4D-Var Method Research Articles

An intercomparison of total column-averaged nitrous oxide between ground-based FTIR TCCON and NDACC measurements at seven sites and comparisons with the GEOS-Chem model

Abstract. Nitrous oxide (N2O) is an important greenhouse gas and it can also generate nitric oxide, which depletes ozone in the stratosphere. It is a common target species of ground-based Fourier transform infrared (FTIR) near-infrared (TCCON) and mid-infrared (NDACC) measurements. Both TCCON and NDACC networks provide a long-term global distribution of atmospheric N2O mole fraction. In this study, the dry-air column-averaged mole fractions of N2O (XN2O) from the TCCON and NDACC measurements are compared against each other at seven sites around the world (Ny-Ålesund, Sodankylä, Bremen, Izaña, Réunion, Wollongong, Lauder) in the time period of 2007–2017. The mean differences in XN2O between TCCON and NDACC (NDACC–TCCON) at these sites are between −3.32 and 1.37 ppb (−1.1 %–0.5 %) with standard deviations between 1.69 and 5.01 ppb (0.5 %–1.6 %), which are within the uncertainties of the two datasets. The NDACC N2O retrieval has good sensitivity throughout the troposphere and stratosphere, while the TCCON retrieval underestimates a deviation from the a priori in the troposphere and overestimates it in the stratosphere. As a result, the TCCON XN2O measurement is strongly affected by its a priori profile. Trends and seasonal cycles of XN2O are derived from the TCCON and NDACC measurements and the nearby surface flask sample measurements and compared with the results from GEOS-Chem model a priori and a posteriori simulations. The trends and seasonal cycles from FTIR measurement at Ny-Ålesund and Sodankylä are strongly affected by the polar winter and the polar vortex. The a posteriori N2O fluxes in the model are optimized based on surface N2O measurements with a 4D-Var inversion method. The XN2O trends from the GEOS-Chem a posteriori simulation (0.97±0.02 (1σ) ppb yr−1) are close to those from the NDACC (0.93±0.04 ppb yr−1) and the surface flask sample measurements (0.93±0.02 ppb yr−1). The XN2O trend from the TCCON measurements is slightly lower (0.81±0.04 ppb yr−1) due to the underestimation of the trend in TCCON a priori simulation. The XN2O trends from the GEOS-Chem a priori simulation are about 1.25 ppb yr−1, and our study confirms that the N2O fluxes from the a priori inventories are overestimated. The seasonal cycles of XN2O from the FTIR measurements and the model simulations are close to each other in the Northern Hemisphere with a maximum in August–October and a minimum in February–April. However, in the Southern Hemisphere, the modeled XN2O values show a minimum in February–April while the FTIR XN2O retrievals show different patterns. By comparing the partial column-averaged N2O from the model and NDACC for three vertical ranges (surface–8, 8–17, 17–50 km), we find that the discrepancy in the XN2O seasonal cycle between the model simulations and the FTIR measurements in the Southern Hemisphere is mainly due to their stratospheric differences.

Radar Data Assimination in WRF Model to Forecast Heavy Rainfall at Ho Chi Minh City

Abstract: This article using high resolution WRF model simulation on a heavy rainfall in summer at Hochiminh city by using radar data to assimilation initial conditions with 3DVAR method, the WRF3Dvar running simulation with two modes: cold start and warm start combine with three cases: only Reflectivity of radar; Reflectivity and Doppler radar radial wind observations; Reflectivity, Doppler radar radial wind, and GTS data. The background error used was CV7 created from 6 months forecast in South Vietnam. Radar data before assimilation was quality control and thinned to remove noise and create the best observation. 24 station rainfall in South Vietnam using to an evaluation of WRF model simulation. Results show assimilation only reflectivity will affect to variable qcloud, qvapor and qrain on the initial condition of model and assimilation only Doppler radar radial wind improve wind. Compare each case show warm start simulation precipitation better than the cold start, assimilation both Doppler radar radial wind observations, the reflectivity of radar and GTS better than another case.
 Key words: WRFDA,RADAR

