How to Make a Potentiometric Surface Map

What a potentiometric surface map actually claims

A potentiometric surface map is a contour map of hydraulic head. Each well gives one number — the elevation, above a datum, that water stands at in that well — and the contours join places where that elevation is estimated to be the same. In an unconfined aquifer the surface it draws is the water table. In a confined one it is the level water would rise to if you put a well there, which is above the top of the aquifer and is not a physical surface at all. The map is the same drawing either way; the sentence you write under it is not.

The reason anybody draws it is the second figure hidden inside it. Groundwater moves from higher head to lower head, down the steepest slope of that surface, so the contours tell you which way the water is going and how hard. That is what decides which wells are up-gradient of a release, where the next well goes, and whether a plume is heading at somebody’s supply well or away from it.

Three things a potentiometric surface map is not, all of which get drawn by accident. It is not a map of depth to water: contour those and the picture follows the ground surface rather than the water. It is not a map of concentrations, which is a plume map and a different figure. And it is not valid across two aquifers at once — heads from a shallow zone and a deep one contoured together produce a surface that exists nowhere.

• Every head on one map should come from the same gauging round. Water levels move with recharge, tides, river stage and the pump next door, so a map built from wells gauged across three weeks is a map of three different days.
• Every head should be relative to the same datum, and the datum should be named on the figure. Two wells surveyed to different vertical datums can differ by a metre with nothing wrong with either measurement.

Why somebody is asking you for one

The federal hazardous-waste monitoring rule says it plainly. A groundwater monitoring programme must include a determination of the groundwater surface elevation each time groundwater is sampled — 40 CFR §264.97(f). What the rule asks for is the measurement. The contour map is the convention that grew up around it, and it is the form a reviewer expects to see.

Underneath that, several state programmes publish report templates and map-guidance documents which name this figure directly — sometimes as a numbered figure in a corrective action plan, sometimes as a requirement that the interpolation method and the date the map was made appear on the sheet itself. That is why the figure recurs quarter after quarter for the same wells, and why the same drawing gets redrawn for thirty years after a landfill closes.

What none of that tells you is what applies to your site. Requirements differ by programme, by state and by the permit in front of you, they are revised, and nothing on this page is legal advice about any of them. Read the guidance that governs your own submittal; what follows is about how the figure is made.

What has to be in the file

One row per well, and four things on it: a name, a position, a water level, and the date it was read. That is the whole requirement, and most field spreadsheets already have it.

The water level is where the work usually is, because a field sheet almost never carries a groundwater elevation. It carries a surveyed top-of-casing elevation, which does not change, and a depth to water measured down from that same reference point, which does. The head is the first minus the second. Doing that subtraction in a spreadsheet column is the single most common step between a field sheet and a figure, and it is the step where a sign error puts the whole map upside down.

A file that looks like the one below is enough to draw from. It is the sample site on this site, and it is deliberately shaped the awkward way round — top of casing and depth to water, no elevation column — because that is the shape a real gauging round arrives in.

• The coordinates need a frame, not just numbers. Latitude and longitude, a UTM easting and northing, or a site grid in metres or feet are all readable, but which one it is has to be stated rather than guessed, because the same pair of numbers means three different distances in the three frames.
• A dry well, a well being pumped and a well screened in a different unit all belong in the file and none of them belongs in the contouring. Leave them in and take them out of the surface deliberately, so that the figure can say it did.

The way it is taught: contouring it by hand

This is the method in every hydrogeology course, and it is worth doing at least once even if you never do it again — a contour you have placed yourself is a contour you can defend, and placing one teaches you what the numbers will and will not support in a way that reading about it does not. It needs the well plan at a known scale, the heads, a straight edge and a pencil.

1. 1

   Plot the wells to scale and post the head beside each one

   The elevation, not the depth to water, to the precision it was measured at. Write it small and to one side so the numbers do not fight the lines you are about to draw.

2. 2

   Choose the contour interval

   Take the range across the site and pick a round interval that gives roughly five to ten lines over it — 0.5 m, 1 m, 5 ft, whatever lands there. Too many contours and the figure claims a precision the wells do not have; too few and the gradient is invisible.

3. 3

   Join the wells into triangles

   Light lines between neighbouring wells, no crossings, favouring short connections over long thin slivers. Each of those lines is a segment along which you are about to assume the head varies linearly, so you are choosing which wells are allowed to talk to each other.

4. 4

   Interpolate along each line

   Between a well at 38.4 and a well at 37.6, the 38.0 contour crosses halfway. Mark the point on the line for every contour value that falls between the two heads. This is the three-point problem done graphically, once per triangle edge.

5. 5

   Join equal values into smooth lines

   Connect the marks of the same value across the map. Contours never cross, never branch, and never simply stop in the middle of the sheet — they close, or they run off the edge of the control. Where they must be extended past the outermost wells, dash them or leave them out.

