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Control volume E in IE (internal energy) E out E in D t = D IE + E out D t Basic energy balance equation: Energy Balance at the Land Surface Energy Balance for a Single Land Surface Slab, Without Snow S w i + L w i = S w h + L w h + H + l E + C p D T + miscellaneous Terms on

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Slide1 l.jpg

Control volume

Ein

IE

(internal energy)

Eout

EinDt = DIE + EoutDt

Basic energy balance equation:

Energy Balance at the Land Surface


Energy balance for a single land surface slab without snow l.jpg

Energy Balance for a Single Land Surface Slab, Without Snow

Swi + Lwi = Swh + Lwh + H +lE + CpDT + miscellaneous

Terms on

LHS come from

the climate model.

Strongly dependent

on cloudiness, water

vapor, etc.

Terms on

RHS come are

determined by

the land surface

model.

Sw Sw Lw Lw H lE

T

where

Swi = Incoming shortwave radiation

Lwi = Downward longwave radiation

Swh = Reflected shortwave radiation

Lwh = Upward longwave radiation

H = Sensible heat flux

l = latent heat of vaporization

E = Evaporation rate

Cp = Heat capacity of surface slab

DT = Change in slab’s temperature, over the time step

miscellaneous = energy associated with soil water freezing, plant

chemical energy, heat content of precipitation, etc.


Slide3 l.jpg

Reflected Shortwave Radiation

# bands

# bands

Assume: Sw = S Swdirect, band b + S Swdiffuse, band b

b=1

b=1

reflectance for

spectral band

Compute: Sw = S Sw direct, band b a direct, band b

+ S Sw diffuse, band b a diffuse, band b

# bands

b=1

# bands

b=1

Simplest description: consider only one band (the whole spectrum) and don’t differentiate between diffuse and direct components:

Sw = Sw a

Typical albedoes (from Houghton):

sand .18-.28

grassland .16-.20

green crops .15-.25

forests .14-.20

dense forest .05-.10

fresh snow .75-.95

old snow .40-.60

urban .14-.18

albedo


Upward longwave radiation l.jpg

Upward Longwave Radiation

Stefan-Boltzmann law: Lw = e s T4

where e = surface emissivity

s = Stefan-Boltzmann constant = 5.67 x 10-8 W/(m2K4)

T = surface temperature (K)

Emissivities of natural surfaces tend to be slightly less than 1, and they vary with water content. For simplicity, many models assume e = 1 exactly.


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r cp (Ts - Tr)

ra

Sensible heat flux (H)

Spatial transfer of the “jiggly-ness” of molecules, as represented by temperature

Equation commonly used in climate models: H = r cp CH |V| (Ts - Tr),

where

r = mean air density

cp = specific heat of air, constant pressure

CH = exchange coefficient for heat

|V| = wind speed at reference level

Ts = surface temperature

Tr = air temperature at reference level (e.g., lowest GCM grid box)

For convenience, we can write this in terms of the aerodynamic resistance, ra:

H =

where ra = 1/ (CH |V|)


Slide6 l.jpg

V1

R

r cp (Ts - Tr)

V2

ra

H=

Why is this form convenient? Because it allows the use of the Ohm’s law analogy:

Tr

Sensible

heat flux

ra

Electric

Current

Ts

r cp (Ts - Tr)

Current = Voltage difference / Resistance

I = (V2 – V1) / R

H=

ra


Slide7 l.jpg

The aerodynamic resistance, ra, represents the difficulty with which heat (jiggliness of

molecules) can be transferred through the near surface air. This difference is strongly

dependent on wind speed, roughness length, and buoyancy, which itself varies with

temperature difference:

10000

r cp (Ts - Tr)

H =

1000

ra

ra (s/m)

100

10

1

-10

0

10

Ts - Tr

Idealized picture


Slide8 l.jpg

LATENT HEAT FLUX: The energy used to tranform

liquid (or solid) water into water vapor.

Latent heat flux from a liquid surface: lvE, where

E = evaporation rate (flux of water molecules away from surface)

lv = latent heat of vaporization

= (approximately) (2.501 - .002361T)106 J/kg

Latent heat flux from an ice surface: lsE, where

ls = latent heat of sublimation

= lv + lm

lm = latent heat of melting = 3.34 x 105 J/kg

For the purpose of this class, lv and lv will both be assumed constant.

We can then discuss the latent heat flux calculation in terms of the

evaporation calculation.


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Now, some definitions.

es(T) = saturation vapor pressure: the

vapor pressure at which the condensation

vapor onto a surface is equal to the upward

flux of vapor from the surface.

Clausius-Clapeyron equation:

es(T) varies as exp(-0.622 )

Useful approximate equation:

es(T) = exp(21.18123 – 5418/T)/0.622,

where T is the temperature in oK.

l

RdT


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Specific humidity, q: Mass of vapor per mass of air

qr = 0.622 er /p (p = surface pressure, er = vapor pressure)

Dewpoint temperature, Tdew: temperature to which air must be reduced to begin

condensation.

Relative humidity, h: The ratio of the amount of water vapor in the atmosphere

to the maximum amount the atmosphere can hold at that temperature.

