A PREDICTION APPROACH A PREDICTION APPROACH TO AGRICULTURAL LAND TO AGRICULTURAL LAND

USE ESTIMATIONUSE ESTIMATION

Ambrosio L. , Marín C., Ambrosio L. , Marín C., Iglesias L., Iglesias L., Montañés J., Rubio L.A.Montañés J., Rubio L.A.

Universidad Politécnica Universidad Politécnica Madrid. Madrid. SpainSpain

Financial support from the Spanish Ministerio de Financial support from the Spanish Ministerio de Ciencia y Tecnología and from the Junta de Ciencia y Tecnología and from the Junta de

Andalucía is gratefully acknowledged. Andalucía is gratefully acknowledged.

INTRODUCTIONINTRODUCTION Farmer land use decisions are modeled using aFarmer land use decisions are modeled using a dynamic dynamic

generalized linear mixed model (multinomial) allowing for generalized linear mixed model (multinomial) allowing for spatiotemporal correlation spatiotemporal correlation

Based on this model, a predictor of agricultural land uses is Based on this model, a predictor of agricultural land uses is defineddefined

The predictor variables are: (i) biological data provided by The predictor variables are: (i) biological data provided by an agrometeorological model, (ii) economical data and (iii) an agrometeorological model, (ii) economical data and (iii) data on last year land usesdata on last year land uses

In order to identify the correlation structure, a In order to identify the correlation structure, a spatiotemporal variogram model is usedspatiotemporal variogram model is used

The predictor performance is evaluated by simulationThe predictor performance is evaluated by simulation

AREA SAMPLING FRAME FOR AREA SAMPLING FRAME FOR GROUND DATA COLLECTIONGROUND DATA COLLECTION

Currently, most of agricultural data are collected Currently, most of agricultural data are collected using spatial sampling (FAO 1996, 1998). using spatial sampling (FAO 1996, 1998).

A spatial sampling scheme, made popular by the A spatial sampling scheme, made popular by the Joint Research Centre of the European Union, Joint Research Centre of the European Union, uses topographic maps as sampling frame and the uses topographic maps as sampling frame and the 1 km by 1 km UTM square as sampling unit 1 km by 1 km UTM square as sampling unit (usually this sampling unit is reduced to a 700 m (usually this sampling unit is reduced to a 700 m by 700 m). by 700 m).

Spatial location of the sampling units.Spatial location of the sampling units.

Sampling units are Sampling units are grouped into 10 km by 10 grouped into 10 km by 10 km blocks with 100 km blocks with 100 sampling units in each sampling units in each

A systematic sample with A systematic sample with three sampling units in the three sampling units in the same positions within each same positions within each block, is selected.block, is selected.

Aerial photographs are Aerial photographs are used to collect data on used to collect data on land uses within sampling land uses within sampling unitsunits

250000

250000

300000

300000

350000

350000

400000

400000

4100000 4100000

4150000 4150000

20 0 20 Km

The ground dataThe ground data

In order to estimate the statistical model In order to estimate the statistical model parameters, ground data are needed and parameters, ground data are needed and the land use observed in the systematic the land use observed in the systematic sample conducted every year by the sample conducted every year by the Spanish Ministry of Agriculture, Fishing and Spanish Ministry of Agriculture, Fishing and Food will be used as ground data. Food will be used as ground data.

PREDICTOR VARIABLESPREDICTOR VARIABLES

StaticsStaticsAgrometeorological models Agrometeorological models output output Economic variables Economic variables

DynamicsDynamicsLast year land uses Last year land uses

CGMSCGMS Agrometeorological Agrometeorological modelmodel

CGMS was designed to produce CGMS was designed to produce quantitative yield forecasts of the quantitative yield forecasts of the crop yield of the main European crop yield of the main European crops. crops. It will be used here to compute an It will be used here to compute an index of crop suitability in each index of crop suitability in each 10 10 km by 10 km blockkm by 10 km block..

The CGMS output dataThe CGMS output data

Some of the model output are:Some of the model output are: The weight biomass generated by the The weight biomass generated by the

crop and the weight dry matter in storage crop and the weight dry matter in storage organs (potential and water limited) organs (potential and water limited)

The total water consumption and The total water consumption and requirement. requirement.

