Hydrology:Soil moisture, Rainfall, and Evapotranspiration

Tarendra LakhankarNOAA-CREST Center, The City University of New York

• Hydrology• Rainfall• Soil moisture• Evapotranspiration• Experiments

– Math Examples: Average precipitation estimation using map– Soil moisture experiment using moisture meter

Overview

The Hydrologic Cycle

Rainfall

Precipitation

• Single strongest variable driving hydrologic processes• Formed water vapor in the atmosphere

snowrain

graupelsleet

freezing rainhail

Water vapor

Droplets form by nucleation

Droplets increase in sizeby condensation

Droplets become heavyenough to fall

Evaporation decreasessize of many droplets

Some droplets increase in size by impact andaggregation

Rain Drops

Larger drops break up

• Point Measurement – Rainfall Gauges• Network of Rainfall Gauges

– The number of stations depend on precipitation and its variability

• Area Measurement – Radar, Satellites• Source of Data

• http://www.crh.noaa.gov/ind/precip.php• http://www.srh.noaa.gov/ridge2/RFC_Precip/• http://water.weather.gov/precip/download.php• http://www.cocorahs.org/ViewData/• Many other publications, Universities, etc.

Precipitation Measurements

Q iCA=

If Q = cubic feet per second, P = inches/hour and A= Acres, Then Q = 1.008CiA

Q = Peak discharge, cfsC = Rational method runoff coefficienti = Rainfall intensity, inch/hourA = Drainage area, acre

Ground Cover Runoff Coefficient, C

Lawns 0.05 - 0.35

Forest 0.05 - 0.25

Cultivated land 0.08-0.41

Meadow 0.1 - 0.5

Parks, cemeteries 0.1 - 0.25

Unimproved areas 0.1 - 0.3

Pasture 0.12 - 0.62

Residential areas 0.3 - 0.75

Business areas 0.5 - 0.95

Industrial areas 0.5 - 0.9

Asphalt streets 0.7 - 0.95

Brick streets 0.7 - 0.85

Roofs 0.75 - 0.95

Concrete streets 0.7 - 0.95

Simplified Table of Rational Method Runoff Coefficients (see references below)

Rational Method for Watershed Discharge

Precipitation Measurement

Precipitation Measurement

Tipping-Bucket: Demonstration

• A rain gauge (also known as an udometer, pluviometer, or an ombrometer) is a type of instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation over a set period of time.

Pluviometer

Precipitation Measurement

Outside CanopyUnder Canopy

Precipitation Measurement

Precipitation Measurement

Ideal rain gage for rainfall with egg-crateStructure (Dingman, 2002)

• Conifer forests in North America Ic = 15-40% of Pg

• Natural teak forests in Thailand Ic = 65% of Pg

• Is influenced by rain:– amount, – duration, – intensity, – and pattern

Rainfall Interception

• Simplest method for determining areal average

Arithmetic Mean Method

P1

P2

P3

P1 = 10 mm

P2 = 20 mm

P3 = 30 mm

• Gages must be uniformly distributed• Gage measurements should not vary greatly about the

mean

∑=

=N

iiP

NP

1

1

mmP 203

302010=

++=

Isohyetal method

• Steps– Construct isohyets (rainfall contours)– Compute area between each pair of

adjacent isohyets (Ai)– Compute average precipitation for each

pair of adjacent isohyets (pi)– Compute areal average using the

following formula

∑=

=M

iii pAP

1

P1

P2

P3

10

20

30

A1=5 , p1 = 5

A2=18 , p2 = 15

A3=12 , p3 = 25

A4=12 , p3 = 35

mmP 6.2147

35122512151855=

×+×+×+×=

∑=

=N

iii PA

AP

1

1

Inverse distance weighting

P1=10

P2= 20

P3=30

• Prediction at a point is more influenced by nearby measurements than that by distant measurements

• The prediction at an ungaged point is inversely proportional to the distance to the measurement points

• Steps– Compute distance (di) from ungaged

point to all measurement points.

