Advancing Climate Modeling through High-Performance Computing: Towards More Accurate and Efficient Simulations

Ensemble simulations have been performed with a climate model constrained to follow temperature histories obtained from a recent compilation of 56 well‐calibrated surface temperature proxy records, using a new data assimilation technique. First, we demonstrate that the data assimilation technique provides a faithful representation in the Northern Hemisphere of the signal recorded by the climate proxies at both the regional and gridbox scales. Second, by varying the external forcing, the parameters of the data assimilation method, and the parameters controlling the equilibrium climate sensitivity of the climate model, we demonstrate that the uncertainty in model results is much lower in simulations using data assimilation than in those without it. This observation implies that the data assimilation, using a set of 56 proxies, is providing an efficient and robust constraint on the simulated climate variability over the past centuries. At the hemispheric and continental scales, the model reconstructions using data assimilation are in good agreement with both the instrumental record of the past 150 years and reconstructions of climate in past centuries derived from the application of traditional statistical approaches to networks of proxy data. This increases the confidence in both the data assimilation and traditional statistical approaches. Our data assimilation method, however, is unable to provide a reliable reconstruction over the North Atlantic Ocean, which we attribute to the paucity of proxy data in that region.

<p>Over the last 40 years remote sensing has significantly changed the way we observe and predict the Earth system, particularly in the oceanographic and meteorological sciences. Today, every General Circulation model (GCM) relies upon advanced and well-established data assimilation (DA) techniques, and Land Surface Models (LSMs) – which are integral components of GCM – have been increasingly using DA to constrain the LSM model predictions with available remote sensing data of hydrological, carbon and energy cycles.</p> <p>Despite this, the use of DA into hydrological models (HMs) is still operationally limited and the reasons for that lie in 1) the considerable variability between different HMs, with much uncertainty in their respective representations of processes (often conceptual) and their sensitivity to changes in key variables, 2) the contrast between the scale of application of HMs (often smaller than LSMs) and the coarse-scale information provided by remote sensing along with their associated accuracy and, 3) the variety of the data assimilation setups, specificity of the study areas, and pre-processing used by a plethora of studies on the topic which provide a blurred picture on the real benefit of DA of relevant hydrological variables into HMs (e.g. soil moisture, precipitation, snow, terrestrial water storage anomalies).</p> <p>The recent exponential grown of high-resolution remote sensing data (the European Union's Earth observation Programme Copernicus with the constellation of the Sentinel satellites is a notable example) has potentially opened new opportunities for improving our HMs also for small scale applications.  However, their usefulness is still limited by our ability to analyse and integrate efficiently a large volume of observations with current hydrologic models. In other words, most of the issues mentioned above have been not overcome with a consequent under-exploitation of potentially useful information to constrain HMs.</p> <p>This contribution aims to summarize the main challenges and opportunities of DA into HMs from a hydrological perspective in light of the availaiblity of new and more skillful Earth observations. It identifies and explains critical challenges by using published literature by the author on European catchments as well as on-going studies, and offers insights for a productive research based on new available models and observations as to build a comprehensive hydrologic data assimilation framework that is a critical component of future hydrologic observation and modelling systems.</p>

Challenges for data assimilation – from convective‐scale to climate

Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is important in many geophysical and engineering applications. In these cases, nonlinearities, high (or infinite) dimensionality of the state space, and sparse observations pose key challenges for deriving efficient and accurate data assimilation (DA) techniques. A number of DA algorithms used commonly in practice, such as the Ensemble Kalman Filter (EnKF) or Ensemble Square Root Kalman Filter (EnSRKF), suffer from serious drawbacks such as catastrophic filter divergence and filter instability. The analysis of stability and accuracy of these DA schemes has thus far focused either on finite-dimensional dynamics, or on complete observations in case of infinite-dimensional dissipative systems. We develop a unified framework for the analysis of several well-known and empirically efficient DA techniques derived from various Gaussian approximations of the Bayesian filtering schemes for geophysical-type dissipative dynamics with quadratic nonlinearities. We establish rigorous results on (time-asymptotic) accuracy and stability of these algorithms with general covariance and observation operators. The accuracy and stability results for EnKF and EnSRKF for dissipative PDEs are, to the best of our knowledge, completely new in this general setting. It turns out that a hitherto unexploited cancellation property involving the ensemble covariance and observation operators and the concept of covariance localization in conjunction with covariance inflation play a pivotal role in the accuracy and stability for EnKF and EnSRKF. Our approach also elucidates the links, via determining functionals, between the approximate-Bayesian and control-theoretic approaches to DA. We consider the ‘model’ dynamics governed by the two-dimensional incompressible Navier–Stokes equations (NSEs) and observations given by noisy measurements of averaged volume elements or spectral/modal observations of the velocity field. In this setup, several continuous-time DA techniques, namely the so-called 3DVar, EnKF and EnSRKF reduce to a stochastically forced NSEs. For the first time, we derive conditions for accuracy and stability of EnKF and EnSRKF. The derived bounds are given for the limit supremum of the expected value of the L 2 norm and of the H 1 Sobolev norm of the difference between the approximating solution and the actual solution as the time tends to infinity. Moreover, our analysis reveals an interplay between the resolution of the observations (roughly, the ‘richness’ of the observation space) associated with the observation operator underlying the DA algorithms and covariance inflation and localization which are employed in practice for improved filter performance.

