According to the Köppen-Geiger climate classification (Kottek et al., 2006), the locality belongs to the subpolar climate Dfc. (snow zone, fully humid with cool summer) and it features long, usually very cold winters, and short, cool to mild summers. Based on the observed meteorological data from the Kvikkjokk station (between the years 1890 and 2001), the Walter climate diagram was constructed in order to express the climate features in the area (Fig. 2).

As shown in the Fig. 2, the climate at locality is rather humid. Annual precipitation is 581 mm. Minimum precipitation sum is observed in March and April (28 mm) and maximum in July (86 mm), respectively. Annual average of temperature is -1.2 ∘C. Maximum monthly average temperature is observed in July (16.8 ∘C), while the minimum takes place in January (-13.9 ∘C) respectively. The coldest monthly average temperature was recorded in January 1893 (-24.4 ∘C) and the maximum average monthly temperature was observed in July 1937 (16.8 ∘C). Because of the humid climate and a relatively low average air temperature due to energy balance of high latitudes, it is anticipated that air temperature represents the main climate driver for ecological processes in the studied area. This is confirmed also by Holtmeier and Broll (2005).

Two groups of databases were assessed in the study. The first one – NORDKLIM is the database of observed climate data. Three data sets of temperature records and six sets for the precipitation records, recorded on the four weather stations situated close to the locality Hårås, were used for comparison.

The second group included eight data sets generated from five gridded databases. The data from this group are hereinafter called modeled data set. The four modeled data sets of temperature were generated from various gridded databases and another four modeled data sets for precipitation.

For both groups of data sets the monthly and seasonal (3 months) temperature means and monthly and seasonal precipitation totals were assessed. All database properties and labels (abbreviations) of assessed data sets are specified in Table 1.

The NORDKLIM database contains homogenized data sets for 12 climate variables, recorded on 114 weather stations distributed in Scandinavian countries, 48 of which are in Sweden Fig. 1. The database was compiled by the Swedish Meteorological and Hydrobiological Institute (Tuomenvirta et al., 2001). Two weather stations (Kvikkjokk and Jokkmokk) located 40 and 70 km away from locality Hårås and two other stations (Tjaamotis and Kiruna), located 18 and 110 km from it, were selected. For Tjaamotis and Kiruna only precipitation data sets (P18, P18agr, P110, P110agr) were provided for the above-mentioned database and both variables (temperature and precipitation data sets) were available for Kvikkjokk and Jokkmokk stations (T40, T40agr, P40, T70, P70).

The second group of climate databases included gridded time series. For the position of both the nearest weather stations and Hårås locality, we generated the data using the web application of the Royal Netherlands Meteorological Institute called KNMI Climate Explorer, which was created in order to enable the statistics analysis of time series of climate data (CLIMEX.KNMI, 2014). One can set the location for required climate time series by coordinates for point, or for points defining rectangular area, or by shapefile to define an irregular polygon mask. Average values or a set of grid points can be selected as an output for areas, whereas percentage of valid points for averaging and land/sea mask are optional. That application enables us to apply monthly or yearly high and/or low-pass filter and aggregates data to a lower time resolution. Other useful tools are the construction of statistical forecast model, the computation of anomalies, and the zonal mean.

For monthly temperature means data from CRU TS 3.21 database (T_CRU) and anomalies from GISS 250 T2m/SST anom (GISS) with grid resolution 0.5 and 1∘, respectively, were generated. The anomaly is a difference between the absolute temperature value and the value of the long-term average determined from the reference period. Seasonal temperature was generated from Luterbacher et al. (2004) database (LT) as well as another one data set was derived by aggregation of CRU TS 3.21 (T_CRUagr). The period overlap for all temperature databases was 100 years (between 1902 and 2001).

Monthly precipitation data sets were generated from GPCC V7 0.5∘ (GPCC), CRU 3.21 database (P_CRU), as well as from Pauling et al. (2008; PP) and aggregated CRU 3.21 database (P_CRUagr) for seasonal precipitation data sets. The assessed period for which all precipitation data sets were available extends from 1910 till 1997, i.e. 88 years. Grid resolution of all utilized precipitation gridded databases is 0.5∘.

