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  • View in gallery

    Schematic view of terrain elevation over Russia. Names refer to locations mentioned in the text.

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    (a) Schematic view of the 2.8° × 2.8° areas and locations of “sites” in the “reference” network over Russia. Location of sites for one of the ten (b) 500-, (c) 400-, (d) 200-, and (e) 100-site networks. (f) Locations of sites in the “real network.”

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    Frequency distribution of (a) land cover type, (b) terrain elevation, and (c) soil type or other surface type in the “reference,” the 500-, 400-, 200-, and 100-site networks and real network over Russia. In the case of the artificial networks, the uppermost, mean, and lowermost frequency of the 10 networks are illustrated for each network density by horizontal lines. In (a) the x axis represents urban (U), cropland/pasture (CLP), cropland/grassland (CLGL), cropland/woodland (CLWL), grassland (GL), shrubland (SL), mixed shrubland/grassland (MSGL), savanna (SV), broadleaf deciduous forest (BDF), needleleaf deciduous forest (NDF), broadleaf evergreen forest (BEF), needleleaf evergreen forest (NEF), mixed forest (MF), water bodies (WB), herbaceous wetlands (HWL), wooded wetlands (WWL), bare or sparsely vegetated (BSV), herbaceous tundra (HT), wooded tundra (WT), mixed tundra (MT), bare ground tundra (BGT), and glacier/ice (GI). In (c), the x axis represents sand (S), loamy sand (LS), sandy loam (SL), silt loam (SLL), silt (SL), loam (L), sandy clay loam (SCL), silty clay loam (SLCL), clay loam (CL), sandy clay (SC), silty clay (SLC), clay (C), organic material (OM), and bedrock (BR). Note that over Russia the average terrain elevation of the 500-, 400-, 200-, and 100-site networks ranges between 405 and 421 m (with on average over all 10 networks 412 m), 390 and 430 m (410 m), 389 and 454 m (415 m), and 379 and 457 m (421 m), respectively; average terrain height of the real network amounts to 387 m; the average terrain height of the reference network is 416 m.

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    Temporal behavior of regional averages of SLP as obtained for the reference data using all data within all 2.8° × 2.8° areas and as derived for various 500-site networks based on the “sites” within the 2.8° × 2.8° areas for (a) July and (b) December, for various 400-site networks for (c) July and (d) December, for various 200-site networks for (e) July and (f) December, and for various 100-site networks in (g) July and (h) December. In (c) and (d) the solid line with filled circles represents the regional averages derived from the real network (411 sites). In (a)–(h), all other lines represent the regional averages with the lowest error values among the ten setups of the respective network of given density; the shaded regions represent the maximum over- and underestimation of the reference regional averages found for the 10 networks of the same density. The letters H and L in (a) and (b) represent the days with high and low pressure situations. Data shown are for 2005, but 2006 and 2007 show similar general behavior with respect to differences among networks of same density, the range of over- and underestimation by networks and among networks of different density, as well as reaction to events (e.g., frontal passages). See text for further details.

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    Spatial distribution of regional averages of SLP in hPa for (a) July and (b) December, biases for (c) July and (d) December between regional averages of SLP estimated from the real network and the reference network, and biases for (e) July and (f) December between regional averages of SLP estimated from the ten 400-site networks and the reference network and scatterplot of spatial differences between regional averages of SLP estimated from the real network and the reference network and spatial differences between terrain elevation (m) estimated from the real network and the reference network for (g) July and (h) December. In (e) and (f), the maximum values for the ten 400-site networks are always shown when several networks have values for the same 2.8° × 2.8° area. Since geographical trends are marginal for all artificial networks as demonstrated by (e) and (f), spatial plots for artificial networks are not presented any further. Data shown are for 2005. The general distribution of errors looks similar for 2006 and 2007 (therefore not shown). Legends differ among panels. White areas in the plot represent areas with no site in the network. Note that no interpolated values are shown to avoid the mix of differences truly due to network density and design (shown here) and those from interpolation methods that are not the focus of this paper (and are therefore not discussed).

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    Temporal evolution of the reference regional average environmental lapse rate for 2005 (black line), 2006 (dark gray line), and 2007 (light gray line) for July (solid lines) and December (dashed lines). The bars indicate the temporal and spatial average standard deviation of the environmental lapse rate on a given day.

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    As in Fig. 4, but for 10-m wind speed (m s−1).

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    Spatial distribution of regional averages of 10-m wind speed in m s−1 for (a) July and (b) December; biases for (c) July and (d) December between regional averages of 10-m wind speed estimated from the real network and the reference network.

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    As in Fig. 4, but for 2-m temperature (K).

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    As in Fig. 8, but for 2-m temperature (K).

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    As in Fig. 8, but for RH (%).

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    As in Fig. 8, but for precipitation (mm day−1).

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    As in Fig. 8, but for shortwave radiation (W m−2).

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    As in Fig. 8, but for longwave radiation (W m−2).

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    As in Fig. 4, but for soil temperature at 0.2-m depth (K).

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    As in Fig. 8, but for soil temperature at 0.2-m depth (K).

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Theoretical Assessment of Uncertainty in Regional Averages due to Network Density and Design

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  • 1 Geophysical Institute, and Department of Atmospheric Sciences, College of Natural Science and Mathematics, University of Alaska Fairbanks, Fairbanks, Alaska
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Abstract

Weather Research and Forecasting (WRF) model simulations are performed over Russia for July and December 2005, 2006, and 2007 to create a “dataset” to assess the impact of network density and design on regional averages. Based on the values at all WRF grid points, regional averages for various quantities are calculated for 2.8° × 2.8° areas as the “reference.” Regional averages determined based on 40 artificial networks and 411 “sites” that correspond to the locations of a real network are compared with the reference regional averages. The 40 networks encompass 10 networks of 500, 400, 200, or 100 different randomly taken WRF grid points as sites. The real network’s site distribution misrepresents the landscape. This misrepresentation leads to errors in regional averages that show geographical and temporal trends for most quantities: errors are lower over shores of large lakes than coasts and lowest over flatland followed by low and high mountain ranges; offsets in timing occur during frontal passages when several sites are passed at nearly the same time. Generally, the real network underestimates regional averages of sea level pressure, wind speed, and precipitation over Russia up to 4.8 hPa (4.8 hPa), 0.7 m s−1 (0.5 m s−1), and 0.2 mm day−1 and overestimates regional averages of 2-m temperature, downward shortwave radiation, and soil temperature over Russia up to 1.9 K (1.4 K), 19 W m−2 (14 W m−2), and 1.5 K (1.8 K) in July (December). The low density of the ten 100-site networks causes difficulties for sea level pressure. Regional averages obtained from the 30 networks with 200 or more randomly distributed sites represent the reference regional averages, trends, and variability for all quantities well.

