Search Results

You are looking at 11 - 20 of 34 items for :

  • Author or Editor: Jeffrey Anderson x
  • Monthly Weather Review x
  • Refine by Access: Content accessible to me x
Clear All Modify Search
Mahsa Mirzargar and Jeffrey L. Anderson

Abstract

Various generalizations of the univariate rank histogram have been proposed to inspect the reliability of an ensemble forecast or analysis in multidimensional spaces. Multivariate rank histograms provide insightful information about the misspecification of genuinely multivariate features such as the correlation between various variables in a multivariate ensemble. However, the interpretation of patterns in a multivariate rank histogram should be handled with care. The purpose of this paper is to focus on multivariate rank histograms designed based on the concept of data depth and outline some important considerations that should be accounted for when using such multivariate rank histograms. To generate correct multivariate rank histograms using the concept of data depth, the datatype of the ensemble should be taken into account to define a proper preranking function. This paper demonstrates how and why some preranking functions might not be suitable for multivariate or vector-valued ensembles and proposes preranking functions based on the concept of simplicial depth that are applicable to both multivariate points and vector-valued ensembles. In addition, there exists an inherent identifiability issue associated with center-outward preranking functions used to generate multivariate rank histograms. This problem can be alleviated by complementing the multivariate rank histogram with other well-known multivariate statistical inference tools based on rank statistics such as the depth-versus-depth (DD) plot. Using a synthetic example, it is shown that the DD plot is less sensitive to sample size compared to multivariate rank histograms.

Full access
Lili Lei and Jeffrey L. Anderson

Abstract

The empirical localization algorithm described here uses the output from an observing system simulation experiment (OSSE) and constructs localization functions that minimize the root-mean-square (RMS) difference between the truth and the posterior ensemble mean for state variables. This algorithm can automatically provide an estimate of the localization function and does not require empirical tuning of the localization scale. It can compute an appropriate localization function for any potential observation type and kind of state variable. The empirical localization algorithm is investigated in the Community Atmosphere Model, version 5 (CAM5). The empirical localization function (ELF) is computed for the horizontal and vertical separately so that the vertical localization is explored explicitly. The horizontal and vertical ELFs are also computed for different geographic regions. The ELFs varying with region have advantages over the single global ELF in the horizontal and vertical, because different localization functions are more effective in different regions. The ELFs computed from an OSSE can be used as the localization in a subsequent OSSE. After three iterations, the ELFs appear to have converged. When used as localization in an OSSE, the converged ELFs produce a significantly smaller RMS error of temperature and zonal and meridional winds than the best Gaspari–Cohn (GC) localization for a dependent verification period using the observations from the original OSSE, and a similar RMS error to the best GC for an independent verification period. The converged ELFs have a significantly smaller RMS error of surface pressure than the best GC for both dependent and independent verification periods.

Full access
Jonathan Poterjoy and Jeffrey L. Anderson

Abstract

This study presents the first application of a localized particle filter (PF) for data assimilation in a high-dimensional geophysical model. Particle filters form Monte Carlo approximations of model probability densities conditioned on observations, while making no assumptions about the underlying error distribution. Unlike standard PFs, the local PF uses a localization function to reduce the influence of distant observations on state variables, which significantly decreases the number of particles required to maintain the filter’s stability. Because the local PF operates effectively using small numbers of particles, it provides a possible alternative to Gaussian filters, such as ensemble Kalman filters, for large geophysical models. In the current study, the local PF is compared with stochastic and deterministic ensemble Kalman filters using a simplified atmospheric general circulation model. The local PF is found to provide stable filtering results over yearlong data assimilation experiments using only 25 particles. The local PF also outperforms the Gaussian filters when observation networks include measurements that have non-Gaussian errors or relate nonlinearly to the model state, like remotely sensed data used frequently in atmospheric analyses. Results from this study encourage further testing of the local PF on more complex geophysical systems, such as weather prediction models.

