Near-surface wind variability over spatiotemporal scales relevant to plume tracking insects

Abstract

Odor plume tracking is important for many organisms, and flying insects have served as popular model systems for studying this behavior both in field and laboratory settings. The shape and statistics of the airborne odor plumes that insects follow are largely governed by the wind that advects them. Prior atmospheric studies have investigated aspects of microscale wind patterns with an emphasis on characterizing pollution dispersion, enhancing weather prediction models, and for assessing wind energy potential. Here, we aim to characterize microscale wind dynamics through the lens of short-term ecological functions by focusing on spatial and temporal scales most relevant to insects actively searching for odor sources. We collected and compared near-surface wind data across three distinct environments (sage steppe, forest, and urban) in Northern Nevada. Our findings show that near-surface wind direction variability decreases with increasing wind speeds and increases in environments with greater surface complexity. Across environments, there is a strong correlation between the variability in the wind speed (i.e., turbulence intensity) and wind direction (i.e., standard deviation in wind direction). In some environments, the standard deviation in the wind direction varied as much as 15°–75° on time scales of 1–10 min. We draw insight between our findings and previous plume tracking experiments to provide a general intuition for future field research and guidance for wind tunnel design. Our analysis suggests a hypothesis that there may be an ideal range of wind speeds and environment complexity in which insects will be most successful when tracking odor plumes over long distances.

I. INTRODUCTION

Across many species and ecosystems, the ability to successfully localize viable food sources or mates through olfactory search is critical for their survival. From shrimp to sharks^1,2 and moths to mammals,^3-5 there are countless examples of aquatic, terrestrial, and aerial animals that rely on the synergy of multiple sensory modalities to track odor plumes to their sources. The sensory experience of a plume tracking animal is determined by their movement as well as the shape and statistics of the plume, which are in turn governed by the characteristics of the fluid medium responsible for its advection. In laminar flow, odor plumes take on a simple ribbon-like shape,^3,6 whereas plumes in more turbulent flow become more dispersed and broken up.^7-9 Field studies in turbulent air flow with moths¹⁰ and fruit flies¹¹ suggest that insects can still be quite successful plume trackers on spatial scales of 10–100 m and time scales of tens of minutes despite the flow complexity caused by turbulence. To better understand both flying insects’ plume tracking algorithms and the ecological pressures that have driven their evolution, it is important that we characterize the spatial and temporal statistics of natural wind on the scale of tens of minutes across 10–100 m and in different environments that flying insects encounter.

The study of wind is quite broad, with applications spanning from the lowest portion of the atmosphere (surface roughness sublayer) through higher altitudes. First introduced in 1954, the Monin–Obukhov similarity theory (MOST) is widely used as a general framework for quantifying atmospheric stability and turbulence.¹² Although MOST is often used to describe the vertical wind profile spanning up to the lower layer of the troposphere, this relationship does not hold within the surface roughness sublayer, posing challenges for successfully classifying near-surface wind conditions in highly vegetated or urban areas.^13,14 The challenge of classifying near-surface wind conditions is often compounded in microscale environments (<1 km²) due to increasing surface heterogeneity caused by land development.^15,16 Efforts have been made toward developing a mathematical framework for describing the wind profile within plant canopies;^17,18 however, these frameworks typically assume a homogeneous environment and require measurement of heat flux induced by vegetation. Furthermore, plant canopy wind models are not generally applicable in other environments, such as cities or sparse-vegetation landscapes.

Prior atmospheric and fluids studies have sought to statistically quantify near-surface wind patterns for applications in weather modeling, urban pollution dispersion, and wind energy production.^19-21 Near-surface nocturnal wind regimes have been of particular interest due to the higher occurrence of submeso motions and other flow phenomena, which become more readily observable in strongly stable nocturnal atmospheric conditions.^22-24 Mahrt²⁵ and Mahrt et al.²⁶ assessed data collected from multiple environments and described temporal changes of wind direction and speed variability over scales of approximately 10–15 min in nocturnal conditions. These studies found that standard deviations in the wind direction are inversely related to the wind speed with directional variability highest in wind speeds less than 2 m/s. There are undoubtedly many nocturnal insect species for which these prior studies would be applicable.

Near-surface wind regimes in complex urban areas are also of particular interest for researchers seeking to improve existing pollution models.^27-29 Both Hanna et al.²⁸ and Pirhalla et al.²⁹ used an array of wind sensors distributed across various heights and distances within areas of less than 1 km to assess patterns in urban wind variability. Since wind profiles in the urban environment are not well understood, these works explored statistical quantities at and above the street level. Hanna et al.²⁸ found horizontal and vertical turbulence intensities measurements from two different cities to be in general agreement, suggesting that near-surface turbulent characteristics may be similar across urban areas. Other case studies have examined wind profiles specific to an area of interest for wind energy assessment.^30-32 Though these efforts have all contributed to our collective knowledge of near-surface wind patterns, we still do not have a comprehensive understanding of the fine-scale wind direction and wind speed variability, which occurs across environments of varying surface complexity in daytime convective processes. Here, we seek to compare short-term wind variability across three distinct environments as a means of gaining intuition on the key differences an insect might experience while actively tracking an odor plume.

