The Community Multiscale Air Quality (CMAQ) system is the Environmental Protection Agency's main modeling tool for atmospheric pollution studies. CMAQ-ADJ, the adjoint model of CMAQ, offers new analysis capabilities such as receptor-oriented sensitivity analysis and chemical data assimilation. This thesis presents the construction, validation, and properties of new adjoint modules in CMAQ, and illustrates their use in sensitivity analyses and data assimilation experiments. The new module of discrete adjoint of advection is implemented with the aid of automatic differentiation tool (TAMC) and is fully validated by comparing the adjoint sensitivities with finite difference values. In addition, adjoint sensitivity with respect to boundary conditions and boundary condition scaling factors are developed and validated in CMAQ. To investigate numerically the impact of the continuous and discrete advection adjoints on data assimilation, various four dimensional variational (4D-Var) data assimilation experiments are carried out with the 1D advection PDE, and with CMAQ advection using synthetic and real observation data. The results show that optimization procedure gives better estimates of the reference initial condition and converges faster when using gradients computed by the continuous adjoint approach. This counter-intuitive result is explained using the nonlinearity properties of the piecewise parabolic method (the numerical discretization of advection in CMAQ). Data assimilation experiments are carried out using real observation data. The simulation domain encompasses Texas and the simulation period is August 30 to September 1, 2006. Data assimilation is used to improve both initial and boundary conditions. These experiments further validate the tools developed in this thesis. / Master of Science

One of the Sustainable Development Goals set in 2015 by the United Nations aims to ensure access to affordable, reliable, sustainable, and modern energy for all, increasing the global share of renewable energy to 32-35% by 2030. Moving towards this goal, the University of Trento funded the interdepartmental strategic project ERiCSol (Energie Rinnovabili e Combustibili Solari), in order to promote the research on renewable energy storage and solar fuels. The research activity presented in this thesis lies in the framework of this project, focusing on the development of new advanced simulation approaches to improve the estimation of the wind resource availability and the related power production for Italian wind farms in complex terrain. The wind farms, operated by the company AGSM S.p.A., are located in two different geographical contexts: Rivoli Veronese and Affi are at the inlet of the Adige Valley, while Casoni di Romagna and Carpinaccio Firenzuola, are on the crest of the Apennines close to the borders between the provinces of Bologna e Firenze. The analysis of data from year-long field measurements highlighted the different peculiarities of these areas. The wind farms at the mouth of the Adige Valley are influenced by a daily periodic thermally-driven circulation, characterised by a nocturnal intense down-valley wind alternating with a diurnal weaker up-valley wind, while the Apennines wind farms are primarily affected by synoptic-scale winds. Simulations, with the mesoscale Weather Research and Forecasting (WRF) model, are performed and compared with field measurements in both cases, to highlight strengths and weaknesses. The results show that the model is able to capture with good accuracy wind speed and direction in the Apennines wind farms, while larger errors arise for Rivoli Veronese and Affi wind farms, where the intensity of the nocturnal down-valley wind is generally underestimated. Considering the former case, modelled and observed yearly wind speed density distributions are compared, in order to evaluate the impact of model errors in the estimation of the wind resource at these sites. Since reliable simulations of the wind resource are also essential to ensure the security in power transmission and to prevent penalties to energy operators, an analysis of the power production is also performed, to evaluate how errors in the estimate of the resource translate into errors in the estimate of the production. Considering the wind farms at the mouth of the Adige Valley, the research work mainly focuses on the evaluation of the impact of data assimilation by means of observational nudging on model results, in order to optimize the setup for operational forecasts. Different configurations are tested and compared, varying the temporal window for the assimilation of local data.

We present a new framework for understanding parameter estimation in dynamical systems. The approach is developed within the modeling approach of continuous data assimilation. We outline the basic assumptions that lead to our derivation. Under these assumptions we show that the parameter estimation turns into a finite dimensional nonlinear optimization problem. We show that our derivation reproduces and extends the algorithm originally developed in [9]. We then implement these methods in three example systems: the Lorenz '63 model, the two-layer Lorenz '96 model, and the Kuramoto Sivashinsky equation. So as to remain sufficiently general, our derivations are largely formal; we leave a more rigorous justification for future work.

