Gregory J. Hakim

Boundary Conditions for Limited-Area Ensemble Kalman Filters

Abstract One aspect of implementing a limited-area ensemble Kalman filter (EnKF) involves the specification of a suitable ensemble of lateral boundary conditions. Two classes of methods to populate a boundary condition ensemble are proposed. In the first class, the ensemble of boundary conditions is provided by an EnKF on a larger domain and is approximately a random draw from the probability distribution function for the forecast (or analysis) on the limited-area domain boundary. The second class perturbs around a deterministic estimate of the state using assumed spatial and temporal covariance relationships. Methods in the second class are relatively flexible and easy to implement. Experiments that test the utility of these methods are performed for both an idealized low-dimensional model and limited-area simulations using the Weather Research and Forecasting (WRF) model; all experiments employ simulated observations under the perfect model assumption. The performance of the ensemble boundary condition ...

Ensemble-Based Sensitivity Analysis

The sensitivity of forecasts to observations is evaluated using an ensemble approach with data drawn from a pseudo-operational ensemble Kalman filter. For Gaussian statistics and a forecast metric defined as a scalar function of the forecast variables, the effect of observations on the forecast metric is quantified by changes in the metric mean and variance. For a single observation, expressions for these changes involve a product of scalar quantities, which can be rapidly evaluated for large numbers of observations. This technique is applied to determining climatological forecast sensitivity and predicting the impact of observations on sea level pressure and precipitation forecast metrics. The climatological 24-h forecast sensitivity of the average pressure over western Washington State shows a region of maximum sensitivity to the west of the region, which tilts gently westward with height. The accuracy of ensemble sensitivity predictions is tested by withholding a single buoy pressure observation from this region and comparing this perturbed forecast with the control case where the buoy is assimilated. For 30 cases, there is excellent agreement between these forecast differences and the ensemble predictions, as measured by the forecast metric. This agreement decreases for increasing numbers of observations. Nevertheless, by using statistical confidence tests to address sampling error, the impact of thousands of observations on forecast-metric variance is shown to be well estimated by a subset of the O(100) most significant observations.

Comparing Adjoint- and Ensemble-Sensitivity Analysis with Applications to Observation Targeting

Abstract The sensitivity of numerical weather forecasts to small changes in initial conditions is estimated using ensemble samples of analysis and forecast errors. Ensemble sensitivity is defined here by linear regression of analysis errors onto a given forecast metric. It is shown that ensemble sensitivity is proportional to the projection of the analysis-error covariance onto the adjoint-sensitivity field. Furthermore, the ensemble-sensitivity approach proposed here involves a small calculation that is easy to implement. Ensemble- and adjoint-based sensitivity fields are compared for a representative wintertime flow pattern near the west coast of North America for a 90-member ensemble of independent initial conditions derived from an ensemble Kalman filter. The forecast metric is taken for simplicity to be the 24-h forecast of sea level pressure at a single point in western Washington State. Results show that adjoint and ensemble sensitivities are very different in terms of location, scale, and magnitud...

The Ohio Valley Wave-Merger Cyclogenesis Event of 25–26 January 1978. Part II: Diagnosis Using Quasigeostrophic Potential Vorticity Inversion

Abstract The dynamical interactions between precursor disturbances during the wave-merger cyclogenesis event of 25–26 January 1978 over eastern North America are diagnosed using quasigeostrophic potential vorticity (QGPV) inversion. This case is characterized by two prominent preexisting upper-level disturbances that induce rapid surface cyclogenesis as they come into close proximity. Static QGPV inversion is used to attribute a particular geopotential height field to the QGPV associated with each precursor disturbance. The full flow is partitioned into the following components: the northern upper precursor, the southern upper precursor, and the background flow. Prognostic QGPV inversion is used to quantify the instantaneous geopotential height tendencies attributable to each of these flow components. The static-inversion results for the upper precursors exhibit the structure of baroclinic vortices with maximum amplitude near the tropopause. During the 48-h period spanning the period of study of this even...

