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

Created by ChrisR

Solve Later

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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,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAoCAYAAABuIqMUAAAC3klEQVRYR+2Yu24UMRSGkzfg1oIiLgUVCHFpQgEF4VIhkAJKk45LR0MkoAOikEgpE+gQEgIeAEhSQEFElYaKAsETAAlPAP+38okOZmfXXnknrDSWfs14xmP//n18fM4MDw1wGR5g7kMN+a1avUb5/0X5vSKyJvwU5oQngdhOXQ8mkFx17e/r/orwUriZ8G12k3Zmc169vA49Tek6KzCpy8KIcCMaZV31mfCMtkx0STgqfBVOCD+ymSV80I48g3933+6KBl+IJnBY9U+u/TXdPw71xX6pTv9VG/a3I3NB929cHVN4EeqoviMSCdXHwrPruprpJWiZ1ySFfExgVEN86ECe/bJ9UMn7Vdtys8lV3pN/pRXAzPpSUswmJtDNbDx581a1ksc3j4cR8fvH3OidyPt3fHJSMN9ffAJVysckvDvsRN670WWxPVucseuwU2zjXSJEJgQOmyryvj2H0yXB+//i8+gWmEH0nmB+G/vHFfpTdlr1MwInKoX6fJhoccK+w27krS3hwXFhjzDiyPvQ4KOef66DtJFKJe8n3M3b9FXtXpRvyJdeksZsSiua2l8vyt9W54/CAHibAz14GGL+i8I74YiwTdgvkLiQseGe8W6nBDsrOPVxx7jlb4yfSx6XuSLsc+rk+HXLsjjE7gQSlrz4CPRheH9VV0hT7BDcfJZK/pBT2/H+63YjDFD13ogzcRRsqadiK+mTHnPHfkJ8/0XYXOlU8lWEcp4byTjEtiDQp5uWivr4iO8p5MmtUhd5IxPvEcwQE4ojV7gRWvOOvUA7gj6Lr2olb38k4tzAVGff3I2WkRgKsImfC/w+MVOrlbyZjLdhNuADgT2Ave8WfLJOIo/HQf1bwj95QV1mYxsQIpPCOeGXcFogYmVF3rchz7vKhKYu8iwzSkMcr/RM4HcKK8IEngrmElsmoYK7fNtOcWtQJ3kbs9i1IV9MysyOGuUzBSvWvFG+mJSZHf0BvpeoKQkEiaYAAAAASUVORK5CYII=" 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,iVBORw0KGgoAAAANSUhEUgAAABoAAAAoCAYAAADg+OpoAAAB50lEQVRYR+1WyS4FURB97wvE8AWGNQliw9b4AUgsXkJi+ADCXkx7w8IaWwlhZcGKWNhjJVbGL+Ccl6pO99Xdr9XVbyF9k5Pq4Xade+pW1e1yqU6jXCeeUkFkjnQRuiJ0QQSyJsMEvmgA9qyxy0LUCecXwHKeRP1wfgw0Am3A418raoXDaWBFHD/AVuT62UIYFzqSbIvTIbHvsNdyPWxRlbZHDNulOB2DPbUQ6DdpRIuYtCETW2Bf8yK6geMe4BwwhSu8sCRFzZj0IhOXYDd91PDbJKJRvDsR5wOwV3kRrcIxU5vZ1uRLkqboHi9ZoEcA24/3SKojFijHHGDub7WSgQoOZFIX7BNwBvT6yIpTxK4wD1BVn5DMwN45RCzoEWBQwrwAWwHaAe7rFBAUeRwRV8/Ww0R4A7ZSwqfdg3PXgX2AxwkXyWcdQLXQ44gYOq7sA1iLURIWNoubXcBNmi+ZFHT8LOdR2LF7fYgH40C41rTYNfSJitIcu++48ohD3GsyRVT6KNL92YFzJoIO3ePIQelDpN1jEgwMIYfu2Y/+6EOk3V1XriGLLXIrkW44U5hqaD8BHiluvVWlWol09e7+JCaSlUi7R+Yj3kqk3T3zL5iFiNnWLTG6hWXbqfm/ZyH6TUEHc/8f0Tfny1wpwHGjIQAAAABJRU5ErkJggg==" 