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Observing and Modeling the Vertical Wind Profile at Multiple Sites in and above the Amazon Rain Forest Canopy.

1. Introduction

There are several issues that have motivated researchers to intensify their studies on the interaction between the Amazon rainforest and the atmosphere [1-4]. Among these issues is the role that the Amazonian forest exerts the liberation of energy in the tropical atmosphere [5], on the hydrological cycle [6], and in the global balance of secondary gaseous components in the atmosphere, such as ozone, carbon dioxide, and hydrocarbons [7]. Furthermore, there are problems associated with deforestation in the Amazon that could have a direct influence on global climate change [8]. In this context, understanding the processes of energy, mass, and momentum exchanges between the Amazon forest and the atmosphere is of fundamental importance. Although considerable progress has been made in this area over the past 30 years [9-12], more details on variables controlling the said exchanges are needed.

According to Yi [13], the vertical profile of the wind velocity, together with the Reynolds stress, is of fundamental importance to the characterization of turbulent flow over vegetated surfaces, an assertion particularly relevant in dense forest areas. Studies conducted in Amazon forests have shown persistent decoupling of the atmospheric flow-between the lower and upper forest canopy [10], due to reduced penetration of direct solar radiation inside the forest and corresponding static stability near the forest floor [9], a condition that often persists over the entire diurnal cycle [11, 12, 14, 15]. Mechanical turbulence generated at canopy top by the rough canopy becomes a determining factor that dominates turbulent mixing processes between the upper and lower forest canopy [16].

An hypothesized, dynamic instability associated with an inflection point in the above-canopy wind profile in what is known as the roughness sublayer [17-20] is another factor that may contribute to the production of turbulence that penetrates into the lower canopy [16, 21]. Dias Junior et al. [22], working in the Amazon, showed the existence of a strong correlation between the inflection point height and time scales of coherent structures, known to contribute to turbulent mixing in forest areas [21].

Only a few previous studies have been done using to describethe wind profile shapeinthe rain forest canopy, combining observational data and modeling. Sa and Pacheco [23], using a third-order polynomial fit, estimated the inflection point height and the average wind speed at the inflection point as well as a characteristic length scale used to normalize the vertical wind profile in an Amazonian forest. Souza et al. [24], using the same data as did Sa and Pacheco [23], proposed an empirical-analytic model that was able to satisfactorily reproduce the vertical wind profile observed.

What is common among most of the work on the vertical wind profile in the Amazon [22-25] is the use of data from a single point of measurements, with good spatial resolution for only part of the profile, raising the question that these studies may be unrepresentative of dense forest areas in the Amazon overall. Thus, the aim of this study was to evaluate the different aspects of the vertical wind profile measured at different experimental sites in the Amazon. In addition, simplified models were used to simulate the profiles. Furthermore, for one of these models, an improvement was proposed in its formulation in order to reduce the input variables necessary for the model to generate the wind profile.

2. Materials and Methods

2.1. Study Area and Data. This research used observational data collected in five experimental sites in the Brazilian Amazon, where micrometeorological observation towers were installed, namely, the Rebio-Jaru Forest Reserve [28], located in the state of Rondonia in the Southwest Amazon; the Cuieiras Biological Reserve (also called site K34, [29]), located next to the city of Manaus, Amazonas; the Tapajos National Forest (FLONA, Km 67 site) near the city of Santarem, Para [30]; the Caxiuana National Forest about 350 km west of the city of Belem, Para [31]; and the Uatuma Sustainable Development Reserve, in the ATTO site (Amazonian Tall Tower Observatory, [3]), city of Santo Antoenio do Uatumaa, Amazonas. For the latter experimental site, data from two measurements towers were used, which will be called triangular tower (TT) and square tower (ST). The experimental design of each site is summarized in Table 1 and the geographical position is shown in Figure 1. The data used in this work consists primarily of wind speed averages at different heights within and above the forest canopy at each experimental site, made by sonic (two- and three-dimensional) and cup (specification of each instrument is listed in Table 1) anemometers.

