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.

Why the interest in carbon? Clearly, for questions of global climate change.

Why the interest in modeling the land’s role in the carbon cycle? Note, for example, the impact of land seasonality on the atmospheric CO2 content.

Land sources and sinks of carbon are net yet well quantified, as indicated by the famous “missing carbon sink”.

(Slightly dated) list of carbon modeling references, from a compilation by Jim Collatz:

“[Third generation models] use modern theories relating photosynthesis and plant water relations to provide a consistent description of energy exchange, evapotranspiration, and carbon exchange by plants…. The third-generation LSPs point the way to future land models that can be coupled with comprehensive atmospheric and ocean models to explore different global exchange scenarios.” -- Sellers et al.

SiB2

IGBP/GAIM REPORT SERIES, REPORT #5, “NET PRIMARY PRODUCTIVITY MODEL INTERCOMPARISON ACTIVITY (NPP)”, Wolfgang Cramer and the participants* of the "Potsdam '95" NPP model intercomparison workshop

Annual net primary production (g C m -2 yr-1) estimated as the average of all model NPP estimates.

Many different types of carbon assimilation models exist. In the particular comparison shown here, only SiB2 is a “SVAT-type” carbon model. All of these models, though, have the same goal: to understand the global distribution and temporal variations of the carbon cycle at the land surface.

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

Mappings between climateand vegetation exist that canbe used for the second approachon the previous page.

The third approach on the previouspage requires a whole new type ofmodel framework.

Figure from Mather, The ClimaticWater Budget in EnvironmentalAnalysis, Lexington Books.

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

DYNAMIC VEGATION (cont.)

What underlies the behavior of a land surface model?PILPS (the Project for the Intercomparison of Landsurface ParameterizationSchemes): a project in which the responses of various land surface models tothe same atmospheric forcing are quantified and compared. Overall goal: abetter understanding of land surface model (LSM) behavior.

Typical PILPS result: widedisparity in LSM response.

How do we explain this disparity?We can’t compare code or evencompare descriptions of the parameterizations -- the LSMs aretoo complex, and such a comparisonwould soon become intractable.

Alternative approach: empiricallycharacterize underlying controls onevaporation and runoff.

Reference: Koster, R. and P. C. D. Milly, The interplaybetween evaporation and runoff formulations in a landsurface model, J. Climate, 10, 1578-1591, 1997.

(Analysis introducing a possible alternative path for LSM development)

Many of the models that performed the experiment on the previous page performed a supplemental experiment that imposed a great many controls:

Prescribed vegetation type and fraction Prescribed albedo Prescribed aerodynamic resistance No seasonal variation in vegetation parameters No snowfall

Model disparity remained high:

In fact, model disparity is even higher than before -- apparently,in the control (on the previous page),differences in the above quantities led to compensating effects.

The experiment to the left, though, simplifies the task of explaining differencesin LSM behavior.

w(root zone

soil moisture)

P (prescribed)

Ew (computed)

Ei (prescribed)

Rs (computed)P - Ei

Q (computed)

Transpiration efficiency = T =

Runoff ratio = R =

Baseflow = Q (mm/day)

E - Ei

Ep - EiRs

P - Ei

0

1

0 200 400 800 1000600

T

R

T = 0 defines lowerlimit of soil moisture

R = 1 defines upperlimit of soil moisture(when no baseflow)

0

1

0 200 400 800 1000600

T

RQ

0

25

Simple case: no baseflow

Consider a simple water balance model: w(n+1) - w(n)

t= P - Ei - Rs - Ew - Q

functions of w

How might these linear relationships look?For each model participating in the PILPS experiment, we can plot monthlyaverage root zone soil moisture (w) against monthly average T, R, and Q,for each of the 12 months. We can then fit, through simple regression, lines that characterize (to first order) the model’s inherently complex relationships between soil moisture and the fluxes.

T vs w for 3 LSMs R vs w for 3 LSMs Q vs w for 3 LSMs

Fits certainly aren’t perfect, butthey do describe the first orderrelationship.