To gain insight into daytime microscale wind conditions, we collected near-surface wind data in three qualitatively distinct environments in Northern Nevada (playa/sage steppe, urban, and forest) and statistically quantified temporal and spatial variability in direction and speed. Since our goal was to understand the significance of wind variability over scales relevant to a plume tracking insect, we focused our analysis on wind patterns occurring over periods of less than 15 min, across distances of less than 200 m, and at an altitude of 2 m above the ground. Prior field research has documented male gypsy moths flying within 1 m from the ground while tracking female pheromones,³³ and other works suggest that insects, such as Drosophila and honeybees, adjust their flight altitude based on the wind speed to maintain a constant optic flow.³⁴ Though the average altitude that insects inhabit may vary based on environment, comparing wind observations at a height of 2 m above the ground level across environments provides insight in the sensory information that a wide variety of insects may be likely to experience while actively tracking an odor. Our findings indicate that near-surface wind patterns over these spaces and time ranges are most consistently variable in low wind speeds and in environments with a higher surface complexity.

II. METHODS

A. Site descriptions

Wind data were recorded across various locations in Northern Nevada (Fig. 1). Three qualitatively distinct environments were chosen for this work: playa/sage steppe, forest, and urban areas. The playa environment (Black Rock Desert) can be characterized as open, flat, and sandy with no vegetation. The sage steppe environment (Lemmon Valley) was an open area with surrounding hills approximately 0.5–1 km away, with an average vegetation height of approximately 0.75 m. Qualitatively, we grouped these environments together as “open” landscapes, though there is a distinction in wind profiles due to differences in surface roughness elements.

FIG. 1.

Locations, descriptions, and dates of data collection. Sensors were generally oriented in “L” shape, though this orientation varied slightly across data collections. Each environment will be referred to as its general landscape in subsequent figures. Surface roughness values were estimated based on prior literature.^14,35 Sagehen Creek Field Station photo image credit to Sebastian Wolf, 06/07/2018.

Both of the forest sites can be characterized as mature coniferous with a mean tree height of approximately 20–30 m. The three urban sites were located within Reno, Nevada. All three sites were enclosed by fences approximately 2 m in height. The fences surrounding urban sites one and two were wooden, whereas urban site three had a mix of chain-link and wooden fencing. The surrounding buildings for all urban sites were approximately 6–12 m tall. Representative pictures are included for each environment in Fig. 1. Additionally, Figs. S1 and S2 show representative horizontal wind speed, horizontal wind direction, and vertical velocity time series for each data collection. Together, these figures demonstrate a diversity of wind speed and direction conditions recorded across days and locations.

B. Instrumentation and setup

Wind recordings were measured with 3D ultrasonic anemometers (TriSonica^™ Mini, Anemoment, Longmont, CO) at a rate of 10 Hz. The TriSonica^™ Mini has a specified accuracy of ±0.2 m/s in wind speeds between 0 and 10 m/s, ±0.2% m/s in wind speeds between 11 and 30 m/s, and ±1° for wind direction. The anemometers were arranged on tripods at approximately 2 m above the ground level and at distances spanning from 1 to 200 m apart. The spatial layout of sensors varied slightly across data collections based on site constraints. Sensors were generally oriented in “L” shape in all data collections aside from the playa, where sensors were arranged in a 3 × 3 grid. The “L” shape configuration allowed for more variation in the distance between sensors while still encapsulating potential differences caused by landscape heterogeneity. These sensors were manually leveled and oriented toward north with compass readings prior to each experiment. Teensy 3.5 controllers with microSD cards were used for data logging. A separate GPS receiver [GP-20U7 (56 Channel), SparkFun] recorded time and location information.

In total, nine anemometers were utilized throughout our collections. Since the TriSonica^™ Mini’s design obstructs some vertical flow, we placed 1–2 sensors in a vertical orientation to obtain more accurate vertical flow measurements (sensor orientations shown in Fig. 1). In some instances, recording malfunctions, adverse weather conditions, and/or wildlife interactions resulted in the loss of recording for certain sensors. In some collections, sensors were set up for multiple days. It is well known that wind regimes shift between night and daytime;³⁶ therefore, for consistency across locations, only daytime data (at least 1 h after sunrise and 1 h before sunset) were utilized for this analysis.

To quantitatively distinguish between each distinct environment, we assigned each environment an estimated aerodynamic surface roughness length based on prior literature.^14,31,35 Though methods for estimating surface roughness with single level anemometer data have previously been proposed,¹⁵ they generally require sensor placement above the roughness elements, which was not possible in our forest and urban experiments.

During data pre-processing, minor time measurement offsets were corrected through interpolation. To verify sensor accuracy and noise levels, we recorded measurements in a laminar flow wind tunnel at three different wind speeds (Fig. S3). Based on these measurements, we chose two different filtering parameters to smooth wind measurements and ran our analysis using both the filtered and unfiltered data. Filtering did not have a strong effect on our results; therefore, all analyses included in this paper were conducted on the unfiltered data. More information about the filtering parameters used can be found Figs. S3 and S4.

