Watershed Water Balance

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

Project Files

• EXCEL workbook for calculations

Requirements and Connections

Hourly time series of streamflow obtained by

• Downloading processed data from DCEW streamflow stations OR
• Calculating streamflow: described in the Streamflow Measurement exercise.

Total annual precipitation (for coincident time periods as the streamflow) obtained by

• Downloading processed data from DCEW weather stations (smaller watersheds) OR
• Areal average precipitation (large watersheds): described in the Spatial Average Precipitation: Hypsometric Method exercise.

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 (GW_in), and release water as streamflow, also called discharge (Q), evapotranspiration (ET), or groundwater (GW_out) (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+ GW_in)-(Q+ET+GW_out) =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 the amount of stored water is 0. For example, the watershed stores very little water in mid-August. Over a year the wetness varies but returns to approximately the same dry state again the following August, or ΔS=0 for the annual time step. There are limitations to this assumption, but we will assume it’s true for this exercise.

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 + GW_net-Q-ET = 0      (3)

In large watersheds it is commonly assumed that GW_net = 0. This assumption takes two forms. First,  any groundwater in the watershed originated as precipitation and discharges to the surface within the watershed boundary. This assumption relegates GW to a storage term rather than a flux term since groundwater movement is restricted to inside the control volume. Secondd, 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.

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 discharge
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 as a demonstration for the LG station draining the entire DCEW (27 km²) for the 2012 water year (Oct 1, 2011 – Sept 30, 2012).

Steps

1. Download and prepare the Excel Template.

a. Open the Site-Discharge tab.

i. Click cell C1. An scroll arrow should appear to the right of the cell. Select the Lower Gage site. You should see the title of plot change to Site: Lower Gage.

ii. Enter the year 2012 in cell B11.

iii. Reproduce cell a11-c18 in subsequent columns for additional water years if assigned by instructor.

b. Open the Site-precipitation tab and prepare the page as you did for streamflow.

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

a. Evaluate the water year 2012  (Oct 1, 2011-Sep 30, 2012) streamflow data at the LG station that is provided in columns A and B of the of the Site-Discharge tab.

i. 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 for short durations.

ii. A hydrograph is automatically generated for WY 2012.  Visually inspect the hydrograph for annual streamflow patterns. Discuss with colleagues, instructor, neighbors, or yourself anything of interest you might see. When is the peak? When is low flow?

b. For additional water years as assigned, obtain streamflow data for additional years of interest by one of the methods below as assigned by your instructor.  Create hydograph plots for each water year similar to what is automatically done for 2012.

i. Download and compile  calendar year data by browsing to Lower Gauge Data Access page. You will need to construct a time series for the water year from the two calendar year data sets. For example, to construct a 2013 water year dataset you will need to combine Oct 1-Dec 31st, 2012 with Jan 1- Sept 30, 2013 into a continuous record.

ii. Download the entire continuous dataset for the period of record Scholarworks (https://scholarworks.boisestate.edu/dcew_data/7/). You can extract the appropriate dates from the LG column.

iii. Use files provided by your instructor.

c. Calculate the streamflow volume (L) by determining the area under the hydrograph. View 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, beginning in the second timestep (cell c20).
ii. Second, in the calculation ‘red cells’, sum the values from  step 1.b.i to obtain the Cumulative Annual Streamflow Volume (L)

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

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

3. Calculate the Total Annual Precipitation

Precipitation is strongly controlled by elevation in the DCEW (see Background). The value for P in equation 5 (Background) 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 to represent the watershed average and follow the steps below
i. Obtain historical records of cumulative precipitation values for Treeline for water year 2012 (October 1, 2011-Sep 30, 2012). To build water year data from calendar year data you can compute the precipitation that fell from Oct 1, 2011 through December 31, 2011 and then add that amount to the total the fell from Jan 1, 2012 through Sep 30, 2012.

ii. Copy your precipitation water year data 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. A plot of cumulative precipitation is automatically generated for 2012. Create additional plots for other water years as assigned.

iv. Determine the total cumulative depth of precipitation for the year. Enter result in cell B12 and in the appropriate cells in the “Answers” workbook tab.

d. Repeat for additional years as assigned

4. Calculate the Total Annual Evapotranspiration

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

• Annual evapotranspiration
• Ratios ET/P and Q/P

5. Questions/Problems

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

b. Review the ET/P ratios that you computed. Explain what these ratios tell you about the dominant export of water from the landscape. How might these computations be different in a more humid and more arid environment?

c. Describe the climatological and geological factors that may determine the ratios ET/P and Q/P.

d. If you completed the exercise for multiple years, comment on the interannual variability of P, Q, ET, and the ratio ET/P and Q/P. Do they all vary the same?

e. Your water balance computations were over an annual time period. You can also perform similar calculations at shorter time periods, or for individual rain storms. Describe some complications that might arise for shorter time durations. Would you expect the ET/P and Q/P ratios for storm events to be similar to annual?

6. Products to hand in

Your instructor will specific instructions for what to turn in and how to do so. In general, expect to turn in

1. Hard copy of ‘Summary of Results’ table(s) found in the “Answers” tab of the accompanying EXCEL workbook
2. Answers to discussion questions as assigned by instructor.
3. Digital copy of your completed excel workbook. Be sure to follow you instructor’s file naming conventions.