Variational Data Assimilation

By applying four-dimensional variational dataassimilation (4-D-Var) to a combined ozone and dynamics Numerical Weather Prediction model (NWP), ozone observations generate wind increments through the ozonedynamics coupling. The dynamical impact of Aura/MLS satellite ozone profiles is investigated using Météo-France operational ARPEGE NWP 4-D-Var assimilation system for a period of 3 months. A data-assimilation procedure has been designed and run on 6-h windows. The procedure includes: (1) 4-D-Var assimilating both ozone and operational NWP standard observations, (2) ARPEGE transporting ozone as a passive-tracer, (3) MOCAGE, the Météo-France chemistry and transport model re-initializing the ARPEGE ozone background at the beginning time of the assimilation window. Using observation minus forecast statistics, it is found that the ozone assimilation reduces the wind bias in the lower stratosphere. Moreover, the Degrees of Freedom for Signal diagnostics show that the MLS data covering the 68.1-31.6 hPa vertical pressure range are the most informative and their information content is nearly of the same order as tropospheric humidity-sensitive radiances. Furthermore, with the help of error variance reduction diagnostics, the ozone contribution to the reduction of the horizontal divergence background-error variance is shown to be better than tropospheric humidity-sensitive radiances.

We have developed a simplified aerosol model together with its tangent linear and adjoint versions for variational assimilation of aerosol optical depth with the aim to optimize aerosol emissions over the globe. The model was derived from the general circulation model LMDz; it groups together the 24 aerosol species simulated in LMDz into 4 species, namely gaseous precursors, fine mode aerosols, coarse mode desert dust and coarse mode sea salt. The emissions have been kept as in the original model. Modifications, however, were introduced in the computation of aerosol optical depth and in the processes of sedimentation, dry and wet deposition and sulfur chemistry to ensure consistency with the new set of species and their composition. The simplified model successfully manages to reproduce the main features of the aerosol distribution in LMDz. Differences between the original and simplified models are mainly associated to the new deposition and sedimentation velocities consistent with the definition of species in the simplified model and the simplification of the sulfur chemistry. Furthermore, simulated aerosol optical depth remains within the variability of AERONET observations for all aerosol types and all sites throughout most of the year. Sensitivity analyses with the tangent linear version show that the simplified sulfur chemistry is the dominant process responsible for the strong non-linearity of the model.

Obtaining an accurate initial state is recognized as one of the biggest challenges in accurate model prediction of convective events. This work is the first attempt in utilizing the India Meteorological Department (IMD) Doppler radar data in a numerical model for the prediction of mesoscale convective complexes around Chennai and Kolkata. Three strong convective events both over Chennai and Kolkata have been considered for the present study. The simulation experiments have been carried out using fifth-generation Pennsylvania State University-National Center for Atmospheric Research (PSU-NCAR) mesoscale model (MM5) version 3.5.6. The variational data assimilation approach is one of the most promising tools available for directly assimilating the mesoscale observations in order to improve the initial state. The horizontal wind derived from the DWR has been used alongwith other conventional and non-conventional data in the assimilation system. The preliminary results from the three dimensional variational (3DVAR) experiments are encouraging. The simulated rainfall has also been compared with that derived from the Tropical Rainfall Measuring Mission (TRMM) satellite. The encouraging result from this study can be the basis for further investigation of the direct assimilation of radar reflectivity data in 3DVAR system. The present study indicates that Doppler radar data assimilation improves the initial field and enhances the Quantitative Precipitation Forecasting (QPF) skill.

Climate change has affected the entire Arctic Ocean and in particular its Pacific Sector where the minimum of the summer ice extent was observed during the last decade. Diminishing sea ice has yielded greater fetch thus affecting surface waves all around the Alaska. To better represent the wave hindcast in the Pacific sector, we present modeling results of the WAM model configured for the Pacific Sector of the Arctic Ocean and a novel way to assimilate wave information into the wave models using the Reduced space 4Dvar (R4Dvar) data assimilation approach. The model results include the validation of several wind products for the region and comparison with in situ and satellite observation. The employed assimilation method does not require development of the tangent linear and adjoint codes for implementation. It is based on minimization of the cost function in a sequence of low-dimensional subspaces of the control space. The twin-data experiments show that assimilation of the wave da...