Corresponding author address: Nicole Mölders, Geophysical Institute, 903 Koyukuk Drive, Fairbanks, AK 99775-7320. Email: molders@gi.alaska.edu

Abstract

Weather Research and Forecasting (WRF) model simulations are performed over Russia for July and December 2005, 2006, and 2007 to create a “dataset” to assess the impact of network density and design on regional averages. Based on the values at all WRF grid points, regional averages for various quantities are calculated for 2.8° × 2.8° areas as the “reference.” Regional averages determined based on 40 artificial networks and 411 “sites” that correspond to the locations of a real network are compared with the reference regional averages. The 40 networks encompass 10 networks of 500, 400, 200, or 100 different randomly taken WRF grid points as sites. The real network’s site distribution misrepresents the landscape. This misrepresentation leads to errors in regional averages that show geographical and temporal trends for most quantities: errors are lower over shores of large lakes than coasts and lowest over flatland followed by low and high mountain ranges; offsets in timing occur during frontal passages when several sites are passed at nearly the same time. Generally, the real network underestimates regional averages of sea level pressure, wind speed, and precipitation over Russia up to 4.8 hPa (4.8 hPa), 0.7 m s−1 (0.5 m s−1), and 0.2 mm day−1 and overestimates regional averages of 2-m temperature, downward shortwave radiation, and soil temperature over Russia up to 1.9 K (1.4 K), 19 W m−2 (14 W m−2), and 1.5 K (1.8 K) in July (December). The low density of the ten 100-site networks causes difficulties for sea level pressure. Regional averages obtained from the 30 networks with 200 or more randomly distributed sites represent the reference regional averages, trends, and variability for all quantities well.

Corresponding author address: Nicole Mölders, Geophysical Institute, 903 Koyukuk Drive, Fairbanks, AK 99775-7320. Email: molders@gi.alaska.edu

1. Introduction

Appropriate meteorological networks are among the important prerequisites to evaluate numerical weather prediction and climate models of various scales, to determine representative regional averages for climatology, and to identify climate changes. Mesoscale-γ/β models are typically evaluated by assuming that measurements at a site are representative for the grid cell the site falls into (Chase et al. 1996; Zhong et al. 2005; Mölders and Kramm 2007). This assumption cannot be made for general circulation models (GCMs) because here fluxes and state variables represent volume and area averages of several hundreds of square-kilometers in the horizontal and several decameters in vertical direction. Furthermore, several sites may often exist within the area represented by a GCM grid cell, making a comparison like in mesoscale modeling ambiguous. Therefore, in climate modeling, it has become common practice for evaluation purposes to use interpolation methods and/or calculate regional averages to produce gridded data for areas of the size of GCM grid cells based on the available measurements (Palutikof et al. 1997; Bauer et al. 2002; Li et al. 2008; PaiMazumder et al. 2008). However, doing so bears uncertainty from the interpolation methods and observations.

Uncertainty in gridded regional averages has been examined with respect to the interpolation methods for precipitation, radiation, air pollutants, and meteorological state variables (Shaw and Lynn 1972; Creutin and Obled 1982; Court and Bare 1984; Lebel et al. 1987; Lindley and Walsh 2004; Luo et al. 2008). Major findings were that 1) any interpolation technique causes uncertainty in regional averages, 2) the choice of interpolation methods should depend on the nature of the region and available data (type, amount), and 3) some interpolation methods are not well suited for regions with strong systematic variations unless the site density is high and the sites are well distributed over the region. Common conclusions were that 1) optimal interpolation methods provide the best results for regional precipitation because they include the spatial correlation structure of precipitation; 2) kriging (a statistical technique based on autocorrelation to interpolate the variables of a random field on a grid from data at observational sites) provides the best results for spatial interpolation of pollutant concentrations, precipitation, and temperature (Tabios and Salas 1985; Lefohn et al. 1987; Holdaway 1996; Phillips et al. 1997; Ninyerola et al. 2000; Jeffrey et al. 2001; Lindley and Walsh 2004); and 3) even with an optimal interpolation method regional precipitation and temperature averages can be biased by observers, poorly sited stations, network design, and/or using data that were originally collected for other purposes. Underreporting and observers’ preferences to report precipitation values divisible by 5 and/or 10, for instance, can cause bias in regional precipitation averages (Daily et al. 2007). Near-surface temperatures obtained from poorly and inhomogeneously sited stations vary stronger in comparison to the North American Regional Reanalysis (Mesinger et al. 2006) than well-sited stations do (Pielke et al. 2007). Changes in site location or network density alter the topography, latitude, and elevation represented by the network, difference in sensors, and their exposures and site exposure to cold air; these changes affect air temperature and minimum and maximum temperature measured (Robeson and Doty 2005; Peterson 2006) with consequences for regional averages calculated by means of these sites. Not representing the topography by the network may cause systematic bias in regional average precipitation because the measurements are made at different terrain heights than those that would reflect the region (Groisman et al. 1991; Groisman and Legates 1994). Network density may also affect regional precipitation averages (Frei and Schär 1998; Tsintikidis et al. 2002); high-density networks are more likely to capture locally high precipitation rates than coarse networks (St-Hilaire et al. 2003). Especially, if a huge fraction of precipitation stems from convection, regional averages determined from high-density networks may be more accurate than those of coarse networks. Uncertainty due to networks becomes particularly problematic in remote areas, where networks are often designed with accessibility and ease of maintenance in mind. Consequently, these networks follow major haulways and are not randomly distributed. Accuracy and reliability of long time series of gridded data compiled from all available stations may be influenced by urbanization, land cover changes, moving, shutting down or adding sites, errors in digitizing old paper records, the procedure of filling missing data, and to a certain degree, by the applied interpolation algorithms (Mitchell et al. 2004).

Today, gridded data from networks with long time series are often used for GCM evaluation; that is, some of these networks already existed before GCMs became available. The gridded soil temperature data (Zhang et al. 2001) used by PaiMazumder et al. (2008) for GCM evaluation, for instance, stem from long-term agricultural monitoring stations; the lysimeter data used by Mölders et al. (2003) for evaluation of the water budget of the Hydro-Thermodynamic Soil Vegetation Scheme (Kramm et al. 1996) were originally collected to assess ground water recharge. Since it takes decades to sample long time series one has to put aside what purpose a long-term monitoring network was designed for (Goody et al. 2002) and assess what one can meaningfully do with its data scientifically, how limited they are, and what uncertainty they bear. Examining this for a real network is one of the goals of this study.

The fluxes that change the state variables in the system earth–atmosphere depend on those states (Entekhabi and Brubaker 1995). Because of the nonlinear dynamical modes of variability and statistical signatures related to these interactions results found for the impact of network design and/or density on regional averages of precipitation, concentration, and temperature cannot be generalized for other state variables and fluxes. Therefore, to separate GCM weaknesses in representing complex processes from uncertainty due to observation-derived climatology, it is essential to understand the potential impact of network density and/or site distribution on gridded regional averages for a broad variety of state variables and fluxes.

