Stochastically Perturbed Bifurcations

1988 ◽  
pp. 169-180
Author(s):  
N. Sri Namachchivaya ◽  
Harry H. Hilton
Keyword(s):  
Stochastically Perturbed

Development of stochastically perturbed parameterization scheme for the Noah Land Surface Model with the optimized random forcing parameters using the micro-genetic algorithm

2021 ◽  
Author(s):  
Sujeong Lim ◽  
Claudio Cassardo ◽  
Seon Ki Park
Keyword(s):  
Genetic Algorithm ◽  
Land Surface ◽  
Weather Forecasting ◽  
Land Surface Model ◽  
Surface Model ◽  
Ensemble Spread ◽  
Near Surface ◽  
Random Forcing ◽  
Micro Genetic Algorithm ◽  
Stochastically Perturbed

<p>The ensemble data assimilation system is beneficial to represent the initial uncertainties and flow-dependent background error covariance (BEC). In particular, the inevitable model uncertainties can be expressed by ensemble spread, that is the standard deviation of ensemble BEC. However, the ensemble spread generally suffers from under-estimated problems. To alleviate this problem, recent studies employed stochastic perturbation schemes to increases the ensemble spreads by adding the random forcing in the model tendencies (i.e., physical or dynamical tendencies) or parameterization schemes (i.e., PBL, convective scheme, etc.). In this study, we focus on the near-surface uncertainties which are affected by the interactions between the land and atmosphere process. The land surface model (LSM) provides various fluxes as the lower boundary condition to the atmosphere, influencing the accuracy of hourly-to-seasonal scale weather forecasting, but the surface uncertainties were not much addressed yet. In this study, we developed the stochastically perturbed parameterization (SPP) scheme for the Noah LSM. The Weather Research and Forecasting (WRF) ensemble system is used for regional weather forecasting over East Asia, especially over the Korean Peninsula. As a testbed experiment with the newly-developed Noah LSM-SPP system, we first perturbed the soil temperature — a crucial variable for the near-surface forecasts by affecting sensible heat fluxes, land surface skin temperature and surface air temperature, and hence lower-tropospheric temperature. Here, the random forcing used in perturbation is made by the tuning parameters for amplitude, length scale, and time scales: they are commonly determined empirically by trial and error. In order to find optimal tuning parameter values, we applied a global optimization algorithm — the micro-genetic algorithm (micro-GA) — to achieve the smallest root-mean-squared errors. Our results indicate that optimization of the random forcing parameters contributes to an increase in the ensemble spread and a decrease in the ensemble mean errors in the near-surface and lower-troposphere uncertainties. Further experiments will be conducted by including soil moisture in the testbed.</p>

Sensitivity of modeled microphysics to stochastically perturbed parameters

2021 ◽  
Author(s):  
Tomislava Vukicevic ◽  
Aleksa Stankovic ◽  
Derek Posselt
Keyword(s):  
Parameter Uncertainty ◽  
Squall Line ◽  
Physical Parameters ◽  
Test Case ◽  
Modeling Framework ◽  
Water Path ◽  
Second Moment ◽  
Ensemble Simulations ◽  
Parameter Perturbations ◽  
Stochastically Perturbed

