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Crop yield estimation explainer

Here, we explain and illustrate the ideas behind our crop yield estimation system. This work builds on core support fromÌý,Ìý, theÌý, and is directly funded by theÌý, throughÌýÌý²¹²Ô»åÌý.

The work arises from a collaboration betweenÌý×î×¼µÄÁùºÏ²ÊÂÛ̳/,Ìý,Ìý,Ìý,Ìý,Ìý.

Some of the team, on fieldwork.

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Earth Observation data

We have designed the monitoring system to be robust to sampling opportunities. This means that it can make use of any satellite data at suitable wavelengths and spatial resolutions. This includes optical data from the USÌýÌýmissions and data from the ChineseÌýÌýsatellites, but the backbone is provided by data from the operationalÌýÌýÌýsatellites. These are part of the EU-fundedÌýÌýprogramme, and use multiple satellites to provide global observations at better than the weekly frequency at a spatial resolution of 10+ m. Such optical data (i.e. from around 400-2500 nm wavelength) are ideal for agricultural monitoring over much of the world, including both large farms and smallholders.

Radiative transfer models

Optical sensors on these satellites do not directly measure information that tells us about crop state. Instead, they measure sunlight, reflected from the Earth's surface and transmitted through the atmosphere. Except when clouds 'get in the way'Ìýwhen they measure the cloud scattering, rather than that of the land surface.

To monitor the land surface, we must clear imagery of artefacts such as clouds, cloud shadows, dead pixels etc., and then try to estimate the land surface reflectance from our measurements of 'top of atmosphere' radiance. We then want to make sure that we are looking at the image pixels we are interested in (crop pixels, in this case).

We next wish to interpret the land surface reflectance in terms of the biophysical (structural and biochemical) properties that control crop reflectance. These can be broadly characterised as theÌýamount of vegetationÌý(given as theÌý), theÌýleaf propertiesÌý(typicallyÌý, dry matter and water content) and theÌýsoil properties.

To deal with atmospheric effects and interpret the surface reflectance, we can use specialisedÌýradiative transfer modelsÌýthat tell us how varying the properties leads to variation in spectral reflectance. That is tricky enough, but harder still in many ways, is 'inverting' such a model, to give the mapping from spectral reflectance to e.g. vegetation properties. In recent years, fast approaches to provide estimates of this have been developed usingÌýmachine learning.

The animation below illustrates the results of such inference over an agricultural field in the UK.

• The top panel shows LAI over the (winter wheat) growing season. The red dots show LAI estimates for dates when Sentinel-2 satellite observations are available. The red bar provides an indication of uncertainty. 'NN' here means Ìý(Artificial) '', a machine learning approach used to estimate LAI (and other properties) from spectral reflectance.
• The second panel shows the spectral reflectance 'measured' by the sentinel-2ÌýMSIÌýinstrument as blue squares, over the range 400-1000 nm. The red dotted line is for a form of quality test on the radiative transfer inference: it shows the spectral reflectance modelled by the radiative transfer model (Ìýhere). A strong mismatch means the inference may be less reliable.
• The lower panel shows images over the field. From left to right, these show: LAI; Chlorophyll concentration; brown pigment concentration (related to senescence), and a 'true colour' (RGB) image of the area. Each pixel represents 10 m in this mapping.

Microwave data

Optical data sources such as those above allow estimates of crop biophysical state to be inferred from the spectral reflectance as we have seen. But,Ìýa lot of the timeÌýclouds get in the way of seeing the land surface from space, so we also make use of observations from the microwave region, here,ÌýÌýdata. TheÌýÌýsends down a radar pulse, and measures how much radiation is scattered back to the sensor. Special processing synthesises a long antenna, allowing for high resolution observations to be made. The backscatter data are sensitive to vegetation amount, moisture, and soil properties, but not (most) cloud. A backscatter ration from two polarisations is found to provide quite a stable signal for tracking vegetation amount. So, even though the data are noisier and of lower information content than optical data, they fulfil the vital role of observing the surface in the presence of cloud.

The figure below shows observations over an agricultural site with a maize crop in central Ghana.

• The upper panel shows LAI inferred from Sentinel-2 optical data. The red bar provides an indication of uncertainty. 'NN' here means Ìý(Artificial) '', a machine learning approach used to estimate LAI (and other properties) from spectral reflectance.
• The central panel shows the measured spectral reflectance over the range 400-2500 nm for Sentinel-2 observations. Note the complete lack of observations in July-September due to high cloud cover.
• The lower panel shows the more regular and reliable microwave polarisation ratio from Sentinel-1. Even though these data have less information than the Sentinel-2 data, they allow us to track the crop biomass over the whole season, at high temporal frequency.

Crop models

Mechanistic models of crop development such asÌýÌýallow us to link relatively simple parameterisations to crop growth, phenology and yield, driven by weather data.

