Identification

Title

Upscale versus “up-amplitude” growth of forecast-error spectra

Abstract

Atmospheric predictability is measured by the average difference (or "error") within an ensemble of forecasts starting from slightly different initial conditions. The spatial scale of the error field is a fundamental quantity; for meteorological applications, the error field typically varies with latitude and longitude and so requires a two-dimensional (2D) spectral analysis. Statistical predictability theory is based on the theory of homogeneous, isotropic turbulence, in which spectra are circularly symmetric in 2D wavenumber space. One takes advantage of this circular symmetry to reduce 2D spectra to one-dimensional (1D) spectra by integrating around a circle in wavenumber polar coordinates. In recent studies it has become common to reduce 2D error spectra to 1D by computing spectra in the zonal direction and then averaging the results over latitude. It is shown here that such 1D error spectra are generically fairly constant across the low wavenumbers as the amplitude of an error spectrum grows with time and therefore the error spectrum is said grow "up-amplitude." In contrast computing 1D error spectra in a manner consistent with statistical predictability theory gives spectra that are peaked at intermediate wavenumbers. In certain cases, this peak wavenumber is decreasing with time as the error at that wavenumber increases and therefore the error spectrum is said to grow "upscale." We show through theory, simple examples, and global predictability experiments that comparisons of model error spectra with the predictions of statistical predictability theory are only justified when using a theory-consistent method to transform a 2D error field to a 1D spectrum.

Resource type

document

Resource locator

Unique resource identifier

code

http://n2t.net/ark:/85065/d7862mct

codeSpace

Dataset language

eng

Spatial reference system

code identifying the spatial reference system

Classification of spatial data and services

Topic category

geoscientificInformation

Keywords

Keyword set

keyword value

Text

originating controlled vocabulary

title

Resource Type

reference date

date type

publication

effective date

2016-01-01T00:00:00Z

Geographic location

West bounding longitude

East bounding longitude

North bounding latitude

South bounding latitude

Temporal reference

Temporal extent

Begin position

End position

Dataset reference date

date type

publication

effective date

2023-01-01T00:00:00Z

Frequency of update

Quality and validity

Lineage

Conformity

Data format

name of format

version of format

Constraints related to access and use

Constraint set

Use constraints

Limitations on public access

None

Responsible organisations

Responsible party

contact position

OpenSky Support

organisation name

UCAR/NCAR - Library

full postal address

PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

name: homepage

responsible party role

pointOfContact

Metadata on metadata

Metadata point of contact