This study examined the level of turbulence in the atmospheric boundary layer in Maiduguri, north-eastern Nigeria. Five years (2011-2015) temperature and wind speed data at 1000 mbar pressure level retrieved from Era-Interim Reanalysis Platform was used. These data were gotten at 6-hourly synoptic hours: 0000H, 0600H, 1200H and 1800H at 0.125 ° grid resolution. The gradient Richardson ( Rig) number method was utilised in analysing turbulence across three layers: 10 - 50 m (surface layer); 50 - 100 m (mid layer) and 100 - 1300 m (upper layer). Findings shows that the surface layer is always in a turbulent state as over 95% of Rig values were below Richardson Critical ( Ric) value of 0.25 with range 0.02 - 0.94. However, all values across the hours were below the Richardson Termination ( RT) value of 1. Laminar conditions exist at the mid layer across the hours as 99.9% of Rig values ranging 0.88 - 8.02 were greater than RT of 1. Rig values for the upper layer were largely negative and ranged between -78.71 to -724.14. This indicates robust turbulent conditions. Turbulence generated through forced and free ascents prevailed at the surface layer and upper layer respectively. This shows that wind shear is dominant at the surface while thermal buoyancy prevails at the upper level. The months of February and September at 1200 and 1800 hours respectively are the periods of maximum (about 134 m) and minimum (below 15 m) heights were free convection destabilises forced convection in the study area. Relating findings to emission dispersion suggests that air pollutants will be transported across far and near distances at the upper layer and surface layers respectively. This is due to the stable nature of the mid layer that will limits vertical emission dispersion. Policy makers should ensure that potential emission sources stacks are above 50 m to ensure pollutants are dispersed aloft in the area.
The atmospheric boundary layer (ABL) and, more essentially, boundary layer turbulence, are indispensable elements of weather and climate [
Boundary layer studies are very important due to the following reasons: creatures cohabit there, energy fluxes mediate creating transfers of air masses and emission dispersion is prevalent. Also, the state of any local weather is predicted from boundary layer processes and clouds within the boundary layer regulates local weather pattern. This study intends to assess the levels of turbulence within the boundary layer in Maiduguri across three vertical layers i.e. 10 - 50 m, 50 - 100 m and 100 - 1300 m. The Gradient Richardson (Rig) number method will be used to assess the levels of turbulence.
Maiduguri is located at the tip of north-eastern Nigeria and roughly positioned between Latitude 11˚47'N to 11˚54'N and Longitude 13˚05'E to 13˚12'E (
throughout the year. The area has two different climatic periods, which are: the hot dry spell with quite high temperatures and the wet season. The wet season is preceded by the very cold, dry and dusty Harmattan winds [
Rainfall amount over the years have ranged between 265.5 - 925.7 mm with mean value of 580.5 mm [
The data for used for this study were obtained from the European Centre for Medium Ranged Weather Forecast (ECMWF) Era-Interim Re-analysis data for five years (2011-2015). The Era-Interim Reanalysis Platform is the up-to-date widespread atmospheric reanalysis data and has been found resourceful in the analysis of atmospheric circulation of tropical Africa. The use of the improved Era-Interim reanalysis data has exceeded prospects and expresses positive views about the achievements in the analysis of weather data realised within the last decade. The data for the indicated period of time acquired at 0.125 degree resolution was retrieved 6-hourly at 0000, 0600, 1200 and 1800 synoptic hours. Tem- perature and wind speed data were obtained at pressure level of 1000 mbar which is an approximation of the surface level data.
Many different models of assessing boundary layer turbulence exist. Researchers have generally combined one destabilizing force with one stabilizing force [
When meteorologist mention the convectional Richardson number what is being referred to is the gradient Richardson number [
where S (a stability parameter) is the restoring force. The stability parameter is of the equation below.
Therefore, the gradient Richardson number is given by:
where,
g is the gravitational acceleration (m/s2)
T is the mean temperature (˚C)
θ is the potential temperature
(du/dz)2, is the mean wind speed (m/s2)
Z is the vertical height (m).
The mean wind speed can be resolved into
where Zm is the mean vertical height considered. The relationship between Monin-Obukhov Length and Richardson number is given by:
The Equation (5) was used to estimate the approximate vertical distance where the restoring force equals the generated force.
The analysed wind component of the gradient Richardson formula at 50 m, 100 m and 1300 m was calculated using Equation (6).
where V0 is the referenced surface wind velocity and V is the estimated wind velocity at the specified vertical height (H). The assumed roughness length for Maiduguri was 0.03 i.e. for open flat terrain with scattered settlements [
The estimated atmospheric pressure at 50 m, 100 m and 1300 m levels was determined with the following equation:
where, P is the atmospheric pressure in bars, h, the height in (km), P0, pressure at height; h = 0 (P0 = 1 bar) and h0 = 7 (an approximate scale height for the atmosphere). The correspondent potential temperature (θ) at the indicated altitudes was calculated with the following equation [
where, “Tz” is the temperature (K) of the air parcel at reference height (z), “R” is the gas constant of air and “Cp” is the specific heat capacity at constant pressure. The ratio (R/Cp) is given as (0.286) for air. At any level, z, there is a temperature (Tz) and a corresponding potential temperature (θz).
