Hydromodule numeracy unlocks the puzzles of irrigation

Forty years ago, on this date (28 Sept 1983), I started my first job on a large-scale irrigation system in the Swaziland/Eswatini lowveld in Southern Africa.  I’ve learnt a lot about irrigation in the intervening time. Given irrigation is a true system, it confronts society and science with considerable cross-disciplinary and cross-scalar puzzles.  I’ve seen irrigation understood in different ways, by myself over my career and by others.  (As an aside, irrigation needs a large tent that welcomes many viewpoints.  However, I think irrigation engineering and science debates are burdened with conventions and precepts that draw from an era when water was abundant, leaky, predictable, abstracted from one source, had one or few functions/costs, and when other sectoral needs were low). As well as excellent managers, colleagues and mentors, and a mix of hardware (sprinkler, gravity, drip), ‘fortunately’ for my career training, the hot lowveld was drought-prone – providing insights for the rest of my career.  

Drawing on this experience, here is the question I pose for myself. “Looking back, what has been your most important piece of irrigation knowledge to help unpack its puzzles?”  In other words, what is irrigation’s ‘intellectual scalpel’ (Robert Pirsig) or ‘sonic screwdriver’ (Doctor Who) that interrogates irrigation when water is multi-sourced, varying, scarce, potentially costly, and demanded by many?  I could provide several answers (good training, lots of fieldwork, meeting farmers, working in a team, and so on). 

But rising to the top, the single answer, I believe, is an ability to understand, calculate and work with the irrigation hydromodule. The hydromodule is the ratio of crop evapotranspiration (mm) per day, expressed as the specific ratio of irrigation flow rate (l/sec) to the area served (ha). The hydromodule is therefore ‘litres per second per hectare’ (l/sec/ha).  The hydromodule can be thought as the water duty, although the latter is usually its inverse, so would be ‘hectares’ per litre per second (or other specified units such as acres and cubic feet per second).  

Importantly for irrigation analyses, there are two hydromodules that can be calculated and compared; one calculates crop/irrigation demand in l/sec/ha, and the other calculates the actual irrigation specific supply in l/sec/ha. Allow me to further define and explain these two remarkable ratios and then finish with some observations and a contentious grumble or two.  You can follow some of the below explanations in this spreadsheet. 

• The demand-side or crop hydromodule is identical to the irrigation need in the depth equivalent millimetres per day (mm/day, allowing for effective rainfall and irrigation losses).  This is because 1.0 mm on one hectare is 10,000 litres (10 cubic metres) and 24 hours contains 86400 seconds. So, they inter-convert; l/sec/ha = [(mm/day) x 10000 / 86400].  Or, the hydromodule in l/sec/ha = [(mm/day) x 0.1157].
• An easy-to-remember rule of thumb for the peak irrigation need/demand of an irrigation system in a hot semi-arid environment is the number ‘one’ because 1.0 l/sec/ha is equivalent to a peak crop demand of about 6-9 mm/day allowing for rainfall and irrigation system losses (inefficiencies).  For example, 7.0 mm/day corrected for an 80% irrigation efficiency is a demand hydromodule of 1.013 l/sec/ha.
• This demand hydromodule then becomes the intended/planned/designed supply hydromodule.  But (see below) the actual supply hydromodule likely differs because the command area and the flow capacity of the turnout (gate) at the head of the command area are changed to simplify design and construction, or to build in extra slack, or is changed during construction and on-going operation and maintenance (or lack of).
• Note, hydromodules always must be calculated in, or corrected to, their 24-hour version; this is because soil and crops continue to evapotranspire water during the night.
• Best to express the hydromodule to three decimal places – this precision is necessary for the way it dictates or reflects large flows for large areas)
• The actual supply hydromodule is the irrigation system’s hard-wired-in provision of water to meet the crop water demand ‘at scale’.   The actual specific supply can be determined by dividing the measured flow rate of the supply (l/sec) to a given command area divided by the latter’s area (ha), correcting for the number of hours in the day that irrigation is supplied for.  A daytime flow rate of 120 litres per second to 60 hectares is 2.000 litres/second/ha. Note, if this irrigation supply is for 12 hours only, the 24-hour supply hydromodule is 1.000 l/sec/ha. And recall, the supply hydromodule is usually ‘gross’, meaning the designs of the flows, canals, pipes, valves, gates, etc. allow for system losses.
• We can now compare different irrigation systems; an irrigation system in relatively cool moist UK might have a peak demand module of 0.250 l/sec/ha. A system in arid Southern Africa may have a peak demand hydromodule of 0.968 l/sec/ha.  This does not necessarily mean the latter’s crops (e.g. sugarcane or rice) are per se ‘thirsty’; rather they happen to be associated with climates that are more evaporative. 
• It also means we can compare changes in both hydromodules over time. The demand hydromodule might increase if different crops are grown (bananas are more consumptive than citrus) and the original planned supply hydromodule might become too generous over time if the system has switched to drip causing its new hydromodule to be lower.  (Rebounds in irrigation consumption can occur via other means principally area expansion).
• We can compare the two hydromodules. If the actual final supply hydromodule exceeds the demand hydromodule (equivalent to the planned intended supply), the irrigation system has been over-designed in terms of how it matches the irrigation water demand (and it will over-supply farms and fields unless manually cut back at the command area’s supply point).  If the actual supply hydromodule is less than the intended demand hydromodule, the system is throttled in terms of its water supply.  In the latter, some farmers might attribute their water shortages to their neighbours’ irrigation practices, whereas the whole group of farmers is under-supplied.