Each of these experimental sites is in dense tropical forest with trees ranging from 30 to 40 meters high. The leaf area index (LAI) values for different sites are relatively close. de Moura [32] found 5.6 [m.sup.2][m.sup.-2] LAI value for Rebio-Jaru, and for the K34 site, Filho et al. [33], using incident solar radiation measurements, estimated LAI at 6.1[m.sup.2][m.sup.-2], and Tota et al. [27] measured 7.3 [m.sup.2][m.sup.-2] using a LIDAR. At the Santarem site, Asner et al. [34] found LAI to be approximately 6.3 [m.sup.2][m.sup.-2] in October (dry season) and 5.8 [m.sup.2][m.sup.-2] for January (rainy season). In Caxiuana, seasonal variation of LAI is quite sharp, reaching a peak in October, larger than 6[m.sup.2][m.sup.-2] [31]. Preliminary measures made in September 2013 at the ATTO site indicate LAI of 5.7 [+ or -] 0.37 (Giordane Martins, personal communication, November, 2016).

2.2. Methodology. To obtain the vertical wind speed profiles, averages of the entire time period for which data were available were taken for each height in each experimental site (Table 1). Data from three-dimensional sonic anemometers were used with the following to calculate the wind speed U:

U = [square root of ([u.sup.2] + [v.sup.2])], (1)

where u and v are zonal and meridional wind velocity components, respectively.

In this work, we use two models to simulate the vertical wind profile above and below the forest canopy. The first, which will be called Yi Model [13, 36], describes the profile:

[??](z) = [[??].sub.h] [c.sup.h.sub.D]/[c.sub.D](z)] exp {-0,5 [LAI - L(z)]}, (2)

where [[??].sub.h] is the average wind speed at h height (h = 35 m is the average canopy height), [c.sub.D](z) is the drag coefficient at z height, [c.sup.h.sub.D] = [c.sub.D](h); LAI is the leaf area index; and L(z) is the cumulative leaf area index, defined as

L(z) = [[integral].sup.z.sub.0] [alpha](z')dz', (3)

where [alpha] is the leaf area density.

The leaf area density was assumed from the values obtained by Tota et al. [27] at the tower K34 site (Figure 2). The drag coefficient was calculated as [10, 37]

[C.sub.D](z) = [u.sup.2]* (z)/[U.sup.2] (z), (4)

where u* = [[[([bar.u'w']).sup.2] + [([bar.v'w']).sup.2]].sup.1]/4 is the friction velocity wherein u', v', and w' are the wind turbulent components. This equation was applied to each height for both K34 and ATTO-TT. We then used the cubic interpolation technique to obtain values at other heights in the vertical profile (Figure 2).

The second model used in this study is an empirical analytical model based on data from sites in the Amazon and mathematical function properties, developed by Souza et al. [24] (called the Souza Model from this point forward), given by the equation:

[mathematical expression not reproducible] (5)

where [mu], [omega], [alpha],[beta], and [gamma] are fit parameters of the equation to the observed data, z is the height, and [z.sub.ip] is the inflection point height in the vertical wind profile. This model used a larger number of fit parameters, a fact that will be further discussed in the next section.

3. Results and Discussion

Figure 3 shows the vertical profile of the wind velocity of the K34 and ATTO triangular tower for the daytime (Figure 3(a)) and nighttime (Figure 3(b)) periods. Such profiles are complementary: whereas the K34 measurements show wind speed behavior inside the canopy, the ATTO data provides more information above the canopy. The shape of the profiles does not change significantly between the daytime and nighttime periods, but in general the speeds recorded during the day, at each height, showed slightly higher values than the nighttime. Due to the vegetation structure below 0.8h wind speed showed very low values, lower than 0.25 [ms.sup.-1], except for at 0.65h in the daytime ATTO profile. This point, in turn, showed the maximum difference between the profiles observed for an equivalent height, probably caused by differences in the vegetation structure between the sites.

The atmospheric stability was close to neutral, and the vertical wind profile above the forest canopy is assumed to be the theoretical logarithmic profile [17]. This assumption is approximate for both K34 and ATTO-TT sites, and Figure 3(c) shows the comparison between said logarithmic profile and the observed data. In this analysis, it is possible to note that from 0.7h to 1.5h the theoretical logarithmic profile overestimates the measured wind speed values; on the other hand, above 1.7h the values observed for the ATTO-TT were slightly higher than said logarithm profile. The reason for these differences is the roughness sublayer just above the forest canopy, and this complicates the effort to estimate accurately the relationship between the mean turbulent variables and the canopy structure [38].

From the K34 and ATTO-TT data, we obtained the fitting constants required for the Souza Model, using the least squares technique (Table 2). The constants were obtained in two ways: first by using the original equation proposed by de Souza et al. [24] (5) in which five constants are required; in the second case, we used a formulation proposed here, where only two constants are used.

