ESSDEarth System Science DataESSDEarth Syst. Sci. Data1866-3516Copernicus PublicationsGöttingen, Germany10.5194/essd-10-235-2018seNorge2 daily precipitation, an observational gridded dataset over Norway from 1957 to the present dayLussanaCristiancristianl@met.nohttps://orcid.org/0000-0003-3159-4895SalorantaTuomoSkaugenThomasMagnussonJanTveitoOle EinarAndersenJessNorwegian Meteorological Institute, Oslo, NorwayNorwegian Water Resources and Energy Directorate, Oslo, NorwayCristian Lussana (cristianl@met.no)1February201810123524930June201723December20176December201728August2017This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://essd.copernicus.org/articles/10/235/2018/essd-10-235-2018.htmlThe full text article is available as a PDF file from https://essd.copernicus.org/articles/10/235/2018/essd-10-235-2018.pdf
The conventional climate gridded datasets based on observations only are
widely used in atmospheric sciences; our focus in this paper is on climate
and hydrology. On the Norwegian mainland, seNorge2 provides high-resolution
fields of daily total precipitation for applications requiring long-term
datasets at regional or national level, where the challenge is to simulate
small-scale processes often taking place in complex terrain. The dataset
constitutes a valuable meteorological input for snow and hydrological
simulations; it is updated daily and presented on a high-resolution grid
(1 km of grid spacing). The climate archive goes back to 1957. The
spatial interpolation scheme builds upon classical methods, such as optimal
interpolation and successive-correction schemes. An original approach based
on (spatial) scale-separation concepts has been implemented which uses
geographical coordinates and elevation as complementary information in the
interpolation. seNorge2 daily precipitation fields represent local
precipitation features at spatial scales of a few kilometers, depending on
the station network density. In the surroundings of a station or in dense
station areas, the predictions are quite accurate even for intense
precipitation. For most of the grid points, the performances are comparable
to or better than a state-of-the-art pan-European dataset (E-OBS), because of
the higher effective resolution of seNorge2. However, in very data-sparse
areas, such as in the mountainous region of southern Norway, seNorge2
underestimates precipitation because it does not make use of enough
geographical information to compensate for the lack of observations. The
evaluation of seNorge2 as the meteorological forcing for the seNorge snow
model and the DDD (Distance Distribution Dynamics) rainfall–runoff model
shows that both models have been able to make profitable use of seNorge2,
partly because of the automatic calibration procedure they incorporate for
precipitation. The seNorge2 dataset 1957–2015 is available at
10.5281/zenodo.845733. Daily updates from 2015 onwards are available at
http://thredds.met.no/thredds/catalog/metusers/senorge2/seNorge2/provisional_archive/PREC1d/gridded_dataset/catalog.html.
Introduction
Conventional climatological datasets are based on observed data
only and they provide valuable information for a large spectrum of
users in modern societies . The
Norwegian Meteorological Institute (MET) produces and maintains the
seNorge collection of high-resolution gridded datasets for daily
mean temperature and total precipitation in support of climate,
hydrology and atmospheric sciences in general.
The object of this paper is the daily total precipitation gridded
fields of the latest seNorge version 2.0 (or simply
seNorge2). It is worth mentioning that the seNorge2 daily
mean temperature dataset has been described in the paper by
. Despite being released only recently,
seNorge2 has already been used in a few applications, such as snow and
permafrost mapping and evaluation of
climate projections . Most
noticeably, the Norwegian Water Resources and Energy Directorate
(NVE) uses seNorge2 as meteorological forcing for the national
forecasting system for floods, avalanches and landslides. As
a consequence, the temperature and precipitation fields are
regularly updated on a daily basis.
The daily precipitation dataset has a focus on the Norwegian
mainland, though it extends into Sweden and Finland too, and it is
produced on a regular grid with 1km grid spacing in both
the Easting and Northing directions. The data are presented as (i) an
historical archive covering the period from 1957 to 2015, which is
available at http://doi.org/10.5281/zenodo.845733; (ii) daily
updates from 2015 onwards, available for public download at
http://thredds.met.no/thredds/catalog/metusers/senorge2/seNorge2/provisional_archive/PREC1d/gridded_dataset/catalog.html.
The current historical archive has been named “release 17.08”,
with reference to the release date August 2017. MET is planning to
make available regular updated releases of this dataset to the
users. The file format chosen is the Network Common Data Form
(netCDF) and the files include numerous descriptive attributes.
The seNorge2 statistical interpolation method is based on a modified optimal
interpolation
OI: scheme,
where innovative ideas on the interaction between precipitation at
different spatial scales have been implemented. OI has been
developed as an objective analysis scheme for meteorological
fields, and then it has been widely used in data assimilation to
provide initial conditions for numerical models
. The availability of a background or
first-guess field is a central component of OI. The concept of
a first-guess field was introduced in the context of objective
analysis during the 1950s
and it
coincided with the prior information used in Bayesian statistical
schemes. In our work, OI has been used as a spatial interpolation
technique and the background field has been estimated from the
in situ observations instead of
being observation-independent
information derived from numerical atmospheric models or
climatology, as for the “classical” OI. Bayesian spatial
interpolation schemes have been applied to precipitation in the
past
.
However, the absence of an independent background motivated us to
adopt an approach inspired by the successive-correction methods
in the form proposed by . The spatial
interpolation scheme developed for seNorge2 is based on an
iteration of a statistical interpolation scheme over a decreasing
sequence of spatial scales. This idea has been widely used for
mesoscale meteorological analysis in successive-correction methods; see
, and references therein. However,
we have adapted this method to the special statistical properties
of precipitation fields, and its implementation can be regarded as
an original contribution to this research field.
