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Insolation Examples

This page demonstrates various use cases of Insolation.jl through visualizations and practical examples. These examples show how to calculate and visualize solar radiation patterns across different timescales and locations.

Diurnal Cycle of Insolation

The diurnal cycle shows how insolation and solar zenith angle vary throughout a day at a specific location. This is useful for understanding the daily energy input and for applications such as solar power forecasting.

Pasadena in Winter: Clear diurnal cycle with peak insolation at solar noon. Solar zenith angle reaches minimum (~35°) at midday.

using Insolation
using Dates

include("plot_diurnal_cycle.jl")

# Load orbital data
od = OrbitalDataSplines()

# Example 1: Pasadena, California in January (mid-latitude winter)
lat, lon = [34.15, -118.14]  # Pasadena coordinates
date = DateTime(2020, 01, 10)
timezone = +8  # Pacific Standard Time (UTC+8)
diurnal_cycle(lat, lon, date, od, timezone, "Pasadena_January.png")

Finland in Summer: At the Arctic Circle, the sun does not set at northern summer solitice, resulting in continuous daylight and non-zero insolation for the 24-hour period. This "midnight sun" phenomenon is visible as the sustained insolation during night hours.

# Example 2: Rovaniemi, Finland in June (Arctic summer - midnight sun)
lat, lon = [66.50, 25.73]  # Rovaniemi coordinates (Arctic Circle)
date = DateTime(2020, 06, 20)  # Summer solstice
timezone = -3  # Eastern European Summer Time (UTC+3)
diurnal_cycle(lat, lon, date, od, timezone, "Finland_June.png")

Latitudinal and Seasonal Variations

The following examples show how daily-averaged insolation varies with latitude and day of year, revealing Earth's seasonal cycles and the role of orbital parameters.

Modern Climate (J2000 Epoch)

import Insolation
import Insolation.Parameters as IP
import ClimaParams as CP

FT = Float64
param_set = IP.InsolationParameters(FT)

include("plot_insolation.jl")

# Get current epoch orbital parameters
γ0 = IP.obliq_epoch(param_set)
ϖ0 = IP.lon_perihelion_epoch(param_set)
e0 = IP.eccentricity_epoch(param_set)
od = Insolation.OrbitalDataSplines()

# Calculate daily-mean insolation across latitudes and days
days, lats, F0 = calc_day_lat_insolation(od, 365, 180, param_set)
plot_day_lat_insolation(days, lats, F0, "YlOrRd", title, "insol_example1.png")

This plot shows daily-averaged TOA insolation as a function of latitude and day of year for modern Earth (J2000 epoch). Key features:

  • Solstices: Maximum insolation at high latitudes during local summer (June in NH, December in SH)
  • Equinoxes: Symmetric insolation distribution around March 21 and September 21
  • Annual Mean: Right panel shows the latitudinal gradient, with maximum near the equator

Effect of Reduced Obliquity

Obliquity (axial tilt) controls the strength of seasonal cycles. Here we reduce obliquity from 23.44° to 20° to demonstrate its impact.

# Reduce obliquity to 20.0° (from current 23.44°)
param_set_low_obliq = IP.InsolationParameters(FT, (; obliq_epoch = deg2rad(20.0)))
γ1 = IP.obliq_epoch(param_set_low_obliq)
days, lats, F2 = calc_day_lat_insolation(od, 365, 180, param_set_low_obliq)

plot_day_lat_insolation(days,lats,F2,"YlOrRd",  title, "insol_example2a.png")
plot_day_lat_insolation(days, lats, F2-F0, "PRGn", title, "insol_example2b.png")

Absolute Insolation (top): With reduced obliquity, polar regions receive less summer insolation, and the tropical regions receive slightly more year-round.

Difference Plot (bottom): Shows that reducing obliquity:

  • Decreases high-latitude summer insolation (blue regions)
  • Increases tropical insolation slightly (purple regions)
  • Results in weaker seasonal cycles overall

This demonstrates that lower obliquity leads to milder seasons - important for understanding climates on other planets or Earth's past climates.

Extreme Obliquity (Uranus-like Configuration)

Uranus has an extreme axial tilt of 97.86°, essentially rotating "on its side." This creates dramatically different seasonal patterns.

# Set obliquity to 97.86° (Uranus's axial tilt)
param_set_uranus = IP.InsolationParameters(FT, (;obliq_epoch = deg2rad(97.86)))
γ4 = IP.obliq_epoch(param_set_uranus)
days, lats, F5 = calc_day_lat_insolation(od, 365, 180, param_set_uranus)

plot_day_lat_insolation(days,lats,F5,"YlOrRd", title, "insol_example3a.png")
plot_day_lat_insolation(days, lats, F5-F0, "PRGn", title, "insol_example3b.png")

Absolute Insolation (top): With extreme obliquity, the insolation pattern is dramatically different:

  • Polar regions receive intense summer insolation, exceeding tropical values
  • Equatorial regions have two insolation peaks per year
  • Extreme seasons with long polar day/night periods

Difference Plot (bottom): Compared to Earth's current configuration:

  • Polar summers receive much more insolation (>500 W/m² increase)
  • Annual-mean distribution shifts toward maxima at the poles

This extreme case illustrates how orbital parameters fundamentally shape a planet's climate. Such configurations help us understand exotic exoplanets and the range of possible planetary climates.

Summary

These examples demonstrate that Insolation.jl can:

  • Calculate diurnal cycles for any location and date
  • Visualize latitudinal and seasonal patterns
  • Explore sensitivity to orbital parameters
  • Model both Earth-like and exotic planetary configurations

For paleoclimate applications with time-varying orbital parameters, see Milankovitch Cycles.