[mathematical expression not reproducible] (6)

For both (5) and (6), the Souza Model fits very well to the K34 and ATTO-TT data, with a coefficient of determination ([r.sup.2]) of 0.98 and 0.97, respectively (Figure 4). Thus, (6) is more advantageous because it has a smaller number of necessary constants for the mathematical fit (the model of (6) will be called Modified Souza Model from this point forward).

An important question is whether the Souza Models (original and modified), which fit the K34 and ATTO-TT data very well, can be used to represent the vertical wind profile for other experimental sites in the Amazon. Also, a good test to see if the model represents such profiles is to compare their performance with that of another model that has already been tested in other conditions, such as the Yi Model.

We can conclude from this analysis that all models represented fairly well the vertical profile of the wind velocity for different Amazonian experimental sites (Figure 5), although there are differences among both the models and simulated and observed wind speed values, to a greater or lesser degree, for some heights. In Figures 6(a), 6(b), and 6(c), the observed wind speed values were plotted against the model output to measure the degree to which data points approach the line with an 45[degrees] angular coefficient, and which model better represents the observations at each point. Among the models, the Yi Model was the one that presented, on average, the greatest distance of observed values. The two versions of the Souza Models have similar behavior, but the Modified Souza Model has a slightly higher coefficient of correlation (0.973) compared to the original Souza Model (0.967).

To verify the ability of each model at different heights, an average of the observed and simulated wind speed values was calculated at intervals of 8 meters in height and then the difference between the modeled and observed values was calculated (Figure 6(d)). The results show that the Yi Model overestimated the wind velocity values above 48 m in height, with a greater difference between 72 and 80 m, while at the same time it underestimated values below 48 m, with a mean-squared error (MSE) of 0.12 [ms.sup.-1]. The Souza Model had its maximum divergence between 32 and 40 m, with a difference of 0.3 [ms.sup.-1] between the modeled value and the observed value. The Modified Souza Model was the one that presented the smallest absolute value at its point of maximum difference between the heights of 8 and 16 m and also presented the lowest MSE, 0.04 [ms.sup.-1]. Again, this shows that a smaller number of fit parameters in the Souza Model do not change the model's ability to simulate the vertical wind profile for different sites in the Amazon.

Each of the three models has satisfactory performance; using one or the other model depends on each situation. In the Souza Model, the constants must be different for other forest types, after which calculations for a given profile maybe extrapolated to others with similar vegetation structure. Since the Yi Model requires, in addition to other input variables, the profile drag coefficient, this, in turn, needs to be calculated for the type of vegetation.

4. Conclusions

In this work, we examined the vertical wind profile measured at different experimental sites in Amazonia. Measurements with high resolution below the canopy, performed at the K34 site, and above the canopy at the ATTO triangular tower represent for the first time that such data have been compiled in a single work and have provided a broader view of the wind vertical profile behavior in the Amazon forest. Under the forest canopy, the wind speed values were very low due to the vegetation structure, while above the canopy wind increases with height in an approximately logarithmic behavior. Furthermore, with data from the two sites mentioned above, it was possible to obtain a new formulation for the Souza Model, with a reduced number of input variables, which facilitates the use of the model for future applications. Both Souza Models (original and modified) and the Yi Model managed to satisfactorily represent the vertical wind profile for different sites in the Amazon.

http://dx.doi.org/ 10.1155/2017/5436157

Competing Interests

The authors declare that they have no competing interests.

Acknowledgments

The authors acknowledge the funding provided by the Coordination of Higher Education and Personnel Training (CAPES) and all who participated in the GoAmazon project at K34 and ATTO IOP-1-2012 for the excellent quality of the collected data.

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Raoni Aquino Silva de Santana, (1) Cleo Quaresma Dias-Junior, (2) Roseilson Souza do Vale, (1) Julio Tota, (1) and David Roy Fitzjarrald (3)

(1) Federal University of Western Para (UFOPA), Santarim, PA, Brazil

(2) Federal Institute of Para (IFPA) Braganca, PA, Brazil

(3) University at Albany, SUNY, Albany, NY, USA

Correspondence should be addressed to Raoni Aquino Silva de Santana; raoniass@gmail.com

Received 4 September 2016; Revised 24 November 2016; Accepted 25 December 2016; Published 18 January 2017

Academic Editor: Enrico Ferrero

Caption: Figure 1: Experimental sites located in the Amazon (source: adapted from Zeri et al. [26]).

