Adjoint Sensitivity Studies Research Articles

Local and Remote Influences on the Heat Content of the Labrador Sea: An Adjoint Sensitivity Study

AbstractThe Labrador Sea is one of the few regions on the planet where the interior ocean can exchange heat directly with the atmosphere via strong, localized, wintertime convection, with possible implications for the state of North Atlantic climate and global surface warming. Using an observationally constrained ocean adjoint model, we find that annual‐mean Labrador Sea heat content is sensitive to temperature/salinity changes (1) along potential source water pathways (e.g., the subpolar gyre, the North Atlantic Current, the Gulf Stream) and (2) along the West African and European shelves, which are not significant source water regions for the Labrador Sea. The West African coastal/shelf adjustment mechanism, which may be excited by changes in along‐shelf wind stress, involves pressure anomalies that propagate along a coastal waveguide toward Greenland, changing the across‐shelf pressure gradient in the North Atlantic and altering heat convergence in the Labrador Sea. We also find that nonlocal (in space and time) heat fluxes (e.g., in the Irminger Sea, the seas south of Iceland) can have a strong impact on Labrador Sea heat content. Understanding and predicting the state of the Labrador Sea and its potential impacts on North Atlantic climate and global surface warming will require monitoring of oceanic and atmospheric properties at remote sites in the Irminger Sea, the subpolar gyre, and along the West African and European shelf/coast system, among others.

Adjoint sensitivity study on idealized explosive cyclogenesis

The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study. The PSU/NCAR limited-area, nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation, respectively. To ensure the explosive development of a baroclinic wave, the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderate-amplitude disturbance, derived from a potential vorticity inversion technique. Firstly, the validity period of the tangent linear model for this idealized baroclinic wave case is discussed, considering different initial moisture distributions and a dry condition. Secondly, the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment, respectively. The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection, and the validity period can last even longer in the dry adjoint integration. Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream. Moreover, the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere, which cannot be depicted in the dry adjoint run.

Inclusion of Linearized Moist Physics in NASA’s Goddard Earth Observing System Data Assimilation Tools

Abstract 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.

Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico

[1] Adjoint model sensitivity analyses were applied for the loop current (LC) and its eddy shedding in the Gulf of Mexico (GoM) using the MIT general circulation model (MITgcm). The circulation in the GoM is mainly driven by the energetic LC and subsequent LC eddy separation. In order to understand which ocean regions and features control the evolution of the LC, including anticyclonic warm-core eddy shedding in the GoM, forward and adjoint sensitivities with respect to previous model state and atmospheric forcing were computed using the MITgcm and its adjoint. Since the validity of the adjoint model sensitivities depends on the capability of the forward model to simulate the real LC system and the eddy shedding processes, a 5 year (2004–2008) forward model simulation was performed for the GoM using realistic atmospheric forcing, initial, and boundary conditions. This forward model simulation was compared to satellite measurements of sea-surface height (SSH) and sea-surface temperature (SST), and observed transport variability. Despite realistic mean state, standard deviations, and LC eddy shedding period, the simulated LC extension shows less variability and more regularity than the observations. However, the model is suitable for studying the LC system and can be utilized for examining the ocean influences leading to a simple, and hopefully generic LC eddy separation in the GoM. The adjoint sensitivities of the LC show influences from the Yucatan Channel (YC) flow and Loop Current Frontal Eddy (LCFE) on both LC extension and eddy separation, as suggested by earlier work. Some of the processes that control LC extension after eddy separation differ from those controlling eddy shedding, but include YC through-flow. The sensitivity remains stable for more than 30 days and moves generally upstream, entering the Caribbean Sea. The sensitivities of the LC for SST generally remain closer to the surface and move at speeds consistent with advection by the high-speed core of the current, while sensitivities to SSH generally extend to deeper layers and propagate more slowly. The adjoint sensitivity to relative vorticity deduced from the sensitivities to velocity fields suggests that advection of cyclonic (positive) relative vorticity anomalies from the YC or the LCFEs accelerate the LC eddy separation. Forward model perturbation experiments were performed to complement and check the adjoint sensitivity analysis as well as sampling the predictability and nonlinearity of the LC evolution. The model and its adjoint can be used in four-dimensional variational assimilation (4D-VAR) to produce dynamically consistent ocean state estimates for analysis and forecasts of the circulation of the GoM.

