Patent Publication Number: US-2023140138-A1

Title: Analyzing data influencing crop yield and recommending operational changes

Description:
BACKGROUND 
     Crop yields may be influenced by myriad factors, both naturally-occurring and induced by humans. Naturally-occurring factors include, but are not limited to, climate-related factors such as temperature, precipitation, humidity, as well as other naturally-occurring factors such as disease, animals and insects, soil composition and/or quality, and availability of sunlight, to name a few. Human-induced or “operational” factors are myriad, and include application of pesticides, application of fertilizers, crop rotation, applied irrigation, soil management, crop choice, and disease management, to name a few. 
     One source of operational data is farm machinery, which are becoming increasingly sophisticated. For example, some tractors are configured to automatically log various data pertaining to their operation, such as where they were operated (e.g., using position coordinate data), how frequently they were operated in various areas, the kinds of operations they perform in various areas at various times, and so forth. In some cases, tractor-generated data may be uploaded by one or more tractors (e.g., in real time or during downtime) to a central repository of tractor-generated data. Agricultural personnel such as farmers or entities that analyze crop yields and patterns may utilize this data for various purposes. 
     In addition to factors that influence crop yields, detailed observational data is becoming increasingly available in the agriculture domain. Myriad observational data related to soil quality, aeration, etc., may be gathered from one or more sensors deployed throughout a geographic area such as a field. As another example, digital images captured from high elevations, such as satellite images, images captured by unmanned aerial vehicles, manned aircraft, or images captured by high elevation manned aircraft (e.g., space shuttles), are becoming increasingly important for agricultural applications, such as estimating a current state or health of a field. 
     However, high-elevation digital imagery presents various challenges, such as the fact that 30-60% of such images tend to be covered by clouds, shadows, haze and/or snow. Moreover, the usefulness of these high-elevation digital images is limited by factors such as observation resolutions and/or the frequency at which they are acquired. For example, the moderate resolution imaging spectroradiometer (“MODIS”) satellite deployed by the National Aeronautics and Space Administration (“NASA”) captures high-elevation digital images at a relatively high temporal frequency (e.g., a given geographic area may be captured daily, or multiple times per week), but at relatively low spatial/spectral resolutions. By contrast, the Sentinel-2 satellite deployed by the European Space Agency (“ESA”) captures high-elevation digital images at a relatively low temporal frequency (e.g., a given geographic area may only be captured once every few days or even weeks), but at relatively high spatial/spectral resolutions. 
     SUMMARY 
     The present disclosure is generally, but not exclusively, directed to using artificial intelligence to diagnose one or more conditions that contribute to crop yields, and/or to generate and provide, as output in various forms, recommended operational changes. For example, in various implementations, one or more neural networks, such as a feed forward neural network, a convolutional neural network, a recurrent neural network, a long short-term memory (“LSTM”) neural network, a gated recurrent unit (“GRU”) neural network, etc., may be trained to generate output that is indicative, for instance, of predicted crop yield. Inputs to such a model may include various combinations of the operational and observational data points described previously. In particular, using a combination of operational and observational data collected over a crop cycle (e.g., a crop year) as inputs, a neural network can be trained to predict an estimated or predicted crop yield in a given geographic area at any point during the crop cycle. Techniques are also described herein for determining how much various observational and/or operational factors contributed to these estimated crop yields, and/or for making operational change recommendations based on these contributing factors. 
     As noted previously, high-elevation digital imagery presents various challenges. At least some ground truth high-elevation digital images may be partially or wholly obscured by transient obstructions, such as clouds, snow, etc. Additionally, it is often the case that high-elevation digital images having a spatial resolution sufficient for meaningful observation are acquired of the geographic area at relatively low temporal frequencies (e.g., once every ten days, once a quarter, etc.). Accordingly, in various implementations, digital images from multiple temporal sequences of digital images acquired at disparate resolutions/frequencies may be processed to remove transient obstructions and/or fused using techniques described herein to generate “synthetic” high-elevation digital images of the geographic area that are free of transient obstructions and/or have sufficient spatial resolutions for meaningful observation. These synthetic high-elevation digital images may then be applied as input across the aforementioned neural networks, in conjunction with the plurality of other data points mentioned previously, to facilitate enhanced crop yield prediction, diagnosis, and/or operational change recommendations. 
     In some implementations, neural networks that are trained to generate crop yield predictions may be leveraged to diagnose contributing factors to the predicted crop yields. For example, in some implementations, a temporal sequence of high-elevation digital images capturing a particular geographic area, such as a field used to grow a particular crop, may be obtained. In some instances, the transient-obstruction and/or data fusion techniques described herein may be employed to ensure the temporal sequence of high-elevation digital images has sufficient temporal frequency and/or spatial resolution. This temporal sequence may cease at a particular time interval into a crop cycle of the particular crop. For example, a crop cycle may begin in March and run through September, and the current date may be June 1 st , such that no high-elevation digital images are yet available for the remainder of the crop cycle. 
     In various implementations, ground truth operational and/or observational data may be obtained for the same geographic area. These ground truth data may include operational data such as how much irrigation was applied, what nutrients were applied, how often treatment was applied, etc. These ground truth data may also include observational data (distinct from the high-elevation digital images) such as soil quality measurements, precipitation reports, sunlight/weather reports, and so forth. These ground truth data may be grouped into temporal chunks, each temporal chunk corresponding temporally with a respective high-elevation digital image of the temporal sequence of high-elevation digital images. The temporal sequence of high-elevation digital images and the ground truth data may be applied as input across the aforementioned model(s) to generate a “ground truth-based crop yield prediction” (i.e. predicted based on ground truth data) of the geographic area at the end of the crop cycle. 
     Various techniques may then be applied in order to diagnose which factors had the greatest influence on the ground truth-based crop yield prediction, and/or to make one or more recommended operational changes that are generated with the goal of increasing the crop yield prediction moving forward. For example, in some implementations, a plurality of distinct “hypothetical crop yield predictions” (i.e., generated based at least in part on hypothetical/altered data) may be generated for the first geographic area. Each distinct hypothetical crop yield prediction may be generated by applying the high-elevation digital images of the first temporal sequence and temporal chunks of “hypothetical” operational data (as opposed to ground truth operational data) as input across the machine learning model, e.g., to generate a candidate predicted crop yield. 
     The hypothetical operational data may include one or more altered data points (or “altered versions”) of the ground truth operational data. For example, the amount of irrigation applied may be artificially increased (or decreased), the amount of nitrogen (e.g., fertilizer) applied may be artificially increased (or decreased), and so forth. Based on those hypothetical crop yield predictions that are greater than the ground truth-based crop yield prediction, one or more recommended operational changes may be identified. In particular, operational data point(s) that were altered to generate a given hypothetical crop yield prediction may be used to determine recommended operational change(s). 
     Suppose a ground truth amount of nitrogen was actually applied to a field and ultimately contributed to a ground truth-based crop yield prediction. Now, suppose an artificially increased (or decreased) amount of nitrogen was substituted for the ground truth amount of nitrogen, and yielded a hypothetical crop yield prediction that is greater than the ground truth-based crop yield prediction. A recommended operational change may be to apply more (or less) nitrogen moving forward. 
     In some implementations, the altered data points may be identified from “reference” geographic areas and their associated observational/operational data. For example, one or more reference geographic areas that are comparable to a geographic area under consideration (e.g., similar observational and/or operational data, same crops planted, etc.) may be identified, e.g., using latent space embeddings and/or various clustering techniques. Additionally or alternatively, these reference geographic areas may be selected based on their having more optimistic crop yield predictions than the geographic area under consideration. Additionally or alternatively, these reference geographic areas may be selected based on a high-elevation reference digital image of the reference geographic area depicting “healthier” crops than a temporally-corresponding high-elevation digital image captured of the geographic area under consideration. However the reference geographic areas are selected, in various implementations, operational data points from these reference geographic areas may be used as substitutions for ground truth operational data points associated with the geographic area under consideration. 
     Other techniques may be employed using ground truth and hypothetical data to diagnose crop yields, in addition to or instead of the crop yield model(s) described previously. For example, in some implementations, differences or “deltas” between operational/observational data from a field under consideration and that of a reference field may be determined. These deltas, e.g., in combination with deltas between the predicted crop yields they generated, may be applied as input across one or more machine learning models (e.g., support vector machines, random forests, etc.) that are trained to identify which individual factors contributed the most to the delta in predicted crop yields. 
     Techniques described herein give rise to various technical advantages. For example, recommended operational changes may be used to generate commands that are provided to farm equipment, such as autonomous tractors. The farm equipment may then be operated (or operate autonomously or semi-autonomously) in accordance with the commands to generate greater crop yields. Additionally, and as noted herein, various machine learning models may be trained to generate data indicative of predicted crop yields at a granular level. For example, given a sequence of high-elevation digital images (which may include synthetic high-elevation digital images generated using techniques described herein), crop yield may be predicted on a pixel-by-pixel basis, e.g., where the high-elevation digital images have pixel resolutions of, for instance, a 10 meters by 10 meters geographic unit. With this pixel-level knowledge, it is possible to diagnose which operational and/or observational data points contributed to a given crop yield in individual geographic units. This granular knowledge may be used to generate recommended operational changes on a geographic unit-level basis. Intuitively, individual geographic units of a field may be treated differently based on the recommendations, rather than treating the whole field the same. 
     In some implementations, a computer implemented method may be provided that includes: obtaining a first temporal sequence of high-elevation digital images, wherein the first temporal sequence of high elevation digital images capture a first geographic area under consideration over a given time interval through a crop cycle of a first type of crop growing in the first geographic area; obtaining ground truth operational data generated through the given time interval that influence a final crop yield of the first geographic area after the crop cycle, wherein the ground truth operational data is grouped into temporal chunks, each temporal chunk of the ground truth operational data corresponding temporally with a respective high-elevation digital image of the first temporal sequence of high-elevation digital images; generating a ground truth-based crop yield prediction of the first geographic area at the end of the crop cycle by applying the high-elevation digital images of the first temporal sequence and the temporal chunks of the operational as input across a machine learning model; identifying one or more recommended operational changes, wherein the identifying includes: generating one or more distinct hypothetical crop yield predictions of the first geographic area, wherein each distinct hypothetical crop yield prediction is generated by applying the high-elevation digital images of the first temporal sequence and temporal chunks of hypothetical operational data as input across the machine learning model, wherein the hypothetical operational data includes one or more altered data points of the ground truth operational data, and identifying the one or more recommended operational changes based on one or more of the altered data points that were used to generate one or more of the hypothetical crop yield predictions that are greater than the ground truth-based crop yield prediction; and causing one or more output components of one or more computing devices to audibly or visually convey one or more of the recommended operational changes. 
     This method and other implementations of technology disclosed herein may each optionally include one or more of the following features. 
     In various implementations, the machine learning model may be a recurrent neural network. In various implementations, the recurrent neural network may be a long short-term memory (“LSTM”) or gated recurrent unit (“GRU”) neural network. 
