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XerxesZorgon/stefan-boltzmann-revisited.ipynb

Created May 28, 2024 19:17
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Earth temperature from the Stefan-Boltzmann Law
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stefan-boltzmann-revisited.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "aea6a10e-28c9-4a56-9685-d3fc96154d95",
"metadata": {},
"source": [
"# The Stefan-Boltzmann Law Revisited\n",
"\n",
"This worksheet calculates the blackbody radiation and Earth temperature due to human industrial activities. See the Wild Peaches article [here](https://wildpeaches.xyz/blog/economics-and-the-stefan-boltzmann-law/).\n",
"\n",
"You will be able to calculate:\n",
"* The average Earth temperature based on incoming solar radiation\n",
"* The temperature increase from radiating away heat caused by human activities\n",
"* The temperature rise assuming constant economic growth over several centuries.\n",
"\n",
"The key physical law needed is the [Stefan-Boltzmann Law](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law):\n",
"\n",
"\\begin{equation}\n",
"J = \\sigma T^4\n",
"\\end{equation}\n",
"\n",
"where \n",
"\n",
"* $J = $ radiant emittance in units of $\\frac{W}{m^2}$\n",
"* $\\sigma = 5.67 \\times 10^{-8} \\; \\frac{W}{m^2 \\cdot T^4}$ is the Stefan-Boltzmann constant\n",
"* $T = $ temperature of the blackbody radiator in degrees Kelvin\n",
"\n",
"Most objects are not blackbodies, or perfect radiators, so the equation is modified to\n",
"\n",
"\\begin{equation}\n",
"J = \\epsilon \\sigma T^4\n",
"\\end{equation}\n",
"\n",
"for some [emissivity](https://en.wikipedia.org/wiki/Emissivity) $\\epsilon \\in [0,1]$.\n",
"\n",
"For details, see [*Energy and Human Ambitions on a Finite Planet*](https://escholarship.org/uc/item/9js5291m#page=2) by Tom Murphy, $\\S 1.3$ [**Thermodynamic Consequences**](https://escholarship.org/uc/item/9js5291m#section.1.3), which uses \n",
"\n",
"\\begin{equation}\n",
"P = A_{surf} \\sigma (T_{hot}^4 - T_{cold}^4)\n",
"\\end{equation}\n",
"\n",
"for the radiated power $P$ from an object with surface area $A_{surf}$ and temperature $T_{hot}$ radiating into a region with temperature $T_{cold}$. Since space is near absolute zero, we can omit $T_{cold}$. \n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "2fc86772-febe-4932-94e8-20491fd3a4df",
"metadata": {},
"source": [
"## Earth temperature from solar radiation\n",
"\n",
"The Earth receives about $F = 1360 \\frac{W}{m^2}$ of solar energy at the top of the atmosphere, but only $960 \\frac{W}{m^2}$ reaches the ground due to the albedo $\\alpha = 0.293$. The area of the disk facing the sun with Earth radius is\n",
"\n",
"\\begin{equation}\n",
"A_{disk} = \\pi R_{\\oplus}^2\n",
"\\end{equation}\n",
"\n",
"where $R_{\\oplus}$ is the Earth radius in meters. The absorbed energy is radiated away from the entire surface\n",
"\n",
"\\begin{equation}\n",
"A_{surf} = 4 \\pi R_{\\oplus}^2\n",
"\\end{equation}\n",
"\n",
"so the power input from the sun can be related to the emitted power output,\n",
"\n",
"Solving for $T$, \n",
"\n",
"\\begin{equation}\n",
"\\begin{aligned}\n",
"P_{in} &= 960 \\frac{W}{m^2} \\times \\pi R_{\\oplus}^2 \\\\\n",
"&= 4 \\pi R_{\\oplus}^2 \\sigma T^4 = P_{out}. \\\\\n",
"T &= \\left( \\frac{960}{4 \\sigma} \\right)^{1/4}\n",
"\\end{aligned}\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "72fe5527-232d-4d4d-904d-2d58184e6a7c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1360"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F = 1360 # Solar power at the top of the atmosphere, W/m^2"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "cd320025-7882-47b0-a169-36df73d9bcb5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.293"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"α = 0.293 # Earth albedo"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "54a08dc8-edb1-4601-8bf5-d887ba813cc2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.670374419e-8"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"σ = 5.670374419e-8 # Stefan-Boltzmann constant"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "8eca0180-0cee-427b-8499-5937c6f2dab6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"255.16532016222948"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T = (F*(1-α)/(4σ))^(1/4) # Temperature derived from Stefan-Boltzmann Law"
]
},
{
"cell_type": "markdown",
"id": "aaa7bae1-060e-4e8a-9675-3d91bf4922b9",
"metadata": {},
"source": [
"This temperature $T = 255 \\degree K$ is colder than the observed average temperature of $288 \\degree K$ because it doesn't include the effects of greenhouse gases. See [*CO2 v. CH4*](https://wildpeaches.xyz/blog/co2-v-ch4/) for how to include the greenhouse effect. Let $\\Delta T_{GHG} = 33 \\degree K$ to get the Earth temperature, "
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "f1118b2e-88e3-4e01-8804-3b0a6f02a899",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"288.1653201622295"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T_GHG = 33 # Temperature correction due to greenhouse gases\n",
"T_Earth = T + T_GHG"
]
},
{
"cell_type": "markdown",
"id": "d0c16c4c-27e7-4417-a97b-3eeb61f397b5",
"metadata": {},
"source": [
"## Temperature increases from energy use\n",
"\n",
"[Energy consumption](https://ourworldindata.org/grapher/global-energy-substitution?facet=none) from primary sources (fossil fuels, nuclear, hydro, renewables, biomass) is $E = 178,889 \\; TWh$ per year (in 2022). To calculate the increase in the Earth's surface temperature, we'll need the power in watts per meter of area of the Earth's disk. \n",
"\n",
"TWh are units of energy (terawatt-hours) where $1 \\; TWh = 1e12 \\; Wh$ so 178,889 TWh = 178.889e15 Wh. Divide this by the number of hours per year to get power, $P_0 = E/H$.\n",
"\n",
"\\begin{equation}\n",
"H = 365 \\frac{days}{year} \\times 24 \\frac{hours}{day}.\n",
"\\end{equation}\n",
"\n",
"Next, divide by the surface area of the disk,\n",
"\n",
"\\begin{equation}\n",
"A_{disk} = \\pi R_{\\oplus}^2.\n",
"\\end{equation}\n",
"\n",
"to find the power per square meter, $p_0 = P_0/A_{disk}$.\n",
"\n",
"The radius of the Earth is $R_{\\oplus} = 6.371e6 \\;m$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "25a9b6e4-2a27-4a1a-b9c6-22abdc129c43",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8760"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"H = 365 * 24 # Number of hours in a year"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "54e6009c-2746-43fd-ab5e-ecd188044e6c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.0421118721461188e13"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"E = 178889e12 # Primary energy consumption, Wh\n",
"P0 = E/H # Power in watts"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "c2f8c44e-1214-48b9-8447-8672d6485139",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"6.371e6"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R_Earth = 6.371e6 # Earth radius in meters"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "b6b9599b-116d-413f-ae0f-d0dc499059fe",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.2751611797744706e14"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A_disk = π * R_Earth^2 # Area of Earth disk, m^2"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "d8d593bc-8198-4afb-9665-4eb47edb5014",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.16014539216974075"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p0 = P0 / A_disk # Power from energy consumption, W/m^2"
]
},
{
"cell_type": "markdown",
"id": "00a18c1a-426b-44a2-8a80-0f5e597d2542",
"metadata": {},
"source": [
"Using the Stefan-Boltzmann Law calculate the increase in Earth temperature from energy consumption.\n",
"\n",
"\\begin{equation}\n",
"\\begin{aligned}\n",
"\\Delta T_{Energy} &= \\left( \\frac{F (1 - \\alpha) + p_0}{4 \\sigma} \\right)^{1/4} + \\Delta T_{GHG} - T_{Earth} \\\\\n",
"&= \\left( \\frac{F (1 - \\alpha) + p_0}{4 \\sigma} \\right)^{1/4} - T.\n",
"\\end{aligned}\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "03ff0a34-7a4d-4c02-9fa8-290513a55358",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.010624063530087824"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dT_Energy = ((F*(1-α) + p0)/(4*σ))^(1/4) - T"
]
},
{
"cell_type": "markdown",
"id": "5ca57fe1-2aa3-4433-a338-9f89982e5f2c",
"metadata": {},
"source": [
"For convenience, let's turn $\\Delta T_{Energy}$ into a function,\n",
"\n",
"$$\n",
"T_E(E) = \\left( \\frac{F(1-\\alpha) + E/(H \\cdot A_{disk})}{4 \\sigma} \\right)^{1/4} + \\Delta T_{GHG}.\n",
"$$\n",
"\n",
"In this form we can test different values for the annual energy consumption measured in TWh. "
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "3b96cd34-9334-4c15-b93a-a2fd22847ed7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"TE (generic function with 1 method)"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TE(E) = map(e -> ((F*(1-α)+e/(H*A_disk))/(4*σ))^0.25 + T_GHG, E)"
]
},
{
"cell_type": "markdown",
"id": "95558bbe-bfdf-4b0f-8abc-ce0b2e8f9e6b",
