Coupling the Planetary Boundary Layer to the Large Scale Dynamics of the Atmosphere: The Impact of Vertical Discretisation

Accurate coupling between the resolved scale dynamics and sub-grid scale physics is essential for accurate modelling of the atmosphere. Previous emphasis has been towards the temporal aspects of this so called physics-dynamics coupling problem, with little attention towards the spatial aspects. When designing a model for numerical weather prediction there is a choice for how to vertically arrange the required variables, namely the Lorenz and Charney-Phillips grids, and there is ongoing debate as to which is the optimal. The Charney-Phillips grid is considered good for capturing the large scale dynamics and wave propagation whereas the Lorenz grid is more suitable for conservation. However the Lorenz grid supports a computational mode. In the first half of this thesis it is argued that the Lorenz grid is preferred for modelling the stably stratified boundary layer. This presents the question: which grid will produce most accurate results when coupling the large scale dynamics to the stably stratified planetary boundary layer? The second half of this thesis addresses this question. The normal mode analysis approach, as used in previous work of a similar nature, is employed. This is an attractive methodology since it allows one to pin down exactly why a particular configuration performs well. In order to apply this method a one dimensional column model is set up, where horizontally wavelike solutions with a given wavenumber are assumed. Applying this method encounters issues when the problem is non normal, as it will be when including boundary layer terms. It is shown that when addressing the coupled problem the lack of orthogonality between eigenvectors can cause mode analysis to break down. Dynamical modes could still be interpreted and compared using the eigenvectors but boundary layer modes could not. It is argued that one can recover some of the usefulness of the methodology by examining singular vectors and singular values; these retain the appropriate physical interpretation and allow for valid comparison due to orthogonality between singular vectors. Despite the problems in using the desirable methodology some interesting results have been gained. It is shown that the Lorenz grid is favoured when the boundary layer is considered on its own; it captures the structures of the steady states and transient singular vectors more accurately than the Charney-Phillips grid. For the coupled boundary layer and dynamics the Charney-Phillips grid is found to be most accurate in terms of capturing the steady state. Dispersion properties of dynamical modes in the coupled problem depend on the choice of horizontal wavenumber. For smaller horizontal wavenumber there is little to distinguish between Lorenz and Charney-Phillips grids, both the frequency and structure of dynamical modes is captured accurately. Dynamical mode structures are found to be harder to interpret when using larger horizontal wavenumbers; for those that are examined the Charney-Phillips grid produces the most sensible and accurate results. It is found that boundary layer modes in the coupled problem cannot be concisely compared between the Lorenz and Charney-Phillips grids due to the issues that arise with the methodology. The Lorenz grid computational mode is found to be suppressed by the boundary layer, but only in the boundary layer region.The EPSRC and The Met Offic

Assessing the tangent linear behavior of common tracer transport schemes and their use in a linearized atmospheric general circulation model

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have non-linear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5

Implementation of Multidomain Unified Forward Operators (UFO) Within the Joint Effort for Data Assimilation Integration (JEDI): Ocean Applications

The Joint Effort for Data assimilation Integration (JEDI) is a collaborative development led by the Joint Center for Satellite Data Assimilation (JCSDA) in conjunction with NASA, NOAA and the Department of Defense (NAVY and Air Force). The (Sea-Ice Ocean and Coupled Assimilation) SOCA as one of the JCSDA projects, focuses on the application of JEDI to marine data assimilation. One of the goals of SOCA is to make use of surface-sensitive radiances to constrain sea-ice and upper ocean fields (e.g., salinity, temperature, sea-ice fraction, sea-ice temperature, etc.). The first elements toward an ocean/atmosphere coupled data assimilation capability within JEDI, with a focus on supporting and developing the assimilation of radiance observations sensitive to the ocean and atmosphere has been implemented. The direct radiance assimilation of surface sensitive microwave radiances focusing on Global Precipitation Measurement (GPM) Imager (GMI) for the SST Constraint and Soil Moisture Active Passive (SMAP) for the Sea Surface Salinity (SSS) has been the main focus. Also, in UFO the capability to calculate the cool skin layer depth and skin temperature has been implemented similar to the GEOS-5. It has been tested with GMI sea surface temperature retrievals. This is important because Satellite and in-situ observations of the Sea-Surface Temperature (SST) show high variability, including a diurnal cycle and very thin, cool skin layer in contact with the atmosphere, and Incorporating a realistic skin SST is essential for atmosphere-ocean coupled data assimilation

Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version

Sensitivity of Different Types of Observations to NASA GEOS Hurricane Analyses and Forecasts

