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  • View in gallery

    Spatial correlation of (left) four atmospheric variables and (right) three soil variables for all available daily records in the period from January 2017 to June 2019 for 21 stations (420 pairs without self-correlation) of the Kansas Mesonet spanning the entire state of Kansas. The period and number of stations were selected to allow inclusion of soil moisture, which was added to the Kansas Mesonet in late 2016. Each point represents the value of the Pearson’s correlation coefficient between the time series of a given variable for two stations separated by a distance d.

  • View in gallery

    (left) Sketch of instrumentation layout and (right) image of the Ottawa 2SE station located at the Kansas State University East Central Research Experiment Station.

  • View in gallery

    Geographic location of the 56 stations of the Kansas Mesonet in 2016.

  • View in gallery

    Diagram with three hypothetical stations illustrating the components involved in the calculation of an empty circle centered at the Voronoi vertex V. The radius of the empty circle is limited by the distance between V and the nearest station (i.e., station 3). Stations 1 and 2 are farther than station 3; therefore, the perimeter of the empty circle does not intersect them.

  • View in gallery

    Map of the Kansas Mesonet showing the 56 stations of the network (filled circles), the Voronoi vertices and points of the state boundary line (open circles) used to compute the empty circles, the resulting web of 56 Voronoi polygons (gray lines connecting open circles), the largest empty circle (blue-shaded circle), the suggested location of the next monitoring station (red cross mark inside the circle), and the largest support area of the network (gray-shaded Voronoi polygon).

  • View in gallery

    Histograms of the (a) 145 empty circle areas and (b) 56 station-support areas of the Kansas Mesonet. Station-support areas are the areas of the Voronoi polygons. The area of the LEC, LSA, and median value (dashed lines) are provided for additional reference.

  • View in gallery

    Numbered sequence of future siting locations for the Kansas Mesonet (open circle followed by sequence number). Numeration starts from a value of 57 (a value one unit higher than the current number of stations) and extends to a maximum value of 105. The maximum value is equal to the number of counties across Kansas, which is a reasonable long-term goal for the network.

  • View in gallery

    (a) Area of the LEC and station-support area for the Kansas Mesonet as a function of increasing number of stations, and (b) Lorenz curves for the support area of the current state (red dot–dashed line) and idealized state of the Kansas Mesonet network with 105 stations (blue dashed line).

  • View in gallery

    Spatial coverage of USDA soil textural classes at 5-cm depth across Kansas. Note that only 8 of the 12 classes are present in the state and that only 4 of the 8 present classes are clearly visible at this level. White pixels represent major lakes.

  • View in gallery

    Largest empty circle with the largest number of wildland fires in the period from 2000 to 2018. The map of wildland fires was created using fire and thermal anomalies at 1-km spatial resolution obtained from the MODIS Fire and Thermal Anomalies daily product generated by the NASA Terra (MOD14) and Aqua (MYD14) satellites.

  • View in gallery

    Map showing 185 stations of the SCAN overlaying the map of severe-or-worse drought frequency using U.S. Drought Monitor data from 2000 to 2018. The map also shows the largest and second largest unmonitored areas, which are located over areas with frequent drought events.

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Optimizing the Spatial Configuration of Mesoscale Environmental Monitoring Networks Using a Geometric Approach

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  • 1 Department of Agronomy, Kansas State University, Manhattan, Kansas
  • | 2 Department of Statistics, Kansas State University, Manhattan, Kansas
  • | 3 Department of Agronomy, Kansas State University, Manhattan, Kansas
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Abstract

The ability of mesoscale environmental monitoring networks to collect spatially unbiased observations and to detect mesoscale environmental phenomena is radically determined by the spatial configuration of the network. However, there is lack of an objective, practical, and amenable method for guiding the spatial configuration of multifunctional, long-term mesoscale networks. The objective of this study is to present and demonstrate the application of a new method based on computational geometry that identifies the optimal location of future monitoring stations by finding the largest unmonitored area of the network. The computation of the method is first illustrated using the spatial distribution of the Kansas Mesonet as a case-study scenario and is then applied to several statewide and nationwide mesoscale networks in the United States. The proposed geometric method was effective to generate a long-term road map with the location of future monitoring stations. The geometric method seamlessly integrated with georeferenced data to identify the largest unmonitored areas with frequent occurrence of wildland fires and severe drought and to identify underrepresented soil types. Spatially dense statewide mesoscale networks with >120 stations across the studied U.S. states resulted in largest unmonitored areas of about 602 km2, whereas nationwide networks had largest unmonitored areas of 5002–6002 km2. The proposed method based on the geometric arrangement of network stations can be used by scientists, network managers, and state climatologists to improve the spatial representability of existing networks, better plan the allocation of limited resources, and increase the preparedness potential of mesoscale networks.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andres Patrignani, andrespatrignani@ksu.edu