– Compute the precipitation at the ungaged point using the following formula

∑

∑

=

=

=N

i i

N

i i

i

d

dP

P

12

12

1ˆ

d1=25

d2=15

d3=10

mmP 24.25

101

151

251

1030

1520

2510

ˆ

222

222=

++

++=

p

( ) ( )221

22112 yyxxd −+−=

Thiessen polygon method

P1

P2

P3

A1

A2

A3

• Any point in the watershed receives the same amount of rainfall as that at the nearest gage

• Rainfall recorded at a gage can be applied to any point at a distance halfway to the next station in any direction

• Steps in Thiessen polygon method1. Draw lines joining adjacent gages 2. Draw perpendicular bisectors to the lines created in

step 13. Extend the lines created in step 2 in both directions

to form representative areas for gages4. Compute representative area for each gage5. Compute the areal average using the following

formula

∑=

=N

iii PA

AP

1

1

P1 = 10 mm, A1 = 12 Km2

P2 = 20 mm, A2 = 15 Km2

P3 = 30 mm, A3 = 20 km2mmP 7.20

47302020151012

=×+×+×

=

Rainfall interpolation in GIS

• Data are generally available as points with precipitation stored in attribute table.

Rainfall maps in GIS

Nearest Neighbor “Thiessen” Polygon Interpolation

Spline Interpolation

Figure 2.14

Storm Patterns (Histograms)

Lets do some calculation

Estimate Average precipitation

Soil Moisture

Soil Moisture

• Meteorological and weather prediction modeling

• Hydrological modeling – Runoff prediction and flood control– Reservoir management – Soil erosion and mud slide

• Agriculture applications– Improving crop yield– Irrigation scheduling

Volumetric vs. Gravimetric Water Content

• In situ field measurement methods only measure volumetric water content

Volumetric Water Content (VWC) Symbol – θ Water volume per unit total volume

Gravimetric Water Content (GWC) Symbol – w Water weight per unit dry soil

weight

50%

35%

15%Air

Water

Soil

• Gravimetric (w) Technique– Sample representative weight of soil

• Take care to limit water draining/evaporating from soil– Weigh sample on balance with adequate accuracy/precision– Dry sample at 105o C for 24 h

• Allow to cool in desiccators – Obtain dry sample weight and take weight

• Generate volumetric water content– Same as gravimetric except soil is sampled with known volume

Direct Water Content Measurements

Direct Water Content Measurements

• Advantages– Simple – Direct measurement– Can be inexpensive

• Disadvantages– Destructive

• does not account for temporal variability

– Time consuming– Requires precision balance & oven

On field how to take sample

Measuring in situ Water Content (indirect)

• Neutron thermalization– Neutron probes

• Dielectric measurement– Capacitance/Frequency Domain Reflectometry (FDR)– Time Domain Reflectometry (TDR)

• Radioactive source– High-energy epithermal neutrons

• Releases neutrons into soil – Interact with H atoms in the soil

• slowing them down– Other common atoms

• Absorb little energy from neutrons

• Low-energy detector– Slowed neutrons collected

• “thermal neutrons”– Thermal neutrons directly related to H

atoms, water content

Neutron Thermalization Probe: How They Work

The probe contains a source of fast neutrons, and the gauge monitors the flux of slow neutrons scattered by the soil. In using the neutron meter, a cased hole in the ground is necessary for lowering the probe to obtain readings.