C. Statistics: multiple linear regression analysis

Microscale wind dynamics can be influenced by the environment’s surface complexity, mean wind speeds, and the distance over which wind travels. To quantitatively compare the way these key variables might impact wind speed and wind direction, we conducted multiple linear regression (MLR) using general least squares. In several cases, model diagnostic plots indicated that residual standard errors varied between data collections. To account for this heteroskedasticity and potential correlation within group observations, we implemented cluster-robust standard errors by assigning a group number to each data collection. Regression covariates were z-score normalized to improve the interpretation of their relative effect size within each MLR model. To verify that independent variables were not strongly correlated within a model, which would impact both the coefficient estimates and the corresponding p-values, variance inflation factor (VIF) was used to assess the covariate structure of our data. All covariates had VIFs between one and four, indicating that there was no significant multicollinearity present. Statistical diagnostic plots for each model are included in Fig. S5.

1. Spatial comparisons: variation in wind characteristics as a function of distance

To visualize the variation of wind direction and speed over distance, we computed the difference in the direction and speed at all points in time between each permutation of two sensor pairs. This resulted in a total of 30 to 42 paired comparisons per experiment, with slight variation across experiments due to sensor malfunctions. Though limited works have sought to quantify the time span over which insects typically track a localized odor in outdoor environments, prior release and recapture studies suggest that a fair few of tracking events on the scale of 0–200 m will occur within 10-min.^11,37 Correspondingly, we chose to average observed differences between sensors over discrete 10-min intervals. We, then, calculated the distance between sensors using the recorded GPS coordinates. To ensure that our GPS recordings were sufficiently accurate, we manually measured the distance between sensors on several experiments and compared those measurements to the GPS readings. The recorded GPS measurements were always within 2–3 m of our manual measurements, which is in agreement with the accuracy specified by the GPS manufacturing company and did not have any impact on the interpretation of our results. Since some data were collected on privately owned land, latitude and longitude information was converted to Cartesian coordinates in preparation for making the data publicly available.

To control for the fact that data were collected on different days, in which atmospheric stability and large scale weather conditions may play a role, we used wind speed and direction data from a nearby weather tower (Sagehen Creek Station, CA) during the dates and times of each of our data collections as a variable in our spatial regression analysis (general location shown in Fig. 1). These data are managed by the Western Regional Climate Center (WRCC) and is publicly available on their website. The automated weather station is positioned at a height of 30 m and records the mean wind speed and standard deviation in the wind direction over discrete 10-min intervals. The distances between this tower and our data collections varied from approximately 10–55 km, with the exception of the Black Rock Desert, which is approximately 225 km from the Sagehen Creek Field Station.

2. Temporal comparisons: variation in wind characteristics over time

It is well known that wind is both spatially and temporally variant. To better understand microscale temporal variation, we investigated the changes in the wind direction and speed for different time intervals. This was done by analyzing time series data from one singular wind sensor, as opposed to comparing differences in data between pairs of sensors. To simplify the interpretation of covariate effects across data collections, MLR was chosen for temporal analysis rather than other available time series analysis methods. To do this, we analyzed how the wind direction and wind speed from each data collection varied over time by computing the standard deviation and mean values of speed and direction over time windows ranging from 0 to 10 min at randomly chosen points throughout each dataset.

Since the standard deviation in wind speed values has no upper limit, we normalized these calculations using the mean horizontal wind speed, giving a non-dimensional value, which is commonly referred to as turbulence intensity³⁸ and can be defined as

$$T_i=\frac{{\sigma }_h}{U},$$ (1)

where ${\sigma }_h$ is the standard deviation of horizontal wind speed, and U is the mean horizontal wind direction.

We implemented similar methods when conducting MLR analysis on the vertical velocity measured by our vertically oriented sensors. To standardize values across datasets, we used vertical turbulence intensity, defined as

$$T_{iw}=\frac{{\sigma }_w}{U}.$$ (2)

This quantity has been used as a proxy for atmospheric stability and as an estimate for vertical shear in prior field studies seeking to quantify wind profiles in the lower atmospheric boundary layer.^28,29

In addition to MLR, we investigated temporal variation across environments using both autocorrelation and frequency domain analysis. These methods, however, were not particularly informative of environment driven differences on the timescale of 0–10 min. Figure S7 shows the mean power spectral densities of horizontal wind speed and direction for each data collection using discrete 10 min intervals. In most cases, the power spectra were similar, with the exception of several days in which wind direction was constant for the majority of sampling time.

The shortcomings of these analyses motivated further visual exploration of the time driven changes in the wind direction, eventually leading to the use of probability density distributions. By calculating the standard deviation in the direction over time windows ranging from 10⁻¹ to 10³s for all points throughout each data collection, we were able to construct density heatmaps, which show the relationship of the standard deviation of wind direction over different time windows for a given time series.