This data can be computed for areas as small This data can be computed for areas as small as a plot.as a plot.

Economic variablesEconomic variables

European Union direct aid per hectare, as European Union direct aid per hectare, as defined in the Common Agricultural Policy.defined in the Common Agricultural Policy.

THE SCALE PROBLEMTHE SCALE PROBLEM

The scale The scale problem arises problem arises because biophysical because biophysical (Land uses and CGMS output) and economic (Land uses and CGMS output) and economic variables are observed at different spatial scales. variables are observed at different spatial scales.

The advances in the techniques of spatial data The advances in the techniques of spatial data collection (collection (satellite images), the advances in satellite images), the advances in geographical information systems (GIS) that allow geographical information systems (GIS) that allow us to put together data from different sources, and us to put together data from different sources, and the use of internet as a data distribution channel, the use of internet as a data distribution channel, makes the scale problem and tmakes the scale problem and the overall problem he overall problem of analysing data collected using different spatial of analysing data collected using different spatial scales a problem common to many sciences.scales a problem common to many sciences.

Modelling the scale problemModelling the scale problem Empirical spatiotemporal Empirical spatiotemporal

semivariograms.semivariograms. In building this model it is In building this model it is

necessary to create meaningful necessary to create meaningful observational units and to observational units and to transform all the data to the transform all the data to the same spatial supportsame spatial support

This is the “change of support This is the “change of support problem” which has two main problem” which has two main effects: “overdispersion” and effects: “overdispersion” and “spatial autocorrelation” “spatial autocorrelation”

The spatiotemporal variogram The spatiotemporal variogram allows us to take account of allows us to take account of these two problems and is used these two problems and is used in order to specify the working in order to specify the working correlation matrix . correlation matrix .

SUNFLOWER

SUGAR BEET

SOFT WHEAT

OTHER

Time (year)

Time (year)

Time (year)

Time (year)

Distance (m)

Distance (m)

Distance (m)

Distance (m)

THE MODELTHE MODEL

The working model is The working model is

where is a row vector of explanatory where is a row vector of explanatory variables of known values, is a column vector of variables of known values, is a column vector of unknown parameters, is the vector of land unknown parameters, is the vector of land uses in last year, is a column vector of unknown uses in last year, is a column vector of unknown parameters and is the correlation matrix parameters and is the correlation matrix defined by the spatiotemporal variogram.defined by the spatiotemporal variogram.

log( )i i i ik kkk s t k s t s t s t k

A A x A Z A

2

1 2 1 2

ˆ ; ; 1,2, , ; 1,2, ,

( ) ( ) ( )

i ik s tk i s

ke ek k

V Var Z s R i n t T

R

ik s tx A

k

ik s tZ A

k

( )kR

EstimationEstimationParameters are estimated by solving the following Parameters are estimated by solving the following system by iteratively reweighted least squaressystem by iteratively reweighted least squares

Where:Where: T TX W X X WY

1TW D V D kV diag V

k

D diag 1Y D Z

1 2

T

k KZ Z Z Z Z

1 2k s k s k stk sTkZ Z Z Z Z

1 2 i N

T

stk k s t k s t k s t k s tZ Z A Z A Z A Z A

The fitted modelThe fitted model

Table 1. Performance of the regression estimators.

Coefficient Standard errors Estimate Bias (%)

