Evaluating Various Energy Balance Aggregation Schemes in Cotton Using Unoccupied Aerial Systems (UASs)-Based Latent Heat Flux Estimates

Highlights

What are the main findings?

• Spatially aggregating the output fluxes was more accurate than spatially aggregating inputs when estimating latent energy using a Two-Source Energy Balance Priestley–Taylor model.
• Spatially aggregating data from unmanned aerial systems to estimate latent energy using the two-source energy model was closer to eddy flux tower measurements than applying manned aircraft and satellite imagery.

What is the implication of the main finding?

• Latent energy estimates from data collected by unmanned aerial systems can be a reliable source of spatial latent energy in a field with variable soil properties.

Abstract

Daily evapotranspiration (ET) estimated from an unoccupied aerial system (UAS) could help improve irrigation practices, but its spatial resolution needs to be upscaled to coarser pixel resolutions before applying surface energy balance models. The purpose of this study was to evaluate the impact of various energy balance-based aggregation schemes on generating spatially distributed latent heat flux (LE), and, in comparison, to existing occupied aircraft and satellite remote sensing platforms. In 2017, UAS multispectral and thermal imagery, along with ground truth data, were collected at various cotton growth stages. These data sources were combined to model LE using a Two-Source Energy Balance Priestley–Taylor (TSEB-PT) model. Several UAS aggregation schemes were tested, including the mode of aggregation (i.e., input image and output flux) as well as the averaging scheme (i.e., simple aggregation vs. Box–Cox). Results indicate that output flux aggregation with Box–Cox averaging produced the lowest relative upscaling pixel-scale variability in LE and the lowest absolute prediction errors (relative to eddy covariance flux tower measurements). Output flux aggregation with simple averaging was also more accurate in reproducing LE from occupied aircraft and satellite imagery. Although results are limited to a single site, UAS LE estimates were reliably aggregated to coarser pixel resolutions, which made for faster image processing for operational applications.

1. Introduction

Actual evapotranspiration (ET_a in mm per unit time) has been estimated using thermal and multispectral imagery from sensors located aboard non-commercial geostationary and polar-orbiting satellites (or SATs collectively) [1]. However, SAT imagery is not guaranteed to be cloud-free [2], and more frequent thermal observations are needed to capture day-to-day variability in ET_a and plant stress, as in the case of combining multi-sensor sources [3]. Furthermore, even ET at the highest SAT pixel resolution (currently 30 m) may not be sufficient to adequately detect crop and soil variability within a single production field in agricultural settings. While alternative platforms such as commercial SATs and occupied aerial systems (OASs) can provide enhanced spatial and temporal information, both have high acquisition costs, as survey companies require a minimum area for coverage to at least break even [4].

Unoccupied aerial systems (UASs) have been proposed as an alternative to monitor ET_a within a given production field [5]. This is because, relative to OASs and commercial/non-commercial SATs, users have the most control over image collection [4]. UASs can offer additional advantages in terms of spatial detail, with imagery as fine as 0.05 m having been reported [6]. The value of such high pixel resolutions can be appreciated within certain applications, such as crop scouting [2]. In other applications, such as irrigation management, this extra spatial detail is usually unnecessary [7]. Mismatches can exist between the observation scale at which UAS images are collected and the application scale at which decisions are implemented. Drip irrigation systems, for example, operate on a spatial scale from 1–10 m², central pivots on 100 m², and furrow irrigation on 1000 m² [8]. If UAS imagery is indeed more detailed than is necessary, prolonged processing times can even delay the delivery of the end product. A customer survey report by [8] indicates that most users require ET_a maps less than a day after image acquisition, a demand that can be met with UASs, given a proper workflow.

In addition to the application scale, UAS images can also present discrepancies with respect to the LE modeling scale. For example, mismatches may result between the defined modeling scale and processes that define these models, such as shear-driven turbulence [9]. These discrepancies are most apparent within LE algorithms such as the two-source energy balance (TSEB) model. TSEB models were initially developed and applied at pixel resolutions associated with non-commercial SATs (e.g., 60–120 m pixel resolution) [10,11,12]. Under the TSEB model, canopy and soil temperatures (T_c and T_s, respectively) are estimated at each pixel, which are then used to find LE as a residual from the energy balance equation. The assumption behind the TSEB-PT model, therefore, is that each pixel contains both vegetation and soil components. However, such assumptions are not always met with UAS imagery, where pixel resolutions can be fine enough to capture both components. Under these conditions, application of the TSEB-PT model, therefore, may not provide reliable estimates of LE, since the model algorithms were not necessarily designed to operate at very fine resolutions.

Discrepancies between observation, management, and modeling scales can be mitigated by transferring information using scaling techniques [13]. In the case of the UAS, one such scaling technique can be performed through up-scaling, or aggregating, images to a coarser pixel resolution [14]. Initial studies quantifying the effects of aggregation on ET (or LE) modeling have been primarily confined to pixel resolutions associated with SAT imagery [15,16]. For example, one study aggregated Landsat 5/7 thermal/multispectral imagery from original resolutions to various pixel resolutions (0.06–1 km) and then ran contextual surface energy balance system (SEBS) ET models at each resolution, a process called input aggregation [17]. In their results, they reported relative canopy ET (or ET_c) pixel-scale errors ranging from 25 to 60 percent, which they attributed to changes in sensible heat (H), specifically roughness length for heat and momentum (z_oh and z_om, respectively). Another study suggests that input aggregation is detrimental when model parameters (such as z_oh and z_om) behave in a non-linear fashion [18]. Ref. [17] also found that pixel-scale ET_c errors were reduced when the fluxes were modeled at the initial Landsat resolution and then aggregated, an alternative process called output aggregation.

Errors from input-aggregated SEBS fluxes could be reduced by applying alternative aggregation rules (e.g., for linear, harmonic, or geometric roughness length averaging) [19]. However, the optimal averaging rule has rarely been analyzed in terms of non-contextual ET models such as TSEB. TSEB can be favorable over the SEBS and contextual models, in general, because it eliminates the need for empirical corrections of excess resistance (i.e., z_om, z_oh) [20]. In one of the few papers on the topic, Ref. [19] showed that, at least with ASTER SAT imagery, ET fluxes using TSEB models were more conservative across spatial scales (i.e., 0.1 to 1 km) than contextual models such as the SEBS. However, such studies have not been extensively evaluated with UAS imagery, except for [21] for a particular crop type, since image quality can vary depending on weather conditions (e.g., wind, radiation, temperature, vapor pressure) and/or sensor quality [22].

The purpose of this study was to investigate the scaling properties of UAS-based LE estimates from a TSEB model. In particular, the interest is in comparing the different modes of UAS aggregation (i.e., input vs. output, linear vs. non-linear averaging) at partial and full canopy cover conditions from a cotton row crop. There is additional interest in determining the contributing sources of error that result from these different aggregation modes. Finally, UAS maps are compared with those obtained from OAS and SAT imagery.