D. Wind direction computations

All calculations involving the wind direction were adjusted to account for circularity. When finding the difference in the direction between sensors, we used the smaller angle such that the difference was always bounded in the range of 0°–180°. The circular mean was computed using the following equation:

$$\overline{\theta }=\text{arctan}\left(\sum _{j=1}^n\sin {\theta }_j,\sum _{j=1}^n\cos {\theta }_j\right),$$ (3)

where $\overline{\theta }$ represents the mean angle. The circular standard deviation in the direction was calculated as

$${\sigma }_{\theta }=\sqrt{2(1-R)},$$ (4)

such that ${\sigma }_{\theta }\in [0,\pi ∕2]$, where

$$R=\Vert \sum _j^n\left(\begin{array}{c}\hfill \cos ({\theta }_j)\hfill \\ \hfill \sin ({\theta }_j)\hfill \end{array}\right)\Vert .$$ (5)

These relations are well documented in the circular statistics literature.^39-41

III. RESULTS

A. Variability of wind speed and direction across space

To understand spatially driven near-surface wind variation, we compared the absolute difference in the horizontal wind direction and speed between pairs of sensors over discrete 10 min periods. Figure 2(a) demonstrates this differencing method for two sensors over a time period of 50 min. By repeating this calculation for all permutations of two sensor pairs across each data collection, we recovered statistics, which provide intuition on how different wind observations were for a given time period over distances ranging from 0 to 200 m. Table I details MLR results using the data shown in Fig. 2(a) where the 10-min mean difference in the direction between sensors is the dependent variable and the independent variables are the 10-min mean wind speed, estimated environment surface roughness, and distance between sensors. Similarly, Table I details MLR results using the data shown in Fig. 2(b) where the 10-min mean difference in the wind speed between sensors is the response variable. The following subsections detail relationships observed as a function of these wind direction and speed differences.

FIG. 2.

Spatial variability in wind direction is primarily correlated with wind speed and environment surface complexity. (a) Visual demonstration of difference in direction calculations between two signals recorded at a distance of 80 m apart. (b) Summary statistics showing the 10-min mean difference in wind direction between sensors as a function of distance, wind speed, and estimated surface roughness. (c) Summary statistics showing the 10-min mean difference in wind speed between sensors as a function of distance, wind speed, and estimated surface roughness.

TABLE I.

Multiple linear regression coefficients, standard errors, and p-values for (a) absolute difference in wind direction between sensors (adjusted $R^2=0.662$) and (b) absolute difference in wind speed between sensors $R^2=0.229$. Estimated surface roughness was used as a proxy for environment as a means of quantifying surface complexity. The 10-min standard deviations in wind direction and 10-min mean wind speeds measured by the Sagehen Creek Field Station were used as a control in regressions A and B, respectively.

Variable	Normalized coefficient	Standard error	P-value
(a)
10-min mean wind speed	−0.7318	0.093	<0.001
10-min mean wind speed × environment	−0.3207	0.073	<0.001
Environment	0.3207	0.094	0.001
Intercept	−0.2999	0.140	0.032
Distance × environment	−0.2364	0.139	0.089
Control × environment	0.1412	0.036	<0.001
Control	−0.0717	0.045	0.108
Distance	0.0712	0.163	0.662
(b)
10-min mean wind speed	0.8563	0.207	<0.001
10-min mean wind speed × environment	0.5491	0.157	<0.001
Environment	0.3326	0.123	0.007
Intercept	0.2826	0.125	0.024
Distance × environment	0.0529	0.067	0.430
Distance	0.0511	0.069	0.459
Control	−0.0305	0.055	0.580
Control × environment	0.0044	0.055	0.936

1. Directional variability decreases with increasing mean wind speed

From our regression analysis, we found the difference in the wind direction between sensors to be most strongly correlated with mean wind speed (normalized coefficient = −0.7318, p-value < 0.001, Table I). Across all data collections, the difference in the wind direction was highest when mean wind speeds were less than 2 m/s, with variability dropping significantly around the 3 m/s threshold [Fig. 2(b)]. This phenomenon is consistent with the prior atmospheric science literature indicating that wind direction variability is highest in low wind speed conditions.^22,25,42

This MLR model contained some residual heteroskedasticity (Fig. S5). While running diagnostics, we found that the majority of heteroskedasticity was due to the transitional relationship between the mean wind speed and wind direction, which occurs when wind speeds increase beyond approximately 2 m/s. Implementing the same regression analysis on a subset of the data in which mean wind speeds were constrained to under 2 m/s corrected for the majority of residual heteroskedasticity. This correction did not strongly impact regression standard errors due to the use of cluster-robust covariance; however, the normalized coefficient for the mean wind speed dropped to −0.4943 (p-value < 0.001). This indicates that the mean wind speed may become a more dominate influence of wind direction variability above the 2 m/s threshold.

2. Environments with higher surface complexity exhibit larger directional variability

Environment complexity (quantified by using estimated surface roughness) also corresponded with greater differences in direction measurements between sensors (normalized coefficient = 0.3027 and p-value = 0.001). There was a clear difference in directional changes observed between the playa and urban environments, whereas directional differences observed in the sage steppe and forest environments had more similar distributions [Fig. 2(b)]. Interestingly, the mean difference in the direction between sensors was higher in sage steppe (43.90°) than in forest (38.86°). Even still, the observed range of minimum and maximum differences was lower in sage steppe, and the spread of the interquartile range was smaller (26.57° vs 32.92° for sage steppe and forest, respectively).

3. Spatial differences in wind direction do not significantly vary over distances less than 200 meters

The 10-min mean difference in the wind direction across sensors did not significantly depend on the distance alone (p-value = 0.662) or on interactions between the distance and environment (p-value = 0.089). Figure 2(b) shows a visible upward linear trend of approximately 5° over 200 m in forest and sage steppe environments, although the range of differences observed between sensors still varied as widely as 20°–100° across all distances. Across all urban experiments, the mean difference in the wind direction between sensors was approximately 30° greater than that in the sage steppe and forest environments, indicating strongly turbulent flow. Though there is no strong linear relationship between difference in the direction and distance between sensors, Fig. 2(b) hints at a non-linear relationship in the forest and steppe environments.