Abstract

The ability of mesoscale environmental monitoring networks to collect spatially unbiased observations and to detect mesoscale environmental phenomena is radically determined by the spatial configuration of the network. However, there is lack of an objective, practical, and amenable method for guiding the spatial configuration of multifunctional, long-term mesoscale networks. The objective of this study is to present and demonstrate the application of a new method based on computational geometry that identifies the optimal location of future monitoring stations by finding the largest unmonitored area of the network. The computation of the method is first illustrated using the spatial distribution of the Kansas Mesonet as a case-study scenario and is then applied to several statewide and nationwide mesoscale networks in the United States. The proposed geometric method was effective to generate a long-term road map with the location of future monitoring stations. The geometric method seamlessly integrated with georeferenced data to identify the largest unmonitored areas with frequent occurrence of wildland fires and severe drought and to identify underrepresented soil types. Spatially dense statewide mesoscale networks with >120 stations across the studied U.S. states resulted in largest unmonitored areas of about 602 km2, whereas nationwide networks had largest unmonitored areas of 5002–6002 km2. The proposed method based on the geometric arrangement of network stations can be used by scientists, network managers, and state climatologists to improve the spatial representability of existing networks, better plan the allocation of limited resources, and increase the preparedness potential of mesoscale networks.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andres Patrignani, andrespatrignani@ksu.edu

1. Introduction

In recent decades, the increasing need for research-grade, near-real-time, and spatially dense environmental observations has propelled the number of in situ mesoscale networks for meteorological, agricultural, and hydrological monitoring. Mesoscale networks record multiple essential climate variables (Bojinski et al. 2014) and operate at a horizontal spatial resolution ranging from a few to several hundred kilometers (American Meteorological Society 2019). Information from mesoscale environmental monitoring networks is critical and has been widely used to track climate trends (Garbrecht et al. 2014), better understand soil moisture–rainfall feedbacks mechanisms (Findell and Eltahir 1997; Ford et al. 2015b), validate remote sensing soil moisture and evapotranspiration products (Liu et al. 2011), quantify surface and subsurface soil water storage (Ochsner et al. 2019; Lollato et al. 2016; Patrignani and Ochsner 2018; Ochsner et al. 2013; Swenson et al. 2008), estimate potential drainage recharge rates (Wyatt et al. 2017), and support natural hazard forecasting such as droughts (Ford et al. 2015a; Mozny et al. 2012), flash flooding (Basara 2001; Terti et al. 2019), wildfires (Carlson et al. 2002; Krueger et al. 2015, 2016; Reid et al. 2010), and severe thunderstorms (Gagne et al. 2012). Furthermore, the decision support tools, outreach programs, and scientific discoveries that stem from mesoscale networks propagate through their surrounding community by helping decision-makers and policy makers and contributing to increasing public safety (Ziolkowska et al. 2017). Thus, the spatial configuration of mesoscale networks plays a pivotal role for collecting spatially unbiased observations and for studying and detecting both large-scale and localized environmental phenomena that may otherwise go undetected.

The World Meteorological Organization and steering committees of mesoscale networks have developed extensive guidelines and protocols detailing best practices for selecting the location of new monitoring stations (Shafer et al. 1993) based on dominant land cover, terrain slope, site accessibility, presence of obstacles, and soil properties [Brock et al. 1995; American Association of State Climatologists (AASC); AASC 2019]. There is, however, a lack of a practical method for guiding and planning the spatial configuration at the network level. The location of additional monitoring stations must be in concert with the spatial arrangement of existing stations and aimed at strengthening the ability of the network to effectively capture environmental phenomena across the spatial domain of the network.

One of the earliest methods used for designing the spatial configuration of mesoscale networks consisted of political boundaries. During the inception of the Oklahoma Mesonet (Brock et al. 1995; McPherson et al. 2007) in the early 1990s, county boundaries were used as a template for defining the location of stations. The initial goal of the network’s steering committee was to deploy a monitoring station in each of the 77 counties across Oklahoma (roughly one station per 32 km). The use of political boundaries is a simple and attractive method that has the advantage of covering the entire geographical domain of the network with nonoverlapping subregions. Additional motivations for the use of political boundaries is that private and public local sponsors commonly take pride of ownership and that usually state and federal emergency and disaster assistance programs are based on county level boundaries. However, areas defined by political boundaries can unevenly represent the spatial domain of the network and may still contain contrasting topographical features, land covers, soil types, and even microclimate patterns that make the selection of siting locations not trivial. For instance, the area of counties within the contiguous United States ranges between 5 and 52 000 km2, with counties of western states having a notoriously larger area than counties of eastern states. So, by following political borders, areas with frequent and potentially hazardous environmental events may end up underrepresented, weakening the ability of the network to increase public safety.

