seNorge observational gridded datasets. seNorge_2018, version 20.05
MMETreport
No. 07/2020ISSN 2387-4201Free seNorge observational gridded datasets seNorge_2018, version 20.05Cristian Lussana
The Norwegian Meteorological Institute, Oslo, Norway a r X i v : . [ phy s i c s . a o - ph ] A ug ETreport
Title Date seNorge observational gridded dataset. seNorge_2018,version 20.05. August 6, 2020
Section Report no.
Division for Climate Services 07/2020
Author(s) Classification
Cristian Lussana (cid:122)
Free (cid:106)
Restricted
Abstract seNorge_2018 is an observational gridded dataset for daily aggregated tempera-tures and precipitation data over the Norwegian mainland. The time interval cov-ered spans more than 60 years, from the 1st of January 1957 to the present day.Version 20.05 of the historical archive (1957-2019) is described in this document,with special emphasis on the variations in the methods with respect to the previousversion of the archive, which is version 18.12.
Keywords observational gridded datasets, temperature, precipitation, climatology, hydrology,statistical interpolationDisciplinary signature Responsible signatureHans Olav Hygen Cecilie Stenersen
Norwegian Meteorological Institute
Oslo
P.O. Box 43, Blindern0313 Oslo, NorwayT. +47 22 96 30 00
Bergen
Allégaten 705007 Bergen, NorwayT. +47 55 23 66 00
Tromsø
P.O. Box 6314, Langnes9293 Tromsø, NorwayT. +47 77 62 13 00
Norwegian Meteorological Institute
Oslo
P.O. Box 43, Blindern0313 Oslo, NorwayT. +47 22 96 30 00
Bergen
Allégaten 705007 Bergen, NorwayT. +47 55 23 66 00
Tromsø
P.O. Box 6314, Langnes9293 Tromsø, NorwayT. +47 77 62 13 00
Norwegian Meteorological Institute
Oslo
P.O. Box 43, Blindern0313 Oslo, NorwayT. +47 22 96 30 00
Bergen
Allégaten 705007 Bergen, NorwayT. +47 55 23 66 00
Tromsø
P.O. Box 6314, Langnes9293 Tromsø, NorwayT. +47 77 62 13 00 ontents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction seNorge indicates a family of observational gridded datasets over Norway. The Norwe-gian Meteorological Institute (MET Norway) started to produce the seNorge datasets ver-sions 1.0 and 1.1 for the Norwegian mainland in the nineties (
Tveito and Førland , 1999;
Tveito et al. , 2000, 2002, 2005;
Mohr , 2008). The version 2.0 has been produced after2015 (
Lussana et al. , 2018b,a). The most recent member of this family is seNorge_2018and this document describes version 20.05. In particular, we focus on the modificationsof methods and data used with respect to version 18.12, which has been documented by
Lussana et al. (2019).The main motivation behind the development of seNorge is to provide gridded datasetsof a few near-surface atmospheric key-variables for climatological and hydrological ap-plications. Observational gridded datasets exploit the information provided by networksof traditional weather stations over a region and they return estimates of the selected vari-ables potentially anywhere within the region.The tag ”2018” in seNorge_2018 indicates that the statistical models used for spatialanalysis and the code have been developed in 2018. An important component of thespatial analysis procedure is Optimal Interpolation (OI
Gandin and Hardin , 1965), andthe reader may refer to
Uboldi et al. (2008) for the description of the modified OI schemeused. The versioning of seNorge_2018 indicates the production date of the datasets, suchthat version 20.05 (or ver. 20.05) refers to May 2020. As stated above, the first version ofseNorge_2018 was ver. 18.12. A new version may include both updated data sources andfurther developments of the methods. Note that the new developments are not consideredsignificant enough to change the name of seNorge_2018, because the Bayesian inferencebehind the statistical methods remains unchanged.seNorge_2018 includes gridded fields of daily mean, maximum and minimum tem-perature, and daily total