2. Materials and Methods

2.1. Study Area and Management

The study site (17 ha, 30.531°N, −96.431°W) is located on the Texas A&M Experimental Farm in central-eastern Texas (Figure 1). The region has a humid subtropical climate (Cfa) according to the Köppen climate classification system. Soil color varies within the field, with darker and lighter soils on the west and east sides of the field, respectively. Soil surface textures include silt loam, silty clay loam, and silty clay [23], and the soils are classified as Vertisols, Inceptisols, and Entisols as they vary across the field [24]. Elevations are relatively constant, with an average elevation of 67.7 ± 0.3 m above ground level (coefficient of variation = 0.44). Total in-season precipitation and average daily air temperatures based on local rain gauges (red circles, Figure 1) were 495 mm and 26.0 °C, respectively.

In past seasons, the field was actively managed with conventional tillage practices and kept in a continuous crop rotation with alternate years of corn (Zea mays L.) and cotton (Gossypium hirsutum L.). On 5 April 2017 (day of year = 95), cotton (variety PHY 444 WRF) was planted at a rate of 111,200 seeds ha⁻¹ and at 1.02 m row spacing. Pre-emerge and post-emergence herbicides (Prowl H₂O, Cotoran 4L, Cornerstone Plus) were applied to ensure uniform stand establishment. In-season management of cotton included fertilization, plant growth regulation, and weed control. Based on field measurements, first flowering was observed on June 8 (64 days after planting, or DAP), with cutout (i.e., 5 nodes above white flower or NAWF) on 1 July 2017. Boll filling occurred approximately between June 29 and July 28 (85-112 DAP, defined here as 2 NAWF). Open bolls for about 90 percent of the field occurred around September 1 (210 DAP). Defoliation occurred on 9 September 2017 (157 days after planting, or DAP), and harvest was conducted on 10 October 2017 (188 DAP).

2.2. Image Acquisition

One of the objectives of this study was to compare UAS-aggregated LE imagery with that from OAS and SAT platforms.

Table 1. Flight times and pixel resolutions for all intensive observation periods. The local times associated with each multispectral and thermal survey are also described by survey platform, along with its reported altitudes and native or original pixel resolutions for each sensor. MS—Multispectral. No SAT data was available on July 28 due to cloud cover.

Growing Stage	Platform	Altitude (km)	Flight Time—Multispectral	Flight Time—Thermal	Native Pixel Resolution (m)
					MS	Thermal
	16 June 2017
Flowering	UAS	0.12	13:48–14:10	13:00–13:15	0.07	0.15
	OAS	1.37	13:58–14:10		0.48	1.32
	SAT	705	11:57		30	100
Boll filling	26 July 2017
	UAS	0.12	11:27–11:48	N/A	0.08	N/A
	28 July 2017
	UAS	0.12	No flight	14:46–15:00	N/A	0.15
	OAS	1.37	15:17–15:31		0.48	1.31

shows the dates of intense observation periods (IOPs) when UAS, OAS, and SAT surveys were conducted over the field in the 2017 growing season. The images collected at these dates and times form the basis of the images for this study. SAT in this study refers to Landsat 8, a satellite that operates in sun-synchronous, near-polar orbit. SAT thermal images are initially collected at 100 m but subsequently resampled to 30 m resolution via cubic convolution [25]. The SAT multispectral bands are defined at 30 m resolution. The main growth stages selected for this study include cotton flowering and boll filling. Note that UAS multispectral and thermal surveys were conducted separately due to platform limitations. Survey altitudes for UAS, OAS, and SAT systems were approximately 0.12, 1.37, and 705 km, respectively (Table 1).

The lag time between the UAS and SAT surveys on 16 June 2017 was about one hour. Previous attempts were made to conduct a UAS thermal survey at the time of the SAT overpass (i.e., 11:57, Table 1) to ensure similar radiative conditions between platforms. However, cloud variability was present during the survey, and partial cloud cover was observed from the SAT imagery (Figure A1). SAT images were not available on July 26 or July 28 (i.e., UAS thermal and multispectral surveys, Table 1) because the next overpass date was not until 3 August 2017. Both multispectral and thermal images were necessary for TSEB-PT modeling (Section 2.4).

Relative to the SAT, OAS surveys were conducted much closer in time to UAS thermal surveys. The average flight time for OAS surveys at 1.37 km was 13 min. All multispectral and thermal afternoon flights were conducted within ±two hours of solar noon, which is defined here as 13:30 local time (Table 1). The pixel resolutions from the multispectral camera were 0.48 m, while those from the thermal camera were 1.31 m (Table 1). Both multispectral and thermal sensors equipped on the OAS platform were flown at the same time. On 26 July 2017, only a UAS multispectral survey was conducted so that the TSEB-PT model could be run from UAS thermal surveys on July 28 (Section 2.4)—no UAS multispectral survey was conducted on July 28 because it was collected two days prior (Table 1).

2.2.1. UAS Sensors

Sensors equipped aboard the Tuffwing UAS platform (Boerne, TX, USA) are given in

Table 2. Remote sensing platform and sensor characteristics used in the study ¹.

Characteristic	Multispectral Sensors			Thermal Sensors
	UAS	OAS	SAT	UAS	OAS	SAT
Platform	Tuffwing UAS Mapper	Cessna 206	Landsat 8	Tuffwing UAS Mapper	Cessna 206	Landsat 8
Sensor	Micasense Rededge	Nikon D810	Operational Land Imager (OLI)	ICI 8640-P	FLIR SC660	Thermal Infrared Sensor
Number of channels	5 (RGB + NIR + Red Edge)	4 (RGB + NIR)	9 (RGB, NIR, SWIR)	1	1	2
Notable spectral wavebands (μm)	0.46–0.50 (Blue)	0.40–0.50 (Blue)	0.45–0.51 (Blue)	7.0–14.0	7.50–13.00	10.6–11.19
	0.54–0.58 (Green)	0.51–0.59 (Green)	0.53–0.59 (Green)
	0.66–0.68 (Red)	0.60–0.70 (Red)	0.64–0.67 (Red)
	0.80–0.88 (NIR)	0.83–1.00 (NIR)	0.85–0.88 (NIR)
Resolution (px)	1280 × 960	7360 × 4912	7541 × 7691	640 × 512	640 × 480	7541 × 7691
Focal length (mm)	5.5	20	886	12.5	37.6	178
FOV (°)	47.9	83.9	15	78	24	15
Output data	16-bit	16-bit	12-bit	14-bit	16-bit	12-bit
Ground image dimension (m)	106 × 79	1204 × 805	185,000 × 180,000	84 × 104	285 × 213	185,000 × 180,000
		2462 × 1646			584 × 437

¹ The use of trade, firm, or corporation names in this article is for the information and convenience of the reader. Such use does not constitute official endorsement or approval by the US Department of Agriculture.

. The multispectral camera used in this study was the Micasense RedEdge (MicaSense, Seattle, WA, USA). The RedEdge camera is a complementary metal–oxide–semiconductor sensor that detects visible and near-infrared radiation. Thermal images were collected using an ICI 8640-P sensor (Infrared Cameras Inc., Beaumont, TX, USA). The 8640-P is an uncooled focal plane array microbolometer with vanadium oxide film. Previous use of the RedEdge and the ICI 8640-P sensors towards vegetation monitoring and plant phenotyping has been documented [26,27].

