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- 1. Yield Gap Analysis and Crop Modeling Workshop Nairobi, Kenya RESEARCH PROGRAMS ON Climate Change, Agriculture and Food Security SYSTEMS ANALYSIS IN AGRICULTURE Integrated Systems for the Humid Tropics Roots, Tubers and Bananas International Potato Center Sub-program: Production Systems and Environment
- 2. SYSTEMS ANALYSIS IN AGRICULTURE
- 3. 1. Collection of elements 2. Connected 3. Forming a unit
- 4. 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
- 5. 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
- 6. Stephen W. Hawking Theoretical Physicist Cambridge University
- 7. Methodology Define objectives Analysis of the system Synthesis 5000 Verification y = 1.0657x - 195.55 R2 = 0.9925 Validation Sensitivity analyses 500 0 -500 Scenario analyses -1000 Y -1500 -2000 Documentation -2500 8.0 5.0 -3000 2.0 -1.0 -3500 1 2 3 4 5 6 7 -4.0 8 9 10 11 12 13 14 15 16 17 X1 18 19 20 21 -7.0 -10.0 X2 Simulados 4000 3000 2000 2000 2500 3000 3500 4000 Observados 4500 5000
- 8. Methodology Defining Objectives Problem to be Addressed Define objectives Analysis of the system Synthesis Verification Defining Effective Measurements Analysis of the System Determine Components of the System Defining model Variables Synthesis Validation Sensitivity analyses Scenario analyses Documentation Defining working hypotheses Abstraction of components Developing the Mathematical Algorithm Programming
- 9. Define objectives Irradiance Day t hour h Analysis of the system Respiration Day t Synthesis Verification Validation Sensitivity analyses Scenario analyses Documentation Biomass Day t-1 GPP Day t NPP Day t
- 10. Linear Regression (Observed vs. Simulated). 5000 y = 1.0657x - 195.55 R2 = 0.9925 Define objectives Simulados 4000 3000 Analysis of the system 2000 2000 Synthesis 2500 3000 3500 4000 Observados 4500 5000 Ho (1) : o = 0 Ha (1) : o 0 Verification Validation Ho (2) : 1 = 1 Ha (2) : 1 1 Residual Analysis (Observed vs. Simulated). Residuales (y-ye) Scenario analyses 150 100 Sensitivity analyses 200 150 100 Residuales (y-ye) 200 50 0 -50 50 0 -50 -100 -100 -150 -150 -200 Documentation -200 Observaciones Observaciones ei = yi – yei
- 11. Define objectives Analysis of the system Synthesis Running the model to generate desired information Find estimated values of input and state variables that maximize (or minimize) ouput variables Verification Validation Sensitivity analyses Scenario analyses Documentation What Happens if
- 12. Basic concepts required to model systems dynamics
- 13. Hierarchy of Yield Drivers and Associated Yield Levels Crop Traits Germplasm Production Situation Defining factors Potential yield (Yp) CO2 Radiation Limiting factors Attainable yield Climate Temperatu re Yield increasing measures Reducing factors Water Actual yield (Ya) Yield protecting measures Nutrients Soils Weeds Pests Dry Matter Yield, Mg/Ha Diseases Modified by R. Quiroz from Penning de Vries & Rabbinge, 1995
- 14. 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.
- 15. 20 0 10 Bacteria, number 30 40 Let us say we put a single bacteria in a culture that divides itself every half minute; in 15 min there will be 45 0 5 10 15 Time,min Most living organism present growth patterns similar to this figure. That is, it follows an exponential increase in number or weight.
- 16. 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: Time, t Weight, w 1 w0 2 2w0 3 3w0 4 4w0 5 5w0 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
- 17. The growth rate at any time is: 30 10 20 dy dx 0 Bacteria, number 40 dw/dt = k* W0 *Exp (k*t) 0 5 10 Time,min 15
- 18. We can calculate now the relative growth rate (RGR), defined as the rate of growth divided by the weight: RGR = dw/dt RGR = k W (t) k* W0 *Exp (k*t) = W0 *Exp (k*t)
- 19. 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
- 20. RGR*= dw/dt W *(1 – g*W) = 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
- 21. 0.000 0.010 0.020 0.030 RGR 0 0 50 Time,days 50 100 Weight 150 100 150 0 10 20 Weight 30 40
- 22. Now, let us say we have a plant growing without restriction (water, climate, pest control, etc.) Irradiance Day t Biomass Day t-1 Respiration Day t GPP Day t W (t)= W0 *e k*t Where: W(t) – weight at any time t W0 – weight at t=0 k – growth constant NPP Day t
- 23. Conceptual representation of a horizontal surface at the top of the canopy G B R NIR
- 24. A. Effect of temperature on the metabolic reaction rate Optimal t° Emergency Rate Reaction Rate % B. Effect of so potato plan Temperature ( °C ) Respiration/photosynthesis rates (gCO2 cm -2 hoja min -1 Total D. Relationship b solar energy u M (gcm -2) C. Effect of temperature on photosynthesis and respiration in potato
- 25. 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.
