One-dimensional Variational Data Assimilation Research Articles

Towards the use of conservative thermodynamic variables in data assimilation: a case study using ground-based microwave radiometer measurements

Abstract. This study aims at introducing two conservative thermodynamic variables (moist-air entropy potential temperature and total water content) into a one-dimensional variational data assimilation system (1D-Var) to demonstrate their benefits for use in future operational assimilation schemes. This system is assessed using microwave brightness temperatures (TBs) from a ground-based radiometer installed during the SOFOG3D field campaign, dedicated to fog forecast improvement. An underlying objective is to ease the specification of background error covariance matrices that are highly dependent on weather conditions when using classical variables, making difficult the optimal retrievals of cloud and thermodynamic properties during fog conditions. Background error covariance matrices for these new conservative variables have thus been computed by an ensemble approach based on the French convective scale model AROME, for both all-weather and fog conditions. A first result shows that the use of these matrices for the new variables reduces some dependencies on the meteorological conditions (diurnal cycle, presence or not of clouds) compared to typical variables (temperature, specific humidity). Then, two 1D-Var experiments (classical vs. conservative variables) are evaluated over a full diurnal cycle characterized by a stratus-evolving radiative fog situation, using hourly TB. Results show, as expected, that TBs analysed by the 1D-Var are much closer to the observed ones than the background values for both variable choices. This is especially the case for channels sensitive to water vapour and liquid water. On the other hand, analysis increments in model space (water vapour, liquid water) show significant differences between the two sets of variables.

WAP-1D-VAR v1.0: development and evaluation of a one-dimensional variational data assimilation model for the marine ecosystem along the West Antarctic Peninsula

Abstract. The West Antarctic Peninsula (WAP) is a rapidly warming region, with substantial ecological and biogeochemical responses to the observed change and variability for the past decades, revealed by multi-decadal observations from the Palmer Antarctica Long-Term Ecological Research (LTER) program. The wealth of these long-term observations provides an important resource for ecosystem modeling, but there has been a lack of focus on the development of numerical models that simulate time-evolving plankton dynamics over the austral growth season along the coastal WAP. Here, we introduce a one-dimensional variational data assimilation planktonic ecosystem model (i.e., the WAP-1D-VAR v1.0 model) equipped with a model parameter optimization scheme. We first demonstrate the modified and newly added model schemes to the pre-existing food web and biogeochemical components of the other ecosystem models that WAP-1D-VAR model was adapted from, including diagnostic sea-ice forcing and trophic interactions specific to the WAP region. We then present the results from model experiments where we assimilate 11 different data types from an example Palmer LTER growth season (October 2002–March 2003) directly related to corresponding model state variables and flows between these variables. The iterative data assimilation procedure reduces the misfits between observations and model results by 58 %, compared to before optimization, via an optimized set of 12 parameters out of a total of 72 free parameters. The optimized model results capture key WAP ecological features, such as blooms during seasonal sea-ice retreat, the lack of macronutrient limitation, and modeled variables and flows comparable to other studies in the WAP region, as well as several important ecosystem metrics. One exception is that the model slightly underestimates particle export flux, for which we discuss potential underlying reasons. The data assimilation scheme of the WAP-1D-VAR model enables the available observational data to constrain previously poorly understood processes, including the partitioning of primary production by different phytoplankton groups, the optimal chlorophyll-to-carbon ratio of the WAP phytoplankton community, and the partitioning of dissolved organic carbon pools with different lability. The WAP-1D-VAR model can be successfully employed to link the snapshots collected by the available data sets together to explain and understand the observed dynamics along the coastal WAP.

A 1D-Var Approach to Retrieve Clear-Sky Wet Tropospheric Correction from Current and Future Altimetry Missions

AbstractStatistical methods are usually used to provide estimations of the wet tropospheric correction (WTC), necessary to correct altimetry measurements for atmospheric path delays, using brightness temperatures measured at two or three low frequencies from a passive microwave radiometer on board the altimeter mission. Despite their overall accuracy over oceanic surfaces, uncertainties still remain in specific regions of complex atmospheric stratification. Thus, there is still a need to improve the methods currently used by taking into account the frequency-dependent information content of the observations and the atmospheric and surface variations in the surroundings of the observations. In this article we focus on the assimilation of relevant passive microwave observations to retrieve the WTC over ocean using different altimeter mission contexts (current and future, providing brightness temperature measurements at higher frequencies in addition to classical low frequencies). Data assimilation is performed using a one-dimensional variational data assimilation (1D-Var) method. The behavior of the 1D-Var is evaluated by verifying its physical consistency when using pseudo- and real observations. Several observing-system simulation experiments are run and their results are analyzed to evaluate global and regional WTC retrievals. Comparisons of 1D-Var-based TWC retrieval and reference products from classical WTC retrieval algorithms or radio-occultation data are also performed to assess the 1D-Var performances.

