3Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.DOI: 10.15201/hungeobull.71.1.1 Hungarian Geographical Bulletin 71 2022 (1) 3–19. Introduction Today there are a number of tools available to translate climate model outputs into vegeta- tion distribution patterns (see e.g., bioclimatic classification methods: Prentice, K.C. 1990; correlative vs. mechanistic biome models: Yates, D.N. et al. 2000; species distribution models: Elith, J. and Leathwick, J.R. 2009). Bioclimatic classification methods (BCMs) 1 Institute of Archaeology, Research Centre for the Humanities, Eötvös Loránd Research Network, Centre of Excellence of the Hungarian Academy of Sciences, Tóth Kálmán u. 4., H–1097 Budapest, Hungary; Depart- ment of Geology and Palaeontology, University of Szeged, Egyetem u. 2–6., H–6722 Szeged, Hungary. Cor- responding author’s e-mail: szelepcsenyi.zoltan@abtk.hu 2 Department of Meteorology, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H–1117 Budapest, Hungary. E-mail: bhajni@nimbus.elte.hu 3 Agricultural Institute, Centre for Agricultural Research, Eötvös Loránd Research Network, Brunszvik u. 2., H–2462 Martonvásár, Hungary. E-mail: fodor.nandor@atk.hu ORCID: https://orcid.org/0000-0002-9844-4958, https://orcid.org/0000-0002-0271-095X, https://orcid.org/0000- 0002-6460-1767 Estimating relative sunshine duration from commonly available meteorological variables for simulating biome distribution in the Carpathian Region Zoltán SZELEPCSÉNYI 1, Hajnalka BREUER 2 and Nándor FODOR 3 Abstract Bright sunshine duration (BSD) data are required for simulating biomes using process-based vegetation models. However, monthly global paleoclimate datasets that can be used in paleo data–model comparisons do not necessarily contain BSD or radiation data. Considering the theoretical and practical aspects, the scheme of Yin, X. (1999) is here recommended to estimate monthly time series of relative BSD using only monthly climate and location data. As a case study for the Carpathian Region, the efficiency of both the original and a variant of that scheme is analysed in this paper. The alternative scheme has high applicability in paleoenvironmental studies. Comparison of the estimated and observed BSD data shows that from May to August, the value of relative root mean squared error in more than 90 percent of the study area does not exceed the threshold of 20 percent, indicating an excellent performance of the original estimation scheme. It is also found that though the magnitude of overestimation for the alternative algorithm is significant in the winter period, the proposed method performs similarly well in the growing season as the original. Furthermore, concerning modelling the distribution of biomes, simulation experiments are performed to assess the effects of modifying some configuration settings: (a) the generation of relative BSD data, and (b) the algorithm used to create quasi-daily weather data from the monthly values. Under both the recent humidity conditions of the study region and the spatial resolution of the climate dataset used, the results can be considered sufficiently robust, regardless of the configuration settings tested. Thus, using monthly temperature and precipitation climatologies, the spatial distribution of biomes can be properly simulated with the configuration settings proposed here. Keywords: sunshine duration, water balance, biome, plant functional types, data–model comparisons, CarpatClim Received November 2021, accepted March 2022 Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.4 are tools used to transform a set of climate and soil variables into an index-class that can be directly related to biome-level vegetation units (Tapiador, F.J. et al. 2019). Correlative models determine a statistical relationship between vegetation distribution and environ- mental variables (e.g., climate, soil, etc.); then this link is applied to simulate the potential distribution of vegetation under the altered conditions (Yates, D.N. et al. 2000; Elith, J. and Leathwick, J.R. 2009). From this point of view, therefore, BCMs (e.g., Köppen, W. 1936) can be considered the simplest correlative biome models. Mechanistic biome models, in contrast, focus on mechanisms determin- ing survival and performance of plants by simulating processes in soil–vegetation–at- mosphere systems, such as water, carbon and nutrient cycles (Prentice, I.C. et al. 2007). Paleoclimatological and paleoenvironmen- tal studies often use both outputs from cli- mate model simulations and proxy archives such as fossil pollen records in a common framework. These studies represent a special area of called paleo data–model comparisons (Harrison, S.P. 2013) that have essentially two distinct purposes: (a) to understand the mechanisms of past climate and environmen- tal shifts (e.g., Miller, P.A. et al. 2008; Mauri, A. et al. 2014), and (b) to provide feedback on the performance of climate/environmental reconstruction approaches (e.g., Prentice, I.C. et al. 1998; Webb, III T. et al. 1998). These comparisons can be made in two ways, ei- ther by collating pollen-inferred climate with that simulated by climate models (e.g., Webb, III T. et al. 1998; Mauri, A. et al. 2014), or by comparing biome/species distribution estimated using paleoclimate model outputs with vegetation reconstructed from pollen assemblages (e.g., Prentice, I.C. et al. 1998; Miller, P.A. et al. 2008). Currently, more and more global datasets are made publicly available that provide bias- corrected monthly climatologies (multi-year averages) from paleoclimate simulations in order to support distribution modelling ex- periments in various research areas (e.g., paleobiogeography, archaeology). However, these datasets differ significantly in terms of spatial resolution, temporal coverage and time step, and in terms of which climate vari- ables they contain information on. Beyer, R.M. et al. (2020), for example, published a monthly global dataset (hereinafter HadCM3-120k), with a horizontal resolution of 0.5°, for tem- perature, precipitation, cloud cover, relative humidity, and wind speed, and additional parameters related to bioclimatic and biogeo- chemical conditions, covering the last 120,000 years at a temporal resolution of 1,000–2,000 years. For this, medium-resolution simula- tions generated by the HadCM3 general circu- lation model (GCM) for the last 120,000 years were combined with high-resolution simula- tions prepared by the HadAM3H GCM for the last 21,000 years and a recent observational dataset. (For details of the above-mentioned GCMs, see Valdes, P.J. et al. 2017.) Then, Krapp, M. et al. (2021) extended access to the climate variables in question for the last 800,000 years by performing a statistical-based reconstruction using the above-mentioned simulations. And recently, Karger, D.N. et al. (in review) shared with the scientific commu- nity their dataset, called CHELSA-TraCE21k v1.0, that includes monthly climatologies for both temperature and precipitation, and other bioclimatic variables, with a spatial resolution of 30 arc-sec at a 100-year time step for the last 21,000 years. For this, a transient simulation generated by the CCSM3 GCM (He, F. 2011) was downscaled considering the temporal change of orography. The HadCM3-120k was specifically gener- ated to feed mechanistic biome models, while the CHELSA-TraCE21k v1.0 was clearly de- veloped to support paleoecological studies using correlative species distribution models (SDMs). In SDMs (e.g., MaxEnt: Phillips, S.J. et al. 2006), bioclimatic variables, i.e., annual and seasonal measures derived from monthly values of temperature and precipitation, are generally used as environmental predictors, besides topographic variables. In contrast, due to the simulation of energy and water fluxes, for applying mechanistic biome mod- els, a meteorological variable directly related 5Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19. to radiation (e.g., cloud cover, sunshine dura- tion) is also required, besides temperature and precipitation data. Beyer, R.M. et al. (2020) and Krapp, M. et al. (2021), relying on their own datasets, also estimated the evolution of the global biome distribution using one of the best-known mechanistic biome models, called BIOME4 (Kaplan, J.O. 2001). The BIOMEn models (e.g., BIOME: Prentice, I.C. et al. 1992; BIOME4) estimate the net radiation as a function of latitude, temperature, and bright sunshine duration (BSD). Thus, to apply the above-mentioned vegetation model to their own datasets, the authors used different em- pirical linear relationships (Doorenbos, J. and Pruitt, W.O. 1977; Hoyt, D.V. 1977) to convert cloud cover data to the percentage of possible sunshine hours. Unfortunately, the CHELSA- TraCE21k v1.0 does not contain cloudiness or BSD data, so it is not directly suitable for feeding the above-mentioned BIOMEn mod- els. However, estimating BSD data from com- monly available meteorological variables may be a solution to overcome the lack of data. Although there are several estimation meth- ods for calculating monthly values of BSD (Kandirmaz, H.M. et al. 2014), in this study, the use of a method developed by Yin, X. (1999) is recommended. Yin, X. (1999) used monthly data of 729 worldwide stations for finding a generic algorithm that captures global variabil- ity of BSD data in relation to temperature, pre- cipitation, and geographic location. Regression models for estimating monthly mean daily values of BSD are usually set only for smaller regions due to limited access to reliable station data (e.g., Italy: Stanghellini, C. 1981), and/or use parameters that are not readily available from global gridded climate datasets (e.g., the number of wet days per month: Castellvi, F. 2001). Thus, what makes the method proposed by Yin, X. (1999) special is that it is globally parameterized and uses only monthly climate and location data that are widely available. To our knowledge, by means of gridded cli- mate datasets, the performance of the estima- tion scheme proposed by Yin, X. (1999) has not yet been evaluated. Our current level of knowl- edge would indicate that there is currently no global gridded observational dataset to which the following three statements are true with- out exception: (i) it contains monthly values for BSD, temperature, and precipitation; (ii) it contains monthly meteorological data for a long period without time averaging; and (iii) it was developed based on station observations. Currently, there is only access to global data- sets that also use remotely sensed and reanaly- sis data to produce gridded climate informa- tion, and for which values of BSD can only be derived from another meteorological variable (e.g., incoming solar radiation: TerraClimate, Abatzoglou, J.T. et al. 2018; cloud cover: CRU TS v4, Harris, I. et al. 2020). However, two re- gional climate databases are known that pro- vide station-based meteorological fields for the above-mentioned three variables for continu- ous periods: CarpatClim (Spinoni, J. et al. 2015) and HadUK-Grid (Hollis, D. et al. 2019). In consideration of the literature discussed above, the first objective of this study is to as- sess the accuracy of the scheme under discus- sion using the monthly climate data provided by the CarpatClim dataset. The second goal of this paper is to test how the quality of esti- mates changes as a result of proposed modifi- cations of the approach, which are justified by its applicability in paleoenvironmental stud- ies. The amount of incoming and outgoing radiation influences the growing conditions of plants, so the error in estimating the rela- tive BSD can cause problems in the modelling of the biome distribution. Therefore, as a case study for the Carpathian Region, evaluation of the impact of the estimated relative BSD on simulation of energy and water fluxes and bi- ome designation is the third aim of this study. Materials and methods Estimation of monthly mean relative sunshine duration The monthly mean daily values of relative BSD (RSD, dimensionless) for a given month is esti- mated using the following parametric regres- sion model as recommended by Yin, X. (1999): Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.6 , with , where , , , , and , where p is the station atmospheric pressure in relation to the pressure at sea level, fo represents global trends, fi gives regional modifications, ∑fi is the summation of values of any regional functions that are applicable to a particular lo- cation, RE is the monthly average of hourly solar irradiance for cloudless-sky conditions (in MJ m−2 hr−1), P is the monthly mean precipitation intensity (in mm dy−1), T is the monthly mean air temperature (in °C), EP is the monthly aver- age of daily potential evapotranspiration (in mm dy−1), ϕ is the latitude (in decimal degrees), IT<0 is a temperature indicator (1 if T ≤ 0 °C, and 0 if T > 0 °C), Tam is the annual mean tempera- ture (in °C), EPam is the annual average of daily potential evapotranspiration (in mm dy−1), Tmin is the lowest monthly mean air temperature (in °C), P7 is the monthly mean precipitation intensity (in mm dy−1) in the warmest month (fixed at July for the Northern Hemisphere, and January for the Southern Hemisphere), P1 is the monthly mean precipitation intensity (in mm dy−1) in the coldest month (fixed at January for the Northern Hemisphere, and July for the Southern Hemisphere), Pam is the annual mean precipitation intensity (in mm dy−1), Tar is the annual range of monthly mean air temperature (annual diurnal range) (in °C). The values of RE are calculated as proposed by Yin, X. (1997a), with a minor modification, using the daytime means of optical air mass and cosine zenith. The former is computed as recommended by Yin, X. (1997a), while the latter is estimated by using Eq. 5 of Yin, X. (1997b). Furthermore, in contrast to the original approach, where the solar constant was fixed at 4.9212 MJ m−2 hr−1, its value is corrected, according to Yin, X. (1999), by cal- endar day for the variable ellipticity of the Earth’s orbit using the scheme of Brock, T.D. (1981). In these calculations, the values of so- lar declination and daylength are derived by using the approach of Brock, T.D. (1981). The values of EP are computed using Eq. A10 of Yin, X. (1998). The value of EPam is calculated as a weighted mean of the EP values using the number of days in months as weights. Simulation of biome distribution In this study, the BIOME model (Prentice, I.C. et al. 1992) is applied to simulate the spatial distribution of biome-level vegeta- tion units. First, the presence of each plant functional type (PFT) that is a group of plant types with similar ecophysiological behav- iour is estimated under given climatic con- ditions. To do this, it is necessary to check which of the 14 PFTs defined can occur con- sidering the environmental constraints as- sociated with their climatic tolerances and requirements (Table 1). After this, the domi- nance class value (D) of each PFT is exam- ined and only those in the highest class (with lowest D) present are retained. Finally, to infer the biome type, retained PFTs are com- bined with each other by taking into account rules formalized in Table 2. (1) (2) (3) (4) (5) (6) (7) 7Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19. In the BIOME model, the plant-available moisture is characterized by the Priestley– Taylor coefficient (α, dimensionless). Here, the values of α at an annual time scale are computed by using the SPLASH v.1.0 model (Davis, T.W. et al. 2017), through the simula- tion of seasonal changes in both surface en- ergy fluxes and climatic water balance. In the BIOME model, in order to quantify heat re- quirement, the growing degree-days (GDD, in °C day) is used, which can be obtained by summing the values of daily tempera- ture above a certain base temperature. To calculate values of GDD, the values of daily mean temperature are required; furthermore, besides temperature and precipitation data, the relative BSD must also be used in the SPLASH v.1.0 model, on a daily basis. The methods for generating these daily values are described in more detail below. Table 1. Dominance class (D) and environmental constraints* for each plant functional type used in the model Abbre- viation Plant functional type D TC GDD0 GDD5 TW α min max min min min min max tr.e.t tr.r.t w-te.e.t te.s.t c-te.c.t bo.e.t bo.s.t sb.suc wa.g.s cl.g.s cd.g.s h.d.s c.d.s p.d Tropical evergreen tree Tropical rain-green tree Warm temperate evergreen tree Temperate summer-green tree Cool temperate conifer tree