2c:null 2d:["$","title",null,{"children":"Synthetic Flow Series | Western Power | Observable"}] 32:T572,{ const peak=correl.filter(c=>c.LagDays==11)[0] var data = [ { x: correl.filter(c=>c.LagDays<=23).map(c=>c.LagDays), y: correl.filter(c=>c.LagDays<=23).map(c=>c.Correl), mode: 'lines', line: {shape: 'spline', color: colr(1)}, type: 'scatter', hovertemplate: '%{x:.0f} days
%{y:.4f}' }, { x: [peak.LagDays], y: [peak.Correl], text:['Maximum correlation ' + d3.format('.4f')(peak.Correl) + '
at ' + peak.LagDays + ' days lag'], mode: 'markers+text', textposition: 'bottom right', hoverinfo:'none', marker: {color: colr(4),size:10}, type: 'scatter' }]; var layout = { width: width>700?670:width-30, margin:{t:10,b:50,l:70,r:5}, height:400, font: font, showlegend: false, xaxis: { showgrid: false, zeroline: false, ticks:'outside', title: 'Days of Lag', range:[-1,24] }, yaxis: { title: 'Correlation', zeroline: false, showline: false, separatethousands:true, range:[0.94,1.01] } } const cap=`Pearson correlation coefficient between daily flow at Victoria Falls and flow at Ngonye with the Victoria Falls flows lagged by between 0 and 23 days.` const div=container(cap, width>700?690:width-10) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }33:T53b,{ var data = [ { y: lagged.map(f => f.Ngonye), x: lagged.map(f => f.VicFalls), name: 'Victoria Falls Flow
Lagged by 11 days', mode: 'markers', marker: { color: colr_b(1), symbol: 'x',size:4 }, type: 'scatter' }, { y: combined.map(f => f.Ngonye), x: combined.map(f => f.VicFalls), name: 'Not lagged', mode: 'markers', marker: { color: colr_b(5), size: 3 }, type: 'scatter' } ]; var layout = { width: width>700?670:width-30, margin:{t:10,b:50,l:70,r:5}, height: 400, font: font, showlegend: true, legend: {x: 1,xanchor: 'left',y: 1}, hovermode:false, xaxis: { showgrid: true, zeroline: false, ticks: 'outside', separatethousands: true, title: 'Flow at Victoria Falls (m\u00b3/s)', range:[0,5000] }, yaxis: { title: 'Flow at Ngonye (m\u00b3/s)', zeroline: false, showline: false, separatethousands: true, ticks:'outside', range:[0,5000] } } const cap=`Flow at Victoria Falls plotted against flow at Ngonye for a) the same day and b) with Victoria Falls flows lagged by 11 days.` const div=container(cap, width>700?690:width-10) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }34:T4be,html`

Procedure

From: Mott MacDonald - Ngonye Falls Hydropower Project - 2018 Feasibility Study Update - Final Report Version D

Calculate Flow Duration Curves (FDCs) from daily data for the following:

The analogue site - Victoria Falls - for the overlapping period of data at the target site (2005 – 2023)
The analogue site for the complete long-term record (1924 -2023)
The target site - Ngonye - for the overlapping period (2005 – 2023)

Compare the FDCs for the analogue site for the two periods and derive factors between the shorter and longer periods
Apply these factors to the target site FDC to produce an estimated long-term FDC for the target site
For each daily flow value at the analogue site, determine its position on the long-term FDC (percentile)
Look up the flow value for this percentile from the estimated long-term FDC for the target site taking into account of the 11-day time lag.

