Sensible and Latent Heat Fluxes Over A Processing Cassava Crop with The Surface Renewal and Energy Balance Method


 There are several methods for determining the sensible heat flux (H) on natural or agricultural surfaces. One such method is the surface renewal (SR) based on ramps of air temperature measured at high frequency by means of an ultra-thin thermocouple. The micrometeorological tower was installed (13°6'39"S, 39°16'46"W, 154 m anm) to assess the suitability of the method in estimating H on industrial cassava cultivation via calibration in relation to the eddy covariance (EC ), this consisted of a 3D anemometer. In both systems, measurements were made at a frequency of 10 Hz and comprised the period from 17/04 to 25/07/2019 (100 days). In addition to high-frequency measurements of air temperature and sonic temperature, measurements of net radiation and ground heat flux were also made, and all data grouped at 30-min intervals for determination of latent heat flux (LE) via balance solution power. It was found that (a) the SR method was adequate to estimate the sensible heat flux (H) over industrial matched with a calibration coefficient equal to 0.96; (b) under conditions of unstable atmospheric stability (daytime) the SR method showed better performance for estimating H compared to stable atmospheric conditions (nighttime); (c) the SR method proved to be adequate for estimating the latent heat flux (LE), in the industrial cassava cultivation with a high degree of correlation (r2 > 0.90), with the EC method as a reference; and (d) in the area cultivated with industrial cassava, it was found that the heat flux in the soil (G) corresponded on average to 6% of the radiation balance.


Introduction
Understanding the fate of radiative exchanges between the surface and the air is fundamental for modeling the turbulent mass and energy exchange processes that occur in the lower atmosphere (BONAN, 2016). At the surface level, the total radiation balance (Rn) is the energy source for heating the air (H), heating the medium below the surface (G) and for evaporating water (LE). This partition is commonly represented by the simpli ed energy balance equation [Rn = G + H + LE], where theoretically the difference (Rn -G) is the energy available for turbulent ows (H + LE).
In vegetated areas, LE represents the energy involved in the evapotranspiration (ET) process, a fundamental concept in the context of crop water requirements and irrigation water management. Rn and G can be easily measured with appropriate instruments under eld conditions (SNYDER et al., 2008).
Obtaining H and LE, on the other hand, is more challenging, as it requires the use of complex and costly instrumentation and requires a method of observation of the turbulence that dominates these two processes in the atmospheric boundary layer (MONTEITH; UNSWORTH, 1990). The method has been used on a wide spectrum of surfaces. Mengistu and Savage (2010) used RAS to estimate evaporation from a lake in South Africa. The method has been used on vegetation with wide variation in its characteristics such as plant height, age, orientation and planting density as well as The area planted with cassava in Brazil in 2017 was 1.4 million hectares with average productivity ranging from 9.8 to 21.9 t ha-1 (EMBRAPA, 2018) and a national average around 15 t ha-1. Cassava is typically cultivated under rainfall, but when irrigated it can yield twice as much (COELHO FILHO, 2020). To date, there are no reports of the use of the air renewal method to measure the sensitive heat ux H on cassava crops, either under irrigation or under rainfall conditions. The objectives of this work were (1) to calibrate a surface air renewal system to determine the sensible heat ux over an industrial cassava area; (2) quantify the sensible heat and latent heat uxes from the crop with the combined methods of surface air renewal and energy balance; and (3) study the partition of the total radiation balance between the components of the energy balance. The plot where this study was conducted has an area of approximately 10 ha, cultivated with the industrial cassava variety BRS Novo Horizonte. The culture was conducted under a rainfall regime with planting spacing of 90 cm between rows and 80 cm between plants in the row.

Weather tower positioning
The main criterion for choosing a point inside the area for positioning the tower was to ensure su cient upwind direction. Ease of access to the tower was also considered as a criterion, considering the growth of plants that would make it di cult for personnel to move.

Instruments and data collection
Fast-response and slow-response sensors taken to the eld for data colLEECion are listed in Table 1.  Fast response sensors were scanned at a frequency of 10 Hz and data summarized at 30-minute intervals. This was also the integration interval for the data from the slow response sensors, except that these were scanned every 5 s.

Determination of energy balance components
Sensitive heat ux (H) In the present study, the sensible heat ux density H (W m-2) was determined by two methods: (1) surface air turnover (RAS) and (2) eddy covariance (hereafter referred to as CT). The second was used as a reference for calibrating the rst.