Boreal evergreen conifer tree Boreal summer-green tree Sclerophyll/succulent Warm grass/shrub Cool grass/shrub Cold grass/shrub Hot desert shrub Cold desert shrub Polar desert 1 1 2 3 3 3 3 4 5 6 6 7 8 9 15.5 15.5 5.0 −15.0 −19.0 −35.0 – 5.0 – – – – – – – – – 15.5 5.0 −2.0 5.0 – – – – – – – – – – – – – – – – – 100 – 100 – – – – 1,200 900 350 350 – – 500 – – – – – – – – – – – 22 – – 22 – – 0.80 0.45 0.65 0.65 0.65 0.75 0.65 0.28 0.18 0.33 0.33 – – – – 0.95 – – – – – – – – – – – – *TC = mean temperature of the coldest month (in °C); GDD0 = growing degree-days above a 0 °C base (in °C day); GDD5 = growing degree-days above a 5 °C base (in °C day); TW = mean temperature of the warmest month (in °C); α = Priestley–Taylor coefficient at an annual time scale (dimensionless). Table 2. A list of biome types used in the model and their generation rules Abbreviation Biome type Plant functional types TRRA TRSE TRDR WAMX TEDE COMX COCO TAIG CLMX CLDE XERO WAST COST TUND HODE SEDE PODE Tropical rain forest Tropical seasonal forest Tropical dry forest/savannah Broad-leaved evergreen/warm mixed forest Temperate deciduous forest Cool mixed forest Cool conifer forest Taiga Cold mixed forest Cold deciduous forest Xerophytic woods/scrub Warm grass/shrub Cool grass/shrub Tundra Hot desert Semi-desert Polar desert tr.e.t tr.e.t + tr.r.t tr.r.t w-te.e.t te.s + c-te.c.t + bo.s.t te.s.t + c-te.c.t + bo.e.t + bo.s.t c-te.c.t + bo.e.t + bo.s.t bo.e.t + bo.s.t c-te.c.t + bo.s.t bo.s.t sb.suc wa.g.s cl.g.s + cd.g.s cd.g.s h.d.s c.d.s p.d Note: Each biome type is arising as a combination of dominant plant functional types. Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.8 Evaluation methodology Monthly time series of the temperature, pre- cipitation and sunshine duration, along with location data, are required for evaluating the performance of the procedure proposed by Yin, X. (1999). The CarpatClim dataset pro- vides access to the three meteorological vari- ables relevant to the assessment for the time period 1960–2010, with a horizontal resolu- tion of 0.1°, covering nine countries with 5,895 grid cells (Figure 1). For this reason, using data derived from this dataset, RSD values for each year in the period 1961–2010 are estimated using the scheme developed by Yin, X. (1999), and the estimates are com- pared to the observed data. Observed values of RSD are determined by a two-step proce- dure, following Spinoni, J. et al. (2015): (i) the monthly amount of BSD to which the Car- patClim dataset provides access is divided by the number of days in a given month to calculate the monthly mean for BSD, and then (ii) this value is divided by the monthly mean for daylength that is calculated using Eq. 8.5.3 of Iqbal, M. (1983). Finally, in each grid cell, values of the root mean square error normalized by the mean value of observed data (RRMSE, in percentages) are computed between the observed and estimated 50-year time series of RSD, separately for each month. To apply the parametric regression model proposed by Yin, X. (1999) to monthly glob- al paleoclimate datasets already described in the introduction, two modifications are needed to use. A feature of such paleoclimate datasets is that they represent climatic con- ditions averaged over a longer period (typi- cally 30 or 50 years) at each time step. For this reason, it is considered necessary to in- Fig. 1. Topography of the Carpathian Region based on the CarpatClim dataset (Spinoni, J. et al. 2015) 9Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19. vestigate how the scheme performs when ap- plied to multi-year averages instead of single year time series. Furthermore, the regression model of Yin, X. (1999) also uses the monthly mean of hourly solar irradiance to estimate the global trend, but uses an algorithm to es- timate the value of RE that cannot be applied without modification in paleoclimatological studies because it does not consider changes in the Earth’s orbital parameters. For this rea- son, here, it is recommended that the value of RE be calculated using the algorithm used in the SPLASH v.1.0 model, with the addition that orbital parameters are calculated using the method of Berger, A. and Loutre, M.F. (1991). In this approach, first, the daily solar radiation at the top of the atmosphere is cal- culated (Eq. 7 in Davis, T.W. et al. 2017), and then this value is multiplied by the atmos- pheric transmissivity to obtain the value of daily surface radiation. In this case, as well, cloudless conditions are assumed, i.e., the transmission coefficient is taken into account with a universal value of 0.75, however, its value is modified as a function of elevation by using the scheme of Allen, R.G. (1996). The daylength is calculated via Eq. 1.6.11 in Duffie, J.A. and Beckman, W.A. (1991), using the sunset hour angle (Eq. 8 in Davis, T.W. et al. 2017). Finally, the mean hourly surface radiation is derived as the quotient of the daily surface radiation and the daylength. In this study, using the CarpatClim dataset, values of RSD for the period 1981–2010 are computed in two ways: (A) by averaging the time series estimated using the initial scheme for each year, and (B) by applying the scheme to 30-year averages, with the provision that the values of RE are calculated for year 1995 using the algorithm described above. When modelling the distribution of bi- omes, monthly climatologies must be con- verted to daily values, in order to simulate seasonal changes in both surface energy fluxes and climatic water balance. In the