In this study, an innovative MODIS fractional snow cover (SCF) data assimilation (DA) prototype framework that invokes machine learning (ML) techniques and Common land model (CoLM) is proposed to improve the estimation of the snow depth (SD) and the SCF. To validate our new framework, we analyzed two snow seasons from 2013 to 2015 at 46 stations in Northern Xinjiang in China. We developed 12 SCF DA schemes that represent different DA methods (direct insertion (DI) and Ensemble Kalman Filter (EnKF)), observational data (original data and gap‐filled MODIS SCF data), and observation operators (five new snow depletion curves (SDCs) defined using traditional multivariate nonlinear regression and four ML methods). While improving the frequency of the SCF observations in the DI‐based DA scheme only resulted in a marginal improvement in the snow estimates, by adding new SDCs fitted by ML techniques (e.g., deep belief network), and the gap‐filled MODIS SCF data to the EnKF‐based DA scheme, we were able to reduce model structural uncertainties of CoLM and achieve marked improvement in the accuracy of the snow estimates (RMSE = 5.92 cm, mean bias error = −1.94 cm, and average degree of improvement = 32.18% for SD estimates and RMSE = 15. 79%, mean bias error = −1.21%, and average degree of improvement = 47.95% for SCF estimates). Our results demonstrate the feasibility of improving snow estimates by combining the ML techniques with physically based snowpack model in a SCF DA framework.

In order to improve the simulation accuracy, it is effective to use a data assimilation technique which is capable of reproducing more realistic simulated states by incorporating observational data into simulation models. One of the simplest ones among data assimilation techniques is a Newtonian relaxation‐type nudging method which has been widely used in mesoscale meteorological models. In this study, we proposed a data assimilation method using a vibration equation which can incorporate turbulence winds toward target mean winds while maintaining small‐scale turbulent fluctuations as a different approach from the conventional nudging method. First, we conducted test simulations in which nudging is applied in a basic turbulent boundary layer (TBL) flow toward a target one. It is shown that the basic TBL flow can be reasonably nudged toward the target one while maintaining the turbulent fluctuations well when prescribing the natural frequency in the vibration equation smaller than the spectral peak frequency in the TBL flow. Then, we applied the proposed nudging method by incorporating data obtained from meteorological observations located in the actual city of Kyoto. The mean wind velocity profiles were reasonably nudged toward the target observed profile and the turbulence statistics were also favorably maintained. It is concluded that the data assimilation method using the vibration equation successfully nudges toward the target mean winds while maintaining small‐scale turbulent fluctuations well.

Abstract. The IGCM4 (Intermediate Global Circulation Model version 4) is a global spectral primitive equation climate model whose predecessors have extensively been used in areas such as climate research, process modelling and atmospheric dynamics. The IGCM4's niche and utility lies in its speed and flexibility allied with the complexity of a primitive equation climate model. Moist processes such as clouds, evaporation, atmospheric radiation and soil moisture are simulated in the model, though in a simplified manner compared to state-of-the-art global circulation models (GCMs). IGCM4 is a parallelised model, enabling both very long integrations to be conducted and the effects of higher resolutions to be explored. It has also undergone changes such as alterations to the cloud and surface processes and the addition of gravity wave drag. These changes have resulted in a significant improvement to the IGCM's representation of the mean climate as well as its representation of stratospheric processes such as sudden stratospheric warmings. The IGCM4's physical changes and climatology are described in this paper.

