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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Error Growth in Operational 10-day Forecasts

The rate of growth of forecast errors has been estimated previously, using as data base 100 consecutive 10-day operational forecasts from the European Center for Medium Range Forecasting (ECMWF). The growth of the difference between two model forecasts verifying the same day was parameterized. This parameterization of error growth was extended by including the effect of model deficiencies as well as their scale dependence. In this way the forecaster are able to fit real forecast error growth and determine the scale dependence of the derived parameters (rate of error growth, external error source due to model errors, and saturation levels). This work is a necessary step in the application of the Lagged Average Forecasting (LAF) technique to the ECMWF 10-day forecasts. It is found that for both the analyses and the forecasts, there is an approximate equipartition of energy between all the zonal wavenumbers m corresponding to the same total wavenumber n.

Kalnay, E.↗
NASA NTRS2013

The Influence of Observation Errors on Analysis Error and Forecast Skill Investigated with an Observing System Simulation Experiment

The Global Modeling and Assimilation Office (GMAO) observing system simulation experiment (OSSE) framework is used to explore the response of analysis error and forecast skill to observation quality. In an OSSE, synthetic observations may be created that have much smaller error than real observations, and precisely quantified error may be applied to these synthetic observations. Three experiments are performed in which synthetic observations with magnitudes of applied observation error that vary from zero to twice the estimated realistic error are ingested into the Goddard Earth Observing System Model (GEOS-5) with Gridpoint Statistical Interpolation (GSI) data assimilation for a one-month period representing July. The analysis increment and observation innovation are strongly impacted by observation error, with much larger variances for increased observation error. The analysis quality is degraded by increased observation error, but the change in root-mean-square error of the analysis state is small relative to the total analysis error. Surprisingly, in the 120 hour forecast increased observation error only yields a slight decline in forecast skill in the extratropics, and no discernable degradation of forecast skill in the tropics.

Observation Error↗
NASA NTRS2020

Evaluation of adjoint-based observation impacts as a function of forecast length using an Observing System Simulation Experiment

Adjoints of numerical weather prediction models may be employed for Forecast Sensitivity to Observation (FSO) in order to monitor the contribution of ingested observation data on short-term forecast skill. However, the calculation of short-term forecast error is difficult due to the lack of a truly independent dataset for verification. In an Observing System Simulation Experiment framework, the Nature Run is able to provide a true and complete verification dataset and allows accurate evaluation of short term forecast errors. In this work, an OSSE developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office is used to explore the impact of observational data on forecasts in the 6 to 48 hour range. An adjoint of the Global Earth Observing System model is employed to compare the observation impacts estimated using both self-analysis verification and the true Nature Run verification. Self-analysis verification is found to inflate the estimated forecast error growth during the early forecast period, resulting in overestimations of observation impacts, particularly in the 6-12 hour forecast range. By 48 hours, the self-analysis verification estimates of forecast error and observation impacts more closely match the true values. The fraction of beneficial observations is also overinflated at short forecast times when self-analysis verification is used. The progression of impacts of an individual observation or data type depends on the character of the growth of the initial condition error that each observation affects.

numerical weather prediction↗
NASA NTRS2004

A Case Study of the Impact of AIRS Temperature Retrievals on Numerical Weather Prediction

Large errors in numerical weather prediction are often associated with explosive cyclogenesis. Most studes focus on the under-forecasting error, i.e. cases of rapidly developing cyclones which are poorly predicted in numerical models. However, the over-forecasting error (i.e., to predict an explosively developing cyclone which does not occur in reality) is a very common error that severely impacts the forecasting skill of all models and may also present economic costs if associated with operational forecasting. Unnecessary precautions taken by marine activities can result in severe economic loss. Moreover, frequent occurrence of over-forecasting can undermine the reliance on operational weather forecasting. Therefore, it is important to understand and reduce the prdctions of extreme weather associated with explosive cyclones which do not actually develop. In this study we choose a very prominent case of over-forecasting error in the northwestern Pacific. A 960 hPa cyclone develops in less than 24 hour in the 5-day forecast, with a deepening rate of about 30 hPa in one day. The cyclone is not versed in the analyses and is thus a case of severe over-forecasting. By assimilating AIRS data, the error is largely eliminated. By following the propagation of the anomaly that generates the spurious cyclone, it is found that a small mid-tropospheric geopotential height negative anomaly over the northern part of the Indian subcontinent in the initial conditions, propagates westward, is amplified by orography, and generates a very intense jet streak in the subtropical jet stream, with consequent explosive cyclogenesis over the Pacific. The AIRS assimilation eliminates this anomaly that may have been caused by erroneous upper-air data, and represents the jet stream more correctly. The energy associated with the jet is distributed over a much broader area and as a consequence a multiple, but much more moderate cyclogenesis is observed.

