Abstract

Atmospheric scintillations cause difficulties for applications where an undistorted propagation of electromagnetic radiation is essential. These scintillations are related to turbulent fluctuations of temperature and humidity that are in turn related to surface heat fluxes. We developed an approach that quantifies these scintillations by estimating Cn2 from surface fluxes that are derived from single-level routine weather data. In contrast to previous methods that are biased to dry and warm air, our method is directly applicable to several land surface types, environmental conditions, wavelengths, and measurement heights (lookup tables for a limited number of site-specific parameters are provided). The approach allows for an efficient evaluation of the performance of, e.g., infrared imaging systems, laser geodetic systems, and ground-to-satellite optical communication systems. We tested our approach for two grass fields in central and southern Europe, and for a wheat field in central Europe. Although there are uncertainties in the flux estimates, the impact on Cn2 is shown to be rather small. The Cn2 daytime estimates agree well with values determined from eddy covariance measurements for the application to the three fields. However, some adjustments were needed for the approach for the grass in southern Europe because of non-negligible boundary-layer processes that occur in addition to surface-layer processes.

© 2014 Optical Society of America

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References

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2014 (3)

B. Maronga, “Monin-Obukhov similarity functions for the structure parameters of temperature and humidity in the unstable surface layer: results from high-resolution large-eddy simulations,” J. Atmos. Sci. 71, 716–733 (2014).
[Crossref]

A. van de Boer, A. F. Moene, A. Graf, D. Schüttemeyer, and C. Simmer, “Detection of entrainment influences on surface-layer measurements and extension of Monin-Obukhov similarity theory,” Bound-Layer Meteor. 152, 19–44 (2014).

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

2013 (3)

A. van de Boer, A. F. Moene, and D. Schuettemeyer, “Sensitivity and uncertainty of analytical footprint models according to a combined natural tracer and ensemble approach,” Agric. Forest. Meteor. 169, 1–11 (2013).

H. C. Ward, J. G. Evans, O. K. Hartogensis, A. F. Moene, H. A. R. De Bruin, and C. S. B. Grimmond, “A critical revision of the estimation of the latent heat flux from two-wavelength scintillometry,” Q. J. R. Meteorol. Soc. 139, 1912–1922 (2013).

M. Sivasligil, C. B. Erol, O. M. Polat, and H. Sari, “Validation of refractive index structure parameter estimation for certain infrared bands,” Appl. Opt. 52, 3127–3133 (2013).
[Crossref]

2012 (2)

M. Braam, F. C. Bosveld, and A. F. Moene, “On Monin Obukhov scaling in and above the atmospheric surface layer: the complexities of elevated scintillometer measurements,” Bound-Layer Meteor. 144, 157–177 (2012).

D. Li, E. Bou-Zeid, and H. A. R. De Bruin, “Monin–Obukhov similarity functions for the structure parameters of temperature and humidity,” Bound-Layer Meteor. 145, 45–67 (2012).

2011 (1)

S. Cheinet, A. Beljaars, K. Weiss-Wrana, and Y. Hurthaud, “The use of weather forecasts to characterise near-surface optical turbulence,” Bound-Layer Meteor. 138, 453–473 (2011).

2010 (2)

T. T. Leclerc, R. L. Phillips, L. C. Andrews, D. T. Wayne, P. Sauer, and R. Crabbs, “Prediction of the ground-level refractive index structure parameter from the measurement of atmospheric conditions,” Proc. SPIE 7685, 76850A (2010).
[Crossref]

A. Graf, D. Schüttemeyer, H. Geiß, A. Knaps, M. Möllmann-Coers, J. H. Schween, S. Kollet, B. Neininger, M. Herbst, and H. Vereecken, “Boundedness of turbulent temperature probability distributions, and their relation to the vertical profile in the convective boundary layer,” Bound-Layer Meteor. 134, 459–486 (2010).

