2 systems analysis in agriculture

RESEARCH PROGRAMS ON

Climate Change,Agriculture andFood Security

Integrated Systemsfor the HumidTropics

Roots, Tubersand Bananas

Yield Gap Analysis and Crop Modeling WorkshopNairobi, Kenya

SYSTEMS ANALYSIS IN AGRICULTURE

International Potato CenterSub-program: Production Systems and Environment

SYSTEMS ANALYSIS IN AGRICULTURE

1. Collection of elements2. Connected3. Forming a unit

A particular attribute of most agricultural systems is their complexity. Therefore, when studying complex systems we should follow Albert Einstein’s rule: Make things as simple as possible, BUT NOT SIMPLER THAN THAT

Mathematics is used to synthesize and understand the behavior of a system:

• Reductionist knowledge of the parts of a system (known as mathematical models)

• Mean of articulating our ideas and formalizing them in an abstract way

Stephen W. HawkingTheoretical PhysicistCambridge University

Methodology

Define objectives

Analysis of the system

Synthesis

Verification

Validation

Sensitivity analyses

Scenario analyses

Documentation

y = 1.0657x - 195.55

R2 = 0.9925

2000

3000

4000

5000

2000 2500 3000 3500 4000 4500 5000

Observados

Sim

ula

do

s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

-10.0

-7.0

-4.0

-1.0

2.0

5.0

8.0

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

Y

X1

X2

Methodology

Define objectives


Synthesis

Verification

Validation


Scenario analyses

Documentation

Defining ObjectivesProblem to be Addressed

Defining Effective Measurements

Analysis of the SystemDetermine Components of the System

Defining model Variables

SynthesisDefining working hypotheses

Abstraction of components

Developing the Mathematical Algorithm

Programming

Define objectives


Synthesis

Verification

Validation


Scenario analyses

Documentation

BiomassDay t-1

NPPDay t

IrradianceDay t hour h

RespirationDay t

GPPDay t

Linear Regression (Observed vs. Simulated).

y = 1.0657x - 195.55

R2 = 0.9925

2000

3000

4000

5000

2000 2500 3000 3500 4000 4500 5000

Observados

Sim

ula

do

s

Ho (1) : o = 0 Ho (2) : 1 = 1

Ha (1) : o 0 Ha (2) : 1 1Residual Analysis (Observed vs.

Simulated).

-200

-150

-100

-50

0

50

100

150

200

Observaciones

Res

idu

ales

(y-

ye)

-200

-150

-100

-50

0

50

100

150

200

Observaciones

Res

idu

ales

(y-

ye)

ei = y

i – ye

i

Define objectives


Synthesis

Verification

Validation


Scenario analyses

Documentation

Running the model to generate desired information

Find estimated values of input and state variables that maximize (or minimize) ouput variables

What Happens if

Define objectives


Synthesis

Verification

Validation


Scenario analyses

Documentation

Basic concepts required to model systems

dynamics

Soils

Climate

Germplasm

CO2

Weeds

Crop Traits

Diseases

Radiation

Temperature

Water

Pests

Nutrients

Potential yield (Yp)

Attainable yield

Actual yield (Ya)

Dry Matter Yield, Mg/Ha

Defining factors

Limiting factors

Reducing factors

Hierarchy of Yield Drivers and Associated Yield Levels

Modified by R. Quiroz from Penning de Vries & Rabbinge, 1995

Yield increasing measures

Yield protecting measures

Pro

du

ctio

n S

itu

atio

n

Growth and development

Growth. The increase of weight or volume of the total plant or various plant organs.

Development. The passing through consecutive phenological phases. Characterized by the order and rate of appearance of vegetative and reproductive plant organs.

Let us say we put a single bacteria in a culture that divides itself every half minute; in 15 min there will be 45

Most living organism present growth patterns similar to this figure. That is, it follows an exponential increase in number or weight.