To determine if there was a statistically significant non-linear trend, we regressed the 10-min mean directional differences on distance for each environment using a quadratic model and used analysis of variance (ANOVA) to compare the result with a linear model (see Fig. S6 and Table SI). In both the forest and sage steppe environments, F-tests rendered significant p-values (<0.001) for the added quadratic term, indicating that the non-linear model better describes the observed directional differences over distances of 0–200 m. In the urban environment, the added quadratic term was not significant (p-value = 0.219). Since the urban experiments were conducted on privately owned land, our spatial distribution of sensors was constrained to areas less than 50 m². It is possible the observed trend in urban data would also show some non-linearity in larger open urban areas, such as city parks.

4. The effects of control data were minimal

The control data from the Sagehen Creek Field Station (10-min standard deviation in the direction observed at 30 m above the ground level) were not significant as a stand-alone predictor for difference in the direction between sensors (p-value = 0.108, Table I). This indicates that collecting data on different days did not strongly influence MLR results. The interaction term between our control data and estimated surface roughness was significant, though the coefficient itself was relatively small (normalized coefficient = 0.1412, p-value < 0.001). This indicates that a portion of the directional variability observed across environments may be attributed to the difference in locations that data were collected.

5. The absolute difference in speed between sensors showed no strong correlations

Figure 2(c) demonstrates that the absolute difference in the horizontal wind speed between sensors is not well described as a function of distance, mean wind speed, or environment. From MLR model results, we find that although several of the terms have significant p-values, the adjusted $R^2$ is quite low ($R^2=0.229$, Table I), suggesting that this model does not explain much of the variability. Further, the residual diagnostic plots in Fig. S5 indicated that this model had a particularly high level of heteroskedasticity and outliers.

To assess the impacts of these residual issues on model estimates and standard errors, we performed a Box Cox transformation $(\lambda =0.326)$ and removed outlier data. This corrected for most of the heteroskedasticity and resulted in an adjusted $R^2$ of 0.153, along with an approximate 10% reduction in normalized coefficient values for environment surface roughness and 10-minute mean wind speed. Though we include the MLR results (Table I) and residual diagnostic plots (Fig. S5) of the original model for ease of interpretation, the reduction in $R^2$ after transformation indicates that the difference in speed between sensors is not well predicted by distance, environment, or mean wind speed.

B. Variability of wind speed and direction over time

We initially investigated temporal driven variations in the wind speed and direction using autocorrelation and power spectral density analyses. Since temporal changes can be affected by both mean wind speed and environment, decoupling and quantifying the relative effects of each variable over small time windows proved challenging when using these methods. Figure S7 shows the 10-min averaged power spectral density for each day of data collected. The −5/3 Kolmogorov spectrum⁴³ roughly holds true for wind speeds in the frequency ranges between 10⁻¹ and 10¹ Hz over most days and environments. Although detailed spectral analysis of wind direction is uncommon, it has been previously addressed in several prior works.^44,45 van Doorn et al.⁴⁴ sought to identify statistical traits of wind direction and found a power curve with slope of −2 to generally fit the spectrum of their experimental data, noting that relationship to be characteristic of Brownian motion. Shishov et al.⁴⁵ observed that the directional spectrum of their data followed the power law with a slope of roughly −1, further noting that it was in the range of the typical −5/3 power law. Thus, we include the −5/3 power curve in both Figs. S7(a) and S7(b) for the reader’s reference. Other spectra characteristics were relatively indistinguishable when directly comparing environments.

The exploration of these two analyses made way for a sliding time window approach, which is illustrated in Fig. 3(a). Figure 3(b) shows three distinct wind direction conditions (consistent, large infrequent shifts, and constant fluctuations), and Fig. 3(c) displays the corresponding density heatmaps obtained by computing the standard deviation in the wind direction over time windows ranging from 10⁻¹ to 10³ s for all points throughout the given time series. It can be seen in all scenarios that there is a positive increase in ${\sigma }_{\theta }$ as the time window increases. In cases of consistent wind direction, ${\sigma }_{\theta }$ levels off within 1–2 s, whereas we see ${\sigma }_{\theta }$ level off at around 100 s in the most variable case. These three examples are included to provide intuition on the time driven variations in the wind direction and the typical time window length at which ${\sigma }_{\theta }$ levels out in different conditions.

FIG. 3.

Temporal variations in wind statistics can be captured by using varying time window lengths across the observed signal. (a) Illustration of sliding window calculations used to compute the temporal variations in ${\sigma }_{\theta }$, $T_i$, and $T_{iw}$ for each dataset. (b) Three examples of wind direction over time: constant, large infrequent shifts, and highly variable. (c) Standard deviation in wind direction over varying time windows from 10⁻¹ to 10³ s, calculated using the method described by A. (d) Summary statistics comparing the standard deviation in direction across environments over linearly spaced time intervals ranging from 0 to 10 min. (e) Summary statistics comparing the turbulence intensity across environments over linearly spaced time intervals ranging from 0 to 10 min. (f) Summary statistics comparing the vertical turbulence intensity across environments over linearly space timed intervals ranging from 0 to 10 min. There were no vertically oriented sensors in the playa, and thus, vertical turbulence intensity values from that data are absent.