More sophisticated optimization approaches such as spatial decorrelation and spatial variance-reduction methods that account for the spatial structure of the observation variables have been widely used to instrument catchment-scale rain gauge networks (Bastin et al. 1984; Bras and Rodríguez-Iturbe 1976; Pardo-Igúzquiza 1998), solar ultraviolet radiation networks (Schmalwieser and Schauberger 2001), groundwater quality monitoring networks (Herrera and Pinder 2005), and air pollution monitoring networks (Kumar 2009). However, these methods have two major drawbacks. The first drawback is that sophisticated optimization approaches are mostly oriented at short-term and application-specific networks, while modern automated mesoscale networks are aimed at long-term (30–50 yr) data collection of multiple variables at several heights (e.g., wind speed at 2 and 10 m), depths (e.g., soil moisture at 5, 10, 20, 50, and 100 cm), and time intervals (e.g., 1, 5, and 60 min along with daily), while also generating numerous value-added products (e.g., reference evapotranspiration, vapor pressure deficit, growing degree days) (Table 1). In application-specific networks, the problem often resides in minimizing a single objective function (e.g., semivariogram, correlogram), but the multivariate character of modern mesoscale networks would require minimization of a complex multiobjective function that not only accounts for a large number of variables, but also for the different degree of spatial autocorrelation of each variable. For instance, daily observations of air and surface soil temperature across Kansas can exhibit a strong (r > 0.9) spatial correlation for stations located even more than 500 km apart, whereas daily precipitation and soil moisture have much noisier and shorter correlation distances (Fig. 1). Multiobjective (Trujillo-Ventura and Hugh Ellis 1991) and entropy-based state-space optimization models (Bueso et al. 1998) have been proposed to integrate multiple observation variables. However, these methods have not gained traction in the community driving the deployment of mesoscale networks. The second drawback is that an existing dataset for the same observation variable and study area is required to compute the parameters of models describing the spatial structure. This is a major limitation in regions where no prior data are available—which may very well be the reason for deploying or augmenting a mesoscale network in that region (Arsenault and Brissette 2014). In the United States, extensive daily records and monthly summaries of precipitation and air temperature are available from nationwide networks such as the National Weather Service (NWS) Cooperative Observer Program (COOP). For instance, monthly air temperature and precipitation from the COOP network have been used to design the spatial configuration of the U.S. Climate Reference Network using an iterative degradation method (Vose and Menne 2004). However, in situ data availability is often limited in other regions of the world, particularly for less ubiquitous variables such as soil moisture and solar radiation.

Table 1.

Essential variables recorded by new 10-m towers of the Kansas Mesonet.

Table 1.
Fig. 1.
Fig. 1.

Spatial correlation of (left) four atmospheric variables and (right) three soil variables for all available daily records in the period from January 2017 to June 2019 for 21 stations (420 pairs without self-correlation) of the Kansas Mesonet spanning the entire state of Kansas. The period and number of stations were selected to allow inclusion of soil moisture, which was added to the Kansas Mesonet in late 2016. Each point represents the value of the Pearson’s correlation coefficient between the time series of a given variable for two stations separated by a distance d.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

In light of these limitations and the multifunctional facet of modern mesoscale environmental monitoring networks, our objective was to study the application of a new method that solely relies on the geometric configuration of the network to identify the largest unmonitored area of the network, and from it, derive the tentative location of a new station. Our idea departs from previous methods that relied on the spatial structure of observation variables and is aimed at demonstrating a practical method that can be used to guide the deployment of future monitoring stations. The specific question that we will try to answer is: What is the optimal siting location of the next N monitoring stations given the current spatial configuration of a given mesoscale network? Note that we are not concerned with finding the optimal density of the network, but rather with searching for the optimal location of future monitoring stations, regardless of any long-term target network density.

We first describe the problem of finding the largest unmonitored area and the method for identifying the optimal location of future stations using the Kansas Mesonet as an example. We also demonstrate how this method can be easily applied as a marching process to create a road map of the location of N future siting locations. We have not found in the literature any other method providing a long-term road map for siting future networks stations. For a more comprehensive analysis, the method was applied to other statewide and nationwide environmental monitoring networks of the United States. Last, we present a few examples on how to extend the proposed approach in combination with georeferenced information of wildland fires, soil type, and frequency of drought events. For convenience, area is represented throughout this paper following the XX2 format to indicate the length of one side of a square of the given area, for example, 1002 km2 = 10 000 km2 (e.g., Ochsner et al. 2013).

2. Materials and methods

a. Description of the Kansas Mesonet

The Kansas Mesonet is a mesoscale environmental monitoring network across Kansas that was established in 1984 when the Kansas State University Kansas Research and Extension network began a small network of 13 automated weather monitoring stations consisting of electronic sensors mounted on 2-m tripods. As a consequence of the growing number of public and private supporters in recent years, the network underwent a major expansion and currently consists of 62 active stations. Most of these stations have been upgraded to 10-m permanent monitoring towers (Fig. 2) to meet the highest standards of scientific research and make observations comparable to surrounding networks (viz., the Oklahoma Mesonet and Nebraska Mesonet). Stations consisting of 10-m towers monitor precipitation, air temperature, relative humidity, barometric pressure, incident solar radiation, wind speed and direction, soil temperature, and soil moisture at multiple vertical levels (i.e., depths and heights) and time intervals (Table 1). As a test-case scenario for this analysis we used the spatial configuration of the network as of 2016, which only consisted of 56 stations (Fig. 3). This choice was made to best represent the scenario that motivated this study.

Fig. 2.
Fig. 2.

(left) Sketch of instrumentation layout and (right) image of the Ottawa 2SE station located at the Kansas State University East Central Research Experiment Station.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

Fig. 3.
Fig. 3.