Let’s assume we have a culture that divides itself every unit of time (t). If we record the weight and we say that the first cell had a weight w0, then when divided into two the weight is 2w0, son on and so forth, we will have:

The shape of the growth response, as a function of time, might be generically described by an exponential function:

W(t) = w0 *e k*t

Time, t Weight, w

1 w0

2 2w0

3 3w0

4 4w0

5 5w0

dw/dt = k* W0 *Exp (k*t)

The growth rate at any time is:

We can calculate now the relative growth rate (RGR), defined as the rate of growth divided by the weight:

dw/dt k* W0 *Exp (k*t)

W (t) W0 *Exp (k*t)==RGR

RGR = k

Now we have a little problem, plants and other biological systems do not grow indefinitely; as the organisms get bigger, their growth rate slows until it reaches its mature size, when RGR becomes zero

Therefore we need to modify our equation for RGR. There are different ways and we will use an arbitrary but convenient way

dw/dt

W ==RGR* k (1 – g*W)

Where: g=1/Wmax

Putting this in words, when W is close to W0 RGR is close to k but as W approaches Wmax RGR also approaches zero

*(1 – g*W)

BiomassDay t-1

GPPDay t

NPPDay t

IrradianceDay t

RespirationDay t

Now, let us say we have a plant growing without restriction (water, climate, pest control, etc.)

W (t)= W0 *e k*t

Where: W(t) – weight at any time t W0 – weight at t=0 k – growth constant

Conceptual representation of a horizontal surface at the top of the

canopy

GB R NIR

A. Effect of temperature on the metabolic reaction rate

Reaction Rate%

B. Effect of soil temperature on the emergency rate of potato plants

Optimal t°

Temperature ( °C )

Em

erg

en

cy

Ra

te

Temperature ( °C )

C. Effect of temperature on photosynthesis andrespiration in potato

Respiration/photosynthesis rates(gCO2 cm -2 hoja min -1

Total photosynthesis

Net

photosynthesis

Respiration

Air temperature ( °C )

D. Relationship between total dry matter and intercepted solar energy under different environmental conditions

Cu

mm

ula

tiv

eD

M (

gc

m-2

)

Cold weather + waterB = 2.0

Warm weather + waterB = 1.2

Warm weather w/o waterB = 0.8

Intercepted solar radiation


Reaction Rate%


Optimal t°

Temperature ( °C )

Em

erg

en

cy

Ra

te

Temperature ( °C )




Net

photosynthesis

Respiration



Cu

mm

ula

tiv

eD

M (

gc

m-2

)






Reaction Rate%


Optimal t°

Temperature ( °C )

Em

erg

en

cy

Ra

te

Temperature ( °C )




Net

photosynthesis

Respiration



Cu

mm

ula

tiv

eD

M (

gc

m-2

)






Reaction Rate%


Optimal t°

Temperature ( °C )

Em

erg

en

cy

Ra

te

Temperature ( °C )




Net

photosynthesis

Respiration



Cu

mm

ula

tiv

eD

M (

gc

m-2

)





Thermal time and growth

Growth and development of crops are strongly dependent on temperature.

Each species requires a specific temperature range for development to occur. They are named cardinal temperatures:

• Base temperature, Tb• Optimum temperature, To• Maximum temperature, Tm

Thermal time are commonly calculated as a Growing Degree Days (GDDs), Growing Degree Units (GDUs), or heat units (HUs). Different methods exist for calculating heat units.

Growing degree days calculation

Classical approach

ET Effective temperatureADD Acummulated degree days

ET = TX-Tb

Where Tx Mean temperature

Tx < To, ET = TX (1-((Tx-To)/(To-Tb))2

Alternative Approach

Tx > To, ET = TX (-((Tx-Tm)/(Tm-To))2 Tm

To

Tb

0

10

20

30

40

-20 -10 0 10 20 30 40 50

Temperature

Effec

tive

tem

pera

ture

0

10

20

-20 -10 0 10 20 30 40 50

Temperature

Effec

tive

tem

pera

ture

Potato phenology

Phase 0 between planting and emergence

Phase 1 between emergence and tuber initiation

Phase 2 between tuber initiation and the moment when 90% of assimilates are partitioned to the tubers

Phase 3 until the end of crop growth

Potato phenologyPatacamaya, La Paz

17°16' S 68°55' W 3800 m.a.s.l.