2004 (1)

2003 (1)

A. F. Moene, “Effects of water vapour on the structure parameter of the refractive index for near-infrared radiation,” Bound-Layer Meteor. 107, 635–653 (2003).

2001 (3)

J. M. Wilczak, S. P. Oncley, and S. A. Stage, “Sonic anemometer tilt correction algorithms,” Bound-Layer Meteor. 99, 127–150 (2001).

F. Chen and J. Dudhia, “Coupling an advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system. Part I: Model implementation and sensitivity,” Mon. Weather Rev. 129, 569–585 (2001).
[Crossref]

R. J. Ronda, H. A. R. de Bruin, and A. A. M. Holtslag, “Representation of the canopy conductance in modeling the surface energy budget for low vegetation,” J. Appl. Meteor. 40, 1431–1444 (2001).

2000 (1)

T. E. Twine, W. P. Kustas, J. M. Norman, D. R. Cook, P. Houser, T. P. Meyers, J. H. Prueger, P. J. Starks, and M. L. Wesely, “Correcting eddy-covariance flux underestimates over a grassland,” Agric. Forest. Meteor. 103, 279–300 (2000).

1999 (2)

T. M. Crawford and C. E. Duchon, “An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling longwave radiation,” J. Appl. Meteor 38, 474–480 (1999).

W. C. de Rooy and A. A. M. Holtslag, “Estimation of surface radiation and energy flux densities from single-level weather data,” J. Appl. Meteor. 38, 526–540 (1999).

1997 (1)

A. Beljaars and F. C. Bosveld, “Cabauw data for the validation of land surface parameterization schemes,” J. Climate 10, 1172–1193 (1997).

1996 (1)

F. Chen, K. Mitchell, J. Schaake, Y. Xue, H. L. Pan, V. Koren, Q. Y. Duan, M. Ek, and A. Betts, “Modeling of land surface evaporation by four schemes and comparison with FIFE observations,” J. Geophys. Res. 101, 7251–7268 (1996).
[Crossref]

1994 (1)

H. Rachele and A. Tunick, “Energy balance model for imagery and electromagnetic propagation,” J. Appl. Meteor. 33, 964–976 (1994).

1993 (2)

H. A. R. De Bruin, W. Kohsiek, and J. J. M. van den Hurk, “A verification of some methods to determine the fluxes of momentum, sensible heat, and water vapour using standard deviation and structure parameter of scalar meteorological quantities,” Bound-Layer Meteor. 63, 231–257 (1993).

A. K. Betts and A. C. Beljaars, “Estimation of effective roughness length for heat and momentum from FIFE data,” Atmos. Res. 30, 251–261 (1993).
[Crossref]

1992 (4)

C. M. J. Jacobs and H. A. R. De Bruin, “The sensitivity of regional transpiration to land-surface characteristics: significance of feedback,” J. Climate 5, 683–698 (1992).

R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves Random Media 2, 179–201 (1992).
[Crossref]

V. Thiermann and H. Grassl, “The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation,” Bound-Layer Meteor. 58, 367–389 (1992).

D. Sadot and N. S. Kopeika, “Forecasting optical turbulence strength on the basis of macroscale meteorology and aerosols: models and validation,” Opt. Eng. 31, 200–212 (1992).
[Crossref]

1989 (1)

J. Stewart and L. Gay, “Preliminary modelling of transpiration from the fife site in Kansas,” Agric. Forest Meteor. 48, 305–315 (1989).

1988 (3)

J. B. Stewart, “Modelling surface conductance of pine forest,” Agric. Forest Meteor. 43, 19–35 (1988).

A. A. M. Holtslag and H. A. R. De Bruin, “Applied modeling of the nighttime surface energy balance over land,” J. Appl. Meteor. 27, 689704 (1988).

