Ein Eout(internal energy)

Control volume

Basic energy balance equation: Eint = IE + Eoutt

Energy Balance at the Land Surface

Energy Balance for a Single Land Surface Slab, Without Snow

Sw + Lw

= Sw

+ Lw

+ H +E + CpT + miscellaneous

where Sw

= Incoming shortwave radiation Lw

= Downward longwave radiation Sw

= Reflected shortwave radiation Lw

= Upward longwave radiation H = Sensible heat flux = latent heat of vaporization E = Evaporation rate Cp = Heat capacity of surface slab T = Change in slab’s temperature, over the time step miscellaneous = energy associated with soil water freezing, plant chemical energy, heat content of precipitation, etc.

Sw Sw Lw Lw H E

T

Terms on LHS come fromthe climate model.Strongly dependenton cloudiness, watervapor, etc.

Terms on RHS come aredetermined by the land surfacemodel.

Reflected Shortwave Radiation

Assume: Sw = Sw direct, band b + Sw diffuse, band b

b=1

# bands # bands

b=1

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

+ Sw diffuse, band b a diffuse, band b

# bands

b=1

# bands

reflectance forspectral band

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

Sw = Sw aalbedo

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

b=1

Upward Longwave Radiation

Stefan-Boltzmann law: Lw = T4

where = surface emissivity = 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 = 1 exactly.

Sensible heat flux (H)

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

cp (Ts - Tr)

ra

where ra = 1/ (CH |V|)

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

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

cp (Ts - Tr)

ra

H=

V1

V2

R

Current = Voltage difference / Resistance I = (V2 – V1) / R

cp (Ts - Tr)

ra

H=

Ts

Tr

raElectricCurrent

Sensibleheat flux

The aerodynamic resistance, ra, represents the difficulty with which heat (jiggliness of molecules) can be transferred through the near surface air. This difference is stronglydependent on wind speed, roughness length, and buoyancy, which itself varies with

temperature difference:

Ts - Tr

ra (s/m)

1

10000

1000

100

0

10

-10 10

cp (Ts - Tr)

ra

H =

Idealized picture

LATENT HEAT FLUX: The energy used to tranform liquid (or solid) water into water vapor.

Latent heat flux from a liquid surface: vE, where E = evaporation rate (flux of water molecules away from surface) v = latent heat of vaporization = (approximately) (2.501 - .002361T)106 J/kg

Latent heat flux from an ice surface: sE, where s = latent heat of sublimation = v + m m = latent heat of melting = 3.34 x 105 J/kg

For the purpose of this class, v and v will both be assumed constant. We can then discuss the latent heat flux calculation in terms of the evaporation calculation.

Now, some definitions.

es(T) = saturation vapor pressure: thevapor pressure at which the condensationvapor onto a surface is equal to the upwardflux 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.

RdT

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 begincondensation.

Relative humidity, h: The ratio of the amount of water vapor in the atmosphereto 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 evaporativedemand”.

Four evaporation componentsTranspiration: 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 soilSnow evaporation: sublimation from the surface of the snowpack

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)

Ep =0.622 es(Ts) - er

p ra

Note: the ra used here is that same as thatused in the sensible heat equation. Does thatmake sense?

es(Ts)

er

ra

Evaporativeflux

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 ofenvironmental stress, rs is modeled so that it increases during times of environmental stress.

Typical approaches to modeling latent heat flux (summary)

Transpiration

Evaporation from bare soil

Interception loss

Snow evaporation

vE = 0.622 es(Ts) - erp ra + rs

vE = 0.622v es(Ts) - erp ra + rsurface

vE = 0.622v es(Ts) - erp ra

sE = 0.622s es(Ts) - erp ra

Note: more complicatedforms are possible, e.g.,inclusion (in series) ofa subcanopy aerodynamicresistance.

Resistance to evaporationimposed by soil

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 isapproximately 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 closeto 1 (rain forests).

HEAT FLUX INTO THE SOIL

One layer soil model: Let G be the residual energy flux at theland surface, i.e.,

G = Sw + Lw

- Sw

- Lw

- H - E

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

G = CpTs/t

where Cp is the heat capacity t is the time step length (s)

The choice of the heat capacity can have a major impact on the surface energy balance.

time of day time of day

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.

