A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general purpose nonhydrostatic compressible model is used with the inclusion of complex multi-class ice microphysics. New aspects compared to previous studies include the demonstration of the ability of EnKF method in retrieving multiple microphysical species associated with a multi-class ice microphysics scheme, and in accurately retrieving the wind and thermodynamic variables. Also new are the inclusion of reflectivity observations and the determination of the relative role of radial velocity and reflectivity data as well as their spatial coverage in recovering the full flow and cloud fields. In general, the system is able to reestablish the model storm extremely well after a number of assimilation cycles, and best results are obtained when both radial velocity and reflectivity data, including reflectivity information outside precipitation regions, are used. Significant positive impact of the reflectivity assimilation

The possibility of estimating fundamental parameters common in single-moment ice microphysics schemes using radar observations is investigated for a model-simulated supercell storm by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, snow, and hail/graupel, and the bulk densities of snow and hail/graupel. These parameters are closely involved in the definition of drop/particle size distributions of microphysical species but often assume highly uncertain specified values. 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

Abstract. We have extended the 3-D ocean based “Grid ENabled Integrated Earth system model ” (GENIE-1) to help understand the role of ocean biogeochemistry and marine sediments in the long-term (∼100 to 100 000 year) regulation of atmospheric CO2, and the importance of feedbacks between CO2 and climate. Here we describe the ocean carbon cycle, which in its first incarnation is based around a simple single nutrient (phosphate) control on biological productivity. The addition of calcium carbonate preservation in deep-sea sediments and its role in regulating atmospheric CO2 is presented elsewhere (Ridgwell and Hargreaves, 2007). We have calibrated the model parameters controlling ocean carbon cycling in GENIE-1 by assimilating 3-D observational datasets of phosphate and alkalinity using an ensemble Kalman filter method. The calibrated (mean) model predicts

We modify the local ensemble Kalman filter (LEKF) to incorporate the effect of forecast model bias. The method is based on augmentation of the atmospheric state by estimates of the model bias, and we consider different ways of modeling (i.e. parameterizing) the model bias. We evaluate the effectiveness of the proposed augmented state ensemble Kalman filter through numerical experiments incorporating various model biases into the model of Lorenz and Emanuel. Our results highlight the critical role played by the selection of a good parameterization model for representing the form of the possible bias in the forecast model. In particular, we find that forecasts can be greatly improved provided that a good model parameterizing the model bias is used to augment the state in the Kalman filter. 1.

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In this paper we review progress towards efficiently estimating parameters in climate models. Since the general problem is inherently intractable, a range of approximations and heuristic methods have been proposed. Simple Monte Carlo sampling methods, although easy to implement and very flexible, are rather inefficient, making implementation only possible in the very simplest models. More sophisticated methods based on random walks and gradient descent methods can provide more efficient solutions, but it is often unclear how to extract probabilistic information from such methods and the computational costs are still generally too high for their application to state of the art GCMs. The ensemble Kalman filter is an efficient Monte Carlo approximation which is optimal for linear problems, but we show here how its accuracy can degrade in nonlinear applications. Methods based on particle filtering may provide a solution to this problem but have yet to be studied in any detail in the realm of climate models. Statistical emulators show great promise for future research and their computational speed would eliminate much of the need for efficient sampling techniques. However, emulation of a full GCM has yet to be achieved and the construction of such represents a substantial computational task in itself.

In this paper, we show how oracle-based optimization can be used effectively for the cal-ibration of an intermidiate complexity climate model. In a fully developed example, we estimate the 12 principal parameters of the C-GOLDSTEIN climate model by using an oracle-based optimization tool, Proximal-ACCPM. The oracle is a procedure which finds, for each query point, a value for the goodness-of-fit function and an evaluation of its gradi-ent. The difficulty in the model calibration problem stems from the need to undertake costly calculations for each simulation and also from the fact that the error function used to assess the goodness-of-fit is not convex. The method converges to a ‘best fit ’ estimate over ten times faster than a comparable test using the ensemble Kalman filter. The approach is sim-ple to implement and potentially useful in calibrating computationally demanding models based on temporal integration (simulation), for which functional derivative information is not readily available.

The impacts of polarimetric radar data on the estimation of uncertain microphysical parameters are investigated through observing system simulation experiments when the effects of uncertain parameters on the observation operators are also considered. Five fundamental microphysical parameters (i.e., the intercept parameters of rain, snow, and hail and the bulk densities of snow and hail) are estimated individually or collectively using the ensemble square root Kalman filter. The differential reflectivity Z DR, specific differential phase KDP, and radar reflectivity at horizontal polarization ZH are used individually or in combinations for the parameter estimation while the radial velocity and ZH are used for the state estimation. In the process, the parameter values estimated in the previous analysis cycles are used in the forecast model and in observation operators in the ensuing assimilation cycle. Analyses are first performed that examine the sensitivity of various observations to the microphysical parameters with and without observation operator error. The results are used to help interpret the filter behaviors in parameter estimation. The experiments in which either a single or all five parameters contain initial errors reveal difficulties in estimating certain parameters using Z H alone when observation operator error is involved. Additional polarimetric measurements are found to be beneficial for both parameter and state estimation in general. It is found that the polarimetric data are more

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of satellite data and products into land surface processes. In this letter, a variational data assimilation scheme is developed based on the weak-constraint concept. It assimilates surface skin temperature into a simple land surface model for the estimation of turbulent fluxes. An automatic differentiation technique is used to derive the adjoint codes to evaluate the gradient of the cost function. After the construction of this assimilation system, numerical experiments are conducted to test its performance with different model errors, and the comparison is also made with the strong constraint scheme. The results show that the land surface turbulent fluxes can be retrieved with highly satisfactory accuracy. Index Terms—Data assimilation, evapotranspiration, land surface temperature (LST), weak constraint. I.