Note: h = er/ es(Tr) = es(Tdew)/ es(Tr) = qs(Tdew)/ qs(Tr)

Potential Evaporation, Ep: The evaporative flux from an idealized, extensive

free water surface under existing atmospheric conditions. “The evaporative

demand”.

Four evaporation components

Transpiration: The flux of moisture drawn out of the soil and then released

into the atmosphere by plants.

Bare soil evaporation: Evaporation of soil moisture without help from plants.

Interception loss: Evaporation of rainwater that sits on leaves and ground

litter without ever entering the soil

Snow evaporation: sublimation from the surface of the snowpack


Slide11 l.jpg

0.622r es(Ts) - er

Ep =

p ra

er

Evaporative

flux

ra

es(Ts)

The Penman equation can be shown to be equivalent to

the following equation, which lies at

the heart of the potential evaporation

calculation used in many climate

models:

vapor pressure at

reference level

=es(Tdew)

Note: the ra used here is that same as that

used in the sensible heat equation. Does that

make sense?


Slide12 l.jpg

Stomatal resistance is not easy to quantify.

rs varies with:

-- plant type and age

-- photosynthetically active radiation (PAR)

-- soil moisture (w)

-- ambient temperature (Ta)

-- vapor pressure deficit (VPD)

-- ambient carbon dioxide concentrations

Effective rs for a full canopy (i.e., rc) varies with leaf density, greenness fraction,

leaf distribution, etc. rc is essentially a spatially integrated version of rs .

Modeling stomatal resistance:

“Jarvis-type” models: rs = rs-unstressed(PAR) f1(w)f2(Ta)f3(VPD)

Many newer models: rs = f(photosynthesis physics)

Key point: Because plants close their stomata during times of

environmental stress, rs is modeled so that it increases during

times of environmental stress.


Slide13 l.jpg

Typical approaches to modeling latent heat flux (summary)

Transpiration

0.622lr es(Ts) - er

lvE =

p ra + rs

Evaporation from bare soil

0.622lvr es(Ts) - er

lvE =

p ra + rsurface

Resistance to

evaporation

imposed by soil

Interception loss

0.622lvr es(Ts) - er

lvE =

p ra

Note: more complicated

forms are possible, e.g.,

inclusion (in series) of

a subcanopy aerodynamic

resistance.

Snow evaporation

0.622lsr es(Ts) - er

lsE =

p ra


Slide14 l.jpg

Bowen Ratio, B: The ratio of sensible heat flux to latent heat flux.

Evaporative Fraction, EF: The ratio of the latent heat flux to the

net radiative energy.

Over long averaging periods, for which the net heating of the ground is

approximately zero, these two fractions are simply related: EF = 1/(1+B).

Maximum B is infinity (deserts).

Minimum EF is 0 (deserts).

Minimum B could be close to zero, maximum EF could be close

to 1 (rain forests).


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HEAT FLUX INTO THE SOIL

One layer soil model: Let G be the residual energy flux at the

land surface, i.e.,

G = Sw + Lw - Sw - Lw - H - lE

Then the temperature of the soil, Ts, must change by DTs so that

G = CpDTs/dt

where

Cp is the heat capacity

dt is the time step length (s)


Slide16 l.jpg

time of day

time of day

The choice of the heat capacity can have a major impact on

the surface energy balance.

Low heat capacity case

High heat capacity case

-- Heat capacity might, for example, be chosen so that it represents the

depth to which the diurnal temperature wave is felt in the soil.

-- Note that heat capacity increases with water content. Incorporating this

effect correctly can complicate your energy balance calculations.


Slide17 l.jpg

T1

G12

Internal

energy

T2

G23

T3

Heat Flux Between Soil Layers

One simple approach:

G12 = L (T1 - T2) / Dz

where

L = thermal conductivity

Dz = distance between

centers of soil layers.

Dz

temperature

-- Using multiple layers rather than a single layer allows

the temperature of the surface layer (which controls

fluxes) to be more accurate.

-- Like heat capacity, thermal conductivity increases with

water content. Accounting for this is comparatively easy.

depth


Slide18 l.jpg

Energy balance in snowpack

Sw Sw Lw Lw H lsE

Internal

energy

Tsnow

lmM

GS1

T1

Snow modeling: Plenty of “If statements”

Albedo is high when

the snow is fresh, but

it decreases as the

snow ages.

Snowmelt occurs only

when snow temperature

reaches 273.16oK.

Internal energy

a function of

snow amount,

snow temperature,

and liquid water

retention

Thermal conductivity

within snow pack

varies with snow age.

It increases with snow

density (compaction

over time) and with

liquid water retention.

1

Solid

fraction

0

Temperature

273.16


Slide19 l.jpg

250oK

260oK

Temperature

profile

snow

270oK

272oK

soil

Critical property of snow: Low thermal conductivity

strong insulation

To capture such properties,

the snow can be modeled

as a series of layers, each

with its own temperature.

snow

soil


Water balance for a single land surface slab without snow e g standard bucket model l.jpg

Water Balance for a Single Land Surface Slab, Without Snow(e.g., standard bucket model)

Terms on

LHS come from

the climate model.

