scholarly journals Using machine learning to correct model error in data assimilation and forecast applications

2021 ◽  
Author(s):  
Alban Farchi ◽  
Patrick Laloyaux ◽  
Massimo Bonavita ◽  
Marc Bocquet
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Data Science ◽  
Weather Prediction ◽  
Realistic Model ◽  
Model Error ◽  
Underlying Assumption ◽  
Correct Model ◽  
Recent Developments ◽  
Spatiotemporal Processes

<p>Recent developments in machine learning (ML) have demonstrated impressive skills in reproducing complex spatiotemporal processes. However, contrary to data assimilation (DA), the underlying assumption behind ML methods is that the system is fully observed and without noise, which is rarely the case in numerical weather prediction. In order to circumvent this issue, it is possible to embed the ML problem into a DA formalism characterised by a cost function similar to that of the weak-constraint 4D-Var (Bocquet et al., 2019; Bocquet et al., 2020). In practice ML and DA are combined to solve the problem: DA is used to estimate the state of the system while ML is used to estimate the full model. </p><p>In realistic systems, the model dynamics can be very complex and it may not be possible to reconstruct it from scratch. An alternative could be to learn the model error of an already existent model using the same approach combining DA and ML. In this presentation, we test the feasibility of this method using a quasi geostrophic (QG) model. After a brief description of the QG model model, we introduce a realistic model error to be learnt. We then asses the potential of ML methods to reconstruct this model error, first with perfect (full and noiseless) observation and then with sparse and noisy observations. We show in either case to what extent the trained ML models correct the mid-term forecasts. Finally, we show how the trained ML models can be used in a DA system and to what extent they correct the analysis.</p><p>Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models, Nonlin. Processes Geophys., 26, 143–162, 2019</p><p>Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization, Foundations of Data Science, 2 (1), 55-80, 2020</p><p>Farchi, A., Laloyaux, P., Bonavita, M., and Bocquet, M.: Using machine learning to correct model error in data assimilation and forecast applications, arxiv:2010.12605, submitted. </p>

Ensemble Data Assimilation to Characterize Surface-Layer Errors in Numerical Weather Prediction Models

2013 ◽  
Vol 141 (6) ◽  
pp. 1804-1821 ◽  
Author(s):  
J. P. Hacker ◽  
W. M. Angevine
Keyword(s):  
Surface Layer ◽  
Data Assimilation ◽  
Atmospheric Surface Layer ◽  
Weather Prediction ◽  
Model Error ◽  
Time Of Day ◽  
Turbulent Heat ◽  
Model Errors ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Abstract Experiments with the single-column implementation of the Weather Research and Forecasting Model provide a basis for deducing land–atmosphere coupling errors in the model. Coupling occurs both through heat and moisture fluxes through the land–atmosphere interface and roughness sublayer, and turbulent heat, moisture, and momentum fluxes through the atmospheric surface layer. This work primarily addresses the turbulent fluxes, which are parameterized following the Monin–Obukhov similarity theory applied to the atmospheric surface layer. By combining ensemble data assimilation and parameter estimation, the model error can be characterized. Ensemble data assimilation of 2-m temperature and water vapor mixing ratio, and 10-m wind components, forces the model to follow observations during a month-long simulation for a column over the well-instrumented Atmospheric Radiation Measurement (ARM) Central Facility near Lamont, Oklahoma. One-hour errors in predicted observations are systematically small but nonzero, and the systematic errors measure bias as a function of local time of day. Analysis increments for state elements nearby (15 m AGL) can be too small or have the wrong sign, indicating systematically biased covariances and model error. Experiments using the ensemble filter to objectively estimate a parameter controlling the thermal land–atmosphere coupling show that the parameter adapts to offset the model errors, but that the errors cannot be eliminated. Results suggest either structural errors or further parametric errors that may be difficult to estimate. Experiments omitting atypical observations such as soil and flux measurements lead to qualitatively similar deductions, showing the potential for assimilating common in situ observations as an inexpensive framework for deducing and isolating model errors.

scholarly journals Special Issue on Selected Papers from IVAPP 2018

Information ◽  
2018 ◽  
Vol 9 (7) ◽  
pp. 171
Author(s):  
Alexandru Telea ◽  
Andreas Kerren
Keyword(s):  
Machine Learning ◽  
Information Visualization ◽  
Visual Analytics ◽  
Data Science ◽  
Time Dependent ◽  
Dependent Data ◽  
Special Issue ◽  
Making Sense ◽  
Recent Developments

Recent developments at the crossroads of data science, datamining,machine learning, and graphics and imaging sciences have further established information visualization and visual analytics as central disciplines that deliver methods, techniques, and tools for making sense of and extracting actionable insights and results fromlarge amounts of complex,multidimensional, hybrid, and time-dependent data.[...]

