Advances in Meteorology

Volume 2017, Article ID 1432672, 8 pages

https://doi.org/10.1155/2017/1432672

## The Influence of the Intermittent Behavior of the Nocturnal Atmospheric Flow on the Prediction of the Diurnal Temperature Range: A Simplified Model Analysis

^{1}Instituto Federal Sul-Rio-Grandense, Campus Pelotas, Pelotas, RS, Brazil^{2}Programa de Pós-Graduação em Engenharia, Universidade Federal do Pampa, Campus Alegrete, Alegrete, RS, Brazil^{3}Departamento de Física, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil^{4}Departamento de Engenharia Mecânica, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil

Correspondence should be addressed to Felipe D. Costa; rb.ude.apmapinu@nidranedf

Received 1 February 2017; Revised 17 April 2017; Accepted 2 May 2017; Published 8 June 2017

Academic Editor: Enrico Ferrero

Copyright © 2017 Leandro L. Gonzales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The variation of the atmospheric temperature near the surface associated with anthropogenic effects is analyzed using a simplified atmospheric model. Local changes in cloud cover and four different scenarios of atmospheric concentration of carbon dioxide are considered. The results show that the highest temperature variability occurs in the weak wind and decoupled state and in the transition between flow regimes. In agreement with previous efforts, the results indicate that the reduction of diurnal temperature range is related to the existence of two distinct flow regimes in the stable boundary layer. However, in the decoupled state, the occurrence of intermittent bursts of turbulence may cause temperature variations among the different scenarios to become unpredictable. It implies that it is difficult to predict the diurnal temperature range in places where low winds are common.

#### 1. Introduction

The increase of the concentration of greenhouse gases, such as methane and CO_{2}, in the atmosphere, has been causing anomalous elevations in the temperature in the last two centuries [1]. Furthermore, the temperature elevation is not homogenous throughout the diurnal cycle. It has been suggested that the daily minimum temperatures may have risen twice as fast as the corresponding maxima since 1950 [2, 3]. Those observations, however, are not generally reproduced by atmospheric models [4, 5]. Reference [4] observed that doubling the concentration of the carbon dioxide was not enough to significantly affect the diurnal temperature range (DTR). Reference [5] found similar results and suggested that the problem resides in the turbulence boundary layer schemes that are used in the atmospheric models, mainly because of their bad performance during nighttime.

In this period, the only source of turbulence is the wind shear, as the stable stratification causes buoyant forces to destroy turbulence. The relative magnitude of those two terms from the turbulent kinetic energy budget equation ultimately leads to two distinct regimes in stable boundary layer (SBL) [6–9]. A decoupled regime is characterized by light winds and weak turbulence that can alternate with periods with more intense turbulence, in a phenomena known as global intermittency, or just intermittency [6]. On the other hand, the coupled state happens for moderate to strong winds, and the turbulence is always well developed and self-sustained [10]. During the same night, the flow can switch regimes, and those changes can occur intermittently or in an organized way and can lead to temperature variability as large as 10 K [11]. Recent studies [8–10] have identified that to a large extent the SBL regime is solely determined by mean wind speed. Anyhow, atmospheric models do not usually represent well the SBL variability of regimes, and it is pointed out as one of the causes of the unsuccessful prediction of the DTR behavior [12].

Reference [13] presented, by using the numerical model proposed by [14], an analysis of the influence of the atmospheric coupling in the nocturnal temperature and its possible impact over the DTR. In this work we use a similar model, proposed by [15], which is able to reproduce the intermittent behavior of the turbulence in the disconnected state, to analyze the impact of the complex behavior of the turbulence over the temperature estimations. It is important to stress that the analysis presented here is simplified in many ways. For example, the model does not take into account the effect of the radiative flux divergence, which exerts partial control over the stability of the layer, especially in weak wind cases [16, 17]. However, it can illustrate the impact of a phenomenon that most of the atmospheric models are not able to reproduce on the DTR. And, it also shows that many additional efforts are necessary to improve such models.

#### 2. Materials and Methods

##### 2.1. Model

For idealized conditions, with no advection, and for a dry and horizontally homogeneous atmosphere, the equations that control the flow in the atmospheric boundary layer (ABL) can be written in simplified form aswhere , , and are, respectively, the wind components and the air temperature, , are the components of the geostrophic wind, and are the components of the moment flux, and is the sensible heat flux. Following [12, 13] the clear air radiative cooling is neglected. Although it is a simplification, as it was stated by [13] and tested here (not shown), the impact of using a simple parametrization for the clear air radiative cooling in the model dynamics is minimal because it does not affect the equilibrium states of the model.

