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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