A set of four-dimensional variational data assimilation (4D-Var) experiments were conducted using both a standard method and an incremental method in an identical twin framework. The full physics adjoint model of the Florida State University global spectral model (FSUGSM) was used in the standard 4D-Var, while the adjoint of only a few selected physical parameterizations was used in the incremental method. The impact of physical processes on 4D-Var was examined in detail by comparing the results of these experiments. The inclusion of full physics turned out to be significantly beneficial in terms of assimilation error to the lower troposphere during the entire minimization process. The beneficial impact was found to be primarily related to boundary layer physics. The precipitation physics in the adjoint model also tended to have a beneficial impact after an intermediate number (50) of minimization iterations. Experiment results confirmed that the forecast from assimilation analyses with the full physics adjoint model displays a shorter precipitation spinup period. The beneficial impact on precipitation spinup did not result solely from the inclusion of the precipitation physics in the adjoint model, but rather from the combined impact of several physical processes. The inclusion of full physics in the adjoint model exhibited a detrimental impact on the rate of convergence at an early stage of the minimization process, but did not affect the final convergence. A truncated Newton-like incremental approach was introduced for examining the possibility of circumventing the detrimental aspects using the full physics in the adjoint model in 4D-Var but taking into account its positive aspects. This algorithm was based on the idea of the truncated Newton minimization method and the sequential cost function incremental method introduced by Courtier et al., consisting of an inner loop and an outer loop. The inner loop comprised the incremental method, while the outer loop consisted of the standard 4D-Var method using the full physics adjoint. The limited-memory quasi-Newton minimization method (L-BFGS) was used for both inner and outer loops, while information on the Hessian of the cost function was jointly updated at every iteration in both loops. In an experiment with a two-cycle truncated Newton-like incremental approach, the assimilation analyses turned out to be better than those obtained from either the standard 4D-Var or the incremental 4D-Var in all aspects examined. The CPU time required by this two-cycle approach was larger by 35% compared with that required by the incremental 4D-Var without almost any physics in the adjoint model, while the CPU time required by the standard 4D-Var with the full physics adjoint model was more than twice that required by the incremental 4D-Var. Finally, several hypotheses concerning the impact of using standard 4D-Var full physics on minimization convergence were advanced and discussed.

The adjoint method application in variational data assimilation provides a way of obtaining the exact gradient of the cost function J with respect to the control variables. Additional information may be obtained by using second order information. This paper presents a second order adjoint model (SOA) for a shallow-water equation model on a limited-area domain. One integration of such a model yields a value of the Hessian (the matrix of second partial derivatives, VzJ) multiplied by a vector or a column of the Hessian of the cost function with respect to the initial conditions. The SOA model was then used to conduct a sensitivity analysis of the cost function with respect to distributed observations and to study the evolution of the condition number (the ratio of the largest to smallest eigenvalues) of the Hessian during the course of the minimization. The condition number is strongly related to the convergence rate of the minimization. It is proved that the Hessian is positive definite during the process of the minimization, which in turn proves the uniqueness of the optimal solution for the test problem. Numerical results show that the sensitivity of the response increases with time and that the sensitivity to the geopotential field is larger by an order of magnitude than that to the u and v components of the velocity field. Experiments using data from an ECMWF analysis of the First Global Geophysical Experiment (FGGE) show that the cost function J is more sensitive to observations at points where meteorologically intensive events occur. Using the second order adjoint shows that most changes in the value of the condition number of the Hessian occur during the first few iterations of the minimization and are strongly correlated to major large-scale changes in the reconstructed initial conditions fields. * A brief description of the FOA model is provided in Appendix A.

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The major accomplishment of this contract has been the successful development of a method for extracting time derivative information from geostationary meteorological satellite imagery. This research is a proof-of-concept study which demonstrates the feasibility of using pattern recognition techniques and a statistical cloud classification method to estimate time rate of change of large-scale meteorological fields from remote sensing data. The cloud classification methodology is based on Typical Shape Function analysis of parameter sets characterizing the cloud fields. The three specific technical objectives, all of which were successfully achieved, are as 1. Develop and test a cloud classification technique based on pattern recognition methods, suitable for the analysis of visible and infrared geostationary satellite VISSR imagery. 2. Develop and test a methodology for intercomparing successive images using the cloud classification technique, so w to obtain estimates of the time rate of change of meteorological fields. 3. Implement this technique in a testbed system incorporating an interactive graphics terminal to determine the feasibility of extracting time derivative information suitable for comparison with numerical weather prediction products. This work should be carried forward in Phase I1 to produce a fully operational standalone work station to enable the benefits of this research to be realized in a real-time numerical weather prediction environment. Forecast verification studies, in conjunction with predictability theories, show that the early hours of numerical weather predictions are typically characterized by a rapid decay of skill. If observational estimates of time derivative, can be compared with numerical computations during this critical period, a PO- tentially valuable new tool will have been made available for improving numerical weather prediction model.