     In various implementations, obtaining the first temporal sequence of high-elevation digital images may include: obtaining a second temporal sequence of high-elevation digital images, wherein the second temporal sequence of high-elevation digital images capture the first geographic area at a first temporal frequency, and wherein each high-elevation digital image of the second temporal sequence is captured at a first spatial resolution; obtaining a third temporal sequence of high-elevation digital images, wherein the third temporal sequence of high-elevation digital images capture the first geographic area at a second temporal frequency that is less than the first temporal frequency, and wherein each high-elevation digital image of the third temporal sequence is captured at a second spatial resolution that is greater than the first spatial resolution; selecting a given high-elevation digital image from the second temporal sequence that is captured during a time interval in which no high-elevation digital images of the third temporal sequence are available; and fusing the given high-elevation digital image of the second temporal sequence with data from one or more high-elevation digital images of the third temporal sequence to generate a synthetic high-elevation digital image of the first geographic area at the second spatial resolution. In various implementations, the synthetic high-elevation digital image of the first geographic area may be included as part of the first temporal sequence of high-elevation digital images. 
     In various implementations, the method may further include: selecting a current high-elevation digital image from the first temporal sequence, wherein the current high-elevation digital image is captured at the given time interval into the crop cycle; determining a current measure of crop health based on the current high-elevation digital image; selecting a reference high-elevation digital image from a second temporal sequence of high-elevation digital images, wherein the second temporal sequence of high elevation digital images capture a reference geographic area over a crop cycle of the first type of crop growing in the reference geographic area, wherein the reference high-elevation digital image is captured at the given time interval into the crop cycle; determining a reference measure of crop health based on the reference high-elevation digital image; and detecting a difference between the current measure of crop health and the reference measure of crop health. In various implementations, the one or more recommended operational changes may be identified in response to the detecting. 
     In various implementations, one or more of the altered data points of the ground truth operational data may be selected based on ground truth operational data generated through the given time interval that influenced a final crop yield of the reference geographic area after the crop cycle. In various implementations, the reference geographic area may be the first geographic area during a previous crop cycle or a different geographic area than the first geographic area. In various implementations, the reference geographic area may be selected by generating a first embedding associated with the first geographic area into latent space, and determining a distance between the first embedding and a second embedding associated with the reference geographic area in latent space. 
     In various implementations, the method may further include: generating a command based on the one or more recommended operational changes; and transmitting the command to an autonomous tractor. In various implementations, the command may cause the autonomous tractor to operate in accordance with the one or more recommended operational changes. 
     Other implementations may include a non-transitory computer readable storage medium storing instructions executable by a processor to perform a method such as one or more of the methods described above. Yet another implementation may include a system including memory and one or more processors operable to execute instructions, stored in the memory, to implement one or more modules or engines that, alone or collectively, perform a method such as one or more of the methods described above. 
     It should be appreciated that all combinations of the foregoing concepts and additional concepts described in greater detail herein are contemplated as being part of the subject matter disclosed herein. For example, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the subject matter disclosed herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    illustrates an example environment in selected aspects of the present disclosure may be implemented, in accordance with various implementations. 
         FIG.  2    depicts an example of how geographic units may be classified into terrain classifications, and how those terrain classifications can be used to generate replacement data for obscured pixels, in accordance with various implementations. 
         FIG.  3    depicts one example of how generative adversarial networks can be used to generate obstruction-free high-elevation digital images. 
         FIG.  4    depicts another example of how generative adversarial networks can be used to generate synthetic transient obstructions, e.g., for purposes of training various machine learning models described herein. 
         FIG.  5    depicts a flow chart illustrating an example method of practicing selected aspects of the present disclosure, in accordance with various implementations. 
         FIG.  6    depicts an example of how techniques described herein may be used to generate a transient-obstruction-free version of a high-elevation digital image that is at least partially obscured by transient obstruction(s). 
         FIG.  7 A ,  FIG.  7 B ,  FIG.  7 C , and  FIG.  7 D  schematically depict another technique for removing transient obstructions from high-elevation digital images, in accordance with various implementations. 
         FIG.  8 A ,  FIG.  8 B ,  FIG.  8 C , and  FIG.  8 D  schematically demonstrate a technique for fusing data from high-elevation digital images at different domain resolutions/frequencies to generate a synthetic high-elevation digital image. 
         FIG.  9    schematically demonstrates an example mapping between high and low spatial resolution images. 
         FIG.  10    depicts a flow chart illustrating an example method of practicing selected aspects of the present disclosure, in accordance with various implementations. 
         FIG.  11    schematically demonstrates one example of how crop yield prediction may be implemented using a temporal sequence of high-elevation digital images. 
         FIG.  12    depicts an example of how a many-to-many machine learning model may be employed to estimate crop yields for individual geographic units, in accordance with various implementations. 
         FIG.  13    depicts a flow chart illustrating an example method of practicing selected aspects of the present disclosure, in accordance with various implementations. 
         FIG.  14    depicts a flow chart illustrating an example method of practicing selected aspects of the present disclosure, in accordance with various implementations. 
         FIG.  15    schematically depicts one example of how various factors contributing to crop yields/predictions may be determined, in accordance with various implementations. 
         FIG.  16 A ,  FIG.  16 B ,  FIG.  16 C , and  FIG.  16 D  depict an example of how factors contributing to crop yield predictions may be identified, in accordance with various implementations. 
         FIG.  17    depicts a flow chart illustrating an example method of practicing selected aspects of the present disclosure, in accordance with various implementations. 
         FIG.  18    schematically depicts an example architecture of a computer system. 
     
    
    
     DETAILED DESCRIPTION 
       FIG.  1    illustrates an environment in which one or more selected aspects of the present disclosure may be implemented, in accordance with various implementations. The example environment includes a plurality of client devices  106   1-N , a high elevation digital image processing system  102 , a crop yield and diagnosis system  144  (which may alternatively be referred to as a “crop yield modeling and diagnosis system”), an operational data clearing house  146 , and one or more data sources  148 . Each of components  106   1-N ,  102 ,  144 , and  146  may be implemented in one or more computers that communicate, for example, through a network. High elevation digital image processing system  102  and crop yield and diagnosis system  144  are examples of information retrieval systems in which the systems, components, and techniques described herein may be implemented and/or with which systems, components, and techniques described herein may interface. 
     An individual (which in the current context may also be referred to as a “user”) may operate a client device  106  to interact with other components depicted in  FIG.  1   . Each component depicted in  FIG.  1    may be coupled with other components through one or more networks  110 , such as a local area network (LAN) or wide area network (WAN) such as the Internet. Each client device  106  may be, for example, a desktop computing device, a laptop computing device, a tablet computing device, a mobile phone computing device, a computing device of a vehicle of the participant (e.g., an in-vehicle communications system, an in-vehicle entertainment system, an in-vehicle navigation system), a standalone interactive speaker (with or without a display), or a wearable apparatus of the participant that includes a computing device (e.g., a watch of the participant having a computing device, glasses of the participant having a computing device). Additional and/or alternative client devices may be provided. 
     Each of client device  106 , high elevation digital image processing system  102 , crop yield and diagnosis system  144 , and operational data clearing house  146  may include one or more memories for storage of data and software applications, one or more processors for accessing data and executing applications, and other components that facilitate communication over a network. The operations performed by client device  106 , high elevation digital image processing system  102 , crop yield and diagnosis system  144 , and/or operational data clearing house  146  may be distributed across multiple computer systems. Each of high elevation digital image processing system  102 , crop yield and diagnosis system  144 , and operational data clearing house  146  may be implemented as, for example, computer programs running on one or more computers in one or more locations that are coupled to each other through a network. 
     Each client device  106  may operate a variety of different applications that may be used, for instance, to view high-elevation digital images that are processed using techniques described herein to remove transient obstructions such as clouds, shadows (e.g., cast by clouds), snow, manmade items (e.g., tarps draped over crops), etc. For example, a first client device  106   1  operates an image viewing client  107  (e.g., which may be standalone or part of another application, such as part of a web browser). Another client device  106   N  may operate a crop prediction application  109  that allows a user to initiate and/or study agricultural predictions and/or recommendations provided by, for example, crop yield and diagnosis system  144 . 
     In various implementations, high elevation digital image processing system  102  may include a transient obstruction detection engine  124 , a terrain classification engine  128 , an obstruction replacement engine  132 , a transient obstruction generation engine  138 , and/or a data fusion engine  142 . In some implementations one or more of engines  124 ,  128 ,  132 ,  138 , and/or  142  may be omitted. In some implementations all or aspects of one or more of engines  124 ,  128 ,  132 ,  138 , and/or  142  may be combined. In some implementations, one or more of engines  124 ,  128 ,  132 ,  138 , and/or  142  may be implemented in a component that is separate from high elevation digital image processing system  102 . In some implementations, one or more of engines  124 ,  128 ,  132 ,  138 , and/or  142 , or any operative portion thereof, may be implemented in a component that is executed by client device  106 . 
     Transient obstruction detection engine  124  may be configured to detect, in high-elevation digital images, transient obstructions such as clouds, shadows cast by clouds, rain, haze, snow, flooding, and/or manmade obstructions such as tarps, etc. Transient obstruction detection engine  124  may employ a variety of different techniques to detect transient obstructions. For example, to detect clouds (e.g., create a cloud mask), transient obstruction detection engine  124  may use spectral and/or spatial techniques. In some implementations, one or more machine learning models may be trained and stored, e.g., in index  126 , and used to identify transient obstructions. For example, in some implementations, one or more deep convolutional neural networks known as “U-nets” may be employed. U-nets are trained to segment images in various ways, and in the context of the present disclosure may be used to segment high elevation digital images into segments that include transient obstructions such as clouds. Additionally or alternatively, in various implementations, other known spectral and/or spatial cloud detection techniques may be employed, including techniques that either use, or don&#39;t use, thermal infrared spectral bands. 
     In some implementations, terrain classification engine  128  may be configured to classify individual pixels, or individual geographic units that correspond spatially with the individual pixels, into one or more “terrain classifications.” Terrain classifications may be used to label pixels by what they depict. Non-limiting examples of terrain classifications include but are not limited to “buildings,” “roads,” “water,” “forest,” “crops,” “vegetation,” “sand,” “ice,” “mountain,” “tilled soil,” and so forth. Terrain classifications may be as coarse or granular as desired for a particular application. For example, for agricultural monitoring it may be desirable to have numerous different terrain classifications for different types of crops. For city planning it may be desirable to have numerous different terrain classifications for different types of buildings, roofs, streets, parking lots, parks, etc. 
     Terrain classification engine  128  may employ a variety of different known techniques to classify individual geographic units into various terrain classifications. Some techniques may utilize supervised or unsupervised machine learning that includes trained machine learning models stored, for instance, in index  130 . These techniques may include but are not limited to application of multivariate statistics to local relief gradients, fuzzy k-means, morphometric parameterization and artificial neural networks, and so forth. Other techniques may not utilize machine learning. 
     In some implementations, terrain classification engine  128  may classify individual geographic units with terrain classifications based on traces or fingerprints of various domain values over time. For example, in some implementations, terrain classification engine  128  may determine, across pixels of a corpus of digital images captured over time, spectral-temporal data fingerprints or traces of the individual geographic units corresponding to each individual pixel. Each fingerprint may include, for instance, a sequence of values within a particular spectral domain across a temporal sequence of digital images (e.g., a feature vector of spectral values). 
