Abstract

The impact of negative dissipation on posttime analysis and forecast correction techniques is examined in a simplified context. The experiments are conducted using a three-level quasigeostrophic model (with a nonsingular tangent propagator matrix) under a perfect-model assumption. Corrections to the initial analysis errors are obtained by operating on the forecast error with (i) the full inverse of the forward tangent propagator, (ii) an inverse composed of a subset of the first leading singular vectors (pseudoinverse), and (iii) the tangent equations with a negative time step (backward integration). When the forecast error is known exactly, using negative dissipation during the full-inverse or backward-integration calculation results in an analysis-error estimate that projects too weakly onto the leading singular vectors and too strongly onto the decaying singular vectors. These discrepancies are small for weak dissipation but increase as the dissipation strength is increased.

When the forecast error is known inexactly, negative dissipation provides a beneficial damping of the backward-in-time growth of uncertainties present in the forecast error. This damping effect is found to be due to a fairly uniform change in the singular values, not changes in the singular vectors. However, even for very strong negative dissipation, the uncertainty in the forecast error still grows during the full inverse or backward integration. Therefore, the analysis error estimate will still be dominated by the trailing singular vectors, which represent the decaying part of the initial error. This is in contrast to the pseudoinverse technique, which, like the adjoint sensitivity, is dominated by the fastest growing part of the initial error, and is therefore relatively insensitive to the analysis uncertainty contained within the forecast error. Thus, while full-inverse and backward-integration calculations may provide an analysis perturbation that results in a significantly improved forecast, the analysis error estimate is accurate only when the forecast error is known exactly (i.e., perfect model experiments), regardless of the sign of the dissipation. These results hold for both global and regional forecast errors.

Abstract

A suite of high-resolution two-dimensional ensemble simulations are used to investigate the predictability of mountain waves, wave breaking, and downslope windstorms. For relatively low hills and mountains, perturbation growth is weak and ensemble spread is small. Gravity waves and wave breaking associated with higher mountains exhibit rapid perturbation growth and large ensemble variance. Near the regime boundary between mountain waves and wave breaking, a bimodal response is apparent with large ensemble variance. Several ensemble members exhibit a trapped wave response and others reveal a hydraulic jump and large-amplitude breaking in the stratosphere. The bimodality of the wave response brings into question the appropriateness of commonly used ensemble statistics, such as the ensemble mean, in these situations. Small uncertainties in the initial state within observational error limits result in significant ensemble spread in the strength of the downslope wind speed, wave breaking, and wave momentum flux. These results indicate that the theoretical transition across the regime boundary for gravity wave breaking can be interpreted as a finite-width or blurred transition zone from a practical predictability standpoint.

Abstract

In this paper it is argued that ensemble prediction systems can be devised in such a way that physical parameterizations of subgrid-scale motions are utilized in a stochastic manner, rather than in a deterministic way as is typically done. This can be achieved within the context of current physical parameterization schemes in weather and climate prediction models. Parameterizations are typically used to predict the evolution of grid-mean quantities because of unresolved subgrid-scale processes. However, parameterizations can also provide estimates of higher moments that could be used to constrain the random determination of the future state of a certain variable. The general equations used to estimate the variance of a generic variable are briefly discussed, and a simplified algorithm for a stochastic moist convection parameterization is proposed as a preliminary attempt. Results from the implementation of this stochastic convection scheme in the Navy Operational Global Atmospheric Prediction System (NOGAPS) ensemble are presented. It is shown that this method is able to generate substantial tropical perturbations that grow and “migrate” to the midlatitudes as forecast time progresses while moving from the small scales where the perturbations are forced to the larger synoptic scales. This stochastic convection method is able to produce substantial ensemble spread in the Tropics when compared with results from ensembles created from initial-condition perturbations. Although smaller, there is still a sizeable impact of the stochastic convection method in terms of ensemble spread in the extratropics. Preliminary simulations with initial-condition and stochastic convection perturbations together in the same ensemble system show a promising increase in ensemble spread and a decrease in the number of outliers in the Tropics.

