Abstract

In this paper the influence of surface type, wind speed, and other environmental conditions on near-surface air temperature, specific humidity, and surface temperature is studied. A wireless sensor network consisting of 13 low-cost meteorological stations was set up as a 2.3-km-long double transect in western Germany during the Fluxes and Patterns in the Soil–Vegetation–Atmosphere Scheme (FLUXPAT2009) campaign. This deployment covered various surface types, including a small river. It was found that the air temperature was mainly influenced by the distance to the river and that its variability is controlled by the wind speed. During the night, a pool of cold air formed in the valley close to the water. The specific humidity is also governed by proximity to the river, especially during the night and for low wind speeds. In contrast, the differences in surface temperature were caused by different land cover. These results can be confirmed by a cluster analysis. Setting up 13 stations in a relatively small area is not always feasible. In this study, an estimation of the error that is made by considering the effect of a reduced number of stations is given. Use of only a single station results in an error of 0.86 K in air temperature, 0.67 g kg−1 in specific humidity, and 1.4 K in surface temperature.

1. Introduction

Meteorological conditions near the surface (e.g., air temperature, specific humidity, and wind speed) vary on small spatial and temporal scales. Hence, the classical approach of using just one highly accurate station is of limited representativeness. A large number of stations need to be deployed over a small area to monitor the variability caused by different land surfaces and environments.

Networks for monitoring meteorological conditions are common among early and more recent studies, but the interstation distance typically exceeds 1 km. For example, Zemel and Lomas (1976) measured the air temperature in the Huleh Valley in Israel with a network of 70 stations. Kawashima and Ishida (1992) examined the temperature close to the surface in a 250 km × 300 km area in Japan with a network consisting of 130 stations, and Hubbard (1994) determined the spatial variability of daily measurements in the high plains in the United States.

On the microscale up to 2 km (Orlanski 1975), smaller meteorological networks are used to monitor local features. With such micronetworks, the air temperature fluctuation, especially nocturnal cooling, is frequently explored. Bodine et al. (2009) investigated this cooling in the Lake Thunderbird Micronet (Shapiro et al. 2009) area with 26 stations in a 120 m × 320 m domain. Hunt et al. (2007) detected a rapid nocturnal cooling and strong inversions at the El Reno Oklahoma Mesonet site using a transect of four portable automated micrometeorological stations. The nocturnal development of air temperature structure along a 22-km transect in complex terrain in Sweden was investigated by Gustavson et al. (1998). Mahrt (2006) studied the spatial variability of surface air temperature in complex terrain within a horizontal range from 200 m up to 1.4 km using six micronetworks. A very dense network of measurements of air, surface, and soil temperature and soil moisture was used by Xu et al. (2002). They constructed a 10-km transect with stations every 10 m to examine the spatial variability of the meteorological conditions.

To be in charge of such a network is a challenging and time-consuming task, because the data have to be collected at each individual station. In recent years, wireless sensor networks have become a common method to investigate small-scale variabilities. The advantage of these wireless networks is their autonomy, which permits their use in almost any environment. For example, sensors were placed on zebras for studying wildlife-tracking systems in Kenya (Zhang et al. 2005). A network of 16 sensors was set up on an active volcano in Ecuador to collect seismic and acoustic data (Werner-Allen et al. 2006a,b). Polastre et al. (2004) placed 43 stations in bird’s nests on Great Duck Island, Maine, for habitat monitoring.

In this paper we study the spatial variability of air and surface temperature, specific humidity, and wind speed. We analyze the factors that cause these variabilities and give an estimation of the error that is made by using less-dense networks.

2. Sensor network

The sensor network used in this study is called SensorScope. It has been developed at the Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland. The network consists of two different kinds of stations: slave stations and master stations. Pictures of a station and the communication scheme of the wireless network are shown in Fig. 1. The slave stations send their data via radio communication at a frequency of 868 MHz to a master station. The master station collects the incoming data and forwards them via global system for mobile communications/general packet radio service (GSM/GPRS) to a central server. The data are uploaded every 15 min to an Internet site (http://sensorscope.epfl.ch/climaps). For a detailed description of the technique of the SensorScope sensor network, see Barrenetxea et al. (2008) and Ingelrest et al. (2010).

Fig. 1.

