1. Introduction

This report provides the background, general methods and results of a project undertaken to investigate the use of remote sensing, agroclimatic and survey data to model reliable crop yield estimates as a preliminary estimate to the November Farm Survey estimates, an occasion of the Crop Reporting Series at Statistics Canada. These estimates are made available before the September Farm Survey estimates are released. The work was completed by the Remote Sensing and Geospatial Analysis Section, Agriculture Division, and by the Business Survey Methods Division at Statistics Canada in collaboration with Agriculture and Agri-Food Canada (AAFC).

2. General methodology for crop yield modelling

A methodology for modelling crop yield was developed and tested on the crops that are typically published at the provincial and national levels by the September Farm Survey, as shown in Table 1. The five provinces listed account for approximately 98% of the agricultural land in Canada, across a diverse range of climate zones and soil types. The crops that account for approximately 85% of the revenue for the 19 crops listed are referred to as the seven major crops.

Table 1. Crops typically published in the results of the September Farm Survey, by province
Table summary
This table displays the results of Table 1. Crops typically published in the results of the September Farm Survey. The information is grouped by Crop type (appearing as row headers), Province (appearing as column headers).

Crop type	Province
	Quebec	Ontario	Manitoba	Saskatchewan	Alberta
7 major crops
Barley	X	X	X	X	X
Canola	X	X	X	X	X
Corn for grain	X	X	X
Durum wheat				X	X
Oats	X	X	X	X	X
Soybeans	X	X	X
Spring wheat	X	X	X	X	X
12 additional crops
Canary seed				X
Chickpeas				X	X
Coloured beans		X	X
Fall rye		X	X	X	X
Field peas			X	X	X
Flaxseed			X	X	X
Lentils				X
Mixed grains	X	X	X	X	X
Mustard seed				X	X
Sunflower seed			X
White beans		X	X
Winter wheat	X	X	X	X	X
Note: Fodder corn is typically published in the September Farm survey. However, it was not modelled due to a lack of July Farm Survey yield estimates.

The goal of the model was to produce a preliminary estimate of the expected harvest yield of the crops in late summer using information from existing data sources.

3. Data sources used in the model

The modelling methodology used three data sources: 1) the coarse resolution satellite data used as part of Statistics Canada's Crop Condition Assessment Program; 2) Statistics Canada's Crop Reporting Series data, and 3) agroclimatic data for the agricultural regions of Canada.

3.1 Normalized Difference Vegetation Index

Since 1987, Statistics Canada has monitored crop conditions across Canada and the northern United States using the Advanced Very High Resolution Radiometer (AVHRR) sensor aboard the National Oceanic and Atmospheric Administration (NOAA) series of satellites. This series of satellites produces a daily image of the entire Earth's surface at a spatial resolution of one kilometre. A spectral vegetation index, the Normalized Difference Vegetation Index (NDVI), was used as a surrogate for photosynthetic potential. NDVI is the normalized ratio of the Near-Infrared (NIR) to Red (R) reflectance (NDVI = (ρNIR − ρR)/(ρNIR + ρR)) and varies from −1 to 1, with values close to one indicating high vegetation content and values close to zero indicating no vegetation over bare ground. Materials such as water which absorb more radiation in the NIR than visible wavelengths, have a negative NDVI.

The NDVI data were processed on a continuous basis throughout the agricultural growing season (April to October) for the entire land mass of Canada. Statistics Canada has a time series of NDVI data from 1987 to present, which includes years of severe drought and record production. The daily NDVI images were processed into seven-day composites as described by Latifovic et al. (2005) and the methodology was further refined by Statistics Canada to minimize or eliminate NDVI errors introduced by the presence of clouds (Bédard 2010).

Cropland NDVI statistics by census agricultural region (CAR) were computed and stored in a relational database for each weekly NDVI composite. Only NDVI picture elements, or pixels, that geographically coincide with an agriculture land cover database produced by AAFC as part of an annual crop inventory were extracted to generate the mean NDVI value for cropland within each of the CARs. The agriculture land cover file and the associated metadata file produced by AAFC were accessible at www.geobase.ca/geobase/en/data/landcover/index.html.

After the mean NDVI values were computed they were imported as one of the input variable databases to the crop models as three-week moving averages from week 18 to 36 (May to August).

3.2 Survey area and yield data

Statistics Canada's Field Crop Reporting Series surveys were another dataset used in the model. These surveys obtain information on grains and other field crops stored on farms (March, July, September and December Farm Surveys), seeded area (March, June, July, September and November Farm Surveys), harvested area, expected yield and production of field crops (July, September and November Farm Surveys). These data provide accurate and timely estimates of seeding intentions, seeded and harvested area, production, yield and farm stocks of the principal field crops in Canada at the provincial level.