Material Dielectric Permittivity

Air 1Soil Minerals 3 - 7Organic Matter 2 - 5Ice 5 Water 80

Dielectric Theory: How it works • In a heterogeneous medium:

– Volume fraction of any constituent is related to the total dielectric permittivity

– Changing any constituent volume changes the total dielectric

– Because of its high dielectric permittivity, changes in water volume have the most significant effect on the total dielectric

Dielectric Mixing Model: FYI

• The total dielectric of soil is made up of the dielectric of each individual constituent– The volume fractions, Vx, are weighting factors that add to

unity

– Where ε is dielectric permittivity, b is a constant around 0.5, and subscripts t, m, a, om, i, and w represent total, mineral soil, air, organic matter, ice, and water.

ibiom

bom

bwa

bam

bm

b VVVVt

εεθεεεε ++++=

• Rearranging the equation shows water content, θ, is directly related to the total dielectric by

• Take home points– Ideally, water content is a simple first-order function of dielectric

permittivity• Generally, relationship is second-order in the real world

– Therefore, instruments that measure dielectric permittivity of media can be calibrated to read water content

5.0

5.05.05.05.05.0

5.0

)(1

w

iiomomaamm

w

VVVVt ε

εεεεεε

θ +++−=

Volumetric Water Content and Dielectric Permittivity

Dielectric Instruments: Time Domain Reflectometry

Dielectric Instruments: Capacitor/FDR Sensor Basics

• Sensor probes form a large capacitor– Steel needles or copper traces in circuit board are capacitor

plates– Surrounding medium is dielectric material– Electromagnetic (EM) field is produced between the positive

and negative plates

Typical Capacitor

Capacitor

Electromagnetic Field

Dielectric Material

Positive Plate Negative Plate

Example: How Capacitance Sensors Function

EM Field

Sensor (Side View)

0 cm

1 cm

2 cm

• Answer: It depends on what you want.– Every technique has advantages and disadvantages– All techniques will give you some information about water content

• So what are the important considerations?– Experimental needs

• How many sites? How many probes at each site? – Current inventory of equipment

• What instruments are available or can by borrowed– Budget

• How much money can be spent to get the data?– Required accuracy/precision– Manpower available to work– Certification

• People available certified to work with radioactive equipment

Question: What Technique is Best for My Research?

• Case: Irrigation scheduling/monitoring– Details

• 20+ sites, measurements from .25 m to 2 m• Spread over field system• Continuous data collection is desirable• Money available for instrumentation• Eventually moving to controlling irrigation water

– Choice• Capacitance sensors

– Good accuracy– Inexpensive– Easy to deploy and monitor– Radio telemetry available to simplify data collection

Examples: Applying Techniques to Field Measurement

• Permanent installation– Horizontal insertion

• Purpose– Measure at specific depths– Useful to see infiltration fronts, drying depths

• Technique– Dig trench– Install probes into side wall

» Installation tools are helpful (see manufacturer)

» Ensure NO air gaps between probes and soil

– Refill trench

Sensor Installation

Sensor Installation

• “Push-in and Read” Sensors– Purpose

• Spot measurements of VWC• Many measurements over large area• No need for data on changes in VWC over time

– Technique• Push probe into soil

– Ensure adequate soil to probe contact• Take reading from on-board display

With Replicates

U.S. Climate Reference Network (USCRN)All 114 Stations Installed/Operational End of FY 08

Installed 7 Pairs (14)Installed Single (92)Awaiting Installation (8)

0

4

8

12

16

20

8/1 8/4 8/7 8/10 8/13 8/16 8/19 8/22 8/25 8/28 8/31August 2006

Volu

met

ric w

ater

Con

tent

(%

)

0

4

8

12

16

20

Rain

fall

(mm

)

EC-5 15cm EC-5 30cm EC-5 45cmEC-5 90cm TE-5(WC) 15cm Rain (mm) 0

Data courtesy of W. Bandaranayake and L. Parsons, Univ. of Florida Citrus Research and Education Center

What can I expect to see in the field?