     As an example, suppose a particular geographic unit includes at least a portion of a deciduous tree. In a temporal sequence of satellite images of the geographic area that depict this tree, the pixel(s) associated with the particular geographic unit in the visible spectrum (e.g., RGB) will sequentially have different values as time progresses, with spring and summertime values being more green, autumn values possibly being orange or yellow, and winter values being gray, brown, etc. Other geographic units that also include similar deciduous trees may also exhibit similar domain traces or fingerprints. Accordingly, in various implementations, the particular geographic unit and/or other similar geographic units may be classified, e.g., by terrain classification engine  128 , as having a terrain classification such as “deciduous,” “vegetation,” etc., based on their matching spectral-temporal data fingerprints. 
     Obstruction replacement engine  132  may be configured to generate obstruction-free versions of digital images in which those pixels that depict clouds, snow, or other transient obstructions are replaced with replacement data that estimates/predicts the actual terrain that underlies these pixels. Obstruction replacement engine  132  may use a variety of different techniques to generate transient-obstruction-free versions of digital images. 
     For example, in some implementations, obstruction replacement engine  132  may be configured to determine, e.g., based on output provided by transient obstruction detection engine  124 , one or more obscured pixels of a high-elevation digital image that align spatially with one or more obscured geographic units of the geographic area that are obscured in the digital image by one or more transient obstructions. Obstruction replacement engine  132  may then determine, e.g., across pixels of a corpus of digital images that align spatially with the one or more obscured geographic units, one or more spectral-temporal data fingerprints of the one or more obscured geographic units. For example, in some implementations, terrain classification engine  128  may classify two or more geographic units having matching spectral-temporal fingerprints into the same terrain classification. 
     Obstruction replacement engine  132  may then identify one or more unobscured pixels of the same high-elevation digital image, or of a different high elevation digital image that align spatially with one or more unobscured geographic units that are unobscured by transient obstructions. In various implementations, the unobscured geographic units may be identified because they have spectral-temporal data fingerprints that match the one or more spectral-temporal data fingerprints of the one or more obscured geographic units. For example, obstruction replacement engine  132  may seek out other pixels of the same digital image or another digital image that correspond to geographic units having the same (or sufficiently similar) terrain classifications. 
     In various implementations, obstruction replacement engine  132  may calculate or “harvest” replacement pixel data based on the one or more unobscured pixels. For example, obstruction replacement engine may take an average of all values of the one or more unobscured pixels in a particular spectrum and use that value in the obscured pixel. By performing similar operations on each obscured pixel in the high-elevation digital, obstruction replacement engine  132  may be able to generate a transient-obstruction-free version of the digital image in which data associated with obscured pixels is replaced with replacement pixel data calculated based on other, unobscured pixels that depict similar terrain (e.g., same terrain classification, matching spectral-temporal fingerprints, etc.). 
     In some implementations, obstruction replacement engine  132  may employ one or more trained machine learning models that are stored in one or more indexes  134  to generate obstruction-free versions of digital images. A variety of different types of machine learning models may be employed. For example, in some implementations, collaborative filtering and/or matrix factorization may be employed, e.g., to replace pixels depicting transient obstructions with pixel data generated from other similar-yet-unobscured pixels, similar to what was described previously. In some implementations, matrix factorization techniques such as the following equation may be employed: 
     
       
      
       {circumflex over (r)} 
       ui 
       =μ+b 
       i 
       +b 
       u 
       +q 
       i 
       T 
       p 
       u  
      
     
     wherein r represents the value of a pixel in a particular band if it were not covered by clouds, μ represents global average value in the same band, b represents the systematic bias, i and u represent the pixel&#39;s id and timestamp, T represents matrix transpose, and q and p represent the low-dimension semantic vectors (or sometimes called “embeddings”). In some implementations, temporal dynamics may be employed, e.g., using an equation such as the following: 
         {circumflex over (r)}   ui ( t )=μ+ b   i ( t )+ b   u ( t )+ q   i   T   p   u ( t )
 
     wherein t represents a non-zero integer corresponding to a unit of time. Additionally or alternatively, in some implementations, generative adversarial networks, or “GANs,” may be employed, e.g., by obstruction replacement engine  132 , in order to train one or more models stored in index  134 . A more detailed description of how GANs may be used in this manner is provided with regard to  FIG.  3   . 
     In some implementations, a transient obstruction generation engine  138  may be provided that is configured to generate synthetic obstructions such as clouds, snow, etc. that may be incorporated into digital images (e.g., used to augment, alter, and/or replace pixel values in one or more spectrums) for a variety of different purposes. In some implementations, digital images with baked-in synthetic transient obstructions may be used as training data to train one or more machine learning models used by other components of high elevation digital image processing system  102 . 
     For example, in some implementations, a machine learning model employed by obstruction replacement engine  132  and stored in index  134  may be trained as follows. An obstruction-free (e.g., cloudless) high-elevation digital image of a geographic area may be retrieved. Based on the obstruction-free digital image, transient obstruction generation engine  138  may generate, e.g., using one or trained more machine learning models described below, a training example that includes the obstruction-free image with baked in synthetic transient obstructions such as clouds. This training example may be applied, e.g., by obstruction replacement engine  132 , as input across one or more machine learning models stored in index  134  to generate output. The output may be compared to the original obstruction-free digital image to determine a difference or error. This error may be used to perform operations such as back propagation and/or gradient descent to train the machine learning model to remove transient obstructions such as clouds and replace them with predicted terrain data. 
     As another example, in some implementations, a machine learning model employed by transient obstruction detection engine  124  and stored in index  126  may be trained as follows. An obstruction-free (e.g., cloudless) high-elevation digital image of a geographic area may be retrieved. Based on the obstruction-free digital image, transient obstruction generation engine  138  may generate, e.g., using one or trained more machine learning models described below, a training example that includes the obstruction-free image with baked-in synthetic transient obstructions such as clouds. The location of the synthetic transient obstruction will be known because it is synthetic, and thus is available, e.g., from transient obstruction generation engine  138 . Accordingly, in various implementations, the training example may be labeled with the known location(s) (e.g., pixels) of the synthetic transient obstruction. The training example may then be applied, e.g., by transient obstruction detection engine  124 , as input across one or more machine learning models stored in index  134  to generate output indicative of, for instance, a cloud mask. The output may be compared to the known synthetic transient obstruction location(s) to determine a difference or error. This error may be used to perform operations such as back propagation and/or gradient descent to train the machine learning model to generate more accurate cloud masks. 
     Transient obstruction generation engine  138  may use a variety of different techniques to generate synthetic transient obstructions such as clouds. For example, in various implementations, transient obstruction generation engine  138  may use particle systems, voxel models, procedural solid noise techniques, frequency models (e.g., low albedo, single scattering approximation for illumination in a uniform medium), ray trace volume data, textured ellipsoids, isotropic single scattering approximation, Perlin noise with alpha blending, and so forth. In some implementations, transient obstruction generation engine  138  may use GANs to generate synthetic clouds, or at least to improve generation of synthetic clouds. More details about such an implementation are provided with regard to  FIG.  4   . Transient obstruction generation engine  138  may be configured to add synthetic transient obstructions to one or more multiple different spectral bands of a high-elevation digital image. For example, in some implementations transient obstruction generation engine  138  may add clouds not only to RGB spectral band(s), but also to NIR spectral band(s). 
     Data fusion engine  142  may be configured to generate synthetic high-elevation digital images by fusing data from high-elevation digital images of disparate spatial, temporal, and/or spectral frequencies. For example, in some implementations, data fusion engine  142  may be configured to analyze MODIS and Sentinel-2 data to generate synthetic high-elevation digital images that have spatial and/or spectral resolutions approaching or matching those of images natively generated by Sentinel-2 based at least in part on data from images natively generated by MODIS.  FIGS.  7 A-D ,  8 A-D,  9 , and  10 , as well as the accompanying disclosure, will demonstrate operation of data fusion engine  142 . 
     In this specification, the term “database” and “index” will be used broadly to refer to any collection of data. The data of the database and/or the index does not need to be structured in any particular way and it can be stored on storage devices in one or more geographic locations. Thus, for example, the indices  126 ,  130 ,  134 ,  140 ,  154 , and  156  may include multiple collections of data, each of which may be organized and accessed differently. 
     Crop yield and diagnosis system  144  may be configured to practice selected aspects of the present disclosure to provide users, e.g., a user interacting with crop prediction client  109 , with data related to crop yield predictions, forecasts, diagnoses, recommendations, and so forth. In various implementations, crop yield and diagnosis system  144  may include a training module  150  and an inference module  152 . In other implementations, one or more of modules  150  or  152  may be combined and/or omitted. 
     Training module  150  may be configured to train one or more machine learning models to generate data indicative of crop yield predictions. These machine learning models may be applicable in various ways under various circumstances. For example, one machine learning model may be trained to generate crop yield predictive data for a first crop, such as spinach, soy, etc. Another machine learning model may be trained to generate crop yield predictive data for a second crop, such as almonds, corn, wheat, etc. Additionally or alternatively, in some implementations, a single machine learning model may be trained to generate crop yield predictive data for multiple crops. In some such implementations, the type of crop under consideration may be applied as input across the machine learning model, along with other data described herein. 
     The machine learning models trained by training model  150  may take various forms. In some implementations, one or more machine learning models trained by training model  150  may come in the form of memory networks. These may include, for instance, recurrent neural networks, long short-term memory (“LSTM”) neural networks, gated recurrent unit (“GRU”) neural networks, and any other type of artificial intelligence model that is designed for application of sequential data, iteratively or otherwise. In various implementations, training module  150  may store the machine learning models it trains in a machine learning model database  154 . 
     In some implementations, training module  150  may be configured to receive, obtain, and/or retrieve training data in the form of observational and/or operational data described herein and iteratively apply it across a neural network (e.g., memory neural network) to generate output. Training module  150  may compare the output to a ground truth crop yield, and train the neural network based on a difference or “error” between the output and the ground truth crop yield. In some implementations, this may include employing techniques such as gradient descent and/or back propagation to adjust various parameters and/or weights of the neural network. 
     Inference module  152  may be configured to apply input data across trained machine learning models contained in machine learning module database  154 . These may include machine learning models trained by training engine  150  and/or machine learning models trained elsewhere and uploaded to database  154 . Similar to training module  150 , in some implementations, inference module  152  may be configured to receive, obtain, and/or retrieve observational and/or operational data and apply it (e.g., iteratively) across a neural network to generate output. Assuming the neural network is trained, then the output may be indicative of a predicted crop yield. In some implementations, and as will be described with regard to  FIGS.  15 - 17   , crop yield and diagnosis system  144  in general, and inference module  152  in particular, may be configured to perform various techniques to identify factors contributing to an undesirable crop yield and/or crop yield prediction, and to generate recommended operational changes for provision to agricultural personal and/or to autonomous or semi-autonomous farm equipment or machinery. 
     Training module  150  and/or inference module  152  may receive, obtain, and/or retrieve input data from various sources. This data may include both observational data and operational data. As noted previously, “operational” data may include any factor that is human-induced/controlled and that is likely to influence crop yields. Operational data relates to factors that can be adjusted to improve crop yields and/or to make other decisions. “Observational” data, on the other hand, may include data that is obtained from various sources (e.g.,  148 ), including but not limited to sensors (moisture, temperature, ph levels, soil composition), agricultural workers, weather databases and services, and so forth. 
