A Comparison of Methods for Calculating Montgomery Streamfunction Using Modern Data

1. A Comparison of Methods for Calculating Montgomery Streamfunction Using Modern Data Patrick S. Market1 and Scott M. Rochette2 1Dept. of Soil, Env., & Atmospheric Science, University of Missouri 2Dept. of the Earth Sciences, The College at Brockport, SUNY Introduction The suggestion has been made recently that Montgomery Streamfunction is now calculable simply by applying the equation Ψ = g Z + cp T , using the observed (or modeled) height and temperature values at the elevation of interest. Historically, this practice has been frowned upon, as radiosonde measurements did not have the accuracy requisite to allow such a practice. This led to inaccurate calculations of Ψ, and therefore geostrophic wind calculations that were in serious error. This history, and the subsequent abandonment of isentropic coordinates in the early 20th century have been well documented (Bleck 1973), and will not be repeated here. As such, since the late 1950s, an integral approach to calculating Ψ has been preferred in order to get workable, usable values, and subsequent geostrophic wind calculations (Danielsen 1959). Yet, there have been marked advancements in the accuracy and reliability of radiosonde measurements, especially with the advent of GPS-verified height data. In this study, we show that nowadays, the values from the simple method and the integral method are, in fact, very similar. Indeed, the difference between calculations of Ψ differ by 0.6%, a value that is quite consistent throughout the depth of the troposphere. This value is well below the 2% difference threshold suggested by previous researchers (Danielsen 1959), beyond which calculations of the geostrophic wind would begin to exhibit the same errors as experienced in the early 20th century. This value is established with high-resolution radiosonde data as well as with output from the Rapid Update Cycle (using both initial fields as well as short-term forecast values). Analysis Table I. Sample data and calculations from 1600 UTC 2011 Mar 22 flight. These analyses demonstrate the similarities between the single-level method for calculating Ψ and the integrated approach (taken as the control). At top: the ratio of the two methods to calculating Ψ. In the first 16 minutes of the radiosonde flight (and lowest ~500 mb). At bottom: the percent error of the simple method, % error = [1 – (Ψsimple / Ψintegrated)] x 100 hovering around 0.6%, and well below the 2.0% threshold suggested by Danielsen (1959). Data and Methodology For this study, we have selected a single radiosonde flight - Data collected by the University of Missouri (UM) sounding system o Intermet iMet-3000 · GPS winds · GPS verified heights - Flight specifications o Launched on 22 March 2011, 1600 UTC o Launched from UM South Farm site - Calculate Montgomery Streamfunction using o Ψsimple = Cp T + g Z , and o Ψintegrated = Ψlower + (Cp x Tmean x ln( θ2 / θ1) ) Geostrophic wind calculations with aid from the Rapid Update Cycle fields are ongoing Conclusions - Most software written in the last few decades already includes the integral approach - Yet, findings shown here allow us to conclude that the simpler method may be employed in the presence of highly accurate height and temperature data References Bleck, R., 1973: Numerical forecasting experiments based on the conservation of potential vorticity on isentropic surfaces. J. Appl. Meteor., 12, 737-752. Danielsen, E. F., 1959: The laminar structure of the atmosphere and its relation to the concept of the tropopause. Arch. Meteor. Geophys., BioKlim, Atol., Ser. A, 11, 232-293.