# Watershed Water Balance

• Water Cycle/Balance Schematic [Source: FISRWG 1998]

## Problem

Watersheds receive water as rain and snowmelt, and loose water as evapotranspiration, streamflow, and groundwater recharge. Differences between the amounts of received and lost water result in changes in the amount of water stored in the watershed. This is an example of the Law of Mass Conservation, known to hydrologists as the water balance.  While some components of the water balance are easily measured, others are not. Can we use the Law of Mass Conservation to estimate unmeasured components of the watershed water balance?

## Goal

The goal of this project is to estimate the amount of annual evapotranspiration from Dry Creek Experimental Watershed (DCEW) using a water balance approach.

## Learning objective(s)

Upon completion of this exercise, students will be able to

• Define important components of a mountain watershed water balance
• Write an algebraic equation expressing the watershed water balance
• Describe the concepts of flux and control volume with respect to conservation of mass
• Estimate the total annual depths (Volume/Area) of precipitation and streamflow from time series records
• Describe errors associated with estimating the magnitude of evapotranspiration (or another water balance component) as a water balance residual
• Describe the hydrometeorological and geological controls on the relative magnitudes of water balance components

## Requirements and Connections

• Hourly time series of streamflow obtained by
• Calculating streamflow: described in the Streamflow Measurement exercise.
• Total annual precipitation (for coincident time periods as the streamflow) obtained by

• ## The Water Balance Equation

Conservation of mass is a fundamental physical concept in hydrologic science (Equation 1). The rate of water flow into a watershed minus the rate water flow out of a watershed equals the rate of change in the amount of water stored within the watershed. A bucket of water is a simple example. If more water comes in through the top of the bucket than leaves through the drain, the water level in the bucket rises.

IN-OUT = Change in storage (1)

Watersheds behave in a similar fashion to the bucket. Over a specified period of time (Δt), a watershed can receive water as rain (R), snowmelt (SN), or groundwater (GWin), and release water as streamflow, also called discharge (Q), evapotranspiration (ET), or groundwater (GWout) (Equation 2). Human influences may also contribute water gains and losses, but this example is restricted to natural watersheds. If the sum of inflows exceeds the sum of outflows, the watershed becomes wetter, that is to say soil moisture increases, groundwater levels rise, and lake levels rise creating a change (Δ) in water storage (S).

(R+ SN+ GWin)-(Q+ET+GWout) =ΔS (2)

Hydrologists must often measure or model the various components of the water balance equation. Precipitation and streamflow are fairly straightforward to measure. Evapotranspiration and groundwater are not. We will make some assumptions about the water balance equation to estimate evapotranspiration as the residual.

Water storage rises and falls within the year, but over the duration of a year we assume that the change in water storage is 0.If we lump rain and snowmelt into one precipitation term (P) and lump groundwater in and out into one net term the annual water balance equation becomes

P + GWnet-Q-ET =0 (3)

In large watersheds it is commonly assumed that GWnet = 0. That is to say that any groundwater in the watershed originated as precipitation in the watershed, or that any groundwater that enters the watershed by subsurface flow from outside the watershed boundaries, also leaves the watershed in an equal amount by subsurface flow . The simplified annual water balance equation then becomes

P-Q-ET =0 (4)

and

ET=P-Q (5)

where P and Q represent the total volumes of precipitation and streamflow entering and exiting the watershed during a year.Q is measured at the watershed outlet and represents the volume of water that drained by streamflow from the entire watershed over the desired duration (one year in this project). Methods to measure Q are presented in the Streamflow Measurement exercise. P is measured at small points in the watershed. For small watersheds it may be appropriate to estimate P from a single point. As watershed size increases, P becomes more variable and a spatial average must be used as described in the Spatial Average Precipitation exercise.

The variables in Equation 5 must have matching units. Precipitation is commonly measured in units of depth (L), whereas streamflow is commonly measured as an instantaneous volume per time (L3/t).  The get an annual total volume of streamflow, we can integrate the instantaneous values of an annual hydrograph. We can then multiply the precipitation depth by the watershed area (L2) to get a precipitation volume, and solve for the volume of ET. A problem with this approach is that volumes of P, Q, and ET for a watershed for a year are very large numbers that are difficult to visualize. Instead of converting P to a volume, it is more common to convert streamflow volume to a depth by dividing by the area of the watershed. ET will then also have depth units.  It is important recognize that this streamflow depth is NOT an actual depth of water in a stream. It is a one-dimensional volume. It is the depth of water that water occur if the entire volume of annual streamflow were collected in a giant container and then spread over the area of the entire watershed.

