9 Catchment Modeling-II

Ranjana Ray Chaudhuri

epgp books

 

 

 

Learning Objectives

  • To assess the problem accurately and then set the objectives of the model
  • To explain the process of model development and evaluation
  • To understand modeling steps in order to get deeper understanding of the natural dynamics of the catchment

 

Introduction

 

The process of model development is best understood from figure 1, the development involves five important steps as shown in the figure. The environment may be taken to mean the entire catchment characteristics broadly. Once the problem is identified a model study plan is developed, then the data collection plan is prepared and conceptualization takes place. After this a model is constructed and then the steps of calibration and validation follow. As seen from the figure the steps of data and conceptualization, model set up and calibration and validation are iterative in nature. For any model to be successful it has been identified that stakeholders are involved, competent authorities are involved and public opinion is considered. All this strengthens the model and makes it robust. Once calibration and validation of the model is done then simulation takes place, this helps to check the efficacy of the model. It is only when the users of the model can take suitable water and eco system management decisions based on the model output, that the model can be considered successful. As seen in figure 1 there are sub steps mentioned against the major steps in the model developing process model developed which shall be explained below.

 

Model Purpose

 

There are a numbers of reasons and purposes for which a model needs to be developed. So it is important to identify the purpose for which the model is to be developed. For example, the rainfall runoff relationship is studied in catchments extensively, the model has been explained in detail in previous module; however, the purpose for which it is being studied may be different depending on the problem that we are trying to solve. The purpose for which the relationship is to be studied could be for any of the following purposes in a catchment (may not be limited to these only):

  • To build rain water harvesting structures (ponds, check dams and the like) so that regular floods or droughts occurring in the particular catchment can be addressed, so it is important to quantify the surface runoff rate. Based on this and the time period, the volume generated will determine the size of the structure.
  • To allocate water in the catchment based on the various water demands, like agricultural water demand, industrial and urban water demand, so it important to understand how much water can be extracted from surface water sources and ground water sources. It is also used to decide when surface water may be used and when ground water may be used. This strengthens the cause of conjunctive use.
  • Forecasting of events when flooding/waterlogging may occur in the catchment, when a certain threshold of precipitation is crossed, the runoff generated causes flooding in the catchment, erosion that may occur because of severe rainfall, quantity of sediment generated.
  • All the three purpose categories mentioned above are part of the water management process in the catchment

Objectives of the model

 

Once the model purpose is defined, the objectives of the model will need to be specified. It is imperative to see who are the people or stakeholders who will be using the model, how will the results of the model be used (application). In order to get a clear perspective of these, the specific outputs needed from the model should be discussed with the users. For example, if the objective of the model is to arrest stream bank erosion problem within the catchment then the model must be able to suggest vegetation measures to be planted on the banks, management measures needed to sustain them and other initiatives that may be taken. For this the annual sediment load, quantity of erosion taking place, nature of rainfall, runoff generated and soil characteristics and vegetation characteristics within the catchment must also be known. Prior knowledge of upstream catchments will also be helpful if the stream is coming from outside the catchment. This kind of model may serve as a sub model for a detail water quality model for the stream or river as well.

 

Data collection

 

Once the purpose and objectives are set, what data already exists must be explored. For this a study plan is prepared and pre- existing information is explored. To go back to the rainfall runoff model, measured data on stream flow if available may be collected (how many years stream flow data is available that are to be seen, if rainfall records are available, that too should be collected). Next the quality, accuracy and completeness of data are to be evaluated. Major constraint faced during the data collection stage is the fact that the model may be designed for different time steps while the spatial and temporal data are available in different temporal and spatial resolution. Analysis has also to be done to determine how to make the available data useful to the model scale, for example how to carry out downscaling of temperature and rainfall data from global or regional climate models (which are used for prediction of future temperature and precipitation trends). One has toanalyse if sufficient expertise is available to analyze and assess such data and how much work is involved. If the data cannot be easily collected then may be the objectives of the model may be revisited. Other kinds of data sets that are used for analysis in catchment modeling are land use data, probability distributions of precipitation, nutrient load, sediment load. In addition data set which is of importance is the knowledge about natural processes in the catchment like direction of stream flow, nature of stream flow during different seasons. To take the example of rainfall runoff model for a catchment, in order to build the model well, if the rainfall runoff data record if available on a daily basis then this gives an idea about storage characteristics of the catchment. In summers and at the onset of monsoons the evapotranspiration, soil moisture, infiltration are all quite high, while during the middle of the monsoon months, the effective rainfall which causes runoff is much higher as the storage facilities are full to the brim. This analysis of effective rainfall and therefore surface runoff helps to build a more robust model.