The evaluation of EnVar method including hydrometeors analysis variables for assimilating cloud liquid/ice water path on prediction of rainfall events

The Weather Research and Forecasting (WRF) model's data assimilation (WRFDA) hybrid ensemble-variational data assimilation (EnVar) system is used to examine the performance of the EnVar method for assimilating cloud liquid/ice water path products. To add flow-dependent features to background error covariance (BEC) of hydrometeors, hydrometeors mixing ratios (Qc, Qi, Qr, Qs) are extended into analysis state vector for the “alpha” control variable. Then the BEC in the updated WRFDA-EnVar system combines the static hydrometeors BEC and flow-dependent hydrometeors BEC derived from ensemble forecasts. The updated system is evaluated by performing a series of single observation tests and two-weeks cycling assimilation and forecasting experiments by assimilating Cloud Liquid/Ice Water Path from NASA. The single observation tests show that the flow-dependent and multivariate BEC is introduced into the updated WRFDA-EnVar system by including extended hydrometeors analysis variables. The cycling assimilation and forecasting experiments demonstrate that by using the updated system included hydrometeors analysis variables, the root mean square errors (RMSEs) of analysis and forecasts are reduced and the Fractions Skill Scores (FSSs) of the precipitation forecasts are increased when compared with 3DVar method and the EnVar method without hydrometeors analysis variables. The diagnostics for a local severe rainfall case in the two-weeks cycling assimilation and forecasting experiments further show that through the application of the EnVar method included hydrometeors analysis variables, the convective available potential energy (CAPE) and humidity are increased effectively, and then better forecasts in terms of spatial distribution and intensity in accumulated precipitation are obtained, as well as cloud component.

Application of a Physical Ensemble Method in the POD-4DEnVar

Abstract The sensitivity of the proper orthogonal decomposition (POD)-based ensemble four-dimensional variational assimilation (4DVar) method (referred to as POD-4DEnVar) to cumulus and microphysics schemes was investigated using the Weather Research and Forecasting (WRF) Model for heavy rainfall in South China. Results show that the choice of the cumulus and microphysics schemes for ensemble samples significantly impacts precipitation prediction and that Doppler radar data assimilation using POD-4DEnVar is sensitive to the parameterization schemes used for the ensemble samples. The cumulus and microphysics schemes primarily affect the vertical velocity and rainwater mixing ratio of the ensemble forecasts. Variations in the ensemble samples caused by different parameterization schemes are introduced into the four-dimensional ensemble variational assimilation by the radar data observation operator. These variations affect the analysis fields and result in variations in precipitation prediction. To obtain the optimal result (smallest forecast error), three methods are designed based on the physical ensemble technique, which can filter out the effects of different parameterization schemes for the ensemble samples through averaging. The results show that the precipitation forecasts from the three assimilation experiments are improved compared with a control experiment, but each physical ensemble method leads to a unique precipitation forecast.

Impact of 3DVAR assimilation of surface PM2.5 observations on PM2.5 forecasts over China during wintertime

Data assimilation is one of the effective ways to improve model predictions. In this study, surface fine particulate matter (PM2.5) observations during 16 December 2015 to 15 January 2016 over China are assimilated in a regional air quality forecasting system using the three-dimensional variational (3DVAR) method. Two parallel experiments with and without data assimilation (DA) are conducted. The results show that 3DVAR can significantly reduce the uncertainties of the initial PM2.5 fields and improve the subsequent PM2.5 forecasts at a certain extent. The influences of DA on both analysis and forecast fields are different in different areas. Overall, the root-mean-square error of analysis field could be reduced by at least 50%, and the correlation coefficient could be improved to more than 0.9. Less improvement appears in the North China Plain. For forecast field, similar with previous studies, the DA is effective only within a certain forecast time. On average, the benefits of DA could last more than 48 h over China. Much longer benefits (>24 h) are found in Sichuan basin, Xinjiang, southern China and part of northern China. In the first 24 h, there are more than half of Chinese cities with their daily mean PM2.5 hit rates increasing greater than 10%. The duration of DA benefits are mainly affected by weather condition and emission intensity. The areas with longer DA benefits generally have more stable weather condition and/or weaker emission intensity. The absence of heterogeneous reactions in chemical transport models may also has negative effects on the durations. In addition, we found that the assimilated observation information could transport along with the air masses, and the downwind areas generally have better DA benefits, indicating that when doing air quality forecasting using nested domains, we should conduct the DA in the largest domain rather than the innermost one.

