seNorge_2018 is a collection of observational gridded datasets over Norway for daily total precipitation: daily mean, maximum, and minimum temperatures.
The time period covers 1957 to 2017, and the data are presented over a high-resolution terrain-following grid with 1 km spacing in both meridional and zonal directions.
The seNorge family of observational gridded datasets developed at the Norwegian Meteorological Institute (MET Norway) has a 20-year-long history and seNorge_2018 is its newest member, the first providing daily minimum and maximum temperatures.
seNorge datasets are used for a wide range of applications in climatology, hydrology, and meteorology.
The observational dataset is based on MET Norway's climate data, which have been integrated by the “European Climate Assessment and Dataset” database.
Two distinct statistical interpolation methods have been developed, one for temperature and the other for precipitation.
They are both based on a spatial scale-separation approach where, at first, the analysis (i.e., predictions) at larger spatial scales is estimated. Subsequently they are used to infer the small-scale details down to a spatial scale comparable to the local observation density.
Mean, maximum, and minimum temperatures are interpolated separately; then physical consistency among them is enforced.
For precipitation, in addition to observational data, the spatial interpolation makes use of information provided by a climate model.
The analysis evaluation is based on cross-validation statistics and comparison with a previous seNorge version.
The analysis quality is presented as a function of the local station density.
We show that the occurrence of large errors in the analyses decays at an exponential rate with the increase in the station density.
Temperature analyses over most of the domain are generally not affected by significant biases.
However, during wintertime in data-sparse regions the analyzed minimum temperatures do have a bias between 2

Long-term observational gridded datasets of near-surface meteorological variables are widely used products.
In climatology, they have been used for example to monitor the regional climate

seNorge_2018 is a collection of four long-term observational datasets over Norway covering the 61-year time period 1957–2017 for daily total precipitation (RR;

Like the previous versions of seNorge, precipitation and temperature data are provided on a high-resolution grid with 1 km grid spacing in both meridional and zonal directions.
seNorge_2018 aims at achieving a higher effective resolution of the analyzed (or predicted) fields than the previous versions.
It is worth spending a few words on effective resolution in OI.
The difference between grid spacing and resolution is described by

The following definitions of spatial scales are used in the text. The regional scale coincides with the whole domain. Given the importance of the observational network, at an arbitrary point we refer to scales that are defined with respect to the station distribution in its surroundings. The subregional scale (or local scale) defines an area – around the point – that includes dozens of observations (10–100). The small scale defines an area that includes few observations (1–10). The unresolved scale refers to those spatial scales that are smaller than the average distance between a station and its closest neighbors, such that atmospheric fields could not be properly represented by the observational network.

The main original aspect of our research is that the spatial interpolation methods automatically adapt OI settings to the local station density, such that in data-dense regions the spatial supports of the areal-averaged analyses are smaller than in data-sparse regions.
In other words, the effective resolution of the analysis fields is higher in data-dense than in data-sparse regions.
Because the spatial analysis depends on station density, the integral data influence

The presented research includes several other original aspects.
In the case of precipitation, the measurements have been adjusted for the wind-induced under-catch in a way that is consistent with the method proposed by

In the case of temperature, seNorge_2018 is the first seNorge dataset that includes daily minimum and maximum temperatures.
The availability of these two additional variables allows for the computation of several more indices for climate variability and extremes, such as the ones reported in the paper by

The structure of the paper is as follows.
Section

The in situ observations are retrieved from MET Norway's climate database and the European Climate Assessment and Dataset

The measured RR value (i.e.,RR

The observational network for the four variables: RR, TG, TX, and TN.
Panel

Figure

The reference fields are derived from long-term averages calculated from the output of a high-resolution numerical model.
The reference datasets used for precipitation are based on hourly precipitation provided by the climate model version of HARMONIE (version cy38h1.2), a seamless NWP model framework developed and used by several national meteorological services.
HARMONIE includes a set of different physics packages adapted for different horizontal resolutions.
For the high-resolution, convection-permitting simulations in this case, the model has been set up with AROME physics

Over our domain, we have chosen not to use precipitation climatologies derived by observational gridded datasets as the reference because in some regions the observational network is extremely sparse (Fig.

IDI is similar to the degrees of freedom introduced by

For the purpose of evaluation in Sect.

A representation of the observational network useful for spatial analysis of TG

In the two maps of Fig.

For temperature, elevation plays a predominant role and even only a few stations at higher elevations can provide a reasonable approximation of the subregional near-surface temperature lapse rate.
Figure

For precipitation, the IDI map in Fig.

Fig.

The notation used is based on both

Precipitation reference field for October, that is,

The same interpolation scheme is used for the mean, the maximum, and the minimum daily temperature.
The physical consistency among the three variables is assured by post-processing the independently analyzed datasets and for each grid point we make sure that TN is always smaller than or equal to TG and TX is always greater than or equal to TG.
The cross-checking is further discussed in Sect.