In our case study, we assess this uncertainty in gridded regional averages for a large variety of quantities for July and December 2005, 2006, and 2007 over Russia (Fig. 1). In doing so, we use the Weather Research and Forecasting (WRF; Skamarock et al. 2005) model to create a “reference dataset.” Regional averages for 2.8° × 2.8°, a common size of GCM grid cells for the last decade’s era of climate modeling, are determined from the WRF-predicted values. These reference regional averages are compared with regional averages derived from 40 different artificial networks, 10 each of 4 different densities (500, 400, 200, and 100 sites) with randomly distributed sites and a nonrandomly distributed network (Fig. 2). The nonrandomly distributed network is based on the site locations of a real network that has over 50 yr of soil temperature data that are frequently used in climate model evaluation and climatological studies (Zhang et al. 2001; Romanovsky et al. 2007; PaiMazumder et al. 2008). Since it has become a classical long-term dataset that is widely used because of its consistency and length, the sites of this dataset are chosen. Advantages of using these sites in the investigation are twofold: the investigations will provide a better sense of errors caused by this network and may help the scientific community to assess differences between their simulations and the gridded soil temperature observations. July and December are chosen because these are the months with the greatest discrepancies between GCM-simulated and observed soil temperatures (PaiMazumder et al. 2008) and locally great changes with time (Romanovsky et al. 2007). The advantage of using WRF-generated values over randomly generated values is that the former not only permits us to assess the degree of potential uncertainty in gridded climatology related to network design and/or density, but also provides hints where/when regional averages of gridded data may be more or less reliable.

2. Experimental design

a. Reference dataset

WRF simulations are performed with the model setup given in Table 1 for July and December 2005, 2006, and 2007. The model domain encompasses 70 × 150 grid points over Russia (Fig. 1) with a 50-km grid increment and 31 vertical layers from the surface to 50 hPa and 6 layers in the soil; in the presence of snow, 5 snow layers are considered. Simulations start daily at 1800 UTC for 30 h of integration. We discard the first 6 h of each simulation as spinup time. The National Centers for Environmental Prediction 1° × 1° and 6-h-resolution global final analyses serve as initial and boundary conditions.

The WRF-simulated quantities are assumed to be “measurements” from an optimal, dense, and spatially equally distributed “observational network” referred to as reference. Regional averages of sea level pressure (SLP), 10-m wind speed, 2-m temperature, minimum and maximum temperature, precipitation, relative humidity, shortwave and longwave radiation, and soil temperature are determined for areas of 2.8° × 2.8° using all WRF-simulated values that fall into these areas and a Cressman-type method as described in PaiMazumder et al. (2008). There are 637 (13 × 49) grid cells of 2.8° × 2.8° areas in the model domain (39.5°–73°N, 22°–157°E). Regional averages calculated for these 637 2.8° × 2.8° areas are called reference hereinafter.

b. Networks

Forty networks, 10 with 500, 400, 200, and 100 sites each, called 500-, 400-, 200-, and 100-site networks hereinafter, are assumed with 500, 400, 200, and 100 randomly taken WRF grid points as “sites” (Fig. 2). These 40 networks are chosen by using a random number generator over land grid cells only. Regional averages for 2.8° × 2.8° areas are calculated based on these networks. If several sites fall within a 2.8° × 2.8° area, the same method as for determining the reference regional averages is used to calculate the regional average. In the following, the term “regional averages” refers to averages for 2.8° × 2.8° areas.

Furthermore, regional averages are determined for 411 sites of an existing Russian network (Fig. 2) called the real network hereafter. In doing so, the WRF variables of the grid cells the sites fall into are assumed to be the “observations.” There are up to 2, 5, 5, 6, and 8 WRF sites within the 2.8° × 2.8° areas of the 100-, 200-, 400-, and 500-site networks and the real network. These values represent the maximum number of WRF sites within the 2.8° × 2.8° areas occurring in the ten artificial networks of different densities and the real network.

The regional averages determined based on the sites of the real and 40 artificial networks are compared with the reference to assess the contribution of network density and/or design to uncertainty in regional averages of gridded data. To reduce uncertainty from interpolations in areas that have no site at all, we only discuss (and show) results for 2.8° × 2.8° areas with at least one site. This procedure leaves us with up to 310, 277, 168, 89, and 231 regional averages of 2.8° × 2.8° areas per time period investigated for the 500-, 400-, 200-, and 100-site networks in all 10 cases and the real network, respectively.

c. Analysis method

We calculate the difference between the reference regional averages and regional averages derived from the various networks to quantify the uncertainty in the gridded data/regional averages caused by network density and/or design. Any regional average calculated from a network will be considered as being in excellent agreement with the reference regional average if it falls within the reference value plus/minus the accuracy of routine measurements given in Table 2.

We determine performance measures (Table 3) to identify reasons for discrepancies in regional averages. In our experimental design, bias indicates systematic errors in regional averages caused by differences in physical and/or geometric factors between the landscape represented by a network and the reference landscape (terrain elevation, vegetation type, vegetation fraction, soil type, etc.). The standard deviation of error (SDE) quantifies random error when the bias is removed. In any actual observational network, measurements have random errors. In our experimental design, random error may stem, among other things, from initialization and boundary conditions. At the bottom of the soil model, for instance, soil temperature and moisture vary spatially, but not with time. Taking a site just one WRF grid point apart may mean a different lower boundary condition with impacts on soil temperature and moisture. Root-mean-square error (RMSE) assesses the overall success of a network in capturing the reference regional average and avoids positive and negative differences canceling each other out. To measure the strength of the various networks in capturing trends and/or phases of regional averages, correlation skill scores r between the regional averages derived for the various networks and the reference regional averages are determined. To determine the overall relative degree to which the regional averages derived from various networks approach the reference regional averages, Willmott’s index of agreement (WIA) (Willmott 1984; Cannon and Whitfield 2002) between the regional averages derived from the reference network and the various artificial networks is calculated. Willmott’s index of agreement ranges from 0 (complete disagreement) to 1 (perfect agreement).

For all networks for all 2.8° × 2.8° areas with at least one site, performance measures are calculated based on hourly values. To examine shifts in regional averages related to the networks’ representation of timing of events [frontal passage, heating (cooling), convection] we examine the averages and measures for the domain at large (Table 4).

3. Results

a. Representation of landscape

WRF uses the strategy of dominant land cover. This strategy assumes that the land cover type dominating in a grid cell is representative of the entire grid cell and can be used to calculate the exchange of momentum, heat, and moisture at the surface–atmosphere interface. Consequently, the landscape assumed in WRF is more homogeneous and much simpler than a natural landscape (Avissar and Pielke 1989). This WRF-assumed reference landscape is a mix of broadleaf and coniferous forest, wetlands, and tundra (Fig. 3a) partly underlain by warm permafrost. The 100-, 200-, 400-, and 500-site networks in all their 10 setups represent the frequency of occurrence of the various land cover types in the reference landscape within ±5%. The real network significantly (95% or higher confidence level) overestimates the fraction of mixed forest (MF), savanna (SV), and needleleaf evergreen forest (NEF), and underestimates the extension of water bodies (WB) by 10%. These misrepresentations of land cover may cause some uncertainty in regional averages of energy balance components, 2-m temperature, wind speed, relative humidity, and precipitation derived from the real network (section 3e). All other land cover types are within ±5% of the fraction found in the reference landscape (Fig. 3a). Note that the real network was originally designed to monitor conditions in agriculturally used land (cf. Zhang et al. 2001); the landscape considered by WRF, however, has a variety of land cover types for the WRF grid cells that the sites of the real network fall into. Thus, any discrepancies found for the real network would probably be greater if WRF assumed cropland/grassland for the grid cells that represent the 411 sites. Since the WRF simulations are all performed with the same simplified landscape, all networks are located in the same reference landscape derived by the strategy of dominant land cover.

