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An ensemble seasonal hindcast approach is used to investigate the development of the equatorial Pacific Ocean cold sea surface temperature (SST) bias and its characteristic annual cycle in the Community Earth System Model, version 1 (CESM1). In observations, eastern equatorial Pacific SSTs exhibit a warm phase during boreal spring and a cold phase during late boreal summer–autumn. The CESM1 climatology shows a cold bias during both warm and cold phases. In our hindcasts, the cold bias during the cold phase develops in less than 6 months, whereas the cold bias during the warm phase takes longer to emerge. The fast-developing cold-phase cold bias is associated with too-strong vertical advection and easterly wind stress over the eastern equatorial region. The antecedent boreal summer easterly wind anomalies also appear in atmosphere-only simulations, indicating that the errors are intrinsic to the atmosphere component. For the slower-developing warm-phase cold bias, we find that the too-cold SSTs over the equatorial region are associated with a slowly evolving upward displacement of subsurface ocean zonal currents and isotherms that can be traced to the ocean component.

The correspondence between mean sea surface temperature (SST) biases in retrospective seasonal forecasts (hindcasts) and long-term climate simulations from five global climate models is examined to diagnose the degree to which systematic SST biases develop on seasonal time scales. The hindcasts are from the North American Multimodel Ensemble, and the climate simulations are from the Coupled Model Intercomparison Project. The analysis suggests that most robust climatological SST biases begin to form within 6 months of a realistically initialized integration, although the growth rate varies with location, time, and model. In regions with large biases, interannual variability and ensemble spread is much smaller than the climatological bias. Additional ensemble hindcasts of the Community Earth System Model with a different initialization method suggest that initial conditions do matter for the initial bias growth, but the overall global bias patterns are similar after 6 months. A hindcast approach is more suitable to study biases over the tropics and subtropics than over the extratropics because of smaller initial biases and faster bias growth. The rapid emergence of SST biases makes it likely that fast processes with time scales shorter than the seasonal time scales in the atmosphere and upper ocean are responsible for a substantial part of the climatological SST biases. Studying the growth of biases may provide important clues to the causes and ultimately the amelioration of these biases. Further, initialized seasonal hindcasts can profitably be used in the development of high-resolution coupled ocean–atmosphere models.

The capability to forecast conditions in the mesosphere and lower thermosphere is investigated based on 30‐day hindcast experiments that were initialized bimonthly during 2009 and 2010. The hindcasts were performed using the Whole Atmosphere Community Climate Model with thermosphere‐ionosphere eXtension (WACCMX) with data assimilation provided by the Data Assimilation Research Testbed (DART) ensemble Kalman filter. Analysis of the WACCMX+DART hindcasts reveals several important features that are relevant to forecasting the middle atmosphere. The results show a clear dependence on spatial scale, with the slowest error growth occurring in the zonal mean and the fastest error growth occurring for small‐scale waves. The error growth rate is also found to be significantly greater in the upper mesosphere and lower thermosphere compared to in the upper stratosphere to lower mesosphere, suggesting that the forecast skill decreases with increasing altitude. The results demonstrate that the errors in the lower thermosphere reach saturation, on average, in less than 5 days, at least with the current version of WACCMX+DART. A seasonal dependency to the error growth is found at high latitudes in the Northern and Southern Hemispheres but not in the tropics or global average. We additionally investigate the error growth rates for migrating and nonmigrating atmospheric tides and find that the errors saturate after ∼5 days for tides in the lower thermosphere. The results provide an initial assessment of the error growth rates in the mesosphere and lower thermosphere and are relevant for understanding how whole atmosphere models can potentially improve space weather forecasting.

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.

Global data assimilation systems for numerical weather prediction (NWP) are characterized by significant uncertainties in tropical analysis fields. Furthermore, the largest spread of global ensemble forecasts in the short range on all scales is in the tropics. The presented results suggest that these properties hold even in the perfect-model framework and the ensemble Kalman filter data assimilation with a globally homogeneous network of wind and temperature profiles. The reasons for this are discussed by using the modal analysis, which provides information about the scale dependency of analysis and forecast uncertainties and information about the efficiency of data assimilation to reduce the prior uncertainties in the balanced and inertio-gravity dynamics. The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully. In addition, it is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is influenced by the applied radius for the covariance localization.

