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The genesis of meteorology at the University of Chicago is reviewed in commemoration of the 60th anniversary of the founding of the Institute of Meteorology. The Institute of Meteorology was founded in October 1940 under the leadership of Carl Rossby and Horace Byers. Although previous attempts failed due to lack of resources, the imminent need for meteorologists in aviation and long-range weather forecasting, particularly for the nation's military needs, provided sufficient motivation for the program, and a $15,000 donation by Sewell Avery provided the necessary funds to get the program started. This article adds to Byers' 1975 account of the founding of the Institute by documenting the exchange of letters in 1939 between C. Rossby, Karl T. Compton (president of Massachusetts Institute of Technology), Arthur H. Compton (professor of Physics at Chicago), and Henry Gale (dean of Physical Sciences at Chicago) regarding the possibility of establishing a meteorology program at Chicago.
The genesis of meteorology at the University of Chicago is reviewed in commemoration of the 60th anniversary of the founding of the Institute of Meteorology. The Institute of Meteorology was founded in October 1940 under the leadership of Carl Rossby and Horace Byers. Although previous attempts failed due to lack of resources, the imminent need for meteorologists in aviation and long-range weather forecasting, particularly for the nation's military needs, provided sufficient motivation for the program, and a $15,000 donation by Sewell Avery provided the necessary funds to get the program started. This article adds to Byers' 1975 account of the founding of the Institute by documenting the exchange of letters in 1939 between C. Rossby, Karl T. Compton (president of Massachusetts Institute of Technology), Arthur H. Compton (professor of Physics at Chicago), and Henry Gale (dean of Physical Sciences at Chicago) regarding the possibility of establishing a meteorology program at Chicago.
Abstract
Area equivalent latitude based on potential vorticity (PV) is a widely used diagnostic for isentropic transport in the stratosphere and upper troposphere. Here, an alternate method for calculating equivalent latitude is explored, namely, a numerical synthesis of a PV-like tracer from a long-term integration of the advection–diffusion equation on isentropic surfaces. It is found that the tracer equivalent latitude (TrEL) behaves much like the traditional PV equivalent latitude (PVEL) despite the simplified governing physics; this is evidenced by examining the kinematics of the Arctic lower stratospheric vortex. Yet in some cases TrEL performs markedly better as a coordinate for long-lived trace species such as ozone. These instances include analysis of lower stratospheric ozone during the Stratospheric Aerosol and Gas Experiment (SAGE) III Ozone Loss and Validation Experiment (SOLVE) campaign and three-dimensional reconstruction of total column ozone during November–December 1999 from fitted ozone-equivalent latitude relationship. It is argued that the improvement is due to the tracer being free from the diagnostic errors and certain diabatic processes that affect PV. The sensitivity of TrEL to spatial and temporal resolution, advection scheme, and driving winds is also examined.
Abstract
Area equivalent latitude based on potential vorticity (PV) is a widely used diagnostic for isentropic transport in the stratosphere and upper troposphere. Here, an alternate method for calculating equivalent latitude is explored, namely, a numerical synthesis of a PV-like tracer from a long-term integration of the advection–diffusion equation on isentropic surfaces. It is found that the tracer equivalent latitude (TrEL) behaves much like the traditional PV equivalent latitude (PVEL) despite the simplified governing physics; this is evidenced by examining the kinematics of the Arctic lower stratospheric vortex. Yet in some cases TrEL performs markedly better as a coordinate for long-lived trace species such as ozone. These instances include analysis of lower stratospheric ozone during the Stratospheric Aerosol and Gas Experiment (SAGE) III Ozone Loss and Validation Experiment (SOLVE) campaign and three-dimensional reconstruction of total column ozone during November–December 1999 from fitted ozone-equivalent latitude relationship. It is argued that the improvement is due to the tracer being free from the diagnostic errors and certain diabatic processes that affect PV. The sensitivity of TrEL to spatial and temporal resolution, advection scheme, and driving winds is also examined.
Abstract
Gravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline nonorographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.
Abstract
Gravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline nonorographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.