Optimization Based Methods for Partially Observed Chaotic Systems

In this paper we consider filtering and smoothing of partially observed chaotic dynamical systems that are discretely observed, with an additive Gaussian noise in the observation. These models are found in a wide variety of real applications and include the Lorenz 96’ model. In the context of a fixed observation interval T, observation time step h and Gaussian observation variance sigma _Z^2, we show under assumptions that the filter and smoother are well approximated by a Gaussian with high probability when h and sigma ^2_Z h are sufficiently small. Based on this result we show that the maximum a posteriori (MAP) estimators are asymptotically optimal in mean square error as sigma ^2_Z h tends to 0. Given these results, we provide a batch algorithm for the smoother and filter, based on Newton’s method, to obtain the MAP. In particular, we show that if the initial point is close enough to the MAP, then Newton’s method converges to it at a fast rate. We also provide a method for computing such an initial point. These results contribute to the theoretical understanding of widely used 4D-Var data assimilation method. Our approach is illustrated numerically on the Lorenz 96’ model with state vector up to 1 million dimensions, with code running in the order of minutes. To our knowledge the results in this paper are the first of their type for this class of models.

Evaluation of Heavy Precipitation Simulated by the WRF Model Using 4D-Var Data Assimilation with TRMM 3B42 and GPM IMERG over the Huaihe River Basin, China

To obtain independent, consecutive, and high-resolution precipitation data, the four-dimensional variational (4D-Var) method was applied to directly assimilate satellite precipitation products into the Weather Research and Forecasting (WRF) model. The precipitation products of the Tropical Rainfall Measuring Mission 3B42 (TRMM 3B42) and its successor, the Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM IMERG) were assimilated in this study. Two heavy precipitation events that occurred over the Huaihe River basin in eastern China were studied. Before assimilation, the WRF model simulations were first performed with different forcing data to select more suitable forcing data and determine the control experiments for the subsequent assimilation experiments. Then, TRMM 3B42 and GPM IMERG were separately assimilated into the WRF. The simulated precipitation results in the outer domain (D01), with a 27-km resolution, and the inner domain (D02), with a 9-km resolution, were evaluated in detail. The assessments showed that (1) 4D-Var with TRMM 3B42 or GPM IMERG could both significantly improve WRF precipitation predictions at a time interval of approximately 12 h; (2) the WRF simulated precipitation assimilated with GPM IMERG outperformed the one with TRMM 3B42; (3) for the WRF output precipitation assimilated with GPM IMERG over D02, which has spatiotemporal resolutions of 9 km and 50 s, the correlation coefficients of the studied events in August and November were 0.74 and 0.51, respectively, at the point and daily scales, and the mean Heidke skill scores for the two studied events both reached 0.31 at the grid and hourly scales. This study can provide references for the assimilation of TRMM 3B42 or GPM IMERG into the WRF model using 4D-Var, which is especially valuable for hydrological applications of GPM IMERG during the transition period from the TRMM era into the GPM era.