The spatial interpolation is implemented on a grid point-by-grid point basis.
It combines a regional pseudo-background field, which is the weighted average of numerous subregional fields, with the observations.
The temperature analysis at the generic

The local Kalman gain in Eq. (

The pseudo-background

The optimization of

TG annual statistics: “

TX annual statistics. See Table

TN annual statistics. See Table

The multi-scale OI analyses are the results of successive approximations of the observations over a sequence of decreasing spatial scales that at station locations converge to the observed values.

The interpolation scheme is not applied directly to the RR values (the vector of the raw observed values adjusted for the wind-induced under-catch is indicated as

The analysis procedure can be written as

The step-by-step description of the model

An OI scheme such as the one presented in Eqs. (

An example of application of the spatial interpolation method described in Sect.

The reference field for October (see Sect.

RR from 24 October 1998. Statistical interpolation of relative anomalies (dimensionless units) over different spatial length scales with the scheme reported in Eqs. (

The first of the three fundamental steps in Eq. (

RR from 24 October 1998. “Critical” scale (Sect.

Figure

Figure

RR analysis field

The evaluation is based mostly on CV exercises and comparison against the seNorge2 datasets of RR and TG. The cross-validation analysis (i.e., CV analysis) is the analysis value at a station location obtained considering a selection of the available observations that does not include the one measured at that location. If CV is applied systematically to all stations and it includes all the remaining observations then it is called leave-one-out cross-validation (LOOCV).

The summary statistics of the following variables are used: CV analysis residuals (i.e, CV analyses minus observations), innovations (i.e., background minus observations), and analysis residuals (i.e, analyses minus background).
The CV analysis, background, and analysis are evaluated through the statistics of CV analysis residuals, innovations, and analysis residuals, respectively.
Note that the background is not considered in the verification of precipitation.
At a generic station location, CV analysis and background are independent of the observation, while the analysis has been computed using the observation.
As a consequence, the statistics of CV analysis residuals and innovations have similar interpretations.
The CV analysis residual distributions are used in place of the unknown analysis error distributions at grid points.
The innovation distributions are used to investigate the properties of the background error at grid points.
On the other hand, the statistics of analysis residuals reveal the filtering properties of the statistical interpolation at station locations that are related to the observation representativeness error

For temperature, we use LOOCV.
The comparison between the statistics of CV analysis residuals and innovations quantifies the improvement of the analysis over the pseudo-background at grid points.
The fraction of errors (i.e., absolute deviations) greater than 3

For precipitation, LOOCV is computationally too expensive. Thus, for each day a random sample of 10 % of the available stations have been reserved for CV and they are not used in the interpolation.
Because precipitation errors follow a multiplicative rather than an additive error model

TG, TX, and TN verification scores as a function of CV IDI for the summer seasons (June–July–August) of the 61-year time period 1957–2017.
With reference to the definitions introduced in Sect.

In Figs.

TG, TX, and TN verification scores as a function of CV IDI for the winter seasons (December–January–February) of the 61-year time period 1957–2017.
See Fig.

For all variables, the spatial interpolation scheme generally performs better during summer than winter when small-scale processes (e.g., strong temperature inversion) are more frequent.
The TG analysis error distribution at grid points, as estimated by CV analysis residuals, shows that during the summer, the MAE is between 0.5 and 1

The seNorge_2018 spatial interpolation procedure builds upon seNorge2. Several modifications have been made, though keeping the scale-separation approach. In seNorge_2018 a single function has been used to model the subregional vertical profile, instead of the three different functions used in seNorge2. At the same time, in seNorge_2018 the blending of subregional fields into a regional pseudo-background field is based on a much larger number of subregional fields.

TG, mean difference between seNorge_2018 and seNorge2 daily analysis during winter (December–January–February).

In Fig.

The variations between seNorge_2018 and seNorge2 having the most significant impacts on the differences shown in Fig.

The evident differences between the two datasets are in the mountains, where seNorge_2018 often presents warmer valley floors and colder ridges.
In particular, according to Fig.

RR and CV analysis verification scores as a function of CV IDI for the 61-year time period 1957–2017.
The terminology used is introduced in Sect.

In Fig.

The close relationship between the terrain and the annual total precipitation is shown in Fig.

Annual total precipitation as derived by summing RR.

Figure

Scale decomposition of precipitation energy based on 2-D discrete Haar wavelet transformation (Sect.

For precipitation, we have stated in the Introduction that seNorge_2018 uses a reference to increase the effective resolution of the field, compared to the resolution given by the spatial distribution of the observational network alone.
In the context of forecast verification,

Next we discuss more in detail the relationships between the occurrence of large errors, as they have been defined at the beginning of Sect.

Expected percentages of large errors on the grid (dimensionless units) based on the summary statistics of the analyses and the spatial distribution of stations of the observational network.
The color scale is the same for all the maps.
Wintertime (DJF) temperatures are considered, and large errors are defined as deviations between analysis and unknown truth larger than 3

In Fig.

As for temperature, the expected percentage of large errors over the precipitation grid is shown in Fig.

Because the presented statistical interpolation methods automatically adapt to the local observation density, the user of the seNorge_2018 dataset must be aware that (i) the comparison between different subregions over the domain is influenced by the respective local station densities, and (ii) variations in the observational network over time will affect temporal trends derived from this dataset

For the four variables, we have investigated the variations in the performances of our interpolation schemes between two different time periods, 1961–1990 (61–90) and 1991–2015 (91–15).
The evaluation scores are similar to the ones presented in Sect.