The artificial networks with 200 or more sites in all their 10 setups represent terrain elevation well (Fig. 3b). In the ten 100-site networks, sites are, on average, located (up to 41 m) higher than in the reference landscape. The real network significantly overrepresents by about 8% sites that represent areas with elevation between 100 and 300 m and underrepresents by about 6% and 3% sites with elevation <100 m and elevation between 300 and 500 m, respectively (Fig. 3b).

Except for the ten 100-site networks and the real network, all networks also represent the frequency of soil-type occurrence well within ±5%. The ten 100-site networks overrepresent clay loam (CL; up to 7%). The real network significantly underrepresents loam (L) and overrepresents CL (Fig. 3c). These misrepresentations of soil types may cause some uncertainty in regional averages of soil temperature with consequences for other quantities (e.g., 2-m temperature) derived from the real network.

b. General findings

Overall, networks with 200 or more randomly distributed sites reproduce the reference regional averages of all quantities in all setups well, while the real network has some difficulties capturing them (Table 4). All ten 100-site networks have difficulty capturing the regional averages of SLP, but reproduce the regional averages of all other quantities well. For the real networks, regional averages of 2-m temperature, relative humidity, precipitation, and shortwave and longwave downward radiation differ most from the reference regional averages during strong convective situations in July and frontal passages in December no matter the year. In July, the real network has difficulties in correctly representing convective situations, whereas its December regional averages are temporally biased during frontal passages (e.g., Fig. 4). Because of its nonrandom site distribution, the majority of the sites within a 2.8° × 2.8° area can be passed by fronts within a short time.

All networks with randomly distributed sites typically reproduce regional averages with lower errors (RMSEs, biases, SDEs) than the real network. While SDEs, biases, and RMSEs for these 40 networks show no distinct area of higher or lower values (therefore only shown for SLP), those of the real network do (e.g., Fig. 5). Regional averages from the real network have high systematic and random errors for all quantities in 2.8° × 2.8° areas located mainly over mountains and/or land water boundaries (therefore only shown for biases). SDEs, biases, and RMSEs between the reference regional averages and regional averages derived from the real network show similar spatial and temporal behavior in all 3 yr (Table 4). In the following, when quantifying errors or skills, we give the worst correlation, WIA, absolute bias, RMSE, and SDE.

c. Sea level pressure

All networks with 200 or more randomly distributed sites reproduce the regional SLP averages and their temporal evolution well (Fig. 4) with biases less than the typical accuracy of routine measurements, correlation skill scores >0.905 (2007), and WIA > 0.901 (2007) in all of their ten setups. For the ten 100-site networks the low density strongly affects capturing the phase and amplitude, while for the real network the nonrandom site distribution causes temporal biases (up to −4.8 hPa) because fronts pass a majority of sites within a short time (Figs. 2, 4c,d; Table 4).

The ten 100-site networks over- and underestimate the reference regional averages up to ±6 and ±5 hPa in July and December, respectively (Fig. 4). That they represent a higher elevated landscape than the reference landscape is a major reason. The real network shows extremely high SLP biases (about ±160 in July, ±104 hPa in December) along the coasts, over the mountains and Arkhangel’sk (Figs. 5c,d; Table 5). The lower biases in December than July of the real network result from the lower or even negative environmental lapse rate in the former [0.4 K (100 m)−1, on average] than later month [0.7 K (100 m)−1, on average] due to the excessive radiative cooling over snow (Fig. 6). This is similar to what was found by Barry and Chorley (1992), for instance, over central Canada and eastern Siberia and by Huang et al. (2008) who examined the relationships between near-surface temperature, lapse rate, and solar radiation. The spatial variation in environmental lapse rate is smaller in December due to the lower horizontal heterogeneity of surface temperature and moisture conditions than in July. Rolland (2003) found a similar result when investigating the seasonal and spatial variation of lapse rates in Alpine regions. Consequently, the real network’s misrepresentation of terrain affects SLP regional averages stronger in July than in December.

According to the correlation skill scores and WIA, regional SLP averages derived from the real network only marginally agree with the reference regional averages (Table 4). Along coasts, regional SLP averages are even negatively correlated with the reference. The fact that sites of the real network represent an, on average, about 29 m flatter terrain than the reference landscape (Fig. 3b) and the strong inverse correlation (>−0.985) between SLP biases and spatial differences between terrain elevation of the real network and the reference (Figs. 5g,h) explain the overall strong systematic errors in regional SLP averages. Thus, reducing pressure measured at mountain sites to SLP assumes an average temperature between the sea level surface and the site that may be incorrect.

RMSEs and SDEs for the real network are greatest over Arkhangel’sk and the Sayan Mountains in all months (Table 5). SLP RMSEs are more than 10 times higher than the SDEs (Table 4). This means random errors are relatively small and the misrepresented terrain causes most of the regional SLP errors. RMSEs and SDEs of the real network are on average higher in December than in July (Table 4).

d. 10-m wind speed

The 40 networks with randomly distributed sites reproduce well the phase and amplitude of the reference regional wind speed averages with errors smaller than the typical errors of routine measurements, correlation skill scores >0.926, and WIA > 0.957 (Fig. 7).

The real network underestimates the amplitude up to 0.7 and 0.5 m s−1 in July and December, respectively, and generally has difficulties in reproducing the phase (Fig. 7). Overall correlation (WIA) exceeds 0.515 and 0.432 (0.468 and 0.481) in July and December, respectively (Table 4), that is, about 55% (45%) lower than for the networks with randomly distributed sites. In both months even negative correlations occur along the coasts and over the Ural Mountains indicating that the real network strongly misrepresents the wind field conditions at boundaries of smooth to rough or vice versa and in complex terrain. In December, regional averages of wind speed derived from the real network become biased when frontal systems pass the majority of the nonuniformly distributed sites.