(a) Station of the SensorScope network: This station is equipped from top to bottom with sensors for measuring wind speed and direction, solar radiation, air temperature, specific humidity, surface temperature, and precipitation. (b) Communication scheme: slave stations (shown here as small symbols) send data via 868-MHz radio communication to the master station (big symbol), as indicated by the thin lines. The master station forwards the data via GSM/GPRS to a server (thick arrows).

Fig. 1.

(a) Station of the SensorScope network: This station is equipped from top to bottom with sensors for measuring wind speed and direction, solar radiation, air temperature, specific humidity, surface temperature, and precipitation. (b) Communication scheme: slave stations (shown here as small symbols) send data via 868-MHz radio communication to the master station (big symbol), as indicated by the thin lines. The master station forwards the data via GSM/GPRS to a server (thick arrows).

Each station is equipped with sensors for measuring air temperature, relative humidity, surface temperature, wind speed, and wind direction (Fig. 1a). Some stations are additionally equipped with devices for measuring the incoming solar radiation and precipitation. All sensors and references are listed in Table 1.

Table 1.

Sensors used in FLUXPAT2009.

Sensors used in FLUXPAT2009.
Sensors used in FLUXPAT2009.

Nadeau et al. (2009) show that it might be possible to estimate the sensible heat flux with measurements of such a sensor network. Ninety-two SensorScope stations were deployed at the campus of the EPFL to estimate the sensible heat flux over different surface types in an urban environment. The heat flux was calculated on the basis of surface temperature measurements made by the network stations and was compared with scintillometer measurements. The technique also relies on additional instruments—for example, a sonic detection and ranging (sodar) radio acoustic sounding system (RASS)—and some assumptions.

To test the accuracy of the low-cost sensors of the SensorScope network, we compared them with more accurate measurements. The temperature and humidity sensors were all placed close to each other at the rooftop of the Meteorological Institute of the University of Hamburg. We compared their data with measurements of a Vaisala, Inc., HMP45 sensor, which has an uncertainty at the 95% confidence level of ±1.5% for relative humidity and ±0.13 K for air temperature. The intercomparison showed that the measurements of the network sensors are consistent but are not highly accurate. We calculated the bias of every network sensor relative to the reference measurements of the HMP45. We also computed the bias for each network sensor relative to all other network sensors; the percentile range Δp90−10, defined by the difference between the 90th and the 10th percentiles; and the mean of their root-mean-square errors (RMSE). The RMSE between two time series of length N from the stations Xa and Xb is defined as

 
formula

The results are listed in Table 2.

Table 2.

Mean difference, RMSE, and percentile range for air temperature, specific humidity, surface temperature, and wind speed during the calibration period.

Mean difference, RMSE, and percentile range for air temperature, specific humidity, surface temperature, and wind speed during the calibration period.
Mean difference, RMSE, and percentile range for air temperature, specific humidity, surface temperature, and wind speed during the calibration period.

The mean bias in air temperature for all network sensors relative to the HMP45 is 0.17 K. The mean difference between all of the network sensors is just 0.04 K, the mean RMSE is 0.25 K, and Δp90−10 is 0.59 K. On the basis of these results, a correction of the temperature measurements is made for each sensor. The sensors are passively ventilated, and therefore the measurements are positively biased when the sun is shining. The correction formula is hence based on the solar radiation:

 
formula

where T is the measured temperature, FSW is the shortwave incoming solar radiation, and a and b are regression coefficients. The mean value of a is −0.0016, and b ranges from −0.31 to 0.21 K.

The mean difference in relative humidity between the reference and the network sensors is −0.43%. Among the network sensors it is halved to 0.21%. To correct the difference between reference and network measurements, we used a formula of the third order:

 
formula

where ΔRH is the mean difference between the network and the reference measurements of relative humidity for 1% intervals and a, b, c, and d are regression coefficients. The mean values of a, b, and c are −8.5 × 10−5, 0.019, and −1.45, respectively. The coefficient d is in the range between −4.91% and 56.5%. On the basis of ΔRHfit, a bias for the relative humidity in 1% steps is calculated. This bias is added to the measurements. The relative humidity is highly influenced by air temperature. To eliminate this influence we calculated the specific humidity using the air temperature mentioned above and air pressure measurements that were only taken at station 01 (see Fig. 2). That leads to a mean difference in specific humidity between the reference and the network sensors of 0.05 g kg−1. The difference between all the sensors of the network is one order of magnitude smaller at 0.004 g kg−1. Their mean RMSE amounts to 0.18 g kg−1, and Δp90−10 amounts to 0.41 g kg−1.

