Search Results

You are looking at 31 - 40 of 68 items for

  • Author or Editor: Jeffrey Anderson x
  • Refine by Access: All Content x
Clear All Modify Search
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
Man-Yau Chan
,
Jeffrey L. Anderson
, and
Xingchao Chen

Abstract

The introduction of infrared water vapor channel radiance ensemble data assimilation (DA) has improved numerical weather forecasting at operational centers. Further improvements might be possible through extending ensemble data assimilation methods to better assimilate infrared satellite radiances. Here, we will illustrate that ensemble statistics under clear-sky conditions are different from cloudy conditions. This difference suggests that extending the ensemble Kalman filter (EnKF) to handle bi-Gaussian prior distributions may yield better results than the standard EnKF. In this study, we propose a computationally efficient bi-Gaussian ensemble Kalman filter (BGEnKF) to handle bi-Gaussian prior distributions. As a proof-of-concept, we used the 40-variable Lorenz 1996 model as a proxy to examine the impacts of assimilating infrared radiances with the BGEnKF and EnKF. A nonlinear observation operator that constructs radiance-like bimodal ensemble statistics was used to generate and assimilate pseudoradiances. Inflation was required for both methods to effectively assimilate pseudoradiances. In both 800- and 20-member experiments, the BGEnKF generally outperformed the EnKF. The relative performance of the BGEnKF with respect to the EnKF improved when the observation spacing and time between DA cycles (cycling interval) are increased from small values. The relative performance then degraded when observation spacing and cycling interval become sufficiently large. The BGEnKF generated less noise than the EnKF, suggesting that the BGEnKF produces more balanced analysis states than the EnKF. This proof-of-concept study motivates future investigation into using the BGEnKF to assimilate infrared observations into high-order numerical weather models.

Full access
Tobias Necker
,
Martin Weissmann
,
Yvonne Ruckstuhl
,
Jeffrey Anderson
, and
Takemasa Miyoshi

Abstract

State-of-the-art ensemble prediction systems usually provide ensembles with only 20–250 members for estimating the uncertainty of the forecast and its spatial and spatiotemporal covariance. Given that the degrees of freedom of atmospheric models are several magnitudes higher, the estimates are therefore substantially affected by sampling errors. For error covariances, spurious correlations lead to random sampling errors, but also a systematic overestimation of the correlation. A common approach to mitigate the impact of sampling errors for data assimilation is to localize correlations. However, this is a challenging task given that physical correlations in the atmosphere can extend over long distances. Besides data assimilation, sampling errors pose an issue for the investigation of spatiotemporal correlations using ensemble sensitivity analysis. Our study evaluates a statistical approach for correcting sampling errors. The applied sampling error correction is a lookup table–based approach and therefore computationally very efficient. We show that this approach substantially improves both the estimates of spatial correlations for data assimilation as well as spatiotemporal correlations for ensemble sensitivity analysis. The evaluation is performed using the first convective-scale 1000-member ensemble simulation for central Europe. Correlations of the 1000-member ensemble forecast serve as truth to assess the performance of the sampling error correction for smaller subsets of the full ensemble. The sampling error correction strongly reduced both random and systematic errors for all evaluated variables, ensemble sizes, and lead times.

Free access
Lili Lei
,
Jeffrey L. Anderson
, and
Glen S. Romine

Abstract

For ensemble-based data assimilation, localization is used to limit the impact of observations on physically distant state variables to reduce spurious error correlations caused by limited ensemble size. Traditionally, the localization value applied is spatially homogeneous. Yet there are potentially larger errors and different covariance length scales in precipitation systems, and that may justify the use of different localization functions for precipitating and nonprecipitating regions. Here this is examined using empirical localization functions (ELFs). Using output from an ensemble observing system simulation experiment (OSSE), ELFs provide estimates of horizontal and vertical localization for different observation types in regions with and without precipitation. For temperature and u- and υ-wind observations, the ELFs for precipitating regions are shown to have smaller horizontal localization scales than for nonprecipitating regions. However, the ELFs for precipitating regions generally have larger vertical localization scales than for nonprecipitating regions. The ELFs are smoothed and then applied in three additional OSSEs. Spatially homogeneous ELFs are found to improve performance relative to a commonly used localization function with compact support. When different ELFs are applied in precipitating and nonprecipitating regions, performance is further improved, but varying ELFs by observation type was not found to be as important. Imbalance in initial states caused by use of different localization functions is diagnosed by the domain-averaged surface pressure tendency. Forecasts from analyses with ELFs have smaller surface pressure tendencies than the standard localization, indicating improved initial balance with ELFs.