Full access
Lili Lei and Jeffrey L. Anderson

Abstract

Two techniques for estimating good localization functions for serial ensemble Kalman filters are compared in observing system simulation experiments (OSSEs) conducted with the dynamical core of an atmospheric general circulation model. The first technique, the global group filter (GGF), minimizes the root-mean-square (RMS) difference between the estimated regression coefficients using a hierarchical ensemble filter. The second, the empirical localization function (ELF), minimizes the RMS difference between the true values of the state variables and the posterior ensemble mean. Both techniques provide an estimate of the localization function for an observation’s impact on a state variable with few a priori assumptions about the localization function. The ELF localizations can have values larger than 1.0 at small distances, indicating that this technique addresses localization but also can correct the prior ensemble spread in the same way as a variance inflation when needed. OSSEs using ELF localizations generally have smaller root-mean-square error (RMSE) than the optimal Gaspari and Cohn (GC) localization function obtained by empirically tuning the GC width. The localization functions estimated by the GGF are broader than those from the ELF, and the OSSEs with the GGF localization generally have larger RMSE than the optimal GC localization function. The GGFs are too broad because of spurious correlation biases that occur in the OSSEs. These errors can be reduced by using a stochastic EnKF with perturbed observations instead of a deterministic EAKF.

Full access
Lili Lei and Jeffrey L. Anderson

Abstract

To investigate the impacts of frequently assimilating only surface pressure (PS) observations, the Data Assimilation Research Testbed and the Community Atmosphere Model (DART/CAM) are used for observing system simulation experiments with the ensemble Kalman filter. An empirical localization function (ELF) is used to effectively spread the information from PS in the vertical. The ELF minimizes the root-mean-square difference between the truth and the posterior ensemble mean for state variables. The temporal frequency of the observations is increased from 6 to 3 h, and then 1 h. By observing only PS, the uncertainty throughout the entire depth of the troposphere can be constrained. The analysis error over the entire depth of the troposphere, especially the middle troposphere, is reduced with increased assimilation frequency. The ELF is similar to the vertical localization function used in the Twentieth-Century Reanalysis (20CR); thus, it demonstrates that the current vertical localization in the 20CR is close to the optimal localization function.

Full access
Hui Liu, Jeffrey Anderson, and Ying-Hwa Kuo

Abstract

Radio occultation (RO) refractivity observations provide information about tropospheric water vapor and temperature in all weather conditions. The impact of using RO refractivity observations on analyses and forecasts of Hurricane Ernesto’s genesis (2006) using an ensemble Kaman filter data assimilation system is investigated. Assimilating RO refractivity profiles in the vicinity of the storm locally moistens the analysis of the lower troposphere and also adjusts the wind analysis in both the lower and upper troposphere through forecast multivariate correlations of RO refractivity and wind. The model forecasts propagate and enhance the added water vapor and the wind adjustments leading to more accurate analyses of the later stages of the genesis of the storm. The root-mean-square errors of water vapor and wind forecasts compared to dropsonde and radiosonde observations are reduced consistently. As a result, assimilating RO refractivity data in addition to traditional observations leads to a stronger initial vortex of the storm and improved forecasts of the storm’s intensification. The benefits of the RO data are much reduced when the RO data in the lower troposphere (below 6 km) are ignored.

Full access
Yue Ying, Fuqing Zhang, and Jeffrey L. Anderson

Abstract

Covariance localization remedies sampling errors due to limited ensemble size in ensemble data assimilation. Previous studies suggest that the optimal localization radius depends on ensemble size, observation density and accuracy, as well as the correlation length scale determined by model dynamics. A comprehensive localization theory for multiscale dynamical systems with varying observation density remains an active area of research. Using a two-layer quasigeostrophic (QG) model, this study systematically evaluates the sensitivity of the best Gaspari–Cohn localization radius to changes in model resolution, ensemble size, and observing networks. Numerical experiment results show that the best localization radius is smaller for smaller-scale components of a QG flow, indicating its scale dependency. The best localization radius is rather insensitive to changes in model resolution, as long as the key dynamical processes are reasonably well represented by the low-resolution model with inflation methods that account for representation errors. As ensemble size decreases, the best localization radius shifts to smaller values. However, for nonlocal correlations between an observation and state variables that peak at a certain distance, decreasing localization radii further within this distance does not reduce analysis errors. Increasing the density of an observing network has two effects that both reduce the best localization radius. First, the reduced observation error spectral variance further constrains prior ensembles at large scales. Less large-scale contribution results in a shorter overall correlation length, which favors a smaller localization radius. Second, a denser network provides more independent pieces of information, thus a smaller localization radius still allows the same number of observations to constrain each state variable.