Model and data reduction for data assimilation: Particle filters employing projected forecasts and data with application to a shallow water model

Data assimilation techniques, developed in the past two decades mainly for weather prediction, produce better forecasts by taking advantage of both theoretical/numerical models and real-time observations. In this paper, we explore the possibility of applying the four-dimensional variational data assimilation (4D-VAR) technique to the prediction of solar flares. We do so in the context of a continuous version of the classical cellular-automaton-based self-organized critical avalanche models of solar flares introduced by Lu and Hamilton (Astrophys. J. 380, L89, 1991). Such models, although a priori far removed from the physics of magnetic reconnection and magnetohydrodynamical evolution of coronal structures, nonetheless reproduce quite well the observed statistical distribution of flare characteristics. We report here on a large set of data assimilation runs on synthetic energy release time series. Our results indicate that, despite the unpredictable (and unobservable) stochastic nature of the driving/triggering mechanism within the avalanche model, 4D-VAR succeeds in producing optimal initial conditions that reproduce adequately the time series of energy released by avalanches and flares. This is an essential first step toward forecasting real flares.

Quantifying continental-scale river discharge is essential to understanding the terrestrial water cycle but is susceptible to errors caused by a lack of observations and the limitations of hydrodynamic modeling. Data assimilation (DA) methods are increasingly used to estimate river discharge in combination with emerging river-related remote sensing products (e.g., water surface elevation [WSE], water surface slope, river width, and flood extent). However, directly comparing simulated WSE to satellite altimetry data remains challenging (e.g., because of large biases between simulations and observations or uncertainties in parameters), and large errors can be introduced when satellite observations are assimilated into hydrodynamic models. In this study we performed direct, anomaly, and normalized value assimilation experiments to investigate the capacity of DA to improve river discharge within the current limitations of hydrodynamic modeling. We performed hydrological DA using a physically-based empirical localization method applied to the Amazon Basin. We used satellite altimetry data from ENVISAT, Jason 1, and Jason 2. Direct DA was the baseline assimilation method and was subject to errors due to biases in the simulated WSE. To overcome these errors, we used anomaly DA as an alternative to direct DA. We found that the modeled and observed WSE distributions differed considerably (e.g., differences in amplitude, seasonal flow variation, and a skewed distribution due to limitations of the hydrodynamic models). Therefore, normalized value DA was performed to improve discharge estimation. River discharge estimates were improved at 24 %, 38 %, and 62 % of stream gauges in the direct, anomaly, and normalized value assimilations relative to simulations without DA. Normalized value assimilation performed best for estimating river discharge given the current limitations of hydrodynamic models. Most gauges within the river reaches covered by satellite observations accurately estimated river discharge, with Nash-Sutcliffe efficiency (NSE) > 0.6. The amplitudes of WSE variation were improved in the normalized DA experiment. Furthermore, in the Amazon Basin, normalized assimilation (median NSE = 0.50) improved river discharge estimation compared to open-loop simulation with the global hydrodynamic model (median NSE = 0.42). River discharge estimation using direct DA methods was improved by 7 % with calibration of river bathymetry based on NSE. The direct DA approach outperformed the other DA approaches when runoff was considerably biased, but anomaly DA performed best when the river bathymetry was erroneous. The uncertainties in hydrodynamic modeling (e.g., river bottom elevation, river width, simplified floodplain dynamics, and the rectangular cross-section assumption) should be improved to fully realize the advantages of river discharge DA through the assimilation of satellite altimetry. This study contributes to the development of a global river discharge reanalysis product that is consistent spatially and temporally.

This paper presents two novel data assimilation (DA) techniques for reconstructing steady turbulent flows at high Reynolds numbers by introducing perturbations to the Reynolds stress tensor computed by the turbulence model of a Favre-averaged Navier–Stokes (FANS) code. These techniques minimize the least-squares difference between an experimentally measured mean flow quantity and the corresponding quantity as computed by the FANS code. The two DA methods differ from each other in the choice of the control parameters: one perturbs the eigenvalues and eigenvectors of a baseline Reynolds stress, whereas the other perturbs the components of a baseline realizable Reynolds stress such that the perturbed result is still realizable. For the optimization procedure, a gradient-based algorithm is used in combination with a discrete adjoint methodology. The DA methods are applied to high-Reynolds-number problems, and their results compared with a reference technique. The results show that the approaches developed in this work are more effective at reconstructing the turbulent flowfield than standard techniques, but are more computationally expensive due to the high dimensionality of the optimization problem. Furthermore, it appears that only small perturbations to the control parameters are necessary to obtain significant improvements over the baseline results.