The survey produces results only when the crop is relatively abundant. If the crop is abundant in a province, the yields are available at a lower geographic level (usually corresponding to the CARs). If there is a crop but it is not abundant, survey data are available at the province level only. Some crops are absent or largely absent in a province and do not have survey data available.

For abundant crops, CAR level crop yield estimates from the July and November Farm Surveys from 1987 to present were used as input variables for the models while yield estimates from the September Farm Survey and the November Farm Survey were used to verify the accuracy of the yield model results. For less abundant crops, the survey data were compiled at the provincial level.

3.3 Agroclimatic indexes

The climate data collected during the growing season were the third data source used for modelling crop yields. The station-based daily temperature and precipitation data provided by Environment Canada and other partner institutions were used to generate the climate-based predictors (Chipanshi et. al. 2015).

Average values of the indexes at all stations within the cropland extent of a specific CAR were used to represent the mean agroclimate of that CAR. If a CAR lacked input climate data, stations from neighbouring CARs were used.

To form a manageable array of potential crop yield predictors, AAFC aggregated the daily agroclimatic indexes into monthly sums and means for the months of May to August. Their standard deviations (Std) over the month were also calculated and included in the modelling methodology (Newlands et al. 2014; Chipanshi et al. 2015). The Std value shows how the daily index varies over the one-month period. The larger the Std, the higher the variability of the parameter in that month.

4. Modelling survey yields

The model was selected by first reviewing the existing models, then by assessing the models available in SAS. Modelling was done at the smallest geographic level for which historical survey data were available. Only the five main crop-producing provinces (Quebec, Ontario, Manitoba, Saskatchewan and Alberta) were modelled.

4.1 Review of existing models

A model must be created for each CAR (or for each province in the case of less abundant crops). Each region has 28 years of data (1987 to 2014) and 80 explanatory variables. For its preliminary evaluation, Statistics Canada used a stepwise multiple linear regression, and showed that the optimal number of explanatory variables to be selected for modelling was five (Bédard and Reichert 2013).

An approach used by AAFC is based on the Bayesian and non-Bayesian methods at different steps (Chipanshi et al. 2015). The variable selection step uses a non-Bayesian approach by the least-angle robust regression algorithm, while cross-validating and keeping the variables that minimize the median of absolute errors. Yields are then estimated using a Bayesian approach.

The Bayesian approach is used to estimate yields at the beginning of the season, when data for the current year are not all available, which will not be the case at Statistics Canada, where estimates are done near the end of the growing season. As shown in Section 5, the methodology used by Statistics Canada generates results that are similar to the AAFC approach (identified as the least-angle robust model).

4.2 An alternative approach to SAS stepwise modelling

It is important to take outliers into account when selecting the explanatory variables (Khan et al. 2007) and performing estimation, and therefore to use robust modelling methods when possible. The objective was to find a robust alternative for both selecting the variables and estimating the yields. It was found that there was no robust selection procedure in the SAS software used at StatCan. An alternative was to use non-robust algorithms at the selection step and then to estimate the model in a robust way. The LASSO (Least Absolute Shrinkage and Selection Operator) method was selected from the five variable selection algorithms available in SAS. The MM method was chosen from the robust regression methods available in SAS, since it processes outliers at both the model and explanatory variable levels (Copt et al. 2006).

In the rest of the document the method retained by StatCan will be referred to as the LASSO robust model and the method used by StatCan for preliminary evaluations will be referred to as the stepwise non-robust model.

4.3 Aggregating model yield estimates to the provincial and national levels

The yield model estimates are created at the CAR level for the majority of crops. The CAR level estimates are weighted based on seeded area and aggregated to produce a provincial estimate. For certain crops that are less common in a province, the model estimates are only created at the provincial level. A similar weighting approach was used to produce a national estimate from provincial estimates.

4.4 Model evaluation method

The November Farm Survey estimates are considered the most accurate estimate of yield for a given year, due to the fact that the data are collected after the majority of harvesting is completed and the sample size is the largest of all six of the survey occasions. The results of the September Farm Survey can be considered a preliminary estimate of the November results. Therefore, the goal of the modelled yield is not to replicate the results of the September Farm Survey but rather to obtain a sufficiently accurate yield estimate in advance of the November survey results. Unless otherwise indicated, the analysis in the following sections was based on the November yield estimate as the benchmark for comparison.