Accurate physical modeling and accelerated numerical simulation of turbulent flows remain primary challenges in CFD for aerospace engineering and related fields. This dissertation tackles these challenges with a focus on Reynolds-Averaged Navier--Stokes (RANS) models, which will continue to serve as the backbone for many practical aircraft applications. Specifically, in RANS turbulence modeling, the challenges include developing more efficient ensemble filters to learn nonlinear eddy viscosity models from observation data that move beyond the classical Boussinesq hypothesis, as well as developing non-equilibrium models that break away from the weak equilibrium assumption while maintaining computational efficiency. For accelerating RANS simulations, the challenges include leveraging existing simulation data to optimize the computational workflow while maintaining the method's adaptability to various computational settings. From a fundamental and mathematical perspective, we view these challenges as problems of modeling and learning complex nonlinear and nonlocal mappings, which we categorize into three types: field-to-point, field-to-field, and ensemble-to-ensemble. To model and resolve these mappings, we build up on recent advancements in machine learning and develop novel neural operator-based methods that not only possess strong representational capabilities but also preserve critical physical and mathematical principles. With the developed tools, we have demonstrated promising preliminary results in addressing these challenges and have the potential to significantly advance the state of the art in RANS turbulence modeling and simulation acceleration. / Doctor of Philosophy / Understanding and accurately predicting turbulent flows, such as those around airplanes or ships, are among the biggest challenges in computational fluid dynamics (CFD). This research aims to improve Reynolds-Averaged Navier--Stokes (RANS) models, which are widely used in practical engineering applications. Traditional RANS turbulence models are based on simplified assumptions that are linear and local, making it difficult to capture the true complexity of turbulent flows. My work addresses this limitation by developing new models that leverage advanced machine learning techniques to better represent turbulence. Specifically, I have focused on developing methods that extend beyond conventional approaches by learning more accurate local nonlinear constitutive relations and incorporating nonlocal effects---an important step toward improving simulation accuracy. In addition, I have explored strategies to accelerate RANS simulations by making more effective use of existing data, providing better initial conditions for simulations, and ultimately reducing computational costs. Preliminary results indicate that these new methods have the potential to push the boundaries of RANS turbulence modeling, enabling more accurate and efficient simulations.

Through a combination of fossil fuel emissions, land use change, and other anthropogenic activities, mankind has dramatically altered global biogeochemical cycles, leading to an unprecedented era of rapid environmental change. To anticipate how the carbon and water cycles will change in the future, and inform decisions about how to adapt and mitigate these changes, we need a better understanding of the inherent predictability of these cycles. To begin to address this challenge I designed, implemented, and analyzed a 35-day iterative forecasting workflow using Harvard Forest as an initial testbed. A key aim of this forecast is to understand the predictability of leaf area index (LAI), net ecosystem exchange (NEE), and latent heat flux (LE), which I assess in terms of how forecast uncertainty changes as a function of forecast lead time, and how the predictability of LAI, NEE and LE is impacted by the assimilation of MODIS LAI observations. I used four metrics of uncertainty (root mean square error, bias, continuous ranked probability score, and mean absolute error) to evaluate the forecast performance. Uncertainty in LAI, LE, and NEE was not positively correlated with forecast lead time. The inclusion of MODIS LAI observations improved predictability of NEE and LE, but had the greatest impact on LAI (~50% uncertainty reduction). Carbon stores (LAI as a proxy for leaf carbon) were more predictable than terrestrial fluxes (NEE, LE).

Today, ocean modeling is fast developing as a versatile tool for the study of earth’s climate, local marine ecosystems and coastal engineering applications. Though the field of ocean modeling began in the early 1950s along with the development of climate models and primitive computers, even today, the state-of-the-art ocean models have their own limitations. Many issues still remain such as the uncertainity in the parameterisation of essential processes that occur on spatial and temporal scales smaller than that can be resolved in model calculations, atmospheric forcing of the ocean and the boundary and initial conditions. The advent of data assimilation into ocean modeling has heralded a new era in the field of ocean modeling and oceanic sciences. “Data assimilation” is a methodology in which observations are used to improve the forecasting skill of operational meteorological models. The study in the present thesis mainly focuses on obtaining a four dimensional realization (the spatial description coupled with the time evolution) of the oceanic flow that is simultaneously consistent with the observational evidence and with the dynamical equations of motion and to provide initial conditions for predictions of oceanic circulation and tracer distribution. A good implementation of data assimilation can be achieved with the availability of large number of good quality observations of the oceanic fields as both synoptic and in-situ data. With the technology in satellite oceanography and insitu measurements advancing by leaps over the past two decades, good synoptic and insitu observations of oceanic fields have been achieved. The current and expected explosion in remotely sensed and insitu measured oceanographic data is ushering a new age of ocean modeling and data assimilation. The thesis presents results of analysis of the impact of data assimilation in an ocean general circulation model of the North Indian Ocean. In this thesis we have studied the impact of assimilation of temperature and salinity profiles from Argo floats and Sea Surface height anomalies from satellite altimeters in a Sigma-coordinate Indian Ocean model. An ocean data assimilation system based on the Regional Ocean Modeling System (ROMS) for the Indian Ocean is used. This model is implemented, validated and applied in a climatological simulation experiment to study the circulation in the Indian Ocean. The validated model is then used for the implementation of the data assimilation system for the Indian Ocean region. This dissertation presents the qualitative and quantitative comparisons of the model simulations with and without subsurface temperature and salinity profiles and sea surface height anamoly data assimilation for the Indian Ocean region. This is the first ever reported data assimilation studies of the Argo subsurface temperature and salinity profile data with ROMS in the Indian Ocean region.