USDA Soil Climate Analysis Network (SCAN)

1970s 1980s 1990s 2000

FieldExperiments

RADARSAT-2SMOS, METOP

RADARSAT-1 ERS-2, ENVISAT

AMSR-ESIR-C/X-SAR JERS-1, ERS-1ESTAR, SSM/I

SEASAT, PBMR, SMMR

Soil

Moi

stur

e Se

nsin

g Te

chno

logy NPOESS

CMIS/VIIRS

2010

Soil Moisture - Microwave Remote Sensing Evolution

AQUARIUSSMAP

Ground truthSM Missions:FIFE’87-89Mansoon’90 OXSOME’90MACHYDRO’90HAPEX’90-92WASHITA’92 WASHITA’94 SGP’97SGP’99 SMEX’02SMEX’03 SMEX’04SMEX’05…Common wavelength L and C band, which penetrate cloud, rain, and vegetation canopies

Active Microwave Passive Microwave

own energy (Reflection) Earth energy (Emission)

High (10’s meter) Low (10-100 Km)

Regional modeling Global modeling

SAOCOMGCOM-W

Advanced Microwave Scanning Radiometer (AMSR-E)

• AMSR-E is Advanced Microwave Scanning Radiometer for NASA’s Earth Observing Systemand JAXA of Japan. It’s onboard the Aqua satellite of EOS that was successfully launchedin May 2002.

Mission AMSR-E

Operational begin

Launched December, 2002

Instrument concept

Passive microwave radiometer

Frequency 6.92, 10.65, 18.7, 23.8, 36.5, 89 GHz

Polarization Dual polarization

Channels 12 channels

Foot print 5 to 60 km

Angular range 55 degrees

Swath 1445 km

http://wwwghcc.msfc.nasa.gov/AMSR/

SMOS (Soil Moisture and Ocean Salinity) Mission

• ESA's Soil Moisture and Ocean Salinity (SMOS) mission has been designed to observe soilmoisture over the Earth's landmasses and salinity over the oceans.

• The goal of the SMOS mission is to monitor surface soil moisture with an accuracy of 4% (at35-50 km spatial resolution).

Mission SMOS

Launch November, 2009

Duration Minimum 3 years

Instrument Microwave Imaging Radiometer using Aperture Synthesis - MIRAS

Instrument concept Passive microwave 2D-interferometer

Frequency L-band (21 cm, 1.4 GHz)

Number of receivers 69

Receiver spacing 0.875 lambda = 18.37 cm

Polarization H & V

Radiometric resolution 35 km at center of field of view

Angular range 0-55 degrees

Temporal resolution 3 days revisit at Equator

http://www.esa.int/esaCP/index.html

SMAP ( Soil Moisture Active Passive) Mission

• SMAP is implemented as a directed mission within the NASA Earth Systematic MissionProgram. The SMAP project is managed by the Jet Propulsion Laboratory (JPL) withparticipation by the Goddard Space Flight Center (GSFC).

• SMAP will use a combined radiometer and high-resolution radar to measure surface soilmoisture and freeze-thaw state, providing new opportunities to enable improvements toweather and climate forecasts, flood prediction and drought monitoring.

Mission SMAP

Launch March, 2013

Duration 3 years

Instrument concept Active microwave - Synthetic Aperture Radar

Passive microwave- Radiometer

Frequency L-band :1.26 GHz (H)1.29 GHz (V)

L-band :1.41 GHz

Polarization HH, VV,HV H, V, U

Radiometric resolution 1 - 3 km 40 km

Angular range 40 degrees

Swath width 1000 km

Temporal resolution global coverage within 3 days at the equator and 2 days at boreal latitudes (>45°N)

http://smap.jpl.nasa.gov

ASCAT (Advanced SCATterometer) Level 2 – Soil Moisture Product

• The ASCAT soil moisture product is produced by EUMETSAT, using the WARPNRTsoftware originally developed by IPF/TU Wien (Institute of Photogrammetry andRemote Sensing, Vienna University of Technology).

• Accuracy: The average RMS error of the soil moisture index is about 25%, whichcorresponds to about 0.03-0.07 m3 water per m3 soil, depending on soil type.

• The ASCAT soil moisture service has been set up to meet the requirements ofNumerical Weather Prediction (NWP) applications. Value-added soil moisture productsfor hydrological users in Europe are currently under development within the SatelliteApplication Facility in Support to Operational Hydrology and Water Management.