The 2017 Atlantic hurricane season was the 5th most active, featuring 17 named storms, the highest number of major hurricanes since 2005, and by far the costliest season on record. African easterly waves often serve as the seeding circulation for a large portion of hurricanes (i.e. tropical storms with wind over 74mph in the Atlantic and Northeast Pacific). Warm SST, moist air, and low wind shear are the main requirements for tropical cyclones to develop and maintain hurricane strength. In terms of hurricane propagation (so called hurricane tracks), Atlantic hurricanes typically propagate around the periphery of the subtropical ridge called the Bermuda High (Azores High), riding along its strongest winds. If the high is positioned to the east, then hurricanes generally propagate northeastward around the high's western edge into the open Atlantic Ocean without making land fall. If the high is positioned to the west and extends far enough to the south, storms are blocked from curving north and forced to continue west towards Florida, Cuba, and the Gulf of Mexico. If we have accurate atmospheric temperature distribution, which is directly related to atmospheric wave patterns, wind distributions, moisture distribution, and SST distribution in the analyses, we will have better NWP skills in hurricane analyses including hurricane intensity and tracks. Assimilating various observation data are supposed to play these roles in the analyses. To examine impacts of different types of observation data on NASA Goddard Earth Observing System (GEOS) model hurricane analyses and forecasts during the period of 2017 summer, this study performs data denial experiments using GEOS Atmospheric Data Assimilation System (ADAS), which is based on the hybrid 4D-EnVar GSI algorithm. Various types of observations such as microwave sounders, infrared sounders, TCvitals, and conventional data are removed in the experiments. In addition, the interaction between the different observation groups as certain instruments are removed from the analysis is investigated in detail using adjoint based forecast sensitivity observation impact (FSOI)

Investigating Sensitivity to Saharan Dust in Tropical Cyclone Formation Using Nasa's Adjoint Model

As tropical cyclones develop from easterly waves coming of the coast of Africa they interact with dust from the Sahara desert. There is a long standing debate over whether this dust inhibits or advances the developing storm and how much influence it has. Dust can surround the storm and absorb incoming solar radiation, cooling the air below. As a result an energy source for the system is potentially diminished, inhibiting growth of the storm. Alternatively dust may interact with clouds through micro-physical processes, for example by causing more moisture to condense, potentially increasing the strength. As a result of climate change, concentrations and amount of dust in the atmosphere will likely change. It it is important to properly understand its effect on tropical storm formation. The adjoint of an atmospheric general circulation model provides a very powerful tool for investigating sensitivity to initial conditions. The National Aeronautics and Space Administration (NASA) has recently developed an adjoint version of the Goddard Earth Observing System version 5 (GEOS-5) dynamical core, convection scheme, cloud model and radiation schemes. This is extended so that the interaction between dust and radiation is also accounted for in the adjoint model. This provides a framework for examining the sensitivity to dust in the initial conditions. Specifically the set up allows for an investigation into the extent to which dust affects cyclone strength through absorption of radiation. In this work we investigate the validity of using an adjoint model for examining sensitivity to dust in hurricane formation. We present sensitivity results for a number of systems that developed during the Atlantic hurricane season of 2006. During this period there was a significant outbreak of Saharan dust and it is has been argued that this outbreak was responsible for the relatively calm season. This period was also covered by an extensive observation campaign. It is shown that the adjoint can provide insight into the sensitivity and reveals a relatively low sensitivity to dust compared to, for example, the thermodynamic variables. However a secondary sensitivity though moisture is seen. If dust dries the air it can significantly reduce the cyclone intensity through the moisture

The Tangent Linear and Adjoint of the FV3 Dynamical Core: Development and Applications

GMAO (NASA's Global Modeling and Assimilation Office) has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR (4-Dimensional Variational Assimilation). In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system

Inclusion of Linearized Moist Physics in Nasa's Goddard Earth Observing System Data Assimilation Tools

Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa-Schubert (RAS) convection scheme has been developed and tested in NASA's Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture

Progress Towards Integrating the Finite-Volume Cubed-Sphere (FV3) Dynamical Core Tangent Linear and Adjoint Models into JEDI

The Joint Effort for Data assimilation Integration (JEDI) -- led by the Joint Center for Satellite Data Assimilation (JCSDA) -- is an inter-organizational endeavor to develop a common framework for performing data assimilation. This extensive framework will ultimately provide solvers, observation operators, interpolation and model interfaces using object oriented modeling. Two partners involved in JEDI use or plan to use the Finite Volume Cubed-Sphere (FV3) dynamical core to produce weather forecasts; these are NASA's Global Modeling and Assimilation Office and NOAA's National Center for Environment Prediction. In this work we present an update on ongoing efforts to integrate the FV3 tangent linear and adjoint models into the prototype JEDI framework. We setup and run a simple cycled data assimilation experiment using 4DVAR on the cubed sphere grid and with the FV3 tangent linear and adjoint models. Development of the observation operators for JEDI is separately underway. Instead of using real observations a simplified set of simulated observations will be used. We discuss the steps required to bring the FV3 linearized model into the object oriented framework and consider what would be the computational requirements of running this configuration for an operational system. FV3 uses a small time-step to ensure that small scales are well resolved, however this presents design challenges when running 4DVAR with the adjoint. An approach to storing the FV3 model trajectory has been developed that maintains the flexibility of using automatic differentiation. We discuss how this approach is incorporated into the framework. Other important uses of adjoint models include computing observation impacts and singular vectors, we consider how these tools can be included in JEDI