Fig. 2.

Deployment within the FLUXPAT2009 project in western Germany: Light markers represent slave stations; dark markers represent master stations (source: Google Earth; ©2009 Google, ©2010 Tele Atlas, ©2010 Europa Technologies, and image ©2010 GeoContent).

Fig. 2.

Deployment within the FLUXPAT2009 project in western Germany: Light markers represent slave stations; dark markers represent master stations (source: Google Earth; ©2009 Google, ©2010 Tele Atlas, ©2010 Europa Technologies, and image ©2010 GeoContent).

The ZyTemp Co. TN901 infrared thermometers, which measure the surface temperature, were compared with a KT19. We used a water quench and started at 45°C. The sensors were aerated by a ventilator while the water was cooling down. In a second experiment, we used ice water to verify the zero point. The sensors provide very similar results, with a mean difference of 0.13 K. Because the instrument’s uncertainty of 0.6 K is very small, no correction was applied here. The mean RMSE between the network stations amounts to 0.38 K; the percentile range is 0.83 K.

The Davis Instruments Co. wind anemometers (model 6410) were calibrated in a wind tunnel. Two sensors were placed simultaneously in the tunnel side by side symmetrical to the middle of the tunnel, so that both sensors were exposed to the same wind speeds. The tunnel produces constant wind speeds for 5 min at 1.2, 1.5, 2, 3, 5, 7.5, 10, and 12 m s−1. All sensors show a similar behavior. They underestimate low wind speeds and get better results at higher wind speeds. The mean difference between the sensors from the network is 0.002 m s−1, the mean RMSE is 0.17 m s−1, and Δp90−10 is 0.42 m s−1. The mean difference between the given wind speed of the wind tunnel and the network measurements is 0.3 m s−1. Therefore, the measurements were corrected using a linear regression of the form

 
formula

where υ is the measured wind speed. The regression coefficient a has a mean value of 0.95, and b ranges between 0.42 and 0.7 m s−1.

For all sensors, these comparative measurements show that the network does not measure with high accuracy but does demonstrate precision. Therefore, we will focus on the differences between the stations more than on the absolute values.

3. FLUXPAT2009

The measurements took place within the Fluxes and Patterns in the Soil–Vegetation–Atmosphere Scheme (FLUXPAT2009) campaign in western Germany in the summer of 2009 (Fig. 2). The research area is located between 50°51′20″N, 6°25′35″E and 50°52′10″N, 6°27′2″E. It is a relatively flat terrain with a mean elevation of ~100 m above sea level. For more information see also Koyama et al. (2010).

Our deployment within the FLUXPAT2009 project is shown in Fig. 2. Our campaign started on 6 August and ended on 27 August 2009. We deployed 13 slave stations (light markers) and two master stations (dark markers) as a double transect perpendicular to the small river Rur and covering different kinds of land use. The transect is 2.3 km long, and the distance between neighboring stations is between 140 and 370 m. Stations 04 and 06 were not operational the whole time because of battery problems, and therefore they are excluded from the analysis. The geographical coordinates, surfaces, vegetation, the distance to the river, and mean fetches for each station are listed in Table 3. Station 01 is the only site that is not used agriculturally. For research purposes, it is covered only by bare soil without any vegetation. Stations 02, 05, 07, and 11 are placed on croplands that have already been harvested and the soil is visible. At the potato field, where station 03 is located, the soil is also visible. Stations 13 and 15 are placed on grassland in a small valley near the river. At the rest of the stations (08, 09, 10, 12, and 17) the crop has also already been harvested, but it still lies on the ground and covers the soil. Because the crop has been harvested at almost all stations, the state of the soil is more important than the type of vegetation. We also calculated mean fetches for each station weighted with the commonness of the wind directions north, east, south, and west. Most of the stations have a fetch between 50 and 100 m. Station 11 has the smallest fetch with only 23 m, followed by stations 10 and 09 with 42 and 49 m, respectively. These stations are located at the edges of fields. The longest fetches occur at station 12 with 113 m and station 05 with 189 m.

Table 3.

Geographical position, land use, distance to the river (dr), vegetation, and mean fetch for each station of the transect.

Geographical position, land use, distance to the river (dr), vegetation, and mean fetch for each station of the transect.
Geographical position, land use, distance to the river (dr), vegetation, and mean fetch for each station of the transect.