For the real network, July and December wind speed absolute biases reach up to 3.2 and 6 m s−1, respectively, along the coasts and over the central Siberian uplands (Figs. 8c,d; Table 5). Here also RMSEs and SDEs are highest (Table 5). July biases and RMSEs are about half the magnitude of those in December (Table 4). The systematic errors may be attributed to differences in surface and terrain roughness represented by the real network and the reference network (Fig. 3a). Except for the coasts, these 2.8° × 2.8° areas represent complex terrain. The nonuniform distribution of the real network has difficulties representing the wind direction/“channeling” situation correctly and hence, the wind speed. In the 2.8° × 2.8° areas over water, the surface is relatively smoother and wind speed is greater than over land. Thus, the reference regional averages exceed those calculated from the real network that only considers land sites. In general, biases exceed the SDEs, indicating that systematic errors due to misrepresentation of surface roughness and terrain by the real network dominate the RMSEs (Table 4).

e. 2-m temperatures

The 40 artificial networks reproduce well the reference regional 2-m temperature averages with biases below the typical accuracy of measurements, correlation skill scores >0.896, and WIA > 0.902 (Fig. 9). The real network has tremendous difficulties in capturing regional 2-m temperature averages (Fig. 9).

In July, based on the real network, regional 2-m temperature averages are overestimated up to about 8 K and underestimated up to about 12 K along coasts and over mountains (Table 5); in December, overestimates and underestimates in these areas are twice as high than in July (Figs. 10c,d). In both months the RMSEs and SDEs of the real network are also highest along the coasts and over the mountains (Table 5). July RMSEs and SDEs reach up to 10 K and 5.2 K, respectively; they more than double for December (Table 4).

For the real network, errors are higher in December than in July because of the strong influence of snow-covered and snow-free surfaces on 2-m temperatures (Table 4). RMSEs and SDEs are comparatively higher in the early afternoon than at other times in July due to the then strong convection not being represented well by the real network. No such obvious pattern exists for RMSE and SDE in December because of the more homogenous temperature distribution under winter high and low pressure than in summer convective situations.

These findings indicate that random errors play a role, but misrepresentation of the landscape by the real network introduces great systematic errors in regional averages of 2-m temperatures for 2.8° × 2.8° areas in complex elevated terrain or that include both water and land. The former finding well agrees with Peterson (2006) and Pielke et al. (2007). The real network’s failure to represent terrain elevation affects the representation of temperature distribution because temperature typically decreases with height (section 3c). Furthermore, the real network has about 15% more MF sites and 10% less “water” sites than required to represent the reference landscape (Fig. 3a). During the day in July MF heats less strongly than areas covered by low vegetation; surface temperatures of lakes and the ocean are typically lower than those of the adjacent vegetation. These facts partly explain the higher regional temperature averages derived from the real network in coastal and shore areas, and the lower values in mountainous forest–covered areas than those obtained from the reference network in July. The real network’s misrepresentation of terrain elevation adds to discrepancies in regional temperature averages. In December, open water is relatively warmer than adjacent snow-covered areas. Thus, heat fluxes from open water to the atmosphere lead to warmer air than over snow-covered land. Furthermore, lakes are frozen, homogeneously snow covered, and have relatively high albedo; high vegetation sticks out of snow, so albedo is lower than over small entirely snow-covered vegetation. Albedo, however, affects 2-m temperature via the snow temperature–albedo feedback. Brighter surfaces reflect more incoming radiation than relatively darker surfaces. Consequently, December regional averages based on the real network, wherein MF is overrepresented at the cost of totally snow-covered small vegetation or no vegetation, are higher than those of the reference network. In the case of 2.8° × 2.8° areas located in coastal regions the fact that the water in these areas is not completely ice covered plays a role.

The real network has difficulties in reproducing the phase especially on days with frontal passages (e.g., 11 July and 21 December 2005) and overestimates the amplitude up to 1.9 and 1.4 K in July and December, respectively (Figs. 9c,d). The systematic errors in the temporal course of 2-m temperature regional averages derived from the real network may partly be explained by the misrepresentation of incoming solar radiation (section 3h).

All networks with randomly distributed sites reproduce the regional averages of maximum 2-m temperatures well for the majority of the 2.8° × 2.8° areas in both months of all 3 yr whereas the real network has substantial difficulties in December (Table 4). Typically errors in the regional averages obtained from the real network are lower in July than in December for all 3 yr. Consequently, WIA and correlation are comparatively higher in July than December (i.e., July regional averages from the real network are more reliable than those derived for December).

The 40 networks with randomly distributed sites capture the regional averages of minimum 2-m temperatures well in both months in all 3 yr whereas the real network shows strong biases of up to about 20 K along coasts, over mountains, and south of Arkangel’sk, Russia (Table 5). RMSEs and SDEs are about twice as high in December than July for the reasons discussed earlier.

In summary, systematic errors due to misrepresentation of the landscape by the real network strongly contribute to RMSEs in regional averages of maximum and minimum temperatures derived from the real network.

f. Relative humidity

In both months of all 3 yr the 40 networks with randomly distributed sites reproduce the temporal evolution of relative humidity regional averages well (not shown). Biases are below the typical accuracy of measurements. Even the lowest correlation skill scores and WIA still exceed 0.932. While the real network also acceptably reproduces the amplitude, it has appreciable difficulties with the phase.

Like for regional SLP and temperature averages, regional relative humidity averages derived from the real network show high errors over mountainous and coastal areas (Figs. 11c,d; Table 5). Errors in the regional averages obtained from the real network are, on average, higher in July than in December (Table 4). Consequently, correlation and WIA are as low as 0.490 and 0.462 in July (0.566 and 0.627 in December), respectively (Table 4). The highest biases and RMSEs in July are about twice as high as the values found for December (Table 4) because of the greater spatial differences in relative humidity in the former than latter month. The lower average correlation (>0.490) in July than December (>0.566) in conjunction with the higher July biases (Table 4) suggests misrepresentation of the convective situation as a contributing factor. In July and December even negative correlations between the regional relative humidity averages derived from the real and reference network occur over the mountains, along the shores of Baikal Lake, and the coasts. The nearly similar SDEs in July (16%) and December (12%) indicate a similar contribution of random errors in both months. The, on average, higher absolute values of biases than SDEs imply that systematic errors due to misrepresentation of the landscape contribute greatly to the RMSEs of relative humidity.

The reasons for these findings are manifold. The disagreement for areas with substantial water fraction results from the differences in surface moisture and water supply to the atmosphere for water and land areas. Whereas over water the saturation deficit and wind speed mainly determine the water supply to the atmosphere, over land vegetative controls, soil moisture, and soil type also impact the water supply and hence relative humidity. Furthermore, since the exchange of heat and moisture at the vegetation–atmosphere interface depends on vegetation type, differences in the vegetation represented cause bias in relative humidity; differences in terrain representation may strongly affect relative humidity due to temperature differences. As aforementioned the nonrandom site distribution in the real network misrepresents the MF and WB frequency with consequences for the exchange of heat and moisture at the surface–atmosphere interface. Consequently, the real network cannot capture the distribution of relative humidity well. As will be discussed in sections 3g and 3h, this shortcoming has consequences for convection, precipitation, and shortwave and longwave radiation with feedback to 2-m temperature. Note that relative humidity nonlinearly depends on temperature; at relatively low temperatures with the same specific humidity a 1 K increase in temperature, for instance, causes a greater decrease in relative humidity than at relatively high temperatures. In all years examined, the environmental lapse rate close to the surface is 0.3 K (100 m)−1 stronger in July than December (Fig. 6).

g. Precipitation

The 40 networks with randomly distributed sites capture the temporal evolution of regional precipitation averages well with biases below the typical errors of routine measurements, WIA > 0.905, and correlations >0.850. While the real network also well reproduces the amplitude, it has difficulties capturing the phase, especially during the frontal passages.

