## 1. Introduction

*k*is the von Kármán constant,

*z*is the height above the ground,

*ζ*=

*z*/

*L*(

*L*is the Obukhov length scale) is the stability parameter,

A number of studies have been carried out to analyze the observational characteristics of

The studies done so far are primarily focused on analyzing the behavior of

The understanding of

## 2. Data

The data used in the present study are obtained from slow- and fast-response sensors mounted over a 32-m micrometeorological tower deployed in a remote grassland area of Birla Institute of Technology, Mesra, Ranchi (23.412°N, 85.440°E), India, with an average elevation of 609 m above mean sea level in a tropical region (Fig. 1). There are few suburban buildings in the area between the east and the northwest. There are hostel buildings, residential houses, and dense trees in the area between the southeast and the east (Tyagi et al. 2012; Dwivedi et al. 2014). A building nearest to the tower is a school to the northwest. There is agricultural land in the area between the northwest and the west. The area between the southeast and the west is relatively flat and free from any obstacle.

The slow-response sensors at logarithmic heights of 1, 2, 4, 8, 16, and 32 m on the tower measure air temperature, wind speed, wind direction, and relative humidity. A fast-response sensor (CSAT3 sonic anemometer) at 10-m height measures the three components of wind and temperature at a 10-Hz frequency (https://www.bitmesra.ac.in/cms-aboutus.aspx?this=1&mid=16&cid=17).

## 3. Analysis and methodology

*u*′,

*υ*′, and

*w*′ are, respectively, the fluctuations in longitudinal, lateral, and vertical wind components.

*U*is the mean wind speed.

The whole dataset is divided based on the wind speed and the stability regimes. As the focus of the study is on unstable conditions, data during the daytime conditions with ^{−1} and the transition period between day and night are excluded. To minimize the effect of the rainfall on the measurements, the data points corresponding to the 1 h before and after rainfall are also excluded. A total of 772 hourly data points with ^{−1}) and moderate (>2 m s^{−1}) winds, respectively. Since most of the data points corresponding to the range

Quantitative description of the data in each of the unstable sublayers according to Bernardes and Dias (2010).

## 4. Results and discussion

### a. The observed behavior of with respect to wind speed in different sublayers

An increasing nature of *U*. Despite these opposing tendencies, *U*.

The regression curves for this dataset are found to be power-law profiles: (i) *U* as a power-law profile: *U* in moderate to strong instability (DCS, DCS–FCS transition, and FCS layers). This indicates that the correlation of *U* in weakly to moderately unstable conditions, suggesting that the relationship appears to be significantly influenced by the stability of the atmospheric surface layer. However, it is not feasible to isolate the effects of instability and the wind speed on the values of drag coefficient because of self-correlation (Mahrt et al. 2001).

### b. The observed behavior of with respect to U in different wind direction sectors

Land-based observations of *U* in different wind-direction sectors. The wind direction is taken as a clockwise angle from the north and is divided into 24 sectors with an interval of 15° and numbered accordingly as 1, 2, …, and 24. There are some buildings and trees in sectors 1–9 and 23 and 24 (denoted as region I) while there is agricultural land lying in sectors 17–22 (region III). Sectors 10–16 (denoted as region II) belong to a relatively flat area. The observed behavior of *U* remains almost similar in each of the regions following the power law (Fig. 3). The average value of

### c. The observed behavior of with

The scatter in *U* than

The variation of drag coefficient with

Table 1 shows the amount of data and the observed average values of *C*_{D} increases in weak to moderate instability, reaching a peak value, beyond which it starts decreasing with increasing instability.

A physical reasoning for the observed decreasing nature of *u*_{*} and *U*. The frictional velocity increases with *u*_{*} with

The behavior of

The analysis of the limited turbulent measurements for April and May 1999 at Anand (22°35′N, 72°55′E) during the Land Surface and Processes Experiment (LASPEX) also reveals a decreasing tendency of

The decreasing tendency of drag coefficient with increasing instability was also observed over the sea surface (Konishi and Nan-niti 1979; Tsukamoto et al. 1991). Konishi and Nan-Niti (1979) cited a personal communication (T. Hanabusa et al. 1976) for pointing out an observed decreasing trend with increasing instability over the land surface under the rough conditions at the Tsukuba meteorological observation tower of the Meteorological Research Institute (Japan).