de- scription of the water balance module used in the initial version of the BIOME model, Prentice, I.C. et al. (1993) have recommended for this that monthly values are interpolated linearly between mid-month days. However, this approach is unsound because it is not mean-preserving (the monthly means of the interpolated daily values will generally not match the original monthly values). When presenting the SPLASH v.1.0 model, Davis, T.W. et al. (2017) simply suggested that monthly mean values are assumed constant over each day of the month. This procedure is suitable in terms of the monthly averages, but it generates unrealistic time series. In the 1990s, several mean-preserving methods (see e.g., Epstein, E.S. 1991; Lüdeke, M.K.B. et al. 1994) were developed to address this issue. Here, quasi-daily values are constructed in two ways: (a) monthly averages of tempera- ture and RSD are assumed constant, and the monthly precipitation sum is divided equal- ly across each day of the month; and (b) for temperature and RSD, the ‘harmonic’ inter- polation technique described by Epstein, E.S. (1991) is used, with a correction of physically impossible values, and in the case of precipi- tation, the temporal scaling using an iterative interpolation technique described by Lüdeke, M.K.B. et al. (1994) is applied, with a damp- ing variable of 0.7 for each month. In this study, we assess the effects of the choice of the method used to generate the quasi-daily values and of the source of the BSD data on the results in terms of the spatial distribution of the bioclimatic variables used in the BIOME model. Finally, biome maps simulated under various model configura- tion settings are compared using the Kappa statistic (Cohen, J. 1960), which value ranges from 0 to 1, with 0 representing totally dif- ferent patterns and 1 indicating complete agreement. Results and discussion One of the key objectives of this study is to attempt to evaluate the performance of the estimation procedure for RSD using data provided by the CarpatClim database. The performance of the scheme proposed by Yin, X. (1999) is assessed based on the root Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.10 mean square error normalized by the mean value of observed data (RRMSE, in percent- ages) calculated between the observed and estimated values for the period 1961–2010, separately for each month (Figure 2). From May to August, the RRMSE value in more than 90 percent of the study area does not ex- ceed the threshold of 20 percent below which the model performance can be considered excellent, according to Bellocchi, G. et al. (2002). In the period from April to October, in nearly 99 percent of the grid cells with el- evation smaller than 500 m a.s.l., the value of RRMSE is less than 40 percent, which is the limit of the model performance still consid- ered acceptable based on the work of Belloc- chi, G. et al. (2002). In the summer months, the RRMSE value in almost 90 percent of the lower regions (elevation < 500 m a.s.l.) does not even exceed the threshold of 15 percent. Interestingly, in the winter months, the esti- mation scheme performs better in the higher than in the lower elevation areas (66 ± 3% and 45 ± 28% of the regions at elevations above and below 500 m a.s.l., respectively, with a threshold of 40%). Although not within the scope of this study, it should be pointed out that the inconsistency between the measured and estimated values found in the Ukrain- ian section of the Carpathians suggests (see Figure 2) that one or even more of the climate fields used in the assessment may contain significant errors in this region. However, an explanation of this requires a more detailed analysis. An important objective of this paper is to assess how the accuracy of the estimates changes when the scheme is adapted for ap- plying to paleoclimate datasets. To study this, values of RSD for the period 1981–2010 are calculated in two ways (Figure 3): (A) by aver- aging the time series estimated using the ini- tial scheme for each year, and (B) by applying the scheme to 30-year averages. The estimated results are compared to the averages of the measured values over the period 1981–2010 (Figure 3, b). For the time window used here, we can see that in the period from March to September, the estimation method proposed here performs even better than the initial algo- rithm. In these months, i.e., in the most impor- tant period in terms of the evapotranspiration processes, with one exception, the value of RRMSE calculated for the whole study area does not exceed the threshold of 10 percent (see the second row in Figure 3, b), which in- dicates a very good quality of the estimates. (As previously indicated, the Ukrainian part of the Carpathians is the main contributor to the observed discrepancies.) In the context of Figure 3, it is important to underline that when applying the modified es- timation scheme to 30-year averages, the over- estimation is very high in the winter months (in January, its value exceeds the value of 0.15 over almost half of the region), which, combined with a low (around 0.254 in January) bench- mark, results in very high values of RRMSE: 60.8 percent in January and almost 30 percent in February. For both estimation methods, the difference in winter months, which is also highlighted above in relation to the Figure 2, is probably related to the formation of condi- tions for cold-air pool (CAP), which is a typi- cal weather situation in the Carpathian Basin (Szabóné André, K. et al. 