Surface Renewal Method (RAS)
Here, this work, the then Surface Renewal, was translated as a method of surface air renewal. Figure 1, adapted from  illustrates the theoretical formation of air temperature ramps. When a parcel of air comes into contact with the elements of the canopy, it is assumed that a period of quiescence occurs in which there is no variation in the temperature of the parcel (Figures 1a, e). If the plot is cooler than the vegetation then it gains energy and experiences a gradual increase in temperature which is then detected by the ultra-thin thermocouple above the crown (Figures 1b, f). Subsequently, the plot ejects and is replaced (renewed) by another one that is cooler than the vegetation, producing a sharp decline in the temperature trace (Figures 1c, g). From this point, the cycle eventually repeats (Figure 1d, h).
Temperature ramps are characterized by an amplitude (A) and the inverse of the ramp frequency (d + s), as shown in Figure 2, for both conditions of atmospheric stability. Sensitive heat ux density is calculated from these characteristics using an average slope representative of a given time interval, eg 30 minutes, according to Equation 1.
where: HSR is the sensible heat ux density after calibration (W m-2); H' is the sensible heat ux density before calibration (W m-2); α is the calibration factor; ρ is the air density (kg m −3 ); Cp is the speci c heat of air at constant pressure (J kg −1 °C −1 ); A is the ramp amplitude (°C); 1 / (d + s) is the ramp frequency (s −1 ) and z is the thermocouple temperature measurement height (m). Snyder et al. (1996) used statistical moments and the Van Atta (1977) structure function (Equation 2) to calculate the A and (d + s) characteristics of the mean slope, as follows: where: m is the number of data points in the 30-minute interval measured at frequency f in Hz; n is the exponent of the function; j is the sampling interval (sample lag) between data points corresponding to a fraction of time (time lag) r given by the ratio (j / f); and Ti is the i-th temperature sample in the 30-minute series. According to Snyder et al. (1996) a condition in Van Atta's (1977) linearized model is that the time fraction r must be much smaller than (d + s).
An estimate of the mean amplitude value A is obtained by solving Equation 3 for real roots.
[ ] ( ) Where: and Once the ramp amplitude is known, the inverse of the ramp frequency (d + s) is calculated according to . In the second method, the sensible heat ux H was obtained using the eddy covariance technique according to Equation 7.
where: HEC is the sensible heat ux density (W m-2) via eddy covariance; ρ is the air density (kg m −3 ); Cp is the speci c heat of air at constant pressure (J kg −1 °C −1 ); w′ is the instantaneous deviation of the vertical wind speed around the mean (ms −1 ); and T′ is the instantaneous deviation of the sonic anemometer temperature around the mean (°C).
Net radiation and soil heat ux (Rn and G) As shown in Table 1, the net radiation Rn at the vegetation level was measured with a radiometer balance positioned 270 cm above the ground and mounted on a metallic arm pointing to geographic north.
Two heat ux plates were used to measure the heat ux 8 cm deep and 200 cm away from the tower tripod. One of the plates was installed between plants in the row and the other between rows to better represent the measurements. Soil temperature variation above each plate was monitored with soil thermocouples inserted at 2 and 6 cm depth while soil moisture within the surface layer was measured with an FDR sensor as described in Table 1.
The heat ux on the soil surface was calculated according to Equation 8.
where: G is the soil surface heat ux (W m −two ); G8 is the ground heat ux measured 8 cm deep; Ts(i) and Ts(i-1) are the mean soil temperatures above the plate at the beginning and end of the time interval Δt, respectively; Δt is the time interval (1800 s); zs is the installation depth of the heat ux plate (m); and Cs is the caloric capacity of the soil (J m −3 °C −1 ) calculated with Equation 9 assuming for the experimental area a mineral soil with a particle density of 2.65 Mg m −3 and negligible organic matter content.

Latent heat ux (LE)
The latent heat ux density was obtained as a residual of the energy balance (Equation 10).

LE = Rn − G − H
where: LE is the latent heat ux density (W m −two ) from vegetation; Rn is the total radiation balance (W m −two ); G is the soil heat ux density (W m −two ); and H is the sensible heat ux density (W m −two ). Since measurements of H with air renewal and eddy covariance were obtained independently, the energy balance could be solved for both methods in order to obtain, respectively, LESR and LEEC.

Footprint analysis
A footprint analysis around the micrometeorological tower to delimit the area contributing to turbulent ows was determined based on the model by Kljun et al. (2015) through the FFPOnline tool (v.1.22) found inhttp://footprint.kljun.net/download.php. Zero plane of displacement (d) was calculated as 2/3 of crop height (hc). The Monin-Obukhov length, which is used to characterize atmospheric stability conditions, was calculated according to Equation 13.

( )
where: ρ is the density of air (kg m−3), Cp is the speci c heat of air at constant pressure (1004 J kg−1 K−1), u* is the friction velocity (ms−1), T is the air temperature (K), g is the acceleration due to gravity (9.81 ms−2), and H is the sensible heat ux density (W m−2).

