Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies

1995 ◽  
Vol 76 (1-2) ◽  
pp. 165-179 ◽  
Author(s):  
Jouko Launiainen
Keyword(s):  
Richardson Number ◽  
Stability Parameter ◽  
Bulk Richardson Number ◽  
Flux Profile ◽  
The Relationship

scholarly journals Local flux-profile relationships of wind speed and temperature in a canopy layer in atmospheric stable conditions

2010 ◽  
Vol 7 (3) ◽  
pp. 4505-4537 ◽  
Author(s):  
G. Zhang ◽  
M. Y. Leclerc ◽  
A. Karipot
Keyword(s):  
Richardson Number ◽  
Forest Canopy ◽  
Similarity Theory ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Canopy Layer ◽  
Stability Parameters ◽  
Stable Conditions ◽  
Flux Profile ◽  
The Relationship

Abstract. The particularities of the physics of the canopy layer pose challenges to the determination and use of traditional universal functions so helpful in the atmospheric surface layer. Progress toward "universal-like functions" such as those provided by Monin-Obukhov similarity theory for the canopy layer has been modest. One of the challenges lies in that the assumptions underlying Monin-Obukhov similarity theory do not hold within a canopy layer. This paper thus examines the local flux-profile relations for wind (φm) and for temperature (φh) using three different stability parameters, i.e., h/L(h) at tree top, local z/L(z), and local bulk Richardson number (Ri), within a tall forest canopy in nighttime stable (indicated by h/L(h)>0) conditions. Results suggest that the in-canopy φm can be described using the local Richardson number Ri. φm is found to increase linearly with Ri in the upper canopy layer for |Ri|<1. When local |Ri|>1, |φm| decreases with |Ri|, a result consistent for all levels of measurements within the canopy. When both local φh and local Ri are positive, i.e., local downward turbulent heat flux is consistent with local temperature gradient, local φh increases with local Ri when Ri<1 but does not change with Ri (or much more scattered) when Ri>1. The relationship between local φh and Ri disappears when counter-gradient heat transfer occurs in strongly stable conditions. A self-correlation analysis is used to examine the influence of self-correlation and the physical meaning of these relationships.

scholarly journals Comparison of Length Scale Parameterization Methodologies

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 89
Author(s):  
Faruk Tuna ◽  
Ferhat Bingöl
Keyword(s):  
Wind Shear ◽  
Richardson Number ◽  
Atmospheric Stability ◽  
The Other ◽  
Length Scale ◽  
Bulk Richardson Number ◽  
Obukhov Length ◽  
Average Value ◽  
Flux Profile

Atmospheric stability has been studied for decades. There are several methodologies that evolved over the years. In this study, a special experimental meteorological mast that has been erected to a complex site has been used to calculate dimensionless Obukhov length ( ζ = z L ) , dimensionless momentum ( φ m ), and heat coefficients ( φ h ). The results are compared with the ones from average value approaches: Richardson number, flux-profile (F-P) relations, and wind shear exponent methods. The results show that the estimated ζ values, using the bulk Richardson number, get along well with the reference ζ within the neutral and stable regimes. F-P relations and wind shear exponent methods result in the best agreement for stable and neutral regimes. Nevertheless, average oriented methods are not reliable for the other regimes.

scholarly journals Local flux-profile relationships of wind speed and temperature in a canopy layer in atmospheric stable conditions

2010 ◽  
Vol 7 (11) ◽  
pp. 3625-3636 ◽  
Author(s):  
G. Zhang ◽  
M. Y. Leclerc ◽  
A. Karipot
Keyword(s):  
Richardson Number ◽  
Forest Canopy ◽  
Similarity Theory ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Canopy Layer ◽  
Stability Parameters ◽  
Stable Conditions ◽  
Flux Profile ◽  
The Relationship

Abstract. The particularities of the physics of the canopy layer pose challenges to the determination and use of traditional universal functions so helpful in the atmospheric surface layer. Progress toward "universal-like functions" such as those provided by Monin-Obukhov similarity theory for the canopy layer has been modest. One of the challenges lies in that the assumptions underlying Monin-Obukhov similarity theory do not hold within a canopy layer. This paper thus examines the local flux-profile relations for wind (Φm) and for temperature (Φh). It uses three different stability parameters, i.e., h/L(h) at tree top, local z/L(z), and the local bulk Richardson number (Ri), within a tall forest canopy in nighttime stable (indicated by h/L(h) > 0) conditions. Results suggest that the in-canopy Φm can be described using the local Richardson number Ri. Furthermore, Φm is found to increase linearly with Ri in the upper canopy layer for |Ri| < 1. When local |Ri| > 1, |Φm| decreases with |Ri| in a power function, a result consistent for all levels of measurements within the canopy. When both local Φh and local Ri are positive, i.e., the local downward turbulent heat flux is consistent with the local temperature gradient, the local Φh increases with the local Ri when Ri < 1. However, Φh does not change with Ri (or much more scattered) when Ri > 1. The relationship between local Φh and Ri disappears when counter-gradient heat transfer occurs in strongly stable conditions. A self-correlation analysis is used to examine the influence of self-correlation and the physical meaning of these relationships.

scholarly journals On the computation of planetary boundary-layer height using the bulk Richardson number method

2014 ◽  
Vol 7 (6) ◽  
pp. 2599-2611 ◽  
Author(s):  
Y. Zhang ◽  
Z. Gao ◽  
D. Li ◽  
Y. Li ◽  
N. Zhang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Planetary Boundary Layer ◽  
Richardson Number ◽  
Potential Temperature ◽  
Bulk Richardson Number ◽  
Stable Boundary Layers ◽  
Stable Boundary ◽  
Field Campaigns ◽  
Weakly Stable

Abstract. Experimental data from four field campaigns are used to explore the variability of the bulk Richardson number of the entire planetary boundary layer (PBL), Ribc, which is a key parameter for calculating the PBL height (PBLH) in numerical weather and climate models with the bulk Richardson number method. First, the PBLHs of three different thermally stratified boundary layers (i.e., strongly stable boundary layers, weakly stable boundary layers, and unstable boundary layers) from the four field campaigns are determined using the turbulence method, the potential temperature gradient method, the low-level jet method, and the modified parcel method. Then for each type of boundary layer, an optimal Ribc is obtained through linear fitting and statistical error minimization methods so that the bulk Richardson method with this optimal Ribc yields similar estimates of PBLHs as the methods mentioned above. We find that the optimal Ribc increases as the PBL becomes more unstable: 0.24 for strongly stable boundary layers, 0.31 for weakly stable boundary layers, and 0.39 for unstable boundary layers. Compared with previous schemes that use a single value of Ribc in calculating the PBLH for all types of boundary layers, the new values of Ribc proposed by this study yield more accurate estimates of PBLHs.

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