Geographic location of the 56 stations of the Kansas Mesonet in 2016.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

b. Method description

The location of a new monitoring station was determined by finding the centroid of the largest unmonitored area of the network. In this paper, we defined the largest unmonitored area as the largest empty circle (LEC) among the existing stations of the network (Fig. 4). Finding the LEC is a problem that belongs to the realms of computational geometry and is a method that solely relies on the spatial configuration of the network (Schuster 2008). Formally, if we let the discrete set of points P = {p1, p2, …, pn}, located on a two-dimensional Euclidean plane, then the problem consists of finding the largest empty circle C, such that no point of P lies in the interior of C (Toussaint 1983). In the context of this study, the set of points P is represented by the set of monitoring stations and the two-dimensional plane is represented by the planar spatial extent of the network. The tentative centroids for the LEC can consist of randomly generated points (i.e., brute force approach) or by simply using the vertices of Voronoi diagrams (also known as Thiessen polygons) (Voronoi 1909; De Berg et al. 2008; Preparata and Shamos 2012) that partition the plane into subregions of convex polygons containing a single monitoring station. We favored the use of Voronoi diagrams, which is another common structure of computational geometry that seamlessly integrates with the LEC method and is computationally faster.

Fig. 4.
Fig. 4.

Diagram with three hypothetical stations illustrating the components involved in the calculation of an empty circle centered at the Voronoi vertex V. The radius of the empty circle is limited by the distance between V and the nearest station (i.e., station 3). Stations 1 and 2 are farther than station 3; therefore, the perimeter of the empty circle does not intersect them.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

Specifically, each station of the network belongs to a single Voronoi polygon and each Voronoi polygon consists of three or more vertices that represent the support area of each station. Each Voronoi vertex is equidistant (i.e., the circumcenter) to three stations determined by a Delaunay triangle. Voronoi vertices are of central importance for solving the LEC problem since they constitute the candidate centroids for the largest empty circle. However, a limitation of using Voronoi diagrams compared to randomly selected points is that Voronoi vertices are confined within the convex hull of the network. To resolve this issue, we intersected the edges of Voronoi polygons that extended beyond the convex hull with the network boundary (e.g., state or country border). The intersected points at the network boundary were added to the existing pool of tentative centroids for searching the largest empty circle.

Given the current spatial configuration of the network, the problem of finding the largest empty circle was solved by following these six steps: (i) partition the spatial domain of the network into P subregions using Voronoi diagrams (the resulting Voronoi vertices constitute the initial pool of tentative centroids for computing the LEC), (ii) intersect Voronoi diagrams with network boundaries and add the intersected boundary points to the existing pool of tentative centroids, (iii) compute the empty circles using each tentative centroid as the center of the circle and using the distance to the nearest station as the radius of the circle (Fig. 4), (iv) intersect circle boundaries with state boundaries if the empty circle extended beyond the spatial extent of the network, (v) compute the area of each empty circle (some intersected circles in the previous step will no longer preserve the shape and perimeter of the initial circle), and (vi) sort empty circle areas and find the LEC for the network. The geographic coordinates of the centroid of the LEC were used as the suggested optimal location of the next station. Once a new station is deployed, the new LEC needs to be recomputed by repeating the same six steps. This recomputation is required since the newly deployed station will change the configuration of the surrounding Voronoi polygons. Another advantage of computing the LEC using Voronoi diagrams is that these diagrams can be used to study the support area of each network station. All computations were programmed using MATLAB R2019a including Mapping Toolbox, version 4.8.

c. Auxiliary datasets

Georeferenced datasets of wildland fires, severe drought, and soil textural class were coupled with the set of empty circles to better capture unmonitored network areas with frequent natural hazards and underrepresented soil types. Soil texture was particularly included in this study because of the growing interest in measuring variables such as soil moisture to improve our understanding of land-atmosphere interactions, increase the forecasting skill of land surface models, and due to the strong connection of soil type with multiple agricultural and hydrological processes (e.g., erosion and runoff) (Ochsner et al. 2013).

Wildland fire records from 2000 to 2018 were obtained at 1-km spatial resolution from the Moderate Resolution Imaging Spectroradiometer (MODIS) Fire and Thermal Anomalies daily product generated by the National Aeronautics Space Administration (NASA) Terra (MOD14) and Aqua (MYD14) satellites that is available through the NASA Fire Information for Resource Management System web portal. The resulting dataset for Kansas contained a total of 78 222 events, which includes human-caused (mostly prescribed fires) and naturally occurring or accidental fires. Other sources of thermal anomalies (e.g., structure fires, industrial sources) are also contained in the dataset, but make up a minimal number of detections. To minimize the number of misclassified pixels due to unusual thermal signatures we used the confidence level associated with each pixel in the MOD14 and MYD14 products to only select fires detected with a confidence equal or higher than 50%. In this study we favored MODIS data due to high geolocation accuracy compared to other sources such as the federal fire occurrence dataset (Brown et al. 2002) that contains unverified location records (Hawbaker et al. 2013).

Drought data for the conterminous United States were obtained from the U.S. Drought Monitor (Svoboda et al. 2002) for the period 2000–18. The drought dataset consisted of weekly (N = 978 weeks) vector maps containing polygon areas delimiting the spatial extent of different drought categories across the United States. The U.S. Drought Monitor generates five drought intensity classes: abnormally dry (D0), moderate drought (D1), severe drought (D2), extreme drought (D3), and exceptional drought (D4). In our case, polygons for classes D2, D3, and D4 were converted from vector to raster using a 1-km grid to approximate the shape of the polygon. The resulting raster maps were stacked and then the total number of weeks under any of these three drought categories were computed for each pixel. This layer was intended to represent the most frequently affected areas of the United States by severe-or-worse droughts.

