A Reexamination of the Emergy Input to a System from the Wind

Emergy Synthesis 9, Proceedings of the 9 th Biennial Emergy Conference (2017) 7 A Reexamination of the Emergy Input to a System from the Wind Daniel E. Campbell, Laura E. Erban ABSTRACT The wind energy absorbed in the global boundary layer (GBL, 900 mb surface) is the basis for calculating the wind emergy input for any system on the Earth s surface. Estimates of the wind emergy input to a system depend on the amount of wind energy dissipated, which can have a range of magnitudes for a given velocity depending on surface drag and atmospheric stability at the location and time period under study. In this study, we develop a method to consider this complexity in estimating the emergy input to a system from the wind. A new calculation of the transformity of the wind energy dissipated in the GBL (900 mb surface) based on general models of atmospheric circulation in the planetary boundary layer (PBL, 100 mb surface) is presented and expressed on the 12.0E+24 sej y -1 geobiosphere baseline to complete the information needed to calculate the emergy input from the wind to the GBL of any system. The average transformity of wind energy dissipated in the GBL (below 900 mb) was 1241±650 sej J -1. The analysis showed that the transformity of the wind varies over the course of a year such that summer processes may require a different wind transformity than processes occurring with a winter or annual time boundary. INTRODUCTION The wind energy absorbed in the global boundary layer (GBL, 900 mb surface) is the basis for calculating the wind emergy input for any system on the Earth s surface. Calculating the wind energy absorbed in the GBL is a more complex problem than has been recognized in most emergy evaluations. In this paper, we examine the factors involved in making an estimate of the wind energy absorbed by a system and develop a simple method to include the major aspects of this complexity in a calculation to obtain a more accurate estimate of the wind energy input. We also present a new calculation of the transformity of the wind energy dissipated in the GBL based on analysis of a general atmospheric circulation model (Wiin-Nielsen and Chen, 1993), which pertains to the planetary boundary layer (PBL, 100 mb surface). Two factors (0.42 and 0.33) for the maximum and minimum energy transfer into the GBL from the PBL (Ellsaesser, 1969) were used to estimate the transformity of the wind energy absorbed in the GBL. The transformity of the wind energy absorbed was calculated and expressed relative to the new geobiosphere baseline, 12.0E+24 sej y -1 (Brown et al. 2016), to complete the information needed to calculate the emergy input to the GBL for any system from the wind. 13

Estimates of the wind emergy input to a system depend on the amount of wind energy dissipated, which can have a range of magnitudes for a given velocity depending on surface drag and atmospheric stability at the location and time period under study. In this study, we develop a method to consider this complexity in estimating the emergy input to a system from the wind. Also, we recalculate the transformity of wind energy dissipated in the GBL using a general circulation model of the atmosphere Wiin-Nielsen and Chen (1993) and the work of Ellsaesser (1969) on energy transfer from the PBL to the GBL. BACKGROUND INFORMATION Odum (1996) estimated the kinetic energy of the wind used annually from 1000 m above the Earth to the Earth s surface from Equation 1. S z=0 Eq. 1. KE = ρ a t A ( D z ) z ( V z ) z Where the air density, a (kg m -3 ), times t, the seconds per year (s y -1 ), times A, the area of the system (m 2 ) multiplied by the eddy diffusion gradient, D z/ z (m 3 s -1 m -1 ) times ( V z/ z) 2, the vertical velocity gradient squared (m s -1 m -1 ) 2 both integrated over the height of the boundary layer, S (m). Data to evaluate this expression depend on the availability of measurements of the two vertical gradients, which are calculated from data taken by radiosonde balloons. Average January and July values for the vertical eddy diffusion gradient and vertical wind velocity gradient were published for 25 locations in the United States (Swaney, 1978; Odum and Odum, 1983). However, because of the lack of radiosonde data for many locations around the world and the somewhat cumbersome calculation method, Odum (unpublished, but see Campbell et al. 2005) developed a second method for estimating the kinetic energy of wind dissipated (D) in the global boundary layer, GBL, using the relationship in Equation 2. Eq. 2. D = ½ρ a C D V g 3 2 dz Where a (kg m -3 ) the air density, times C D, a dimensionless geostrophic drag coefficient, times (V g) 3 the cube of the geostrophic wind velocity (m 3 s -3 ). This expression depends on knowledge of 1) an appropriate drag coefficient, which is a function of surface roughness, form drag for a given atmospheric stability, and 2) the geostrophic wind speed V g. METHODS At the global scale, kinetic energy dissipation may be isolated from the flux terms in a general atmospheric circulation model (Fig. 1, D(K Z) + D(K E)). In this paper, we used the estimates of Wiin- Nielsen and Chen (1993) to quantify the storages and transformations of potential and kinetic wind energy in the PBL. Wiin-Nielsen and Chen report data from the northern hemisphere, thus to make estimates for the whole Earth, we have assumed that the southern hemisphere will have similar average values for atmospheric circulation. To obtain a more robust estimate of the transformity of the wind using the general circulation models of Wiin-Nielsen and Chen, we considered the wind energy dissipation as estimated from measurements and as occurred under the assumption that the conversion from mean potential to mean kinetic energy averages to zero over a year s time. This gave maximum and minimum scenarios for winter and summer wind energy dissipated in the PBL (Figs. 1 and 2). 14