Strongly dependent

on cloudiness, water

vapor, etc.

Terms on

RHS come are

determined by

the land surface

model.

P = E + R + CwDw/Dt + miscellaneous

P E

R

w

where

P = Precipitation

E = Evaporation

R = Runoff (effectively consisting of surface runoff and baseflow)

Cw = Water holding capacity of surface slab

Dw = Change in the degree of saturation of the surface slab

Dt = time step length

miscellaneous = conversion to plant sugars, human consumption, etc.


Slide21 l.jpg

Precipitation, P

Getting the land surface hydrology right in a climate model is difficult

largely because of the precipitation term. At least three aspects of

precipitation must be handled accurately:

a. Spatially-averaged precipitation amounts (along

with annual means and seasonal totals)

b. Subgrid distribution.

c. Temporal variability and temporal correlations.

Otherwise, even with a perfect land surface model,

Perfect land

surface model

Garbage

in

Garbage

out


Slide22 l.jpg

Precipitation: subgrid variability (1)

The bottom storm is more

evenly distributed over the

catchment than the top storm.

Intuitively, the top storm will

produce more runoff, even

though the average storm

depth over the catchment

(E(Yo)) is smaller.

Key points:

-- Specifying subgrid

variability of precipitation

is critical to an accurate

modeling of surface hydrology.

-- A GCM is typically unable

to specify the spatial structure

of a given storm. The LSM

typically has to “guess” it.

From Fennessey, Eagleson,

Qinliang, and Rodriguez-Iturbe,

1986.


Slide23 l.jpg

Precipitation: subgrid variability (2)

Here, the two storms have

similar spatial structure

and total precipitation

amounts. The locations of

the storms, however, are

different. If the top storm

fell on more mountainous

terrain than the bottom

storm, the top storm might

produce more runoff

Key point: A GCM is

typically unable to specify

the subgrid location of a

given storm. The LSM

typically has to “guess” it.

From Fennessey, Eagleson,

Qinliang, and Rodriguez-Iturbe,

1986.


Slide24 l.jpg

time step 2

time step 3

time step 1

Case 1: No temporal

correlation in storm

position -- the storm is

placed randomly with the

grid cell at each time step.

Case 2: Strong temporal

correlation in storm

position between time steps.

Precipitation: temporal correlations

Temporal correlations are very important -- but are largely ignored --

in GCM formulations that assume subgrid precipitation distributions.

This is especially true when the time step for the land calculation is of

the order of minutes. Why are temporal correlations important?

Consider three consecutive time steps at a GCM land surface grid cell:

Case 2 should produce, for example, stronger runoff.


Slide25 l.jpg

Throughfall

Simplest approach: represent the interception reservoir as a bucket that gets filled during

precipitation events and emptied during subsequent evaporation. Throughfall occurs

when the precipitation water “spills over” the top of the bucket.

Capacity of bucket is

typically a function

of leaf area index, a

measure of how many

leaves are present.

This works, but because it ignores subgrid precipitation

variability (e.g., fractional wetting), it is overly simple.


Slide26 l.jpg

Spatial precipitation variability and interception loss

SiB’s approach

(Seller’s et al, 1986)

Precipitation assumed

to fall according

to some prescribed

distribution

Area above line

is considered

throughfall

Capacity of

reservoir

Note: SiB allows

some of the

precipitation to fall

to the ground without

touching the canopy.

Original water in reservoir


Slide27 l.jpg

Temporal precipitation variability and interception loss

Mosaic LSM’s approach:


Slide28 l.jpg

Runoff

a. Overland flow:

(i) flow generated over permanently saturated zones near a river

channel system: “Dunne” runoff

(ii) flow generated because precipitation rate exceeds the infiltration

capacity of the soil (a function of soil permeability, soil water

content, etc.): “Hortonian” runoff

b. Interflow (rapid lateral subsurface flow through macropores and seepage

zones in the soil

c. Baseflow (return flow to stream system from groundwater)

Runoff (streamflow) is affected by such things as:

-- Spatial and temporal distributions of precipitation

-- Evaporation sinks

-- Infiltration characteristics of the soil

-- Watershed topography

-- Presence of lakes and reservoirs


Slide29 l.jpg

Modeling runoff: GCM scale

Surface runoff formulations in GCMs are generally very crude, for at least

two reasons:

(i) Developers of GCM precipitation schemes have focused on producing

accurate precipitation means, not on producing accurate subgrid spatial

and temporal variability.

(ii) GCM land surface models generally represent the hydrological state of

the grid cell with grid-cell average soil moistures -- the time evolution of

subgrid soil moisture distributions is not monitored.

At best, we can expect first-order success with these

runoff formulations


Slide30 l.jpg

Soil Moisture Transport, Baseflow

First, some useful definitions:

Porosity (n): The ratio of the volume of pore space in the soil to the total volume of the soil. When a soil with a porosity of 0.5 is completely dry, it is 50% rock by volume and 50% air by volume.

Volumetric moisture content (q): The ratio of the volume of water in the soil to the total volume of soil. When the soil is fully saturated, q = n.