The Joint Center for Satellite Data Assimilation (JCSDA) was established by NASA and NOAA in 2001, with the DoD becoming a partner in 2002. The goal of the JCSDA is to accelerate the use of observations from earth-orbiting satellites in operational numerical analysis and prediction models for the purpose of improving weather forecasts, improving seasonal to interannual climate forecasts, and increasing the accuracy of climate data sets. Advanced instruments of the current and planned satellite missions, do and will increasingly provide large volumes of data related to atmospheric, oceanic, and land surface state. These data will exhibit accuracies and spatial, spectral and temporal resolutions never before achieved. The JCSDA will ensure that the maximum benefit from investment in space is realised from the advanced global observing system. It will also help accelerate the use of satellite data from both operational and experimental spacecraft for weather and climate related activities. To this end the advancement of data assimilation science by JCSDA has included the establishment of the JCSDA Community Radiative Transfer Model (CRTM) and continual upgrades including, the incorporation of AIRS and snow and ice emissivity models for improving the use of microwave sounding data over high latitudes, preparation for use of METOP IASI/AMSU/HSB, DMSP SSMIS and CHAMP GPS data, real-time delivery of EOS-Aqua AMSR-E to NWP centers, and improved physically based SST analyses. Eighteen other research projects are also being supported by the JCSDA (e.g. use of cloudy radiances from advanced satellite instruments) to develop a state of-the-art satellite data assimilation system. The work undertaken by the JCSDA represents a key component of GEOSS. In particular data assimilation, data impact studies, OSSEs, THORPEX and network design studies are key activities of GEOSS. Recent advances at the JCSDA including the demonstration of the benefits in the Northern and Southern Hemisphere of AIRS radiance assimilation on NCEP GFS forecasts, demonstration of the benefits of MODIS Polar atmospheric motion vector assimilation on NCEP GFS forecasts and the beneficial impact of the CRTM's modeling of sea ice and snow emissivity are recorded below.

Many meteorological disasters such as landslides with torrential rain have been reported. Monitoring and a prediction of the precipitation activity are very important to mitigate these disasters. However, in the developing countries such as Indonesia and the Philippines, the observation with the radars is difficult in the present conditions due to the cost and the maintenance. The water vapor tomography using a GPS and/or broadband satellite is considered to be effective for the precipitation monitoring system instead of the radars in the above countries. When the rain cloud bringing the damage of a heavy rain and the thunderstorm is developing, there is an apparent flow of the water vapor from the neighborhood. It is possible that the GPS can detect the flow and distribution of water vapor. Therefore, in this study, we develop a water vapor tomography from GPS and AMeDAS data using algorithm of residual minimization learning neural network (RMTNN). The numerical simulation demonstr...

This paper describes the direct assimilation of water vapour radiances at ECMWF, the emphasis being put on the usage of the clear-sky water vapour radiances from geostationary satellites, which became operational in April 2002 using data from Meteosat–7. Currently, experiments are being carried out to extend the coverage by geostationary radinaces using data from the GOES satellites. As the four–dimensional variational assimilation includes the time dimension, the high temporal resolution of the geostationary radiance data can be exploited to provide information not only on the upper tropospheric humidity but also on the upper tropospheric wind field. Extensive pre-operational monitoring of the geostationary clear–sky radiance data has been carried out. It shows a systematic warm bias of approximately 2– 3 K for the Meteosat water vapour radiances compared to the model first guess fields, while the bias of water vapour radiances from the GOES satellites and both HIRS and AMSUB with ...

The re-analysis programmes of numerical weather prediction (NWP) centres provide global, comprehensive descriptions of the atmosphere and of the Earth surface over long periods of time. The high realism of their representation of key NWP parameters, like temperature and winds, implies some realism for less emblematic parameters, such as cloud cover, but the degree of this realism needs to be documentated. This study aims to evaluate the high clouds over open oceans in the ECMWF 15-yr and 45-yr re-analyses. The assessment is based on a new 23-yr climatology of monthly frequencies of high cloud occurrence retrieved from the infrared radiances measured by operational polar satellites. It is complemented by data from the International Satellite Cloud Climatology Project. It is shown that the 45-yr ECMWF re-analysis dramatically improves on the previous 15-yr re-analysis for the realism of seasonal and interannual variations in high clouds, despite remaining systematic errors. More than ...

The assimilation of SEVIRI water vapour radiance data improves the fit of radiosonde data; figure shows that the biases of sonde humidity data against both the background and analysis are reduced in the area observed by Met-8. The fit of AMSU-B data in the same area is also improved; figure shows the difference in standard deviation of first guess departure of AMSU-B channel 3 on NOAA-16 for the trial and control. The area observed by Met-8 is clearly visible, showing that the background is closer to AMSU-B in this area. A similar result is found for HIRS channel 12. When RMS error in vector winds are studied, we find that winds, particularly at upper tropospheric levels, show a small but statistically significant improvement; table 1 shows the t-test significance of RMS error reduction. No indications were found that the RMS error grew when SEVIRI data are assimilated.

