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Unit 5.1 - Water Balance of a Tree

Martha Conklin, SSCZO staff and students (University of California, Merced)
Based on material from Physical Hydrology and journal articles; also see Peterson, E.W. (2005) for another catchment-level water balance activity.

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The assignment is to calculate an annual water balance for a tree using data gathered at the Southern Sierra Critical Zone Observatory. In the framework of experimental design, students will organize around a research question "Is there enough water in the soil to account for transpiration?" After gathering and organizing data, students will calculate the annual water fluxes and reservoirs using a mass balance approach. Later these lessons can be expanded to catchment-scale calculations.

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Learning Goals

Concepts and Content

  • Students will integrate CZO data from multiple sensors to calculate a water balance centered on a tree. They will apply concepts of fluxes and reservoirs to complete a mass balance equation on an annual time scale.

Thinking skills

  • Critical thinking will be employed in designing the research question framework and connecting disparate data sets. While data can be pre-gathered and presented to the students, the class or groups must first think through which data sets are necessary for the completion of the assignment.

Context for Use

This is a weeklong unit in an upper-level undergraduate course on the Critical Zone. Students should have basic understanding of soil structure, vegetation physiology, and mathematical skills needed for the calculations. It will cover two 75-minute periods and require the use of calculators and/or computers. If you have a longer or less-frequent class time, adjustments can be made to the suggested activities as needed. The unit can be scaled up in complexity by having students find and process data from the CZO digital libraries, or scaled down by providing simplified numbers in a graphical context (diagram of water balance around tree indicating fluxes and reservoirs for water mass balance, could be appropriate for a 5th grade student).

Description and Teaching Materials

Lecture topics that need to be covered during the two periods:

  1. Water cycle basics: Precipitation / Evaporation & Transpiration / Groundwater and soil-water storage / Surface waters, Oceans / Magnitude of reservoirs, fluxes
  2. Background for calculating water balance
  • Formulating the equation (balance between inputs and outputs)
  • Reworking the equation (what components do we know, what do we need to find?)
  • Spending some time on the units. It is easy for the student to think about cm of water in a precipitation gauge. It might be less obvious to think of cm of water in a stream.
  • CZO hydrology and meteorology network and measurements
    • Southern Sierra CZO network and measurements
    • Where and how to access data, what it looks like and how to modify it

    Possible other topics:

    1. Differences in water cycles among climates
    • Timing, amount of precipitation across climates (mean monthly temperature, precipitation graphs)
    • Evapotranspiration differences based on climate, vegetation (rainforests vs. grasslands, seasonality)
    • Storage and timing of groundwater fluxes, especially relative to other quantities
  • How to quantify or track the hydrological cycle in the field: applicable methods for meteorology, water stress, stable isotopes, hydrology, remote sensing
  • Pre-class reading:

    • Dingman, S. Lawrence. Chapters 1 and 2. "Introduction to Hydrologic Science" and "Basic Hydrologic Concepts." Physical Hydrology. Second Ed. Prentice Hall: New Jersey, 2002.
    • The USGS Water Science School
    • Students should answer the following guided questions as they read chapters and browse the website:
      • How do water properties and cycling processes vary spatially? Temporally?
      • How do scientists measure water properties and processes?
      • How does water cycling impact Critical Zone function and properties?
      • How do processes in the Critical Zone affect water balance?

    Unit 5.1 - Part 1 (75 minutes total)