2.2.2. OAS Sensors

OAS multispectral images were collected with a Nikon D810 camera (Melville, NY, USA). Thermal images were collected using a FLIR SC660 sensor, which, like the ICI 8640-P, is an uncooled focal plane array microbolometer (Wilsonville, OR, USA, https://www.flir.com/ (accessed on 19 October 2025)). The FLIR SC660 has a slightly smaller range for detecting thermal radiation (7.5–13 μm) than the ICI 8640-P (7.0–14.0 μm, Table 2). The D810 multispectral sensor was set under manual settings, with an exposure time of 0.001 s. The D810 and SC660 have previous applications in monitoring crop water status [28,29].

2.2.3. SAT Sensors

Landsat 8 SAT imagery was obtained on 16 June 2017, from multispectral and thermal sensors aboard the platform, namely the Operational Land Imager (OLI) and the Thermal Infrared Sensor (TIRS), respectively. The OLI was manufactured by Ball Aerospace & Technologies Corporation, while the TIRS was built by the NASA Goddard Space Flight Center. More detailed information on the characteristics of these two sensors beyond Table 2 can be found elsewhere in the literature [30]. While Landsat has two thermal bands, only band 10 (i.e., 10.6–11.19 μm) was used, as band 11 (11.5–12.51 μm) has documented stray light issues [31].

2.3. Image Post-Processing

Discussion of UAS post-processing, including geometric/radiometric corrections, can be found in Appendix A and is omitted here for the sake of brevity.

2.3.1. OAS

The goal of orthomosaicking OAS imagery was to only analyze images that cover the area spanned by the eddy covariance tower footprints for LE comparisons. While the entire field was captured in a single shot with OAS multispectral imagery, such was not the case with the thermal imagery. Because thermal images define the ET modeling domain (Section 2.5), and to simplify processing times, all OAS analysis was only conducted over these smaller portions of the field.

After data acquisition, multispectral images were first corrected from RAW to 16-bit TIFF files using the provided software (Capture NX-D 1.2.1). Because the multispectral sensor captured the entire field in one shot, mosaicking was not needed. Instead, only geo-referencing was needed using known coordinates of objects identified within the image. RGB and NIR images were first geo-referenced separately and then stacked together within ArcGIS Version 10.8.1 (ESRI, Redlands, CA, USA).

Multispectral radiometric calibrations were conducted using the empirical line calibration in order to obtain surface reflectance [32]. The main interest was in estimating red and NIR reflectance (ρ_Red, ρ_NIR) alone so that the Normalized Difference Vegetation Index (NDVI) could be calculated for later use in the LE modeling phase (Section 2.4). Ground-truth reflectance measurements were obtained with a Handheld 2 spectroradiometer instrument, which has a spectral range of 325–1075 nm, a spectral resolution of <3 nm, and a 25° FOV (ASD Inc., Boulder, CO, USA). Four 8 × 8 m tarpaulins were used for radiometric calibration, with reported nominal reflectance values of 4, 16, 32, and 48 percent [33]. The Handheld 2 collected reflectance data from these tarps during each OAS IOP, as well as measurements of soil and cotton reflectance for validation. In addition to measured reflectance values, raw sensor information (i.e., digital numbers, or DNs) was extracted from a 9 × 9-pixel box within each tarp in order to convert DNs to percent reflectance values.

All images collected by the thermal FLIR SC660 sensor were first processed to generate camera-calibrated temperatures using the provided software (ExaminIR Version 1.10.0, FLIR, Wilsonville, OR, USA). The settings supplied in ExaminIR were the same as those from the UAS processing software, mainly: (1) emissivity or ε = 1.00, (2) transmissivity or τ = 1.00, and (3) obtained air temperatures or T_a. At 1.37 km altitude, most of the field was captured in one shot (Figure A1); therefore, like the multispectral imagery, image registration was only required, and this was performed using the geo-referenced multispectral imagery as a visual aid. OAS thermal radiometric corrections were performed at each pixel by calculating emissivity (ε) values weighted by vegetation fraction cover [34], followed by estimation of surface temperature (T_r) from brightness temperature (T_br) and background air temperature (or T_bg, via local weather data) [35].

2.3.2. SAT

Surface reflectance data from the visible/near-infrared wavelengths were obtained through the Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS). Raw thermal DNs were first obtained from the level one product using the United States Geological Survey Global Visualization Viewer (GLOVIS). Raw DNs, along with the surface reflectance data, were used to estimate T_r—detailed information regarding the conversion of SAT DN to T_r can be found in Appendix B.

2.4. Model Formulation

The purpose of this study was to evaluate how UAS LEs change as a function of coarsening pixel resolution and how such information compares with that from OASs and SATs. Within this context, LEs needed to be obtained across the entire production field. To do this, LEs were estimated using a combination of remote sensing and energy balance modeling techniques. The energy balance model used here was the TSEB model [36]. Contextual energy balance models, while popular [6,37], were hypothesized as unfavorable in this study because satellites were not expected to properly identify hot/cold temperature endmembers within the small study area (17 ha or 0.17 km²).

The general approach to TSEB models is to estimate LE as a residual of the energy balance equation, which is based on the difference between net radiation and soil heat fluxes (R_n-G) and sensible heat (H). In the original TSEB-PT formulation from [36], H is expressed from both soil and vegetation components as follows:

$$\mathrm{H}={ \mathrm{\rho }\mathrm{C}}_{\mathrm{p}}{\displaystyle \frac{{\mathrm{T}}_0-{\mathrm{T}}_{\mathrm{a}}}{{\mathrm{r}}_{\mathrm{a}}}},$$

(1)

where ρC_p is the volumetric capacity of air (J m⁻³ K⁻¹), T₀ is the surface aerodynamic temperature (K), T_a is the air temperature (K), and r_a is the resistance to heat transport or aerodynamic resistance (s m⁻¹). In practice, T₀ is unknown and replaced with T_r, although this approach can result in an overestimation of H fluxes [38]. Ref. [36] explicitly considers the aerodynamic resistance of the soil and canopy elements originally through a parallel resistance network, and to obtain a solution, estimates LE from the canopy using the TSEB Priestley–Taylor approximation (TSEB-PT). Unlike other versions of the TSEB model (i.e., TSEB-DTD and TSEB-2T; [21]), the TSEB-PT model allows for comparisons between UAS, OAS, and SAT LEs because it uses thermal imagery comprising a mixture or composite of soil and vegetation temperatures at one point in time (Table 1). The original model formulation begins with an initial approximation of LE_c based on the transpiration equation from [39] as follows:

$${\mathrm{LE}}_{\mathrm{c}}={ \mathrm{\alpha }}_{\mathrm{PT}}{\mathrm{f}}_{\mathrm{g}}{\displaystyle \frac{\mathrm{\Delta }}{\mathrm{\Delta }+\mathrm{\gamma }}}{\mathrm{R}}_{\mathrm{n},\mathrm{c}},$$

