Samuel S.P. Shen is Distinguished Professor of Mathematics and Statistics, San Diego State University and Visiting Research Mathematician, Scripps Institution of Oceanography, UCSD. In 2006, he left the McCalla Professorship position at the University of Alberta, Canada, and became the SDSU department chair of mathematics and statistics. In the same year, he founded the SDSU Climate Infomratics Lab (SCIL), which has trained a large number of data and AI scientists and attracted research fundings from NSF, NOAA, NASA, DOE and ONR. In 2013, he co-founded the SDSU Center for Climate and Sustainability Studies (C2S2), an SDSU Area of Excellence. In 2019, he co-founded the SDSU Big Data Analytics MS program.

Dr. Samuel Shen is an applied mathematician with current research interests in climate data science and interactive math instruction. He directs the SDSU Climate Informatics Lab (SCIL), which conducts research in 4D climate data visualization, fast delivery of big climate data, climate data reconstruction, machine learning/AI applications in climate science, uncertainty quantification, nonlinear water waves, interactive math instruction, and Python and R tutorial products. Their spectral optimal averaging (SOA) method for inhomogeneous fields and their findings of multiple solutions of forced nonlinear waves in the 1990s have influenced the international community’s research in the relevant fields. The first uncertainty quantification for the global warming assessments in the United Nations’ Inter-governmental Panel for Climate Change (IPCC) report was made in 2001 using their SOA theory (IPCC Report 2001, Figs. 2.7 and 2.8). The report cited six of Shen’s papers.

His paper “North, G.R., K.Y. Kim, S.S.P. Shen, and J.W. Hardin: Detection of forced climate signals, Part I: Theory” studied the same topic as the 2021 physics Nobel laureate paper (K. Hasselmann 1993). The Hasselmann and North teams communicated their research results in advance before submitting their papers to the same Journal of Climate and cited each other’s papers. Shen’s method of ensemble canonical correlation analysis (ECCA) algorithm developed at NASA in 2001 was the first linear climate prediction method that can take the nonlinear process into account. NASA Goddard Space Flight Center announced the results on January 15, 2002 in its press release, citing it as a TOP STORY. The NOAA Climate Prediction Center has adopted ECCA in its operational forecasts His paper “North, G.R., K.Y. Kim, S.S.P. Shen, and J.W. Hardin: Detection of forced climate signals, Part I: Theory” studied the same topic as the 2021 physics Nobel laureate paper (K. Hasselmann 1993). The Hasselmann and North teams communicated their research results in advance before submitting their papers to the same Journal of Climate and cited each other’s papers. Shen’s method of ensemble canonical correlation analysis (ECCA) algorithm developed at NASA in 2001 was the first linear climate prediction method that can take the nonlinear process into account. NASA Goddard Space Flight Center announced the results on January 15, 2002 in its press release, citing it as a TOP STORY. The NOAA Climate Prediction Center has adopted ECCA in its operational forecasts.

Professor Shen has patterned two technologies: (i) Spectral Optimal Averaging Algorithm (SOA), and (ii) 4-Dimensional Visual Delivery of Big Climate Data (4DVD). Professor Shen has been awarded 48 research grants from various US and Canadian funding agencies. Among the awards, six are major research projects with multi-million dollars. Presently he is the lead PI of a $2.7 million AI grant from the National Science Foundation. This project is from 2023 – 2027 and does research on 4D space-time organization of geophysical processes and visualization tools.

Professor Shen has published 5 books and more than 140 refereed papers with top journals and publishers, including Nature Geoscience and Cambridge University Press. He has been recognized with international honors and awards. He was elected as President-elect of the Canadian Applied and Industrial Mathematics Society in 1999, and Vice-President of the Canadian Mathematical Society in 2003. In 2001, he received the honor of “Well-known Overseas Chinese Scholar” from the Chinese Academy of Sciences. In 2014, SDSU honored Dr. Shen with a Distinguished Professorship, which is the top SDSU research prize issued to one SDSU faculty per year. Now only 14 Distinguished Professors are still active SDSU employees.

