number when implementing a new one
  MO: Q: 1st objective: absolute difference in FDC's low-segment volume
  Q: 2nd objective: 1.0 - NSE of discharge of months DJF
• 21 (reserved) please use the next number when implementing a new one
  SO: Q: ( (1.0-lnNSE(Q_highflow))**6 + (1.0-lnNSE(Q_lowflow))6 )(1/6)
  where Q_highflow and Q_lowflow are calculated like in objective (19)
• 22-26 (reserved MC/JM/ST) please use the next number when implementing a new one
• 27 SO: ET: 1.0 - KGE of catchment average evapotranspiration
• 28 SO: Q + SM: weighted OF using SM (OF12) and Q (OF14) equally weighted
• further functions can be implemented in mo_objective_function and mo_mrm_objective_function
• 29 SO: Q + ET: weighted OF using ET (OF27) and Q (OF14) equally weighted
• 30 SO: Q + domain_avg_ET: [1.0-KGE(Q)]*RMSE(domain_avg_ET) - objective function using Q and domain average ET (standard score)$
• 31 SO: Q: 1 - weighted NSE (NSE is weighted with observed discharge)

further functions can be implemented in mo_objective_function and mo_mrm_objective_function

You can read more about that in the documentation: https://mhm.pages.ufz.de/mhm/stable/calopt.html

Hope that helps!

Cheers, Sebastian