OK, that’s the basic introduction. You can see vigilant numeracy is required!

With reference to the linked spreadsheet, let’s say that a mono-cropped gravity irrigation system of 1000 hectares has a uniform demand hydromodule of 1.042 /sec/ha.  This gives us the design/intended supply hydromodule of 1.042 l/sec/ha.  Let’s say the 1000 ha is divided into four farms each of 100 hectares (= 400 ha), 10 farms of 50 hectares (= 500 ha), and 20 small farms on the remaining 100 ha. Each larger farm should be supplied with approximately 100 litres/second on a 24-hour basis, each 50-ha farm should be supplied with about 50 l/sec, and each 5-ha farm should be supplied with 5 l/sec (in this instance they rotate and share the flow of 100 l/sec).

Furthermore, let’s say our irrigation scheme is improved but sticks with gravity supply.  In the before T1 scenario, the irrigation scheme is less efficient (70%) and in the T2 scenario the irrigation has been upgraded by a number of means (changing to 12 hour daytime irrigation, and tighter and more equitable design of water control to mention a few) bringing a turnout efficiency of 85%.  

The demand and actual supply hydromodules allow you to analyse and comment on the following 14 matters: 

1. The two hydromodules immediately unpack the equity of supply (and farmer protestations about supply). Farms receiving approximately 100 l/sec are notionally getting more water than the farms getting 50 l/sec. But their specific supply may be very similar, meaning they are equally supplied.  But take a look at the spreadsheet, via the actual supply hydromodule, Farm 5 in the T1 before scenario is abundantly supplied at 1.600 l/sec/ha and Farm 14 is the least supplied at 0.600 l/sec/ha.
2. They allow you to question and fix poor irrigation design. We might assume the demand hydromodule and the final supply hydromodule are uniform and match precisely. But in real world systems, various influences often result in markedly different designs across space and time. Even with uniform demand hydromodules (in mono-cropped systems), I’ve found supply-side ratios vary hugely.  In other words, engineers don’t take sufficient care to design-in actual specific supplies that closely match demand; their final constructions over- and under-supply different farms/command units.  Read the details and acknowledgements in this 1992 paper. Add that crop demand hydromodules also change over time and space, and you have the beginnings of a real puzzle – all of which can be patiently solved with the scalpel of the two hydromodule ratios.
3. Related to the previous point, hydromodules allow you to see different schools of irrigation engineering for water control. You can work out how these schools prioritise different ways of controlling water. Related, I believe there is a pecking order of water control; from the hydromodule (l/sec/ha), to flows (l/sec) to water levels (mm) to visual or no indicators at all. And there will be farmer indicators and measures – these are not absent or irrelevant! The idea of a hydromodule and its means of control allows you to see why this excellent Bolding et al 1995 paper was award-winning.
4. The hydromodule allows you to see the architecture of water control, asking how modular is the irrigation system in terms of a hierarchy of command areas, flow rates and flow control technology. The 100 ha and 50 ha farms have their own module gate and flow – each is one module. But each of the 5-hectare farms share one modular flow of 100 l/sec with 19 other farms. Here the module is the 100 ha of 20 farms, rather than 20 modules each of 5 ha.  A lack of structured sub-division between the 20 x 5-ha farms may be giving those farmers real headaches sharing water. It is no coincidence that these are similar words; hydromodule (a ratio), modules (gates/turnouts), and modular (a structured architecture).
5. The hydromodule stops you from over-emphasising the meaning of visible leaks in irrigation systems.  In the spreadsheet, Farm 9 in T1 is supplied with 0.700 l/sec/ha (so is under-supplied) but it still could be leaking return flows or have ponds of standing water; and from these clues, might be considered inefficiently over-supplied with water.
6. With hydromodules, you can begin to explore irrigation scheduling, especially during drought periods. You can check if the farmers’ inability to complete and rotate irrigation on time is caused by a low specific water supply to the head of their modular unit, or by internal inadequacies and inequities in intra-unit distribution.  The spreadsheet calculates both the rotation interval and areal progress per day (ha per day) to deliver a required irrigation dose that fits the soil profile (see next point).  You can see that the tighter ‘more efficient’ designs in the modernised T2 system deliver rotational schedules that more precisely match the desired dose for the soil profile. 
