Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 William J. Gutowski, Jr. Iowa State University

Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 GOAL: Understand basis for modeling climate from (almost) first principles

Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 Review (Part 1): Symbolism Conservation Laws mass (r, rq) thermodynamic energy (T, q) momentum ( ) Equation of State (p = rRT) Water in the Atmosphere

Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 OUTLINE (Part 2): Radiation Surface Processes Earth System

RNET FSH RNET

Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 OUTLINE (Part 2): Radiation

Radiation Spectrum Black Body Curves Emission 255 K 6,000 K Wavelength [m]

Radiation Spectrum Solar (shortwave, visible) Terrestrial Black Body Curves Emission 6,000 K 255 K Wavelength [m] Solar (shortwave, visible) Terrestrial (longwave, infrared)

Radiation Spectrum Solar Terrestrial Absorption [%] Wavelength [m] Entire atmosphere Absorption [%] Above 11 km Wavelength [m] Solar Terrestrial

Radiation Spectrum Solar Terrestrial CH4 N2O Absorptivity [%] O2 & O3 CO2 H2O Wavelength [m] Solar Terrestrial

Energy Balance for Earth

Energy Balance for Earth Planetary Albedo

Energy Balance for Earth

Energy Balance for Earth

Solar Constant At photosphere surface, solar flux ~ 6.2.107 W-m-2

Solar Constant At photosphere surface, solar flux ~ 6.2.107 W-m-2 At Earth’s orbit, solar flux ~ 1360 W-m-2

Daily Solar Radiation at Top of Atmos. [106 J-m-2] Note high latitude annual cycle, esp. maximum values in summer. This is at top of atmosphere. This is not radiation reaching the surface. Raidation reaching the surface is reduced from this by reflection. High-latitude reflection will be larger because (1) large amount of snow and ice cover and (2) oblique angle of incoming radiation.

Planetary Albedo Scattering: air molecules, aerosols Reflection: clouds Surface albedo Ocean 2-6% Snow 40-95% Crop 15-25% Forest 5-10% Cities 14-18%

What is Earth’s temperature? Balance: Radiation in = Radiation out a Incoming = 1360 W-m-2 x (1-albedo) x (area facing sun) = 1360 x (1-0.3) x pa2 = 1.2.10+17 W

What is Earth’s temperature? Balance: Radiation in = Radiation out a Incoming = 1360 W-m-2 x (1-albedo) x (area facing sun) = 1360 x (1-0.3) x pa2 = 1.2.10+17 W Outgoing = sT4 x (area emitting) ; i.e., black body = sT4 x 4 pa2

What is Earth’s temperature? Balance: Radiation in = Radiation out a Incoming = 1360 W-m-2 x (1-albedo) x (area facing sun) = 1360 x (1-0.3) x pa2 = 1.2.10+17 W Outgoing = sT4 x (area emitting) ; (i.e., black body) = sT4 x 4 pa2 Balance implies T = {0.7(1360 W-m-2)/4s}1/4 = 255 K = -18 oC

What is Earth’s temperature? Balance: Radiation in = Radiation out a Balance implies T = -18 oC Observed surface T = +15 oC Difference? Must account for atmosphere (greenhouse effect).

What is Earth’s temperature? Balance: Radiation in = Radiation out a Balance implies T = -18 oC Observed surface T = +15 oC Difference? Must account for atmosphere (greenhouse effect). Perspective 1. Atmosphere reduces effective emissivity of surface. Use radiation = esT4. Then e = (255/288)4 = 0.61

What is Earth’s temperature? Balance: Radiation in = Radiation out a Balance implies T = -18 oC Observed surface T = +15 oC Difference? Must account for atmosphere (greenhouse effect). Perspective 1. Atmosphere reduces effective emissivity of surface. Use radiation = esT4. Then e = (255/288)4 = 0.61 Perspective 2. Where is T = 255 K? (Effective black body level) Approximately 5 km above surface (above most q).

Greenhouse Effect IR radiation absorbed & re-emitted, partially toward surface Solar radiation penetrates

Greenhouse Effect IR radiation absorbed & re-emitted, partially toward surface Net IR: ~50-100 W-m Emitted IR: ~200-500 W-m

Radiative Cooling vs. Height

Absorbed Solar Radiation High influx in tropical oceans, esp. where cloud cover low. Rapdi drop with latitude: high zenith angle, ice/snow cover

Outgoing Terrestrial Radiation Note effect of high clouds in the tropics. Variation with latitude (temperature), but weaker gradient than absorbed solar. Also, net surface longwave (not shown) has even less of a gradient.