In the scientific literature, numerous approaches have been
described to address spatial interpolation of precipitation for
different combinations of spatial and temporal resolutions. In the
article by , a review and
inter-comparison of six interpolation methods can be found. Not
surprisingly, a number of inter-comparison studies have found
“inhomogeneities in the gridded data that are primarily caused by
inhomogeneities in the underlying station data”
.
describes a three-step process
interpolation technique, aimed at establishing E-OBS:
a pan-European archive of observational gridded datasets at monthly
and daily timescales, available on a 0.25∘ by
0.25∘ latitude–longitude grid. First, monthly totals are
interpolated using thin-plate splines . Second,
daily values are obtained using Kriging
and taking into account the
monthly totals. The third step aims at obtaining uncertainty
estimates for E-OBS. In this paper, we will use E-OBS as
a reference dataset to evaluate seNorge2. The conclusions of the
work by favor the use of statistical
interpolation schemes based on a two-step approach, where the
background is estimated from the data, such as Kriging with external drift
that is rather similar to OI. In addition, they
conclude that the inclusion of a single topographic predictor may
be sufficient in the interpolation, and they support “the common
practice of using a climatological mean field as a background in
the interpolation of daily precipitation”. OI combined with
principal component analysis have been used to reconstruct
historical climate datasets of precipitation in Switzerland
. In the paper by
, an interpolation approach based on local
weighted linear regression (LWLR) has been compared with local
regression Kriging (RK). This last method (RK) uses only
geographical coordinates and elevation, while LWLR uses several
additional geographical parameters, such as slope steepness, slope
orientation and distance from the sea. LWLR shows better results
than RK at high-elevation sites provided that the data density is
sufficiently high, while “RK is more robust in performing
extrapolation over areas with complex orography and scarce data
coverage, where LWLR may provide unrealistic precipitation
values”, thus indicating that the inclusion of additional
geographical information in complex terrain can actually improve
the interpolation results, though once again the results of
a method over a specific domain strongly depend on the station
network available. The paper by contains
important remarks and recommendations on the use of gridded
datasets for computing temporal trends of precipitation, which is
not at all straightforward because of “artifacts in trend patterns
due to local inhomogeneities in the data and the station network”.
The previous seNorge versions (v1.0 and v1.1) were based on
a linear estimation of precipitation on the grid
: for
each point, the three closest observations are identified by means
of a triangulation procedure, and then the (linear) estimated value is
adjusted taking into account both the elevation differences and the
geographical characteristics of the site surrounding the grid point
that may cause undercatch of precipitation due to the effect of
wind (i.e., “wind field deformation and deflection of hydrometeors over the
gauge orifice results in a systematic measurement bias” –
).
seNorge2 uses the information from much more than the three closest
stations to estimate precipitation in a location; in addition,
geographical information such as elevation, latitude and longitude
has been incorporated into the statistical interpolation scheme.
seNorge2 has been evaluated by means of several complementary
approaches, such as analysis of a case study; accumulation over a temporal
period much longer than 1 day; verification of the
performances at station locations by using summary statistics and
skill scores; and verification of the performances over grid points by
comparing seNorge2 to E-OBS, which was recently chosen by the
Copernicus Climate Change Service as a reference dataset for Europe
(https://insitu.copernicus.eu/news/the-european-climate-assessment-dataset-and-copernicus).
Because of the importance of seNorge2 as input for hydrological
applications, the indirect evaluation of the precipitation fields
as components of the water cycle by means of snow and hydrological models has
been included in the paper. Indirect evaluation relies
on the fact that successful modeling of hydrological processes
requires reliable meteorological forcing data, which is a crucial
but often undervalued element of the model chain
e.g.,. Indirect evaluation has proven useful in the
verification of surface models
, for example. Our approach is similar to
the one described by to evaluate long-term
precipitation.
The outline of the paper is as follows. Section
presents the geographical area and the observations used. In
Sect. the seNorge2 statistical interpolation
method is described. The evaluations of the precipitation fields
at station locations and over the grid points are reported in
Sect. . The indirect evaluation of precipitation as
a component of the water cycle is reported in
Sect. , together with brief descriptions of the
seNorge snow model and the DDD (Distance Distribution Dynamics)
rainfall–runoff model that have been used for the indirect
evaluation.
seNorge2 domain, topography (gray shades, meters
above mean sea level) and station locations (blue triangles, valid for the
date: 24 November 2014). The total number of station locations in the example
is 737. The top-left inset shows the time series for the number of available
observations for the whole period covered by the dataset: 1957–2015; the red
line marks the day 24 November 2014. The two lateral panels show the
distributions of elevations for both the digital elevation model (gray dots)
and stations (blue dots) along the Easting (bottom panels) and Northing
(lateral panel) coordinates.
Geographical area and data
The seNorge2 domain is shown in Fig. . The geographical area of interest is
the Norwegian mainland, plus a strip of land extending into Sweden
and Finland that has been added so as to properly cover the Norwegian
catchments stretching along the national borders. The domain is
characterized by a complex topography, with the highest peaks above
2000m in southern Norway and in northern Sweden. The
steep topography is known to cause pronounced orographic
enhancement of precipitation along the Norwegian coast, especially
along the western coast of southern Norway.
The daily precipitation for day D has been defined as the
accumulated precipitation between 06:00 UTC of day
D-1 and 06:00 UTC of day D. The dataset
is based on in situ observations from the Norwegian Climate
Database (data.met.no). We also include data from the European
Climate Assessment Dataset ECA&D: for
regions neighboring Norway. The original non-homogenized time series
have been used, to have a larger dataset than the one provided by
the homogenized time series. The number of stations used for the
interpolation varies with time due to data availability and the
station distribution is uneven throughout the spatial domain. As
an example, in Fig. the spatial distribution of
stations for 24 November 2014 is shown, together with the
time series of the number of available observations for the whole
period covered by the dataset. In the case of 24 November 2014,
which is close to the end of the period covered by the historical
dataset, 737 observations were available. The number of
observations vary between 600, before 1960, and approximately 900 during the
seventies and the nineties, and then the number of
observations gradually decrease to approximately 700 before
increasing again after 2010. In general, the station network is
denser in the southern part of the domain, while it becomes sparser
in its northernmost part. With reference to the hierarchy of
atmospheric motions proposed by , the average
distances between nearby station locations correspond to the lower
boundary of the mesoscale (meso-γ), and they are consistent with the
representation of thunderstorms, thunderstorm groups and
fronts. The two panels in Fig. show the distribution
of station elevations together with the domain topography; the
stations are located at elevations that seldom exceed
1000m, so that it might be expected that predicted
precipitation fields would be more representative and accurate for
lower elevations than in the highest mountains.