Simulating Arctic sea ice conditions up to the present and predicting them several months in advance has high stakeholder value, yet remains challenging. Advanced data assimilation (DA) methods combine real observations with model forecasts to produce sea ice reanalyses and accurate initial conditions for sea ice prediction. This study introduces a sea ice DA framework for a sea ice model with a parameterization of the ice thickness distribution by resolving multiple thickness categories. Specifically, the Los Alamos Sea Ice Model, version 5 (CICE5), is integrated with the Data Assimilation Research Testbed (DART). A series of perfect model observing system simulation experiments (OSSEs) are designed to explore DA algorithms within the ensemble Kalman filter (EnKF) and the relative importance of different observation types. This study demonstrates that assimilating sea ice concentration (SIC) observations can effectively remove SIC errors, with the error of total Arctic sea ice area reduced by about 60% annually. When the impact of SIC observations is strongly localized in space, the error of total volume is also modestly improved. The largest simulation improvements are produced when sea ice thickness (SIT) and SIC are jointly assimilated, with the error of total volume decreased by more than 70% annually. Assimilating multiyear sea ice concentration (MYI) can reduce error in total volume by more than 50%. Assimilating MYI produces modest improvements in snow depth (errors are reduced by around 16%), while assimilating SIC and SIT has no obvious influence on snow depth. This study also suggests that different observation types may need different localization distances to optimize DA performance.

We present results pertaining to the assimilation of real lower, middle, and upper atmosphere observations in the Whole Atmosphere Community Climate Model (WACCM) using the Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter. The ability to assimilate lower atmosphere observations of aircraft and radiosonde temperature and winds, satellite drift winds, and Constellation Observing System for Meteorology, Ionosphere, and Climate refractivity along with middle/upper atmosphere temperature observations from SABER and Aura MLS is demonstrated. The WACCM+DART data assimilation system is shown to be able to reproduce the salient features, and variability, of the troposphere present in the National Centers for Environmental Prediction/National Center for Atmospheric Research Re-Analysis. In the mesosphere, the fit of WACCM+DART to observations is found to be slightly worse when only lower atmosphere observations are assimilated compared to a control experiment that is reflective of the model climatological variability. This differs from previous results which found that assimilation of lower atmosphere observations improves the fit to mesospheric observations. This discrepancy is attributed to the fact that due to the gravity wave drag parameterizations, the model climatology differs significantly from the observations in the mesosphere, and this is not corrected by the assimilation of lower atmosphere observations. The fit of WACCM+DART to mesospheric observations is, however, significantly improved compared to the control experiment when middle/upper atmosphere observations are assimilated. We find that assimilating SABER observations reduces the root-mean-square error and bias of WACCM+DART relative to the independent Aura MLS observations by ∼50%, demonstrating that assimilation of middle/upper atmosphere observations is essential for accurate specification of the mesosphere and lower thermosphere region in WACCM+DART. Last, we demonstrate that WACCM+DART is able to follow the dynamical and chemical variability during the 2009 sudden stratosphere warming, illustrating the capability of WACCM+DART to generate high-quality atmospheric reanalysis from the surface to the lower thermosphere.

In this study, ensemble sensitivity analysis has been applied to examine the evolution of two extreme extratropical cyclones over the Pacific. Sensitivity using, as forecast metrics, forecast cyclone minimum pressure and location, as well as principal components (PCs) of the leading EOFs in forecast SLP variations near the cyclone center, has been computed for medium-range forecasts of up to 7.5 days. Results presented here show that coherent sensitivity patterns can be tracked from the forecast validation time back in time to at least day −6, with the sensitivity signal exhibiting downstream development characteristics in most cases. Comparing the different forecast metrics, sensitivity patterns derived from the PCs of the leading EOFs in forecast SLP variations are apparently more coherent than those derived from cyclone parameters. To test whether the linear sensitivity analyses provide quantitatively accurate guidance under the highly nonlinear evolution of the atmospheric flow, perturbed initial condition experiments have been conducted using initial condition perturbations derived based on ensemble sensitivity. Results of this study suggest that in the medium range, perturbations derived from cyclone parameters are quite effective in modifying the evolution of the cyclones out to 5.5 days, but are largely ineffective for 7.5-day forecasts. On the other hand, perturbations derived based on the PCs of the leading EOFs are still quite effective in modifying forecast cyclone location out to 7.5 days. These results suggest that EOF-based sensitivities perform better than cyclone parameter-based sensitivities in the medium range.