Sensitivity of Western Boundary Transport at the Mean North Equatorial Current Bifurcation Latitude to Wind Forcing

Abstract The bifurcation of the North Equatorial Current (NEC) plays an important role in the heat and water mass exchanges between the tropical and subtropical gyres in the Pacific Ocean. The variability of western boundary transport (WBT) east of the Philippine coast at the mean NEC bifurcation latitude (12°N) is examined here. A tropical Pacific regional model is set up based on the Massachusetts Institute of Technology general circulation model and its adjoint, which calculates the sensitivities of a defined meridional transport to atmospheric forcing fields and ocean state going backward in time. The adjoint-derived sensitivity of the WBT at the mean NEC bifurcation latitude to surface wind stress is dominated by curl-like patterns that are located farther eastward and southward with increasing time lag. The temporal evolution of the adjoint sensitivity of the WBT to wind stress resembles wind-forced Rossby wave dynamics but propagating with speeds determined by the background stratification and current, suggesting that wind-forced Rossby waves are the underlying mechanism. Interannual-to-decadal variations of the WBT can be hindcast well by multiplying the adjoint sensitivity and the time-lagged wind stress over the whole model domain and summing over time lags. The analysis agrees with previous findings that surface wind stress (especially zonal wind stress in the western subtropical Pacific) largely determines the WBT east of the Philippines, and with a time lag based on Rossby wave propagation. This adjoint sensitivity study quantifies the contribution of wind stress at all latitudes and longitudes and provides a novel perspective to understand the relationship between the WBT and wind forcing over the Pacific Ocean.

Adjoint Sensitivity of the Niño-3 Surface Temperature to Wind Forcing

Abstract The evolution of sea surface temperature (SST) over the eastern equatorial Pacific plays a significant role in the intense tropical air–sea interaction there and is of central importance to the El Niño–Southern Oscillation (ENSO) phenomenon. Effects of atmospheric fields (especially wind stress) and ocean state on the eastern equatorial Pacific SST variations are investigated using the Massachusetts Institute of Technology general circulation model (MITgcm) and its adjoint model, which can calculate the sensitivities of a cost function (in this case the averaged 0–30-m temperature in the Niño-3 region during an ENSO event peak) to previous atmospheric forcing fields and ocean state going backward in time. The sensitivity of the Niño-3 surface temperature to monthly zonal wind stress in preceding months can be understood by invoking mixed layer heat balance, ocean dynamics, and especially linear equatorial wave dynamics. The maximum positive sensitivity of the Niño-3 surface temperature to local wind forcing usually happens ~1–2 months before the peak of the ENSO event and is hypothesized to be associated with the Ekman pumping mechanism. In model experiments, its magnitude is closely related to the subsurface vertical temperature gradient, exhibiting strong event-to-event differences with strong (weak) positive sensitivity during La Niña (strong El Niño) events. The adjoint sensitivity to remote wind forcing in the central and western equatorial Pacific is consistent with the standard hypothesis that the remote wind forcing affects the Niño-3 surface temperature indirectly by exciting equatorial Kelvin and Rossby waves and modulating thermocline depth in the Niño-3 region. The current adjoint sensitivity study is consistent with a previous regression-based sensitivity study derived from perturbation experiments. Finally, implication for ENSO monitoring and prediction is also discussed.

Validation of a Tropical Cyclone Steering Response Function with a Barotropic Adjoint Model

Abstract The steering of a tropical cyclone (TC) vortex is commonly understood as the advection of the TC vortex by an “environmental wind.” In past studies, the environmental steering wind vector has been defined by the horizontal and vertical averaging of the horizontal winds in a box centered on the TC. The components of this environmental steering have been proposed as response functions to derive adjoint-derived sensitivities of TC zonal and meridional steering. The appropriateness of these response functions in adjoint sensitivity studies of TC steering is tested using a two-dimensional barotropic model and its adjoint for a 24-h forecast. It is found that these response functions do not produce sensitivities to TC steering because perturbations to the model initial conditions that change the final-time location of the TC also change the response functions in ways that have nothing to do with the steering of the TC at model verification. An alternate response function is proposed wherein the environmental steering vector is defined as the wind averaged over the response function box attributed to vorticity outside of that box. By redefining the response functions for the zonal and meridional steering as components of this environmental steering vector, the effect of small changes to the final-time location of the TC is removed, and the resultant sensitivity gradients can be shown to truly represent the sensitivity of TC steering to perturbations of the model forecast state.

Application of an Adiabatic WRF Adjoint to the Investigation of the May 2004 McMurdo, Antarctica, Severe Wind Event

The tangent linear and adjoint of an adiabatic version of the Weather Research and Forecasting (WRF) Model with its Advanced Research WRF (ARW) dynamic core have been developed. The source-to-source automatic differentiation tool [i.e., the Transformation of Algorithm (TAF) in FORTRAN] was used in the development. Tangent linear and adjoint checks of the developed adiabatic WRF adjoint modeling system (WAMS) were conducted, and all necessary correctness verification procedures were passed. As the first application, the adiabatic WAMS was used to study the adjoint sensitivity of a severe windstorm in Antarctica. Linearity tests indicated that an adjoint-based sensitivity study with the Antarctic Mesoscale Prediction System (AMPS) 90-km domain configuration for the windstorm is valid up to 24 h. The adjoint-based sensitivity calculation with adiabatic WAMS identified sensitive regions for the improvement of the 24-h forecast of the windstorm. It is indicated that the windstorm forecast largely relies on the model initial conditions in the area from the south part of the Trans-Antarctic Mountains to West Antarctica and between the Ross Ice Shelf and the South Pole. Based on the sensitivity analysis, the southerly or southeasterly wind at lower levels in the sensitivity region should be larger, the cyclone should be stronger, and the atmospheric stratification should be more stable over the north slope of the Trans-Antarctic Mountain to the Ross Ice Shelf, than the AMPS analyses. By constructing pseudo-observations in the sensitivity region using the gradient information of forecast windstorm intensity around McMurdo, the model initial conditions are revised with the WRF three-dimensional variational data assimilation, which leads to significant improvement in the prediction of the windstorm. An adjoint sensitivity study is an efficient way to identify sensitivity regions in order to collect more observations in the region for better forecasts in a specific aspect of interest.