Abstract
The 2002 Southern Hemisphere final warming occurred early, following an unusually active winter and the first recorded major warming in the Antarctic. The breakdown of the stratospheric polar vortex in October and November 2002 is examined using new satellite observations from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument aboard the European Space Agency (ESA) Environment Satellite (ENVISAT) and meteorological analyses, both high-resolution fields from the European Centre for Medium-Range Weather Forecasts and the coarser Met Office analyses. The results derived from MIPAS observations are compared to measurements and inferences from well-validated solar occultation satellite instruments [Halogen Occultation Experiment (HALOE), Polar Ozone and Aerosol Measurement III (POAM III), and Stratospheric Aerosol and Gas Experiments II and III (SAGE II and III)] and to finescale tracer fields reconstructed by transporting trace gases based on MIPAS or climatological data using a reverse-trajectory method. These comparisons confirm the features in the MIPAS data and the interpretation of the evolution of the flow during the vortex decay revealed by those features. Mapped ozone and water vapor from MIPAS and the analyzed isentropic potential vorticity vividly display the vortex breakdown, which occurred earlier than usual. A large tongue of vortex air was pulled out westward and coiled up in an anticyclone, while the vortex core remnant shrank and drifted eastward and equatorward over the South Atlantic. By roughly mid-November, the vortex remnant at 10 mb had shrunk below scales resolved by the satellite observations, while a vortex core remained in the lower stratosphere.
Abstract
The 2002 Southern Hemisphere final warming occurred early, following an unusually active winter and the first recorded major warming in the Antarctic. The breakdown of the stratospheric polar vortex in October and November 2002 is examined using new satellite observations from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument aboard the European Space Agency (ESA) Environment Satellite (ENVISAT) and meteorological analyses, both high-resolution fields from the European Centre for Medium-Range Weather Forecasts and the coarser Met Office analyses. The results derived from MIPAS observations are compared to measurements and inferences from well-validated solar occultation satellite instruments [Halogen Occultation Experiment (HALOE), Polar Ozone and Aerosol Measurement III (POAM III), and Stratospheric Aerosol and Gas Experiments II and III (SAGE II and III)] and to finescale tracer fields reconstructed by transporting trace gases based on MIPAS or climatological data using a reverse-trajectory method. These comparisons confirm the features in the MIPAS data and the interpretation of the evolution of the flow during the vortex decay revealed by those features. Mapped ozone and water vapor from MIPAS and the analyzed isentropic potential vorticity vividly display the vortex breakdown, which occurred earlier than usual. A large tongue of vortex air was pulled out westward and coiled up in an anticyclone, while the vortex core remnant shrank and drifted eastward and equatorward over the South Atlantic. By roughly mid-November, the vortex remnant at 10 mb had shrunk below scales resolved by the satellite observations, while a vortex core remained in the lower stratosphere.
Abstract
The Australian bushfires of 2019/20 produced an unusually large number of pyrocumulonimbus (pyroCb) that injected huge amounts of smoke into the lower stratosphere. The pyroCbs from 29 December 2019 to 4 January 2020 were particularly intense, producing hemispheric-wide aerosol that persisted for months. One plume from this so-called Australian New Year (ANY) event evolved into a stratospheric aerosol mass ~1000 km across and several kilometers thick. This plume initially moved eastward toward South America in January, then reversed course and moved westward passing south of Australia in February and eventually reached South Africa in early March. The peculiar motion was related to the steady rise in plume potential temperature of ~8 K day−1 in January and ~6 K day−1 in February, due to local heating by smoke absorption of solar radiation. This heating resulted in a vertical temperature anomaly dipole, a positive potential vorticity (PV) anomaly, and anticyclonic circulation. We call this dynamical component of the smoke plume “smoke with induced rotation and lofting” (SWIRL). This study uses Navy Global Environmental Model (NAVGEM) analyses to detail the SWIRL structure over 2 months. The main diagnostic tool is an anticyclone edge calculation based on the scalar Q diagnostic. This provides the framework for calculating the time evolution of various SWIRL properties: PV anomaly, streamfunction, horizontal size, vertical thickness, flow speed, and tilt. In addition, we examine the temperature anomaly dipole, the SWIRL interaction with the large-scale wind shear, and the ozone anomaly associated with lofting of air from the lower to the middle stratosphere.