The Community Atmosphere Model (CAM) has been interfaced to the Data Assimilation Research Testbed (DART), a community facility for ensemble data assimilation. This provides a large set of data assimilation tools for climate model research and development. Aspects of the interface to the Community Earth System Model (CESM) software are discussed and a variety of applications are illustrated, ranging from model development to the production of long series of analyses. CAM output is compared directly to real observations from platforms ranging from radiosondes to global positioning system satellites. Such comparisons use the temporally and spatially heterogeneous analysis error estimates available from the ensemble to provide very specific forecast quality evaluations. The ability to start forecasts from analyses, which were generated by CAM on its native grid and have no foreign model bias, contributed to the detection of a code error involving Arctic sea ice and cloud cover. The potential of parameter estimation is discussed. A CAM ensemble reanalysis has been generated for more than 15 yr. Atmospheric forcings from the reanalysis were required as input to generate an ocean ensemble reanalysis that provided initial conditions for decadal prediction experiments. The software enables rapid experimentation with differing sets of observations and state variables, and the comparison of different models against identical real observations, as illustrated by a comparison of forecasts initialized by interpolated ECMWF analyses and by DART/CAM analyses.

This paper quantifies the linear mass–wind field balance and its temporal variability in the global data assimilation system Data Assimilation Research Testbed/Community Atmosphere Model (DART/CAM), which is based on the ensemble adjustment Kalman filter. The part of the model state that projects onto quasigeostrophic modes represents the balanced state. The unbalanced part corresponds to inertio-gravity (IG) motions. The 80-member ensemble is diagnosed by using the normal-mode function expansion. It was found that the balanced variance in the prior ensemble is on average about 90% of the total variance and about 80% of the wave variance. Balance depends on the scale and the largest zonal scales are best balanced. For zonal wavenumbers greater than k = 30 the balanced variance stays at about the 45% level. There is more variance in the westward- than in the eastward-propagating IG modes; the difference is about 2% of the total wave variance and it is associated with the covariance inflation. The applied inflation field has a major impact on the structure of the prior variance field and its reduction by the assimilation step. The shape of the inflation field mimics the global radiosonde observation network (k = 2), which is associated with the minimum variance reduction in k = 2. Temporal variability of the ensemble variance is significant and appears to be associated with changes in the energy of the flow. A perfect-model assimilation experiment supports the findings from the real-observation experiment.

This paper explores the degree to which short-term forecasts with global models might be improved if clouds were fully included in a data assimilation system, so that observations of clouds affected all parts of the model state and cloud variables were adjusted during assimilation. The question is examined using a single ensemble data assimilation system coupled to two present-generation climate models with different treatments of clouds. “Perfect-model” experiments using synthetic observations, taken from a free run of the model used in subsequent assimilations, are used to circumvent complications associated with systematic model errors and observational challenges; these provide a rough upper bound on the utility of cloud observations with these models. A series of experiments is performed in which direct observations of the model’s cloud variables are added to the suite of observations being assimilated. In both models, observations of clouds reduce the 6-h forecast error, with much greater reductions in one model than in the other. Improvements are largest in regions where other observations are sparse. The two cloud schemes differ in their complexity and number of degrees of freedom; the model using the simpler scheme makes better use of the cloud observations because of the stronger correlations between cloud-related and dynamical variables (particularly temperature). This implies that the impact of real cloud observations will depend on both the strength of the instantaneous, linear relationships between clouds and other fields in the natural world, and how well each assimilating model’s cloud scheme represents those relationships.