The relative difference (presented as a percentage) between the yield estimate of a given method (i.e., September Farm Survey or the model) and the November survey yield estimate was the measure of quality. A negative relative difference indicated that the given yield estimate was smaller than the November survey estimate, while a positive relative difference indicated that the given yield estimate was larger than the November survey estimate.

$\mathrm{Relative difference}=100*\frac{\mathrm{Given estimate}-\mathrm{November survey estimate}}{\mathrm{November survey estimate}}$

Many of the summary tables were shown in terms of the absolute relative difference to demonstrate the magnitude of the difference between two estimates and did not take into account the direction of the difference. These absolute relative differences were summarized in terms of the median, 75th percentile, 90th percentile and maximum value calculated over the range of years for which estimates were compared.

5. Results of the model evaluations

Two studies were undertaken to evaluate the quality of the models. The first compared the LASSO robust model with the stepwise non-robust model while the second compared the LASSO robust model approach to the least-angle robust model.

5.1 Comparing results between the LASSO robust model and stepwise non-robust model

The LASSO robust model results were compared with results from the stepwise non-robust model by comparing the relative differences with the November survey yields. Results were generated for the seven major crops from 1987 to 2014 inclusive at the national level.

In general, the LASSO robust model, when compared with the November survey yields, produced results with smaller absolute relative differences than the stepwise non-robust model (Table 2). It was retained for the second study.

Table 2. Median, 75th and 90th percentiles of absolute relative difference of the LASSO robust and the stepwise non-robust models with November survey yields at the national level for 1987 to 2014 for seven major crops
Table summary
This table displays the results of Table 2. Median. The information is grouped by Crop (appearing as row headers), Median, 75 percentile and 90 percentile (appearing as column headers).

Crop	Median		75th percentile		90th percentile
	LASSO robust (%)	Stepwise non-robust (%)	LASSO robust (%)	Stepwise non-robust (%)	LASSO robust (%)	Stepwise non-robust (%)
Barley	3.9	3.3	5.0	6.0	7.7	8.2
Canola	6.4	5.0	10.7	8.0	14.6	15.0
Corn for grain	4.3	6.6	6.2	8.5	8.8	11.6
Durum wheat	3.8	4.9	6.6	8.0	10.3	10.2
Oats	3.8	7.0	5.8	12.5	8.3	18.6
Soybeans	4.3	7.2	10.0	12.4	16.9	19.0
Spring wheat	3.1	4.0	7.0	6.2	9.1	8.8

5.2 Comparing results of the LASSO robust model with the least-angle robust models

For the yield model estimates, the LASSO robust model using SAS was compared with the least-angle robust model using R statistical language software. Statistics Canada, in collaboration with AAFC, determined that the LASSO robust model produced comparable results to those produced by the least-angle robust model. Table 3 indicates that the median absolute differences in yield over 28 years at the national level between the two models were all close to 1% for six of the seven major crops analyzed, and at 2.4% for soybeans.

Table 3. Median absolute difference between yields from the LASSO robust model and the least-angle robust model, national level, for seven major crops
Table summary
This table displays the results of Table 3. Median absolute difference between yields from the LASSO robust model and the least-angle robust model. The information is grouped by Crop (appearing as row headers), Median absolute difference (%) (appearing as column headers).

Crop	Median absolute difference (%)
Barley	0.9
Canola	1.0
Corn for grain	1.4
Durum wheat	1.3
Oats	0.9
Soybeans	2.4
Spring wheat	0.9

Statistics Canada made the decision to adopt the SAS LASSO robust model not only because it produced similar results to the least-angle robust model, but also because SAS is the standard programming tool used at the agency.

6. Comparisons of modelled yields with September survey yield results

The yield estimates produced by the SAS LASSO robust model were compared with the September survey yield in terms of relative differences from the November survey yields. Multiple comparisons were completed to evaluate how the modelled and survey yields performed at national and provincial levels over the long term (1987 to 2014), in a year with normal conditions (2014), and in a year of record production (2013).

6.1 Comparing absolute relative differences with November survey yields at the national level (1987 to 2014)

The series of graphs in Figure 2 show the relative difference of both the September survey estimates and the LASSO robust modelled estimates with the November survey yields, at the national level, for the seven major crops separately from 1987 to 2014.

As can be seen by comparing these seven graphs, there is no consistent pattern when the estimates of the two methods are compared. Neither method is consistently closer to the November survey estimates for any crop. For soybeans and corn for grain, the two methods follow a similar pattern of estimates over the 28 years with regard to how the estimates change from year to year. However, this pattern is not present for the other crops. Additionally, for any given year one method does not consistently perform better for all crops. In general, both methods have comparable relative differences from the November survey estimates. However, the modelled estimates tend to have larger relative differences in cases where an extreme relative difference is observed (e.g., the maximum and minimum relative differences are larger).