7. With the hydromodule in your back-pocket, you can question the efficacy of irrigation tools that purportedly help manage irrigation.  I believe there is no need to give farmers soil moisture meters (as well as being a bit of a pain to use, they cannot accurately capture soil-moisture variability or wetting profiles across thousands of irrigated hectares – FYI my first degree was Soil Science). Instead, we can use hydromodules to arrange a supply-dictated schedule that doses the right depth of water (say 70 mm) at the right interval (every 7-11 days).  This schedule will work ‘at scale’ – it can apply to tertiary units of say 5 to 500 hectares, and thus by extension to thousands of hectares.  And the calculations can be changed over time if needed.  The spreadsheet shows the various calculations including the irrigation scheduling delay (in days) caused by an under-supply of water. Farmers generally know their command areas (and can be grabbed from satellite images); the trick is finding ways of stabilising pre-set flows or accurately measuring varying flows – but with practice this is not difficult, also using short-cuts via simple stage-discharge recording points). 
8. The hydromodule also allows the calculation of the potential areal expansion for each of the 15 outlets should the actual supply exceed the planned designed supply.  Two calculations are conducted; the area expansion via using the surplus supply (the overplus); and the areal expansion using the overplus combined with an increase in future efficiency taken from T2 or T3.  
9. Hydromodules allow you to speak to farmers in ways that stretch everyone’s knowledge. Starting with conversations such as “how do you know if you personally have enough water?”; “how do you know you collectively have enough water?”; “what determines your rate of irrigation?”; and ‘how do you share scarce water?” begins a journey that unpacks vernacular terms for frugal or excessive irrigation, and moves towards fleshing out meaningful numbers. Also, knowing about hydromodules means knowing when they are not useful or needed. 
10. Hydromodules reveal how new lower water withdrawals (so called paper water savings) applied at the headworks of the 1000 ha system are cascaded through the system to the different farms. In the spreadsheet, a 350 l/sec cut in withdrawals is realised, with the result that the new T2 average actual supply hydromodule is 0.803 l/sec/ha, down from T1’s 1.042 l/sec/ha. The spreadsheet shows how new smaller turnouts are required for each farm in order to equitably distribute this lower specific supply.  See next point.
11. Hydromodules tell us how important it is to work with real farmers and real water flows – rather than directly managing consumed water which seems to be the current fashion (and personally does not make sense to me). In the future, frugal flourishing systems will arise out accurately manging real water – afforded by hydromodule analyses.  In the spreadsheet, the cut in withdrawals from T1 to T2 of 350 l/sec means that the river retains that 350 l/sec.  The now-extra 350 l/sec does not need to pass through the irrigation system to magically recycle back to the river (very hydrologically illiterate). If the 350 l/sec overplus was withdrawn into the system, it will likely be used to expand consumptive irrigation, or result in non-recovered water and non-beneficial consumption. Make no mistake though; a final accounting of aggregate depletion/consumption is needed, but this requires a different set of water accounts (see this paper). 
12. Hydromodules indicate priority actions to improve and revitalise irrigation systems.  They help you begin to respond to this apposite observation from Rien Bos in 1987 “water management in future irrigation schemes could be improved if systems were designed in such a way that their proper management would be as easy as the mismanagement of existing systems.”  They also help with new calculations of rejigged designs if an irrigation system seeks to equitably distribute smaller flows within the system. When sequencing performance improvements, I usually start with checking and fixing the demand and actual supply hydromodules before moving to causes of leaks, runoff, ponding etc. My 1992 paper explains my experience in this regard.
13. Hydromodules give you the means to examine water licences for irrigation and the legal framework for water allocation (especially the legal flexibility to meet new patterns of water withdrawals and consumption). Generous licences handed out in the past are likely one of the causes of today’s arguments about over-allocated catchments.
14. Hydromodules allow you to build bespoke irrigation spreadsheets that become intellectual scalpels.  These spreadsheets can be simple as given in the linked example, or highly complex as given in the Appendix of this 2023 paper on irrigation resilience to drought.  Knowledge of hydromodules reveals when you don’t need them, how to use them to cross-check other water calculations, and what you may have missed out.  For the latter, in the accompanying spreadsheet, the irrigation management of the 20 farms under outlet number 15 needs their own set of calculations but they are not shown here).