At Hårås locality, 20 increment cores were taken from spruce tree stems at a height of 1.3 m. After pre-processing of samples, they were analyzed in WinDENDRO computer image analysis system. The analysis consisted of measuring tree-ring widths and their dating. The created tree-ring series were synchronized with the regional curve derived from the tree-ring series, which showed the highest correlation. We used visual synchronization supported by a graphical method known as “skeleton plot” (Cropper, 1979). The series was considered to be satisfactorily synchronized if the value of coefficient of parallelism (GLK) exceeded 70 %. Tree-ring series, which did not exceed this threshold, were excluded from further analyses. The occurrence of potential misdating of tree-ring series was evaluated by the software COFECHA (Grissino-Mayer, 2001). With regard to the open crown canopy of the stands, the high-frequency signal of mean chronology was detrended using a modified negative exponential function. The final tree-ring chronology was performed with the method of robust double-weighted-averaging of tree ring indices that included the removal of temporal autocorrelation. The values of tree-ring indices were calculated using the formula of Cook and Kariukstis (1990). Basic descriptive statistics were calculated to assess the potential of measured tree ring series for its accurate dating and for extraction of climatic signal.

The comparison of climate databases gives us information about the systematic and random error of the modeled climate data. As reference data observed data sets of temperature means and precipitation totals were used, which were recorded at the weather stations and located the closest to Hårås, i.e. Tjaamotis and Kvikkjokk. For these locations were generated modeled data sets from gridded databases. From the differences between the modeled and observed data we calculated the mean error (e‾) and the standard error (SE). Student t test was applied to test the significance of the systematic error at 5 and 1 % significance levels. The final accuracy of the modeled data was quantified by root mean square error (RMSE). The above-described evaluation was performed separately for the mean temperature and precipitation totals and separately for monthly and seasonal climatic data sets. The observed seasonal data were derived by aggregating the observed monthly records.

The impact of climate on increment formation was evaluated by deriving the cross-correlation function between monthly or seasonal series of climate variables (temperature, precipitation) and tree-ring indices within an 18-month long (April_preceding year to September) or a 7-season long (March–April–May_preceding year to September–October–November) dendroclimatic year. Student t test was used to evaluate the significance of the coefficients of correlation at 5 and 1 % significance level. With regard to the objective of the study, we compared the results of growth response derived from the observed climate data and from the modeled climate data sets. We wanted to reveal the cases with different statistical significance of correlation coefficients compared to ρ= 0, caused by different climate databases and the significant differences between correlation coefficients derived for the same month or season, however using various climate databases. For evaluations thus created, regional tree ring chronology was considered as a reference data set.

Question 1: what is the bias, precision, and overall accuracy of modeled data sets at the location of a weather station for monthly and/or seasonal average temperature and precipitation totals?

The differences between the modeled and observed climate data were calculated separately for monthly and seasonal data of mean temperatures and precipitation totals. We analyzed the significance of deviation of the modeled data from the observed records, the presence of the random error and the overall accuracy of the modeled data. Presented statistics are valid for the specific combination of reference observed data and grid point of modeled data. It is due to a different scale of climatic information received by observed and modeled data. The grid point of modeled data represent the same climatic value for the whole cell of grid (area 0.5∘ × 0.5∘ or 1∘ × 1∘ of latitude × longitude), and observed data are valid for the location of the weather station (one point). Maximum distance between grid point and weather station for this latitude is up to 30 or 60 km in the case of GISS database. For our evaluation the Kvikkkjokk weather station, as a temperature reference data set, is 11.6 km away from the nearest grid point of gridded databases and for Tjaamotis station (precipitation reference data) it is 9.4 km. The final values of the errors of the analyzed databases are presented in Tables 2 and 3.