"metadata": {},
"source": [
"Check the solution above with E = 178,889 TWh."
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "6483b108-7f25-4b81-816c-40da40a01dde",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"288.17594422575957"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TE(E) # Expected temperature including waste heat"
]
},
{
"cell_type": "markdown",
"id": "910552f4-215a-483a-964a-9fdf8cfb29c8",
"metadata": {},
"source": [
"Now we can compare the temperature with no additional energy input, $E = 0$ and the difference."
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "d64412d9-aed0-47e1-a282-727caffdec04",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"288.1653201622295"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TE(0)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "c064f4ba-fe0c-4d30-9efd-b569dc846e0d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.010624063530087824"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TE(E) - TE(0) # Temperature increase due to energy consumption in 2022."
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "fa2d01bf-c56c-4484-80e1-b7a07f2edf0f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.1006447190978825e14"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A_surf = 4*A_disk"
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "be259087-65e8-4146-a7d5-4d77471998f7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.468164773929745e18"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"EEI = 1.0 * H *A_surf # Earth Energy Imbalance in Wh per year"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "60f4a4f8-a6dd-4636-bdcb-2884c55ae4b6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.2649640338803465"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TE(EEI) - TE(0) # Temperature increase due to greenhouse gases and waste heat"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "0a9466f4-916c-472b-825b-377c87a80f3e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.04009624768501781"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(TE(E) - TE(0)) / (TE(EEI) - TE(0)) # Ratio of waste heat temperature increase to EEI heating"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "e210ae0a-a8bc-48a0-a36a-0187aa913435",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.04003634804243519"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"E/EEI # Ratio of energies"
]
},
{
"cell_type": "markdown",
"id": "70f572b4-5a65-4f14-8e2c-60ca60e7f068",
"metadata": {},
"source": [
"## Single Layer Model\n",
"\n",
"The single layer model of the atmosphere used in [CO2 v. CH4](https://wildpeaches.xyz/blog/co2-v-ch4/) lets us calculate the temperature with an emissivity term $\\epsilon = 0.78$. The equation is\n",
"\n",
"$$\n",
"T_e = \\left( \\frac{(1-\\alpha)S}{(1 - \\frac{\\epsilon}{2}) \\sigma} \\right)^{1/4}\n",
"$$\n",
"\n",
"and by including a power term $p$ for greenhouse gas forcings and waste heat we can get a more accurate estimate of the expected changes in Earth's temperature."
]
},
{
"cell_type": "code",
"execution_count": 55,
"id": "0ddc465b-74a6-4c22-afc3-ed42e756612f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"340.0"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S = F/4 # Average solar power received over entire surface of Earth"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "73d782a4-f3a3-4759-9813-bf90f63acb36",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.78"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ϵ = 0.78 # Atmosphere emissivity"
]
},
{
"cell_type": "code",
"execution_count": 59,
"id": "f4a9e332-e6d0-4f54-9515-a303d480d9ab",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Te (generic function with 1 method)"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Te(p) = map(pe -> ( ((1-α)*S + pe)/((1 - ϵ/2) * σ))^0.25, p)"
]
},
{
"cell_type": "code",
"execution_count": 61,
"id": "b8dddf3c-422f-40c9-9d84-3b40f35e4e85",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"288.7281909796797"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Te(0) # Earth temperature without additional sources"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "cbf399f8-368d-4706-8a0c-4231b2f81e90",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.2998157670028263"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Te(1) - Te(0) # Increase in temperature from greenhouse gases assuming 1 W/m^2"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "cccdd98a-1af7-40f6-bc2f-fb2de74e073f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.0120214872536053"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Te(P0/A_surf) - Te(0) # Temperature increase due to waste heat"
]
},
{
"cell_type": "markdown",
"id": "f82c2e49-26dc-42d7-a7e1-03f6767ea6f0",
"metadata": {},
"source": [
"## Exponential growth\n",
"\n",
"Using the model $T_e(p)$ we can estimate the Earth's temperature over time, assuming a constant exponential growth of the economy, and thus energy. Let $q(t)$ be the instantaneous power at time $t$ measured in Watts and $q_0$ the power at time $t_0$, then\n",
"\n",
"$$\n",
"q(t) = q_0 e^{r (t - t0)}\n",
"$$\n",
"\n",
"where $r$ is the constant growth rate. For convenience, you should input $r$ as a percentage, and the equation will convert it to the correct growth rate."
]
},
{
"cell_type": "code",
"execution_count": 67,
"id": "7187892b-ee2a-41ee-9c93-f401c3b8684b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.3"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"r = 2.3 # Constant growth rate, equivalent to 10 x over a century"
]
},
{
"cell_type": "code",
"execution_count": 76,
"id": "1ac6ea30-1f7e-4d57-92c7-efa033356958",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.027496076401843934"
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q0 = 122857e12 / (H * A_surf) # Initial power at time t0 = 2000, W/m^2"
]
},
{
"cell_type": "code",
"execution_count": 84,
"id": "b0a1afad-426f-44f5-affd-fcaa61c862c2",
"metadata": {},
"outputs": [],
"source": [
"t0 = 2000; # First year in the sequence"
]
},
{
"cell_type": "code",
"execution_count": 92,
"id": "f0f31374-5e1c-4293-98f3-358bd1d69827",
"metadata": {},
"outputs": [],
"source": [
"tf = 3000; # Last year in the sequence"
]
},
{
"cell_type": "code",
"execution_count": 93,
"id": "945703ea-b1d0-4914-9e6e-cb3b9a1b3539",
"metadata": {},
"outputs": [],
"source": [
"t = t0:tf;"
]
},
{
"cell_type": "code",
"execution_count": 71,
"id": "7fb45a46-0300-4f7f-a34e-39a500a64068",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"q (generic function with 1 method)"
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"q(T) = map(t -> q0*exp(r/100*(t-t0)),T) # Intantaneous power function "
]
},
{
"cell_type": "code",
"execution_count": 94,
"id": "86f67863-fce0-46fe-a922-ae58f396d423",
"metadata": {},
"outputs": [],
"source": [
"Q = q(t); # Power consumption in each year, Watts"
]
},
{
"cell_type": "markdown",
"id": "32cc13ab-c2f2-4c6d-8a9f-12c1891d223d",
"metadata": {},
"source": [
"The Stefan-Boltzmann Law requires the extra power generated to be balanced by increased temperatures."
]
},
{
"cell_type": "code",
"execution_count": 95,
"id": "601962ae-c6af-4045-82e9-be5375d94adc",
"metadata": {},
"outputs": [],
"source": [
"T_growth = Te(Q); # Increased temperature over the timespan"
]
},
{
"cell_type": "code",
"execution_count": 79,
"id": "865eccfa-e595-4abf-b3e0-3d3d09a27d32",
"metadata": {},
"outputs": [],
"source": [
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 99,
"id": "c813e918-3db7-4da7-ad1d-324df5a6fe64",
"metadata": {},
"outputs": [],
"source": [
"water = 373.1; # Water boils\n",
"paper = 505.9; # Paper burns\n",
"gold = 1337; # Gold melts\n",
"sun = 5778; # Surface temperature of the Sun"
]
},
{
"cell_type": "code",
"execution_count": 100,
"id": "c38717d7-2776-4baf-8ff4-892b22622153",
"metadata": {},
"outputs": [
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" 462.361,1384.23 464.33,1384.23 466.299,1384.23 468.268,1384.23 470.238,1384.23 472.207,1384.23 474.176,1384.23 476.145,1384.23 478.114,1384.23 480.083,1384.23 \n",
" 482.052,1384.23 484.022,1384.23 485.991,1384.23 487.96,1384.23 489.929,1384.23 491.898,1384.23 493.867,1384.23 495.837,1384.23 497.806,1384.23 499.775,1384.23 \n",
" 501.744,1384.23 503.713,1384.23 505.682,1384.23 507.652,1384.23 509.621,1384.23 511.59,1384.23 513.559,1384.23 515.528,1384.23 517.497,1384.23 519.467,1384.23 \n",
" 521.436,1384.23 523.405,1384.23 525.374,1384.23 527.343,1384.23 529.312,1384.23 531.282,1384.23 533.251,1384.23 535.22,1384.23 537.189,1384.23 539.158,1384.22 \n",
" 541.127,1384.22 543.096,1384.22 545.066,1384.22 547.035,1384.22 549.004,1384.22 550.973,1384.22 552.942,1384.22 554.911,1384.22 556.881,1384.22 558.85,1384.22 \n",
" 560.819,1384.22 562.788,1384.22 564.757,1384.22 566.726,1384.22 568.696,1384.22 570.665,1384.22 572.634,1384.22 574.603,1384.22 576.572,1384.22 578.541,1384.22 \n",
" 580.511,1384.22 582.48,1384.22 584.449,1384.21 586.418,1384.21 588.387,1384.21 590.356,1384.21 592.326,1384.21 594.295,1384.21 596.264,1384.21 598.233,1384.21 \n",
