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Last active November 16, 2024 15:42
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Modeling Tide Heights and Kayaker's Heuristics
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"cell_type": "markdown",
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"<center>\n",
"<figure>\n",
" <img src=\"https://austinrochford.com/resources/img/kayak_sunrise.png\" width=\"60%\" alt=\"Sunrise over back bay in a kayak\">\n",
" <figcaption>Sunrise over <a href=\"https://maps.app.goo.gl/rnDzaFEQLJ1mrFNk9\">Jenkins Sound</a>, New Jersey</figcaption>\n",
"</figure>\n",
"</center>\n",
"\n",
"Just over a year ago, I moved to the [beach](https://en.wikipedia.org/wiki/Cape_May_Court_House,_New_Jersey), partly to be able to indulge in my passion of sea kayaking more frequently. As a result of this move, I have become much more aware of the tidal rythym of both the local Atlantic Ocean and [Delaware Bay](https://en.wikipedia.org/wiki/Delaware_Bay) coasts.\n",
"\n",
"While there are many websites that will provide detailed tide tables, and I have aqcuired a nice, decorative [tide clock](https://en.wikipedia.org/wiki/Tide_clock) featuring a landscape of our [local lighthouse](https://en.wikipedia.org/wiki/Cape_May_Lighthouse), I found myself wanting a digital display that cycled through the tidal status at several locations.\n",
"\n",
"<center>\n",
"<figure>\n",
" <img src=\"https://images.squarespace-cdn.com/content/v1/54a17af0e4b0f0443677e561/1605620839653-J9N5X4D3I9XZFUFWJDV0/CMNV.jpg?format=2500w\" alt=\"Tide clock showing the Cape May Point lighthouse\" width=\"60%\">\n",
" <figcaption>Cape May Point Lighthouse tide clock from <a href=\"https://www.tidepieces.com/shop/cape-may-lighthouse-new-jersey\">Tidepieces</a></figcaption>\n",
"</figure>\n",
"</center>\n",
"\n",
"After a bit of searching, I found the relatively inexpensive [Ulanzi TC001 Smart Pixel Clock 2882\n",
"](https://www.ulanzi.com/products/ulanzi-pixel-smart-clock-2882?srsltid=AfmBOorD9ZhQLOUcCRKgU15xK_4bjLfW_N0RdtBl8H-NloLi4KvFQz-V) and the corresponding open source firmware [AWTRIX 3](https://blueforcer.github.io/awtrix3/#/). In the process of writing software to turn this device into a digital tide clock, I stumbled upon the fun little math problem that is the subject of this post.\n",
"\n",
"<center>\n",
" <img src=\"https://austinrochford.com/resources/img/tidetrix.png\" alt=\"Prototype digital tide clock\" width=\"60%\">\n",
"</center>\n",
"\n",
"In this post, we will derive a function that approximates the water level between low and high tides in an idealized, semi-[diurnal](https://en.wikipedia.org/wiki/Diurnal_cycle) tide region. This approximation is sufficient for my purposes, as most areas of the Atlantic ocean (including New Jersey, where I live) are subject to such a tide pattern. We will spend the rest of this post deriving the water level approximation and comparing its predictions to several heuristics frequently used by kayakers (and other boaters) to predict tide height and flow rate."
]
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"## Deriving the approximation\n",
"\n",
"We will denote the water height at time $t$ after the most recent low tide as $h(t)$. The units of the domain and range of the function $h$ are not particularly important here, as we can scale the inputs to reflect the local intertidal time for the location in question and shift and scale the output to reflect the local intertidal range.\n",
"\n",
"Under this simplifying assumption, we assume a low tide of height zero occurs at time $t = 0$, and high tide of height one occurs at time $t = 1$, resulting in the constraints\n",
"\n",
"$$\n",
"\\begin{align}\n",
" h(0) & = 0 \\\\\n",
" h(1) & = 1.\n",
"\\end{align}\n",
"$$\n",
"\n",
"We also assume that there are [slack tides](https://en.wikipedia.org/wiki/Slack_tide) at times $t = 0$ and $t = 1$, meaning that water is completely still (not rising or falling) at those times. This assumption results in the constraints on the derivative, $h'$,\n",
"\n",
"$$\n",
"\\begin{align}\n",
" h'(0) & = 0 \\\\\n",
" h'(1) & = 0.\n",
"\\end{align}\n",
"$$\n",
"\n",
"Finally, we also assume that the height of the water is changing the fastest halfway between low ($t = 0$) and high ($t = 1$) tide. This assumption results in the constraint on the second derivative, $h''$,\n",
"\n",
"$$h''\\left(\\tfrac{1}{2}\\right) = 0.$$\n",
"\n",
"For simplicity, we will assume that $h(t)$ is a polynomial, so we seek the unique quartic polynomial that satisfies the above five constraints. We write\n",
"\n",
"$$h(t) = a_0 + a_1 t + a_2 t^2 + a_3 t^3 + a_4 t^4,$$\n",
"\n",
"so the first and second derivatives are\n",
"\n",
"$$\n",
"\\begin{align}\n",
" h'(x) & = a_1 + 2 a_2 t + 3 a_3 t^2 + 4 a_4 t^3 \\\\\n",
" h''(x) & = 2 a_2 + 6 a_3 t + 12 a_4 t^2.\n",
"\\end{align}$$\n",
"\n",
"Expressing the five constraints in terms of these coefficients, we get\n",
"\n",
"$$\n",
"\\begin{matrix}\n",
" 0 & = & h(0) & = & a_0 \\\\\n",
" 1 & = & h(1) & = & a_0 & + & a_1 & + & a_2 & + & a_3 & + & a_4 \\\\\n",
" 0 & = & h'(0) & = & & & a_1 \\\\\n",
" 0 & = & h'(1) & = & & & a_1 & + & 2 a_2 & + & 3 a_3 & + & 4 a_4 \\\\\n",
" 0 & = & h''\\left(\\frac{1}{2}\\right) & = & & & & & 2 a_2 & + & 3 a_3 & + & 3 a_4.\n",
"\\end{matrix}\n",
"$$\n",
"\n",
"While we could use software to solve this system of five linear equations in the five unknown coefficients, the first and third equations imply that $a_0 = 0 = a_1$, which reduces the system to three equations in three unknowns,\n",
"\n",
"$$\n",
"\\begin{matrix}\n",
" 1 & = & a_2 & + & a_3 & + & a_4 \\\\\n",
" 0 & = & 2 a_2 & + & 3 a_3 & + & 4 a_4 \\\\\n",
" 0 & = & 2 a_2 & + & 3 a_3 & + & 3 a_4,\n",
"\\end{matrix}\n",
"$$\n",
"\n",
"which is straightforward to solve by hand. Subtracting the third equation from the second shows that $a_4 = 0$ as well, so we are left with a system of two equations in two unknowns,\n",
"\n",
"$$\n",
"\\begin{matrix}\n",
" 1 & = & a_2 & + & a_3 \\\\\n",
" 0 & = & 2 a_2 & + & 3 a_3.\n",
"\\end{matrix}\n",
"$$\n",
"\n",
"From here it is easy to work out that $a_2 = 3$ and $a_3 = -2$. Therefore, our function for approximate water height is\n",
"\n",
"$$h(t) = 3 t^2 - 2 t^3.$$\n",
"\n",
"We define this function in Python and visualize it below."
]
},
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"cell_type": "code",
"execution_count": 1,
"id": "75db4e8c-cfd8-4c48-aead-7d6dce5e4ac7",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3c1b4ab7-d9c1-4bd5-be02-a283aa8f9d14",
"metadata": {},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt, ticker\n",
"import numpy as np\n",
"import seaborn as sns\n",
"from sympy import lambdify\n",
"from sympy.abc import t"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "96111de3-f0ff-4eff-a577-6495c3732025",
"metadata": {},
"outputs": [],
"source": [
"sns.set(color_codes=True)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "944ae4a3-746d-43a1-88f4-e8a37812ec1f",
"metadata": {},
"outputs": [],
"source": [
"def h(t):\n",
" return 3 * t**2 - 2 * t**3"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4192bcb5-4612-450d-894b-2ce6b0d0cc52",
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{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"t_ = np.linspace(0, 1)\n",
"\n",
"ax.plot(t_, h(t_));\n",
"\n",
"ax.xaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_ylabel(\"$h(t)$\");"
]
},
{
"cell_type": "markdown",
"id": "beabd6fe-c76f-45f9-8b19-fc6fb9417eff",
"metadata": {},
"source": [
"We can also use [SymPy](https://www.sympy.org/en/index.html) to verify this function satsifies our five constraints."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8c8e63b4-c48a-4cd3-92a1-959396821452",
"metadata": {},
"outputs": [],
"source": [
"# function constraints\n",
"assert h(0) == 0\n",
"assert h(1) == 1"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "8fe66603-ba7b-44f9-91f7-70404734271d",
"metadata": {},
"outputs": [],
"source": [
"dh = lambdify(t, h(t).diff(t))\n",
"\n",
"# derivative constraints\n",
"assert dh(0) == 0\n",
"assert dh(1) == 0"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "96c5d939-42d4-4ecf-8953-c4cce5c7d0fc",
"metadata": {},
"outputs": [],
"source": [
"d2h = lambdify(t, h(t).diff(t).diff(t))\n",
"\n",
"# second derivative constraint\n",
"assert d2h(0.5) == 0"
]
},
{
"cell_type": "markdown",
"id": "a07e2cd8-cd2f-4b15-9620-5e8118be261a",
"metadata": {},
"source": [
"Thankfully, we have done the math correctly and $h$ satisfies all of our constraints."
]
},
{
"cell_type": "markdown",
"id": "24731717-f4d3-441e-b6da-b5596076f8ef",
"metadata": {},
"source": [
"## Kayaker's heuristics\n",
"\n",
"While the plot of water height above is plausible and the function satisfies our constraints, kayakers use a number of heuristics to predict the water height and flow rate based on the time since the most recent slack tide. In the rest of this post we will compare the predictions of our function $h$ with these heuristics.\n",
"\n",
"For these heuristics we will use [Kayarchy](https://www.kayarchy.com/), my favorite online resource for sea kayaking information, as our reference. Note that in this section we assume there are six hours between low tide at time $t = 0$ and the subsequent high tide at time $t = 1$ for simplicity. In reality, due to the fact that the moon takes slightly more than one day to orbit the earth completely, these tides are about [six hours and twelve minutes apart](https://en.wikipedia.org/wiki/Tide#Example_calculation:~:text=the%20time%20between%20semi%2Ddiurnal%20tides%20is%20not%20twelve%20but%2012.4206%20hours), on average. Since six is much easer to do mental math with than 6.2 while paddling a kayak in wind and waves, the following heuristics all make this simplifying assumption."
]
},
{
"cell_type": "markdown",
"id": "2fa457b2-de5a-461a-bdc1-8080bff509fe",
"metadata": {},
"source": [
"### Rule of Twelfths\n",
"\n",
"The [Rule of Twelfths](https://www.kayarchy.com/html/03thesea/005tides.htm#ruleoftwelfths) sates\n",
"\n",
"> In the first hour after low tide, the water level rises by 1/12 of the tidal range. In the second hour, it rises by 2/12. In the third hour it rises by 3/12. In the fourth hour it is 3/12 again, then 2/12, then 1/12 in the last hour before high tide.\n",
"\n",
"We define these hourly increments in a NumPy array."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "c939ff90-0881-42d6-a6ea-30c666b348ae",
"metadata": {},
"outputs": [],
"source": [
"TWELFTHS_HEIGHT_INC = np.array([1, 2, 3, 3, 2, 1]) / 12"
]
},
{
"cell_type": "markdown",
"id": "24c1cf18-76d2-460c-9793-f49bce9af6a3",
"metadata": {},
"source": [
"With this array, we can compare the tide height predicted by the Rule of Twelfths to the predictions of $h$ at each hour after high tide."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "18a69de2-972d-4c89-be9b-9ca4ae696af7",
"metadata": {},
"outputs": [],
"source": [
"HOURS = np.linspace(0, 1, 7)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "98bebc40-d7d2-4dc0-8f3f-447ec4140ecd",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.plot(t_, h(t_));\n",
"\n",
"ax.scatter(HOURS[1:], TWELFTHS_HEIGHT_INC.cumsum(),\n",
" c=\"C1\", zorder=5, label=\"Rule of twelfths\");\n",
"\n",
"ax.xaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_ylabel(\"$h(t)$\");\n",
"\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"id": "490a6a32-7adc-4b29-b662-647e0a883d3d",
"metadata": {},
"source": [
"We see that $h$ and the Rule of Twelfths are in fairly close agreement."