Full access
Hisashi Nakamura, Mototaka Nakamura, and Jeffrey L. Anderson

Abstract

Time evolutions of prominent blocking flow configurations over the North Pacific and Europe are compared based upon composites for the 30 strongest events observed during 27 recent winter seasons. Fluctuations associated with synoptic-scale migratory eddies have been filtered out before the compositing. A quasi-stationary wave train across the Atlantic is evident during the blocking amplification over Europe, while no counterpart is found to the west of the amplifying blocking over the North Pacific. Correlation between the tropopause-level potential vorticity (PV) and meridional wind velocity associated with the amplifying blocking is found to be negative over Europe in association with the anticyclonic evolution of the low-PV center, but it is almost zero over the North Pacific. Feedback from the synoptic-scale eddies, as evaluated in the form of 250-mb geopotential height tendency due to the eddy vorticity flux convergence, accounts for more than 75% of the observed amplification for the Pacific blocking and less than 45% for the European blocking. This difference is highlighted in two types of “contour advection with surgery” experiments. In one of them PV contours observed four days before the peak blocking time were advected by composite time series of the low-pass-filtered observational wind, and in the other experiment they were advected by the low-pass-filtered wind from which the transient eddy feedback evaluated as above had been removed at every time step. Hence, the latter data should be dominated by low-frequency dynamics. For the European blocking both experiments can reproduce the anticyclonic evolution of low-PV air within a blocking ridge as observed. For the Pacific blocking, in contrast, the observed intrusion of low-PV air into the higher latitudes cannot be reproduced without the transient feedback. Furthermore, in a barotropic model initialized with the composite 250-mb flow observed three days before the peak time, a simulated blocking development over the North Pacific is more sensitive to the insertion of the observed transient feedback than that over Europe. These results suggest that the incoming wave activity flux associated with a quasi-stationary Rossby wave train is of primary importance in the blocking formation over Europe, whereas the forcing by the synoptic-scale transients is indispensable to that over the North Pacific.

Full access
Mohamad El Gharamti, Kevin Raeder, Jeffrey Anderson, and Xuguang Wang

Abstract

Sampling errors and model errors are major drawbacks from which ensemble Kalman filters suffer. Sampling errors arise because of the use of a limited ensemble size, while model errors are deficiencies in the dynamics and underlying parameterizations that may yield biases in the model’s prediction. In this study, we propose a new time-adaptive posterior inflation algorithm in which the analyzed ensemble anomalies are locally inflated. The proposed inflation strategy is computationally efficient and is aimed at restoring enough spread in the analysis ensemble after assimilating the observations. The performance of this scheme is tested against the relaxation to prior spread (RTPS) and adaptive prior inflation. For this purpose, two model are used: the three-variable Lorenz 63 system and the Community Atmosphere Model (CAM). In CAM, global refractivity, temperature, and wind observations from several sources are incorporated to perform a set of assimilation experiments using the Data Assimilation Research Testbed (DART). The proposed scheme is shown to yield better quality forecasts than the RTPS. Assimilation results further suggest that when model errors are small, both prior and posterior inflation are able to mitigate sampling errors with a slight advantage to posterior inflation. When large model errors, such as wind and temperature biases, are present, prior inflation is shown to be more accurate than posterior inflation. Densely observed regions as in the Northern Hemisphere present numerous challenges to the posterior inflation algorithm. A compelling enhancement to the performance of the filter is achieved by combining both adaptive inflation schemes.

Open access
Jeffrey L. Anderson and Huug M. van den Dool

Abstract

The skill of a set of extended-range dynamical forecasts made with a modern numerical forecast model is examined. A forecast is said to be skillful if it produces a high quality forecast by correctly modeling some aspects of the dynamics of the real atmosphere; high quality forecasts may also occur by chance. The dangers of making a conclusion about model skill by verifying a single long-range forecast are pointed out by examples of apparently high “skill” verifications between extended-range forecasts and observed fields from entirely different years.

To avoid these problems, the entire distribution of forecast quality for a large set of forecasts as a function of lead time is examined. A set of control forecasts that clearly have no skill is presented. The quality distribution for the extended-range forecasts is compared to the distributions of quality for the no-skill control forecast set.

The extended-range forecast quality distributions are found to be essentially indistinguishable from those for the no-skill control at leads somewhat greater than 12 days. A search for individual forecasts with a “return of skill” at extended ranges is also made. Although it is possible to find individual forecasts that have a return of quality, a comparison to the no-skill controls demonstrates that these return of skill forecasts occur only as often as is expected by chance.

Full access