Systems Analysis and Environmental Modeling Lecture Notes PDF

Systems Analysis and Environmental Modeling 040918401 Fall 2024  General Circulation Models or GCMs Numerical models (General Circulation Models or GCMs), a.k.a. Global Climate Model, representing physical processes in the atmosphere, ocean, cryosphere and land surface, are the mo...

Systems Analysis and Environmental Modeling 040918401 Fall 2024  General Circulation Models or GCMs Numerical models (General Circulation Models or GCMs), a.k.a. Global Climate Model, representing physical processes in the atmosphere, ocean, cryosphere and land surface, are the most advanced tools currently available for simulating the response of the global climate system to increasing greenhouse gas concentrations only GCMs, have the potential to provide geographically and physically consistent estimates of regional climate change which are required in impact analysis  General Circulation Models or GCMs Climate models are important tools for improving our understanding and predictability of climate behavior on seasonal, annual, decadal, and centennial time scales. Models investigate the degree to which observed climate changes may be due to natural variability, human activity, or a combination of both. Their results and projections provide essential information to better inform decisions of national, regional, and local importance, such as water resource management, agriculture, transportation, and urban planning.  General Circulation Models (GCMs) are mathematical models used to simulate the Earth's climate system by representing physical, chemical, and biological processes. They help predict how the climate will respond to various factors like greenhouse gases, aerosols, and changes in land use. Importance Predict future climate scenarios. Assess impacts of climate change on ecosystems, agriculture, and human societies. Aid in developing mitigation and adaptation strategies. Components of GCMs 1. Atmospheric Models Simulate atmospheric dynamics, radiation, and water vapor processes. 2. Ocean Models Represent currents, heat transport, and ocean-atmosphere interactions. 3. Land Surface Models Account for soil moisture, vegetation, and land use changes. 4. Cryosphere Models Include glaciers, ice sheets, and sea ice dynamics. Basic Working Principles 1.Grid System 1. The Earth's surface is divided into a 3D grid of horizontal and vertical cells. 2. Climate variables (temperature, humidity, wind) are calculated for each grid cell. 3. Smaller grid sizes (higher resolution) provide more detailed results but require more computational power. 2.Time Steps 1. GCMs simulate changes over time, usually in hourly to annual increments. 3.Input Parameters 1. Natural forcings: Solar radiation, volcanic eruptions. 2. Anthropogenic forcings: Greenhouse gas emissions, deforestation.  Types of GCMs 1.Atmosphere-Ocean General Circulation Models (AOGCMs) 1. Coupled systems of atmospheric and oceanic models. 2. Used to study interactions between the atmosphere and oceans. 2.Earth System Models (ESMs) 1. Extend AOGCMs by including carbon cycles, biogeochemical processes, and vegetation dynamics. 3.Regional Climate Models (RCMs) 1. High-resolution models for specific regions, embedded within GCMs. Recent Developments in GCMs 1.High-Resolution Models 1. Resolve finer-scale features like hurricanes and urban heat islands. 2.Coupling with AI 1. Use machine learning to improve parameterization and reduce computation time. 3.CMIP6 Models 1. Latest generation of models for IPCC's Sixth Assessment Report.  General Circulation Models or GCMs The Geophysical Fluid Dynamics Laboratory has been one of the world leaders in climate modeling and simulation for the past 50 years. Beginning in the 1960s, GFDL scientists developed the first coupled ocean- atmosphere general circulation climate model, and have continued to pioneer improvements and advances in a growing modeling community. State-of-the art climate modeling at GFDL requires vast computational resources, including supercomputers with thousands of processors and petabytes of data storage. one of the important aspects of GCMs is that they calculate the precipitation, and this provides another means of evaluating how good the models are. The figure shows a comparison of the observed mean annual precipitation for the time period 1961-1990 and the average of the 14 models used by the IPCC study. he models, on average, do quite well at simulating the global pattern of precipitation  Climate Scenarios and Predictions 1.Representative Concentration Pathways (RCPs) 1. RCP 2.6: Low emissions scenario with aggressive mitigation. 