Case I.1
Real-time precipitation analysis using information on spatial covariance and
circulation type (Reinhard Schiemann, Christoph Frei, and Mark A. Liniger) 1
Introduction
There is an obvious need for quantitative and spatially resolved information on precipitation in
applications such as runoff forecasting, water resources management, and avalanche warning
systems. In Switzerland, the climatological rain-gauge network is very dense and serves many
applications with high-resolution data of the past. Yet, only a rather small part of the gauges can
provide measurements on a real-time basis and in an automated fashion. Most of the observations are
taken manually and typically become available with a delay of some days or weeks. Therefore,
gridding methods have to rely on a coarse network of stations when applied in a real-time context,
which may severely limit the quality of interpolated analyses.
In this study, we investigate a method for improving the quality of near real-time spatial analysis of
daily precipitation from a sparse gauge network. To this end, the nested application of two approaches
is investigated:
First, in addition to the observations from the sparse network, we incorporate information on the spatial
covariance in the daily precipitation fields determined from high-resolution measurements of the past.
In a mountainous region, precipitation patterns have a strongly convoluted spatial structure [e.g., 2,3],
which is hardly resolved by real-time rain-gauge networks, but could be estimated from past data.
Second, we introduce information on the large-scale atmospheric circulation in the form of circulation
types (CTs). Precipitation patterns are recurrent in time due to characteristic orographic forcing in
situations with similar large-scale atmospheric circulation. Consequently, it appears promising to test,
for the territory of Switzerland, if the gridding performance improves if information on the large-scale
atmospheric flow is explicitly taken into account in terms of CTs.
Several authors have exploited CT information for mesoscale precipitation analysis. For example, [4]
have determined CT dependent lapse rates and semi-variograms in an ordinary kriging, [5] uses CT
stratification in the deterministic component of a gridding scheme, and [6] have modified the classical
Shepard approach [7,8,9] by introducing CT dependent station weights. Herein, we follow these ideas
and stratify the spatial analysis with respect to the types of two classifications of the circulation in
Central Europe.
Method and data
The method we use is reduced-space optimal interpolation [RSOI; 10]. Previous applications of this
technique have been concerned with the reconstruction of global historical monthly sea surface
temperatures, night marine air temperature, and sea ice [11,12], of monthly marine and global mean
sea level pressure [13,14], of daily mean sea level pressure for the European-North Atlantic region
[15], of Pacific sea surface temperatures from proxy data [16], and of monthly precipitation in the Alps
[17,18]. To the knowledge of the authors, this is the first study to test the feasibility of reconstructing
daily, i.e. strongly skewed, precipitation data by means of RSOI. While the above studies are
1
More information can be found in [1]: Schiemann, R., Frei, C., & Liniger M. A., Reduced-space optimal interpolation of daily
rain-gauge precipitation in Switzerland. J. Geophys. Res., submitted.
Figure Error! No text of specified style in
document.-1. Overview of the study area. (a)
Gauges of the sparse network (51 stations; blue
circles), the dense network (typically 420 stations
on individual days; red dots) and height of
topography (shading). (b) Long term mean
precipitation (mm d-1).
concerned with the reconstruction of historical climate data, the idea behind this study is a near realtime application of RSOI where the reconstruction period corresponds to a “very recent past”.
The optimal interpolation technique exploits the statistical relationship between the coarse real-time
and the dense climatic networks. It consists of two main parts. First, principal component analysis is
used to obtain a reduced-space description of the high-resolution precipitation data during a
calibration period. Second, data from the low-density real-time rain-gauge network are used to
estimate the scores of the leading principal components in the reconstruction period. In this way, the
method considers both the temporal evolution of the precipitation field during the reconstruction period
and the spatial covariance structure that is known from the long-term high-resolution climatology. A
detailed description of the method and its present application is provided in [1].
The domain considered in this study is Switzerland (Figure Error! No text of specified style in
document.-1Error! Reference source not found.a). We define two networks of rain gauges. The red
dots show a dense network of gauges with typically 420 precipitation totals available on individual
days. This corresponds to a median nearest neighbor distance of ~5 km. Furthermore, an ad-hoc
choice of a sparse network is shown by the blue circles. It has 51 gauges and a median nearestneighbor distance of ~20 km. The dense network data have been used for the construction of daily
precipitation grids by means of a modified SYMAP algorithm as described in [19] and [20, section 4].