Ensemble-based methods have gained widespread popularity in the field of data assimilation. An ensemble of model realizations encapsulates information about the error correlations driven by the physics and the dynamics of the numerical model. This information can be used to obtain improved estimates of the state of non-linear dynamical systems such as the atmosphere and/or the ocean. This work develops efficient ensemble-based methods for data assimilation. A major bottleneck in ensemble Kalman filter (EnKF) implementations is the solution of a linear system at each analysis step. To alleviate it an EnKF implementation based on an iterative Sherman Morrison formula is proposed. The rank deficiency of the ensemble covariance matrix is exploited in order to efficiently compute the analysis increments during the assimilation process. The computational effort of the proposed method is comparable to those of the best EnKF implementations found in the current literature. The stability analysis of the new algorithm is theoretically proven based on the positiveness of the data error covariance matrix. In order to improve the background error covariance matrices in ensemble-based data assimilation we explore the use of shrinkage covariance matrix estimators from ensembles. The resulting filter has attractive features in terms of both memory usage and computational complexity. Numerical results show that it performs better that traditional EnKF formulations. In geophysical applications the correlations between errors corresponding to distant model components decreases rapidly with the distance. We propose a new and efficient implementation of the EnKF based on a modified Cholesky decomposition for inverse covariance matrix estimation. This approach exploits the conditional independence of background errors between distant model components with regard to a predefined radius of influence. Consequently, sparse estimators of the inverse background error covariance matrix can be obtained. This implies huge memory savings during the assimilation process under realistic weather forecast scenarios. Rigorous error bounds for the resulting estimator in the context of data assimilation are theoretically proved. The conclusion is that the resulting estimator converges to the true inverse background error covariance matrix when the ensemble size is of the order of the logarithm of the number of model components. We explore high-performance implementations of the proposed EnKF algorithms. When the observational operator can be locally approximated for different regions of the domain, efficient parallel implementations of the EnKF formulations presented in this dissertation can be obtained. The parallel computation of the analysis increments is performed making use of domain decomposition. Local analysis increments are computed on (possibly) different processors. Once all local analysis increments have been computed they are mapped back onto the global domain to recover the global analysis. Tests performed with an atmospheric general circulation model at a T-63 resolution, and varying the number of processors from 96 to 2,048, reveal that the assimilation time can be decreased multiple fold for all the proposed EnKF formulations.Ensemble-based methods can be used to reformulate strong constraint four dimensional variational data assimilation such as to avoid the construction of adjoint models, which can be complicated for operational models. We propose a trust region approach based on ensembles in which the analysis increments are computed onto the space of an ensemble of snapshots. The quality of the resulting increments in the ensemble space is compared against the gains in the full space. Decisions on whether accept or reject solutions rely on trust region updating formulas. Results based on a atmospheric general circulation model with a T-42 resolution reveal that this methodology can improve the analysis accuracy. / Ph. D.

Land surface processes play an important role when modeling weather and climate, and understanding and representing such processes in South America is a particular challenge because of the large variations in regional climate and surface features such as vegetation and soil. Numerical models have been used to explore the climate and weather of continental South America, but without appropriate initiation of land surface conditions model simulations can rapidly diverge from reality. This initiation problem is exacerbated by the fact that conventional surface observations over South America are scarce and biased towards the urban centers and coastal areas. This dissertation explores issues related to the apt representation of land surface processes and their impacts in numerical simulations with a regional atmospheric model (specifically the Eta model) over South America. The impacts of vegetation heterogeneity in regional weather forecast were first investigated. A South American Land Data Assimilation System (SALDAS) was then created analogous to that currently used in North America to estimate soil moisture fields for initializing regional atmospheric models. The land surface model (LSM) used in this SALDAS is the Simplified Simple Biosphere (SSiB). Precipitation fields are critical when calculating soil moisture and, because conventional surface observations are scarce in South America, some of the most important remote sensed precipitation products were evaluated as potential precipitation forcing for the SALDAS. Spin up states for SSiB where then compared with climatological estimates of land surface fields and significant differences found. Finally, an assessment was made of the value of SALDAS-derived soil moisture fields on Eta model forecasts. The primary result was that model performance is enhanced over the entire continent in up to 72h forecasts using SALDAS surface fields