Evaluation of Lightning Forecasting Based on One Lightning Parameterization Scheme and Two Diagnostic Methods

Lightning forecasting is a vital item in server convective system short-time forecasting. However, lightning parameterization in mesoscale numerical prediction models is still in its early stages of development. Several lightning parameterization schemes are implemented in the Weather Research and Forecasting (WRF) model. Data assimilation can provide a more accurate initial field, which could be useful for subsequent lightning forecasting. To evaluate its effect on lightning forecasting, a severe convective case that influenced Jiangsu and Anhui Province on 5 June 2009 is utilized and a series of experiments are conducted including assimilating radar reflectivity and lightning location network data via the three-dimensional variational (3DVar) method. Results show that data assimilation can effectively improve reflectivity forecasting and subsequent lightning forecasting. Lightning forecasting based on the PR92 lightning parameterization scheme, which is based on the convective cloud top height, offers a weaker magnitude forecast. The diagnostic method based on reflectivity and temperature has some spatial displacement. The potential forecast provided by lightning threat indexes produced an improvement in Anhui Province, while in other regions, it is located further east than the observation.

Idealized Experiments for Optimizing Model Parameters Using a 4D-Variational Method in an Intermediate Coupled Model of ENSO

Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational (4D-Var) data assimilation system was developed for an intermediate coupled model (ICM) and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer (Te), which is empirically and explicitly related to sea level (SL) variation. The strength of the thermocline effect on SST (referred to simply as “the thermocline effect”) is represented by an introduced parameter, αTe. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Var data assimilation system implemented in the ICM are also discussed.

Reconstructing Large- and Mesoscale Dynamics in the Black Sea Region from Satellite Imagery and Altimetry Data—A Comparison of Two Methods

Two remote sensing methods, satellite altimetry and 4D-Var assimilation of satellite imagery, are used to compute surface velocity fields in the Black Sea region. Surface currents derived from the two methods are compared for several cases with intense mesoscale and large-scale dynamics during low wind conditions. Comparison shows that the obtained results coincide well quantitatively and qualitatively. However, satellite imagery provides more reasonable results on the spatial variability of coastal dynamics than altimetry data. In particular, this is related to the reconstruction of eddy coastal dynamics, such as Black Sea near-shore anticyclones. Current streamlines in these eddies are not closed near the coast in altimetry data, which we relate to the extrapolation during mapping procedure in the absence of coastal along-track measurements. On the other hand, in offshore areas, imagery-derived currents can be underestimated due to the absence of thermal contrasts and smoothing during the procedure of the 4D-Var assimilation. Wind drift currents are another source of inconsistency, as their impact is directly observed in satellite imagery but absent in altimetry data. The advantage of the 4D-Var method for reconstructing coastal dynamics is used to compute surface currents in the Marmara Sea on the base of 250 m resolution Modis optical data. The results reveal the very complex dynamics of the basin, with a large number of mesoscale and sub-mesoscale eddies. 4D-Var assimilation of Modis imagery is used to obtain information about dynamic characteristics of these small eddies with radiuses of 4–10 km.

Nonlinear Least Squares En4DVar to 4DEnVar Methods for Data Assimilation: Formulation, Analysis, and Preliminary Evaluation

Abstract The En4DVar method is designed to combine the flow-dependent statistical covariance information of EnKF into the traditional 4DVar method. However, the En4DVar method is still hampered by its strong dependence on the adjoint model of the underlying forecast model and by its complexity, maintenance requirements, and the high cost of computer implementation and simulation. The primary goal of this paper is to propose an alternative approach to overcome the main difficulty of the En4DVar method caused by the use of adjoint models. The proposed approach, the nonlinear least squares En4DVar (NLS-En4DVar) method, begins with rewriting the standard En4DVar formulation into a nonlinear least squares problem, which is followed by solving the resulting NLS problem by a Gauss–Newton iterative method. To reduce the computational and implementation complexity of the proposed NLS-En4DVar method, a few variants of the new method are proposed; these modifications make the model cheaper and easier to use than the full NLS-En4DVar method at the expense of reduced accuracy. Furthermore, an improved iterative method based on the comprehensive analysis on the above NLSi-En4DVar family of methods is also proposed. These proposed NLSi-En4DVar methods provide more flexible choices of the computational capabilities for the broader and more realistic data assimilation problems arising from various applications. The pros and cons of the proposed NLSi-En4DVar family of methods are further examined in the paper and their relationships and performance are also evaluated by several sets of numerical experiments based on the Lorenz-96 model and the Advanced Research WRF (ARW) Model, respectively.

