What is an Empirical Model – and How Does it Differ from a Theoretical Process-Based Model?

Understanding different scientific models for measuring complex soil systems

Soil systems are very complex. Soil, vegetation, climate, land management and landscape history all interact in ways that are difficult to fully measure using equations alone. That’s why different scientific modelling approaches exist — and why understanding them matters for achieving sustainable land management.

At Downforce Technologies, we use an empirical model for measuring and reporting on carbon removals from farm scale upwards to the landscape. This sets us apart from traditional theoretical or process-based models which simulate how soil systems work. Our empirical approach underpins Downforce’s ability to deliver Soil Organic Carbon (SOC) data that is accurate, scalable and affordable and suitable for sustainable land management, resilient supply chains and cost-effective reporting.

Empirical models: built from real-world measurements

The use of measurement and observation to make sense of the world – empiricism- has a long history. An empirical model relies on measurements to develop predictions about outcomes, based on observed patterns and repeatability.

Empirical models make very few assumptions about how a system behaves, beyond the relationship between a dependent variable and a set of independent variables. The exact nature of this relationship is established by measurement: how does the value of the dependent variable change as the independent variables vary?

Key characteristics of empirical models

• Bottom-up: They begin with data collected in the real world — such as soil carbon measurements, observations of environmental and physical parameters from satellite-based instruments and surveys.
• Minimal assumptions: They do not require a full understanding of the underlying physics or biology.
• Pattern based: They identify statistical relationships between variables (e.g. how soil carbon changes with vegetation, climate or land use).
• Continuously improving: As more data becomes available, empirical models are retrained and refined.

If repeated soil samples show that areas with certain vegetation patterns consistently have higher soil carbon, an empirical model “learns” from the data to strengthen the relationship — even if the exact physical processes underpinning it are too complex to model directly. This is the foundation of Downforce’s modelling approach.

Theoretical Process-Based Models: built from theory and scientific principles

Theoretical models, also known as process-based models, make up-front assumptions and rules about the behaviour of a system. Although some of the rules are established empirically, many are the result of assumptions, educated guesswork and/or physical reasoning. This means that these types of models require a complex set of rules to function. Examples include DAYCENT, DNDC and Roth C.

Key characteristics of theoretical models

• Top-down: The models start with known scientific principles (e.g. soil physics, decomposition rates, hydrology).
• Mechanistic: They describe how variables should interact based on theory.
• Mathematically defined: They use equations to represent processes such as carbon turnover, microbial activity or water movement.
• Useful when data is sparse: They can operate even with limited real-world measurements.

A process-based soil carbon model might use equations describing decomposition rates, temperature sensitivity, and carbon pools to predict how soil carbon should change over time. These models are powerful, but they rely on assumptions — and those assumptions may not hold across diverse and variable diverse landscapes.

Downforce’s empirical approach

The main independent variable in the Downforce empirical model is the measure of how much organic carbon is present in topsoil - SOC%. The level of SOC comes out of an empirical relationship with Sentinel-2 multispectral data and a range of control parameters. The data from the Sentinel -2 satellite is derived from a multispectral imaging device, which detects the reflectance intensity over a set of wavelength bands in the visible to infrared part of the electromagnetic spectrum. The data have a spatial resolution of 10m, and a temporal resolution of 10 days, which means that for a 100ha site, 370,000 primary data points are collected per spectral band per year.

Downforce uses a functional classification based on the elements of SCORPAN[1] to minimise the influence of different parameters on SOC variation. In this way, the quality of the measured relationship between the satellite data and SOC can be improved and the uncertainty reduced. There are four key steps to Downforce’s SOC measurement approach. At each step, different primary data is used:

1.Ingestion of SOC samples for Digital Soil Mapping

This makes use of thousands of soil samples. Each sample point is categorised by location, land-use and soil type. Relevant climatological data (temperature and rainfall) as well as the topology of the sampled area is also gathered and recorded. This geospatial metadata is used to drive a machine learning model to build a regional digital soil map.

2. Functional classification

Soils are highly complex, and a host of environmental forces play their part in shaping soil and influencing how its constituent parts (including SOC) change over time. Rather than try to directly account for all of these drivers in the model, their individual influence is minimised by creating functional classes based on soil type and texture, land use, topology and climate, to identify land which is statistically similar within the wider region.

3. Remote sensing and empirical model

Once the functional classification is complete, soil carbon data (the dependent variable) are collected from within the same functional class and related to geolocated satellite data (the independent variable). A model relating how the satellite data varies for the different SOC values within each functional class can then be constructed. This model is then applied to the whole area of interest based on satellite data collected for every 10m x 10m “pixel”, every dekad (10 day period) and used to predict the SOC values. Large-scale averages remove the influence of noisy data and give a robust picture of the soil carbon stocks as seen through the lens of the model.

4. Linking SOC to Farming Practices and Activities

Empowered with accurate SOC measurements, farmers, landowners and supply chain companies can implement more sustainable agricultural solutions to drive farmer profitability, improve resilience and remove carbon from the atmosphere. Our empirical model can be constructed a priori for different management practices or used to detect their outcomes.

Connect with our team to learn more about our approach for delivering Soil Organic Carbon data: info@downforce.tech

[1] The SCORPAN parameters - Soil, Climate, Organism (biome), Relief (terrain), Parent material, Age and eNvironmental factors. These parameters are used to describe the development and distribution of soils and improve the accuracy of soil property predictions A. McBratney, M. Mendonça Santos, B. Minasny (2003). On digital soil mapping. Geoderma, 117 (2003), pp. 3-52, 10.1016/S0016-7061(03)00223-4.

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