Full access
Xiu-Qun Yang
,
Jeffrey L. Anderson
, and
William F. Stern

Abstract

An approach to assess the potential predictability of the extratropical atmospheric seasonal variations in an ensemble of atmospheric general circulation model (AGCM) integrations has been proposed in this study by isolating reproducible forced modes and examining their contributions to the local ensemble mean. The analyses are based on the monthly mean output of an eight-member ensemble of 10-yr Atmospheric Model Intercomparison Project integrations with a T42L18 AGCM.

An EOF decomposition applied to the ensemble anomalies shows that there exist some forced modes that are less affected by the internal process and thus appear to be highly reproducible. By reconstructing the ensemble in terms of the more reproducible forced modes and by developing a quantitative measure, the potential predictability index (PPI), which combines the reproducibility with the local variance contribution, the local ensemble mean over some selective geographic areas in the extratropics was shown to result primarily from reproducible forced modes rather than internal chaotic fluctuations. Over those regions the ensemble mean is potentially predictable. Extratropical potentially predictable regions are found mainly over North America and part of the Asian monsoon regions. Interestingly, the potential predictability over some preferred areas such as Indian monsoon areas and central Africa occasionally results primarily from non-ENSO-related boundary forcing, although ENSO forcing generally dominates over most of the preferred areas.

The quantitative analysis of the extratropical potential predictability with PPI has shown that the preferred geographic areas have obvious seasonality. For the 850-hPa temperature, for example, potentially predictable regions during spring and winter are confined to Alaska, northwest Canada, and the southeast United States, the traditional PNA region, while during summer and fall they are favored over the middle part of North America. It has also been shown that the boreal summer season (June–August) possesses the largest potentially predictable area, which seems to indicate that it is a favored season for the extratropical potential predictability. On the contrary, boreal winter (December–February) appears to have a minimum area of extratropical potential predictability.

The results have been compared with the more traditional statistical tests for potential predictability and with observations from the National Centers for Environmental Prediction reanalysis, which indicates that the PPI analysis proposed here is successful in revealing extratropical potential predictability determined by the external forcing.

Full 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
Nicholas F. Anderson
,
Cedric A. Grainger
, and
Jeffrey L. Stith

Abstract

Airborne in situ measurements of updrafts in tropical convective storms were analyzed to determine the similarities and differences between updrafts in a tropical continental and a tropical oceanic region. Two hundred fifteen updraft cores from the Tropical Rainfall Measuring Mission (TRMM) component of the Large Scale Biosphere–Atmosphere (LBA) experiment (tropical continental wet season) and 377 updraft cores from the Kwajalein Experiment (KWAJEX) (tropical oceanic) were analyzed in a similar manner to that of previous studies of tropical updrafts. Average speed, maximum speed, width, and mass flux of the updraft cores from the TRMM-LBA and KWAJEX were generally similar to each other and also were similar to results from previous studies of tropical updrafts.