precipitation amounts. The time period covered by the datasetsbegins the 1st of January 1957 (1957-01-01) and continues to the present day. The datasetis updated on a daily basis. seNorge_2018 datasets can be divided into two archives: anhistorical archive and an operational archive. The historical archive includes data from1957-01-01 to a date in the recent past, which is 2019-12-31 for ver. 20.05. The historicalarchive is re-built periodically. Then, a new version of the archive is created and new Dig-ital Object Identifiers (DOIs) are assigned to the corresponding datasets. The operationalarchive is updated every day based on the data of the last few days. In addition, each time4 new historical archive is built, the operational archive is also modified, such that thereis a seamless transition between the most recent version of the historical archive and theoperational archive. In this sense, the operational archive is a provisional archive. In thecase of ver. 20.05, the operational archive starts at 2020-01-01.The motivations that led us to change parts of the methods used for spatial analysisin ver. 20.05 with respect to ver. 18.12 are different for temperature and precipitation.In the case of precipitations, the gridded fields of a regional climate model are used asinput data to scale precipitation in the spatial analysis. Since a climate model coveringthe same region but spanning a longer time period is available, the gridded fields from thismodel are used to replace those previously used for ver. 18.12. In the case of temperature,the OI in ver. 18.12 was configured to achieve the best agreement -on average- between(independent) observations and cross-validation analyses. However, the optimization pro-cedure favoured some regions and penalized others, depending on the spatial distributionsof the observational network. In particular, since most of the stations used are located atlow elevations, the optimization procedure was biased towards ensuring the optimal per-formances for those regions, while the uncertainties in mountainous regions and in datasparse regions was considered only marginally in the optimization. As a consequence, thevariability of ver. 18.12 analyses fields in data sparse regions is rather large, larger thanin seNorge2 (or seNorge version 2.0) for instance. The ideal situation would be to rely onthe OI performances of seNorge_2018 ver. 18.12 in data dense regions and, at the sametime, reduce the uncertainty of the temperature fields in data sparse regions down to thelevel of seNorge2. seNorge_2018 ver. 20.05 has exactly this objective. The variability ofthe gridded analysis field in data sparse regions is reduced by blending together the resultsof several different OIs based on slightly different configurations.The document is organized as follows. Sec. 2 defines seNorge_2018 variables andpresents the data used. Sec. 3 describes the variations in the spatial analysis with respectto the methods implemented for ver. 18.12. Sec. 4 compares the gridded fields of ver.20.05 with those of ver. 18.12 with the aim of studying the effects of variations in theinput data and methods over the results. Sec. 5 summarizes the main messages of thedocument. The data access is then described in the Appendix. After the Appendix, asection with supplementary material is included, in order to make the reading of the maintext more fluent by avoiding the interruptions caused by pages and pages of figures.5
Data and Definitions seNorge covers the Norwegian mainland and it includes all the catchments of rivers flow-ing in the Norwegian territory, as a consequence seNorge extends also into parts of Swe-den and Finland bordering Norway. The domain of seNorge_2018 ver. 20.05 is the sameof ver. 18.12. More details and figures on the domain can be found in previous pa-pers, such as
Lussana et al.