" 600.202,1384.21 602.171,1384.21 604.141,1384.21 606.11,1384.21 608.079,1384.21 610.048,1384.21 612.017,1384.21 613.986,1384.2 615.955,1384.2 617.925,1384.2 \n",
" 619.894,1384.2 621.863,1384.2 623.832,1384.2 625.801,1384.2 627.77,1384.2 629.74,1384.2 631.709,1384.2 633.678,1384.2 635.647,1384.19 637.616,1384.19 \n",
" 639.585,1384.19 641.555,1384.19 643.524,1384.19 645.493,1384.19 647.462,1384.19 649.431,1384.19 651.4,1384.19 653.37,1384.18 655.339,1384.18 657.308,1384.18 \n",
" 659.277,1384.18 661.246,1384.18 663.215,1384.18 665.185,1384.18 667.154,1384.18 669.123,1384.17 671.092,1384.17 673.061,1384.17 675.03,1384.17 676.999,1384.17 \n",
" 678.969,1384.17 680.938,1384.16 682.907,1384.16 684.876,1384.16 686.845,1384.16 688.814,1384.16 690.784,1384.15 692.753,1384.15 694.722,1384.15 696.691,1384.15 \n",
" 698.66,1384.15 700.629,1384.14 702.599,1384.14 704.568,1384.14 706.537,1384.14 708.506,1384.14 710.475,1384.13 712.444,1384.13 714.414,1384.13 716.383,1384.13 \n",
" 718.352,1384.12 720.321,1384.12 722.29,1384.12 724.259,1384.11 726.229,1384.11 728.198,1384.11 730.167,1384.11 732.136,1384.1 734.105,1384.1 736.074,1384.1 \n",
" 738.043,1384.09 740.013,1384.09 741.982,1384.09 743.951,1384.08 745.92,1384.08 747.889,1384.07 749.858,1384.07 751.828,1384.07 753.797,1384.06 755.766,1384.06 \n",
" 757.735,1384.05 759.704,1384.05 761.673,1384.05 763.643,1384.04 765.612,1384.04 767.581,1384.03 769.55,1384.03 771.519,1384.02 773.488,1384.02 775.458,1384.01 \n",
" 777.427,1384.01 779.396,1384 781.365,1384 783.334,1383.99 785.303,1383.99 787.273,1383.98 789.242,1383.97 791.211,1383.97 793.18,1383.96 795.149,1383.95 \n",
" 797.118,1383.95 799.087,1383.94 801.057,1383.93 803.026,1383.93 804.995,1383.92 806.964,1383.91 808.933,1383.91 810.902,1383.9 812.872,1383.89 814.841,1383.88 \n",
" 816.81,1383.87 818.779,1383.87 820.748,1383.86 822.717,1383.85 824.687,1383.84 826.656,1383.83 828.625,1383.82 830.594,1383.81 832.563,1383.8 834.532,1383.79 \n",
" 836.502,1383.78 838.471,1383.77 840.44,1383.76 842.409,1383.75 844.378,1383.74 846.347,1383.73 848.317,1383.71 850.286,1383.7 852.255,1383.69 854.224,1383.68 \n",
" 856.193,1383.66 858.162,1383.65 860.131,1383.64 862.101,1383.62 864.07,1383.61 866.039,1383.6 868.008,1383.58 869.977,1383.57 871.946,1383.55 873.916,1383.54 \n",
" 875.885,1383.52 877.854,1383.5 879.823,1383.49 881.792,1383.47 883.761,1383.45 885.731,1383.43 887.7,1383.42 889.669,1383.4 891.638,1383.38 893.607,1383.36 \n",
" 895.576,1383.34 897.546,1383.32 899.515,1383.3 901.484,1383.28 903.453,1383.26 905.422,1383.23 907.391,1383.21 909.361,1383.19 911.33,1383.17 913.299,1383.14 \n",
" 915.268,1383.12 917.237,1383.09 919.206,1383.07 921.176,1383.04 923.145,1383.01 925.114,1382.99 927.083,1382.96 929.052,1382.93 931.021,1382.9 932.99,1382.87 \n",
" 934.96,1382.84 936.929,1382.81 938.898,1382.78 940.867,1382.75 942.836,1382.71 944.805,1382.68 946.775,1382.64 948.744,1382.61 950.713,1382.57 952.682,1382.54 \n",
" 954.651,1382.5 956.62,1382.46 958.59,1382.42 960.559,1382.38 962.528,1382.34 964.497,1382.3 966.466,1382.26 968.435,1382.22 970.405,1382.17 972.374,1382.13 \n",
" 974.343,1382.08 976.312,1382.04 978.281,1381.99 980.25,1381.94 982.22,1381.89 984.189,1381.84 986.158,1381.79 988.127,1381.74 990.096,1381.68 992.065,1381.63 \n",
" 994.034,1381.57 996.004,1381.52 997.973,1381.46 999.942,1381.4 1001.91,1381.34 1003.88,1381.28 1005.85,1381.22 1007.82,1381.16 1009.79,1381.09 1011.76,1381.03 \n",
" 1013.73,1380.96 1015.7,1380.89 1017.66,1380.82 1019.63,1380.75 1021.6,1380.68 1023.57,1380.61 1025.54,1380.53 1027.51,1380.45 1029.48,1380.38 1031.45,1380.3 \n",
" 1033.42,1380.22 1035.39,1380.14 1037.36,1380.05 1039.33,1379.97 1041.29,1379.88 1043.26,1379.8 1045.23,1379.71 1047.2,1379.62 1049.17,1379.52 1051.14,1379.43 \n",
" 1053.11,1379.34 1055.08,1379.24 1057.05,1379.14 1059.02,1379.04 1060.99,1378.94 1062.96,1378.83 1064.92,1378.73 1066.89,1378.62 1068.86,1378.51 1070.83,1378.4 \n",
" 1072.8,1378.29 1074.77,1378.18 1076.74,1378.06 1078.71,1377.94 1080.68,1377.82 1082.65,1377.7 1084.62,1377.58 1086.59,1377.46 1088.55,1377.33 1090.52,1377.2 \n",
" 1092.49,1377.07 1094.46,1376.94 1096.43,1376.8 1098.4,1376.66 1100.37,1376.53 1102.34,1376.39 1104.31,1376.24 1106.28,1376.1 1108.25,1375.95 1110.22,1375.8 \n",
" 1112.18,1375.65 1114.15,1375.5 1116.12,1375.34 1118.09,1375.19 1120.06,1375.03 1122.03,1374.86 1124,1374.7 1125.97,1374.53 1127.94,1374.37 1129.91,1374.2 \n",
" 1131.88,1374.02 1133.84,1373.85 1135.81,1373.67 1137.78,1373.49 1139.75,1373.31 1141.72,1373.13 1143.69,1372.94 1145.66,1372.75 1147.63,1372.56 1149.6,1372.37 \n",
" 1151.57,1372.17 1153.54,1371.97 1155.51,1371.77 1157.47,1371.57 1159.44,1371.37 1161.41,1371.16 1163.38,1370.95 1165.35,1370.74 1167.32,1370.52 1169.29,1370.3 \n",
" 1171.26,1370.09 1173.23,1369.86 1175.2,1369.64 1177.17,1369.41 1179.14,1369.18 1181.1,1368.95 1183.07,1368.72 1185.04,1368.48 1187.01,1368.24 1188.98,1368 \n",
" 1190.95,1367.76 1192.92,1367.51 1194.89,1367.26 1196.86,1367.01 1198.83,1366.75 1200.8,1366.5 1202.77,1366.24 1204.73,1365.98 1206.7,1365.71 1208.67,1365.44 \n",
" 1210.64,1365.17 1212.61,1364.9 1214.58,1364.63 1216.55,1364.35 1218.52,1364.07 1220.49,1363.79 1222.46,1363.5 1224.43,1363.22 1226.4,1362.92 1228.36,1362.63 \n",
" 1230.33,1362.34 1232.3,1362.04 1234.27,1361.74 1236.24,1361.43 1238.21,1361.13 1240.18,1360.82 1242.15,1360.51 1244.12,1360.19 1246.09,1359.88 1248.06,1359.56 \n",
" 1250.03,1359.23 1251.99,1358.91 1253.96,1358.58 1255.93,1358.25 1257.9,1357.92 1259.87,1357.58 1261.84,1357.24 1263.81,1356.9 1265.78,1356.56 1267.75,1356.21 \n",
" 1269.72,1355.86 1271.69,1355.51 1273.66,1355.15 1275.62,1354.8 1277.59,1354.44 1279.56,1354.07 1281.53,1353.71 1283.5,1353.34 1285.47,1352.96 1287.44,1352.59 \n",
" 1289.41,1352.21 1291.38,1351.83 1293.35,1351.45 1295.32,1351.06 1297.29,1350.67 1299.25,1350.28 1301.22,1349.89 1303.19,1349.49 1305.16,1349.09 1307.13,1348.69 \n",
" 1309.1,1348.28 1311.07,1347.87 1313.04,1347.46 1315.01,1347.04 1316.98,1346.63 1318.95,1346.21 1320.92,1345.78 1322.88,1345.35 1324.85,1344.93 1326.82,1344.49 \n",
" 1328.79,1344.06 1330.76,1343.62 1332.73,1343.18 1334.7,1342.73 1336.67,1342.28 1338.64,1341.83 1340.61,1341.38 1342.58,1340.92 1344.55,1340.46 1346.51,1340 \n",
" 1348.48,1339.53 1350.45,1339.06 1352.42,1338.59 1354.39,1338.11 1356.36,1337.63 1358.33,1337.15 1360.3,1336.67 1362.27,1336.18 1364.24,1335.69 1366.21,1335.19 \n",
" 1368.18,1334.69 1370.14,1334.19 1372.11,1333.69 1374.08,1333.18 1376.05,1332.67 1378.02,1332.16 1379.99,1331.64 1381.96,1331.12 1383.93,1330.59 1385.9,1330.06 \n",
" 1387.87,1329.53 1389.84,1329 1391.81,1328.46 1393.77,1327.92 1395.74,1327.38 1397.71,1326.83 1399.68,1326.28 1401.65,1325.72 1403.62,1325.16 1405.59,1324.6 \n",
" 1407.56,1324.03 1409.53,1323.47 1411.5,1322.89 1413.47,1322.32 1415.44,1321.74 1417.4,1321.15 1419.37,1320.57 1421.34,1319.98 1423.31,1319.38 1425.28,1318.78 \n",
" 1427.25,1318.18 1429.22,1317.58 1431.19,1316.97 1433.16,1316.36 1435.13,1315.74 1437.1,1315.12 1439.06,1314.5 1441.03,1313.87 1443,1313.24 1444.97,1312.6 \n",
" 1446.94,1311.96 1448.91,1311.32 1450.88,1310.67 1452.85,1310.02 1454.82,1309.36 1456.79,1308.71 1458.76,1308.04 1460.73,1307.38 1462.69,1306.71 1464.66,1306.03 \n",
" 1466.63,1305.35 1468.6,1304.67 1470.57,1303.98 1472.54,1303.29 1474.51,1302.59 1476.48,1301.89 1478.45,1301.19 1480.42,1300.48 1482.39,1299.77 1484.36,1299.05 \n",
" 1486.32,1298.33 1488.29,1297.61 1490.26,1296.88 1492.23,1296.15 1494.2,1295.41 1496.17,1294.66 1498.14,1293.92 1500.11,1293.17 1502.08,1292.41 1504.05,1291.65 \n",
" 1506.02,1290.89 1507.99,1290.12 1509.95,1289.34 1511.92,1288.56 1513.89,1287.78 1515.86,1286.99 1517.83,1286.2 1519.8,1285.41 1521.77,1284.6 1523.74,1283.8 \n",
" 1525.71,1282.99 1527.68,1282.17 1529.65,1281.35 1531.62,1280.52 1533.58,1279.69 1535.55,1278.86 1537.52,1278.02 1539.49,1277.17 1541.46,1276.32 1543.43,1275.47 \n",
" 1545.4,1274.61 1547.37,1273.74 1549.34,1272.87 1551.31,1272 1553.28,1271.12 1555.25,1270.23 1557.21,1269.34 1559.18,1268.45 1561.15,1267.54 1563.12,1266.64 \n",
" 1565.09,1265.73 1567.06,1264.81 1569.03,1263.89 1571,1262.96 1572.97,1262.03 1574.94,1261.09 1576.91,1260.14 1578.88,1259.19 1580.84,1258.24 1582.81,1257.28 \n",
" 1584.78,1256.31 1586.75,1255.34 1588.72,1254.36 1590.69,1253.38 1592.66,1252.39 1594.63,1251.39 1596.6,1250.39 1598.57,1249.39 1600.54,1248.37 1602.51,1247.36 \n",
" 1604.47,1246.33 1606.44,1245.3 1608.41,1244.27 1610.38,1243.22 1612.35,1242.18 1614.32,1241.12 1616.29,1240.06 1618.26,1238.99 1620.23,1237.92 1622.2,1236.84 \n",
" 1624.17,1235.76 1626.14,1234.67 1628.1,1233.57 1630.07,1232.46 1632.04,1231.35 1634.01,1230.24 1635.98,1229.11 1637.95,1227.98 1639.92,1226.85 1641.89,1225.7 \n",
" 1643.86,1224.55 1645.83,1223.4 1647.8,1222.23 1649.77,1221.06 1651.73,1219.89 1653.7,1218.7 1655.67,1217.51 1657.64,1216.32 1659.61,1215.11 1661.58,1213.9 \n",
" 1663.55,1212.68 1665.52,1211.46 1667.49,1210.22 1669.46,1208.99 1671.43,1207.74 1673.4,1206.48 1675.36,1205.22 1677.33,1203.96 1679.3,1202.68 1681.27,1201.4 \n",
