This proposal focuses upon two interconnected and equally important problems. The first of them is developing a new Statistical Learning Theory (SLT) dedicated to modeling specific complex systems. The second one is to develop a new convection representation for numerical climate models. Understanding climate and weather is important to science, society and the economy. The processes we focus upon (clouds, and particularly convection) are critical to climate and weather. The proposal involves a novel approach to improving the representation of those processes. Our goal is to combine a team of mathematical scientists with expertise in SLT, and atmospheric scientists with expertise in cloud modeling and climate system modeling to produce an innovative representation for convection in the atmospheric models used for numerical weather prediction and climate change studies. The project will develop an SLT system that emulates the statistical behavior of a more realistic but very expensive high resolution Cloud System Resolving Model (CSRM) in a variety of cloud regimes. Employing even the simplest of these CSRM frameworks in a large scale model increases the cost of today?s atmospheric models by factors of thousands, which make their use impractical for many studies. By emulating the behavior of these more realistic frameworks in a large scale model we develop a new SLT parameterization, dramatically reducing the cost of the more realistic representations of model convection, and providing an opportunity to address problems currently viewed as critical within the scientific community. By developing the application-oriented SLTs we hope to make the more realistic cloud and convective formulations currently being explored, computationally feasible and use them in climate models.
This proposal combines research used in the computational statistics scientific community with climate science. One of the most important components of the climate system is the representation of clouds. They control many aspects of the energy and heat that enter and leave the climate system, and they interact with many components of the earth system (agriculture, weather, society, and the economy). But clouds are so complex that they can not be treated very precisely in models that are used for understanding climate and weather. The equations required to represent clouds are so complex that a precise treatment would slow down current models by factors of thousands or millions. Current computational climate and weather models cannot afford a precise representation of clouds so faster approximate treatments of clouds are needed. Traditional representations for clouds in climate and weather models are not sufficiently accurate, and progress has been slow in improving these model components. This proposal employs advanced statistical-mathematical methods to try and improve the situation. These methods (called Statistical Learning Theory or SLT) allow one to represent very complex systems with accurate, and very fast approximations. We are going to try to approximate very detailed, complex and expensive models of convective clouds using SLT to produce an accurate approximation for clouds with the goal of using this approximation (these approximations are frequently called a parameterization in climate and weather models). This research will push forward the knowledge base used in both the SLT community, and the climate community.