One pattern that can be seen is that the September survey results tend to be low when compared with the November survey results (below the x-axis) more often than the model results.

Figure 1. Relative difference from November survey yields at the national level, 1987 to 2014, seven major crops.

Table 4 summarizes the graphical information. At the national level, the median absolute relative differences from the November Farm Survey yields for the seven major crops modelled (barley, canola, corn for grain, durum wheat, oats, soybean, and spring wheat) were very similar to those from the September Farm Survey for the period from 1987 to 2014. In both cases, the median absolute relative difference was 4.1%. The median absolute relative difference results were comparable for some of the 12 additional crops, although larger relative differences were seen for crops that have a limited amount of historical data available. For the 12 additional crops, the overall median absolute relative difference of the modelled estimates (4.4%) was similar to the modelled median of the seven major crops but the overall median absolute relative difference of the September survey for the 12 crops (3.0%) was much lower than its median for the seven major crops.

In general, when larger relative differences were observed, the model's relative differences tended to be larger than those of the September survey. The maximum national absolute relative difference from the November Farm Survey yields for the 19 crops modelled was 39.4%, compared with 31.5% for the September Farm Survey.

Table 4. Median, 75th and 90th percentile and maximum of the absolute relative difference between the September survey yields and the LASSO robust modelled yields and the November survey yields at the national level for 19 crops
Table summary
This table displays the results of Table 4. Median. The information is grouped by  Crop (appearing as row headers), Median, 75th percentile, 90th percentile, Maximum and Years of Nov historical data (appearing as column headers).

Crop	Median		75th percentile		90th percentile		Maximum		Years of November historical data
	LASSO robust (%)	Sept. survey (%)	LASSO robust (%)	Sept. survey (%)	LASSO robust (%)	Sept. survey (%)	LASSO robust (%)	Sept. survey (%)
Barley	3.9	2.4	5.0	3.5	7.7	5.4	17.8	8.4	28
Canola	6.4	5.5	10.7	8.6	14.6	11.5	26.1	17.4	28
Corn for grain	4.3	6.4	6.2	8.4	8.8	10.7	22.6	16.1	28
Durum wheat	3.8	4.7	6.6	6.1	10.3	7.2	15.9	13.0	28
Oats	3.8	3.6	5.8	4.6	8.3	9.1	14.2	14.8	28
Soybeans	4.3	4.3	10.0	6.9	16.9	14.0	39.4	31.5	28
Spring wheat	3.1	4.0	7.0	5.3	9.1	7.3	16.8	12.6	28
Canary seed	7.2	5.6	14.3	13.3	19.2	19.9	20.6	27.6	16
Chickpeas	5.4	8.3	12.9	13.7	22.0	17.3	22.8	23.9	10
Coloured beans	7.9	5.4	11.9	6.8	13.5	11.2	13.9	16.9	7
Fall rye	4.5	2.6	7.6	4.4	10.0	8.3	27.7	10.4	27
Field peas	4.0	2.3	6.1	5.1	11.6	7.2	21.7	19.7	28
Flax	6.0	4.1	10.6	6.8	14.4	9.0	29.6	12.3	28
Lentils	2.8	3.2	6.9	5.0	12.3	6.6	15.4	11.7	22
Mixed grains	2.4	1.7	4.0	2.8	5.9	5.5	11.4	9.7	28
Mustard seed	3.4	4.6	8.8	8.3	13.6	11.4	21.3	13.5	11
Sunflower	15.9	7.7	25.5	16.7	29.9	22.6	35.5	31.1	10
White beans	11.9	5.0	12.9	6.1	15.4	7.3	19.1	8.8	7
Winter wheat	2.2	1.0	4.3	2.1	7.6	3.7	16.1	12.2	28
Overall (7 major crops)	4.1	4.1	6.9	6.4	13.1	10.3	39.4	31.5
Overall (12 additional crops)	4.4	3.0	8.3	6.0	14.2	11.0	35.5	31.1
Overall (all crops)	4.2	3.6	7.6	6.2	13.7	10.5	39.4	31.5

6.2 Comparing absolute relative differences with November survey yields at the provincial level (1987 to 2014)

Similar comparisons were done at the provincial level. For each crop, only provinces that had at least 10% of the national total area for the crop were included in the summary statistics. The median absolute relative difference from the November Farm Survey yields for the seven major crops modelled was 5.1%, compared with 4.4% for the September Farm Survey; the maximum absolute relative differences were 44.5% and 35.5%, respectively (Table 5). For the 12 additional crops the median absolute relative difference at the provincial level for the modelled estimates was 5.6%, compared with 3.7% for the September Farm Survey. Significantly larger overall maximums of 112.2% for the model and 79.3% for the September survey were observed.