This study documents and evaluates the boundary layer and energy budget response to record low 2007 sea ice extents in the Community Atmosphere Model version 4 (CAM4) using 1-day observationally constrained forecasts and 10-yr runs with a freely evolving atmosphere. While near-surface temperature and humidity are minimally affected by sea ice loss in July 2007 forecasts, near-surface stability decreases and atmospheric humidity increases aloft over newly open water in September 2007 forecasts. Ubiquitous low cloud increases over the newly ice-free Arctic Ocean are found in both the July 2007 and the September 2007 forecasts. In response to the 2007 sea ice loss, net surface [top of the atmosphere (TOA)] energy budgets change by +19.4 W m−2 (+21.0 W m−2) and −17.9 W m−2 (+1.4 W m−2) in the July 2007 and September 2007 forecasts, respectively. While many aspects of the forecasted response to sea ice loss are consistent with physical expectations and available observations, CAM4’s ubiquitous July 2007 cloud increases over newly open water are not. The unrealistic cloud response results from the global application of parameterization designed to diagnose stratus clouds based on lower-tropospheric stability (CLDST). In the Arctic, the well-mixed boundary layer assumption implicit in CLDST is violated. Requiring a well-mixed boundary layer to diagnose stratus clouds improves the CAM4 cloud response to sea ice loss and increases July 2007 surface (TOA) energy budgets over newly open water by +11 W m−2 (+14.9 W m−2). Of importance to high-latitude climate feedbacks, unrealistic stratus cloud compensation for sea ice loss occurs only when stable and dry atmospheric conditions exist. Therefore, coupled climate projections that use CAM4 will underpredict Arctic sea ice loss only when dry and stable summer conditions occur.

This paper applies the normal-mode functions for the three-dimensional diagnosis of systematic analysis increments in the operational systems of ECMWF and NCEP, in the NCEP/NCAR reanalyses and in the ensemble data assimilation system DART/CAM which is developed at NCAR. Non-zero systematic increments are interpreted as the analysis system bias. The main region of tropospheric biases in all systems is the Tropics; most of the large-scale tropical bias resides in the unbalanced (inertio-gravity) motion with the eastward-propagating component being dominant in some datasets. The magnitudes of tropospheric wind-field biases in July 2007 were in the range between 1 ms−1 and 2 ms−1, illustrating the importance of diagnosing analysis systems in the Tropics where magnitudes of the large-scale variability are of the same order. The systematic increments integrated over the whole models' atmosphere appear predominantly balanced; this balance is associated with biases in the zonally averaged balanced state and, in case of ECMWF and NCEP, with the biases at the model top levels. Spectra of analysis increments averaged over one month show that, on average, 20% to 45% of total energy in increment fields belongs to the inertio-gravity motions. Copyright © 2010 Royal Meteorological Society

The Data Assimilation Research Testbed (DART) is an open-source community facility for data assimilation education, research, and development. DART's ensemble data assimilation algorithms, careful ...

© 2016. American Geophysical Union. All Rights Reserved. We examine in detail a 1 year global reanalysis of carbon monoxide (CO) that is based on joint assimilation of conventional meteorological observations and Measurement of Pollution in The Troposphere (MOPITT) multispectral CO retrievals in the Community Earth System Model (CESM). Our focus is to assess the impact to the chemical system when CO distribution is constrained in a coupled full chemistry-climate model like CESM. To do this, we first evaluate the joint reanalysis (MOPITT Reanalysis) against four sets of independent observations and compare its performance against a reanalysis with no MOPITT assimilation (Control Run). We then investigate the CO burden and chemical response with the aid of tagged sectoral CO tracers.We estimate the total tropospheric CO burden in 2002 (from ensemble mean and spread) to be 371 ± 12%Tg for MOPITT Reanalysis and 291 ± 9%Tg for Control Run. Our multispecies analysis of this difference suggests that (a) direct emissions of CO and hydrocarbons are too low in the inventory used in this study and (b) chemical oxidation, transport, and deposition processes are not accurately and consistently represented in the model. Increases in CO led to net reduction of OH and subsequent longer lifetime of CH4 (Control Run: 8.7 years versus MOPITT Reanalysis: 9.3 years). Yet at the same time, this increase led to 5-10% enhancement of Northern Hemisphere O3 and overall photochemical activity via HOx recycling. Such nonlinear effects further complicate the attribution to uncertainties in direct emissions alone. This has implications to chemistry-climate modeling and inversion studies of longer-lived species.

