Evaluation and optimization of sampling errors for the Monte Carlo Independent Column Approximation

2004 ◽  
Vol 130 (601) ◽  
pp. 2069-2085 ◽  
Author(s):  
Petri Räisänen ◽  
Howard W. Barker
Keyword(s):  
Monte Carlo ◽  
Sampling Errors ◽  
Independent Column

The Monte Carlo Independent Column Approximation’s Conditional Random Noise: Impact on Simulated Climate

2005 ◽  
Vol 18 (22) ◽  
pp. 4715-4730 ◽  
Author(s):  
P. Räisänen ◽  
H. W. Barker ◽  
J. N. S. Cole
Keyword(s):  
Monte Carlo ◽  
Global Climate ◽  
Random Noise ◽  
Radiative Heating ◽  
Time Interval ◽  
Additional Time ◽  
Time Step ◽  
Order Of Magnitude ◽  
Independent Column ◽  
The Impact

Abstract The Monte Carlo Independent Column Approximation (McICA) method for computing domain-average radiative fluxes is unbiased with respect to the full ICA, but its flux estimates contain conditional random noise. Results for five experiments are used to assess the impact of McICA-related noise on simulations of global climate made by the NCAR Community Atmosphere Model (CAM). The experiment with the least noise (an order of magnitude below that of basic McICA) is taken as the reference. Two additional experiments help demonstrate how the impact of noise depends on the time interval between calls to the radiation code. Each experiment is an ensemble of seven 15-month simulations. Experiments with very high noise levels feature significant reductions to cloudiness in the lowermost model layer over tropical oceans as well as changes in highly related quantities. This bias appears immediately, stabilizes after a couple of model days, and appears to stem from nonlinear interactions between clouds and radiative heating. Outside the Tropics, insignificant differences prevail. When McICA sampling is confined to cloudy subcolumns and when, on average, 50% more samples, relative to basic McICA, are drawn for selected spectral intervals, McICA noise is much reduced and the results of the simulation are almost statistically indistinguishable from the reference. This is true both for mean fields and for the nature of fluctuations on scales ranging from 1 day to at least 30 days. While calling the radiation code once every 3 h instead of every hour allows the CAM additional time to incorporate McICA-related noise, the impact of noise is enhanced only slightly. In contrast, changing the radiative time step by itself produces effects that generally exceed the impact of McICA’s noise.

scholarly journals Tests of Monte Carlo Independent Column Approximation in the ECHAM5 Atmospheric GCM

2007 ◽  
Vol 20 (19) ◽  
pp. 4995-5011 ◽  
Author(s):  
P. Räisänen ◽  
S. Järvenoja ◽  
H. Järvinen ◽  
M. Giorgetta ◽  
E. Roeckner ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Water Content ◽  
Beta Distribution ◽  
Cloud Fraction ◽  
Total Water Content ◽  
Subgrid Scale ◽  
Total Water ◽  
Distribution Scheme ◽  
Independent Column ◽  
The Impact

Abstract The Monte Carlo Independent Column Approximation (McICA) method for computing domain-average radiative fluxes allows a flexible treatment of unresolved cloud structure, and it is unbiased with respect to the full ICA, but its flux estimates contain conditional random noise. Here, tests of McICA in the ECHAM5 atmospheric GCM are reported. ECHAM5 provides an interesting test bed for McICA because it carries prognostic variables for the subgrid-scale probability distribution of total water content, which allows us to determine subgrid-scale cloud variability directly from the resolved-scale model variables. Three experiments with differing levels of radiative noise, each consisting of ten 6-yr runs, are performed to estimate the impact of McICA noise on simulated climate. In an experiment that attempted to deliberately maximize McICA noise, a systematic reduction in low cloud fraction occurred. For a more reasonable implementation of McICA, the impact of noise is very small, although statistically discernible. In terms of the impacts of noise, McICA appears to be a viable approach for use in ECHAM5. However, to improve the simulation of cloud radiative effects, realistic representation of both unresolved and resolved cloud structures is needed, which remains a challenging problem. Comparison of ECHAM5 data with a global cloud system–resolving model dataset and with International Satellite Cloud Climatology Project data suggested two problems related to unresolved cloud structures. First, ECHAM5 appears to underestimate subgrid-scale cloud variability. This problem seems partly related to the use of the beta distribution scheme for total water content in ECHAM5: in its current form, the scheme is unable to generate highly inhomogeneous clouds (relative standard deviation of condensate amount >1). Second, it appears that in ECHAM5, overcast cloud layers occur too frequently and partially cloudy layers too rarely. This problem is not unique to the beta distribution scheme; in fact, it is more pronounced when using an alternative, relative humidity–based cloud fraction scheme.