Full access
Hui Liu
,
Jeffrey L. Anderson
,
Ying-Hwa Kuo
, and
Kevin Raeder

Abstract

The importance of multivariate forecast error correlations between specific humidity, temperature, and surface pressure in perfect model assimilations of Global Positioning System radio occultation (RO) refractivity data is examined using the Ensemble Adjustment Filter (EAF) and the NCAR global Community Atmospheric Model, version 3. The goal is to explore whether inclusion of the multivariate forecast error correlations in the background term of 3D and 4D variational data assimilation systems (3DVAR and 4DVAR, respectively) is likely to improve RO data assimilation in the troposphere. It is not possible to explicitly neglect multivariate forecast error correlations with the EAF because they are not used directly in the algorithm. Instead, the filter only makes use of the forecast error correlations between observed quantities (RO here) and model state variables. However, because the forecast error correlations for RO observations are dominated by correlations with a subset of state variable types in certain regions, the importance of multivariate forecast error correlations between state variables can be indirectly assessed. This is done by setting the forecast error correlations of RO observations and some state variables (e.g., temperature) to zero in a set of assimilation experiments. Comparing these experiments to a control in which all state variables are impacted by RO observations allows an indirect assessment of the importance of multivariate correlations between state variables not impacted by the observations and those that are impacted. Results suggest that proper specification of the multivariate forecast error correlations in 3DVAR and 4DVAR systems should improve the analysis of specific humidity, surface pressure, and temperature in the troposphere when assimilating RO data.

Full access
Joshua P. Hacker
,
Jeffrey L. Anderson
, and
Mariusz Pagowski

Abstract

Strategies to improve covariance estimates for ensemble-based assimilation of near-surface observations in atmospheric models are explored. It is known that localization of covariance estimates can improve conditioning of covariance matrices in the assimilation process by removing spurious elements and increasing the rank of the matrix. Vertical covariance localization is the focus of this work, and two basic approaches are compared: 1) a recently proposed hierarchical filter approach based on sampling theory and 2) a more commonly used fifth-order piecewise rational function. The hierarchical filter allows for dynamic estimates of localization functions and does not place any restrictions on their form. The rational function is optimized for every analysis time of day and for every possible observation and state variable combination. The methods are tested with a column model containing PBL and land surface parameterization schemes that are available in current mesoscale modeling systems. The results are expected to provide context for assimilation of near-surface observations in mesoscale models, which will benefit short-range mesoscale NWP applications. Results show that both the hierarchical and rational function approaches effectively improve covariance estimates from small ensembles. The hierarchical approach provides localization functions that are irregular and more closely related to PBL structure. Analysis of eigenvalue spectra show that both approaches improve the rank of the covariance matrices, but the amount of improvement is not always directly related to the assimilation performance. Results also show that specifying different localization functions for different observation and state variable combinations is more important than including time dependence.

Full access
Robert Pinkel
,
Jeffrey Sherman
,
Jerome Smith
, and
Steven Anderson

Abstract

In this work a profiling CTD, operated from the research platform FLIP, is used to monitor the fine-scale density field as a function of both depth and time. A sequence of 10 000 CTD profiles from the surface to 560 m is examined. The data were obtained off the Southern California coast in the 1986 PATCHEX experiment. The vertical separation between successive isopycynal surfaces is tracked. The separation is related to the vertical derivative of vertical displacement, and is here referred to as the strain. The purpose of this work is to present a simple picture of the fine scale strain field as it evolves in time as well as depth.

When viewed in isopycnal following coordinates, the qualitative nature of the strain field depends on the characteristic vertical scale over which it is estimated. The “20 m strain” field has a wavelike character, dominated by inertial and semidiurnal tidal motion. Wavelike fluctuations are seen in the 20 m strain field even at subinertial frequencies. This suggests that nonlinear processes are significant even at these relatively large vertical scales. The “2 m strain” more closely resembles the classic picture of fine structure. Lenses of low density gradient fluid are separated by sheets of higher gradient water. The lenses are seen to persist up to eight hours. They can propagate with respect to the density field over tens of meters. The low gradient regions evolve into regions of high gradient and visa versa. The probability density function (PDF) of isopycnal separation is Gaussian for isopycnal pairs of large (∼20 m) mean separation. As mean separation distance is decreased, the skewness of the distribution increases.

Since all scalar fields in the sea are strained by the same velocity field, fluctuations in the fine-scale vertical gradients of a variety of quantities are correlated. Averages of the products of fine scale gradients can differ significantly from products of the averages.

Full access