Degree of saturation (w): The ratio of the volume of water in the soil to the volume of water at saturation. By definition, w= q /n.

Pressure head (y): A measure of the degree to which the soil holds on to its water through tension forces. More specifically, y =p/rg, where r is the density of water, g is gravitational acceleration, and p is the fluid pressure.

Elevation head (z): The height of soil element above an arbitrary baseline.

Hydraulic head (h): The sum of the pressure head and the elevation head.

Wilting point: The soil moisture content (measured either in degree of saturation or pressure head) at which plants can no longer draw the moisture from the soil. When modeling the root zone, this is often considered to be the lowest moisture content possible.

Field capacity: The water content obtained when a saturated soil drains to the point where the surface tension on the soil particles balances the gravitational forces causing drainage.


Slide31 l.jpg

L

h2

h1

Estimating water transport in the saturated zone (i.e., below water table)

Darcy’s Law states that

Q/A = flow per unit normal area = - K

where K = hydraulic conductivity

h = hydraulic head

L = separation distance

h2 - h1

L

More generally, q = - K h

q = specific discharge = Q/A

Generalized Darcy’s Law:

relates flow to gravitational

and pressure forces.

(Recall: h = y + z)


Slide32 l.jpg

krg

K =

m

Hydraulic conductivity, K, is related to the soil’s specific permability:

Where r is the fluid’s density and m is its dynamic viscosity. K is thus a

function of soil and fluid properties.

K varies tremendously with

soil type. Small variations in

soil type, say across a field site,

could lead to orders of magnitude

difference in the ability to

transport moisture.

From Freeze and Cherry


Slide33 l.jpg

y(w) = ysaturated w -b

K(w) = Ksaturated w 2b+3

b = empirical coefficient

Unsaturated zone

equations (from

Clapp and Hornberger)

Moisture transport in the unsaturated zone (e.g., in the soil near

the surface) can also be computed with Darcy’s law, if appropriate

corrections are made to pressure head and hydraulic conductivity.

qr = residual moisture

“specific retention”

Z

If atmospheric

pressure defined

to be 0.

qr

Recall: q = ratio of water volume

to soil volume,

n = porosity

Soil moisture

profile

capillary

fringe

p < 0

p = 0

q=n

q

p > 0

Water table

Recall: w= degree of saturation,

= q/n


Slide34 l.jpg

w1

d1

surface layer

w2

d2

root layer

d3

w3

recharge layer

One possible discretization of Darcy’s law (continued)

Characterize the soil as stacked layers

(d = thickness)

Compute for each layer i:

yi = ysat wi-b

Ki = Ksat wi 2b+3

Compute flow from layer i to layer i+1:

yi - yi+1

qz i,i+1 = K

+ 1

d

K = “average” K across distance = (diKi + di+1Ki+1)/(di+di+1)

d = effective depth for computing gradient = 0.5 (di+di+1)

For drainage out the bottom of the soil column (QD), one might equate it

to the hydraulic conductivity in the lowest layer. SiB, for example, goes

beyond this by also applying a “mean slope angle” term, sin x: QD = K3 sin x


Slide35 l.jpg

Energy balance versus water balance

Water balance:

Implicit solution usually not necessary

Results in updated water storage prognostics

Energy balance:

Implicit solution usually necessary

Results in updated temperature prognostics

How are the energy and water budgets connected?

1. Evaporation appears in both.

2. Albedo varies with soil moisture content.

3. Thermal conductivity varies with soil moisture content.

4. Thermal emissivity varies with soil moisture content.

Question: Can we address how the energy and water budgets

together control evaporation rates?


Slide36 l.jpg

Budyko’s analysis of energy and water controls over evaporation

These assymptotes

act as barriers to

evaporation.


Slide38 l.jpg

What determines the shape of Budyko’s curve?

If only annual means mattered,

the observed curve should look

like this:


Slide39 l.jpg

Seasonality, however, is important.


Slide40 l.jpg

Note that if these seasonal effects

alone were considered, the

observed curve would actually

look like this:


Slide41 l.jpg

This effect can bring the curve in line with the observed curve. Note, though,

that other effects also contribute to a region’s evaporation rate, including land

surface properties and the temporal variation of precipitation.


Slide42 l.jpg

Budyko’s analysis: discussion

1. Annual precipitation and net radiation control, to first order, annual

evaporation rates.

2. The spread of points around the Budyko curve is large, though, due to

various additional factors:

-- phasing of seasonal P and Rnet cycles

-- interseasonal storage of moisture

-- Other land surface or meteorological effects (vegetation type and

resistance, topography, rainfall statistics, …)

3. Note also:

-- Land surface processes affect the precipitation and net radiation

forcing -- there’s not truly a clean separation between land

and atmospheric effects.

-- The land’s effects on hourly, daily and monthly evaporation are

relatively much more important than they are on annual

evaporation.


Slide43 l.jpg

Structure of a Mosaic LSM tile: Water Balance

precipitation

evaporation +

transpiration

INTERCEPTION RESERVOIR

throughfall

surface runoff

infiltration

SURFACE LAYER

ROOT ZONE LAYER

soil moisture

diffusion

RECHARGE LAYER

drainage


Slide44 l.jpg

GCM

P, radiation,

Tair, etc.