Reale, O.↗
NASA NTRS1994

Suboptimal schemes for atmospheric data assimilation based on the Kalman filter

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.

Todling, Ricardo↗
NASA NTRS2019

Assessing the Impact of Observations in a Multi-Year Reanalysis (MERRA-2)

Operational and quasi-operational weather prediction centers have been routinely assessing the contribution from various observing systems to reducing errors in short-range forecasts for a number of years now. The original technique, Forecast Sensitivity-based Observation Impact (FSOI), involves definition of a forecast error measure and evaluation of sensitivities with respect to changes in the observations that require adjoint operators of both the underlying tangent linear model and corresponding analysis technique. The present work applies FSOI to reanalysis and aims at providing an expanded view of the contribution of various observing systems over nearly 40 years of assimilation. Specifically, this study uses MERRA-2 given that its supporting software includes all ingredients necessary to calculate FSOI. Part of this work shows how the quality of forecasts improves over the course of the reanalysis, and examines forecast sensitivities relevant to FSOI. The assessment here finds, for example, that: conventional observations are a major player in reducing forecast error throughout the 40 years of reanalysis, even when their volume reduces from 45\% in the earlier periods to about 5% in the modern era; satellite radiances, especially microwave instruments are major contributors to error reduction from the early single platform TIROS-N days to the current multi-platform scenario, though their fractional contribution reduces slightly from the early 2000's onward after the increased availability of wind observation from aircraft and atmospheric motion vectors, and the introduction of GPSRO; infrared instruments play a secondary role to microwave but are significant still, with the peculiar result of fractional impacts contribution from modern hyperspectral instruments being roughly similar to those from early infrared instruments. The dependence of results on the chosen error measure is emphasized throughout.

Todling, Ricardo↗
NASA NTRS2019

Assessing the Impact of Observations in a Multi-Year Reanalysis

Operational and quasi-operational weather prediction centers have been routinely assessing the contribution from various observing systems to reducing errors in short-range forecasts for a number of years now. The original technique, Forecast Sensitivity Observation Impact (FSOI), involves definition of a forecast error measure and evaluation of sensitivities with respect to changes in the observing system that require adjoint operators of both the underlying tangent linear model and corresponding analysis technique. The present work applies FSOI to Reanalysis and aims at providing an expanded view of the contribution of various observing systems over nearly 40 years of assimilation. Specifically, this study uses MERRA-2 given that its supporting software includes all ingredients necessary to calculate FSOI. Part of this work shows how the quality of forecasts improves over the course of the reanalysis, and examines forecast sensitivities relevant to FSOI. The assessment here finds, for example, that: conventional observations are a major player in reducing forecast error throughout the 40 years of reanalysis, even when their volume reduces from 45% in the earlier periods to about 5% in the modern era; satellite radiances, especially microwave instruments are major contributors to error reduction from the early single platform TIROS-N days to the current multi-platform scenario; infrared instruments play a secondary role to microwave but are significant still, with the peculiar result of fractional impacts contribution from modern hyperspectral instruments being roughly similar to those from early infrared instruments. The dependence of results on the chosen error measure is emphasized throughout.

Fabio L R Diniz↗
NASA NTRS1987

Error growth and predictability in operational ECMWF forecasts

The forecast error growth in the 100-day ECMWF data set of 10-day forecasts previously utilized by Lorenz (1982) is studied, separating the square of the error into systematic and random components. The nature of the errors is analyzed in the spherical harmonics wavenumber domain, and a new parametrization and its application to global errors are presented. The wavenumber dependence of the error growth is studied.

Dalcher, Amnon↗
NASA NTRS1991

Simplification of the Kalman filter for meteorological data assimilation

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Dee, Dick P.↗
NASA NTRS1985

Application of lagged averaged forecasting to medium range forecasting

The lagged average forecast (LAF) method for predicting and compensating for forecast error growth is applied to two 100 day samples of 10 day forecasts at the 500 mb altitude for winter-summer 1980-81. The LAF parameterizes the forecast error growth in order to weight the forecast with regression calculations. A 5 day LAF forecast was generated for a 10 day forecast made with a 1681 d.o.f. model which produced predictions using a truncated spherical harmonic expansion. A 100 day data set was employed, with the first 90 days serving for LAF forecasts for the model forecast. Significant improvements were obtained in the model forecast when the LAF weightings were introduced into the model variables.