6. 6

   Bring the hydrogeology to it

   This is the step that is not arithmetic and is the reason the method survives. A gaining stream is a line of known head and pulls contours towards it; a pumping well makes a cone the well network may barely see; a low-permeability boundary steepens the gradient against it. None of that is in the numbers, and you know it.

7. 7

   Label the lines and finish the sheet

   Every contour labelled with its value, an arrow or two down the steepest slope, the interval stated, the gauging date, a north arrow, a scale bar and the datum. A figure that does not say when it was measured cannot be checked against anything.

• What it costs is time and repeatability. Two competent people given the same fourteen heads produce two different maps — usually similar, occasionally not — and neither can reconstruct exactly how the other placed a line. Next quarter starts from a blank sheet, and a revised water level means redrawing the part of the map it touched.
• What it buys is judgement in the right place. An interpolator has no idea the north edge is a river. If you contour by machine, that knowledge has to arrive some other way — an added control point, an excluded well, or a sentence in the report saying what the surface does not know.

The way it is done here, step by step

The same figure, from the same file, with the interpolation done for you and stated on the sheet. Nothing below asks you to configure anything before you see a map: the first drawing appears from the file alone, and every setting is a correction to something already on screen.

1. 1

   Get the round into one sheet

   One row per well, headers on a row of their own. Comma, tab, semicolon or pipe-separated text, a pasted block, or an Excel workbook — the separator, the decimal mark and the text encoding are worked out from the file, and there is no parser setting anywhere to get wrong.

2. 2

   Drop it in and read the detection table

   Every column is listed with the role it was given and the reason it was given it. This is the screen to actually read: it says which columns became the coordinates, what frame they are in, which column is the date and which is the water level. Any one of them is one click to change.

3. 3

   Check the arithmetic it did for you

   If the file had a top-of-casing elevation and a depth to water, the head was computed and the subtraction is written out in your own header spellings. If the file already had an elevation column, it is checked against that subtraction instead, and a row where the two disagree is named.

4. 4

   Look at the map that has already drawn itself

   Contours at an interval derived from your own range, wells posted and labelled, flow arrows pointing down the slope of the computed surface, and the contours clipped to the convex hull of the wells — with anything drawn beyond them hatched and named on the figure rather than presented as measurement.

5. 5

   Correct what needs correcting

   Click a well to take it out of the contouring: it stays posted, gets a legend row saying it was not used, and the method note counts it. Switch the interpolation from inverse distance weighting to ordinary kriging, which fits a variogram to your wells and needs at least eight of them. Set the contour interval yourself if the derived one is not the one your last report used.

6. 6

   Fill in the title block and place the furniture

   The block arrives filled in — site, figure, value mapped, date, well count, interval — and every cell is editable by clicking it on the sheet. The title block, the legend, the scale bar and the north arrow drag where you want them. The arithmetic does not: the method note, the gradient readout and the contour labels have no text box over them.

7. 7

   Export it

   SVG or PNG for the report. DXF or GeoJSON when somebody wants the geometry rather than the picture — the same contours, hull and wells in your file’s own coordinates. All four are free.

Where a water-table map goes wrong

Most bad potentiometric maps are not bad arithmetic. They are a correct surface fitted to numbers that should not have been fitted together, and the figure looks exactly as convincing either way. These are the ones worth checking before a map leaves your desk.

• Wells in different aquifers on one map. If some wells are screened in a shallow zone and others in a deeper one, the surface between them is an average of two things that are not the same thing. Make two maps.
• A well that was being pumped, or had just been. The head in it is a fact about the pump and not about the aquifer, and one such well drags the contours across half the site.
• A dry well, or one where the tape did not reach water. There is no head there. Post the well and leave it out of the surface rather than letting a blank become a zero.
• Contouring straight across a river, a canal or a lake. A surface-water body is usually a boundary of known head, and an interpolator will happily draw a smooth surface through one as though it were not there.
• Extrapolation past the wells. A contour drawn where there is no control is a guess, and the further out it goes the more confident it looks. Here everything past the hull of the wells is hatched and captioned; on a hand-drawn sheet, dash it.
• Different units, quietly. Feet of casing elevation and metres of depth to water subtract to a number, and it is not a head. Check that the two columns you are subtracting are measured in the same thing.

The numbers that come after the figure

The map is usually not the end of the job. The report text wants the hydraulic gradient as a number and the flow direction as a bearing, which is the three-point problem worked on three wells or a least-squares plane fitted through more. If you have two rounds rather than one, the difference between the two surfaces is its own figure and answers a different question — seasonal change, recovery, or the effect of whatever started pumping in between.

Once the flow direction is settled it becomes the thing every chemistry figure is read against. A plume that runs up-gradient is either a second source or a mistake in this map. Whoever reviews your report will check that before anything else.