E. L. Andreas, “Estimating Cn2 over snow and sea ice from meteorological data,” J. Opt. Soc. Am. A 5, 481–495 (1988).
[Crossref]

1984 (1)

W. R. Rouse, “Microclimate at arctic tree line 3. The effects of regional advection on the surface energy balance of upland tundra,” Water Resour. Res. 20, 74–78 (1984).
[Crossref]

1983 (2)

P. Schotanus, F. Nieuwstadt, and H. de Bruin, “Temperature measurement with a sonic anemometer and its application to heat and moisture fluxes,” Bound-Layer Meteor. 26, 81–93 (1983).

A. A. M. Holtslag and A. P. Van Ulden, “A simple scheme for daytime estimates of the surface fluxes from routine weather data,” J. Climate Appl. Meteor. 22, 517–529 (1983).

1981 (1)

S. B. Idso, “A set of equations for full spectrum and 8 to 14  μm and 10.5 to 12.5  μm thermal radiation from cloudless skies,” Water Resour. Res. 17, 295–304 (1981).
[Crossref]

1980 (2)

E. Webb, G. Pearman, and R. Leuning, “Correction of flux measurements for density effects due to heat and water vapour transfer,” Quart. J. Roy. Meteor. Soc. 106, 85–100 (1980).

F. Kasten and G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24, 177–189 (1980).
[Crossref]

1978 (2)

R. J. Hill and S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).

K. L. Davidson, T. M. Houlihan, C. W. Fairall, and G. E. Schacher, “Observation of the temperature structure function parameter, C T 2, over the ocean,” Bound-Layer Meteor. 15, 507–523 (1978).

1977 (2)

C. A. Friehe, “Estimation of the refractive-index temperature structure parameter over the ocean,” Appl. Opt. 16, 334–340 (1977).
[Crossref]

J. C. Wyngaard and S. F. Clifford, “Taylor’s hypothesis and high-frequency turbulence spectra,” J. Atmos. Sci. 34, 922–929 (1977).
[Crossref]

1976 (2)

M. L. Wesely, “The combined effect of temperature and humidity fluctuations on refractive index,” J. Appl. Meteor. 15, 43–49 (1976).

P. G. Jarvis, “The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field,” Phil. Trans. 273, 593–610 (1976).

1971 (1)

J. C. Wyngaard, O. R. Coté, and Y. Izumi, “Local free convection, similarity, and the budgets of shear stress and heat flux,” J. Atmos. Sci. 28, 1171–1182 (1971).
[Crossref]

1970 (1)

C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer,” J. Appl. Meteor. 9, 857–861 (1970).

1954 (1)

A. S. Monin and A. M. Obukhov, “Basic laws of turbulent mixing in the surface layer of the atmosphere,” Tr. Geofiz. Inst. Akad. Nauk. SSSR 24, 163–187 (1954).

1946 (1)

A. M. Obukhov, “Turbulence in an atmosphere with a non-uniform temperature,” Tr Geofiz. Inst. Akad. Nauk. SSSR 1, 95–115 (1946).

Alexander, D. C.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Andreas, E. L.

Andrews, L. C.

T. T. Leclerc, R. L. Phillips, L. C. Andrews, D. T. Wayne, P. Sauer, and R. Crabbs, “Prediction of the ground-level refractive index structure parameter from the measurement of atmospheric conditions,” Proc. SPIE 7685, 76850A (2010).
[Crossref]

Angevine, W. M.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

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M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

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M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Barrié, J.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Bazile, E.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

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Darbieu, C.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Davidson, K. L.

K. L. Davidson, T. M. Houlihan, C. W. Fairall, and G. E. Schacher, “Observation of the temperature structure function parameter, C T 2, over the ocean,” Bound-Layer Meteor. 15, 507–523 (1978).

de Bruin, H.

P. Schotanus, F. Nieuwstadt, and H. de Bruin, “Temperature measurement with a sonic anemometer and its application to heat and moisture fluxes,” Bound-Layer Meteor. 26, 81–93 (1983).

De Bruin, H. A. R.

H. C. Ward, J. G. Evans, O. K. Hartogensis, A. F. Moene, H. A. R. De Bruin, and C. S. B. Grimmond, “A critical revision of the estimation of the latent heat flux from two-wavelength scintillometry,” Q. J. R. Meteorol. Soc. 139, 1912–1922 (2013).