Klein Tank et al. , 2002) are alsoused.The definitions of the variables available in seNorge_2018 are: • RR at a given date is the total amount of precipitation accumulated from 06 UTC ofthe day previous to that date to 06 UTC of the day in the date. RR is also referred toas daily precipitation. Note that RR at a station location does not correspond to thevalue observed by the corresponding ombrometer, not only because of the adjust-ment made by the spatial analysis but also because observations are adjusted for thewind-induced under-catch according to the relationships reported by
Lussana et al. (2019) and based on
Wolff et al. (2015). • TG at a given date is the mean averaged temperature from 06 UTC of the dayprevious to that date to 06 UTC of the day in the date. TG is also referred to asdaily mean temperature. In detail, it is the arithmetic mean of 24 hourly values or aformula based mean value computed from fewer observations (
Førland and Tveito ,1997). • TX at a given date is the maximum temperature from 18 UTC of the day previous to6hat date to 18 UTC of the day in the date. TX is also referred to as daily maximumtemperature. • TN at a given date is the minimum temperature from 18 UTC of the day previous tothat date to 18 UTC of the day in the date. TX is also referred to as daily minimumtemperature.The 63-year time period covered by the historical archive of seNorge_2018 ver. 20.05ranges from January 1957 to December 2019. In such a long period of time the observa-tional network has continuously changed. The data availability is shown in Fig. 1. Thereare more observations for precipitation than for temperature. In the case of temperature,there are no significant differences between TG, TX and TN. The area of seNorge_2018spatial domain measures 606579 km . In the idealized case of a completely uniform spa-tial distribution of the observational network, the ratio (area) / (number of observations)corresponds to the area around each observation where that observation is the closest datasource. In this sense, that area can be referred to as a sort of ”area of influence” of anobservation. The radius of the circle equivalent to the area of influence is a measure of theaverage distance we need to travel in every direction before meeting another observation.This radius is a rough indicator of the observation spatial density. Suppose the number ofavailable observations is 100, then the radius is equal to 44 km. With numbers of availableobservations equal to 200, 300, 600 and 900, then we get circle radii of, respectively: 31km, 25 km, 18 km and 15 km. For all variables, it is possible to identify three differentregimes in the time series. From 1957 to 1975, there was an increase in the number ofavailable observations. From 1975 to 2000-2005, there was a gradual, slow decrease inthe number of observations. The decrease is rather sharp for RR in the period from 2000to 2005. From 2005 to 2020, the situation is different between the two quantities. Inthe case of precipitation, there is an oscillatory trend with an average of approximately700 observations, while for temperature a sharp increase from 300 to 500 observations isshown.The in-situ data shown in Fig. 1 has been quality controlled according to MET Nor-way’s quality assurance system specifications. In addition, for temperature, a spatial con-sistency test such as those described by Lussana et al. (2010) has been applied. For pre-cipitation, the time series have been visually inspected to identify anomalies with respectto neighbouring stations.By comparing Fig. 1 with Fig. 1 of
Lussana et al. (2019), it can be noted that on7igure 1: Time series of number of observations used for spatial analysis that are in theseNorge_2018 domain after the data quality control. The left panel shows RR observa-tions. The right panel shows TG (black dots) and TX, TN (gray dots) observations. Notethe different scales on the y-axes between the two panels.average ver. 20.05 is based on more observations than ver. 18.12. However, similarly tover. 18.12, the in-situ data used in ver. 20.05 are not evenly distributed across the altituderange. More stations are located in the lowlands, while in the mountains the observationalnetwork is quite sparse. This should have an influence on the uncertainties of the spatiallyinterpolated fields of ver. 20.05 similar to what reported for ver. 18.12 and documentedby
Lussana et al. (2019).
