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, stochastic downscaling is not a substitute for physically based models, but it is a way to introduce rainfall variability at scales not resolved by physical models. In this paper we discuss the results of the application of a robust stochastic downscaling procedure [Rainfall Filtered Autoregressive Model (RainFARM); Rebora et al. 2006b ], originally devised for spatiotemporal rainfall downscaling of meteorological predictions, to the output of a state-of-the-art regional climate model (Protheus; Artale
, stochastic downscaling is not a substitute for physically based models, but it is a way to introduce rainfall variability at scales not resolved by physical models. In this paper we discuss the results of the application of a robust stochastic downscaling procedure [Rainfall Filtered Autoregressive Model (RainFARM); Rebora et al. 2006b ], originally devised for spatiotemporal rainfall downscaling of meteorological predictions, to the output of a state-of-the-art regional climate model (Protheus; Artale
model the onset of precipitation as a fixed critical threshold of CWV. Instead, it may be appropriate to model onset as a stochastic switch that has a mean “critical value” as in the notion of conditional instability, but which also has some random variance about this mean critical value. Such a model would be a “stochastic trigger” for the onset of precipitation/convection. The observations described above should be useful in guiding and constraining the development of convective parameterizations
model the onset of precipitation as a fixed critical threshold of CWV. Instead, it may be appropriate to model onset as a stochastic switch that has a mean “critical value” as in the notion of conditional instability, but which also has some random variance about this mean critical value. Such a model would be a “stochastic trigger” for the onset of precipitation/convection. The observations described above should be useful in guiding and constraining the development of convective parameterizations
), stochastic approximations ( Zidihkeri and Frederiksen 2008 ), and the subsequent identification of universal scaling laws for subgrid dynamics in atmospheric and oceanic flows ( Kitsios et al. 2016 ). Various approaches to incorporating stochastic kinetic energy (KE) backscatter have for some time now been applied to reduce systematic model errors in operational weather prediction and atmospheric models ( Berner et al. 2012 ; Franzke et al. 2015 ; Berner et al. 2017 ). One unavoidable consequence of
), stochastic approximations ( Zidihkeri and Frederiksen 2008 ), and the subsequent identification of universal scaling laws for subgrid dynamics in atmospheric and oceanic flows ( Kitsios et al. 2016 ). Various approaches to incorporating stochastic kinetic energy (KE) backscatter have for some time now been applied to reduce systematic model errors in operational weather prediction and atmospheric models ( Berner et al. 2012 ; Franzke et al. 2015 ; Berner et al. 2017 ). One unavoidable consequence of
between the annual cycle and ENSO indicates the need for a unifying theoretical framework within which many (if not all) of these mechanisms can be examined simultaneously. In this study, we propose an extension of the conceptual recharge oscillator model of ENSO ( Jin 1997 ) that includes a statistical–dynamical representation of the seasonally varying background state. We refer to the model as the seasonal stochastic recharge model (SSRM). The SSRM is derived based on a seasonally varying
between the annual cycle and ENSO indicates the need for a unifying theoretical framework within which many (if not all) of these mechanisms can be examined simultaneously. In this study, we propose an extension of the conceptual recharge oscillator model of ENSO ( Jin 1997 ) that includes a statistical–dynamical representation of the seasonally varying background state. We refer to the model as the seasonal stochastic recharge model (SSRM). The SSRM is derived based on a seasonally varying
interpolations. This requires the offline computation of interpolation positions. The method is illustrated within a one-dimensional test bed. The note is organized as follow. Section 2 recalls the correlation model based on the diffusion equation and its link with probabilities. The relationship between stochastic differential equations (SDEs) and elliptic partial differential equations (EPDEs) is described in section 3 . This section also gives details about the numerical stochastic resolution of SDE
interpolations. This requires the offline computation of interpolation positions. The method is illustrated within a one-dimensional test bed. The note is organized as follow. Section 2 recalls the correlation model based on the diffusion equation and its link with probabilities. The relationship between stochastic differential equations (SDEs) and elliptic partial differential equations (EPDEs) is described in section 3 . This section also gives details about the numerical stochastic resolution of SDE