What if temperature decreases? The same: Incoming = 1.2.10+17 W Outgoing = sT4 x (area emitting) = sT4 x 4 pa2

What if temperature decreases? These are the same: Incoming = 1.2.10+17 W Outgoing = sT4 x (area emitting) = sT4 x 4 pa2 But for T < 255 K: imbalance Incoming solar exceeds outgoing IR net energy input T increases ~ Negative Feedback ~

Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 BREAK

Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 OUTLINE (Part 2): Radiation Surface Processes

Key Energy Fluxes at Surface Net Radiation Sensible Heat Latent Heat Deep Soil/Ocean

Key Energy Fluxes at Surface Sensible Heat FSH = r Cp(wT)s Tair Ts

Key Energy Fluxes at Surface Sensible Heat FSH ≈ - r CpCH(Tair-Ts) CH = CH(V, zo, dq/dz) FSH = r Cp(wT)s Tair Ts

Key Energy Fluxes at Surface Latent Heat Note various water pathways. Magnitude of ET depends on land use (vegetation) and soil type.

FLH ~ - rCpCW{eair-esat(Ts)} Key Energy Fluxes at Surface FLH ~ - rCpCW{eair-esat(Ts)} Latent Heat Note various water pathways. Magnitude of ET depends on land use (vegetation) and soil type.

FLH ~ - rCpCW{eair-esat(Ts)} Key Energy Fluxes at Surface FLH ~ - rCpCW{eair-esat(Ts)} Latent Heat CW = CW(V, zo, dq/dz) but also CW = CW(physiology) soil moisture CW µ leaf temp. sunlight CO2 level Note various water pathways. Magnitude of ET depends on land use (vegetation) and soil type.

Key Energy Fluxes at Surface Deep Ocean Deep Soil Important for global climate Generally small

Cycles Diurnal FLH FSH FSH FLH Grassland - Net Radiation Dry Lake Note magnitudes of fluxes. FLH

Cycles Diurnal FLH FSH Less cooling by evaporation Ts increases FSH Grassland - Net Radiation Cycles FLH FSH Diurnal Dry Lake - Net Radiation Less cooling by evaporation Ts increases FSH larger FSH Note magnitudes of fluxes. FLH

Cycles Annual Soil Temperature at depths marked Note magnitudes of fluxes.

Cycles Annual Note magnitudes of fluxes.

Subsurface Water Root Zone Vadose Zone Ground Water Impermeable Layer Note effect of high clouds in the tropics. Variation with latitude (temperature), but weaker gradient than absorbed solar. Also, net surface longwave (not shown) has even less of a gradient. Water Table Ground Water Impermeable Layer

Subsurface Water

Water Cycle Q Q P P E E River flow (dishcarge) can pool, creating inland bodies of water that produce ET. Groundwater can also give groundwater-supported ET, when water table is near surface. R

Climate Modeling Theory - 2 Module 5 Climate Modeling Theory - 2 OUTLINE (Part 2): Radiation Surface Processes Earth System

Earth Climate System Q P E E R

Plant B Plant A Scales of Climate Human Influences Global Regional Regional Regional Regional Microscale Microscale Microscale Microscale Microscale Microscale Microscale Microscale Microscale Microclimate A Microclimate B Microclimate C Air-Transported Pathogen B Air-Transported Pathogen A CO2, CO, NOx,SO2, trace gases, shading, H2O, temperature, Solar, IR, wind, particulate matter CO2, CO, NOx,SO2, trace gases, shading, H2O, temperature, Solar, IR, wind, particulate matter CO2, CO, NOx,SO2, trace gases, shading, H2O, temperature, Solar, IR, wind, particulate matter Surface slope, IR Radiation, Evaporation, Biogeochemicals Crop A Crop B Chemicals Chemicals Chemicals Plant A Plant B Human Influences Insect A Management Management Particulate Deposition, Precipitation, Solar Radiation, IR Insect B Soil Pathogen B Erosion Chemicals Soil Pathogen D Detritus Soil A H2O, temperature, nutrients, microbes, soil carbon, trace chemicals Soil A H2O, temperature, nutrients, microbes, soil carbon, trace chemicals Soil C H2O, temperature, nutrients, microbes, soil carbon, trace chemicals Soil B H2O, temperature, nutrients, microbes, soil carbon, trace chemicals Soil B H2O, temperature, nutrients, microbes, soil carbon, trace chemicals Hydrology, Soil Microbiology, Soil Biochemistry Field Field Field Field Field Field Field Field Field Field Regional Regional Regional Regional Continental Scales of Landforms

Climate Modeling Theory Modules 3 & 5 Climate Modeling Theory Acknowledgements Dingman (1994) Physical Hydrology Haltiner (1971) Numerical Weather Prediction Holton (1992) An Introduction to Dynamic Meteorology Oort & Peixoto (1992) Physics of Climate Wallace & Hobbs (1977) Atmospheric Science: An Introductory Survey Colleagues at Iowa State University