Caption: Figure 2: Leaf area density vertical profile (source: Tota et al. [27]) and drag coefficient profile.

Caption: Figure 3: Vertical wind profile for K34 (blue line) and ATTO triangular tower (red line). The horizontal lines represent the standard deviation for each measurement point. The logarithmic profile was obtained through the equation u = (u*/k) ln((z - d)/[z.sub.0]), where k is von Karman's constant, [z.sub.0] = (1/30)h is roughness length, and d = 0.75h is displacement height [17].

Caption: Figure 4: Observed and modeled vertical wind profiles.

Caption: Figure 5: Vertical wind profile observed and modeled in different experimental sites in the Amazon.

Caption: Figure 6: Wind speed (U) observed versus modeled for the three models used in this study ((a), (b), and (c)). Part (d) shows the modeled minus observed wind speed for different intervals of heights, above and below the forest canopy.
Table 1: Instruments and data periods used.

Experimental       Instruments                    Reference
sites

K34 [4]        3D-sonic anemometer       CSAT3, Campbell scientific

Rebio-Jaru        Cup anemometer          Low Power A100L2, Vector
[22]                                          Instruments Inc.

                  Cup anemometer          5103, R.M. Young Company
Santarem       3D-sonic anemometer       CSAT, Campbell scientific
[30]           2D-sonic anemometer      CATI/2, Applied Technologies,
                                                    Inc.

               3D-sonic anemometer     ATI, Applied Technologies, Inc.

Caxiuana        sonic anemometers         CSAT, Campbell scientific
[31]

               3D-sonic anemometer    WindMaster, Gill Instruments Ltd.

ATTO--         2D-sonic anemometer    WindSonic, Gill Instruments Ltd.
Triangular      Automatic weather               MetPak, Gill
tower [35]           station                  Instruments Ltd.

ATTO Square    3D-sonic anemometer    R3, Gill Instruments Ltd. 5103,
tower [3]         Cup anemometer             R.M. Young Company

Experimental       Instruments            Measurement         Sampling
sites                                        heights            rate

K34 [4]        3D-sonic anemometer     1.5, 7.0,13.5,18.4,      20 Hz
                                        22.1, 24.5, 31.6,
                                        34.9, 40.4, 48.2

Rebio-Jaru        Cup anemometer       55.0, 50.55, 47.7,       0.1Hz
[22]                                   42.9, 40.25, 37.8,
                                       32.8, 26.65, 14.30

                  Cup anemometer      64.1, 52, 38.2, 30.7       1Hz
Santarem       3D-sonic anemometer            57.8             10 Hz
[30]           2D-sonic anemometer             1.8               1Hz

               3D-sonic anemometer              5               10 Hz

Caxiuana        sonic anemometers             57.8              10 Hz
[31]

               3D-sonic anemometer         78, 41 e 30          10 Hz

ATTO--         2D-sonic anemometer       23, 36, 45 e 50         4Hz
Triangular      Automatic weather          57, 60 e 72           1Hz
tower [35]           station

ATTO Square    3D-sonic anemometer          23 40 80           10 Hz
tower [3]         Cup anemometer           30, 42, 55            1Hz

Experimental       Instruments              Measurement period
sites

K34 [4]        3D-sonic anemometer      June 2014 to January 2015

Rebio-Jaru        Cup anemometer              February 1999
[22]

                  Cup anemometer
Santarem       3D-sonic anemometer        July to November 2013
[30]           2D-sonic anemometer

               3D-sonic anemometer

Caxiuana        sonic anemometers           April 18-24, 1999
[31]

               3D-sonic anemometer

ATTO--         2D-sonic anemometer        February to April 2012
Triangular      Automatic weather
tower [35]           station

ATTO Square    3D-sonic anemometer       January to February 2012
tower [3]         Cup anemometer

Table 2: Souza Models fit constants.

Constants    Souza Model    Modified Souza Model

[micro]       1.016            1.012
[beta]        0.1583            0.1
[alpha]       0.7275             --
[omega]         1                --
[gamma]       1.973              --
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Title Annotation:Research Article
Author:de Santana, Raoni Aquino Silva; Dias-Junior, Cleo Quaresma; do Vale, Roseilson Souza; Tota, Julio; F
Publication:Advances in Meteorology
Article Type:Report
Date:Jan 1, 2017
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