1. Standard deviations in direction increase with increasing time windows

As can be seen in Fig. 3(d), the standard deviation in the direction $({\sigma }_{\theta })$ generally increased over time in all environments (normalized coefficient = 0.1809 and p-value < 0.001), though the relative effect size indicates that time window is less important than the mean wind speed and environment surface roughness (Table II). The temporal variations of each data collection can be seen with more detail in Fig. 4, which is organized as a function of overall mean horizontal wind speed and environment.

TABLE II.

Multiple linear regression coefficients, standard errors, and p-values for (a) standard deviation in wind direction (adjusted $R^2=0.519$), (b) turbulence intensity (adjusted $R^2=0.714$), and (c) vertical turbulence intensity (adjusted $R^2=0.610$). Estimated surface roughness is used as a proxy for environment. Corresponding residual diagnostic plots are included in Fig. S5.

Variable	Normalized coefficient	Standard error	P-value
(a)
Mean wind speed	−0.5640	0.141	<0.001
Environment	0.4068	0.114	<0.001
Mean wind speed × environment	−0.2365	0.121	0.050
Time window	0.1809	0.028	<0.001
Intercept	−0.1067	0.179	0.550
Mean wind speed × time window	−0.0440	0.012	<0.001
(b)
Std. deviation in direction	0.7667	0.072	<0.001
Environment	0.0988	0.050	0.049
Time window	0.0562	0.013	<0.001
Environment × std. deviation in direction	−0.0501	0.085	0.556
Intercept	0.0358	0.049	0.464
Time window × std. deviation in direction	−0.0293	0.014	0.037
(c)
Std. deviation in direction	0.5898	0.063	<0.001
Environment	0.3115	0.086	<0.001
Environment × std. deviation in direction	0.0967	0.077	0.207
Intercept	−0.0397	0.098	0.685
Time window	0.0544	0.019	0.004
Time window × std. deviation in direction	−0.0339	0.018	0.053

FIG. 4.

The standard deviation in wind direction generally increases for larger time windows and is a function of both wind speed and environment. We computed the standard deviation in wind direction over varying time window lengths for all points throughout each data collection. Each subplot (a)–(p) represents the probability distribution corresponding to a time series, which can be found in Figs. S3 and S4. Subplot (b) corresponds to data collected in the playa, but is grouped with the steppe environment for visual simplicity.

2. Standard deviations in direction are largely a function of environment and mean wind speed

From MLR results, we found that ${\sigma }_{\theta }$ was negatively correlated with the mean wind speed (normalized coefficient = −0.5640 and p-value < 0.001). Figure 3(d) shows that the relationship between ${\sigma }_{\theta }$ and mean wind speed was similar to the directional variability observed in our spatial analysis [Fig. 2(b)]. Furthermore, Fig. 4 demonstrates that the maximum value of ${\sigma }_{\theta }$ decreased with increasing mean wind speed across environments.

Environment surface complexity also played a sizable role in temporal variations of ${\sigma }_{\theta }$ (normalized coefficient = 0.4068 and p-value < 0.001). Although we collected wind data over a variety of days with differing conditions, the overall mean horizontal wind speed in forest and urban environments never exceeded 3 m/s. These observations indicate that near-surface mean wind flow may generally be lower in environments with more surface roughness elements.

Our results are consistent with prior temporal analysis of surface wind patterns in the nocturnal stable boundary layer.^25,27 Mahrt²⁵ reported values of near-surface ${\sigma }_{\theta }$ around 50° in nocturnal conditions under low wind speeds. Mahrt also found that ${\sigma }_{\theta }$ decreases substantially around the 2 m/s wind speed threshold. Although Mahrt primarily focused on nocturnal wind regimes, he did note that the standard deviation in the direction would typically be higher in day time regimes due to convective processes, as well as in more complex environments. These ranges are in agreement with our findings, though we see some higher values of ${\sigma }_{\theta }$ (up to approximately 75°) in the urban data.

3. Horizontal and vertical turbulence intensity are not impacted by time window length

Table II shows that although the relationship between the horizontal turbulent intensity $(T_i)$ and time window in our MLR model was statistically significant (p-value < 0.001), the normalized coefficient is very small (0.0562). The effect size of time window is equally small with respect to the vertical turbulent intensity $(T_{iw})$ (normalized coefficient = −0.0544, p-value = 0.004, and Table II). These results indicate that the time window size has very little effect on $T_i$ and $T_{iw}$ over the scale of 0–10 min. In addition to Figs. 3(e) and 3(f), direct relationships between the horizontal and vertical wind speed are included in Fig. S8 and demonstrate a general correlation between mean speeds and standard deviations in speed across environments.

4. Horizontal and vertical turbulence intensities are generally higher in environments with greater surface complexity

Figures 3(e) and 3(f) demonstrate that values of $T_i$ and $T_{iw}$ were generally larger in environments with higher estimated surface roughness. However, MLR results in Table II indicate that the relative effects of environment surface complexity appear to be much stronger with respect to $T_{iw}$ (normalized coefficient = 0.3115, p-value < 0.001) than with $T_i$ (normalized coefficient = 0.0988 and p-value = 0.049). Overall, values of $T_i$ were higher in the sage steppe environment than in the forest environment, whereas values of $T_{iw}$ were much closer in the steppe and forest environments. It is worth noting that these wind statistics were taken at a height of 2 m above the ground level and would likely be different for winds observed at canopy top in forest environments.