The steps of the procedure used for the production of daily gridded datasets for an ar-bitrary day are listed in the Algorithm 1. The mathematical notation and the symbolsused are defined in Tab. 1. The objective of this Section is to describe the modificationsin the methods of seNorge_2018 ver. 20.05 compared to ver. 18.12, while the generaldescription of the methods documented by
Lussana et al. (2019) is still the reference forseNorge_2018.In the Algorithm 1, we made it clear that a number of data are required for the pro-duction of seNorge_2018. The fixed datasets used are not reported in the algorithm andthose are the digital elevation model and the land area fraction over the 1 km regular grid.The gridded fields of wind speed are derived from numerical model output, in this wayit is possible to associate a value of wind speed to each observation, independently of8he actual availability of an observed value of wind speed. In fact, observed wind speedvalues would have been more accurate data but we would have inevitably lost some ofthe precious observations of temperature and precipitation. We estimated that data losswould have been a worse solution than the less accuracy for the wind speed. The numer-ical models used are described in the paper
Lussana et al. (2019) and they are based onMET Norway’s products (
Reistad et al. , 2011;
Müller et al. , 2017;
Frogner et al. , 2019). seNorge_2018 statistical interpolation of precipitation is based on an iterative OI schemethat uses the relative anomalies between observed and reference precipitation values. Thereferences are long-term monthly averages of precipitation obtained through numericalmodels. In the case of ver. 18.12, the reference datasets used for precipitation are basedon hourly precipitation provided by the climate model version of HARMONIE (versioncy38h1.2), a seamless NWP model framework developed and used by several nationalmeteorological services. For ver. 20.05, the reference dataset has changed. The long-termmonthly averages of precipitation have been derived by the "NorCP" simulation, whichprovides high-resolution (3 km) climate model data covering the 21-year time period from1998-2018 by an updated climate model version of HARMONIE (
Lind et al. , 2020).In Fig. 2, the typical annual total precipitation fields for the references of ver. 20.05and ver. 18.12 are compared. First thing to notice is that the domain of the reference forver. 20.05 is wider than that of ver. 18.12. As a consequence, the Norwegian mainland inver. 20.05 reference is less likely to be affected by those border effects that may affect ver.18.12, especially in Southern Norway. Besides, the wider domain of ver. 20.05 shouldalso allow for a better development of the high-resolution dynamics of the dynamicaldownscaling procedure. As shown in the right panel, the reference of ver. 20.05 has -onaverage- larger values of precipitation, though the situation can vary significantly betweenmonths and regions, as shown in Figs. 11- 22. seNorge_2018 statistical interpolations of temperature are all based on a two-step spatialanalysis scheme. The first step aims at representing the temperature field at a point asthe average over a spatial support larger than the local station density, where this is char-acterized as the average distance between a station and its closest neighbouring stations9igure 2: Comparison of typical annual total precipitation fields of the seNorge_2018reference fields. Left panel: ver. 20.05 reference field. Middle panel: ver. 18.12 referencefield. Right panel: relative deviations as percentages of the ver. 18.12 reference field (i.e.,ref(ver 20.05) / ref(ver 18.12)).in the surroundings of that point. The second step refines the temperature representationat a point by including those effects that are observed only by a small number of neigh-bouring stations. The first step is implemented through the elaboration of sub-regionalpseudo-background fields. This part has remained unchanged from ver. 18.12. The sec-ond step is implemented by means of an Optimal Interpolation (OI) scheme and this parthas been significantly changed, as it is described in the following of this Section.For each of the three variables TG, TX and TN, the OI runs with more than a singleconfiguration, as it is instead for ver. 18.12. In particular, four different OI are performed.The parameter that is varying within the different OI runs is D z , which is the verticaldecorrelation length used in the definition of the background error covariance matrix. Forver. 