" 1683.24,1200.11 1685.21,1198.81 1687.18,1197.5 1689.15,1196.19 1691.12,1194.87 1693.09,1193.54 1695.06,1192.2 1697.03,1190.86 1698.99,1189.51 1700.96,1188.15 \n",
" 1702.93,1186.78 1704.9,1185.41 1706.87,1184.02 1708.84,1182.63 1710.81,1181.23 1712.78,1179.83 1714.75,1178.41 1716.72,1176.99 1718.69,1175.56 1720.66,1174.12 \n",
" 1722.62,1172.67 1724.59,1171.21 1726.56,1169.75 1728.53,1168.27 1730.5,1166.79 1732.47,1165.3 1734.44,1163.8 1736.41,1162.29 1738.38,1160.78 1740.35,1159.25 \n",
" 1742.32,1157.72 1744.29,1156.17 1746.25,1154.62 1748.22,1153.06 1750.19,1151.49 1752.16,1149.91 1754.13,1148.32 1756.1,1146.73 1758.07,1145.12 1760.04,1143.5 \n",
" 1762.01,1141.88 1763.98,1140.24 1765.95,1138.6 1767.91,1136.95 1769.88,1135.28 1771.85,1133.61 1773.82,1131.93 1775.79,1130.24 1777.76,1128.53 1779.73,1126.82 \n",
" 1781.7,1125.1 1783.67,1123.37 1785.64,1121.63 1787.61,1119.88 1789.58,1118.11 1791.54,1116.34 1793.51,1114.56 1795.48,1112.77 1797.45,1110.97 1799.42,1109.15 \n",
" 1801.39,1107.33 1803.36,1105.5 1805.33,1103.65 1807.3,1101.8 1809.27,1099.93 1811.24,1098.05 1813.21,1096.17 1815.17,1094.27 1817.14,1092.36 1819.11,1090.44 \n",
" 1821.08,1088.51 1823.05,1086.56 1825.02,1084.61 1826.99,1082.64 1828.96,1080.67 1830.93,1078.68 1832.9,1076.68 1834.87,1074.67 1836.84,1072.65 1838.8,1070.61 \n",
" 1840.77,1068.57 1842.74,1066.51 1844.71,1064.44 1846.68,1062.36 1848.65,1060.27 1850.62,1058.16 1852.59,1056.04 1854.56,1053.91 1856.53,1051.77 1858.5,1049.62 \n",
" 1860.47,1047.45 1862.43,1045.27 1864.4,1043.08 1866.37,1040.87 1868.34,1038.65 1870.31,1036.42 1872.28,1034.18 1874.25,1031.93 1876.22,1029.66 1878.19,1027.37 \n",
" 1880.16,1025.08 1882.13,1022.77 1884.1,1020.45 1886.06,1018.11 1888.03,1015.76 1890,1013.4 1891.97,1011.03 1893.94,1008.64 1895.91,1006.23 1897.88,1003.82 \n",
" 1899.85,1001.39 1901.82,998.94 1903.79,996.481 1905.76,994.007 1907.73,991.519 1909.69,989.017 1911.66,986.501 1913.63,983.969 1915.6,981.424 1917.57,978.863 \n",
" 1919.54,976.288 1921.51,973.698 1923.48,971.093 1925.45,968.473 1927.42,965.838 1929.39,963.188 1931.36,960.523 1933.32,957.842 1935.29,955.145 1937.26,952.433 \n",
" 1939.23,949.706 1941.2,946.963 1943.17,944.203 1945.14,941.428 1947.11,938.637 1949.08,935.83 1951.05,933.007 1953.02,930.167 1954.99,927.311 1956.95,924.439 \n",
" 1958.92,921.55 1960.89,918.644 1962.86,915.722 1964.83,912.782 1966.8,909.826 1968.77,906.853 1970.74,903.862 1972.71,900.855 1974.68,897.83 1976.65,894.787 \n",
" 1978.62,891.727 1980.58,888.65 1982.55,885.554 1984.52,882.441 1986.49,879.31 1988.46,876.16 1990.43,872.993 1992.4,869.807 1994.37,866.603 1996.34,863.38 \n",
" 1998.31,860.139 2000.28,856.879 2002.25,853.601 2004.21,850.303 2006.18,846.987 2008.15,843.651 2010.12,840.296 2012.09,836.922 2014.06,833.528 2016.03,830.115 \n",
" 2018,826.682 2019.97,823.229 2021.94,819.756 2023.91,816.263 2025.88,812.751 2027.84,809.217 2029.81,805.664 2031.78,802.09 2033.75,798.495 2035.72,794.88 \n",
" 2037.69,791.244 2039.66,787.587 2041.63,783.908 2043.6,780.209 2045.57,776.488 2047.54,772.746 2049.51,768.982 2051.47,765.196 2053.44,761.389 2055.41,757.56 \n",
" 2057.38,753.708 2059.35,749.835 2061.32,745.939 2063.29,742.02 2065.26,738.079 2067.23,734.116 2069.2,730.129 2071.17,726.119 2073.13,722.087 2075.1,718.031 \n",
" 2077.07,713.951 2079.04,709.848 2081.01,705.722 2082.98,701.571 2084.95,697.397 2086.92,693.199 2088.89,688.976 2090.86,684.729 2092.83,680.458 2094.8,676.162 \n",
" 2096.76,671.841 2098.73,667.495 2100.7,663.124 2102.67,658.728 2104.64,654.307 2106.61,649.86 2108.58,645.388 2110.55,640.889 2112.52,636.365 2114.49,631.815 \n",
" 2116.46,627.238 2118.43,622.635 2120.39,618.006 2122.36,613.35 2124.33,608.667 2126.3,603.957 2128.27,599.219 2130.24,594.455 2132.21,589.663 2134.18,584.843 \n",
" 2136.15,579.996 2138.12,575.121 2140.09,570.217 2142.06,565.285 2144.02,560.325 2145.99,555.336 2147.96,550.319 2149.93,545.272 2151.9,540.197 2153.87,535.092 \n",
" 2155.84,529.957 2157.81,524.793 2159.78,519.6 2161.75,514.376 2163.72,509.122 2165.69,503.838 2167.65,498.524 2169.62,493.178 2171.59,487.802 2173.56,482.395 \n",
" 2175.53,476.957 2177.5,471.488 2179.47,465.986 2181.44,460.454 2183.41,454.889 2185.38,449.292 2187.35,443.663 2189.32,438.001 2191.28,432.307 2193.25,426.58 \n",
" 2195.22,420.82 2197.19,415.027 2199.16,409.2 2201.13,403.34 2203.1,397.446 2205.07,391.518 2207.04,385.555 2209.01,379.559 2210.98,373.528 2212.95,367.462 \n",
" 2214.91,361.361 2216.88,355.224 2218.85,349.053 2220.82,342.846 2222.79,336.603 2224.76,330.324 2226.73,324.009 2228.7,317.657 2230.67,311.269 2232.64,304.844 \n",
" 2234.61,298.382 2236.58,291.883 2238.54,285.346 2240.51,278.771 2242.48,272.159 2244.45,265.508 2246.42,258.819 2248.39,252.092 2250.36,245.326 2252.33,238.52 \n",
" 2254.3,231.676 2256.27,224.792 2258.24,217.868 2260.21,210.904 2262.17,203.901 2264.14,196.856 2266.11,189.772 2268.08,182.646 2270.05,175.479 2272.02,168.271 \n",
" 2273.99,161.022 2275.96,153.73 2277.93,146.397 2279.9,139.021 2281.87,131.603 2283.84,124.141 2285.8,116.637 2287.77,109.09 2289.74,101.499 2291.71,93.8644 \n",
" 2293.68,86.1857 \n",
" \"/>\n",
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" 324.52,1372.19 326.489,1372.19 328.458,1372.19 330.427,1372.19 332.396,1372.19 334.365,1372.19 336.335,1372.19 338.304,1372.19 340.273,1372.19 342.242,1372.19 \n",
" 344.211,1372.19 346.18,1372.19 348.15,1372.19 350.119,1372.19 352.088,1372.19 354.057,1372.19 356.026,1372.19 357.995,1372.19 359.964,1372.19 361.934,1372.19 \n",
" 363.903,1372.19 365.872,1372.19 367.841,1372.19 369.81,1372.19 371.779,1372.19 373.749,1372.19 375.718,1372.19 377.687,1372.19 379.656,1372.19 381.625,1372.19 \n",
" 383.594,1372.19 385.564,1372.19 387.533,1372.19 389.502,1372.19 391.471,1372.19 393.44,1372.19 395.409,1372.19 397.379,1372.19 399.348,1372.19 401.317,1372.19 \n",
" 403.286,1372.19 405.255,1372.19 407.224,1372.19 409.194,1372.19 411.163,1372.19 413.132,1372.19 415.101,1372.19 417.07,1372.19 419.039,1372.19 421.008,1372.19 \n",
" 422.978,1372.19 424.947,1372.19 426.916,1372.19 428.885,1372.19 430.854,1372.19 432.823,1372.19 434.793,1372.19 436.762,1372.19 438.731,1372.19 440.7,1372.19 \n",
" 442.669,1372.19 444.638,1372.19 446.608,1372.19 448.577,1372.19 450.546,1372.19 452.515,1372.19 454.484,1372.19 456.453,1372.19 458.423,1372.19 460.392,1372.19 \n",
" 462.361,1372.19 464.33,1372.19 466.299,1372.19 468.268,1372.19 470.238,1372.19 472.207,1372.19 474.176,1372.19 476.145,1372.19 478.114,1372.19 480.083,1372.19 \n",
" 482.052,1372.19 484.022,1372.19 485.991,1372.19 487.96,1372.19 489.929,1372.19 491.898,1372.19 493.867,1372.19 495.837,1372.19 497.806,1372.19 499.775,1372.19 \n",
" 501.744,1372.19 503.713,1372.19 505.682,1372.19 507.652,1372.19 509.621,1372.19 511.59,1372.19 513.559,1372.19 515.528,1372.19 517.497,1372.19 519.467,1372.19 \n",
" 521.436,1372.19 523.405,1372.19 525.374,1372.19 527.343,1372.19 529.312,1372.19 531.282,1372.19 533.251,1372.19 535.22,1372.19 537.189,1372.19 539.158,1372.19 \n",
" 541.127,1372.19 543.096,1372.19 545.066,1372.19 547.035,1372.19 549.004,1372.19 550.973,1372.19 552.942,1372.19 554.911,1372.19 556.881,1372.19 558.85,1372.19 \n",
" 560.819,1372.19 562.788,1372.19 564.757,1372.19 566.726,1372.19 568.696,1372.19 570.665,1372.19 572.634,1372.19 574.603,1372.19 576.572,1372.19 578.541,1372.19 \n",
" 580.511,1372.19 582.48,1372.19 584.449,1372.19 586.418,1372.19 588.387,1372.19 590.356,1372.19 592.326,1372.19 594.295,1372.19 596.264,1372.19 598.233,1372.19 \n",
" 600.202,1372.19 602.171,1372.19 604.141,1372.19 606.11,1372.19 608.079,1372.19 610.048,1372.19 612.017,1372.19 613.986,1372.19 615.955,1372.19 617.925,1372.19 \n",
" 619.894,1372.19 621.863,1372.19 623.832,1372.19 625.801,1372.19 627.77,1372.19 629.74,1372.19 631.709,1372.19 633.678,1372.19 635.647,1372.19 637.616,1372.19 \n",
" 639.585,1372.19 641.555,1372.19 643.524,1372.19 645.493,1372.19 647.462,1372.19 649.431,1372.19 651.4,1372.19 653.37,1372.19 655.339,1372.19 657.308,1372.19 \n",
" 659.277,1372.19 661.246,1372.19 663.215,1372.19 665.185,1372.19 667.154,1372.19 669.123,1372.19 671.092,1372.19 673.061,1372.19 675.03,1372.19 676.999,1372.19 \n",
" 678.969,1372.19 680.938,1372.19 682.907,1372.19 684.876,1372.19 686.845,1372.19 688.814,1372.19 690.784,1372.19 692.753,1372.19 694.722,1372.19 696.691,1372.19 \n",
" 698.66,1372.19 700.629,1372.19 702.599,1372.19 704.568,1372.19 706.537,1372.19 708.506,1372.19 710.475,1372.19 712.444,1372.19 714.414,1372.19 716.383,1372.19 \n",
" 718.352,1372.19 720.321,1372.19 722.29,1372.19 724.259,1372.19 726.229,1372.19 728.198,1372.19 730.167,1372.19 732.136,1372.19 734.105,1372.19 736.074,1372.19 \n",
" 738.043,1372.19 740.013,1372.19 741.982,1372.19 743.951,1372.19 745.92,1372.19 747.889,1372.19 749.858,1372.19 751.828,1372.19 753.797,1372.19 755.766,1372.19 \n",
" 757.735,1372.19 759.704,1372.19 761.673,1372.19 763.643,1372.19 765.612,1372.19 767.581,1372.19 769.55,1372.19 771.519,1372.19 773.488,1372.19 775.458,1372.19 \n",
" 777.427,1372.19 779.396,1372.19 781.365,1372.19 783.334,1372.19 785.303,1372.19 787.273,1372.19 789.242,1372.19 791.211,1372.19 793.18,1372.19 795.149,1372.19 \n",