• ## Goal

Estimate the amount of annual evapotranspiration from Dry Creek Experimental Watershed (DCEW) and its subwatersheds using a water balance approach. Students will

1. Calculate the effective depth of annual streamflow
2. Determine the annual depth of precipitation
3. Calculate the annual depth of evapotranspiration
4. Answer discussion questions, as assigned by instructor

Prior to completing the steps below, students should ensure that they understand the project by reading the information in the INTRODUCTION and BACKGROUND tabs.

This exercise can be completed for all watersheds within the DCEW. A watershed is defined as the area draining to one of the steam gauging stations (BS, TL, C1W, C1E, C2E, C2M, and LG). The following steps are written for the LG station draining the entire DCEW (27 km2).  Q and P in Equation 5 are single values representing annual total volumes or depths of streamflow and precipitation, respectively. Step 1 outlines how to obtain Q and Step 2 outlines how to obtain P.

## Steps

1. Calculate the Total Annual Depth of Streamflow (Q)

a. Obtain a record of hourly streamflow values for the LG station for the 2012 calendar year by one of two methods indicated by your instructor
i. Download data by browsing to the watershed of interest from the Data Access page, OR
ii. Complete the Streamflow Measurement exercise.

b. Copy the obtained streamflow data (1a) into the first column, ‘Date/Time’, and second column, ‘Q (L/s)’, of the “Site-Discharge” tab in the EXCEL workbook provided. Make sure to update and rename the “Site-Discharge” workbook tab with the site name, as outlined in the worksheet procedures.

c. Inspect the streamflow data for missing values, denoted as -6999. Replace missing values with your best estimate of streamflow. A simple average of neighboring values will suffice.

d. Calculate the streamflow volume (L) by determining the area under the hydrograph. Here is an example of how to perform this calculation. The general steps are
i. First calculate the volume of streamflow within each time step in Column C.
ii. Second, in the calculation ‘red cells’, sum the values from (1.d.i) to obtain the Cumulative Annual Streamflow Volume (L)

e. Convert the volume of streamflow to a depth (cm) (Cell C14).

f. Repeat steps 1a-1e for other years as indicated by your instructor
i. Copy headers and data into neighboring columns in the same re-named “Site-Discharge” workbook tab.
ii. Enter the year in the appropriate highlighted cell.

g. Record your results in the appropriate cell in the “Answers” workbook tab.

h. If other sites are specified by the instructor
i. Duplicate the “Site-Discharge” workbook tab.
ii. Repeat steps 1a-1g

2. Calculate the Total Annual Precipitation

Precipitation is strongly controlled by elevation in the DCEW (see Background). The value for P in equation 5 should be the elevation-weighted average over the entire watershed.  The best way to obtain the elevation-weighted average is to complete the Spatial Average Precipitation exercise.   If your instructor does not assign the precipitation exercise, you can either use a direct average of several stations within the watershed or assume that the precipitation collected at the Treeline site approximates the average precipitation that falls over the entire DCEW. To complete this Watershed Water Balance exercise

a. Complete the Spatial Average Precipitation exercise, OR

b. Compute the average of 3 stations, or

c. Use precipitation collected at the Treeline Site and follow the steps below
i. Obtain historical records of hourly precipitation values for Treeline for the appropriate calendar year.
ii. Copy obtained data (2b-i) into the first column, ‘Date/Time’, and second column, ‘Cumulative Precipitation (mm)’, of the “Site-Precipitation” workbook tab. Make sure to update and rename the “Site-Precipitation” tab with the site name, as outlined in the worksheet procedures.
iii. Determine the total cumulative depth of precipitation for the year. Enter result in cell B12
iv. Repeat steps (2b-i) through (2b-iii) for additional years as indicated by your instructor. Copy data into neighboring columns in the same “Site-Precipitation” workbook tab. Enter the year in the appropriate highlighted cell.
v. Record your results in the appropriate cells in the “Answers” workbook tab.

3. Calculate the Total Annual Evapotranspiration

For each year and watershed(s) in your analysis, use the annual streamflow and precipitation estimates from above to compute the variables below and record your results in the “Answers” workbook tab:

• Annual evapotranspiration using equation: ET=P-Q
• Ratios ET/P and Q/P

4. Questions for Discussion

a. What are the sources and potential magnitudes of error in the estimation of evapotranspiration by the water balance method?

b. What are the climatological and geological factors that determine the ratios ET/P and Q/P and contribute to variability of computed water balance components?

5. Products to hand in

Unless instructed otherwise, turn in:

• Completed ‘Summary of Results’ table(s) found in the “Answers” tab of the accompanying EXCEL workbook.
• Answers to discussion questions as assigned by instructor.
• Evaluation survey for this module.