(2)

where α_PT is the Priestley–Taylor parameter with an initial value of 1.26, f_g is the fraction of green vegetation (typically assumed = 1 during the growing season), Δ is the slope of the saturation vapor pressure–temperature curve (Pa K⁻¹), γ is the psychrometric constant (Pa K⁻¹), and R_n,c is the net radiation of the canopy computed by a procedure summarized in [38]. After LE_c is initialized using Equation (1), H_c is then computed as R_n,c–LE_c which then allows for T_c to be found as follows:

$${\mathrm{H}}_{\mathrm{c}}={ \mathrm{\rho }\mathrm{C}}_{\mathrm{p}}{\displaystyle \frac{{\mathrm{T}}_{\mathrm{c}}-{\mathrm{T}}_{\mathrm{a}}}{{\mathrm{r}}_{\mathrm{a}}}}\to {\mathrm{T}}_{\mathrm{c}}={\displaystyle \frac{{\mathrm{H}}_{\mathrm{c}}{\ast \mathrm{r}}_{\mathrm{a}}}{{\mathrm{\rho }\mathrm{C}}_{\mathrm{p}}}}+{\mathrm{T}}_{\mathrm{a}},$$

(3)

where r_a is the aerodynamic resistance to momentum and heat transfer (s m⁻¹), ρ is the air density (kg m⁻³), C_p is the specific heat of air (J kg⁻¹ K⁻¹), and T_a is the air temperature at the time of overpass (K). With an initial T_c from Equation (3), T_s, or soil temperature, is found by rearranging a mixing model weighted by the vegetation fraction cover (f_c) and T_r values obtained from the sensor [36]:

$${\mathrm{T}}_{\mathrm{r}}={\left[{\mathrm{f}}_{\mathrm{c}}{\ast \mathrm{T}}_{\mathrm{c}}^4+\left(1-{\mathrm{f}}_{\mathrm{c}}\right){\ast \mathrm{T}}_{\mathrm{s}}^4\right]}^{1/4} ,$$

(4)

Note that, in order to obtain an initial T_c value, fraction canopy cover (f_c) is calculated from [40] as follows:

$${\mathrm{f}}_{\mathrm{c}}\left(\mathrm{\theta }\right)= 1-\exp \left[{\displaystyle \frac{-0.5\mathrm{\Omega }\left(\mathrm{\theta }\right)\mathrm{LAI}}{\cos \left(\mathrm{\theta }\right)}}\right],$$

(5)

where Ω is a vegetative clumping factor calculated at a given sensor viewing angle θ [41], and the leaf area index (LAI) is calculated from multispectral imagery (see Section 2.5). A check on these T_c and T_s values is then performed by applying these newly found T_s values to find H_s:

$${\mathrm{H}}_{\mathrm{s}}={ \mathsf{\rho }\mathrm{C}}_{\mathrm{p}}{\displaystyle \frac{{\mathrm{T}}_{\mathrm{s}}-{\mathrm{T}}_{\mathrm{a}}}{{\mathrm{r}}_{\mathrm{s}}+{\mathrm{r}}_{\mathrm{a}}}},$$

(6)

where r_s is the soil resistance to momentum and heat transfer (s m⁻¹). Finally, LE_s is found from the energy balance of the soil (LE_s = R_n,s − G − H_s), where G = 0.35*R_n,s is from [41]. A valid solution is reached when LE_s is positive. If a valid solution is found, the latent and sensible fluxes from both canopy (i.e., LE_c = R_n,c − H_c) and soil sources are, respectively, added together to compute the LE and H terms. A more detailed description of this model can be found in [36,41]. The modeling scheme described above is the version of TSEB-PT using parallel resistance as opposed to the more complicated series resistance formulation, which is available in the Python package pyTSEB, version 2.0 (https://github.com/hectornieto/pyTSEB (accessed on 15 October 2018), Source: Hector Nieto) and applied to the imagery in this study. Details of the original series resistance formulation are in [36], while updates are described in detail in [21]. For the range of canopy cover conditions existing in this study, both parallel and series resistance formulations would yield similar results [11].

2.5. Model Inputs and Processing

To run TSEB-PT models for UAS, OAS, and SAT imagery, both image and non-image data need to be generated. Image inputs refer to spatially varying parameters such as T_r (Section 2.3), f_c, and LAI. Non-image inputs refer to model inputs such as weather data (e.g., incoming solar radiation, wind speed, and air temperature) and agronomic data such as canopy height (hc) and canopy width (wc). The following sections detail the derivation of these inputs separately.

2.5.1. Image Inputs

All further discussion of input derivation applies to UAS, OAS, and SAT platforms. The fc was derived from NDVI imagery by scaling between the ‘infinite’ NDVI (NDVI_∞) and soil NDVI (NDVI_s) [42]:

$$f_c= {\left({\displaystyle \frac{NDVI-NDV{I}_s}{NDV{I}_{\infty }-NDV{I}_s}}\right)}^2,$$

(7)

where NDVI_∞ was taken to be the maximum NDVI observed from the native pixel size (0.976). NDVI_s was based on average NDVI values at a time before squaring occurred, just prior to planting (0.2).

LAI maps were then generated by regressing in situ LAI (Figure 1) against the f_c maps generated from above. LAI measurements were taken with an LAI-2200C sensor (LI-COR, Lincoln, NE, USA), either one hour before sunrise or one hour before sunset. All LAI campaigns were collected in a two-day span from a UAS thermal overpass (Table 1). LAI measurements were taken in an area spanning three meters by three rows. In accordance with LICOR recommendations, all LAI observations were collected directly underneath cotton plants along a row and at one-fourth, one-half, and three-fourths distance from the cotton row.

Table 3. Agronomic and weather data collected at the IOPs, along with their respective units. Abbreviations are as follows: (1) LAI—leaf area index; (2) h_c—canopy height; (3) w_c—canopy width; (4) T_a—air temperature; (5) u—wind speed; (6) S_dn—downward incoming solar radiation; (7) VPD—vapor pressure deficit. No SAT data was available on July 28 due to cloud cover. Flight times are for thermal sensor flights only.

Date	Time	Platform	LAI	hc	wc	Ta	u	Wind Direction	Sdn	VPD
			m2 m−2	m	m	K	m s−1	°	W m−2	kPa
16 June 2017	11:57	SAT	1.03	0.44	0.14	304.3	3.78	213	878	1.79
	13:00–13:15	UAS				306.1	3.88	205	1014	2.40
	13:58–14:10	OAS				306.7	3.11	191	998	2.58
28 July 2017	14:46–15:00	UAS	2.37	0.8	0.92	309.6	1.84	166	945	3.55
	15:17–15:31	OAS				310.1	1.77	189	898	3.73

shows field average characteristics of agronomic data collected at site locations shown in Figure 1 (dark blue circles). The field average LAI values on June 16 and July 28 were 1.03 ± 0.22 and 2.37 ± 0.34 m² m⁻², respectively.

2.5.2. Non-Image Inputs

Weather data were collected using 15-minute averaged sensor data obtained across both eddy flux towers. Weather parameters include (but are not limited to) (1) air temperature (T_a, K), (2) wind speed (u, m s⁻¹), (3) vapor pressure deficit (VPD, kPa), (4) incoming shortwave radiation (S_dn, W m⁻²), and (5) longwave radiation (L_dn, W m⁻²). Specific weather data on June 16 and July 28 (Table 1) are shown in Table 3.