Abstract. Climate proxy data provide noisy, and spatially incomplete information on some aspects of past climate states, whereas palaeosimulations with climate models provide global, multi-variable states, which may however differ from the true states due to unpredictable internal variability not related to climate forcings, as well as due to model deficiencies. Using data assimilation for combining the empirical information from proxy data with the physical understanding of the climate system represented by the equations in a climate model is in principle a promising way to obtain better estimates for the climate of the past. Data assimilation has been used for a long time in weather forecasting and atmospheric analyses to control the states in atmospheric General Circulation Models such that they are in agreement with observation from surface, upper air, and satellite measurements. Here we discuss the similarities and the differences between the data assimilation problem in palaeoclimatology and in weather forecasting, and present and conceptually compare three data assimilation methods that have been developed in recent years for applications in palaeoclimatology. All three methods (selection of ensemble members, Forcing Singular Vectors, and Pattern Nudging) are illustrated by examples that are related to climate variability over the extratropical Northern Hemisphere during the last millennium. In particular it is shown that all three methods suggest that the cold period over Scandinavia during 1790–1820 is linked to anomalous northerly or easterly atmospheric flow, which in turn is related to a pressure anomaly that resembles a negative state of the Northern Annular Mode.

Regional climate modeling is a dynamical downscaling technique applied to the results of global climate models (GCMs) in order to acquire more information on climate simulations and climate change projections. GCMs and regional climate models (RCMs) have undergone considerable development over the past few decades, and both have increased in resolution. The higher‐resolution edge of RCMs compared to GCMs still remains, however. This has been demonstrated in a number of specific studies. As GCMs operate on relatively coarse resolutions, they do not resolve more variable land forms and similar features that shape regional‐scale climates. RCMs operate on higher resolutions than GCMs, by a factor of 2–10. Some RCMs now explore resolutions down to 1–5 km. This adds value in regions with variable orography, land–sea and other contrasts, as well as in capturing sharp, short‐duration and extreme events. In contrast, large‐scale and time‐averaged fields, not least over smooth terrain and on scales that have been already skillfully resolved in GCMs, are not much affected. RCMs also generate additional detail compared to GCMs when in climate projection mode. Compared to the present‐day climate for which observations exist, here the added value aspect is more complex to evaluate. Nevertheless, added value is meaningfully underlined when there is a clear physical context for it to appear in. In addition to climate modeling and model evaluation‐related added value considerations, a significant relevant aspect of added value is the provision of regional scale information, including climate change projections, for climate impact, adaptation, and vulnerability research. WIREs Clim Change 2016, 7:145–159. doi: 10.1002/wcc.378This article is categorized under: Climate Models and Modeling > Knowledge Generation with Models

Ensuring a reliable water supply in the face of changing conditions and growing demand is a critical global challenge. Water distribution networks (WDNs) are essential infrastructure, but traditional modeling methods based on historical data often struggle to adapt in real-time and integrate new information. In order to lower model errors in WDN models, this study explores the use of a Data Assimilation (DA) method that makes use of the Ensemble Kalman Filter. The study explores the effectiveness of the DA method, and a novel Greedy Algorithm (GA) for optimizing the location of sensors. The study shows that the DA method improves the WDN model and the GA is able to successfully determine optimal sensor locations. It was observed that increasing the number of sensors in the WDN increased the effectiveness of the DA method. This study highlights the potential of data assimilation to improve WDN modeling. Water utilities can gain from more precise predictions, greater system performance, and efficient decision-making for the management and maintenance of water distribution networks by allowing models to adapt and improve dynamically

Global glacier mass loss is accelerating, yet considerable spread in projected glacier changes remains due to model structure, forcing, and parameter uncertainty. Most global glacier projections rely on relatively simple models where calibration approaches are essential to constrain uncertainty by using scarce observations. Probabilistic calibration strategies that help with quantifying uncertainities have recently incorporated into a limited number of global glacier models. As a next step, we suggest employing Bayesian data assimilation methods with untapped potential to integrate multi source observations (in-situ, satellite, reanalysis) when calibrating global glacier model projections.Here, we present a probabilistic calibration framework for the Python Glacier Evolution Model (PyGEM) based on ensemble-based data assimilation. Two data assimilation techniques (PBS and AdaPBS) are used to calibrate mass balance parameters to constrain future projections of glacio-hydrological variables (surface mass balance and runoff) between 2015 and 2100 under four SSP climate scenarios across the Scandinavian region. In this work, we compare our calibration results with commonly used deterministic and probabilistic glacier model calibration algorithms which are already in use in PyGEM. Our probabilistic calibration framework based on data assimilation has the potential to quantify and disentangle uncertainties from climate forcing, model structure, and parameters. Better constrained and uncertainty-aware glacier models increases confidence in projections of future glacier change and their relevant impacts. This work paves the way for producing policy relevant global glacier projections and scenarios with their uncertainty estimates within the ERC-AdG GLACMASS project.