Accounting for land model error in numerical weather prediction ensemble systems: toward ensemble-based coupled land/atmosphere data assimilation

2021 ◽  
Author(s):  
Clara Sophie Draper
Keyword(s):  
Soil Moisture ◽  
Data Assimilation ◽  
Numerical Weather Prediction ◽  
Weather Prediction ◽  
Model Error ◽  
Model Parameters ◽  
Ensemble Spread ◽  
Numerical Weather ◽  
Vegetation Fraction ◽  
Ensemble Systems

AbstractThe ensembles used in the NOAA National Centers for Environmental Prediction (NCEP) global data assimilation and numerical weather prediction (NWP) system are under-dispersed at and near the land surface, preventing their use in ensemble-based land data assimilation. Comparison to offline (land-only) data assimilation ensemble systems suggests that while the relevant atmospheric fields are under-dispersed in NCEP’s system, this alone cannot explain the under-dispersed land component, and an additional scheme is required to explicitly account for land model error. This study then investigates several schemes for perturbing the soil (moisture and temperature) states in NCEP’s system, qualitatively comparing the induced ensemble spread to independent estimates of the forecast error standard deviation in soil moisture, soil temperature, 2m temperature, and 2m humidity. Directly adding perturbations to the soil states, as is commonly done in offline systems, generated unrealistic spatial patterns in the soil moisture ensemble spread. Application of a Stochastically Perturbed Physics Tendencies scheme to the soil states is inherently limited in the amount of soil moisture spread that it can induce. Perturbing the land model parameters, in this case vegetation fraction, generated a realistic distribution in the ensemble spread, while also inducing perturbations in the land (soil states) and atmosphere (2m states) that are consistent with errors in the land/atmosphere fluxes. The parameter perturbation method is then recommended for NCEP’s ensemble system, and it is currently being refined within the development of an ensemble-based coupled land/atmosphere data assimilation for NCEP’s NWP system.

A machine learning approach to the observation operator for satellite radiance data assimilation

2021 ◽  
Author(s):  
Jianyu Liang ◽  
Koji Terasaki ◽  
Takemasa Miyoshi
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Bias Correction ◽  
Reference System ◽  
Weather Prediction ◽  
Learning Model ◽  
Correction Procedure ◽  
Observation Operator ◽  
Machine Learning Model ◽  
Physically Based

<p>The ‘observation operator’ is essential in data assimilation (DA) to derive the model equivalent of the observations from the model variables. For satellite radiance observations, it is usually based on complex radiative transfer model (RTM) with a bias correction procedure. Therefore, it usually takes time to start using new satellite data after launching the satellites. Here we take advantage of the recent fast development of machine learning (ML) which is good at finding the complex relationships within data. ML can potentially be used as the ‘observation operator’ to reveal the relationships between the model variables and the observations without knowing their physical relationships. In this study, we test with the numerical weather prediction system composed of the Nonhydrostatic Icosahedral Atmospheric Model (NICAM) and the Local Ensemble Transform Kalman Filter (LETKF). We focus on the satellite microwave brightness temperature (BT) from the Advanced Microwave Sounding Unit-A (AMSU-A). Conventional observations and AMSU-A data were assimilated every 6 hours. The reference DA system employed the observation operator based on the RTTOV and an online bias correction method.</p><p>We used this reference system to generate 1-month data to train the machine learning model. Since the reference system includes running a physically-based RTM, we implicitly used the information from RTM for training the ML model in this study, although in our future research we will explore methods without the use of RTM. The machine learning model is artificial neural networks with 5 fully connected layers. The input of the ML model includes the NICAM model variables and predictors for bias correction, and the output of the ML model is the corresponding satellite BT in 3 channels from 5 satellites. Next, we ran the DA cycle for the same month the following year to test the performance of the ML model. Two experiments were conducted. The control experiment (CTRL) was performed with the reference system. In the test experiment (TEST), the ML model was used as the observation operator and there is no separate bias correction procedure since the training includes biased differences between the model and observation. The results showed no significant bias of the simulated BT by the ML model. Using the ECMWF global atmospheric reanalysis (ERA-interim) as a benchmark to evaluate the analysis accuracy, the global-mean RMSE, bias, and ensemble spread for temperature in TEST are 2% higher, 4% higher, and 1% lower respectively than those in CTRL. The result is encouraging since our ML can emulate the RTM. The limitation of our study is that we rely on the physically-based RTM in the reference DA system, which is used for training the ML model. This is the first result and still preliminary. We are currently considering other methods to train the ML model without using the RTM at all.</p>

scholarly journals Beating the Uncertainties: Ensemble Forecasting and Ensemble-Based Data Assimilation in Modern Numerical Weather Prediction

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Hailing Zhang ◽  
Zhaoxia Pu
Keyword(s):  
Data Assimilation ◽  
Numerical Weather Prediction ◽  
Weather Forecasting ◽  
Weather Prediction ◽  
Ensemble Forecasting ◽  
Atmospheric Flow ◽  
Numerical Weather ◽  
Recent Developments ◽  
Numerical Weather Forecasting ◽  
Chaotic Nature

Accurate numerical weather forecasting is of great importance. Due to inadequate observations, our limited understanding of the physical processes of the atmosphere, and the chaotic nature of atmospheric flow, uncertainties always exist in modern numerical weather prediction (NWP). Recent developments in ensemble forecasting and ensemble-based data assimilation have proved that there are promising ways to beat the forecast uncertainties in NWP. This paper gives a brief overview of fundamental problems and recent progress associated with ensemble forecasting and ensemble-based data assimilation. The usefulness of these methods in improving high-impact weather forecasting is also discussed.