E, H, upward

longwave

LSM

How do we evaluate the performance of such an LSM?

“Online” approach: test GCM output against observations.

Advantage: The coupling effects can be

studied, and various sensitivity tests can

be performed.

Disadvantage: The model forcing

(precipitation, radiation, etc.) can be wrong,

so validating the land surface model can be

very difficult. (“Garbage in -- Garbage out”)

Example from GISS

GCM/LSM: The Amazon

river is poorly simulated,

but we can’t tell if this is

due to a bad LSM or poor

precipitation from the GCM.


Slide45 l.jpg

Better approach: Offline forcing (one-way coupling)

Forcing

Data

Advantage: Land surface model can be

driven with realistic atmospheric forcing, so

that the impact of the LSM’s formulations

on the surface fluxes can be isolated.

Disadvantage: Deficient behavior of the LSM

may seem small in offline tests but may grow

(through feedback) in a coupled system.

Thus, offline tests can’t get at all of the

important aspects of a land surface model’s

behavior.

Output

File

P, radiation,

Tair, etc.

E, H, Rlw ,

diagnostics

LSM

PILPS model intercomparisons (to be discussed in a later lecture) have

largely focused on such offline evaluations.


Slide46 l.jpg

DYNAMIC VEGATION: Yet another step forward in model development

Typical GCM approach:

ignore effects of climate

variations on vegetation

Early attempts at

accounting for vegetation/

climate consistency

Fully integrated dynamic

vegetation model

Figure from Foley et al., “Coupling dynamic

models of climate and vegetation”,

Global Change Biology, 4, 561-579, 1998.


Slide47 l.jpg

as described by bT and fR

Thus, it is the relative positions of the runoff and evaporation functions

that determine the annual transpiration rate -- not the average soil moisture.

Most important take-home lesson: soil moisture in one model need

not have the same “meaning” as that in another model. As long as the

transpiration and runoff curves have the same relative positions, two

models (e.g., Models A and B below) will behave identically, even if

they have different soil moisture ranges.

(True for simple models in simple

water balance framework and for

complex LSMs running in AGCMs.)

Model A

Model B

1

1

bT

bT

R

R

0

0

0

200

400

600

800

1000

0

200

400

600

800

1000


Slide48 l.jpg

Sure enough, the LSMs in PILPS

have different soil moisture ranges...

…and there is no evidence that LSMs

with higher soil moistures produce

higher evaporations.


Slide49 l.jpg

Important aside: What does “model-produced soil moisture” mean? What are the implications of a misinterpreted soil moisture?

Common problem: GCM “A” needs to initialize its land model with realistic soil moistures for some application (e.g., a forecast).

Misguided, dangerous, and all too common solution: Use soil moistures generated by GCM “B” during a reanalysis or by land model “C” in an offline forcing exercise (e.g., GSWP), after correcting for differences in layer depths and possibly soil type.

This solution is popular because of a misconception of what “soil moisture” means in a land model. Contrary to popular belief,

-- model “soil moisture” is not a physical quantity that can

be directly measured in the field.

-- model “soil moisture” isbest thought of as a model- specific

“index of wetness” that increases

during wet periods and decreases

during dry periods.


Slide50 l.jpg

Should a land modeler be concerned that modeled soil moisture has a nebulous meaning – that it doesn’t match observations?

It depends on one’s outlook.Consider that in the real world:

(1) soil moisture varies

tremendously across the

distances represented by

GCM grid cells,

(2) surface fluxes (evaporation, runoff, etc.) vary nonlinearly with soil moisture.

and

dry

evaporation

efficiency

wet

wet

hundreds of km

soil moisture


Slide51 l.jpg

Wet:

s=1.0

Dry:

s=0.5

Simple example based on the nonlinear response of the “beta function” (evaporation efficiency) to soil moisture. (Such nonlinearity has indeed been measured locally in the real world.)

Consider a region split into a wet half (degree of saturation = 1) and a drier half (degree of saturation = 0.5). The average soil moisture is 0.75.

Under the simplifying assumption that the potential evaporation is the same over both sides, we have:

0.6

Ewet = 0.6 Ep

Edry = 0.4 Ep

Eave = 0.5 Ep

average soil moisture = 0.75

E based on average soil moisture = 0.55 Ep

0.55

evaporation

efficiency

0.4

0.5

0.75

1.0

soil moisture


Slide52 l.jpg

Clearly, inserting a soil moisture from Model A into Model B is dangerous, even if the Model A product is a trusted reanalysis. Extreme, idealized example:

A very wet condition for Model A is a very dry condition for Model B

soil moisture range for Model B

soil moisture range for Model A

200.

400.

0.

“soil moisture in top meter of soil” (mm)


Slide53 l.jpg

Recall from 3rd lecture: runoff cannot be

represented realistically with a one-

dimensional vertical framework.

In a typical LSM, the soil

moisture is effectively

assumed uniform in layers

a few centimeters thick

spanning hundreds of

kilometers!

