Problem 57800. Compute infiltration and runoff under constant precipitation with the Green-Ampt method

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Problem statement</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function that computes infiltration, depression storage, and runoff using the </w:t></w:r><w:hyperlink w:docLocation=\"https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt\"><w:r><w:rPr><w:u/></w:rPr><w:t>Green-Ampt method</w:t></w:r></w:hyperlink><w:r><w:t>. It should take as input the rainfall intensity </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"i\"/></w:customXmlPr><w:r><w:t>i</w:t></w:r></w:customXml><w:r><w:t>, saturated hydraulic conductivity </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Ks\"/></w:customXmlPr><w:r><w:t>K_s</w:t></w:r></w:customXml><w:r><w:t>, initial moisture content </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"thetai\"/></w:customXmlPr><w:r><w:t>\\theta_i</w:t></w:r></w:customXml><w:r><w:t>, saturated moisture content </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"thetas\"/></w:customXmlPr><w:r><w:t>\\theta_s</w:t></w:r></w:customXml><w:r><w:t>, average suction head </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Psi_av\"/></w:customXmlPr><w:r><w:t>\\Psi_{av}\n</w:t></w:r></w:customXml><w:r><w:t>, maximum available depression storage </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Smax\"/></w:customXmlPr><w:r><w:t>S_{max}</w:t></w:r></w:customXml><w:r><w:t>, and a vector of times </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"t\"/></w:customXmlPr><w:r><w:t>t</w:t></w:r></w:customXml><w:r><w:t>. If ponding occurs, the function should insert the ponding time </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>t_p</w:t></w:r></w:customXml><w:r><w:t> into the time vector. It should then compute the cumulative infiltration </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"F\"/></w:customXmlPr><w:r><w:t>F</w:t></w:r></w:customXml><w:r><w:t> and depression storage </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"S\"/></w:customXmlPr><w:r><w:t>S</w:t></w:r></w:customXml><w:r><w:t> at each of the times, as well as the runoff </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Q\"/></w:customXmlPr><w:r><w:t>Q</w:t></w:r></w:customXml><w:r><w:t> during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. </w:t></w:r><w:r><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Background</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>To compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"f\"/></w:customXmlPr><w:r><w:t>f</w:t></w:r></w:customXml><w:r><w:t> is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"fp\"/></w:customXmlPr><w:r><w:t>f_p</w:t></w:r></w:customXml><w:r><w:t>, and the cumulative infiltration </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"F\"/></w:customXmlPr><w:r><w:t>F</w:t></w:r></w:customXml><w:r><w:t> is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The infiltration capacity predicted by the Green-Ampt method is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"fp = Ks(1+Psi_av(thetas-thetai)/F)\"/></w:customXmlPr><w:r><w:t>f_p  = K_s\\left(1+\\frac{\\Psi_{av}(\\theta_s - \\theta_i)}{F}\\right)</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The cumulative infiltration </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>F_p</w:t></w:r></w:customXml><w:r><w:t> at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p\"/></w:customXmlPr><w:r><w:t>t = \\frac{1}{K_s}\\left[F-\\Psi_{av}(\\theta_s - \\theta_i) \\ln\\left(1+\\frac{F}{\\Psi_{av}(\\theta_s-\\theta_i)}\\right)\\right]+t_p-t^\\prime_p</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>where</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))\"/></w:customXmlPr><w:r><w:t>t^\\prime_p = \\frac{F_p}{K_s} – (\\theta_s - \\theta_i)\\frac{\\Psi_{av}}{K_s} \\ln\\left(1+\\frac{F_p}{\\Psi\n_{av} (\\theta_s - \\theta_i)}\\right)</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>is the time to infiltrate </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Fp\"/></w:customXmlPr><w:r><w:t>F_p</w:t></w:r></w:customXml><w:r><w:t> from the start of the storm under immediate ponding. </w:t></w:r><w:r><w:t> </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 572.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 286.3px; transform-origin: 407px 286.3px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">Problem statement</span></span></div><div style="block-size: 129px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 64.5px; text-align: left; transform-origin: 384px 64.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257.242px 8px; transform-origin: 257.242px 8px; unicode-bidi: normal; "><span style="">Write a function that computes infiltration, depression storage, and runoff using the </span></span><a target='_blank' href = "https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/6.1/overview-of-optional-capabilities/modeling-precipitation-and-infiltration/green-ampt"><span style=""><span style="text-decoration-line: underline; ">Green-Ampt method</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.775px 8px; transform-origin: 56.775px 8px; unicode-bidi: normal; "><span style="">. It should take as input the rainfall intensity </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">i</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.467px 8px; transform-origin: 103.467px 8px; unicode-bidi: normal; "><span style="">, saturated hydraulic conductivity </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="Ks" style="width: 17px; height: 20px;" width="17" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.4583px 8px; transform-origin: 75.4583px 8px; unicode-bidi: normal; "><span style="">, initial moisture content </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="thetai" style="width: 13px; height: 20px;" width="13" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; "><span style="">, saturated moisture content </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="thetas" style="width: 14px; height: 20px;" width="14" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; "><span style="">, average suction head </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="Psi_av" style="width: 23.5px; height: 20px;" width="23.5" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.208px 8px; transform-origin: 127.208px 8px; unicode-bidi: normal; "><span style="">, maximum