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

Conventional climatological datasets are based on observed data
only and they provide valuable information for a large spectrum of
users in modern societies

The object of this paper is the daily total precipitation gridded
fields of the latest seNorge version

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

The seNorge2 statistical interpolation method is based on a modified optimal
interpolation

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

The previous seNorge versions (v1.0 and v1.1) were based on
a linear estimation of precipitation on the grid

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
(

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

The outline of the paper is as follows. Section

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.

The seNorge2 domain is shown in Fig.

The daily precipitation for day

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

OI relies on the assumptions of Gaussian distribution for both the
observation error

The analysis is also a random variable with a Gaussian
distribution

The equations for the weight matrices

Given our assumptions about the error covariance matrices, the
expressions for the weight matrices are derived directly from the
theory of linear Kalman filters

Two elements of the OI diagnostics are introduced in this
paragraph, because they have been used in the optimization of
parameters (Sect.

Second, the leave-one-out cross-validation (CV) analysis

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

An individual event on the grid is a connected zone of grid points
where the precipitation exceeds the predefined threshold of

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.,

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.

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.

As stated in Sect.

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

The application of the OI iterative scheme requires the definition
of two further elements: (1) a spatial averaging operator

The iterative OI algorithm is based on two nested loops.

The

The

Out of the

The final analyses are

In Fig.

Figure

seNorge2 examples.

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,

Daily precipitation comparison between E-OBS
and seNorge2, which has been upscaled to the E-OBS grid (

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

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

In Fig.

As highlighted by the boxplots in the two insets of
Fig.

Note that Fig.

In Fig.

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

The datasets considered in the comparison are (i) seNorge2 and (ii)
seNorge1.1

The model underestimation (

The bias index B for SCA in the seNorge grid cells for the two
gridded dataset versions (v.1.1. in

Daily updated maps of snow conditions have been produced for
Norway since 2004 by using the seNorge snow model

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

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;

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 (

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 (

The regional model underestimation and overestimation (

The maps of the bias index B (Fig.

The DDD rainfall–runoff model

Geographical distribution of

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

The correction factor

In general, the water balance seems reasonable, although the
simulated actual evapotranspiration (AE) shows lower values when compared
with the ones reported in Sect.

Figure

The seNorge2 dataset 1957–2015 is available at

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

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

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

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

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

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