Several prior studies have been conducted within the urban surface roughness sublayer in an attempt to better understand the complexities of disturbed urban flow.^28,29 Hanna et al.²⁸ reported values of 0.3 for $T_{iw}$ in three different cities. Here, we report values closer to 0.4 for our urban data. Though these differences could be due to atmospheric stability on the days we collected data, Hanna and Chang⁴⁶ noted that the overall effects of atmospheric stability are expected to be minimal due to the strong mechanical mixing of wind forced by the surrounding buildings. Thus, we speculate that a possible reason for this discrepancy may be the positioning of our vertically oriented sensors, which were typically within 1–2 m of a fence or building and may have resulted in an increased vertical flow due to recirculating winds created by the surrounding fencing and infrastructures.

5. Horizontal and vertical turbulence intensity is strongly correlated with standard deviation in direction

From Figs. 3(e) and 3(f) and MLR results in Table II, it can be seen that both $T_i$ and $T_{iw}$ are strongly correlated with ${\sigma }_{\theta }$. These relationships are logical, given that $T_i$, $T_{iw}$, and ${\sigma }_{\theta }$ are often used as general indicators of near-surface turbulence. This relation may be of particular interest to researchers interested in replicating natural wind conditions in wind tunnels, since it is possible to increase $T_i$ by manipulating wind shear through changes in the wind speed (e.g., Ref. 47) without inducing large values of ${\sigma }_{\theta }$ due to the geometry of typical wind tunnels constraining flow to move on average in one direction.

IV. DISCUSSION

Our results highlight that near-surface wind variability over spatial and temporal scales relevant to foraging insects is primarily influenced by the mean wind speed and environment surface complexity. Consistent with prior literature, we find that wind directional variability is inversely proportional to the mean wind speed. We further observe that increases in surface complexity contribute to higher variation in the wind direction both temporally and spatially. Notably, there was a strong relationship between turbulence intensity and the standard deviation in the direction. Though our results indicated that spatial variation and timescale have some impact on wind variability, these impacts are much smaller than those caused by both environment and wind speed.

A. Significance of wind speed on near-surface wind variability

Across environments, wind direction variability decreases with increasing wind speeds. This effect becomes increasingly pronounced when mean speeds surpass the 2 m/s threshold. Though insects can passively travel in higher wind speeds, they must actively navigate through wind when tracking an odor plume. The range of wind speeds in which insects have been observed performing these tasks varies based on the size of the insect. Wind tunnel experiments with moths show that they can successfully navigate mechanically induced turbulent conditions in 1 m/s wind speeds,⁴⁸ whereas Drosophila tracking tasks are typically conducted in wind speeds around 0.4 m/s.^49,50 Field studies suggest that at wind speeds higher than 1 m/s, Drosophila are likely to be substantially advected by the wind.¹¹ Furthermore, field based studies with bees show that flower foraging rates drop in higher wind speeds.^51-53 Hennessy et al.⁵³ found a 38% decrease in flower visits by bees when wind speeds increased in the range of 0–1 to 2.5–3.5 m/s. Together, these prior studies suggest that many insects are most likely to perform odor plume tracking behaviors in wind speeds of less than 3 m/s.

From our results, we expect that insects tracking odor plumes in the 0–2 m/s wind speed range will also experience higher levels of directional variability, leading to more meandering and disperse plume shapes. Talley et al.⁴⁸ reported that moths in wind tunnels performed better with mechanically induced turbulence than in purely laminar flow due to the two to threefold increase in the plume’s cross-sectional area 1 m downwind. Though $T_i$ was not quantified in this study, Talley⁵⁴ gave more information on the turbulence intensity observed in their setup, with reported values of $T_i$ around 5%–20% depending on measurement location within the tunnel. ${\sigma }_{\theta }$ was not quantified, but was likely small compared to the values we observe in outdoor environments due to the constraints of a unidirectional wind tunnel. In a recent field study, Crall et al.⁵⁵ found that temporal changes in the wind speed and turbulence increased the amount of bee visits to fragmented forested sites due to increases in odor dispersion. Both of these results support the idea that insects may be better equipped to extract odor plume information in wind conditions with higher directional variability. In wind tunnels, generating larger values of $T_i$ is generally easier than creating higher fluctuations in ${\sigma }_{\theta }$ due to fan orientation constraints. Since we see that $T_i$ is strongly correlated with ${\sigma }_{\theta }$, the ability to increase ${\sigma }_{\theta }$ in future wind tunnel experiments will be important for uncovering insect tracking strategies in more natural wind conditions.

B. Significance of surface complexity on near-surface wind variability

Estimated surface roughness had the second largest effect size in both spatial and temporal regressions, indicating that the wind direction is largely a function of both wind speed and surface complexity. There was a distinct separation in directional variability and turbulence intensity between the least complex (playa) and most complex (urban) environments. This separation was not as clear when comparing differences between the sage steppe and forest environments. This may, in part, be due to the height of our sensor placement, which was approximately 1 m above the mean roughness element in the steppe experiments and approximately +20 m below the mean roughness element in the forest experiments.