If we had a well-calibrated model and weather data, expressing the conditions local to a particular part of a particular field, we might expect the model to perform well, and allow for good tracking of crop status and any stresses, and good predictions of crop yield. Model calibration however requires quite a large set of agronomic data, so these models are only ever calibrated in a broad sense, for a particular crop with a particular set of practices.

A regionally-calibrated agronomic model with somewhat localised weather data is of great use in management and planning for farmers, regional and national authorities, as well as insurers etc. But it doesn't directly relate to what is happening in a particular area of a particular field. Even though they will be tied to the weather in the year simulated and so show the right broad seasonal effects, differentÌýlocalÌýconditions could give rise to a range of different scenarios of LAI development. This is illustrated in the figure below, which shows an ensemble of plausible LAI trajectories, each of which corresponds to a slightly different set of model parameters and/or weather conditions thatÌýare likelyÌýrepresentative of those found on the ground.

Most often in the past, crop model calibration has been used to produce aÌýsetÌýof model parameters, i.e. the parameters that 'best' represent the range of agronomy data used in the calibration (typically with variations over space and time). That concept of calibration tends to ignore the fact that, taking into account the uncertainties in the data and model, we should more properly represent the calibration result by a set of statistical distributions of model parameters: some representation of their probability distribution functions (PDFs). We can provide better calibrations of the crop models then, by taking into account uncertainty. This gives us the ability to estimate output uncertainty.

The figure below shows a PDF of the yield for winter wheat in Hengshui, in the North China Plain. Note that the distribution is quite wide, meaning that quite a range of different yields might arise in this area. We are still able to quantify the 'most likely' from the peak of the PDF, but it doesn't tell us about any particular field.

Data Assimilation

We can provide some improvement on using regional models, with associated calibrated PDFs, by usingÌý, and we have learned how to useÌýÌýtechniques to combine model and observational information. But the agricultural landscape in many countries varies at a higher resolution than this, so complicated 'scaling effects' must be taken into account in trying to use e.g. 1 km observations over fields that are smaller than this. The advantage of the coarse resolution data has been that it is high temporal frequency, typically giving observations every day or so.

We have used this combination of data and models to improve regional yield estimates in China by providing information through the Government CHARMS system. In addition, when we have only a partial set of observations and some predictions of the likely weather, we can make predictions of crop yield whilst the crop is still in the ground. As time advances and we get more information, we can refine and improve these predictions. We have also provided this sort of information for regional government in China. An example is given below.

Thanks toÌý, we now have satellite observations at the right spatial and temporal frequency for agricultural monitoring.

The figure below illustrates how the regionally-calibrated crop models, with somewhat coarse resolution weather dataÌýprovide a set of probable crop states (LAI in this case). The satellite data then provide spatially-localised 'measurements' of the actual crop state (LAI here), The combination of the data and model information then refines the model calibration and gives spatially localised estimates of yield, and a probability distribution function - PDF expressing the uncertainty of the yield estimate. The data model 'merging' is down usingÌý.

The figure below shows the impact of the data assimilation on the crop yield PDF. Here we have moved the mean and shrunk the uncertainty.

Results

The use of the system inÌýforecastingÌýis shown below. The lector's panel shows plausible LAI trajectories over time. The red dots illustrate Sentinel-2 LAI estimates (with uncertainty bar). The right panel shows the PDF of the yield. Early in the season, the yield could take on a wide range of states. As we get more observations, the ensemble of possible states shrinks, and the uncertainty in yield prediction also shrinks. This would be further improved if observed weather were used to replace expected weather. Around a month before harvest, the yield estimate is quite stable, but even before then, we are limiting the range of expected yield considerably.

There are various outputs of the system, but the one of most general interest to users is a spatial map of yield (at 10m or so spatial resolution).

We can visualise this at a range of spatial scales to show the level of detail obtained. The images below show the estimated yield (kg/ha) of winter wheat in 2017 over Hengshui in the North China Plain. We can visualise the data at different spatial resolutions. At the broad scale, we see a North-West to South-East gradient in crop productivity. This is driven by weather and soil. This regional information is needed mainly for reporting and planning.

As we zoom in, we can now see the full resolution of the Sentinel data coming into play. We can see individual fields: some performing better than others due to very local conditions and farmer decisions on variety, fertiliser inputs, irrigation etc. We can also see within-field variations from these data, showing areas of higher- or lower productivity. This is the sort of detailed information needed for local management and insurance.

We have developed a capability to produce similar data in almost real-time using our models on theÌý.

a. National Scale

b. County Scale

c. Farm Scale

Because we are using data assimilation, we can also estimate the uncertainty associated with our predictions.

The figures below show the mean predicted yield for Hengshui 2017Ìýand the (per pixel) uncertainty in yield. The uncertainty here is given as the standard error, a measure of the width of the PDF.

Mean yield over Hengshui (kg/ha)

Std yield over Hengshui (kg/ha)

It is interesting to see that there are 'stripes' in the uncertainty image. This results from the number of samples of LAI available in different parts of the image, from different satellite orbits. In essence, where there are fewer (or poorer) samples, the uncertainty is higher.

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