Training a supermodel with noisy and sparse observations: a case study with CPT and the synch rule on SPEEDO – v.1

Abstract

Abstract. As an alternative to using the standard multi-model ensemble (MME) approach to combine the output of different models to improve prediction skill, models can also be combined dynamically to form a so-called supermodel. The supermodel approach enables a quicker correction of the model errors. In this study we connect different versions of SPEEDO, a global atmosphere-ocean-land model of intermediate complexity, into a supermodel. We focus on a weighted supermodel, in which the supermodel state is a weighted superposition of different imperfect model states. The estimation, “the training”, of the optimal weights of this combination is a critical aspect in the construction of a supermodel. In our previous works two algorithms were developed: (i) cross pollination in time (CPT)-based technique and (ii) a synchronization-based learning rule (synch rule). Those algorithms have so far been applied under the assumption of complete and noise-free observations. Here we go beyond and consider the more realistic case of noisy data that do not cover the full system's state and are not taken at each model's computational time step. We revise the training methods to cope with this observational scenario, while still being able to estimate accurate weights. In the synch rule an additional term is introduced to maintain physical balances, while in CPT nudging terms are added to let the models stay closer to the observations during training. Furthermore, we propose a novel formulation of the CPT method allowing the weights to be negative. This makes it possible for CPT to deal with cases in which the individual model biases have the same sign, a situation that hampers constructing a skillfully weighted supermodel based on positive weights. With these developments, both CPT and the synch rule have been made suitable to train a supermodel consisting of state of the art weather and climate models.

Analog data assimilation for the selection of suitable general circulation models

“…Another possible application of the AnDA-CME framework is in the context-weighted supermodels (Schevenhoven et al, 2019;Schevenhoven and Carrassi, 2022), which provides a way to combine the time derivatives of different models resulting in improved short-range and long-range predictions.…”

A Multi‐Model Ensemble Kalman Filter for Data Assimilation and Forecasting

“…In a weighted supermodel, the individual models are not directly connected through coupling terms; rather, the supermodel tendency is taken to be a weighted average of the individual model tendencies, and the individual models compute their tendencies based on the supermodel state (Schevenhoven et al, 2019). CPT and weighted supermodels were compared by Schevenhoven et al (2019) and Schevenhoven and Carrassi (2022). Sengupta et al (2020) used a Bayesian neural network to infer model weights.…”

“…Previously, MM‐DA was only tested on very low‐dimensional models with non‐chaotic behavior (Narayan et al., 2012; Yang et al., 2017), and recursive multi‐step forecasts were not tested. Methods for multi‐model forecasting have often been tested with perfect observations for calibration, single forecasts for each model rather than ensembles, and models that all share the same space (Schevenhoven & Selten, 2017; Schevenhoven et al., 2019); several papers, though, have extended this work to noisy observations (Du & Smith, 2017; Schevenhoven & Carrassi, 2022). Here, we conduct twin experiments of the proposed method for both DA and forecasting in various settings, including models of different dimensionality and different‐sized ensembles.…”

“…CPT and weighted supermodels were compared by Schevenhoven et al. (2019) and Schevenhoven and Carrassi (2022).…”

Framework for an Ocean‐Connected Supermodel of the Earth System

“…Models are connected as they run via their state variables or their tendencies. Models can either be connected to each other (e.g., Mirchev et al., 2012; Smith, 2001) or toward their weighted mean (Schevenhoven & Carrassi, 2021; Wiegerinck et al., 2013). During a training phase, the connection terms are optimized to formulate a new synchronised dynamical system that achieves enhanced performance.…”