Three cold fronts passed the measurement site and caused rain events during the campaign on the first, fifth, and last days. The intensity of rainfall was similar at all stations, with a total amount of approximately 20 mm for each event. The mean soil moisture at the site is between 19% and 36%. It rises by approximately 7% after each rain event but decreases within three days to its initial amount. Most days were occasionally overcast; five days were cloud free. It was a warm summer period, with daily mean temperatures between 16° and 26°C. The highest temperature reached was 37.2°C; the lowest temperature was 8.3°C.

Each station is equipped with sensors for measuring 1-min means of air temperature, relative humidity, surface temperature, wind speed, and wind direction. The air temperature and relative humidity sensor is placed at 1.5-m height, and the wind sensor is at 2-m height. Stations 01, 03, 09, 10, 12, 13, and 15 are additionally equipped with devices for monitoring 1-min means of solar radiation.

4. Results

a. Variability of atmospheric conditions

To examine the variability of the atmospheric conditions, we use 1-min means of air temperature, specific humidity, surface temperature, and wind speed. Because there is no reference in our deployment that is considered to be the truth, we calculate the differences ΔTair, Δq, ΔTsurf, and Δυ between each station and every other station. The statistics of these samples are summarized in terms of the mean value and the 10th and 90th percentiles depicted by Fig. 3 for each station. The mean value represents the systematic deviation between two stations, and the percentile range reflects random deviations for an arbitrary 1-min interval.

Fig. 3.

Mean differences of (a) air temperature, (b) specific humidity, (c) surface temperature, and (d) wind speed over the whole measurement period for each station. The 10th and 90th percentiles are illustrated as error bars.

Fig. 3.

Mean differences of (a) air temperature, (b) specific humidity, (c) surface temperature, and (d) wind speed over the whole measurement period for each station. The 10th and 90th percentiles are illustrated as error bars.

The mean difference in air temperature in Fig. 3a ranges from −0.50 K for station 13 closest to the river to 0.31 K for station 01 farthest from the river, leading to a mean difference of 0.81 K between these two stations. The percentile range is 2–3 times the mean difference, ranging from 1.52 K at station 09 to 2.51 K at station 15. Therefore, the random deviations in air temperature variability are in general larger than systematic effects. Because the mean difference and Δp90−10 between the sensors during the calibration period were much smaller at 0.04 and 0.59 K, respectively (see Table 2), the differences between the stations are induced by the environment and not by sensor inaccuracies.

For the specific humidity in Fig. 3b the mean difference varies between −0.26 g kg−1 for station 05 and 0.24 g kg−1 for station 17. Only four stations, namely stations 11, 13, 15, and 17, show distinctly positive mean differences. Station 13 (07) shows the highest (lowest) variability with a percentile range of 1.36 (0.88) g kg−1. That is 2–3 times the percentile range during the calibration period. Thus, the variation in specific humidity is also mainly caused by random deviations.

In Fig. 3c the mean difference in surface temperature ranges from −2.37 K for station 15 to 1.09 K for station 03, leading to a mean difference of 3.46 K between these two stations. The percentile range varies from 4.00 K at station 09 to 5.63 K at station 15. That is less than 2 times the mean difference. For surface temperature the systematic errors play a more important role than for air temperature and specific humidity. Again these errors are barely caused by inaccuracies of the measurements. The percentile range during the calibration period was smaller by a factor of more than 4 at 0.83 K, and the mean difference was just 0.13 K.

The mean difference in wind speed in Fig. 3d ranges from −0.7 m s−1 at station 15 to 0.56 m s−1 at station 02, resulting in a difference of 1.26 m s−1. The percentile range is slightly higher, with values between 1.85 m s−1 at station 08 and 2.07 m s−1 at station 17. Both mean difference and percentile range are distinctly larger than during the calibration (0.002 and 0.42 m s−1, respectively). This result suggests that the systematic deviations have a great impact on wind speed variability.

These results raise the question of which factors cause the variabilities in the measurements. In Fig. 4 the mean differences and 10th and 90th percentiles are shown for day (left column) and night (right column) separately. For each station we divided the measurements into three different classes of wind speed: low wind speeds up to 1.2 m s−1 represented by the light-gray squares, moderate wind speeds between 1.2 and 2.5 m s−1 represented by the dark-gray circles, and high wind speeds of more than 2.5 m s−1 represented by the black diamonds. For the daytime, the moderate wind speed class includes almost 10 000 measurements for each station. Half that many data are available for high wind speeds, and the class of low wind speed is smaller by a factor of 3, with approximately 3200 measurements. During the nighttime low wind speeds dominate, with a total amount of 9000 measurements for each station. The class of moderate wind speed contains almost 2700 data points, and the class of high wind speed includes only 323 measurements.