D. Li, E. Bou-Zeid, and H. A. R. De Bruin, “Monin–Obukhov similarity functions for the structure parameters of temperature and humidity,” Bound-Layer Meteor. 145, 45–67 (2012).

R. J. Ronda, H. A. R. de Bruin, and A. A. M. Holtslag, “Representation of the canopy conductance in modeling the surface energy budget for low vegetation,” J. Appl. Meteor. 40, 1431–1444 (2001).

H. A. R. De Bruin, W. Kohsiek, and J. J. M. van den Hurk, “A verification of some methods to determine the fluxes of momentum, sensible heat, and water vapour using standard deviation and structure parameter of scalar meteorological quantities,” Bound-Layer Meteor. 63, 231–257 (1993).

C. M. J. Jacobs and H. A. R. De Bruin, “The sensitivity of regional transpiration to land-surface characteristics: significance of feedback,” J. Climate 5, 683–698 (1992).

A. A. M. Holtslag and H. A. R. De Bruin, “Applied modeling of the nighttime surface energy balance over land,” J. Appl. Meteor. 27, 689704 (1988).

A. van Dijk, A. F. Moene, and H. A. R. de Bruin, “The principles of surface flux physics: theory, practice and description of the ECPACK library,” (Meteorology and Air Quality Group, 2004).

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M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

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M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Delbarre, H.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Derrien, S.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Duan, Q. Y.

F. Chen, K. Mitchell, J. Schaake, Y. Xue, H. L. Pan, V. Koren, Q. Y. Duan, M. Ek, and A. Betts, “Modeling of land surface evaporation by four schemes and comparison with FIFE observations,” J. Geophys. Res. 101, 7251–7268 (1996).
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T. M. Crawford and C. E. Duchon, “An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling longwave radiation,” J. Appl. Meteor 38, 474–480 (1999).

Dudhia, J.

F. Chen and J. Dudhia, “Coupling an advanced land surface-hydrology model with the Penn State-NCAR MM5 modeling system. Part I: Model implementation and sensitivity,” Mon. Weather Rev. 129, 569–585 (2001).
[Crossref]

Durand, P.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Ek, M.

F. Chen, K. Mitchell, J. Schaake, Y. Xue, H. L. Pan, V. Koren, Q. Y. Duan, M. Ek, and A. Betts, “Modeling of land surface evaporation by four schemes and comparison with FIFE observations,” J. Geophys. Res. 101, 7251–7268 (1996).
[Crossref]

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Evans, J. G.

H. C. Ward, J. G. Evans, O. K. Hartogensis, A. F. Moene, H. A. R. De Bruin, and C. S. B. Grimmond, “A critical revision of the estimation of the latent heat flux from two-wavelength scintillometry,” Q. J. R. Meteorol. Soc. 139, 1912–1922 (2013).

Fairall, C. W.

K. L. Davidson, T. M. Houlihan, C. W. Fairall, and G. E. Schacher, “Observation of the temperature structure function parameter, C T 2, over the ocean,” Bound-Layer Meteor. 15, 507–523 (1978).

Faloona, I.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Flament, P.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Fourmentin, M.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Friehe, C. A.

Garai, A.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

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Gibert, F.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Gioli, B.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

Graf, A.