    • Time: A 75 minute class period (30 minutes for presentation; 15 minutes to cover examples and talk through differences in climate with effects on the water balance; 20 minutes to start worksheet in class - potentially in groups; 10 minutes to reconvene and discuss progress).
    • Setting: Prior to class, students should have read the two Hydrology textbook chapters (see above). Much of the class will be devoted to in-class lecture on water cycle background and implications for human interaction with the critical zone, and discussion of climate (mean monthly temperature and precipitation graphs), measuring and tracking water flows, and how water balance measurements vary according to climate. The worksheet can be completed by students in groups during lecture or outside of class after the lecture.
    • Materials: Bring hard copies of the Water Balance Worksheet (Microsoft Word 200kB Apr17 17).
    • Lecture 5.1 - Part 1: Introduction to Measuring the Water Cycle in the Sierra Nevada (covers water balance equation, fluxes, and reservoirs, and how to think about the water balance in the context of a forested catchment; introduces the Southern Sierra Critical Zone Observatory; gives background for activity 5.1)
    • Activity 5.1 - Part 1 Summary: The water balance worksheet assesses the students' understanding of the conceptual aspects of the water balance (including fluxes, reservoirs, equations), and requires the students to analyze a generalized water cycle of a forest in a Mediterranean climate and compare that to one in a temperate climate. Students are asked to identify what data needs to be collected for a water balance and to write down an equation. The lecture covers a Mediterranean climate, though the instructor should initiate a discussion about how another climate (e.g. temperate climate) is different in terms of amount and timing of precipitation, temperatures, and types of vegetation. Answers are provided in a separate document. The answers are basic and simple. For question 2 (Q2): not all fluxes are required, though at minimum students should show all fluxes and reservoirs listed in the answer to Q1. Students should clearly compare the effects of the two climates in Q3, providing at least two detailed examples (ET, snowpack storage, timing of forest activity, etc.). It may be helpful to have students draw annual graphs depicting mean monthly temperature and precipitation to compare and contrast the two climates.
      • First complete the first two questions in the water balance worksheet (Microsoft Word 200kB Apr17 17) in class. Students will need to briefly identify the needed data and identify the terms in the water balance.
          • Learning outcome: Identify the components in the water balance of a tree and the measurements needed to obtain the needed data.
          • Key concept – Trees have a sphere of influence where they impact the water balance. The water balance involves fluxes (such as precipitation, transpiration) and reservoirs in the critical zone. The magnitude and timing of these fluxes and reservoirs will change for different climates.
    • Homework Assignment 5.1 - Day 1: Complete the rest of the water balance worksheet (questions 3-5).

    Unit 5.1 - Part 2 (75 minutes total)

    • Time: A 75 minute class period (30 minute lecture, 30 minutes group work, 15 minutes discussion at end). Groups will work together on calculations, though calculations may need to be finished outside of class).
    • Setting: Students will need computers to complete this activity. If possible, this is a good day for access to a computer lab; otherwise students can work through questions and activity on their own computers in class.
    • Materials: Bring hard copies of the tree water budget activity or project on a screen.
    • Lecture 5.1 - Part 2: Water Cycles at the CZO: making measurements and using water balance data at the Southern Sierra Critical Zone Observatory
    • Activity 5.1 - Part 2: This activity uses data from the Southern Sierra Critical Zone Observatory's flux towers, soil sensors, and Critical Zone Tree in a framework for estimating contributions to stream discharge. The students will end up using a selection of the data files. However, a larger set of data files is presented. Students need to evaluate and choose which files to work with, as researchers do. More data can be explored at the SSCZO digital library (links in Directions and Additional Resources below). Students may all complete the same calculations. For instance, use a select month, compare different seasons, or compare different years (additional data from the digital library will be needed for this last option). To encourage discussion in the class, students may be divided into multiple groups, with each group receiving data for a distinct season. In the Mediterranean climate where these data were obtained, precipitation is largely limited to the winter months. Water used by vegetation during the summer months must come from another source, generally soil moisture storage or water storage in deep soils and porous bedrock.