Field agronomic information was obtained by averaging spatially distributed field measurements at each IOP (Figure 1). Relevant information includes canopy height, canopy width, leaf width, leaf spectral properties, and leaf angle distribution. All canopy height and width measurements were visually observed across ten different plants at each site using measuring tape. Leaf width was visually observed from the widest points between select leaves on each plant. Leaf spectral properties were obtained using local ground-truth reflectance data. Leaf angle distribution was calculated from leaf tip angle measurements collected alongside LAI data [43].

The use of a constant G/R_n,s was based on the observation that most PM thermal UAS surveys were collected around solar noon, which is supported by observations by [44], indicating that the use of a constant ratio is appropriate for several hours around solar noon. Green vegetation fraction, f_g, was set to one for all model runs. View zenith angle was set to nadir or zero degrees.

2.6. General Design of the Experiments

The purpose of this study was to address the effect of UAS aggregation on LE estimations. The overall methodology used to address this question is shown in Figure 2. Two basic aggregation rules, either from the input imagery or output fluxes, were applied to UAS imagery. Before these aggregation rules were applied, however, all image inputs (e.g., T_r, LAI, f_c) were first aggregated to a pixel resolution of 1.33 m—this step was performed so that assumptions of TSEB modeling of having a mixed pixel of soil and vegetation (i.e., >1 m) were satisfied. The choice of 1.33 m was based on the nearest multiple of UAS thermal imagery relative to the OAS (Table 1). Next, an input aggregation scheme was applied, whereby the initially aggregated imagery (at 1.33 m) was aggregated again to a coarser pixel resolution (5, 10, 30, and 90 m), followed by a TSEB-PT model run at each resolution. To address the effect of different input image aggregation schemes, only one set of image inputs can be modified at a time. Therefore, initial analyses were focused on identifying the most sensitive image input parameters via field histograms. The two candidate input variables were T_r and f_c. The 30 m resolution reflects the SAT Tr disaggregation approaches using concurrent multispectral imagery [10]. The 90 m resolution reflects Landsat 8 thermal imagery satellite images aggregated to the closest multiple of its original resolution (i.e., 100 m)—this approach has precedence within the literature [45].

The other aggregation scheme tested in this study was output flux aggregation, whereby the fluxes were first modeled at 1.33 m, followed by flux aggregation to the desired pixel resolution. The output-aggregated flux resolution was aggregated to the same values as those from the input-aggregated approaches. This experimental design is like other studies addressing aggregation properties from satellite sensors [15,16,17,18].

Within a given aggregation scheme (i.e., input/output), additional sub-schemes were used to address the effect of field statistical distributions on aggregation. First, a simple mean, or arithmetic average, was calculated, with the assumption that image inputs or outputs behave linearly (labeled as SA in Figure 2a). Second, a non-linear scheme was addressed by using a Box–Cox approach, whereby values were transformed to an optimal transformation power, arithmetically averaged, and subsequently back transformed to obtain values in the original units (labeled as BC in Figure 2a)—further description of the BC approach is given in Appendix C. Collectively, four individual aggregation schemes were tested for a given IOP date (hereafter referred to as In-SA, In-BC, Out-SA, and Out-BC in Figure 2a). Examples of UAS Out-SA LE images across both IOP dates are shown in Figure 3.

One of the primary goals of this study was to address which aggregation scheme (i.e., In-SA, In-BC, Out-SA, or Out-BC) produced the lowest (1) pixel-scale errors and (2) prediction errors (with respect to eddy flux towers). First, pixel-scale relative errors were calculated, which compare the value at the selected aggregated resolution against the individual pixels from which it is comprised. Relative error (R_e) is calculated as R_e = RMSE/μ [46], where RMSE is the root-mean-square error difference between the coarse resolution pixel and its constituent fine resolution pixels, and μ is the spatial mean value of all the fine resolution pixels. Second, the modeled fluxes (i.e., In-SA, In-BC, Out-SA, Out-BC) were compared to the LE measured by the eddy covariance towers installed within the field during each IOP (Figure 1). Quality of fit was assessed in terms of mean absolute percentage error (MAPE):

$$MAPE= {\displaystyle \frac{100}{n}}{{\displaystyle \sum }}_{j=1}^n\left|{\displaystyle \frac{\widehat{y}-y}{y}}\right|,$$

(8)

where ŷ and y are the UAS/OAS modeled and eddy covariance LEs, respectively. Appendix D provides a description of flux tower data and the method used to obtain remotely sensed weighted fluxes within the footprint of each eddy tower, as well as the extraction of energy balance components (i.e., R_n, G, LE, H) from the flux towers.

3. Results

3.1. Comparing UAS Aggregation Approaches

The purpose of this study was to evaluate the different aggregation approaches (Figure 2) in terms of (1) R_e on the pixel scale and (2) absolute errors with respect to eddy flux towers. Analysis begins by first presenting histograms for T_r and f_c on different dates and resolutions, as shown in Figure 4. Because LAI is derived from f_c (Section 2.5.1), it is omitted here for the sake of brevity. The purpose here is to determine the relative sensitivity of these parameters to aggregation, as this will determine which parameter will then be tested in terms of averaging rules (e.g., In-SA, In-BC, Figure 2). Each panel in Figure 4 has the distribution of f_c and T_r at the native resolution as black lines (i.e., 0.07 and 0.15 m, respectively, Table 1), as well as the aggregated resolution, either using SA (green lines) or BC (pink lines) averaging approaches.

One observation that can be made from Figure 4 is that the distribution of the f_c and T_r curves for the native and aggregated images shifts in time. For example, on June 16, the f_c curves are primarily right-skewed (Figure 4a), while on July 28, these f_c curves shift to left-skewed distributions (Figure 4c). On June 16, T_r curves were approximately normal (Figure 4b), while on July 28 these distributions shifted towards right-skewed distributions (Figure 4d). These shifts in f_c and T_r correspond with the increased vegetative cover (and decreased soil exposure) during the two sampling dates (Table 3). On July 28, the distributions from f_c and T_r behave in a somewhat opposite manner, as both show left- and right-skewed distributions, respectively, (Figure 4c,d), likely because of changes in crop phenology throughout the growing season.

In comparing distributions within and across aggregation methods, several observations can be made. On June 16, and to a lesser degree, July 28, f_c-SA (green line) and f_c-BC (pink line) field distributions are visually different from each other, particularly for the low-medium values of f_c (0–0.5, Figure 4a). In particular, the f_c-SA distribution on June 16 contains a greater amount of f_c pixels between 0.1 and 0.5 than the f_c-BC or f_c-native imagery (Figure 4a). Moving from June 16 to July 28, f_c differences between SA/BC and native resolution (0.15 m) become less noticeable, although both aggregated distributions are shifted slightly to the left from the native distribution (Figure 4c). The f_c-SA shows a greater proportion of pixels associated with vegetation than that of f_c-BC (Figure 4c). This result may have occurred because In-SA effectively mixes high- and low-end values (from vegetation and soil, respectively), while In-BC weights values more towards high values (based on the greater proportion of vegetation via the transformation power, Appendix B).