Surfzone State Estimation, with Applications to Quadcopter-Based Remote Sensing Data

AbstractA one-dimensional variational data assimilation (1DVar) method is presented based on the depth- and time-averaged alongshore-uniform surfzone wave and current equations, for simultaneous estimation of three uncertain variables: bathymetry, incident wave boundary conditions, and bed roughness. The method is validated using twin tests and in situ field observations, and its results are shown to be comparable to those of an existing ensemble-based bathymetry inversion technique. Unlike existing techniques, the ability to simultaneously estimate boundary conditions and bed roughness along with bathymetry also means the 1DVar method can produce full state estimates without the requirement for additional supporting measurements (e.g., direct measurements of the incident waves). A proof-of-concept field application is shown using observations collected from an unmanned quadcopter sensor package that measures surfzone wave height from a fixed-beam lidar range finder, and time-averaged longshore current from particle image velocimetry of drifting surface foam.

Precipitation Analysis over the French Alps Using a Variational Approach and Study of Potential Added Value of Ground-Based Radar Observations

Abstract A one-dimensional variational data assimilation (1DVar) method to retrieve profiles of precipitation in mountainous terrain is described. The method combines observations from the French Alpine region rain gauges and precipitation estimates from weather radars with background information from short-range numerical weather prediction forecasts in an optimal way. The performance of this technique is evaluated using measurements of precipitation and of snow depth during two years (2012/13 and 2013/14). It is shown that the 1DVar model allows an effective assimilation of measurements of different types, including rain gauge and radar-derived precipitation. The use of radar-derived precipitation rates over mountains to force the numerical snowpack model Crocus significantly reduces the bias and standard deviation with respect to independent snow depth observations. The improvement is particularly significant for large rainfall or snowfall events, which are decisive for avalanche hazard forecasting. The use of radar-derived precipitation rates at an hourly time step improves the time series of precipitation analyses and has a positive impact on simulated snow depths.

Retrieval of Cloud Water Variables by 1D-Var Algorithm

Data assimilation of satellite observations in cloud and rain regions is a worldwide problem. In the paper, we designed the background field and their error covariance of three cloud water variables (cloud cover, cloud liquid water and cloud ice water) at first. The experiment results demonstrate that 1D-Var (One-dimensional variational data assimilation) can retrieve the three variables efficiently. The cloud liquid water and cloud ice water can be obviously improved by 1D-Var. However, the retrieved effect of low cloud cover is still to be improved. It has the positive potential to assimilate the satellite observations in cloud and rain regions.

30-Year atmospheric temperature record derived by one-dimensional variational data assimilation of MSU/AMSU-A observations

In the past, satellite observations of the microwave radiation emitted from the atmosphere have been directly utilized for deriving the climate tends of vertical-layer-averaged atmospheric temperatures. This study presents the 30-year atmospheric temperature trend derived by one-dimensional variational (1D-Var) data assimilation of Microwave Sounding Unit/Advanced Microwave Sounding Unit-A (MSU/AMSU-A) observations. Firstly, the radiance measurements from MSU on board the early National Oceanic and Atmospheric Administration (NOAA)-6 to NOAA-14 and AMSU-A on board NOAA-15 to -19 have been inter-calibrated to form a fundamental climate data record. A 1D-Var method is then employed to establish the thematic climate data record of atmospheric temperature profiles that are appropriate for climate change study. Verification of the MSU/AMSU-A derived temperature profiles with collocated Global Positioning System radio occultation data confirms a reasonable good accuracy of the derived atmospheric temperature profiles in the troposphere and low stratosphere. Finally, the global climate trend of the atmospheric temperature in clear-sky conditions is deduced, showing not only a global warming in the troposphere and a cooling in the stratosphere, but also a stronger warming in the upper troposphere than in the low troposphere.

