10 Catchment Modeling-III

Ranjana Ray Chaudhuri

epgp books

 

 

 

Objectives:

  • To provides an idea about various models normally used to describe and explain catchment characteristics.
  • To make student understand about use of models in understanding water balance, rainfall-runoff, and groundwater.
  • To learn the application of common range of models in use today.

 

Introduction

 

Some most popular models used in catchment modeling are discussed below:

 

Types of models:

 

1. Water balance models

 

The difference in input and output of the system is change in storage in the catchment, whether it is a pond, lake or the entire catchment. This is based on the principle of conservation of mass and cover in detail in the previous modules.

 

2. Rainfall-Runoff models

 

This kind of model reproduces the relationship between rainfall and runoff on a catchment scale depending on the characteristics of the catchment. These models account for some or all the various components which account for the difference in rainfall and runoff like volume of evapotranspiration, ground water storage, evaporation amongst others. There are currently models which account for even small-scale storage within the catchment like farm ponds, tanks and other rain water harvesting structures. These are important because they are altering stream flow patterns downstream and many times resulting in smaller storage in large reservoirs which have been designed for must larger capacities originally. A certain temporal time interval is chosen in which the catchment dynamics is studied, it can be hourly, daily, weekly, monthly, seasonally, and annually (sometimes even decadal shifts are also studied). In India studying the catchment seasonally is extremely important as the monsoon period governs the storage properties of the catchment. Rainfall runoff models give good results when rain gauge data and stream flow data are available for sufficiently long period of time. A part of the data set is used to establish the model while another is used to calibrate the model (minimum 1 year of data for daily modeling, while a longer data set is needed for calibrating seasonal modeling). While relying on the predictions of stream flow due to rainfall events it is important to note that the predictions are valid for the conditions of the catchment established during calibration stage only.

 

Rainfall runoff models are extensively used for the following purposes.

 

1.    Generally rainfall data is available for longer periods of time than stream flow records, so once the model it established and calibrated, the balance stream flow can be simulated using the rainfall records. Similarly missing stream flow data are also generated with the help of these models.

2.    Rainfall runoff models are used for flood forecasting in the catchment.

3.    There are spatial and temporal changes which occur in the catchment due to change in land use and land cover. This results in change in spatial and temporal distribution of runoff over a period of change in land use. For example, with the extensive advocacy of farm scale rain water harvesting measures like ponds, tanks and check dams at farm level or village level, which were not there earlier in the catchment, the interception of water in the catchment has changed. Similarly, wherever there has been large scale deforestation or afforestation, the interception of water has led to changes in sub surface flow after a rainfall event. It is widely studied through models now that large scale presence of rain water harvesting measures in catchments of a river basin are leading to reduced stream flow. Thus, impacts of such changes at catchment level are not just felt at catchment level but also at river basin scale level. The ecological characteristics of the stream may have altered due to change in environmental flow in the stream. The change in the flow of the stream, like volume and duration can be modeled taking into account the volume of rainfall and volume of original stream flow and change in stream flow due to change in catchment characteristics.

 

Two models are described below, one is a model for flood or peak discharge estimation (Rational formula) in small catchments which is developed based on rainfall intensity and catchment characteristics while the other is a computer algorithm based (IHACRES) model.

4.      Rational formula is commonly used to understand the peak overland flow or surface runoff due to a storm event. The peak over land flow (also known as peak discharge) is estimated for a return period or frequency of occurrence (say for a return period of 1 in 100 years or 1 in 50 years).The design of culvert, small check dams within the catchment would necessitate the estimation of such peak discharge for which we may have storage structures or in case of culverts, carry the flood flow away from the catchment so as not to cause water logging.

 

The model relates the peak discharge to t the area of catchment (A), the rainfall intensity (i) for a duration tc and an exceedance probability (P) and runoff coefficient C which depends on the land use land cover of the catchment. The model is as shown below

In order to estimate the peak discharge, the three parameters are rainfall intensity for the desired frequency, the time of concentration of the catchment and the runoff coefficient.

 

Qp = peak discharge (m3/s)

 

C= coefficient of runoff

 

i= mean intensity of precipitation (mm/hr) for a duration of rainfall tc and an exceedance probability of P

 

A= drainage area measured in km2, (can be in hectares as well to be converted tokm2 to apply in this model)

 

The intensity I is related to the time of concentration tc as explained below.