Abstract
The Australian bushfires of 2019/20 produced an unusually large number of pyrocumulonimbus (pyroCb) that injected huge amounts of smoke into the lower stratosphere. The pyroCbs from 29 December 2019 to 4 January 2020 were particularly intense, producing hemispheric-wide aerosol that persisted for months. One plume from this so-called Australian New Year (ANY) event evolved into a stratospheric aerosol mass ~1000 km across and several kilometers thick. This plume initially moved eastward toward South America in January, then reversed course and moved westward passing south of Australia in February and eventually reached South Africa in early March. The peculiar motion was related to the steady rise in plume potential temperature of ~8 K day−1 in January and ~6 K day−1 in February, due to local heating by smoke absorption of solar radiation. This heating resulted in a vertical temperature anomaly dipole, a positive potential vorticity (PV) anomaly, and anticyclonic circulation. We call this dynamical component of the smoke plume “smoke with induced rotation and lofting” (SWIRL). This study uses Navy Global Environmental Model (NAVGEM) analyses to detail the SWIRL structure over 2 months. The main diagnostic tool is an anticyclone edge calculation based on the scalar Q diagnostic. This provides the framework for calculating the time evolution of various SWIRL properties: PV anomaly, streamfunction, horizontal size, vertical thickness, flow speed, and tilt. In addition, we examine the temperature anomaly dipole, the SWIRL interaction with the large-scale wind shear, and the ozone anomaly associated with lofting of air from the lower to the middle stratosphere.
Abstract
An essential component of four-dimensional variational data assimilation is the tangent linear model (TLM), which is a linearized version of the full nonlinear forecast model. A relatively new approach to calculating the TLM is a regression model called the ensemble tangent linear model (ETLM). Here we validate the ETLM for linearizing a nonorographic gravity wave drag (NGWD) subgrid-scale model. The regression is applied to an ensemble created by perturbing the atmospheric state and calculating one time step of the NGWD model. The ETLM is validated using independent perturbations based on archived analysis increments. We examine how the skill of the NGWD ETLM depends on the choice of ensemble perturbation, ensemble size, amount of ensemble inflation/deflation, and the size of the localization stencil. After examining the nearly perfect results using a large ETLM ensemble (100 000 members), optimal tuning is then performed for 150–500 members. For smaller ETLM ensembles, spurious noise due to sampling error could be reduced either by downscaling the perturbations or by localizing the ETLM. The impact of localization decreases as the ETLM ensemble size increases. We then validate the ETLM using one year of archived DA analysis increments. The skill varies over time with percentage errors relative to persistence forecasts (where 100% is no skill, 0% is a perfect forecast) generally ranging from ∼50% to 90% (∼40% to 80%) for ETLMs with 150 (500) members. The ETLM is also shown to propagate small increments (1% of the size of analysis increments) with fractional errors of ∼10%.
Abstract
An essential component of four-dimensional variational data assimilation is the tangent linear model (TLM), which is a linearized version of the full nonlinear forecast model. A relatively new approach to calculating the TLM is a regression model called the ensemble tangent linear model (ETLM). Here we validate the ETLM for linearizing a nonorographic gravity wave drag (NGWD) subgrid-scale model. The regression is applied to an ensemble created by perturbing the atmospheric state and calculating one time step of the NGWD model. The ETLM is validated using independent perturbations based on archived analysis increments. We examine how the skill of the NGWD ETLM depends on the choice of ensemble perturbation, ensemble size, amount of ensemble inflation/deflation, and the size of the localization stencil. After examining the nearly perfect results using a large ETLM ensemble (100 000 members), optimal tuning is then performed for 150–500 members. For smaller ETLM ensembles, spurious noise due to sampling error could be reduced either by downscaling the perturbations or by localizing the ETLM. The impact of localization decreases as the ETLM ensemble size increases. We then validate the ETLM using one year of archived DA analysis increments. The skill varies over time with percentage errors relative to persistence forecasts (where 100% is no skill, 0% is a perfect forecast) generally ranging from ∼50% to 90% (∼40% to 80%) for ETLMs with 150 (500) members. The ETLM is also shown to propagate small increments (1% of the size of analysis increments) with fractional errors of ∼10%.