MethodsOptimal interpolation
The OI aims at providing the best (i.e., minimum error variance for
the analysis), linear, unbiased estimate of the unknown
meteorological field by combining prior information (i.e., background) on the
grid with in situ observations. In the
following, we use the same notation as (based on
): the vector y indicates
the m
observations of either air temperature or precipitation, and the
vector x represents the n grid cells. Superscripts
o, b and a denote observation,
background and analysis, respectively, while the superscript
t indicates the unknown true value. Matrices are in
bold roman type (capital letters). Scalar variables are in italic
type, so the ith component of a vector x is xi,
while for a generic matrix W, components are indicated
as Wij.
OI relies on the assumptions of Gaussian distribution for both the
observation error
εo≡yo-yt
and the background error
εb≡yb-yt
(or
ηb≡xb-xt
for grid points). As a consequence, their distributions are
completely defined by their mean values and covariance matrices
only. Both the observations and the background are assumed to be
unbiased estimates of the true value and their error covariance
matrices are specified by means of analytical functions, such
that εo∼N(0,R),
εb∼N(0,S) and
ηb∼N(0,B). Furthermore, observations and background are regarded
as uncorrelated variables.
The analysis is also a random variable with a Gaussian
distribution and its mean values on the grid
and at station locations can be written as
xa=xb+Kyo-yb,ya=yb+Wyo-yb,
where the two matrices of interpolation weights are K, the gain
matrix, and W, the influence matrix.
The equations for the weight matrices K and W
depend on our choices for the error covariance matrices. The
observation error covariance matrix R is assumed to be
diagonal and all the observations are assumed to have the same
error variance σo2; then,
R≡σo2I (I
is the identity matrix). The background error covariance matrices
requires the specification of the correlation between two generic
points ri=(xi,yi,zi) and
rj=(xj,yj,zj), which for us is
the correlation function ρ:
ρ(ri,rj)=exp-12d(ri,rj)Dh2+Δz(ri,rj)Dz2,
where d(ri,rj) is the horizontal
distance between the two points; Δz(ri,rj) is the difference between their
elevations; Dh and Dz are the horizontal and vertical
de-correlation lengths, respectively. The generic component
Sij of the background error covariance matrix at
station locations (a similar expression holds for B too)
is
Sij≡σb2ρ(ri,rj),
where ri and rj indicate the locations of
the ith and jth stations, and the background error variance
σb2 is assumed to be the same for all the
points. The components of the background error correlation matrix
at station locations S̃ can be written as
S̃ij≡ρ(ri,rj),
while the background error correlation matrix between grid points
and station locations is the n×m matrix with
components
G̃ij≡ρ(ri,rj), where
ri indicates the spatial location of the ith grid
point and rj is the jth station location.
Given our assumptions about the error covariance matrices, the
expressions for the weight matrices are derived directly from the
theory of linear Kalman filters :
K=G̃S̃+ε2I-1,W=S̃S̃+ε2I-1,
where ε2 is the ratio
σo2/σb2.
Two elements of the OI diagnostics are introduced in this
paragraph, because they have been used in the optimization of
parameters (Sect. ). First, the integrated data influence
IDI: is the
sensitivity of the analysis in a generic point on the domain to
variations in the observations, independently of the actual
observed values. In practice, the IDI field is the result of an OI
scheme where the observations are set to 1 and the background is
set to 0, such that regions where the observations effectively introduce
information have IDI values close to 1. On the other
hand, for data-void regions the IDI values are close to 0.
Second, the leave-one-out cross-validation (CV) analysis
yˇa: each component of the m-vector
yˇa is the analysis value obtained for
the corresponding station location by using all the other
observations, but without using the observation measured at that
station location. The equation for yˇa
can be written as yˇa=yo+wTya-yo,
where the vector w has components wi=(1-Wii)-1. The deviation between the
CV analysis and its corresponding observation represents an
estimate of the analysis error based on the idea that each
observation is used as an independent verification of the analysis
field. Because not all the available information is used, the error
estimate can be regarded as a conservative one.
Spatial interpolation of daily accumulated precipitation
The precipitation field is regarded as a composition of several
(precipitation) events, which are considered individually, in the
sense that the statistical properties of the field are allowed to
change between events.
For each event, the statistical interpolation scheme has been
implemented by means of an iterative algorithm on
a cascade of spatial scales, ranging from the synoptic
scale down to the small scale. As stated in ,
given the filtering properties of OI, the choice of the scale
parameters Dh and Dz in the correlation function ρ
(Eq. ) determines a minimum distance scale
(wavelength) resolved by the analysis. In addition, the spatial
resolution of the observational network dictates a minimum for
that choice because those small spatial features not resolved by the
observational network will not be accurately represented by the analysis. The iterative algorithm
presented
exploits the OI filtering properties. Starting from a first-guess
of the average precipitation value (i.e., the largest scale), several
successive iterations of OI-derived corrections (over a decreasing
sequence of values for Dh) are applied to the predicted
precipitation field.
Identification of events
An individual event on the grid is a connected zone of grid points
where the precipitation exceeds the predefined threshold of
0.1mmday-1.