Heat Flux Between Soil Layers

T2

T1

T3

G12

G23

Internalenergy

One simple approach:

G12 = (T1 - T2) / z

where = thermal conductivity z = distance between centers of soil layers.

z

-- 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.

temperature

depth

Snow modeling: Plenty of “If statements”

Energy balance in snowpack

T1

Sw Sw Lw Lw H sE

Tsnow mMInternalenergy GS1

Snowmelt occurs onlywhen snow temperaturereaches 273.16oK.

Internal energya function of snow amount,snow temperature,and liquid water retention

Albedo is high whenthe snow is fresh, butit decreases as thesnow ages.

Thermal conductivitywithin snow pack varies with snow age.It increases with snowdensity (compactionover time) and withliquid water retention.

Solidfraction

0

1

Temperature 273.16

Critical property of snow: Low thermal conductivity strong insulation

soil

snow

soil

snow

Temperatureprofile

250oK

260oK

270oK

272oK

To capture such properties,the snow can be modeled as a series of layers, eachwith its own temperature.

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

P = E + R + Cww/t + miscellaneous

where P = Precipitation E = Evaporation R = Runoff (effectively consisting of surface runoff and baseflow) Cw = Water holding capacity of surface slab w = Change in the degree of saturation of the surface slab t = time step lengthmiscellaneous = conversion to plant sugars, human consumption, etc.

P E

w

Terms on LHS come fromthe climate model.Strongly dependenton cloudiness, watervapor, etc.

Terms on RHS come aredetermined by the land surfacemodel.

R

Precipitation, P

Getting the land surface hydrology right in a climate model is difficultlargely 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 landsurface model

Garbagein

Garbageout

The bottom storm is more evenly distributed over thecatchment than the top storm.Intuitively, the top storm willproduce more runoff, eventhough the average stormdepth over the catchment (E(Yo)) is smaller.

Key points: -- Specifying subgridvariability of precipitationis critical to an accuratemodeling of surface hydrology.-- A GCM is typically unableto specify the spatial structureof a given storm. The LSMtypically has to “guess” it.

From Fennessey, Eagleson,Qinliang, and Rodriguez-Iturbe,1986.

Precipitation: subgrid variability (1)

Here, the two storms havesimilar spatial structureand total precipitationamounts. The locations ofthe storms, however, aredifferent. If the top stormfell on more mountainousterrain than the bottomstorm, the top storm mightproduce more runoff

Key point: A GCM is typically unable to specifythe subgrid location of agiven storm. The LSM typically has to “guess” it.

From Fennessey, Eagleson,Qinliang, and Rodriguez-Iturbe,1986.

Precipitation: subgrid variability (2)

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 ofthe order of minutes. Why are temporal correlations important? Consider three consecutive time steps at a GCM land surface grid cell:

time step 1 time step 2 time step 3Case 1: No temporalcorrelation in storm position -- the storm isplaced randomly with thegrid cell at each time step.

Case 2: Strong temporalcorrelation in storm position between time steps.

Case 2 should produce, for example, stronger runoff.

Throughfall

Simplest approach: represent the interception reservoir as a bucket that gets filled duringprecipitation events and emptied during subsequent evaporation. Throughfall occurs when the precipitation water “spills over” the top of the bucket.

This works, but because it ignores subgrid precipitationvariability (e.g., fractional wetting), it is overly simple.

Capacity of bucket istypically a functionof leaf area index, ameasure of how manyleaves are present.

Spatial precipitation variability and interception loss

SiB’s approach (Seller’s et al, 1986)

Original water in reservoir

Precipitation assumed to fall accordingto some prescribeddistributionArea above line

is consideredthroughfall

Capacity of reservoir

Note: SiB allowssome of the precipitation to fallto the ground withouttouching the canopy.

Temporal precipitation variability and interception loss

Mosaic LSM’s approach:

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

Modeling runoff: GCM scaleSurface runoff formulations in GCMs are generally very crude, for at leasttwo 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

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

Pressure head (): A measure of the degree to which the soil holds on to its water through tension forces. More specifically, =p/g, where 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.

