United States
Environmental Protection
Agency
Environmental Sciences
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S3-84-086 Sept. 1984
&EPA Project Summary
Spatial and Temporal
Interpolation of NEROS
Radiosonde Winds
0. Russell Bullock, Jr.
This text summarizes a research
program whose objective was the
determination of a most appropriate
numerical method for the spatial and
temporal analysis of free atmospheric,
radiosonde derived wind observations
for the North-East Regional Oxidant
Study (NEROS) pollutant transport
model being developed at the Environ-
mental Sciences Research Laboratory
of the U.S. Environmental Protection
Agency, Research Triangle Park, North
Carolina. The analysis was performed
by automated data processing with
some restrictions in computer execution
time and storage area.
Previously developed methods of
spatial and temporal data analysis were
reviewed and their applicability to the
NEROS effort evaluated. Evaluation
was based on tests with actual radio-
sonde data and with data sets produced
through numerical model initialization
procedures. In all cases, the desired
result was a 7 by 6 grid of wind vectors
in latitude and longitude space at
discrete pressure levels for every hour
during a three data test period.
Optimization of applicable spatial
analysis schemes was completed and
error statistics were calculated based
on agreement between the analyzed
gridpoint values and the data values at
various locations within the NEROS
test region. Two types of input values
were used during the optimization
tests. Actual observational data were
obtained from the National Weather
Service radiosonde network for one
test, and artificially generated data
were produced for a second separate
test.
Linear and curvilinear time interpola-
tion methods were tested two ways.
For one test, time interpolation proce-
dures were applied to the input data
sets to produce artificial hourly radio-
sonde sounding data that were then
spatially analyzed. For the other test,
spatial analysis was performed with the
data available at the actual observation
times and the resulting gridpoint values
were then interpolated in time to pro-
duce the hourly analyses.
This Project Summary was developed
by EPA's Environmental Sciences
Research Laboratory, Research Triangle
Park, NC, to announce key findings of
the research project that is fully docu-
mented in a separate report of the same
title (see Project Report ordering infor-
mation at back).
Introduction
As a part of the development of the
North-East Regional Oxidant Model
(NEROS) atmospheric pollution transport
model, a technique for the spatial and
temporal analysis of radiosonde derived
wind observations was required. For this
study, two-dimensional spatial grids of
wind values were desired at various
constant pressure levels and at hourly
intervals The idea of producing one
three-dimensional grid for every hour
does not apply m this case because the
analyses at each pressure level were
performed separately, using only the data
available on the pressure level of the
analysis. In the same respect, the
temporal analysis was performed sepa-
rately due to lack of a generally applicable
scaling relation between space and time
for radiosonde winds
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As the name implies, the NEROS
project is primarily investigating oxidant
transport in the Great Lakes and North-
east regions of the United States and in
the southernmost portions of Ontario,
Canada. Figure 1 shows this region of
interest within the interior solid outline.
Also shown is the placement of the 7 by
6 computational grid-point array desig-
nated for the study of radiosonde wind
analysis Notice that the exterior grid
points are located outside the NEROS
region in order to isolate any boundary
value assumptions that are often required
for numerical analysis schemes.
Measurements of wind are usually
taken in terms of the direction from which
the air is flowing and the speed of flow
However, most applications in numerical
modeling required that the wind be
defined in terms of the orthogonal
spatial components of the air flow vector.
Nevertheless, many philosophical reasons
have been proposed for the use of both
vector decompositions, the spatial com-
ponents of the wind vector (u,v) and the
wind direction and speed. Therefore, an
investigation of both schemes was
performed.
Some contemporary schemes for the
spatial analysis of wind use separate
scalar analyses of vorticity (f) and
divergence (6) to define the final wind field
using the Helmholtz equation. By analyzing
these parameters defined by the total
wind field, ambiguous vector decomposi-
tion is not a concern.
However, the Helmholtz equation
V="k-V¥+V* (1)
relates the fields of the stream function
(ili) and the velocity potential (\) to the
wind field, not to £ and 8. The definitions
Va^ = £ and V2x = & (2)
present two intermeshed Dinchlet prob-
lems. Many methods have been proposed
to solve various permutations of this
multiple boundary value problem, and
some of the more popular solutions were
tested for their applicability to the spatial
analysis of radiosonde winds on the grids
chosen for this research effort.
Time interpolation of radiosonde winds
can be accomplished by schemes as
simple as linear interpolation or as
complex as forward-backward numerical
atmospheric modeling For the purposes
of this research, temporal analysis was
limited to schemes of linear interpolation
or curve fitting of the individual data
points at the observation times. The most
important question with respect to time
interpolation is whether to use it on radio-
sonde sounding data to create artificial
hourly soundings that are then spatially
analyzed, or to use time interpolation on
the grid-point values previously obtained
from spatial analyses of actual data.
Procedure
Radiosonde data were obtained from
normal 0000 Greenwich mean time
(GMT) and 1200 GMT National Weather
Service observations and from special
0600 GMT and 1800 GMT observations
taken specifically for the NEROS project.