This study aims to assess the potential and limits of an advanced inversion method to estimate pollutant precursor sources mainly from observations. Ozone, sulphur dioxide, and partly nitrogen oxides observations are taken to infer source strength estimates. As methodology, the fourdimensional variational data assimilation technique has been generalised and employed to include emission rate optimisation, in addition to chemical state estimates as usual objective of data assimilation. To this end, the optimisation space of the variational assimilation system has been complemented by emission rate correction factors of 19 emitted species at each emitting grid point, involving the University of Cologne mesoscale EURAD model. For validation, predictive skills were assessed for an August 1997 ozone episode, comparing forecast performances of pure initial value optimisation, pure emission rate optimisation, and joint emission rate/initial value optimisation. Validation procedures rest on both measurements withheld from data assimilation and prediction skill evaluation of forecasts after the inversion procedures. Results show that excellent improvements can be claimed for sulphur dioxide forecasts, after emission rate optimisation. Significant improvements can be claimed for ozone forecasts after initial value and joint emission rate/initial value optimisation of precursor constituents. The additional benefits applying joint emission rate/initial value optimisation are moderate, and very useful in typical cases, where upwind emission rate optimisation is essential. In consequence of the coarse horizontal model grid resolution of 54 km, applied in this study, comparisons indicate that the inversion improvements can rest on assimilating ozone observations only, as the inclusion of NO x observations does not provide additional forecast skill. Emission estimates were found to be largely independent from initial

Estimating surface circulation from satellite images is a hot subject for a large range of applications. Motion estimation from image data has been studied for long in the literature of Image Processing, and more recently in that of Data Assimilation (DA). This paper describes how the construction of dedicated spaces for projecting motion and image fields allows applying DA methods with a reduced model and eases the estimation of surface circulation on the whole Black Sea basin.

Résumé: Les réseaux de contraintes pondérées offrent un cadre de représentation et de résolution permettant d'exprimer des contraintes dites" molles", utiles pour modéliser un très large champ d'applications. La plupart des solveurs que l'on trouve actuellement implantent un algorithme de séparation et évaluation en profondeur d'abord qui maintient une cohérence locale durant la phase d'exploration de l'arbre. Les résultats empiriques tendent à prouver que maintenir FDAC* semble être le meilleur choix en pratique. Nous ...

RESUME This paper examines how satellite altimeter and scatterometer measurements could be jointly used in a numerical ocean model in an attempt to simulate a rea­ listic ocean circulation. The aim of the study is to determine quantitatively how sensitive the efficiency of the assimilation process may be to the variability of the wind stress curl and to evaluate the ability of the Topex/Poseidon altimetric data to correct for the sampling of scatterometer wind data that is to be provided by the forthcoming ERS 1 and NSCAT satellite missions. The model is quasigeostrophic, eddy-resolving and multi-layered, and is applied . to the prognostic description of the mid-latitude ocean circulation in a schematic box ocean. Satellite altimeter data are simulated from model runs (forced by ECMWF winds) under the conditions of the Topex/Poseidon mission and are assimilated into the model by using a Newtonian relaxation or nudging tech­ nique. Satellite scatterometer wind data are simulated from...

The Developmental Testbed Center (DTC) provides a link between the research and operational communities in order to more efficiently transfer new technologies in numerical weather prediction (NWP) from research to operations. Extensive testing and evaluation must be performed to ensure that these new techniques are indeed ready for operational consideration. At the DTC, NWP research and operational communities interact to test and evaluate new developments in the Weather and Research Forecasting (WRF) model, for both research applications and operational implementation (Bernardet et al. 2008).

Many applications in geosciences require solving inverse problems to estimate the state of a physical system. Data assimilation provides a strong framework to do so when the system is partially observed and its underlying dynamics is known to some extent. In the variational flavor, it can be seen as an optimal control problem where initial conditions are the control parameters. Such problems being often ill-posed, regularization may be needed using explicit prior knowledge to enforce satisfying solution. In this work we propose to use a deep prior, a neural architecture that generates potential solution and acts as implicit regularization. The architecture is trained in an fully-unsupervised manner using the variational data assimilation cost so that gradients are backpropagated through the dynamical model and then through the neural network. To demonstrate its use, we set a twin experiment using a shallow-water toy model, where we test various variational assimilation algorithms on a ocean-like circulation estimation.

Inverse problems are of utmost importance in many fields of science and engineering. In the variational approach inverse problems are formulated as PDE-constrained optimization problems, where the optimal estimate of the uncertain parameters is the minimizer of a certain cost functional subject to the constraints posed by the model equations. The numerical solution of such optimization problems requires the computation of derivatives of the model output with respect to model parameters. The first order derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through first order adjoint sensitivity analysis. Second order adjoint models give second derivative information in the form of matrix-vector products between the Hessian of the cost functional and user defined vectors. Traditionally, the construction of second order derivatives for large scale models has been considered too costly. Consequent...