Dalcher, A.↗
NASA NTRS2003

Comparison of Flow-Dependent and Static Error Correlation Models in the DAO Ozone Data Assimilation System

In a data assimilation system the forecast error covariance matrix governs the way in which the data information is spread throughout the model grid. Implementation of a correct method of assigning covariances is expected to have an impact on the analysis results. The simplest models assume that correlations are constant in time and isotropic or nearly isotropic. In such models the analysis depends on the dynamics only through assumed error standard deviations. In applications to atmospheric tracer data assimilation this may lead to inaccuracies, especially in regions with strong wind shears or high gradient of potential vorticity, as well as in areas where no data are available. In order to overcome this problem we have developed a flow-dependent covariance model that is based on short term evolution of error correlations. The presentation compares performance of a static and a flow-dependent model applied to a global three- dimensional ozone data assimilation system developed at NASA s Data Assimilation Office. We will present some results of validation against WMO balloon-borne sondes and the Polar Ozone and Aerosol Measurement (POAM) III instrument. Experiments show that allowing forecast error correlations to evolve with the flow results in positive impact on assimilated ozone within the regions where data were not assimilated, particularly at high latitudes in both hemispheres and in the troposphere. We will also discuss statistical characteristics of both models; in particular we will argue that including evolution of error correlations leads to stronger internal consistency of a data assimilation ,

Wargan, K.↗
NASA NTRSDate not supplied

Complementarities of GEO and LEO IR Sounders for Numerical Weather Prediction in an OSSE Framework

Preparations are underway for the United States’ weather satellite program and the expected advancements in the coming decade. Among these changes is the launch of the proposed NOAA/NASA Geostationary eXtended Observations (GeoXO) Sounder (GXS), coordinated with international counterparts, to form a global ring of hyperspectral infrared (IR) sounders. Coincident with the progress of IR sounders from GEO platforms, the future of low Earth orbit (LEO) sounders is being re-envisioned after decades of beneficial impact in numerical weather prediction (NWP) systems. To address questions about the utility of the two platform types in concert, the Global Modeling and Assimilation Office (GMAO) Observing System Simulation Experiment (OSSE) framework was used to examine the roles of GEO and LEO sounders and their impact on forecast error reduction. Overall, inclusion of both types of platforms in the satellite program produces the largest forecast error reduction with LEO sounders having a strong impact on global skill and GEO sounders providing the most benefit on the scale of targeted regions.

Erica McGrath-Spangler↗
NASA NTRS2003

Satellite Detection of Precipitation over the North Pacific

Intense extratropical winter cyclones often impact the West Coast of North America with strong winds and heavy precipitation. Several times during a winter season, short-term forecasts (24 - 48 hours) of these storms are seriously deficient with central pressure errors in the 10's of hPa and surface low position errors in the 100's of km. For example, 48-hr sea level pressure errors (forecast - observation) at buoy 46005 off the Oregon coast for the 2001 - 2002 winter season is plotted. In addition, two times the standard deviation (determined from pressure errors from the last four winter seasons) are also shown. It is evident from this figure that large forecast errors (i.e. greater than 10 hPa) occurred about 10 times this past winter at buoy 46005 with three events where the errors were 20 hPa. Beside large forecast errors of sea level pressure, numerical forecasts of precipitation for land falling cyclones can also be flawed. This is due in large part to the lack of accurate precipitation information over the ocean. Therefore, remote sensing techniques are the only viable option for obtaining accurate information on the distribution and intensity of precipitation over the North Pacific. Due to the radiative characteristics of precipitation sized hydrometeors at microwave frequencies, microwave sensors are able to detect precipitation over oceanic regions. Past studies have demonstrated the utility of passive microwave rainrate data for locating intense rainfall in rapidly deepening cyclones, in detecting developing polar mesocyclones and in determining frontal bands. There are currently many sources of microwave rainrate data: the Special Sensor Microwave Imager (SSM/I) (currently flying on three platforms), the Advanced Microwave Sounding Unit (AMSU-B) (currently flying on NOAA-15, NOAA-16, and NOAA-17), and the Tropical Rainfall Measuring Mission Microwave Imager (TMI). Data will soon be available from the Advanced Microwave Radiometer-EOS (AMSR-E) on the Aqua platform. In this paper, we present a new technique for mapping rainrate distributions over the North Pacific utilizing rainrate estimates from several microwave sensors and upper-tropospheric winds derived from geosynchronous satellite IR data. The goal of this work is to develop a way to obtain high temporal and spatial rainfall information over the North Pacific. This information will be used to support the verification of model derived precipitation distributions and to support the analysis of in situ measurements of rainfall during the Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE) field campaigns.