Furthermore, to estimate the amount of wind energy in the PBL that is found in the GBL, we used the maximum and minimum estimates for the fraction of the total kinetic energy below the 100 mb surface that is dissipated in the GBL (i.e., below 900 mb) from Ellsaesser (1969) to estimate the transformity of the wind energy dissipated there. Local kinetic energy dissipation (Equation 3) may be estimated through integration of the missing wind in the vertical wind profile. The missing wind refers to wind speed lost from the vertical profile extending to the Earth s surface relative to the gradient wind speed at the top of the GBL. Theoretically, this profile has a logarithmic form (Equation 4), with a curvature that depends on the drag coefficient and atmospheric stability conditions. We fit vertical profiles for five combinations of these conditions (Figs. 3 & 4) using 1) typical ratios of the 10-m to gradient ( geostrophic) wind speeds (http://www.metoffice.gov.uk/media/pdf/p/l/chapter_1._wind.pdf ), 2) average 10-m (surface) wind speeds for land and sea (Archer and Jacobsen, 2005) and 3) reasonable values of the stability parameter were chosen to fit the logarithmic velocity profile (see Eq. 4). We integrate kinetic energy dissipation to 900 mb (approximately 1000m) and then calculate appropriate drag coefficients for these conditions using Equation 3. Eq. 3. Kinetic energy dissipation: D = 1 2 ρc DV gr 3 where: D is the dissipation per unit area, ρ is air density, C D is the drag coefficient and V gr is the gradient wind velocity. Note that in Eq. 3 we have substituted the gradient wind for the geostrophic wind and that for our purposes the two are approximately equal, but the data used in curve fitting below was reported relative to the gradient wind. Eq. 4. Logarithmic wind profile: V(z) = V fr [ln ( z ) ψ ( z )] k z 0 L where: V fr is the friction velocity, k is the von Kármán constant, z 0 is the roughness length, z is the height above the land surface, L is the Monin-Obukhov length, which is the height above the Earth s surface at which turbulence is generated more by buoyancy forces than by wind shear. The dimensionless stability parameter, z, takes on positive and negative values for stable and unstable L atmospheric conditions, respectively. The stability function ψ ( z ) is determined empirically and takes L on different forms. Here we use: ψ unstable ( z L ) = (1 16 z L )0.25 1 or ψ stable ( z L ) = 4.7 z L RESULTS & DISCUSSION Estimates of the wind energy dissipated in the atmosphere below the 100 mb surface (Wiin-Nielsen and Chen, 1993) made from their general atmospheric circulation models ranged from 0.95 W m -2 (northern hemisphere summer under conditions in Figure 1) to 2.95 W m -2 (northern hemisphere winter, under conditions in Fig. 2.). Table 1 shows the transformities of the wind in the PBL and the GBL for maximum and minimum estimates of summer and winter winds from the general circulation model of Wiin-Nielsen and Chen (1993) and for maximum and minimum estimates of the amount of kinetic energy in the atmosphere that occurs below the 900 mb surface (Ellsaesser, 1969). 15