Table 5. Median, 75th and 90th percentile and maximum of the absolute relative difference between the September survey yields and the LASSO robust modelled yields and the November survey yields at the provincial level for 19 crops
Table summary
This table displays the results of Table 5. Median. The information is grouped by  Crop (appearing as row headers), Median, 75th percentile, 90th percentile and Maximum (appearing as column headers).

Crop	Median		75th percentile		90th percentile		Maximum
	LASSO robust (%)	Sept. survey (%)	LASSO robust (%)	Sept. survey (%)	LASSO robust (%)	Sept. survey (%)	LASSO robust (%)	Sept. survey (%)
Barley	3.6	3.0	7.5	5.0	10.8	8.0	26.4	12.3
Canola	6.0	6.2	13.4	9.9	18.3	12.6	38.7	21.8
Corn for grain	5.5	5.8	7.7	8.9	9.7	12.5	33.1	26.1
Durum wheat	4.6	4.6	7.6	6.3	10.2	8.2	24.5	14.7
Oats	5.0	3.5	8.4	6.9	13.5	10.4	27.8	22.4
Soybeans	7.1	4.6	10.3	8.9	19.5	14.5	43.1	35.5
Spring wheat	5.0	4.2	8.7	6.5	14.0	9.7	44.5	15.9
Canary seed	7.2	5.6	14.3	13.3	19.2	19.9	20.6	27.6
Chickpeas	5.4	8.3	12.9	13.7	22.0	17.3	22.8	23.9
Coloured beans	8.8	7.3	17.2	13.7	24.0	17.8	112.2	21.1
Fall rye	5.9	4.3	13.2	10.5	21.8	14.5	74.8	79.3
Field peas	5.5	3.6	7.6	7.6	13.6	9.9	34.3	42.3
Flax	7.1	5.2	9.7	8.0	14.3	10.1	40.6	15.4
Lentils	2.8	3.2	6.9	5.0	12.3	6.6	15.4	11.7
Mixed grains	2.9	0.5	5.1	3.5	7.5	6.0	11.2	10.6
Mustard seed	8.1	4.7	14.5	11.4	20.8	17.0	33.8	23.5
Sunflower	15.9	7.7	25.5	16.7	29.9	22.6	35.5	31.1
White beans	12.6	5.9	18.8	8.9	21.0	12.3	31.9	18.6
Winter wheat	4.6	1.8	11.7	5.5	17.7	13.9	43.9	39.9
Overall (7 major crops)	5.1	4.4	8.9	7.4	14.7	11.5	44.5	35.5
Overall (12 additional crops)	5.6	3.7	11.6	8.1	18.5	14.1	112.2	79.3
Overall (All crops)	5.3	4.1	9.8	7.7	16.4	12.4	112.2	79.3

6.3 Comparing relative differences with November survey yields at the national level, 2014

There is nothing unique about the year 2014 in terms of the growing conditions throughout the year or the amount of each crop harvested. It is presented as a "typical" year. In 2014, at the national level, four of the seven major crops modelled and four of the 12 additional crops had smaller relative differences than the September Farm Survey when compared with the November Farm Survey results (Table 6).

Table 6. 2014 national yield estimates for the LASSO robust model and survey (September and November), with relative differences with the November survey estimates for 19 crops
Table summary
This table displays the results of Table 6. 2014 national yield estimates for the LASSO robust model and survey (September and November). The information is grouped by Crop (appearing as row headers), November survey, LASSO robust and September survey (appearing as column headers).