Initially, a first guess for the distribution of events both on
the grid and for station locations is obtained. The observations
measuring precipitation (i.e., wet observations) are
tentatively grouped in events by using a triangulation-based
procedure: two wet observations are assigned to the same event if
a direct connection between them exists (i.e., they lie on the
vertices of the same triangle) or if they are connected through
only one observation not measuring precipitation (i.e., vertices of
adjacent triangles). In this latter case, the observation not
measuring precipitation (i.e., dry observation) is also
included in the first guess of that event. Then, an interpolation
procedure based on the nearest neighbor is used to group grid points
into events. The precipitation is set to 0mm for all
the grid points outside the event areas.
In the second step, each event is considered individually, aiming
at determining those grid points where precipitation is most
likely to occur. The question is to decide whether the analysis
at a grid point is more influenced by the surrounding wet
observations or by the dry ones. As described in
Sect. , the influence on the analysis of a set of
observations can be quantified through the IDI value. Suppose
that the ith grid point has been assigned in our first guess to
a specific event: then precipitation is most likely to occur there
if the IDI of the wet observations (xIDIw)
included in the event under consideration is greater than or equal to
a fraction of the IDI of the dry observations
(xIDId):
xiIDIw≥0.6⋅xiIDId→precipitation occurs at theith grid point.
We require that the influence of the dry observations
xiIDId must be considerably larger than
xiIDIw for a grid point to be considered “dry”.
This can be regarded as a conservative choice; in case of uncertainty (i.e.,
when xiIDId and xiIDIw are not too different),
we prefer to estimate
a precipitation value for the ith grid point instead of taking
the more drastic decision of setting it to 0. The factor 0.6
in Eq. () has been set as in
, because it improves the agreement
between the model results and the observations. As described in
Sect. , the IDI values are obtained as the analysis
values (Eq. ) with the background set to 0 and the
observed values set to 1. In this case, the OI parameters used
in the IDI elaboration can vary from grid point to grid point:
Dh is the horizontal distance to the closest available station
location (irrespective of the observed value); Dz is the
maximum elevation within the event first-guess (a minimum value of
500m is pre-set); ε2≡σo2/σb2=0.1, which means
that we impose the IDI field to fit the value 1 in the
surroundings of observation locations.
Finally, adjacent (connected) grid points where the precipitation
is most likely to occur are assigned to the same event and the
event gets a unique label. The wet observations are assigned to
the same event of the surrounding grid points. In the special case
of a wet observation surrounded by dry grid points only, a new
event is created. The isolated wet observation is associated with
this new event, together with the closest grid points. This special
situation may occur in dense station areas (i.e., station density
comparable to the grid resolution) when, for example, only one
station measures precipitation.
Iterative optimal interpolation
As stated in Sect. , the iterative algorithm
operates on a cascade of spatial scales, which is defined through
a decreasing sequence of K values for Dh=large
scale,…,local scale. The largest scale
D1h is set to the semi-major axis of the ellipsoid of
minimal area enclosing all grid points of the event under
consideration (i.e., its ellipsoid hull), and then
Dk+1h=Dkh-10km (k=1,…,K) and the
local scale DKh are set to the minimum distance between two
stations (the minimum allowed value is 10km).
The regional topography influences the precipitation patterns,
and consequently points at the same elevation tend to be more
correlated than points at different elevations. Because of that,
we have decided to include elevation differences in our
(de)correlation functions ρ (Eq. ). The sequence
of K vertical scales Dkz is not predefined, such as for
Dh. On the contrary, they are optimized every time step and
for each Dkh value. The optimal Dkz is chosen
among four possible values Dz={5000m,2000m,1000m,500m}. A value
of Dz=5000m means that the de-correlation of
precipitation along the vertical is actually not needed; then, the
de-correlation gradually increases with decreasing Dz. By
decreasing the correlation ρ between points, we also reduce the spatial
extent of the area of influence that every
observation has on the analysis. Because our method is based only
on observations, a predefined lower limit of 500m has
been set for Dz; otherwise, the total extension of data-sparse
areas may become too large.
The application of the OI iterative scheme requires the definition
of two further elements: (1) a spatial averaging operator
…h,v to process the vector-observed
values. The operator is applied to its components to
obtain for each station location a “processed observation” meant
to represent the average precipitation in a neighborhood of a predefined size
around that location. The neighborhood
considered is a cylinder of radius h and height v, having its
center of mass at the station location; (2) ε2
(Eqs. –), the ratio between the
observation and background error covariances ε2, specifies the
weight of the new information (i.e., the processed
observations) compared to the background. At each iteration, the
background is the result of previous iteration steps, and it
represents the integrated effect of the larger spatial scales.
ε2 is set to 0.1, as in the IDI calculation of
Sect. , and its value is kept constant in the
elaboration.
The iterative OI algorithm is based on two nested loops.
The outer loop over the Dh={large
scale,…,local scale} scales (index
k=1,…,K). For the k iteration, the background is the
analysis obtained at iteration k-1: xkb=xk-1a and ykb=yk-1a. As initial conditions, the vectors
x1b and y1b are set to
the mode of the distribution of observed precipitation values.
The inner loop over Dz={5000m,2000m,1000m,500m}
(index c=1,…,4). The observation vector used is the
processed observation yk,co≡yoDkh,Dcz. First, the cross-validation
analysis yˇk,ca is computed as in
Eq. (), where the influence matrix W is
computed using the pair (Dkh,Dcz) in
Eq. () to define the correlation function. Then, the
optimal value for Dz (D̃z) is chosen as the one
that minimizes the relative error between
yˇk,ca and
yk,co (i.e., relative error = prediction/observation). However, we are not using the actual (CV)
predicted and (processed) observed values in the definition
of relative error. In fact, the “started logs” (st.log)
of those values have been
used, so as “to ensure an equal scaling of positive and negative
deviations of prediction from observations and because the
relative error is highly sensitive to small observations that
might be under or overestimated by a large factor in the
prediction” . The relative error is written asrelsk,c=1m⋅∑j=1mst.logyˇj,k,ca-st.logyj,k,co2,where …j,k,c indicates the jth vector component for iteration
(k,c) and the started logs are defined asst.logx=log10xif x>lc,log10lc+x-lc/lc⋅ln(10)if x≤lc.The critical threshold has been set to lc≡1.5mm.
