NWP models simulate the atmospheric state on a given model grid, thereby principally

limiting the representation of atmospheric phenomena to scales larger than the grid point

distance. However, in addition such models generally filter away small-scale phenomena (of

several grid lengths) in order to avoid numerical instability of the discrete numerical model

equations, which also prevents upscale error growth originating from the relatively uncertain

small scales (section 3 of [R5] and [R22]). Moreover, data assimilation systems act as socalled

low pass filters on the information provided by the observations, thereby essentially

rejecting observed information on scales smaller than the typical error structure of the NWP

model (background error covariance). So, observations do generally not affect the spectrum

of NWP model scales, but rather replace error variance with observed (true) variance. As a

consequence the simulated atmospheric state by NWP models is a smooth representation of

the true atmospheric state, lacking atmospheric variance in particular on the smallest

(turbulent) scales. Observing systems sample the true atmospheric state and thus do

measure small-scale atmospheric phenomena. This variance in the measured atmospheric

scales which is not part of the NWP model atmospheric state is called the spatial observation

spatial representativeness error [R3]. It is not an error in the sense of a deficiency of the

observing system such as e.g. instrument noise, but it merely describes that part of the

observation that cannot be well represented by the model and should therefore be treated as

an observation error when compared to the NWP model state, e.g., in data assimilation.

The smallest spatial scale of atmospheric phenomena that a NWP model can reasonably

represent is called the effective model resolution here. This should not be confused with the

sampling or grid distance which the NWP community usually refers to as “resolution”. The

discrete numerical equations actually cannot generally resolve atmospheric variance on the

sampling scale, but use higher-order closures that allow realistic atmospheric variance only

on scales 5-10 times the grid size [R5]. The effective model resolution differs for different

NWP models and is in fact not well defined in the literature. [R5] defines effective model

resolution as the wavelength (i.e., the inverse of the wave number) where the NWP model

spectra first deviates from the atmospheric spectrum, the latter obtained from high-resolution

observations. [R15] on the other hand uses a statistical description of atmospheric

turbulence. Structure functions and wind energy spectra are derived from these and a 2-

dimensional box-car averaging technique is applied to the turbulence data. The length of the

box-car for which the averaged structure function (or spectrum) compares best with the NWP

model structure function (or spectrum) defines the effective resolution. From the structure

functions, typical values found for the effective model resolution are 117 km for a global

model with 35 km grid size and 80 km for a mesoscale model with 13 km model grid size.

When using wind energy spectra 8 times larger values of about 650 km for the mesoscale

model are found.

Results from the recently issued survey [A3] among NWP centers show a large spread and

uncertainty of reported numbers for the effective model resolution, indicating that NWP

centers worldwide do not have a clear picture of this quantity. It is very relevant in data

assimilation though, for the quantification of the observation representativeness error

variance that substantially contributes to the total observation error variance. It is clear that a

correct specification of the observation representativeness error is needed to subscribe a

correct weight of the observation in the analysis.

From the above it is clear that the observation representation error depends on how the

observation is spatially accumulated. The change from Aeolus burst-mode (BM) to

continuous-pulsed mode (CM) laser operation offers an increased flexibility for the

accumulation of measured data. For BM operation the horizontal accumulation was limited to

50 km along track. Continuously measured satellite information (both horizontally and

vertically) may be processed and accumulated to optimally represent the effective resolution

of the NWP model as this would increase the accumulated signal and reduce the total

observation error, both the measurement error and the spatial representation error parts. It

is, thus, of interest to study the effects of accumulation, both horizontally and vertically, for

the Aeolus CM.

This report describes the use of high-resolution observations of various parts of the

atmosphere to quantify i) the effective model resolution of a global (ECMWF) and regional

(HiRLAM) model and ii) the expected observation representativeness error for Aeolus-CM

measurements as a function of horizontal accumulation length and vertical accumulation

depth.

GJ Marseille, A Stoffelen. 2Observation Representativeness Error

published, 2012

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