ocmw.core.statsTools module

A set of functions for generating validation statistics based on timeseries of modelled and observed values.

The circ_ functions apply the metrics to circular parameters, e.g. heading or wave direction.

corr_coef	Validation Metric: Correlation Coefficient
bias	Validation Metric: Bias
mean_bias	Validation Metric: Mean Bias
norm_mean_bias	Validation Metric: Normalised mean bias
mean_norm_bias	Validation Metric: Mean normalised bias
mean_absolute_error	Validation Metric: Mean absolute error
norm_ma_error	Validation Metric: Normalised mean absolute error
rms_error	Validation Metric: Root-mean-square error
norm_rmse	Validation Metric: Normalised root-mean-square error
goodness_of_fit	Validation Metric: Goodness-of-fit
scatter_index	Validation Metric: Scatter index
reliability_index	Validation Metric: Reliability index
skill_score	Validation Metric: Skill score
model_efficiency	Validation Metric: Model efficiency
circ_mod_pi	Fix angular range in radians to -pi <= theta <= pi
circ_mean	Calculate mean of angular data for range (-180 to 180)
circ_std	Calculate standard deviation of angular data for range (-180 to 180)
circ_corr	Validation Metric (Circular): Correlation Coefficient
circ_mean_bias	Validation Metric (Circular): Mean Bias
circ_norm_mean_bias	Validation Metric (Circular): Normalised mean Bias
circ_mean_abs_error	Validation Metric (Circular): Mean absolute error
circ_norm_ma_error	Validation Metric (Circular): Normalised mean absolute error
circ_rms_error	Validation Metric (Circular): Root-mean-square error
circ_norm_rmse	Validation Metric (Circular): Normalised root-mean-square error
circ_goodness_of_fit	Validation Metric (Circular): Goodness-of-fit
circ_scatter_index	Validation Metric (Circular): Scatter index
stats_metrics_circular	Calculate circlar validation metrics for a pair of modelled and observation time series
stats_metrics	Calculate standard validation metrics for a pair of modelled and observation time series
initialize_results	Initialise a dictionary for collecting validation results
store_results	Store validation results record in the results dictionary
save_results	Save tabulated validation results as an ASCII file
display_metrics	Display validation results as a table on the standard output
display_results_metrics	Display validation results as a table on the standard output

Functions for generating validation statistics based on timeseries of modelled and observed values.

ocmw.core.statsTools.corr_coef(model, obs)

Validation Metric: Correlation Coefficient

Parameters:

• model (numpy.array, float) – model data time series

• floatobs (numpy.array,) – observation time series mapped onto model time stamps

Returns:

correlation coefficient (R)

Return type:

float

ocmw.core.statsTools.bias(model, obs)

Validation Metric: Bias

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

bias (b)

Return type:

float

ocmw.core.statsTools.mean_bias(model, obs)

Validation Metric: Mean Bias

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

mb

Return type:

float

ocmw.core.statsTools.norm_mean_bias(model, obs)

Validation Metric: Normalised mean bias

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

nmb

Return type:

float

ocmw.core.statsTools.mean_norm_bias(model, obs)

Validation Metric: Mean normalised bias

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

mnb

Return type:

float

ocmw.core.statsTools.mean_absolute_error(model, obs)

Validation Metric: Mean absolute error

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

mae

Return type:

float

ocmw.core.statsTools.norm_ma_error(model, obs)

Validation Metric: Normalised mean absolute error

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

nmae

Return type:

float

ocmw.core.statsTools.rms_error(model, obs)

Validation Metric: Root-mean-square error

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

rmse

Return type:

float

ocmw.core.statsTools.norm_rmse(model, obs)

Validation Metric: Normalised root-mean-square error

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

nrmse

Return type:

float

ocmw.core.statsTools.goodness_of_fit(model, obs)

Validation Metric: Goodness-of-fit

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

R2

Return type:

float

ocmw.core.statsTools.scatter_index(model, obs)

Validation Metric: Scatter index

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

si

Return type:

float

ocmw.core.statsTools.reliability_index(model, obs)

Validation Metric: Reliability index

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

ri

Return type:

float

ocmw.core.statsTools.skill_score(model, obs)