inflation ( Whitaker and Hamill 2012 ), though the latter can mitigate the effects of many different kinds of errors in ensemble filtering, like sampling errors. Covariance inflation techniques attempt to account for model error in the analysis, but they do not reduce the model error. Additive inflation is analogous to stochastic parameterization, the difference being that random perturbations are added to the forecast before every assimilation cycle, versus being added at every time step of the
inflation ( Whitaker and Hamill 2012 ), though the latter can mitigate the effects of many different kinds of errors in ensemble filtering, like sampling errors. Covariance inflation techniques attempt to account for model error in the analysis, but they do not reduce the model error. Additive inflation is analogous to stochastic parameterization, the difference being that random perturbations are added to the forecast before every assimilation cycle, versus being added at every time step of the
11401 . doi:10.1029/2006WR005714 . Bárdossy, A. , and Plate E. J. , 1992 : Space-time model for daily rainfall using atmospheric circulation patterns. Water Resour. Res. , 285 , 1247 – 1259 . Brissette, F. P. , Khalili M. , and Leconte R. , 2007 : Efficient stochastic generation of multi-site synthetic precipitation data. J. Hydrol. , 345 , 121 – 133 . 10.1016/j.jhydrol.2007.06.035 Eischeid, J. K. , Pasteris P. A. , Diaz H. F. , Plantico M. S. , and Lott N. J. , 2000
11401 . doi:10.1029/2006WR005714 . Bárdossy, A. , and Plate E. J. , 1992 : Space-time model for daily rainfall using atmospheric circulation patterns. Water Resour. Res. , 285 , 1247 – 1259 . Brissette, F. P. , Khalili M. , and Leconte R. , 2007 : Efficient stochastic generation of multi-site synthetic precipitation data. J. Hydrol. , 345 , 121 – 133 . 10.1016/j.jhydrol.2007.06.035 Eischeid, J. K. , Pasteris P. A. , Diaz H. F. , Plantico M. S. , and Lott N. J. , 2000
convection, unresolved processes at smaller scales such as deep convective clouds show some particular features in space and time, such as high irregularity, high intermittency, and low predictability. Some good candidates to account for those processes while remaining computationally efficient appear to be suitable stochastic parameterizations ( Majda et al. 2008 ; Palmer 2012 ). Generally speaking, these models consist of coupling some simple stochastic triggers (e.g., birth–death, spin–flip, coarse
convection, unresolved processes at smaller scales such as deep convective clouds show some particular features in space and time, such as high irregularity, high intermittency, and low predictability. Some good candidates to account for those processes while remaining computationally efficient appear to be suitable stochastic parameterizations ( Majda et al. 2008 ; Palmer 2012 ). Generally speaking, these models consist of coupling some simple stochastic triggers (e.g., birth–death, spin–flip, coarse
effective predictors in each equation is a priori unknown, there still remains hope for at least hypothetical feasibility of constructing an empirical model that is able to capture the full spectrum of observed variability in select atmospheric fields. For example, the intermediately sized empirical model of Kravtsov et al. (2011) demonstrated capability of reproducing various aspects of high-dimensional air–sea interaction over the Southern Ocean. In this respect, stochastic modeling of sea level
effective predictors in each equation is a priori unknown, there still remains hope for at least hypothetical feasibility of constructing an empirical model that is able to capture the full spectrum of observed variability in select atmospheric fields. For example, the intermediately sized empirical model of Kravtsov et al. (2011) demonstrated capability of reproducing various aspects of high-dimensional air–sea interaction over the Southern Ocean. In this respect, stochastic modeling of sea level
subgrid-scale fluctuations must be included explicitly via a stochastic term, or if it is sufficient to include their mean influence by improved deterministic physics parameterizations. Palmer (2001) suggests that we use stochastic dynamic models ( Epstein 1969 ) such as cellular automata or Markov models to represent model uncertainty due to improperly represented processes in the deterministic models. Others have promoted physics tendency perturbations ( Buizza et al. 1999 ), multiple physics
subgrid-scale fluctuations must be included explicitly via a stochastic term, or if it is sufficient to include their mean influence by improved deterministic physics parameterizations. Palmer (2001) suggests that we use stochastic dynamic models ( Epstein 1969 ) such as cellular automata or Markov models to represent model uncertainty due to improperly represented processes in the deterministic models. Others have promoted physics tendency perturbations ( Buizza et al. 1999 ), multiple physics