Unlike f_c, differences in T_r distributions by aggregation rule were not observed. On June 16, for example, the T_r distributions for both SA and BC aggregation were almost identical (Figure 4b), and this was also observed on July 28 (Figure 4d). From these observations, two main points can be made. First, the sensitivity of f_c to the aggregation rule (i.e., SA vs. BC) was greater during partial than full vegetation coverage. Second, f_c was more sensitive to the selected aggregation rule than T_r, and this may have occurred because f_c is expressed on a much smaller scale relative to T_r (i.e., 0−1). For this reason, all further results for input aggregation will be discussed in terms of f_c input aggregation only. In other words, In-SA and In-BC refer to aggregation techniques from f_c imagery only (Figure 2).

Figure 5 shows histograms from LEs across the field at two different pixel resolutions (5 m and 10 m) and IOPs. Within each panel, field distributions at the initial aggregation level (1.33 m, black) are plotted alongside input (i.e., f_c)-aggregated images (blue) and output flux-aggregated images (orange). Note that the T_r arithmetic averaging was consistently used for all aggregation schemes (see Appendix A). The peak LE encountered on June 16 and July 28 was around 400 W m⁻² and 500 W m⁻², respectively. On June 16, LE histograms become generally narrower as the pixel resolution is aggregated from its native counterpart (Figure 5a,b). The most likely reason for this result is that soil and vegetation pixels are being increasingly averaged when pixel resolutions become greater than the width of the soil row (~0.5 m), resulting in less variation relative to the finer resolution imagery. When moving from June 16 to July 28, the LE field histograms across native and aggregation types shift from approximately normal to left-skewed, indicating greater vegetation coverage (Figure 5a vs. Figure 5c, Figure 5b vs. Figure 5d). A general trend that persists across all aggregation distributions on July 28, relative to the native distribution, is that the former has a larger proportion of pixels in the mid-range (i.e., 400–600 W m⁻²), presumably due to averaging of vegetation and soil pixels, regardless of aggregation/averaging approach.

Unlike the f_c field distributions (Figure 4a,c), the LE field distributions by aggregation and averaging methods (In-BC, Out-BC, In-SA, Out-SA) are pretty similar to each other on both sampling dates (Figure 5). While this may suggest that the selection of the correct aggregation and averaging approach has a minor impact, large differences (as much as 100 W m⁻²) were visually observed between the approaches on a per-pixel basis (Figure 6). Further visual inspection revealed that these differences were more prevalent within less densely vegetated areas. In other words, the selection of the aggregation and averaging approach is mostly relevant to heterogeneous surfaces, and this observation is in line with previous findings [47].

Based on these observations, as well as Figure 5 and Figure 6, further insights into LE aggregation behavior were quantified by calculating R_e for each of the scenarios shown in Figure 2. In particular, LE pixel-scale errors (R_e, Section 2.6) are plotted as a function of four different pixel resolutions (5 m, 10 m, 30 m, and 90 m) in Figure 7, and these errors are given in

Table 4. Mean pixel-scale relative errors from plots shown in Figure 7 (scaled between 0 and 1).

Resolution	16 June 2017				28 July 2017
	In-SA	In-BC	Out-SA	Out-BC	In-SA	In-BC	Out-SA	Out-BC
5	0.10	0.20	0.10	0.19	0.13	0.15	0.12	0.14
10	0.11	0.22	0.11	0.20	0.14	0.16	0.14	0.16
30	0.13	0.24	0.13	0.23	0.16	0.19	0.16	0.19
90	0.21	0.30	0.17	0.25	0.24	0.27	0.21	0.24
Average	0.14	0.24	0.13	0.22	0.17	0.19	0.16	0.18

. As expected, the magnitude of relative error, regardless of aggregation method, increased with increasing pixel resolution—this is because the signal/noise ratio is diminished as the pixel size increases relative to the sensed objects (i.e., crops/soils) [7]. R_e values for all aggregation methods were lower on July 28 (Figure 7b) than on June 16 (Figure 7a), as the median R_e from Table 4 was 0.16 and 0.20, respectively. Differences between the 25th and 75th percentiles of different aggregation methods are more noticeable on June 16 than on July 28 as well (Figure 6 and Figure 7). These results most likely occurred because of the relatively high R_e errors on June 16 from both In-BC and Out-BC (Figure 7a).

R_e differences were exhibited not only across dates but within dates as well. For a given sampling date, differences in relative errors between the SA vs. BC transformation were smaller than those between input vs. output aggregation (Table 4). In other words, aggregated LEs were more sensitive to the selection of the averaging rule than the selection of the aggregation method. In terms of comparison, relative errors from simple averaging (i.e., Out-SA, In-SA) were generally lower than BC (i.e., Out-BC, In-BC). For example, the median relative error for SA on June 16 was 0.14, while for BC it was 0.20. With respect to the individual models, the magnitude of R_e was (from lowest to highest): Out-SA < In-SA < In-BC < Out-BC (Figure 7, Table 4). Thus, output flux aggregation produced slightly lower pixel-scale errors than using input aggregation with respect to SA. These trends are particularly apparent on June 16 (Figure 7a), although differences are diminished on July 28 (Figure 7b), presumably because of more homogenous (vegetated) surfaces. Therefore, it can be concluded that SA averaging (preferably with output flux aggregation) performed the best at upscaling UAS imagery under these conditions for this study, despite the apparent non-normal distributions presented in the inputs (Figure 4c,d) and output fluxes (Figure 5c,d).

The second criterion used to determine which aggregation method was optimal was through comparisons with LE from eddy flux towers. Figure 8 shows plots of UAS-aggregated LEs (i.e., In-SA, In-BC, Out-SA, Out-BC) against the LE measured by the eddy covariance-based LEs, across both towers and dates (n = 4).

Table 5. Mean absolute errors (MAEs, expressed as a %) of different LE-aggregated flux configurations between the UAS and eddy flux towers. In-SA: LAI input simple average aggregation; In-BC: LAI input Box–Cox aggregation; Out-SA: LE native simple average aggregation; Out-BC: LE native Box–Cox aggregation.

Resolution (m)	In-SA	In-BC	Out-SA	Out-BC
5	7.2	8.0	6.0	7.9
10	7.8	8.1	6.2	8.6

provides the MAPE values from each configuration and is expressed as error from the mean LE (467 W m⁻²). One consistent result that appeared across all resolutions was that the errors from output flux aggregation (i.e., Out-SA, Out-BC) were lower than those from input LAI aggregation (i.e., In-SA, In-BC). For example, at 5 m, the MAPE for In-SA was 7.2 percent, while for Out-SA it was 6.0 percent (Table 5). When comparing SA vs. BC averaging, the former was more accurate relative to eddy fluxes—the average BC MAPE for input aggregation was 8.2 percent, while for SA it was 6.8 percent (Table 5). In fact, the trends in MAPE are the same as the relative errors from Table 4: MAPE (Out-SA) < MAPE (In-SA) < MAPE (In-BC) < MAPE (Out-BC). Output aggregation approaches had slightly lower median MAPE values than input approaches (7.2 vs. 7.8 percent, respectively, on average).