Smith, Jeremy↗
NASA NTRS1981

Applications systems verification and transfer project. Volume 1: Operational applications of satellite snow cover observations: Executive summary

Both LANDSAT and NOAA satellite data were used in improving snowmelt runoff forecasts. When the satellite snow cover data were tested in both empirical seasonal runoff estimation and short term modeling approaches, a definite potential for reducing forecast error was evident. A cost benefit analysis run in conjunction with the snow mapping indicated a $36.5 million annual benefit accruing from a one percent improvement in forecast accuracy using the snow cover data for the western United States. The annual cost of employing the system would be $505,000. The snow mapping has proven that satellite snow cover data can be used to reduce snowmelt runoff forecast error in a cost effective manner once all operational satellite data are available within 72 hours after acquisition. Executive summaries of the individual snow mapping projects are presented.

Rango, A.↗
NASA NTRS2005

A Posteriori Correction of Forecast and Observation Error Variances

Proposed method of total observation and forecast error variance correction is based on the assumption about normal distribution of "observed-minus-forecast" residuals (O-F), where O is an observed value and F is usually a short-term model forecast. This assumption can be accepted for several types of observations (except humidity) which are not grossly in error. Degree of nearness to normal distribution can be estimated by the symmetry or skewness (luck of symmetry) a(sub 3) = mu(sub 3)/sigma(sup 3) and kurtosis a(sub 4) = mu(sub 4)/sigma(sup 4) - 3 Here mu(sub i) = i-order moment, sigma is a standard deviation. It is well known that for normal distribution a(sub 3) = a(sub 4) = 0.

Rukhovets, Leonid↗
NASA NTRS2013

Ensemble Data Assimilation Without Ensembles: Methodology and Application to Ocean Data Assimilation

Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.

Data Assimilation↗
NASA NTRS2003

Impact of Flow-Dependent Error Correlations and Tropospheric Chemistry on Assimilated Ozone

The presentation compares different versions of a global three-dimensional ozone data assimilation system developed at NASA's Data Assimilation Office. The Solar Backscatter Ultraviolet/2 (SBUV/2) total and partial ozone column retrievals are the sole data assimilated in all of the experiments presented. We study the impact of changing the forecast error covariance model from a version assuming static correlations with a one that captures a short-term Lagrangian evolution of those correlations. This is further combined with a study of the impact of neglecting the tropospheric ozone production, loss and dry deposition rates, which are obtained from the Harvard GEOS-CHEM model. We compare statistical characteristics of the assimilated data and the results of validation against independent observations, obtained from WMO balloon-borne sondes and the Polar Ozone and Aerosol Measurement (POAM) III instrument. Experiments show that allowing forecast error correlations to evolve with the flow results in positive impact on assimilated ozone within the regions where data were not assimilated, particularly at high latitudes in both hemispheres. On the other hand, the main sensitivity to tropospheric chemistry is in the Tropics and sub-Tropics. The best agreement between the assimilated ozone and the in-situ sonde data is in the experiment using both flow-dependent error covariances and tropospheric chemistry.

Wargan, K.↗
NASA NTRS2020

A Brief Assessment of the Impact of Nearly 40 Years of Assimilated Observations Over the Amazon Basin

Adding a Forecast Sensitivity-based Observation Impact component to Version 2 of the Modern Era Retrospective-analysis for Research and Applications, the present study provides an assessment of the impact of nearly 40 years of observations on short-range (24-hr) forecasts over the Amazon basin. Under self-verification, forecast errors are found to slightly increase from the early data-sparse days to the more recent years, when data dramatically increase. Throughout the reanalysis, satellite radiances dominate in volume, but only before 1999 they dominate the impacts. Beyond 1999, over 50% of forecast error reduction is associated with conventional observations (radiosondes). Atmospheric Motion Vectors are also found to be large contributors to error reduction, but their contribution reduces in dry periods. In opposition to Atmospheric Motion Vectors, satellite radiances tend to contribute more in the dry season. Results provide motivation for additional conventional observations and the use of all-sky treatment of radiances.

F. L. R. Diniz↗