# How to match mean and standard deviation of 2 datasets for data that cannot be less than 0

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Hi all,

I have two datasets of monthly precipitation sums at a certain location. One of them is observed, the other is modelled by a climate model. I want to match the mean and standard deviation of both datasets, so that the time series from the model matches with those from the observations. However, when I apply the formula, some negative values occur in the time series of the modelled monthly precipitation sums in order to make the standard deviation fit. I wonder whether there is a solution for this or if anyone knows how I can solve this.

Thanks!

data_mod=[70.74191271 66.54238669 28.60091702 55.56554018 66.04186858 77.06576381 72.57394329 99.62497103 42.51156832 22.81012399 107.3993961 48.45702239 33.71119171 61.09975519 74.43277952 39.14433747 113.1039794 67.93592923 96.95537867 12.99913771 53.6158074 48.05637989 52.27533536 99.27060261 54.73806827 148.462539 17.94473213 93.65016815 32.89454535 52.36015655];

data_obs=[27 38.6 146.1 61.8 44.6 7.5 50.4 23.2 8.1 89.7 23.1 83.3 86.5 46 14.5 27.7 81 30 50.3 165.7 15.5 106.7 56.7 52.5 75.1 100.1 6.9 18.7 93.4 16.6];

data_transformed = mean(data_obs(:)) + (data_mod - mean(data_mod(:)))*(std(data_obs(:))/std(data_mod(:)));

mean(data_transformed(:))

std(data_transformed(:))

##### 0 Comments

### Answers (1)

Les Beckham
on 7 Feb 2024

Edited: Les Beckham
on 7 Feb 2024

Your model data doesn't look at all like the observed data, so I'm not surprised that trying to force their statistics to match gives you unexpected results.

data_mod=[70.74191271 66.54238669 28.60091702 55.56554018 66.04186858 77.06576381 72.57394329 99.62497103 42.51156832 22.81012399 107.3993961 48.45702239 33.71119171 61.09975519 74.43277952 39.14433747 113.1039794 67.93592923 96.95537867 12.99913771 53.6158074 48.05637989 52.27533536 99.27060261 54.73806827 148.462539 17.94473213 93.65016815 32.89454535 52.36015655];

data_obs=[27 38.6 146.1 61.8 44.6 7.5 50.4 23.2 8.1 89.7 23.1 83.3 86.5 46 14.5 27.7 81 30 50.3 165.7 15.5 106.7 56.7 52.5 75.1 100.1 6.9 18.7 93.4 16.6];

plot(1:numel(data_obs), data_obs, '.-', 1:numel(data_mod), data_mod, 'o-')

legend('Observed', 'Modeled')

grid on

mean(data_mod) % <<< Model mean is much higher than observed mean!

mean(data_obs)

data_transformed = mean(data_obs(:)) + (data_mod - mean(data_mod(:)))*(std(data_obs(:))/std(data_mod(:)));

mean(data_transformed(:))

std(data_transformed(:))

##### 2 Comments

Les Beckham
on 8 Feb 2024

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