Estimation of optical turbulence with standard weather-station observations

We present a robust model that is able to estimate surface fluxes of heat, moisture and momentum, and from those optical turbulence via the structure parameter of the refractive index of air, Cn2. Our model differs from previous models (Sadot and Kopeika, 1992; Rachele and Tunick, 1994; Bendersky et al., 2004) in that it does not use empirical parameters, and that it makes use of standard weather-station data (temperature, humidity, shortwave radiation and wind speed) measured at (or, potentially, forecasted for) one height only. Our model mainly depends on the Penman-Monteith equation (an implementation of de Rooij and Holtslag (1999) to calculate fluxes from the input) and Monin-Obukhov similarity theory (to calculate Cn2 from the surface fluxes).

The model was tested for two crop types and two climates through three datasets (daytime data only); over a grass field in the Netherlands (Haarweg, Wageningen; one year), over a grass field in southern France (BLLAST experiment, Lannemezan; a summer period), and over a wheat field in western Germany (Transregio experiment, Merken; a growing season).

We validated the modelled sensible and latent heat fluxes and the modelled Cn2 for the various fields with values derived from 30-minute high-frequency wind, temperature and humidity data from sonic anemometers and gas analysers. Despite many underlying assumptions regarding field conditions, the model performs well for both grass fields. The model is also able to represent the fluxes and Cn2 over the wheat field, albeit with some more deviations from the observed fluxes and Cn2. These deviations are mainly caused by the uncertainty in the approximation of the canopy resistance of the growing wheat, which in our model only depends on leaf area index and water vapour deficit.

Estimates for Cn2 that are derived from our model could for example be used in the planning phase of microwave-link networks for communicational purposes or campaigns using imaging systems, since the propagation of electromagnetic radiation suffers from strong atmospheric turbulence. Furthermore, the derived Cn2 from our model could be tested in equations that specify the image quality achieved by a ground-based telescope. The robust estimates of evaporation could for instance be used in crop studies if direct flux measurements are not available.

Bendersky, S., N. S. Kopeika, and N. Blaunstein: 2004, ‘Atmospheric optical turbulence over land in middle east coastal environments: prediction modeling and measurements.'. Appl Opt 43(20), 4070–9.

Rachele, H. and A. Tunick: 1994, ‘Energy balance model for imagery and electromagnetic propagation'. J Appl Meteor 33, 964–976.

de Rooy,W. C. and A. A. M. Holtslag: 1999, ‘Estimation of surface radiation and energy flux densities from single-level weather data'. J Appl Meteor 38(5), 526–540.

Sadot, D. and N. S. Kopeika: 1992, ‘Forecasting optical turbulence strength on the basis of macroscale meteorology and aerosols : models and validation'. Opt Eng 31(2), 200–212.