" 797.118,1372.19 799.087,1372.19 801.057,1372.19 803.026,1372.19 804.995,1372.19 806.964,1372.19 808.933,1372.19 810.902,1372.19 812.872,1372.19 814.841,1372.19 \n",
" 816.81,1372.19 818.779,1372.19 820.748,1372.19 822.717,1372.19 824.687,1372.19 826.656,1372.19 828.625,1372.19 830.594,1372.19 832.563,1372.19 834.532,1372.19 \n",
" 836.502,1372.19 838.471,1372.19 840.44,1372.19 842.409,1372.19 844.378,1372.19 846.347,1372.19 848.317,1372.19 850.286,1372.19 852.255,1372.19 854.224,1372.19 \n",
" 856.193,1372.19 858.162,1372.19 860.131,1372.19 862.101,1372.19 864.07,1372.19 866.039,1372.19 868.008,1372.19 869.977,1372.19 871.946,1372.19 873.916,1372.19 \n",
" 875.885,1372.19 877.854,1372.19 879.823,1372.19 881.792,1372.19 883.761,1372.19 885.731,1372.19 887.7,1372.19 889.669,1372.19 891.638,1372.19 893.607,1372.19 \n",
" 895.576,1372.19 897.546,1372.19 899.515,1372.19 901.484,1372.19 903.453,1372.19 905.422,1372.19 907.391,1372.19 909.361,1372.19 911.33,1372.19 913.299,1372.19 \n",
" 915.268,1372.19 917.237,1372.19 919.206,1372.19 921.176,1372.19 923.145,1372.19 925.114,1372.19 927.083,1372.19 929.052,1372.19 931.021,1372.19 932.99,1372.19 \n",
" 934.96,1372.19 936.929,1372.19 938.898,1372.19 940.867,1372.19 942.836,1372.19 944.805,1372.19 946.775,1372.19 948.744,1372.19 950.713,1372.19 952.682,1372.19 \n",
" 954.651,1372.19 956.62,1372.19 958.59,1372.19 960.559,1372.19 962.528,1372.19 964.497,1372.19 966.466,1372.19 968.435,1372.19 970.405,1372.19 972.374,1372.19 \n",
" 974.343,1372.19 976.312,1372.19 978.281,1372.19 980.25,1372.19 982.22,1372.19 984.189,1372.19 986.158,1372.19 988.127,1372.19 990.096,1372.19 992.065,1372.19 \n",
" 994.034,1372.19 996.004,1372.19 997.973,1372.19 999.942,1372.19 1001.91,1372.19 1003.88,1372.19 1005.85,1372.19 1007.82,1372.19 1009.79,1372.19 1011.76,1372.19 \n",
" 1013.73,1372.19 1015.7,1372.19 1017.66,1372.19 1019.63,1372.19 1021.6,1372.19 1023.57,1372.19 1025.54,1372.19 1027.51,1372.19 1029.48,1372.19 1031.45,1372.19 \n",
" 1033.42,1372.19 1035.39,1372.19 1037.36,1372.19 1039.33,1372.19 1041.29,1372.19 1043.26,1372.19 1045.23,1372.19 1047.2,1372.19 1049.17,1372.19 1051.14,1372.19 \n",
" 1053.11,1372.19 1055.08,1372.19 1057.05,1372.19 1059.02,1372.19 1060.99,1372.19 1062.96,1372.19 1064.92,1372.19 1066.89,1372.19 1068.86,1372.19 1070.83,1372.19 \n",
" 1072.8,1372.19 1074.77,1372.19 1076.74,1372.19 1078.71,1372.19 1080.68,1372.19 1082.65,1372.19 1084.62,1372.19 1086.59,1372.19 1088.55,1372.19 1090.52,1372.19 \n",
" 1092.49,1372.19 1094.46,1372.19 1096.43,1372.19 1098.4,1372.19 1100.37,1372.19 1102.34,1372.19 1104.31,1372.19 1106.28,1372.19 1108.25,1372.19 1110.22,1372.19 \n",
" 1112.18,1372.19 1114.15,1372.19 1116.12,1372.19 1118.09,1372.19 1120.06,1372.19 1122.03,1372.19 1124,1372.19 1125.97,1372.19 1127.94,1372.19 1129.91,1372.19 \n",
" 1131.88,1372.19 1133.84,1372.19 1135.81,1372.19 1137.78,1372.19 1139.75,1372.19 1141.72,1372.19 1143.69,1372.19 1145.66,1372.19 1147.63,1372.19 1149.6,1372.19 \n",
" 1151.57,1372.19 1153.54,1372.19 1155.51,1372.19 1157.47,1372.19 1159.44,1372.19 1161.41,1372.19 1163.38,1372.19 1165.35,1372.19 1167.32,1372.19 1169.29,1372.19 \n",
" 1171.26,1372.19 1173.23,1372.19 1175.2,1372.19 1177.17,1372.19 1179.14,1372.19 1181.1,1372.19 1183.07,1372.19 1185.04,1372.19 1187.01,1372.19 1188.98,1372.19 \n",
" 1190.95,1372.19 1192.92,1372.19 1194.89,1372.19 1196.86,1372.19 1198.83,1372.19 1200.8,1372.19 1202.77,1372.19 1204.73,1372.19 1206.7,1372.19 1208.67,1372.19 \n",
" 1210.64,1372.19 1212.61,1372.19 1214.58,1372.19 1216.55,1372.19 1218.52,1372.19 1220.49,1372.19 1222.46,1372.19 1224.43,1372.19 1226.4,1372.19 1228.36,1372.19 \n",
" 1230.33,1372.19 1232.3,1372.19 1234.27,1372.19 1236.24,1372.19 1238.21,1372.19 1240.18,1372.19 1242.15,1372.19 1244.12,1372.19 1246.09,1372.19 1248.06,1372.19 \n",
" 1250.03,1372.19 1251.99,1372.19 1253.96,1372.19 1255.93,1372.19 1257.9,1372.19 1259.87,1372.19 1261.84,1372.19 1263.81,1372.19 1265.78,1372.19 1267.75,1372.19 \n",
" 1269.72,1372.19 1271.69,1372.19 1273.66,1372.19 1275.62,1372.19 1277.59,1372.19 1279.56,1372.19 1281.53,1372.19 1283.5,1372.19 1285.47,1372.19 1287.44,1372.19 \n",
" 1289.41,1372.19 1291.38,1372.19 1293.35,1372.19 1295.32,1372.19 1297.29,1372.19 1299.25,1372.19 1301.22,1372.19 1303.19,1372.19 1305.16,1372.19 1307.13,1372.19 \n",
" 1309.1,1372.19 1311.07,1372.19 1313.04,1372.19 1315.01,1372.19 1316.98,1372.19 1318.95,1372.19 1320.92,1372.19 1322.88,1372.19 1324.85,1372.19 1326.82,1372.19 \n",
" 1328.79,1372.19 1330.76,1372.19 1332.73,1372.19 1334.7,1372.19 1336.67,1372.19 1338.64,1372.19 1340.61,1372.19 1342.58,1372.19 1344.55,1372.19 1346.51,1372.19 \n",
" 1348.48,1372.19 1350.45,1372.19 1352.42,1372.19 1354.39,1372.19 1356.36,1372.19 1358.33,1372.19 1360.3,1372.19 1362.27,1372.19 1364.24,1372.19 1366.21,1372.19 \n",
" 1368.18,1372.19 1370.14,1372.19 1372.11,1372.19 1374.08,1372.19 1376.05,1372.19 1378.02,1372.19 1379.99,1372.19 1381.96,1372.19 1383.93,1372.19 1385.9,1372.19 \n",
" 1387.87,1372.19 1389.84,1372.19 1391.81,1372.19 1393.77,1372.19 1395.74,1372.19 1397.71,1372.19 1399.68,1372.19 1401.65,1372.19 1403.62,1372.19 1405.59,1372.19 \n",
" 1407.56,1372.19 1409.53,1372.19 1411.5,1372.19 1413.47,1372.19 1415.44,1372.19 1417.4,1372.19 1419.37,1372.19 1421.34,1372.19 1423.31,1372.19 1425.28,1372.19 \n",
" 1427.25,1372.19 1429.22,1372.19 1431.19,1372.19 1433.16,1372.19 1435.13,1372.19 1437.1,1372.19 1439.06,1372.19 1441.03,1372.19 1443,1372.19 1444.97,1372.19 \n",
" 1446.94,1372.19 1448.91,1372.19 1450.88,1372.19 1452.85,1372.19 1454.82,1372.19 1456.79,1372.19 1458.76,1372.19 1460.73,1372.19 1462.69,1372.19 1464.66,1372.19 \n",
" 1466.63,1372.19 1468.6,1372.19 1470.57,1372.19 1472.54,1372.19 1474.51,1372.19 1476.48,1372.19 1478.45,1372.19 1480.42,1372.19 1482.39,1372.19 1484.36,1372.19 \n",
" 1486.32,1372.19 1488.29,1372.19 1490.26,1372.19 1492.23,1372.19 1494.2,1372.19 1496.17,1372.19 1498.14,1372.19 1500.11,1372.19 1502.08,1372.19 1504.05,1372.19 \n",
" 1506.02,1372.19 1507.99,1372.19 1509.95,1372.19 1511.92,1372.19 1513.89,1372.19 1515.86,1372.19 1517.83,1372.19 1519.8,1372.19 1521.77,1372.19 1523.74,1372.19 \n",
" 1525.71,1372.19 1527.68,1372.19 1529.65,1372.19 1531.62,1372.19 1533.58,1372.19 1535.55,1372.19 1537.52,1372.19 1539.49,1372.19 1541.46,1372.19 1543.43,1372.19 \n",
" 1545.4,1372.19 1547.37,1372.19 1549.34,1372.19 1551.31,1372.19 1553.28,1372.19 1555.25,1372.19 1557.21,1372.19 1559.18,1372.19 1561.15,1372.19 1563.12,1372.19 \n",
" 1565.09,1372.19 1567.06,1372.19 1569.03,1372.19 1571,1372.19 1572.97,1372.19 1574.94,1372.19 1576.91,1372.19 1578.88,1372.19 1580.84,1372.19 1582.81,1372.19 \n",
" 1584.78,1372.19 1586.75,1372.19 1588.72,1372.19 1590.69,1372.19 1592.66,1372.19 1594.63,1372.19 1596.6,1372.19 1598.57,1372.19 1600.54,1372.19 1602.51,1372.19 \n",
" 1604.47,1372.19 1606.44,1372.19 1608.41,1372.19 1610.38,1372.19 1612.35,1372.19 1614.32,1372.19 1616.29,1372.19 1618.26,1372.19 1620.23,1372.19 1622.2,1372.19 \n",
" 1624.17,1372.19 1626.14,1372.19 1628.1,1372.19 1630.07,1372.19 1632.04,1372.19 1634.01,1372.19 1635.98,1372.19 1637.95,1372.19 1639.92,1372.19 1641.89,1372.19 \n",
" 1643.86,1372.19 1645.83,1372.19 1647.8,1372.19 1649.77,1372.19 1651.73,1372.19 1653.7,1372.19 1655.67,1372.19 1657.64,1372.19 1659.61,1372.19 1661.58,1372.19 \n",
" 1663.55,1372.19 1665.52,1372.19 1667.49,1372.19 1669.46,1372.19 1671.43,1372.19 1673.4,1372.19 1675.36,1372.19 1677.33,1372.19 1679.3,1372.19 1681.27,1372.19 \n",
" 1683.24,1372.19 1685.21,1372.19 1687.18,1372.19 1689.15,1372.19 1691.12,1372.19 1693.09,1372.19 1695.06,1372.19 1697.03,1372.19 1698.99,1372.19 1700.96,1372.19 \n",
" 1702.93,1372.19 1704.9,1372.19 1706.87,1372.19 1708.84,1372.19 1710.81,1372.19 1712.78,1372.19 1714.75,1372.19 1716.72,1372.19 1718.69,1372.19 1720.66,1372.19 \n",
" 1722.62,1372.19 1724.59,1372.19 1726.56,1372.19 1728.53,1372.19 1730.5,1372.19 1732.47,1372.19 1734.44,1372.19 1736.41,1372.19 1738.38,1372.19 1740.35,1372.19 \n",
" 1742.32,1372.19 1744.29,1372.19 1746.25,1372.19 1748.22,1372.19 1750.19,1372.19 1752.16,1372.19 1754.13,1372.19 1756.1,1372.19 1758.07,1372.19 1760.04,1372.19 \n",
" 1762.01,1372.19 1763.98,1372.19 1765.95,1372.19 1767.91,1372.19 1769.88,1372.19 1771.85,1372.19 1773.82,1372.19 1775.79,1372.19 1777.76,1372.19 1779.73,1372.19 \n",
" 1781.7,1372.19 1783.67,1372.19 1785.64,1372.19 1787.61,1372.19 1789.58,1372.19 1791.54,1372.19 1793.51,1372.19 1795.48,1372.19 1797.45,1372.19 1799.42,1372.19 \n",
" 1801.39,1372.19 1803.36,1372.19 1805.33,1372.19 1807.3,1372.19 1809.27,1372.19 1811.24,1372.19 1813.21,1372.19 1815.17,1372.19 1817.14,1372.19 1819.11,1372.19 \n",
" 1821.08,1372.19 1823.05,1372.19 1825.02,1372.19 1826.99,1372.19 1828.96,1372.19 1830.93,1372.19 1832.9,1372.19 1834.87,1372.19 1836.84,1372.19 1838.8,1372.19 \n",
" 1840.77,1372.19 1842.74,1372.19 1844.71,1372.19 1846.68,1372.19 1848.65,1372.19 1850.62,1372.19 1852.59,1372.19 1854.56,1372.19 1856.53,1372.19 1858.5,1372.19 \n",
