MODELLING APPROACHES – STELLA & HYDROLOGICAL MODELS

STELLA is a modelling platform with a wide range of applications. In A formal approach to hydrological model conceptualization (1993), Jin Lee applies the use of STELLA to hydrological models. By dividing the process of modelling into 1) conceptualization and 2) programming and testing, Lee describes how hydrological model conceptualization can be integrated into STELLA.

Representing a model as a diagram of states and rates, or equivalently as stores and flows, Lee gives an example of such a diagram as reproduced below.

States are represented as rectangles; rates as opposing triangle pairs; and dependencies as arrows. For example, the amount of daily evaporation (upper right) depends on the evaporation rate, which is itself a function of climatic variables, soil conductivity and the amount of soil moisture. Representing a model conceptualization in such a way communicates which real-world phenomena are incorporated, which are idealized, and which are neglected. For example, the daily evaporation depends on the weather, which is neglected. Which phenomena are incorporated often depends on the desired complexity of the model, as well as the researcher’s background knowledge on the relative importance of different factors. Both of these were discussed in the Occam’s Razor post centred around Domingos (1999), and the post on model validity centred around Oreskes et al. (1994).

Lee points out how such a representation links easily to a mathematical formulation for each of the states and rates. Indeed, STELLA allows equations to be defined for each state and rate, incorporating all the relevant dependencies. For example, the equation for daily evaporation would take the evaporation rate as an input.

In Singh et al. (2010), the authors use a water balance model to assess the impact of climate change on the level of Loktak Lake in Northeast India. Water supply is important in the region, given the large population and dwindling groundwater reserves (Tiwari et al. (2009), also source of image with caption below). 

Dividing climate change projections into two groups, defined as A) 2 deg. C global warming from 7 different global climate models (GCMs) and B) 1 to 6 deg. C global warming from the HadCM3 GCM, the authors find that nearly all of the projections from group A, and all from group B, predict increasing lake levels. The authors point out that water management of the lake has already taken place, with two sub-catchments being isolated to reduce lake level rise. The results indicate that more work is needed, or communities and wetlands around the lake may be flooded.

The authors summarise their modelling approach in 3 stages: a calibrated model of the hydrological system dependent on climate data, which is then perturbed by altering the original climate data along the lines of the GCM projection, and then comparing the output with a baseline model defined by projecting current climatic conditions.

Finally, a stochastic hydrological model developed by Dincer et al. (1987) uses a conception similar to Lee’s, by representing a swamp as a series of stores along a line of flow. Each store, or cell, has an outflow dependent on the amount of water in the store. The water balance of each cell in turn depends on the sum of inflows minus outflows. By perturbing the inflow, the changes in swamp capacity and outflow can be measured, and the model was applied to changes to the Okavango swamp in Botswana. 

An interesting aspect of the model is its calibration procedure. The authors note that the long term independent variables (precipitation, inflow and evapotranspiration) are not stationary but probabilistic, meaning that different periods cannot be compared with each other. This leads to a systematic error whereby changes in flow distribution inside the swamp may be missed. The model is more reliably calibrated, however, over the discharge, water level and area variables. The authors conclude on the power of such network models, and the importance of groundwater to the Okavango Swamp.