[1] The adjoint and tangent linear models in the traditional four-dimensional variational data assimilation (4DVAR) are difficult to obtain if the forecast model is highly nonlinear or the model physics contains parameterized discontinuities. A new method (referred to as POD-E4DVAR) is proposed in this paper by merging the Monte Carlo method and the proper orthogonal decomposition (POD) technique into 4DVAR to transform an implicit optimization problem into an explicit one. The POD method is used to efficiently approximate a forecast ensemble produced by the Monte Carlo method in a 4-dimensional (4-D) space using a set of base vectors that span the ensemble and capture its spatial structure and temporal evolution. After the analysis variables are represented by a truncated expansion of the base vectors in the 4-D space, the control (state) variables in the cost function appear explicit so that the adjoint model, which is used to derive the gradient of the cost function with respect to the control variables in the traditional 4DVAR, is no longer needed. The application of this new technique significantly simplifies the data assimilation process and retains the two main advantages of the traditional 4DVAR method. Assimilation experiments show that this ensemble-based explicit 4DVAR method performs much better than the traditional 4DVAR and ensemble Kalman filter (EnKF) method. It is also superior to another explicit 4DVAR method, especially when the forecast model is imperfect and the forecast error comes from both the noise of the initial field and the uncertainty in the forecast model. Computational costs for the new POD-E4DVAR are about twice as the traditional 4DVAR method but 5% less than the other explicit 4DVAR and much lower than the EnKF method. Another assimilation experiment conducted within the Lorenz model indicates potential wider applications of this new POD-E4DVAR method.

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.

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A B S T R A C T This paper presents a novel non-linear least squares enhanced proper orthogonal decomposition (POD)-based 4DVar algorithm (referred as NLS-4DVar) for the non-linear ensemble-based 4DVar. In the algorithm, the GaussÁNewton iterative method is employed to handle the non-quadratic non-linearity of the 4DVar cost function while the overall structure of the algorithm still resembles the original POD-4DVar algorithm. It is proved that the original POD-4DVar algorithm is a special case of the proposed NLS-4DVar algorithm under the assumption of the linear relationship between the model perturbations (MPs) and the simulated observation perturbations (OPs). Under the assumption it is also shown that the solution of POD-4DVar algorithm coincides with the solution of the proposed NLS-4DVar algorithm. On the contrary, if the linear relationship assumption is dropped, the solution of the POD-4DVar algorithm is only the first iteration of the proposed NLS-4DVar algorithm. As a result, our analysis provides an explanation for the degraded and inaccurate performance of the POD-4DVar algorithm when the underlying forecast model or (and) the observation operator is strongly non-linear. The potential merits and advantages of the proposed NLS-4DVar are demonstrated by a group of Observing System Simulation Experiments with Advanced Research WRF (ARW) using accumulated rainfall-observations.

Abstract. Satellite retrievals of the column-averaged dry air mole fractions of CO2 (XCO2) could help to improve carbon flux estimation due to their good spatial coverage. In this study, in order to assimilate the GOSAT (Greenhouse Gases Observing Satellite) XCO2 retrievals, the Global Carbon Assimilation System (GCAS) is upgraded with new assimilation algorithms, procedures, a localization scheme, and a higher assimilation parameter resolution. This upgraded system is referred to as GCASv2. Based on this new system, the global terrestrial ecosystem (BIO) and ocean (OCN) carbon fluxes from 1 May 2009 to 31 December 2015 are constrained using the GOSAT ACOS (Atmospheric CO2 Observations from Space) XCO2 retrievals (Version 7.3). The posterior carbon fluxes from 2010 to 2015 are independently evaluated using CO2 observations from 52 surface flask sites. The results show that the posterior carbon fluxes could significantly improve the modeling of atmospheric CO2 concentrations, with global mean bias decreases from a prior value of 1.6 ± 1.8 ppm to −0.5 ± 1.8 ppm. The uncertainty reduction (UR) of the global BIO flux is 17 %, and the highest monthly regional UR could reach 51 %. Globally, the mean annual BIO and OCN carbon sinks and their interannual variations inferred in this study are very close to the estimates of CarbonTracker 2017 (CT2017) during the study period, and the inferred mean atmospheric CO2 growth rate and its interannual changes are also very close to the observations. Regionally, over the northern lands, the strongest carbon sinks are seen in temperate North America, followed by Europe, boreal Asia, and temperate Asia; in the tropics, there are strong sinks in tropical South America and tropical Asia, but a very weak sink in Africa. This pattern is significantly different from the estimates of CT2017, but the estimated carbon sinks for each continent and some key regions like boreal Asia and the Amazon are comparable or within the range of previous bottom-up estimates. The inversion also changes the interannual variations in carbon fluxes in most TransCom land regions, which have a better relationship with the changes in severe drought area (SDA) or leaf area index (LAI), or are more consistent with previous estimates for the impact of drought. These results suggest that the GCASv2 system works well with the GOSAT XCO2 retrievals and shows good performance with respect to estimating the surface carbon fluxes; meanwhile, our results also indicate that the GOSAT XCO2 retrievals could help to better understand the interannual variations in regional carbon fluxes.

