ABSTRACT:We present a critique of Emanuel's steady-state hurricane model, which is a precursor to his theory for hurricane potential intensity (PI). We show that a major deficiency of the theory is the tacit assumption of gradient wind balance in the boundary layer, a layer that owes its existence to gradient wind imbalance in the radial momentum equation. If a more complete boundary-layer formulation is included using the gradient wind profiles obtained from Emanuel's theory, the tangential wind speed in the boundary layer becomes supergradient, invalidating the assumption of gradient wind balance. We show that the degree to which the tangential wind is supergradient depends on the assumed boundarylayer depth. The full boundary-layer solutions require a knowledge of the tangential wind profile above the boundary layer in the outer region where there is subsidence into the layer and they depend on the breadth of this profile. This effect is not considered in Emanuel's theory. We argue that a more complete theory for the steady-state hurricane would require the radial pressure gradient above the boundary layer to be prescribed or determined independently of the boundary layer.The issues raised herein highlight a fundamental problem with Emanuel's theory for PI, since that theory makes the same assumptions as in the steady-state hurricane model. Our current findings together with recent studies examining intense hurricanes suggest a way forward towards a more consistent theory for hurricane PI.

Abstract. Dynamically downscaled precipitation fields from regional climate models (RCMs) often cannot be used directly for regional climate studies. Due to their inherent biases, i.e., systematic over-or underestimations compared to observations, several correction approaches have been developed. Most of the bias correction procedures such as the quantile mapping approach employ a transfer function that is based on the statistical differences between RCM output and observations. Apart from such transfer functionbased statistical correction algorithms, a stochastic bias correction technique, based on the concept of Copula theory, is developed here and applied to correct precipitation fields from the Weather Research and Forecasting (WRF) model. For dynamically downscaled precipitation fields we used high-resolution (7 km, daily) WRF simulations for Germany driven by ERA40 reanalysis data for 1971-2000. The REG-NIE (REGionalisierung der NIEderschlagshöhen) data set from the German Weather Service (DWD) is used as gridded observation data (1 km, daily) and aggregated to 7 km for this application. The 30-year time series are split into a calibration (1971-1985) and validation (1986-2000) period of equal length. Based on the estimated dependence structure (described by the Copula function) between WRF and REGNIE data and the identified respective marginal distributions in the calibration period, separately analyzed for the different seasons, conditional distribution functions are derived for each time step in the validation period. This finally allows to get additional information about the range of the statistically possible bias-corrected values. The results show that the Copula-based approach efficiently corrects most of the errors in WRF derived precipitation for all seasons. It is also found that the Copula-based correction performs better for wet bias correction than for dry bias correction. In autumn and winter, the correction introduced a small dry bias in the northwest of Germany. The average relative bias of daily mean precipitation from WRF for the validation period is reduced from 10 % (wet bias) to −1 % (slight dry bias) after the application of the Copula-based correction. The bias in different seasons is corrected from 32 % March-April-May (MAM), −15 % June-July-August (JJA), 4 % September-October-November (SON) and 28 % December-January-February (DJF) to 16 % (MAM), −11 % (JJA), −1 % (SON) and −3 % (DJF), respectively. Finally, the Copula-based approach is compared to the quantile mapping correction method. The root mean square error (RMSE) and the percentage of the corrected time steps that are closer to the observations are analyzed. The Copula-based correction derived from the mean of the sampled distribution reduces the RMSE significantly, while, e.g., the quantile mapping method results in an increased RMSE for some regions.

Abstract. This paper presents a new Copula-based method for further downscaling regional climate simulations. It is developed, applied and evaluated for selected stations in the alpine region of Germany. Apart from the common way to use Copulas to model the extreme values, a strategy is proposed which allows to model continuous time series. As the concept of Copulas requires independent and identically distributed (iid) random variables, meteorological fields are transformed using an ARMA-GARCH time series model. In this paper, we focus on the positive pairs of observed and modelled (RCM) precipitation. According to the empirical copulas, significant upper and lower tail dependence between observed and modelled precipitation can be observed. These dependence structures are further conditioned on the prevailing large-scale weather situation. Based on the derived theoretical Copula models, stochastic rainfall simulations are performed, finally allowing for bias corrected and locally refined RCM simulations.

A simple slab model for the boundary layer of a hurricane is re-examined and a small error in the original calculation is corrected. With this correction, the development of supergradient winds is a ubiquitous feature of the solutions. The boundary layer shows two types of behaviour in the inner core of the vortex depending on the depth of the layer and the maximum tangential wind speed above the layer. For small depths and/or large tangential wind speeds, large supergradient winds develop and lead to a rapid deceleration of the inflow such that the inflow becomes zero at some radius inside the radius of maximum tangential wind speed above the boundary layer. For large depths and/or small tangential wind speeds, the solutions do not become singular until within a few kilometres of the rotation axis. The transition between the two regimes is very abrupt. Interpretations are given for the foregoing behaviour. Other aspects of the boundary-layer dynamics and thermodynamics are investigated including: the dependence on mixing by shallow convection; the effects of a radially varying boundary-layer depth; the effects of downward momentum transport; the dependence of thermodynamical quantities on the boundary-layer depth; and the radial variation of equivalent potential temperature. Predicted values of the last quantity are in acceptable agreement with observations made in category-five hurricane Isabel (2003). The version with radially varying depth gives more realistic vertical velocities in the inner-core region of the vortex. The limitations and strengths of the slab model are discussed.

This paper presents a new Copula-based method for further downscaling regional climate simulations. It is developed, applied and evaluated for selected stations in the alpine region of Germany. Apart from the common way to use Copulas to model the extreme values, a strategy is proposed which allows to model continous time series. In this paper, we focus on the positive pairs of observed and modelled (RCM) precipitation. As the concept of Copulas requires <i>independent and identically distributed</i> (<i>iid</i>) random variables, meteorological fields are transformed using an ARMA-GARCH time series model. The dependence structures between modelled and observed precipitation are conditioned on the prevailing large-scale weather situation. The impact of the altitude of the stations and their distance to the surrounding modelled grid cells is analyzed. Based on the derived theoretical Copula models, stochastic rainfall simulations are performed, finally allowing for bias corrected and locally refined RCM simulations