18.12, D z was set to 210 m. In the case of ver. 20.05 the four values used are: 210m; 400 m; 600 m and 800 m. For each combination of the pair variable/OI configuration,a dataset of gridded fields is produced.There are two more steps that must be performed in order to obtain the final dataset ofTG, TX and TN. The first step is the merging of the four datasets into a single dataset foreach variable. The second step is the check for consistency between the three variables,specifically to ensure that TX is greater or equal to TG and, at the same time, TN issmaller or equal to TG. Note that such a check is needed, because the spatial analysis isperformed for each variable independently from the others, therefore in regions where theanalysis uncertainty at a given time is greater than the difference between variables, theconsistency between TG, TX and TN may be violated. The check for consistency was10mplemented already in ver. 18.12 and it first replaces TX with TG for those grid pointswhere TG is greater than TX, then it replaces TN with TG for those grid points where TGis smaller than TX. This simple and practical solution might not always yield satisfactoryresults, for this reason it is one of the points that should be improved in future versions ofseNorge_2018.The merging of datasets into a single one is a new feature of ver. 20.05 compared tover. 18.12. Statistical interpolation schemes produce fields where each value is an averageover a spatial support and the sizes of those spatial supports vary across the domain. TheOI settings influence the sizes of the three-dimensional spatial supports. The vector of OIsettings λ includes D z =
210 m (same as ver. 18.12), then: λ includes D z =
400 m; λ includes D z =
600 m (same as seNorge2); λ includes D z =
800 m. Apart from D z , all theparameters in the four OI settings do share the same values. The variables considered areTG, TX and TN, they are further abbreviated as g , x and n , respectively. For example,the notation for the analysis of TG at the j th grid point for the OI configuration with D z =
800 m is x g , aj ( λ ) (see also Tab. 1). In addition to the analysis, the Integral DataInfluence (IDI, Uboldi et al. , 2008) is available for each point in each field. IDI is anindicator ranging from 0 to 1 that summarizes the amount of information used in the OIthat is derived from nearby observations. At the j th grid point, if we consider for instanceTX, the notation x x , IDI j ( λ ) indicates IDI obtained with D z =
400 m. Given a particularset of λ values, grid points where the IDI values are close to 0 will have the analysisalmost identical to the large-scale pseudo-background, since no information from nearbyobservations has been used in the analysis. Then, the spatial support of the analysis ismostly determined by the pseudo-background characteristics. On the other hand, gridpoints where the IDI values are close to 1 will use nearby observations to adjust theanalysis. In this case, the spatial support of the analysis is mostly determined by the OIsettings and the spatial support of the analysis temperature field is smaller for smallervalues of D z .The merging is done such that more weight is given to the field with smaller spatialsupport (i.e. λ ) and weight has been given to the other (coarser) fields only where theyprovide additional information. In this way, we make use of the observational networkin an optimal way by providing a higher resolution field where the network is denser.The relative content of information of a field with respect to another field is evaluatedthrough a function inspired by Shannon’s measure of information content, similarly towhat reported for the probability density functions in Tarantola (2005), Sec. 1.2.5. In11ur equations, IDI will replace probability density functions. The fields are ordered fromthe one with the smallest spatial supports, which is that obtained with λ , to the one withthe largest spatial supports, when the OI is performed with λ . Then, relative content ofinformation in one field with respect to its immediate antecedent field with smaller spatialsupports is computed. The first field, the one with λ , is assigned the complementary ofthe relative content of information of the second field. The weights are the normalizedrelative contents of information. The procedure is described in mathematical terms in theequations that follows.The TG analysis at the j th grid point is obtained as a weighted average of the four OIanalysis: x g , aj = ∑ l = w lj · x g , aj ( λ l ) (1)where the weights with l = , . . . , w lj = α − j · x g , IDI j ( λ l ) · log (cid:32) x g , IDI j ( λ l ) x g , IDI j ( λ l − ) (cid:33) (2)The weight for l = w = α − · ( − w ) (3)and α is the vector of normalization factors used to enforce that ∑ l = w lj = , ∀ j = , . . . , m . Note that to avoid problems in Eq. (2), all the IDI values smaller than 0.0000001have been replaced with 0.0000001.In Figs. 3- 6 examples of the normalized weights of Eqs. (2)- (3) are shown. Thefigures show the averaged weights over the days within year 2019 for TG. In the rightpanels, the fields on the original seNorge_2018 grid are shown. In the left panels, thefields have been aggregated on a coarse resolution grid with square boxes of side length50 km. In this way, we focus on averages over regions and not on small-scale details. Theweight w in Fig. 3 is by far the largest one and for a few boxes on the coarser grid itsvalue is equal to 1. The OI analysis obtained with λ should have more weight than theothers, especially close to an observation. In mountainous regions where the observationalnetwork is sparse, w reaches its smallest values. The weight w in Fig. 4 has maximumvalues in the range 0.25-0.5 exactly in those regions where w has its smallest values.The other two weights, w and w , are shown in Figs. 5- 6 and the information of thecorresponding OIs are used to integrate the higher-resolutions OI only in mountainous12egions where the observational network is sparse. The maximum value of w is 0.25,while the maximum value for w is 0.16.Figure 3: Normalized weights w ( D z =
210 m) for TG, averaged over 2019. The leftpanel shows the aggregated field over square boxes with sides of 50 km. The right panelshows the original field on the 1 km grid.Figure 4: Same as Fig. 3 but for w ( D z =
400 m).13igure 5: Same as Fig. 3 but for w ( D z =
600 m).Figure 6: Same as Fig. 3 but for w ( D z =
800 m).14
Results
A comparison between seNorge_2018 ver. 20.05 and ver. 18.12 is reported in this sectionfor the four variables RR, TG, TX and TN. In particular, the comparison is based onthe most recent 30-year period common to both datasets, which is the time period 1988-2017. Note that a complete study to characterize estimation uncertainties based on cross-validation experiments has not been performed yet for ver. 20.05, while it is available inthe paper by
Lussana et al. (2019) for ver. 18.12.The comparison of total precipitation amounts is shown in Fig. 7 for winter monthsand in Figs. 23- 25 for the other seasons. The comparison is performed on monthly pre-cipitation totals averaged over the period 1988-2017. The results show the amounts of ver.20.05 as percentages of the amounts of ver. 18.12. For example, where the monthly totalprecipitation of ver. 20.05 is approximately equal to the amount of ver. 18-12 ( ± ± ± ± . ◦ C. Fig. 8 shows thatduring winter: ver. 20.05 is colder than ver. 18.12 on the Scandinavian mountains in theNorthern part of Sweden; ver. 20.05 is warmer than ver. 18.12 on the northernmost partof Norway, in the region of East-Finnmark.The comparison of the daily maximum temperature is shown in Fig. 9 for wintermonths and Figs. 29- 31 for the other months. The quantity considered is the monthly15igure 7: Monthly total precipitation amounts for seNorge_2018 ver. 20.05, as percentageof ver. 18.12, averaged over the 30-year period from 1988 to 2017 for winter months:December, in the left panel; January, in the middle; February, in the right panel. Thefields of averaged values over square boxes with sides of 50 km are shown in the panels.Figure 8: Differences between monthly mean daily temperature of seNorge_2018 ver.20.05 and ver. 18.12, as ◦ C, averaged over the 30-year period from 1988 to 2017 forwinter months: December, in the left panel; January, in the middle; February, in the rightpanel. The fields of averaged values over square boxes with sides of 50 km are shown inthe panels.mean of daily maximum temperatures. The monthly mean is based on the period 1988-2017. Then, the differences between ver. 20.05 and ver. 18.12 are shown in the figures.In general, the two seNorge_2018 versions are rather similar. The situation is similar tothat of daily mean temperature, but the differences between the two versions are even lesspronounced.The comparison of the daily minimum temperature is shown in Fig. 10 for wintermonths and Figs. 32- 34 for the other months. The quantity considered is the monthly16igure 9: Differences between monthly average of maximum daily temperature ofseNorge_2018 ver. 20.05 and ver. 18.12, as ◦ C, averaged over the 30-year period from1988 to 2017 for winter months: December, in the left