Water Year is defined as running Oct to Sept as is usual in the region. `35:T4f3,{ var data = [ { x: fdcs.map(c=>1-c.exceedance), y: fdcs.map(c=>c.vicFallsFull), mode: 'lines', line: {shape: 'spline', color: colr_b(1), width:2.5}, type: 'scatter', name:'Full FDC' }, { x: fdcs.map(c=>1-c.exceedance), y: fdcs.map(c=>c.vicFallsOverlap), name:'Overlap FDC', mode: 'lines', line: {shape: 'spline', color: colr_b(3), width:2,dash:'dashdot'}, type: 'scatter', } ]; var layout = { width: width>700?670:width-30, margin:{t:10,b:50,l:70,r:15}, height:270, font: font, showlegend: true, legend: {x: 1,xanchor: 'right',y: 1}, xaxis: { showgrid: false, zeroline: false, ticks:'outside', tickformat: ',.0%', visible:true }, yaxis: { title: 'Flow (m\u00b3/s)', zeroline: false, showline: false, type:'log', hoverformat:'.0f', separatethousands:true, } }; const cap=`Flow duration curves for Victoria Falls for the full period of the data (1924-) and the period overlapping with the data for the Sioma gauge (2005-).` const div=container(cap, width>700?690:width-10) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }36:T4b8,{ var data = [ { x: fdcs.map(c=>1-c.exceedance), y: fdcs.map(c=>c.sioma), mode: 'lines', line: {shape: 'spline', color: colr_b(1), width:2.5}, type: 'scatter', name:'Gauged FDC' }, { x: fdcs.map(c=>1-c.exceedance), y: fdcs.map(c=>c.ngonyeScaled), name:'Scaled FDC', mode: 'lines', line: {shape: 'spline', color: colr_b(3), width:2,dash:'dashdot'}, type: 'scatter', } ]; var layout = { width: width>700?670:width-30, margin:{t:10,b:50,l:70,r:15}, height:270, font: font, showlegend: true, legend: {x: 1,xanchor: 'right',y: 1}, xaxis: { showgrid: false, zeroline: false, ticks:'outside', tickformat: ',.0%', visible:true }, yaxis: { title: 'Flow (m\u00b3/s)', zeroline: false, showline: false, type:'log', separatethousands:true, hoverformat:'.0f' } } const cap=`Flow Duration Curves for Sioma, gauged and scaled according to the derived conversion factor for Victoria Falls.` const div=container(cap, width>700?690:width-10) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }37:[{"id":"44425f801f53844b47d9cd6b6e89d083808f2d43edc0fbdcbf0c681eb58d22aeb7fb9c3f734721788981b71a86e7d4cf7bd11926f19f4c451b7905fe2edec443","href":"https://static.observableusercontent.com/files/44425f801f53844b47d9cd6b6e89d083808f2d43edc0fbdcbf0c681eb58d22aeb7fb9c3f734721788981b71a86e7d4cf7bd11926f19f4c451b7905fe2edec443","name":"ngonye_vicfalls@2.jpg","type":"image/jpeg","lastModified":1594279909229.566,"size":25326}] 30:{"id":"d587c297826eb5eb","slug":"synthetic-flow-series","title":"Synthetic Flow Series","thumbnail":"cc02c8c4d2e88a2d9c4b77f0fe524b298d827bb23d96bc76559e9c767b6871e3","access_level":"public","create_time":"$D2020-07-08T18:51:21.785Z","update_time":"$D2025-08-13T07:57:10.234Z","view_time":null,"first_public_time":"$D2020-07-09T12:46:37.684Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"3aaf4970407a12be","login":"westernpower","name":"Western Power","avatar_url":"https://avatars-next.observableusercontent.com/0c11a3086911e8caa71a7767a24de09ff93d85f36798166fa6c2d0b61107b761","tier":"starter_2024"},"version":437,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"96924893937b5930","login":"andyflem","name":"Andy Fleming","avatar_url":"https://avatars-next.observableusercontent.com/fd3844143a4c29872f0df28a8ebce77bb56cebf2fa74bb669872e4def82ad809","tier":null}],"members":[{"type":"team","id":"3aaf4970407a12be","login":"westernpower","name":"Western Power","avatar_url":"https://avatars-next.observableusercontent.com/0c11a3086911e8caa71a7767a24de09ff93d85f36798166fa6c2d0b61107b761","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"042ea7275c7e9c32","slug":"ngonye-falls","title":"Ngonye Falls","owner":{"id":"3aaf4970407a12be","login":"westernpower","name":"Western Power"}},"type":"notebook","body":{"titling":"auto","title":"Synthetic Flow Series","cells":[{"id":0,"value":"html`\n