- 26. Growing degree days calculation Classical approach ET = TX-Tb Effective temperature 40 Where Tx Mean temperature 30 20 10 0 -20 -10 0 10 20 30 40 50 40 50 Temperature Tx < To, ET = TX (1-((Tx-To)/(To-Tb))2 Effective temperature Alternative Approach To 20 10 Tx > To, ET = TX (-((Tx-Tm)/(Tm-To))2 Tb Tm 0 ET Effective temperature ADD Acummulated degree days -20 -10 0 10 20 Temperature 30
- 27. 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
- 28. Potato phenology Patacamaya, La Paz 17°16' S 68°55' W 3800 m.a.s.l. 100% Canopy Cover 80% 60% 40% 20% GDD Luk'y Waycha Alpha Ajanhuiri Gendarme Phase 1 350 - 450 GDD Phase 2 800 – 1000 GGD Phase 3 1200 – 1400 GDD 1400 1200 1000 800 600 400 200 0 0%
- 29. SOLANUM Conceptual framework Light Light Interception LUE (—) DM PAR Kg DM.ha¨¹.d ¨¹ Photosynthetic Apparatus T GC LAI Light Reflectance Tubers Roots Stems Leaves
- 30. 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)
- 31. The main growth processes Light interception Light use efficiency Tuber partitioning
- 32. 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).
- 33. Fraction of light intercepted (FLINT) MCC 1.0 0.8 0.6 Canopy cover 0.4 0.2 R0 f0 0.0 0 500 1000 Thermal time 1500 2000
- 34. Model parameters Radiation use efficiency P6 light use efficiency, RUE (gr MJ-1) Partitioning harvest index function HI=M/(1+(t_ac/A)b) P7 asymptotic harvest index, M P8 initial slope of the harvest index curve, b (ºCd-1), P9 thermal time at the initial harvest index curve, A (ºCd) Tuber dry matter P10 tuber dry matter content (DMcont)
- 35. Radiation use efficiency - RUE 3000 y = 5.552x R² = 0.933 Total dry matter (gr. m-2) 2000 1000 0 0 100 200 300 Intercepted PAR (MJ.m-2) 400
- 36. Asymptotic harvest index 1.0 M 0.8 0.6 Tuberization index b 0.4 0.2 A 0.0 0 500 1000 Thermal time 1500 2000
- 37. The soil - plant - atmosphere system CO2 Temperature Radiation Rainfall Photosynthesis Respiration Photorespiration Transpiration Dry matter Atmosphere Plant Farmer practices Water Nutrients Evaporation Soil
- 38. Model parameterization ―Minimum data set‖ What to measure? When to measure? How to measure?
- 39. What to measure for estimating potential production? Solar radiation Temperature Planting date Emergence date Harvest date Canopy cover/LAI/VI Dry matter by plant organ Dry matter content of tubers Atmosphere Plant
- 40. When to measure? Daily meteorological data Periodic crop growth measurements Weekly 10 days 15 days
- 41. How to measure?
- 42. Meteorological data and equipment • Minimum and maximum air temperature • Solar incoming radiation • Rainfall • Reference evapotranspiration • Soil temperature
- 43. Leaf area data acquisition
- 44. Determining leaf area index (LAI) from NDVI NIR - R NDVI = NIR + R Where: NIR: Near Infrarred R: Red
- 45. Relationship between LAI and NDVI data simulated
- 46. Canopy cover data acquisition Grid method
- 47. Canopy cover data acquisition Segmented image method Post-processing
- 48. Measuring dry matter Leaves Stems Tubers Roots
- 49. Parameter calculation example La Molina, Peru Latitude 12º 04’39‖ S Longitude 76º 56’53‖ W Altitude 280 m.a.s.l. June - November 2006
- 50. Thanks

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