We present a global chemical data assimilation system using a global atmosphere model, the Community Atmosphere Model (CAM3) with simplified chemistry and the Data Assimilation Research Testbed (DART) assimilation package. DART is a community software facility for assimilation studies using the ensemble Kalman filter approach. Here, we apply the assimilation system to constrain global tropospheric carbon monoxide (CO) by assimilating meteorological observations of temperature and horizontal wind velocity and satellite CO retrievals from the Measurement of Pollution in the Troposphere (MOPITT) satellite instrument. We verify the system performance using independent CO observations taken on board the NSF/NCAR C-130 and NASA DC-8 aircrafts during the April 2006 part of the Intercontinental Chemical Transport Experiment (INTEX-B). Our evaluations show that MOPITT data assimilation provides significant improvements in terms of capturing the observed CO variability relative to no MOPITT assimilation (i.e. the correlation improves from 0.62 to 0.71, significant at 99% confidence). The assimilation provides evidence of median CO loading of about 150 ppbv at 700 hPa over the NE Pacific during April 2006. This is marginally higher than the modeled CO with no MOPITT assimilation (~140 ppbv). Our ensemble-based estimates of model uncertainty also show model overprediction over the source region (i.e. China) and underprediction over the NE Pacific, suggesting model errors that cannot be readily explained by emissions alone. These results have important implications for improving regional chemical forecasts and for inverse modeling of CO sources and further demonstrate the utility of the assimilation system in comparing non-coincident measurements, e.g. comparing satellite retrievals of CO with in-situ aircraft measurements.

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.

© 2015. American Geophysical Union. All Rights Reserved. We show the results and evaluation with independent measurements from assimilating both MOPITT (Measurements Of Pollution In The Troposphere) and IASI (Infrared Atmospheric Sounding Interferometer) retrieved profiles into the Community Earth System Model (CESM). We used the Data Assimilation Research Testbed ensemble Kalman filter technique, with the full atmospheric chemistry CESM component Community Atmospheric Model with Chemistry. We first discuss the methodology and evaluation of the current data assimilation system with coupled meteorology and chemistry data assimilation. The different capabilities of MOPITT and IASI retrievals are highlighted, with particular attention to instrument vertical sensitivity and coverage and how these impact the analyses. MOPITT and IASI CO retrievals mostly constrain the CO fields close to the main anthropogenic, biogenic, and biomass burning CO sources. In the case of IASI CO assimilation, we also observe constraints on CO far from the sources. During the simulation time period (June and July 2008), CO assimilation of both instruments strongly improves the atmospheric CO state as compared to independent observations, with the higher spatial coverage of IASI providing better results on the global scale. However, the enhanced sensitivity of multispectral MOPITT observations to near surface CO over the main source regions provides synergistic effects at regional scales.

In dynamic meteorology, singular vectors (SVs) are the structures that maximize a given norm of a forecast perturbation given a tangent linear model and a quadratic constraint on the initial perturbation. That constraint is a prescription of the value of either the same or a different norm applied to the initial perturbations. In the sense that SVs maximize the forecast perturbations according to a specified measure, they may be considered as optimal perturbations. SVs are used to characterize predictability, to identify and correct possible initial errors given forecast errors, to create a set of significant perturbations for ensemble forecasting, or to determine locations for observation targeting. They are a specific application of generally defined singular vectors in mathematics.