0%

20%

40%

60%

80%

100%

0

200

400

600

800

1000

1200

1400

GDD

Can

opy

Cov

er

Luk'y Waycha Alpha Ajanhuiri Gendarme

Phase 1 350 - 450 GDD

Phase 2 800 – 1000 GGD

Phase 3 1200 – 1400 GDD

SOLANUM Conceptual framework

Roots Stems Leaves

GC LAI

Light Reflectance

PhotosyntheticApparatus

Tubers

Light

Interception

Kg DM.ha¨¹.d ¨¹

Light

LUE( )DMPAR—

T

Dry matter accumulation equation

The growth model, based on light interception and utilization as proposed by Spitters (1987, 1990) and Kooman (1995), was used to simulate the daily dry matter accumulation, through the following general equation: Wt = flint*PAR*LUE Where:

• Wt Growth rate at day t (g DM.m-2.d-1) • flint Fraction of PAR intercepted by the foliage• PAR Photosynthetically active radiation (MJ.m-2.d-1)• LUE Light utilization efficiency (g DM.MJ-1 PAR)

The main growth processes

Light interceptionLight use efficiencyTuber partitioning

Model parameters

Fraction of light intercepted (FLINT)

Growth phase:FLINT = (MCC * N * f0 * exp (R0*t)) / (N *f0 * exp(R0*T) + 1 – N *f0).

P1 maximum canopy cover, MCC P2 initial light interception capacity, f0 (m2 pl-1) P3 initial relative crop growth rate R0 (ºCd-1)

Senescence phase:Ft = 0.5 – (t - t0.5) / d.

P4 duration of leaves senescence, d (ºCd), P5 time when light interception was reduced to 50%, t0.5 (ºCd).

Fraction of light intercepted (FLINT)

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000

Thermal time

Canopy cover

f0

R0

MCC

Radiation use efficiencyP6 light use efficiency, RUE (gr MJ-1)

Partitioning harvest index functionHI=M/(1+(t_ac/A)b) P7 asymptotic harvest index, MP8 initial slope of the harvest index curve, b (ºCd-1), P9 thermal time at the initial harvest index curve, A (ºCd)

Tuber dry matterP10 tuber dry matter content (DMcont)

Model parameters

Radiation use efficiency - RUE

y = 5.552xR² = 0.933

0

1000

2000

3000

0 100 200 300 400

To

tal d

ry m

att

er

(g

r. m-2

)

Intercepted PAR (MJ.m-2)

Asymptotic harvest index

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000

Thermal time

Tuberization index

A

M

b

The soil - plant - atmosphere system

Atmosphere

Plant

Soil

CO2

TemperatureRadiation

Rainfall

PhotosynthesisRespiration

PhotorespirationTranspiration

Dry matter

WaterNutrients

Evaporation

Farmerpractices

Model parameterization“Minimum data set”

What to measure? When to measure?How to measure?

Atmosphere

Plant

Planting dateEmergence dateHarvest dateCanopy cover/LAI/VIDry matter by plant organDry matter content of tubers

Solar radiation Temperature

What to measure for estimating potential production?

When to measure?

Daily meteorological data

Periodic crop growth measurements Weekly 10 days15 days

How to measure?

Meteorological data and equipment

• Minimum and maximum air temperature

• Solar incoming radiation• Rainfall• Reference -

evapotranspiration• Soil temperature

Leaf area data acquisition

Determining leaf area index (LAI) from NDVI

Where:

NIR: Near Infrarred

R: Red

NDVI =NIR - R

NIR + R

Relationship between LAI and NDVI

data

simulated

Canopy cover data acquisition

Grid method

Post-processingSegmented image method

Canopy cover data acquisition

Measuring dry matter

Leaves Stems Tubers

Roots

Parameter calculation example

La Molina, Peru

Latitude 12º 04’39” SLongitude 76º 56’53” W

Altitude 280 m.a.s.l.

June - November 2006

Thanks

2 systems analysis in agriculture

Technology