In the case of mean temperature, T_CRU data set as well as T_CRUagr underestimated the monthly as well as seasonal data by 1.43 ∘C, and seasonal data LT by 1.39 ∘C, as documented by the values of mean error (e‾) in Table 2. The significance of bias was proved with the statistical test at α= 1 % significance level. GISS data set was biased the least (-0.15 ∘C) due to its use of anomalies rather than absolute values. However the significance at 1 % level was also proved because of big sample size (n= 1200). For the purpose of differences calculation, the GISS anomalies were recalculated to absolute values using Kvikkjokk data set for reference period 1950–1981 (Hansen et al., 2010).

The random error was quantified with the standard error of differences (SE). It describes the variation of the differences around the average difference e‾ and it is considered a measure of precision of the modeled temperature data sets. The precision of the modeled monthly temperatures was found to be ±0.69 ∘C (±27.26 %) for T_CRU data and ±1.56 ∘C (±126 %) for GISS data. Precision of the seasonal data was ±1.19 ∘C (±46.49 %) for LT data and ±1.17 ∘C (±46.57 %) for T_CRUagr data set. The comparison of the relative standard errors shows that the monthly temperature data were approximately by 50 % more precise than the seasonal data. However, this comes from the fact that SE of the seasonal data was calculated from the differences, the number of which was probably two thirds smaller (n= 400) than the amount of the monthly data (n= 1200). The advantage of the database of the modeled seasonal temperatures is that it encompasses the reconstructed time series of more than 500 years (starting in the year 1500). If it had been possible to calculate the differences for such a long time series, the mean error of the seasonal data would have probably decreased.

The overall accuracy (RMSE) of the modeled monthly temperature data sets was ±1.59 and ±1.57 ∘C, and of the modeled seasonal temperature data it was ±1.83 and ±1.85 ∘C respectively.

Table 3 presents the statistical comparison of the differences between the observed and the modeled data of monthly and seasonal precipitation totals.

Similar to temperature, the results of the statistical test proved a systematic deviation of the modeled data from the observed data. On the contrary to temperature, the modeled precipitation data sets mostly overestimated the observed records. In the monthly database, the P_CRU data biased the records by 4.62 mm (11 %) on average, while in the case of seasonal data the overestimation was 15.75 mm (12.5 %) for PP data and 14.1 mm for P_CRUagr data, respectively. The only GPCC data were underestimated by 0.73 mm. Bigger deviation of the seasonal data results from the nature of the data, since they were calculated as a sum of precipitation of 3 months in one season.

The standard error of the monthly precipitation data sets were ±5.12 mm (±11 %) for P_CRU and ±6.77 mm (±16 %) for GPCC. The precision of seasonal data sets amounted to ±31.84 mm (±22 %) for PP and ±17.05 mm (±12 %) for P_CRUagr data, respectively. The final accuracy of the modeled monthly and seasonal data sets of precipitation totals is presented in Table 3.

Based on results presented in Table 3, we conclude 99 % confidence that the modeled data of both climatic variables were significantly different from the observed data. This bias can be eliminated from the data by extracting the mean deviation value (e‾) from every value of the modeled climatic series. Bigger variability of differences for modeled and observed data around its average difference was found in GISS temperature data set (±126 %).

Question 2: how does the tightness of correlation change between modeled and observed climate data sets with increasing distance of weather station from the locality of radial increment formation? Does this correlation decrease faster with increasing distance of weather station for precipitation data sets due to its higher spatial variability compared to temperature?

At this section of results the correlation was examined between the monthly data observed at the weather stations and the modeled data generated for the location of Hårås by the KNMI Climate Explorer application. The correlation was examined on the sample size 1056 records. We investigated the correlation changes for modeled data with increasing distance of the weather station to the Hårås locality.

The relationship between the monthly temperatures of various climate databases is shown in Fig. 3a. For the both modeled data (T_CRU, GISS) we revealed equal strength of correlation (r= 0.99) within the data (T_40, T_70) of both weather stations (Kvikkjokk, Jokkmokk) located 40 and 70 km from Hårås. It means that 98 % (r2= 0.98) of variability of modeled temperature data can be explained by data of both used weather stations and the increasing distance of about 30 km between weather stations does not significantly influence the tightness of correlation.