An adjoint model that includes precipitation physics is applied to four synoptic cases in order tocompare the sensitivities of both convective and non-convective precipitation rates with respect to initialperturbations of temperature, water vapor mixing ratio, vorticity or divergence. These are contrastedwith sensitivities of barotropic vorticity. Forecast periods between 1 and 24 h are investigated. Rootmean-square values of the sensitivities as a function of vertical coordinate and field are presented aswell as time series of impacts of optimal perturbations weighted by initial variances of uncertaintiesin the fields. For all the forecast aspects and cases considered, the greatest sensitivity and impacts arewith regard to the temperature field. Precipitation is equally sensitive to vorticity and divergence, butwhen their relative uncertainties are considered, impacts of the vorticity dominate those of divergence.Precipitation is sensitive to initial specific humidity, but so is barotropic vorticity within a cyclone. Thesensitivities of precipitation were not found to increase with forecast periods as much as the sensitivitiesto vorticity, suggesting that even within the same synoptic feature, different processes are responsiblefor the development of these distinct characteristics. Although comparison with corresponding impactsin the nonlinear model suggests that a 24 h period is too long for the adjoint-estimated precipitationimpacts to be good approximations to the nonlinear results in some of the cases, 6-h adjoint-estimatedresults appear useful. DOI: 10.1034/j.1600-0870.2003.201394.x

If a parametrization scheme for convective precipitation is to be used for assimilating observations of precipitation using a statistically based technique, then statistics of the errors produced by that scheme are required. These are the errors produced by the scheme's formulation itself, not counting any errors in the scheme's input. Such errors are extremely difficult to estimate, but examination of differences produced by various suitable schemes can yield qualitative descriptions of such errors. Here, hourly accumulated convective precipitation fields produced from six different versions of a short-term forecast model are compared. The versions have identical initial and boundary conditions, but vary in the schemes used for either the convection or the planetary boundary layer, or both. The distribution of differences, or differences in logarithms of accumulations, between corresponding precipitating grid points for pairs of forecasts are examined using a simple binning technique. When the convection schemes differ, results reveal that if either a log-normal or normal distribution is a better characterization of the distributions, it is the log-normal one. The standard deviations of these logarithmic distributions correspond to different schemes at identical grid points producing values differing by factors of 2 or more. A large proportion of grid points that have non-zero hourly accumulations using one model version may have no accumulation using another version. For most pairs of forecasts examined, however, grid points having larger values of accumulation for one scheme tend to have a smaller fraction of values having no accumulation in the other scheme. These results suggest that the finite probability that the model produces no precipitation when the corresponding, true atmospheric state does, should be considered in the statistical description of the model errors and that, because of the large standard deviation of model errors as well as large possible errors of hourly precipitation observations, the quantitative usefulness of assimilating such observations may be very limited.

Finite-time growth of perturbations in the presence of moist physics (specifically, precipitation) is investigated using singular vectors (SVs) in the context of a primitive equation regional model. Two difficulties appear in the explicit consideration of the effect of moist physics when studying such optimal growth. First, the tangent-linear description of moist physics may not be as straightforward and accurate as for dry-adiabatic processes; second, because of the consideration of moisture, the design of an appropriate measure of growth (i.e., norm) is subject to even more ambiguity than in the dry situation. In this study both of these problems are addressed in the context of the moist version of the National Center for Atmospheric Research Mesoscale Adjoint Modeling System, version 2, with emphasis on the second problem. Leading SVs are computed in an iterative fashion, using a Lanczos algorithm, for three norms over an optimization interval of 24 h; these norms are based on an expression re...

The accuracy of tangent linear and adjoint versions of a primitive-equation model with moist physics is examined with respect to growing perturbations having significant initial magnitudes. The Jacobians for the convective parametrizations are approximated using a perturbation method. These Jacobians are then quality controlled to ensure that the approximations are suitable. Results show that: (I) linearization of the diabatic moist physics can have a significant impact; (2) even where such impacts are large, the linearized versions of the model can yield good approximations to the nonlinear behaviour for significant perturbations, especially if there is sufficient dynamical influence: (3) poor approximations can be obtained when convection dominates the results; and (4) a straightforward linearization of some parametrization schemes may be inadequate. The results are encouraging for quantitative applications of some moist adjoint models to extratropical cyclones in the winter, but suggest some tangent linear approximations may be unsuitable in the tropics or over continents in the summer, except if qualitative agreements with nonlinear results are sufficient. Detailed comparisons of linear and nonlinear results should be made. particularly using optimal perturbations, prior to any applications of tangent linear or adjoint models.