Soil texture for Kansas was determined based on 1-km gridded maps of sand and clay content at 5-cm depth obtained from the International Soil Reference and Information Centre SoilGrids product (Hengl et al. 2014), which for the United States is largely based on the U.S. Department of Agriculture (USDA) Natural Resources Conservation Service (NRCS) Soil Survey Geographic Database (Soil Survey Staff 2014). Soils were classified into one of the 12 soil textural classes defined by the U.S. Department of Agriculture.

Simplification of boundary density points for the conterminous United States was achieved using the Douglas–Peucker line-simplification algorithm setting a tolerance of 0.11° of arc. This was necessary to reduce the number of points and speed the computation process at the national level. For instance, the number of points defining the border of the United States was simplified from 301 839 points to 706 points, resulting in nearly identical boundaries and a difference in area of 1.5%, a value that can be assumed to be negligible for the purpose of this study.

To provide a broader context for the results of our study, we also included five statewide networks [Oklahoma Mesonet (McPherson et al. 2007; Brock et al. 1995), Nebraska Mesonet (Shulski et al. 2018), South Dakota Mesonet, North Dakota Mesonet, and New York Mesonet] and two nationwide networks [the U.S. Climate Reference Network (Diamond et al. 2013; Bell et al. 2013) and the Soil Climate Analysis Network (SCAN; Schaefer et al. 2007)].

d. Distribution analysis of unmonitored areas and station-support areas

Uniformity in the distribution of the station-support areas was evaluated using Lorenz curves and the Gini coefficient (Gini 1921). The Gini coefficient is a statistical metric for dispersion commonly used in economics to quantify income or wealth inequality. In the context of this paper, the Gini coefficient provides a comprehensive and intuitive framework for quantifying the degree of spatial uniformity of the support area of a monitoring network. The Gini coefficient ranges from 0 to 1, where a value of 0 means that the support areas of all of the stations are equally distributed and a value of 1 represents maximal inequality. In this context, the latter situation would only occur when the network has a single station accounting for the entire spatial extent. The Gini coefficient was computed as the ratio between the area under the Lorenz curve (Lorenz 1905) and the area under the curve denoting perfect equality (perfect spatial distribution or 1:1 line) using the following equation:
G=(AB)/A,
where A has a value of 0.5 and represents the area under the line of perfect equality and B is the area under the Lorenz curve. Lorenz curves represent the distribution of station-support areas and were created by first sorting the support areas of the stations given by the Voronoi polygons in ascending order, then calculating the cumulative areal sum, and then normalizing the cumulative areal sum by the total area. The area under the Lorenz curve was computed by numerical integration using the trapezoidal rule.

3. Results and discussion

a. Unmonitored network area

On the basis of the spatial configuration of the Kansas Mesonet we identified a total of 145 empty circles with an area ranging from 252 to 1312 km2 (shaded circle in Fig. 5) and a median area of 622 km2 (Fig. 6a). Our findings revealed that the largest unmonitored area represents a stunning 8% of the area of the state, a value that is also comparable to the total area of about eight Kansas counties. The centroid of the LEC (red cross mark in Fig. 5) represents the point farthest (i.e., remotest) from any station across the entire network and indicates the ideal siting location of the next monitoring station of the Kansas Mesonet. The LEC centroid is located at geographic coordinates 38.3456°, −96.3599°, about 13 km to the southeast of Emporia, Kansas and right at the intersection of Lyon and Chase counties. The method of finding the LEC only provides tentative siting coordinates since the definitive location of the station will depend on land availability and network-specific site selection criteria that typically account for land cover, depth of the soil profile, landscape position, and presence of obstacles. The resulting LEC is almost entirely circumscribed into the Flint Hills ecoregion, an area dominated by natural grassland vegetation, rolling landscapes, and rocky soils that stretches about 400 km in the north–south direction between the northern part of Oklahoma and the Kansas–Nebraska border. The absence of Kansas Mesonet stations across much of this region is mostly due to the lack of Kansas Research and Extension Experiment Stations, low interest from public and private sponsors, and frequent prescribed wildland fires that increase the risk of accidental station damage.

Fig. 5.
Fig. 5.

Map of the Kansas Mesonet showing the 56 stations of the network (filled circles), the Voronoi vertices and points of the state boundary line (open circles) used to compute the empty circles, the resulting web of 56 Voronoi polygons (gray lines connecting open circles), the largest empty circle (blue-shaded circle), the suggested location of the next monitoring station (red cross mark inside the circle), and the largest support area of the network (gray-shaded Voronoi polygon).

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

Fig. 6.
Fig. 6.

Histograms of the (a) 145 empty circle areas and (b) 56 station-support areas of the Kansas Mesonet. Station-support areas are the areas of the Voronoi polygons. The area of the LEC, LSA, and median value (dashed lines) are provided for additional reference.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

On the other hand, station-support areas for the Kansas Mesonet ranged from 202 to 932 km2, with a median value of 602 km2 (Fig. 6b). The largest support area was for the Hill City station in the northwest portion of the state (shaded gray area in Fig. 5), which did not overlap with the largest unmonitored area and represented only 50% of the area of the LEC. This unexpected finding infringes upon the perception that new stations should be deployed so as to “split” the largest support area. In this particular case, the largest empty circle and the largest support area are on opposite sides of the network, meaning that the largest support area would remain unchanged after deploying the next monitoring station at the centroid of the LEC.