A New Surface Model for Cyclone–Anticyclone Asymmetry

Cyclonic vortices on the tropopause are characterized by compact structure and larger pressure, wind, and temperature perturbations when compared to broader and weaker anticyclones. Neither the origin of these vortices nor the reasons for the preferred asymmetries are completely understood; quasigeostrophic dynamics, in particular, have cyclone‐anticyclone symmetry. In order to explore these and related problems, a novel small Rossby number approximation is introduced to the primitive equations applied to a simple model of the tropopause in continuously stratified fluid. This model resolves dynamics that give rise to vortical asymmetries, while retaining both the conceptual simplicity of quasigeostrophic dynamics and the computational economy of two-dimensional flows. The model contains no depth-independent (barotropic) flow, and thus may provide a useful comparison to two-dimensional flows dominated by this flow component. Solutions for random initial conditions (i.e., freely decaying turbulence) exhibit vortical asymmetries typical of tropopause observations, with strong localized cyclones, and weaker diffuse anticyclones. Cyclones cluster around a distinct length scale at a given time, whereas anticyclones do not. These results differ significantly from previous studies of cyclone‐anticyclone asymmetry in the shallow-water primitive equations and the periodic balance equations. An important source of asymmetry in the present solutions is divergent flow associated with frontogenesis and the forward cascade of tropopause potential temperature variance. This thermally direct flow changes the mean potential temperature of the tropopause, selectively maintains anticyclonic filaments relative to cyclonic filaments, and appears to promote the merger of anticyclones relative to cyclones.

Performance Characteristics of a Pseudo-Operational Ensemble Kalman Filter

The 2-yr performance of a pseudo-operational (real time) limited-area ensemble Kalman filter (EnKF) based on the Weather Research and Forecasting Model is described. This system assimilates conventional observations from surface stations, rawinsondes, the Aircraft Communications Addressing and Reporting System (ACARS), and cloud motion vectors every 6 h on a domain that includes the eastern North Pacific Ocean and western North America. Ensemble forecasts from this system and deterministic output from operational numerical weather prediction models during this same period are verified against rawinsonde and surface observation data. Relative to operational forecasts, the forecast from the ensemble-mean analysis has slightly larger errors in wind and temperature but smaller errors in moisture, even though satellite radiances are not assimilated by the EnKF. Time-averaged correlations indicate that assimilating ACARS and cloud wind data with flow-dependent error statistics provides corrections to the moisture field in the absence of direct observations of that field. Comparison with a control experiment in which a deterministic forecast is cycled without observation assimilation indicates that the skill in the EnKF’s forecasts results from assimilating observations and not from lateral boundary conditions or the model formulation. Furthermore, the ensemble variance is generally in good agreement with the ensemble-mean error and the spread increases monotonically with forecast hour.

Developing Wave Packets in the North Pacific Storm Track

Developing wave packets in the western North Pacific storm track are diagnosed observationally. An abrupt upstream edge to baroclinic wave activity over the western North Pacific facilitates comparisons between the observational results and previous theoretical predictions on the spatiotemporal evolution of an impulse disturbance. Results show that surface cyclogenesis events are preceded by a sharply peaked wave packet that originates poleward of the Himalaya Plateau and develops rapidly across the North Pacific to North America. Composite wave-packet structure is broadly consistent with linear theory for idealized models such as Eady’s. The longitude‐height structure of the mature packet reveals deep growing waves with horizontal wavelengths of approximately 4000 km near the packet peak. Downstream from the peak, amplitude decays exponentially, and wavelength decreases approximately linearly to about 2500‐3000 km at the leading edge. Meridional potential vorticity gradients are concentrated near the tropopause. In contrast to linear theory, the packets show an abrupt upstream edge and no evidence of upstream development. As the packet travels through the along-stream variations of the Pacific jet stream, the packet-peak and leading-edge group velocity vary. These accelerations change the packet length and suggest that the Pacific jet may act to focus the packets. A sample of North Atlantic storm track events reveals similar results and suggests that the Atlantic storm track is often seeded by wave packets that originate over the western North Pacific Ocean. In contrast, Atlantic packets refract equatorward and become trapped on the subtropical jet to the south of Himalaya Plateau, suggesting perhaps less potential for seeding disturbances in the Pacific storm track.