scholarly journals The Impact of Model Resolution on Differences between Independent Column Approximation and Monte Carlo Estimates of Shortwave Surface Irradiance and Atmospheric Heating Rate

2005 ◽  
Vol 62 (8) ◽  
pp. 2939-2951 ◽  
Author(s):  
William O’Hirok ◽  
Catherine Gautier
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Grid Cell ◽  
Horizontal Resolution ◽  
Model Resolution ◽  
Radiative Effects ◽  
Heating Rates ◽  
Atmospheric Heating ◽  
Surface Irradiance ◽  
Independent Column

Abstract Within general circulation models (GCMs), domain average radiative fluxes are computed using plane-parallel radiative transfer algorithms that rely on cloud overlap schemes to account for clouds not resolved at the horizontal resolution of a grid cell. These parameterizations have a strong statistical approach and have difficulty being applied well to all cloudy conditions. A more physically based superparameterization has been developed that captures subgrid cloud variability using an embedded cloud system resolving model (CSRM) within each GCM grid cell. While plane-parallel radiative transfer computations are generally appropriate at the scale of a GCM grid cell, their suitability for the much higher spatially resolved CSRMs (2–4 km) is unknown because they ignore photon horizontal transport effects. The purpose of this study is to examine the relationship between model horizontal resolution and 3D radiative effects by computing the differences between independent column approximations (ICA) and 3D Monte Carlo estimates of shortwave surface irradiance and atmospheric heating rate. Shortwave radiative transfer computations are performed on a set of six 2D fields composed of stratiform and convective liquid water and ice clouds. To establish how 3D effects vary with the size of a grid cell, this process is repeated as the model resolution is progressively degraded from 200 to 20 km. For shortwave surface irradiance, the differences between the 3D and ICA results can reach 500 W m−2. At model resolutions of between 2.0 and 5.0 km the difference for almost all columns is reduced to a maximum of ±100 W m−2. For atmospheric heating rates assessed at the level of individual model cells, 3D radiative effects can approach a maximum value of ±1.2 K h−1 when the horizontal column size is 200 m. However, between model resolutions of 2.0 and 5.0 km, 3D radiative effects are reduced to well below ±0.1 K h−1 for a large majority of the cloudy cells. While this finding seems to bode well for the CSRM, the results ultimately need to be understood within the context of how 3D radiative effects impact not only heating rates but also cloud dynamics.

Sampling Errors of Variance Components in Small Sample Multifacet Generalizability Studies

1978 ◽  
Vol 3 (4) ◽  
pp. 319-346 ◽  
Author(s):  
Philip L. Smith
Keyword(s):  
Monte Carlo ◽  
Variance Components ◽  
Variance Component ◽  
Generalizability Theory ◽  
Small Sample ◽  
Least Square ◽  
Sampling Errors ◽  
Sample Stability ◽  
Sampling Behavior ◽  
Variance Component Estimates

The paper describes the small sample stability of least square estimates of variance components within the context of generalizability theory. Monte Carlo methods are used to generate data conforming to some selected multifacet generalizability designs to illustrate the sampling behavior of variance component estimates. Based on the findings, recommendations are made concerning the design of efficient small sample generalizability studies.

scholarly journals Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 50 ◽  
Author(s):  
Francesca Greselin ◽  
Fabio Piacenza ◽  
Ričardas Zitikis
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Sampling Error ◽  
Risk Measure ◽  
Simulated Data ◽  
Operational Risk ◽  
Computational Effort ◽  
Risk Measurement ◽  
Sampling Errors ◽  
Eu Regulation

We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization.

The Monte Carlo Independent Column Approximation: an assessment using several global atmospheric models

2008 ◽  
Vol 134 (635) ◽  
pp. 1463-1478 ◽  
Author(s):  
H. W. Barker ◽  
J. N. S. Cole ◽  
J.-J. Morcrette ◽  
R. Pincus ◽  
P. Räisänen ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Atmospheric Models ◽  
Independent Column

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

Sign in / Sign up

Export Citation Format

Share Document