# Atmospheric State

The observation and representation in general circulation models (GCMs) of cloud vertical overlap is the object of active research due to its impact on the Earth radiative budget. Previous studies have found that vertically contiguous cloudy layers show a maximum overlap between layers up to several kilometers apart but tend towards a random overlap as separations increase. The decorrelation length-scale that characterizes the progressive transition from maximum to random overlap changes from one location and season to another and thus may be influenced by large-scale vertical motion, wind shear or convection. Observations from the U.S. Department of Energy Atmospheric Radiation Measurement Program ground-based radars and lidars in midlatitude and tropical locations in combination with reanalysis meteorological fields are used to evaluate how dynamics and atmospheric state influence cloud overlap. For midlatitude winter months, strong synoptic scale upward motion maintains conditions closer to maximum overlap at large separations. In the tropics, overlap becomes closer to maximum as convective stability decreases. In midlatitude subsidence and tropical convectively stable situations, where a smooth transition from maximum to random overlap is found on average, large wind shears sometimes favor minimum overlap. Precipitation periods are discarded from the analysis but, when included, maximum overlap occurs more often at large separations. The results suggest that a straightforward modification of the existing GCM mixed maximum-random overlap parameterization approach that accounts for environmental conditions can capture much of the important variability and is more realistic than approaches only based on an exponential decay transition from maximum to random overlap.

## atmospheric state

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The sensitivity of model forecast within data assimilation cycles to the parameter values, and the issue of solution uniqueness of the estimation problem, are examined. The ensemble square root filter (EnSRF) is employed for model state estimation. Sensitivity experiments show that the errors in the microphysical parameters have a larger impact on model microphysical fields than on wind fields; radar reflectivity observations are therefore preferred over those of radial velocity for microphysical parameter estimation. The model response time to errors in individual parameters are also investigated. The results suggest that radar data should be used at about 5-min intervals for parameter estimation. The response functions calculated from ensemble mean forecasts for all five individual parameters show concave shapes, with unique minima occurring at or very close to the true values; therefore, true values of these parameters can be retrieved at least in those cases where only one parameter contains error.

The accuracy of numerical weather prediction (NWP) depends very much on the accuracy of the initial state estimation and the accuracy of the prediction model. Various advanced data assimilation techniques have been developed in the recent decades that improve the estimation of model initial conditions. Among these methods are four-dimensional variational data assimilation (4DVAR; Le Dimet and Talagrand 1986; Courtier and Talagrand 1987) and the ensemble-based assimilation methods (Evensen 1994; Evensen and van Leeuwen 1996; Burgers et al. 1998; Houtekamer and Mitchell 1998; Anderson 2001; Bishop et al. 2001; Whitaker and Hamill 2002; Evensen 2003; Tippett et al. 2003), which have the advantage of closely involving a numerical model in the data assimilation process. However, errors in the model can directly affect the effectiveness of these data assimilation methods.

Because of many assumptions involved, the microphysical parameterization can be a significant source of model error for convective-scale data assimilation and prediction. Parameter estimation is a common approach to dealing with model error associated with uncertain parameters. The inverse problem of parameter estimation concerns the optimal determination of the parameter by observing the dependent variable(s) collected in the spatial and time domains (Yeh 1986). Various methods have been used for parameter estimation, among which variational parameter estimation with an adjoint model is popular in the literature of meteorology and oceanography (Navon 1998). The ensemble Kalman filter method (hereafter EnKF) has recently been tested successfully for the atmospheric state estimation at the convective scale with simulated (Snyder and Zhang 2003; Zhang et al. 2004; Tong and Xue 2005; Xue et al. 2006) and real (Dowell et al. 2004; Tong 2006) radar data. The results with simulated data, under the perfect model assumption, have been excellent, while the quality of state estimation with real data, when model error inevitably exists, is generally not as good. More recently, Aksoy et al. (2006) used EnKF for the simultaneous estimation of state variables and up to six parameters in a relatively simple two-dimensional sea-breeze model with encouraging success.

In this study, we set out to investigate the ability of the EnKF in correcting the errors in some of the fundamental parameters in model microphysics, where complex process interactions and high nonlinearities usually exist. In the framework of EnKF, parameter estimation is realized by treating the uncertain parameters as independent model variables and using the covariance information sampled from the ensemble to estimate the parameters given available observations (Anderson 2001). This is often referred to as state vector augmentation technique where the model parameters are considered part of the augmented state vector. Model state variables and parameters are estimated simultaneously, through continuous assimilation cycles. The latest estimation will be used for subsequent forecast.

Although sophisticated microphysical schemes are attractive and represent the future direction of convective-scale modeling and NWP, they are expensive and much research is still needed on the treatment of processes involving the additional moments before they can be widely used. The increased number of prognostic variables in the model also poses a larger challenge for state estimation or model initialization. The single-moment bulk schemes are widely used in current research and operational models; the ultimate goal of our current line of study is therefore to overcome, to the extent possible, the shortcomings of such single-moment schemes by constraining uncertain microphysical parameters using data, that is, by estimating the parameters as well as the model state variables using radar observations of the convective storms.

The sensitivity analysis in this part and the parameter estimation in Part II are based on a simulated supercell storm. The configurations of the forecast model and truth simulation are mostly inherited from Tong and Xue (2005, hereafter TX05). Briefly, the ARPS (Xue et al. 2000, 2001, 2003), a fully compressible and nonhydrostatic atmospheric prediction system, is used. The truth simulation is initialized from a modified observed supercell sounding as used in Xue et al. (2001). The LFO83 ice microphysics and 1.5-order turbulent kinetic energy (TKE)-based subgrid-scale turbulence schemes are the only physics options included. The model domain is 64 km 64 km 16 km in size. The horizontal grid spacing is 2 km and the vertical grid spacing is 0.5 km. A 4-K ellipsoidal thermal bubble centered at x = 48 km, y = 16 km, and z = 1.5 km, with radii of 10 km in the x and y directions and 1.5 km in the z direction is used to initiate the storm. The length of simulation is up to 3 h. The assumed true parameter values, which are the default values of the LFO83 scheme, are used in the truth simulation (Table 1).

The ensemble-based forecast and assimilation results are sensitive to the realization of the initial ensemble perturbations. To increase the robustness of the results to be presented in this paper, we performed five parallel sets of experiments, with the only difference being the initialization of ensembles. All the response functions shown in this paper are averaged over the five parallel sets of experiments. The results of the CNTL data assimilation experiments are first presented to show the behavior of the EnKF state estimation without parameter error.

In Part II, the details of the simultaneous estimation of the microphysical parameters and model state variables using the EnSRF algorithm from radar data will be presented. The sensitivity analysis and parameter identifiability discussed here will guide us with the experiment design and help us understand the results of estimation. The parameter identifiability issue will be further discussed there based on the estimation results. 041b061a72