Abstract
The local ensemble tangent linear model (LETLM) provides an alternative method for creating the tangent linear model (TLM) and adjoint of a nonlinear model that promises to be easier to maintain and more computationally scalable than earlier methods. In this paper, we compare the ability of the LETLM to predict the difference between two nonlinear trajectories of the Navy’s global weather prediction model at low resolution (2.5° at the equator) with that of the TLM currently used in the Navy’s four-dimensional variational (4DVar) data assimilation scheme. When compared to the pair of nonlinear trajectories, the traditional TLM and the LETLM have improved skill relative to persistence everywhere in the atmosphere, except for temperature in the planetary boundary layer. In addition, the LETLM was, on average, more accurate than the traditional TLM (error reductions of about 20% in the troposphere and 10% overall). Sensitivity studies showed that the LETLM was most sensitive to the number of ensemble members, with the performance gradually improving with increased ensemble size up to the maximum size attempted (400). Inclusion of physics in the LETLM ensemble leads to a significantly improved representation of the boundary layer winds (error reductions of up to 50%), in addition to improved winds and temperature in the free troposphere and in the upper stratosphere/lower mesosphere. The computational cost of the LETLM was dominated by the cost of ensemble propagation. However, the LETLM can be precomputed before the 4DVar data assimilation algorithm is executed, leading to a significant computational advantage.
Abstract
The local ensemble tangent linear model (LETLM) provides an alternative method for creating the tangent linear model (TLM) and adjoint of a nonlinear model that promises to be easier to maintain and more computationally scalable than earlier methods. In this paper, we compare the ability of the LETLM to predict the difference between two nonlinear trajectories of the Navy’s global weather prediction model at low resolution (2.5° at the equator) with that of the TLM currently used in the Navy’s four-dimensional variational (4DVar) data assimilation scheme. When compared to the pair of nonlinear trajectories, the traditional TLM and the LETLM have improved skill relative to persistence everywhere in the atmosphere, except for temperature in the planetary boundary layer. In addition, the LETLM was, on average, more accurate than the traditional TLM (error reductions of about 20% in the troposphere and 10% overall). Sensitivity studies showed that the LETLM was most sensitive to the number of ensemble members, with the performance gradually improving with increased ensemble size up to the maximum size attempted (400). Inclusion of physics in the LETLM ensemble leads to a significantly improved representation of the boundary layer winds (error reductions of up to 50%), in addition to improved winds and temperature in the free troposphere and in the upper stratosphere/lower mesosphere. The computational cost of the LETLM was dominated by the cost of ensemble propagation. However, the LETLM can be precomputed before the 4DVar data assimilation algorithm is executed, leading to a significant computational advantage.
Abstract
An ensemble-based linearized forecast model has been developed for data assimilation applications for numerical weather prediction. Previous studies applied this local ensemble tangent linear model (LETLM) to various models, from simple one-dimensional models to a low-resolution (~2.5°) version of the Navy Global Environmental Model (NAVGEM) atmospheric forecast model. This paper applies the LETLM to NAVGEM at higher resolution (~1°), which required overcoming challenges including 1) balancing the computational stencil size with the ensemble size, and 2) propagating fast-moving gravity modes in the upper atmosphere. The first challenge is addressed by introducing a modified local influence volume, introducing computations on a thin grid, and using smaller time steps. The second challenge is addressed by applying nonlinear normal mode initialization, which damps spurious fast-moving modes and improves the LETLM errors above ~100 hPa. Compared to a semi-Lagrangian tangent linear model (TLM), the LETLM has superior skill in the lower troposphere (below 700 hPa), which is attributed to better representation of moist physics in the LETLM. The LETLM skill slightly lags in the upper troposphere and stratosphere (700–2 hPa), which is attributed to nonlocal aspects of the TLM including spectral operators converting from winds to vorticity and divergence. Several ways forward are suggested, including integrating the LETLM in a hybrid 4D variational solver for a realistic atmosphere, combining a physics LETLM with a conventional TLM for the dynamics, and separating the LETLM into a sequence of local and nonlocal operators.