 

Conceptualization

 

At this stage it is important to identify the types of variables to be covered and the expected output based on the data availability, so the decision regarding whether the model will be empirical, conceptual, physical, lumped or distributed, event based or continuous, probabilistic, stochastic or deterministic can to be taken. Once the conceptual model is chosen another set of iteration with the objectives, plan, data availability is carried out involving the various stakeholders’ needs to be carried out so that all the hypotheses may be checked.

 

After conceptualization of the entire system (in this case the catchment), design for a site specific model begins. The model at this stage is represented in mathematical terms. So variables have to be defined, a variable is one which changes with time (in our case the rainfall event measured in mm   or cm changes with time). Variables normally are measured in units of mass, volume, length and time. The other components of a model are constants, parameters and mathematical operators. Constants have fixed value in the model which does not change with time while parameter values may vary with time, they are either measured or are inferred from secondary data (for instance, hydraulic conductivity used for groundwater models are either measured through experiments or are obtained from secondary data depending on properties of the aquifer). Mathematical operators like addition, multiplication, division, subtraction express the relationship amongst variables.

 

The chosen model structure is guided by prior knowledge of science in the relationship between the variables for which the model is being developed and the governing principle is to keep the model simple. If it is possible to explain the relationship with one dimensional equation, two and three dimensional are very rarely used, one dimensional differential equation will be used for example instead of three dimensional differential equation if there is scope to explain the relationship adequately with this.

 

Every model has a few assumptions which are justified based on the understanding of the natural system of the area under study (for example, usually point rainfall data is available this is used to derive catchment area average rainfall data based on certain assumptions or assigned weights that are given to different point rainfall station data).

 

Model performance

 

Once the model is set up (mathematical equation is identified), variables, parameters and constants are identified and assigned values, the model is run and the performance of the model is evaluated. The model performance is evaluated essentially based on the variation in measured values and model simulated values. Often the model cannot predict the extremes of highs and lows with equal precision. For example in case of rainfall runoff model when the model results of stream flow is compared with observed stream flow results there will be variation in the low flows and high flow events. This results in large residual differences between predicted (model values) and observed stream flows. This is because often the measured low stream flow data at stream gauging stations are unreliable; same may be the case with recording high stream flows during flood events. Typically the difference between observed and modeled stream flows for a stream flow at a catchment gauging station is shown below in figure 2, as shown both for high and low flows the difference is high.

 

Measurement of performance of a model

 

The root mean square (RMS) is a measure of error or difference between observed and modeled values. It is calculated as shown below:

 

The errors have the same units as the data measurements, therefore if it is stream flow the unit of measurement will be m3/ day or m3/sec as the case may be. This method works best for high value deviations because of the squaring effect, than the lower values.

 

The Nash and Sutcliffe efficiency (NSE) is also a measure of the performance of hydrological models.

 

 

Qo, Qm are observed/ measured discharge and model discharge values. ¯Qo is mean observed discharge for the time period T over which the model values are tested. Nash-Sutcliffe efficiencies can range from – to 1, an efficiency of E=1, means that the observed and model values have a perfect match, while E=0 indicates that the models predictions are similar to the mean of the observed data. However, if the value of E is negative (- < E < 0), it means that the observed mean is a better predictor than the model values of discharge. It means the model is unable to simulate the stream flow and iterative steps must be repeated to revise the model equation. In short closer the value of efficiency is to 1, more accurate is the model. WHAT-Web based hydrograph analysis tool may be used to carry out model performance (https://engineering.purdue.edu/mapserve/WHAT/compute_r2_nash_sutcliffe.html).

 

 

There are a number of statistical methods used to check model errors, only two are discussed here. Once the model code logic is verified and model behavior is accepted a sensitivity analysis is carried out. If the sensitivity analysis reveals over parameterization, which is indicated if the sensitive analysis reveals that the model is insensitive to a few parameters, then it is better to remove those parameters and simplify the model. Saltelli et. al. (2000) give an idea about various methods of sensitivity analysis and their necessity. At this stage review and dialogue with relevant stake holders may be carried out and if need be further iterations can be carried out. Once the performance of the model is established, then the step of validation is taken up, Klemes, 1986 explained model validation tests which are widely adopted today.

 

One of the model validation methods is explained here. Models are widely used to understand ungauged catchments as the catchment data is insufficient. So what is done is two similar catchments are chosen (say X and Y), which have similar properties between them and similar to the ungauged catchment. The model is calibrated using data (e.g. stream flow data) from one and validated using the catchment data of Y. Only if the two validation results are acceptable, then the credibility of the model is established to simulate stream flow in the ungauged catchment too, as was explained in the previous module. However, it is not always possible to have sets of data for validation of model especially for ground water contaminant problems, as there may not be any previous history of contamination in the catchment. That does not mean that the model is not acceptable, only that a greater degree of uncertainty has to be built in the model output, as the historical dataset is not available or is available for a very short period in time.