Synthetic Flow Series

Ngonye Falls Hydroelectric Project

\n\n${book_index('synthetic-flow-series')}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":124,"value":"html `\n

Introduction

\nTo produce a long time series (1924-2023) of daily flow for the Ngonye Falls site, a correlation is carried out between the overlapping portions of the Zambezi River Authority (ZRA) gauge at Ngonye Falls (2005-2023) and a portion of the record of the Victoria Falls gauge at Livingstone (1924-2023).\n

\nOnce correlated, the full Victoria Falls gauge record is extrapolated to produce a synthetic record for Ngonye Falls.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"html`\n

Flow Lag

\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":140,"value":"html`\nThe Zambezi river flows over 350km southwest from Ngonye to Victoria Falls (Livingstone town) and part of this reach of river includes the wide floodplains between Sesheke and Kazungula.\n

\nAlthough river flows at Ngonye correlate very closely with flows at Victoria Falls, there is a lag in changes in flow due to the time it takes the water to travel between the two points.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":133,"value":"html`\n\n

\n\n`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":153,"value":"html`\nTo determine the time lag between changes in flow at Ngonye and Victoria Falls a standard correlation coefficient between the two sets of flows is calculated with the flows at Victoria Falls lagged by an increasing number of days. The lag with the highest correlation coresponds with the time taken for flows to travel from Ngonye to Victoria Falls.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"html`\nThe highest correlation between the two sets of flows is where the Victoria Falls flows are lagged by 11 days which shows that, on average, flows take 11 days to travel from Ngonye to Victoria Falls.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":81,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":159,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":407,"value":"

Victoria Falls

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":181,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":359,"value":"{ \n \n var data = [\n {\n x: fdcs.map(c=>1-c.exceedance),\n y: fdcs.map(c=>c.vicFallsRatioSmoothed),\n mode: 'lines',\n line: {shape: 'spline', color: colr(6), width:1.5},\n type: 'scatter',\n name:'Full to overlap FDC Factor'\n } \n ];\n \n var layout = {\n width: width>700?670:width-30,\n margin:{t:10,b:50,l:70,r:15}, \n height:250,\n font: font,\n showlegend: true, \n legend: {x: 1,xanchor: 'right',y: 1},\n xaxis: {\n showgrid: false,\n zeroline: false,\n ticks:'outside',\n tickformat: ',.0%',\n title: 'Exceedance',\n },\n yaxis: {\n title: 'Factor',\n zeroline: false,\n showline: false,\n separatethousands:true,\n hoverformat:'.2f',\n }\n }\n const cap=`Conversion factor between the full FDC and overalapping FDC at Victoria Falls.`\n const div=container(cap, width>700?690:width-10)\n \n plt.newPlot(div, data, layout,{displayModeBar: false});\n \n return div\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":410,"value":"

Sioma

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":235,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":412,"value":"

Conversion Factor

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":366,"value":"{ \n \n \n var data = [\n {\n x: fdcs.map(c=>1-c.exceedance),\n y: fdcs.map(c=>c.conversionFactor),\n mode: 'lines',\n line: {shape: 'spline', color: colr(6), width:1.5},\n type: 'scatter',\n name:'Victoria Falls to Ngonye Conversion Factor'\n } \n ];\n \n var layout = {\n width: width>700?670:width-30,\n margin:{t:10,b:50,l:70,r:15}, \n height:170,\n font: font,\n showlegend: true, \n legend: {x: 1,xanchor: 'right',y: 1},\n xaxis: {\n showgrid: false,\n zeroline: false,\n ticks:'outside',\n tickformat: ',.0%',\n title: 'Exceedance',\n },\n yaxis: {\n title: 'Factor',\n zeroline: false,\n showline: false,\n separatethousands:true,\n hoverformat:'.2f',\n }\n }\n const cap=`Conversion factor between the Victoria Falls Flows and Ngonye Falls Flows..`\n const div=container(cap, width>700?690:width-10)\n \n plt.newPlot(div, data, layout,{displayModeBar: false});\n \n return div \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":414,"value":"