The authors propose a new procedure, designated the adjoint-based genesis diagnostic (AGD) procedure, for studying triggering mechanisms and the subsequent genesis of the synoptic phenomena of interest. This procedure makes use of a numerical model sensitivity to initial conditions and the nonlinear evolution of the initial perturbations that are designed using this sensitivity. The model sensitivity is evaluated using the associated adjoint model. This study uses the dry version of the National Center for Atmospheric Research Mesoscale Adjoint Modeling System (MAMS) for the numerical experiments. The authors apply the AGD procedure to two cases of Alpine lee cyclogenesis that were observed during the Alpine Experiment special observations period. The results show that the sensitivity fields that are produced by the adjoint model and the associated initial perturbations are readily related to the probable triggering mechanisms for these cyclones. Additionally, the nonlinear evolution of these initial perturbations points toward the physical processes involved in the lee cyclone formation. The AGD experiments for a weak cyclone case indicate that the MAMS forecast model has an underrepresented topographic forcing due to the sigma vertical coordinate and that this model error can be compensated by adjustments in the initial conditions that are related to the triggering mechanisms, which is not associated with the topographic blocking mechanism.

The accuracy of a tangent linear version of a 3-dimensional mesoscale primitive equation model (the PSU/NCAR MM4) is investigated by comparing its results with those produced by identical perturbations introduced in nonlinear forecasts of the original model. Moist physical processes are not considered in this study. For perturbation magnitudes as large as typical current analysis errors, the perturbation tendencies are shown to be very accurately estimated by the tangent linear model (TLM), with greater relative error in a summer case than in a winter one. The evolutions of perturbations in forecasts out to 72 h are also accurately estimated, although the unperturbed lateral boundary conditions that act to sweep perturbations out of the domain are an artificial means of perturbation constraint. It is shown that for many cases it is sufficient to approximate a true TLM by using an infrequent update of the basic state, thereby reducing the amount of stored fields and input required by the TLM software. For perturbations not smaller than one-tenth the size of typical analysis errors, a 30-min update appears sufficient. The TLM accuracy is related to the accuracy of adjoint sensitivity calculations with regard to finite-amplitude perturbations. An example of an adjoint application is shown to have two-digit accuracy for a moderately sized perturbation. All these results indicate that our TLM and corresponding adjoint yield quantitatively accurate results for many important uses. DOI: 10.1034/j.1600-0870.1993.00010.x

This paper presents the application of the normal-mode functions to diagnose the atmospheric energy spectra in terms of balanced and inertia–gravity (IG) contributions. A set of three-dimensional orthogonal normal modes is applied to four analysis datasets from July 2007. The datasets are the operational analysis systems of NCEP and ECMWF, the NCEP–NCAR reanalyses, and the Data Assimilation Research Testbed–Community Atmospheric Model (DART–CAM), an ensemble analysis system developed at NCAR. The differences between the datasets can be considered as a measure of uncertainty of the IG contribution to the global energetics. The results show that the percentage of IG motion in the present NCEP, ECMWF, and DART–CAM analysis systems is between 1% and 2% of the total energy field. In the wave part of the flow (zonal wavenumber k ≠ 0), the IG energy contribution is between 9% and 15%. On the contrary, the NCEP–NCAR reanalyses contain more IG motion, especially in the Southern Hemisphere extratropics. Each analysis contains more energy in the eastward IG motion than in its westward counterpart. The difference is about 2%–3% of the total wave energy and it is associated with the motions projected onto the Kelvin wave in the tropics. The selected truncation parameters of the expansion (zonal, meridional, and vertical truncation) ensure that the projection provides the optimal fit to the input data on model levels. This approach is different from previous applications of the normal modes and under the linearity assumption it allows the application of the inverse projection to obtain details of circulation associated with a selected type of motion. The bulk of the IG motion is confined to the tropics. For the successful reproduction of three-dimensional circulations by the normal modes it is important that the expansion includes a number of vertical modes.