available depression storage </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="Smax" style="width: 27px; height: 20px;" width="27" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.775px 8px; transform-origin: 70.775px 8px; unicode-bidi: normal; "><span style="">, and a vector of times </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">t</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.725px 8px; transform-origin: 72.725px 8px; unicode-bidi: normal; "><span style="">. If ponding occurs, the function should insert the ponding time </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 13px; height: 20px;" width="13" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.25px 8px; transform-origin: 216.25px 8px; unicode-bidi: normal; "><span style=""> into the time vector. It should then compute the cumulative infiltration </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">F</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; "><span style=""> and depression storage </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">S</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.933px 8px; transform-origin: 130.933px 8px; unicode-bidi: normal; "><span style=""> at each of the times, as well as the runoff </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">Q</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.983px 8px; transform-origin: 169.983px 8px; unicode-bidi: normal; "><span style=""> during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths. </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; "><span style=""> </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">Background</span></span></div><div style="block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.342px 8px; transform-origin: 378.342px 8px; unicode-bidi: normal; "><span style="">To compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">f</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.025px 8px; transform-origin: 140.025px 8px; unicode-bidi: normal; "><span style=""> is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="fp" style="width: 13px; height: 20px;" width="13" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.4667px 8px; transform-origin: 96.4667px 8px; unicode-bidi: normal; "><span style="">, and the cumulative infiltration </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">F</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126.408px 8px; transform-origin: 126.408px 8px; unicode-bidi: normal; "><span style=""> is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.65px 8px; transform-origin: 195.65px 8px; unicode-bidi: normal; "><span style="">The infiltration capacity predicted by the Green-Ampt method is</span></span></div><div style="block-size: 39.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.9px; text-align: left; transform-origin: 384px 19.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-15px"><img src="data:image/png;base64,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" alt="fp = Ks(1+Psi_av(thetas-thetai)/F)" style="width: 162.5px; height: 40px;" width="162.5" height="40"></span></div><div style="block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.3px 8px; transform-origin: 81.3px 8px; unicode-bidi: normal; "><span style="">The cumulative infiltration </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 18px; height: 20px;" width="18" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 290.558px 8px; transform-origin: 290.558px 8px; unicode-bidi: normal; "><span style=""> at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by</span></span></div><div style="block-size: 39px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.5px; text-align: left; transform-origin: 384px 19.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p" style="width: 344.5px; height: 39px;" width="344.5" height="39"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.0667px 8px; transform-origin: 19.0667px 8px; unicode-bidi: normal; "><span style="">where</span></span></div><div style="block-size: 40.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.4px; text-align: left; transform-origin: 384px 20.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))" style="width: 264px; height: 41px;" width="264" height="41"></span></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.0583px 8px; transform-origin: 68.0583px 8px; unicode-bidi: normal; "><span style="">is the time to infiltrate </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="Fp" style="width: 18px; height: 20px;" width="18" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 166.85px 8px; transform-origin: 166.85px 8px; unicode-bidi: normal; "><span style=""> from the start of the storm under immediate ponding. </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; "><span style=""> </span></span></div></div></div>

Problem statement
Write a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity , saturated hydraulic conductivity , initial moisture content , saturated moisture content , average suction head , maximum available depression storage , and a vector of times . If ponding occurs, the function should insert the ponding time  into the time vector. It should then compute the cumulative infiltration  and depression storage  at each of the times, as well as the runoff  during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.  
Background
To compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate  is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) , and the cumulative infiltration  is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface. 
The infiltration capacity predicted by the Green-Ampt method is

The cumulative infiltration  at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by

where

is the time to infiltrate  from the start of the storm under immediate ponding.

Solve

Solution Stats

5 Solutions
2 Solvers

Last Solution submitted on Apr 24, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers2

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 57800. Compute infiltration and runoff under constant precipitation with the Green-Ampt method

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author216

Problem Tags

Community Treasure Hunt

Problem 57800. Compute infiltration and runoff under constant precipitation with the Green-Ampt method

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author216

Problem Tags

Community Treasure Hunt

Players