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.
Clouds and convection are among the most important and complex phenomena of the Earth’s physical climate system. The processes that control clouds, and through which they interact with other components of the Earth system involve slow and fast fluid motions carrying heat, moisture, affecting winds, gases, and particals in the atmosphere. They influence other important physical processes through phase changes of water substances, radiative transfer, chemistry, and produce and remove gases and aerosols. Clouds are strong regulators of radiant energy, sites for chemistry, participate in many climate feedbacks, and are potentially very susceptible to anthropogenic change (indirect aerosol effects). They figure prominently in all climate change assessments. In spite of intense studies for centuries, clouds still provide an intellectual and computational challenge. Because of the vast range of time and space scales involved in clouds processes they are very complicated to represent. Often scientists know how to represent cloud more accurately than afford in climate models. Drastic simplifications in the treatment of clouds are often made in climate and weather models to speed up computer calculations. These simplifications speed up calculations, but the result is a less accurate and realistic model. We have explored a novel approach to the representation of clouds that use a computational approach called "Neural Networks". Neural Networks (NNs) are used to "mimic" complicated phenomena using non-linear statistical data modeling tools. They can be used to model complex relationships between inputs and outputs. In this case we are using NNs to reproduce the behavior of a very detailed and computationally expensive model of clouds, to make the calculation go much more quickly than it would otherwise. We produced a "training dataset" with the costly model, and then used it to train the NN to mimic its behavior. A variety of "input" and "output" variables were examined in the NN framework to identify the accuracy and consistency of the NN in reproducing the more complicated and costly parent model behavior for one location on the planet, the tropical western pacific. We explored the NNs ability to represent: 1) the heating and moistening terms associated with convection; 2) associate precipitation fluxes at the surface; and 3) volume of air occupied by condensed water (the cloud fraction). Our research indicates that it is possible to produce useful estimates of the changes in temperature, water vapor, and estimates of precipitation and cloud fraction associated with deep convection in the tropical ocean with this technique. The training dataset was quite limited (appropriate only for a particular region of the planet for a brief period in time), and the parameterization has not yet been trained with a sufficiently large dataset to be useful for global climate simulations, but the approach still looks promising.
