Conceptual model of unit hydrology
A simplified conceptual model of hydrologic processes may be presented in the following way:
This diagram is only the top of an iceberg, with a lot of fairly complex processes that may be further described in much more detail and complexity. You may click on the diagram to see some more details about the variables and processes involved. At this point it is important to decide what are the most important features of the system that need be considered.
We chose the following 4 variables for this general model:
The major processes and assumptions we make to create a model:
Like in other models, it is very important to decide what are the spatial and the temporal scales that are to be used in our hydrologic model. At different temporal scales processes look fairly different. Consider a major rainfall event, when, say, during a thunderstorm you had a downpour that brought 3 cm of precipitation in one hour. Then the storm moved away and there was no more rain over the next 23 hours.
If you assume a 1 minute time step in your model, you will need to take into account the accumulation of water on the surface, its gradual infiltration into the soil, which will happen as some of the water is also removed by overland flow. If you look deeper into the unsaturated layer, you will see how the front of moisture produced by the infiltrating water will be moving downwards through the layer of soil eventually to reach the saturated layer. After the rain stops in a while all the surface water will be removed, either by the horizontal flows, or by infiltration. A new equilibrium will be reached in the insaturated layer, some of the water accumulating on top of the saturated layer and effectively rising it somewhat, the rest of the water staying in the unsaturated layer, increasing the content of soil moisture (the sponge analogy).
Suppose that the model time step is 1 day. The picture will be totally different. In 1 day we will see no surface water at all. It will already either get into the soil, or run downhill to a nearby stream, river or pond. The unstaurated layer will not show any of the water front propagation, it will already equilibrate at the new state of moisture content and groundwater level. The processes look quite different in the model.
Similarly, the spatial resolution is important. In the unit model presented in the diagram above, we assume a spatially homogeneous location. That is all the variables are averages over a certain area. Within this area we do not distinguish any variability, the amounts of Surface Water, Snow/Ice, Unsaturated and Saturated Water are the same. If we are looking at a 1 m2 cell this does not cause any problem and it is easy to imagine how to measure and track these variables. However, if we are considering a much larger area, say 1 km2, then within one cell we may find hills, depressions, rivers and ravines. The geology and soils may be also quite different and need be averaged across the landscape.
After looking at individual processes and variables, we can put together the whole model for the hydrologic cycle, assuming that we can single out an area that is more or less independent of the adjacent regions. We assume that we are looking at an area of approximately 1 km2, located in a relatively flat terrain that is not too much affected by horizontal fluxes of groundwater. There is a certain gradient of elevation that is sufficient to remove all the excess of surface water that did not get a chance to infiltrate into the ground over one time step. The groundwater table is rather stable and tends to be at equilibrium at the initial conditions. The climatic data that we have is at a daily time step, therefore there is no reason to assume a finer time step in the model. Thus, our time step is 1 day and our spatial resolution is 1 km2.
The model diagram gets quite complex, but you will certainly recognize some of the modules and submodels previously considered. By clicking on individual groups of processes you can go to the corresponding pages for a review.
The Globals sector contains climatic data that are input as graphs and the empirical model for solar radiation. Here we also define the elevation of the area considered. This might not be very important for the unit model, but it will become crucial when combining the unit models into a spatial simulation.
The Input/Output sector presents all the model parameters and the graphic output generated by the model.
The model is fairly complex and it is hard to understand its structure and
equations without looking at the real Stella model.
Click here to download the Stella model
EXERCISES
In reality hydrologic processes are very much spatial and their description within the framework of a spatially uniform unit model is quite limited. Stella is certainly not a proper tool to build spatial models, that may get very complex and require direct links to maps and Geographic Information Systems (GIS). There are two basic approaches used for modeling spatial hydrology:
Each of the two approaches has its advantages and disadvantages.
This decision is made based on
Once the spatial units are picked, they are assumed homogeneous. Certain empirical or process based equations are assumed to define the amounts of water and constituents that these hydrologic units may generate. These quantities are then fed into a network model that represents the transport along the river and it's tributaries. The network model links together the individual models for the spatial units.
One of the classic examples of this approach is the HSPF, which is available for download from a variety of sites.
An outgrowth of HSPF, is the BASINS model.
See - http://www.epa.gov/OST/BASINS/
A major improvement is the user-friendly interface,
which allows you to build a project for a watershed that you are
intersted in. At this site you may even find data sets, which are
needed for the model, for most of the USA.
TOPMODEL is another classical model that has been used for
a variety of rivers and watersheds.
See - http://es-sv1.lancs.ac.uk/es/research/hfdg/topmodel.html
The Patuxent Landscape Model is a grid-based spatial landscape model. See the description of the spatial hydrology in that model at http://kabir.cbl.umces.edu/PLM/MODEL/Hydrology.html
Another excellent example of the grid-based approach is the Everglades model at http://kabir.cbl.umces.edu/Glades/ELM.html
Both these models use an ecosystem-level "unit" model built in Stella, that is replicated in each of the unit cells representing the landscape. For each different habitat type the model is driven by a different set of parameter values (e.g. percolation rate, infiltration rate, etc. are different for a forest vs. an agricultural field, vs. a residential lot).
The hydrologic unit model in PLM is designed very much similar to the
hydrologic model described above. To see more details on the algorithms
of spatial fluxing that link the cells together, check out these two papers:
It should be noted that the methods described there are simplified in order to handle large areas and complex ecological models. The methods suggested can be considered as an empirical approach to surface water routing. It is certainly very much based on some empirical assumptions and common sense. The requirements of a landscape modeling framework, where hydrology is only a part of a much more complex and sophisticated model structure, do not allow the time step to be reduced in order to accommodate the instabilities occuring in the numerical methods used. For that same reason, plus because of the complicated spatial patterns that we encounter, we cannot employ the stable implicit scheme. The methods suggested certainly sacrifice some of the precision, especially in the transfer processes, but they represent the quasi-equilibrium state well and substantially gain in model efficiency in terms of the CPU time required. In this case we have to rely more on the comparison of the model output with the data available, and be ready to switch from the more process based description to a more empirical one.
Certainly by choosing this approach, by diverging from the process-based approach and by allowing more parameter and formulae calibration, we decrease the generality of the model, thus requiring additional testing and calibration when switching to other scales or areas. The question is what is a truly process-based model as against an empirical, regression one. In any process-based model there is a certain level of abstraction at which we actually utilize certain empirical generalizations, rather than true process description. For example, there is hardly an adequate detailed description of the photosynthesis process to be found among the models of vegetation growth, instead some variations of Michaelis-Menten kinetics are applied, which are already empirical generalizations of the process. Nevertheless these models claim to be process-based. As we go to larger systems, such as landscapes, we will need to employ even more generalized formalizations, as was done above for modeling hydrology.
E-mail to Alexey Voinov