2021). Namely, the CAP conditions are extremely favourable for the formation of fog which lead to less surface solar radiation. Considering that the model is globally parameterized, it is impractical to ex- pect it to capture such local effects, but fortu- nately, this model weakness has little relevance in simulating important processes for plants, as it will also be shown later. The ultimate goal of this study is to examine how sensitive the BIOME model is to change configuration settings. We are interested in how the results change when on the one hand, the measured time series of RSD are replaced by estimates produced by different algo- rithms, and on the other hand, the technique for generating daily weather data is made more sophisticated. For the latter aspect, the simulations are performed in two ways: (a) monthly means are assumed constant over each day of the month, and (b) different mean-preserving interpolation techniques are applied (for details, see evaluation methods). 11Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19. Fig. 2. Performance of the regression model developed by Yin, X. (1999) to estimate monthly time series of the relative sunshine duration (RSD, dimensionless), based on the root mean square error normalized by the mean value of observed data (RRMSE, in percentages). RRMSE values are calculated between the observed and estimated values for the period 1961–2010 using the CarpatClim dataset, separately for each month. The presence of PFTs is fundamentally dependent on the plant-available moisture, which in the BIOME model is characterized by the α ranging from 0 to 1.26. Its value for the period 1981–2010 is calculated at an annual time scale using the SPLASH v.1.0 model, with a total of six settings (Figure 4). The simulation performed using the mea- sured values of RSD and assuming constant monthly means of each meteorological vari- able over each day of the month is consid- ered as a reference (Figure 4, a). Based on this, it can be concluded that there is suffi- cient moisture in the study area for all woody PFTs related to mid-latitudes (cf. Figure 4, a, and Table 2), with the spatial resolution and Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.12 Fi g. 3 . S pa tia l d is tr ib ut io n pa tte rn s o f m on th ly m ea n of re la tiv e su ns hi ne d ur at io n (R SD , d im en si on le ss ) i n th e C ar pa th ia n Re gi on fo r t he p er io d 19 81 –2 01 0: b y av er ag in g th e ob se rv ed ti m e se ri es fo r e ac h ye ar (O ); by a ve ra gi ng th e tim e se ri es e st im at ed u si ng th e sc he m e pr op os ed b y Yi n, X . ( 19 99 ) f or e ac h ye ar (P A ); an d by a pp ly in g th e sc he m e to 3 0- ye ar a ve ra ge s, w ith th e pr ov is io n th at th e te rm r el at ed to th e so la r ir ra di an ce in th e m od el (s ee R E i n Eq . 3 ) i s ca lc ul at ed fo r y ea r 1 99 5 us in g th e al go ri th m u se d in th e SP LA SH v .1 .0 m od el (f or d et ai ls s ee e va lu at io n m et ho do lo gy ) ( PB ). In a dd iti on to th e va lu es (a ), th e di ffe re nc es fr om th e va ri ou s so ur ce s ar e al so m ap pe d (b : P A −O , P B− O , a nd P B− PA ), in th e la tte r c as e sh ow in g th e ro ot m ea n sq ua re e rr or n or m al iz ed b y th e m ea n va lu e of re fe re nc e da ta (R RM SE , i n pe rc en ta ge s) o ve r t he w ho le ta rg et d om ai n. 13Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19. time window used here. The change in the methodology for generating daily weather data has little effect on the spatial distributions of this bio- climatic index over the study period: for only 13 out of the 5,895 grid cells, the value of α changes by more than 0.005 when the daily data required for the simulation are generated us- ing more sophisticated techniques (see the first row of the second col- umn in Figure 4, b). Regardless of the settings, the value of α for the period 1981–2010 does not change over at least one-third of the target domain, however, the spatial distribution of these unchanged areas varies de- pending on the choice of source for Fig. 4. Spatial distributions of the Priestley– Taylor coefficient (α, dimensionless) in the Carpathian Region for the period 1981– 2010: (a) the values of α are simulated by the SPLASH v.1.0 model using the ob- served values of monthly means of relative sunshine duration (RSD, dimensionless), assuming monthly means for each mete- orological variable to be constant over each day of the month; and (b) the differences of α values modelled by the initial algorithm and estimated under various model con- figurations. In each cell of the panel (b), the references are derived from the panel (a). In each row of the panel (b), the estimates are calculated using the RSD values derived from various sources: (O) by averaging the single year time series of the observations; (PA) by averaging the time series estimated using the initial scheme for each year; and (PB) by applying the scheme to 30-year av- erages. In each column of the panel (b), the estimates are calculated using quasi-daily values of each meteorological variable gen- erated by different approaches: (constant) monthly means are assumed constant over each day of the month; and (interpolated) different mean-preserving interpolation techniques are applied (for details, see evaluation methodology). In the panel (b), the root mean square error normalized by the mean value of reference data (RRMSE, in percentages) over the whole target do- main is shown above each map. Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.14 the RSD data. When using the model driven by sunshine data estimated using multi-year averages, the unchanged areas are limited to the Carpathians that are the wettest regions of the target domain (see the third row in Figure 4, b). At this setting, wetter conditions compared to the reference are simulated over more than two-thirds of the study area (66.9% and 63.2%, respectively, for constant and interpolated daily data). While simula- tions using estimated single year time series of RSD show an underestimation in an area of a similar extent (see the second row in Figure 4, b). Overall, changing the configura- tion settings does not have a significant effect on this bioclimatic index, with the RRMSE for this index hovering around 1.5 percent, considering all simulation experiments. Considering all five bioclimatic indices used in the BIOME model, in addition to α, the growing degree-days can also be signifi- cantly influenced by the approach used to generate daily temperature values. Thus, a sensitivity analysis is also performed for these two indices. Values of GDD5 and GDD0 for the period 1981–2010 are calculated using the two approaches described above, and their spatial distribution (Figure 5) is plotted (mostly) us- ing the thresholds used in the BIOME model (see Table 1). Except for the highest peaks of the Carpathians, in the target domain, the value of GDD5 exceeds the threshold of Fig. 5. Spatial distributions of growing degree-days above base temperatures of 5 °C and 0 °C (GDD5 and GDD0, in °C day) in the Carpathian Region for the period 1981–2010. Panels (a) and (b) show the spatial distribution of respectively GDD5 and GDD0 depending on how the quasi-daily temperature values required to compute these bioclimatic indices are constructed: (constant) monthly means are assumed constant over each day of the month; and (interpolated) the ‘harmonic’ interpolation technique described by Epstein, E.S. (1991) is applied. Panels (c) and (d) show the spatial distributions of the differences between growing degree-days calculated from interpolated and constant daily values, respectively, for GDD5 and GDD0. 15Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19. 1,200 °C day, regardless of the settings (see Figure 5), and thus, in these regions, the PFT “temperate summer-green tree” (te.s.t) can occur (see Table 2), due to the availability of sufficient moisture (see Figure 4). Although, in relation to the spatial distribution of these indices (Figure 5, a and b), a large difference between the two approaches cannot be ob- served, inter alia due the thresholds used to plotting, but the distribution maps for the differences (Figure 5, c and d) provide ad- ditional valuable information. In the case of GDD5 (GDD0), the areas with a difference of greater than 30 °C day are mostly located at altitudes lower (higher) than 500 m a.s.l. (cf. Figure 5, c and d, and Figure 1). For growing degree-days, the difference between the two algorithms is greater in grid cells where the monthly mean temperatures in the first and last months of the growing season are spread around the given base temperature and the annual diurnal range is relatively large. It is easy to understand that under a typical an- nual temperature course, in cases where the monthly mean temperature is equal to or slightly greater than 5 °C in both April and November, for the GDD5, a larger amount of heat can be generated from interpolated val- ues than from constant daily data. As a final step in this study, it is checked how changing the configuration settings af- fects the biome designation. Thus, the main results of this study include the distribution maps of biomes under different configura- tion settings (Figure 6). Here again, the refer- ence simulation is prepared using the meas- ured values of RSD and assuming constant monthly means (the first row of the first col- umn in Figure 6). For the period 1981–2010, 5 out of the 14 extratropical biome types used by the BIOME model can be observed in the Carpathian Region, at a horizontal resolution of 0.1°. More than half (55%) of the target area is covered by the biome type “temperate deciduous forest” (TEDE), mostly limited to the lowlands (elevation < 250 m a.s.l.). With an areal proportion of 40.7 percent, the sec- ond most dominant biome type in the target domain is the “cool mixed forest” (COMX), covering significant areas in Slovakia, Ukraine and the mountains of Romania. The types “taiga” (TAIG) and “cool conifer forest” (COCO) together cover a total of 4.2 percent of the study area. As shown in Figure 6, these types appear most markedly in the Eastern Carpathians. The type “tundra” (TUND) cov- ers slightly more than 0.1 percent of the target area (7 grid cells). Comparing the simulation experiments, it can be found that the choice of source for the time series of RSD has no effect on the biome distribution under giv- en space and time conditions: values of the Kappa statistic between the maps derived from the reference simulation and from the remaining two experiments are equal to one, i.e., the spatial distribution patterns of biomes are completely identical (see the first column in Figure 6). Biome maps generated using in- terpolated daily values are consistent with each other (see the second column in Figure 6). Comparing them to the reference map, only a slight mismatch can be found (Kappa statistic = 0.9923). There is a disagreement between biome maps for only 24 of the 5,895 grid cells derived using different