Out of the inner loop and back to the outer loop. The analyses xka (Eq. ) and
yka (Eq. ) are obtained; the
weight matrices K and W
(Eqs. –) used in the analysis
procedure are computed with the correlation function ρ
(Eq. ) defined by the two parameters Dh and
D̃z.
The final analyses are xa=xKa and ya=yKa.
Evaluation of the precipitation fieldsCase studies
In Fig. , two examples of precipitation fields are
shown. In the top panel, a case study for daily precipitation is
presented, which has been chosen because it is representative of
a typical situation where intense precipitation occurs. The presence of
a low-pressure system over southern Norway causes the
advection of moist air from over the ocean towards the mainland,
thus determining intense precipitation along the coast, especially
in the presence of steep topography (see Fig. ). The figure also
gives an idea of the range of spatial scales involved
in such a precipitation event. In this case, the most intense part
of the precipitation takes place in the south, over an area of
about 500km by 500km; inside this region, precipitation
hotspots of different sizes are present, with the most intense ones
(red colors) having an extension of no more than 50km by
50km and often far less than that. The higher the
station density, the finer would be the effective spatial
resolution (i.e., spatial detail) of the final prediction. In the
bottom panel, the seNorge2 mean annual accumulated precipitation
field for the 30-year period 1981–2010 is shown. The
precipitation patterns agree quite well with the expected
climatology e.g.,. The highest
precipitation amounts of more than 3000mm are recorded
along the western coast in southern Norway. The regions with the
lowest annual precipitation amounts are recorded inland in the
north and on the leeward side of the highest Norwegian mountains in
the south.
Verification at station locations
Figure shows the equitable threat score
ETS:, which “measures the
fraction of observed events that were correctly predicted,
adjusted for hits associated with random chance” (see the WWRP/WGNE
Joint Working Group on Forecast Verification Research website at
http://www.cawcr.gov.au/projects/verification). Three
gridded datasets of daily precipitation have been considered: (i)
seNorge2; (ii) E-OBS (described in the introduction; version 16.0 has been
used); and (iii) seNorge2 upscaled onto the E-OBS coarser
grid of about 20km by 20km
(i.e., 0.25∘ by 0.25∘ regular latitude–longitude grid),
so as to allow for a comparison between
E-OBS and seNorge2 performances when both datasets have a similar
representativeness (i.e., represents same spatial scales). Because
a grid point value represents area mean conditions across (at
least) one grid box, the upscaling has been done by averaging all
the seNorge2 grid points within the coarser E-OBS boxes (as
recommended by Christoph Frei and Phil D. Jones; see the Appendix
of the UERRA report
http://uerra.eu/component/dpattachments/?task=attachment.download&id=42).
The ETS has been computed by taking into account all the available
Norwegian data in the period 1981–2010 (i.e., approximately
5 000 000 observations) and the values extracted from the
precipitation datasets have been evaluated against the
observations. By taking into account a 30-year period, the
dataset should include enough extreme precipitation events, such
that the statistics of those rare events can be considered
meaningful. Note that the observations have been used in the
spatial interpolation, so they do not constitute independent information, and
for this reason such an evaluation provides
information only for the performance at station locations and not
over grid points.
seNorge2 examples. (a) Total precipitation for the day
24 November 2014. (b) Mean annual precipitation, based on the annual
precipitation from 1981 to 2010.
Equitable threat score (ETS) for daily precipitation over all the
available Norwegian stations. Datasets are seNorge2 (red); seNorge2 upscaled
to the E-OBS grid (blue, 0.25∘×0.25∘ geographical
latitude–longitude coordinate reference system); and E-OBS (green). Several
precipitation thresholds have been considered: 1, 2, 4, 8, 16, 32, 64 and
128mmday-1. Time interval: 30 years, from 1981 to 2010.
Daily precipitation comparison between E-OBS
and seNorge2, which has been upscaled to the E-OBS grid (0.25∘×0.25∘ geographical latitude–longitude coordinate reference system).
(a) Fitted linear regression coefficient, seNorge2=coeff⋅EOBS; regions where the coefficient values are
smaller than 0.8 or larger than 1.2 are highlighted by thick contouring
lines. (b) Correlation coefficient. The two insets in the top-left
corners in the panels show the elevation dependence of the corresponding
variable; note that the box width is proportional to the number of points in
the elevation range.
seNorge2 considered at its original resolution clearly shows the
benefits of a finer effective resolution, if compared to E-OBS,
especially for intense precipitation. The ETS is generally above
0.9, and even for precipitation amounts higher than
128mmday-1 the fraction of observed events that
were correctly predicted is approximately 0.8. The best
performances are obtained for daily precipitation amounts around
10mmday-1, probably because such intensities are
often (i.e., more frequently than for the other intensities)
related to large-scale precipitation and the uncertainties
associated with intermittency are less significant. The
comparison of seNorge2 and E-OBS over the same (coarser) grid shows that the
two datasets perform rather similarly. seNorge2 has
higher ETS values than E-OBS for most of the thresholds, though
E-OBS presents slightly better ETS for the most intense
precipitation amounts.