" 1860.47,1372.19 1862.43,1372.19 1864.4,1372.19 1866.37,1372.19 1868.34,1372.19 1870.31,1372.19 1872.28,1372.19 1874.25,1372.19 1876.22,1372.19 1878.19,1372.19 \n",
" 1880.16,1372.19 1882.13,1372.19 1884.1,1372.19 1886.06,1372.19 1888.03,1372.19 1890,1372.19 1891.97,1372.19 1893.94,1372.19 1895.91,1372.19 1897.88,1372.19 \n",
" 1899.85,1372.19 1901.82,1372.19 1903.79,1372.19 1905.76,1372.19 1907.73,1372.19 1909.69,1372.19 1911.66,1372.19 1913.63,1372.19 1915.6,1372.19 1917.57,1372.19 \n",
" 1919.54,1372.19 1921.51,1372.19 1923.48,1372.19 1925.45,1372.19 1927.42,1372.19 1929.39,1372.19 1931.36,1372.19 1933.32,1372.19 1935.29,1372.19 1937.26,1372.19 \n",
" 1939.23,1372.19 1941.2,1372.19 1943.17,1372.19 1945.14,1372.19 1947.11,1372.19 1949.08,1372.19 1951.05,1372.19 1953.02,1372.19 1954.99,1372.19 1956.95,1372.19 \n",
" 1958.92,1372.19 1960.89,1372.19 1962.86,1372.19 1964.83,1372.19 1966.8,1372.19 1968.77,1372.19 1970.74,1372.19 1972.71,1372.19 1974.68,1372.19 1976.65,1372.19 \n",
" 1978.62,1372.19 1980.58,1372.19 1982.55,1372.19 1984.52,1372.19 1986.49,1372.19 1988.46,1372.19 1990.43,1372.19 1992.4,1372.19 1994.37,1372.19 1996.34,1372.19 \n",
" 1998.31,1372.19 2000.28,1372.19 2002.25,1372.19 2004.21,1372.19 2006.18,1372.19 2008.15,1372.19 2010.12,1372.19 2012.09,1372.19 2014.06,1372.19 2016.03,1372.19 \n",
" 2018,1372.19 2019.97,1372.19 2021.94,1372.19 2023.91,1372.19 2025.88,1372.19 2027.84,1372.19 2029.81,1372.19 2031.78,1372.19 2033.75,1372.19 2035.72,1372.19 \n",
" 2037.69,1372.19 2039.66,1372.19 2041.63,1372.19 2043.6,1372.19 2045.57,1372.19 2047.54,1372.19 2049.51,1372.19 2051.47,1372.19 2053.44,1372.19 2055.41,1372.19 \n",
" 2057.38,1372.19 2059.35,1372.19 2061.32,1372.19 2063.29,1372.19 2065.26,1372.19 2067.23,1372.19 2069.2,1372.19 2071.17,1372.19 2073.13,1372.19 2075.1,1372.19 \n",
" 2077.07,1372.19 2079.04,1372.19 2081.01,1372.19 2082.98,1372.19 2084.95,1372.19 2086.92,1372.19 2088.89,1372.19 2090.86,1372.19 2092.83,1372.19 2094.8,1372.19 \n",
" 2096.76,1372.19 2098.73,1372.19 2100.7,1372.19 2102.67,1372.19 2104.64,1372.19 2106.61,1372.19 2108.58,1372.19 2110.55,1372.19 2112.52,1372.19 2114.49,1372.19 \n",
" 2116.46,1372.19 2118.43,1372.19 2120.39,1372.19 2122.36,1372.19 2124.33,1372.19 2126.3,1372.19 2128.27,1372.19 2130.24,1372.19 2132.21,1372.19 2134.18,1372.19 \n",
" 2136.15,1372.19 2138.12,1372.19 2140.09,1372.19 2142.06,1372.19 2144.02,1372.19 2145.99,1372.19 2147.96,1372.19 2149.93,1372.19 2151.9,1372.19 2153.87,1372.19 \n",
" 2155.84,1372.19 2157.81,1372.19 2159.78,1372.19 2161.75,1372.19 2163.72,1372.19 2165.69,1372.19 2167.65,1372.19 2169.62,1372.19 2171.59,1372.19 2173.56,1372.19 \n",
" 2175.53,1372.19 2177.5,1372.19 2179.47,1372.19 2181.44,1372.19 2183.41,1372.19 2185.38,1372.19 2187.35,1372.19 2189.32,1372.19 2191.28,1372.19 2193.25,1372.19 \n",
" 2195.22,1372.19 2197.19,1372.19 2199.16,1372.19 2201.13,1372.19 2203.1,1372.19 2205.07,1372.19 2207.04,1372.19 2209.01,1372.19 2210.98,1372.19 2212.95,1372.19 \n",
" 2214.91,1372.19 2216.88,1372.19 2218.85,1372.19 2220.82,1372.19 2222.79,1372.19 2224.76,1372.19 2226.73,1372.19 2228.7,1372.19 2230.67,1372.19 2232.64,1372.19 \n",
" 2234.61,1372.19 2236.58,1372.19 2238.54,1372.19 2240.51,1372.19 2242.48,1372.19 2244.45,1372.19 2246.42,1372.19 2248.39,1372.19 2250.36,1372.19 2252.33,1372.19 \n",
" 2254.3,1372.19 2256.27,1372.19 2258.24,1372.19 2260.21,1372.19 2262.17,1372.19 2264.14,1372.19 2266.11,1372.19 2268.08,1372.19 2270.05,1372.19 2272.02,1372.19 \n",
" 2273.99,1372.19 2275.96,1372.19 2277.93,1372.19 2279.9,1372.19 2281.87,1372.19 2283.84,1372.19 2285.8,1372.19 2287.77,1372.19 2289.74,1372.19 2291.71,1372.19 \n",
" 2293.68,1372.19 \n",
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" 344.211,1353.24 346.18,1353.24 348.15,1353.24 350.119,1353.24 352.088,1353.24 354.057,1353.24 356.026,1353.24 357.995,1353.24 359.964,1353.24 361.934,1353.24 \n",
" 363.903,1353.24 365.872,1353.24 367.841,1353.24 369.81,1353.24 371.779,1353.24 373.749,1353.24 375.718,1353.24 377.687,1353.24 379.656,1353.24 381.625,1353.24 \n",
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" 403.286,1353.24 405.255,1353.24 407.224,1353.24 409.194,1353.24 411.163,1353.24 413.132,1353.24 415.101,1353.24 417.07,1353.24 419.039,1353.24 421.008,1353.24 \n",
" 422.978,1353.24 424.947,1353.24 426.916,1353.24 428.885,1353.24 430.854,1353.24 432.823,1353.24 434.793,1353.24 436.762,1353.24 438.731,1353.24 440.7,1353.24 \n",
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" 678.969,1353.24 680.938,1353.24 682.907,1353.24 684.876,1353.24 686.845,1353.24 688.814,1353.24 690.784,1353.24 692.753,1353.24 694.722,1353.24 696.691,1353.24 \n",
" 698.66,1353.24 700.629,1353.24 702.599,1353.24 704.568,1353.24 706.537,1353.24 708.506,1353.24 710.475,1353.24 712.444,1353.24 714.414,1353.24 716.383,1353.24 \n",
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" 757.735,1353.24 759.704,1353.24 761.673,1353.24 763.643,1353.24 765.612,1353.24 767.581,1353.24 769.55,1353.24 771.519,1353.24 773.488,1353.24 775.458,1353.24 \n",
" 777.427,1353.24 779.396,1353.24 781.365,1353.24 783.334,1353.24 785.303,1353.24 787.273,1353.24 789.242,1353.24 791.211,1353.24 793.18,1353.24 795.149,1353.24 \n",
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" 1013.73,1353.24 1015.7,1353.24 1017.66,1353.24 1019.63,1353.24 1021.6,1353.24 1023.57,1353.24 1025.54,1353.24 1027.51,1353.24 1029.48,1353.24 1031.45,1353.24 \n",
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" 1112.18,1353.24 1114.15,1353.24 1116.12,1353.24 1118.09,1353.24 1120.06,1353.24 1122.03,1353.24 1124,1353.24 1125.97,1353.24 1127.94,1353.24 1129.91,1353.24 \n",
" 1131.88,1353.24 1133.84,1353.24 1135.81,1353.24 1137.78,1353.24 1139.75,1353.24 1141.72,1353.24 1143.69,1353.24 1145.66,1353.24 1147.63,1353.24 1149.6,1353.24 \n",
" 1151.57,1353.24 1153.54,1353.24 1155.51,1353.24 1157.47,1353.24 1159.44,1353.24 1161.41,1353.24 1163.38,1353.24 1165.35,1353.24 1167.32,1353.24 1169.29,1353.24 \n",
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" 1190.95,1353.24 1192.92,1353.24 1194.89,1353.24 1196.86,1353.24 1198.83,1353.24 1200.8,1353.24 1202.77,1353.24 1204.73,1353.24 1206.7,1353.24 1208.67,1353.24 \n",
" 1210.64,1353.24 1212.61,1353.24 1214.58,1353.24 1216.55,1353.24 1218.52,1353.24 1220.49,1353.24 1222.46,1353.24 1224.43,1353.24 1226.4,1353.24 1228.36,1353.24 \n",
" 1230.33,1353.24 1232.3,1353.24 1234.27,1353.24 1236.24,1353.24 1238.21,1353.24 1240.18,1353.24 1242.15,1353.24 1244.12,1353.24 1246.09,1353.24 1248.06,1353.24 \n",
" 1250.03,1353.24 1251.99,1353.24 1253.96,1353.24 1255.93,1353.24 1257.9,1353.24 1259.87,1353.24 1261.84,1353.24 1263.81,1353.24 1265.78,1353.24 1267.75,1353.24 \n",
" 1269.72,1353.24 1271.69,1353.24 1273.66,1353.24 1275.62,1353.24 1277.59,1353.24 1279.56,1353.24 1281.53,1353.24 1283.5,1353.24 1285.47,1353.24 1287.44,1353.24 \n",
" 1289.41,1353.24 1291.38,1353.24 1293.35,1353.24 1295.32,1353.24 1297.29,1353.24 1299.25,1353.24 1301.22,1353.24 1303.19,1353.24 1305.16,1353.24 1307.13,1353.24 \n",
" 1309.1,1353.24 1311.07,1353.24 1313.04,1353.24 1315.01,1353.24 1316.98,1353.24 1318.95,1353.24 1320.92,1353.24 1322.88,1353.24 1324.85,1353.24 1326.82,1353.24 \n",
" 1328.79,1353.24 1330.76,1353.24 1332.73,1353.24 1334.7,1353.24 1336.67,1353.24 1338.64,1353.24 1340.61,1353.24 1342.58,1353.24 1344.55,1353.24 1346.51,1353.24 \n",
" 1348.48,1353.24 1350.45,1353.24 1352.42,1353.24 1354.39,1353.24 1356.36,1353.24 1358.33,1353.24 1360.3,1353.24 1362.27,1353.24 1364.24,1353.24 1366.21,1353.24 \n",
" 1368.18,1353.24 1370.14,1353.24 1372.11,1353.24 1374.08,1353.24 1376.05,1353.24 1378.02,1353.24 1379.99,1353.24 1381.96,1353.24 1383.93,1353.24 1385.9,1353.24 \n",
" 1387.87,1353.24 1389.84,1353.24 1391.81,1353.24 1393.77,1353.24 1395.74,1353.24 1397.71,1353.24 1399.68,1353.24 1401.65,1353.24 1403.62,1353.24 1405.59,1353.24 \n",
" 1407.56,1353.24 1409.53,1353.24 1411.5,1353.24 1413.47,1353.24 1415.44,1353.24 1417.4,1353.24 1419.37,1353.24 1421.34,1353.24 1423.31,1353.24 1425.28,1353.24 \n",
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" 1446.94,1353.24 1448.91,1353.24 1450.88,1353.24 1452.85,1353.24 1454.82,1353.24 1456.79,1353.24 1458.76,1353.24 1460.73,1353.24 1462.69,1353.24 1464.66,1353.24 \n",
" 1466.63,1353.24 1468.6,1353.24 1470.57,1353.24 1472.54,1353.24 1474.51,1353.24 1476.48,1353.24 1478.45,1353.24 1480.42,1353.24 1482.39,1353.24 1484.36,1353.24 \n",
" 1486.32,1353.24 1488.29,1353.24 1490.26,1353.24 1492.23,1353.24 1494.2,1353.24 1496.17,1353.24 1498.14,1353.24 1500.11,1353.24 1502.08,1353.24 1504.05,1353.24 \n",
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" 1565.09,1353.24 1567.06,1353.24 1569.03,1353.24 1571,1353.24 1572.97,1353.24 1574.94,1353.24 1576.91,1353.24 1578.88,1353.24 1580.84,1353.24 1582.81,1353.24 \n",
" 1584.78,1353.24 1586.75,1353.24 1588.72,1353.24 1590.69,1353.24 1592.66,1353.24 1594.63,1353.24 1596.6,1353.24 1598.57,1353.24 1600.54,1353.24 1602.51,1353.24 \n",
" 1604.47,1353.24 1606.44,1353.24 1608.41,1353.24 1610.38,1353.24 1612.35,1353.24 1614.32,1353.24 1616.29,1353.24 1618.26,1353.24 1620.23,1353.24 1622.2,1353.24 \n",