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

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 = + z)

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

K = kg

Where is the fluid’s density and is its dynamic viscosity. K is thus a function of soil and fluid properties.

K varies tremendously withsoil type. Small variations insoil type, say across a field site,could lead to orders of magnitude difference in the ability totransport moisture.

From Freeze and Cherry

Moisture transport in the unsaturated zone (e.g., in the soil nearthe surface) can also be computed with Darcy’s law, if appropriatecorrections are made to pressure head and hydraulic conductivity.

Water table

Z

=n

Soil moisture profile

capillary fringe

r

r = residual moisture

“specific retention”

Recall: = ratio of water volume to soil volume, n = porosity

p < 0

p = 0

p > 0

If atmospheric pressure defined to be 0.

(w) = saturated w -b

K(w) = Ksaturated w 2b+3

b = empirical coefficient

Unsaturated zoneequations (from

Clapp and Hornberger)

Recall: w= degree of saturation, = /n

One possible discretization of Darcy’s law (continued)

Characterize the soil as stacked layers(d = thickness)

d1

d3

d2

w1

w2

w3 recharge layer

surface layer

root layerCompute for each layer i:i = sat wi -b

Ki = Ksat wi

2b+3

Compute flow from layer i to layer i+1:

qz i,i+1 = K i - i+1

d+ 1

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

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 budgetstogether control evaporation rates?

Energy balance versus water balance

Energy balance:Implicit solution usually necessaryResults in updated temperature prognostics

Water balance:Implicit solution usually not necessaryResults in updated water storage prognostics

Budyko’s analysis of energy and water controls over evaporation

These assymptotesact as barriers to evaporation.

What determines the shape of Budyko’s curve?

If only annual means mattered,the observed curve should look like this:

Seasonality, however, is important.

Note that if these seasonal effects alone were considered, theobserved curve would actually look like this:

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 landsurface properties and the temporal variation of precipitation.

Budyko’s analysis: discussion

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

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

Structure of a Mosaic LSM tile: Water Balance

precipitation

throughfall

INTERCEPTION RESERVOIR

SURFACE LAYER

ROOT ZONE LAYER

RECHARGE LAYER

surface runoffinfiltration

drainage

soil moisturediffusion

evaporation + transpiration

How do we evaluate the performance of such an LSM?

“Online” approach: test GCM output against observations.

GCM

LSM

P, radiation, Tair, etc.

E, H, upwardlongwave

Advantage: The coupling effects can bestudied, and various sensitivity tests canbe 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 GISSGCM/LSM: The Amazonriver is poorly simulated, but we can’t tell if this isdue to a bad LSM or poorprecipitation from the GCM.

Better approach: Offline forcing (one-way coupling)

ForcingData

LSM

P, radiation, Tair, etc.

Advantage: Land surface model can bedriven with realistic atmospheric forcing, sothat the impact of the LSM’s formulationson the surface fluxes can be isolated.

Disadvantage: Deficient behavior of the LSMmay 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’sbehavior.

OutputFile

E, H, Rlw ,

diagnostics

PILPS model intercomparisons (to be discussed in a later lecture) havelargely focused on such offline evaluations.

Figure from Foley et al., “Coupling dynamicmodels of climate and vegetation”, Global Change Biology, 4, 561-579, 1998.

Typical GCM approach:ignore effects of climatevariations on vegetation

Early attempts at accounting for vegetation/climate consistency

Fully integrated dynamicvegetation model

DYNAMIC VEGATION: Yet another step forward in model development

Most important take-home lesson: soil moisture in one model need not have the same “meaning” as that in another model. As long as thetranspiration and runoff curves have the same relative positions, twomodels (e.g., Models A and B below) will behave identically, even ifthey have different soil moisture ranges.

0

1

0 200 400 800 1000600

T

R

0

1

0 200 400 800 1000600

T

R

Model A Model B

(True for simple models in simplewater balance framework and for complex LSMs running in AGCMs.)

Thus, it is the relative positions of the runoff and evaporation functionsthat determine the annual transpiration rate -- not the average soil moisture.

as described by T and fR

Sure enough, the LSMs in PILPShave different soil moisture ranges...

