Mathematics
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Item A Data Assimilation System for Lake Erie Based on the Local Ensemble Transform Kalman Filter(2024) Russell, David Scott; Ide, Kayo; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Data assimilation (DA) is the process by which a model forecast is adjusted to account for recent observations, taking into account both forecast and observation uncertainties. Although DA is common in numerical weather prediction (NWP) and other applications at global and regional scales, DA for large lakes such as North America's Great Lakes is still at an early stage of research and is not yet used operationally. In particular, the use of an ensemble-based approach to DA has scarcely been explored for large lakes, despite its growing popularity in operational NWP centers worldwide due to its dynamic estimation of the forecast covariance. Using Lake Erie as a test case, this study investigates the potential of ensemble DA to i) propagate forecast improvements throughout the lake and across forecast variables, and ii) inform the design of in-situ observing systems. The local ensemble transform Kalman filter (LETKF) is an efficient, localized, flexible variant of the ensemble Kalman filter (EnKF) that is used in multiple operational NWP centers. This work presents the development of a DA system for Lake Erie, which uses the LETKF to adjust forecasts of temperatures, currents, and water levels throughout the lake, using only lake surface temperature (LST) and temperature profile (TP) observations. The impact of both types of observations on all three forecast variables is evaluated within the framework of observing system simulation experiments (OSSEs), in which a DA system attempts to reconstruct a nature run (NR) by assimilating simulated observations of the NR. Observing system design questions are explored by comparing three different TP configurations. Assimilation of LST observations alone produces strong improvements to temperatures throughout the epilimnion (upper layer), while assimilation of TP observations extends these improvements to the hypolimnion (lower layer) near each profile. TP assimilation also shows improved representation of strong gyre currents and associated changes to thermocline depth and surface height, particularly when profiles sample from locations and depths where the thermal stratification in the forecast has been strongly affected by erroneous gyre currents. This work shows that the LETKF can be an efficient and effective tool for improving both forecasts and observing systems for large lakes, two essential ingredients in predicting the onset and development of economically and ecologically important phenomena such as harmful algal blooms (HABs) and hypoxia.Item Developments in Lagrangian Data Assimilation and Coupled Data Assimilation to Support Earth System Model Initialization(2019) Sun, Luyu; Carton, James A.; Penny, Stephen G.; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The air-sea interface is one of the most physically active interfaces of the Earth's environments and significantly impacts the dynamics in both the atmosphere and ocean. In this doctoral dissertation, developments are made to two types of Data Assimilation (DA) applied to this interface: Lagrangian Data Assimilation (LaDA) and Coupled Data Assimilation (CDA). LaDA is a DA method that specifically assimilates position information measured from Lagrangian instruments such as Argo floats and surface drifters. To make a better use of this Lagrangian information, an augmented-state LaDA method is proposed using Local Ensemble Transform Kalman Filter (LETKF), which is intended to update the ocean state (T/S/U/V) at both the surface and at depth by directly assimilating the drifter locations. The algorithm is first tested using "identical twin" Observing System Simulation Experiments (OSSEs) in a simple double gyre configuration with the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model version 4.1 (MOM4p1). Results from these experiments show that with a proper choice of localization radius, the estimation of the state is improved not only at the surface, but throughout the upper 1000m. The impact of localization radius and model error in estimating accuracy of both fluid and drifter states are investigated. Next, the algorithm is applied to a realistic eddy-resolving model of the Gulf of Mexico (GoM) using Modular Ocean Model version 6 (MOM6) numerics, which is related to the 1/4-degree resolution configuration in transition to operational use at NOAA/NCEP. Atmospheric forcing is first used to produce the nature run simulation with forcing ensembles created using the spread provided by the 20 Century Reanalysis version 3 (20CRv3). In order to assist the examination on the proposed LaDA algorithm, an updated online drifter module adapted to MOM6 is developed, which resolves software issues present in the older MOM4p1 and MOM5 versions of MOM. In addition, new attributions are added, such as: the output of the intermediate trajectories and the interpolated variables: temperature, salinity, and velocity. The twin experiments with the GoM also show that the proposed algorithm provides positive impacts on estimating the ocean state variables when assimilating the drifter position together with surface temperature and salinity. Lastly, an investigation of CDA explores the influence of different couplings on improving the simultaneous estimation of atmosphere and ocean state variables. Synchronization theory of the drive-response system is applied together with the determination of Lyapunov Exponents (LEs) as an indication of the error convergence within the system. A demonstration is presented using the Ensemble Transform Kalman Filter on the simplified Modular Arbitrary-Order Ocean-Atmosphere Model, a three-layer truncated quasi-geostrophic model. Results show that strongly coupled data assimilation is robust in producing more accurate state estimates and forecasts than traditional approaches of data assimilation.Item Proactive Quality Control based on Ensemble Forecast Sensitivity to Observations(2014) Hotta, Daisuke; Kalnay, Eugenia; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Despite recent major improvements in numerical weather prediction (NWP) systems, operational NWP forecasts