# Estimating the Total Annual Evapotranspiration depth using the Annual Watershed Balance concept

Initial Publication Date: September 8, 2015

#### Introduction

The objective of this step is to estimate the total annual evapotranspiration depth in the study area by applying the law of mass conservation in the watershed. Using a simple bucket model, the change in watershed storage can be expressed as the net difference in influx and outflux of water in the system i.e. IN-OUT= ∆S. Besides the total evapotranspiration (ET) depth, the total annual streamflow depth and the total annual precipitation calculated earlier in Step 3 and Step 4 are the major fluxes in the system. We make certain reasonable assumptions about the other unknown fluxes to arrive at our final estimate of ET.

## Conceptual Outcomes

- Students demonstrate the understanding of law of mass conservation in watershed hydrology along with the concepts of control volume and flux.

- Students demonstrate the understanding of different components of a watershed balance.

- Students develop the understanding of relative magnitudes of different fluxes of water leaving and entering the watershed.

## Practical Outcomes

- Students learn to account for different fluxes as they develop the watershed balance equation for their study areas.

- Students learn to make reasonable assumptions in their analysis of watershed hydrology.

30 minutes

## Computing/Data Inputs

Numerical data: Total annual streamflow depth at the watershed outlet = 15.3 inches
Numerical data: Total annual precipitation in the watershed = 43.1 inches

## Computing/Data Outputs

Numerical value: Estimated total annual evapotranspiration depth

Calculator

## Instructions

Conservation of mass in watershed: Bucket model

Water balance in a watershed is obtained by applying a simple bucket model to the watershed system. According to this model, the net difference in influx and outflow of water in the system is equal to the change in watershed storage.

IN-OUT= ∆S

Incoming and Outgoing water fluxes

Now, Precipitation (R) and Infiltration (GW_in) form the major influxes, where as Streamflow at the outlet (Q), Evapotranspiration (ET) and Groundwater leaving the watershed (GW_out) are the main outfluxes in the watershed system.

Thus,

(R+GW_in )-(Q+ET+GW_out )= ∆S

Final expression for ET

Assuming that the net change in watershed storage over a year is very small, ∆S can be approximated to zero. Similarly, one can approximate GW_in to be nearly equal to GW_out for a large watershed so that the above equation reduces down to

R-Q-ET= 0 or ET=R-Q

Lets substitute the values of total annual streamflow depth (Q = 15.3 inches) and total annual precipitation (R = 43.1 inches) calculated in step 3 and step 4 to get the estimates of total annual evapotranspiration depth (ET).

i.e. ET = 43.1 inches - 15.3 inches = 27.8 inches !

Did you expect the ET to be that high for this watershed?
Note that the above number is only a rough "estimate", as there were several simplifications and assumptions involved in our calculations.