Scale: hundreds of kilometers


Slide54 l.jpg

Lecture 9

Land and Climate: Modeling Studies

What is land-atmosphere feedback on precipitation?

…which affects the overlying atmosphere (the boundary layer structure, humidity, etc.)...

…causing soil

moisture to

increase...

Precipitation

wets the

surface...

…which causes

evaporation to

increase during

subsequent days

and weeks...

…thereby (maybe)

inducing additional precipitation


Slide55 l.jpg

Perhaps such feedback contributes to predictability.

Short-term weather prediction with numerical models (e.g., those shown on the news every night) are limited by chaos in the atmosphere.

Initialize model

with that state;

integrate into

future

Establish

atmospheric

state

Short-term

(~several days)

weather

prediction

Decay reflects short

timescale of atmospheric

“memory”

Relevance

of initial

conditions

Atmosphere

Saturday’s forecast for Tuesday (March 23, 2004):

sunny, high of 46F (8C).

days


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Relevance

of initial

conditions

Ocean

Land

months

For longer term prediction, we must rely on slower moving components of the Earth’s system, such as ocean heat content and soil moisture.

Associated

prediction of

weather, if

weather

responds to

these states

Establish

ocean state,

land moisture

state

Initialize model

with those states;

integrate into

future

Long-term

(~weeks to years)

prediction of ocean

and/or land states

For soil moisture to contribute to precipitation predictability, two things must happen:

1. A soil moisture anomaly must be “remembered” into the forecast period.

2. The atmosphere must respond in a predictable way to the remembered soil moisture anomalies


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Part 1: Soil Moisture Memory

Observational soil moisture measurements give some indication of soil moisture memory.

Vinnikov and Yeserkepova, 1991

Soil moisture timescales of several months are possible. “The most important part of upper layer (up to 1 m) soil moisture variability in the middle latitudes of the northern hemisphere has … a temporal correlation scale equal to about 3 months.” (Vinnikov et al., JGR, 101, 7163-7174, 1996.)

Vinnikov and Yeserkepova, 1991


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Koster et al. (2001) (cont.)

Boreal summer

Boreal winter

Results for SST and

soil moisture control

over precipitation

coherence

Differences: an

indication of the

impacts of soil

moisture control

alone


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Koster et al. (2001) (cont.)

Why does land moisture have an effect where it does? For a large effect, two things are needed:

a large enough evaporation signal

a coherent evaporation signal – for a given soil moisture anomaly, the resulting evaporation

anomaly must be predictable.

Both conditions can be related to

relative humidity:

The dots show where the land’s signal is strong.

From the map, we see a strong signal in the

transition zones between wet and dry climates.

Evap.

coherence


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Why does land-atmosphere

feedback occur where it

does?

One control: Budyko’s

dryness index

variance

amplification

factor

The results of this study could be highly model-dependent. A critical question about a critical issue: how does the atmosphere’s response to soil moisture anomalies vary with AGCM? We address this with...


Can we explain what controls ac p in the gcm l.jpg

Can we explainwhat controls ac(P) in the GCM?

GCM

obs

correlates

with

Pn

Pn+2

means that

Pn

Pn+2

Breaks down in western US

correlates

with

correlates

with

En+2

correlates

with

wn

wn+2

Breaks down in eastern US

correlates

with

Breaks down in western US


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Illustration of point 6:

The ensemble mean is off,

but some of the ensemble

members do give a

reasonable forecast


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What happens when the atmosphere is initialized (via reanalysis) in addition to the land variables? Supplemental 9-member ensemble forecasts, for June only (1979-1993):

1. Initialize atmosphere and land

2. Initialize atmosphere only

Warning: Statistics are based on only 15 data pairs!

June r2 values, averaged over area of focus

AMIP runs:

SSTs only

SSTs + land

initialization

+ atmosphere

initialization

SSTs +

atmosphere

initialization

GLDAS runs:

SSTs + land

initialization


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Outlook

Presumably, skill associated with land initialization can only increase with:

-- improvements in model physics

-- improved data for initialization

satellite sensors (HYDROS, GPM, …)

ground networks

data assimilation

-- improved data for validation

In other words, we’ve demonstrated only a “minimum” skill associated with land initialization.

Current

increase in skill

Idealized potential

increase in skill

We have a lot

of untapped

potential!


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DATA ASSIMILATION: THE OPTIMAL MERGING OF OBSERVATIONS AND MODEL RESULTS

strengths

weaknesses

Key motivation: observations and model results have their own strengths and weaknesses. By combining them optimally, we get the best of both worlds.

Measures of real-world states. “What we’re after in the first place. ”

Inadequate coverage, significant measurement error.

obs

Based on trustworthy physics. Complete space/ time coverage, including unmeasurable states.

Results subject to myriad inadequacies of model parameterizations

model

Decide how much you believe model result (estimate model error)

Integrate model forward in time

Combined model/ observational state at time t

Combined model/ observational state at time t+1

Model state at time t+1

Decide how much you believe obser-vation (estimate observational error)

Observation at time t+1

The actual mathematics involved here can be very complicated...