Through these fits, we see that each LSM is characterized bydifferent relationships between root zone moisture and the fluxes.

heavy line:T

dashed line:R

dotted line:Q

In the simple water balance model, take Rs = R(w) (P - Ei) Ew = T(w) (Ep - Ei) G = G(w)When the fitted curves are used to define the coefficient of the Rs, Ew, andG functions, and when the simple water balance model is used with thesevalues, the resulting transpiration fluxes agree very well with thefluxes the original models simulated.

Key interpretation:the simple linear fitscapture much of theintrinsic behavior of the different LSMs.

Note the the success of the simple water balance model (with coefficientsfrom linear fits) extends beyond the annual scale -- it also applies to the models’ simulation of seasonal transpiration rates.

We can extend this analysis further by considering the annual mean of the water balance equation: P - Ei = Rs + Ew = R(w) (P - Ei) + T(w) (Ep - Ei)

The unique solution can be written:

where D = ( Ep - Ei ) / ( P - Ei ) (a climatic “index of dryness”)

T = Average of beta function across soil moisture range

fR = Fraction of soil moisture range over which runoff occurs.

Ew

P - Ei

2 D T

1 + 2 D T fR

=

0

1

T

R

wO wr w1

fR = (w1-wr)/(w1-w0)

fR

1T = shaded area / (w1-w0)

Assume for nowthat the drainageterm can be “folded into” the runoff term.

Although the equation produces a biased evapotranspiration, it neverthelessexplains (in large part) the variability amongst the models.

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 moisture0.5

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

The example suggests that if a land modeler is forced to represent the soil with vertical layers, with a single variable representing the moisture in a tremendously large area, and without any representation of subgrid process variability, the following is the best that can be hoped for:

Unrealistic soil moisture andRealistic areally-averaged

surface fluxes

Realistic soil moisture andUnrealistic areally-averaged surface fluxes

or

Arguably, for AGCM applications, a modeler would strive for this –given the restrictions of model resolution, the modeler may choose to live with a nebulous soil moisture variable.

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

Approaches do exist for mapping one model’s soil moisture into that of another, for purposes of initialization. For example, we can scale using standard normal deviates:

pdf of soil moisture:

Model “A”

pdf ofsoil moisture:

Model “B”

A

aA

B

aB

XA XB

XA - A

A

XB - B

B=

These pdfs, of course, will vary with region. A caveat: for some applications, particularly those that employ a constantly evolving modeling system (e.g., data assimilation and forecasting), the decadal model output needed to generate the pdf descriptions will probably be unavailable.

While soil moisture has a nebulous meaning in land surface models, the time change in soil moisture should be well-defined – e.g., the monthly change of moisture below the land-atmosphere interface can be calculated with

Monthly change = Monthly Precipitation – Monthly Evaporation – Monthly Runoff,

and all terms on the R.H.S. of this equation have precise, unambiguous meanings.

In practice, intermodel differences in “monthly soil moisture change” are much smaller than intermodel differences in absolute soil moisture (e.g., Entin et al., 1999). Still, -- some differences do exist, due to differences in the size of the soil

moisture dynamic range, a function of model parameterization. -- in any case, the transformation of a soil moisture / t value to a

model initialization is not necessarily straightforward.

Note on the meaning of soil moisture / t

In actuality (in nature and in most models), the T function isn’t simply linear; the value of T plateaus out at high soil moisture. (The linearity assumption was used mostly for convenience.) Athigh enough soil moisture, the plant is no longer water stressed, and increased soil moisture does not increase transpiration.

Nevertheless, the same arguments apply: it is the relative positions of the runoff and evaporation functions that determine the annual transpiration rate.

In many recent LSMs, the value of the non-water stressed T is given considerable attention. It might, for example be effectively computed as a function of: Vegetation type, LAI, greenness Environmental stresses (e.g., temperature) CO2, photosynthesis Aerodynamic properties Other quantities

0

1

0 200 400 800 1000600

T

R

0

1

0 200 400 800 1000600

T

R

0

1

0 200 400 800 1000600

T

R

0

1

0 200 400 800 1000600

T

R

Relatively little attention hasbeen given to the formulation of runoff -- a big mistake, if accurateannual evaporations are desired.