A deep scientific understanding of complex physical systems, such as the atmosphere, can be achieved neither by direct measurements nor by numerical simulations alone. Data assimilation is a rigorous procedure to fuse information from a priori knowledge of the system state, the physical laws governing the evolution of the system, and real measurements, all with associated error statistics. Data assimilation produces best (a posteriori) estimates of model states and parameter values, and results in considerably improved computer simulations. The acquisition and use of observations in data assimilation raises several important scientific questions related to optimal sensor network design, quantification of data impact, pruning redundant data, and identifying the most beneficial additional observations. These questions originate in operational data assimilation practice, and have started to attract considerable interest in the recent past. This dissertation advances the state of knowledge in four dimensional variational (4D-Var) data assimilation by developing, implementing, and validating a novel computational framework for estimating observation impact and for optimizing sensor networks. The framework builds on the powerful methodologies of second-order adjoint modeling and the 4D-Var sensitivity equations. Efficient computational approaches for quantifying the observation impact include matrix free linear algebra algorithms and low-rank approximations of the sensitivities to observations. The sensor network configuration problem is formulated as a meta-optimization problem. Best values for parameters such as sensor location are obtained by optimizing a performance criterion, subject to the constraint posed by the 4D-Var optimization. Tractable computational solutions to this "optimization-constrained" optimization problem are provided. The results of this work can be directly applied to the deployment of intelligent sensors and adaptive observations, as well as to reducing the operating costs of measuring networks, while preserving their ability to capture the essential features of the system under consideration.

Data assimilation is an important data-driven application (DDDAS) where measurements of the real system are used to constrain simulation results. This paper describes a methodology for dynamically configuring sensor networks in data assimilation systems based on numerical models of time-evolving differential equations. The proposed methodology uses the dominant model singular vectors, which reveal the directions of maximal error growth. New sensors are dynamically placed such as to minimize an estimation error energy norm. A shallow water test problem is used to illustrate our approach.

The error in mesoscale model forecasts on the West Coast of the United States often depends strongly on the quality of the synoptic scale forecast. Kuypers (2000) demonstrated that small differences in synoptic scale initial analyses due to different random samples of the large scale structure are sufficient to cause large errors in the mesoscale forecast. This dependence of the mesoscale on the synoptic scale is often mirrored in statements like, “A good mesoscale forecast requires a good synoptic scale forecast.” The method by which a good synoptic scale forecast is achieved is the subject of numerous efforts at improving the observations over the Pacific through targeting of observations.

The 183-GHz water vapor absorption band measurements from the Advanced Microwave Sounding Unit B (AMSU-B) and Microwave Humidity Sounder (MHS) on board polar-orbiting satellites were processed to produce a bias-corrected, intersatellite calibrated microwave brightness temperature data set suitable for longterm climate monitoring. The data set generation involves radiative transfer simulations to adjust for biases arising from satellite orbital drift and difference in local observation time between satellites. − Grid resolution: 1.5°×1.5°. − Contained fields: inter-satellite calibrated 183.31±1 GHz channel monthly mean brightness temperatures [K]. − Time span: January 1999 December 2014.

A method is developed for the optimal estimation of the parameters in a ji@ nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The method is based on the adjoint method of optimal control. It is shown that accurate ualues of the parameters can be estimated, and the estimates are stable with respect to random perturbations of the data provided that data from a suficient number of locations are available for assimilation.

We have developed a variational data assimilation technique for the Sun using a toy αΩ dynamo model. The purpose of this work is to apply modern data assimilation techniques to solar data using a physically based model. This work represents the first step toward a complete variational model of solar magnetism. We derive the adjoint αΩ dynamo code and use a minimization procedure to invert the spatial dependence of key physical ingredients of the model. We find that the variational technique is very powerful and leads to encouraging results that will be applied to a more realistic model of the solar dynamo.

For a linearized system such as ��/�t � M�, singular vector analysis can be used to find patterns that give the largest or smallest ratios between the sizes of M � and �. Such analyses have applications to a wide range of atmosphere–ocean problems. The resulting singular vectors, however, depend on the norm used to measure the sizes of M � and �, as noted in various applications. This causes complications because the choices of norm are generally nonunique. Based on perturbation theory, a derivation of how singular vectors change with norms typically used in the atmosphere–ocean literature is provided, and it is shown that the norm dependences observed in previous studies can be understood as general properties of singular vectors. This will hopefully clarify the interpretation of these observed norm dependencies, and provide guidance to new studies on how singular vectors would vary for different norms. It is further argued, based on these results, that there may not be as much nor...