     A highly beneficial source of observational data may be a temporal sequence of high-elevation digital images that have sufficient spatial resolution and temporal frequency such that when they are applied as input across one or more machine learning models in database  154 , the models generate output that is likely to accurately predict crop yield. As noted previously, a ground truth temporal sequence of high-elevation digital images that meets these criteria may be hard to find, due to transient obstructions such as clouds, as well as due to the disparate spatial resolutions and temporal frequencies associated with various satellites. Accordingly, in some implementations, a temporal sequence of high-elevation digital images applied by training module  150  and/or inference module  152  across a machine learning model may include digital images generated and/or modified using techniques described herein to be transient-obstruction-free and/or to have sufficient spatial resolutions and/or temporal frequencies. One example demonstrating how this may be accomplished is provided in  FIG.  11    and the accompanying description. 
     Operational data clearing house  146  may receive, store, maintain, and/or make available, e.g., in database  156 , various operational data received from a variety of different sources. In some implementations, one or more sources of data  148 , including farm equipment such as tractors, may log their operation and provide this data to operational data clearing house  146 , e.g., by uploading their log data during downtime (e.g., every night). Additionally or alternatively, agricultural personnel such as farmers may periodically input operational data based on their own activities. This operational data may include factors such as which fertilizers or pesticides were applied, when they were applied, where they were applied, how much irrigation was applied, when irrigation was applied, which crops were planted in prior years, what/when/where other chemicals were applied, genetic data related to crops, and so forth. Additionally or alternatively, in some implementation, some operational data may be obtained from other sources, such as from the farm equipment itself ( 148 ), from individual farmers&#39; computers (not depicted), and so forth. 
     Another form of observational data that may be obtained from one or more data sources  148  is ground truth data about actual crop yields achieved in the field. For example, when a crop is harvested, an accounting may be made as to what percentages, weights, or other units of measure of the total planted crops were successfully harvested, unsuccessfully harvested, spoiled, etc. This ground truth data may be used as described herein, e.g., by training engine  150 , to train one or more machine learning models. 
       FIG.  2    depicts an example of how a ground truth high-elevation digital image (top) may be processed to classify the constituent geographic units that correspond to its pixels. In the top image, which schematically represents a high elevation digital image capturing a geographic area, a T-shaped road is visible that divides two plots of land at bottom left and bottom right. The bottom left plot of land includes a cluster of vegetation, and so does the bottom right plot. The bottom right plot also features a building represented by the rectangle with cross hatching. 
     The middle image demonstrates how the digital image at top may be classified, e.g., by terrain classification engine  128 , into discrete terrain classifications, e.g., based on geographic units that share spectral-temporal fingerprints. The middle image is subdivided into squares that each represent a pixel that aligns spatially with a geographic unit of the top digital image. Pixels that depict roadway have been classified accordingly and are shown in a first shading. Pixels that depict the building have also been classified accordingly and are shown in black. Pixels that represent the vegetation in the bottom left and bottom right plots of land are also classified accordingly in a second shading that is slightly darker than the first shading. 
     The bottom image demonstrates how techniques described herein, particularly those relating to terrain classification and/or spectral-temporal fingerprint similarity, may be employed to generate replacement data that predicts/estimates terrain underlying a transient obstruction in a high elevation digital image. In the bottom images of  FIG.  2   , a cloud has been depicted schematically primarily over the bottom left plot of land. As indicated by the arrows, two of the vegetation pixels (five columns from the left, three and four rows from bottom, respectively) that are obscured by the cloud can be replaced with data harvested from other, unobscured pixels. For example, data associated with the obscured pixel five columns from the left and three rows from bottom is replaced with replacement data that is generated from two other unobscured pixels: the pixel four columns from left and four rows from top, and the pixel in the bottom right plot of land that is five rows from bottom, seven columns from the right. Data associated with the obscured pixel five columns from the left and four rows from bottom is replaced with replacement data that is generated from two other unobscured pixels: the pixel five columns from left and three rows from top, and the pixel in the bottom right plot of land that is five rows from top and nine columns from the right. 
     Of course these are just examples. More or less unobscured pixels may be used to generate replacement data for obscured pixels. Moreover, it is not necessary that the unobscured pixels that are harvested for replacement data be in the same digital image as the obscured pixels. It is often (but not always) the case that the unobscured pixels may be contained in another high elevation digital image that is captured nearby, for instance, with some predetermined distance (e.g., within 90 kilometers). Or, if geographic units that are far away from each other nonetheless have domain fingerprints that are sufficiently similar, those faraway geographic units may be used to harvest replacement data. 
       FIG.  3    depicts an example of how GANs may be used to train a generator model  250  employed by obstruction replacement engine  132 , in accordance with various implementations. In various implementations, obstruction replacement engine  132  may retrieve one or more high elevation digital images  248  and apply them as input across generator model  250 . Generator model  250  may take various forms, such as an artificial neural network. In some implementations, generator model  250  may take the form of a convolutional neural network. 
     Generator model  250  may generate output in the form of synthetically cloud-free (or more generally, transient obstruction-free) images. These images may then be applied as input across a discriminator model  252 . Discriminator model  252  typically will take the same form as generator model  250 , and thus can take the form of, for instance, a convolutional neural network. In some implementations, discriminator model  252  may generate binary output that comprises a “best guess” of whether the input was “synthetic” or “natural” (i.e., ground truth). At the same time, one or more natural, cloud-free (or more generally, transient obstruction-free) images (i.e., ground truth images) may also be applied as input across discriminator model  252  to generate similar output. Thus, discriminator model  252  is configured to analyze input images and make a best “guess” as to whether the input image contains synthetic data (e.g., synthetically-added clouds) or represents authentic ground truth data. 
     In various implementations, discriminator model  252  and generator model  250  may be trained in tandem, e.g., in an unsupervised manner. Output from discriminator model  252  may be compared to a truth about the input image (e.g., a label that indicates whether the input image was synthesized by generator  250  or is ground truth data). Any difference between the label and the output of discriminator model  252  may be used to perform various training techniques across both discriminator model  252  and generator model  250 , such as back propagation and/or gradient descent, to train the models. 
     In other implementations, one or more recurrent neural networks or other memory networks (e.g., long short-term memory, or “LSTM”) that are able to account for multi-temporal input may be used, e.g., by obstruction replacement engine  132 , to generate replacement data that “fills in the gaps” as described in the summary. For example, in some implementations, each spatio-spectral “slice” of the 3D array structure described elsewhere herein (i.e., data extracted from each digital image of multiple digital images captured over time) may be applied as input across a recurrent neural network to generate output. This output may be combined (e.g., concatenated) with a “next” slice of the 3D array structure and applied, e.g., by obstruction replacement engine  132 , as input across the same recurrent neural network to generate additional output. This may continue across a whole temporal sequence of digital images captured of a geographic area. At each turn, the output may “predict” what the next slice will look like. When the next slice in actuality includes transient obstruction(s) such as clouds, the predicted output can be used to generate replacement data for the obscured pixels. 
       FIG.  4    schematically depicts an example of how GANs may be used to train one or more machine learning models employed by transient obstruction generation engine  138 , in accordance with various implementations. Similar to  FIG.  3   , transient obstruction generation engine  138  may utilize a generator model  350  and a discriminator model  352 , which may or may not take similar forms as models  250 - 252 . In this example, transient obstruction generation engine  138  may retrieve one or more obstruction-free ground truth high-elevation digital images  348  and apply them as input across generator model  350  to generate synthetic images that include baked-in synthetic obstructions such as clouds. These synthetic images may then be applied as input across discriminator model  352 , along with natural, ground truth images that also include obstructions. Similar to before, discriminator model  352  may be configured to generate output that constitutes a “guess” as to whether an input digital image is “synthetic” (e.g., generated by generator model  350 ) or “natural.” These models  350 - 352  may be trained in a manner similar to that described above with regard to models  250 - 252 . 
     Referring now to  FIG.  5   , one example method  500  of performing selected aspects of the present disclosure is described. For convenience, the operations of the flow chart are described with reference to a system that performs the operations. This system may include various components of various computer systems, including various engines described herein. Moreover, while operations of method  500  are shown in a particular order, this is not meant to be limiting. One or more operations may be reordered, omitted or added. 
     At block  502 , the system may obtain a digital image of a geographic area captured from an elevated vantage point. In various implementations, the digital image may include a plurality of pixels that align spatially with a respective plurality of geographic units of the geographic area. 
     At block  504 , the system, e.g., by way of transient obstruction detection engine  124 , may identify one or more obscured pixels of the digital image that align spatially with one or more obscured geographic units of the geographic area that are obscured in the digital image by one or more transient obstructions. Put another way, pixels that depict a portion of a cloud or other transient obstruction are identified, e.g., by transient obstruction detection engine  124  using one or more techniques described previously. 
     At block  506 , the system, e.g., by way of terrain classification engine  128 , may determine, across pixels of a corpus of digital images that align spatially with the one or more obscured geographic units, one or more spectral-temporal data fingerprints of the one or more obscured geographic units. For example, in some implementations, a (“3D”) array structure may have been assembled previously for the geographic area, e.g., based on multiple digital images captured of the geographic area. Each row of the 3D array may represent a particular pixel (and spatially corresponding geographic unit). Each column of the array may correspond to, for instance, a different digital image captured at a different time. Each unit in the third dimension of the 3D array may correspond to different spectral frequencies that are available in the digital images, such as red, green, blue, near infrared (“IR”), mid-IR, far-IR, thermal IR, microwave, and/or radar. In various implementations, this 3D array structure may be used at block  306  to determine domain fingerprints, such as spectral-temporal fingerprints, of individual geographic units. 
     At block  508 , the system, e.g., by way of obstruction replacement engine  132 , may identify one or more unobscured pixels of the same digital image or a different digital image that align spatially with one or more unobscured geographic units of the same or different geographic area that are unobscured by transient obstructions. In various implementations, the unobscured geographic units may have one or more spectral-temporal data fingerprints that match the one or more spectral-temporal data fingerprints of the one or more obscured geographic units that were determined at block  506 . 
     At block  510 , the system may calculate replacement pixel data based on the one or more unobscured pixels. For example, an average of values across the unobscured pixels within a particular spectrum, or across multiple spectra, may be used. Additionally or alternatively, in some implementations, a single pixel that is “closest” (e.g., has a most similar domain fingerprint) to the unobscured pixel may simply be cloned into the obscured pixel. At block  512 , the system may generate a transient-obstruction-free version of the digital image in which data associated with the one or more obscured pixels is replaced with the replacement pixel data. 
       FIG.  6    depicts an example of how techniques described herein may be used to generate a transient-obstruction-free version of a high-elevation digital image. On the left, a digital image captured from a high elevation (e.g., a satellite) depicts a geographic area. It also can be seen that a number of clouds are positioned between the ground surface and the vantage point of the satellite, and therefore obstruct portions of the geographic area from view. In addition it can be seen the shadows cast by the clouds also obstruct additional portions of the geographic area. 