###### 2.1.1. Surface Parameterization

The surface parameterization is an important aspect to determine the nature and the behavior of the boundary layer. In this work a method proposed by [18] is used, which considers the energy balance of the soil substrate, a slab layer of soil, and the surface atmospheric layer [14, 18]. In this way, the prognostic equation for the soil temperature can be written aswhere is the flux incoming longwave radiation, is the ground temperature, is the substrate temperature, is the surface sensible heat flux, is the heat exchange coefficient between the substrate and the slab, and is the Stefan-Boltzmann constant. The thermal capacity per area unit of the surface (J K m^{2}) depends on the soil thermal conductivity , the Earth angular frequency , and the soil volumetric thermal capacity , where and are the soil specific heat and density, respectively [18]:

###### 2.1.2. Radiative Balance

The radiative forcing related to a perturbation in the concentration of a gas is defined by the net change of the radiative flux induced in the Tropopause, which is generally recognized as a gain (positive) or loss (negative) of energy to the whole system. The justification for this concept rises from experiments with radiative-convective one-dimensional model, in which the temperature surface changes can be only related to the net changes of the radiative flux in the Tropopause [19].

In a situation of clear skies, the surface radiative flux is, for convenience, interpreted in terms of the definition of effective atmospheric emissivity, , given by the nondimensional relation , where is the temperature in the lower limit of the atmosphere. According to [20], the incoming longwave radiation is given bywhere is the cloud fraction, is the specific humidity, and is the temperature in a reference level. It is important to notice that the term GHGS is added due to greenhouse gas concentration [13], and it defines the radiative forcing due to the carbon dioxide concentration in the atmosphere [21]: where corresponds to current values of CO_{2} in the atmosphere.

###### 2.1.3. Turbulence Closure

Usually, simplified models use the flux-gradient theory to solve the turbulence closure problem. When a first-order closure is used, those models use prescribed stability functions on the diffusion coefficients, or on the mixing lengths, which reduces the degrees of freedom of a dynamical system. Then, a possible complex relation between two variables is replaced by mean relation that may “kill” any possibility of the model to reproduce complex solutions. In this way [15] proposed not to use any stability function. In this way, in the whole boundary layer the turbulent fluxes are determined bywhere is the direction of the mean Wind and is the friction velocity. Following [22], the friction velocity is directly evaluated from the turbulent kinetic energy (TKE) (), with being a constant that relates the local shear and the turbulence intensity [23]. The value of this constant depends on the local stability; however, for simplicity, we use in this work [24].

The temperature scale is defined byThe diffusion coefficient of heat () is defined as , where Pr is the turbulent Prandtl number, assumed to be one for simplicity, and is the diffusion coefficient of momentum. In the latter expression is a constant and is the mixing length, taken as the neutral case to avoid the use of stability functions. It is important to stress that it is a very simplified model in many aspects, and it is necessary to keep the idea of not using stability functions at this point.

A variable that plays a key role in this turbulent closure is the TKE, and for these idealized conditions its budget equation can be written aswhere LHS is the local TKE budget, the two first RHS terms are the shear production terms, the third RHS term is the buoyant production/destruction of TKE, the fourth RHS term is turbulent transport of turbulence, with being the local turbulent flux of TKE, and the last RHS term is the viscous dissipation of TKE.

Using (6) and (7), and following [25], the following relation can be obtained:where . In the same way the thermal production/destruction of turbulence can be parameterized as and following [22], the transport term is parameterized aswhere is a constant that is equivalent to the Prandtl number [22]. Here, this value is taken as 2.5, the same value used by [15]. The viscous dissipation of TKE is parameterized by the Kolmogorov equation [26, 27]:In the former expression is turbulent mixing length for the dissipation, which, for simplicity, is considered to be the same as the turbulent mixing length. It is important to stress that (14) was derivate for conditions of continuous, homogenous, and isotropic turbulence; and such conditions are not present in the very stable regime of the SBL. Then, a constant that represents the presence of anisotropy of turbulence is added to (14). The value of this constant can vary in order of magnitude in models [28]. In this work, we use the same value as [15] ().

Finally, the set of equations that is integrated on the model is

###### 2.1.4. Discretization and Integration

In the model, the top of the boundary layer () and the ground surface () are used as boundaries of the SBL. Between those two points levels are considered, the first one being fixed at 5 m and the others being equally spaced between this and the domain top ( m). The prognostic equation for wind components and temperature is evaluated for these levels. However, the turbulent flux divergence is evaluated where every flux depends on TKE. In this way, the prognostic equation for is calculated in intermediate levels () between the main levels (). The intermediate levels are defined by . So, the set of equations (15) is solved using the lines method, which uses the fourth-order Runge-Kutta as the time integrator, with 0,01 s for time step.

*(1) Initial Conditions and Constants*. In the boundary layer’s top the variables are assumed as constants: , , K. In the surface the no-slip condition , is assumed. In all levels , while is assumed to increase linearly from its surface value until . The soil temperature and the air temperature are considered to be the temperature of reference: K and K.

The initial value of TKE is assumed also as minimum possible value in all levels, m^{2} s^{−2}. It is important to notice that it is common to use a minimum value of TKE in atmospheric models [28, 29], but cut-off value does not affect the results as shown by [15]. The other constants used in the model are presented in Table 1.