daily weather data. In all cases, this mismatch is explained by the discrepancy in the spatial distribution of GDD5 (see Figure 5, c). The difference is ulti- mately due to the fact that in some grid cells of the Carpathians, certain heat-demanding woody PFTs (e.g., te.s.t) can occur in the case of the reference simulation, in contrast to the experiments using interpolated daily values. In summary, the BIOME model is not sensi- tive to modify configuration settings consid- ered here. Conclusions In this paper, as a case study for the Carpathi- an Region, we inspect the efficiency of biome distribution simulation using only monthly temperature and precipitation climatologies. The biome maps were constructed by using a simple process-based vegetation model, the BIOME model, with one minor amendment: the water balance module of the model was Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19.16 Fig. 6. Spatial distribution patterns of biomes simulated by the BIOME model in the Carpathian Region for the period 1981–2010. In each row, the biomes are derived using the sunshine duration data derived from different sources: (O) by averaging the single year time series of the observations; (PA) by averaging the time series estimated using the initial scheme for each year; and (PB) by applying the scheme to 30-year averages. In each column, the biomes are derived using quasi-daily values of each meteorological variable generated by different approaches: (constant) monthly means are assumed constant over each day of the month; and (interpolated) different mean-preserving interpolation techniques are applied (for details, see evaluation meth- odology). Above each map, the Kappa statistic reflecting the degree of similarity of the distribution patterns is shown, using the map in the first column of the first row as a reference in each case. The abbreviations of biome types can be found in Table 2. 17Szelepcsényi, Z. et al. Hungarian Geographical Bulletin 71 (2022) (1) 3–19. replaced by the SPLASH v.1.0 model, thus switching to analytical expressions for cal- culating daily radiation, evapotranspiration and soil moisture. Monthly temperature and precipitation data, which were required to create the biome maps, were taken from the CarpatClim dataset for the period 1981–2010. The relative BSD data required to run the SPLASH v.1.0 model were taken from the CarpatClim dataset and also estimated by the scheme proposed by Yin, X. (1999) us- ing the above-mentioned temperature and precipitation data. Comparisons between the observed and estimated relative BSD time series for the period 1961–2010 showed that the estimation procedure performed rela- tively well from late spring to early autumn, i.e., in the most important period in terms of the evapotranspiration processes. It was also examined the effects of two modifications justified by the applicability of the estima- tion method to paleoclimate datasets: (a) to apply the scheme of Yin, X. (1999) to multi- year averages instead of single year time se- ries, and (b) to calculate the term related to the solar irradiance in the scheme by apply- ing the algorithm used in the SPLASH v.1.0 model under changing orbital parameters of the Earth. It was found that although the magnitude of overestimation for the modi- fied algorithm is significant in the winter period, the proposed procedure performs similarly well as the initial procedure in the period from March to October. When mod- elling the distribution of biomes, simulation experiments were performed to assess the effects of modifying some configuration settings of the model: (a) the generation of relative BSD data, and (b) the algorithm used to create quasi-daily weather data from the monthly climatologies. We found that under both the recent humidity conditions of the study region and the spatial resolution of the climate dataset used, the results can be considered sufficiently robust, regardless of the configuration settings tested. The choice of source for BSD data had no effect on the results, while the choice of the method for temporal downscaling of monthly tempera- ture data had little effect on the distribution patterns of biomes. Thus, the main message of this paper is that using climate data avail- able for Quaternary studies (i.e., monthly temperature and precipitation climatolo- gies), the spatial distribution of biomes can be properly simulated via more sophisticated biome models than BCMs. We believe that by applying the modelling framework outlined here to the data provided by the CHELSA- TraCE21k v1.0, the evolution of biomes over the past millennia can be properly mapped. Acknowledgements: The work of the first author was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4. A/2-11-1-2012- 0001 ‘National Excellence Program’. The work of the second author was partly financed by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The authors would like to thank the creators of the CarpatClim dataset (http://www.carpatclim-eu. org/) used in this study for sharing their datasets with the scientific community. The authors are also grate- ful to the software developers of the SPLASH model (https://bitbucket.org/labprentice/splash) for making available to everyone their source codes. REFERENCES Abatzoglou, J.T., Dobrowski, S.Z., Parks, S.A. and Hegewisch, K.C. 2018. TerraClimate, a high- resolution global dataset of monthly climate and climatic water balance from 1958–2015. Scientific Data 5. 170191. 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