Variable True Monte Carlo

Estimate

Bias (%) Monte Carlo

Taking into account

spatiotemporal correlation

Ignoring spatiotemporal correlation

Intercept 9.1001 8.659229 4.844685 0.440988 -45.46569 -92.76641 SF_CGMS 0.00001 -1.4E-05 -42.5478 3.69E-06 -11.43039 -43.86269 SF_AID 0.0054 0.005249 2.80384 0.000363 -4.415354 -48.51866 SW_CGMS -0.0001 -7.8E-05 21.62265 3.4E-05 3.22893 -7.741224 SW_AID 0.0125 0.007995 36.04109 0.005054 3.6277 -11.07378 SB_CGMS 0.0007 0.000713 -1.79788 0.000131 -15.63028 -62.14043 SF_1_SF -0.0002 -0.00014 31.14396 6.39E-05 -45.43592 -73.62034 SF_1_SW -0.0002 -0.00023 -15.2744 3.41E-05 16.8306 18.1274 SF_1_SB -0.0005 -0.00043 14.48989 8.26E-05 -37.67078 -69.19964 SF_1_OT -0.0003 -0.00025 15.08629 4.62E-05 -45.12375 -86.46224 SW_1_SF -0.0004 -0.0002 51.0962 0.000111 3.56241 8.21527 SW_1_SW -0.0003 -0.0005 -65.8324 0.000102 17.3498 20.0379 SW_1_SB -0.0004 -0.00025 37.44093 0.000168 -4.497496 -14.71085 SW_1_OT -0.0007 -0.00059 15.98533 0.000121 -29.30296 -70.27814 SB_1_SF -0.0004 -0.00032 19.4779 8.99E-05 -25.00327 -59.71163 SB_1_SW -0.0003 -0.00043 -43.0977 0.000137 27.395 40.0811 SB__1_SB 0.0001 0.000162 -61.9125 4.83E-05 -26.52534 -60.92722 SB_1_OT -0.0005 -0.00048 3.905174 6.07E-05 15.8015 -78.27985

THE PREDICTORTHE PREDICTOR

Based on the model a land use estimator is defined, which Based on the model a land use estimator is defined, which makes optimal use of the available data, according to statistical makes optimal use of the available data, according to statistical criteria.criteria.

The predictor is The predictor is

where,where,

with with

If beta, and V are known, then the predictor is unbiased and If beta, and V are known, then the predictor is unbiased and its error is minimum.its error is minimum.

0 0 0 0 0 0

1ˆ ˆ ( ˆ )s t

T

s t s tZ A A C V Z

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 2 0 0 0 0

0 0 0 0 0 0

1 2

,1 ,2 , ,

, , , , ,

1 2 1 2, 0 0, ( , , ; )

i N

i i

T

s t s t s t s t k s t K

T

s t k s t k s t k s t k t s t k T

T

s t k t s t k s t s t k s t s t k s t s t k s t

ks t k s t k s t k s t s t k i

C C C C C

C C C C C

C C C C C

C Cov Z A Z A dist s s t t

is tk

0 0 0 0

, 0;s t k s t kCov C C k k

SMALL AREA ESTIMATIONSMALL AREA ESTIMATIONThere is a growing demand for There is a growing demand for reliable estimates over small areas reliable estimates over small areas (counties). (counties). Due to the small sample size in small Due to the small sample size in small areas, the design-based approach areas, the design-based approach does not provide sufficiently precise does not provide sufficiently precise estimates for most uses.estimates for most uses. The proposed model- based The proposed model- based approach provides estimations approach provides estimations (predictions) of land uses in areas as (predictions) of land uses in areas as small as 10Km by 10 Km. small as 10Km by 10 Km.

PredictionsPredictions

Mapping predictions of crop areas of the main crops within Mapping predictions of crop areas of the main crops within 10Km by 10Km blocks in a Spanish zone.10Km by 10Km blocks in a Spanish zone.

WITHOUT DIRECT AIDWITH DIRECT AID

SOFT

W

HEA

TSU

NFL

OW

ER

< 540540 - 585585 - 620620 - 665985 - 15551555 - 18551855 - 21652165 - 2805

Area (ha)

Area (ha)

100 - 20020 - 100

200 - 325325 - 540

< 1010 - 1515 - 20

PREDICTOR PERFORMANCEPREDICTOR PERFORMANCE

Table 2. Predictor performace

Standard error bias (%) Quantiles Predictor Bias (%) Taking into

account spatiotemporal

correlation

Ignoring spatiotemporal

correlation

Coefficient of Variation (%)

1 25%Q -5.06 -24.87 -47.34 4.01

50%Median -1.49 -14.92 -33.79 10.51

3 75%Q 1.95 -4.67 -23.66 16.13