Verification over grid points
The quality assessment of seNorge2 precipitation fields over grid
points has been done by comparing them against the pan-European
reference E-OBS dataset (version 16.0). The dataset is compared
on the E-OBS 0.25∘ by 0.25∘ regular
latitude–longitude grid. Figure shows the results regridded
over the original seNorge2 grid with a nearest-neighbor interpolation, such
that the sizes of the boxes reflect the E-OBS grid resolution. As for
Sect. , the 30-year
period 1981–2010 has been considered in the verification, such
that the statistics should be robust and resistant. E-OBS and
seNorge2 are based on different spatial interpolation methods, but
they use the same observations. seNorge2 makes use of more
observations over Norway, in addition to the ECA&D dataset that
is the E-OBS archive of observations. As a consequence, the
assessment of seNorge2 presented in this section is relative to
the E-OBS performances, rather than being in absolute terms.
In Fig. , the comparison between E-OBS and seNorge2
daily precipitation shows that the two datasets are rather similar
over most of the domain. The fitted linear regression coefficient
shows that for most grid points seNorge2 precipitation is within
±20% of E-OBS precipitation and often very close to
1. Note that in the work by , the
precipitation biases in a high-resolution gridded dataset over
the Alps (underestimate) due to measurement biases and network
biases (i.e., “distribution of rain gauges is biased, with
high-elevation areas being undersampled in comparison to lowland
and valley-floor conditions”) is estimated to be within 5 and
25% (up to 40% in winter for elevations
higher than 1500m). A multiplicative bias of up to ±20% between seNorge2 and E-OBS daily precipitation can
be considered a satisfactory agreement between the dataset. The
correlation coefficient is also above 0.9 for a large portion of
the domain.
As highlighted by the boxplots in the two insets of
Fig. , the significant differences between the two
datasets are found in southern Norway; in the mountain area where
the highest peaks are located, seNorge2 underestimates
precipitation compared to E-OBS. For elevation higher than
1000m, the linear regression coefficient gradually
decreases, and it reaches the value of approximately 0.6 at
2000m. Analogously, the correlation coefficients
decrease to values of about 0.8 at 2000m. As an
explanation, we have verified that in our interpolation method
(Sect. ), as Dh becomes smaller and smaller, the
optimization of Dz also favors the smallest value of
500m, so that the adjustments at local scales involve
a smaller number of grid points (i.e., in both the horizontal and vertical
directions) than the ones for the larger spatial
scales. By design, the interpolation scheme reconstructs local
precipitation features only in the surroundings of station
locations, where these features can be trusted, while in data-void
areas the precipitation field is determined by the large-scale
signal recovered by the available network of gauges. However, for
those regions where the average difference between station
elevations and topography is twice the Dz value or more,
elevation differences matter much more than differences in the
horizontal distances. Given the raingauge network bias towards
the lowest elevations (see Fig. ), we may argue that
the biases (underestimation) shown in Fig. result
from the fact that seNorge2 in the (almost) data-void areas of the
mountains in southern Norway is representative of larger spatial
scales than the ones recovered by E-OBS.
Note that Fig. also shows a few grid points where
seNorge2 predictions significantly overestimate precipitation
compared to E-OBS (red colors in the top panels) and the
correlation reaches values between 0.7 and 0.8. Most likely,
these are the local effects of observations that have been
included in seNorge2 only, thus bringing valuable information on
a local scale that is not present in E-OBS.
Indirect evaluation of precipitation as a component of the water cycle Comparison to hydrological observations
In Fig. , the annual average catchment water
balance is shown as the sum of runoff and actual
evapotranspiration (i.e., sinks of water) against precipitation (i.e.,
input). The years from 2000 to 2013 have been considered
and the 151 runoff measurements capture the outflow from
catchments without artificial influence (e.g., hydropower) and
glaciers. The actual evapotranspiration estimates were obtained
from the MODIS Global Evapotranspiration Project
.
Average yearly precipitation (inputs of water to the catchment)
against the sum of average yearly runoff and actual evapotranspiration
(losses of water from the catchment) for the period from 1 January 2000 to
31 December 2013 for seNorge1.1 (blue) and seNorge2 (red). The upper left box
shows the distribution of regression residuals when the sum of runoff and
actual evapotranspiration exceeds 2000mmyr-1.
The datasets considered in the comparison are (i) seNorge2 and (ii)
seNorge1.1 (see the introduction). The
regression lines are obtained through the application of a robust
and resistant procedure as described in
. seNorge1.1 shows higher annual
total precipitation than the water losses for most catchments
(coefficient of regression 1.08), while seNorge2 underestimates
the input term in the water balance (coefficient of regression
0.63). The linear regressions between precipitation and the sum
of runoff and evapotranspiration show a higher coefficient of
determination (r2) for seNorge1.1 than seNorge2. On the
other hand, the seNorge2 points tend to lie closer to the
regression line, as shown in the box on the upper left of
Fig. where the regression residuals are
reported for both versions. The sum of squares of residuals
(i.e., residual = precipitation - predicted value by the linear
regression) for seNorge1.1 is twice as large as the one for
seNorge2: 12 958 521.8 (mmyr-1)2 for
seNorge2 against 25 435 946.8 (mmyr-1)2 for
seNorge1.1. As a consequence, seNorge2 provides less accurate
(i.e., higher bias) but more precise (i.e., lower spread) estimates
of the annual averaged precipitation than seNorge1.1.
The model underestimation (Fu, red circles) and
overestimation (Fo, blue circles) areas of SCA (% of all grid
cells) in the three regions (Fig. ) and for the two grid data
versions (v.1.1 in the left column and v.2 in the right column) in 2001–2015
(on the days when a MODIS satellite image is available for comparison). The
solid lines denote GAM curves (with standard error) fitted to the cloud of
points. The horizontal dashed lines denote the 5% deviation level
within which the model results are considered “good” in NVE operational
snow mapping .
The bias index B for SCA in the seNorge grid cells for the two
gridded dataset versions (v.1.1. in a and v.2 in b) in
March–July 2001–2015. In (a), the three regions used in
Fig. are shown.
