
-- Daisy growth rate function is a function of temperature. Maximum growth
-- occurs at 22.5 degrees Celsius, and daisies grow from a minimum of 5 C to
-- a maximum of 40 C.
local function daisyGrowthRate(tempK) -- daisyGrowthRate as function of temperature.
	local gr = 0.0
	local temp = tempK - 273
	if temp > 5.0 and temp < 40.0 then
		gr = 1 - 0.003265 * (22.5 - temp)^2
	end
	return gr
end

-- Calculates the average planet temperature using Boltzmann's law
-- "The amount of thermal radiation emitted increases rapidly and the principal frequency of the radiation becomes higher with increasing temperatures"
-- TempK^4 = average solar flux * luminosity (1 - albedo)
-- Watson and Lovelock used 3668 watts per square meter as the solar flux,
-- which is much higher than the average solar flux incident on the Earth today,
-- because the Earth has a relatively low planetary albedo and
-- a significant greenhouse effect.
local SIGMA = 5.67E-08    -- Joules / per sec * square meters * TempK^^4 -- Stephen Boltzmann constant
local SOLAR_FLUX = 3668   -- Watts/square meter

local function calcTemp(lum, albedo)
	local tempK = (lum * SOLAR_FLUX * (1 - albedo) / (4*SIGMA)) ^0.25
	return tempK
end

-- Calculates the temperatures near the daisies
--
-- The local temperatures Tw and Tb are defined by making a simplifying assumption about
-- the heat transfer: a linearization of a diffusion term.
-- A parameter q is defined as the heat transfer coefficient,
-- thereby defining the local temperatures as
-- TempK^4 (daisy) = q (planet_albedo - daisy_albedo) + tempK^4 (planet)

local HEAT_TRANSFER_COEF = 2.06E09  -- Kelvins^4  -- used by Watson and Lovelock

local function tempNearDaisy(planet_temp, planet_albedo, daisy_albedo)
	local temp_daisy = (HEAT_TRANSFER_COEF * (planet_albedo - daisy_albedo) +
		planet_temp ^ 4 ) ^ 0.25
	return temp_daisy
end

-- actual growthRate is constained by the empty area of the planet
local function growthReduction(baseRate, emptyArea)
	local newRate = baseRate * emptyArea
	return newRate
end

--- An implementation of the daisy world model.
-- Wood, A. J., G. J. Ackland, J. G. Dyke, H. T. P. Williams, and T. M. Lenton (2008),
-- Daisyworld: A review, Rev. Geophys., 46.
-- Daisyworld consists of two different types of daisy, which may be considered distinct species
-- (because there is no possibility of mixed replication of the types) or, alternatively, as
-- distinct phenotypes of the same species. The two types are identified as either black or
-- white according to their reflectivity or albedo.
-- @arg data.sunLuminosity Sun luminosity (this is the main variable of the model).
-- Values beteween 0.70 and 1.6  support life in Daisyworld.
-- @arg data.planetArea The total area of the planet. The sum of the arguments
-- whiteArea, blackArea, and emptyArea should be equals to this value. The default value is 1.
-- @arg data.whiteArea The initial area of white daisies. The default value is 0.4.
-- @arg data.blackArea The initial area of black daisies. The default value is 0.273.
-- @arg data.emptyArea The initial empty area. The default value is 0.327.
-- @arg data.whiteAlbedo The albedo of white area. The default value is 0.75.
-- @arg data.blackAlbedo The albedo of black area. The default value is 0.25.
-- @arg data.soilAlbedo The albedo of empty area. The default value is 0.5.
-- @arg data.decayRate The death rate for all daisies.
-- @arg data.finalTime The final time of the simulation. The default value is 100.
-- @image daisyworld.bmp
Daisyworld = Model{
	-- sun luminosity (this is the main variable of the model)
	-- values beteween 0.70 and 1.6  support life in Daisyworld
	sunLuminosity         = 0.7,

	-- variables
	-- default values are approximate equilibrium values
	-- when sun luminosity is equal to 1.0
	-- hint: change the starting conditions when changing the sun luminosity
	-- increase the white area for a strong sun
	-- increase the black area for a faint sun
	planetArea           = 1.0,
	whiteArea            = 0.40,
	blackArea            = 0.273,
	emptyArea            = 0.327,

	-- params (fixed assumptions)
	whiteAlbedo          = 0.75,
	blackAlbedo          = 0.25,
	soilAlbedo           = 0.50,
	decayRate            = 0.3,

	-- simulation time
	finalTime  =  100,
    planetAlbedo = function(model)
		return model.whiteArea * model.whiteAlbedo +
			model.blackArea * model.blackAlbedo +
			model.emptyArea * model.soilAlbedo
	end,
    daisyArea = function(model)
        return model.blackArea + model.whiteArea
    end,
	init = function(model)
		model.chart1 = Chart{
			target = model,
			select = {"blackArea", "whiteArea", "emptyArea"}
		}

		model.chart2 = Chart{
			target = model,
			select = "planetAlbedo",
		}

        model.aveTemp = calcTemp(model.sunLuminosity, model:planetAlbedo())

		model.chart3 = Chart{
			target = model,
			select = "aveTemp",
		}

		model.chart4 = Chart{
			target = model,
			select = "daisyArea"
		}

		model.timer = Timer{
			Event{action = function()
				-- function that calculates the planet Temperature
				model.aveTemp = calcTemp(model.sunLuminosity, model:planetAlbedo())

				-- temperature near he white daisies
				model.tempNearWhite = tempNearDaisy(model.aveTemp,
					model:planetAlbedo(), model.whiteAlbedo)

				-- indicated growth rate for the white daisies
				model.indWhiteGrowthRate = daisyGrowthRate(model.tempNearWhite)

				-- actual growthRate is constained by the empty area of the planet
				model.whiteGrowthRate = growthReduction(model.indWhiteGrowthRate, model.emptyArea)

				-- white area
				model.whiteArea = model.whiteArea + model.whiteArea *
					(model.whiteGrowthRate - model.decayRate)

				-- temperature near the black daisies
				model.tempNearBlack = tempNearDaisy(model.aveTemp,
                    model:planetAlbedo(), model.blackAlbedo)

				-- indicated growth rate for the white daisies
				model.indBlackGrowthRate = daisyGrowthRate(model.tempNearBlack)

				-- actual growthRate is constained by the empty area of the planet
				model.blackGrowthRate = growthReduction(model.indBlackGrowthRate, model.emptyArea)

				-- black area
				model.blackArea = model.blackArea + model.blackArea *
					(model.blackGrowthRate - model.decayRate)

				model.emptyArea = model.planetArea - (model.blackArea + model.whiteArea)
			end},
			Event{action = model.chart1},
			Event{action = model.chart2},
			Event{action = model.chart3},
			Event{action = model.chart4}
		}
	end
}