The March 1993 Superstorm Cyclogenesis: Incipient Phase Synoptic- and Convective-Scale Flow Interaction and Model Performance

Abstract The incipient stages of the 12–14 March 1993 “superstorm” (SS93) cyclogenesis over the Gulf of Mexico are examined. Noteworthy aspects of SS93 include 1) it is the deepest extratropical cyclone ever observed over the Gulf of Mexico during the 1957–96 period, and 2) existing operational prediction models performed poorly in simulating the incipient cyclogenesis over the northwestern Gulf of Mexico. A dynamic-tropopause (DT) analysis shows that SS93 is triggered by a potent potential vorticity (PV) anomaly as it crosses extreme northern Mexico and approaches the Gulf of Mexico. The low-level environment over the western Gulf of Mexico is warmed, moistened, and destabilized by a persistent southerly flow ahead of the approaching PV anomaly. Ascent and a lowering of the DT (associated with a lowering of the potential temperature) ahead of the PV anomaly contributes to further destabilization that is realized in the form of a massive convective outbreak. An examination of the National Centers for Envi...

Assimilation of Time-Averaged Pseudoproxies for Climate Reconstruction

The efficacy of a novel ensemble data assimilation (DA) technique is examined in the climate field reconstruction (CFR) of surface temperature. A minimalistic, computationally inexpensive DA technique is employed that requires only a static ensemble of climatologically plausible states. Pseudoproxy experiments are performed with both general circulation model (GCM) and Twentieth Century Reanalysis (20CR) data byreconstructingsurfacetemperaturefieldsfromasparsenetworkofnoisypseudoproxies.TheDAapproach is compared to a conventional CFR approach based on principal component analysis (PCA) for experiments on global domains. DA outperforms PCA in reconstructing global-mean temperature in all experiments and is more consistent across experiments, with a range of time series correlations of 0.69‐0.94 compared to 0.19‐ 0.87 for the PCA method. DA improvements are even more evident in spatial reconstruction skill, especially in sparsely sampled pseudoproxy regions and for 20CR experiments. It is hypothesized that DA improves spatialreconstructionsbecauseitreliesoncoherent,spatiallylocaltemperaturepatterns,whichremainrobust even when glacial states are used to reconstruct nonglacial states and vice versa. These local relationships, as utilized by DA, appear to be more robust than the orthogonal patterns of variability utilized by PCA. Comparing results for GCM and 20CR data indicates that pseudoproxy experiments that rely solely on GCM data may give a false impression of reconstruction skill.

Ensemble Data Assimilation Applied to RAINEX Observations of Hurricane Katrina (2005)

An ensemble Kalman filter (EnKF) based on the Weather Research and Forecasting model is applied to generate ensemble analyses and forecasts of Hurricane Katrina (2005) and the surrounding area every 6 h over the lifetime of the storm on a nested domain. Analyses are derived from assimilating conventional in situ observations, reconnaissance dropsondes, including data taken during the Hurricane Rainband and Intensity Exchange Experiment (RAINEX), and tropical cyclone position estimates. Observation assimilation at individual times consistently reduces errors in tropical cyclone position, but not necessarily in intensity; however, withholding observations leads to significantly larger errors in both quantities. Analysis increments for observations near the tropical cyclone are dominated by changes in vortex position, and these increments increase the asymmetric structure of the storm. Data denial experiments indicate that dropsondes deployed in the synoptic environment provide minimal benefit to the outer domain; however, dropsondes deployed within the tropical cyclone lead to significant reductions in position and intensity errors on the inner domain. Specifically, errors in the inner domain ensemble-mean 6-h forecasts of minimum pressure are 70% larger when dropsonde data is not assimilated. Precipitation fields are qualitatively similar to Tropical Rainfall Measuring Mission (TRMM) satellite estimates, although model values are double the values of the satellite estimate. Moreover, the spinup period and initial imbalance in EnKF-initialized WRF forecasts is less than starting the model from a GFS analysis. Ensemble-mean 48-h forecasts initialized with EnKF analyses have track and intensity errors that are 50% smaller than GFS and NHC official forecasts.