Data assimilation method consists in combining all available pieces of information about a system to obtain optimal estimates of initial states. The different sources of information are weighted according to their accuracy by the means of error covariance matrices. Our purpose here is to evaluate the efficiency of variational data assimilation for the xenon induced oscillations forecasts in nuclear cores. In this paper we focus on the comparison between 3DVAR schemes with optimised background error covariance matrix B and a 4DVAR scheme. Tests were made in twin experiments using a simulation code which implements a mono-dimensional coupled model of xenon dynamics, thermal, and thermal-hydraulic processes. We enlighten the very good efficiency of the 4DVAR scheme as well as good results with the 3DVAR one using a careful multivariate modelling of B.

Many applications in geosciences require solving inverse problems to estimate the state of a physical system. Data assimilation provides a strong framework to do so when the system is partially observed and its underlying dynamics is known to some extent. In the variational flavor, it can be seen as an optimal control problem where initial conditions are the control parameters. Such problems being often ill-posed, regularization may be needed using explicit prior knowledge to enforce satisfying solution. In this work we propose to use a deep prior, a neural architecture that generates potential solution and acts as implicit regularization. The architecture is trained in an fully-unsupervised manner using the variational data assimilation cost so that gradients are backpropagated through the dynamical model and then through the neural network. To demonstrate its use, we set a twin experiment using a shallow-water toy model, where we test various variational assimilation algorithms on a ocean-like circulation estimation.

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Observing System Experiments (OSEs) were conducted to analyze the impact of assimilation of Megha-Tropique's (MT) Sounder for Probing Vertical ProBles of Humidity (SAPHIR) radiances on the simulation of tracks and intensity of three tropical cyclones (Kyant, Vardah, and Maarutha) formed over the Bay of Bengal during 2016-2017 North Indian Ocean cyclone period. National Centre for Medium Range Weather Forecast (NCMRWF) UniBed Model (NCUM) Hybrid-4DVAR assimilation and forecast system was used for the OSEs. Assimilation of SAPHIR radiances produced an improvement of 9% and 12%, respectively, in the cyclones' central sea level pressure (CSLP) and the maximum sustained wind (MSW), while an improvement of 38% was seen in the cyclone tracks within the forecast lead time of 120 hrs. Initial assessment shows that the improvement in the cyclone intensity is due to the assimilation of the unique surface peaking channel of SAPHIR (channel-6), whereas the improvement in the cyclone track is due to the assimilation remaining Bve channels of SAPHIR. Thus, the assimilation of SAPHIR radiances in the NCUM system showed improvement in both intensity and track of the cyclones over the Bay of Bengal; however, more cyclone cases over different ocean basins have to be analyzed to make a robust conclusion. This study speciBes the importance of similar microwave humidity instruments in the same frequency range for the detailed exploration of cyclone track and structure.

The Indian sub-continent often receives heavy rainfall events, especially during active phases of the southwest monsoon (SWM). The accurate prediction of such events requires a high-resolution model with data assimilation techniques which can assimilate high-density spatial and temporal observed data, like radar observations. This study is undertaken to evaluate the impact of assimilation of radial velocity from multiple Doppler weather radars (DWRs) for simulation of three convective rainfall events during the SWM using the high-resolution (4 km) National Centre for Medium Range Weather and Forecasting (NCMRWF) Unified Model (NCUM) with a three-dimensional variational (3DVAR) data assimilation system. Two numerical experiments are carried out viz. control simulation (CNTL) and a second experiment (RAD, assimilation of all observations used in CNTL plus radial winds from Indian DWRs). The study clearly shows that the assimilation of DWR data has a positive impact in the simulation of heavy rainfall events by the model. The root mean square error (RMSE) of the analyzed (simulated) u-and v-components of wind is reduced by 46% (25%) and 37% (19%) in the RAD experiment as compared to the CNTL experiment. The simulated wind fields at different pressure levels are stronger after assimilation of DWR observations, and it is also successfully produced the cyclonic circulation as compared to the CNTL simulation. The skew-T plots suggested that the convection is more properly represented by the RAD experiment than the CNTL. The value of stability parameters is properly simulated in the RAD experiment, while compared with the CNTL, the values are reasonably well matched with the observed values in all cases. The intensity of the rainfall is reasonably well simulated by the RAD as compared to the CNTL experiment. The statistical skill scores of rainfall with different thresholds are significantly improved in the RAD experiment for all the cases.