To put the analysis of the Kansas Mesonet into a broader perspective, we applied the method of identifying the LEC to five additional statewide and two nationwide mesoscale networks (Table 2). Not surprisingly, the Oklahoma Mesonet and the New York Mesonet with more than 120 stations each had the smallest LEC with an area of 612 km2. The LEC from these two networks are lower by almost a factor of 5 relative to that of the Kansas Mesonet (i.e., 1312 km2) and are smaller by nearly a factor of 100 relative to the LEC area for nationwide networks such as the SCAN and the U.S. Climate Reference network. The small unmonitored areas and the more uniform distribution of support areas give the Oklahoma Mesonet and the New York Mesonet the ability to capture localized natural phenomena such as convective storms, tornadic supercells, and even the development of flash droughts associated with patched irregular areas of coarse-textured soils, that in sparser networks may go completely undetected.

Table 2.

Summary of network area, LEC area, station-support area, and support area distribution as represented by the Gini coefficient for multiple statewide and nationwide mesoscale environmental monitoring networks across the United States. The areas are represented by XX2 to indicate the length of one side of a square of the given area; e.g., 1002 km2 = 10 000 km2. Station counts are for 2016.

Table 2.

The Kansas Mesonet, despite being one of the studied statewide networks with the lowest number of stations, resulted in a more uniform (lower Gini coefficient) support area distribution than comparable and denser networks. For instance, the Kansas Mesonet resulted in a Gini coefficient of 0.27 (Table 2), while the Nebraska Mesonet with 68 stations and the North Dakota Mesonet with 69 stations resulted in Gini coefficients of 0.35 and 0.28, respectively. Something similar occurred with nationwide networks, where the uneven distribution of the 185 stations of the SCAN resulted in a 47% greater Gini coefficient compared to the U.S. Climate Reference Network with just 110 stations across the conterminous United States (Table 2), highlighting the effectiveness of the iterative degradation method supporting the design of the U.S. Climate Reference Network (Vose and Menne 2004). From this analysis, it seems logical to us that the spatial resolution of mesoscale networks should not be only characterized by the mean size of the station-support area, but also by including a metric of spatial uniformity of the station-support areas (e.g., Gini coefficient) and the size of the largest unmonitored area.

b. Station deployment road map

The computation of the LEC can also be applied recursively to identify the optimal sequence of future stations (Fig. 7). The recursive implementation consisted of finding the centroid of the LEC to deploy the next monitoring station and then adding this new station to the list of all stations before starting the next iteration. In practice, it could take several years or even decades for a mesoscale network to reach its largest size, but the recursive implementation of the LEC method can enable researchers and network managers to plan the evolution of the network, identify priority areas, and create a long-term road map for better allocation of limited resources. The recursive analysis could be expanded to deploy N number of stations, but in practice mesoscale networks are often limited by funding and manpower, making this maximum value a complex variable that strongly depends on contemporaneous political–economic situation of the supporting institution.

Fig. 7.
Fig. 7.

Numbered sequence of future siting locations for the Kansas Mesonet (open circle followed by sequence number). Numeration starts from a value of 57 (a value one unit higher than the current number of stations) and extends to a maximum value of 105. The maximum value is equal to the number of counties across Kansas, which is a reasonable long-term goal for the network.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

The recursive method was applied to the Kansas Mesonet by growing the network from 56 stations to an idealized maximum of 105 stations, which equals the number of Kansas counties and is an arbitrary, but reasonable, number of long-term stations for this network. Deploying additional 49 stations resulted in a reduction of the largest empty circle from 1312 to 642 km2, a change of 76% relative to the current value (Fig. 8a). The deployment of the first station had the greatest impact, reducing the LEC area by 17%. To a lesser extent, the largest support area (LSA) was reduced from 932 to 602 km2, which is equivalent to a 58% percent reduction compared to the current value. After nearly doubling the size of the network, the areas of the LEC and the LSA tended to converge, suggesting that the configuration of the network tends to have similar and uniformly distributed monitored and unmonitored areas. This increased in uniformity can be clearly visualized by a decreased Gini coefficient from 0.27 for the current spatial configuration of the network to 0.14 for the hypothesized future configuration of the network. This change is also depicted by the reducing gap between the Lorenz curve corresponding to the network with 105 stations and the line of perfect support area distribution (Fig. 8b). The Gini coefficient is a useful metric to quantify the progress of the spatial support of the network during the augmentation stage, but the Gini coefficient is only a relative measure of support area distribution. Thus, it provides little information about the absolute magnitude of the spatial support of the stations, which is important from the point of view of capturing mesoscale phenomena. In other words, two networks with identical Gini coefficients can have completely different support areas.

Fig. 8.
Fig. 8.