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" 1643.86,1353.24 1645.83,1353.24 1647.8,1353.24 1649.77,1353.24 1651.73,1353.24 1653.7,1353.24 1655.67,1353.24 1657.64,1353.24 1659.61,1353.24 1661.58,1353.24 \n",
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" 1722.62,1353.24 1724.59,1353.24 1726.56,1353.24 1728.53,1353.24 1730.5,1353.24 1732.47,1353.24 1734.44,1353.24 1736.41,1353.24 1738.38,1353.24 1740.35,1353.24 \n",
" 1742.32,1353.24 1744.29,1353.24 1746.25,1353.24 1748.22,1353.24 1750.19,1353.24 1752.16,1353.24 1754.13,1353.24 1756.1,1353.24 1758.07,1353.24 1760.04,1353.24 \n",
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" 1781.7,1353.24 1783.67,1353.24 1785.64,1353.24 1787.61,1353.24 1789.58,1353.24 1791.54,1353.24 1793.51,1353.24 1795.48,1353.24 1797.45,1353.24 1799.42,1353.24 \n",
" 1801.39,1353.24 1803.36,1353.24 1805.33,1353.24 1807.3,1353.24 1809.27,1353.24 1811.24,1353.24 1813.21,1353.24 1815.17,1353.24 1817.14,1353.24 1819.11,1353.24 \n",
" 1821.08,1353.24 1823.05,1353.24 1825.02,1353.24 1826.99,1353.24 1828.96,1353.24 1830.93,1353.24 1832.9,1353.24 1834.87,1353.24 1836.84,1353.24 1838.8,1353.24 \n",
" 1840.77,1353.24 1842.74,1353.24 1844.71,1353.24 1846.68,1353.24 1848.65,1353.24 1850.62,1353.24 1852.59,1353.24 1854.56,1353.24 1856.53,1353.24 1858.5,1353.24 \n",
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" 1880.16,1353.24 1882.13,1353.24 1884.1,1353.24 1886.06,1353.24 1888.03,1353.24 1890,1353.24 1891.97,1353.24 1893.94,1353.24 1895.91,1353.24 1897.88,1353.24 \n",
" 1899.85,1353.24 1901.82,1353.24 1903.79,1353.24 1905.76,1353.24 1907.73,1353.24 1909.69,1353.24 1911.66,1353.24 1913.63,1353.24 1915.6,1353.24 1917.57,1353.24 \n",
" 1919.54,1353.24 1921.51,1353.24 1923.48,1353.24 1925.45,1353.24 1927.42,1353.24 1929.39,1353.24 1931.36,1353.24 1933.32,1353.24 1935.29,1353.24 1937.26,1353.24 \n",
" 1939.23,1353.24 1941.2,1353.24 1943.17,1353.24 1945.14,1353.24 1947.11,1353.24 1949.08,1353.24 1951.05,1353.24 1953.02,1353.24 1954.99,1353.24 1956.95,1353.24 \n",
" 1958.92,1353.24 1960.89,1353.24 1962.86,1353.24 1964.83,1353.24 1966.8,1353.24 1968.77,1353.24 1970.74,1353.24 1972.71,1353.24 1974.68,1353.24 1976.65,1353.24 \n",
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" 1368.18,600.616 1370.14,600.616 1372.11,600.616 1374.08,600.616 1376.05,600.616 1378.02,600.616 1379.99,600.616 1381.96,600.616 1383.93,600.616 1385.9,600.616 \n",
" 1387.87,600.616 1389.84,600.616 1391.81,600.616 1393.77,600.616 1395.74,600.616 1397.71,600.616 1399.68,600.616 1401.65,600.616 1403.62,600.616 1405.59,600.616 \n",
" 1407.56,600.616 1409.53,600.616 1411.5,600.616 1413.47,600.616 1415.44,600.616 1417.4,600.616 1419.37,600.616 1421.34,600.616 1423.31,600.616 1425.28,600.616 \n",
" 1427.25,600.616 1429.22,600.616 1431.19,600.616 1433.16,600.616 1435.13,600.616 1437.1,600.616 1439.06,600.616 1441.03,600.616 1443,600.616 1444.97,600.616 \n",
" 1446.94,600.616 1448.91,600.616 1450.88,600.616 1452.85,600.616 1454.82,600.616 1456.79,600.616 1458.76,600.616 1460.73,600.616 1462.69,600.616 1464.66,600.616 \n",
" 1466.63,600.616 1468.6,600.616 1470.57,600.616 1472.54,600.616 1474.51,600.616 1476.48,600.616 1478.45,600.616 1480.42,600.616 1482.39,600.616 1484.36,600.616 \n",
" 1486.32,600.616 1488.29,600.616 1490.26,600.616 1492.23,600.616 1494.2,600.616 1496.17,600.616 1498.14,600.616 1500.11,600.616 1502.08,600.616 1504.05,600.616 \n",
" 1506.02,600.616 1507.99,600.616 1509.95,600.616 1511.92,600.616 1513.89,600.616 1515.86,600.616 1517.83,600.616 1519.8,600.616 1521.77,600.616 1523.74,600.616 \n",
" 1525.71,600.616 1527.68,600.616 1529.65,600.616 1531.62,600.616 1533.58,600.616 1535.55,600.616 1537.52,600.616 1539.49,600.616 1541.46,600.616 1543.43,600.616 \n",
" 1545.4,600.616 1547.37,600.616 1549.34,600.616 1551.31,600.616 1553.28,600.616 1555.25,600.616 1557.21,600.616 1559.18,600.616 1561.15,600.616 1563.12,600.616 \n",
" 1565.09,600.616 1567.06,600.616 1569.03,600.616 1571,600.616 1572.97,600.616 1574.94,600.616 1576.91,600.616 1578.88,600.616 1580.84,600.616 1582.81,600.616 \n",
" 1584.78,600.616 1586.75,600.616 1588.72,600.616 1590.69,600.616 1592.66,600.616 1594.63,600.616 1596.6,600.616 1598.57,600.616 1600.54,600.616 1602.51,600.616 \n",
" 1604.47,600.616 1606.44,600.616 1608.41,600.616 1610.38,600.616 1612.35,600.616 1614.32,600.616 1616.29,600.616 1618.26,600.616 1620.23,600.616 1622.2,600.616 \n",
" 1624.17,600.616 1626.14,600.616 1628.1,600.616 1630.07,600.616 1632.04,600.616 1634.01,600.616 1635.98,600.616 1637.95,600.616 1639.92,600.616 1641.89,600.616 \n",
" 1643.86,600.616 1645.83,600.616 1647.8,600.616 1649.77,600.616 1651.73,600.616 1653.7,600.616 1655.67,600.616 1657.64,600.616 1659.61,600.616 1661.58,600.616 \n",
" 1663.55,600.616 1665.52,600.616 1667.49,600.616 1669.46,600.616 1671.43,600.616 1673.4,600.616 1675.36,600.616 1677.33,600.616 1679.3,600.616 1681.27,600.616 \n",
" 1683.24,600.616 1685.21,600.616 1687.18,600.616 1689.15,600.616 1691.12,600.616 1693.09,600.616 1695.06,600.616 1697.03,600.616 1698.99,600.616 1700.96,600.616 \n",
" 1702.93,600.616 1704.9,600.616 1706.87,600.616 1708.84,600.616 1710.81,600.616 1712.78,600.616 1714.75,600.616 1716.72,600.616 1718.69,600.616 1720.66,600.616 \n",
" 1722.62,600.616 1724.59,600.616 1726.56,600.616 1728.53,600.616 1730.5,600.616 1732.47,600.616 1734.44,600.616 1736.41,600.616 1738.38,600.616 1740.35,600.616 \n",
" 1742.32,600.616 1744.29,600.616 1746.25,600.616 1748.22,600.616 1750.19,600.616 1752.16,600.616 1754.13,600.616 1756.1,600.616 1758.07,600.616 1760.04,600.616 \n",
" 1762.01,600.616 1763.98,600.616 1765.95,600.616 1767.91,600.616 1769.88,600.616 1771.85,600.616 1773.82,600.616 1775.79,600.616 1777.76,600.616 1779.73,600.616 \n",
" 1781.7,600.616 1783.67,600.616 1785.64,600.616 1787.61,600.616 1789.58,600.616 1791.54,600.616 1793.51,600.616 1795.48,600.616 1797.45,600.616 1799.42,600.616 \n",
" 1801.39,600.616 1803.36,600.616 1805.33,600.616 1807.3,600.616 1809.27,600.616 1811.24,600.616 1813.21,600.616 1815.17,600.616 1817.14,600.616 1819.11,600.616 \n",
" 1821.08,600.616 1823.05,600.616 1825.02,600.616 1826.99,600.616 1828.96,600.616 1830.93,600.616 1832.9,600.616 1834.87,600.616 1836.84,600.616 1838.8,600.616 \n",
" 1840.77,600.616 1842.74,600.616 1844.71,600.616 1846.68,600.616 1848.65,600.616 1850.62,600.616 1852.59,600.616 1854.56,600.616 1856.53,600.616 1858.5,600.616 \n",
" 1860.47,600.616 1862.43,600.616 1864.4,600.616 1866.37,600.616 1868.34,600.616 1870.31,600.616 1872.28,600.616 1874.25,600.616 1876.22,600.616 1878.19,600.616 \n",
" 1880.16,600.616 1882.13,600.616 1884.1,600.616 1886.06,600.616 1888.03,600.616 1890,600.616 1891.97,600.616 1893.94,600.616 1895.91,600.616 1897.88,600.616 \n",
" 1899.85,600.616 1901.82,600.616 1903.79,600.616 1905.76,600.616 1907.73,600.616 1909.69,600.616 1911.66,600.616 1913.63,600.616 1915.6,600.616 1917.57,600.616 \n",
" 1919.54,600.616 1921.51,600.616 1923.48,600.616 1925.45,600.616 1927.42,600.616 1929.39,600.616 1931.36,600.616 1933.32,600.616 1935.29,600.616 1937.26,600.616 \n",
" 1939.23,600.616 1941.2,600.616 1943.17,600.616 1945.14,600.616 1947.11,600.616 1949.08,600.616 1951.05,600.616 1953.02,600.616 1954.99,600.616 1956.95,600.616 \n",
" 1958.92,600.616 1960.89,600.616 1962.86,600.616 1964.83,600.616 1966.8,600.616 1968.77,600.616 1970.74,600.616 1972.71,600.616 1974.68,600.616 1976.65,600.616 \n",
" 1978.62,600.616 1980.58,600.616 1982.55,600.616 1984.52,600.616 1986.49,600.616 1988.46,600.616 1990.43,600.616 1992.4,600.616 1994.37,600.616 1996.34,600.616 \n",
" 1998.31,600.616 2000.28,600.616 2002.25,600.616 2004.21,600.616 2006.18,600.616 2008.15,600.616 2010.12,600.616 2012.09,600.616 2014.06,600.616 2016.03,600.616 \n",
" 2018,600.616 2019.97,600.616 2021.94,600.616 2023.91,600.616 2025.88,600.616 2027.84,600.616 2029.81,600.616 2031.78,600.616 2033.75,600.616 2035.72,600.616 \n",
" 2037.69,600.616 2039.66,600.616 2041.63,600.616 2043.6,600.616 2045.57,600.616 2047.54,600.616 2049.51,600.616 2051.47,600.616 2053.44,600.616 2055.41,600.616 \n",
" 2057.38,600.616 2059.35,600.616 2061.32,600.616 2063.29,600.616 2065.26,600.616 2067.23,600.616 2069.2,600.616 2071.17,600.616 2073.13,600.616 2075.1,600.616 \n",
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]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nt = length(t);\n",
"plot(t,T_growth, linecolor = :red, linewidth = 3, xlabel = \"Year\", ylabel = \"Earth Temperature, deg K\", legend = :topleft, label = \"Temperature\")\n",
"plot!(t,water*ones(nt), linecolor = :blue, linewidth = 3, linestyle = :dash, label = \"Water boils\")\n",
"plot!(t,paper*ones(nt), linecolor = :black, linewidth = 3, linestyle = :dash, label = \"Paper burns\")\n",
"plot!(t,gold*ones(nt), linecolor = :yellow, linewidth = 3, linestyle = :dash, label = \"Gold melts\")\n",
"plot!(t,sun*ones(nt), linecolor = :orange, linewidth = 3, linestyle = :dash, label = \"Surface of the Sun\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.9.4",
"language": "julia",
"name": "julia-1.9"
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@uablrek