A case study of aerosol data assimilation with the Community Multi-scale Air Quality Model over the contiguous United States using 3D-Var and optimal interpolation methods

Abstract. This study applies the Gridpoint Statistical Interpolation (GSI) 3D-Var assimilation tool originally developed by the National Centers for Environmental Prediction (NCEP), to improve surface PM2.5 predictions over the contiguous United States (CONUS) by assimilating aerosol optical depth (AOD) and surface PM2.5 in version 5.1 of the Community Multi-scale Air Quality (CMAQ) modeling system. An optimal interpolation (OI) method implemented earlier (Tang et al., 2015) for the CMAQ modeling system is also tested for the same period (July 2011) over the same CONUS. Both GSI and OI methods assimilate surface PM2.5 observations at 00:00, 06:00, 12:00 and 18:00 UTC, and MODIS AOD at 18:00 UTC. The assimilations of observations using both GSI and OI generally help reduce the prediction biases and improve correlation between model predictions and observations. In the GSI experiments, assimilation of surface PM2.5 (particle matter with diameter < 2.5 µm) leads to stronger increments in surface PM2.5 compared to its MODIS AOD assimilation at the 550 nm wavelength. In contrast, we find a stronger OI impact of the MODIS AOD on surface aerosols at 18:00 UTC compared to the surface PM2.5 OI method. GSI produces smoother result and yields overall better correlation coefficient and root mean squared error (RMSE). It should be noted that the 3D-Var and OI methods used here have several big differences besides the data assimilation schemes. For instance, the OI uses relatively big model uncertainties, which helps yield smaller mean biases, but sometimes causes the RMSE to increase. We also examine and discuss the sensitivity of the assimilation experiments' results to the AOD forward operators.

Weak-norm posterior contraction rate of the 4DVAR method for linear severely ill-posed problems

Inspired by the artificial dynamic, we solve the linear severely ill-posed problems based on the 4DVAR method arising in data assimilation. To obtain the consistency of the posterior distribution in the weak norm by a fractional order of the forward operator, we are interested in asymptotic behavior of the weak norm squared posterior contraction (SPCL) function. By assuming exponentially decaying spectrum of the forward operator, the estimate of the SPCL function is established for a Sobolev-like source condition. Such a result is further extended to a general source condition. In both cases, we verify that the severe ill-posedness of the inverse problem can be reduced to moderate ill-posedness by the weak norm.

Assimilating Conventional and Doppler Radar Data with a Hybrid Approach to Improve Forecasting of a Convective System

A hybrid ensemble adjustment Kalman filter—three-dimensional ensemble—variational (EAKF-En3DVar) system is developed to assimilate conventional and radar data, and is applied to a convective case in Colorado and Kansas, USA. The system is based on the framework of the Weather Research and Forecasting model’s three-dimensional variational (3DVar) and Data Assimilation Research Testbed. A two-step assimilation procedure with a shorter length scale and analysis cycle is used to reduce analysis noise in radar data assimilation. Results show that the hybrid experiment assimilating only conventional data improves the quantitative precipitation forecast (QPF) and quantitative reflectivity forecast over those of a 3DVar experiment, and the improvements are also evident after assimilating radar data. The assimilation of radar data substantially improves the QPF up to seven hours, with either the 3DVar or hybrid method. The hybrid experiment assimilating both conventional and radar data forecasts a more accurate convective system in terms of structure, spatial extent and intensity and produces increased low-level cooling and mid-level warming in the convective region. These improvements are attributable to an improved forecast background field of wind, temperature and water vapor mixing ratio, with maximum root mean square error reduction at the tropopause and near the surface.

