PythonDA

This is a Python Data Assimilation tool. It contains classes for DA experiments, twin experiments, DA filters and metrics.

Installation:

PythonDA requires the following Python modules:

• numpy
• scipy

The following modules are highly recommended but not mandatory (they are used by the table() method to format results and by the plot() method to plot results):

• tabulate
• matplotlib

Usage:

Prepare a list of ensemble filters for a twin experiment:

from Filters import Seik, Ghosh

EnsSize=31
forgettin_factor=0.7
ens_filters=[Seik(EnsSize, forget=forgettin_factor), 
             Ghosh(EnsSize, forget=forgettin_factor)]

Each filter needs to know the ensemble size. Other customizations are possible by specifying other arguments (e.g., the chosen forgetting factor, which is 1.0 by default).

Choose a model:

import Models

model=Models.Lorenz96()

Choose metrics to be compared:

import Metrics

metrics=[Metrics.RmpeByTime(name='RMSE_by_time'),
         Metrics.TimeMean(Metrics.RmpeByTime(), name='Total_RMSE')]

The first metric RmpeByTime is a metric over time, suitable to be represented in a plot. It computes the p-norm of the error (p is 2 by defalut, giving the Root Mean Square Error, but it can be specified as argument, e.g., Metrics.RmpeByTime(p=1)). The second one, TimeMean, takes a metric over time as argument (e.g., RmpeByTime), and computes its p-norm in the time window. TimeMean is a subclass of Summary metrics, which are suitable to summarize the results with a single number and usually are represented in tables better than plots.

Define a twin experiment in the time window between 0 and 20:

import DA

t_span=[0.0,20.0]
test=DA.TwinExperiment(t_span=t_span, model=model, ens_filters=ens_filters, metrics = metrics)

Compute climatlogical moments (mean and covariance) for the model and build the truth of the twin experiment:

N=62
IC_truth=model.climatological_moments(N)
test.build_truth(IC_truth)

Here N is the number of variables of the Lorenz96 model. The climatological_moments method:

1. build an history by integrating the model for a long period (default is history_len=1000.0),
2. computes climatological mean and covariance,
3. returns the last state of the history. The build_truth method create the truth of the twin experiment integrating the model in the time window test.t_span, with initial condition IC_truth.

Build observations:

import numpy as np

obs_template=DA.Observation(obs=np.zeros(N), std=np.ones(N))
obs_times=np.arange(t_span[0]+0.2,t_span[1], 0.2)
test.build_obs(times=obs_times, template=obs_template)

The observations in the twin experiment are built given an observation template and observation times.

Initialize 100 experiments at once, build error affected initial conditions and launch the twin experiments:

test.build_tests()
n_experiments=100
test.build_climatological_ICs(n_experiments=n_experiments)
test.run()

Present results by using a table and a plot:

test.table()
test.plot()

See examples in single_twin.py and multi_twin.py.