panel; January, in the middle;February, in the right panel. The fields of averaged values over square boxes with sidesof 50 km are shown in the panels.mean of daily maximum temperatures. The monthly mean is based on the period 1988-2017. Then, the differences between ver. 20.05 and ver. 18.12 are shown in the figures. Asfor the other two temperature variables, the largest differences between the two versionsare observed for the winter months, even though in the case of minimum temperaturethere are still significant differences in the northern part of the domain also for September,October and March. The patterns of the deviations resemble also those observed for thedaily mean temperature, with a region in northern Norway where ver. 20.05 is warmer(more than 1 ◦ C) than ver. 18.12 and a region of the Scandinavian mountains in northernSweden where ver. 20.05 is colder than ver. 18.12. In addition, the deviations betweenminimum temperatures over South-Norway in winter are also significant for a few squareboxes, up to ± . ◦ C. seNorge_2018 version 20.05 has been released and it is described in this document. Theobservational gridded datasets include daily mean, minimum and maximum temperaturesand daily total precipitation amounts over the Norwegian mainland for the time period1957-2019. The gridded fields are made available over a regular grid with 1 km of spacingbetween grid nodes in both easting and northing directions.Version 20.05 is an update of ver. 18.12, which covers the same spatial domain but17igure 10: Differences between monthly average of maximum daily temperature ofseNorge_2018 ver. 20.05 and ver. 18.12, as ◦ C, averaged over the 30-year period from1988 to 2017 for winter months: December, in the left panel; January, in the middle;February, in the right panel. The fields of averaged values over square boxes with sidesof 50 km are shown in the panels.spans a smaller time period, from 1957 to 2017. The data sources for the in-situ observa-tions are the same for the two versions, however the observational datasets for ver. 20.05have been collected from scratch, that is independently from ver. 18.12. The in-situ ob-servations have been quality controlled based on both visual inspection of the time seriesand the application of automatic procedures. The set of in-situ observations used for ver.20.05 is rather similar to the one used for ver. 18.12. A bit more observations have beenused in ver. 20.05.Version 20.05 includes some changes in the methods with respect to ver. 18.12. In thecase of precipitation, the reference fields used to scale the daily precipitation amounts inthe statistical interpolation have been changed. In the case of temperature, the statisticalinterpolation has been modified such that the pseudo-background, large-scale, field isadjusted locally on the basis of the surrounding observations over wider regions in ver.20.05 than in ver. 18.12.The combined impacts over the results of the updated input observational datasetsand the modifications in the methods have been evaluated for the period 1988-2017 byconsidering monthly averaged deviations between ver. 20.05 and ver. 18.12. Instead ofconsidering grid points, we have aggregated deviations over square boxes with sides of50 km. In general, the deviations are rather small, especially in data dense regions, andthis fact indicates a stability of the methods with respect to variations in some procedures.However, in data sparse regions or where some new observations have been used in ver.180.05, the differences between the two versions are evident even over 30-year averages.For all variables, the largest differences occur during winter and they are more pronouncedover few square boxes that are characterized by complex terrain and a sparse observationalnetwork. Future plans include a complete evaluation of seNorge_2018 ver. 20.05 basedon cross-validation to estimate the improvements in accuracy and precision with respectto ver. 18.12. 19 ppendix: Data Access seNorge_2018 version 20.05 datasets are available for public download under the Nor-wegian Licence for Open Government Data (NLOD, https://data.norge.no/nlod/en/ ). The data can be accessed from two distinct sources: Zenodo zenodo.org andMET’s Norway THREDDS data server thredds.met.no . A detailed description on howto access the data is available at the seNorge wiki-pages: • https://github.com/metno/seNorge_docs/wiki/seNorge_2018 In the wiki, it is also possible to get the latest news on the datasets and contact the devel-opers by opening issues about specific topics.The digital object identifiers (DOIs) of the datasets are: • TG, daily mean temperature (