Abstract

The rate at which the leading singular vectors converge toward a single pattern for increasing optimization times is examined within the context of a T21 L3 quasigeostrophic model. As expected, the final-time backward singular vectors converge toward the backward Lyapunov vector, while the initial-time forward singular vectors converge toward the forward Lyapunov vector. Although there is significant case-to-case variability, in general this convergence does not occur over timescales for which the tangent approximation is valid (i.e., less than 5 days). However, a significant portion of the leading Lyapunov vector is contained within the subspace spanned by an ensemble composed of the first 30 singular vectors optimized over 2 or 3 days. Also as expected, the final-time leading singular vectors become independent of metric as optimization time is increased. Given an initial perturbation that has a white spectrum with respect to the initial-time singular vectors, the percent of the final-time perturbation explained by the leading singular vector is significant and increases as optimization time increases. However, even for 10-day optimization times, the leading singular vector accounts for, on average, only 23% to 28% of the total evolved global perturbation variance depending on the metric and trajectory.

Abstract

Two versions of the Navy Operational Global Atmospheric Prediction System (NOGAPS) global ensemble, with and without a stochastic convection scheme, are compared regarding their performance in predicting the development and evolution of tropical cyclones. Forecasts of four typhoons, one tropical storm, and two selected nondeveloping tropical systems from The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign and Tropical Cyclone Structure 2008 (T-PARC/TCS-08) field program during August and September 2008 are evaluated. It is found that stochastic convection substantially increases the spread in ensemble storm tracks and in the vorticity and height fields in the vicinity of the storm. Stochastic convection also has an impact on the number of ensemble members predicting genesis. One day prior to the system being declared a tropical depression, on average, 31% of the ensemble members predict storm development when the ensemble includes initial perturbations only. When stochastic convection is included, this percentage increases to 50%, but the number of “false alarms” for two nondeveloping systems also increases. However, the increase in false alarms is smaller than the increase in correct development predictions, indicating that stochastic convection may have the potential for improving tropical cyclone forecasting.

Abstract

The statistics of model temporal variability ought to be the same as those of the filtered version of reality that the model is designed to represent. Here, simple diagnostics are introduced to quantify temporal variability on different time scales and are then applied to NCEP and CMC global ensemble forecasting systems. These diagnostics enable comparison of temporal variability in forecasts with temporal variability in the initial states from which the forecasts are produced. They also allow for an examination of how day-to-day variability in the forecast model changes as forecast integration time increases. Because the error in subsequent analyses will differ, it is shown that forecast temporal variability should lie between corresponding analysis variability and analysis variability minus 2 times the analysis error variance. This expectation is not always met and possible causes are discussed. The day-to-day variability in NCEP forecasts steadily decreases at a slow rate as forecast time increases. In contrast, temporal variability increases during the first few days in the CMC control forecasts, and then levels off, consistent with a spinup of the forecasts starting from overly smoothed analyses. The diagnostics successfully reflect a reduction in the temporal variability of the CMC perturbed forecasts after a system upgrade. The diagnostics also illustrate a shift in variability maxima from storm-track regions for 1-day variability to blocking regions for 10-day variability. While these patterns are consistent with previous studies examining temporal variability on different time scales, they have the advantage of being obtainable without the need for extended (e.g., multimonth) forecast integrations.

Abstract

Potential vorticity streamers (PVSs) are elongated filaments of high-PV air near the tropopause. In the warm season, anticyclonic Rossby wave breaking (AWB) produces enhanced PVS activity, which in turn modifies the equatorward tropical environment by enhancing vertical wind shear (VWS). This enhanced VWS can play an important role in suppressing nearby tropical cyclone (TC) activity. Given the important role that PVSs play in modifying their local environment, forecasts of PVS activity on subseasonal time scales may also influence forecasts of TC activity. This study uses Navy Earth System Prediction Capability (Navy ESPC) 45-day forecasts initialized during boreal summer 2009–15 to investigate subseasonal predictability of PVSs and TCs in the North Atlantic. PVSs are identified on the 350-K isentropic surface bounded by the 2 PV unit (PVU; 1 PVU = 10⁻⁶ K kg⁻¹ m² s⁻¹) contour and defined as the high-PV trough axis downstream of the AWB axis. TCs are identified in the forecasts using the TempestExtremes detection algorithm that tracks warm-core lows. PVS and TC activity metrics that sum the number and intensity of events for a given time period are also computed. We first use skill scores and mean-state biases to determine the typical predictability of PVS activity, and then subselect high- and low-PVS-activity forecasts to determine how PVS forecast errors impact TC activity forecast errors. Results show that PVS activity can modulate TC activity at subseasonal time scales, with over-forecasted PVS activity corresponding to underestimated forecasts of TC activity and vice versa. This inverse correlation is consistent with enhanced VWS occurring equatorward of PVS troughs in the high-PVS forecasts.