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,iVBORw0KGgoAAAANSUhEUgAAArEAAABOCAYAAAA3gU7IAAAex0lEQVR4Xu1d2+tuV3XVPyBoU5+KhEPbPPShtMQ0irYBhXhpoQgmTbWlBCLWaAkUbWu8UErTxsS0gg+tlQiHoLY1kYBYbSMY0LwEm2CwpYWmFwTf1Fr6B7Rz5HzDM8/+7cu677X2NzZMcvL79l5rrrFuY80111wvfYkeISAEhIAQEAJCQAgIASEwGAIvHUxfqSsEhIAQEAJCQAgIASEgBF4iEqtGIASEgBAQAkJACAgBITAcAiKxw1WZFBYCQkAICAEhIASEgBAQiVUbEAJCQAgIASEgBISAEBgOAZHYNlX2i5bNN1ay+gf77c1tVFEuQkAI7IDAr1ue95u80eQ/dshfWQqBvRH4cVPg30zeY/I3BZX5fUvrwZX0fsl+e7pgfkqqIwREYttUBknsv1t2L8xk+az97UNtVFEuQkAINEYABPYvTF5v8nzjvJWdEOgJgZ8zZZ4qTGTRv+6aKSRI880mIrE9tYDCuojEFgZ0ITmS2D+w3x9qk6VyEQJCoAMEMMH+tcnbTUpanzoomlQQAkkI/LJ99XcN+gTnXZHYpGoa4yOR2Db1JBLbBmflIgR6QoD9/t2m1F/1pJh0EQI7I/Dblv8nKxNZkdidK7lF9udOYrHdcHuDCUYktkVrVh5CoB8EuG36pKkEa6yeYyGAOr0hsUg4AyG3kisuNsCxlpuNSGxiAx3ps3MlsSCvd5t84FRZ11euNJHYygAreSHQGQLfNH1+zOTVJt/vTDepUwaBn7Rk/tTkTpfc39q/n5skf8n+Hwf6fur0958XiX0RCczDz5wwqdFPRGLLtPOuUzlHEottjAdOEwwq579NRGK7bqZSTggMhcCfmLYfNJEv3lDVlqSsPxmPg7s/vZLK39tvt5jcaKKFzRWgSDRB/kvvWIjEJjXpsT46NxILAvvPJv9yWgFiZSwSO1ablbZCoGcEOHH+pSmJUEJ6jo0AiOmbTkXcqnMQ3jtMfuHYkESXDm4F95j8ismXo79e/kAktiCYvSZ1biTW1wMHH5HYXlun9BIC4yEANwIsjhHaR/Fgx6u/WI1/YB/AbQTPFgkDiX2ZicIpXosy48cCy5JuBSKxsa15wPdFYmWJHbDZSmUh0CUCPHGtUHpdVk9xpaaX2LzCclhzEwBZA4nV4uZiVdAto2TfEYkt3uT7S1AkViS2v1YpjYTAeAjQmgTN5fM4Xv2laOz9YZduXcQ7ig2+jW6N/iMSu4378G+IxIrEDt+IVQAh0AECJDQ4ra7t4g4qpIEK3h92zoLIm6R0pXhYZZS2xorEhuE+9FsisSKxQzdgKS8EOkGAvpHwh9V2cSeVUlENWA6/59KfRqJgnOD77B1ddBFWEQhZhggPOKdSYjdDJDYM96HfEokViR26ATdWHtclftdEgcrTgYff6NEmdV4tWyNMUDrS+rImArw6lXnAEovnJpOXmzBigRY1cbWAq5kRd7eEb6xIbBz2Q74tEisSO2TD3UFpEJVbTRQ2KQ98TP73mvyGyVFiZSIiAaIRbJ1Oz0NOX/eEAGMBQ6