The grids obtained in this way are available through 1960–2007. They are provided at a resolution of
~2x2 km and their effective spatial resolution is ~15x15 km [21,22]. These fields are the best estimate
of the daily precipitation distribution in Switzerland that we currently dispose of. We attempt to
reproduce these fields as closely as possible and therefore refer to them as the observations (OBS).
The long-term mean of OBS is shown in Figure Error! No text of specified style in
document.-1Error! Reference source not found.b.
Furthermore, we consider daily precipitation grids constructed from the sparse network (51 instead of
420 stations) in terms of two different interpolation methods. These methods are (i) reduced-space
optimal interpolation whose application is the focus of this study and incorporates the spatial
covariance structure of the OBS data, and (ii) the modified SYMAP algorithm, which is used as a
reference method (and is the same method used to construct the OBS fields from the dense network).
The corresponding grids are referred to as RSOI and SIMPLE, respectively, and are evaluated by
quantifying their agreement with OBS.
Finally, we test if the RSOI skill improves when the method is calibrated only with days of the same
weather type as the day for which the reconstruction is carried out (stratified application of RSOI; see
[1] for details). To this end, two classifications from version 1.1 of the COST 733 catalogue of CT
Figure Error! No text of specified style in
document.-2. Mean squared error skill score
(MSESS) of interpolated precipitation maps at
each grid point. (a) SIMPLE, (b) RSOI. Circles
show the locations of gauges in the sparse
network.
classifications [23] are used: the PCACA classification [24,25] distinguishing 5 CTs and the SANDRA
classification [26] with 22 types.
Main conclusions
RSOI is a statistical procedure which allows reconstructing daily precipitation fields from
measurements of sparse station networks. It is inherent to RSOI that it yields spatially smoothed
precipitation fields. Nevertheless, gridding in terms of RSOI clearly outperforms the SIMPLE reference
interpolation method (based on contemporaneous gauge data only) for the study domain and the
networks considered herein (Error! Reference source not found.). The improvement over the
reference method is particularly strong for locations at greater distance from the gauge locations.
Consequently, RSOI lends itself to gridding in a quasi real-time context, when only measurements of a
small part of the full gauge network are available. In fact, MeteoSwiss has started using RSOI to
operationally derive a preliminary spatial precipitation analysis for the previous day (with a slightly
denser real-time network than the one used in this feasibility study). The interpolation presented herein
is entirely based on gauge measurements and their covariance in space; it does not use other sources
of data such as radar measurements [e.g., 27,28]. Thus, RSOI is attractive as a reference for methods
using additional data sources, or in situations when no additional data are available.
It has been shown that the improvement due to the inclusion of weather type information is
comparatively small and depends strongly on the weather type. Stratification is generally more
beneficial for wet weather types than for dry types (Table Error! No text of specified style in
document.-1).
CT 1 CT 2 CT 3 CT 4 CT 5
MSESS (unstratified)
0.717 0.817 0.841 0.689 0.845
MSESS (stratified)
0.709 0.826 0.857 0.693 0.856
mean precipitation (mm d-1) 1.2
7.1
6.5
2.3
5.3
Table Error! No text of specified style in document.-1. Median mean-squared error skill score
(MSESS) for days of the five CTs of the PCACA classification, for unstratified RSOI (top row)
and RSOI stratified with respect to the circulation type (2nd row). The mean daily Swiss
precipitation for each CT is also shown.
Arguably, the following two reasons explain this finding: first, the estimation of the scores of the
leading principal components of the precipitation field is an integral part of RSOI. These leading scores
inherently contain information on the CT and an explicit stratification with respect to CTs appears to
add only relatively little extra information. Second, there is indication that the reduction in sample size
associated with the stratification may offset the potential benefits from circulation-type information.
Recommendation
CT information can – in principle – be introduced in procedures of spatial interpolation, via stratification
of the underlying statistical relationships and parameters. The added value that can be expected from
such a procedure depends on how complementary CT information is to other input data (notably the
station data), and on how strong the relationship is between circulation and the field of interest.
Moreover, the stratification can introduce sampling uncertainties which could (partly) offset the gain
from the CT information. Even though the added value was minor in the application studied, the
understanding we gained from this exercise suggests: Incorporation of CT information in spatial
analysis is worth being tested in areas where station density is very sparse, in combination with more
simple interpolation methods (e.g. those not exploiting covariance structures from past data), with
meteorological parameters that have a stronger (less variable) relationship to circulation than
precipitation (e.g. pressure, possibly temperature and sunshine duration), and when the interest is on
specific conditions with a known signal. Care should be exercised when using CT classifications with a
large number of types. A long calibration period might be important to avoid sampling uncertainty in
such applications.
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