(a) Area of the LEC and station-support area for the Kansas Mesonet as a function of increasing number of stations, and (b) Lorenz curves for the support area of the current state (red dot–dashed line) and idealized state of the Kansas Mesonet network with 105 stations (blue dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

The resulting road map contained some stations right at the network boundary. This is a consequence of including boundary points into the pool of tentative empty circle centroids. We identified at least three different ways of addressing the area between the convex hull and the boundary of the network. Our first alternative was to identify the intersecting points between the Voronoi polygons and the network boundaries (i.e., state line). A second alternative involved the generation of random points on the area between the convex hull and the network boundaries. A third alternative involved the use of stations from neighboring mesonet networks. We favored the addition of points from the intersection between Voronoi polygons and the network border (i.e., state border) to allow the network to grow beyond the boundaries imposed by the convex hull and improve the spatial coverage of unmonitored gaps near network boundaries. However, the selected approach is slightly more computationally demanding since borders delimited by natural boundaries often require more points than straight political boundaries. Our analysis treated mesoscale networks in isolation from other networks, but with the increasing number of mesoscale networks it is advisable that the deployment of new monitoring stations should involve the location of stations from neighboring networks as if any given network is part of a network of networks.

Two alternative geometric methods for finding the largest unmonitored area of a network considered in earlier stages of this study included computing the largest empty rectangle and the largest empty convex polygon. A common weakness of these two alternative methods is the susceptibility to detect large and elongated unmonitored areas, in which the polygon centroid can result adjacent to existing stations.

c. Application of the LEC with georeferenced environmental information

Up to this point the selection of the next monitoring station was solely determined by the geometric configuration of the existing stations. In this section we take the LEC method a step further and we demonstrate how it can be applied with georeferenced data of natural hazards and resources.

With the growing interest in monitoring soil-related variables such as soil moisture (Ochsner et al. 2013), knowledge of the spatial distribution of the predominant soil and detailed characterization of soil physical properties are becoming essential for accurate measurements (Scott et al. 2013). Soil textural class is a variable that synthesizes many of the continuous soil physical properties into a manageable and practical number of soil classes that have been widely used in hydrology and agriculture. Eight of the 12 USDA soil textural classes are present in Kansas as based on the percentage of sand and clay content at the 5-cm depth (Fig. 9). The predominant soil classes are loam (38.5%), silty clay loam (26.9%), and silt loam (24.8%), which together account for about 90% of the land area of the state (Table 3). The Kansas Mesonet currently represents five of the eight soil textural classes. Most monitoring stations are deployed in loam (28 stations), silt loam (18 stations), and silty clay loam (7 stations) soils. Silty clay loam is the predominant soil within the LEC, accounting for 91% (22 702 km2/24 981 km2) of the LEC area and representing nearly 27% (22 702 km2/84 555 km2) of the total area of silty clay loam soils across Kansas (Table 3, Fig. 9). Deploying a new station in the centroid of the LEC shown in Fig. 9 will not only decrease the size of the largest unmonitored area of the network, but will also increase the representativeness of the third most common soil textural class across Kansas, which is clearly underrepresented. In fact, eleven additional stations would need to be deployed in silty clay loam soils [100(7 + 11)/(56 + 11) = 26.9%, Table 3] to align the proportion of stations in each soil textural class with the areal proportion of each soil textural class across the state.

Fig. 9.
Fig. 9.

Spatial coverage of USDA soil textural classes at 5-cm depth across Kansas. Note that only 8 of the 12 classes are present in the state and that only 4 of the 8 present classes are clearly visible at this level. White pixels represent major lakes.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

Table 3.

Area of the eight USDA soil textural classes present in Kansas and the LEC.

Table 3.

The utilization of prescribed fires over the Flint Hills ecoregion is another prominent use of weather data in the state. These prescribed fires are a useful management strategy to suppress invasive plants and improve grassland yield and palatability for cattle grazing. Accurate environmental monitoring is equally important over areas with prescribed fires to guide firefighters, land managers, smoke management, and increase awareness for conditions conducive for wildland fire. Wind speed and direction, air temperature, relative humidity, antecedent precipitation, and dry soil and vegetation conditions are primary variables utilized for prescribed burning and fire danger models (Carlson et al. 2002), all of which are variables monitored by modern mesoscale networks. The LEC with the greatest number of satellite-detected thermal anomalies was the same as the LEC identified using the spatial configuration of the network (Fig. 10). There were a total of 19 711 MODIS pixels representing fires in the period 2000–18 within the LEC. While the population density within this area is low with about 1.15 people per square kilometer (total of 96 937 people), there are multiple actively growing urban areas near the edge of the LEC. Deploying new monitoring stations within this LEC will not only enhance the ability of the network to better track and warn about the risk of wildland fires and air pollution in the region, but it will also complement the monitoring of underrepresented soil types.

Fig. 10.
Fig. 10.

Largest empty circle with the largest number of wildland fires in the period from 2000 to 2018. The map of wildland fires was created using fire and thermal anomalies at 1-km spatial resolution obtained from the MODIS Fire and Thermal Anomalies daily product generated by the NASA Terra (MOD14) and Aqua (MYD14) satellites.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