]
},
{
"cell_type": "markdown",
"id": "dd0bf587-be4a-4681-9214-d48fcd3dc84f",
"metadata": {},
"source": [
"### Rule of Thirds\n",
"\n",
"We now turn from predicting tide height with the rule of twelfths to three heuristics for predicting tidal flow rates. The [Rule of Thirds](https://www.kayarchy.com/html/03thesea/006currents.htm#:~:text=At%20slack%20water%2C%20there,water%2C%20so%200/3.) states that\n",
"\n",
"> At slack water, there may be a few confused currents but the overall mass of water is stationary. The Rule of Thirds describes the flow at this time as 0/3. An hour later the rate of flow is 1/3 of the maximum printed on the chart. At two hours it is 2/3, at three it is 3/3, at four it is 2/3, at five it is 1/3 again, and after six it is slack water, so 0/3.\n",
"\n",
"We define the expected flow rates from the Rule of Thirds below."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "fb2ca99f-1494-4ccc-bb93-fdbd8140547f",
"metadata": {},
"outputs": [],
"source": [
"THIRDS_FLOW_RATE = np.array([0, 1, 2, 3, 2, 1, 0]) / 3"
]
},
{
"cell_type": "markdown",
"id": "2701f139-5b6f-4f95-88b9-82ff6fc78f61",
"metadata": {},
"source": [
"Note that the rule of thirds expresses the flow rate at each hour as a fraction of the maximum flow rate, which, according to our second derivative assumption, occurs at $t = \\tfrac{1}{2}$."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "423b955c-687c-4414-98e3-d97d863c148c",
"metadata": {},
"outputs": [],
"source": [
"MAX_FLOW = dh(0.5)"
]
},
{
"cell_type": "markdown",
"id": "ba6f8b3f-1719-4b7e-8002-1511a5f29e33",
"metadata": {},
"source": [
"We now compare the flow rate predictions from the Rule of Thirds to those from $h'$."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "62f34cbd-989c-414e-93c1-e44fb99b1617",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"t_ = np.linspace(0, 1)\n",
"\n",
"ax.plot(t_, dh(t_) / MAX_FLOW);\n",
"\n",
"ax.scatter(HOURS, THIRDS_FLOW_RATE,\n",
" c=\"C1\", zorder=5, label=\"Rule of Thirds\");\n",
"\n",
"ax.xaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_ylabel(\"$h'(t)$\");\n",
"\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"id": "15a176ab-d638-4c64-8bc5-7fae626c4156",
"metadata": {},
"source": [
"We see that where it matters most, at one, two, four, and five hours after low tide, the predictions of the Rule of Thirds are directionally correct, but not particularly close to the predictions of $h'$. It remains to be seen if this is a deficiency of either the Rule of Thirds or of $h$."
]
},
{
"cell_type": "markdown",
"id": "d90cedd3-156e-4358-9c22-15dd0cd96075",
"metadata": {},
"source": [
"### The 50/90 Rule\n",
"\n",
"Per [Kayarchy](https://www.kayarchy.com/html/03thesea/006currents.htm#:~:text=Alternatively%20there%20is,six%20hours%200%25.),\n",
"\n",
"> Alternatively there is the 50/90 Rule which is often more accurate but perhaps not quite so easy to use in high wind and waves. It states that an hour after slack water the rate of flow is 50% of the maximum, at two hours it is 90%, at three hours 100%, at four hours 90% again, at 5 hours 50% and at six hours 0%.\n",
"\n",
"Kayarchy raises an interesting point here, if it is indeed the rule of thirds that could stand to be improved, that improvement is likely to come with the tradeoff of higher complexity.\n",
"\n",
"We define the expected flow rates for the 50/90 Rule below."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "eb2c7bf5-fb05-45f0-899f-1297149628cc",
"metadata": {},
"outputs": [],
"source": [
"FLOW_RATE_50_90 = np.array([0, 0.5, 0.9, 1, 0.9, 0.5, 0])"
]
},
{
"cell_type": "markdown",
"id": "e689cf04-71f8-412c-aa99-1590c3e76fb2",
"metadata": {},
"source": [
"We now compare the Rule of Thirds, the 50/90 Rule, and $h'$."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "b2ed4e40-6edc-404b-b4f6-78056d4fb34a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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cjoKyOigVMsQO9sVf74jG20+Mw11TB6G/v6tdTXj21KhxY3wwXnk4Fi8+GIOpMYFwdVJCW9eIbQk5WPzBAfxvdyYqqjtXrsSeCTIZVGPvueo+qrF39/ik7SYPP/woAgOD8NZbS1FXZ078o6KGYvfunTh9+iSys89i6dIlV+ytHDAgFGPHTsCbby7F77/vxYULefjyy8/wxRefom/fwFbvM23aDLi5ueNf//o7UlOTkZWViSVLXkB9fX2nJpB3hylTboCnpxdeeukfyMzMwPHjR/Hee29bbndwcEBqagqWLXsNSUmnUVCQj23btqK+vh5RUdFXOXLn2URPEhHZr3qdAXuOX8DPh85bhtQ8XFWYGReEsVEBvWaOjiAICPbXINhfgz9NGohTZ8rw48FzyC6oxo7Dufjl2AVMGBaAmXFBnOjdCmVIDDDtCegOfNmsR0lw9oRq7N3dfvn/1ahUKjz33D+xaNGj+OijlfjrX/+GP//5L9Bqq/DXvz4OFxdXzJt3L6qra654jCVLluKjj/6LN998DdXVWvTpE4i///1fmDnzplb3d3FxwfLlq7BixX/w1FOPAwCio4fhgw/WoE+fvt3yPDvK0dER7733Ad59dxkef/xhuLpq8Mgjj+K111627LNkyVK8//47+Pvf/w+1tTUICgrGiy++gmHDRnRrbIJ4tUFDuiZz/YaWlx13hkIh67ZufuoZbMNrq2toxK6jedh5OBe1DealPrzd1Lgxvj/GDQ2QfD6ONbShKIpIPleOLfvPIfPilXxymYCxUf64Mb4/fD06d9m2NWhs1KOsrABeXgFQKjs/rNhUcVusq4LC1QPwGSRZDxJ1nkIh69D5d63Xlaenc++pk0REtqOmvhE7Dp/H7qN5qNeZJ6r6eTrhpvj+iBviJ3lyZE0EQUBUiBcigz2Rfr4SWw6cQ2pOBfadKsDvpwswZogfbhobjACv7qn6b4sEmcxymX9HP2CJmjBJIqIeYRJF7D2Zj+9/PWPpOerr44ybxwYjJtzXsgwDtSQIAiL6eyCivweyLlRh64FzOHWmDAeTi5CYUoxpowNxy7gQOKr4lk7UlXhGEVG3yymsxrod6Tibb16+I9DHGbeOH4ARYd6Q2dEk7J4wsK8b/nrHMJwr1GLz7+dwIqsUPx/KxaHUYtw1ZRBGhfvY1cR2IikxSSKiblPXYMAP+87il2N5EEXzWmmzJwzAlFF9Iec8kU4J9tdg0dxonDpTii93ZqCksgErNyYhKsQT90wLg5+n7c9XIpIakyQi6nKiKCIhpQhf/5IFba15YenYwb64c/KgNi8TQm0THeqNiCAPbEvIwbaEHCRll+NfaxIxa0x/zBrTHw7Kri8cSNRbMEkioi6VX1qLL3akI+18JQDA39MJ904Pw5CL1aap6zkozT108ZH++HJnBpKyy7F5/zkcTC7EPdPCEB3a+bW5iHojJklE1CUMRhM278/GTwnnYTSJUCpkuHlsMG6IDYJSwaG1nuDn6YSn/zQMR9NL8NXuTJRUNuA/357CyDAf3H9DOCt3E7UTkyQi6rTiynqs2pSM7ALzxOzhA71x19RB8HFn0cOeJggCYiJ8ERniic37s7HzcB6OZZTgzIUqPHLzEESyR4+ozZgkEVGnJKQU4vPt6WjQG+GkUuDBmRGIifCVOqxez1GlwJ2TB2FsVAA+2pyMC6W1eOd/JzBzTH/MnhDCelREbcAkiYg6pEFvwPqdmfj9dAEAYFCgGxbeHAkvN7XEkdGl+vm64IUHYvD17kz8eiIf2xJykHa+An++JZI9fV2spKQYt902q8X2f/zj35g162YAQGZmOt57722kpaXA3d0Dd955D+64Y16z/