As well as their importance to nutrition, fatty acids (FA) represent a unique group of quorum sensing chemicals that modulate the behavior of bacterial population in virulence. However, the way in which full-length, membrane-bound receptors biochemically detect FA remains unclear. Here, we provide genetic, enzymological and biophysical evidences to demonstrate that in the phytopathogenic bacterium Xanthomonas campestris pv. campestris, a medium-chain FA diffusible signal factor (DSF) binds directly to the N-terminal, 22 amino acid-length sensor region of a receptor histidine kinase (HK), RpfC. The binding event remarkably activates RpfC autokinase activity by causing an allosteric change associated with the dimerization and histidine phosphotransfer (DHp) and catalytic ATP-binding (CA) domains. Six residues were found essential for sensing DSF, especially those located in the region adjoining to the inner membrane of cells. Disrupting direct DSF-RpfC interaction caused deficiency in bacterial virulence and biofilm development. In addition, two amino acids within the juxtamembrane domain of RpfC, Leu172 and Ala178, are involved in the autoinhibition of the RpfC kinase activity. Replacements of them caused constitutive activation of RpfC-mediated signaling regardless of DSF stimulation. Therefore, our results revealed a biochemical mechanism whereby FA activates bacterial HK in an allosteric manner, which will assist in future studies on the specificity of FA-HK recognition during bacterial virulence regulation and cell-cell communication.

[1] To overcome the difficulties in determining the optimal parameters needed for a radiative transfer model (RTM), which acts as the observational operator in a land data assimilation system, we have designed a dual-pass assimilation (DP-En4DVar) framework to optimize the model state (volumetric soil moisture content) and model parameters simultaneously using the gridded Advanced Microwave Scanning Radiometer-EOS (AMSR-E) satellite brightness temperature data. This algorithm embeds a dual-pass (the state assimilation pass and the parameter optimization pass) optimization technique based on an ensemble-based four-dimensional variational assimilation method and a shuffled complex evolution approach (SCE-UA). The SCE-UA method optimizes the parameters using observational information, thereby leading to improved simulations. The RTM is used to estimate brightness temperature from surface temperature and soil moisture. This algorithm is implemented differently in two phases: the parameter calibration phase and the pure assimilation phase. Both passes are applied in each assimilation time window during the parameter calibration phase. However, only the state assimilation pass is used in the pure assimilation phase after the parameters are determined during the parameter calibration phase. Several experiments conducted using this framework coupled partially with a land surface model (the NCAR CLM3) show that volumetric soil moisture content can be significantly improved to be comparable with in situ observations by assimilating only daily satellite brightness temperature. Furthermore, the improvement in surface soil moisture also propagates to lower layers where no observations are available.Citation: Tian, X., Z. Xie, A. Dai, C. Shi, B. Jia, F. Chen, and K. Yang (2009), A dual-pass variational data assimilation framework for estimating soil moisture profiles from AMSR-E microwave brightness temperature,

[1] To make use of satellite microwave observations for estimating soil moisture, a dual-pass land data assimilation system (DLDAS) is developed in this paper by incorporating a dual-pass assimilation framework into the Community Land Model version 3 (CLM3). In the DLDAS, the model state (volumetric soil moisture content) and model parameters are jointly optimized using the gridded Advanced Microwave Scanning Radiometer-EOS (AMSR-E) satellite brightness temperature (T b ) data through a radiative transfer model (RTM), which acts as an observation operator to provide a link between the model states and the observational variable (i.e., Tb). The DLDAS embeds a state assimilation pass and a parameter calibration pass. In the assimilation pass, the whole soil moisture profiles are assimilated from the T b data using an ensemble-based four-dimensional variational assimilation method (En4DVar). Simultaneously, several key parameters in the RTM are also optimized using the ensemble Proper Orthogonal Decomposition-based parameter calibration approach (EnPOD_P) in the parameter optimization pass to account for their high variability or uncertainty. To quantify the impacts of the T b assimilation on CLM3-calculated soil moisture, the original CLM3 (Sim) and the DLDAS (Ass) were run separately over China on a 0.5°grid forced with identical, observation-based atmospheric forcing from 2004 to 2008. Soil moisture data from 226 stations over China are averaged over seven different climate divisions and compared with the soil moisture from the Sim and Ass runs. It is found that the assimilation of the AMSR-E T b data through the DLDAS greatly improves the soil moisture content within the top 10 cm with reduced mean biases and enhanced correlations with the station data in all divisions except for southwest China, where the current satellite sensors may have difficulties in measuring soil moisture due to the dense vegetation and complex terrain over this region. The results suggest that the AMSR-E T b data can be used to improve soil moisture simulations over many regions and the DLDAS is a promising new tool for estimating soil moisture content from satellite T b data.