M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

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M. Lothon, F. Lohou, D. Pino, F. Couvreux, E. R. Pardyjak, J. Reuder, J. Vilà-Guerau de Arellano, P. Durand, O. Hartogensis, D. Legain, P. Augustin, B. Gioli, I. Faloona, C. Yagüe, D. C. Alexander, W. M. Angevine, E. Bargain, J. Barrié, E. Bazile, Y. Bezombes, E. Blay-Carreras, A. van de Boer, J. L. Boichard, A. Bourdon, A. Butet, B. Campistron, O. de Coster, J. Cuxart, A. Dabas, C. Darbieu, K. Deboudt, H. Delbarre, S. Derrien, P. Flament, M. Fourmentin, A. Garai, F. Gibert, A. Graf, J. Groebner, F. Guichard, M. A. Jimenez Cortes, M. Jonassen, A. van den Kroonenberg, D. H. Lenschow, V. Magliulo, S. Martin, D. Martinez, L. Mastrorillo, A. F. Moene, F. Molinos, E. Moulin, H. P. Pietersen, B. Piguet, E. Pique, C. Román-Cascón, C. Rufin-Soler, F. Saïd, M. Sastre-Marugán, Y. Seity, G. J. Steeneveld, P. Toscano, O. Traullé, D. Tzanos, S. Wacker, N. Wildmann, and A. Zaldei, “The BLLAST field experiment: Boundary-layer late afternoon and sunset turbulence,” Atmos. Chem. Phys. Discuss. 14, 10789–10852 (2014).

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Figures (9)

Fig. 1.
Fig. 1.

Daily course of observed values of Cn2 (from an eddy-covariance station) for λ=670nm [(a) and (c)] and λ=2mm [(b) and (d)] for different weather types (blue asterisk is clear sky, red circle is cloudy) and seasons: (a) and (b) two summer days; (c) and (d) two autumn days above grass in The Netherlands (Haarweg Wageningen, 2005).

Fig. 2.
Fig. 2.

Reaction of rc to water vapor deficit Δq according to different schemes for the observed range of Δq. The reactions by dRH99 and BB97 were defined for the same grass area (Cabauw, The Netherlands), and are therefore both calculated by rcLAI/rs,min (LAI=2, rs,min=110sm1, being representative for Cabauw).

Fig. 3.
Fig. 3.

Validation of estimates (model) of ra, rc, Ts, H, LvE, and QnG with measurements (obs) at a grass field in The Netherlands (GC) in 2005. Dark markers indicate clear-sky conditions, whereas light markers indicate very cloudy conditions.

Fig. 4.
Fig. 4.

Validation of estimates (model) of the structure parameters of n for (a) an optical and (b) a millimeter wavelength, with derivations from measurements (obs) at a grass field in The Netherlands in 2005. Dark markers indicate clear-sky conditions, whereas light markers indicate very cloudy conditions.

Fig. 5.
Fig. 5.

Validation of estimates (model) of the structure parameters of n for an optical [(a) and (c)] and a millimeter wavelength [(b) and (d)], with derivations from measurements (obs). Above, a grass field in southern France in 2011 for adjusted Monin–Obukhov parameters. Below, a wheat field in the ripening phase in western Germany in 2009. Dark markers indicate clear-sky conditions, whereas light markers indicate very cloudy conditions.

Fig. 6.
Fig. 6.

Cn2 measured (markers) and estimated (lines) for a clear (circles and dashed) and cloudy (asterisks) summer day (June 19, 12 UTC, 2005) at the Haarweg (similar to Fig. 1).

Fig. 7.
Fig. 7.

Sensitivity of derivations of Cn2 using the algorithm given in [49], to RH and Ta. Diamond markers indicate the 25th and 75th percentile of RH and Ta for the grass data of the Haarweg in 2005.

Fig. 8.
Fig. 8.

rc and LvE estimates (model) versus measurements (obs) for the Haarweg (GC) using the approach for rc from dRH99, colored by Δq (light is 0, dark is 10gkg1).

Fig. 9.
Fig. 9.

Validation of derivations of Cn2 from measured values for CT2, Cq2, CTq, and rTq, with derivations from flux measurements (T* and q*) at a grass field in The Netherlands in 2005. Dark markers indicate an optical wavelength; light markers indicate a millimeter wavelength.