Observability of Flow-Dependent Structure Functions for Use in Data Assimilation

Abstract One of the objectives of data assimilation is to produce initial conditions that will improve the quality of forecasts. Studies on singular vectors and sensitivity studies have shown that small changes to the initial conditions can sometimes lead to exponential error growth. This has motivated research to include flow-dependent structures within the assimilation that would have the characteristics to correctly predict the growth or decay of meteorological systems. This relates to the characterization of precursors to atmospheric instability. In this paper, the observability of such structures by observations is discussed. Several studies have shown that deploying observations over regions where changes in the initial conditions may impact the forecast the most do not lead to the expected benefit. In this paper, it is shown that given the small magnitude of the signal to be detected, it is important to take into account the accuracy of the observations. If the signal-to-noise ratio is too low, observations cannot detect and characterize precursors to forecast error growth. From that perspective, the assimilation only has the possibility to extract information about evolved structures of error growth. Experiments with a simple one-dimensional variational data assimilation (1D-Var) system are presented and, then, an adapted three-dimensional variational data assimilation (3D-Var) system with different sensitivity structure functions is used. The results have been obtained by adapting the variational assimilation system of Environment Canada.

Evaluation of the Impact of Observations on Analyses in 3D- and 4D-Var Based on Information Content

Abstract The degrees of freedom for signal (DFS) is used in data assimilation applications to measure the self-sensitivity of analysis to different observation types. This paper describes a practical method to estimate the DFS of observations from a posteriori statistics. The method does not require the consistency of the error statistics in the analysis system and it is shown that the observational impact on analyses can be estimated from observation departures with respect to analysis or the forecast. This method is first introduced to investigate the impact of a complete set, or subsets, of observations on the analysis for idealized one-dimensional variational data assimilation (1D-Var) analysis experiments and then applied in the framework of the three dimensional (3D)- and four-dimensional (4D)-Var schemes developed at Environment Canada.

High-Repetition Millimeter-Wave Passive Remote Sensing of Humidity and Hydrometeor Profiles from Elliptical Orbit Constellations

AbstractThe potential of an elliptical-orbit Flower Constellation of Millimeter-Wave Radiometers (FLORAD) for humidity profile and precipitating cloud observations is analyzed and discussed. The FLORAD mission scientific requirements are aimed at the retrieval of hydrological properties of the troposphere, specifically water vapor, cloud liquid content, rainfall, and snowfall profiles. This analysis is built on the results already obtained in previous works and is specifically devoted to evaluate the possibility of (i) deploying an incremental configuration of a Flower constellation of six minisatellites, optimized to provide the maximum revisit time over the Mediterranean area or, more generally, midlatitudes (between ±35° and ±65°); and (ii) evaluating in a quantitative way the accuracy of a one-dimensional variational data assimilation (1D-Var) Bayesian retrieval scheme to derive hydrometeor profiles at quasi-global scale using an optimized set of millimeter-wave frequencies. The obtained results show that a revisit time over the Mediterranean area (latitude 25° 45′, longitude −10° 35′°) of less than about 1 and 0.5 h can be obtained with four satellites and six satellites in Flower elliptical orbits, respectively. The accuracy of the retrieved hydrometeor profiles over land and sea for a winter and summer season at several latitudes shows the beneficial performance from using a combination of channels at 89, 118, 183, and 229 GHz. A lack of lower frequencies, such as those below 50 GHz, reduces the sounding capability for cloud lower layers, but the temperature and humidity retrievals provide a useful hydrometeor profile constraint. The FLORAD mission is fully consistent with the Global Precipitation Mission (GPM) scope and may significantly increase its space–time coverage. The concept of an incremental Flower constellation can ensure the flexibility to deploy a spaceborne system that achieves increasing coverage through separate launches of member spacecrafts. The choice of millimeter-wave frequencies provides the advantage of designing compact radiometers that comply well with the current technology of minisatellites (overall weight less than 500 kg). The overall budget of the FLORAD small mission might become appealing as an optimal compromise between retrieval performances and system complexity.

A New Technique for Estimation of Lower-Tropospheric Temperature and Water Vapor Profiles from Radio Occultation Refractivity

Abstract An empirical technique is proposed to obtain temperature and humidity profiles over the tropics using radio occultation refractivity profiles and surface/available lower-altitude temperature and pressure measurements over humid tropical regions. The technique is tested on a large number of diverse radiosonde-derived refractivity profiles over the tropics (30°S–30°N) and selected Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) radio occultation refractivity profiles that have collocated radiosonde observations over the region 10°S–30°N during the boreal summer of 2006. In a number of cases, the results were in good agreement with the collocated radiosonde data. The error statistics of temperature and humidity profiles obtained from the proposed technique are discussed and compared with the previously published results from another technique and also with the results of a one-dimensional variational data assimilation (1DVAR) technique given with COSMIC data. It is found that the previously published results and proposed technique are marginally better (worse) in reproducing observed relative humidity (specific humidity) when compared to the 1DVAR technique. The proposed new technique is applied on COSMIC refractivity profiles over the Bay of Bengal during summer 2007 to derive changes in vertical thermal and moisture changes in the troposphere between active and break phases of the monsoon pattern and many of the observed features are captured reasonably well.

