Fragmented Corrections to the van Genuchten–Mualem Model Diverge by 24–68% from a Consistent Coupled Parameterization: A Quantitative Demonstration for Thermal, Osmotic, and Hysteretic Conditions

Water does not move through soil the way it flows down a smooth pipe. In the ground, water clings to tiny grains, navigating a labyrinth of pores that shrink and expand as the soil dries out or gets wet. To predict how this water moves—whether it is rain soaking into a field, salt spreading from irrigation, or moisture shifting through a clay barrier—scientists rely on a standard set of rules known as the van Genuchten–Mualem model. This model acts as the default calculator for water movement in variably saturated soil, describing how tightly water holds on to dirt particles and how easily it can slip past them. For decades, this calculator has worked well under simple, stable conditions. But the real world is rarely simple. Soil temperatures fluctuate, irrigation water often contains dissolved salts, and the path water takes when soaking in is rarely the same as the path it takes when draining out.

When these complex conditions arise, researchers have traditionally tried to fix the standard model by applying separate, isolated corrections. They would adjust the numbers for heat, then apply a different adjustment for salt, and finally add a third tweak for the difference between wetting and drying. The problem is that these patches were often stitched together without checking if they fit the same underlying logic. In a new study, researchers from Ho Chi Minh City University of Natural Resources and Environment and Ho Chi Minh City University of Technology have shown that this piecemeal approach leads to significant errors. By unifying these corrections into a single, consistent framework and running detailed computer simulations, they demonstrated that the old, fragmented way of calculating water movement can be wrong by tens of percent, drastically altering predictions of how deep water will penetrate and how much soil it will saturate.

The researchers focused on three specific environmental factors that change how water behaves in the ground: temperature, salinity, and the history of whether the soil is getting wet or drying out. First, they looked at heat. As soil warms up, water becomes less viscous, meaning it flows more easily, much like honey thinning out on a hot day. The standard model often ignores this change, treating water as if it has the same thickness regardless of temperature. Second, they examined salt. When water contains dissolved salts, it develops an osmotic pressure that can either pull water toward it or hold it back, depending on whether the soil acts like a filter that blocks the salt. Many existing models assume the soil always blocks the salt completely, a condition that rarely happens in common sandy or silty soils. Third, they considered hysteresis, a phenomenon where soil holds onto water differently depending on its past. A soil that is drying out holds water tighter than the same soil that is currently soaking up water, yet many calculations ignore this distinction and use a single curve for both states.

To test how much these separate adjustments matter, the team built a unified computer model that handles temperature, salt, and wetting history all at once, ensuring the rules for each factor were consistent with one another. They then ran a simulation of a realistic scenario: a column of dry loam soil being irrigated with salty water under a summer heat gradient, where the surface is hot and the deeper layers are cooler. They compared the results of their unified model against the results of the traditional, fragmented approach, where each correction was applied in isolation or with incorrect assumptions. The differences were stark and physically distinct. When the simulation ignored the fact that warm water flows faster, it underestimated the total amount of water soaking into the soil by 27 percent. When it ignored the difference between wetting and drying paths, it predicted the wetting front would travel 68 percent deeper than it actually did, suggesting water would reach much further underground than it really would.

Perhaps the most dramatic error came from how the models handled salt. In the real world, most common soils like sand and silt do not act as perfect filters for salt; they allow salt to move freely with the water. However, the traditional fragmented approach often assumes the soil acts as a perfect membrane, blocking all salt and creating a massive, artificial suction that holds water back. The researchers found that even a small, incorrect assumption that the soil blocks just a tiny fraction of the salt could suppress the predicted water infiltration by 24 to 51 percent. If the model assumed the soil was a perfect membrane, it essentially stopped the water from moving at all, injecting a fictitious pressure equivalent to a column of water tens or even hundreds of meters high. This error is not just a small calculation mistake; it fundamentally changes the physical picture of what is happening underground.

The study also validated the new unified approach against real-world data to ensure the corrections were grounded in reality. For the temperature effect, they used independently measured data to show that simply adjusting for surface tension is not enough; a more complex relationship is needed to match observed behavior. For the salt effect, they reviewed measurements from various soils and confirmed that the "membrane" effect is near zero in sands and silts, only becoming significant in highly compacted clays. For the wetting and drying difference, they tested their unified model against laboratory measurements of soil moisture curves, finding that a simple adjustment factor could predict the wetting behavior of medium-to-fine soils with reasonable accuracy, though the exact value varies by soil type.

The core finding is that consistency matters. Because temperature, salinity, and hysteresis affect water movement through different physical mechanisms, applying them in a disjointed way does not allow the errors to cancel each other out. Instead, the mistakes stack up, leading to predictions that are off by large margins. The researchers have provided a single, closed-form mathematical framework that incorporates all three factors without needing new, unknown parameters. This new formulation collapses back to the standard model when conditions are normal, ensuring it fits with existing data, but it remains robust when conditions change. The result is a more reliable tool for engineers and scientists who need to predict how water moves through the ground, whether they are managing irrigation in salt-affected fields, designing barriers to contain contaminants, or understanding how moisture moves through the earth's crust. By unifying these corrections, the study ensures that the numbers used to describe the ground are not just a collection of patches, but a coherent picture of reality.