For the real network the greatest errors (biases, SDEs, RMSEs) in regional precipitation averages occur in 2.8° × 2.8° areas that represent water or complex terrain. SDEs are only slightly lower than RMSEs (15 m day−1 versus 15.5 mm day−1 in July; 12 mm day−1 versus 13 mm day−1 in December; cf. Table 4), indicating that random errors dominate the performance of the real network in reproducing regional precipitation averages. The highest biases reach up to −4.8 and 5.1 mm day−1 in July (Figs. 12c,d; Table 4).

On average, biases, RMSEs, and SDEs of the real network are higher in July than in December for all 3 yr (Table 4). The higher July than December biases mean that misrepresentation of terrain elevation has a stronger impact than that of the convective situation. The greater precipitation biases at high elevation and greater biases in summer than in winter well agree with results from Groisman and Legates (1994) who found similar behavior for U.S. meteorological networks. Misrepresentation of terrain height yields systematic errors related to precipitation caused by orographic lifting, while along the coasts the misrepresentation of atmospheric moisture supply goes along with misrepresentation of precipitation.

On average, in July, correlation skill scores are appreciably lower than in December because the real network misrepresents convection and hence convective precipitation. Moreover, there is more precipitation in July than December. With more areas receiving no precipitation, the likelihood of “correctly” obtaining zero precipitation for the regional averages by pure chance increases. The notably lower WIA than correlation skill scores (Table 4) indicates an offset in the regional precipitation averages featured by the real and reference network.

h. Downward radiation

All 40 networks with randomly distributed sites capture well the temporal evolution of shortwave radiation regional averages. Regional averages of shortwave radiation derived from the artificial networks have smaller biases than the typical measurement errors; correlation skill scores and WIA exceed 0.932 and 0.931, respectively.

The real network has notable difficulties in reproducing the regional averages of shortwave radiation (r > 0.315, WIA > 0.149; Table 4). It overestimates regional averages up to about 100 W m−2 along coasts and underestimates up to about 120 W m−2 over mountains in July, whereas in December, overestimates reach up to 100 W m−2 over Arkhangel’sk (Figs. 13c,d; Table 5). These systematic errors can be explained as follows: in July the misrepresentation of the landscape by the real network (Fig. 3a) leads to an inadequate representation of the regional exchange of heat and moisture at the vegetation–atmosphere interface with consequences for relative humidity and temperature (sections 3f, 3g) and feedback on cloud formation. Note that cloud occurrence differs slightly among the artificial networks and the reference network, but strongly deviates from the reference for the real network. Differences in cloudiness in turn affect incoming shortwave radiation. Thus, the placement of sites in the real network causes a misrepresentation of cloudiness, especially in partly ocean-covered 2.8° × 2.8° areas under convective situations as evidenced from satellite imagery. Shifts in the timing of high and low insolation occur. In December the real network’s misrepresentation of the reference terrain height feeds back to misrepresentation of temperature and humidity distributions with impacts for cloudiness, and finally shortwave radiation. Overall, the real network underestimates shortwave radiation regional averages up to 19 and 14 W m−2 in July and December, respectively (Table 4).

For the real network, shortwave radiation RMSEs are high along coasts (up to 180 W m−2) in July and over Arkhangel’sk (up to 100 W m−2) in December (Table 5). July SDEs of shortwave radiation are greatest (up to 150 W m−2) along coasts and over high mountains (Table 5); December SDEs are greatest (up to 26 W m−2) over mountains (Table 5). On average, SDEs are about 80 W m−2 higher in July than in December. The higher absolute values of biases than SDE values imply that systematic errors due to misrepresentation of the reference landscape and in July convection by the real network dominate RMSEs of shortwave downward radiation.

In both months of all 3 yr, all 40 artificial networks reproduce well the temporal evolution of regional longwave radiation averages with biases below the typical accuracy of measurement errors. Thus, WIA and correlation skill scores exceed 0.905 and 0.945, respectively. As documented by the skill scores (Table 4), the real network has some difficulties reproducing the phase and regional averages of longwave radiation.

Regional averages of longwave radiation derived from the real network are biased during frontal passages. Thus, due to the nonrandom site distribution of the real network, a great majority of the sites is passed at nearly the same time, shifting the averages toward lower/higher values than the reference regional averages. The real network overestimates and underestimates the reference regional averages up to ±60 W m−2 along coasts and over mountains in July; in December it overestimates (underestimates) up to 80 W m−2 (100 W m−2) over mountains (along the coast of the Sea of Okhotsk) (Figs. 14c,d; Table 5). The reasons for these systematic errors in longwave radiation are similar to those for shortwave radiation. In addition, misrepresentation of terrain height can contribute to misrepresentation of snow cover with consequences for temperature (via the albedo–temperature effect), moisture, cloud, and finally longwave radiation distribution in December.

In July for the real network, longwave radiation RMSEs are highest (up to 68 W m−2) over Arkhangel’sk; SDEs are greatest (up to 45 W m−2) over mountains (Table 5). In December for the real network, RMSEs and SDEs are highest (up to 100 and 56 W m−2, respectively) over mountains and along the coasts (Table 5).

Errors for the real network are higher in December than in July for most of the 2.8° × 2.8° areas. Consequently, correlation between the averages derived from the real and reference network is notably lower in December than in July, similar to WIA (Table 4).

The nearly equal SDEs and absolute biases in regional averages of longwave radiation found for the real network indicate that systematic and random errors contribute nearly equally to RMSEs (Table 4).

i. Soil temperature

Generally, the 40 networks with randomly distributed sites reproduce regional soil temperature averages at all depths and capture the temporal evolution in the upper soil well (Fig. 15), with correlation skill scores >0.943 and WIA > 0.921.