Adjoint Sensitivity of Surface Precipitation to Initial Conditions

Abstract The adjoint version of the Global Environmental Multiscale model including a comprehensive package of simplified and linearized physical processes (large-scale condensation, deep moist convection, vertical diffusion, and subgrid-scale orographic effects) is used to evaluate the sensitivity of surface precipitation to initial conditions for up to 24 h for two meteorological systems: a midlatitude front and a tropical cyclone. Such diagnostics are useful to improve the understanding on variational assimilation of precipitation data. In agreement with a similar study, the largest sensitivity is found with respect to the temperature field for both stratiform and convective precipitation. Close to the observation time and for stratiform precipitation, the sensitivity with respect to specific humidity is rather large, which corroborates conclusions from previous one-dimensional variational data assimilation experimentations. The sensitivity is then reduced significantly after the observation time. The sensitivities of surface precipitation to the wind components and to specific humidity are comparable and are at a maximum at the observation time. The sensitivity to the surface pressure is always much smaller than the sensitivity to the other variables. In general, sensitivities are largest at the observation time and then decrease. However, for the midlatitude perturbation, the sensitivity is enhanced after 12 h for stratiform precipitation and also for convective precipitation using a scheme based on the moisture convergence closure. This results from a dynamical coupling upstream of the area of interest through baroclinic instability as evidenced by vertically backward-tilted sensitivities. Such enhancement is not observed for the tropical case. The tangent-linear approximation remains acceptable for accumulated precipitation up to 24 h but is rather poor for instantaneous rain rates. The variational assimilation of accumulated precipitation should thus be favored.

From Near-Surface to Root-Zone Soil Moisture Using Different Assimilation Techniques

Abstract Root-zone soil moisture constitutes an important variable for hydrological and weather forecast models. Microwave radiometers like the L-band instrument on board the European Space Agency’s (ESA) future Soil Moisture and Ocean Salinity (SMOS) mission are being designed to provide estimates of near-surface soil moisture (0–5 cm). This quantity is physically related to root-zone soil moisture through diffusion processes, and both surface and root-zone soil layers are commonly simulated by land surface models (LSMs). Observed time series of surface soil moisture may be used to analyze the root-zone soil moisture using data assimilation systems. In this paper, various assimilation techniques derived from Kalman filters (KFs) and variational methods (VAR) are implemented and tested. The objective is to correct the modeled root-zone soil moisture deficiencies of the newest version of the Interaction between Soil, Biosphere, and Atmosphere scheme (ISBA) LSM, using the observations of the surface soil moisture of the Surface Monitoring of the Soil Reservoir Experiment (SMOSREX) over a 4-yr period (2001–04). This time period includes contrasting climatic conditions. Among the different algorithms, the ensemble Kalman filter (EnKF) and a simplified one-dimensional variational data assimilation (1DVAR) show the best performances. The lower computational cost of the 1DVAR is an advantage for operational root-zone soil moisture analysis based on remotely sensed surface soil moisture observations at a global scale.

One-Dimensional Variational Data Assimilation of SSM/I Observations in Rainy Atmospheres at MSC

Abstract Currently, satellite radiances in the Canadian Meteorological Centre operational data assimilation system are only assimilated in clear skies. A two-step method, developed at the European Centre for Medium-Range Weather Forecasts, is considered to assimilate Special Sensor Microwave Imager (SSM/I) observations in rainy atmospheres. The first step consists of a one-dimensional variational data assimilation (1DVAR) method. Model temperature and humidity profiles are adjusted by assimilating either SSM/I brightness temperatures or retrieved surface rain rates (derived from SSM/I brightness temperatures). In the second step, 1DVAR column-integrated water vapor analyses are assimilated in four-dimensional variational data assimilation (4DVAR). At the Meteorological Service of Canada, such a 1DVAR assimilation system has been developed. Model profiles are obtained from a research version of the Global Environmental Multi-Scale model. Several issues raised while developing the 1DVAR system are addressed. The impact of the size of the observation error is studied when brightness temperatures are assimilated. For two case studies, analyses are derived when either surface rain rate or brightness temperatures are assimilated. Differences in the analyzed fields between these configurations are discussed and shortcomings of each approach are identified. Results of sensitivity studies are also provided. First the impact of observation error correlation between channels is investigated. Second, the size of the background temperature error is varied to assess its impact on the analyzed column-integrated water vapor. Third, the importance of each moist physical scheme is investigated. Finally, the portability of moist physical schemes specifically developed for data assimilation is discussed.