Monsoon depressions form over the sea, which is a typical data-sparse region for conventional observations. The Moderate Resolution Imaging Spectroradiometer (MODIS) provides for very high-horizontal resolution temperature and humidity soundings. Such high-resolution satellite data can improve the poorly analyzed depressions. The objective of this study is to investigate the impact of ingesting and assimilating the MODIS temperature and humidity profiles on the prediction of a monsoon depression, which formed over the Bay of Bengal during September 2006 using threedimensional variational data assimilation (3DVAR). The NCAR Weather Research and Forecast model (WRF) has been utilized in this study. The results of the study indicate that the simulated sea level pressure fields from the 3DVAR run is in better agreement with the sea level pressure field from the NCEP-FNL analysis as compared to the control run. Higher spatial correlation and the lower rms errors of the sea level pressure field are associated with the 3DVAR run. The simulated structure of the spatial precipitation pattern for the assimilation experiments (3DVAR) are closer to the TRMM observations with more rainfall simulated over the east coast regions in the assimilation experiments. The 3DVAR runs clearly shows lower number of false alarms, higher probability of detection and larger value of equitable threat score for the 48 hours accumulated precipitation as compared to the control run. The results also indicate that the 3DVAR has larger positive bias values for precipitation as compared to the control run. For the 3DVAR run, the results reveal lower rms errors for temperatures at all levels and dew point temperatures, except for the upper troposphere. However, the rms errors for the wind speeds are not lower for the 3DVAR run. Overall, the results of this study indicate a very positive impact of the 3DVAR assimilation of MODIS observations on the simulation of a monsoon depression over India.

Pre-monsoon rainfall around Kolkata (northeastern part of India) is mostly of convective origin as 80% of the seasonal rainfall is produced by Mesoscale Convective Systems (MCS). Accurate prediction of the intensity and structure of these convective cloud clusters becomes challenging, mostly because the convective clouds within these clusters are short lived and the inaccuracy in the models initial state to represent the mesoscale details of the true atmospheric state. Besides the role in observing the internal structure of the precipitating systems, Doppler Weather Radar (DWR) provides an important data source for mesoscale and microscale weather analysis and forecasting. An attempt has been made to initialize the stormscale numerical model using retrieved wind fields from single Doppler radar. In the present study, Doppler wind velocities from the Kolkata Doppler weather radar are assimilated into a mesoscale model, MM5 model using the three-dimensional variational data assimilation (3DVAR) system for the prediction of intense convective events that occurred during 0600 UTC on 5 May and 0000 UTC on 7 May, 2005. In order to evaluate the impact of the DWR wind data in simulating these severe storms, three experiments were carried out. The results show that assimilation of Doppler radar wind data has a positive impact on the prediction of intensity, organization and propagation of rain bands associated with these mesoscale convective systems. The assimilation system has to be modified further to incorporate the radar reflectivity data so that simulation of the microphysical and thermodynamic structure of these convective storms can be improved.

Performance evaluation metrics B Performance evaluation on the stations C AMHG 35 D Usual parameterizations of flow resistance References Highlights • Method for hydraulic model derived stage fall discharge • Spatially distributed variational calibration of a hydraulic network model 40 • Multi-mission altimetry data assimilation • Stage-fall-discharge laws amenable to satellite altimetry

The 2D shallow water equations adequately model some geophysical flows with wet-dry fronts (e.g. flood plain or tidal flows); nevertheless deriving accurate, robust and conservative numerical schemes for dynamic wet-dry fronts over complex topographies remains a challenge. Furthermore for these flows, data are generally complex, multi-scale and uncertain. Robust variational inverse algorithms, providing sensitivity maps and data assimilation processes may contribute to breakthrough shallow wet-dry front dynamics modelling. The present study aims at deriving an accurate, positive and stable finite volume scheme in presence of dynamic wet-dry fronts, and some corresponding inverse computational algorithms (variational approach). The schemes and algorithms are assessed on classical and original benchmarks plus a real flood plain test case (Lèze river, France). Original sensitivity maps with respect to the (friction, topography) pair are performed and discussed. The identification of inflow discharges (time series) or friction coefficients (spatially distributed parameters) demonstrate the algorithms efficiency.

This study addresses the problem of 4D estimation of cloudy atmosphere on cloud resolving scales using satellite remote sensing measurements. The motivation is to develop a methodology for accurate estimation of cloud properties and associated atmospheric environment on small spatial scales but over large regions to aid in better understanding of the clouds and their role in the atmospheric system. The problem is initially approached by study of assimilation of the GOES imager observations into a cloud resolving model with explicit bulk cloud microphysical parameterization. A new 4DVAR research data assimilation system with the cloud resolving capability is applied to a case of a multi-layered cloud evolution without convection. In the experiments the information content of the IR window channels is addressed as well as the sensitivity of estimation to lateral boundary condition errors, model first guess, decorrelation length in the background statistical error model and the use of a generic linear model error. The assimilation results are compared with independent observations from the ARM central facility archive. The modeled 3D spatial distribution and short term evolution of the ice cloud mass is significantly improved by the assimilation of IR window channels when the model already contains conditions for the ice cloud formation. The assimilated ice cloud in this case is in good agreement with the independent cloud radar measurements. The simulation of liquid clouds below the thick ice clouds is not influenced by the IR window observations. The assimilation results clearly demonstrate that increasing the