 

The time of concentration (tc) is defined as the time taken for a drop of water from the remotest part of the catchment to reach the outlet of the catchment, should the rainfall episode continues beyond the time of concentration, the runoff value will be constant and equal to the peak value of discharge. It is calculated empirically using Kirpich formula (1940) as:

 

tc =0.01947 L 0.77 S-0.385

 

where time of concentration (tc) is in minutes

 

L=maximum length of travel of water (m)

 

S=slope of the catchment defined as ∆H/L

 

∆H=difference in elevation between the most remote point on the catchment and the outlet

 

The rainfall intensity i corresponding to the duration tc and the desired exceedance probability P     (return period T years, where T=1/P) is found from the rainfall-frequency-duration relationship for the given catchment area as follows:

 

Itc,p= KTα/( tc+a)n

The coefficients K, a, x and n are specific to a given area (Subramanya, 2008). The runoff coefficient “C” represents the combined effect of catchment losses and is dependent on the nature of the surface, slope of the catchment, soil characteristics and land use cover. The value of C is also given in the above mentioned reference. The runoff coefficient C for catchments is given for agricultural and forest land covers and urban built up areas as well. The Rational formula is used for catchments with are of 50km2 and below.

 

5.      IHACRES (Identification of Unit Hydrographs and Component flows from Rainfall, Evaporation and Stream flow data) is a simple rainfall runoff computer model. It is a spatially lumped model (so the spatial characteristics do not change), it also comes in the category of conceptual rainfall runoff model. The model has two modules; a nonlinear module which determines the rainfall excess from the total rainfall episode or storm event which is calculated after determining how much water is taken up by evapotranspiration, infiltration etc. The linear module then follows which converts the excess rainfall to stream flow or overland runoff. The total rainfall to excess rainfall module is not linear because every time a rainfall episode happens the excess rainfall depends on the antecedent moisture condition, as in how dry or wet the soil is before the rainfall episode. This depends on which time of the year the event occurs and the number of rainfall events that have happened in the past few days. Thus, each different type of catchment condition will result in different stream flow ultimately. Thus, the relationship is nonlinear. The second module which converts the excess rainfall to runoff is linear. In this case the concept used is the unit hydrograph theory, which is each unit of excess rainfall produces one unit of stream flow. The stream flow many times is modeled as the overland flow (surface runoff) and shallow sub surface flow and the deeper sub surface flow which is a delayed flow. This component contributes to the base flow in the stream.

6.      CROPWAT model

 

This is a decision support system model developed by Food and Agriculture Organization (FAO) in its land and water division in order to assist in irrigation planning and crop management. It is a model used in planning irrigation schedules, under different water supply conditions, helps to understand the evapotranspiration requirement of each crop in the catchment due to different agrarian patterns. It is a popular excel based software which does crop modeling, it is readily available from the FAO website. The evaporation transpiration rate of a crop is estimated season wise; this helps in planning for the crop water requirement. The basic parameters incorporated in the model are daily soil moisture balance; root growth, effective rainfall and deep percolation. The model has separate interfaces where climate input factors like maximum and minimum temperature, rainfall, humidity, wind speed & sunlight hours are admitted, while in the other interfaces rainfall, type of crop, crop coefficients for different stages of growth and type of soil can be given as input. The potential evapotranspiration is estimated using Penman Montieth formula using climate factors. The crop water requirement is estimated by subtracting the estimated potential evapotranspiration from effective rainfall. The CROPWAT model is an excellent decision support system used for crop water demand management, it is used extensively for effective agriculture water management in catchments, so as to be able to adopt deficit irrigation techniques if the catchment requires it.

 

The FAO Penman-Monteith method to estimate ETo can be derived as follows:

 

where

 

 

ETo reference evapotranspiration [mm day-1],

 

Rn net radiation at the crop surface [MJ m-2 day-1],

 

G soil heat flux density [MJ m-2 day-1],

 

T mean daily air temperature at 2 m height [°C],

 

u2 wind speed at 2 m height [m s-1],

 

es saturation vapour pressure [kPa],

 

ea actual vapour pressure [kPa],

 

es – ea saturation vapour pressure deficit [kPa],

 

D slope vapour pressure curve [kPa °C-1],

 

g psychrometric constant [kPa °C-1].

 

The reference evapotranspiration, ETo, provides a standard to which:

 

·  evapotranspiration at different periods of the year or in other regions can be compared;

 

·  evapotranspiration of other crops can be related.

(Source: http://www.fao.org/docrep/X0490E/x0490e06.htm#penman monteith equation, the text book, Irrigation:Theory and Practice, AM Michael can also be referred for details in India)

 

7.      Groundwater models

 

A catchment is either serviced by surface water like a stream, river system or lake or by a groundwater system. Ground water extractions are on the increase and studying ground water models in order to understand the catchment is gaining importance. Though ground water is sometimes difficult to model, but it is needed. Groundwater flows through confined or unconfined aquifers. In case of unconfined aquifers, the groundwater has an impermeable boundary at the bottom while the top is the exposed soil surface. In case of unconsolidated soil or sand deposits the unconfined aquifers store large quantities of fresh water. The flood plains of the entire Gangetic basin are unconsolidated aquifers which are natural reservoirs of fresh water. Confined aquifers have impermeable boundaries both at the top and bottom. Extraction of groundwater through wells is carried out from both these types of aquifers. Groundwater models are developed in order to understand the water flow direction in aquifers, change in water levels, change in gradient in aquifer, ground water models are also used to model travel of contaminants, pollutants, simulate salinity levels in aquifers.