RsbG3HTTVOxfv338PDwxDffrMfGjRtQVlaCwYMj8fjjTyEiYrBl/4KCfLz77jKcOHEcjo5q3HTTbDz00ELI5a1P2t+2bUuzJT8AQCaTwcnJGRERg/H444uaLaR7LePHxzR7jvaESRIRtdv5omp8uCkZheV1EATg5rHBuHlcMC/rt1IqpRz3z4jAkGBPfPpTGs7ma/HS2kN4YEYEYgf7SR2e3cjKyoSDgwrffLMJl5aqcnFxAQBUVVXi6af/gnHjrsPf/vY8kpNP4+2334CTkxNuvPEWy/4nTx5H37794OXljXXr1mLt2tVYtOj/MHLkaOza9TOeeGIBPvnkCwQFBcNgMOD//u8J9OsXhA8/XIO8vDy8/vorkMlkePjhP1813k2btlv+bzQacf58DpYvfwf/939P4ptvNsHJiWUkmCQRUZuJoohdR/Pw7Z4sGIwiPFxVWHjzEIQHeUgdGrVBTIQvggNc8dHmFGRdqMKHm5KRcq4cd00Jg8rBPkoFmEQTsiqzodVp4eHkhhDXYMiEnknez57NQr9+QfD2bv1qws2bf4BCocSzz/4DCoUCwcEhyMvLxRdffNosSTp4cD/GjBkLAPjyy89xxx13YfbsuQCAhx5aiFOnTuCLLz7DP/7xb+zZswtFRYVYtepTaDQaDBgwEBUV5Vi58j3cd998ODhcebK+l1fzOH19/fD004vxxBMLcezYYYwff31n/yQ2j1/7iKhNquv0WP79aXy1KxMGo4jhA73x0vzRTJBsjLebI567ZwRuGtsfAoC9Jwuw5LPDyC2+8gr0tuJE8Wn868BSvHd8FdamfIV3jnyIfx1YihPFp3vk8c+cyUJwcPAVbz958jiGDx8JheKP/omRI2OQm3se5eVllm0JCfsRHz8OFRUVqKmpbrHSfVhYOI4fP3bxmCcQFhYBjUZjuX3UqNGora1FZmZGu59DU1Ill5tjXLNmFebObT6M1tq2S+3fvw8PPXQvJk8ehzvvnI3Vqz+AXq9vdyzWgEkSEV3TuUItXlp7GCeySqGQC7h76iA8eftQuDrxknJbJJfJMOe6UPxt3nC4uTigoKwOr3x2BPsvzi+zRSeKT2N10jpU6qqaba/UVWF10roeSZTOnMlCZWUl/vKXBbj55ul47LGHkZBwwHJ7SUkxfH2bD296e/sAAIqLiwAA+fkXUFFRgSFDoqDRaODg4ICiosJm9ykoKEBlZfnFYxZd5ZjN73ct+fkXsHLl+/Dz88fw4SPbdd8mCQkH8OKLf8ctt9yGdeu+xjPP/B2//LITr7zyYoeOJzUOtxHRVR3LKMFHW5KhbzTB39MJj94aiSA/V6nDoi4wONgTSx6KxZofU3HqTBnW/JiKooo6zJ4wwKbW1DOJJnybufmq+3yXuRnRPpHdNvRmMBhw/vw5yGQhePLJ/4OTkzN27foZzz77FN5997+IiYlFQ0NDi+Gvpt91OnNPS0LCAYweHWeZdD116g347LM1CA+PQHj4YOzduwf79++DyWQEADQ06ODi4trqMa/VezNt2oRm8SsUSsTGxuGf/3wJjo4dm9T/+eef4JZb5mD27NsBAH37BuLZZ/+BRYseRUFBPgIC+nTouFJhkkRErRJFET8fysW3e7IgAogK8cSjt0bBSc23DXvi6uSARXOj8cPes/jxYA62HshBcUU9Hpo12GaWNMmqzG7Rg3S5Cl0VsiqzEeYR2i0xKBQK/PjjbsjlMqhU5is8IyIGIzv7LL766gvExMRCpVK1SFyafnd0NN8nIWE/Jk2aarl90aJn8Oabr+Kxxx6GKIqIiorGnXfejS1bfgAAqFQqNDY2tnpMtfrqic7atesBABUV5Vi9+gOUl5dj4cK/dCqRychIQ2pqMrZu3WjZJooiAODcuWwmSURk+wxGE77YkYG9J/MBAJNG9sXdUwfx6jU7JRME3H59KPw8nPDZ9jQcSi1GWVUDnrg9Gm42UKVbq9N26X4d1drVYAMGhCIx0Tzk5uvrh7Kykma3l5aaf/fx8YVOp8Px48fw/PN/DE25uLjg5ZeXoqGhAfX19fDw8MDKle+hT59AyzHPns26wjF9rhpvYGA/y7/Llv0HCxbcj6ef/gvWrv0Sbm7uV7yf0Wi84m0mk4i7774fM2fe1OK2yyeK2wK+4xFRM3UNjXj3m5PYezIfAoC7pgzCvdPCmCD1AuOjA/DMncPhrFbgTL4W/++zI7hQYv0TujUqzbV3asd+HXH27BlMn349jh070mx7amoyQkIGAACGDRuJkydPNEsyjh07gqCg/vDw8MTx40fRv38wPDz+qIq+dOkSbN26CWq1Gh4eHjAajdi79zfExo4BAAwfPgIZGWmorf2jnY4ePQwnJ2cMGhTe5vjVajVefPH/oby8DO+884Zlu1KpRF1dXbN98/Jyr3icAQNCcf58DgID+1l+iouL8N//voe6uto2x2Mt+K5HRBbFlfV4dd1RpOZUQKWU48nbozFtdD8INjQ/hTonor8H/nl/DHw9HFGmbcBrXxxFUnbZte8ooYHuIXBXuV11Hw+VGwa6h3RbDMHBIejfvz/eeWcZTp48jpycc1i+/B2kpCThgQceBgDcdNMtqK2txeuvv4Ls7LPYtm0Lvv56Pe67bz6AP65qu5SPjy/WrFmFEyeO4fz5HCxZ8i/U19daClBOmDARXl7eePHFfyArKxP79v2KVav+i3nz7oFSqWzXcxg0KAz33PMAdu/eid9/3wsAiIqKhlZbhfXr16GgIB8bN37fbDL65e655378+uturF27GufP5+DIkUN47bWXUVtbY5M9SYLYNFhIHWI0mlBe3rXZsUIhg4eHMyoqamEwmLr02NQzrK0NL60do1FpMNA9pMUE1qy8Krz//SnU1DfCw1WFp+ZG9+oJ2tbWhj2tpr4RKzacRkZuJWSCgHumh2HSiL4t9mvLa+tqGhv1KCsrgJdXAJTKjg/tNV3ddiULou7DcN+hHT5+W5SXl+HDD1cgMfEAqqtrEB4ejkcffbLZJfypqcn4z3/eQmZmOry8vDFv3j24/fY7AQDz5t2GF15YgqioP+I0GAz44IPl2LlzO3S6BgwbNhJPPvk0+vULsuyTl5eLt99+HSdPnoBGo8FNN92Khx5aCNkVen+bKm7//vuRFrfp9XrMn3836uvr8cUX38DJyRlr167GDz98h9raGowZMxbR0cPx7bf/w3ffbQHQsuL2L7/swrp1n+DcuWxoNBqMG3cdHntsEVxd2/9+olDIOnT+Xet15enpDHkbluZhktRJTJKoNdbUhieKT+PbzM3NJra6q9xwx6BbLB8aCSmF+OTHNBiMJvT3c8WiudHwcFVJFbJVsKY2lEqjwYTPtqfhQJL5UvLpo/vhT5MGQiYz9yy25bV1zcfooiTpSvF4qNwwtx3xkHVhkmTjmCRRa6ylDdvy7br4nBv+94t54ueIQd5YeHOk3VRf7gxraUOpiaKIrQdz8MPeswDMVbsX3jwESWXJXdJz05VJEiBtxW3qelInSby6jchOtaV2zLqkH1BxaBwAwdxLMHmgTdXHoe4nCAJuHhsMPw9HfLw1BUfSimEwGlDk9+NV79fddYmuRCbILJf5d/QDlqgJ02siO9WW2jENqIHMtRyzx4dg3pRBTJDoimIH++HJ26OhkMtwqjATlfq21SUismVMkojsVFtrwsRFu+OW8d131Q/Zj6EDvPDXO6KhVDdee2d0f10iou7GJInITrW1Jsz1UQO6ORKyJ0OCPTF33JA27duddYmIegKTJCI7ZQ21Y8g+TQqPhovCFbjKZT/tfW3xGiLqSl31emKSRGSnZIIMdwy65ar7zB10C6/8oXaTCTLcFTEbEHDFRKmtr62mhVz1el3XBUi9XtPrSS7v3PVpvLqNyI4N9x2KhyPvw+env0ej7I+lBVg7hjpruO9QLIi6D/9L24hqQ7Vlu5uDG/4U1vbXlkwmh6OjC2pqKgAADg6qLqvwbjIJMBrZQ2XL2tuGoihCr9ehpqYCjo4uVyyo2VZMkojsmNFkwpFEGbQpEyDXVGBynDdGDejX7qrIRK0Z7jsU0T6ROJidgq/3JaGuRg65uh8GjGj7mmEAoNGY1yprSpS6ikwmg8nEEgC2rKNt6OjoYnlddQaLSXYSi0lSa6yhDU2iiI+3pCAhpQhymYA/3xKJmAhfSWKxRdbQhrYkv7QWb/7vOKpq9Ojr7Yzn7hkJF8f2rR1mMplgNBq6JB65XICbmxOqqurYm2SjOtqGcrnimj1ILCZJ1IuJooj/7cq0JEiPz47CiDAfqcMiO9bH2xl/v3sk3lh/DBdKa/Hedyfxt3kjoFK2vXq7TCaDTNb5qtuAOclVq9WorzcyybVR1tCG7G8nskM/HszBrqN5AICHbhzMBIl6hJ+nE/7vzuFwUilw5oIWH2xMgsHIBIVsF5MkIjvz24kL2HBxna27pgxCfKS/xBFRbxLo44Kn7oiGg0KGU2fKsHZbGkyc1UE2ikkSkR05ml6Cz39OBwDcGN8f00b3kzgi6o0GBbrjsdlRkAkCDiYX4ptfslgHiWwSkyQiO5GWU4FVm5MhisCE6ADMuY6VtEk6wwZ6Y/6sCADAjsO52J54XuKIiNqPSRKRHcgprMb735+CwWjCiEHeuH9GeJfVmiHqqHFDA/CnSQMBAN/+egb7TuZLHBFR+zBJIrJxxRV1ePfbk2jQGxHezx2P3hoJeScLqBF1lRlxQZgZFwQA+HR7Go5nlkgcEVHb8Z2UyIZV1ejw9tcnoK3Vo5+vC568PRpKRdsvuSbqCXMnhmLcUH+IIvDhpmRk5FZKHRJRmzBJIrJRdQ0GvPPNSZRUNsDHXY3/+9MwOKlZ+oysjyAIeHBmBIaFeqHRYMJ7351CbnGN1GERXROTJCIbZDCasGKD+YNG4+yAZ+4cDjcXldRhEV2RXCbDo7OjMCjQDfU6A9755gTKtQ1Sh0V0VUySiGzQV7szkXa+EioHOZ6+Yxh8PZykDonomlRKOZ6aG42+Ps6oqtFj+YbT0DcapQ6L6IqYJBHZmD3HL2DPsQsQAPz55kj093eVOiSiNnNSK7Ho9mi4OCqRU1iNT7alsoYSWS0mSUQ2JC2nAut3ZgAA5lw/AMMHeUscEVH7+bg74i+3RUEuE3AotRg/HsyROiSiVjFJIrIRxZX1WLkxCUaTiLghfpg1pr/UIRF1WHiQB+6ZFgYA2LD3LI5nsDQAWR8mSUQ2oF5nwPLvT6GmvhHB/q6YPzOCxSLJ5k0c0ReTRvYFAHy0NQV5vOKNrAyTJCIrZxJFrN6SggsltXBzdsCTt0fDQclaSGQf7poyCBFB7tDpjXj/+1OortNLHRKRBZMkIiv3w96zOJFVCoVchiduHwoPV17qT/ZDIZfh8duGwttNjdKqBnywMQkGo0nqsIgAMEkismoJKYWWSa0PzgxHaB83iSMi6noujko8NTcaKgc50s5X4qtdmVKHRASASRKR1cou0GLttjQA5vWvxkYFSBwRUffp6+OCP98cCQFNZS7ypA6JiEkSkTWqrNFhxYbTaDSYEB3qhbnXh0odElG3Gz7IG3OuHwAAWL8rE6k5FRJHRL0dkyQiK2MwmvDfDadRUa1DgJcTFt4cCZmMV7JR7zBrTH/EDfGD0SRi5Q+nUVpZL3VI1IsxSSKyMt/9egZn8rVwUimw6PZoLlpLvYogCJg/MwLB/q6obTDgw83JnMhNkmGSRGRFjmeUYMfhXADAwzcOhp8n12Sj3sdBKcfjs6PgpFLgbL4W3/16RuqQqJdikkRkJUqr6rHmx1QAwPTR/TAizEfiiIik4+3