Crop	November survey	LASSO robust		September survey
	YieldTable 6 note 1Table 6 note 2	YieldTable 6 note 1Table 6 note 2	Relative difference (%)	YieldTable 6 note 1Table 6 note 2	Relative difference (%)
Barley	62.4Table 6 note 1	61.8Table 6 note 1	-1.0	62.1Table 6 note 1	-0.5
Canola	34.4Table 6 note 1	34.1Table 6 note 1	-0.9	32.2Table 6 note 1	-6.4
Corn for grain	149.2Table 6 note 1	156.9Table 6 note 1	5.2	147.4Table 6 note 1	-1.2
Durum wheat	41.0Table 6 note 1	42.3Table 6 note 1	3.2	37.9Table 6 note 1	-7.6
Oats	84.1Table 6 note 1	80.9Table 6 note 1	-3.8	80.1Table 6 note 1	-4.8
Soybeans	41.2Table 6 note 1	43.8Table 6 note 1	6.3	41.0Table 6 note 1	-0.5
Spring wheat	45.8Table 6 note 1	44.3Table 6 note 1	-3.1	43.5Table 6 note 1	-5.0
Canary seed	1038.8Table 6 note 2	1034.8Table 6 note 2	-0.4	1074.0Table 6 note 2	3.4
Chickpeas	1770.6Table 6 note 2	1833.1Table 6 note 2	3.5	1780.0Table 6 note 2	0.5
Coloured beans	20.3Table 6 note 1	17.6Table 6 note 1	-13.3	19.3Table 6 note 1	-5.0
Fall rye	38.2Table 6 note 1	38.0Table 6 note 1	-0.5	36.2Table 6 note 1	-5.2
Field peas	34.9Table 6 note 1	36.8Table 6 note 1	5.4	35.0Table 6 note 1	0.4
Flax	22.1Table 6 note 1	24.0Table 6 note 1	8.6	24.1Table 6 note 1	9.0
Lentils	1373.1Table 6 note 2	1421.5Table 6 note 2	3.5	1324.0Table 6 note 2	-3.6
Mixed grains	66.4Table 6 note 1	58.8Table 6 note 1	-11.4	64.8Table 6 note 1	-2.5
Mustard Seed	908.7Table 6 note 2	954.9Table 6 note 2	5.1	883.0Table 6 note 2	-2.8
Sunflower	1775.2Table 6 note 2	1330.0Table 6 note 2	-25.1	1737.0Table 6 note 2	-2.2
White beans	20.4Table 6 note 1	16.5Table 6 note 1	-19.1	19.4Table 6 note 1	-5.0
Winter wheat	64.5Table 6 note 1	67.2Table 6 note 1	4.2	63.1Table 6 note 1	-2.2
Table 6 note 1 Bushels per acre Return to the first table 6 note 1 referrer Table 6 note 2 Pounds per acre Return to the first table 6 note 2 referrer

6.4 Comparing relative differences with November survey yields at the national level, 2013 (a year of record production)

In 2013 —a year of record production for most crops— the model had smaller relative differences than the September Farm Survey compared with the November Farm Survey for two of the seven major crops analyzed and three of the nine additional crops for which comparable 2013 data were available (Table 7).

Table 7. 2013 national yield estimates for the model and survey (September and November), with relative differences with the November survey estimates for 19 crops
Table summary
This table displays the results of Table 7. 2013 national yield estimates for the model and survey (September and November). The information is grouped by Crop (appearing as row headers), November survey, LASSO robust and September survey (appearing as column headers).

Crop	November survey	LASSO robust		September survey
	YieldTable 7 note 1Table 7 note 2	YieldTable 7 note 1Table 7 note 2	Relative difference (%)	YieldTable 7 note 1Table 7 note 2	Relative difference (%)
Barley	72.0Table 7 note 1	64.0Table 7 note 1	-11.0	68.4Table 7 note 1	-5.0
Canola	40.0Table 7 note 1	35.9Table 7 note 1	-10.4	36.9Table 7 note 1	-7.7
Corn for grain	146.9Table 7 note 1	154.9Table 7 note 1	5.5	137.7Table 7 note 1	-6.2
Durum wheat	48.4Table 7 note 1	41.6Table 7 note 1	-14.1	42.1Table 7 note 1	-13.0
Oats	92.8Table 7 note 1	79.6Table 7 note 1	-14.2	82.7Table 7 note 1	-10.8
Soybeans	43.2Table 7 note 1	43.0Table 7 note 1	-0.4	40.7Table 7 note 1	-5.6
Spring wheat	52.9Table 7 note 1	44.0Table 7 note 1	-16.8	47.5Table 7 note 1	-10.3
Canary seed	1395.1Table 7 note 2	1108.3Table 7 note 2	-20.6	1103.0Table 7 note 2	-20.9
Chickpeas	2093.1Table 7 note 2	1616.5Table 7 note 2	-22.8	1799.0Table 7 note 2	-14.1
Coloured beans	--	--	--	--	--
Fall rye	--	--	--	--	--
Field peas	43.7Table 7 note 1	38.3Table 7 note 1	-12.4	43.0Table 7 note 1	-1.6
Flax	27.6Table 7 note 1	23.7Table 7 note 1	-14.1	26.5Table 7 note 1	-3.8
Lentils	1816.4Table 7 note 2	1536.7Table 7 note 2	-15.4	1604.0Table 7 note 2	-11.7
Mixed grains	61.7Table 7 note 1	58.6Table 7 note 1	-5.0	62.2Table 7 note 1	0.8
Mustard seed	950.1Table 7 note 2	934.2Table 7 note 2	-1.7	1013.0Table 7 note 2	6.6
Sunflower	1660.5Table 7 note 2	1368.0Table 7 note 2	-17.6	1619.0Table 7 note 2	-2.5
White beans	--	--	--	--	--
Winter wheat	63.1Table 7 note 1	58.1Table 7 note 1	-7.9	55.4Table 7 note 1	-12.2
Table 7 note 1 Bushels per acre Return to the first table 7 note 1 referrer Table 7 note 2 Pounds per acre Return to the first table 7 note 2 referrer