Recently, Peng and Sun (2014) have also observed a decrease in *C*_{D} over a forest canopy with peak value at

On the other hand, a systematic mathematical analysis (appendix A) shows that

Rao and Narasimha (2006) also pointed out the inadequacy of MOS theory to explain the MONTBLEX-90 data at Jodhpur in low-wind convective conditions and proposed a subregime of weakly forced convection within the regime of mixed convection, which is governed by velocity scales determined by the heat flux.

By analyzing the CASES-99 dataset, Vickers and Mahrt (2003) observed the decreasing nature of

Thus, it seems that the decreasing nature of

## 5. Issues and limitations

In this study, the observed behavior of drag coefficient is analyzed with respect to the wind speed and stability parameter. Some underlying issues and the limitations associated with the analysis are discussed.

### a. Misalignment of wind and stress vector

In a constant flux layer, if the coordinate system is aligned with the mean wind, the stress vector should be parallel to the mean wind direction. However, a significant angle between mean wind and stress vectors is observed over sea as well as land surfaces (Geernaert 1988; Rieder et al. 1994; Weber 1999; Bernardes and Dias 2010). The misalignment of mean wind and stress vectors increases with increasing instability that might be attributed to an Ekman-layer effect of momentum transport by large eddies (Mahrt et al. 2001; Bernardes and Dias 2010). The angle *U* as well as on

### b. Nonavailability of mixed-layer height and convective velocity scale

In the case of strong instability when the surface stress becomes small, the surface-layer scaling appears to break down; in this situation, an alternative scaling, such as either mixed-layer similarity or local free-convection similarity scaling, can be used. However, in the present study, it is not possible to use these scales because of the nonavailability of mixed-layer height *z*_{i} and convective velocity scale *w*_{*}. The velocity scale based on the heat flux rather than frictional velocity, as suggested by Rao and Narasimha (2006), needs to be evaluated as an alternative to the MOS theory using the slow measurements along with the turbulent measurements used here.

### c. Self-correlation

Self-correlation is referred to, in the literature, as spurious correlation or the shared variable problem that arises when one (dimensionless) group of variables is plotted against another and the two groups under consideration have one or more common variables (Klipp and Mahrt 2004). Although MOS theory is widely used to compute surface fluxes, physical interpretation of MOS can be ambiguous because of circular dependencies and self-correlation (Hicks 1978; Kenney 1982; Andreas and Hicks 2002; Klipp and Mahrt 2004; Baas et al. 2006; Vickers et al. 2015). In the present analysis, both *u*_{*} as a common variable, causing spurious self-correlation between *U* as well as between *u*_{*} while keeping the values of *U* and *U* as well as those of *U* as well as the

Mahrt (2008) also observed that the correlation between *u*_{*}, and its physical significance cannot be evaluated from the data. We hasten to point out here that the analysis of the dataset suffers from the problem of self-correlation.

## 6. Conclusions

The observed behavior of the drag coefficient is analyzed with respect to wind speed and stability parameter in the different unstable sublayers from the turbulent measurements taken at Ranchi in a tropical region. The average value of *U* is observed to follow the power-law profile. The parameterizations of *U* are proposed in five unstable sublayers, as suggested by Kader and Yaglom (1990) and Bernardes and Dias (2010).

The variation of

The authors wish to thank Dr. Manoj Kumar for providing observational data. This work is partially supported by the Ministry of Earth Sciences, Government of India under the CTCZ program. We also thank Dr. Larry Mahrt for his valuable comments. The authors wish to thank the reviewers for their comments and suggestions.

# APPENDIX A

## Mathematical Analysis of with

Thus, the above arguments show that (i)

# APPENDIX B

## An Illustration with an Alternative Form of

Notice that the results presented in appendix A hold well as long as the similarity function

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