Abstract
An ensemble-based linearized forecast model has been developed for data assimilation applications for numerical weather prediction. Previous studies applied this local ensemble tangent linear model (LETLM) to various models, from simple one-dimensional models to a low-resolution (~2.5°) version of the Navy Global Environmental Model (NAVGEM) atmospheric forecast model. This paper applies the LETLM to NAVGEM at higher resolution (~1°), which required overcoming challenges including 1) balancing the computational stencil size with the ensemble size, and 2) propagating fast-moving gravity modes in the upper atmosphere. The first challenge is addressed by introducing a modified local influence volume, introducing computations on a thin grid, and using smaller time steps. The second challenge is addressed by applying nonlinear normal mode initialization, which damps spurious fast-moving modes and improves the LETLM errors above ~100 hPa. Compared to a semi-Lagrangian tangent linear model (TLM), the LETLM has superior skill in the lower troposphere (below 700 hPa), which is attributed to better representation of moist physics in the LETLM. The LETLM skill slightly lags in the upper troposphere and stratosphere (700–2 hPa), which is attributed to nonlocal aspects of the TLM including spectral operators converting from winds to vorticity and divergence. Several ways forward are suggested, including integrating the LETLM in a hybrid 4D variational solver for a realistic atmosphere, combining a physics LETLM with a conventional TLM for the dynamics, and separating the LETLM into a sequence of local and nonlocal operators.
Abstract
A high-altitude version of the Navy Operational Global Atmospheric Prediction System (NOGAPS) spectral forecast model is used to simulate the unusual September 2002 Southern Hemisphere stratospheric major warming. Designated as NOGAPS-Advanced Level Physics and High Altitude (NOGAPS-ALPHA), this model extends from the surface to 0.005 hPa (∼85 km altitude) and includes modifications to multiple components of the operational NOGAPS system, including a new radiative heating scheme, middle-atmosphere gravity wave drag parameterizations, hybrid vertical coordinate, upper-level meteorological initialization, and radiatively active prognostic ozone with parameterized photochemistry. NOGAPS-ALPHA forecasts (hindcasts) out to 6 days capture the main features of the major warming, such as the zonal mean wind reversal, planetary-scale wave amplification, large upward Eliassen–Palm (EP) fluxes, and splitting of the polar vortex in the middle stratosphere. Forecasts beyond 6 days have reduced upward EP flux in the lower stratosphere, reduced amplitude of zonal wavenumbers 2 and 3, and a middle stratospheric vortex that does not split. Three-dimensional EP-flux diagnostics in the troposphere reveal that the longer forecasts underestimate upward-propagating planetary wave energy emanating from a significant blocking pattern over the South Atlantic that played a large role in forcing the major warming. Forecasts of less than 6 days are initialized with the blocking in place, and therefore are not required to predict the blocking onset. For a more thorough skill assessment, NOGAPS-ALPHA forecasts over 3 weeks during September–October 2002 are compared with operational NOGAPS 5-day forecasts made at the time. NOGAPS-ALPHA forecasts initialized with 2002 operational NOGAPS analyses show a modest improvement in skill over the NOGAPS operational forecasts. An additional, larger improvement is obtained when NOGAPS-ALPHA is initialized with reanalyzed 2002 fields produced with the currently operational (as of October 2003) Naval Research Laboratory (NRL) Atmospheric Variational Data Assimilation System (NAVDAS). Thus the combination of higher model top, better physical parameterizations, and better initial conditions all yield improved forecasting skill over the NOGAPS forecasts issued operationally at the time.