The Richardson number (Ri) is very important because it can identify the onset and cessation of turbulence. Theoretical and laboratory studies recommend that lamina flow turn out to be turbulent when Ri is smaller than the critical Richardson (Ric) number of 0.25 [
It has been disclosed [
The results from analysis of the mean gradient Richardson (Rig) number across the layers for the respective hours are shown on
Month | 0000HR | 0600HR | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
10 - 50 m | 50 - 100 m | 100 - 1300 m | L | 10 - 50 m | 50 - 100 m | 100 - 1300 m | L | |||
JAN | 0.24 | 2.03 | −141.32 | 41.99 | 0.15 | 2.06 | −186.97 | 60.77 | ||
FEB | 0.12 | 1.99 | −139.15 | 74.37 | 0.15 | 2.03 | −184.01 | 61.75 | ||
MAR | 0.09 | 2.97 | −121.98 | 84.53 | 0.12 | 2.01 | −158.69 | 74.3 | ||
APR | 0.02 | 1.97 | −137.00 | 75.54 | 0.15 | 2.99 | −159.12 | 58.69 | ||
MAY | 0.02 | 1.26 | −137.14 | 82.19 | 0.12 | 1.28 | −109.76 | 80.91 | ||
JUN | 0.08 | 1.27 | −98.15 | 109.14 | 0.07 | 1.29 | −81.18 | 123.54 | ||
JUL | 0.24 | 2.01 | −139.67 | 42.49 | 0.09 | 1.29 | −111.24 | 92.99 | ||
AUG | 0.19 | 2.02 | −212.69 | 51.36 | 0.12 | 2.03 | −160.94 | 73.26 | ||
SEP | 0.18 | 5.35 | −248.32 | 44.37 | 0.15 | 3.60 | −213.55 | 56.71 | ||
OCT | 0.24 | 3.54 | −245.98 | 37.45 | 0.24 | 3.58 | −248.78 | 37.02 | ||
NOV | 0.24 | 2.01 | −180.96 | 42.72 | 0.19 | 3.59 | −128.96 | 45.89 | ||
DEC | 0.09 | 2.03 | −125.39 | 86.09 | 0.15 | 2.06 | −187.10 | 60.73 | ||
1200H | 1800H | |||||||||
JAN | 0.08 | 1.28 | −98.61 | 108.64 | 0.12 | 1.28 | −138.78 | 81.22 | ||
FEB | 0.07 | 0.88 | −79.48 | 134.42 | 0.23 | 1.26 | −136.61 | 50.19 | ||
MAR | 0.14 | 1.25 | −78.71 | 73.39 | 0.23 | 1.94 | −135.28 | 43.87 | ||
APR | 0.14 | 1.86 | −153.69 | 64.81 | 0.28 | 1.94 | −176.13 | 37.99 | ||
MAY | 0.47 | 3.46 | −288.49 | 22.37 | 0.47 | 3.45 | −240.04 | 22.35 | ||
JUN | 0.18 | 3.49 | −288.81 | 47.73 | 0.24 | 5.23 | −291.14 | 35.79 | ||
JUL | 0.14 | 1.98 | −180.30 | 63.02 | 0.48 | 3.54 | −354.59 | 21.94 | ||
AUG | 0.18 | 2.00 | −181.80 | 51.72 | 0.33 | 8.02 | −440.79 | 25.46 | ||
SEP | 0.65 | 3.53 | −436.89 | 17.89 | 0.94 | 7.97 | −724.14 | 10.75 | ||
OCT | 0.47 | 3.49 | −289.59 | 22.13 | 0.24 | 5.25 | −350.32 | 35.76 | ||
NOV | 0.14 | 1.26 | −87.55 | 71.89 | 0.23 | 1.97 | −155.74 | 43.46 | ||
DEC | 0.07 | 1.92 | −89.77 | 118.22 | 0.09 | 1.99 | −123.22 | 87.61 | ||
below the Richardson Termination point of 1. However, over 96% of the Rig values in this layer were below the Richardson critical level of 0.25. The Rig values across the second layer (50 - 100 m) have indicated an entirely lamina condition except at 1200H in February when mean Rig value was below the RiT of 1 i.e. 0.88.