Impact on the seNorge snow model simulations
Daily updated maps of snow conditions have been produced for
Norway since 2004 by using the seNorge snow model
www.seNorge.no; and the seNorge conventional
climatological datasets as model forcing data. The simulated snow
maps are used among others by the avalanche and flood forecasting
services, hydropower energy situation analysis, as well as the
general public.
Briefly described, the seNorge snow model (v.1.1.1) uses
a threshold air temperature to separate between snow and rain
precipitation, handles separately the ice and liquid water
fractions of the total SWE, and keeps track of the accumulation and melting
of snow. The daily snowmelt rate is a function of air
temperature and solar radiation. The two melt model parameters are
estimated using the extensive melt rate data from Norwegian snow
pillows . Moreover, the average grid cell
snowmelt rates are also affected by the simulated fraction of
snow-covered area (SCA) in the model grid cells.
In the evaluation, the seNorge snow model is run with the
temperature and precipitation from the seNorge1.1 and seNorge2
conventional climatological datasets as forcing in the period
2001–2015, and the simulated SCA values in the grid cells are
compared to the corresponding SCA values derived from MODIS
(MODerate resolution Imaging Spectroradiometer;
http://modis.gsfc.nasa.gov/) satellite images using the
Normalized Difference Snow Index (NDSI) and the Norwegian Linear
Reflectance to snow cover algorithm (NLR)
. No specific
model calibration has been done prior to this evaluation. For
each day when a satellite image is available, each grid cell is
classified into three categories: model underestimation or overestimation, or
good match. A good match is defined here as when the difference in the
simulated and observed SCA does not exceed
±50%-points. These three categories are
also assigned scores of -1, 0 and +1, respectively. This
type of classification is applied in order to make the analysis
more robust to systematic errors that can be present in the
observed satellite-based SCA, e.g., due to the effect of forest
canopy over the snow-covered area.
In order to make regional summaries of the evaluation results,
Norway is divided into eastern, western and northern regions and
the fraction of the region's grid cells where the model
simulations significantly underestimate (Fu) and
overestimate (Fo) in comparison to the observed SCA
(i.e., a deviation exceeding ±0.5) are calculated for each
day a satellite image is available.
As the maximum deviation between observed and simulated SCA may
occur at different times in different elevations and regions,
a monthly mean of the model fit category scores (-1,0,+1)
is calculated for each seNorge grid cell and month (if at least
15 score values are available for the particular grid cell and
month). Then, a bias index B is defined for each grid cell by
summing up the minimum and the maximum values (i.e., the largest
underestimations and overestimations) of the monthly mean scores (if at
least three monthly means are available). This index B should
reflect the systematic bias (if any) in simulated SCA in the
particular grid cell encountered during the period from March to
July.
90% percentile values of the model underestimation
(Fu) and overestimation (Fo) (in % of grid
cells) in the three regions and for the two versions of the conventional
climate dataset.
* Based only on data from the Norwegian climate database, without using ECA&D data outside Norway.
The regional model underestimation and overestimation (Fu,
Fo) of the SCA, based on a total of 369, 318 and
265 MODIS images in eastern, western and northern Norway,
respectively, are shown in Fig. . The
90% percentile values of Fu and
Fo are shown in Table . These
results show that the snow model run with seNorge1.1 data forcing
clearly overestimates the SCA in the main melting season
(May–June) in eastern and western Norway (Fig. ).
When the snow model is run with the seNorge2 data forcing, the
average Fu and Fo are roughly within
a 5% deviation level for the whole analysis period
from March to July in eastern and western Norway
(Fig. ). In northern Norway, however, the
results show a different pattern, where the snow model run with
seNorge1.1 data forcing performs rather well, while the model
application based on seNorge2 data forcing significantly
underestimates the SCA in May–June (Fig. ;
Table ).
The maps of the bias index B (Fig. ) reveal the
patterns of SCA overestimation in eastern and western Norway when
using seNorge1.1 data, and of SCA underestimation in northern
Norway when using seNorge2 data.
Impact on the DDD hydrological model simulations
The DDD rainfall–runoff model
has been
calibrated using the seNorge2 meteorological grid over 136
Norwegian catchments (see Fig. ). Input to the DDD
model is only precipitation and temperature; the model is semi-distributed in
that the moisture accounting (rainfall and snowmelt) is performed for 10
elevation zones of equal area. DDD has a two-dimensional representation of
the subsurface reservoir allowing
for spatial variability of groundwater levels as a function of
distance from the river network. Similar to the seNorge snow model,
snowmelt is estimated using a calibrated temperature index model
(without the additional solar radiation term) and a calibrated
threshold temperature separating solid and liquid precipitation.
The runoff dynamics of the DDD are characterized by a parsimonious
parameter regime where the parameters are individually estimated
from Geographical Information Systems (GIS) or from observed runoff
records (recession analysis) and not collectively against observed
runoff. Estimating the parameters in such a way reduces the
tendency of model parameters when calibrated as a set, to
collectively compensate for errors in input data and model
structure, and hence acquire unrealistic values. DDD is calibrated by
optimizing the Kling–Gupta efficiency (KGE) skill score
where the parameters are optimized so that
correlation is maximized, variability is reproduced and bias is
minimized.
Geographical distribution of Pcorr. The
inset shows
the histograms with the distribution of Pcorr values; the mean
value is reported.
The model parameters for the catchments have been calibrated for
the period 1 September 2000 to 31 December 2014 and validated for
the period 1 September 1985 to 31 August 2000. Then, in total,
about 30 years of data are involved in the evaluation.
The mean KGE for the 136 catchments is 0.87, and the mean bias
is 0.1%, indicating that the volume of observed and
simulate runoff was practically the same. The ability in DDD to adjust the
amount of precipitation obtained from the meteorological grids was crucial
for obtaining such a low bias. The
adjustment is made through a correction factor that linearly
increases/decreases the precipitation in the course of the
calibration. DDD has the ability to use different correction
factors for precipitation as liquid (rain Pcorr) or solid
(snow Scorr).