The SCIL lab, under Professor Shen’s direction, has been conducting climate data analysis research in collaboration with distinguished climatologists. We have developed a suite of theories and methods for climate science. A few are described as follows:

- 4DVD software: The 4DVD technology (4-Dimensional Visual Delivery of Big Climate Data: www.4dvd.org) was developed by SCIL. The software was first released in 2016. The 4DVD uses the technologies of video games and Amazon shopping and puts climate data at users’ fingertips. 4DVD uses various kinds of computing resource optimization in database and distributed computing so that the climate data selected by a user can be quickly visualized and delivered. In this way, 4DVD can deliver climate modeling and observational data to classrooms and households. The Shen lab SCIL has trained schoolteachers under an NSF Noyce program to use 4DVD in mathematics and science teaching.

- SOA method: The spectral optimal averaging (SOA) method, also known as the reduced space optimal averaging (RSOA), was developed in 1994 (Shen et al. 1994, Journal of Climate). The SOA theory provides an approach for using climate model data and modern high-quality observations to optimally analyze historical climate data. Through empirical orthogonal functions (EOFs), the SOA can adequately treat spatial inhomogeneity, making the conventional objective analysis approach, which assumes a homogeneous covariance function, obsolete. The editor of the Journal of Climate highly praised our contribution to climate data analysis: “
*This work makes an important advance over previous studies involving optimal averaging in its consideration of inhomogeneous, anisotropic covariance structure. The continued use of obviously inappropriate assumptions about this structure will do nothing more than delay the optimum exploitation of existing historical data networks or the optimum design of future ones. Your point about the relative insensitivity of error reductions to the exact shapes of the eigenvectors is extremely important.*em>” Some further developments and applications of the method were made in subsequent years (Shen et al., 1998; Folland et al., 2001). This method is now widely used for climate data error analysis, including that for the IPCC reports.

- Space-time optimal detection theory: In early 1990s, Dr. Shen collaborated with Jerry North of Texas A&M University and developed a space-time spectral filter to detect signals of forced climate change (North et al. 1995, Journal of Climate). This method can overcome the problem of stationarity assumption present in other detection methods, such as K. Hasselmann’s fingerprint method. The method successfully detected the carbon dioxide signal in the global average surface air temperature. The filter is a solution of an integral equation with space-time EOFs. This rather general scheme establishes the mathematical foundation for constructing an iteration scheme for future nonlinear detection strategies. The IPCC considered this work as one of the three major advances toward statistical climate change detection methods in the early 1990s (IPCC 1995 report, p. 416; IPCC 2001 report, Appendix 12.2).

- Random clouds and stochastic climate models: In collaboration with Scripps Institution of Oceanography, SCIL developed a Bayesian statistical framework to describe cloud fractions (Shen et al. 2013). This approach provides a path forward for the next generation of climate models: complete stochastic modeling, in which every climate parameter is treated as a random variable and hence, parameterization closure for turbulent flows is turned into physical and stochastic closures.

- Error estimate theory in the optimal reconstruction: This theory helps quantify uncertainties in climate change assessments due to sampling errors and was developed in collaboration with Tom Smith, Chet Ropelewski, and Bob Livezey of the U.S. Climate Prediction Center (CPC) (Shen et al. 1998, 2007, and 2012, Journal of Climate; Smith et al., 1998, Journal of Climate The optimal averaging method uses extrapolated eigenvalues, the area factor in computing EOFs, and cross-validation. This method is considered the most accurate regional averaging scheme currently available and has been applied to the Tropical Pacific SST (sea surface temperature) field and others. The work improved the CPC scheme for interpolating sparse observation data onto grid points. Their SST test showed that 4% of data could recover the original field with an error of less than 10%.

- RVC method: The equivalence between the point observations and the grid box data defined in the climate model output is a fundamental problem in model validation. One example is to use surface rain gauges to measure the rain rate over a grid box and to answer a question: What is the ground truth? (North et al. 1994, J. Atmos. Ocean. Tech.) Shen’s group randomized the locations of the rain gauges in a grid box. This general mathematical method helps objectively compare point observational data with climate model output to avoid apple-to-orange comparisons.

- Randomization theory for point observations of grid box data: The equivalence between the point observations and the grid box data defined in the climate model output is a fundamental problem in model validation. One example is to use surface rain gauges to measure the rain rate over a grid box and to answer a question: What is the ground truth? (North et al. 1994, J. Atmos. Ocean. Tech.) Shen’s group randomized the locations of the rain gauges in a grid box. This general mathematical method helps objectively compare point observational data with climate model output to avoid apple-to-orange comparisons.