      A good discussion point is the time frame to do a water balance. Since this site does not receive summer precipitation, some of the water is stored in the ground over the summer. So if one does a balance over a winter month, storage becomes positive and then the soil becomes saturated. If one does a balance over a summer month, with no precipitation, then the storage term becomes negative as the vegetation uses up the water. If one does an annual balance, the change in storage is minimal. During shorter time periods the storage term is important; during longer time periods, the storage is a minor term in the water balance.
      • Start the Tree Scale Water Budget worksheet (Microsoft Word 37kB Apr17 17). This activity uses streamlined data from the Southern Sierra CZO flux towers, soil sensors, and Critical Zone Tree in a framework for estimating contributions to stream discharge.
        • Learning outcome: Assess the role of trees in moving water from subsurface to atmosphere, and the fraction that flows to the stream. Investigate differences in the water balance between seasons as changing soil water, precipitation, and ET shift in response to seasonal shifts in precipitation and temperature.
        • Key concept: Trees have a sphere of influence where they impact the water balance. In a seasonally snow-covered environment, snow accumulation and retention is dependent on energy balance (snow subliming due to a tree as a heat source and trees as shade), which is tied to tree density on the landscape.

    Directions (redundant with worksheet, although links are unique)

    • Purpose: Calculate the water balance for a tree. This tree is in 1) a montane setting (limited soils) 2) Mediterranean climate (no precipitation in summer) 3) has the following fluxes and reservoirs: reservoirs: soil moisture, snow, tree water, fluxes: transpiration, infiltration. This exercise has data from 2010, a year with average snowpack, for the SSCZO.
    • Modified Data sets: transpiration (radiation, tree parameters), infiltration (soil moisture and soil characteristics), time period for infiltration (time of snow cover), discharge from stream (Providence (P300) and smaller subcatchments). These data sets contain more than enough data to do the calculation.

    Teaching Notes and Tips

    Notes on provided data for 5.1 Part 2 Activity:

    The data sets provided are for the Providence Watershed at the SSCZO for 2010 (a normal water year). These spreadsheets contain a significant amount of data and the students will need help navigating them and understanding the units. In the end all the fluxes should be in depth of water, these can be converted to volume by multiplying times the area of interest (e.g. the area of plot or the area of the watershed).

    Precipitation: For precipitation there are various measurements and it is worth walking the students through them. There is a shielded precipitation gauge in a forest near basin P303, a Providence subbasin. Forests tend be low wind environments, so this precipitation gauge would accurately collect both rain and snow. There are wind data in the spreadsheet with precipitation measurements, for the flux tower, also in a forested environment that do not exceed 3.5 m/s. The precipitation is recorded as depth of precipitation. We also measure snow depth around the basin, this is converted into snow water equivalents (SWE) by using the density of snow as measured on the snow pillows. There is a snow pillow co-located with the precipitation gauge and snow depth sensors. A discussion topic could be to look at the percent of annual precipitation that falls as snow. SWE is reported in depth of water (similar to precipitation). To calculate the annual accumulation of snow, one should only add up the days that the snow pack increased water content (typically on days below freezing and when there is precipitation, or a day or two after a snow event and that the snow is blown around).

    Soil Moisture: For soil moisture, the data are for the "Critical Zone tree" (czt). It is a tree that has been heavily instrumented with multiple soil moisture probes located in P301 (a Providence subbasin). As the Providence Watershed has granitic bedrock, the soils are shallow, typically 1 m in depth. We have provided the students with data from 3 depths (15, 30 and 90 cm). The data are dimensionless (volume water/volume soil). The students can average the data for each depth and obtain an average moisture content for the soil column. To change this into a depth of water, multiple by the average soil depth (1 m). To look at change in soil moisture over an interval of time (e.g. a year), subtract the soil moisture at the beginning of the year from the end of the year. Typically there is not much change in soil moisture from year to year (it drains or the vegetation uses it up).

    Evapotranspiration: Evapotranspiration is measured at the flux tower located in P301 (a Providence subbasin). These data are not currently available on the SSCZO data library as they are updated and recalculated as we obtain more data. On the spreadsheet with these data, there is a sheet labelled "metadata". It provides a publication reference where the data can be found, the units for the various columns of data. Evapotranspiration (H2O_Flux) is in cm/day. To determine the annual evapotranspiration, sum up the daily values and obtain a depth of water flux.