Therefore, it was concluded that aggregating using SA (with output aggregation) had the lowest MAE when upscaling LE from 1.33 m, and this is in agreement with the pixel-scale results reported earlier (Figure 7, Table 4). Input image aggregation can be unstable if all inputs do not present similar statistical distributions, as was shown here (Figure 4). Considering that many previous papers have opted for the input aggregation approach [48,49], the use of output aggregation may need to be considered for future UAS aggregation studies, as was also found by [50].

3.2. Aggregation Properties of the UAS In-SA, In-BC

Because input aggregation schemes, on average, underperformed relative to output aggregation schemes (Section 3.1), possible sources of aggregation errors were explored with respect to both fluxes and model parameters. Input image parameters (T_r, f_c) and output ancillary parameters (r_a, u^*) were investigated by plotting R_e values as a function of pixel resolution (i.e., 5 m, 10 m, 30 m, 90 m). The r_a and u^* were included in this study because they have been cited as contributing sources in regard to aggregation [47].

R_e values from the same set of inputs and outputs are provided in Figure 9. The data presented in Figure 9 are parameters obtained from arithmetic averaging (i.e., In-SA). R_n-G errors were less than 10 percent across resolutions and were very low relative to the turbulent fluxes (i.e., LE/H, Figure 9a,b). This finding has been observed across both non-contextual and contextual models, as R_n is affected more by solar properties than vegetation/soil properties [19,37]. The LE relative error values were similar on June 16 (partial vegetation cover) and July 28 (near-full vegetation cover) (Figure 9c,d). Because LE is calculated as a residual from R_n-G and H, it stands to reason that H errors are contributing to LE aggregation errors, and this was in fact observed from the data, particularly on July 28 (Figure 9f). The effect of this H error on July 28 resulted in greater LE R_e values ranging from two to five percent.

With respect to model parameters, r_a errors were relatively low, ranging from one to five percent (Figure 9i,j). The f_c relative errors were much higher than r_a, although these errors decreased from June 16 to July 28 (Figure 9k,l). The u^* relative errors were lower than both r_a and LAI, although their errors similarly decreased in time (Figure 9m,n). The T_r relative errors were low and constantly close to zero across both dates (Figure 9g,h). Thus, f_c appears to be the main source of aggregation error during partial canopy and full canopy stages, as was the case in previous studies [19]. These findings reaffirm the importance of f_c as stated by the original model developers [36]. However, given that input image aggregation was not the optimum approach in this study (Figure 7 and Figure 8), f_c (and LAI) errors can be avoided through the use of output flux aggregation, preferably by first choosing a pixel resolution suitable for TSEB-PT modeling, which will be dependent on the canopy structure and distribution [9].

3.3. UAS Aggregation as Compared with OAS and SAT Imagery

Next, we compared LEs from one UAS-aggregated technique (Out-SA, Figure 2) with those predicted from OAS and SAT imagery. This is first shown in Figure 10, where UAS Out-SA and OAS LEs (at their resolution, Table 1) are plotted against eddy covariance LEs at the time of the UAS and OAS flights. Figure 10 shows that, across both sampled OAS altitudes, the UAS Out-SA was more similar to eddy LEs. For example, the MAPE values from UAS LEs are 7.0 percent at the 1.33 m pixel resolution. In contrast, the MAPE value from OAS was at 19.6 percent. The scatterplot between the UAS Out-SA and eddy LEs is not outwardly biased (Figure 10). Therefore, aggregated UAS LEs, given the limited number of sampling points, might be a more suitable approach towards accurately estimating LE than using OAS remote sensing.

Trends observed at the flux towers (Figure 10) were also observed across the whole field (Figure 11), whereby modeled LEs were greater from OAS than UAS imagery. One potential reason why this trend might be occurring is that measured T_r decreases as the survey altitude increases from UAS (purple) to OAS (orange) surveys (Figure 12). All things being equal, lower T_r signatures result in higher LEs due to lower T_s and T_c values, which reduce H and result in higher LEs. Figure 12 also shows that the UAS-aggregated T_r encompasses a greater range than that encountered by the OAS T_r. In this situation, therefore, the OAS uncooled microbolometer may be unsuitable for accurately determining T_r, and as a result, estimating LE, especially when UAS-aggregated solutions offer promise.

In addition to the OAS, UAS-aggregated LEs via Out-SA were compared with SAT LEs, both across the field and compared to the eddy flux towers. Figure 13 shows the spatial correlation between UAS LE (y-axis) and SAT LE (x-axis) fluxes on 16 June 2017, from the limited sample area (Figure A1). Whole-field comparisons between UAS and SAT LE reveal large differences in modeled LE, with UASs ranging from 315 to 506 W m⁻², while SAT only ranges from 430 to 472 W m⁻². Note that this data is coming from areas that do not fall under clouds and/or cloud shadow on June 16 (Figure A1). While the LEs between platforms are not entirely comparable due to differences in thermal acquisition times (Table 1), UAS-aggregated LEs, at the very least, are more spatially variable than SAT LEs. To address the differences in acquisition times, SAT/UAS LEs were normalized by tower-measured R_n-G (i.e., available energy). The resulting ratios approximately normalize the effect of different available energy conditions between UAS and Landsat overpass times. These ratios were then compared with the associated available energy fraction from the tower around the overpass time. Through this analysis, the resulting flux ratios can be better compared between the platforms and the towers by reducing the effect of the different radiation conditions for the two overpass times. Results indicate that the flux tower ratio fell within the UAS LE/R_n-G fraction distribution, while it did not for the corresponding SAT LE/R_n-G fraction distribution. Specifically, the UAS LE/Rn-G fraction distribution was 0.70 ± 0.09 (n = 11), and the tower LE/R_n-G fraction was 0.56; the SAT LE/R_n-G fraction distribution was 0.88 ± 0.03 (n = 11), and the tower LE/R_n-G fraction was 0.59. Therefore, any errors induced in the UAS aggregation process may be acceptable because they may capture intra-row variability and its patterns [4].

Flux comparisons between the UAS and SAT platforms at the tower were performed as in Figure 10, except here fluxes were extracted from single pixels encompassing eddy flux tower B (Figure 1, flux tower B) at the time of the UAS and SAT flights. Given the one tower data point on June 16, the residual error between the UAS and eddy flux LE was −52 W m⁻², while between the SAT and eddy flux it was 126 W m⁻². Therefore, while the number of data points is very limited, there is initial evidence to suggest that aggregated UAS fluxes (via Out-SA) might be more accurate than SAT approaches—such a study should aim to collect and compare UAS and SAT imagery beyond the single overpass date presented here.