- ECCA method: To overcome the “spring barrier” in U.S. seasonal precipitation predictions, Professor Shen worked with the NASA Lab for Atmosphere Chief Bill Lau and developed the ensemble canonical correlation analysis (ECCA) method (Shen et al. 2001, NASA Tech. Memo.; Shen et al. 2002, Chin. J. Atmos. Sci.; Lau et al. 2002, Geophys. Rev. Lett.). Different from the traditional linear statistical forecasting methods, the ECCA incorporates global atmospheric circulation dynamics and is a quasi-nonlinear scheme. NASA Goddard Space Flight Center announced the results on January 15, 2002 in its press release, citing it as a TOP STORY. The U.S. Climate Prediction Center has adopted this method as one of its operational forecasts.

- Nonlinear theory of critical precipitation for forest fires: Professor Shen and his student Robert Field developed a nonlinear theory and a new dataset for Indonesian forest fires dating back to 1960. Airport visibility data, satellite remote sensing data, and precipitation data were used to determine the parameters of the nonlinear model. A paper was published in Nature Geoscience (Field et al. 2009). The journal also published a backstory on the research. Nature distributed an official press release about the paper on February 22, 2009. The research has since been covered by many news media around the world, including The New York Times, New Scientist, and Science Daily.

- Degrees of freedom of a climate field: Professor Shen and his student Xiaochun Wang developed a more accurate theory to answer an important climate assessment question: What is the minimum number of stations needed to reliably measure a climate field? (Wang and Shen 1999, Journal of Climate). They found that other authors’ earlier estimates of the degrees of freedom for annual mean surface air temperature anomalies were too low.

- Agroclimate database services: (a) Through eight years of collaboration with Alberta Agriculture, Food and Rural Development (AAFRD), the Shen group created the first comprehensive agroclimate database for Alberta province, called ABClim 1.0. It includes many variables, such as temperature, precipitation, and growing degree days. Nationally, ABClim 1.0 serves as a prototype model for the climate component of Canada’s digital agriculture system, called NLWIS (National Land and Water Information Service). Professor Shen became one of the conceptual designers of this Oracle database system, which has a GIS (Geographic Information System) interface. (b) The Shen team analyzed the long-term (1901-2002) temporal trends in Alberta’s agroclimate, exploring spatial variations and potential crop-growing areas. This information is important to AAFRD’s climate adaptation strategies. AAFRD distributed a press release on Shen’s research results, and several local newspapers reported the work (Shen et al. 2005, J. Appl. Meteo.) (c) Generation of the Agroclimatic Atlas of Alberta: The Agroclimatic Atlas of Alberta is a 97-page document that presents climatic information of importance to Alberta’s agriculture community. The atlas has been well distributed to Alberta farm communities, schools, and relevant governmental ministries, as well as relevant research centers worldwide. It is also displayed on the AAFRD website. The atlas is a significant advancement in information technology for Alberta’s agricultural industry. See S. Chetner and the Agroclimatic Atlas Working Group, Agroclimatic Atlas of Alberta, 2003.

In his earlier career, Professor Shen was interested in the research on nonlinear waves modeled by forced evolution equations, such as the forced Korteweg-de Vries (fKdV) equations, forced nonlinear Schrodinger equations, and forced sine-Gordon equations. The mathematical difficulty of this research was from a lack of group symmetries associated with unforced problems. This was due to the non-conservation of momentum or other quantities. The forced systems supported some surprising phenomena, such as periodic upstream soliton radiation and hydraulic fall in fKdV equations, which do not occur in unforced cases. The mathematical community then recognized the importance of this research direction. In 1997, the American Mathematical Society held a special session on nonlinear waves with an emphasis on forced evolution equations. Shen’s results attracted the attention of many leading researchers in applied mathematicians and nonlinear waves, such as Ted Wu, David McLaughlin, Jerry Bona, Mark Ablowitz, and Peter Lax.

- Comprehensive bifurcation diagram for fKdV When a water flow over a bump in a channel has an upstream uniform velocity close to the characteristic speed of shallow water waves, the free-surface profiles of the flow can demonstrate some intriguing phenomena: trans-critical upstream soliton radiation waves, a sub-critical hydraulic fall, and super-critical multiple solitary waves. Using asymptotic analysis, Shen demonstrated that the forcing due to the bump could be modeled by a Dirac delta function. An analytic expression of the bifurcation diagram was found to classify the types of surface waves (Shen et al. 1992, J. Fluid Mech.; Gong and Shen 1994, SIAM J. Appl. Math).