Now: Back to the discussion of evaporation, runoff, and soil moisture

These two examples (from an application with the simple water balancemodel) illustrate that even with the same T function, differentevaporation rates stem from different assigned runoff functions.

Different runofffunctions lead todifferent transpirationrates

Again, relatively little attention has been given to runoff formulations, as compared to evaporation formulations. This suggests an alternative pathof model evolution.

Current stateof LSMs

Improved representationof point processes (canopystructure, soil levels, photosynthesis physics…)

Focus on vertical, 1-D representation

Improved representation ofsubgrid variability (e.g., ofsoil moisture and its effectson runoff and evaporation)

Focus on horizontal, 3-D representation

Path 1 Path 2

This path is useful for improving runoff formulations.Why? Because the main reasonfor poor runoff formulations isthe inability to treat subgridvariability accurately (seewater balance lecture).

Essentially thepath outlined in the Sellers et alpaper.

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!

An example of a land surface model that follows this second path: the“NSIPP catchment LSM”.

Approach:

1. Use the hydrological catchment as the fundamental land surface unit.

Don’t assume land surface element has a shape defined by the overlying atmospheric grid

2. Within each catchment, use hydrologicalmodels for dealing with subgrid-scale soilmoisture distributions.

TOPMODEL, with a special treatment of the unsaturated zone. (We employ many of the ideas introduced by Famiglietti and Wood, 1994.)

References:Koster et al., J. Geophys. Res., 105, 24809-24822, 2000.Ducharne et al., J. Geophys. Res., 105, 24823-24838, 2000.

Basic idea behind catchment model:

Different moisture levels (shown here as differentwater table depths)…

…lead to different arealpartitionings of the catchment into saturated,unstressed, and wiltingregimes.

Based on the values of these two prognostic variables (and a third [MSD], analogousto MRZ but related to the moisture close to the surface) we can explicitlyresolve three hydrological regimes:

the saturated zone the unsaturated but unstressed zone the wilting zone

Different physics applies in each zone. Unlike one-dimensional, “vertical column” LSMs, we can explicitly apply these different physics.

Evaporation Saturated area: allow unstressed transpiration, unstressed bare soil evaporation. Unsaturated area: allow unstressed transpiration, stressed bare soil evaporation. Wilting zone: Zero transpiration, allow stressed bare soil evaporation.

Runoff Saturated area: All rainfall becomes surface runoff. Unsaturated area: Infiltration allowed. Wilting zone: Infiltration allowed.

Baseflow Computed based on water table distribution (TOPMODEL)

Saturated zone

Unsaturated zone

Wilting zone

A similar (thoughnon-spatially integrated)calculation is performedto determine the flux ofmoisture between the thin surface reservoirand the root zone.

Topographic Data Requirements

1. Catchment delineations (global)

2. Statistics of topographic index within each catchment: -- mean -- standard deviation -- skew

3. Scaling approaches: what would the statistics look like if we had higher resolution data?

These data are not used directly in the model;rather, they are transformed into a number ofmodel parameters.

Figure courtesy of Colin Stark,LDEO, Columbia University

Model parameters are derived from basic topographic statistics. In essence,the model parameters are empirical fits to very complicated calculations.

The catchment model has beentested in various venues, includingthe PILPS 2c Red-Arkansas test.

Unstressedfraction

UnstressedfractionStressed fraction

Stressed fraction

overland flow

stormflow

baseflow

New formulations for “stormflow” and for the effectsof variable depth to bedrock.

depth to bedrock istypically smaller athilltop…

…than at valley bottom

The NSIPP Catchment LSMis continually undergoing…

…development …validation

The model described above represents just one possible way of treating explicitly the subgrid variation of soil moisture in a land surface grid cell and its impact on evaporation and (especially) runoff. Other ways certainly exist, e.g., VIC:

The point is, the importance of modeling this subgrid variability must not get lost in our zeal to improve the one-dimensional physics in a land surface model. Take-home lesson: more than one “evolutionary path” is needed.

Notes on output files generated in computer lab