The real network overestimates soil temperature amplitudes (up to 1.4 and 1.8 K in July and December, respectively). It has notable difficulties capturing the phase. For example, on 11 and 28 July 2005, regional averages of upper soil temperatures fail to show the cold snap seen in the reference regional averages (Fig. 15). These phase differences occur when frontal systems come through and pass the majority of sites within a short time because of the nonrandom site distribution. Generally, biases are greatest along the coast of the Barents Sea, over most mountains in July, and along the coasts and over mountains in December (Figs. 16c,d; Table 5). On average, in July 2005, for instance, regional soil temperature averages are overestimated by 2.3, 1.5, 0.8, and 1.7 K, at 0.05-, 0.2-, 0.4-, and 1.6-m depths, respectively; in December 2005, the real network overestimates regional soil temperature averages by 2.1, 1.8, 1.3, and 1 K at these depths. Biases of regional soil temperature averages decrease with depth for the real network because the differences related to differences in vegetation, terrain height, and atmospheric conditions between the real and reference network become less important for deeper than upper soil layers. The higher bias found for upper than lower soil layers may be partly due to misrepresentation of terrain height, vegetation, and atmospheric conditions by the real network. Differences in vegetation cover/fraction and terrain elevation, namely, have consequences for soil heating. At all depths, some bias stems from the misrepresentation of the soil-type distribution by the real network. The aforementioned difficulties in capturing the temporal evolution of soil temperatures in the upper soil also result from differences between the soil heat capacity and thermal conductivity of soils represented by the real network and those of the reference landscape. As shown by Mölders et al. (2005), small differences in these parameters can significantly (at the 95% or higher confidence level) affect soil temperatures. Soils with a high sand fraction heat/cool much quicker than those with a low sand fraction. In December the high bias found for the real network is also affected by regional differences in snow cover and/or snow depth. Here failure to represent terrain height and vegetation distribution plays a role for snow conditions. More MF instead of low vegetation, for instance, means a lower albedo and snow depth with consequences for insulation of the soil. Secondary differences may be associated with the temperature–albedo feedback. As precipitation increases with height, differences in represented snow conditions may also occur.

Consequently, in the upper soil, soil temperatures obtained from the real network are poorly correlated (>0.315) with the reference regional soil temperature averages and WIA > 0.265 in both months. In July and December, RMSEs and SDEs for the real network are highest (up to 18 K, 4 K) over the mountains and along the coast of the Barents Sea (Table 5). In 2005, for instance, 0.05-, 0.2-, 0.4- and 1.6-m depth July RMSEs amount to 4.4, 3.5, 3.2, and 3.9 K and July SDEs at these depths are 2.9, 1.7, 0.7, and 0.2 K; December RMSEs reach 5.8, 4.6, 3.6, and 2.7 K and December SDEs are 3.1, 2, 0.8, and 0.2 K at these depths. The higher absolute biases than SDEs (Table 4) suggest that systematic errors due to misrepresentation of soil type mainly contribute to RMSEs.

In the natural landscape differences between the regional averages derived from the real network and the true regional averages may be even greater than in our theoretical study because the real network was designed for agricultural purposes (i.e., the real network represents the fertile soils within the 2.8° × 2.8° areas). Consequently, it may be even more biased to a soil type than in the simplified WRF-created landscape assumed in this case study.

Note that PaiMazumder et al. (2008) showed that in December, biases between a GCM-simulated and gridded soil temperature climatology reach up to 6 K at 0.2-m depth, of which about 2.5 K of bias may result from incorrectly simulated atmospheric forcing. Considering the results of our case study, uncertainty due to network design can explain about 2 K of their total bias in winter; thus about 1.5 K of their bias may be attributed to measurement errors and/or model deficits.

4. Conclusions

Simulations performed with the Weather Research and Forecasting model over Russia for July and December 2005, 2006, and 2007 are used to produce a reference dataset to examine the degree of uncertainty in regional averages caused by network density and/or design. Ten networks with four different densities of randomly distributed sites (100, 200, 400, and 500) are assumed. The WRF quantity simulated for the location of an assumed “site” of these 40 networks is assumed to be a “measurement” within the respective network. Regional averages valid for 2.8° × 2.8° areas are calculated based on the values of the sites that fall within these 2.8° × 2.8° areas. These regional averages are compared to the reference regional averages that are determined based on all WRF-simulated values within a 2.8° × 2.8° area. Furthermore, regional averages obtained from WRF-simulated values at the locations of an existing network with 411 sites (“real network”) are compared to the reference regional averages.

Networks with 200 or more randomly distributed sites reliably reproduce regional averages of the examined quantities with errors smaller than the typical accuracy of measurements and show high correlation values and Willmott’s index of agreement. The ten 100-site networks have difficulties in capturing the regional averages of SLP because of higher terrain elevation than the reference landscape.

The real network has difficulties in capturing the reference regional averages of all quantities examined. The reasons differ for the different state variables and fluxes, with sometimes secondary effects involved. Historically the real network was designed to collect soil temperature measurements for agricultural purposes. Thus, its soil-type distribution is skewed toward more fertile soils than the soil-type distribution in the reference landscape. The differences in soil physical properties (e.g., heat capacity, conductivity) lead to systematic error in regional soil temperature averages determined from the real network with biases up to about 20 K. The nonrandom site distribution of the real network also yields temporal offsets in soil temperature, SLP, precipitation, and shortwave and longwave radiation during frontal passages when the majority of sites within a 2.8° × 2.8° area is passed nearly at once. Since the exchange of heat and moisture at the vegetation–atmosphere interface affects 2-m temperature and relative humidity, misrepresentation of vegetation frequency, soil type, and terrain elevation propagates into misrepresentation of convection, precipitation, and shortwave and longwave radiation. Convective activity over forest and cropland, for instance, strongly differs, for which the nonrandomly distributed real network cannot represent well the convective situation of 2.8° × 2.8° areas. The results also show that for most quantities there are geographic trends in regional averages determined from the real network. Errors are lower for regional averages over flatland than for low mountain ranges, the errors for which are themselves lower than for high mountain ranges. Furthermore, errors in regional averages are greater in coastal areas than in areas along the shores of large lakes. No such geographical trends exist for random distributed networks. Thus, one may conclude that high priority should be given to the random placement of sites when designing new networks if possible.

Our case study shows that nonrandom network design like low site density can introduce substantial uncertainty in gridded data and that networks with randomly distributed sites might only need about half the points of the nonrandom distributed real network over Russia to determine gridded data. However, maintenance of such networks with randomly distributed sites can be extremely expensive, especially when sampling is to be performed over several decades, because many of the sites would be difficult to access in remote areas.

Based on these findings we further conclude that when evaluating GCMs with gridded data from “imperfect” existing networks or networks that were not designed with this purpose in mind, one has to develop intelligent strategies to guarantee meaningful conclusions on model performance and for model improvement. Similarly, in determining regional averages from nonrandom networks, strategies have to be developed to assess and remove geographical/temporal trends if possible. Sampling from model-generated values as demonstrated in our study can help to evaluate geographical and temporal trends. However, additional facts may have to be considered. In the case of using soil temperature from the real network for evaluation, for instance, one could restrict the comparison to the patches within a GCM grid cell that represent agriculturally used land.

Acknowledgments

We thank U. S. Bhatt, P. A. Bieniek, M. E. Brown, R. Dlugi, T. Fathauer, G. Kramm, S. E. Porter, J. E. Walsh, and the anonymous reviewers for fruitful discussion, and ARSC and NCAR for computational support. This research was supported by EPSCoR Grant 0701898 and NSF Cooperative Agreements OPP-0327664 and ARC0652838.

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Fig. 1.
Fig. 1.

Schematic view of terrain elevation over Russia. Names refer to locations mentioned in the text.

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 2.
Fig. 2.

(a) Schematic view of the 2.8° × 2.8° areas and locations of “sites” in the “reference” network over Russia. Location of sites for one of the ten (b) 500-, (c) 400-, (d) 200-, and (e) 100-site networks. (f) Locations of sites in the “real network.”