Ngonye Synthetic Flows

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":255,"value":"{ \n var data = [\n {\n x: fdc.map(c=>c.exceedance),\n y: fdc.map(c=>c.flow),\n mode: 'lines',\n line: {shape: 'spline', color: colr_b(1), width:2},\n type: 'scatter',\n name:''\n } \n ];\n \n var layout = {\n width: width>700?670:width-30,\n margin:{t:10,b:50,l:70,r:15}, \n height:320,\n font: font,\n\n showlegend: false, \n legend: {x: 1,xanchor: 'right',y: 1},\n xaxis: {\n showgrid: false,\n zeroline: false,\n ticks:'outside',\n tickformat: ',.0%',\n visible:true\n },\n yaxis: {\n title: 'Flow (m\\u00b3/s)',\n zeroline: false,\n showline: false,\n type:'log',\n separatethousands:true,\n hoverformat:'.0f'\n }\n }\n const cap=`Ngonye Falls synthetic Flow Duration Curve.`\n const div=container(cap, width>700?690:width-10)\n plt.newPlot(div, data, layout,{displayModeBar: false});\n \n return div \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":173,"value":"html`\n

\n

Appendix

\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":179,"value":"fdcs = await d3.csv(hydrologyFolder + \"ngonyeFDCs.csv?\" + Math.floor(Math.random() * 1000),d3.autoType)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":385,"value":"fdc = await d3.csv(hydrologyFolder + \"processed/fdc.csv?\" + Math.floor(Math.random() * 1000),d3.autoType)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"correl = await d3.csv(hydrologyFolder + \"ngonye_vicfalls_correl.csv?\" + Math.floor(Math.random() * 1000),d3.autoType)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"lagged = (await d3.csv(hydrologyFolder + \"ngonye_vicfalls_lagged.csv?\" + Math.floor(Math.random() * 1000),d3.autoType)).slice(0,1000)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":79,"value":"combined = (await d3.csv(hydrologyFolder + \"ngonye_vicfalls_combined.csv?\" + Math.floor(Math.random() * 1000),d3.autoType)).slice(0,1000)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":294,"value":"

Sources

Style

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":319,"value":"function formatFlow(flow) {\n return d3.format(',.2r')(flow) + ' m\\u00b3/s'\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":317,"value":"function colr_b(i = 1, a = 1) {\n return d3hsv.hsv(215, 1, ((6 - i + 1.5) * 15)/120, a).toString();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":313,"value":"function colr(i = 1, a = 1) {\n return d3hsv.hsv(26, 0.85, ((6 - i + 1.5) * 15)/100, a).toString();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":311,"value":"container = function(captionText, width_over) {\n const div=DOM.element('div')\n div.setAttribute(\"class\",\"border m-2 p-2\")\n div.setAttribute(\"style\",`width: ${width_over?width_over:(width>800?800:width)}px`)\n if (captionText) {\n const caption=DOM.element('figcaption')\n caption.setAttribute(\"style\",\"max-width:100%\")\n caption.append(captionText)\n div.append(caption)\n }\n return div\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":309,"value":"html`\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":307,"value":"style=html`css `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":305,"value":"makeTrans=function(col,opacity) {\n let c=d3.color(col)\n c.opacity=opacity\n return c.formatRgb()\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":296,"value":"

Import

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":284,"value":"import {book_index} from \"@westernpower/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"import {font} from \"@westernpower/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"d3 = require(\"d3@7\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"plt = require(\"https://cdn.plot.ly/plotly-latest.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":315,"value":"d3hsv = require(\"d3-hsv@0.1\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1"}} 31:"$30:body"