A. B. Figure 1. Atmospheric circulation model as described by Wiin-Nielsen and Chen (1993), where G(x) is generation of available energy, C(x,y) is conversion of available energy and D(x) is dissipation of available energy in the atmosphere. A Z is the zonal average potential energy, A E is the potential energy in the deviations from the mean or the eddy potential energy, K Z is the mean zonal kinetic energy and K E is the energy of the deviations from the mean or the eddy kinetic energy. Flows are in W m -2 of the Earth s surface (i.e., 5.10E+14 m 2 ). Arrows indicate the direction of the energy flow. A. Conditions in the Northern Hemisphere during winter (January). B. conditions in the Northern hemisphere during summer (July). The flows between the tank symbols C(x,y) were obtained from data; however, the generation of available energy G(x) and the dissipation of kinetic energy D(x) were obtained by assuming that the tanks or state variables are in a steady state. Figure 2. Model components and flows are defined in Figure 1. A. Conditions in the Northern Hemisphere during winter (January). B. Conditions in the Northern Hemisphere during summer (July). Wiin-Nielsen and Chen (1993) provide calculations to show that the flow C(A Z, K Z) is probably not significantly different from zero considering the uncertainty in the data and the time scale of the measurements. In this regard, the models shown in this figure provide an alternative estimate of the global atmospheric circulation assuming that C(A Z, K Z) is zero. Flows are in W m -2 of the Earth s surface. 16

Table 1. Estimation of the average transformity of wind dissipated in the global boundary layer (GBL) calculated from models of the atmosphere (Wiin-Nielson and Chen, 1993) by applying Ellsaesser (1969) to estimate the portion of the total atmospheric kinetic energy below 100 mb dissipated in the GBL. Source: Wiin- Nielsen & Chen (1993) Kinetic Energy Dissipated Atmosphere PBL, (15.8 km) Dissipation below 100 mb Transformity Atmosphere PBL Wind Fraction of total in GBL Ellsaesser (1969) Atmosphere GBL (1 km) Dissipation below 900 mb Transformity GBL Wind Items W m -2 J y -1 sej J -1 Fraction J y -1 sej J -1 Minimum Dissipation (Fig. 1) Summer 0.95 1.53E+22 785 0.42 6.38E+21 1880 Winter 2.73 4.39E+22 273 0.42 1.83E+22 654 Summer 0.95 1.53E+22 785 0.33 5.05E+21 2378 Winter 2.73 4.39E+22 273 0.33 1.45E+22 828 Maximum Average Transformity 529 1435 Maximum Dissipation (Fig. 2) With C(Az,Kz) set to 0 Summer 1.43 2.30E+22 521 0.42 9.67E+21 1241 Winter 2.95 4.75E+22 253 0.42 1.99E+22 602 Summer 1.43 2.30E+22 521 0.33 7.59E+21 1580 Winter 2.95 4.75E+22 253 0.33 1.57E+22 766 Minimum Average Transformity 387 1047 Overall Average Transformity 458 1241 The fraction of this energy dissipated in the GBL is 0.42 to 0.33 based on the maximum and minimum dissipation estimates of Ellsaesser (1969). The global mean annual transformity of wind in the boundary layer is estimated to be 1241 650 sej J -1. The analysis showed that the transformity of the wind varies over the course of a year such that summer processes may require a different wind transformity than processes occurring with a winter or annual time boundary. Therefore, the appropriate transformity to be used in a particular evaluation will depend on the spatial and temporal boundaries of the system. Local wind energy dissipation as calculated from a suite of representative vertical wind speed profiles ranges from < 0.1 to 1.5 W m -2 (Figure 3). Drag coefficients determined from the integrated dissipation profile calculated by Eq. 3, which uses energy dissipation as determined in Eq. 4, range from 1E-5 to 2.5E-3 across profiles (Figure 3). Equation 4 reveals the dependence of these profiles on 1) a roughness length scale, z 0, which is valued from 2E-4 m to >2 m for the roughness range from open seas to cityscapes (WMO, 2008); 2) the friction velocity, V fr, determined from wind speed observations and 3) the Monin-Obukhov stability function (Eq. 4). All three parameters are difficult to determine, as is the drag coefficient. A simpler approach may be to construct a typical wind profile using Eq. 4, 10-m (surface) wind speed data and a ratio of the surface to gradient wind speed appropriate to observed surface roughness and atmospheric stability conditions (Figure 3). Atmospheric stability may be generalized using daily cloud formation data and a weighted average of conditions over the time period of interest. The drag coefficient may be calculated and compared to typical drag coefficients for the surface of the system evaluated. 17