     In the middle image a cloud mask has been detected, e.g., by transient obstruction detection engine  124 . The cloud mask has been used to remove obscured pixels that correspond to the clouds or their respective shadows. Put another way, the obscured pixels that align spatially with the geographic units that are obscured by the clouds or their respective shadows have been removed (e.g., values set to black, zeroed out, etc.). In the right image, the removed pixels have been replaced with replacement data generated using techniques described herein. As explained herein, this replacement data estimates the terrain underlying the obscured pixels. 
       FIGS.  7 A-D  schematically demonstrate another similar technique for performing transient obstruction removal. In  FIGS.  7 A-D  (and in  FIGS.  8 A-D ), the axes are meant to represent feature (e.g., green, blue, red, etc.) spaces, e.g., in latent space. In various implementations, the input for this transient obstruction removal technique may include: 1) a cloud free digital image; 2) a cloud-obstructed digital image; and 3) a cloud mask. The cloud mask may be computed, e.g., by transient obstruction detection engine  124 , from the cloud-obstructed digital image using various techniques, such as those described herein. 
     For the cloud free image, clustering may be performed, e.g., on all of the sub-bands of the image data. Various clustering techniques may be employed, such as K-means and/or other clustering techniques described herein. In some implementations, it is not required that the clusters be generated across a temporal sequence of high-elevation images, as was the case with some of the other transient obstruction-removal techniques described herein. Instead, clusters may be identified in a single cloud-free high-elevation digital image, and then those clusters may be used as described below to remove a transient obstruction from another high-elevation digital image that includes transient obstruction(s). The cluster centers (e.g., centroids) may be calculated, as depicted in  FIG.  7 A  (which only depicts two cluster centers for the sake of brevity and clarity). In some implementations, these clusters may be classified, e.g., by terrain classification engine  128 , as terrain types, e.g., using crop types from the CDL layer. 
     For the cloud-free high-elevation digital image, a distance or delta (Δ) may be computed from each individual pixel of the cluster to the centroid. This is demonstrated in  FIG.  7 B , in which three example pixels and their respective deltas from the pixel cluster centroid are depicted. These deltas may be preserved, e.g., in memory, for subsequent operations described below. Next, for the cloud-obstructed digital image and cloud mask, pixel clusters and their respective centroids may be computed for pixels that are unobstructed. Two examples of such unobstructed centroids are depicted in  FIG.  7 C . Finally, with the cloud-obstructed digital image and cloud mask, the values of the obstructed pixels in the cloud-obstructed digital image may be computed for each spectral sub-band. For example, and as shown in  FIG.  7 D , the values of the obstructed pixels in the cloud-obstructed digital image may be computed by offsetting the pixel cluster centroids computed as depicted in  FIG.  7 C  by the deltas depicted in  FIG.  7 B . 
     In another aspect, and as noted previously, techniques are described herein for generating, e.g., by data fusion engine  142 , synthetic high-elevation digital images by fusing data from multiple temporal sequences of high-elevation digital images, e.g., with disparate resolutions in the temporal, spatial, and/or spectral domains. For example, various data temporal sequences of high-elevation images acquired by MODIS (lower spatial resolution, higher temporal frequency) and the Sentinel-2 (higher spatial resolution, lower temporal frequency) systems may be fused to generate synthetic high-elevation digital images at spatial and/or spectral resolutions that approach or match those of the Sentinel-2 digital images. 
     In various implementations, a first temporal sequence of high-elevation digital images, e.g., acquired by MODIS or another airborne vehicle with relatively high temporal frequency, may be obtained, e.g., directly from the vehicle or from one or more databases that store high elevation digital images captured by the vehicle. The first temporal sequence of high-elevation digital images may capture a geographic area, such as one or more farms, at a first temporal frequency. Each high-elevation digital image of the first temporal sequence may include a plurality of pixels that align spatially with a respective first plurality of geographic units of the geographic area. The first plurality of geographic units may have a size that corresponds to a first spatial resolution of the individual pixels of the first temporal sequence. 
     Similarly, a second temporal sequence of high-elevation digital images, e.g., acquired by Sentinel-2 or another airborne vehicle, may be obtained, e.g., directly from the different vehicle or from one or more databases that store high elevation digital images captured by the different vehicle. Like the first temporal sequence, the second temporal sequence of high-elevation digital images capture the geographic area, except at a second temporal frequency that is less than the first temporal frequency, and at a second spatial resolution that is greater than the first spatial resolution. In various implementations, high-elevation digital images from the first and second temporal sequences may be registered (e.g., spatially aligned) on the same geographic area using a variety of techniques, such as various mathematical models for matching corresponding features on specific spectral sub-bands, Fourier methods, GPS metadata, mutual information, relaxation methods, and so forth. As with the first temporal sequence, each high-elevation digital image of the second temporal sequence may include a plurality of pixels that align spatially with a second plurality of geographic units of the geographic area (which due to the higher resolution of the pixels may be smaller than the first plurality of geographic units). 
     In various implementations, a mapping may be generated of the pixels of the high-elevation digital images of the second temporal sequence to respective sub-pixels of the first temporal sequence. The mapping may be based on spatial alignment of the geographic units of the second plurality of geographic units that underlie the pixels of the second temporal sequence with portions of the geographic units of the first plurality of geographic units that underlie the respective sub-pixels. 
     An example of this mapping is demonstrated schematically in  FIG.  9   . At top, a two-by-two matrix of low-spatial resolution pixels (e.g., acquired by MODIS) is depicted in solid lines, and captures an underlying geographic area. For this example, assume that each pixel is α×α meters in size. At bottom, a four-by-four matrix of high-spatial-resolution pixels (e.g., acquired by Sentinel-2) is depicted in solid lines, and also capture the same geographic area. For this example, assume that each pixel of the bottom matrix is β×β meters in size. For the sake of simplicity, assume further that β is half of α. Thus, four pixels of the bottom matrix fit into one pixel of the top matrix. In various implementations, pixels of the top matrix (i.e., the first temporal sequence) may be subdivided into sub-pixels (shown in dashed lines) that correspond in size to pixels of the bottom matrix. Then, the bottom pixels may be mapped to the sub-pixels of the top matrix, as indicated by the arrows. 
     In some implementations, a next step may be to select a point in time for which a synthetic high-elevation digital image of the geographic area at the second spatial resolution will be generated. For example, a point in time at which no high-elevation digital image of the second temporal sequence, such as between two available images, may be selected, e.g., by a user operating crop prediction client  109  or another remote sensing application. A low-resolution reference digital image that was captured in closest temporal proximity to the point in time may also be selected from the first temporal sequence. 
     Then, in various implementations, a first deviation of ground-truth data forming the low-resolution reference digital image from corresponding data interpolated for the point in time from the first temporal sequence of high-elevation digital images may be determined. Based on the first deviation, a second deviation may be predicted of data forming the synthetic high-elevation digital image from corresponding data interpolated for the point in time from the second temporal sequence of high-elevation digital images. Then, the synthetic high-elevation digital image may be generated based on the mapping and the predicted second deviation. 
     This data fusion process is demonstrated schematically in  FIGS.  8 A-D . The input for the data fusion process includes satellite images from two sources: 1) high resolution low frequency (i.e., the second temporal sequence acquired, for example, by Sentinel-2); and 2) low resolution high frequency (i.e., the first temporal sequence acquired by, for instance, MODIS). 
       FIG.  8 A  demonstrates a first step. For the high spatial resolution data (e.g., second temporal sequence acquired by Sentinel), cloud free high-elevation digital images across a time interval such as a crop year may be identified. Then clustering may be performed on one or more of the sub-bands of all the high-elevation digital images of the second temporal sequence to identify pixel clusters having comparable spectral-temporal traces. Centroids of the pixel clusters may be computed and recorded, as illustrated in  FIG.  8 A  (which only depicts two cluster centroids for the sakes of brevity and clarity). In some cases these pixel clusters may be terrain classified, e.g., using CDL layer data for the classes. Notably, these clustering operations are different from those of  FIGS.  7 A-D  (cloud removal) because temporal data is taken into account (i.e. spectral-temporal traces). 
       FIG.  8 B  demonstrates the next step, in which cloud-free digital images of the second temporal sequence are used to compute deltas (Δ) from each pixel to a centroid of the pixel cluster of which they are members. These deltas may be preserved for future use. This operation may be similar to those described with regard to  FIGS.  7 A-D  in many respects. 
     Next, and as demonstrated in  FIG.  8 C , for high-elevation digital images of the first temporal sequence (low spatial resolution, high temporal frequency, e.g., captured by MODIS) that are free of transient obstructions such as clouds, the pixel clusters may identified, similar to described above with respect to  FIGS.  7 A-D . Then, and as demonstrated in  FIG.  8 D , for the synthetic high-elevation digital image being computed (represented in  FIG.  8 D  by the dark grey circle  866  in the center), its deviation (B in  FIG.  8 D ) from an interpolated value  870  (e.g., linearly interpolated from first and second high-resolution anchor images  880 A,  880 B) is set to be proportionate to a deviation (A in  FIG.  8 D ) of the temporally-corresponding low resolution image  868  (ground truth data from first temporal sequence) from an interpolated value  872  (e.g., interpolated from first and second low-resolution anchor images  882 A,  882 B). 
       FIG.  10    illustrates a flowchart of an example method for practicing selected aspects of the present disclosure, including operations performed by data fusion engine  142 . The steps of  FIG.  10    can be performed by one or more processors, such as one or more processors described herein. Other implementations may include additional steps than those illustrated in  FIG.  10   , may perform step(s) of  FIG.  10    in a different order and/or in parallel, and/or may omit one or more of the steps of  FIG.  10   . For convenience, the operations of  FIG.  10    will be described as being performed by a system configured with selected aspects of the present disclosure. 
     At block  1002 , the system may obtain a first temporal sequence of high-elevation digital images, e.g., from MODIS or another source of relatively high temporal frequency, low spatial/spectral resolution digital images. At block  1004 , the system may obtain a second temporal sequence of high-elevation digital images, e.g., from Sentinel-2 or another source of relatively low temporal frequency but relatively high spatial/spectral resolution images. 
     At block  1006 , the system may generate a mapping of the pixels of the high-elevation digital images of the second temporal sequence to respective sub-pixels of the first temporal sequence, e.g., as depicted in  FIG.  8   . In various implementations, the mapping may be based on spatial alignment of the geographic units of the second plurality of geographic units that underlie the pixels of the second temporal sequence with portions of the geographic units of the first plurality of geographic units that underlie the respective sub-pixels. 
     At block  1008 , the system (e.g., based on user input) may select a point in time for which a synthetic high-elevation digital image of the geographic area at the second spatial resolution will be generated. For example, a point in time may be selected at which no Sentinel-2 image is available. At block  1010 , the system may select, as a low-resolution reference digital image, the high-elevation digital image from the first temporal sequence that was captured in closest temporal proximity to the point in time. 