d/NHnMKYcwWmgPS36yPZWjN124ONiKuRuit0hsCEqDvyMSKxLbqgljhY3nUZOcWIAYmN5xSuth+2+LrVsQ2LeaxATjxnbjbafvYJmBnq30bVGnOeUDju8zga9gDpHFhIcnpz3lYuW3QGtfmpKrq74vh8ALlhRv4Hq3/Xu6uwD3ko+a6FBXPOZ0zcldFIrExmM/3Bcisf2SWHTAt5hga4WDZWgD6/FwCXzEvnUqgNcPhyNAiGC5mD6wcIDkYGsJW/jctsV7uQNcKJaohy+axPhooaxfMIFv1ztPGbHsR7hyskT5cIjjkkmMZRvt5HYT3LWOazwRn3PvLXxa5LYC3ce0tw/by0+YHM3tIhSD3t/jwoV6zvXp/7Mfj9DX96gLXn6Q26dEYveovcZ5isT2S2LZFKaxCN9uP9CqyXcwuSNI9B+Z9Lyt6a0X0wHeh6tBuaYDmJ84WlxQAR0Y9gVEa4r5UlcF0cYgjO0wLEBoKaav1+hbjKXKx3vT4VoQaknFNz9j8lqTB08VsDeJZZue65cxwzn6OcgrfSnnrHsx6endegj4xfTStjdcTHQzV1od0KUgd5wXiU3Df6ivRGL7J7F+wNw6tcnO3+thgrWQNN5Si040JbkMJI/fWhEXEOt3mazdh+47PE8kw0I4Pa3sSfpWUPReB5HS5SMhjrFyExtYulq2hbk68Qur1DoFMb/b5NKJ9HBHQiS2115wZUGLBSqeXGthv6XcTzMf+WE6jsZoJRIbg1Y/70a5iYWSWExe15k83U85szUZ5dpZf4Bgi7yh0142KXl1XzbQLgFPYufKQmKCT6YklltMrYhLrBWW74PAzrlzeBKbMzCXrI+YtGqUj2mmhCHqgcRyYQW3l1SrGzDAA7cZv+tSi8RiPHmVySdMQi3gMe3kHN71V83mWuDPAa+UMnKuyHGNa0FiwY2wK/RDk5gzEzGYgNT9q0mL8x8xeuW+u8QrsbsFCYqvHEJiue33KUv0SE7qo5DYrQMEviHBMvR+kxg/w9yGGPN9Don13+aQhlB9SVBCLWy0zsBaDmvadMDxJLaVP29oWUPeq1U+LE7g3xpq7aauPZBYYpIz0XrsW5BY9qNaJDmkLY38znTHKHR8GLnMe+jO8TJnrG9BYplHruvDEsZsbyMaPtbazRKvZHmD58gtEouMMOhhUj6ak/oIJDbkAMEeA0xqnqVIbK0Bw5cLPm14QixsnnwsERpvUQ/uoKlAF/6uZvnoLhM7vvRAYmmRK2WNE4kt3HArJOfdmnIIVgXVDpWkj8O7xVOWCj46iaX7FsaZXndXUxrdGq/kTlFwCMa1xoFG9BkTbI/Cef1IIAJ4xnZsQYjYmWIDOHt/WAyYcyGJYKmFJWuErQZPYucORKy5E7S0xNInK9TCxraEdrXkj+z1H21VXbN8XHnHWgbXSCzS/DUT+C1+zORxE/idwr8Z9YM+nxv+yFvkYgn41qSL32PxCJ1MZIkNRWr+Pd8XQseHvBzP82tvwEkdL0cmsX7nbsuNcKQWssUr0b/+0CTY1WmOxKLxPHka7OfA6fXQUGhFonwI08PTzfgO5PLTJjkxK9fyTyWx3g907gABrAII4ZQbbzMUu9z3vDUSaU3b3xqJ9X5otSePmPry1rO1wcZPfiNtQbYoH+o99oDMHIlF3wZZ9WHpkC7+Dp+150zeYMIIALGLSt/+/QIz1VI07U+yxOaOMHW/91ZY5IRII3DdGsGAUBeZOqlzzE/tpyOSWE/ypqguGbLqoF821RBeiRwxt783houtDb7e0pCyXeYJSSocpVcgaNQIz7P0/JP9ELwCiChUDCnyyc4dIEBj+IlTOUDEUzt4hPrFXp26