Carbon flux bias estimation employing Maximum Likelihood Ensemble Filter (MLEF)

We evaluate the capability of an ensemble based data assimilation approach, referred to as Maximum Likelihood Ensemble Filter (MLEF), to estimate biases in the CO2 photosynthesis and respiration fluxes. We employ an off-line Lagrangian Particle Dispersion Model (LPDM), which is driven by the carbon fluxes, obtained from the Simple Biosphere - Regional Atmospheric Modeling System (SiB-RAMS). The SiB-RAMS carbon fluxes are assumed to have errors in the form of multiplicative biases. Our goal is to estimate and reduce these biases and also to assign reliable posterior uncertainties to the estimated biases. Experiments of this study are performed using simulated CO2 observations, which resemble real CO2 concentrations from the Ring of Towers in northern Wisconsin. We evaluate the MLEF results with respect to the 'truth' and the Kalman Filter (KF) solution. The KF solution is considered theoretically optimal for the problem of this study, which is a linear data assimilation problem involving Gaussian errors. We also evaluate the impact of forecast error covariance localization based on a new 'distance' defined in the space of information measures. Experimental results are encouraging, indicating that the MLEF can successfully estimate carbon flux biases and their uncertainties. As expected, the estimated biases are closer to the 'true' biases in the experiments with more ensemble members and more observations. The data assimilation algorithm has a stable performance and converges smoothly to the KF solution when the ensemble size approaches the size of the model state vector (i.e., the control variable of the data assimilation problem

Development of a hybrid variational-ensemble data assimilation technique for observed lightning tested in a mesoscale model

Abstract. Lightning measurements from the Geostationary Lightning Mapper (GLM) that will be aboard the Geostationary Operational Environmental Satellite – R Series will bring new information that can have the potential for improving the initialization of numerical weather prediction models by assisting in the detection of clouds and convection through data assimilation. In this study we focus on investigating the utility of lightning observations in mesoscale and regional applications suitable for current operational environments, in which convection cannot be explicitly resolved. Therefore, we examine the impact of lightning observations on storm environment. Preliminary steps in developing a lightning data assimilation capability suitable for mesoscale modeling are presented in this paper. World Wide Lightning Location Network (WWLLN) data was utilized as a proxy for GLM measurements and was assimilated with the Maximum Likelihood Ensemble Filter, interfaced with the Nonhydrostatic Mesoscale Model core of the Weather Research and Forecasting system (WRF-NMM). In order to test this methodology, regional data assimilation experiments were conducted. Results indicate that lightning data assimilation had a positive impact on the following: information content, influencing several dynamical variables in the model (e.g., moisture, temperature, and winds), and improving initial conditions during several data assimilation cycles. However, the 6 h forecast after the assimilation did not show a clear improvement in terms of root mean square (RMS) errors. </jats:p

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods

An ensemble data assimilation system to estimate CO2 surface fluxes from atmospheric trace gas observations

We present a data assimilation system to estimate surface fluxes of CO2 and other trace gases from observations of their atmospheric abundances. The system is based on ensemble data assimilation methods under development for Numerical Weather Prediction (NWP) and is the first of its kind to be used for CO2 flux estimation. The system was developed to overcome computational limitations encountered when a large number of observations are used to estimate a large number of unknown surface fluxes. The ensemble data assimilation approach is attractive because it returns an approximation of the covariance, does not need an adjoint model or other linearization of the observation operator, and offers the possibility to optimize fluxes of chemically active trace gases (e.g., CH4, CO) in the same framework. We assess the performance of this new system in a pseudodata experiment that resembles the real problem we will apply this system to. The sensitivity of the method to the choice of several parameters such as the assimilation window size and the number of ensemble members is investigated. We conclude that the system is able to provide satisfactory flux estimates for the relatively large scales resolved by our current observing network and that the loss of information in the approximated covariances is an acceptable price to pay for the efficient computation of a large number of surface fluxes. The full potential of this data assimilation system will be used for near–real time operational estimates of North American CO2 fluxes. This will take advantage of the large amounts of atmospheric data that will be collected by NOAA-CMDL in conjunction with the implementation of the North American Carbon Program (NACP)

The maximum likelihood ensemble filter performances in chaotic systems

The performance of the maximum likelihood ensemble filter (MLEF), is investigated in the context of generic systems featuring the essential ingredients of unstable dynamics and on a spatially extended system displaying chaos. The main objective is to clarify the response of the filter to different regimes of motion and highlighting features which may help its optimization in more realistic applications. It is found that, in view of the minimization procedure involved in the filter analysis update, the algorithm provides accurate estimates even in the presence of prominent non-linearities. Most importantly, the filter ensemble size can be designed in connection to the properties of the system attractor (Kaplan–Yorke dimension), thus facilitating the filter setup and limiting the computational cost by using an optimal ensemble. As a corollary, this latter finding indicates that the ensemble perturbations in the MLEF reflect the intrinsic system error dynamics rather than a sampling of realizations of an unknown error covariance

A simplified method for the detection of convection using high resolution imagery from GOES-16