Lussana , 2020b). DOI is 10.5281/zenodo.3923706. • RR, daily total precipitation amount (
Lussana , 2020a). DOI is 10.5281/zenodo.3923703.In addition to RR, the archive also provides RRa (RR alternative), which is the fieldof daily total precipitation without the correction for the wind-induced undercatch. • TX, daily maximum temperature (
Lussana , 2020d). DOI is 10.5281/zenodo.3923700.In addition to TX, the archive also provides TXa (TX alternative), which is the fieldof daily maximum temperature without the check for consistency against TG andTN. • TN, daily minimum temperature (
Lussana , 2020c). DOI is 10.5281/zenodo.3923697.In addition to TN, the archive also provides TNa (TN alternative), which is the fieldof daily minimum temperature without the check for consistency against TG andTX. 20 upplementary Material
Figure 11: same as Fig. 2 but for the typical January.Figure 12: same as Fig. 2 but for the typical February.Figure 13: same as Fig. 2 but for the typical March.21igure 14: same as Fig. 2 but for the typical April.Figure 15: same as Fig. 2 but for the typical May.Figure 16: same as Fig. 2 but for the typical June.22igure 17: same as Fig. 2 but for the typical July.Figure 18: same as Fig. 2 but for the typical August.Figure 19: same as Fig. 2 but for the typical September.23igure 20: same as Fig. 2 but for the typical October.Figure 21: same as Fig. 2 but for the typical November.Figure 22: same as Fig. 2 but for the typical December.24igure 23: Same as Fig. 7 but for spring months: March, in the left panel; April, in themiddle; May, in the right panel.Figure 24: Same as Fig. 7 but for summer months: June, in the left panel; July, in themiddle; August, in the right panel.Figure 25: Same as Fig. 7 but for autumn months: September, in the left panel; October,in the middle; November, in the right panel.25igure 26: Same as Fig. 8 but for spring months: March, in the left panel; April, in themiddle; May, in the right panel.Figure 27: Same as Fig. 8 but for summer months: June, in the left panel; July, in themiddle; August, in the right panel.Figure 28: Same as Fig. 8 but for autumn months: September, in the left panel; October,in the middle; November, in the right panel.26igure 29: Same as Fig. 9 but for spring months: March, in the left panel; April, in themiddle; May, in the right panel.Figure 30: Same as Fig. 9 but for summer months: June, in the left panel; July, in themiddle; August, in the right panel.Figure 31: Same as Fig. 9 but for autumn months: September, in the left panel; October,in the middle; November, in the right panel.27igure 32: Same as Fig. 10 but for spring months: March, in the left panel; April, in themiddle; May, in the right panel.Figure 33: Same as Fig. 10 but for summer months: June, in the left panel; July, in themiddle; August, in the right panel.Figure 34: Same as Fig. 10 but for autumn months: September, in the left panel; October,in the middle; November, in the right panel.28able 1: Overview of variables and mathematical notation. All the vectors are columnvectors if not otherwise specified. If X is a matrix, X i is its i th column (column vector)and X i , : is its i th row (row vector). If x is a column vector, x j is its j th element.symbol description dimension m number of grid points - p number of observations - l index of OI configuration l = , . . . , λ OI parameters not specified x g , a ( λ ) TG analysis over the grid, obtained with OI parameters λ m x x , a ( λ ) TX analysis over the grid, obtained with OI parameters λ m x n , a ( λ ) TN analysis over the grid, obtained with OI parameters λ m x g , IDI ( λ ) TG IDI over the grid, obtained with OI parameters λ m x x , IDI ( λ ) TX IDI over the grid, obtained with OI parameters λ m x n , IDI ( λ ) TN IDI over the grid, obtained with OI parameters λ m w l weight for OI with λ l , used in the merging m α normalization factor for the merging m29 lgorithm 1 seNorge_2018 procedure for the production of daily gridded datasets for anarbitrary day. Require: daily observations of temperature and precipitation collected from the datasources
Require: daily averaged wind speed gridded field from numerical model output
Require:
Gridded fields of long-term monthly averages of precipitation from numericalmodel outputProduction of 4 provisional versions of TG fields, OI with λ l , l = , . . . , λ l , l = , . . . , λ l , l = , . . . , eferences Førland, E., and O. Tveito (1997), Temperatur og snødata for flomberegning,
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