1. Announcements Will return Temp labs when they are all done. 9-noon March 6, 2015 field trip to NIST for pressure laboratory World’s best manometer. Friday we will do the RH lab. Think about how to calibrate the Davis RH probe; the Vaisala T & RH probes are on the Cessna for now. You should be working or the precip lab – esp the part with variability with height and distance. 1

2. AOSC 634 Air Sampling and Analysis Lecture 4 Measurement Theory Dynamic Performance of Sensor Systems Response of a first order instrument to Sinusoidal input See Brock et al. Chapter 2. Copyright Brock et al. 1984; Dickerson 2015 2

3. Goal Geophysical fluid phenomena often occur in waves. Weather depends on the flux of heat, momentum, and moisture from or into the surface. The soil flux of trace gases such as CO 2, CH 4, NO, N 2 O, is critical to understanding air quality and climate. What is required to measure those fluxes? 3

4. Objective We need to analyze geophysical wave processes. In a useful instrument, the steady state response to sinusoidal input should be predictable. The amplitude will be diminished and the phase shifted, but we want all spectral components to have the same relative amp. and phase angle as the input. We are looking for: A flat amplitude response (independent of frequency). A linear phase response (change in phase proportional to input freq. and lag independent of frequency). A Fourier transform of the output should return the input freq distribution. 4

5. Dynamic Response Sensor output in response to changing input. 5

6. Dynamic Response 6

7. Response to input with  I ≈  b 7 Phase shift  Normalized input and output

8. Dynamic Response 8 After a few time constants, the transient part goes to zero and the response is characterized by: Output angular frequency A(  ) Phase shift  (  ) in radians. When the response (output) angular freq >> input ang freq the amplitude is nearly the same and there is no discernable phase lag. When the response (output) angular freq << input ang freq the amplitude is zero. When  b    then  √  Output lags input by 0 to  /2 radians, and this increases with increasing . When  = 1 (or  b    then 

9. Dynamic Response 9 When  = 1 (or  b    then  Remember the argument of a trig fnx is always in degrees or radians. And that power is proportional to amplitude squared. Therefore the output power is ½ input power when  = 1. The next diagrams show that the output amplitude is always less than the input amplitude.

10. 10  = ratio input/output freq =  I /  b )A(  ) = Output Amplitude (normalized 

11. 11 Phase lag (radian)  =  I /  b )

12. Applications Anderson et al. CH 4 flux from melting Arctic Tundra. http://www.arp.harvard.edu/publication/ NO and N 2 O emissions form fertilized corn fields. 12

13. Real world example Civerolo et al., 1999. 13

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18. Summary Because all real measurement systems have a finite response time, response to sinusoidal input will be, at best, sinusoidal output with reduced amplitude and a phase shift. If the input frequency in the same as the response freq of the system the amplitude will be reduced to 1/√2 (~70%) of the input. The phase shift will be in the desirable range only for input frequencies of a few times the instrument response freq. For input frequencies > about 10 times the response frequency the output will be barely discernable as a sine wave. Peak power in vertical flux of water, momentum, heat, CO 2, O 3 etc. is about 5Hz. Good instruments can measure these fluxes! 18