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  • COMPUTER LAB: RUNNING A LAND SURFACE MODEL

  • This model is designed to simulate a tropical forest’s response to prescribed atmospheric forcing over a repeated full seasonal cycle. The relevant files are:

  • Model: gm_model.f (Includes driver; written in FORTRAN.)

  • Forcing file: TRF.DAT.30 (Includes rainfall rates, radiation forcing, etc., at a 30 minute time step over a full annual cycle. Model automatically interpolates to a 5 minute time step.)

  • Initialization file: input/lsm_input.dat (Includes parameter values to change for class experiments.)

  • How to run the model:

  • 1. Create input and output directories below the current directory. (This assumes a UNIX system.)

  • 2. Place lsm_input.dat in the input directory.

  • 3. Find a directory that can comfortably hold trf.dat.30.diur (1.4 Mb)

  • 4. Compile the program gm_model.f

  • 5. Modify the model parameters in lsm_input.dat as appropriate.

  • 6. Run the program.

  • 7. Four output files will be produced in the output directory:

  • mosaic.trf.mon.xxxx (4.5 Kb)

  • mosaic.trf.dat.xxxx (388 Kb)

  • mosaic.trf.tra.xxxx (12.9 Kb for 3-year run)

  • mosaic.trf.123.xxxx (291 Kb)

  • where xxxx is the label for the particular experiment.

  • 8. For new experiments, start at instruction 5.


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INPUT FILE:/land/koster/pilps/TRF.DAT.30 This is the forcing data: modify path as necessary.

VEGETATION IDENTIFIER:trf Leave as is

EXPERIMENT IDENTIFIER:gp7 By changing this according to your own system of codes, you control the labeling of the output files of different experiments.

 TIME STEPS   T.S. LENGTH   DIAGS   1ST FORCING    ALAT    534529           300.    2880              0     -3.

534529 = (365x3 + 31) x 24 x 12 + 1

= # of time steps in 3 years + 1 January + 1 time step.

300 = number of seconds in the 5 minute time step.

DIAGS, 1ST FORCING, ALAT do not need to be changed.

NUMBER OF TILES:          1

               TYPE   FRACTION                  1        1.0 Type 1 = tropical forest

Fraction = 1 means a homogeneous cover

 INITIALIZATION:          TC      TD      TA     TM                        300.0   300.0   300.0   300.0

TC = Initial canopy temperature

TD = Initial deep soil temperature

TA = Initial near-surface atmospheric temperature

TM = Initial assumed first forcing temperature

               WWW(1)   WWW(2)  WWW(3) CAPAC    SNOW                0.5000  0.5000   0.5000   0.5       0.

WWW(i) = Initial degree of saturation in soil layer i

CAPAC = Initial fraction of interception reservoir filled

SNOW = Initial snow amount


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 EXPERIMENT 1    HEAT CAPACITY     WATER CAPACITY FACTOR     TURBULENCE FLAG           70000.                         1.                   0

Heat capacity is in J/oK.

If water capacity factor is 0.5, then the default capacity is halved; if it is 2, then the default capacity is doubled, etc.

Turbulence flag: you won’t need this.

 EXPERIMENT 2    INTERCEPTION PARAMETER   PRECIP. FACTOR                       1.                1.

Interception parameter: you won’t need this.

Precip. factor: factor by which to multiply all precipitation forcing.

 EXPERIMENT 3    ALBFIX    RGHFIX   STOFIX        0          0         0

ALBFIX: If this is 1, you are using tropical forest albedo.

RGHFIX: If this is 1, you are using tropical forest roughness heights

STOFIX: If this is 1, you are using tropical forest water holding capacities.

 EXPERIMENT 4    FRAC. WET     PRCP CORRELATION          0.3                   0.

FRAC. WET: The assumed fractional coverage of a storm; equivalent here to the assumed probability that a rainfall event will be applied to the land surface model.

PRCP CORRELATION: Imposed time-step-to-time-step autocorrelation of precipitation events.


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  • EXPERIMENT 1: CHANGE IN MODEL PARAMETERS

  • Background:

  • The heat capacity of the soil surface has an important effect on the land surface model’s surface energy budget calculations. Presumably, the higher the heat capacity, the more slowly the surface temperature will change under a given forcing, leading to a smaller amplitude of the diurnal temperature cycle. This could have profound effects on the annual energy balance.

  • The water holding capacity of the soil has an important effect on the annual water balance and thus on the annual energy balance. A larger water holding capacity, for example, means that high precipitation rates in the spring can more easily lead to high evaporation rates during a subsequent dry summer.

  • Possible experiments:

    • .Modify the heat capacity. You may have to modify it by an order of magnitude or so to see significant effect on the energy budget terms.

    • .Modify the water capacity factor. For starters, try 0.5 and 2.

  • Questions to answer (choose 1)

    • 1. How does varying the heat capacity affect the diurnal energy balance, in particular the amplitude of the diurnal temperature cycle? How large does the change have to be to see an effect? Is the effect in the expected direction?

    • 2. How does varying the heat capacity affect the annual energy balance?

    • 3. How does varying the water holding capacity affect the diurnal and annual energy and water budgets? Does a higher capacity imply a larger annual evaporation?