 

Under such circumstances, a matrix is used to understand the sources of uncertainty in the modeling process, it provides an identification of all relevant sources of uncertainty and a prioritising based on a qualitative assessment of their importance. The matrix provides a framework to keep track of all sources of uncertainty during the modeling process. The source of uncertainty could be in the input data, model structure, parameters chosen, numerical method or software chosen. Though uncertainty is not discussed in great detail here, it may be studied from elsewhere (Refsgaard, 2007).

 

In order to understand the success of the model, following points must be satisfied.

 

  • The purpose of modeling is satisfied
  • The model behavior is approximately the same as the catchment system under study
  • The space and time steps chosen in the model are sufficient to understand the real catchment scale problems
  • The model boundaries are chosen correctly
  • The model implementation follows all steps including calibration and validation if possible
  • Sensitive parameters must be identified
  • Uncertainty analysis must be performed

 

Role of models in decision making process

 

Scientists now have a more clear understanding of the physical complexities of a catchment and river basin, however, it is not enough to understand the catchment only scientifically today. The level of public involvement is high and the objectives of the models have to be communicated to the stake holders as well. Decision support models play a significant role in that. The CROPWAT model of Food and Agriculture Organization (FAO) explained in the next module is one such model which helps in decision making. The scientific part of the model helps in assessing the evapotranspiration requirements of the crop through analysis of climate data, and then the other interface of the model looks at optimum use of water (water allocation) through irrigation scheduling. Should less water be available in a particular season due to drought, it allows the model to decide deficit irrigation techniques. All stake holders can be communicated the output of the model and a collective decision taken. It is one of the most successful decision support methods that are used now to choose a sustainable cropping pattern in different agro climatic zones of the world.

 

The key issues related to use of quantitative models such as CROPWAT as a decision support method may be as follows:

 

  • Before adopting quantitative methods, qualitative thinking has to take place. Only then, the decision making process can be made robust with the help of the model.
  • The quantitative model may not be able to take care of all the stakeholders in the catchment. However, all stakeholder groups should be involved in the decision-making process as far as possible.
  • At all times, it must be remembered that a model is a simplified version of reality. No model can perfectly represent the complex natural catchment system completely. It is thus important that the assumptions must be clearly stated in the model (for example, the rational formula which is used to measure peak discharge in a catchment is valid for small catchments only – this is clearly mentioned as an assumption in the model, please refer to the next module for details).
  • Models today are sophisticated with high computational power, however, quantitative models can do only what they are specified to do. Therefore, it is important that the objectives of the model are clearly specified. Only then the model outputs can be clearly used in the decision-making process. For example, the rational formula gives peak discharge which the probability of exceedance or return period that is mentioned (flood return period of 50 years,100 years) which is then used to design structures for flood protection or proper channelization so that minimal waterlogging takes place.

 

Summary

 

Models allow a deeper understanding of the dynamics of the natural catchment system and are therefore widely used in integrated water resource management of the catchment. This allows for the concept of sustainability to be widely practiced, especially in the context of water resource management and natural resource management. Models allow use of resource without causing long-term degradation of the environmental, economic, and social systems.

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References

 

  • CROPWAT, FAO, Land and Water Development Division, 2002, www.fao.org/nr/water/infores_databases_cropwat.html
  • Chow, VenTe, David R. Maidment, and Larry W. Mays. 1988. Applied Hydrology. McGraw-Hill.
  • Klemes V., 1986. Operational testing of hydrological simulation models. Hydrological Sciences Journal 31(1): 986.
  • Moriasi, D. N., et.al, Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations, Vol. 50(3): 885−900 2007 American Society of Agricultural and Biological Engineers, ISSN 0001−2351 885.
  • Nash, J. E., and J. V. Sutcliffe. 1970. River flow forecasting through conceptual models: Part 1. A discussion of principles. J. Hydrology 10(3): 282-290.
  • Refsgaard, et.al., 2007. Uncertainty in the environmental modelling processes: A framework and guidance. Environmental Modelling & Software 22 (2007) 1543e1556
  • Subramanya K., Engineering Hydrology, Third edition, Tata McGraw Hill, 2008, http://www.mhhe.com/subramanya/eh3e
  • Saltelli, A., et. al., 2004. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. John Wiley Sons Publishers.