Fig. 4.

Mean difference, 10th percentile, and 90th percentile of (a),(d) air temperature, (b),(e) specific humidity, and (c),(f) surface temperature for every station during (left) daytime and (right) nighttime. The light-gray squares refer to wind speeds lower than 1.2 m s−1, the dark-gray circles refer to wind speeds between 1.2 and 2.5 m s−1, and the black diamonds refer to wind speeds higher than 2.5 m s−1. On the x axis, the stations are ordered according to their distance to the river, starting with the one closest to the river. The letters refer to the different surfaces at the stations: G stands for grassland, V is for visible soil, C is for covered soil, and N indicates no vegetation.

Fig. 4.

Mean difference, 10th percentile, and 90th percentile of (a),(d) air temperature, (b),(e) specific humidity, and (c),(f) surface temperature for every station during (left) daytime and (right) nighttime. The light-gray squares refer to wind speeds lower than 1.2 m s−1, the dark-gray circles refer to wind speeds between 1.2 and 2.5 m s−1, and the black diamonds refer to wind speeds higher than 2.5 m s−1. On the x axis, the stations are ordered according to their distance to the river, starting with the one closest to the river. The letters refer to the different surfaces at the stations: G stands for grassland, V is for visible soil, C is for covered soil, and N indicates no vegetation.

The mean differences of the air temperature are shown in Fig. 4a for daytime and Fig. 4d for nighttime. The variability in air temperature is highest for low wind speeds. For moderate and high wind speeds, the mean values and percentiles are almost identical for day and night. The variability, however, is clearly lower for high wind speeds at night. Wind speed is obviously more important for mixing during stable nighttime situations. The influence of the river on nearby stations is largest for low wind speeds: Stations 11–15 are colder than the others during the daytime for low wind speeds and also during the nighttime for all wind speeds. Station 15 is coldest during the nighttime for all wind speeds. The nocturnal cooling is stronger at station 15 than at other sites, because this station is located in a valley. For low wind speeds the mean difference is −0.83 K. On the contrary, during the day it is one of the warmest stations for moderate and high wind speeds. The surface type and the fetch seem to have no impact on the air temperature for all wind speeds.

In Figs. 4b and 4e the specific humidity is shown for day and night, respectively. The most obvious difference between day and night is the variability. During the nighttime, Δp90−10 ranges from 0.43 to 1.04 g kg−1. In the daytime, it is 2 times as large, with 1.06–1.96 g kg−1. The river also seems to have an impact on the specific humidity during the daytime, especially for low wind speeds. Stations 11–17, closest to the river, are consistently more moist than the network mean. At night the influence of the river vanishes. For example, station 13, adjacent to the river, is drier than the average for all wind speeds. As with air temperature, the surface type and the fetch do not influence the specific humidity.

In contrast, the daytime surface temperature in Fig. 4c is clearly influenced by the land use. Stations 13 and 15 in the grassland area provide the lowest surface temperatures for all wind speeds. Their mean difference to the other stations is more than −2 K. The surface temperature at stations 08, 09, 10, 12, and 17, where the soil is covered with harvested corn, is higher than for the grassland stations. The mean difference ranges from −1.09 to 0.61 K. The highest temperatures for all wind speeds occur at stations where the soil is visible. The warmest temperatures are observed at station 07, which is more than 2 K warmer than the network average. The variability is lowest for low wind speeds. Otherwise, the wind speed does not have any clear effect on the surface temperature. At night, in Fig. 4f, the surface temperatures at the grassland stations are again distinctly lower than the network average. For the other stations, there is no noticeable influence of the surface type. The variability is smaller by a factor of 2–3 than during the daytime for moderate and high wind speeds. For low wind speeds, the difference remains almost the same. The highest anomalies of surface temperature are also seen for low wind speeds: Station 13 is 2.4 K colder than the network average, and station 01 is 1.67 K warmer. Therefore, the nocturnal wind speed has a greater influence on the surface temperature than does the surface type, likely because wind plays an important role in the exchange of air masses under stable stratification. The fetch and the distance to the river do not influence the surface temperature here. Indeed, the two stations closest to river show the lowest surface temperatures, but this effect is more due to the surface type than to the distance to the river.