R0y31ZdIrJ/cYUX7VZOahww5WYVYAPxJ5bV+wrJtRZgoBnahhFqUD9jEhh5bs8T6rUhY/BG6yodIo595zq1AXJDF6r1WLSKxhRpthWRgGVt6vjNpXxWyP8skuWsQu8AlWCOSWOruF0yjGw59483llRc6whqJzQWxRxK710iQQmKnBwiWdC+1ldkKm7UYi3Mk1vvPQMcWpJ1bOVsk1oeCWSOnnpyUJD2166xV+TBZ4WBXzOGuNRK7RQb9jkDqBMEJtuRCe0vvEvUtd4ISKCqNFghwJzJ1zByZxNJ4MLL1da6N5PLKKBJ7VBBbdL5pHikkdu0Agb8xaRRXAo8JLGUI8QMCAWsYiMBXTL7hXoJP4MtM6MeI9+Df2OIWo1AS6wl5aLtqQcJDddl6r1X5SKxituVzSKz3N0tdBNKaW7I+RWK3WqR+PycEfD+NGRuI0cgklruwqVboXttJcV651jA4SdT2P+wV7JJ6pZBYfxBorg7QGNDQc8Np5VrMcw7Ggcy+zgRxK/HQVxH/xuobz7Mm3zb5qkktn+VpXYeSWG/RWyMz3h82lTR5HVvVWavyjUhiWQe9kdjpzXep41iJdpqat74TAkAg1++8FInNHW9RlpgdG7+YrRnJxueT2uJiyoU8ivPKJRLbCsRU4Eb7LoXE+o4zt62Nif9+k1zf0NwOmkNip/W4drCrZZ2Hkli/0Fia9L0fMIh5cOiQlQK3qrNW5YsJZ0ZY9rTEljg5PVe9JSyxIrEtRwrlVRMB3x+2XLvW+lPKtyWNBrEkttXtjq1JbBVeuURiCeJoh1BqdqictGNJrD+YslQHeOcZk1bWyZzyh37bC4mlBWBr8OOWz1o/GfmSgxLlIxFes+yVPti1RQZz3QlyJ9el/rCld2g/WntPPrElUFQaLRDI7WelLLFrZWUeJY057KOpvsAt6iYljyq8conEcvszB8Rca1Hs6iUF1FbfxJJYv42bUwetylcqn15IbGh9Ud+loOf+qtZSVthSWIekU6J8GJBvMVmLKIF8Yt2W9rTE5k6uIrEhrU/vnDsC/mBpyrb6iCTWl7mkq1IPbakEr7xQjjkSWwrEliQWB4TWQqCUrkAcuop5QkkR0/Q+lLWCnsfo3+rdXkgsyhsSu3SL5HmL35ZVtxXGMfm0KB/7RmwYvz1JbK6v3hFI7G9ZIeDPrkcIhCDwn/YSLhiJfXJ8z0cksX4XdsQ5Y6l+S/HKIBI7ByJCXeQeIIptvDHvo3Ng1dLqiW1cMSTWVzbKc04HLHoisTg4h8XR2rWzPKE+Z4nllYG48W7UhUiL8jEKR2yoqz1JbO6p6SOQWEQSwbimRwiEIIALIdDHY59zI7HchaWLGiL04HKmh2KB6+z9arxyzhJLEHnV7B8bGF838cHCO8One3ViSOw0jurRrvtdqqxpXNwU8o4FwG0mP2sC8oh2+1aTR02+a/IaE+TzORMeiEPnutdkeuCK9bBGrvyNar4v+di2CJHyEZM532W8h/6FAQv53HzSpcaFGymdJKd8wO8GE9yQ9YTJUmg0uBvgQai4mEckNgatq+/KJzYNN321DwLnRmK5C4tT/7i56rMmMNA9P4Gf4+ul0/yBEJW/Y/JyE0T0+XOTns7LVOOVcySWgxwmVlw/WyKM0z7Nv59cY0isPxG+5GvZT8nKaTI9VR0bH4+xc9H52YF5MImEmFY/nzZXiNP86M8KK//SKhin1FFHIMz02SKBBSm9z2Qtri2D/GOh8kqTb5nEWiTL1cDFlEqUD2HTlvzZeMo/1pXA+6TO9RG/EJzztfV9LMXXrpYl1qcb6yMc2g5EYkOR0ns9IHBuJNa7cAH/PzNZMiByvGCsdcx7uHYbN3nGzp+167oar1yzxILEYhJ+3KQnRl8b7Brph5BYTLx3mfhYqdAFB4K+ZjL6dsISrmjcIH6wQk4fdE5saW/dT86teyy6gCMfDAjcUUAbpqvGlPhAh8sm08ECgwQuW1i7SQp5P3LSH3WFPKDH502mq+dp+ThgsR8i/w+a9HQXe075sIjAg7qdKxPwvcNkzWXDYwbS+/5THWPhwAf1iTrAggEr/ntM/O8Y0PHb/5rAuuz7GMa5tYXKtM7w/6VJLHGY9gH2/U9bnqXGYJHYa2sUi1js0mz11bl2oL9dQQDGgVqX0JwbiaUlFvMWdgjXduW4U+YJK7lGzpXaNdq1d5MoyitTbsGoUcCjpxlCYo+OQc3ygejieZubjGjlm65I8e71J8E3eA/W26WbzzCoPGZSYxHBQaiW1a0m5ltp0z1kKboGrbxrUQu28tjr99IktmU5MJngcpHLJufuIoYF760mPZ/3aNk2UvNacslKTc9/1zuJxTgHyyeeWJeoXHw4l3kjAbnG2UQ1EonNbUZh34vEhuGU8taciwDSIdGYblXTEsVte0zk8JldWvHSTcET5BQ9577xIbhit9RL6VArHdbLUpgY1MOoOwwjk9iS9U0SvNZ/QvLD+PiO04sP239b7ESAwMJf3u/cbOlKn3t8B99D6NlK3y3dSvyeUz7g+L4TkSu1a4Ay9U5iS+CeksaSkYAWz6OF51rE6MgkFhPNTSZ3TkoPM/unTLBSwRYSBtC3mMxtQX7J/l7ikI1IbEo3DfuGpNRHjPDkcOpj6kks4pfi8NGWlRX19/EKAzRKSJ/c3rZ/wtBffmvtkgP0zUsmo1rARGKv1Ls/jOl3E9ZchOD6AZLDwyrefznFPzmlnaI/f9HkxpMuIWlwMQv3k3eePoAPO56UQ6ghebZ8p0T5avRrkdj5VkAjwTTyzdyuZMt21DyvI5NYguljrmIABamdW+nzPQxSv2lSgrxSB5HYek2bg5wnq9ympz8swpSwzklAMOniG5wADbEccNuoxLWx0OE7JrRkMZRVT4e6cmvM+yPj4Br70xG2cEVir7YOtt05Mrd1WNNf31vyxqO1tssFLhZQoe4UaLMYUzCe+PkD3+P/R9+6LVU+YItbJLd8OWPGFpHYebTY9vwCiv1t1JCOMe3iR++eG4ldqlySnjWSmwTw6SOR2Bz01r/lJAorDgZQhKz6LxP4KcHXFdt+PkQJOzpDmIQQWGqASfc6k9xDIBiAoBd9qLCAwrPkl1sPvTops73DHxmP39GA5bnkArFOCdZTpRUEb53DGLqGho/0MN3C3Aqb53FEf4zZ2k+t95DDmj5tH+95Gh/ck/RX2EcxY0mq/qW/K10+EuIYK/damURi59GZHlrmjsbZuBEQlqMPwH6ljzLPWbr84ZpasdVEYksPvVfTA7aXT3ULi8gnTHDaGFt9cyc86WYSaoGtoTlILE/uwwKFgzZzsQBr5N0iTR7aQl5bYcZa6FM6Dx/iK/bik9K67J2eJ7FzRHTtAhOOvShDCxIba4X1bklzhy89iR2xHdQoH9Ms0e/9/J3iasJ+OmLdrPVrlgtzBwwFjMRSyv1x7zEF5XutCXZQwdkeMMGCF+3hhybXRPA5Oon1/lawsnpLV0w8z9xKFYnNRVDfC4F+EBCJvVoXOSS2dUxsWn5DrabcsgVZmAsT50lsCsnau0XXKh8WJ280WQtNGFL23H52VBLLw1tHdhvwRB3tFCHcsAuKmwKvOT9ydBLrV/rTAPefOYHxu/Zf3t4U0rFS3hGJTUFN3wiBPhHwFqKjWXliES9FYlv4xNJtJyQusSdQSyHwSCaA2Wgktmb5aDzKPfAmEjvfG3l+Jxff2L7e8n22oanx8cIZmKOTWN7YBPAZwogDD7avWgWWF4lt2fyVlxCoj0COr1597drl4EnsXISNNXeClpZYXnQSGpPZHwheOnDp9R9tMVOzfPSFzrUU+p3UFK5yREss2/HRotlMRywaIKeLQ/oCw9L/4mHtlIbRbnjMy2nuUMEjliS2hdC5Wt5EJhKbV5f6Wgj0hgAXyGd3kGJSEd4aOTenrJFYb2QIJZep7SBmDPYWwDVfXU8EQ10UUvUv+V2L8qHec68+pbtGqpX+aCQWO0DoJwwbeuSxB2MD5Edk1f7NcJTXRAM5Mon1J1/RCfDAATp3dZgymMQMoCnp6xshIATaIkArXIsDSW1LFpfb9PDsnOWEKfrtT0+kMD7XvrmN80GIxZS+otB77RISEnToX+o0fhz6aW+3KB+wyQ09RmtcajpHI7FptT3eVzRATsfWWevskUms76i+GuFjEeITVbLqRWJLoqm0hMD+CNACucd4sn/pr9XAb/tOtznnLLE8VItdMTwtLEq06m2RWG7XQq81cupJeCrJ2qMeW5UPizwc7Mo53MWFYqpFVyR2jxaWn+fcRQ6sywtGgyOTWD94YjUNFs9QFK2d8EVi8xu2UhACPSGgWLHX1ga2+hDeDv6jILKYbL5igtPEfLALhrA573Lvfcz+jZPHtZ9QEusJeahOLUh4qC5b77UqHwloDsegu0nq7qlI7FZr6PP36W2PjGX8pKl7ITRmTgPrs/hXtJpuVWGr524TBMDH09opWiS259Yi3YRAPAJ+jDnyKeFYZEBmX2eC2Md43uQSgMUSz7Mm3zb5qkmrCwJCSaz38V0jp94ftkT9e6NLLOZ4P9RvtFX5cklsiQggIrEpLWn/b9AX0J5BWsHVsDB+ymR2sXtUEus7Krd6fGBnVFPq6i6likViU1DTN0KgbwRIPNb8JvsuQX3t1g521c/9ag6hJNZHHFgip55gYX4pcRV1KxLbqnwx4czm2gEP8eC3VJ4iEtuyh5XJi/UefNYgtXGUUbdeKn6V7FfTfiulpTO+SGy9ulbKQmAvBEgIap+s36t8JfLthcRy7N/yieUW9tr8MPIlByXKN93unWsnuQe7iHGOv7FIbIke3DaN6IscjkhiveM64J+upl+wv8E8jafV5CMS27YjKDch0AIBTrQ63LWMdi8kNnQMpr5Ldep39EpZYVu0VeZRonwgsbeYrEWUQD458yuJco6/sUhsy5ZVJi8aIJdiM1/I5YgkdnpS9tVWau935X3ZAEgwWBl1FDqAZmShT4WAEGiMgI9FPVKc0JYw9UJiUeaQ2KVbJM9bYbesui1xDs2rRfk43+W42VDPHH9jkdjQVtHHe94NFBEpHjZ58UKDteeIJNZfNbvkV7F1VeIWbrG/i8TGIqb3hcAYCHBnJ2fCHqOkaVr2RGIRdhFGi7UQi6zPOUssT0nvFW88rQau/apF+Ri5I9VARL/I3APYIrElWkznaRyRxHp3gaXDW1Nr7NqKGgPXfSbPmbzBBHHv/C0SIVUsEhuCkt4RAuMh4K+xxi6QnqsIzN2a+HwkQDhEdZvJDSYgj183ucvkPSbXmbzGBPl8zuTpU9ogQfeaTA9ccZdujVx5I4ifH31sW1iJPmIyF1mhxHwRCVHU6znlA36oB8yDT5gshUaDkQjPm6M0u/oydcxxR0BqIrGJFTDSZ0cjsVNyGnLbCupracVH/yeEekAHxgrz90xiAziLxI7UK6SrEAhHgEQtNMRReMrjv+m33lGa2KD1GHPvN2EsWWKN8ZpuYrT6+bRpyZvmx/H8o/b9QwvwgjTDCgvCzHjiJLAgvzBoLJG3UvNFzZrPKR/04