The correlation between the databases of monthly precipitation totals was lower than that of temperature. The variance of the modeled precipitation data sets (P_CRUGPCC) explained by the data observed at four weather stations (P_18, P_40, P_70, P_110) was decreasing with increasing distance to the Hårås locality, as documented in Fig. 3b. The highest correlation coefficient (r= 0.96) was explored for the both modeled data sets in relation to the Tjaamotis station, located 18 km away from Hårås. Increasing distance to Kvikkjokk station (40 km) resulted in a lower correlation (r= 0.90 for P_CRU and r= 0.92 for GPCC). Decreasing trend of correlation coefficients continues with the increase of distance (70 km) for Jokkmokk station to r= 0.88 (P_CRU) and r= 0.89 (GISS) respectively. The lowest correlation (r= 0.83 for P_CRU and r= 0.85 for GPCC) was revealed with the precipitation data of the farthest weather station located in Kiruna, 110 km from Hårås. All differences between correlation coefficients for both model data sets were confirmed as statistically significant at the significant level 1 %, except for the difference between P_40 and P_70 data related to the P_CRU data set. This difference is significant at α= 3 %. Results of temperature relationship mentioned above, together with results of decreasing correlation of precipitation data with increasing distance of weather stations confirm the well-known knowledge about greater spatial variability of precipitation variable compared to temperature.

Question 3: what is the growing response of spruce to monthly and/or seasonal temperature and precipitation? The climate of which months and/or seasons is significant (positively or negatively) for radial increment formation? Which of the two examined climatic variables is the more important factor for radial increment formation? Are there any significant differences between climate databases regarding the analysis of growing response of spruce?

Derived mean indexed chronology from measured tree-ring widths (radial increment) of spruce are considered a reference data for comparison of suitability of climate databases for dendroclimatic analysis. Eighteen individual tree-ring series with GLK > 70 % were selected to derive mean chronology. The check of measured series in software COFECHA has detected no crucial errors and misdated series. Series inter-correlation of mean chronology was 0.729 and average mean sensitivity 0.204. Based on the statistics, we consider cross-dating process to be successful enough and derived mean indexed chronology has a high potential for extraction of climate signal.

The first step was to evaluate the cross-correlation function derived from the mean indexed chronology and individual climate data sets. The values of correlation coefficients presented in Fig. 4 quantify the tightness and the trend of the relationship between the indices of radial increment and the mean of monthly (Fig. 4a) or seasonal (Fig. 4b) temperatures within the 18-month long or 7-season long dendroclimatic year. The values of the correlation coefficients were tested at α= 1 and 5 % significance level.

From Fig. 4a we can see that the radial increment was significantly negatively correlated with the temperatures in June and August of the preceding year at the level α= 5 % and in July of the preceding year at 1 % significance level. This means that with 99 % confidence, high values of temperatures in July of the preceding year negatively affected increment formation in the next year. On the other hand, temperatures in the summer season in the year of increment formation were positively correlated with the amount of increment. Particularly June and July were the months that significantly promoted the formation of the radial increment at 1% significance level. However, the differences between growth responses of spruce depending on the database used were not revealed with only two exceptions. The exceptions were presented in the observed data set T_40 and T_70. August of preceding year for T_70 was not considered significant (r= 0.18) for radial increment formation in contrast with all the other databases and vice versa; December of the preceding year was significant at α= 5 % but only for T_40 data set (r= 0.20). Real differences of the correlation coefficients with the other databases, however, were less than Δr≤ 0.03 (August_preceding) and Δr≤ 0.07 (December_preceding) respectively.

Similar results can be interpreted from Fig. 4b. Aggregation of monthly climate data to the seasons has removed the small differences between databases in the months mentioned above. The radial increment is significantly negatively affected (α= 1 %) by high temperatures in the season JJA of preceding year and vice versa; it is significantly positively affected by JJA temperature in the year of increment formation. No differences in interpreting the growth response of spruce were found and no significant differences between the values of correlation coefficients depending on used climate database were detected.