- Confirmation of the fKdV as an accurate model equation: Since the fKdV equations were derived based on the assumption of small amplitude and long wave, many researchers believed that these models could provide only qualitative results. Using numerical calculations, experimental data, and mathematical theory, Shen demonstrated otherwise: The fKdV model can actually yield quantitatively accurate solutions with an error of less than 10% compared with experiments. Such an unexpected, high accuracy of the fKdV as a model equation encouraged further fKdV studies (Shen 1995, Quarterly Appl. Math.)

- Spectral scheme, stability of solitary waves and collision of uniform soliton trains: A user-friendly C++ software was developed as a tool for both research and teaching. This package solves the forced KdV equations, forced nonlinear Schrodinger equations and forced sine-Gordon equations. This rather unique software can render numerical, graphic, and animated output. The tool is very convenient for checking the stability of the multiple stationary solutions and for simulating the collision process of the solitons of the same size (Danohue and Shen, 2010, J. Engr. Math.).

- Mechanical energy for transcritical flows: In the transcritical regime, solitons are periodically generated and radiated upstream, and depression zones and modulated wake zones are simultaneously generated downstream. Shen found that the depth of depression can be determined by the solvability condition of a boundary value problem for an ordinary differential equation. Upon obtaining the depression depth, the flow characteristics, such as the period of the soliton generation, can be analytically determined (Shen 1993, A Course on Nonlinear Waves, Ch. 6; Shen 1996, Wave Motion).

- UCLA TV 2019: A collaboration with Professor Yongkang Xue at UCLA for the the research of Tibetan Plateau environment and its influence on the global climate system via the NSF program of Earth System Modeling (EaSM3).

- Spectral optimal gridding for precipitation (SOGP) 2014: Spectral optimal gridding for precipitation (SOGP) product release on October 6, 2014: . This MATLAB-based product democratizes the accessibility of the historical precipitation data back to 1900 for the entire globe (excluding the polar regions). It is known in general public as Weather History Time Machine and is well reported by media around the world, such as Science Daily (10/15/2014),
NSF News
(10/15/2014), and San Diego KUSI NEWS TV (a live interview by the KUSI Meteorologist Mark Mathis) (10/23/2014).

- History Channel 2010: Sam Shen arranged a collaboration between the SDSU Mathematics Department and The History Channel in 2010, with a worldwide broadcast from the SDSU campus. The TV program can be viewed from the URL link here,
YouTube, and many other sites. Search the video by the following keywords: Stan Lees Superhumans with The Human Calculator Scott Flansburg on The History Channel.

- Fight Fire with Mathematics: A
Nature Press Release on February 22, 2009, and SDSU News Report on March 9, 2009: Nature distributed an official press release on Feb 22, 2009. Many news media around the world, including The New York Times, New Scientist, and Science Daily, followed the release and reported the research.
SDSU also distributed a news report
on this work. “When thinking of the common tools used to fight a fire, mathematics does not make it on most people's lists. But a recent paper published in Nature Geoscience has proven that thinking wrong.”
For the complete research paper, go to
the Nature website. Nature also published a backstory on the paper.

- Agri-News by Alberta Agriculture, Food and Rural Development Ministry, August 22, 2005

Alberta Agriculture, Food and Rural Development Ministry made a press release on August 22, 2005 about Sam Shen group's research on the agroclimate changes over Alberta (Shen et al., 2005, J. Appl. Meteo.) Newspapers from many cities and communities in Alberta reported this research release.

- Exclusive 12-minute radio interview by CBC Radio-Canada in 2004, and an exclusive 15-minute CCTV-China interview in 2003. They were about the education of the children in rural China.

- NASA Goddard Space Flight Center’s Top Story Press Release on January 15, 2002: New Method Greatly Improves U.S. Seasonal Forecasts: A new technique could raise the bar for predicting seasonal precipitation by 10 to 20 percent for all seasons in the United States, a NASA-funded study finds. It raises the bar for seasonal and inter-annual climate forecasts. The paper was published in Geophysical Research Letters. Professor Shen was responsible for developing the statistical theory of forecasting. For the complete theory, see Shen et al. (2001), NASA Technical Memorandum.