Mission ASCAT

Operational begins 11 December, 2008

Instrument concept Active microwave – Real aperture radar

Frequency Radar C-band (5.255 GHz)

Polarization VV polarization

Spatial Resolution 50 km (25 km grid spacing)

35 km(12.5 km grid spacing)

Angular range 25º - 65 º

Swath Width 550 km

Source: http://www.eumetsat.int, http://www.ipf.tuwien.ac.at

NOAA-CREST Microwave Radiometer

Specification:L-Band Radiometer• Frequency: 1.40 to 1.55 GHz (SMAP Frequency)• polarization : Dual (H, V)• Antenna System: 1.5 x 0.7 meters• Delivery date: September 2009• Manufacturer: Radiometrics Corporation, Boulder CO.High frequency Radiometers• 37, 89 GHz radiometer for snow related research.

Research Objective: • Improve our understanding of scattering and emission.• Evaluate the vegetation (NDVI, VWC) effect on soil moisture.• Evaluate spatial and temporal variability of soil moisture.

We looking for suitable field location for

radiometer.

Evaporation

• Process by which the phase of water is changed from liquid to a vapor.

• It occurs at the evaporating surface, the contact between water body and overlaying air.

Evaporation

• Evaporation rate is a function of several meteorological and environmental factorsThe two main factors from an engineering standpoint are:

– Solar energy: it provides latent heat of vapor

– Advective energy: it is the ability to transport

Evaporation

• Pan evaporation• Water budget• Correlations to climate data (empirical)

Evaporation Measures

• Pan evaporation methodAn evaporation pan is a device designed to measure

evaporation by monitoring the loss of water in the pan during a given time period, usually one (1) day.

Evaporation

Pan coefficient = 0.60 to 0.85 on an annual basis

L c pE p E=

Standard 4 foot diameter pan

http://www.ametsoc.org

• Correlations to Climate Data– General Empirical Formula

( , )E f e U= ∆

Evaporation

– General Theoretical Formula

– Empirical Formula for Lake Hefner

8 80.00241( )L o aE e e U= −1. EL = evaporation rate in inches per day2. eo = saturation vapor pressure at the water

surface in inches of mercury3. eo8 = vapor pressure in air over the lake at

an elevation of 8 m, in inches of mercury4. U8 = wind speed over the lake at an

elevation of 8 m, in miles per day

• As an engineer, you have to find an empirical formula for surface waters in your area of interest

– Empirical Formula for Class A pan

( ) ( )np o aE e e m bU= − +

1. Ep = daily pan evaporation, (in./day)2. eo = saturation vapor pressure at the water

surface, (in. of mercury)3. eo = atmospheric vapor pressure at air

temperature, (in. of mercury)4. U = wind speed at 6 inches above pan rim,

(mpd)5. n, m, and b = 0.88, 0.37, 0.0041, respectively.

• Note: saturated vapor pressure is a function of temperature.

• Transpiration is the process by which plants transfer water from the root zone to the leaf surface, where it eventually evaporates into atmosphere.

• The process by which transpiration takes place can be described as follows:

– Water is extracted by a plants roots, transported upward through its stem and diffused into the atmosphere through stoma.

Transpiration

• Contributing factors:a. Moisture availableb. Vegetation typec. Vegetation densityd. Vegetation health

Transpiration

• Measured with phytometer (plant used as a measuring device)• Phytometer is a device for measuring transpiration, consisting of a

vessel containing soil in which one or more plants are rooted and sealed so that water can escape only by transpiration from the plant.

