I created a correlation matrix, and it seems that the major interactions are among X, Y and Z (I was expecting it). However, I now want to improve the method, and take into account interaction among the parameters. If I run these new 500 simulations with this new parameter set, and compare them with the observations, the number of simulations closer to the observations increase considerably. Parameter_sets = gamma(a=a_T, loc=loc_T, scale=scale_T).ppf(parameter_sets) Parameter_sets = gamma(a=a_R, loc=loc_R, scale=scale_R).ppf(parameter_sets) Parameter_sets = gamma(a=a_Z, loc=loc_Z, scale=scale_Z).ppf(parameter_sets) Parameter_sets = gamma(a=a_Y, loc=loc_Y, scale=scale_Y).ppf(parameter_sets) Parameter_sets = gamma(a=a_X, loc=loc_X, scale=scale_X).ppf(parameter_sets) # Create my new LHS design using the LHS function from pyDOE: # Fit the parameters with a gamma distribution: So, for now without considering interaction, I am operating like this: ```python The data are skewed and Gamma is a good fit. I use the parameters ranges from these retained simulations to fit new distributions and resample each parameter in a Latin hypercube for a new ensemble.
Therefore the ensemble members closer to the observations will help in constraining my input model parameters ranges. The comparison between forecasts and real observations (satellite data), however, will allow me to see which forecast is closer to the observations. However, the observations do not provide any information about these parameters.Īmong the 5 parameters, I am expecting correlation especially among X, Y and Z as all the three parameters are used to calculate the source strength in the model.
I have observations available for comparing the forecasts to the real event, satellite data that detected the plume. The parameters are input model parameters, and I have limited knowledge of them. The 500 members are initially created by generating a Latin hypercube with 5 dimensions, sampled 500 times from uniform distributions. I have an initial ensemble of 500 simulations, where I perturb 5 parameters. I initially posted this on Stack Overflow, but it seems more relevant here. However, I can't understand how, probably also because - not being my field - I never used these methods. I am attempting to take into account the interaction among 5 different parameters in a Latin hypercube design in Python 3.8.
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