There is evidence to support that the wind variability is elevated directly above surface roughness elements. The atmospheric layer just above the roughness elements is often referred to as the “mixing layer.”^38,56 Hanna et al.²⁸ observed consistently higher values of turbulence quantities “near and above H,” where H is the mean building height. Conversely, Drake et al.⁵⁷ noted less wind direction variability within the “bole-space” spanning from the ground to the lower canopy of a conifer forest when compared to wind direction observations above the canopy. From these works, we posit that less variability may have been observed in the steppe environment if wind was measured below the mean roughness element. Future field work aimed toward collecting data in various other environments, and geographical locations would help to fill the knowledge gap surrounding near-surface wind variability in environments of middling surface complexity.

Some of the analyses presented herein were limited due to the use of one sensor height. This impacted our ability to determine the atmospheric stability and more accurately estimate surface roughness values for each data collection. Even still, insects are typically not inhabiting higher air-spaces unless migrating. More information about the atmospheric conditions affecting these migration events are documented by Wainwright et al.^58,59 Though insects inhabit various levels of air space, an insect’s flight altitude while tracking an odor plume will generally be dictated by the height from which the odor is dispersed.⁶⁰ Since prior works suggest that insects will often travel closer to the ground while tracking an odor plume,^3,33 limiting analysis to the lowest level of the surface boundary layer provides insight on sensory information that an insect would have access to while actively pursuing an odor plume. Though there may be some large scale impacts on the local wind due to non-localized atmospheric instability, topography, and daytime heat convection, both the MLR control estimates in Table I and power spectral density analysis in Fig. S7 indicate that these impacts were not largely discernible on the timescale of 10 min.

C. How might wind variability relate to insect plume tracking success?

Figures S1 and S2 demonstrate the variability of wind speed and direction measurements observed across environments and days. In some cases, wind speeds were quite low, with highly variable wind direction. In other cases, the wind direction was fairly consistent. Overall, the wind conditions an insect might encounter are quite diverse, suggesting that insects may implement different odor tracking strategies based on prevailing flow conditions. Additionally, the time and length scales over which canonical cast-and-surge plume tracking can occur may be impacted by the wind variability an insect encounters. In open spaces, such as playa and sage steppe, overall mean wind speeds can often reach higher values than those in environments with greater obstructions. In these scenarios, insects may be utilizing the higher wind speeds and less variable wind direction to track plumes over larger distances than they would in more spatially complex areas. Though our findings suggest that the wind direction becomes less variable with increasing speed, prior studies indicate that insects can struggle to fly in high wind speeds. Taken together, we hypothesize that there may be an optimal range of conditions in which wind speeds do not present significant bio-mechanical disadvantages and environment surface complexity does not greatly obstruct wind direction, thus providing the optimal ratio of foraging options and wind conditions for successful long distance odor plume tracking (Fig. 5).

FIG. 5.

Optimal long distance plume tracking conditions are likely found at intermediate wind speeds and environmental complexities.

Insect populations have seen major declines over the past century, with habitat loss due to agriculture and urbanization conversion being a key driver.^61,62 Farmland wind erosion has been a growing concern over the past century and is caused by strong winds over bare soils.^63,64 Conversely, urbanization drastically increases surface roughness and creates strong disturbances in natural wind flow. These types of land developments drastically alter environment surface roughness and wind flow in ways that are likely to impede an insect’s ability to successfully track odor plumes over long distances.

D. Implications for future plume tracking experiments

Although spatially driven directional variability was assessed by finding the observed difference in direction recorded at two locations, whereas temporal variability was assessed using the standard deviation over varying time windows, our results show that the corresponding relationships between environment and wind speed are remarkably similar. This indicates that the use of temporal statistics with one sensor may be sufficient for future studies aimed at further quantification of environment specific differences. That said, the spatially driven non-linear relationship observed in directional variability over distances between 100 and 200 m in the forest and steppe environments [Fig. 2(b)] may warrant future studies with similar sensor setups.

Our knowledge of how insects successfully track odor plumes in outdoor spaces remains limited due to the underlying complexities of near-surface wind dynamics, which influence odor plume dispersion and insect flight strategies. The observed near-surface wind conditions presented in this study demonstrate significant diversity of wind conditions across environments and days of sampling. In many cases, the standard deviation in the wind direction ranged from 15 to 75 on the timescale of 1–10 min. Under such conditions, odor plumes will be more dispersed and meandering, and the canonical cast-and-surge behavior that insects employ in laminar wind conditions^3,65 is unlikely to be effective. Instead, insects may need to rely on a time history of odor and wind information^49,66,67 or a different strategy altogether. Discovering what these strategies are will require controlled laboratory settings in novel wind tunnel assays where directional variability can be controlled to match the linear relationship with turbulence intensity that we describe in Figs. 3(e) and 3(f).

DATA AVAILABILITY

Data is available through Figshare: https://doi.org/10.6084/m9.figshare.21111610. Geographical coordinates were masked out of respect for land owners who allowed us to collect data on their private property. Code associated with this paper is provided publicly in GitHub at https://github.com/JaleesaHoule/wind_environment_characterization, Ref. 68.