A python-based linear inverse modeling suite.

pyLIM is based on the linear inverse model (LIM) described by Penland & Sardeshmukh (1995). This package provides the machinery to both calibrate and forecast/integrate a LIM from the publications Perkins & Hakim (2017, submitted-2019).

The documentation and test updates are still in progress, but I hope to update those in the near future.

pyLIM requires Python 3.6+ and the following packages: numpy, numexpr, netCDF4, dask, pytables, scipy, and scikit-learn.

To install pyLIM, cd into the package directory after downloading or cloning this repository.

$ cd /path/to/pylim
$ python setup.py install
# -- or if altering pyLIM code --
$ python setup.py develop

This will install pyLIM for the current python environment.

When working with with pyLIM, we start with some data which is well approximated as a predictably linear system forced by white noise. Sea-surface temperatures are a good example of this type of field. This data will be processed to convert the data to anomalies and remove seasonal information / long-term drift (if desired). After pre-processing we convert the data to its components of primary variability using PCA (specific to geospatial fields). pylim.DataTools has some generally helpful tools to process data and load from netCDF and HDF5 sources. (These are quite specific to CMIP5 climate model data currently)

Pre-processing from a netCDF file

import pylim.DataTools as DT

sst = DT.BaseDataObject.from_netcdf('sst_dat.nc', 'sst')
sst.calc_anomaly(12) # calculate monthly anomalies
sst.time_average_resample('annual', 12) # annual average
sst.detrend_data() # linearly detrend data
sst.area_weight_data(use_sqrt=True) 
sst.eof_proj_data(num_eofs=10)
# sst.data now has dimensions of ntimes x 10

If the data is too large for the system to hold in memory, Hdf5DataObject stores intermediate data in an HDF5 container using pytables. Use DT.netcdf_tohdf5_container to convert the netCDF to HDF5, which I found to be more compatible with Dask.

import tables as tb 
dobj_h5 = tb.open_file('tmp_sst_dobj.h5', mode='w',
                       filters=tb.Filters(complib='blosc', complevel=2))
sst_h5 = DT.Hdf5DataObject.from_hdf5('sst_dat.h5', 'sst', dobj_h5)

LIM calibration takes in data of shape ntimes x nfeatures and by default calibrates the LIM using lag-1 covariance statistics. If data are annually averaged, the base forecast unit would be 1-year.

import pylim.LIM as LIM

# data should be ntimes x features
lim = LIM.LIM(tau0_data=sst.data, fit_noise=True)

For other lags, one can specify the lagged data to calibrate to:

lim = LIM.LIM(tau0_data=sst.data[:-3], tau1_data=sst.data[3:], fit_noise=True)

Deterministic forecasts for different leads can be done using

# 1- and 2-year forecasts initialized for every year of the first 10 from SSTs
t0_data = sst.data[0:10]
fcast_out = lim.forecast(t0_data, [1, 2])

Noise integration for two years at ~3 hr timestep. (t0_data can be considered a 10-member ensemble for this integration)

final_state = lim.noise_integration(t0_data, 2, timesteps=2880)