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T. Vukicevic and D. Posselt

Abstract

In this study, the relationship between nonlinear model properties and inverse problem solutions is analyzed using a numerical technique based on the inverse problem theory formulated by Mosegaard and Tarantola. According to this theory, the inverse problem and solution are defined via convolution and conjunction of probability density functions (PDFs) that represent stochastic information obtained from the model, observations, and prior knowledge in a joint multidimensional space. This theory provides an explicit analysis of the nonlinear model function, together with information about uncertainties in the model, observations, and prior knowledge through construction of the joint probability density, from which marginal solution functions can then be evaluated. The numerical analysis technique derived from the theory computes the component PDFs in discretized form via a combination of function mapping on a discrete grid in the model and observation phase space and Monte Carlo sampling from known parametric distributions. The efficacy of the numerical analysis technique is demonstrated through its application to two well-known simplified models of atmospheric physics: damped oscillations and Lorenz’s three-component model of dry cellular convection. The major findings of this study include the following: (i) Use of a nonmonotonic forward model in the inverse problem gives rise to the potential for a multimodal posterior PDF, the realization of which depends on the information content of the observations and on observation and model uncertainties. (ii) The cumulative effect of observations over time, space, or both could render the final posterior PDF unimodal, even with the nonmonotonic forward model. (iii) A greater number of independent observations are needed to constrain the solution in the case of a nonmonotonic nonlinear model than for a monotonic nonlinear or linear forward model for a given number of degrees of freedom in control parameter space. (iv) A nonlinear monotonic forward model gives rise to a skewed unimodal posterior PDF, implying a well-posed maximum likelihood inverse problem. (v) The presence of model error greatly increases the possibility of capturing multiple modes in the posterior PDF with the nonmonotonic nonlinear model. (vi) In the case of a nonlinear forward model, use of a Gaussian approximation for the prior update has a similar effect to an increase in model error, which indicates there is the potential to produce a biased mean central estimate even when observations and model are unbiased.

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T. Vukicevic, M. Sengupta, A. S. Jones, and T. Vonder Haar

Abstract

This study addresses the problem of four-dimensional (4D) estimation of a 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 the 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 the study of the assimilation of the Geostationary Operational Environmental Satellite (GOES) imager observations into a cloud-resolving model with explicit bulk cloud microphysical parameterization. A new 4D variational data assimilation (4DVAR) research system with the cloud-resolving capability is applied to a case of a multilayered 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 Atmospheric Radiation Measurement (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 thick ice clouds is not influenced by the IR window observations. The assimilation results clearly demonstrate that increasing the observational constraint from individual to combined channel measurements and from less to more frequent observation times systematically improves the assimilation results. The experiments with the model error indicate that the current specification of this error in the form of a generic linear forcing, which was adopted from other data assimilation studies, is not suitable for the cloud-resolving data assimilation. Instead, a parameter estimation approach may need to be explored in the future. The experiments with varying decorrelation lengths suggest the need to use the model horizontal grid spacing that is several times smaller than the GOES imager native resolution to achieve equivalent spatial variability in the assimilation.

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T. Vukicevic, T. Greenwald, M. Zupanski, D. Zupanski, T. Vonder Haar, and A. S. Jones

Abstract

This study focuses on cloudy atmosphere state estimation from high-resolution visible and infrared satellite remote sensing measurements and a mesoscale model with explicit cloud prediction. The cloud state is defined as 3D spatially distributed hydrometeors characterized with microphysical properties: mixing ratio, number concentration, and size distribution. The Geostationary Operational Environmental Satellite-9 (GOES-9) imager visible and infrared measurements were used in a new four-dimensional variational data assimilation (4DVAR) mesoscale algorithm for a warm continental stratus cloud system case to test the impact of these observations on the cloud simulation. The new data assimilation algorithm includes the Regional Atmospheric Modeling System (RAMS) with explicit cloud state prediction, the associated adjoint system, and an observational operator for forward and adjoint integrations of the GOES radiances. The results show positive impact of GOES imager measurements on the 3D cloud short-term simulation during and after the assimilation. The impact was achieved through sensitivity of the radiances to the cloud droplet mixing ratio at observation time and a 4D correlation between the cloud and atmospheric thermal and dynamical environment in the forecast model. The dynamical response to the radiance observations was through enhanced large mesoscale vertical mixing while horizontal advection was weak in the case of stable continental stratus evolution.

Although the current experiments show measurable positive impact of the cloudy radiance measurements on the stratus cloud simulation, they clearly suggest the need to further address the problem of negative cloud cover forecast errors. These errors were only weakly corrected in the current study because of the small sensitivity of the visible and infrared window radiances to the cloud-free atmosphere.

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T. Koyama, T. Vukicevic, M. Sengupta, T. Vonder Haar, and A. S. Jones

Abstract

Information content analysis of the Geostationary Operational Environmental Satellite (GOES) sounder observations in the infrared was conducted for use in satellite data assimilation. Information content is defined as a first-order response of the top-of-atmosphere brightness temperature to perturbations of simulated temperature and humidity profiles, obtained from a cloud-resolving model, both in the presence and absence of clouds. Sensitivity to the perturbations was numerically evaluated using an observational operator for visible and infrared radiative transfer developed within a research satellite data assimilation system. The vertical distribution of the sensitivities was analyzed as a function of cloud optical thickness covering the range from a cloud-free scene to an optically thick cloud. The clear-sky sensitivities to temperature and humidity perturbations for each channel are representative of the corresponding channel weighting functions for a clear-sky case. For optically thin–moderate ice clouds, the vertical distributions of the sensitivities resemble clear-sky results, indicating that the use of infrared sounding observations in data assimilation can potentially improve temperature and humidity profiles below those clouds. This result is significant, as GOES infrared sounder data have until now only been used in cloud-cleared scenes. It is expected that the use of sounder data in data assimilation, even in the presence of optically thin to moderate high clouds, will help reduce errors in temperature and water vapor mixing ratio profiles below the clouds.

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