An observational operator and its adjoint have been created that are suitable for use within variational data assimilation using polarized 6-and 10-GHz passive microwave satellite observations. When used within a variational data assimilation system, the operator will facilitate NWP soil moisture initialization using existing and future satellite datasets [e.g., NASA Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E), Advanced Earth Observing Satellite-II (ADEOS-II), Department of Defense (DoD) WindSat, and the National Polar Orbiter Environmental Satellite System (NPOESS) Conical Microwave Imager Sounder (CMIS)]. Five primary control variables are used within the operator, and surface soil moisture is explicitly included as one of the control variables. In future studies, this operator and its adjoint will be used to perform land surface model data assimilation experiments to better determine important NWP surface characteristics. In the current study, the adjoint model development and analysis of the potential information content of passive microwave measurements sensitive to the land surface and soil parameters are focused on. The multivariate results clarify the effects of masking phenomena upon the soil moisture signal. Also included is a useful transformation of the adjoint between real and complex number spaces. The transformations are necessary when higher-level mathematical operators, such as powers, use complex number arguments. This can be a common occurrence within radiative transfer models. Thus, the adjoint of this particular observational operator serves as an example of this behavior. Various observational operator results and sensitivity analyses are presented, demonstrating significant utility of the operator for NWP soil moisture data assimilation studies.

A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Prediction (NCEP) Eta 4DVAR system, however with added improvements addressing its use in a research environment. Preliminary results with RAMDAS are presented, focusing on the minimization performance and the impact of vertical correlations in error covariance modeling. A three-dimensional formulation of the background error correlation is introduced and evaluated. The Hessian preconditioning is revisited, and an alternate algebraic formulation is presented. The results indicate a robust minimization performance.

This study addresses the problem of 4D estimation of cloudy atmosphere on cloud resolving scales using satellite remote sensing measurements. The motivation is to develop a methodology for accurate estimation of cloud properties and associated atmospheric environment on small spatial scales but over large regions to aid in better understanding of the clouds and their role in the atmospheric system. The problem is initially approached by study of assimilation of the GOES imager observations into a cloud resolving model with explicit bulk cloud microphysical parameterization. A new 4DVAR research data assimilation system with the cloud resolving capability is applied to a case of a multi-layered cloud evolution without convection. In the experiments the information content of the IR window channels is addressed as well as the sensitivity of estimation to lateral boundary condition errors, model first guess, decorrelation length in the background statistical error model and the use of a generic linear model error. The assimilation results are compared with independent observations from the ARM central facility archive. The modeled 3D spatial distribution and short term evolution of the ice cloud mass is significantly improved by the assimilation of IR window channels when the model already contains conditions for the ice cloud formation. The assimilated ice cloud in this case is in good agreement with the independent cloud radar measurements. The simulation of liquid clouds below the thick ice clouds is not influenced by the IR window observations. The assimilation results clearly demonstrate that increasing the

An observational operator and its adjoint have been created that are suitable for use within variational data assimilation using polarized 6-and 10-GHz passive microwave satellite observations. When used within a variational data assimilation system, the operator will facilitate NWP soil moisture initialization using existing and future satellite datasets [e.g., NASA Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E), Advanced Earth Observing Satellite-II (ADEOS-II), Department of Defense (DoD) WindSat, and the National Polar Orbiter Environmental Satellite System (NPOESS) Conical Microwave Imager Sounder (CMIS)]. Five primary control variables are used within the operator, and surface soil moisture is explicitly included as one of the control variables. In future studies, this operator and its adjoint will be used to perform land surface model data assimilation experiments to better determine important NWP surface characteristics. In the current study, the adjoint model development and analysis of the potential information content of passive microwave measurements sensitive to the land surface and soil parameters are focused on. The multivariate results clarify the effects of masking phenomena upon the soil moisture signal. Also included is a useful transformation of the adjoint between real and complex number spaces. The transformations are necessary when higher-level mathematical operators, such as powers, use complex number arguments. This can be a common occurrence within radiative transfer models. Thus, the adjoint of this particular observational operator serves as an example of this behavior. Various observational operator results and sensitivity analyses are presented, demonstrating significant utility of the operator for NWP soil moisture data assimilation studies.

A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Prediction (NCEP) Eta 4DVAR system, however with added improvements addressing its use in a research environment. Preliminary results with RAMDAS are presented, focusing on the minimization performance and the impact of vertical correlations in error covariance modeling. A three-dimensional formulation of the background error correlation is introduced and evaluated. The Hessian preconditioning is revisited, and an alternate algebraic formulation is presented. The results indicate a robust minimization performance.