Tables (7)

Tables Icon

Table 1. Vegetation Types and Parameter Values after the ERA40 Surface Scheme (TESSEL) Used in the ECMWF Model

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Table 2. Instrumentation Specifications Per Input or Validation Variable for the Three Measurement Sites

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Table 3. Land-Surface Input Variables per Datasetd

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Table 4. Regression Results of Estimated Versus Observed Fluxes, Structure Parameters, and Variables at the Haarweg (GC left) and in Lannemezan (GS right)a

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Table 5. Regression Results of Estimated Versus Observed Fluxes, Structure Parameters, and Variables During the Growing Season (Left) and Ripening Season (Right) in Merken (WC)a

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Table 6. Sensitivity Estimates of Cn2 to the Main Input Parameters and Constants (or Parameters Directly Derived from Sin) for June 19, 2005, 12 UTC at the Haarwega

Tables Icon

Table 7. Land Surface Input Variables Used for All Sitesa

Equations (50)

Equations on this page are rendered with MathJax. Learn more.

LvE=s(QnG)+ρcpra(esatea)s+γ(1+rcra),
H=QnGLvE.
rc=104Δq=104esateapRdRv,
rc=rs,minLAIfdqfradfTfθ.
rc=25.9fdqfradfθ,
frrs,minLAICabauwfdq=25.9(1+hs(ΔqΔq0)),
(κz)2/3CT2T*2=6.7κ2/3(114.9zL)2/3,
(κz)2/3Cq2q*2=3.5κ2/3(14.5zL)2/3.
CTq=rTqCT2Cq2,
Cn2=AT2T¯a2CT2+Aq2q¯2Cq2+2ATAqT¯aq¯CTq,
AT=p¯T¯a(b1+b2q¯RvR¯),
Aq=p¯Ta¯bq2q¯RvR¯(1q¯(RvRd)R¯),
Ts=(Lout(1ϵs)Linϵsσ)1/4,
ra=ρcpTaTsH,
rc=ra(s(QnG)+ρcp(esatea)raγLvEsγ1),
rc=frrs,minLAIfdqfrad,
fdq=1+hs(ΔqΔq0),
frad=1000Sin+230(10002Sin)Sin(1000230).
Sout=aSin,
a=amax(1N)sin(α)(amaxamin)N(amaxacloud).
N=Sin,0SinSin,00.20.8,
Sin,0=I¯0(d¯sundsun)2cosθz.
Lin=ϵaσTa4,
ϵa,clear=0.63+5.95×107eae1500/Ta,
ϵa=N+(1N)ϵa,clear.
H=Qn,0+Qn,T(TsTa)G0GT(TsTa)LvE0LvET(TsTa),
TsTa=Hraρcp.
H=Qn,0G0LvE01+Qn,T+GT+LvET,
Qn,0=(1a)Sin+(ϵa1)ϵeσTa4,
G0=Ag(TaT24h).
LvE0=ρcpγesat(Ta)era+rc.
Qn,T=raρcpϵsσ4Ta3,
GT=raρcpAg,
LvET=raγs(Ta)ra+rc.
ra=1κu*(lnzz0hΨT(zL)+ΨT(z0hL)).
u*=uκln(zz0m)Ψu(zL)+Ψu(z0mL),
L=Tau*2κgTv*,
Tv*=Hvcpρu*,T*=Hcpρu*,q*=LvELvρu*,
Hv=H(1+0.61q)+0.61cpTaLvE0Lv,
Ts=Ta+Hraρcp+zΓd,
Lout=ϵsσTs4+(1ϵs)Lin,
Qn=SinSout+LinLout=Q0ϵsσ4Ta3(TsTa),
G=Ag(T24hTs)=G0+Ag(TsTa),
LvE=s(QnG)+ρcpra(esatea)s+γ(1+rcra)=LvE0+ρcpγs(Ta)(TsTa)ra+rc.
b1=106(0.237134+68.39397130λ2+0.4547338.9λ2),
b2=106(0.648731+5.8058×103λ27.115×105λ4+8.851×106λ6)b1,
bq2=b2,
b1=0.776×106,
b2=106(7500Ta0.056),
bq2=106(3750Ta0.056).

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