b. Cluster analysis and error estimation

Setting up 13 stations in an area of 1.7 km × 1.4 km is not possible for most deployments, because it is very expensive. In this chapter, we describe the error that would emerge if a smaller number of stations was used. We analyze the following setup: Time series at all 13 sites are of interest, but direct measurements at certain sites are replaced by time series from another station. Two resulting questions will be addressed: 1) Which sites are more or less redundant and need to be observed only once? 2) How large is the resulting error in comparison with the full network? As a distance measure between the time series from two stations we use the RMSE.

To identify redundant stations we perform cluster analyses based on the average-linkage method [see textbooks like Wilks (2005)]. This is a hierarchical and agglomerative method: It starts with one cluster for each element and then progressively merges the elements or clusters whose centers are closest to each other. As a measure of distance between two clusters X and Y with NX and NY elements, respectively, we used the root-mean-square distance (RMSD):

 
formula

where dist(Xa, Yb) is the Euclidean distance between Xa and Yb.

This method always gives the same result, and the user can decide how many clusters are reasonable by looking at the RMSD values. Once an element is placed into one cluster, however, it cannot be relocated. To avoid this effect, we also performed a nonhierarchical method: the k-means method (e.g., Wilks 2005). Here the number of clusters k has to be given a priori. Then, k clusters are generated randomly and cluster centers are determined. Each element will be assigned to the nearest cluster center according to the lowest RMSE. After assigning each element to its nearest cluster, new cluster centers are computed and the elements are reassigned. These steps are repeated until there is no more reassigning. For this method, the results depend on the first random distribution in clusters. Therefore, the clustering varies from run to run. Both types of cluster analysis gave similar results, and therefore we will only show the average-linkage method here.

In Fig. 5, the results of the average-linkage cluster analysis are shown on the left-hand side for air temperature (Fig. 5a), specific humidity (Fig. 5b), and surface temperature (Fig. 5c). On the right-hand side, the error for using 2–13 clusters that are based on the average-linkage clustering is shown. We calculated the RMSE between each station and all other stations in a certain cluster. The mean RMSE is the average of the RMSEs of all stations in a certain cluster, represented by the solid black line. For the optimal RMSE, instead of calculating the mean RMSE of all stations, we chose the station that has the smallest RMSE and is therefore most representative for a certain cluster. The optimal RMSE is plotted as the dotted gray line.

Fig. 5.

(left) Cluster analysis and (right) RMSE of (a),(d) air temperature, (b),(e) specific humidity, and (c),(f) surface temperature for 1–13 clusters.

Fig. 5.

(left) Cluster analysis and (right) RMSE of (a),(d) air temperature, (b),(e) specific humidity, and (c),(f) surface temperature for 1–13 clusters.

The clustering for air temperature is displayed in Fig. 5a. For a better overview we look at the figure from top (1 cluster) to bottom (13 clusters). First stations 13 and 15 close to the river are separated from the others. In the next steps the rest is split into two clusters consisting of stations 01–09 and stations 10–12 plus 17. Later stations 01 and 02 are separated. Stations 03 and 05 are the most-alike stations. The RMSE and the optimal RMSE in Fig. 5d get smaller with increasing cluster number, except for 6 clusters. Using just one station to represent the whole area, the RMSE is 0.86 K. Choosing the most representative station (station 09) reduces the RMSE to 0.79 K. Adding stations leads to a decrease of RMSE between 0.07 and 0.1 K per station until a total number of five stations. After that the reduction of RMSE for one additional station is smaller.

The optimal number of clusters depends on the researcher’s requirements. One additional station increases the accuracy but also the costs. Although the choice of station number is subjective, a clustering with five stations gives reasonable results. The RMSD between these five clusters is more than 0.68 K. That is 0.43 K more than the mean RMSE between the sensors during the calibration period (see Table 2) and, therefore, a significant difference between the clusters. The distribution into these particular clusters can be explained by their geographical position and, therefore, their distance to the river. Cluster 1 includes the two stations that are farthest from the river. Cluster 2 consists of stations that are more than 0.6 km but less than 1.3 km from the river. The distance between the stations in cluster 3 and the river ranges between 0.26 and 0.57 km. Station 13, the one closest to the river, and station 15, located on the grassland next to the river, constitute their own clusters. The mean RMSE for this clustering is 0.52 K. For each cluster the stations with the lowest RMSEs are chosen to calculate the optimal RMSE. For cluster 1, with only two stations, no decision can be made; clusters 4 and 5 only consist of one station. Stations 08 and 11 are most representative for clusters 2 and 3, respectively. The optimal RMSE for using only stations 01 or 02, 08, 11, 13, and 15 is reduced to 0.49 K.