 

Analytical models are the simplest groundwater models used to understand the movement of groundwater. Darcy’s law is the most commonly modeled analytical model..

 

Q= -KA (dh/dl)

 

Where Q is discharge measured in m3/sec or in m3 /day as groundwater movement is slow as compared to surface water flow, K is the hydraulic conductivity measured in m/day, A is the cross sectional area through which the groundwater flow is being studied measured in m2, dh/dl is the hydraulic gradient where dh is the fall in water level over a distance dl. Darcy’s law is valid for laminar flow only, which is normally the case for groundwater flow as it is very slow. The negative sign denotes flow of water from higher to lower gradient. Only under certain circumstances the flow is turbulent, when Darcy’s law is not valid. Darcy’s law is used to determine sustainable ground water extractions from confined and unconfined aquifers.

Thiem’s equation

 

This is the other popular groundwater equation. It is also based of Darcy’s law and used to analyse pumping discharge data, aquifer properties like hydraulic conductivity or transmissivity (T=Kb). In case of confined aquifers, the hydraulic conductivity (K) is multiplied with the thickness(b) of the aquifer, so has units of m2/day instead of m/day unlike hydraulic conductivity. It is used to understand the cone of depression created by the drawdown condition. It is one of the most commonly used methods to understand the extraction of ground water in confined aquifers. The assumptions of Theim’s equations are as follows:

 

The aquifer is confined, isotropic and homogeneous

 

The areal extent of the aquifer is infinite

 

The hydraulic head of the aquifer is a straight line

 

The pumping rate remains the constant, it does not change with time Mathematical form of the equation

Q=2π rTdh/dr

 

In this the radial extent of the aquifer is considered as the well is circular.

 

MODFLOW

 

MODFLOW allows groundwater to be modeled both in steady state and under transient conditions. It is the most commonly used software model for ground water modeling. It is a spatially distributed physically based ground water model, which allows flow of groundwater to be modeled in both two dimensions and three dimensions.

 

MODFLOW is based on Darcys law in three dimension and incorporates parameters of storage as well. The Kx, Ky, Kz are hydraulic conductivity in x, y and z directions, W accounts for recharge, pumping, even taking into account source of water from other places or system, so it is a flux term. The hx, hy and hz terms are hydraulic heads in x,y and z directions is termed as specific storage (defined as amount of water per unit of saturated storage volume which can be extracted from aquifer storage) and t is the time in which we are considering the model. The MODFLOW equation is based on the law of conservation of mass, such that the rate of fluid mass flow through the elemental control volume is equal to the rate of change fluid mass storage within the elemental control volume (https://notendur.hi.is/thorstur/teaching/VMOD28/VMODST_Tutorial_Guide.pdf).

 

This groundwater flow in three dimensions is solved using finite difference method where the entire flow region under consideration, is divided into small blocks and mass balance is computed at each time step. The initial conditions, hydraulic properties must be known and with these the hydraulic heads (output) at specific points and times are determined, so that both spatial and temporal conditions are satisfied. Many times the vertical flow component is assumed negligent, then the flow equation becomes two dimensional.

 

8.   Models to understand interconnection between surface water and ground water

 

Surface water and groundwater have generally been considered as two separate components of the hydrological cycle, yet they are systems which are inter-connected hydrologically, geologically and topographically. Understanding and establishing the interconnectivity between ground water and river systems or lake systems in a catchment will help us to management the catchment water system better, it is in this endeavour that models are being developed in this sector.

 

Surface water ground water interactions take place wherever there is permeable material. Normally when the river flow is above the groundwater level, the outflow is from the river to the groundwater till equilibrium is established between the two (this is the losing stream scenario). Whenever, the groundwater table is higher that the stream flow, the water flows from the groundwater storage to the river (this is the gaining stream scenario). The two conditions may happen along various reaches of the river and also at the same reach but at different times. This is the field in which latest models are being developed in order to understand conjunctive use of water for long term sustainable development.

 

Summary:

 

The models that have been discussed in this module are very typical models used for understanding various aspects of the catchment. It is an overview which gives an understanding of the tools used to assess the surface water and groundwater quantities commonly. They are all application based and students can access these models through internet and practice on them for varying catchment properties.

you can view video on Catchment Modeling-III

References

 

  • CROPWAT, FAO, land and water development division, 2002, Available at:www.fao.org/nr/water/infores_databases_cropwat.html
  • Chow, Ven Te, David R. Maidment, and Larry W. Mays. 1988. Applied Hydrology. McGraw-Hill.
  • Michael A.M., Irrigation: Theory and Practice,2009. Vikas Publishing House Pvt Limited.
  • MODFLOW, https://notendur.hi.is/thorstur/teaching/VMOD28/VMODST_Tutorial_Guide.pdf
  • Subramanya  K.,  Engineering  Hydrology,  third  edition,  Tata  McGraw  Hill,  2008.  Aavailable  at: http://www.mhhe.com/subramanya/eh3e