Validation Metric: Skill score

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

ss

Return type:

float

ocmw.core.statsTools.model_efficiency(model, obs)

Validation Metric: Model efficiency

Parameters:

• model (numpy.array, float) – model data time series

• obs (numpy.array, float) – observation time series mapped onto model time stamps

Returns:

mef

Return type:

float

ocmw.core.statsTools.circ_mod_pi(theta)

Fix angular range in radians to -pi <= theta <= pi

Parameters:

theta (numpy.array, float) – vector of angular values in radians

Returns:

theta in range -pi to pi

Return type:

numpy.array, float

ocmw.core.statsTools.circ_mean(theta, degrees=True)

Calculate mean of angular data for range (-180 to 180)

Parameters:

• theta (numpy.array, float) – vector of angular values.

• degrees (bool, optional) – angular data units flag. The default is degrees = True.

Returns:

mean_theta (float) – mean of the angular data in same units as passed in.

ocmw.core.statsTools.circ_std(theta, degrees=True)

Calculate standard deviation of angular data for range (-180 to 180)

Parameters:

• theta (numpy.array, float) – vector of angular values.

• degrees (bool, optional) – angular data units flag. The default is degrees = True.

Returns:

std_theta (float) – stanadrd deviation of the angular data in same units as passed in.

ocmw.core.statsTools.circ_corr(theta1, theta2, degrees=True)

Validation Metric (Circular): Correlation Coefficient

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular correlation coefficient (c_corr)

Return type:

float

ocmw.core.statsTools.circ_mean_bias(theta1, theta2, degrees=True)

Validation Metric (Circular): Mean Bias

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular mean bias (mb)

Return type:

float

ocmw.core.statsTools.circ_norm_mean_bias(theta1, theta2, degrees=True)

Validation Metric (Circular): Normalised mean Bias

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular normalised mean bias (nmb) as a percentage

Return type:

float

ocmw.core.statsTools.circ_mean_abs_error(theta1, theta2, degrees=True)

Validation Metric (Circular): Mean absolute error

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular mean absolute error (mae)

Return type:

float

ocmw.core.statsTools.circ_norm_ma_error(theta1, theta2, degrees=True)

Validation Metric (Circular): Normalised mean absolute error

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular normalised mean absolute error (mae) as a percentage.

Return type:

float

ocmw.core.statsTools.circ_rms_error(theta1, theta2, degrees=True)

Validation Metric (Circular): Root-mean-square error

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular RMS error (circ_rmse)

Return type:

float

ocmw.core.statsTools.circ_norm_rmse(theta1, theta2, degrees=True)

Validation Metric (Circular): Normalised root-mean-square error

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular normalised RMS error (circ)nrmse as a percentage

Return type:

float

ocmw.core.statsTools.circ_goodness_of_fit(theta1, theta2, degrees=True)

Validation Metric (Circular): Goodness-of-fit

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular goodness-of-fit R2

Return type:

float

ocmw.core.statsTools.circ_scatter_index(theta1, theta2, degrees=True)

Validation Metric (Circular): Scatter index

Parameters:

• theta1 (numpy.array,float) – vector of angular data (modelled)

• theta1 – vector of angualr data (observed)

• degrees (bool) – angular data units flag. The default is degrees = True

Returns:

circular scatter index (circ_si)

Return type:

float

ocmw.core.statsTools.stats_metrics_circular(model, obs, varName, degrees=True)

Calculate circlar validation metrics for a pair of modelled and observation time series

ocmw.core.statsTools.stats_metrics(model, obs, varName)

Calculate standard validation metrics for a pair of modelled and observation time series

ocmw.core.statsTools.initialize_results()

Initialise a dictionary for collecting validation results

ocmw.core.statsTools.store_results(store, results)

Store validation results record in the results dictionary

ocmw.core.statsTools.save_results(store, prefix, paramName, outpath)

Save tabulated validation results as an ASCII file

ocmw.core.statsTools.display_metrics(metrics, paramName, testName=None)

Display validation results as a table on the standard output

ocmw.core.statsTools.display_results_metrics(metrics, paramName, testName=None)

Display validation results as a table on the standard output