Abstract

The impact of stochastic convection on ensembles produced using the ensemble transform (ET) initial perturbation scheme is examined. This note compares the behavior of ensemble forecasts based only on initial ET perturbations with the behavior of ensemble forecasts based on the ET initial perturbations and forecasts that include stochastic convection. It is illustrated that despite the fact that stochastic convection occurs only after the forecast integrations have started, it induces changes in the initial perturbations as well. This is because the ET is a “cycling” scheme, in which previous short-term forecasts are used to produce the initial perturbations for the current forecast. The stochastic convection scheme induces rapid perturbation growth in regions where convection is active, primarily in the tropics. When combined with the ET scheme, this results in larger initial perturbation variance in the tropics, and, because of a global constraint on total initial perturbation variance, smaller initial perturbation variance in the extratropics. Thus, the inclusion of stochastic convection helps to mitigate a problem found in the practical implementation of the ET, namely, that of too little initial variance in the tropics and too much in the extratropics. Various skill scores show that stochastic convection improves ensemble performance in the tropics, with little impact to modest improvement in the extratropics. Experiments performed using the initial perturbations from the control ensemble run but forecast integrations using the stochastic convection scheme indicate that the improved performance of the stochastic convection ensemble at early forecast times is due to both “indirect” changes in the initial perturbations and “direct” changes in the forecast. At later forecast times, it appears that most of the improvement can be gained through stochastic convection alone.

Abstract

The ensemble transform (ET) scheme changes forecast perturbations into analysis perturbations whose amplitudes and directions are consistent with a user-provided estimate of analysis error covariance. A practical demonstration of the ET scheme was undertaken using Naval Research Laboratory (NRL) Atmospheric Variational Data Assimilation System (NAVDAS) analysis error variance estimates and the Navy Operational Global Atmospheric Prediction System (NOGAPS) numerical weather prediction (NWP) model. It was found that the ET scheme produced forecast ensembles that were comparable to or better in a variety of measures than those produced by the Fleet Numerical and Oceanography Center (FNMOC) bred-growing modes (BGM) scheme. Also, the demonstration showed that the introduction of stochastic perturbations into the ET forecast ensembles led to a substantial improvement in the agreement between the ET and NAVDAS analysis error variances. This finding is strong evidence that even a small-sized ET ensemble is capable of obtaining good agreement between the ET and NAVDAS analysis error variances, provided that NWP model deficiencies are accounted for. Last, since the NAVDAS analysis error covariance estimate is diagonal and hence ignores multivariate correlations, it was of interest to examine the ET analysis perturbations’ spatial correlation. Tests showed that the ET analysis perturbations exhibited statistically significant, realistic multivariate correlations.

Abstract

The impacts of assimilating dropwindsonde data and enhanced atmospheric motion vectors (AMVs) on tropical cyclone track forecasts are examined using the Navy global data assimilation and forecasting systems. Enhanced AMVs have the largest impact on eastern Pacific storms, while dropwindsonde data have the largest impact on Atlantic storms. Results in the western Pacific are mixed. Two western Pacific storms, Nuri and Jangmi, are examined in detail. For Nuri, dropwindsonde data and enhanced AMVs are at least as likely to degrade as to improve forecasts. For Jangmi, additional data improve track forecasts in most cases. An erroneous weakening of the forecasted subtropical high appears to contribute to the track errors for Nuri and Jangmi. Assimilation of enhanced AMVs systematically increases the analyzed heights in this region, counteracting this model bias. However, the impact of enhanced AMVs decreases rapidly as the model biases saturate at similar levels for experiments with and without the enhanced AMVs after the first few forecast days. Experiments are also conducted in which the errors assigned to synthetic tropical cyclone observations are increased. Moderate increases in the assigned errors improve track forecasts on average, but larger increases in the assigned errors produce mixed results. Both experiments allow for reductions in innovations and residuals when compared to dropwindsonde observations. These experiments suggest that a reformulation of the synthetic tropical cyclone observation scheme may lead to improved forecasts as more in situ and remote observations become available.