The results for specific humidity are shown in Figs. 5b and 5e. First station 13 closest to the river is split from the rest. In the next two steps stations 15 and 17 are first separated from the other stations and then form their own clusters. Then the big cluster is subdivided into two smaller clusters containing stations 01–09 and stations 10–12 and 17. The two sites most similar are stations 07 and 08. As a reasonable number of clusters, we chose again five. According to the average-linkage method the RMSD between these clusters is at least 0.46 g kg−1. This is considerably larger than the mean RMSE of 0.18 g kg−1 between the sensors during the calibration period. The cluster analysis provides the following five clusters: cluster 1 includes stations 01–09; cluster 2 includes stations 10–12; and clusters 3, 4, and 5 consist of station 13, station 15, and station 17, respectively. This is again a distribution that depends on the geographical position of the stations and, therefore, the distance to the river. Cluster 1 includes the most-northern stations that are more than 0.6 km from the river. The distance between the stations in cluster 2 and the river is between 0.26 and 0.57 km, and the stations are all located east of the river but southwest of cluster 1. The two stations closest to the river constitute their own clusters. Station 13 is located less than 20 m away from the river on the western side. Station 15 stands about 100 m west of the river. Station 17, which is located more than 0.45 km west of the river, forms its own cluster, too. The mean RMSE for these clusters is 0.5 g kg−1. For the optimal RMSE, stations 07 and 11 are selected as most representative for clusters 1 and 2, respectively. The optimal RMSE for a deployment with only stations 07, 11, 13, 15, and 17 is 0.47 g kg−1.

The cluster analysis and RMSEs for surface temperature are shown in the bottom panels of Fig. 5. The clustering in Fig. 5c starts identically to the clustering for air temperature. Initially, the two stations closest to the river, 13 and 15, are separated from the rest. Then the primary cluster is subdivided into two smaller clusters, independent of their geographical position. Station 17 again constitutes its own cluster. Stations 07 and 11 are most alike. The RMSE in Fig. 5f decreases with increasing number of clusters. For using just one station it is 1.4 K, but for three clusters it decreases by almost one-third to 1.04 K. Adding more stations reduces the RMSE by less than 0.1 K per station. Therefore, we chose three clusters as our reasonable example: Cluster 1 consists of stations 02, 03, 05, 07, 11, and 17; cluster 2 includes stations 01, 08, 09, 10, and 12; and the third cluster consists of stations 13 and 15. The RMSD between these three clusters is, at 2 K, 5 times the mean RMSE between the sensors during the calibration. In contrast to the clustering for air temperature and relative humidity, this classification depends on the surface type. As described in Table 3, all stations that form cluster 1 are located at sites where the soil is visible, except for station 17, which is added to that cluster at the highest RMSD level for these three clusters. The cluster-2 stations stand on surfaces for which the soil is covered with harvested crop or for which there is no vegetation at all. In contrast, stations 13 and 15 of the third cluster are placed on grassland. Having one station on each of these surface types gives a mean RMSE of 1.04 K. It is reduced to 0.97 K when using only the most representative stations for each cluster (station 05 for cluster 1 and station 08 for cluster 2).

The clustering of surface temperature time series can also be explained by the surface energy balance: It is reasonable to expect that the latent heat flux is highest for grass and decreases successively from sparse vegetation to bare soil, since plant evaporation becomes less relevant. If we assume that the net radiation is similar at all sites, the sensible flux will vary the other way around. Following the commonly used flux–gradient relations, the sensible heat flux is proportional to the temperature gradient. If we assume similar drag coefficients at the sites and neglect atmospheric temperature variability since it is only one-third of the surface temperature variability (see Fig. 3), high daytime surface temperatures will result in large sensible heat fluxes. Indeed, Fig. 4 indicates that daytime surface temperatures are highest for the bare-soil cluster (stations 02, 03, 05, 07, 11, and 17) followed by the sparsely vegetated cluster (stations 08, 09, 10, and 12), and the grassland cluster exhibits the smallest surface temperatures (station 13 and 15).