uiIduHAwA2HE4FycySyWOiHojJklEVsBgNGHVpmTU6QwICdBg7kRO1CYaGeaDqTGBAIA1P6agrKpB4oiot2GSRGQFNvx2FmfytXBUKfDorZFQyHlqEgHAnyYNvGR+EgtNUs/iOzGRxE5klWL7ofMAgIdmDYaPu6PEERFZD4VchkdnR8FRJceZC1ps2HtW6pCoF2GSRCShcm0D1mxNAQBMHRWIUeGch0R0OV93R8yfaZ6ftD3xPE5mcX4S9QwmSUQSMRhN+HBTMmobDOjv74o7Jg2UOiQiqxUT4YspI5vmJ6WiXMv5SdT9mCQRSeSHfWeRdaEKjio5HpsdBaWCpyPR1fxp8kD093NFTX0jVm1OhtHE+UnUvfiuTCSBU2fK8FOCeR7S/JmD4ct5SETXpFTI8OjsSKgd5MjMq8LGfdlSh0R2jkkSUQ8r1zbg44vzkCaP7IuYCF+JIyKyHX4eTnhwZgQA4MeDOTh9tkziiMieMUki6kFGkwmrNiejpr4RQX4uuHMy5yERtVfsYD9MGtEXALB6SwoqqnUSR0T2ikkSUQ/alnAemXlVUDs0zUOSSx0SkU2aN2UggnxdUFPfiE+2pUIURalDIjvEJImoh+QUVmPz7+Y5FPdMC4OfB9dlI+oopUKOP98aCaVChuTscvx6/ILUIZEdYpJE1AMaDSZ8/GMKjCYRI8N8MDbKX+qQiGxegJcz5l5vXsLn6z1ZKKqokzgisjdMkoh6wMZ9Z3GhpBauTkrcPyMcgiBIHRKRXZgSE4iIIHfoG034eGsKTCYOu1HXYZJE1M0yciuxPdF8uf+DMyKgcXKQOCIi+yETBDx042CoHczLlvyUmCN1SGRHrDZJMplMeP/99zFhwgQMHz4cCxYsQG5ubqv7Ll++HOHh4a3+PP/885b95s+f3+L2++67r6eeEvVCDXoD1vyYAhHAuCh/jAjjsiNEXc3bzRF3TR0EANi4Lxu5xTUSR0T2QiF1AFeycuVKrF+/Hq+//jr8/f3x5ptv4pFHHsGWLVvg4ND8m/hDDz2EefPmNdu2du1afPXVV3jwwQct29LT0/HSSy9h6tSplm1KpbJbnwf1bv/blYmSygZ4alS4a2qY1OEQ2a3xQwNwPKMUJ7JKsXpLCl5+OFbqkMgOWGVPkl6vxyeffIJFixZh4sSJiIiIwLvvvovCwkLs2LGjxf7Ozs7w8fGx/JSUlODzzz/Hiy++iPDwcABAWVkZysrKMGzYsGb7uru79/Czo97iaFoRfjlmvuLmoVmD4aS22u8kRDZPEAQ8MDMCLo5K5JXUYOPes1KHRHbAKpOktLQ01NbWIj4+3rJNo9FgyJAhOHz48DXvv2TJEsTExOC2226zbEtPT4cgCAgJCemWmIkuVVvfiPe/PgEAmDIqEEOCPaUNiKgXcHN2wP03mL8Ybz14DmnnyiWOiGydVX61LSwsBAAEBAQ02+7r62u57Ur27NmD48ePY+PGjc22Z2RkwNXVFUuWLMH+/fvh5OSEGTNm4PHHH28xfNdeii5emFQulzX7l2zPxz+moFzbgAAvJ8ybOqjLXyPU/Xge2qYxUf44kVWKA0mFePerY3hlQRwXj7ZR1nAOWmWSVF9fDwAtkheVSoWqqqqr3nft2rWYNGkSBg8e3Gx7RkYGdDodoqOjMX/+fKSmpmLZsmXIz8/HsmXLOhyrTCbAw8O5w/e/Go2Gi57aot9PXsCB04WQCcAz94yCv69G6pCoE3ge2p4n541E+pu/IL+0Fhv2ZuPROdFSh0SdIOU5aJVJklqtBmCem9T0fwDQ6XRwdLzyHys/Px+JiYn46KOPWty2ZMkSPPfcc3BzcwMAhIWFQalU4umnn8bixYvh7e3doVhNJhFabdcWMJPLZdBoHKHV1sNoNHXpsal7VVbr8N9vTwIA5k4JQ4CHIyoqaiWOijqC56Fte+TmIXjji2P4cX82Ivu7I2qAl9QhUTt15zmo0Ti2qYfKKpOkpmG24uJiBAUFWbYXFxdbJmK3ZteuXfD09MS4ceNa3KZQKCwJUpNBg8yXjBYWFnY4SQIAg6F73kCNRlO3HZu6niiK+HhrimXx2nnTwlFTXc82tHE8D21TZLAnZo0NxrYD57B6SwpeeTgWTmpezWyLpDwHrXKgNiIiAi4uLkhMTLRs02q1SElJwejRo694vyNHjiA2NhYKRcvc77777mtWMwkATp8+DaVSieDg4C6LnXqv/acLcepMGRRyAY/eGsV5EEQSm39TJPw8HFFRrcNXuzOlDodskFW+izs4OODee+/FW2+9hd27dyMtLQ1PP/00/P39MX36dBiNRpSUlKChoaHZ/VJSUhAREdHqMW+44QZs2rQJX331FXJzc7Ft2zYsW7YMDz/8MFxcXHriaZEd09bq8fUv5jfhW8eHINCXrykiqalVCiy4JRICzF9iUnm1G7WTVQ63AcCiRYtgMBjwwgsvoKGhAaNHj8aaNWugVCqRl5eHKVOmYOnSpZgzZ47lPiUlJVese3TvvfdCEASsW7cOr732Gnx8fPDggw9i4cKFPfSMyJ7975dM1DYY0M/XBTfEBl37DkTUI8L6uWPiyL7Yc+wCPvs5HUseioWDUi51WGQjBFEUuRpgJxiNJpSXd+3EXIVCBg8PZ1RU1HIuhA1IOluGd745CQHACw/EICRAwza0A2xD23Zp+2lr9Hjh4wRU1uhxY3x/3H59qNThURt05zno6encponbVjncRmQrdHojPv85HYB5NfKQAF7uT2RtnNQK3DPNfNHP9sTzyOPabtRGTJKIOmHT/myUVpnXZrttwgCpwyGiKxgV7oMRg7xhNIn4dHsaTCYOotC1MUki6qCcwmrsOJQLALh3WjgcVVY7xY+IANwzLQxqBznO5mux5/gFqcMhG8AkiagDTCYRn21Pg0kUERPhi+GDOl5ni4h6hqdGbZmP9P1vZ1BRrZM4IrJ2TJKIOmD30TycK6yGo0qBu6cOkjocImqjSSP6IrSPBg16I77cmSF1OGTlmCQRtVNZVQM27D0LALhjUijcXVQSR0REbSWTCXhgRgTkMgHHMkpwNL1E6pDIijFJImoHURSxbkc6dI1GDAp0w3XD+kgdEhG1U6CvC2bEmeuZfbkzHfU6g8QRkbVikkTUDkfSS3DqTBnkF7+NygRB6pCIqANuHhsMXw9HVNbo8f1vZ6QOh6wUkySiNqptaLTMYbgxvj/6eDtLHBERdZSDUo77bzDXTtpz7AKyLlRJHBFZIyZJRG303a9noK3Vw9/TCTfG95c6HCLqpCHBnhgX5Q8RwGfb02AwsrI6NcckiagNMnIr8duJfADAAzPCoVRw7Scie/CnyQPh4qjEhZJabE88L3U4ZGWYJBFdg9Fkwrod5qVHrhsWgPAgD4kjIqKu4urkgLummMt4bDlwDqVV9RJHRNaESRLRNfx6PB8XSmrhrFZg7sSBUodDRF1sTKQfIoLc0Wgw4ZtfsqQOh6wIkySiq9DW6fHDxZpIc64PhYujUuKIiKirCYKAu6eGQRDMV7CmnCuXOiSyEkySiK7ih71nUaczoJ+vC65nTSQiuxXo64LJIwIBAF/tyuQkbgLAJInoinIKq7H34mTte6aFQSZjTSQie3brhBDzJO7SWi6ASwCYJBG1ShRFfLkzAyKAMUP8ENbPXeqQOkU0mWDIT0VjVgIM+akQTfyWTF3Dnl5bLo5KzLl+AABg475saGv1EkdEUlNIHQCRNUpILkLWhSqolHLcMcm2J2s3Zh+B7sCXEGsrLNsEZw+oxt4DZUiMhJGRrbPH19Z10X3w6/ELOF9Ugw17z+DBmYOlDokkxJ4kosvU6wz45lfzFS43je0PD1fbXcC2MfsIGnauaPYhBgBibQUadq5AY/YRiSIjW2evry2ZTMA908IAAPtOFiC7QCtxRCQlJklEl9l64ByqavTwdXfE9NFBUofTYaLJBN2BL6+6j+7AepseHiFp2Ptra1CgO8ZE+kEEsH5nBkyiKHVIJBEmSUSXKCyvw47DuQCAeVMHQamw3VPEWJje4lv+5cTachgL03soIrIXveG1dcfEgVAp5TiTr8XBpEKpwyGJ2O4nAFE3+N/uTBhNIoYO8MKwUC+pw+kUsa5tC3a2dT+iJr3hteXhqsLN44IBmNdtrNcZpA2IJMEkieiiE1mlOHWmDHKZgLumDoIg2PYl/4KTW5fuR9Skt7y2psX0g5+HI6pq9diy/5zU4ZAEmCQRAWg0mPC/XZkAgOmj+8Hf00niiDpP7h8Owfnq68wJzp6Q+4f3UERkL3rLa0upkOGuqeZ13XYeyUVBWa3EEVFPY5JEBGDH4fMorqyHm7MDbhobLHU4XUKQyaAae89V91GNvRuCjG8D1D696bUVHeqN6FAvGE0ivtqVCZGTuHsV238FE3VSRbUOWw/kAADumBQKR5X9lA9ThsRAPe2JFt/6BWdPqKc9YbO1bEh6vem1ddeUQVDIBSRll+NEVqnU4VAPsp9PA6IO+vbXLOgajQjtq0F8pL/U4XQ5ZUgMFP1Hmq9IqquC4ORmHi6xg2/5JK3e8try83TC9NFB2JaQg//tzkRUiJdNX/lKbcckiXq17AItEpKLIMC8PputT9a+EkEmg6IPKwdT1+str62bxvbH/qQClFQ2YM+xPEyPtd0aatR2TIWp1xJFEd/uMVfWHhPpj2B/jcQREZG1UjsocNsE87puWw6cQ21Do8QRUU9gkkS91qkzZUg7XwmFXIbbrguROhwisnLjhvqjr7czahsM+PFgjtThUA9gkkS9ktFkwre/ngEATI0JhLebo8QREZG1k8tkmDsxFACw60geSqvqJY6IuhuTJOqV9p8uRH5pLZzVCtwU31/qcIjIRkSHeiEiyB0Gowk/7M2WOhzqZkySqNfR6Y34Yd9ZAMDNY4PhpFZKHBER2QpBEHDHpIEAgITkQuQUVkscEXUnJknU6+w4fB5VNXp4u6kxaWSg1OEQkY0JCdAgbogfRADf7MligUk7xiSJehVtrR7bEs8DAOZcP4C1ToioQ+ZcNwAKuYDUnAokZ5dLHQ51E35CUK+yeX82dHojgv1dETvYT+pwiMhG+bg7YvLFnuhv9pyBycTeJHvEJIl6jcLyOvx2Ih8AcMekgZDZaeFIIuoZN40NhpNKgbySGhxIKpQ6HOoGTJKo1/j+1zMwmkREh3phcP+rr2BORHQtLo5K3DjWfHXsD/vOQt9olDgi6mpMkqhXyMqrwtGMEggCcMfFOidERJ01dVQgvDQqVFTrsPNIrtThUBdjkkR2TxRFfHNx+ZEJ0QHo6+MicUREZC+UCjnmXGf+4rUtIQfVdXqJI6KuxCSJ7N6xjBJkXaiCg0KGW8cPkDocIrIzcZF+CPJ1Qb3OiC37z0kdDnUhJklk1wxGE767uPzI9NggeLiqJI6IiOyNTBBwx2Rzgck9xy+gqKJO4oioqzBJIru292Q+iirq4eqkxMy4IKnDISI7FRnsiagBnjCaRGz47azU4VAXYZJEdqtBb8Dm381rK906PgSOKoXEERGRPbtj4kAIAA6nFeNsvlbqcKgLMEkiu7X7aB60dY3w9XDEdcP6SB0OEdm5fr4uGBvlDwDYuI+9SfaASRLZpboGA7ZfXH7k1vEhUMj5Uiei7nfL+BDIZQKSssuRkVspdTjUSfzkILu04/B51DYY0MfbGXFcfoSIeoiPuyMmRAcAAH7Ye5aL39o4Jklkd2rqG7HjsLmo2+zxIZDJuPwIEfWcm8YGQyEXkJ5bidScCqnDoU5gkkR2Z3vieTTojQjydcHIcB+pwyGiXsZTo8bE4X0BmJcrYW+S7WKSRHalqlaPXUcv9iJNGMBFbIlIEjfG94eDQoYzF7Q4fbZM6nCog5gkkV3ZdjAH+kYTQgI0GDbQS+pwiKiXcnNRYfKoQADAD3uz2Ztko5gkkd2oqNZhz/ELAIDbrguBwF4kIpLQzLggqBzkyCmqxrGMUqnDoQ5gkkR2Y+uBczAYTQgLdENksKfU4RBRL+fq5IBpMf0AABt/PwsTe5NsDpMksgullfXYezIfAHDbdQPYi0REVuGG2H5wVClwoaQWh1OLpQ6H2olJEtmFzQfOwWgSMSTYA+FBHlKHQ0QEAHBWKzEjtqk3KRtGk0niiKg9mCSRzSsqr8OB04UAgNsmDJA4GiKi5qbG9IOLoxJF5XVISC6SOhxqByZJZPM27c+GSRQRHeqF0L5uUodDRNSMo0qBmWOCAACbfs+GwcjeJFvBJIls2oXSWiRe/GbGXiQislaTRwZC4+yA0qoG/H66QOpwqI2YJJFN27TvLEQAo8J80N/fVepwiIhapVLKcWN8fwDAlv3n0GgwShwRtQWTJLJZ54uqcSS9BAKAWyeESB0OEdFVTRzeBx6uKlRU6/DbiXypw6E2YJJENmvjvmwAQOwQPwT6uEgcDRHR1SkVctw8NhgAsPVgDnSN7E2ydkySyCZlF2hxIqsUggDcMi5Y6nCIiNpkfHQAvN3U0NbqsefYBanDoWvosiRJp9NBr9d31eGIrmrrgXMAgPhIfwR4OUsbDBFRGynkMktv0s+HzkPP3iSrpujoHRMTE7F7924cO3YMZ86cQUNDAwBArVYjNDQUI0aMwNSpUxEXF9dlwRIBQF5xDY5nlkIALBMhiYhsRXyUPzbvz0aZVod9pwow5eJCuGR92pUkNTY24uuvv8batWtx4cIFuLm5ITIyEjfffDPc3NwgiiK0Wi3y8vKwefNmrFu3Dn369MFDDz2EO++8E0qlsrueB/UiWw+eAwDERPiyF4mIbI5CLsPMMf3xxY4MbE/MwfXD+0Ah5+wXa9SuJGn69OlobGzE7NmzMXPmTERGRl51/6SkJGzfvh0ffvghPvnkE/zyyy+dCpaooOyP9Y9uuthlTURkayZEB2DL/nMo0+pwMKkQE4b1kTokakW7kqQ///nPmDNnDhwcHNq0f1RUFKKiorBo0SJs2LChQwESXWpbQg5EAMMHeqOfL69oIyLbpFTIMSMuCF//koUfE3Iwdqg/5DL2JlmbdrXIvHnzmiVIsbGx+O233655PwcHB8ybN6/90RFdorSyHgeTzNW12YtERLZu4vC+cHFUorii3tJDTtalU2mrVquFVqu94u3Jycn48ssvO/MQRBbbEs/DJIqIDPbAgD4aqcMhIuoUlYMc00b3A2Cum2QSRYkjosu1O0k6evQotm/fjtzcXACAIAhX3PfMmTP4f//v/3U8OqKLKqp1+P2UuUIte5GIyF5MGRkIR5UC+aW1OJ5RKnU4dJl2lwBISEjA8uXLIQgCBEHAihUrcODAAYSHhyM8PBwRERFwd3cHABQXF8PJyamrY6Ze6OdD52EwiggLdEN4kIfU4RARdQkntQJTRgVi64Fz2HrgHEaGeV+184F6VruTpL/85S+YNWsWkpKS8Oyzz0KpVCIhIcEyMVsQBPj4+MDf3x9paWmsk0Sdpq3T49fj5sq0N7G6NhHZmWkxgdh5OBc5RdU4fbYc0aFeUodEF3WomGRISAhCQkLw+eefY+HChZg2bRpqamqQlpaG9PR0pKeno6CgALfffjsee+yxDgVmMpmwYsUKfPvtt6iursbo0aPx4osvol+/fq3uv3nzZjz77LMttu/evRuBgeZCXT/99BOWL1+OvLw8DBgwAM899xzi4+M7FB/1nJ2Hc6E3mBAS4IrIYE/LdpNoQlZlNrQ6LTQqDQa6h0Am8OoQIrJOV3rPcnVywKQRfbH90HlsPXAOQwd4sjfJSnS44jYAfPvtt5b/u7i4ICYmBjExMZ0OCgBWrlyJ9evX4/XXX4e/vz/efPNNPPLII9iyZUurJQjS09MRGxuLd955p9l2T0/zh2pCQgKeffZZLF68GOPGjcN3332HhQsXYuPGjQgNDe2SmKnr1TY0YvfRPADATfHBljeOE8Wn8W3mZlTqqiz7uqvccMegWzDcd6gksRIRXcm13rOmx/bDrqN5yLpQhfTzlYjoz2kF1sAqv3br9Xp88sknWLRoESZOnIiIiAi8++67KCwsxI4dO1q9T0ZGBsLDw+Hj49PsRy6XAwBWr16NqVOn4v7770doaCiee+45REZG4rPPPuvJp0bttPtoHhr0RgT6OGPYIG8A5jeb1Unrmr3ZAEClrgqrk9bhRPFpKUIlImpVW96z3F1UuG5YAABgy8W1KUl6VpkkpaWloba2ttlQmEajwZAhQ3D48OFW75Oenn7FHiGTyYRjx461GFqLi4u74vFIevU6A3YeNl9FedPYYMgEASbRhG8zN1/1ft9lboZJNPVEiEREV9We96yZcf0hlwlIzalA1oWqq96Heka7httmzZqFhQsXYtasWW2uuq3X67FlyxasWbMG27Zta9N9CgsLAQABAQHNtvv6+lpuu1RVVRWKiopw5MgRrF+/HhUVFYiOjsazzz6LkJAQaLVa1NXVwd/fv03Hay+FomtzTfnFNXzkvXwtn72H81HbYIC/pxPGRPpDJhOQXn62xbexy1XoqpBdfQ7hngN7KNKW2Ia2j21o26yl/dr1nuU1EOOjA/DbiXz8eDAHz8wb3jNBWilraMN2JUm33XYbli5dildffRWTJ09GfHw8IiMjERgYCEdHRwBAXV0d8vLykJSUhAMHDmDPnj1QKpV4+OGH2/w49fX1ANAiEVOpVKiqavliy8zMBACIooilS5eioaEBH3zwAe6++25s2bIFBoPhisfT6XRt/wO0QiYT4OHRPYusajSO3XJcW6BrNOLnQ+ZepDunhcPLy7wEiUGrb9P9DQp9t7VLe/TmNrQXbEPbJnX7tfc96+6Zg7HvZD5OZpWivLYRoYHu3RugDZCyDduVJC1YsAB33XUXvvvuO/zwww/YtGmTZSJt09wfo9EIwJywDBo0CE8++STmzp0LF5e2r7OlVqsBmHuhmv4PADqdzpKMXSomJgYHDx6Eh4eHJZ4VK1Zg4sSJ2LBhA+644w7L8S51peO1h8kkQqut69QxLieXy6DROEKrrYfR2DuHjXYezkVltQ7ebmoMG+CBiopaAIDC0LYeTIXBwXIfKbANbR/b0LZZS/u19z3LUS4gbog/DiYX4svtqXjy9uhujtB6dWcbajSObeqhavfVbS4uLnjwwQfx4IMPIi8vD8ePH8fZs2dRWVkJAHB3d8eAAQMwfPjwK16ufy1Nw2zFxcUICgqybC8uLkZ4eHir92m6iq2Jo6MjAgMDUVRUBHd3dzg5OaG4uPnaOMXFxfDz8+tQjJcyGLrnBDQaTd12bGtmMJqw9eLExZlj+gPiH3/jENdguKvcrtp97aFyQ4hrsFX87XprG9oTtqFtk7r9OvKeNWtMEA4mF+JIajFyCqvR11v6XnEpSdmGnSoBEBgYaKlB1JUiIiLg4uKCxMRES5Kk1WqRkpKCe++9t8X+X3/9Nd555x3s2bPHUuG7pqYG586dw9y5cyEIAkaOHIlDhw5ZepUAIDExsctKFlDXOZBUiIpqHdxdHDB+aPN5ZDJBhjsG3YLVSeuueP+5g25hvSQisgodec/q6+OCUWE+OJpRgm0Hc7Dg5iE9ESq1ol2fJGIPLb7n4OCAe++9F2+99RZ2796NtLQ0PP300/D398f06dNhNBpRUlKChoYGAMB1110Hk8mExYsXIzMzE6dPn8aTTz4JT09PzJkzBwAwf/58/Pjjj1i7di3OnDmDZcuWITU1FQ888ECPPCdqG5MoYnvieQDA9NFBUCrkLfYZ7jsUC6Lug7vKrdl2D5UbFkTdxzpJRGRVOvKedePY/gCAQ6lFKNc29Eic1FKbe5I2btyIV199FbNmzcLcuXMxdGj3fhAtWrQIBoMBL7zwAhoaGjB69GisWbMGSqUSeXl5mDJlCpYuXYo5c+YgICAAn376Kd5++23cddddEEUR48aNw+effw6VSgUAGD9+PF577TWsXLkS7777LgYOHIgPP/yQhSStzMmsUhSW18FRpcD1w/tccb/hvkMR7RPJittEZBPa+54V7K9BRJA70s5XYsfhXMybMqiHIyYAEMQ2dg/V19dj165dOHToEA4dOgSVSoW5c+filltusSxo2xsZjSaUl3ftBGGFQgYPD2dUVNT2urkQr39xFBl5VZg5Jgh3TJTuEv7O6s1taC/YhrbNHtrv1Jky/Ofbk1A5yPH242PhpFZKHVKP6s429PR0btPE7TZ/7XZ0dMTNN9+MV155BT///DM+/vhjeHp6Yu3atZ0KlKjJmfwqZORVQS4TMHVUxyb9ExHZi6EDPNHXxxk6vRG/nciXOpxeqcNjE76+vrjpppvw9NNPd2U81Is1zUWKj/SHh6tK4miIiKQlCAJmxJovXtp5JBcGlqLocZ2ewJGZmYlNmzZh27ZtSEtLQ2NjY1fERb1MUUUdjqWXAABuiGUvEhERAMQN8YO7iwMqa/RISC6SOpxep1MlAD7//HO8/vrrMJnM2a0gCJDL5QgJCUFYWBjCw8MRHh6O66+/vkuCJfu141AuRADRoV7o69P2wqNERPZMIZdhWkw/fPvrGfx86DzGDfW3FE2m7tepJOnjjz/GkCFD8MYbb0CpVOLs2bNIS0tDeno6UlJSsH37dphMJqSmpnZVvGSHtHV6/H66AAAsXctERGR2/fC+2HLgHC6U1uL02TJEh3pLHVKv0akkqaamBk888YTlMvqgoCBMnDjRcrtOp0NGRkanAiT798vRPDQaTAj2d0V4kLvU4RARWRUntbkkys+HcrE98TyTpB7UqTlJo0aNQn7+lWfcq1Sqbq+nRLZN12jEL8cuAABmxAWxG5mIqBXTYvpBLhOQdr4S2QVaqcPpNdqVJH366afYv38/iorMk8eefvppbNiwwfI7UXvtP12AmvpGeLupMSrcR+pwiIiskqdGjdjB5rVGm64Epu7XruG2N954w/J/FxcXhIaGQqPR4LbbbsNTTz2FqVOnwsvLq8uDJPtkMonYcSgXAHBDbBDkMlbLJiK6khlxFxe+TS9GSWU9fNwdpQ7J7rUrSTp69CgyMzORkZGB9PR0ZGRkoLS0FJWVlfj3v/+Nl156CX5+fggPD0dERITl6jYu/UGtOZZRguLKejirFRg/NEDqcIiIrFo/XxdEhXgiKbscOw7n4p5pYVKHZPfalSQ5OTlh2LBhGDZsWLPtJSUllqSp6SchIQE6nQ6CIPDqNmpBFEVsP2TuMp40MhAqh5YL2RIRUXM3xAUhKbsc+07l49bxIXBx7F1LlfS0Tl3d1sTHxwc+Pj4YP368ZZvJZMK5c+d4dRu1KjOvCmfztVDIZZgyKlDqcIiIbMKQ/h4I8nXB+eIa7DmWh5vHhUgdkl3rtkkgMpkMAwYMwIwZM7rrIciGNU08HDfUH27ODhJHQ0RkGwRBwIw4cz253Ufz0GgwShyRfeNMWepx+aW1OJFVCgHmCdtERNR2MRG+8NKooK1rxP6kQqnDsWtMkqjH/XxxLtLwQd7w93SSOBoiItuikMswbbT5C+bPh3JhEkWJI7JfTJKoR1XW6HAw2fzNZ2Zcf4mjISKyTdcNC4CTSoGi8jqcyCyVOhy7xSSJetTuo3kwGEUM7OuGgYFuUodDRGST1A4KTBrZFwAsVwpT12OSRD1G32jEbyfMy9jcENtP4miIiGzblFGBkMsEZOVVcamSbsIkiXpMQkqRZQmSEYO4BAkRUWe4u6gQO9gXALDrSK7E0dgnJknUI0RRtJzEk0cGQibjQrZERJ01NcbcK38otRhVNTqJo7E/TJKoR6Sdr0ReSS0clDJcN4xLkBARdYWQAA0G9nWD0SRiz/ELUodjd5gkUY9o6kUaFxUAJzXL6BMRdZWpMeZVC349fgGNBpPE0dgXJknU7Yor6y2XqDadzERE1DVGhvnAw9VcXPJQapHU4dgVJknU7X45mgcRQFSIJwK8nKUOh4jIrijkMky+WA5g19E8iCwu2WWYJFG3atAbsO9UAYA/JhgSEVHXum5YHygVMuQUViPrQpXU4dgNJknUrfafLkS9zgA/TydEDfCUOhwiIrvk6uSAMUP8AAA7j+RJHI39YJJE3cYkith11HyyTh0VCJnAy/6JiLrLtIu99cfSS1CubZA4GvvAJIm6TXJ2OYrK6+CokmNslL/U4RAR2bVAXxdEBLnDJIr45RjLAXQFJknUbXZevOx/QnQfOKoUEkdDRGT/mnqTfjtxAbpGo8TR2D4mSdQtCspqkXS2HAKAyaN42T8RUU8YNtAb3m5q1DYYkJBcKHU4No9JEnWLprlIwwZ6w9fdUeJoiIh6B5lMwJSLX0x3HWE5gM5ikkRdrq6hEQdOm7/BTGPxSCKiHjUhOgAqpRwXSmuRllMhdTg2jUkSdbl9pwqgazSir48zIvp7SB0OEVGv4qRWYtxQ88UyLAfQOUySqEuZTCJ2X3LZv8DL/omIelzTkNvJrFIUV9RJHI3tYpJEXepEVilKqxrgrFZgTCQv+ycikkKAlzOiBnhCBLD7KMsBdBSTJOpSuy5e9n/98L5QKeUSR0NE1Hs1lQP4/XQ+6nUGiaOxTUySqMvkFtcg7XwlZIJgWWyRiIikERniCX9PJ9TrjDiQxHIAHcEkibpMUy/SyHAfeGrUEkdDRNS7yYRLywHkwsRyAO3GJIm6RG1DIxJTigCYJ2wTEZH0xg31h6NKgaKKeqScK5c6HJvDJIm6xP7ThdAbTOjn64JBgW5Sh0NERADUDgqMu7h25h6u59ZuTJKo00RRxJ7j5pNv0oi+vOyfiMiKTBxhniN6IqsU5doGiaOxLUySqNNScypQVF4HtYMcYyL9pA6HiIgu0cfbGRFB7hBF4LcT+VKHY1OYJFGnNfUixUf5Q+2gkDgaIiK6XFNv0t5T+TAYTRJHYzuYJFGnVFTrcDyjFIB5qI2IiKzPyDAfaJwdUFWjx4nMUqnDsRlMkqhT9p7Mh0kUERbohkAflx59bNFkgiE/FY1ZCTDkp0I08dsREVkvKd+zFHIZrhvWBwDwyzGu59ZWHBuhDjOaTNh70jy+PbGHi0c2Zh+B7sCXEGv/WOFacPaAauw9UIbE9GgsRETXYg3vWROH98GPB88h7XwlCspqEeDl3COPa8vYk0QddiKzDBXVOrg6KTEqzLfHHrcx+wgadq5o9mYDAGJtBRp2rkBj9pEei4WI6Fqs5T3LU6PGsFBvAH/MJaWrY5JEHfbrcXOX7YToPlAqeualJJpM0B348qr76A6s59AbEVkFa3vPmnSx13//6ULo9MYeeUxbxiSJOqSovA7J5yogwNyF21OMhektvo1dTqwth7EwvYciIiK6Mmt7z4oM8YSPuxr1OgMSU4t65DFtGZMk6pCmrtqhoV7wdnfssccV66q6dD8iou5kbe9ZMkGwlAPgkNu1MUmidtM3GrH/dAGAnr/sX3Bq25Inbd2PiKg7WeN71vihAVDIZcgprEZ2gbbHHtcWMUmidjucVozaBgO8NGoMHeDVo48t9w+H4Oxx1X0EZ0/I/cN7KCIioiuzxvcsVycHjI7wAcD13K6FSRK12y8XT6qJI/pAJuvZddoEmQyqsfdcdR/V2LshyPjSJiLpWet71qQRgQCAxNQi1NQ39uhj2xJ+klC7NHXPymUCJkT33ITtSylDYqCe9kSLb2eCsyfU055gnSQisirW+J4V2leDfr4uaDSYcODi9AlqicUkqV32XLzsPybCFxpnB8niUIbEQNF/pPnKkboqCE5u5m5t9iARkRWytvcsQRAwaURffP5zOvacyMe00f0gCD07MmALmCRRm9U1GJCQYr5k1BrWaRNkMij6DJY6DCKiNrG296wxkX74Zk8WisrrkJpTgSHBnlKHZHX4tZva7EBSAfSNJvT1dsagQF49RkRky9QOCsRH+QNgOYArYZJEbSKKouUkmjSyL7tliYjsQNOowPGMUlRU6ySOxvowSaI2ST9fiYKyOqiUcsRH+ksdDhERdYFAHxeEBbrBJIqWBcvpD0ySqE2aepHiI/3gqOJUNiIiezHx4npue0/mw8h1L5thkkTXVFWrx7GMEgCwlLMnIiL7MCrMF65OSlRU63Ayq0zqcKwKkyS6pgNJBTCaRAzoo0GQn6vU4RARURdSKmQYHx0AABxyuwyTJLoqURSx96S50Nh1w6QpHklERN3ruovFgU+fLUO5tkHiaKwHkyS6qozcShSV10HlIEfsYF+pwyEiom7g5+mE8H7uEEXgd1bgtmCSRFfV1IsUN9gXagdO2CYisldNowX7ThbAJIoSR2MdmCTRFdU1NOJIejEAYAKH2oiI7NqocB84qRQo0zYg9VyF1OFYBSZJdEUJKUVoNJgQ6OOMAQEaqcMhIqJu5HBJHTxO4DZjkkStEkURe0+YT5IJw/qwwjYRUS8wYZj5KrdjGSXQ1ukljkZ6TJKoVTlF1ThfXAOFXMYK20REvUSQnyuC/V1hNIk4mFQodTiSY5JErWqasD0q3AcujkqJoyEiop7SNIF778l8iL18AjeTJGpBpzciMcX8DeK6iwXGiIiod4gb4gcHpQwFZXU4c0ErdTiSYpJELRxJL0a9zghfd0eE9/eQOhwiIupBjioFYiP8AHACt9UmSSaTCe+//z4mTJiA4cOHY8GCBcjNzb3i/pmZmVi4cCHi4uIQHx+PRYsWIT//j8Y1Go2Ijo5GeHh4s5/ly5f3xNOxKb+dbJqwHQAZJ2wTEfU6TUNuh9KKUK8zSByNdKw2SVq5ciXWr1+PV155Bf/73/9gMpnwyCOPQK9vOdu+oqIC8+fPh1qtxrp167B69WqUl5fjkUcegU6nAwCcO3cOOp0OmzZtwu+//275eeihh3r6qVm1/NJaZOVVQSYIGBvFoTYiot4otK8GAV5O0DeakJhSJHU4krHKJEmv1+OTTz7BokWLMHHiRERERODdd99FYWEhduzY0WL/Xbt2oa6uDsuWLUNYWBiioqLw5ptv4syZMzh27BgAID09HS4uLoiIiICPj4/lx9nZuaefnlXbd8rcixQd6gUPV5XE0RARkRQEQWg2gbu3ssokKS0tDbW1tYiPj7ds02g0GDJkCA4fPtxi//j4eKxcuRJqtdqyTSYzPzWt1jzpLD09HaGhod0cuW0zGE3Yf/rihG1W2CYi6tXio/whlwk4V1iN80XVUocjCatcjKuw0PxBHRDQfLjH19fXctulAgMDERgY2GzbRx99BLVajdGjRwMAMjIyYDAY8PDDDyMtLQ1+fn544IEHcOutt3Y6XoWia3NNuVzW7N+eciyzBDX1jfBwVWFEuDfkMqvMoW2CVG1IXYdtaNvYfp3nqVFjVLgPDqUW4/fTBbi/r1uPPr41tKFVJkn19fUAAAcHh2bbVSoVqqqqrnn/devW4YsvvsALL7wAT09PAOaJ3SaTCYsWLYK/vz9+++03PP/882hsbMTcuXM7HKtMJsDDo3uG7DQax2457pU09SJNi+sPby/XHn1se9XTbUhdj21o29h+nXPThFAcSi3GweQiPDp3OFRKeY/HIGUbWmWS1DRsptfrmw2h6XQ6ODpe+Y8liiLee+89fPDBB3jsscdw3333WW7bunUrjEajZQ5SREQE8vPzsWbNmk4lSSaTCK22rsP3b41cLoNG4witth5Go6lLj30lJZX1OJFRAgCIDfdGRUVtjzyuvZKiDalrsQ1tG9uvawT5OMHbTY3SqgbsPJiNcUN77oKe7mxDjcaxTT1UVpkkNQ2zFRcXIygoyLK9uLgY4eHhrd6nsbERzz//PLZu3Yrnn38eDz74YLPbL022moSFhWHz5s2djtdg6J4T0Gg0dduxL/fb8QsQAQzu7wFPV3WPPa6968k2pO7BNrRtbL/OGx8dgI37svHrsQuIG+zX448vZRta5WBtREQEXFxckJiYaNmm1WqRkpJimWN0ucWLF2P79u14++23WyRIWq0WsbGx2LBhQ7Ptp0+fxqBBg7o8fltjMonYd8q8DAknbBMR0aXGDw2AIADpuZUoLO/akRNrZ5U9SQ4ODrj33nvx1ltvwdPTE3379sWbb74Jf39/TJ8+HUajEeXl5XB1dYVarcaGDRuwbds2LF68GLGxsSgpKbEcy9XVFRqNBmPGjMG7774LLy8v9O/fHzt27MDmzZuxatUqCZ+pdUjKLkdFtQ7OagVGhnlLHQ4REVkRT40aQwd44dSZMuw7lY87Jg6UOqQeY5U9SQCwaNEizJ07Fy+88ALuuusuyOVyrFmzBkqlEgUFBRg/fjy2bdsGwDzfCACWLVuG8ePHN/tp2ue1117DrFmz8O9//xs333wztm3bZqno3ds11cAYGxUApaLnJ+UREZF1axpl2H+6EIZeNMdLEHv7Er+dZDSaUF7etZOcFQoZPDycUVFR2+3jsFW1evztv/thNIlY8nAsAn1cuvXxeouebEPqHmxD28b261oGowl/W3kA2lo9/nJbFEaF+3b7Y3ZnG3p6Ordp4rbV9iRRzziYVAijScSAPhomSERE1CqFXIZxUf4A/igX0xswSerFRFHE/iTzhO3xPXhZJxER2Z6my/9PnSlDVW3LdVTtEZOkXux8UQ0ulNRCIZchdnD3d50SEZHt6uPtjJAADUyiiMTk3tGbxCSpF/v9tLkXaWSYN5zUSomjISIiazd+qHnI7fdeMuTGJKmXMhhNSEwpAoAeraBKRES2K3aIHxRyAXklNb1i0VsmSb3Uyawy1NQ3ws3FAZHBnlKHQ0RENsBZrcTwQT4A/hiNsGdMknqp/Rdf3GMj/SGTCRJHQ0REtqJpyC0hucjuayYxSeqFtLV6nD5bBgAYy6E2IiJqh8gQT7g5O6CmvhGnz5RJHU63YpLUCyWkFMFoEhES4Iq+3s5Sh0NERDZELpMhPrJpArd9D7kxSeqFmobaOGGbiIg6YuzFIbdTZ8qgrbPfmklMknqZ80XVyC2ugUIuIHawn9ThEBGRDQr0cUF/f1cYTaLlSml7xCSpl2kqJz98oDdcHFkbiYiIOqZppYb9djzkxiSpFzEYTUhIMSdJHGojIqLOiBviB7lMwPmiGuQW10gdTrdgktSLnD5bhuq6RmicHRA1gLWRiIio41wclRg+0BuA/fYmMUnqRZqG2uIj/SCXsemJiKhzmkYlEpIL7bJmEj8pe4nqOj1OZpUCAMZFcaiNiIg6L2qAJzROSmjrGpF0tlzqcLock6ReIvFibaT+fq4I9HWROhwiIrIDCrkMYy7WTNqfZH9DbkySeommobZxF2tbEBERdYWmIbcTmaWoqW+UOJquxSSpF8grrkFOUTXkMgFxQ1gbiYiIuk4/XxcE+brYZc0kJkm9QFMX6LCB3nB1cpA4GiIisjfj7LRmEpMkO2c0mXAw2ZzZc6iNiIi6Q1ykuWbSucJqXCixn5pJTJLsXNLZcmhr9XB1UmLoAC+pwyEiIjukcXJAdKj5M2Z/UqHE0XQdJkl2rqnrc8wQfyjkbG4iIuoeTUNuB5MKYTTZR80kfmrasZr6Rpxoqo3EoTYiIupG0aFecHFUoqpWj+Rs+6iZxCTJjh1KLYLBKJqvPPBzlTocIiKyYwq5DGMuXkHdVHbG1jFJsmMHk80v0rFR7EUiIqLuN/biqMWJrFLU6wwSR9N5TJLsVHFlPc5c0EIQgNjBrI1ERETdr7+fKwK8nNBoMOFoeonU4XQakyQ7lXCxF2lIfw94uKokjoaIiHoDQRAsy5Q0jWbYMiZJdkgURSRcrI3U9GIlIiLqCU3zktJyKlBRrZM4ms5hkmSHzhVWo7C8Dg4KGUaG+UgdDhER9SI+7o4YGOgGEbD5ZUqYJNmhpl6k4YO84ahSSBwNERH1NvEXe5MSUmx7yI1Jkp0xmkxITOVQGxERSWf0YPMyJeeLanChtFbqcDqMSZKdSc2pgLZWDxdHJaJCPKUOh4iIeiEXxz+Wwkqw4QncTJLszMEkcy/S6MG+XIaEiIgkMyby4pBbchFMoihxNB3DT1E7otMbcSzTXJcifgiH2oiISDrDB3pD7SBHmbYBWXlVUofTIUyS7MjxrBLo9EZ4u6kR2lcjdThERNSLOSjlGBVuvsLaVofcmCTZkUtrIwmCIHE0RETU2zVdQHQ4rRgGo0niaNqPSZKd0Nb9sepyfCSXISEiIukNDvKAm4sDahsMOH22TOpw2o1Jkp04nFoMo0lEf39XBHg5Sx0OERERZDIBcRfXDz2YbHuFJZkk2Ymmgl3xrI1ERERWpOlz6WRWKeoaDBJH0z5MkuxAcUUdzlzQQhCAuMG+UodDRERkEeTnggAvJzQaTDiaUSx1OO3CJMkOJFxcG2dIsCfcXFQSR0NERPQHQRAsvUkJNjbkxiTJxomiaBnnbVp5mYiIyJo0fT6l5VSgoloncTRtxyTJxp0rrEZReR0cFDKMDPOROhwiIqIWvN0dMSjQDSKAxBTb6U1ikmTjDl4s0DV8kDccVQqJoyEiImrdGMuQm+0UlmSSZMOMJhMOpZonwfGqNiIismajI3whlwk4X1yDCyU1UofTJkySbFjquQpoa/VwcVQiMsRT6nCIiIiuyMVRiaEDvAD8ccGRtWOSZMOaJmzHDvaFQs6mJCIi6xYf9cdVbiZRlDiaa+Mnq43S6Y04llEC4I9xXiIiIms2LNQLagc5yrQNyMqrkjqca2KSZKOOZ5VA12iEj7saoX00UodDRER0TQ5KOWLCzUWPbWECN5MkG5VgqY3kD0EQJI6GiIiobcZcXIT9cFoxDEaTxNFcHZMkG1RT34jk7HIAQBwLSBIRkQ2JCPKAm7MDahsMSDlXLnU4V8UkyQYdyyiB0SQi0McFfbydpQ6HiIiozWQyATER5iG3xBTrXsuNSZINOpRqHmqLG8LFbImIyPbEDTaPghzPLEGjwShxNFfGJMnGaGv1SM2pAACMHsyhNiIisj0D+mrgpVGhQW/EqTPWO+TGJMnGHEkvhigCIQGu8HV3lDocIiKidpMJAkZHmL/oN42OWCMmSTbmUEpTAUn2IhERke2KvThl5GRWKRr0BomjaR2TJBtSrm1AxsXiW6MjOB+JiIhsV38/V/h6OEJvMOFEVqnU4bSKSZINOZJmvgpgUKAbPDVqiaMhIiLqOEEQEDvY/IX/cKp1XuXGJMmGJF58EXGojYiI7EHT59nps2Woa2iUOJqWmCTZiOLKemQXaCEIsNSXICIismWBPi7o6+0Mg1HEsQzrG3JjkmQjDl+c/d9UqZSIiMgejL445HYozfqucmOSZCMOXRxq4zIkRERkT5qG3FKyK1Bdp5c4muaYJNmAgrJa5BbXQC4TMDLMR+pwiIiIuoy/pxP6+7nCJIo4ml4idTjNMEmyAU29SJEhnnBxVEocDRERUddqusrN2gpLMkmycqIoWl40TS8iIiIie9JU+y/9fCUqa3QSR/MHJklWLre4BgVldVDIZRgxiENtRERkf7zdHRHaVwMRwOE066mZxCTJyjUNtUWHesFRpZA4GiIiou4Ra4VruTFJsmIcaiMiot4iJsIXAoAzF7QoraqXOhwATJKs2tl8LUqrGqBSyjEs1FvqcIiIiLqNh6sK4UHuAKxnyI1JkhVLSDH3Ig0b6AWVg1ziaIiIiLrX6Is1kw6lMEmiqzCZRBy6mCTFca02IiLqBUaF+0AmCMgpqkZheZ3U4VhvkmQymfD+++9jwoQJGD58OBYsWIDc3Nwr7l9RUYFnnnkGo0ePRmxsLF5++WXU1zcf0/zpp58wa9YsREdHY/bs2Th48GB3P412MxoNSM74Bd9t/xgu8iQ4qgREDfCSOiwiIqJup3FywJBgDwgw4rfErdi1fx2SM36B0WiQJB6rvVxq5cqVWL9+PV5//XX4+/vjzTffxCOPPIItW7bAwaHl2mWLFi1CfX09Pv30U2i1Wvzzn/9EXV0d3njjDQBAQkICnn32WSxevBjjxo3Dd999h4ULF2Ljxo0IDQ3t6afXqiNJG7GhYD+q5IJ5QxigMWTiZFoVYqJmSxobERFRTxjgm4Ri9xP4RS7DL3nmbW5nfsScgHE9/llolT1Jer0en3zyCRYtWoSJEyciIiIC7777LgoLC7Fjx44W+x8/fhyHDh3CG2+8gcjISMTHx2PJkiXYtGkTiorMQ1arV6/G1KlTcf/99yM0NBTPPfccIiMj8dlnn/X002vVkaSNWFu0H1WXtYhWLmBt0X4cSdooSVxEREQ95UjSRuw0nUS1Qmi2vUoGST4LrTJJSktLQ21tLeLj4y3bNBoNhgwZgsOHD7fY/8iRI/Dx8WnWIxQbGwtBEHD06FGYTCYcO3as2fEAIC4urtXj9TSj0YANBfvNvwjNXxhNv28o2C9ZdyMREVF3s8bPQqscbissLAQABAQENNvu6+true1SRUVFLfZ1cHCAu7s7CgoKoNVqUVdXB39//zYdr70Uis7lmulnf/9jiK01goAqOZCV8zsiwyZ36rGoZ8jlsmb/ku1hG9o2tp/tscbPQqtMkpomXF8+90ilUqGqqqrV/Vubp6RSqaDT6dDQ0HDF4+l0nVsjRiYT4OHh3KljNBgq27xfZx+LepZG4yh1CNRJbEPbxvazHdb4WWiVSZJarQZgnpvU9H8A0Ol0cHRs+YJXq9XQ6/Uttut0Ojg5OUGlUlmOd/ntrR2vPUwmEVpt5y5TVCvc27xfRUVtpx6LeoZcLoNG4witth5Go0nqcKgD2Ia2je1ne3rys1CjcWxTL6NVJklNQ2fFxcUICgqybC8uLkZ4eHiL/f39/bFr165m2/R6PSorK+Hr6wt3d3c4OTmhuLh5cari4mL4+XW+BpHB0LkTcGD/8XA786N50vbl47AAIIpwM5n36+xjUc8yGk1sMxvHNrRtbD/bYY2fhVY5WBsREQEXFxckJiZatmm1WqSkpGD06NEt9h89ejQKCwuRk5Nj2Xbo0CEAwKhRoyAIAkaOHGnZ1iQxMRExMTHd9CzaTi5XYE7AOPMvotj8xou/zwkYB7ncKnNaIiKiTrPGz0Kr/NR1cHDAvffei7feeguenp7o27cv3nzzTfj7+2P69OkwGo0oLy+Hq6sr1Go1hg0bhpEjR+Lpp5/GSy+9hLq6Orz44ouYPXu2pado/vz5WLhwIYYMGYLrrrsO33//PVJTU/Hqq69K/GzNmmo/mOsk/bHdzQRJakMQERH1NGv7LBRE8fJ0zToYjUa888472LBhAxoaGjB69Gi8+OKLCAwMRF5eHqZMmYKlS5dizpw5AICysjK8/PLL2LdvH1QqFWbMmIHnn3/eMh8JADZu3IiVK1eisLAQAwcOxLPPPtuiLED74zShvLzr5gkZjQZk5fyOBkMl1Ap3DOw/nj1INkihkMHDwxkVFbXs6rdRbEPbxvazbd39Wejp6dymOUlWmyTZiq5OkgCe3PaAbWj72Ia2je1n+7qzDduaJFnlnCQiIiIiqTFJIiIiImoFkyQiIiKiVjBJIiIiImoFkyQiIiKiVjBJIiIiImoFkyQiIiKiVjBJIiIiImoFkyQiIiKiVrDidieJogiTqev/hHK5DEYjq8TaMrah7WMb2ja2n+3rrjaUyQQIgnDN/ZgkEREREbWCw21ERERErWCSRERERNQKJklERERErWCSRERERNQKJklERERErWCSRERERNQKJklERERErWCSRERERNQKJklERERErWCSRERERNQKJklERERErWCSRERERNQKJklERERErWCS1ANMJhPef/99TJgwAcOHD8eCBQuQm5t7xf0rKirwzDPPYPTo0YiNjcXLL7+M+vr6Zvv89NNPmDVrFqKjozF79mwcPHiwu59Gr9beNszMzMTChQsRFxeH+Ph4LFq0CPn5+ZbbjUYjoqOjER4e3uxn+fLlPfF0ep32tt/mzZtbtE14eDjy8vIs+/Ac7FntacPly5e32n7h4eF4/vnnLfvNnz+/xe333XdfTz2lXm3VqlXX/FtbxWehSN1u+fLlYlxcnLhnzx4xNTVVfOihh8Tp06eLOp2u1f3vvfde8fbbbxeTkpLEAwcOiJMmTRIXL15suf3gwYNiZGSk+Nlnn4lZWVni66+/LkZFRYlZWVk99ZR6nfa0YXl5uThu3DjxySefFNPT08XTp0+L99xzjzhz5kyxoaFBFEVRzMrKEsPCwsTU1FSxuLjY8lNTU9PTT61XaO85uGzZMvHee+9t1jbFxcWiwWAQRZHnoBTa04Y1NTUt2u6NN94Qhw8fLqalpVn2i4+PF9evX99sv4qKih58Vr3TF198IUZERIj33nvvVfezhs9CJkndTKfTiSNGjBC//PJLy7aqqioxOjpa3LJlS4v9jx07JoaFhTVr5H379onh4eFiYWGhKIqi+NBDD4lPPfVUs/vdeeed4r/+9a/ueRK9XHvb8JtvvhFHjBgh1tfXW7bl5+eLYWFh4oEDB0RRFMUff/xRHDlyZPcHT+1uP1EUxUceeUR85ZVXrnhMnoM9qyNteKnk5GQxMjJS3LBhg2VbaWmpGBYWJiYnJ3dLzNRSYWGh+Oc//1kcPny4OGPGjKsmSdbyWcjhtm6WlpaG2tpaxMfHW7ZpNBoMGTIEhw8fbrH/kSNH4OPjg9DQUMu22NhYCIKAo0ePwmQy4dixY82OBwBxcXGtHo86r71tGB8fj5UrV0KtVlu2yWTmU02r1QIA0tPTm7UxdZ/2th9w9fbhOdjzOtKGl1qyZAliYmJw2223Wbalp6dDEASEhIR0S8zUUnJyMpRKJTZv3oxhw4ZddV9r+SxUdNmRqFWFhYUAgICAgGbbfX19LbddqqioqMW+Dg4OcHd3R0FBAbRaLerq6uDv79+m41HntbcNAwMDERgY2GzbRx99BLVajdGjRwMAMjIyYDAY8PDDDyMtLQ1+fn544IEHcOutt3bTs+i92tt+VVVVKCoqwpEjR7B+/XpUVFQgOjoazz77LEJCQngOSqC9bXipPXv24Pjx49i4cWOz7RkZGXB1dcWSJUuwf/9+ODk5YcaMGXj88cfh4ODQpfGT2eTJkzF58uQ27Wstn4VMkrpZ0ySzy086lUqFqqqqVvdv7QRVqVTQ6XRoaGi44vF0Ol1XhU2XaG8bXm7dunX44osv8MILL8DT0xOAeWK3yWTCokWL4O/vj99++w3PP/88GhsbMXfu3K5/Er1Ye9svMzMTACCKIpYuXYqGhgZ88MEHuPvuu7FlyxYYDIYrHo/nYPfozDm4du1aTJo0CYMHD262PSMjAzqdDtHR0Zg/fz5SU1OxbNky5OfnY9myZV37BKjdrOWzkElSN2sactHr9c2GX3Q6HRwdHVvdX6/Xt9iu0