On the variation of divergent flow: an eddy-flux form equation based on the quasi-geostrophic balance and its application

Bijlsma, S. J., L. M. Hafkenscheid, and P. Lynch, 1986: Computation of the streamfunction and velocity potential and reconstruction of the wind field. Mon. Wea. Rev., 114, 1547–1551.

Buechler, D. E., and H. E. Fuelberg, 1986: Budgets of divergent and rotational kinetic energy during two periods of intense convection. Mon. Wea. Rev., 114, 95–114.

Cao, J., and Q. Xu, 2011: Computing streamfunction and velocity potential in a limited domain of arbitrary shape. Part II: Numerical methods and test experiments. Adv. Atmos. Sci., 28, 1445–1458, doi: 10.1007/s00376-011-0186-5.

Chen, T. C., 1980: On the energy exchange between the divergent and rotational components of atmospheric flow over the tropics and subtropics at 200 mb during two northern. Mon. Wea. Rev., 108, 896–912.

Chen, T. C., and A. C. Wiin-Nielsen, 1976: On the kinetic energy of the divergent and nondivergent flow in the atmosphere. Tellus, 28, 486–498.

Chen, T. C., and M. C. Yen, 1991: Interaction between intraseasonal oscillations of the midlatitude flow and tropical convection during 1979 northern summer: The Pacific Ocean. J. Climate, 4, 653–671.

Chen, T. C., J. C. Alpert, and T. W. Schlatter, 1978: The effects of divergent and nondivergent winds on the kinetic energy budget of a mid-latitude cyclone: A case study. Mon. Wea. Rev., 106, 458–468.

Chen, Q. S., and Y. H. Kuo, 1992: A consistency condition for wind-field reconstruction in a limited area and a harmoniccosine series expansion. Mon. Wea. Rev., 120, 2653–2670.

Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

Daley, R., and E. Barker, 2001: NAVDAS: Formulation and diagnostics. Mon. Wea. Rev., 129, 869–883.

Ding, Y. H., and Y. Z. Liu, 1985: On the analysis of typhoon kinetic energy, Part II Conversion between divergent and nondivergent wind. Science in China (B), 15, 1045–1054.

Fu, S. M., J. H. Sun, S. X. Zhao, and W.-L. Li, 2011: The energy budget of a southwest vortex with heavy rainfall over South China. Adv. Atmos. Sci., 28, 709–724, doi: 10.1007/s00376-010-0026-z.

Fu, S. M., F. Yu, D. H. Wang, and R. D. Xia, 2013: A comparison of two kinds of eastward-moving mesoscale vortices during the Mei-yu period of 2010. Science China Earth Sciences, 56, 282–300.

Fu, S.-M., J.-H. Sun, J. Ling, H.-J. Wang, and Y.-C. Zhang, 2016: Scale interactions in sustaining persistent torrential rainfall events during the Mei-yu season. J. Geophys. Res. Atmos., 121, 12 856–12 876, doi: 10. 1002/2016JD025446.

Graham, R. D., 1953: A new method of computing vorticity and divergence. Bull. Amer. Meteor. Soc., 34, 68–74.

Grist, J. P., R. Marsh, and S. A. Josey, 2009: On the relationship between the North Atlantic meridional overturning circulation and the surface-forced overturning streamfunction. J. Climate, 22, 4989–5002.

Hawkins, H. F., and S. L. Rosenthal, 1965: On the computation of stream functions from the wind field. Mon. Wea. Rev., 93, 245–253.

Hendon, H. H., 1986: Streamfunction and velocity potential representation of equatorially trapped waves. J. Atmos. Sci., 43, 3038–3042.

Hoskins, B., I. Draghici, and H. C. Davies, 1978: A new look at the ω-equation. Quart. J. Roy. Meteor. Soc., 104, 31–38.

Hoskins, B., M. McIntyre and A. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877–946.

Holton, J. R., 1979: An Introduction to Dynamic Meteorology. Academic Press, 391 pp.

Krishnamurti, T. N., and Y. Ramanathan, 1982: Sensitivity of the monsoon onset to differential heating. J. Atmos. Sci., 39, 1290–1306.

Landers, H., 1956: On the magnitude of divergence and vorticity. J. Meteor., 13, 121–122.

Lynch, P., 1988: Deducing the wind from vorticity and divergence. Mon. Wea. Rev., 116, 86–93.

Parrish, D. F., and J. C. Derber, 1992: The national meteorological center’s spectra statistical interpolation analysis system. Mon. Wea. Rev., 120, 1747–1763.

Qu, X., and G. Huang, 2012: An enhanced influence of tropical Indian Ocean on the South Asia High after the late 1970s. J. Climate, 25, 6930–6941.

Reiter, E. R., and D. Y. Gao, 1982: Heating of the Tibet Plateau and movements of the south Asian high during spring. Mon. Wea. Rev., 110, 1694–1711.

Saha, S., and Coauthors, 2010: The NCEP climate forecast system reanalysis. Bull. Amer. Meteor. Soc., 91, 1015–1057.

Sangster, W. E., 1960: A method of representing the horizontal pressure force without reduction of station pressures to sea level. J. Meteor., 17, 166–176.

Tao, S. Y., and Y. H. Ding, 1981: Observational evidence of the influence of the Qinghai-Xizang (Tibet) Plateau on the occurrence of heavy rain and severe convective storms in China. Bull. Amer. Meteor. Soc., 62, 23–30.

Trenberth, K. E., and Chen, S. C., 1988: Rotational and divergent geopotential components. J. Atmos. Sci., 45, 2949–2960.

Wiin-Nielsen, A., and M. Drake, 1966: The contribution of divergent wind components to the energy exchange between the baroclinic and barotropic components. Mon. Wea. Rev., 94, 1–8.

Xu, Q., 2005: Representations of inverse covariances by differential operators. Adv. Atmos. Sci., 22, 181–198, doi: 10.1007/BF 02918508.

Xu, Q., S. Liu, and M. Xue, 2006: Background error covariance functions for vector wind analyses using Doppler-radar radial-velocity observations. Quart. J. Roy. Meteor. Soc., 132, 2887–2904.

Xu, Q., K. Nai, and L. Wei, 2007: An innovation method for estimating radar radial-velocity observation error and background wind error covariances. Quart. J. Roy. Meteor. Soc., 133, 407–415.

Xu, Q., J. Cao, and S. T. Gao, 2011: Computing streamfunction and velocity potential in a limited domain of arbitrary shape. Part I: Theory and integral formulae. Adv. Atmos. Sci., 28, 1433–1444.

Ye, D. Z., 1981: Some characteristics of the summer circulation over the Qinghai-Xizang (Tibet) Plateau and its neighborhood. Bull. Amer. Meteor. Soc., 62, 14–19.