Turbulence conditions within the atmospheric boundary layers differs beginning from the surface layer to the outer layer [
Results from the third layer (100 - 1300 m) with more vertical stretch than the other layers have indicated more turbulent conditions across the hours. All Rig values were largely negative. This indicates strongly unstable situations over the layer. It has been emphasised that largely negative Ri values indicates turbulent or unstable situations [
Results from
A correlation of surface layer wind shear values based on Richardson number [
Furthermore, Rig values from this study at the first layer (10 - 50 m) compare well with the wind shear outcomes on
Additionally, the Rig results for the study area indicated turbulent patterns in two dimensional grade: the first at the surface layer (10 - 50 m) and at the upper layer (100 - 1300 m) during 0000, 0600, 1200 and 1800 hours. Results for the surface layer were minor positives while that at the upper layer were largely negative. This implies that turbulence due to wind shear dominated the surface layer while that resulting from thermal or free ascent prevailed at the upper layer considered in this study. However, turbulence due to free convention is stronger than that due to wind shear. The mid layer was in a state of laminar condition throughout the period considered. Wind velocity pattern at the surface shows a mean range of 2 - 6 m/s for specified night and day hours (Figures 2-5) and this
Stability Categories | Wind Shear (Ri Values) | |
---|---|---|
In-land Site | Coastal Site | |
Very Unstable | 0.14 | 0.08 |
Unstable | 0.22 | 0.13 |
Near Neutral | 0.36 | 0.16 |
Stable | 0.38 | 0.20 |
Very Stable | 0.34 | 0.27 |
Source: Vieira and Sampaio, 2012.
is capable of modifying thermals that may arise at night and during the day. Therefore, turbulence could be regulated by the intervention of varying wind velocity across layers. Massive sensible heat exchange takes place at tropical desert where above 60 kly per annum is transferred to the atmosphere [
The monthly trends of Rig for the various layers in relation to the specified synoptic hours are displayed on Figures 6-8. During the 0000H on
1300 m) during the same hour, September and October reveals the most turbulent periods due to free convection (
During 0600H period, June experiences slightly higher turbulence than the rest months at the 10 - 50 m layer while laminar conditions is stronger during the months of September to November at the 50 - 100 m layer (
The turbulence pattern at 1200H on
While September maintains high turbulence pattern due to free ascent at the upper layer (100 - 1300 m), the months of November-March is least in the fray (
Result analysis from the expression of relationship between Richardson number and Monin-Obukhov Length which estimates the mean height where free ascent of air mass starts dominating forced ascents is shown on
shows that the months of February and September at 1200 and 1800 hours are the periods of maximum and minimum heights were free convection destabilises forced convection in the study area. It has been disclosed [
Rig results indicate that the strength of turbulence within the boundary layer of the study location changes amid layers. The application of Rig as a turbulent indicator also reveals the pattern of atmospheric stability conditions prevalent in the study area. This will be critical to the events that occur at the planetary layer such as emissions from various anthropogenic and natural sources, micrometeorological variations as well as the level of comfort experienced by inhabitants of the boundary layer most especially at the surface layer. The most critical factor in air pollution analysis is the level of turbulence within the boundary layer as it has intense effect on the dispersion of ground level emissions. Result analysis show that pollutant dispersions will be enhanced at 1800H from February to November due to the lower level (below 50 m) at which free ascent destabilises forced ascent (
Turbulence activities in the atmospheric boundary layer affect both weather processes and other vital activities that take place within the layer. Maiduguri, an urban centre located in northeastern Nigeria responds to such realities. Using the Era-Interim Re-analysis data (2011-2015), examining turbulence pattern across the boundary layers in the area have shown that the surface layer (10 - 50 m) is always in a turbulent state. The analysed gradient Richardson number (Rig) across the synoptic hours: 0000H, 0600H, 1200H and 1800H show that over 95% of values were small positive and below the Richardson critical (Ric) value of 0.25. However, all Rig values at the surface layer were below the Richardson Termination (RT) value of 1. Studies has revealed that turbulence exist due to more of wind shear when Rig values are lesser than RT. On the other hand, Rig findings shows that the mid layer (50 - 100 m) indicates laminar situation as a results of Rig values greater than 1. It was a different pattern at the upper level considered in this study (100 - 1300 m) as Rig values were largely negative indicating a strongly turbulent layer. In the study area, turbulence due to forced and free convention was prevalent. While the former was more prevalent at the surface layer, the later was prevalent at the upper layer. Turbulence due to forced ascent results from surface wind shear. That of free ascent could be as a result of the subsidence of high-pressure stable air mass that descends to the surface from across the Sahara desert. This creates unstable conditions as the air mass gains heat and assumes horizontal flow to low-pressure area. The turbulence pattern at the area suggest that air pollution will be transported to longer distance at the upper layer due to the laminar situations at the mid layer. Also, air pollution will be dispersed within the surface layer if the emission source stack is below 50 m both at low and high wind speeds. However, if the emission source stack is above 50 m, emission dispersion will take place aloft. Results also suggest that wind turbines development for power generation will be appropriate within the surface layer when compared to Ri wind shear values in northeast Brazil.
The authors show profound appreciation to the anonymous reviewers whose observations have improved the content of this study. Also the authors appreciate this Journal platform for the opportunity given to publish this study.
Edokpa, D.O. and Weli, V.E. (2017) An Assessment of Atmospheric Boundary Layer Turbulence in Maiduguri, Nigeria. Open Journal of Air Pollution, 6, 27-43. https://doi.org/10.4236/ojap.2017.62003