Dr. Wu's research and its influence are summarized by Google Scholar
| Tropical Dynamics | Modulated Annual Cycle | Climate Change |
| Data Analysis Methods | Engineering and Medicine | Other Studies |
Tropical Dynamics
My journey to tropical atmospheric dynamics wasn't a planned one. After four years of struggle in working on three PhD research topics (monsoon-ENSO interaction, cumulus convection parameterization, and ENSO irregularity), my mentor, Edward Sarachik, told me that the problem of tropical atmosphere under different momentum damping and thermal damping had not been solved. At that time, Ed had also been haunted by the question on whether elevated convective heating can drive surface winds. Based on the seminal paper of Lindzen (1967), the answer is a solid "no" at low frequency end. However, the Zebiak-Cane model (Zebiak & Cane 1987) for ENSO had demonstrated that including the interaction between surface winds and convective heating is crucial to succesfully predict ENSO. This puzzle needed to be solved.
I was lucky enough to get helps from my mentors, Ed, David Battisti, and Dennis Moore to solve this collection of problems. First, I proved that the solutions obtained by Lindzen (1967) were not complete. His solutions contained only the class of eigenfunctions with discrete positive "equivalent depths" which are largely irrelevant to Ed's question at the low frequency end. I discovered the class of eigenfunctions with continuous negative "equivalent depths" which can effectively account for large-scale forcing at low frequencies. When thermal damping is much stronger than momentum damping, the large-scale elevated forcing can drive strong surface wind response (Wu et al. 1999). This theoretical inference was confirmed by numerical model experiments (Wu et al. 2000a).
The results obtained above only gave a partial explanation for how elevated heating drives surface winds. In Zebiak-Cane model (Zebiak & Cane 1987), the atmospheric component is a Gill-type model (Gill 1980), which contains only one vertical mode, corresponding to a sinusoidal vertical heating structure with zero heating at surface and at the top of the atmosphere and a maximum at middle troposphere. This simplification artificially brought the heating down from above cloud base to surface. Whether the surface response in such type of model is caused by this simplification or is a realistic response wasn't answered at that time. In a more general interpretation, this simplification is a result of imposing an artificial lid (for the purpose of easier mathematical treatment) at the top of the atmosphere (which in reality does not exist). A side effect of imposing a lid is the response of the atmosphere to elevated heating having preferred vertical structures, just like a case of pushing a finger at different locations to make different sound by a string instrument. Thus, to fully address this problem, I must remove the lid and eliminate the side effect of preferred vertical structures caused by imposing an artificial lid in mathematical treatment. In Wu et al. (2000b), I solved that problem (for an tropical atmosphere without an artificial lid) mathematically. The results point to that the vertical structure of elevated convective heating determines largely the three-dimentional structure of the atmospheric response. At the meantime, I also obtained mathematically the solutions to Gill-type of model but with different thermal and momentum dampings (Wu et al. 2001) . These solutions explain (pp 738 of that paper) why, in upper troposphere but not in lower troposphere, the temperature and pressure are largely zonally symmetric at low-frequencies, which is now widely known as "weak temperature gradient approximation" (Sobel at al. 2001).
The final note of my PhD study was the proof of the completeness of eigenfunctions of the tidal equation on an equatorial beta-plane (Wu & Moore 2004). To accomplish that, I used the complex forms of some special functions, spectral representation of a differential operator, concept of analytical continuation, and Hilbert space theory. The above mentioned works earned me a PhD from the Department of Atmospheric Sciences , University of Washington.
My dissertation superisory committee included Profs. Edward Sarachik, David Battisti, Mike Wallace, Dennis Hartmann, Ka-Kit Tung, and Charlie Eriksen. Ed and David were my official advisors, and Mike and Dennis were my dissertation reading committee members. Prof. Dennis Moore was not in the supervisory committee due the the formation of the committee was earlier than I first met him. But his inspiration and guidance were crucial to me, especially his introduction of some mathematical books to me.
After a lengthy stay of eight years and three months (including one year postdoc research) in Seattle, which I considered my second home town, I left for the Center of Ocean-Land-Atmosphere Studies (COLA), where I began to learn climate modeling. However, my work along the PhD study continued for a short while. In the final paragraph of Wu et al. (2000b), I discussed the implication of these solutions for the eastward acceleration of Madden-Julian Oscillation (MJO) (Madden & Julian 1972). However, the more important inference from Wu et al. (2000b) is that the interactions among shallow convective heating, deep convective heating, and circulation can provide explanations, from a perspective of pure atmospheric dynamics, for slow eastward propagation of MJO, eastward acceleration of MJO, and why MJO has dominant intraseasonal time scale. At that time, the observation of shallow convective heating was very scarce and not believed to be a major player in MJO. In Wu (2003), I proposed shallow CISK, deep equilibrium mechanism to formalize these explanations and predict the fraction of shallow convection heating in the total of the tropical convective heating. The number obtained, 24%, has largely been confirmed by later observational studies.
After more than a decade on leave from tropical dynamics, I came back to this field recently, working parallelly on two topics: (1) Tropical wave diagnoses and their dynamical interpretations; and (2) Interaction between convective heating and circulation and their parameterization. Traditionally, tropical waves are diagnosed using Fourier transform based methods, such as in the influential work of Wheeler & Kiladis (1999). However, some results of this type of work are hard to be reconciled with physical understanding. For example, in Wheeler-Kiladis diagram, the dominant mixed Rossby-gravity (MRG) wave energy emerges at wave numbers 0 to 4. Since MRG waves have small group velocities, they are physically expected to attenuate away from their sources in a dissipative atmosphere and are not likely to have dominant wave engergy on the above mentioned wave number range. Taking advantages of most recently developed adaptive and local data analysis methods (ALDAMs), we revealed the MRG wave energy distribution in wavenumber-frequency-energy space that is more consistent with physical arguments Sun & Wu(2020). At the same time, we have been building a Dynamics-Based Analysis of Wave (DBA-Wave) package for community usage. Ongoing works in this line include the searching for general characteristics of waves in a spatially varying mean flow.
On the topic of interaction between convective heating and circulation, we modified the conditional instability of the second kind (CISK) theory (Charney & Eliassen 1964) and the cumulus parameterization scheme based on this theory (Kuo 1974). One of the widely criticized drawbacks was "CISK catastrophe", the strongest instability occurred at the smallest scale that a numerical model can resolve. On the other hand, the previous formulations of CISK or its variations assumed that the local convective heating varies simultaneously with local convergence, which has little physical base since the loop of local heat exciting waves, waves changing circulations, circulations feeding back to local moisture convergence at the heating location, and the changing of the local heat takes time. We corrected this drawback in previous CISK theories (Liu et al. 2019) and in the parameterization scheme (Liu et al. 2021) by adding non-instantaneous response and shallow heating. These corrections led to better MJO simulations.
Back to Reseach