In the year 2000, croplands covered about 12% of the Earth’s ice-free land surface. Through cropland management, humankind momentarily appropriates about 25% of terrestrial ecosystem productivity. Not only are croplands a key element of human food supply, but also bear potential in increased carbon (C) uptake when best-practice land management approaches are adopted. A detailed assessment of the impact of land use on terrestrial ecosystems can be achieved by modelling, but the simulation of crop C cycling itself is a relatively new discipline. Observational data on crop net ecosystem exchange (NEE) are available only recently, and constitute an important tool for model development, diagnosis, and validation. Before crop functional types (CFT) had been introduced, however, large-scale biogeochemical models (BGCM) lacked crop-specific patterns of phenology, C allocation, and land management. As a consequence, the influence of cropland C cycling on biosphere-atmosphere C exchange seasonality and magnitude is currently poorly known. To date, no regional assessment of crop C cycling and yield formation exists that specifically accounts for spatially and temporally varying patterns of sowing dates within models. In this thesis, I present such an assessment for the first time. In the first step (chapter 2), I built a crop C mass balance model (SPAc) that models crop development and C allocation as a response to ambient meteorological conditions. I compared model outputs against C flux and stock observations of six different sites in Europe, and found a high degree of agreement between simulated and measured fluxes (R2 = 0.83). However, the model tended to overestimate leaf area index (LAI), and underestimate final yield. In a model comparison study (chapter 3), I found in cooperation with further researchers that SPAc best reproduces observed fluxes of C and water (owed to the model’s high temporal and process resolution), but is deficient due to a lack in simulating full crop rotations. I then conducted a detailed diagnosis of SPAc through the assimilation of C fluxes and biometry with the Ensemble Kalman Filter (EnKF, chapter 4), and identified potential model weaknesses in C allocation fractions and plant hydraulics. Further, an overestimation of plant respiration and seasonal leaf thickness variability were evident. Temporal parameter variability as a response to C flux data assimilation (DA) is indicative of ecosystem processes that are resolved in NEE data but are not captured by a model’s structure. Through DA, I gained important insights into model shortcomings in a quantitative way, and highlighted further needs for model improvement and future field studies. Finally, I developed a framework allowing for spatio-temporally resolved simulation of cropland C fluxes under observational constraints on land management and canopy greenness (chapter 5). MODIS (Moderate Resolution Imaging Spectroradiometer) data were assimilated both variationally (for sowing date estimation) and sequentially (for improved model state estimation, using the EnKF) into SPAc. In doing so, I was able to accurately quantify the multiannual (2000-2006) regional C flux and biometry seasonality of maize-soybean crop rotations surrounding the Bondville Ameriflux eddy covariance (EC) site, averaged over 104 pixel locations within the wider area. Results show that MODIS-derived sowing dates and the assimilation of LAI data allow for highly accurate simulations of growing season C cycling at locations for which groundtruth sowing dates are not available. Through quantification of the spatial variability in biometry, NEE, and net biome productivity (NBP), I found that regional patterns of land management are important drivers of agricultural C cycling and major sources of uncertainty if not appropriately accounted for. Observing C cycling at one single field with its individual sowing pattern is not sufficient to constrain large-scale agroecosystem behaviour. Here, I developed a framework that enables modellers to accurately simulate current (i.e. last 10 years) C cycling of major agricultural regions and their contribution to atmospheric CO2 variability. Follow-up studies can provide crucial insights into testing and validating large-scale applications of biogeochemical models.

As sensor data becomes more and more available, there is an increasing interest in assimilating real time sensor data into spatial temporal simulations to achieve more accurate simulation or prediction results. Particle Filters (PFs), also known as Sequential Monte Carlo methods, hold great promise in this area as they use Bayesian inference and stochastic sampling techniques to recursively estimate the states of dynamic systems from some given observations. However, PFs face major challenges to work effectively for complex spatial temporal simulations due to the high dimensional state space of the simulation models, which typically cover large areas and have a large number of spatially dependent state variables. As the state space dimension increases, the number of particles must increase exponentially in order to converge to the true system state. The purpose of this dissertation work is to develop localized particle filtering to support PFs-based data assimilation for large-scale spatial temporal simulations. We develop a spatially dependent particle-filtering framework that breaks the system state and observation data into sub-regions and then carries out localized particle filtering based on these spatial regions. The developed framework exploits the spatial locality property of system state and observation data, and employs the divide-and-conquer principle to reduce state dimension and data complexity. Within this framework, we propose a two-level automated spatial partitioning method to provide optimized and balanced spatial partitions with less boundary sensors. We also consider different types of data to effectively support data assimilation for spatial temporal simulations. These data include both hard data, which are measurements from physical devices, and soft data, which are information from messages, reports, and social network. The developed framework and methods are applied to large-scale wildfire spread simulations and achieved improved results. Furthermore, we compare the proposed framework to existing particle filtering based data assimilation frameworks and evaluate the performance for each of them.