7. Publishing provincial and national yield estimates

Modelled yield estimates are produced for crops at the provincial and national levels. A set of rules were established to determine which modelled yields are of an acceptable level of quality to publish. These rules are based both on data availability and the coefficient of variation (CV) calculated for each estimate at the provincial level. These rules are applied to each crop.

7.1 Publication rules for modelled yields

A minimum of 12 years of historical survey yield data for both November and July must be available as well as June survey area estimates and July survey yield estimates for the current year. If these conditions are not met, then a modelled yield estimate will not be produced for that region.

A second rule was established: the provincial estimate for a crop will not be published if the total cultivated area from suppressed regions (based on the previous set of conditions) exceeds 10% of the provincial area for the crop. Similarly, if provincial estimates for a crop were not published, the national-level estimate (of the five provinces considered) will not be published if the total cultivated area for the suppressed provinces exceeds 10% of the national area.

In cases where the estimates for certain provinces were suppressed due to quality, but a national level estimate was still produced, only provincial estimates that were of an acceptable level of quality were used.

Finally, if the CV of the provincial or national estimate from the model was greater than 10%, the estimate was not published at that level. Model based CVs are calculated differently than those for survey estimates, and different thresholds are used to determine quality than those used in the Field Crop Reporting Series.

7.2 Publication simulation for 2014

The rules listed in the preceding subsection were applied during a simulation of the production of modelled yields for 2014. Table 8 shows which crops produced publishable results for each province and at the national level, as well as the percentage of the crop area from regions that were suppressed. The results for 2015 and the years to come may be different from this simulation, given that the application of the publication rules will be repeated each year.

Table 8. Crops with publishable yields during the 2014 simulation at the provincial and national levels
Table summary
This table displays the results of Table 8. Crops with publishable yields during the 2014 simulation at the provincial and national levels. The information is grouped by Region Crop (appearing as row headers), Quebec, Ontario, Manitoba, Saskatchewan, Alberta and National (appearing as column headers).

Region Crop	Quebec		Ontario		Manitoba		Saskatchewan		Alberta		National
	Published	Supp. (%)	Published	Supp. (%)	Published	Supp. (%)	Published	Supp. (%)	Published	Supp. (%)	Published	Supp. (%)
Barley	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0
Canola	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0
Canary seed	Absent	N/A	Absent	N/A	Absent	N/A	Yes	0.8	Absent	N/A	Yes	0
Chickpeas	Absent	N/A	Absent	N/A	Absent	N/A	No	100	Absent	N/A	No	100
Dry coloured beans	Absent	N/A	No	100	No	100	Absent	N/A	No	100	No	100
Corn for grain	Yes	0.5	Yes	0	Yes	0	Absent	N/A	No	100	Yes	1.1
Durum wheat	Absent	N/A	Absent	N/A	Absent	N/A	Yes	0	Yes	0.5	Yes	0
Fall rye	Absent	N/A	Yes	0	Yes	6.3	Yes	0	Yes	0	Yes	0
Dry peas	Absent	N/A	Absent	N/A	Yes	0	Yes	0	Yes	0	Yes	0
Flaxseed	Absent	N/A	Absent	N/A	Yes	0	Yes	0	Yes	5	Yes	0
Lentils	Absent	N/A	Absent	N/A	Absent	N/A	Yes	0	Absent	N/A	0	0
Mustard seed	Absent	N/A	Absent	N/A	Absent	N/A	Yes	0	No	100	No	27.1
Mixed grains	Yes	0	Yes	0	Absent	N/A	Absent	N/A	No	100	Yes	8.2
Oats	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0
Soybeans	Yes	1.3	Yes	0	Yes	0	Absent	N/A	Absent	N/A	Yes	0
Spring wheat	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0	Yes	0
Sunflower seeds	Absent	N/A	Absent	N/A	No	100	Absent	N/A	Absent	N/A	No	100
Dry white beans	Absent	N/A	No	100	No	100	Absent	N/A	Absent	N/A	No	100
Winter wheat	Yes	0	Yes	0	Yes	2.9	Yes	0	Yes	0	Yes	0
Number of crops published	8	N/A	9	N/A	10	N/A	12	N/A	9	N/A	13	N/A
Note: Supp (%): Percentage of the area for which modelled yields were suppressed. Absent: indicates that the crop is absent or largely absent in this province. N/A: means Not Applicable.

