1. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 The atmospheric moisture budget in the Arctic – introducing and applying a consistent method to use radiosonde data Reinhard Hagenbrock, Andreas Hense, Felix Ament Meteorological Institute, University of Bonn, Germany Martin Göber Met Office, Bracknell, UK

2. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Outline Motivation: Why the Arctic? Why fresh water? Why radiosondes? Method Use of radiosonde data Calculation of moisture flux convergence (MFC) Results MFC north of 70° Horizontal distribution of MFC Summary and outlook

3. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Why Arctic? Why fresh water? Why radiosondes? The freshwater input into the Arctic Ocean......has strong effect on the thermohaline circulation...is expected to alter under climate change conditions...is difficult to determine: Direct measurements of evaporation E and precipitation P are sparse (or not available at all). Reanalyses are not designed to evaluate the Arctic moisture budget. Radiosondes...

4. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Method: Use of radiosonde data Radiosonde stations used Source: Historical Arctic Rawinsonde Archive (HARA)

5. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Method: Use of radiosonde data The atmospheric moisture budget:

6. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Method: Use of radiosonde data There exists a discrepancy between existing estimates based on radiosondes and those calculated from reanalysis data! Different horizontal scales Large uncertainties in the analyses model Reanalysis uses additional information

7. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Calculation of Moisture Flux Convergence Interpolate to a regular grid Calculate Differentiations Conventional way to calculate moisture flux divergence/convergence: 2 Problems!!!

8. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Calculation of Moisture Flux Convergence Problem No. 1: Mass consistency Problem turns up whenever (moisture) flux divergences are calculated Error in calculated flux divergence is dominated by a term proportional to the (erroneous) mass divergence Solution: remove divergent parts of the wind field! → variational approach, “mass consistent model“

9. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Calculation of Moisture Flux Convergence Variational approach: Set up of a cost function

10. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Calculation of Moisture Flux Convergence Problem No. 2: Irregular grid What you should do: first to differentiate, then to interpolate Change of this order results in serious errors in data sparse regions Solution: Do calculations on irregular grid! Discretize with finite elements

11. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Calculation of Moisture Flux Convergence Discretization: All scalar fields are expanded in linear basis functions h i.

12. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Calculation of Moisture Flux Convergence With this expansion, the contributions to the volume integral read: … so the cost function reads (in 1D):

13. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Calculation of Moisture Flux Convergence The minimization of the cost function leads to a linear equation system. This is solved with a preconditioned conjugate residual solver. boundary conditions (BCs) not necessary for solvability physically motivated BCs may be included by introducing an extra term in the cost function We prevent mass flux through the lower boundary.

14. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Method  (P - E) We combined the variational approach with a FE method in order to calculate the volume integrated moisture flux divergence (or rather: -convergence)... to sum up:

15. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results Typical numbers: ~ 70 stations ~ 800 nodes ~ 1500 tetrahedra

16. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results 1. The effect of missing mass consistency of the MFC north of 70°N.

17. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results: MFC north of 70°N from mass consistent radiosonde data average: 0.461 mm d -1

18. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results: MFC north of 70°N from unmodified radiosonde data average: 0.547 mm d -1

19. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results 2. MFC north of 70°N: Compare radiosonde and reanalysis based results. Use data of (ERA-15) reanalysis precisely where radiosonde data is given. Use radiosonde data on 11 mandatory pressure levels.

20. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 average: 0.449 mm d -1 from mass consistent radiosonde data (on mandatory pressure levels) Results: MFC north of 70°N average: 0.461 mm d -1

21. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 average: 0.480 mm d -1 from mass consistent reanalysis data (on mandatory pressure levels) Results: MFC north of 70°N

22. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results: MFC north of 70°N radiosonde data (average: 0.449 mm d -1 ) ERA-15 reanalysis data (average: 0.480 mm d -1 ) Cullather et al.: radiosonde data (average: 0.45 mm d -1 ) Cullather et al.:ERA-15 reanalysis data (average: 0.50 mm d -1 )

23. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results 3. Horizontal distribution of vertically integrated MFC (ave. 1979-93)

24. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results: Horizontal distribution of vertically integrated MFC from mass consistent radiosonde data

25. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 from mass consistent radiosonde data (smoothed to T42) Results: Horizontal distribution of vertically integrated MFC

26. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Results: Horizontal distribution of vertically integrated MFC from full resolution reanalysis data (smoothed to T42)

27. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Summary (1) A method to analyze atmospheric moisture flux convergence (MFC) is introduced. In order to receive a mass consistent wind field on the irregular grid of the radiosonde data, a variational approach is combined with the Finite Element method. The effect of missing mass consistency is not negligible, neither or average, nor when looking at spatial or temporal variability.

28. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Summary (2) The method allows to compare budgets based on reanalysis and radiosonde data without the problem of different resolutions. The differences observed so far are strongly reduced. There remains a difference of ~ 0.03 mm d -1 (~7 %). For the first time it is possible to make an estimate of the horizontal distribution of the MFC based solely on radiosonde data, thus validating the estimated from reanalyses. Major patterns coincide, yet noticeable differences remain.

29. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Summary (3) As a ”spin-off product“ of the method, several other aspects of the moisture budget (e.g. storage of moisture, storage and transport of energy) are easily analyzed.

30. WATER VAPOR OBSERVATIONS AND PROCESSES Long Beach, 11. Feb. 2003 Outlook The data is used to examine the connection between the moisture budget and large scale circulation.