**Mapes, B. E.**, P. E. Ciesielski, and R. H. Johnson, 2003: Sampling
errors in rawinsonde-array budgets. *J. Atmos. Sci.*, **60**,
2697-2714.

**ABSTRACT**

Rawinsonde data used for sounding-array budget computations have random errors, both instrumental errors and errors of representativeness (here called sampling errors). The latter are associated with the fact that radiosondes do not measure large-scale mean winds and state variables, but are contaminated by small-scale variations as well. Data from the western Pacific and the summer monsoon of southeast Asia are used to estimate these random errors, and to propagate them through budget computations to assign error bars to derived quantities.

The statistics of sampling errors in directly measured variables are estimated
from station pair analysis, in which variance is partitioned into contributions
by resolved and unresolved scales. Resolved scales contribute the portion that
is contained in averages of adjacent sounding stations and/or adjacent launch
times (6-h intervals), while the rest of the total variance is defined as
unresolved. Magnitudes of unresolved variability for typical rawinsonde-array
spacings are ~0.5 K for temperature; ~5% for relative humidity at low levels,
rising to nearly 15% in the middle-upper troposphere; and ~2 m s^{-1}
for winds, rising to 3 m s^{-1} in the upper troposphere. These are
much larger than random instrumental errors, as estimated from pairs of
simultaneous rawinsondes launched very close together. Vertical correlation
scales of unresolved variability are 100-200 hPa. Up to 50% of the variance of
humidity is unresolved, while for zonal wind the unresolved portion is only a
few percent. Spatial and temporal sampling errors become about equal for
6-hourly rawinsondes ~200 km apart.

The effects of sampling errors on budget computations are estimated by a
perturbed-observation ensemble approach. All computations are repeated 20
times, with random realizations of unresolved variability added to the
rawinsonde data entering the analysis. The ensemble standard deviation serves
as an estimate of sampling error, which naturally decreases as the results are
averaged over larger areas and longer time periods. For example, rainfall
estimates on ~500 km scales have sampling errors of ~5 mm day^{-1} in
daily means, and ~1 mm day^{-1} in monthly means. The ensemble spread
of 120-day time integrations of the vertically averaged moist enthalpy equation
with rawinsonde-array-derived advective sources exceeds 20 K, implying that
sampling error could be responsible for substantial biases in column models
forced with such source terms.