The correction factor Scorr should be higher than
Pcorr due to the expected greater gauge undercatch for
snow compared to liquid precipitation. However, for a calibrated
parameter set, this is not always the case. For this study, the
calibrated correction factors for precipitation and snow are meant
to evaluate the seNorge2 dataset.
In general, the water balance seems reasonable, although the
simulated actual evapotranspiration (AE) shows lower values when compared
with the ones reported in Sect. , and
it displays a rather high variability. Values of AE lower than
the expected ones indicate that the correction factors are also too
low, since the runoff volumes have reasonable values. So, with the
understanding of a possible underestimation of AE, we interpret
the calibrated corrections as indicators of underestimation/overestimation of
precipitation in the seNorge2 meteorological grid.
Figure shows the calibrated Pcorr values
plotted according to the centroid of the catchment they represent.
The histograms of the calibrated Pcorr are also displayed.
We see that the mean value for Pcorr (1.25) is well
beyond 1.0. The geographical distribution of Pcorr
reveals that seNorge2 underestimates liquid precipitation on the
western coast along the country and in the mountains. These results
are consistent with the analysis of Sect. .
Scorr behaves rather similarly to Pcorr, with
a mean value of 1.18.
The seNorge2 dataset 1957–2015 is available at
https://doi.org/10.5281/zenodo.845733. The observations of daily
precipitation measured by the network of stations managed by the Norwegian
Meteorological Institute can be downloaded at frost.met.no. Some of the
agreements signed with the station data providers (i.e., other than the
Norwegian Meteorological Institute) restrict the redistribution of the station data
and they cannot be made freely available through frost.met.no. Please
contact the corresponding author for further information.
Conclusions
The seNorge version 2.0 (seNorge2) high-resolution observational
gridded dataset for daily total precipitation over Norway is
described in this paper. The main objective of the dataset is to
support climate and hydrology applications and is presented on
a high-resolution grid with 1 km of grid spacing in both the zonal
and meridional directions.
The MET observational network of raingauges is denser in the
southern part of the domain and sparser in the north. The number of
observations varies between 600 and 900, depending on the
year. In addition, the distribution of observations has a bias towards
the lower elevations and the highest densities are found locally
along the coast. Most of the mountainous regions present a very
sparse measurement network, especially for elevations above
1000m.
The climatological archive goes back to 1957 and is distributed
in a single large file covering the time period 1957–2015, which
is available for public download at
http://doi.org/10.5281/zenodo.845733. Daily updates are
stored and made available for public download at
http://thredds.met.no/thredds/catalog/metusers/senorge2/seNorge2/provisional_archive/PREC1d/gridded_dataset/catalog.html.
Furthermore, the data are shown on the web portals senorge.no
and xgeo.no.
The spatial interpolation scheme relies on statistical (Bayesian)
methods and is based on a combination of two classical interpolation schemes,
namely optimal interpolation and
successive-correction methods. An original multi-scale-separation
approach has been implemented by means of a statistical
interpolation scheme where the information is passed through
a cascade of (decreasing) spatial scales, which covers a wide range
of scales from the synoptic motions down to the lower boundary of
the mesoscale. seNorge2 does not include the correction for
undercatch due to the wind and the relation between precipitation
and elevation is introduced only locally around the station
locations. As a consequence, the predicted precipitation field may
potentially underestimate the actual precipitation, especially at
higher elevations where the station network is sparser.
The evaluation of the seNorge2 daily precipitation fields is based
on a 30-year dataset (1981–2010); the time period is long enough
to provide useful information for extreme precipitation events too.
The dataset of daily totals can properly represent both large-scale
precipitation and small-scale features down to spatial scales of
a few kilometers, depending on the network density. At station
locations, the fraction of observed events that were correctly
predicted is above 0.9 for precipitation intensities of about
10mmday-1, and it decreases to approximately 0.8 in the case
of heavy precipitation (i.e., above
128mmday-1). Intense precipitation is more likely
to be underestimated than weak precipitation. seNorge2 is
especially well suited for those applications requiring a finer
effective resolution of the predicted precipitation field, higher
than the effective resolution of pan-European datasets or global
reanalysis. Over the grid points thus not necessarily
corresponding to station locations, the quality of the seNorge2
predicted precipitation is comparable to state-of-the-art
pan-European datasets, though seNorge2 is expected to represent
local scale features that cannot be included in coarser datasets.
However, the uncertainties increase considerably for the data-void
area on the mountains in southern Norway where seNorge2 seems to
significantly underestimate precipitation. The precipitation
climatology derived from seNorge2 provides reasonable results,
though it is not the focus of this paper to evaluate the derived
climatological fields.
The comparison of seNorge2 with the measurements of the long-term
water balance shows that seNorge2 tends to underestimate
precipitation. The indirect evaluations of seNorge2 by considering
the performances of the seNorge snow model and of the DDD model
show that, for snow, a significant underestimation has been
detected in northern Norway, while for the rest of the country the
estimates are in reasonable agreement with the observations; for
liquid precipitation, underestimation occurs along the western coast
of Norway and in the mountains.
The seNorge project at MET has the objective of maintaining and
improving the conventional (observational) climate gridded datasets
of daily temperature and precipitation. Future developments will
focus on increasing the performances in data-sparse regions, e.g., following
the recommendations of on
the use of climatological precipitation fields for the
interpolation of daily precipitation. Furthermore, the issue of
wind-induced underestimation of solid precipitation will be
addressed.
Acknowledgements
Work at MET Norway and NVE on the activities presented in the article has
been funded by Norwegian project “Felles aktiviteter NVE-MET tilknyttet
nasjonal flom- og skredvarslingstjeneste” and NVE project
“FoU-80200”. Edited by: David
Carlson Reviewed by: three anonymous referees
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