     At block  1012 , the system may determine a first deviation (e.g., A in  FIG.  8 D ) of ground-truth data forming the low-resolution reference digital image from corresponding data interpolated ( 872 ) for the point in time from the first temporal sequence of high-elevation digital images, e.g., as depicted in  FIG.  8 D . For example, in some implementations, the system may select, as first and second low-resolution anchor digital images, two high-elevation digital images (e.g.,  882 A,  882 B) from the first temporal sequence that were captured in closest temporal proximity to, respectively, high-elevation digital images (e.g.,  880 A,  880 B) from the second temporal sequence that were acquired before, and after, respectively. In some implementations, these high-elevation digital images from the second temporal sequence may also be selected, e.g., as first and second high-resolution anchor digital images ( 880 A,  880 B). In some implementations, the corresponding interpolated data ( 872 ) calculated from the first temporal sequence of high-elevation images is calculated based on the first and second low-resolution anchor images ( 882 A,  882 B). 
     At block  1014 , the system may predict, e.g., based on the first deviation determined at block  1012 , a second deviation (e.g., B in  FIG.  8 D ) of data forming the synthetic high-elevation digital image from corresponding data interpolated for the point in time from the second temporal sequence of high-elevation digital images. In some implementations, the corresponding interpolated data calculated for the point in time from the second temporal sequence may be calculated based on the first and second high-resolution anchor digital images ( 880 A,  880 B). For example, in some implementations, a plurality of pixel clusters may be identified across the high-elevation digital images of the second temporal sequence. Each pixel cluster of the plurality of pixel clusters may include pixels with comparable spectral-temporal traces across the second temporal sequence of high-elevation digital images. In some implementations, the corresponding data interpolated from the second temporal sequence may include one or more centroids calculated from one or more of the pixel clusters. And as noted previously, in some cases, deltas between each pixel and a centroid of a pixel cluster of which the pixel is a member may be stored and used to determine the pixel&#39;s final value in the synthetic high-elevation digital image. 
     At block  1016 , the system may generate the synthetic high-elevation digital image based on the mapping and the predicted second deviation. In various implementations, the generating may include interpolating a spectral sub-band of the pixels of the synthetic high-elevation digital image that exists in the pixels of the second temporal sequence of high-elevation digital images, but is missing from the pixels of the first temporal sequence of high-elevation digital images. In some such implementations, the spectral sub-band missing from the pixels of the first temporal sequence of high-elevation digital images may be near infrared (which may be present in the second temporal sequence). Additionally or alternatively, in some implementations, the generating of block  1016  may be further based on a difference between a first elevation at which one or more digital images of the first temporal sequence was taken and a second elevation at which one or more digital images of the second temporal sequence was taken. 
     In addition to or instead of the techniques demonstrated by  FIGS.  7 A-D ,  8 A-D,  9 , and  10 , in some implementations, other machine learning techniques may be employed to generate synthetic high-elevation digital images by fusing data from two or more temporal sequences of high-elevation digital images. For example, in some implementations, various deep learning techniques may be employed to facilitate “super-resolution” image processing. For example, in some implementations, deep convolutional neural networks may be trained using ground truth images to generate “enhanced” or “super-resolution” images. Additionally or alternatively, in some implementations, perceptual loss functions may be defined and/or optimized, e.g., based on high-level features extracted from pre-trained networks. 
     As noted previously, techniques described herein for transient obstruction removal and/or generation of synthetic high-elevation digital images may be employed to improve a variety of applications. One application for which these techniques are particularly useful is crop yield prediction. Referring now to  FIG.  11   , a process is depicted schematically to demonstrate one example of how crop yield prediction may be implementing using a temporal sequence of high-elevation digital images. The high-elevation digital images of the temporal sequence may have sufficiently high spatial resolution and temporal frequency to facilitate accurate crop yield prediction. To this end, in some implementations, one or more high-elevation digital images of the temporal sequence may be transient-obstruction-free, synthetic high-elevation digital images generated using one or of the aforementioned techniques. However, if a ground truth (i.e. non-synthetic) temporal sequence of high-elevation digital images has sufficient spatial resolution and temporal frequency, then the aforementioned techniques may not be required. 
     In  FIG.  11   , a first temporal sequence of high-elevation digital images  1170  may capture a geographic area under consideration, such as a field growing a particular type of crop (e.g., spinach, green beans, potatoes, etc.). First temporal sequence of high-elevation digital images  1170  may have relatively high spatial resolutions but may be acquired at a relatively low temporal frequency, such as once every 2-3 days, once a week, once a month, once a quarter, etc. For example, first temporal sequence of high-elevation digital images  1170  may be acquired by the MODIS satellite described previously. 
     By contrast, a second temporal sequence of high-elevation digital images  1171  may capture the same geographic area under consideration and may have relatively low spatial resolutions but may be acquired at a relatively high temporal frequency, such as daily. For example, second temporal sequence of high-elevation digital images  1171  may be acquired by the Sentinel-2 satellite described previously. Other sources of high-elevation digital images are contemplated herein in addition to or instead of MODIS and Sentinel-2. Moreover, more than two temporal sequences of high-elevation digital images may be provided from a variety of other sources, such as satellites other than MODIS/Sentinel-2, unmanned aerial vehicles, airplanes, balloons, spacecraft, and so forth. 
     First and second temporal sequences  1170  and  1171  may include at least some images that are wholly or partially obstructed by transient obstructions, such as clouds. Accordingly, in various implementations, first and second temporal sequences  1170  and  1170  may be processed using various cloud-removal techniques known in the art and/or described herein to remove transient obstructions and/or replace them with inferred data. For example, in  FIG.  11   , first and second temporal sequences  1170  and  1171  are processed by transient obstruction detection engine  124  and/or transient obstruction replacement engine  132  as described previously to generate, respectively, transient-obstruction-free first and second temporal sequences  1170 ′ and  1171 ′. It should be understood that not all high-elevation images in either sequence will necessarily be obstructed, and in fact there may be many images that are cloud free. Accordingly, transient-obstruction-free first and second temporal sequences  1170 ′ and  1171 ′ may still include original, unaltered (i.e. ground truth) high-elevation digital images. 
     Transient-obstruction-free first and second temporal sequences  1170 ′ and  1171 ′ may then be processed by data fusion engine  142  as described herein to generate a third temporal sequence of high-elevation digital images  1172 . In many cases, third temporal sequence of high-elevation digital images  1172  may include synthetic (and transient-obstruction-free) high-elevation digital images generated based on transient-obstruction-free first and second temporal sequences  1170 ′ and  1171 ′ as described herein. However, in other implementations, if a high spatial resolution temporal sequence of high-elevation digital images is captured at a sufficient frequency, then it may not be necessary to generate synthetic high-elevation digital images. Additionally, in many cases, third temporal sequence of high-elevation digital images  1172  may include, interspersed among the synthetic images, one or more non-synthetic images (or synthetic only inasmuch as transient obstructions have been removed) that include ground truth data captured in the original first temporal sequence of high-elevation digital images  1170 . 
     In various implementations, third temporal sequence of high-elevation digital images  1172  may be applied as input across one or more machine learning models  1174 , along with other data  1173 , to generate output. In various implementations, the output may be indicative of a predicted crop yield. For example, in  FIG.  11   , machine learning model  1174  takes the form of a recurrent neural network that generates output y based on iterative application of the inputs x ( 1172  and  1173 ) across one or more neural networks. As is typical with recurrent neural networks, recurrent neural network  1174  includes an internal state h that is used at each iteration of applied input x to take into account inputs of previous iterations. This is depicted at an unfolded version  1175  of the recurrent neural network, where time t runs down. Some function ƒ is applied after each iteration to update the state h based on the current iteration&#39;s input x. In this example, each iteration of output y may be indicative of an estimated crop yield that is predicted based on the input data x applied up to that point in time. 
     In some implementations, recurrent neural network  1174  may be trained as follows. A third temporal sequence of high-elevation digital images  1172  that captures a geographic region over a predetermined time interval, such as a crop year, may be obtained as described previously. Preferably the third temporal sequence  1172  includes high-elevation digital images leading right up to harvest, when ground truth crop yield can be determined, although this is not necessarily required. 
     Other data  1173  may be obtained that includes operational and/or observational data (besides third temporal sequence  1172 ) for the same geographic area and crop year. In some implementations, other data  1173  may include a plurality of other data points that are grouped into temporal chunks. Each temporal chunk of the plurality of other data points may correspond temporally with a respective high-elevation digital image of third temporal sequence  1172 . For example, if a particular high-elevation digital image of third temporal sequence  1172  was captured on or generated to represent June 1, then other data  1173  that corresponds to this digital image may include precipitation on June 1, irrigation applied on June 1, temperature ranges on June 1, sunshine on June 1, soil quality measurements obtained on June 1, data related to plowing or other agricultural operations performed on June 1, and so forth. 
     These data may be iteratively applied as input x, e.g., day by day, across recurrent neural network  1174  to generate output y for each day. The output y on the last day (e.g., the day(s) of harvest), which may be indicative of an estimated crop yield of the geographic area under consideration, may then be compared to the ground truth crop yield. The different, or “error,” between the two may be determined based on the comparing. Recurrent neural network  1174  may then be trained based on the error, e.g., using techniques such as gradient descent, back propagation, etc. 
     In various implementations, recurrent neural network  1174  may be trained using historical data (e.g.,  1172 - 1173 ) acquired for multiple (e.g., numerous) geographic areas over multiple time intervals (e.g., crop years). The more geographic areas and/or time intervals for which training data is available, the more accurate recurrent neural network  1174  will become for predicting crop yield. In some implementations, separate recurrent neural networks (or more generally, machine learning models) may be trained for different scenarios, such as different types of crops. For example, one machine learning model may be trained for one crop, another for another crop, and so forth. Additionally or alternatively, in some implementations, a single machine learning model may be trained to predict crop yields for multiple types of crops. In some such embodiments, information about the type of crop, such as genetic information, type, genus, etc., may be applied as input across the model along with the other data (e.g.,  1172 - 1173 ). 
     In other implementations, machine learning model  1174  may take other forms. For example, in some implementations, machine learning model  1174  may take the form of long short-term memory (“LSTM”) neural networks, gated recurrent unit (“GRU”) recurrent networks, and other types of memory networks. Additionally or alternatively, in some implementations, feed-forward neural network  1174  may be a feed-forward neural network without memory elements. In some such implementations, the feed-forward neural network may include a large number of inputs that can accommodate input data x (e.g.,  1172 - 1173 ) associated with a set number of days. For example, data from every day (or other periodic time unit) may be applied as input at the same time, with one day&#39;s data being applied at inputs 1 to n, the next day&#39;s data being applied at inputs n+1 to n+n, and so forth. 
     As yet another example, in some implementations, a feed forward neural network may include enough inputs for a single day&#39;s data, plus some additional inputs. Each day&#39;s data may be applied across the feed forward neural network to generate output (e.g., y) that takes the form of a latent space embedding. This latent space embedding may be preserved, e.g., in a memory node or elsewhere. At the next iteration/day, the latent space embedding generated during the previous iteration/day may be applied at the additional inputs mentioned previously, along with the next day&#39;s data, to generate a further latent space embedding. This may repeat for as many days (or other units of time) for which data is available. 