Improved Site-Specific Numerical Prediction of Fog and Low Clouds: A Feasibility Study

Abstract Accurate short-term forecasts of low ceiling and visibility are vital to air traffic operation, in order to maximize the use of an airport. The research presented here uses specific local observations and a detailed numerical 1D model in an integrated approach. The goal of the proposed methodology is to improve the local prediction of poor visibility and low clouds at Paris’s Charles de Gaulle International Airport. In addition to the development of an integrated observations and model-based forecasting system, this study will try to assess whether or not the increased local observing network yields improvements in short-term forecasts of low ceiling and poor visibility. Tests have been performed in a systematic manner during 5 months (the 2002/03 winter season). Encouraging results show that the inclusion of dedicated observations into the local 1D forecast system provides significant improvement to the forecast. Inspection of events indicates that the improvement in very short-term forecasts is a consequence of the ability of the forecast system to more accurately characterize the boundary layer processes, especially during night. Accurate forecast of low cloud seems more difficult since it strongly depends on the 3D mesoscale flow. This study also demonstrates that the use of a 1D model to forecast fogs and low clouds could only be beneficial if it is associated with local measurements and with a local assimilation scheme. The assimilation procedure used in this study is based on different steps: in the first step the atmospheric profiles are estimated in a one-dimensional variational data assimilation (1DVAR) framework, in the second step these atmospheric profiles are modified when fog and/or low clouds are detected, and in the third step the soil profiles are estimated in order to keep the consistency between the soil state and atmospheric measurements.

MAJOR ADVANCES FORESEEN IN HUMIDITY PROFILING FROM THE WATER VAPOUR LIDAR EXPERIMENT IN SPACE (WALES)

The need for an absolute standard for water vapor observations, in the form of a global dataset with high accuracy and good spatial resolution, has long been recognized. The European Space Agency's Water Vapour Lidar Experiment in Space (WALES) mission aims to meet this need by providing high-quality water vapor profiles, globally and with good vertical resolution, using a differential absorption lidar (DIAL) system in a low earth-orbit satellite. WALES will be the first active system to measure humidity from space routinely. With launch envisaged in the 2008–2010 time frame and a minimum duration of two years, the primary mission goals are to (a) contribute to scientific research and (b) demonstrate the feasibility of longer-term operational missions. This paper assesses the benefits of the anticipated data to NWP through quantitative analysis of information content. Good vertical resolution and low random errors are shown to give substantial improvements in analysis error in one-dimensional variational data assimilation (1DVAR) comparisons with advanced infrared sounders. In addition, the vertical extent of the profiles is shown to reach 16.5 km or ~100 hPa, well above the limit of radiance assimilation (13 km or 200 hPa). Also highlighted are important applications in atmospheric sciences and climate research that would benefit from the low bias promised by spaceborne DIAL data and their complementarity to other types of humidity observations.

One-Dimensional Variational Retrievals from SSMIS-Simulated Observations

Retrievals using synthetic background fields and observations for the Special Sensor Microwave Imager Sounder (SSMIS) instrument are performed using a one-dimensional variational data assimilation (1DVAR) scheme for clear and cloudy nonprecipitating skies over open oceans. Two retrieval techniques are implemented in the 1DVAR and are extensively tested. Profiles of temperature, marine surface wind speed, and skin temperature are retrieved with both techniques. In addition, with technique A, profiles of the natural logarithm of specific humidity and liquid water path are also retrieved. With technique B, the natural logarithm of total water content (sum of specific humidity and liquid cloud water content) is retrieved instead of the natural logarithm of humidity and liquid water path. A function specifies how total water content is split among its two components. In essence, excess water vapor oversaturation leads to cloud formation. Retrievals in clear and cloudy conditions for a variety of experiments thoroughly demonstrate how technique A works. The choice of humidity control variable, the presence of biases in the moisture retrievals, and the impact of applying a supersaturation constraint are also discussed. Furthermore, in the presence of clouds, it is shown that little temperature information can be extracted with this technique if the a priori cloud vertical distribution is not known well. With technique B, however, temperature information can be extracted from the observations even in the presence of clouds. Because of its more physically based parameterization, it has some skill at positioning the cloud in the vertical direction.