uablrek commented Mar 3, 2025

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The result for P0 = E/H = 14e13 watts is incorrect in the post:
https://wildpeaches.xyz/blog/stefan-boltzmann-revisited/

The correct value, as in this gist, is 2.0421118721461188e13 (~20.42 TW)

This is in line with https://en.wikipedia.org/wiki/World_energy_supply_and_consumption (19.6TW 2021).

14e13 watts is around 7 times higher, which made me jump a bit

@XerxesZorgon

XerxesZorgon commented Mar 3, 2025 via email

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@uablrek

uablrek commented Mar 3, 2025

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Yes, I think it's a typo. A bit further down in p0=P0/Adisk, the value of E (178889) instead of P0 is written. Again, I think the correct value is used in computations.

@XerxesZorgon

XerxesZorgon commented Jul 7, 2025 via email

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@uablrek

uablrek commented Jul 7, 2025

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do these numbers represent useful energy to society, or total consumption?

Good question, but I don't think it matters all that much. In the case of fossil fuels (~87%) it should be simple: it should be based on extraction. For example, a coal power plant may have an efficiency of 35%, but the statistics should be based on the amount of coal used, not electricity produced. And I think that's the case. Statistics on extractions should be fairly easy to get.

For wind, solar, bio and hydro, I think the stats are based on electricity produced. But they should not be included in your temperature calculations anyway, since the energy is already received by earth, just transformed to electricity.

Nuclear is trickier. I think (and I am guessing) that the stats are based on electricity produced. But a nuclear power plant has an efficiency around 35%, so the thermal effect is around 3 times the electricity output. But then again, nuclear is a small contributor (yet).

@XerxesZorgon

XerxesZorgon commented Jul 8, 2025 via email

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