     After the machine learning model is trained, new input data may be applied across it in the same way(s) as described above. However, there may be cases when ground truth ( 1173 ) data expected at one or more inputs is not available for a particular geographic area under consideration. In some such cases, this missing data may be inferred or otherwise replaced with substitute data in various ways. In some implementations, the missing data may be extrapolated from another geographic area or geographic region as a whole (e.g., other farms in the same state, average data for the state, etc.) In some implementations, the missing data may be extrapolated from another geographic area that is used to grow the same type of crop. In some implementations, the missing data may be inferred using techniques such as expectation-maximization. For example, if only high elevation digital images are available for a geographic area, the other factors that contributed to the observed results in those images may be latent. These latent variables may be inferred by finding a maximum likelihood or maximum a posteriori estimates of the missing data. In yet other implementations, averages of data provided for other similar geographic regions, and/or averages (or other statistical measures) of data may be used. For example, different farmers in a region likely applied different amounts of fertilizer. In some cases, the average amount of fertilizer applied by farmers in the region may be used in place of missing data for a particular farmer&#39;s field. 
     In some implementations, one or more attention mechanisms may be employed with machine learning model  1174  for a variety of reasons. For example, it may be the case that for a given crop year, a particular time period within the crop year has a far greater influence on the ultimate crop yield than other times of the crop year. This may be determined based on various signals, such as input from an agricultural worker (e.g., a farmer indicates the most important week(s) of the crop year). In some such implementations, an attention mechanism may be incorporated into machine learning model  1174  to cause input data associated with the particular time period to be weighted more heavily than input data associated with other time periods within the crop year. 
     In the examples above, the output (y) of machine learning model  1174  was indicative of predicted crop yield. This output may take various forms. In some implementations, machine learning model  1174  may be a many-to-one model such that, for example, the output comprises a single value that indicates a predicted crop yield for an entire geographic area. However, as noted previously, third temporal sequence  1172  may have a spatial resolution that is relatively granular, such as ten meters by ten meters per pixel, or even more granular. Accordingly, in some implementations, machine learning model  1174  may be designed as a many-to-many machine learning model that provides multiple outputs, each output corresponding to a particular geographic unit underlying each pixel of the third temporal sequence of high-elevation digital images  1172 . 
     This is demonstrated schematically in  FIG.  12   . In  FIG.  12   , other data  1173  and third temporal sequence of high-elevation digital images  1172  are depicted being applied as input across machine learning model  1174  to generate output y. However, each high-elevation digital image of third temporal sequence  1172  is depicted in  FIG.  12    as a five-by-five matrix of twenty-five pixels. This is not meant to be limiting, and each high-elevation digital image may have any number of pixels greater or less than that depicted in  FIG.  12   . 
     Machine learning model  1174  in this example takes the form of some flavor of neural network. Some inputs of machine learning model  1174  receive other data  1173 . Other inputs of machine learning model  1174  receive individual pixel values from third temporal sequence of high-elevation digital images  1172 . Each output of the output layer (bottom layer in  FIG.  12   ) of machine learning model  1174  yields, as a constituent part of output y, a pixel-level value that can represent, for instance, a predicted crop yield for the geographic unit underlying the corresponding pixels of third temporal sequence  1172 . In  FIG.  12   , values of 10, 11, and 12 are shown in each “pixel” as representing example crop yield predictions for the underlying geographic units. These values are selected for illustrative purposes only and are not meant to be limiting. It can be seen that, for instance, the top right area of the geographic area, which has mostly 10s, is getting less yield than, say, a diagonal strip from top left to bottom right, which has mostly 12s. That may suggest, e.g., to a farmer, that some remedial action should be taken for the top right area of the geographic area. Thus, generating pixel-level, or more particularly, geographic unit-level crop yield predictions may be useful for a variety of purposes, such as identifying underperforming areas of fields, and/or diagnosing factors that contributed to those underperforming areas. 
     Referring now to  FIG.  13   , an example method  1300  of practicing selected aspects of the present disclosure is described, including inferring predicted crop yields using a trained machine learning model. For convenience, the operations of the flowchart are described with reference to a system that performs the operations. This system may include various components of various computer systems, such as inference module  152  in  FIG.  1   . Moreover, while operations of method  1300  are shown in a particular order, this is not meant to be limiting. One or more operations may be reordered, omitted or added. 
     At block  1302 , the system may obtain a first temporal sequence of high-elevation digital images. In various implementations, the first temporal sequence of high-elevation digital images may capture a first geographic area, such as one or more fields of interest to a farmer or other agricultural personnel. The first temporal sequence of high-elevation digital images may be acquired over a first predetermined time interval, such as a crop year. During the first predetermined time interval, the first geographic area may include at least a first type of crop (e.g., spinach, potato, romaine lettuce, radishes, turnips, rutabaga, corn, wheat, soy, squash, cilantro, etc.) that was planted with the intent to harvest. As noted above, the first temporal sequence of high-elevation digital images may have spatial resolutions and be acquired at a temporal frequency that satisfy one or more criterion. For example, the spatial resolution may be, for instance, ten meters by ten meters per pixel, and the temporal frequency may be daily, hourly, weekly, etc. Moreover, the first temporal sequence may include only original, ground truth images and/or may include synthetic images in which transient obstructions have been removed and/or that are wholly generated (e.g., inferred) using data fusion techniques described herein. 
     At block  1304 , the system may obtain a first plurality of other data points. In various implementations, the first plurality of other data points may be data points that influence a ground truth crop yield of the first geographic area after the first predetermined time interval. These may include observational and/or operational data as described herein. In various implementations, the first plurality of other data points may be grouped into temporal chunks, with each temporal chunk of the first plurality of other data points corresponding temporally with a respective high-elevation digital image of the first temporal sequence of high-elevation digital images. For example, if there are daily high-elevation digital images available, then other daily may be provided in daily chunks. 
     At block  1306 , the system may iteratively apply the high-elevation digital images of the first temporal sequence and the temporal chunks of the first plurality of other data points as input across a machine learning model. The machine learning model may take various forms, such as a recurrent neural network, an LSTM neural network, a GRU neural network, and so forth. In other embodiments, the machine learning model may not be a memory-based network, in which case the input data may not necessarily be applied iteratively, but could for instance be applied all at once. The result of the iterative application may be to generate first output indicative of an estimated crop yield of the first geographic area at the end of the first predetermined time interval. 
     At block  1308 , the system may cause one or more output components of one or more computing devices to audibly or visually convey the estimated crop yield of the first geographic area at the end of the first predetermined time interval. For example, a report may be generated for the farmer or other personnel that are stewards of the one or more fields in the first geographic area. As noted above, the output may come in various forms. In implementations in which a many-to-one machine learning model is employed, the output may be a single value indicative of the estimated crop yield over a geographic area. Additionally or alternatively, in some implementations in which a many-to-many machine learning model is employed, the output may be at the pixel level and may include values corresponding to geographic units underlying individual pixels of the first temporal sequence. 
     Referring now to  FIG.  14   , an example method  1400  of practicing selected aspects of the present disclosure is described, including training the machine learning model. For convenience, the operations of the flowchart are described with reference to a system that performs the operations. This system may include various components of various computer systems, such as training module  150  in  FIG.  1   . Moreover, while operations of method  1400  are shown in a particular order, this is not meant to be limiting. One or more operations may be reordered, omitted or added. 
     At block  1402 , the system may obtain a first temporal sequence of high-elevation digital images, similar to block  1302 . In various implementations, the first temporal sequence of high-elevation digital images may capture a first geographic area and are acquired over a first predetermined time interval. During the first predetermined time interval, the first geographic area may include a first type of crop, again, similar to block  1302 . 
     At block  1404 , the system may obtain a first plurality of other data points, similar to block  1304 . In various implementations, the first plurality of other data points may influence a ground truth crop yield of the first geographic area at the end of the first predetermined time interval. Similar to block  1304 , the first plurality of other data points may be grouped into temporal chunks, each temporal chunk of the first plurality of other data points corresponding temporally with a respective high-elevation digital image of the first temporal sequence of high-elevation digital images. 
     At block  1406 , the system may iteratively apply the high-elevation digital images of the first temporal sequence and the temporal chunks of the first plurality of other data points as input across the machine learning model to generate first output indicative of an estimated crop yield of first geographic area at the end of the first predetermined time interval. This may be similar to block  1306 . 
     At block  1408 , the system may compare the estimated crop yield of the first geographic area at the end of the first predetermined time interval to the ground truth crop yield of the first geographic area. At block  1410 , the system may train the machine learning model based on the comparing, e.g., using techniques such as back propagation, gradient descent, etc. 
     As noted previously, in various implementations, factors that contribute to a ground truth crop yield and/or that contribute to a crop yield prediction made during the middle of a crop cycle may be identified and used to make recommended operational changes. These operational changes may include, for instance, irrigation recommendations, fertilizing recommendations, soil treatment recommendations, crop rotation recommendations, and so forth. And because techniques described herein generate pixel-level (or more particularly, geographic unit-level) crop yield predictions, recommended operational changes can also be made at a pixel (or geographic) level, in addition to at a field level (or larger geographic area). 
     In some cases, recommended operational changes may be presented to agricultural personnel as audio and/or visual output on one or more computing devices, e.g., as part of a computer-generated report that provides farmers with various statistics, charts, projections, etc. In some such cases, the recommendations may be presented in the context of crop yield projections that likely would be achieved should the recommended operational changes be followed. In some cases, pixel-level recommended operational changes may be presented to agricultural personnel in real time, e.g., as they approach a portion of a field for which an operational change is recommended. For example, personnel driving a tractor that is applying nitrogen to the soil may receive a notification, e.g., on a display or via a speaker, that instructs the personnel to increase/decrease a nitrogen application rate for the next five minutes (or the next few rows of the field). 
     Additionally or alternatively, in some implementations, the recommendations may be used to generate commands that are provided to autonomous or semi-autonomous farm machinery, such as autonomous or robotic tractors, drones, unmanned aerial vehicles, etc. These commands may be transmitted to the machinery in the field, e.g., using various wireless communication technologies (e.g., Wi-Fi, cellular, Bluetooth, mesh networks such as ZigBee or Z-Wave, etc.), and/or may be uploaded to the machinery when the machinery is offline, e.g., while batteries are charged, during the night, etc. These commands may cause the farm machinery to operate in accordance with the recommended operational changes. For example, an autonomous tractor may receive commands that indicate how much fertilizer should be applied to each individual geographic unit (corresponding to a pixel of high-elevation digital imagery). As another example, an unmanned aerial vehicle may selectively spread different amounts of pesticides on different portions of a field based on recommended operational changes. 
     In some implementations, the neural networks (e.g.,  1174 ) described previously that are trained to generate crop yield predictions may be leveraged to diagnose how much individual factors (especially operational factors) contribute to crop yield predictions, and/or to generate recommended operational changes. This may be done in a variety of different ways. Referring now to  FIG.  15   , in some implementations, a neural network  1574  may once again take the form of a feed-forward neural network, a memory network such as a recurrent neural network, LSTM network, GRU network, or any combination thereof, and may be trained as described previously to predict crop yields based on third sequence of high-elevation digital images ( 1172  in  FIG.  11   ) and other data that includes observational and/or operational data. 
     As shown in  FIG.  15   , ground truth (“GT”) other data  1573  (similar to  1173 ), which may include observational and/or operational data, may be applied (e.g., iteratively, all at once) as input across the neural network  1574 , along with a sequence of high-elevation digital images  1572  (similar to  1172 ), to generate what will be referred to herein as a “ground truth-based crop yield prediction”  1590 . It may be the case that these data are only available for a portion of the crop cycle, e.g., because the crop yield prediction is being made mid-crop cycle and no future data yet exists. 