The three main factors determining the quality of the temperature datasets are the season of the year, the station density and the terrain complexity. The last two factors are correlated, as shown by Figs.

The two main factors determining the quality of the precipitation dataset are the station density and the terrain complexity. The season of the year seems to have a smaller impact on the verification scores.

With respect to seNorge2, seNorge_2018 presents several methodological improvements and two additional variables, TX and TN.
Furthermore, it should be mentioned that there had been variations in the observational datasets used for the production of the two gridded datasets.
Even though the data sources are the same for both seNorge datasets, seNorge2 is based on an observational dataset that was produced in 2016, while seNorge_2018 benefits from the latest efforts in data collection and quality control made by MET and the ECA&D team.
The verification results show that seNorge_2018 temperature predictions are on average more accurate than seNorge2, especially along the coast.
With respect to the predictions of precipitation, as described in the seNorge2 paper by

The cross-checking is mentioned at the beginning of Sect.

Because of the 12 h offset in the definitions of TG and either TX or TN, the cross-check can be wrong. Nevertheless, it is a useful check to identify those situations where the interpolation of daily extremes is not convincing.
In fact, despite the offset in the definitions of the 24 h aggregation period, for a typical day TN is smaller than TG and TX is greater than TG.
We have found very rare exceptions to these rules in the surroundings of station locations.
In the vast majority of cases, the cross-check flags those grid points in the mountains (i.e., far from station locations) where the extrapolation of the vertical profile cannot be adjusted by means of observed data, which are located in large part on the valley floors (Fig.

The number of grid points flagged by the cross-checking vary seasonally and it is higher in winter and lower in summer. In the case of TN, the cross-check flags on average 9 % of the grid points in winter and 1 % in summer. In the case of TX, the cross-check flags on average 7 % of the grid points in winter and 1 % in summer.

Future developments will focus on improving the cross-check, in order to properly handle those exceptional situations that are currently erroneously flagged as physical inconsistencies among the three variables.

The spatial interpolation software is available

The open-access datasets are available for public download as follows:

daily total precipitation

daily mean temperature

daily maximum temperature

daily minimum temperature

seNorge_2018 provides 61-year (1957–2017) datasets of daily mean, maximum, and minimum temperatures, as well as daily total precipitation, over Norway and parts of Finland, Sweden, and Russia. The plan at MET Norway is to update the historical dataset once a year, while at the same time provisional daily estimates for the current year are computed every day. MET Norway has an open data policy and all the datasets, as well as most of the observations used in the calculations, are available for public download via its web services.

The observational datasets have been obtained through statistical methods that build upon our previous works. The interpolation schemes automatically adapt their settings to the local station density and this allows for a higher effective resolution in data-dense areas, while in data-sparse regions the analysis is always the estimate of at least a few stations.

The main factors determining the quality of the temperature analysis are the season of the year, the station density and the terrain complexity. In the case of precipitation, those factors are the station density and the terrain complexity. Because of the importance of the combination of station density and terrain, we have widely used the IDI concept in our evaluation.

The new seNorge_2018 shows significant differences when compared to its predecessor seNorge2, for both TG and especially RR. While first qualitative evaluations indicate that this is an improvement, an indirect evaluation where seNorge_2018 would be used as the forcing data for snow- and hydrological modeling is needed to confirm this.

seNorge_2018 is MET Norway's first observational dataset providing TX and TN from 1957. The temperature analysis has the largest errors during winter and the TN is the most challenging variable to represent. For TG and TX, large analysis errors are expected only in winter and limited to almost data-void areas such as mountain tops. TN may present large analysis errors more often than TG and TX and for larger portions of the domain, especially in mountainous regions.

To fill commonly occurring spatial gaps for RR in data-sparse regions, the interpolation uses monthly fields of a high-resolution numerical model and adjusts this to an optimal fit with the measurements that are available in the area. As a result, seNorge_2018 has a finer effective resolution than seNorge2. The ability of the method to correctly distinguish between precipitation and no-precipitation depends critically on the station density. In the north, the sparser observational network is associated with a high occurrence of large analysis errors. The evaluation shows that large analysis errors are unlikely in the data-dense regions of southern Norway, even for intense precipitation.

CL developed the spatial analysis methods and code for statistical interpolation and created the datasets. OET developed the analysis methods. AD performed the simulations with the climate model. KT developed the code for the daily updates of seNorge_2018. CL prepared the manuscript with contributions from all co-authors.

The authors declare that they have no conflict of interest.

This research has been partially funded by the Norwegian project “Felles aktiviteter NVE-MET tilknyttet nasjonal flom- og skredvarslingstjeneste”.

This research has been supported by The Norwegian Water Resources and Energy Directorate and The Norwegian Meteorological Institute (project “Felles aktiviteter NVE-MET tilknyttet: nasjonal flom- og skredvarslingstjeneste”).

This paper was edited by Scott Stevens and reviewed by two anonymous referees.