Figure 3. Vertical wind profiles determined using Eq. 4, based on average 10-m (surface) wind speeds for land (3.28 m s -1 ) and sea (6.64 m s -1 ), and a range of representative ratios (numbers on curves) of the surface to gradient wind speeds for different surfaces and atmospheric stability conditions. Figure 4. Kinetic energy dissipation rates corresponding to scenarios in Figure 3, determined as the area of missing wind under each curve. Rates are much higher over land than sea. Drag coefficients (C D) for each scenario are shown above each column. 18

CONCLUSION The range of wind energy dissipation estimated for the same wind velocity and a discussion of the complex factors controlling the velocity profile indicate that care should be taken in calculating the wind energy input to systems in emergy evaluations. We have provided guidance on how to estimate the wind energy dissipated for various conditions and how to apply appropriate wind transformities to systems and processes. The transformity of wind energy dissipated in the GBL (below 900 mb) as determined from a general circulation model of the atmosphere was 1241 650 sej J -1. The analysis also showed that the transformity of the wind varies over the course of a year such that summer processes may require a different wind transformity than processes occurring in a winter or annual time frame. REFERENCES Archer, C.L. and Jacobson, M.Z. (2005) Evaluation of global wind power. Jour. Geophy. Res. - Atmo, 110(D12), doi:10.1029/2004jd005462 Brown, M.T., Campbell, D.E., DeVilbiss, C., Ulgiati, S. 2016. The geobiosphere emergy baseline: A synthesis, Ecological Modelling 339, 92-95. Campbell, D.E., Brandt-Williams, S.L., Meisch, M.E.A. 2005. Environmental Accounting Using emergy: Evaluation of the State of west Virginia. United States Environmental Protection Agency Project Report, EPA/600/R-05/006. Ellsaesser, H.W. 1969. A climatology of Epsilon (atmospheric dissipation). Monthly Weather Review 97(6), 414-423. Met Office, UK http://www.metoffice.gov.uk/media/pdf/p/l/chapter_1._wind.pdf Odum, H.T. (1996), Environmental Accounting: Emergy and Environmental Decision Making, New York: John Wiley and Sons Odum, H.T. and Odum, E.C. (1983), Energy Analysis Overview of Nations. Working Paper WP-83-82, International Institute for Applied Systems Analysis, Austria: Laxenburg Swaney, D. 1978. Energy Analysis of Climatic Inputs to Agriculture. MS Thesis University of Florida, Gainesville, FL. Wiin-Nielsen, A. and Chen, T-S. (1993) Fundamentals of Atmospheric Energetics. Oxford University Press, New York, NY World Meteorological Association (2008) Guide to Meteorological Instruments and Methods of Observation WMO-No. 8 p I.5-12. 19

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