Abstract
A high-altitude version of the Navy Operational Global Atmospheric Prediction System (NOGAPS) spectral forecast model is used to simulate the unusual September 2002 Southern Hemisphere stratospheric major warming. Designated as NOGAPS-Advanced Level Physics and High Altitude (NOGAPS-ALPHA), this model extends from the surface to 0.005 hPa (∼85 km altitude) and includes modifications to multiple components of the operational NOGAPS system, including a new radiative heating scheme, middle-atmosphere gravity wave drag parameterizations, hybrid vertical coordinate, upper-level meteorological initialization, and radiatively active prognostic ozone with parameterized photochemistry. NOGAPS-ALPHA forecasts (hindcasts) out to 6 days capture the main features of the major warming, such as the zonal mean wind reversal, planetary-scale wave amplification, large upward Eliassen–Palm (EP) fluxes, and splitting of the polar vortex in the middle stratosphere. Forecasts beyond 6 days have reduced upward EP flux in the lower stratosphere, reduced amplitude of zonal wavenumbers 2 and 3, and a middle stratospheric vortex that does not split. Three-dimensional EP-flux diagnostics in the troposphere reveal that the longer forecasts underestimate upward-propagating planetary wave energy emanating from a significant blocking pattern over the South Atlantic that played a large role in forcing the major warming. Forecasts of less than 6 days are initialized with the blocking in place, and therefore are not required to predict the blocking onset. For a more thorough skill assessment, NOGAPS-ALPHA forecasts over 3 weeks during September–October 2002 are compared with operational NOGAPS 5-day forecasts made at the time. NOGAPS-ALPHA forecasts initialized with 2002 operational NOGAPS analyses show a modest improvement in skill over the NOGAPS operational forecasts. An additional, larger improvement is obtained when NOGAPS-ALPHA is initialized with reanalyzed 2002 fields produced with the currently operational (as of October 2003) Naval Research Laboratory (NRL) Atmospheric Variational Data Assimilation System (NAVDAS). Thus the combination of higher model top, better physical parameterizations, and better initial conditions all yield improved forecasting skill over the NOGAPS forecasts issued operationally at the time.
Abstract
An ensemble-based tangent linear model (TLM) is described and tested in data assimilation experiments using a global shallow-water model (SWM). A hybrid variational data assimilation system was developed with a 4D variational (4DVAR) solver that could be run either with a conventional TLM or a local ensemble TLM (LETLM) that propagates analysis corrections using only ensemble statistics. An offline ensemble Kalman filter (EnKF) is used to generate and maintain the ensemble. The LETLM uses data within a local influence volume, similar to the local ensemble transform Kalman filter, to linearly propagate the state variables at the central grid point. After tuning the LETLM with offline 6-h forecasts of analysis corrections, cycling experiments were performed that assimilated randomly located SWM height observations, based on a truth run with forced bottom topography. The performance using the LETLM is similar to that of the conventional TLM, suggesting that a well-constructed LETLM could free 4D variational methods from dependence on conventional TLMs. This is a first demonstration of the LETLM application within a context of a hybrid-4DVAR system applied to a complex two-dimensional fluid dynamics problem. Sensitivity tests are included that examine LETLM dependence on several factors including length of cycling window, size of analysis correction, spread of initial ensemble perturbations, ensemble size, and model error. LETLM errors are shown to increase linearly with correction size in the linear regime, while TLM errors increase quadratically. As nonlinearity (or forecast model error) increases, the two schemes asymptote to the same solution.
Abstract
An ensemble-based tangent linear model (TLM) is described and tested in data assimilation experiments using a global shallow-water model (SWM). A hybrid variational data assimilation system was developed with a 4D variational (4DVAR) solver that could be run either with a conventional TLM or a local ensemble TLM (LETLM) that propagates analysis corrections using only ensemble statistics. An offline ensemble Kalman filter (EnKF) is used to generate and maintain the ensemble. The LETLM uses data within a local influence volume, similar to the local ensemble transform Kalman filter, to linearly propagate the state variables at the central grid point. After tuning the LETLM with offline 6-h forecasts of analysis corrections, cycling experiments were performed that assimilated randomly located SWM height observations, based on a truth run with forced bottom topography. The performance using the LETLM is similar to that of the conventional TLM, suggesting that a well-constructed LETLM could free 4D variational methods from dependence on conventional TLMs. This is a first demonstration of the LETLM application within a context of a hybrid-4DVAR system applied to a complex two-dimensional fluid dynamics problem. Sensitivity tests are included that examine LETLM dependence on several factors including length of cycling window, size of analysis correction, spread of initial ensemble perturbations, ensemble size, and model error. LETLM errors are shown to increase linearly with correction size in the linear regime, while TLM errors increase quadratically. As nonlinearity (or forecast model error) increases, the two schemes asymptote to the same solution.