{"id":2503,"date":"2024-04-16T14:56:55","date_gmt":"2024-04-16T14:56:55","guid":{"rendered":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/?post_type=ht_kb&p=2503"},"modified":"2025-09-07T17:45:25","modified_gmt":"2025-09-07T17:45:25","slug":"create-idf-equation-coefficients","status":"publish","type":"ht_kb","link":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/knowledge-base\/create-idf-equation-coefficients\/","title":{"rendered":"Create IDF Equation Coefficients"},"content":{"rendered":"\n

On certain occasions, it is possible that the IDF curves derived by the software may not precisely align with the inputted data. The software modifies (smooths) the input data to calculate coefficients B, D, and E, which are utilized in an Intensity vs. Tc equation. In simpler terms, the data must be plotted in a straight line on a logarithmic scale. If this is not the case, the software will make necessary adjustments to the data, usually focusing on the 5 or 15 minute values, in order to ensure that it conforms to the equation.<\/p>\n\n\n\n

The modifications are consistently confined within the lower and upper limits of the 90% confidence interval, as indicated on the NOAA data tables. It is important to note that NOAA derives this data by interpolating data points on a GIS grid, which may result in some irregularities and may require the software to smooth.<\/p>\n\n\n\n

Nevertheless, if it is crucial for your data to accurately align with the original points, you can employ the charting capabilities in Microsoft Excel. By doing so, you can generate your own coefficients for use in Stormwater Studio’s Third-degree Polynomial equation.<\/p>\n\n\n\n

Example<\/h2>\n\n\n\n

The example below will illustrate how to generate IDF coefficients for use in the third-degree polynomial.<\/p>\n\n\n\n

Step 1.<\/strong> Open Excel and type your data into two columns as shown below, using your own data.<\/p>\n\n\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t
Time (min)<\/th>Intensity (in\/hr)<\/th>\n<\/tr>\n<\/thead>\n
5<\/td>3.3<\/td>\n<\/tr>\n
10<\/td>2.62<\/td>\n<\/tr>\n
20<\/td>1.89<\/td>\n<\/tr>\n
30<\/td>1.48<\/td>\n<\/tr>\n
40<\/td>1.25<\/td>\n<\/tr>\n
50<\/td>1.08<\/td>\n<\/tr>\n
60<\/td>0.96<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n

Step 2.<\/strong> Select the data and choose “Recommended Chart” on the Insert tab.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Choose “Scatter” chart.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Step 3.<\/strong> Add a Trendline. Click anywhere on the new Chart, click the “+” button, and select “Add Trendline –> “Linear”.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Step 4.<\/strong> Select a new equation type. Select “Logarithmic” under the Trendline Options. Also check “Display Equation on chart” as shown below.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Your chart will then look like the following with the equation displayed where Y represents Intensity and X-axis the Tc.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Polynomial Equation employed by Stormwater Studio is: I = A + Bx + Cx^2 + Dx^3 <\/strong><\/p>\n\n\n\n

The Excel-generated equation shown in the chart can be rewritten to match as:<\/p>\n\n\n\n

I = 4.8118 – 0.959x + 0x^2 + 0x^3<\/strong><\/p>\n\n\n\n

Based on the Excel-generated equation, your coefficients are as follows:<\/p>\n\n\n\n

A = 4.8118
B = -0.959
C = 0
D = 0<\/p>\n\n\n\n

Repeat Steps 1 through 4 for each return period.<\/p>\n\n\n\n

Step 5.<\/strong> Enter these coefficients (A, B, C & D) into Stormwater Studio as described here<\/a>. Use the Third-degree Polynomial option.<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Learn how to create your own equation coefficients to match your rainfall data.<\/p>\n","protected":false},"author":1,"comment_status":"open","ping_status":"closed","template":"","format":"standard","meta":{"footnotes":""},"ht-kb-category":[25],"ht-kb-tag":[],"class_list":["post-2503","ht_kb","type-ht_kb","status-publish","format-standard","hentry","ht_kb_category-rainfall-idf-curves"],"_links":{"self":[{"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/ht-kb\/2503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/comments?post=2503"}],"version-history":[{"count":13,"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/ht-kb\/2503\/revisions"}],"predecessor-version":[{"id":2874,"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/ht-kb\/2503\/revisions\/2874"}],"wp:attachment":[{"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/media?parent=2503"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/ht-kb-category?post=2503"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/learn.hydrologystudio.com\/stormwater-studio\/wp-json\/wp\/v2\/ht-kb-tag?post=2503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}