Ensemble-Mean Dynamics of Low-Frequency Variability and Cloud Temperature Profile Retrieval Using GPS RO Data

The second-order closure for the ensemble-mean dynamics is validated using the approach of direct numerical ensemble simulations of a linear barotropic model with stochastic basic flows in extratropics. For various configurations of the stochastic basic flow and external forcing, the deterministic solutions under the second-order closure capture, with remarkable accuracy, the ensemble means and the associated eddy covariance fields of forced responses simulated by a 500-member numerical ensemble. Thus, the second-order closure is found to be adequate for describing the ensemble-mean linear dynamics with stochastic basic flows. Example of ensemble-mean solution shows the important role played by the stochastic synoptic eddy component of the basic flow in determining the ensemble-mean responses to external forcing. This study supports the notion that linear frameworks of ensemble-mean dynamics under second-order closure are useful tools for describing and understanding the dynamics of the synoptic eddy and the low-frequency flow (SELF) feedback and extratropical atmospheric low-frequency variability. Following a similar concept, the conceptual recharge oscillator model for the El Niño-Southern Oscillation phenomenon (ENSO) is utilized to study the influence of fast variability such as that associated with westerly wind bursts (WWB) on dynamics of ENSO and predictability. The ENSO-WWB interaction is simply represented by stochastic forcing modulated by ENSO-related sea surface temperature (SST) anomalies. An analytical framework is developed to describe the ensemble-mean dynamics of ENSO under stochastic forcing. Numerical ensemble simulations verify the main results derived from the analytical ensemble-mean theory: the state-dependent stochastic forcing enhances the instability of ENSO and its ensemble spread, generates asymmetry in the predictability of the onsets of cold and warm phases of ENSO, and leads to an ensemble-mean bias that may eventually contribute to a climate mean state bias. Clouds contribute greatly to the atmospheric variability within weather systems. Measurements of thermodynamic properties in cloudy airs are required to improve numerical weather forecasting models and for the study of the global radiation and hydrology budget. The Global Positioning System (GPS) radio occultation (RO) technique is not affected by clouds and has a high vertical resolution, making it ideally suited for cloud study. Temperatures retrieved from Constellation Observing System for Meteorology Ionosphere & Climate (COSMIC) RO measurements are compared with two operational weather assimilation models including the Prediction and National Center for Atmospheric Research (NCEP/NCAR) reanalysis and European Centre for Medium-Range Weather Forecasts (ECMWF) analysis. The cloudy GPS ROs during June 2007 and June to September 2006 are identified based on the collocated CloudSat data. Systematic bias of opposite sign between large-scale global analyses and observed RO profiles are found for cloudy and clear-sky conditions. It is also found that GPS wet retrieval lapse rate is nearly constant (~6oC/km) in the vertical while that from ECMWF increases with height from cloud middle to cloud top. A new GPS RO cloudy profile retrieval algorithm is proposed. A relative humidity parameter is introduced through an empirical relationship between CloudSat ice-water content and ECMWF relative humidity. The new cloudy temperature retrieval tends to be warmer than the GPS wet retrieval within the cloud and slightly colder near the cloud top, resulting in a cloudy lapse rate that agrees more closely with that of the ECMWF in the lower part of the cloud and increases with height (but faster than that of the ECMWF), and reaches a value of about 7.6oC/km near the cloud top. When the ice-water content measurements are absent, an empirical value of 0.85 is shown to be a good approximation for the relative humidity parameter.