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    EXPERIMENT 2: CHANGE IN MODEL INITIALIZATION

    Background:

    All models require a “spin-up” period to remove the effects of initialization. In other words, the initial conditions imposed in a model may be inconsistent with the preferred model state, and this inconsistency may lead to energy and water budget terms that are unrealistic – they reflect the inappropriate initial conditions imposed rather than the model parameterizations or the atmospheric forcing. The length of the spin-up period is a function of the model (in particular its heat and moisture capacities) and the forcing.

    Possible experiments:

    Initialize the soil moisture reservoirs to complete saturation: set WWW(1), WWW(2), and WWW(3) to 1.

    Initialize the soil moisture reservoirs to be completely dry: set WWW(1), WWW(2), and WWW(3) to 0.0001.

    Initialize the soil moisture reservoirs to be completely dry, and double the water holding capacity: set WWW(1), WWW(2), and WWW(3) to 0.0001, and set the “water capacity factor” (from experiment 1) to 2. Complete drydown. Set WWW(1), WWW(2), and WWW(3) to 1, and set the “precip. factor” to 0. (This turns off all precipitation.)

    Note: for these experiments, you may want to increase the number of time steps. (You won’t know if you need to until you run them.) If n is the number of years you want the model to run, set the # of time steps to [(365*n)+31)]*24*12+1.

    Questions to answer (Choose 1):

    1. How does the transient model response differ in the drydown and wet-up simulations (1 & 2)?

    2. How does doubling the water holding capacity affect the wet-up period?

    3. How long does complete drydown take (simulation 4)? Is equilibrium ever really achieved? Can you define a time scale for the drydown?


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    • EXPERIMENT 3: CHANGE IN MODEL BOUNDARY CONDITIONS

    • Background:

    • GCM deforestation experiments have examined how replacing the Amazon’s forest with grassland can affect the regional climate. In a land surface model, forest and grassland are distinguished from each other only by the values used for various parameters. The experiments below examine “deforestation” in an offline environment. (Of course, deforestation effects in a fully coupled GCM environment may be different.)

    • Possible experiments:

      • .Perform a control simulation, using TYPE =1 (tropical forest).

      • .Replace the tropical forest with grassland: set TYPE=4.

      • .Replace the tropical forest with grassland, but maintain tropical forest albedo: set TYPE=4 and ALBFIX=1.

      • .Replace the tropical forest with grassland, but maintain tropical forest roughness: set TYPE=4 and RGHFIX=1.

      • .Replace the tropical forest with grassland, but maintain tropical forest water holding capacity: set TYPE=4 and STOFIX=1.

      • .Replace the tropical forest with grassland, but maintain tropical forest albedo, surface roughness, and water holding capacity: set TYPE=4, ALBFIX=1, RGHFIX=1, and STOFIX=1.

  • Questions to answer (choose 1)

    • 1. What is the effect of deforestation on the annual energy and water budget? What effect does it have on diurnal cycles?

    • 2. How do albedo change, roughness change, and storage change contribute to the tropical forest / grassland differences? Which effect is largest?

    • 3. Are the impacts of albedo change, roughness change, and storage change linear? E.g., do the changes induced by these three parameters alone add up to the changes seen in simulation 6?


  • Slide72 l.jpg

    • EXPERIMENT 4: CHANGE IN MODEL FORCING

    • Background:

    • The precipitation forcing, which comes from a GCM, need not be assumed to fall uniformly within the GCM’s grid cell area. If the typical areal storm coverage is, say, only half the grid cell’s area, then one can consider an alternative interpretation: that whenever the GCM provides precipitation for a grid cell, the probability that it occurs at a given point within the cell is ½, and when it does occur there, the GCM’s precipitation intensity is doubled. A further consideration is the temporal autocorrelation of storm events, i.e., the probability that a point gets wet during one time step given that it was wetted in the previous time step.

    • Possible experiments:

      • .Perform a control simulation.

      • .Perform simulations that assume a fractional storm coverage of ranging from .1 to .9 (i.e., set FRAC. WET = x, where x ranges from .1 to .9).

      • .Perform simulations that assume a fractional storm coverage of .1 and a time step to time step autocorrelation that ranges from .1 to .9. (i.e., set FRAC. WET=0.5 and PRCP CORRELATION=x, where x ranges from .1 to .9).

  • Questions to answer (Choose 1):

    • 1. How does runoff ratio (runoff / precipitation) change with the assumed fractional coverage?

    • 2. How do runoff ratios change when temporal autocorrelations are included?


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    NEW DIRECTIONS IN LAND SURFACE MODELING

    Sellers et al. (1997) list 3 generations of land surface models:

    1. Simple (e.g., “bucket”) models (see previous lecture)

    2. SVAT models (like Mosaic; see previous lecture)

    3. Models handling carbon

    In this lecture, we will:

    -- Take a brief look at generation #3. (Thanks to Jim Collatz for

    various carbon cycle figures.)

    -- Go over an analysis of evaporation and runoff formulations that

    suggests an alternative path of model evolution.

    -- Describe a new land surface model that follows this alternative

    path.


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    Notes on output files generated in computer lab


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