+ng5OQElUplOd7lt7d2POq89rZhE1EU8d577+GDDz7AY4891uxKjq1bt8JoNMLZ2RkAEBERgfz8fKxZs4ZJUhdrb/vFxMTg4MGD8PDwgCAIAIAVK1Zg4sSJ2LBhA+644w7L8S7Fc7D7dPQczM/PR2JiIj766KMWty1ZsgTPPfcc3NzcAABhYWFQKpV4+umnsXjxYnh7e3fxs6D2sJbPQs5J6mZN3YXFxcXNthcXF8PPz6/F/v7+/i321ev1qKyshK+vL9zd3eHk5NTm41HntbcNAaCxsRHPPvssPvzwQzz//PP461//2ux2tVptSZCahIWFcbimG3Sk/Tw9PS0JEgA4OjoiMDAQRUVFPAcl0JE2BIBdu3bB09MT48aNa3GbQqGwJEhNBg0aBAA8D62AtXwWMknqZhEREXBxcUFiYqJlm1arRUpKimV+yqVGjx6NwsJC5OTkWLYdOnQIADBq1CgIgoCRI0datjVJTExETExMNz2L3q29bQgAixcvxvbt2/H222/jwQcfbHabVqtFbGwsNmzY0Gz76dOnLW/S1HXa235ff/014uLiUFdXZ9lWU1ODc+fOYeDAgTwHJdCRcxAwT/6NjY2FQtFy0OS+++5rVjMJMJ+DSqUSwcHBXRY7dYzVfBZ22XVydEXvvPOOGBsbK+7atatZfQ+9Xi8aDAaxuLjYcrm4yWQS582bJ952223iyZMnxYMHD4qTJk0S//73v1uOt2/fPnHw4MHiJ598ImZlZYlvvPGGGB0dzRot3ag9bfj999+LYWFh4scff9yiVkvTPk8++aQ4fvx48ddffxWzs7PFVatWiYMHDxb37t0r5dO0W+1pv/z8fDEmJkb8y1/+ImZkZIinTp0SH3zwQXHq1KmWOlc8B3tee9qwyZQpU8SVK1e2erx169aJgwcPFtevXy+eP39e/PHHH8W4uDjxnXfe6Ymn0+s999xzzUoAWOtnIZOkHmAwGMRly5aJY8aMEYcPHy4uWLBAzM3NFUVRFHNzc8WwsDDx+++/t+xfWloqPvnkk+Lw4cPFuLg48d///rflzbnJDz/8IE6bNk0cOnSoeNttt1nq71D3aE8bzp8/XwwLC2v1p2mf6upq8bXXXhOvv/56MSoqSrz11lvFnTt3Svb87F17z8GkpCRx/vz54qhRo8SRI0eKTz75pJifn9/smDwHe1Z721AURTE6Olpcv379FY/5xRdfiDNnzhSjoqLESZMmiR988IFoNBq79XmQ2eVJkrV+FgqiKIpd1y9FREREZB84J4mIiIioFUySiIiIiFrBJImIiIioFUySiIiIiFrBJImIiIioFUySiIiIiFrBJImIiIioFUySiIiIiFrBJImI6DKiKGLFihU4cuSI1KEQkYSYJBERXSY7OxvLly9vscI4EfUuTJKIiC6TnJwMAIiMjJQ4EiKSEtduIyK6xNy5c3H69Olm21xdXTn0RtQLKaQOgIjImixYsAArVqyAXq/H448/DgDQaDQSR0VEUmBPEhHRZSZNmoQxY8Zg6dKlUodCRBLinCQioktUV1cjPz8f4eHhUodCRBJjkkREdIn09HQAYJJEREySiIguxSSJiJowSSIiukR6ejp8fHzg6ekpdShEJDEmSUREl8jPz4e/v7/UYRCRFWAJACKiSwQGBiIhIQGrV6+Gr68vQkNDERUVJXVYRCQBJklERJd47LHHkJubi5UrV6Kurg4vvPACkySiXop1koiIiIhawTlJRERERK1gkkRERETUCiZJRERERK1gkkRERETUCiZJRERERK1gkkRERETUCiZJRERERK1gkkRERETUCiZJRERERK1gkkRERETUCiZJRERERK1gkkRERETUiv8Pe4h7OcLlvWUAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"t_ = np.linspace(0, 1)\n",
"\n",
"ax.plot(t_, dh(t_) / MAX_FLOW);\n",
"\n",
"ax.scatter(HOURS, THIRDS_FLOW_RATE,\n",
" c=\"C1\", zorder=5, label=\"Rule of Thirds\");\n",
"\n",
"ax.scatter(HOURS, FLOW_RATE_50_90,\n",
" c=\"C2\", zorder=5, label=\"50/90 Rule\");\n",
"\n",
"ax.xaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_ylabel(\"$h'(t)$\");\n",
"\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"id": "6423f518-da85-41e7-a5d8-4e089aae7379",
"metadata": {},
"source": [
"We see that the 50/90 Rule agrees much more closely with $h'$ than the Rule of Thirds, suggesting that it was indeed the Rule of Thirds that was in need of improvement."
]
},
{
"cell_type": "markdown",
"id": "76292859-8f75-494f-b7ac-290a02293350",
"metadata": {},
"source": [
"### Règle des Sixièmes\n",
"\n",
"One final rule, popular in France, is the [Règle des Sixièmes](https://www.kayarchy.com/html/03thesea/006currents.htm#:~:text=(slack%20water%20%2D%20zero%20flow.%20First%20hour%20after%2C%203/6%20flow.%20In%20the%20second%20hour%20after%2C%205/6%20flow%2C%20in%20the%20third%20hour%2C%206/6%20flow%2C%20then%205/6%2C%20then%203/6).)\n",
"\n",
"> \\[S\\]lack water - zero flow. First hour after, 3/6 flow. In the second hour after, 5/6 flow, in the third hour, 6/6 flow, then 5/6, then 3/6.\n",
"\n",
"We define the expected flow rates for the Règle des Sixièmes below."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "0cbf6465-085b-4c85-bf6e-1ab3d3db2cb9",
"metadata": {},
"outputs": [],
"source": [
"SIXIEMES_FLOW_RATE = np.array([0, 3, 5, 6, 5, 3, 0]) / 6"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "825818c0-04c2-48ad-80d1-b7f3134b42ea",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"t_ = np.linspace(0, 1)\n",
"\n",
"ax.plot(t_, dh(t_) / MAX_FLOW);\n",
"\n",
"ax.scatter(HOURS, THIRDS_FLOW_RATE,\n",
" c=\"C1\", zorder=5, label=\"Rule of Thirds\");\n",
"\n",
"ax.scatter(HOURS, FLOW_RATE_50_90,\n",
" c=\"C2\", zorder=5, label=\"50/90 Rule\");\n",
"\n",
"ax.scatter(HOURS, SIXIEMES_FLOW_RATE,\n",
" c=\"C3\", zorder=5, label=\"Règle des\\nSixièmes\");\n",
"\n",
"ax.xaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_xlabel(\"$t$\");\n",
"\n",
"ax.yaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
"ax.set_ylabel(\"$h'(t)$\");\n",
"\n",
"ax.legend(loc=\"upper right\");"
]
},
{
"cell_type": "markdown",
"id": "ea5ef394-005c-4f54-a7b4-afb04f99a159",
"metadata": {},
"source": [
"We see that the Règle des Sixièmes is slightly further from $h'$ than the 50/90 Rule two and four hours after high tide, but is still much closer than the Rule of Thirds."
]
},
{
"cell_type": "markdown",
"id": "791548bf-fc90-483f-bbf0-561f9468ee58",
"metadata": {},
"source": [
"I find it quite rewarding that the simple polynomial function, $h$, that we derived from five physics-based constraints agrees reasonably well with time-tested kayker's heuristics. Certainly this agreement is enough validation for me to use $h$ to model tidal water levels for my digital tide clock.\n",
"\n",
"This post is available as a Jupyter notebook [here](https://nbviewer.org/gist/AustinRochford/c52b0104a842eb3232c237a89bd1671a)."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "a4f999f7-f94b-43b9-9ae9-31e602a8173b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Last updated: Sat Nov 16 2024\n",
"\n",
"Python implementation: CPython\n",
"Python version : 3.10.10\n",
"IPython version : 8.11.0\n",
"\n",
"sympy: 1.12\n",
"\n",
"seaborn : 0.12.2\n",
"matplotlib: 3.7.1\n",
"numpy : 1.24.2\n",
"\n"
]
}
],
"source": [
"%load_ext watermark\n",
"%watermark -n -u -v -iv -p sympy"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.10"
},
"nikola": {
"date": "2024-11-16",
"slug": "model-tide-kayak",
"title": "Modeling Tide Heights and Kayaker's Heuristics"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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