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 3.
Fig. 3.

Frequency distribution of (a) land cover type, (b) terrain elevation, and (c) soil type or other surface type in the “reference,” the 500-, 400-, 200-, and 100-site networks and real network over Russia. In the case of the artificial networks, the uppermost, mean, and lowermost frequency of the 10 networks are illustrated for each network density by horizontal lines. In (a) the x axis represents urban (U), cropland/pasture (CLP), cropland/grassland (CLGL), cropland/woodland (CLWL), grassland (GL), shrubland (SL), mixed shrubland/grassland (MSGL), savanna (SV), broadleaf deciduous forest (BDF), needleleaf deciduous forest (NDF), broadleaf evergreen forest (BEF), needleleaf evergreen forest (NEF), mixed forest (MF), water bodies (WB), herbaceous wetlands (HWL), wooded wetlands (WWL), bare or sparsely vegetated (BSV), herbaceous tundra (HT), wooded tundra (WT), mixed tundra (MT), bare ground tundra (BGT), and glacier/ice (GI). In (c), the x axis represents sand (S), loamy sand (LS), sandy loam (SL), silt loam (SLL), silt (SL), loam (L), sandy clay loam (SCL), silty clay loam (SLCL), clay loam (CL), sandy clay (SC), silty clay (SLC), clay (C), organic material (OM), and bedrock (BR). Note that over Russia the average terrain elevation of the 500-, 400-, 200-, and 100-site networks ranges between 405 and 421 m (with on average over all 10 networks 412 m), 390 and 430 m (410 m), 389 and 454 m (415 m), and 379 and 457 m (421 m), respectively; average terrain height of the real network amounts to 387 m; the average terrain height of the reference network is 416 m.

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 4.
Fig. 4.

Temporal behavior of regional averages of SLP as obtained for the reference data using all data within all 2.8° × 2.8° areas and as derived for various 500-site networks based on the “sites” within the 2.8° × 2.8° areas for (a) July and (b) December, for various 400-site networks for (c) July and (d) December, for various 200-site networks for (e) July and (f) December, and for various 100-site networks in (g) July and (h) December. In (c) and (d) the solid line with filled circles represents the regional averages derived from the real network (411 sites). In (a)–(h), all other lines represent the regional averages with the lowest error values among the ten setups of the respective network of given density; the shaded regions represent the maximum over- and underestimation of the reference regional averages found for the 10 networks of the same density. The letters H and L in (a) and (b) represent the days with high and low pressure situations. Data shown are for 2005, but 2006 and 2007 show similar general behavior with respect to differences among networks of same density, the range of over- and underestimation by networks and among networks of different density, as well as reaction to events (e.g., frontal passages). See text for further details.

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 5.
Fig. 5.

Spatial distribution of regional averages of SLP in hPa for (a) July and (b) December, biases for (c) July and (d) December between regional averages of SLP estimated from the real network and the reference network, and biases for (e) July and (f) December between regional averages of SLP estimated from the ten 400-site networks and the reference network and scatterplot of spatial differences between regional averages of SLP estimated from the real network and the reference network and spatial differences between terrain elevation (m) estimated from the real network and the reference network for (g) July and (h) December. In (e) and (f), the maximum values for the ten 400-site networks are always shown when several networks have values for the same 2.8° × 2.8° area. Since geographical trends are marginal for all artificial networks as demonstrated by (e) and (f), spatial plots for artificial networks are not presented any further. Data shown are for 2005. The general distribution of errors looks similar for 2006 and 2007 (therefore not shown). Legends differ among panels. White areas in the plot represent areas with no site in the network. Note that no interpolated values are shown to avoid the mix of differences truly due to network density and design (shown here) and those from interpolation methods that are not the focus of this paper (and are therefore not discussed).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 6.
Fig. 6.

Temporal evolution of the reference regional average environmental lapse rate for 2005 (black line), 2006 (dark gray line), and 2007 (light gray line) for July (solid lines) and December (dashed lines). The bars indicate the temporal and spatial average standard deviation of the environmental lapse rate on a given day.

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 7.
Fig. 7.

As in Fig. 4, but for 10-m wind speed (m s−1).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 8.
Fig. 8.

Spatial distribution of regional averages of 10-m wind speed in m s−1 for (a) July and (b) December; biases for (c) July and (d) December between regional averages of 10-m wind speed estimated from the real network and the reference network.

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 9.
Fig. 9.

As in Fig. 4, but for 2-m temperature (K).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 10.
Fig. 10.

As in Fig. 8, but for 2-m temperature (K).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 11.
Fig. 11.

As in Fig. 8, but for RH (%).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 12.
Fig. 12.

As in Fig. 8, but for precipitation (mm day−1).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 13.
Fig. 13.

As in Fig. 8, but for shortwave radiation (W m−2).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 14.
Fig. 14.

As in Fig. 8, but for longwave radiation (W m−2).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 15.
Fig. 15.

As in Fig. 4, but for soil temperature at 0.2-m depth (K).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Fig. 16.
Fig. 16.

As in Fig. 8, but for soil temperature at 0.2-m depth (K).

Citation: Journal of Applied Meteorology and Climatology 48, 8; 10.1175/2009JAMC2022.1

Table 1.

Physical packages used in the WRF simulations to create the reference dataset assumed to be an ideal reference network.

Table 1.
Table 2.

Typical accuracy of routine measurements of SLP, 10-m wind speed, 2-m temperature, RH, precipitation, shortwave and longwave radiation, and soil temperature. Note that routine measurements have greater errors than measurements of special field campaigns (cf. Spindler et al. 1996).

Table 2.
Table 3.

Equations to calculate the performance measures (e.g., Anthes 1984; Anthes et al. 1989; Hanna 1994; Wilks 1995) used in this study. Here φi(xiyi) is the difference between the regional average of a quantity obtained from the various network and reference network at the ith hour for a given 2.8° × 2.8° area and n is the total number of hours within a month. Furthermore, xi is the regional average of a quantity for a 2.8° × 2.8° area obtained from a network and yi is the regional average of a quantity obtained for the 2.8° × 2.8° area from the reference network for the ith hour.

Table 3.
Table 4.

Range of biases, SDEs, RMSEs, correlation skill scores, and WIA between regional averages for 2.8° × 2.8° areas of SLP, 10-m wind speed (υ), 2-m temperature (T), minimum (Tmin) and maximum temperature (Tmax), RH, precipitation (P), shortwave radiation (Rs), longwave radiation (Rl), and soil temperature at 0.2-m depth (Ts) as obtained from the real network and the reference network for July and December of all 3 yr. The first, second, and third value within the bracket represents mean value of a given performance skill for 2005, 2006, and 2007, respectively.

Table 4.
Table 5.

Locations of highest biases, RMSEs, and SDEs between regional averages for 2.8° × 2.8° areas of the various quantities obtained from the real network and the reference network for July and December. Areas of highest values are independent of years.

Table 5.
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