0 2 4 6 80

200

400

600

800

1000

Wa

ter-

op

tima

l ro

ot d

ep

th [m

m]

Tpot

= 4 mm/day

A = 1x10-4 mm-1 Constantfrequency =0.2 events/day

Constantmean depth = 15 mm/storm

Sensitivity of water-optimal root depth to precipitation constant rain frequency, variable mean depth

constant mean depth, variable frequency

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized root depth, Zr/ [-]

T/T

po

t [-]

W = 0.5

W = 0.8

W = 1.2W = 2.0

0 10% 20% 30% 40% 50%0.5

1

1.5

2

Normalized Precipitation Loss, / [-]

W/A

I [-]

AI = 0.25

AI = 0.75

AI = 1.25

AI = 2.0

Multiple factors including climate, vegetation characteristics, soil properties, and nutrient availability influence the morphology and extent of plant roots. This work aims to provide insight specifically to the control of climate and rainfall variability on the depth of plant roots. A simple stochastic model of precipitation forcing and plant uptake is used to balance the carbon costs and benefits of plant roots and to determine an optimal rooting depth. Precipitation events arrive instantaneously as a Poisson process, and rainfall depths are exponentially distributed; the variability in precipitation is thus characterized by two parameters: mean arrival rate and mean rainfall depth.

This model produces an analytical solution for root depth as a function of three variables: mean rainfall depth normalized by plant-available water content, aridity of the climate (determined as the ratio of mean annual rainfall to potential evapotranspiration), and a parameter that combines potential evapotranspiration and vegetation characteristics (root respiration rate, specific root length, root-length density, and water-use efficiency). Consistent with observations, this model predicts the deepest roots when annual rainfall is approximately equal to potential evapotranspiration. In drier environments, plant roots are limited by the availability of water; in wetter environments, the roots are shallower for reasons of efficiency. Except in very dry environments, root depth tends to increase with decreasing frequency of rain events for a given annual rainfall. As the cost of plant roots increases, root depth decreases as does the sensitivity of root depth to climate variability. Results from this simple model can provide insight to the effect of a changing climate on root depth.

B41E-0235 The Influence of Climate on Root DepthAndrew J. Guswa

Picker Engineering Program, Smith College, Northampton, MA, aguswa@email.smith.edu

AbstractR

ain

dept

h

time

Model for Soil-Moisture Dynamics

Sw Sfc

Tra

nspi

ratio

n

Tpot

PrecipitationRain events are stochastic (Poisson), instantaneous, and depths are exponentially distributed. The rainfall regime is quantified by the frequency () and mean depth () of events.

When interception and bare-soil losses are accounted for, the frequency of events that produce water available to the vegetation becomes

EvaporationInterception and bare-soil evaporation have priority over transpiration and are prescribed as maximum depths

soilintercept

Potential TranspirationWater is withdrawn from the root zone at the potential transpiration rate until the root-zone saturation reaches the wilting point.

The potential rate of transpiration is equal to PET minus the average rate at which water is lost to bare-soil and interception evaporation.

InfiltrationWater instantly fills the root zone up to a maximum field-capacity saturation, Sfc; any excess water is lost to drainage and runoff.

Premise• Root depth is determined by the

depth at which the marginal carbon cost of roots is equal to the marginal benefit.

• Roots will respond plastically to their environment at time scales of weeks to months.

• Roots will find and use water within the root-zone.

Goals• Predict root depth as a function of

the intermittency and depth of rain events in both wet and dry environments.

• Develop a simple model that enables analytical solution.

• Illustrate the impacts of a changing climate on root depth if water acquisition drives morphology.

Primary Conclusions• For a given mean storm depth and vegetation and soil characteristics, root

depth is greatest when rainfall and PET are approximately equal. In drier environments, there is not enough water to justify deeper roots; in wet environments, shallow roots are sufficient to meet potential transpiration.

• The sensitivity of root depth to mean precipitation is roughly symmetric if the change in precipitation is due to a change in rain frequency; if the change in rainfall is due to a change in the depth of rain events, the sensitivity of root depth to rain is much greater in dry environments than in wet.

Root zone

Depth, Zr

Porosity, n

Field capacity, Sfc

Wilting point, Sw

Plant-available

water content: wfc SSn

WWZ

WZW

T

T

r

r

1exp

11exp

pot

exp*

Mean TranspirationThe normalized mean transpiration rate as a function of the wetness index, W, the plant available water content, , and the root depth, Zr, is based on

Milly, P. C. D., 1993, An analytical solution of the stochastic storage problem applicable to soil water, Water Resources Research, 29(11), 3755-3758.

PET

Tpot

22*

expexp11

PET

potTW

PETAI

*

The wetness index, W, is a stretched version of the aridity index, AI.

Wetness of the climate

Characteristic infiltrationdepth

Relative root cost

pot

rr

TWUE

RLDA

wfc SSn

potTW

Water-optimal root depth depends on three variables

XW

Z r ln1

221 YYYWX

pot

rr

TWUE

RLDA

A

WY

2

1 2

Water-Optimal Root Depth

Carbon Benefit and Cost of Roots

dzRLDZCrZ

rrr 0

rr ZTWUEZB

WUE Water-use efficiency [mmol C / cm3 H2O]

r Root respiration rate [mmol C / g DM / day]

r Specific root density [g DM / cm of root length]

RLD Root-length density [cm root length / cm3 of soil]

T(Zr) Average transpiration rate [mm H2O / day]

Zr Root depth [mm]

Water-optimal root depth is achieved when the marginal benefit of deeper roots equals the marginal cost, i.e., when the carbon cost of adding deeper roots is just balanced by the incremental increase in photosynthesis due to access to additional water:

RLD

dZ

ZdTWUE rr

r

r

Using the solution for T(Zr) from the stochastic model for soil-moisture dynamics

A = 2 x 10-4 mm-1A = 5 x 10-5 mm-1

Water-optimal root depth

Efficiency of uptake

Water-optimal root depth

Efficiency of uptake

Results

Zr [mm] Zr [mm] T/min(Tpot,) [-]T/min(Tpot,) [-]

0 0.5 1.0 1.5 2.0

Mean precipitation [mm/day]

Wetness Index, W [-]