Data-driven parametrizations in numerical models using data assimilation and machine learning.

2020 ◽  
Author(s):  
Julien Brajard ◽  
Alberto Carrassi ◽  
Marc Bocquet ◽  
Laurent Bertino
Keyword(s):  
Machine Learning ◽  
High Resolution ◽  
Data Assimilation ◽  
Physical Model ◽  
Hybrid Model ◽  
Numerical Models ◽  
Coarse Graining ◽  
Model Error ◽  
Data Driven ◽  
Model Combining

<p>Can we build a machine learning parametrization in a numerical model using sparse and noisy observations?</p><p>In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most of the cases, ML is trained by coarse-graining high-resolution simulations to provide a dense, unnoisy target state (or even the tendency of the model).</p><p>Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data. Furthermore, we intentionally place ourselves in the realistic scenario of noisy and sparse observations.</p><p>The algorithm proposed in this work derives from the algorithm presented by the same authors in https://arxiv.org/abs/2001.01520.The principle is to first apply data assimilation (DA) techniques to estimate the full state of the system from a non-parametrized model, referred hereafter as the physical model. The parametrization term to be estimated is viewed as a model error in the DA system. In a second step, ML is used to define the parametrization, e.g., a predictor of the model error given the state of the system. Finally, the ML system is incorporated within the physical model to produce a hybrid model, combining a physical core with a ML-based parametrization.</p><p>The approach is applied to dynamical systems from low to intermediate complexity. The DA component of the proposed approach relies on an ensemble Kalman filter/smoother while the parametrization is represented by a convolutional neural network.  </p><p>We show that the hybrid model yields better performance than the physical model in terms of both short-term (forecast skill) and long-term (power spectrum, Lyapunov exponents) properties. Sensitivity to the noise and density of observation is also assessed.</p>

scholarly journals Combining data assimilation and machine learning to infer unresolved scale parametrization

2021 ◽  
Vol 379 (2194) ◽  
pp. 20200086
Author(s):  
Julien Brajard ◽  
Alberto Carrassi ◽  
Marc Bocquet ◽  
Laurent Bertino
Keyword(s):  
Machine Learning ◽  
High Resolution ◽  
Data Assimilation ◽  
Hybrid Model ◽  
Numerical Models ◽  
Model Error ◽  
Climate Modelling ◽  
Combining Data ◽  
Full State ◽  
Direct Data

In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrization model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrization is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases, the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model. This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

Bayesian inference of dynamics from partial and noisy observations using data assimilation and machine learning

2020 ◽  
Author(s):  
Marc Bocquet ◽  
Julien Brajard ◽  
Alberto Carrassi ◽  
Laurent Bertino
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Data Assimilation ◽  
Loss Function ◽  
Surrogate Model ◽  
Model Error ◽  
Approximate Algorithm ◽  
Error Statistics ◽  
Long Time Series ◽  
Long Time

<p>The reconstruction from observations of the dynamics of high-dimensional chaotic models such as geophysical fluids is hampered by (i) the inevitably partial and noisy observations that can realistically be obtained, (ii) the need and difficulty to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has recently been suggested to combine data assimilation and machine learning in several ways. We first rigorously show how to unify these approaches from a Bayesian perspective, yielding a non-trivial loss function.</p><p>Existing techniques to optimize the loss function (or simplified variants thereof) are re-interpreted here as coordinate descent schemes. The expectation-maximization (EM) method is used to estimate jointly the most likely model and model error statistics. The main algorithm alternates two steps: first, a posterior ensemble is derived using a traditional data assimilation step using an ensemble Kalman smoother (EnKS); second, both the surrogate model and the model error are updated using machine learning tools, a quasi-Newton optimizer, and analytical formula. In our case, the spatially extended surrogate model is formalized as a neural network with convolutional layers leveraging on the locality of the dynamics.</p><p>This scheme has been successfully tested on two low-order chaotic models with distinct identifiability, namely the 40-variable and the two-scale Lorenz models. Additionally, an approximate algorithm is tested to mitigate the numerical cost, yielding similar performances. Using indicators that probe short-term and asymptotic properties of the surrogate model, we investigate the sensitivity of the inference to the length of the training window, to the observation error magnitude, to the density of the monitoring network, and to the lag of the EnKS. In these iterative schemes, model error statistics are automatically adjusted to the improvement of the surrogate model dynamics. The outcome of the minimization is not only a deterministic surrogate model but also its associated stochastic correction, representative of the uncertainty attached to the deterministic part and which accounts for residual model errors.</p>

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