occasionally suffer from an abrupt drop in forecast skill, a phenomenon called "forecast skill dropout." Recent studies have shown that the "dropouts" occur not because of the model's deficiencies but by the use of flawed observations that the operational quality control (QC) system failed to filter out. Thus, to minimize the occurrences of forecast skill dropouts, we need to detect and remove such flawed observations. A diagnostic technique called Ensemble Forecast Sensitivity to Observations (EFSO) enables us to quantify how much each observation has improved or degraded the forecast. A recent study (Ota et al., 2013) has shown that it is possible to detect flawed observations that caused regional forecast skill dropouts by using EFSO with 24-hour lead-time and that the forecast can be improved by not assimilating the detected observations. Inspired by their success, in the first part of this study, we propose a new QC method, which we call Proactive QC (PQC), in which flawed observations are detected 6 hours after the analysis by EFSO and then the analysis and forecast are repeated without using the detected observations. This new QC technique is implemented and tested on a lower-resolution version of NCEP's operational global NWP system. The results we obtained are extremely promising; we have found that we can detect regional forecast skill dropouts and the flawed observations after only 6 hours from the analysis and that the rejection of the identified flawed observations indeed improves 24-hour forecasts. In the second part, we show that the same approximation used in the derivation of EFSO can be used to formulate the forecast sensitivity to observation error covariance matrix R, which we call EFSR. We implement the EFSR diagnostics in both an idealized system and the quasi-operational NWP system and show that it can be used to tune the R matrix so that the utility of observations is improved. We also point out that EFSO and EFSR can be used for the optimal assimilation of new observing systems.Item DATA ASSIMILATION OF THE GLOBAL OCEAN USING THE 4D LOCAL ENSEMBLE TRANSFORM KALMAN FILTER (4D-LETKF) AND THE MODULAR OCEAN MODEL (MOM2)(2011) Penny, Stephen G.; Kalnay, Eugenia; Carton, Jim; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The 4D Local Ensemble Transform Kalman Filter (4D-LETKF), originally designed for atmospheric applications, has been adapted and applied to the Geophysical Fluid Dynamics Laboratory's (GFDL) Modular Ocean Model (MOM2). This new ocean assimilation system provides an estimation of the evolving errors in the global oceanic domain for all state variables. Multiple configurations of LETKF have been designed to manage observation coverage that is sparse relative to the model resolution. An Optimal Interpolation (OI) method, implemented through the Simple Ocean Data Assimilation (SODA) system, has also been applied to MOM2 for use as a benchmark. Retrospective 7-year analyses using the two systems are compared for validation. The oceanic 4D-LETKF assimilation system is demonstrated to be an effective method for data assimilation of the global ocean as determined by comparisons of global and regional `observation minus forecast' RMS, as well as comparisons with temperature/salinity relationships and independent observations of altimetry and velocity.Item Quantitative aspects of the stability of some dynamical systems(2010) Gonzalez Tokman, Cecilia; Hunt, Brian R; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis is concerned with the study of quantitative aspects of the stability of some dynamical systems that exhibit hyperbolic features. Results include scaling laws for bubbling bifurcations, description of limit invariant measures for metastable systems and shadowing properties of a data assimilation algorithm in the context of hyperbolic systems.Item Ensemble Data Assimilation and Breeding in the Ocean, Chesapeake Bay, and Mars(2009) Hoffman, Matthew Joseph; Kalnay, Eugenia; Carton, James A; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)My dissertation focuses on studying instabilities of different time scales using breeding and data assimilation in the oceans, as well as the Martian atmosphere. The breeding method of Toth and Kalnay finds the perturbations that grow naturally in a dynamical system like the atmosphere or the ocean. Here breeding is applied to a global ocean model forced by reanalysis winds in order to identify instabilities on weekly and monthly timescales. The method is extended to show how the energy equations for the bred vectors can be derived with only very minimal approximations and used to assess the physical mechanisms that give rise to the instabilities. Tropical Instability Waves in the tropical Pacific are diagnosed, confirming the existence of bands of both baroclinic and barotropic energy conversions indicated by earlier studies. For regional prediction of smaller timescale phenomena, an advanced data assimilation system has been developed for the Chesapeake Bay Forecast System, a regional Earth System Prediction model. To accomplish this, the Regional Ocean Modeling System (ROMS) implementation on the Chesapeake Bay has been interfaced with the Local Ensemble Transform Kalman Filter (LETKF). The LETKF is among the most advanced data assimilation methods and is very effective for large, non-linear dynamical systems in both sparse and dense data coverage situations. In perfect model experiments using ChesROMS, the filter converges quickly and reduces the analysis and subsequent forecast errors in the temperature, salinity, and velocity fields. This error reduction has proved fairly robust to sensitivity studies such as reduced data coverage and realistic data coverage experiments. The LETKF also provides a method for error estimation and facilitates the investigation of the spatial distribution of the error. This information has been used to determine areas where more monitoring is needed. The LETKF framework is also applied here to a global model of the Martian atmosphere. Sensitivity experiments are performed to determine the dependence of the assimilation on observational data. Observations of temperature are simulated at realistic vertical and horizontal levels and LETKF performance is evaluated. Martian instabilities that impact the assimilation are also addressed.