Abstract. The ability to detect convective regions and assimilating the proper heating in these regions is the most important skill in forecasting severe weather systems. Since radars are most directly related to precipitation and are available in high temporal resolution, their data are often used for both detecting convection and estimating latent heating. However, radar data are limited to land areas, largely in developed nations, and early convection is not detectable from radars until drops become large enough to produce significant echoes. Visible and Infrared sensors on a geostationary satellite can provide data that are less sensitive to drop size, but they also have shortcomings: their information is almost exclusively from the cloud top. Relatively new geostationary satellites, GOES-16 and GOES-17, along with Himawari-8, can make up for some of this lack of vertical information through the use of very high spatial and temporal resolutions. This study develops two algorithms to detect convection at different life stages using 1-minute GOES-16 ABI data. Two case studies are used to explain the two methods, followed by results applied to one month of data over the contiguous United States. Vertically growing clouds in early stages were detected using decreases in brightness temperatures over ten minutes. Of the detected clouds, the method correctly identifies 71.0 % to be convective. For mature convective clouds which no longer show decreases in brightness temperature, the lumpy texture, and rapid temporal evolution can be observed using 1-minute high spatial resolution reflectance data. The algorithm that uses texture and evolution for mature convection detects with an accuracy of 85.8 %. 54.7 % of clouds that are identified as convective by the ground-based radars are missed by the satellite. These convective clouds are largely under optically thick cloud shields. </jats:p

A simplified method for the detection of convection using high-resolution imagery from GOES-16

Abstract. The ability to detect convective regions and to add latent heating to drive convection is one of the most important additions to short-term forecast models such as National Oceanic and Atmospheric Administration's (NOAA's) High-Resolution Rapid Refresh (HRRR) model. Since radars are most directly related to precipitation and are available in high temporal resolution, their data are often used for both detecting convection and estimating latent heating. However, radar data are limited to land areas, largely in developed nations, and early convection is not detectable from radars until drops become large enough to produce significant echoes. Visible and infrared sensors on a geostationary satellite can provide data that are more sensitive to small droplets, but they also have shortcomings: their information is almost exclusively from the cloud top. Relatively new geostationary satellites, Geostationary Operational Environmental Satellite-16 and Satellite-17 (GOES-16 and GOES-17), along with Himawari-8, can make up for this lack of vertical information through the use of very high spatial and temporal resolutions, allowing better observation of bubbling features on convective cloud tops. This study develops two algorithms to detect convection at vertically growing clouds and mature convective clouds using 1 min GOES-16 Advanced Baseline Imager (ABI) data. Two case studies are used to explain the two methods, followed by results applied to 1 month of data over the contiguous United States. Vertically growing clouds in early stages are detected using decreases in brightness temperatures over 10 min. For mature convective clouds which no longer show much of a decrease in brightness temperature, the lumpy texture from rapid development can be observed using 1 min high spatial resolution reflectance data. The detection skills of the two methods are validated against Multi-Radar/Multi-Sensor System (MRMS), a ground-based radar product. With the contingency table, results applying both methods to 1-month data show a relatively low false alarm rate of 14.4 % but missed 54.7 % of convective clouds detected by the radar product. These convective clouds were missed largely due to less lumpy texture, which is mostly caused by optically thick cloud shields above. </jats:p

Latent heating profiles from GOES-16 and its impacts on precipitation forecasts

Abstract. Latent heating (LH) is an important quantity in both weather forecasting and climate analysis, being the essential factor driving convective systems. Yet, inferring LH rates from our current observing systems is challenging at best. For climate studies, LH has been retrieved from the Precipitation Radar on the Tropical Rainfall Measuring Mission (TRMM) using model simulations in the look-up table (LUT) that relates instantaneous radar profiles to corresponding heating profiles. These radars, first on TRMM and then Global Precipitation Measurement Mission (GPM), provide a continuous record of LH. However, temporal resolution is too coarse to have a significant impacts on forecast models. In operational forecast models such as High-Resolution Rapid Refresh, convection is initiated from LH derived from ground based radar. Despite the high spatial and temporal resolution of ground-based radars, one disadvantage of using these sources is that its data are only available over well observed land areas. This study develops a method to derive LH from the Geostationary Operational Environmental Satellite-16 (GOES-16) in near-real time. Even though the visible and infrared channels on the Advanced Baseline Imager (ABI) provide mostly cloud top information, rapid changes in cloud top visible and infrared properties, when formulated as a LUT similar to those used by the TRMM and GPM radars, can equally be used to derive LH profiles for convective regions based on model simulations with a convective classification scheme and channel 14 (11.2 μm) brightness temperatures. Convective regions detected by GOES-16 are assigned LH from the LUT, and they are compared with LH from the Next Generation Weather Radar (NEXRAD) and one of the Dual-frequency Precipitation Radar (DPR) products, the Goddard Convective-Stratiform Heating (CSH). LH obtained from GOES-16 show similar magnitude with NEXRAD and CSH, and vertical distribution of LH is also very similar with CSH. One month analysis of total LH from convective clouds from GOES-16 and NEXRAD shows good correlation between the two products. Finally LH profiles from GOES-16 and NEXRAD are applied to WRF simulations for convective initiation and their results are compared to investigate their impacts in precipitation forecasts. Results show that LH from GOES-16 have similar impacts as NEXRAD, and improves the forecast significantly. </jats:p