8. Summary

The estimates produced by the SAS LASSO robust model were comparable to those produced by the September survey in terms of relative difference from the November survey estimates for the seven major crops and many of the 12 additional crops published in September. On rare occasions, both the model and the September survey produced extreme relative differences from the November survey estimates, but not necessarily for the same crops/years. These extreme relative differences tended to be larger for the model than for the September survey.

Larger relative differences were observed in the model estimates for crops that have a limited amount of historical data available. Estimates derived from models that were constructed with only a limited number of data points were at risk of being statistically unreliable. Statistics Canada has established three criteria based on the availability of the input data, as well as quality indicators that must be met to ensure the statistical integrity of the estimates and to determine which of the modelled crop yields were of acceptable quality to be published at provincial and national levels. For each year, the yield model estimates for each crop would be evaluated to determine whether their quality is sufficient for publication.

In 2015, modelled yield estimates for crops deemed to have a sufficient level of quality were published as a preliminary estimate to the September Farm Survey estimates. In the longer term, survey managers must determine what is an acceptable level of risk for the published September estimates, and whether the risk of the larger relative differences produced by the model estimates in extreme cases is worth the benefits of eventually replacing the September survey occasion.

9. References

AAFC (circa 2000). http://www.geobase.ca/geobase/en/data/landcover/index.html

Baier, W., Boisvert, J.B., Dyer, J.A., 2000. The versatile soil moisture budget (VSMB) reference manual [computer software], ECORC contribution no. 1553. In:Agriculture and Agri-Food Canada. Eastern Cereal and Oilseed Research Centre, Ottawa, ON, Canada, pp. A1–D4.

Bédard, F. and Reichert, G., 2013. Integrated Crop Yield and Production Forecasting using Remote Sensing and Agri-Climatic data. Analytical Projects Initiatives final report. Remote Sensing and Geospatial Analysis, Agriculture Division, Statistics Canada

Chipanshi, A., Zhang, Y., Kouadio, L., Newlands, N., Davidson, A., Hill, H., Warren, R., Qian, B., Daneshfar, B., Bedard, F. and Reichert, G., 2015. Evaluation of the Integrated Canadian Crop Yield Forecaster (ICCYF) Model for In-season Prediction of Crop Yield across the Canadian Agricultural Landscape. Agricultural and Forest Meteorology, 206:137-150. DOI: http://dx.doi.org/10.1016/j.agrformet.2015.03.007

Copt, S., and Heritier, S., 2006. Robust MM-Estimation and Inference in Mixed Linear Models.Cahiers du département d'économétrie, Faculté des sciences économiques et sociales, Université de Genève

Khan, J. A., Aelst, S. V., and Zamar, R. H., 2007. Robust Model Selection Based on Least Angle Regression. Journal of the American Statistical Association, Vol. 102, No 480, pp. 1289-1299

Latifovic, R., Trishchenko, A.P., Chen J., Park W.B., Khlopenkov, K.V., Fernandes, R., Pouliot, D., Ungureanu, C., Luo, Y., Wang, S., Davidson, A., Cihlar, J., 2005. Generating historical AVHRR 1 km baseline satellite data records over Canada suitable for climate change studies. Canadian Journal of Remote Sensing, vol. 31, no 5, pp 324-346.

Newlands, N.K., Zamar, D., Kouadio, L., Zhang, Y., Chipanshi, A., Potgieter, A., Toure, S., Hill, H.S.J., 2014. An integrated model for improved seasonal forecasting of agricultural crop yield under environmental uncertainty. Front. Environ. Sci. 2, 17, http://dx.doi.org/10.3389/fenvs.2014.00017.

*Reference documents are available in English only

This bar graph shows Statistics Canada's budgetary authorities and expenditures, in thousands of dollars, as of September 30, 2014 and 2015:

• As at September 30, 2014
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• As at September 30, 2015
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