Juxtaposing the spatial configuration of the SCAN with historical records of severe-or-worse drought events from the U.S. Drought Monitor revealed that some of the largest unmonitored areas of the SCAN also match regions with frequent and persistent droughts. The SCAN stems from the need to better monitor agricultural areas of the United States susceptible to drought conditions and currently consists of 185 stations within the conterminous United States. The SCAN effectively covers most agricultural areas within the United States susceptible to drought, but our analysis also revealed noticeable gaps in the network. The two largest and nonoverlapping unmonitored circles in the SCAN are located in areas of the country that also exhibit some of the highest frequency of severe-or-worse droughts (Fig. 11) in the period from 2000 to 2018. Both of these regions have a low population density and are characterized by rocky mountainous terrain dominated by bare soil or natural grasslands and shrublands. The centroid of the LEC area is located at coordinates 43.8749°, −107.9829° (cross mark in Fig. 11), which point is in Wyoming. The LEC has an area of 6352 km2 and encompasses parts of Wyoming, Montana, Idaho, and South Dakota. The median number of weeks under severe or worse drought conditions within the LEC was 280 weeks, with some localized areas reaching a maximum of 403 weeks, which is about 41% of the studied period. The second largest empty circle was located on Arizona and New Mexico. This is somewhat expected since part of this area belongs to the Sonoran Desert. Although the SCAN was deployed with the goal of monitoring environmental conditions and encourage research and decision making in agricultural areas of the United States (Schaefer et al. 2007), deployment of new stations may be required in the identified gaps to better understand the onset, development, and persistence of droughts as natural phenomena beyond the realms of agricultural production.

Fig. 11.
Fig. 11.

Map showing 185 stations of the SCAN overlaying the map of severe-or-worse drought frequency using U.S. Drought Monitor data from 2000 to 2018. The map also shows the largest and second largest unmonitored areas, which are located over areas with frequent drought events.

Citation: Journal of Atmospheric and Oceanic Technology 37, 5; 10.1175/JTECH-D-19-0167.1

While the SCAN does not have presence in certain drought-prone areas of the United States, the Snowpack Telemetry (SNOTEL) network also developed and maintained by the USDA NRCS has multiple stations within these unmonitored SCAN regions. The SNOTEL network was developed to supply near-real-time snowpack information to forecast streamflow volumes and many sites also monitor soil moisture, soil temperature, solar radiation, and wind speed similar to sites of the SCAN, highlighting the importance of generating a network of networks to complement environmental observations. Another important remark from our network analysis of the Kansas Mesonet and SCAN suggests that, in addition to the spatial variability of essential variables, the design of future mesoscale environmental monitoring networks should account for the spatial distribution of natural resources and environmental hazards.

The previous analyses also exposed some of the limitations of the proposed geometric method for siting future monitoring stations. The method was described using the Kansas Mesonet, which is located inland surrounded by a rather flat landscape with gradual elevation changes, and may not be adequate to guide the placement of future monitoring stations in regions dominated by a large number of islands or by mountainous terrain. In regions presenting high elevation, meteorological processes such as orographic precipitation events may not be accurately represented. In coastal environmental monitoring networks, such as the National Observatory of Athens Automatic Network in Greece that extends to numerous islands, the limitation of the LEC method could be circumvented by considering islands as separate spatial domains. Then, the size of the different continental and insular LEC could be ranked to define the optimal location across the entire domain of the environmental monitoring network. Similarly, subregions of mesoscale monitoring networks characterized by mountainous terrain could be delineated and treated separately. In this context, an alternative solution that requires further exploration may consist of generating elevation-weighted LEC.

4. Conclusions

We investigated the problem of identifying the optimal location of future monitoring stations in modern automated mesoscale networks. The method consisted of finding the largest unmonitored area of the network by searching for the largest empty circle, in which its center represents the remotest location of the network and the tentative location for siting a new station. We demonstrated that simple and well-established concepts from computational geometry and statistical economics can be used to analyze the spatial distribution of stations and to objectively determine the siting location of future monitoring stations across an existing network, removing the need for subjective decisions and complicated optimization functions.

Spatially dense statewide mesoscale networks in the United States with more than 120 stations per state had largest unmonitored areas of about 60 km2, while nationwide mesoscale monitoring networks had largest unmonitored areas of 500–600 km2. Across multiple statewide and nationwide networks, the largest unmonitored area was spatially unrelated to the station-support area, which implies that both concepts are somewhat independent and should be considered together to characterize the spatial resolution of mesoscale networks. The proposed method was effective to generate a long-term road map of the location of future monitoring stations to help scientists, network managers, and state climatologists better plan the spatial coverage of the network and the allocation of limited resources for network growth and maintenance. The road map for the case of the Kansas Mesonet generated the optimal geographic location of the next 49 stations of the network. To our knowledge this is the first paper describing the location of N monitoring stations within an existing mesoscale network.

While we still recommend the use of geostatistical approaches that account for the spatial structure of one or few variables for siting stations in application-specific networks, the proposed method of identifying the largest unmonitored area solely based on the geometric configuration of the network provides an alternative, more practical, and amenable method for siting new stations in multivariate mesoscale networks. Due to the geometric nature, the proposed approach can be easily integrated with network boundaries and georeferenced information of natural resources and environmental phenomena such as soil type, wildland fires, and severe droughts. Future studies could focus on environmental hazards not covered in our study such as flooding events and severe thunderstorms. Our study focused on terrestrial environmental monitoring networks, but we do not see any major obstacle on why the proposed approach could not be extended to multifaceted oceanic networks.

Acknowledgments

Partial support for this project has been provided by the Kansas State University Agricultural Experiment Station (Contribution 20-175-J), the Kansas Soybean Commission through Agreement KSC/KSU 1782 and Award A00-0635; and the Kansas Corn Commission through Awards A00-0767-001 and A00-1110. The authors also thank three anonymous reviewers for their helpful and constructive feedback.

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