Effects of 4D-Var Data Assimilation Using Remote Sensing Precipitation Products in a WRF Model over the Complex Terrain of an Arid Region River Basin

Individually, ground-based, in situ observations, remote sensing, and regional climate modeling cannot provide the high-quality precipitation data required for hydrological prediction, especially over complex terrains. Data assimilation techniques can be used to bridge the gap between observations and models by assimilating ground observations and remote sensing products into models to improve precipitation simulation and forecasting. However, only a small portion of satellite-retrieved precipitation products assimilation research has been implemented over complex terrains in an arid region. Here, we used the weather research and forecasting (WRF) model to assimilate two satellite precipitation products (The Tropical Rainfall Measuring Mission: TRMM 3B42 and Fengyun-2D: FY-2D) using the 4D-Var data assimilation method for a typical inland river basin in northwest China’s arid region, the Heihe River Basin, where terrains are very complex. The results show that the assimilation of remote sensing precipitation products can improve the initial WRF fields of humidity and temperature, thereby improving precipitation forecasting and decreasing the spin-up time. Hence, assimilating TRMM and FY-2D remote sensing precipitation products using WRF 4D-Var can be viewed as a positive step toward improving the accuracy and lead time of numerical weather prediction models, particularly over regions with complex terrains.

Improved Prediction of the Indian Ocean Dipole Mode by Use of Subsurface Ocean Observations

Abstract The numerical seasonal prediction system using the Scale Interaction Experiment–Frontier version 1 (SINTEX-F) ocean–atmosphere coupled model has so far demonstrated a good performance for prediction of the Indian Ocean dipole mode (IOD) despite the fact that the system adopts a relatively simple initialization scheme based on nudging only the sea surface temperature (SST). However, it is to be expected that the system is not sufficient to capture in detail the subsurface oceanic precondition. Therefore, the authors have introduced a new three-dimensional variational ocean data assimilation (3DVAR) method that takes three-dimensional observed ocean temperature and salinity into account. Since the new system has successfully improved IOD predictions, the present study is showing that the ocean observational efforts in the tropical Indian Ocean are decisive for improvement of the IOD predictions and may have a large impact on important socioeconomic activities, particularly in the Indian Ocean rim countries.

Evaluating the Role of the EOF Analysis in 4DEnVar Methods

The four-dimensional variational data assimilation (4DVar) method is one of the most popular techniques used in numerical weather prediction. Nevertheless, the needs of the adjoint model and the linearization of the forecast model largely limit the wider applications of 4DVar. 4D ensemble-variational data assimilation methods (4DEnVars) exploit the strengths of the Ensemble Kalman Filter and 4DVar, and use the ensemble trajectories to directly estimate four-dimensional background error covariance. This study evaluates the role of the empirical orthogonal function (EOF) analysis in 4DEnVars. The widely-recognized 4DEnVar method DRP-4DVar (the Dimension-reduced projection 4DVar) is adopted as the representation of EOF analyses in this study. The performance of the Dimension-reduced projection 4DVar (DRP-4DVar), 4DEnVar (i.e., another traditional 4DEnVar scheme without EOF transformation), and the Ensemble Transform Kalman Filter (ETKF) was compared to demonstrate the effect of the EOF analysis in DRP-4DVar. Sensitivity experiments indicate that EOF analyses construct basis vectors in eigenvalue space and the dimension reduction in the DRP-4DVar approach helps improve computational efficiency and analysis accuracy. When compared with 4DEnVar and the ETKF, the DRP-4DVar demonstrates similar analysis root-mean-square error (RMSE) to 4DEnVar, whereas it surpasses the ETKF by 22.3%. In addition, sensitivity experiments of DRP-4DVar on the ensemble size, the assimilation window length, and the standard deviation of the initial perturbation imply that the DRP-4DVar with the optimized EOF truncation number is robust to a wide range of the parameters, but extremely low values should be avoided. The results presented here suggest the potential wide application of EOF analysis in the hybrid 4DEnVar methods.