…and there is no evidence that LSMswith higher soil moistures producehigher evaporations.

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” is best thought of as a model- specific “index of wetness” that increases

during wet periods and decreases during dry periods.

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

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:

hundreds of km

(1) soil moisture varies tremendously across the distances represented byGCM grid cells,

and

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

wet

evaporationefficiency

soil moisture

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:

Wet:s=1.0

Dry:s=0.5

evaporationefficiency

soil moisture

0.5

0.4

1.0

0.6

0.75

Ewet = 0.6 Ep

Edry = 0.4 Ep

Eave = 0.5 Ep

average soil moisture = 0.75E based on average soil moisture = 0.55 Ep

0.55

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:

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

0. 400.200.

soil moisture range for Model A

soil moisture range for Model B

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

Recall from 3rd lecture: runoff cannot be represented realistically with a one-dimensional vertical framework.

Scale: hundreds of kilometers

In a typical LSM, the soilmoisture is effectivelyassumed uniform in layersa few centimeters thick spanning hundreds ofkilometers!

What is land-atmosphere feedback on precipitation?

Precipitation wets thesurface...

…causing soilmoisture toincrease...

…which causesevaporation to increase duringsubsequent daysand weeks...

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

…thereby (maybe) inducing additional precipitation

Lecture 9

Land and Climate: Modeling Studies

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.

Establishatmospheric

state

Initialize modelwith that state;integrate into

future

Short-term(~several days)

weatherprediction

days

Relevanceof initialconditions

Decay reflects shorttimescale of atmospheric “memory”Atmosphere

Saturday’s forecast for Tuesday (March 23, 2004): sunny, high of 46F (8C).

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

Establishocean state,land moisture

state

Initialize modelwith those states;

integrate intofuture

Long-term(~weeks to years)

prediction of oceanand/or land states

Associatedprediction ofweather, ifweather

responds tothese states

months

Relevanceof initialconditions

Ocean

Land

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

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

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

Vinnikov and Yeserkepova, 1991

Part 1: Soil Moisture Memory

Koster et al. (2001) (cont.)

Boreal summer Boreal winter

Results for SST andsoil moisture control over precipitationcoherence

Differences: an indication of theimpacts of soilmoisture controlalone

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.

Koster et al. (2001) (cont.)

Evap.coherence

Why does land-atmospherefeedback occur where itdoes?

One control: Budyko’sdryness index

varianceamplificationfactor

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 explainwhat controls

ac(P) in the GCM?

Pn Pn+2

correlateswith

means that

correlateswith

Pn Pn+2

wn

En+2

wn+2

correlateswith

correlateswith

correlateswith

Breaks down in western US

Breaks down in eastern US

Breaks down in western US

GCM obs

Illustration of point 6:The ensemble mean is off,but some of the ensemblemembers do give areasonable forecast

June r2 values, averaged over area of focus

AMIP runs: SSTs only

GLDAS runs:SSTs + landinitialization

SSTs + landinitialization + atmosphereinitialization

SSTs + atmosphereinitialization

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 land2. Initialize atmosphere only

Warning: Statistics are based on only 15 data pairs!

Outlook

Presumably, skill associated with land initialization can only increase with:-- improvements in model physics-- improved data for initialization

satellite sensors (HYDROS, GPM, …)ground networksdata 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 lotof untapped

potential!

DATA ASSIMILATION: THE OPTIMAL MERGING OF OBSERVATIONS AND MODEL RESULTS

Combined model/ observational state at time t

Model state at time t+1

Observation at time t+1

Combined model/ observational

state at time t+1

Integrate model forward in time

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

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

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

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

obs

model

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

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

Results subject to myriad inadequacies of model parameterizations

Inadequate coverage, significant measurement error.

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.f5. 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.

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

 EXPERIMENT 1    HEAT CAPACITY     WATER CAPACITY FACTOR     TURBULENCE FLAG           70000.                         1.                   0Heat 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         0ALBFIX: If this is 1, you are using tropical forest albedo.RGHFIX: If this is 1, you are using tropical forest roughness heightsSTOFIX: 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.

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?

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?

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?

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?

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.

Notes on output files generated in computer lab