Adjoint sensitivity analysis of regional air quality models

The task of providing an optimal analysis of the state of the atmosphere requires the development of efficient computational tools that facilitate an efficient integration of observational data into models. In a variational approach the data assimilation problem is posed as a minimization problem, which requires the sensitivity (derivatives) of a cost functional with respect to problem parameters. The direct decoupled method has been extensively applied for sensitivity studies of air pollution. Adjoint sensitivity is a complementary approach which efficiently calculates the derivatives of a functional with respect to a large number of parameters. In this paper, we discuss the mathematical foundations of the adjoint sensitivity method applied to air pollution models, and present a complete set of computational tools for performing three-dimensional adjoint sensitivity studies. Numerical examples show that three-dimensional adjoint sensitivity analysis provides information on influence areas, which cannot be obtained solely by an inverse analysis of the meteorological fields. Several illustrative data assimilation results in a twin experiments framework, as well as the assimilation of a real data set are also presented.

Direct and adjoint sensitivity analysis of chemical kinetic systems with KPP: II—numerical validation and applications

The Kinetic PreProcessor KPP was extended to generate the building blocks needed for the direct and adjoint sensitivity analysis of chemical kinetic systems. An overview of the theoretical aspects of sensitivity calculations and a discussion of the KPP software tools is presented in the companion paper. In this work the correctness and efficiency of the KPP generated code for direct and adjoint sensitivity studies are analyzed through an extensive set of numerical experiments. Direct-decoupled Rosenbrock methods are shown to be cost-effective for providing sensitivities at low and medium accuracies. A validation of the discrete–adjoint evaluated gradients is performed against the finite difference estimates. The accuracy of the adjoint gradients is measured using a reference gradient value obtained with a standard direct-decoupled method. The accuracy is studied for both constant step size and variable step size integration of the forward/adjoint model and the consistency between the discrete and continuous adjoint models is analyzed. Applications of the KPP-1.2 software package to direct and adjoint sensitivity studies, variational data assimilation, and parameter identification are considered for the comprehensive chemical mechanism SAPRC-99.

Variational assimilation of radar reflectivities in a cirrus model. I: Model description and adjoint sensitivity studies

AbstractThis paper presents an ice microphysics model to be used in variational assimilation of cloud‐radar data. The model predicts the vertical and temporal evolution of the parameters of a modified gamma size distribution describing an ice‐cloud crystal population, given an initial atmospheric state. Microphysical variables are mapped onto radar reflectivities using an explicit radar forward model. Evolution equations take into account microphysical processes relevant to ice‐crystal growth, such as vapour‐diffusion growth, aggregation, and gravitational sedimentation. The thermodynamic and dynamic state is specified from a numerical forecast or a radiosonde sounding and is assumed constant over the model integration time. Due to this assumption, the model provides no feedback to the environmental state and thus cannot be used for long‐term cloud forecasts. However, when the model is integrated over a short time interval, and the atmospheric conditions are close to water saturation at cloud levels, the model is shown to compare well with observations. An adjoint of a linearized version of the cloud model is derived and applied to investigate model sensitivities to input variables and model parameters. Results show a large sensitivity of model outputs to temperature and selected parameters related to the crystal fall‐velocity parametrization. Copyright © 2003 Royal Meteorological Society

An Adjoint Sensitivity Study of the Efficacy of Modal and Nonmodal Perturbations in Causing Model Block Onset*

Abstract With a blocking index as the response function, the adjoint sensitivity formalism is used to assess the impact of normal modes, adjoint modes, and regional singular vectors on prediction of block onset in a two-layer model. The authors focus on three blocks excited by perturbing the model’s state vector at times preselected using the maximal perturbation that defines the direction in phase space associated with the largest possible change in the response function. The sets of normal modes, adjoint modes, and regional singular vectors (using the total energy or the L2 norm) are computed on instantaneous basic-state flows for the preselected times and sensitivity results are presented for a time window of 3 days. When ordered by decreasing values of the growth rates of the normal modes, the authors find that some distant normal modes and adjoint modes can produce larger changes in the response function than some of their leading counterparts. In contrast, the sets of regional singular vectors conta...