## RegEM: Regularized Expectation Maximization

RegEM is a software package that provides regularized variants of the classical expectation maximization algorithm for estimating statistics from and filling in missing values in incomplete datasets. It is widely used, for example, for imputing missing values in climate and other datasets and for estimating information about past climates from proxies such as tree-ring widths.

## ARfit: Multivariate Autoregressive Model Fitting

ARfit is a software package for autoregressive (AR) time series modeling. It can estimate multivariate AR models from time series data, analyze spectral information (eigenmodes or principal oscillation patterns) of fitted models, and simulate time series. It is widely used, for example, for modeling and analyzing climate and finance time series and electroencephalograms.

## GCMs: General Circulation Models

We use a variety of GCMs for our research, from dry atmosphere models to relatively complex coupled atmosphere-ocean models. Our model codes are freely available.

## PyCLES: A Python-Based Large-Eddy Simulation Infrastructure

PyCLES is a Python-based large-eddy simulation (LES) code for the simulation of clouds and boundary layers.

## RegEM: Regularized Expectation Maximization

### Purpose

RegEM is a collection of Matlab modules for

- the estimation of mean values and covariance matrices from incomplete datasets, and
- the imputation of missing values in incomplete datasets.

The modules implement the regularized EM algorithm described in

T. Schneider, 2001: Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. *Journal of Climate*, **14**, 853-871.

The EM algorithm for Gaussian data is based on iterated linear regression analyses. In the regularized EM algorithm, a regularized estimation method replaces the conditional maximum likelihood estimation of regression parameters in the conventional EM algorithm for Gaussian data. The modules here provide truncated total least squares (with fixed truncation parameter) and ridge regression with generalized cross-validation as regularized estimation methods.

The implementation of the regularized EM algorithm is modular, so that the modules that perform he regularized estimation of regression parameters (e.g., ridge regression and generalized cross-validation) can be exchanged for other regularization methods and other methods of determiningca regularization parameter. Per-Christian Hansen’s Regularization Tools contain Matlab modules implementing a collection of regularization methods that can be adapted to fit into the framework of the EM algorithm. The generalized cross-validation modules of the regularized EM algorithm are adapted from Hansen’s generalized cross-validation modules.

In the Matlab implementation of the regularized EM algorithm, more emphasis was placed on the modularity of the program code than on computational efficiency.

The U.S. National Science Foundation’s Paleo Perspectives on Climate Change program provided funding for recent further developments of the RegEM algorithm.

### Installation

The program package consists of several Matlab modules, all available on Github. To install the programs, download the package into a directory that is accessible by Matlab.

Starting Matlab and invoking Matlab’s online help function

`help filename`

displays information on the module `filename.m`

.

## ARfit: Multivariate Autoregressive Model Fitting

### Purpose

ARfit is a collection of Matlab modules for

- estimating parameters of multivariate autoregressive (AR) models,
- diagnostic checking of fitted AR models, and
- analyzing eigenmodes of fitted AR models.

The algorithms implemented in ARfit are described in the following papers, which should be referenced if you use ARfit in publications:

A. Neumaier and T. Schneider, 2001: Estimation of parameters and eigenmodes of multivariate autoregressive models. *ACM Trans. Math. Softw*., **27**, 27-57.

T. Schneider and A. Neumaier, 2001: Algorithm 808: ARfit – A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models. *ACM Trans. Math*. Softw., **27**, 58-65.

ARfit includes support for multiple realizations (trials) of time series and can estimate parameters of multivariate AR models taking all available realizations into account.

Last ARfit revision: 1 December 2010

### Installation

The ARfit package consists of a number of Matlab modules, all available on Github. To install Matlab, download the package and copy it into a directory accessible by Matlab.

Starting Matlab and invoking Matlab’s online help function

`help filename`

calls up detailed information on the purpose and the calling syntax of the module `filename.m`

. The script ardem.m demonstrates the basic features of the modules contained in ARfit.

### Scilab version

ARfit is also available for Scilab (provided by Holger Nahrstaedt).

## PyCLES

PyCLES is a Python-based large-eddy simulation (LES) code, whose development is led by Kyle Pressel. The source code, including test cases, can be downloaded from Github. We welcome further development of the code by the user community.

PyCLES is described in:

Pressel, K. G., C. M. Kaul, T. Schneider, Z. Tan, and S. Mishra, 2015: Large-eddy simulation in an anelastic framework with closed water and entropy balances. *Journal of Advances in Modeling Earth Systems*, **7**, 1425–1456, doi:10.1002/2015MS000496.

A novel forcing framework with closed surface energy balance has been implemented in PyCLES as described in:

Tan, Z., T. Schneider, J. Teixeira, and K. G. Pressel, 2016: Large-eddy simulation of subtropical cloud-topped boundary layers. Part I: A forcing framework with closed surface energy balance. *Journal of Advances in Modeling Earth Systems*, in press.