• Based on monthly consumptive use (if available) and monthly evaporation

1. T = transpiration rate (mm/time)2. ET = evapotransipiration rate (mm/time)3. E = Evaporation rate (mm/time)

T ET E= −

Transpiration

http://www.ictinternational.com.au/hrm30.htm

Evapotranspiration

• ET = evaporation from soils, plant surfaces, and water bodies combined with water losses through plant leaves

• Evaporation: net loss of water from a surface resulting from a change in state from liquid to vapor and the net transfer of vapor to the atmosphere

• Transpiration: net loss of water from plant leaves by evaporation through plant stomata

Impacts on Hydrology

• > 70% of annual PPT in US• > 95% in semi-arid and arid regions • For dry areas, ET/P ~ 1

– Q/P is very small– ET is limited by plant water availability

• For humid areas, ET/P is smaller– Q/P is higher– ET is limited by energy

• Mass balance

Evapotranspiration

S P R F ET∆ = − − −

pET kE=• k = 0.35 to 0.85 = f(soil/plant condition, location of the

pan, wind speed, upwind fetch, and humidity)

• Based on Pan Evaporation

• For example, k = 0.7 if wind speed = 170-425 km/day, upwind fetch of green crop = 1,000 m, and low relative humidity = 20-40 percent.

Example–Assume the following situations for a small watershed in northern Indiana. The six-month seasonal precipitation is 70 cm, runoff is 20 cm, and the change in groundwater storage is 15 cm. What are the monthly evapotransipiration rates?

S P R ET∆ = − −15 70 20 ET= − −

70 20 15 35 /6 5.83 /

ET cm monthcm month

= − − ==

Evapotranspiration• Irrigation needs based on evapotranspiration

S P I R F ET∆ = + − − −

I ET P= −

Known Known000

Evapotranspiration

• Potential Evapotranspiration (PET) is the amount of evapotranspiration that would take place under the assumption of an ample supply of moisture at all times.

• PET is an indication of optimum crop water requirements.

Can be measured using - evaporation pan

- weighing lysimeter

Allows for estimation of E from measurements of - Global radiation- Wind speed- Air temperature- Relative humidity

Combination Approach

Evaporation and Evapotranspiration

Well watered grass

Radiation TemperatureWind speed Humidity

Crop evapotranspiration under standard conditions

For ryegrass Kc mid=1.65

Crop evapotranspiration under non-standard conditions(actual evapotranspiration)

Water & environmental stress

Well watered crop

optimal agronomic comditions

Reference Evapotranspiration ET0

Evaporation and Evapotranspiration

0ETKET cc =

csactual ETKET =

• initial stage.• development stage• Mid-season stage• Late season stage

Crop growth stages

Evaporation and Evapotranspiration

Crop Coefficient

• Crop growth stages• Single crop coefficient approaches

(Kc)• Dual crop coefficient approaches

(Kcb+ Ke )• basal crop coefficient (Kcb) • soil water evaporation coefficient

(Ke) • Kc=Kcb+Ke

Evaporation and Evapotranspiration

Drought Videos

• Western U.S. drought puts big strain on reservoirshttps://youtu.be/W_nZmt7xmaQ (2.56 min)

• NASA | Mega-droughts Projected for American Westhttp://youtu.be/ToY4eeWsdLc (2.40 min)

• NASA launches Earth-observing satellite helps Measuring Soil Moisture Cycle and floods conditionshttp://youtu.be/Jj8pKIkOxpk (3.00 min)

• California's Extreme Drought, Explained | The New York Timeshttp://youtu.be/rHWHuP91c7Y (3.36 min)

• Real World: What Is Soil Moisture? http://youtu.be/aJ3KaDJ9chM (5.28 min)

Drought Videos to Watch

Experiment

National Weather Stations in New York

Thiessen Method for Average Rain

Step 1

Thiessen Method for Average Rain

Step 2

Thiessen Method for Average Rain

Step 3

Thiessen Method for Average Rain

Step 4

Soil Moisture Experiment

• Mark the glass 5 levels.• Fill soil in plastic glass 50%• Pour the ¼ glass of water in soil.• Allow water to infiltrate to soil.• Take a moisture meter • Check the video how this moisture meter works

(Earth Battery) https://youtu.be/aCCK132OIGA• Measure wetness of soil on scale of 1-10.• Pour more water slowly to make soil completely

saturate.• Estimate approx. how much water you poured to soil

get saturate?