2. RCP 4.5: Intermediate stabilization scenario. 3. RCP 8.5: High emissions scenario ("business as usual"). 2.Shared Socioeconomic Pathways (SSPs) 1. Integrate socioeconomic factors like population growth and economic trends. The SIR Model for Spread of Disease mathematical modelling of infectious diseases Statistical/empirical models Why Use Mathematical /Statistical Models After developing a conceptual model, it is natural to develop a mathematical model that will allow one to estimate the quantitative behavior of the system. Models consist of two basic components, (1) the factors or forces that constitute the model and (2) the relationships between these factors and forces [(101 X 3) - 6 + 7] X 102 - 50 = 260 (Q1) The numbers represent the factors themselves, such as the number of animals, the amount of forage available, or some other biological quantity. The mathematical signs (X, - , + ) represent the relationships between these quantities. Some are multiplicative; others are additive, either positive or negative. The parenthesis and brackets indicate the mathematical order that must be followed in arriving at an answer. The final output (260) represents the cumulative relationship between all factors in the model. Why Use Mathematical and Statistical Models The model represented by equation (Q1) is a very simple one. Complex models can be built only after simpler ones have been assembled and tested. Quantitative results from mathematical models can easily be compared with observational data to identify a model's strengths and weaknesses. Mathematical models are an important component of the final "complete model" of a system which is actually a collection of conceptual, physical, mathematical, visualization, and possibly statistical sub-models. Statistical / empirical models Basis: simple theoretical analysis or empirical investigation gives evidence for relationship between variables E.g. a scatter plot with a trend Basis is generally simplistic or unknown, but general trend seems predictable Using this, a statistical relationship is proposed Scatter plot Rectangular coordinate Two quantitative variables One variable is called independent (X) and the second is called dependent (Y) Points are not joined No frequency table Y * * * X Scatter plot Graphically depicts the relationship between two variables in two dimensional space The pattern of data is indicative of the type of relationship between your two variables: positive relationship negative relationship no relationship Direct Relationship: positive relationship Scatterplot:Video Games and Alcohol Consumption 20 Average Number of Alcoholic Drinks 18 16 14 12 Per Week 10 8 6 4 2 0 0 5 10 15 20 25 Average Hours of Video Games Per Week  18 16 14 12 Height in CM 10 8 6 4 2 0 0 10 20 30 40 50 60 70 80 90 Age in Weeks Inverse Relationship: Negative relationship Scatterplot: Video Games and Test Score 100 90 80 70 Exam Score 60 50 40 30 20 10 0 0 5 10 15 20 Average Hours of Video Games Per Week Reliability Age of Car No relation An Example Trend? Does smoking 170 cigarettes increase 160 systolic blood pressure? 150 Plotting number of 140 cigarettes smoked per 130 day against systolic blood pressure 120 SYSTOLIC Fairly moderate 110 relationship 100 Relationship is positive 0 10 20 30 SMOKING Heart Disease and Cigarettes The Data Data on heart disease and Country Cigarettes CHD 1 11 26 cigarette smoking in 21 2 9 21 developed countries 3 4 9 24 9 21 (Landwehr and Watkins, 1987) 5 8 19 6 8 13 Data have been rounded for 7 8 19 computational convenience. 8 6 11 9 6 23 The results were not affected. 10 5 15 11 5 13 12 5 4 13 5 18 14 5 12 15 5 3 16 4 11 17 4 15 18 4 6 19 3 13 20 3 4 21 3 14  30 Country Cigarettes CHD 1 11 26 2 9 21 3 9 24 4 9 21 CHD Mortality per 10,000 5 8 19 20 6 8 13 7 8 19 8 6 11 9 6 23 10 5 15 10 11 5 13 12 5 4 {X = 6, Y = 11} 13 5 18 14 5 12 15 5 3 16 4 11 0 17 4 15 2 4 6 8 10 12 18 4 6 19 3 13 Cigarette Consumption per Adult per Day 20 3 4 21 3 14