    Discharge: Discharge is measured in four subbasins in Providence basin (P301, P303, P304, and D102). Any of these basins can be used in the calculations, as the Precipitation, Soil Moisture and Evapotranspiration are relevant to all the basins. In the activity, the area for P301 is given. The units for discharge are m3/s. These can be converted to annual discharge by summing over the year and to discharge depth by dividing by the basin area.


    After the pre-class reading and the first lecture, students should be able to complete the water balance activity (Activity 5.1.1). Complete answers should identify the different parts of the water balance and their relationships, particularly the influence of climate and precipitation timing on evapotranspiration and runoff. A well-justified experimental design for the last question will need a research question, background reasoning to support the question, and a hypothesis. Brief research methods would be a bonus. This activity can be graded according to the 5.1.1 grading rubric (Acrobat (PDF) 114kB Apr17 17).

    To be awarded full credit, students completing Activity 5.1.2 need to answer all questions, import and use data to calculate the water balance, and estimate discharge to the streams from the area of interest. Even if the ultimate value is not correct, students should evaluate and discuss the amount of estimated runoff/discharge relative to other terms. This activity can be graded according to the 5.1.2 rubric (Acrobat (PDF) 109kB Apr17 17).

    References and Resources

    Pre-class reading:

    Dingman, S. Lawrence. Chapters 1 and 2. "Introduction to Hydrologic Science" and "Basic Hydrologic Concepts". Physical Hydrology. Second Ed. Prentice Hall: New Jersey, 2002.

    The USGS Water School:

    Additional References:

    Bales, R.C., J.W. Hopmans, A.T. O'Geen, M. Meadows, P.C. Hartsough, P. Kirchner, C.T. Hunsaker, and D. Beaudette. 2011. Soil Moisture Response to Snowmelt and Rainfall in a Sierra Nevada Mixed-Conifer Forest. Vadose Zone J. 10:786–799. doi:10.2136/vzj2011.0001.

    Baldocchi, Dennis D., Xu, Liukang, and Kiang, Nancy, 2004. How Plant Functional-Type, Weather, Seasonal Drought, and Soil Physical Properties Alter Water and Energy Fluxes of an Oak-Grass Savanna and an Annual Grassland. Agricultural and Forest Meteorology, 123, 13-39.

    Fernandez-Illescas, C. P., A. Porporato, F. Laio, and I. Rodriguez-Iturbe. 2001. The ecohydrological role of soil texture in a water-limited ecosystem. Water Resources Research 37:2863-2872.

    Le Maitre, David C., Scott, David F., and Colvin, C., 1999. A Review of Information on Interactions between Vegetation and Groundwater. Water SA, 25 (2), 137-152.

    Lutz, James, A., van Wagtendonk, Jan W., and Franklin, Jerry F., 2010. Climatic Water Deficit, Tree Species Ranges, and Climate Change in Yosemite National Park. Journal of Biogeography, 37, 936-950.

    Neilson, Ronald P., 1995. A Model for Predicting Continental-scale Vegetation Distribution and Water Balance. Ecological Applications, 5(2), 362-385.

    Royce, E.B. and Barbour, M.G., 2001. Mediterranean Climate Effects. I. Conifer Water Use Across a Sierra Nevada Ecotone. American Journal of Botany, 88(5), 911-918.

    Stephenson, Nathan L., 1998. Actual Evapotranspiration and Deficit: Biologically Meaningful Correlates of Vegetation Distribution Across Spatial Scales. Journal of Biogeography, 25, 855-870.

    Stephenson, Nathan L., 1990. Climatic Control of Vegetation Distribution – The role of the Water Balance. The American Naturalist, 135, 649-670.

    Seyfried, M. S. and B. P. Wilcox. 2006. Soil water storage and rooting depth: key factors controlling recharge on rangelands. Hydrological Processes 20:3261-3275.

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    These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. The materials engage students in understanding the earth system as it intertwines with key societal issues. The collection is freely available and ready to be adapted by undergraduate educators across a range of courses including: general education or majors courses in Earth-focused disciplines such as geoscience or environmental science, social science, engineering, and other sciences, as well as courses for interdisciplinary programs.
    Explore the Collection »