5. Summary and conclusions

This study demonstrates that a wireless sensor network is an appropriate tool to examine the small-scale variability of atmospheric conditions near the surface. Using measurements of 13 stations, we studied the influence of the environment on air temperature, specific humidity, and surface temperature over a summer period of 22 days in western Germany. The error that is made by the traditional approach of using only a single station can also be estimated by using measurements of a network.

It turned out that for this deployment the air temperature is mainly influenced by the distance to the river that is crossing the site and by the wind speed. For wind speeds of less than 1.2 m s−1 the air temperature variability is 2 times that for wind speeds of more than 1.2 m s−1. The mean difference between the station closest to and farthest from the river amounts to 0.8 K. One reason is the formation of cold air during nighttime close to the river. The total amount of specific humidity is also mainly influenced by the distance to the river, especially during the day and for low wind speeds. The five stations closest to the water are distinctly more moist than all other stations. The variability of specific humidity is halved during the night relative to daytime measurements. In contrast, the surface temperature is mainly affected by the surface type and land use. At stations where the soil is visible, the surface temperature is clearly higher than at stations where the soil is covered. The surface temperatures are lowest over grassland. The variability in surface temperature is 2–3 times as high during daytime as it is during nighttime for wind speeds higher than 1.2 m s−1. For low wind speeds the variability is almost the same for day and night.

Because such dense networks are not available in general (e.g., owing to cost), we investigated the error evolving from using a smaller set of stations. We used cluster analyses to design these smaller sets. The mean error in air temperature for using just one station instead of all 13 is 0.86 K. Selecting the most representative stations reduces this uncertainty only marginally to 0.79 K. For five stations the mean error is reduced by more than 0.3 K, to 0.52 K, and for the optimal stations it is reduced to 0.49 K. For the specific humidity the mean error for using only one station is 0.67 g kg−1. Adding more stations reduces this error by approximately 0.045 g kg−1 per station. The mean error in surface temperature for using one station is 1.4 K. Adding two more stations reduces this error to 1.04 K. Using only the most representative stations leads to errors of 1.24 and 0.97 K for one and three stations, respectively. It is up to the user to decide how many stations should be erected at a site and, therefore, how accurate the measurements will be.

Wireless sensor networks can also be helpful to validate model results, since they allow for more accurate estimates of gridbox means. Our sensor network provides measurements of air temperature, humidity, surface temperature, wind, and solar radiation at a high spatial and temporal resolution. For many micro- and mesoscale models that consider the surface energy balance, precise information about these meteorological conditions is inevitable. With datasets from our network an independent validation of these kinds of models is feasible.

Furthermore, information about the small-scale variability is becoming increasingly important for models. Recently proposed turbulence schemes (e.g., Mauritsen et al. 2007) consider in addition to the turbulent kinetic energy also the turbulent potential energy, that is, temperature variabilities, which are now directly observable by the sensor network. Resolving the surface heterogeneity explicitly by refining the model grid is computationally too expensive. Thus many models make use of mosaic or tiling approaches. These approaches assume that only the land surface needs to be refined and that the atmospheric variability can be neglected. Many details of such parameterizations are still under debate (e.g., Ament and Simmer 2006), however: Is it sufficient to subdivide an atmospheric grid box into fractions of different land use (“tiling approach”; Avissar and Pielke 1989), or do we need an explicit subgrid (“mosaic approach”; Seth et al. 1994)? Is it necessary to consider the atmospheric variability by a statistical scheme as, for example, proposed by Schomburg et al. (2010)? For instance, the finding of this study that surface temperature variability is dominated by the land-cover type clearly supports the tiling technique. In this way, future analysis and applications of the sensor network will provide new observational guidance for the development of parameterizations of exchange processes of heterogeneous land surfaces.

Acknowledgments

The data used in this studied were collected within the Transregional Collaborative Research Center (SFB/TR) 32 project Patterns in Soil–Vegetation–Atmosphere Scheme: Monitoring, Modelling and Data Assimilation. We thank the organizers for giving us the opportunity to be part of the project. Especially we are grateful to Jan Schween and Alexander Graf for their assistance in the field work. We also acknowledge the landowners, who allowed us to deploy our stations on their fields. We thank Peter Hoffmann and Andrea Lammert-Stockschläder for fruitful scientific discussions and David Flagg for careful proofreading.

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