4. Discussion

The purpose of this study was to evaluate ultra-high (cm-scale) UAS-aggregated imagery within the context of LE modeling. Out of the parameters selected in this study, the largest aggregation errors were predominantly attributed to f_c across both IOP dates (Figure 7 and Figure 8). Here, it was assumed that f_c could be used as a proxy for LAI, based on the methodology described in this paper (Section 2.5.1). This study reinforces previous observations that, even with high-resolution UAS imagery, the surface heterogeneity of the site is a major factor that controls remotely sensed LE aggregation properties [47]. These findings agree with other TSEB aggregation studies [19], although their study was restricted to SAT imagery. The f_c and associated LAI affect several components of the TSEB-PT model, including (1) aerodynamic roughness length (or z_om), (2) zero-plane displacement height (or d), (3) shortwave canopy/soil net radiation (S_n,c/S_n,s), (4) longwave canopy/soil net radiation (L_n,c/L_n,s), (5) clumping index (Ω₀), and (6) canopy layer boundary resistance (or R_x) [36,39,40,41].

Because R_n-G aggregation errors were relatively low (Figure 9), f_c aggregation errors were most likely not manifested through the components of R_n (i.e., S_n,c/S_n,s, L_n,c/L_n,s). Other parameters of R_n that could potentially contribute to aggregation errors, such as shortwave albedo and emissivity, relative to other parameters (such as H), are minimal (Figure 9a,b). Other papers have reported substantial error (greater than 50 percent) due to differences in surface roughness alone [47]. Therefore, it is likely that LAI aggregation errors will have an impact on aerodynamic resistance parameters and either directly or indirectly affect the estimation of H, and this could contribute to the relatively large pixel-scale errors observed (Figure 9e,f). However, prior studies evaluating the sensitivity of TSEB-PT to model inputs find that T_r and f_c/LAI can cause the largest uncertainty in H estimation [51,52].

The topic of the effects of aggregation also has relevance within crops other than cotton. For example, olive orchards and vineyards present additional modeling challenges, as the latter exhibit vertically non-uniform leaf area distribution, requiring modification to radiation and wind extinction algorithms used in uniform canopies [12,53]. Based on a study by [54], there may be cases where a different soil resistance (r_s) scheme may be more appropriate for sparsely vegetated and clumped canopies. Future studies, therefore, might consider the potential influence on estimating aerodynamic resistance based on aggregation schemes. Given that the output flux aggregation was a better approach for this study, however, the question may not be of utmost importance, at least within these given conditions.

Another significant finding in this study was that the f_c aggregation properties (Figure 4), as well as the LE aggregation errors in general (Figure 5 and Figure 7), were more prominent during partial vegetation cover than full vegetation cover. Note that spatial variability in f_c can occur due to changes in soil moisture, soil type, management practices, etc. Such challenges could be addressed by collecting at a finer scale and then aggregating the flux output via output aggregation, as shown in this study. Furthermore, the statistical distribution of the native LE output should be addressed before aggregating LEs. Output flux aggregation is expected to play a role in the validation of coarser-scale flux products provided by Landsat and Sentinel [55]. The finding here that calculating LE or ET_a at the original resolution, rather than an aggregated resolution, has been found elsewhere, at least with satellite imagery [15,56]. In fact, this approach of output flux aggregation is similar in concept to that used in the disaggregation scheme of the DisALEXI (Disaggregation Atmosphere Land Exchange Inverse) model [57]. The downside of these findings, however, is that greater resources (i.e., time, money, etc.) will need to be spent on post-processing operations, such as GCP deployment, high-grade GPS collection, and orthomosaicking. UASs also present LE challenges in terms of finer resolution, amplifying sources of noise such as shadows, canopy glint, and blurriness from wind [58].

Beyond the model parameterization, it is possible that f_c errors are exaggerated due to the UAS data collection process. Multispectral surveys were conducted at different times than the thermal survey, indicating potential differences in illumination conditions between multispectral and thermal surveys (Table 1). These temporal differences can result in image misregistration and, therefore, LE estimation errors. However, given that the model results were less than 10 percent on these two dates (Table 5) and that UASs were more accurate than OASs (Figure 10), this potential error does not appear to be substantial. Recent technological improvements have allowed for multispectral and thermal cameras to collect data at the same time, and preliminary results in the literature suggest this platform setup may be useful for future UAS studies that aim to model LE via TSEB models [59].

In this study, the aggregated UAS was more accurate in replicating eddy flux tower LE measurements relative to OAS (Figure 10). One hypothesis for this result may be that the differences in altitude between the UAS and OAS. As the survey altitude increases further from the ground, outgoing longwave radiation will be attenuated through interaction with water vapor and gases in the atmospheric column, requiring a greater atmospheric correction [60]. The thermal correction approach described here for the OAS is more uncertain due to relatively large pixel resolutions. It is hypothesized that there is more uncertainty in estimations of OAS T_r because the size of the cold object used for correction (i.e., polystyrene blocks) was at or slightly smaller than the OAS thermal pixel resolution. Therefore, the average of polystyrene predicted T_r could not be extracted with OAS thermal images. Another reason why the UAS may have outperformed the OAS sensor could be differences in thermal sensor quality. Both cameras in this study were uncooled microbolometers and are known for producing image blur while the sensor is in motion [61]. Given that the OAS was traveling much faster than the UAS, the resulting blur could increasingly degrade the former’s image quality. Thermal image blur can be reduced using cooled thermal infrared sensors, but these systems cannot currently be equipped aboard UAS platforms, nor are they cost-effective [62]. Future studies might consider comparing UAS LE aggregation properties using output aggregation against those of OAS cooled sensors.

In this study, the land use type was mainly uniform, as a uniform seeding rate and a single variety were growing under a uniformly irrigated field. It would be interesting to evaluate the UAS LE aggregation properties under production fields with multiple land use types [11], for example, found that LE discrimination between corn and soybean fields was diminished beyond a pixel resolution of 960 m. The effects of these studies will be determined by the nature of the objects themselves, as well as their spatial pattern [61], for example, found that high pixel-scale relative errors were linked with areas that show highly contrasting surface roughness properties, such as irrigation canals and production field boundaries. If there is interest beyond a single production field, the approach described in this study could be used to validate platform sensors, such as satellites. While this study was limited to Landsat 8, the launch of Landsat 9 is now available for future studies. Validation could also be applied for fused satellite products, such as Sentinel-2 and Sentinel-3, as proposed by [63] and disaggregation techniques described using multiple satellite sources, including ECOSTRESS and Landsat [3].

5. Conclusions

The purpose of this study was to evaluate the impact of aggregation methods on spatially distributed latent heat flux (LE) when compared to more established occupied aircraft (OAS) and satellite (SAT) remote sensing platforms. The UAS data was aggregated from a fine scale (1.3 m) up to 90 m to compare with OAS and SAT imagery. Although this study was on only one field, results indicate that aggregating the UAS LE output with simple averaging (Out-SA) produced the lowest relative pixel-scale errors and lowest absolute prediction errors for LE when compared to the eddy covariance flux tower measurements. Aggregating UAS imagery-based estimates of LE using the TSEB-PT model was also more accurate in reproducing LEs from eddy flux towers than applying OAS and satellite imagery. This study suggests that UAS LE estimates, despite their data complexity, can be a reliable source of spatial LE, and if reliably extrapolated, spatial daily ET_a, as shown by [50] for evaluating coarser resolution LE and daily ET_a products from SAT data. UAS can also potentially provide ET_a maps over targeted fields at critical stages in crop development when SAT data may be unavailable. Additional studies on other crops, crop growth stages, and land use types would strengthen these conclusions.