And now for my contentious grumble:

Worryingly, we face a global lack of irrigation Masters degrees. When I did my excellent degree at Newcastle University in 1992, I could count at least six degrees across the UK, Netherlands and USA.  They have all gone. This lack of capacity in a sector that withdraws some 5-7 cubic kilometres of water per day is alarming. Reflecting this lack of capacity is the absence of hydromodules in our contemporary water discussions.  

Three summary points follow: 1) I cannot see how future irrigation (frugal, flourishing, equitable, low-carbon, giving up water to other sectors, not cutting crop production) can be delivered without Masters-level irrigation literacy and numeracy.  2). Concerned about depletion-based water reallocation, we should ask scientists “where/what are your hydromodules (and how did you derive them?) in your water accounts and satellite analyses of water productivity and consumption that claim to solve the puzzles of irrigation management?” 3) These hydromodule gaps and omissions tell me that global science, policy and funding debates still do not see water-stressed irrigated catchments as sufficiently problematic and urgent. 

To cite this blog

Lankford B. A. (2023). Hydromodule numeracy unlocks the puzzles of irrigation. Posted 28 Sept 2023. https://brucelankford.org.uk/2023/09/28/hydromodule-numeracy-unlocks-the-puzzles-of-irrigation/

(Blog photo credit, Bruce Lankford. Small modular gates and weir controlling the supply to individual farms in a smallholder irrigation scheme, called VIF, in Eswatini).

Also see:

Bos M. G., 1987. Water management aspects of irrigation system design, in Irrigation design for management Asian regional symposium, Volume II, Discussions and Special Lectures, Kandy, Sri Lanka, 16-18 February 1987.  Hydraulics Research, Wallingford, UK, pp.67-76.

Lankford, B.A. and McCartney, M. Due 2023. Managing the irrigation efficiency paradox to “free” water for the environment. In Knox, J.W. (Ed). Improving water management in agriculture. Burleigh Dodds Science Publishing Limited. Cambridge.