<p>This study investigates sensitivity of  cloud and precipitation parameterized microphysics  to stochastic representation of parameter uncertainty as formulated by the stochastically perturbed parameterization (SPP) scheme.  SPP is applied to multiple microphysical parameters within a lagrangian column model, used in several prior published studies to characterize  parameter uncertainty by means of multivariate nonlinear inversions using remote sensing observations. The 1D column microphysics model is forced with prescribed time-varying profiles of temperature, humidity and vertical velocity.  This modeling framework allows for investigation of the effect of changes in model physics parameters on the model output in isolation from any feedback to the cloud-scale dynamics.</p><p>The test case selected in this study of an idealized representation of mid-latitude squall-line convection is the same as in the prior studies. This enabled using the estimates of multi-parameter distributions from the inversions in the prior studies as the basis for setting the second-moment statistics in the SPP scheme implementation. Additionally impacts of the non-stochastic and stochastic multi-parameter representation of parameterization uncertainty on the microphysics model solution could be directly compared.</p><p>The sensitivity experiments with the SPP scheme involve ensemble simulations where each member is evolved with a different stochastic sequence of parameter perturbations, as is done in the standard practice with this scheme.  The experiments explore impacts of using different decorrelation times and different estimates of second moment statistics for the parameter perturbations.  These include uncorrelated perturbations between the parameters for several values of variance for each parameter and correlated perturbations based on multi-parameter empirical statistical distributions from the prior studies.  The selection of physical parameters for the perturbations is based on the significance of their impacts derived from the prior studies . </p><p>The results are evaluated in terms of changes to the ensemble mean and variance of time evolving profiles of hydrometeor mass quantities, the microphysics processes within the model as well as in terms of the simulated column integral microphysics-sensitive satellite-based  observables. The latter include PR (Precipitation Rate) , LWP (Liquid Water Path), IWP (Ice water path), TOA-LW and TOA-SW (-Long and -Short Wave, respectively).  In each experiment six parameters were perturbed.</p><p>The analyses performed so far indicate a high sensitivity of the microphysics model to the SPP scheme. The ensemble simulations with the standard uncorrelated parameter perturbations exhibit a significant bias relative to the control simulation which uses the unperturbed parameters.  For the selected test case the skewness toward small parameter values in the SPP sampling based on the underlying log-normal distributions leads to less precipitating ice and more precipitating liquid and accumulated precipitation. The response is due to nonlinear relationships between the parameters and modeled microphysics output. The changes in microphysics output result in large mean changes in PR, LWP, IWP, TOA- LW and SW, suggesting a potential for using these and other microphysics sensitive satellite observations to evaluate and if needed correct properties of the underlying sampling distribution in the stochastic scheme.  Further analyses will be presented at the conference.</p>

A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

2012 ◽  
Vol 28 (5) ◽  
pp. 1416-1423 ◽  
Author(s):  
Chun-Biao Gan ◽  
Shi-Xi Yang ◽  
Hua Lei
Keyword(s):  
Dynamical System ◽  
Noisy Chaos ◽  
Stochastically Perturbed

scholarly journals The Impact of a Stochastically Perturbing Microphysics Scheme on an Idealized Supercell Storm

2017 ◽  
Vol 146 (1) ◽  
pp. 95-118 ◽  
Author(s):  
Xiaoshi Qiao ◽  
Shizhang Wang ◽  
Jinzhong Min
Keyword(s):  
Stochastic Methods ◽  
Microphysics Scheme ◽  
Advanced Regional Prediction System ◽  
Recursive Filters ◽  
Supercell Storm ◽  
Regional Prediction ◽  
Double Moment ◽  
The Impact ◽  
Temperature Tendency ◽  
Stochastically Perturbed

Abstract The concept of stochastic parameterization provides an opportunity to represent spatiotemporal errors caused by microphysics schemes that play important roles in supercell simulations. In this study, two stochastic methods, the stochastically perturbed temperature tendency from microphysics (SPTTM) method and the stochastically perturbed intercept parameters of microphysics (SPIPM) method, are implemented within the Lin scheme, which is based on the Advanced Regional Prediction System (ARPS) model, and are tested using an idealized supercell case. The SPTTM and SPIPM methods perturb the temperature tendency and the intercept parameters (IPs), respectively. Both methods use recursive filters to generate horizontally smooth perturbations and adopt the barotropic structure for the perturbation r, which is multiplied by tendencies or parameters from this parameterization. A double-moment microphysics scheme is used for the truth run. Compared to the multiparameter method, which uses randomly perturbed prescribed parameters, stochastic methods often produce larger ensemble spreads and better forecast the intensity of updraft helicity (UH). The SPTTM method better predicts the intensity by intensifying the midlevel heating with its positive perturbation r, whereas it performs worse in the presence of negative perturbation. In contrast, the SPIPM method can increase the intensity of UH by either positive or negative perturbation, which increases the likelihood for members to predict strong UH.

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