Comparison between 3D-Var and 4D-Var data assimilation methods for the simulation of a heavy rainfall case in central Italy

Abstract. This work aims to provide a comparison between three dimensional and four dimensional variational data assimilation methods (3D-Var and 4D-Var) for a heavy rainfall case in central Italy. To evaluate the impact of the assimilation of reflectivity and radial velocity acquired from Monte Midia Doppler radar into the Weather Research Forecasting (WRF) model, the quantitative precipitation forecast (QPF) is used.The two methods are compared for a heavy rainfall event that occurred in central Italy on 14 September 2012 during the first Special Observation Period (SOP1) of the HyMeX (HYdrological cycle in Mediterranean EXperiment) campaign. This event, characterized by a deep low pressure system over the Tyrrhenian Sea, produced flash floods over the Marche and Abruzzo regions, where rainfall maxima reached more than 150 mm 24 h−1.To identify the best QPF, nine experiments are performed using 3D-Var and 4D-Var data assimilation techniques. All simulations are compared in terms of rainfall forecast and precipitation measured by the gauges through three statistical indicators: probability of detection (POD), critical success index (CSI) and false alarm ratio (FAR). The assimilation of conventional observations with 4D-Var method improves the QPF compared to 3D-Var. In addition, the use of radar measurements in 4D-Var simulations enhances the performances of statistical scores for higher rainfall thresholds.

Estimation of the Tropical Pacific Ocean State 2010–13

AbstractA data-assimilating ⅓° regional dynamical ocean model is evaluated on its ability to synthesize components of the Tropical Pacific Ocean Observing System. The four-dimensional variational data assimilation (4DVAR) method adjusts initial conditions and atmospheric forcing for overlapping 4-month model runs, or hindcasts, that are then combined to give an ocean state estimate for the period 2010–13. Consistency within uncertainty with satellite SSH and Argo profiles is achieved. Comparison to independent observations from Tropical Atmosphere Ocean (TAO) moorings shows that for time scales shorter than 100 days, the state estimate improves estimates of TAO temperature relative to an optimally interpolated Argo product. The improvement is greater at time scales shorter than 20 days, although unpredicted variability in the TAO temperatures implies that TAO observations provide significant information in that band. Larger discrepancies between the state estimate and independent observations from Spray gliders deployed near the Galápagos, Palau, and Solomon Islands are attributed to insufficient model resolution to capture the dynamics in strong current regions and near coasts. The sea surface height forecast skill of the model is assessed. Model forecasts using climatological forcing and boundary conditions are more skillful than climatology out to 50 days compared to persistence, which is a more skillful forecast than climatology out to approximately 20 days. Hindcasts using reanalysis products for atmospheric forcing and open boundary conditions are more skillful than climatology for approximately 120 days or longer, with the exact time scale depending on the accuracy of the state estimate used for initializing and on the reanalysis forcing. Estimating the model representational error is a goal of these experiments.

A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 2: Optimization scheme and identical twin experiment of atmospheric CO<sub>2</sub> inversion

Abstract. A four-dimensional variational method (4D-Var) is a popular technique for source/sink inversions of atmospheric constituents, but it is not without problems. Using an icosahedral grid transport model and the 4D-Var method, a new atmospheric greenhouse gas (GHG) inversion system has been developed. The system combines offline forward and adjoint models with a quasi-Newton optimization scheme. The new approach is then used to conduct identical twin experiments to investigate optimal system settings for an atmospheric CO2 inversion problem, and to demonstrate the validity of the new inversion system. In this paper, the inversion problem is simplified by assuming the prior flux errors to be reasonably well known and by designing the prior error correlations with a simple function as a first step. It is found that a system of forward and adjoint models with smaller model errors but with nonlinearity has comparable optimization performance to that of another system that conserves linearity with an exact adjoint relationship. Furthermore, the effectiveness of the prior error correlations is demonstrated, as the global error is reduced by about 15 % by adding prior error correlations that are simply designed when 65 weekly flask sampling observations at ground-based stations are used. With the optimal setting, the new inversion system successfully reproduces the spatiotemporal variations of the surface fluxes, from regional (such as biomass burning) to global scales. The optimization algorithm introduced in the new system does not require decomposition of a matrix that establishes the correlation among the prior flux errors. This enables us to design the prior error covariance matrix more freely.