The data obtained for normal sounding
times were from 24 stations scattered in
and around the NEROS modeling region;
data for special times were observed at
only 7 of these 24 stations. The locations
of all stations sampled for this study are
shown in Figure 2
All analysis was performed using
ASCII-FORTRAN programming on the
UNIVAC 1183 computer at the National
Computer Center, Research Triangle
Park, North Carolina. The first task per-
formed was a survey of contemporary
spatial analysis schemes for scalar
quantities. Next, an investigation of wind
decomposition into orthogonal spatial
components and direction-speed compo-
nents was undertaken. This investigation
included a comparison of accuracies in
the matching of known values of wind to
results obtained by both methods. An
optimum procedure for the spatial
analysis of wind using the Helmholtz
equation was developed, and its accuracy
was compared with that of the wind
decomposition schemes. Finally, the
accuracy of a combination of the optimum
spatial analysis scheme and a linear time
interpolation scheme was tested by
attempting to match 0600 GMT and 1800
GMT observations using data from only
0000 GMT and 1200 GMT. The testing of
this combination of schemes was per-
formed by using spatial analysis as the
first phase of the operation, followed by
the temporal analysis, and also by using
the reversed order of analysis.
Results
The survey of spatial analysis schemes
showed that a distance-based data point
weighting scheme performed well for all
applications to radiosonde data. While
there are other such schemes that use a
less complicated formulation for data
point weighting, none of them were able
to produce results with such spatial
consistency while conserving the impor-
tant features present in the data.
No significant difference was found be-
tween the "u-v" and "direction-speed" wind
decomposition schemes in their ability to
match known wind values in both ordered
and scattered position arrays. However, it
is understood that the complexity of the
actual wind field has an important effect
on the relative ability of these schemes tc
adequately describe the wind field.
It was found that spatial wind analysis
using the Helmholtz equation can be very
complicated and founded on a number of
inconspicuous assumptions. The bound-
ary value problem for the stream function
may be solved by making various assump
tions about the velocity potential and the
wind vectors at the boundary of the
analysis region. Similarly, the velocity
potential can be determined with an
assumption about the stream function
and the boundary wind.
A contemporary scheme for generaliz-
ing these assumptions, was found tc
produce acceptable results. In this
procedure, a preliminary wind analysis is
performed by any means preferred. An
adjustment is then made to this wind f ie/c
by forcing it to have the vorticity anc
divergence content determined by a
separate analysis of each. Vorticity anc
divergence analyses were based on poim
estimates as determined by a computa-
tional method in which triangular config-
urations of wind observations are used.
Some investigators have noted that the
size and shape of these data pom!
triangles may have an effect on the
quality of the vorticity and divergent
estimates obtained. Therefore, perform-
ance statistics were obtained for the wmc
analysis scheme using these estimates
and an optimum triangle size and shape
criterion was determined for the applica
'tions of this study. A maximum size
restriction of 100,000 km2 was deter
mined to be appropriate. A measure o'
triangle shape was based on the ratio o
the maximum triangle vertex angle to the
minimum vertex angle. A maximurr
restriction of about 4 0 was found tc
produce the best results.
Time interpolation results using curve
fitting of the grid-point values obtained a
0000 GMT and 1200 GMT showed grea
spatial discontinuity in the interpolatec
grids for 0600 GMT and 1800 GMT
Therefore, simple linear time interpola
tion was used for the purposes of thi:
study. The results suggest that the bes
performance is obtained by first perform
ing the spatial analysis to produce grid;
for the data times and then using tirru
interpolation of the grid point values. Thi
differences are somewhat dependent or
the pressure level of analysis, but thi
statistics invariably show that thi
procedure using spatial analysis first i:
most accurate. |
Records of computing time used to J
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these tests showed that the most accu-
rate procedure was also the fastest. The
spatial analysis requnes a complete
inventory of all data points and rather
time costly mathematical operations.
Performing the spatial analyses first
eliminates the need for a full spatial
analysis for every time that the grids are
needed. Instead, the spatial analyses are
done only for the times when data is
actually available and the time interpola-
tion produces the final grids.
Conclusions
The wavelength dependent filtering
efficiency offered by the Barnes analysis
scheme is a useful tool for the production of
spatially consistent wind fields that
contain the important features found
in the actual data.
The decision of which wind decomposi-
tion method to use must be made based
on the complexity of the data field and the
scale of the features desired in the final
analysis.
The use of the Helmholtz equation to
determine wind fields allows vorticity and
divergency constraints to be applied to
the final wind analysis. These constraints
may be very useful for operations such as
modeling wind flow over complex terrain
When time and space must be disso-
ciated in the radiosonde wind analysis
due to lack of a scaling parameterization
between them, the spatial analysis should
usually be performed first because of the
advantages of computation speed, and
the possibility of improved accuracy.
Recommendations
Results of the work described in this
document pertaining to the use of the
Helmholtz equation to defifie the wind
field and the use of separate time and
space analyses should be considered
preliminary.
Suggestions for further research work
include the following.
1. Investigation into more specialized
cases in which the manipulation of
vorticity and/or divergence as they
apply in the Helmholtz equation
would be most productive. An exam-
ple would be the modeling wind flow
over complex terrain.
2. Further study into the use of curvilin-
ear time interpolation of spatial grid
points. Preliminary indications are
that a control on the field of time rate
changes used to define the spline or
polynomial curves at the data points
would greatly improve the spatial
continuity obtained in the grids for
the intermediate times.
O. Russell Bullock. Jr. is with Environmental Sciences Research Laboratory,
U.S. Environmental Protection Agency. Research Triangle Park. NC 27711.
Francis S. Binkowski is the EPA Project Officer (see below).
The complete report entitled "Spatial and Temporal Interpolation of NEROS
Radiosonde Winds," (Order No. PB 84-232 545; Cost: $11.50, subject to
change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
it U S GOVERNMENT PRINTING OFFICE, 1984 —759-015/7829
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