Results And Discussion
Wind direction and footprint analysis Figure 3 shows different aspects of the experiment site. Figure 3A is a picture of the tower obtained on 04/30/2019, showing the relative position of the instruments, including the 3D sonic anemometer and the ultra-thin thermocouple (TPUF). Figure 3B shows the compass rose made from 30-minute average data obtained with the sonic anemometer in the period from April 17 to July 25.
The compass rose in Figure 3B shows that the wind blew predominantly (63% of frequency) from the east-south sector with the following distribution: 21% from the south-southeast direction (SSE), 17.4% from the SE direction, 11, 5% from the east-southeast direction (ESE) and 13.2% from the E direction. In each direction, the average wind speeds were 1.13 m s-1 (SSE and SE), 1.23 m s-1 (ESS) and 1.5 m s-1 (E). Figure 3C shows an average footprint for the entire measurement period on an image of the experimental area obtained from Bing, regardless of the change in sonic anemometer height during the period. Overall, the compass rose and the footprint of the turbulent ows are in agreement.
The distance "seen" by the sonic anemometer in the upwind direction totals approximately 50 m on average from the micrometeorological tower. In the prevailing wind direction (SSE) the area of contribution of 90% of turbulent ows is more pronounced.
Calibration of surface air renewal method Table 2 shows the calibration factor (α), the coe cient of determination (R2) for the regressions through the origin when H of the eddies covariance (HEC) was plotted against the H estimated by air renewal (H'). Data are presented separately for each atmospheric stability condition according to crop growth and change in heights of rapid response sensors and are also presented for the entire measurement period.   Figures 4A and 4B show that the agreement between HEC and H' was excellent even before calibration, with a coe cientα of 0.98 as previously shown in Table 2. Under stable atmosphere condition ( Figures 4A and 4B Figure 5B shows the calibration result with excellent agreement between HEC and HSR. The correlation between LEEC and LESR is high (R2 > 0.95) ( Figure 5C) as expected as the agreement between HEC and HSR was also high and both LEEC and LESR are calculated from the same set of values of Rn and G. The data suggest that a single calibration coe cient equal to 0.96 can be used for cultivation conditions and climate similar to those presented in this work, with the aim of estimating the sensible heat ux (HSR) in other years of planting provided that the conditions are approximately the same, that is, the same variety is cultivated in the same spacing conducted under rainfed conditions. Furthermore, the value found for the calibration coe cient α being very close to 1, there is the possibility of using the surface air renewal method with this crop and under the conditions mentioned above without the need for calibration, which in principle would be An ultra-thin thermocouple installed around 50 cm above the crop is su cient to colLEEC air temperature data and direct application of the air renewal method to determine H.

Energy balance components
The diurnal variations of these components for the months of May and June are shown in Figure 7. For the months under study, the maximum LE values were observed on 05/03/2019 and 06/16/2019, respectively, in the order of 460 .56 and 332.45 W m-2. From the data on global solar radiation, days (13/05 and 17/06) different from those mentioned above were identi ed, these have high cloudiness, whose LE values represent the lowest for the period, 180.34 and 65.23 W m-2. For 05/13/2019 and 06/17/2019, the sensible heat uxes are practically equivalent to the heat ux in the soil, which indicates that there was little energy available to heat the air and the soil, and that 90% de Rn was used for the processes of loss of water to the atmosphere, which is in agreement with Jensen and Allen, (2016) and Gao et. al. (2020).
For both dates 05/03/2019 and 06/16/2019 observed in Figure 7, daily average of G was negative, therefore, all the heat was released to the ground.  Figure 8 shows the relationship between components of the radiation/energy balance in the cultivation of industrial cassava from hourly averages of the data collection period in the experimental area. Figure 8B shows the relationship between soil heat ux (G) and net radiation (Rn). During the entire period of data collection, which coincided with the vegetative phase of the cassava crop, the degree of ground cover was visually signi cant, especially because measurements started when the plants had an average height of 60 cm and a predominance of cloudy days. The average value found for the G/Rn ratio was only 6%, which is explained not only by the soil cover by the crop, but also by the proliferation of weeds, considering that the crop was conducted under rainy conditions. In addition to the change in soil water content, the type of cover is a factor responsible for variations in soil heat ux. Figure 8C shows the relationship between the sensible heat ux obtained via air renewal on the HSR surface and the net radiation Rn. The average H/Rn ratio with this method was around 22%, indicating that most of the available energy must have been used for water evaporation, whose LE/Rn ratio was around 72%, considering that the culture was conducted under rainfall conditions. The period from March to September is the wettest in the region with over 70% of annual precipitation concentrated in these months. Rain data were not collected during the experimental period.

Author Contributions and participate
All authors contributed to the study conception and design. Material preparation, data colLEECion and analysis were performed by Neilon Duarte da Silva, Aureo Silva de Oliveira and Mauricio Antonio Coelho Filho. The rst draft of the manuscript was written by Neilon Duarte da Silva, and all authors commented on previous versions of the manuscript. All authors read and approved the nal manuscript.

Data Availability
The datasets generated during and/or analysed during the current study are not publicly available due to as they are source of the University Federal oh the Reconcavo of Bahia but are available from the corresponding author on reasonable request..

Code availability
Not applicable

Ethics approval
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Consent for publication
The authors agree with the publication of the article and are responsible for the content Figure 2 Linearized model of temperature ramps for both unstable and stable conditions, where A is amplitude and (d+s) inverse ramp frequency.    Relationship between net radiation (Rn) and energy balance components (G, H and LE)