The evaluation of the growth response of spruce to precipitation showed an opposite trend compared to temperature. The increasing amount of precipitation in the spring season (MAM_pre) of the preceding year positively correlated with the radial increment (Fig. 5b), and its impact on increment formation was confirmed with 95 % confidence. This result was found using a PP database. Data sets from the remaining three seasonal databases did not confirm the positive impact of precipitation in the spring of the previous year. In the year of the increment formation, the amount of precipitation in the summer season (JJA) had a significant (α= 5 %) negative impact on increment formation. This conclusion is confirmed by two of the four compared data sets, namely modeled PP data and observed P_110agr data set. It is a surprising finding since the data observed the furthest away (110 km) from the locality of increment formation were more tightly correlated (r= -0.25) with data observed 18 km from Hårås (r= -0.09).

Monthly precipitation databases most closely correlate with the radial increment in May of the preceding year and in May and June the year of increment formation. For all those months and concerned data sets, the significant effect on increment formation was confirmed at 5 % significance level or even at 1 % level for the May of the actual year (Fig. 5a).

Regarding the interpretation of the growth response of spruce to precipitation within the mentioned significant months, its significance confirmed only two of the six data sets (Fig. 5a), modeled P_CRU and observed P110 data set. The result observed on seasonal precipitation totals was repeated itself for P110 data set. The overall highest correlation coefficient (r= -0.32), i.e. in May of the actual year, occurred for the data observed at the most remote station (Kiruna), while precipitation at the nearest station (Tjaamotis) correlated only with r= -0.15.

The highest difference between correlation coefficients derived with all six precipitation data sets for 1 month was Δr= 0.18. With sample size equaled 88 records per month, the difference is statistically significant at α= 0.22. Therefore no significant difference of correlation coefficients could be recognized at conventional significance levels α= 5 % or α=1 %. This applies to all differences derived on the base of cross-correlation functions of all temperature and precipitation data sets examined at our study.

Higher correlation coefficients derived by cross-correlation function for the average temperature within the area of interest point to it as more limiting factor for the radial increment formation of spruce compared to precipitation. The highest correlation coefficient r= 0.44 for monthly temperature data was obtained from a modeled T_CRU data set in June and from an LT data set in the JJA season as r= 0.48. For comparison, the correlation of increment and precipitation rendered the highest correlation coefficients r= -0.32 in May as mentioned above and r= 0.27 for modeled PP data set in the MAM season of the preceding year.

Question 4: what is the correlation between temperature and precipitation in months and seasons which were shown significant for radial increment formation?

For the monthly data sets, temperature and precipitation have inverse trends with regard to increment formation in June (Figs. 4a and 5a). Similarly inverse trend could be observed for the JJA season (Figs. 4b and 5b). We investigated climate regime of the study area by correlating mean temperature and precipitation totals from the data sets with the tightest relationship to radial increment formation (Fig. 6a and b). Low correlation between the climatic characteristics in both cases (r= 0.12 and r= 0.11) confirms that climate regime for growing processes of spruce is not inversely proportional function of precipitation and temperature.

The data sets of the gridded climate databases are publicly available for; CRU TS 3.23 (Harris et al., 2014) at https://crudata.uea.ac.uk/cru/data/hrg/cru_ts_3.23/, for GISS 250 T2m/SST anom (Hansen et al., 2010) at https://climexp.knmi.nl/select.cgi?id=someone@somewhere&field=giss_temp_250, for Luterbacher et al. Temperature (Luterbacher et al., 2004) at https://crudata.uea.ac.uk/cru/projects/soap/data/recon/#luter04, for CPCC V7 (Schneider et al., 2015) at ftp://ftp.dwd.de/pub/data/gpcc/html/fulldata_v7_doi_download.html and Pauling et al. Precipitation (Pauling et al., 2006) at https://www.ncdc.noaa.gov/cdo/f?p=519:1:::::P1_study_id:6342.