i7mUqx1Rm7I2Zng4bMcVwKR2JqtqKO0j0Ji0XEQB/ae0+BDiDGxYMB63AS+FXjvdhOsJH38Qrw/fdd3Ah+m67P2Q+wKUyS2o0YvVYRAYQR4GCFn4i6s0q7JgeiA0PFGLq8MCCh2y2BJXfN3o9XU76bN3drDg7zT7X/ocNkELgT+AbHGZQtrhgiQ5UdO+mPsRx4wZHzeZM2STP1y54valZdaPugFgokHdTtXf8D3DpPUWzG5AClxWFKW2NotqYP0j0Jia0JJ94ScW75EYmvWkNIWAvsiQMKVEw5o3xL0lTutedPT/8R5uljAGH39SVASfI/zEDA2zG35Y9HxmMmSNTYHjRLzRU7+Nb+lJXypndPKuxa1YEs/uhKUWBCKxG6hfYDfRWK3K9G7KKQ6qovEbuOsN4TAqAj4sEupY8SoZa+hN6ynd5pMiQy3sqcYT/+O7x81+fKCciBjXzB5m0msj+5WeUvMF1t57PU7XTeWwl6hHr6WsTigVb1UDHeR2L1aSsN8RWLDwObhjVifLqYuEhuGs94SAqMiQP/P1DFi1HLX0BsRDeB24A/QcgydO7/gSSzil+Lw0ZaVFel93GTJWptTrtz5Iifvmt+uXXKA9n/JBG4iqQ/7UE5sWJ+3SGxqTQz0nUjscmWhw9Jvi9tbqSE/RGIH6hRSVQgkIEBrLD690WRuGzsh2bP7ZI6sTiMDIH7k/ziMSX5wmh1W2vcG4g+L7IMmJa6NLTlf9FrpXFzgUB2Elm64edyaSWBr9B+R2F5bUkG9RGKXwYQDO0+xcpsj1coiEluw0SopIdApAqUtSZ0Ws6paNBggE1wg8UoTbGPjwcFdENVXTYgncYcfbCiBZSGQH0J15boVlJwvqgKcmDjnMMyBeL5kQhKLw1hLrhuh2dXoOyKxoegP/J5I7HLlwfkfllcIVvcYpJZiA241AZHYLYT0uxA4BgI82CPf2PT6BGl9wARhrkCaENIK8WA/aYJDRdhu9qQTBOgmk1gCm67hxS9Lzhcl9SqVFg9tIb21MGMp+dEKizk2NnzlWn4isSm1Mdg3IrFtKkwktg3OykUI7I3AXBiovXVS/kKgZwToQ1z6Gl+R2J5rvZBuIrGFgNxIRiS2Dc7KRQj0gECtSbmHskkHIVASAc6NubdzzekkEluypjpNSyS2TcWIxLbBWbkIgR4Q8Dc86ZBXDzUiHXpEAP3kGROE1KoRJUIktsdaL6yTSGxhQBeSE4ltg7NyEQK9IICT70+Z8MrqXvSSHkKgFwRwsQEiG7zeJPdgnSyxvdRqYz1EYtsALhLbBmflIgR6QoBXaJaKe9lT2aSLEMhBgLev5dyEuZW/LLFbCB3gd5HYNpUoEtsGZ+UiBHpDYOmq1N70lD5CoBUCXNyVuFp2TWeR2FY1umM+IrFtwPcBvBGCZ/o8a3/4UBtVlIsQEAKNESCRLX36unExlJ0QyEaAbja4SAjXA5d40L/umkkIPrc3m6jflUC50zREYttUjL9Pey5HxD6EY7seISAEjokAJtr7TfxVqscsqUolBOYR4EGuDxcksMiJFyUs4S4Se+AWKRJ74MpV0YSAEBACQkAICAEhcFQE/h+NmgvW0AkCswAAAABJRU5ErkJggg==" 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.

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

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

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