This paper analyzes the spectra and spatiotemporal features of the large-scale inertia-gravity (IG) circulations in four analysis systems in the tropics. Of special interest is the Kelvin wave (KW), which represents between 7% and 25% of the total IG wave (zonal wavenumber k ≠ 0) energy. The mixed Rossby–gravity (MRG) mode comprises between 4% and 15% of the IG wave energy. At the longest scales, the KW spectra are fitted by a law while the MRG energy spectrum appears flat. At shorter scales both modes follow a −3 law. Energy spectra of the total IG wave motion at long zonal scales (zonal wavenumber smaller than 7) have slopes close to −1. The average circulation associated with KW is characterized by reverse flows in the upper and lower troposphere consistent with the ideas behind simple tropical models. The inverse projection is used to quantify the role of Kelvin and MRG waves in current analysis systems in the upper troposphere over the Indian Ocean. At these levels, easterlies between 10°S and 30°N are represented by the KW to a significant degree while the cross-equatorial flow toward the descending branch of the Hadley cell at 10°S is associated with the MRG waves. The transient structure of equatorial waves is presented in the space of normal modes defined by the zonal wavenumbers, meridional Hough functions, and the vertical eigenfunctions. The difference in the depth of the model domain in DART–CAM and NCEP–NCAR on one hand and ECMWF and NCEP on the other appears to be one reason for different wave propagation properties. In the latter case the vertical energy propagation is diagnosed by filtering the propagating KW modes back to physical space. The results agree with the linear theory of vertically propagating equatorial waves.

Stationary vertically propagating mountain waves generated by flow over a bell-shaped ridge are considered. Dissipation by momentum diffusion is introduced when the disturbed isentropes become nearly vertical. Momentum diffusion, characterized by a constant eddy diffusion coefficient, partially suppresses the amplitude growth of the wave that is a consequence of conservation of wave-energy density. The propagating wave can continue to grow in amplitude until neutral static stability is achieved. At higher levels, wave overturning could be expected to occur. The present solution is contrasted with the solution over a sinusoid. In the latter case, wave saturation can occur, whereby a constant wave amplitude can be maintained by a balance between exponential growth and dissipative decay. Wave momentum flux and its divergence, calculated from each type of solution, are compared. The results are relevant to the parameterization of wave drag associated with the vertical propagation of internal gravity waves. It is concluded that parameterization schemes that incorporate wave drag by use of a monochromatic wave response need to be modified to include the presence of a spectrum of waves from realistic wave sources, such as orography. It appears that the required modifications are principally quantitative adjustments to eddy diffusion coefficients, which take account of the fact that a saturation wave-amplitude cannot be attained for a unique value of the diffusion coefficient. DOI: 10.1034/j.1600-0870.1991.t01-2-00005.x

Large portions of the spectra of singular values are determined for both moist and dry versionsof a tangent linear, regional model for 4 different synoptic cases. Norms considered include theusual energy norm and versions of a norm measuring only the energy in some set of rotationalmode perturbations. At most, only a few percent of the singular vectors possible with any ofthe norms are growing ones. Inclusion of moist physics in the tangent linear model greatlyaffects the leading singular vectors but does not increase the number of growing singular vectorsmuch. Most singular vectors are damping ones, and therefore random perturbations drawnfrom a white-noise distribution will likely damp during the 24-h forecast periods considered.Only a few singular vectors are required to explain a significant portion of the final-time varianceof such perturbations, however, because the leading singular values are so large compared withthe rest. The truncated rotational mode norm is shown to be very useful for investigating theseproperties. DOI: 10.1034/j.1600-0870.2001.01199.x

The sensitivities of two forecast aspects with respect to perturbations of initial and lateral boundary conditions are determined using an adjoint of a limited-area model. Sensitivities are presented as gradient fields. Some characteristics of the sensitivity fields have simple dynamical explanations, such as their strong dependence on winds, and do not require an adjoint model to reveal them. Other characteristics would be difficult to ascertain without an adjoint model, although they, too, in retrospect, have simple dynamical explanations. Still others, although equally important and undoubtedly dependent on the dynamics, would be practically impossible to determine without an adjoint. The quantity and quality of information provided by the adjoint solutions render the adjoint model a tool that is indispensable for sensitivity analysis. DOI: 10.1034/j.1600-0870.1993.00015.x