     In various implementations, one or more data points of the ground truth other data (also referred to as “ground truth data set”)  1573  set may be altered in various ways (e.g., increased, decreased, replaced with randomly- or quasi-randomly selected values, replaced with reference data from other “reference” geographic areas, etc.) to generate first hypothetical input data  1573   1 . This first hypothetical input data set  1573   1  may be applied as input across neural network  1574 , along with sequence of high-elevation digital images  1572 , to generate a first hypothetical crop yield prediction  1590   1 . First hypothetical crop yield prediction  1590   1  may represent a crop yield that would likely be obtained if the ground truth data were replaced with the hypothetical data. 
     As an example, suppose that until now, a first amount of nitrogen has been applied to the geographic area under consideration. This ground truth first amount of nitrogen, along with various other factors (operational and observational), contributes to the ground truth-based crop yield prediction  1590 . Now, suppose in first hypothetical data set  1573   1 , the first amount of nitrogen has been replaced with a greater or lesser second amount of nitrogen, and the remainder of first hypothetical input data set  1573   1  remains the same as ground truth data set  1573 . Suppose further that first hypothetical crop yield prediction  1590   1  is greater than ground truth-based crop yield prediction  1590 . That strongly suggests that the amount of nitrogen applied was not ideal, and that perhaps a different amount of nitrogen should be applied moving forward in the hopes of increasing the ultimate ground truth crop yield. Accordingly, in various implementations, a recommended operational change may be generated, e.g., by crop yield and diagnosis system  144 , which suggests altering the amount of nitrogen applied moving forward, e.g., to compensate for the less-than-optimal amount of nitrogen applied up to this point in time. 
     Referring back to  FIG.  15   , and as indicated by the ellipses, any number N (positive integer) of hypothetical input data sets may be generated and applied, along with the temporal sequence of high-elevation digital images, as input across neural network  1574  to generate any number N of distinct hypothetical crop yield predictions. Any observational and/or operational data point may be altered to calculate a hypothetical crop yield prediction. However, for purposes of generated recommended operational changes, it may be preferable to alter operational data points, since those are controlled by humans and therefore are more easily adjustable by humans. 
     In some implementations, a “brute force” approach may be applied in which numerous hypothetical crop yield predictions are calculated, each based on a different set of one or more input data points being tuned to a different value, to determine the impacts of those respective tunings. In some implementations, one or more hypothetical crop yield predictions that are greater than ground truth-based crop yield prediction  1590  may be used to generate recommended operational changes. For example, the greatest hypothetical crop yield prediction may be selected from multiple candidate hypothetical crop yield predictions. The data points that were altered to generate the hypothetical input data set (selected from  1573   1-N ) that yielded the selected hypothetical crop yield prediction (selected from  1590   1-N ) may be identified as the factors that made the heaviest contributions to the (perhaps less than ideal) ground truth-based crop yield prediction  1590 . These factors and/or the amounts they were altered may be used to generate recommended operational changes. 
     Depending on how many distinct inputs are considered (e.g., a dimension of an input layer of neural network  1574 ), the brute force approach may be cumbersome. A large number of input data points may effectively define a large search space for which brute force requires considerable computing resources and/or time to identify which factors were highly influential, and hence, which operational changes should be recommended. Additionally, the more layers in machine learning model  1574  (e.g., a deep learning neural network), the more computationally expensive it is to apply it to data. 
     Accordingly, various techniques may be employed to effectively reduce the search space of all possible input data points. In some implementations, rather than tuning input data points systematically, randomly, and/or arbitrarily, input data points may be tuned based on “reference data points” obtained from data associated with other, “reference” geographic areas. These “reference” geographic areas may be selected based on various criteria, such as being used to grow the same crop as the geographic area under consideration (particularly if they were successfully used to grow the same crop), being geographically proximate to the geographic area under consideration, being temporally proximate (e.g., data from last year or the year before), being the same geographic area but during a previous crop cycle (e.g., the same crop was more successful in the same geographic area last year), having similar climates/weather patterns, and so forth. 
     In some implementations, data associated with the geographic area under consideration and data associated other geographic areas that are candidates for consideration as reference geographic areas may be used to generate embeddings in latent space. These embeddings may then analyzed to determine which should be used as reference geographic areas for the geographic area under consideration. For example, an embedding of the geographic area under consideration may tend to cluster with other embeddings in the latent space associated with other similar geographic areas. These other similar geographic areas in the same cluster (which may be heavily influenced in some cases by a crop type input) may be suitable for use as reference geographic areas. 
     Once one or more reference geographic areas are identified, input data associated with these reference geographic area(s), and especially operational data, may be substituted for one or more data points in ground truth input data set  1573  to generate a hypothetical input data set  1573   1 , as described previously. The hypothetical crop yield prediction  1590   1  generated from the hypothetical input data set  1573   1  may then indicate whether the substituted data points were, in fact, a highly influential contributor to ground truth crop yield  1590 . 
     As noted previously, repeatedly applying potentially large amounts of data as input across a neural network such as a recurrent neural network in brute force fashion may be cumbersome. Accordingly, various techniques may be employed to identify highly-influential input factors, e.g., by shrinking the search space. 
       FIGS.  16 A-D  demonstrate schematically one example of how highly influential data points may be identified using latent spaces. In  FIGS.  16 A-D , assume that the same four input data points (observational and/or operational), I 1-4 , are used in conjunction with temporal sequence of high-elevation digital images (e.g.,  1572 ,  1172 ) to generate crop yield predictions for ten geographic areas, including the geographic area under consideration. In reality, a far greater number of input data points would likely be considered, but four is used here for demonstrative purposes. These four operational data points could include one or more of units (e.g., gallons) of water applied (e.g., to each geographic unit underlying a pixel of the high-elevation digital imagery), nitrogen or fertilizer applied, prior years&#39; crop choices (e.g., it may be beneficial to use a field to grow a particular sequence of crops over a given number of years), seed application density, tillage measure(s), precipitation received (e.g., cumulative per geographic unit), sunlight received, wind, pest population, or any other data point that might influence crop yield. 
     In various implementations, the geographic area under consideration may be embedded into one or more latent or reduced-dimensionality spaces based on various combinations of the four input data points. Each of  FIGS.  16 A-D  represents one of those latent spaces. The white circle represents the geographic area (or even geographic unit) under consideration and the nine black circles represent nine reference geographic areas/units. For this example, assume that the geographic area under consideration experienced a lower-than-expected crop yield, or that a lower-than-expected crop yield prediction has been made mid-crop cycle. Assume further that the nine reference geographic areas were selected because they had better yields and/or generated better yield predictions. 
     In various implementations, one or more of the four input data points I 1-4  associated with the geographic area under consideration, and the same one or more of the four input data points associated with each of the nine reference geographic areas, may be muted or omitted (e.g., zeroed out, or dropped). The remaining input data points for each geographic area may then be used to generate a respective embedding into a latent space. For example, in  FIG.  16 A , assume that input data input I 1  is muted, and that input data points I 2-4  are used to generate the embeddings depicted in  FIG.  16 A . Likewise, in  FIG.  16 B , assume that input data input I 2  is muted, and that input data points I 1, 3-4  are used to generate the embeddings depicted in  FIG.  16 B . In  FIG.  16 C , assume that input data input I 3  is muted, and that input data points I 1-2, 4  are used to generate the embeddings depicted in  FIG.  16 C . In  FIG.  16 D , assume that input data input I 4  is muted, and that input data points I 1-3  are used to generate the embeddings depicted in  FIG.  16 D . 
     As is seen in  FIGS.  16 A-D , the embeddings generated from the reference geographic areas (black circles in  FIGS.  16 A-D ) form clusters of varying tightness or cohesion. In some cases, the clusters (or “Gaussian blobs”) are tightly packed and have relatively small radii. This is seen, for instance, in  FIGS.  16 B  and C, in which the clusters have relatively small radii that suggests low variance between the input data points selected to generate those embeddings. In other cases, the clusters are less tightly packed and have greater radii, suggesting greater variance between the input data points selected to generate those embeddings. 
     In various implementations, a centroid of the embeddings generated from the reference geographic areas may be determined, and is represented in each of  FIGS.  16 A-D  as a star. In various implementations, a distance d of the embedding generated for the geographic area under consideration (the white circle) from the centroid may be determined. In some such implementations, if the distance dis greater than a variance or “radius” of the cluster of embeddings generated for the reference geographic areas, that may indicate that one or more of the remaining input data points selected for the embeddings varied significantly between the geographic area under consideration and the reference geographic areas. Put another way, the omitted data point was not a highly influential factor in the predicted/ground truth crop yield for the geographic area under consideration, and in fact, one or more of the remaining input data points appears heavily influence different crop yields between the geographic area under consideration and the reference geographic areas. An example of this is seen in  FIGS.  16 B and  16 D , wherein the distances d 2  and d 4  between the embedding (white dot) of the geographic area lies far outside of the respective cluster of reference geographic areas. 
     By contrast, suppose the distance dis less than or similar to the variance/radius of the cluster. This may suggest the omitted input data point contributed significantly to the less-than-idea yield or predicted yield. Examples of this are seen in in  FIGS.  16 A and  16 C , in which the distances d 1  and d 3 , respectively, are similar to, or even less than, a radius or variance of the respective cluster. In  FIG.  16 A , for instance, data point I 1  is omitted, and as a consequence, the remaining data points I 2-4  of the geographic area under consideration generate an embedding (white dot in  FIG.  16 A ) that is d 1  from the cluster centroid. d 1  is approximately equal to the radius of the cluster. Thus, it can be inferred that input data point I 1  contributed (alone or in combination with other data points) to the less-than-optimal crop yield/prediction of the geographic area under consideration. 
     This is even more pronounced in  FIG.  16 C , where d 3  is less than the radius of the cluster. In  FIG.  16 C , data point I 3  is omitted, and the resulting cluster is more tightly packed than that of  FIG.  16 A . In some implementations, both the compactness of the cluster and the distance d may be considered in determining how much an omitted data point contributes to a particular crop yield/prediction. For example, the facts that (i) the cluster in  FIG.  16 C  is tightly packed and (ii) d 3  is less than the radius of the tightly-packed cluster may be a strong indicator that the omitted data point, I 3 , was an even greater contributor to the less-than-ideal crop yield/prediction of the geographic area under consideration than the omitted data point in  FIG.  16 A , I 1 . 
     When data point I 4  is omitted as depicted in  FIG.  16 D , the resulting embedding (white dot) generated for the geographic area under consideration is a distance d 4  from the centroid of the relatively loosely-packed cluster of embeddings generated for the reference geographic areas. The distance d 4  is significantly greater than the radius or variance of the loosely-packed cluster. Accordingly, data point I 4  may not necessarily have been a large contributor to the less-than-ideal crop yield, at least by itself. 
     In the examples of  FIGS.  16 A-D , only one input data point is omitted in each test case. However, this is not meant to be limiting. In various implementations, more than one input data point may be omitted at the same time to generate embeddings for the geographic area under consideration and the reference geographic areas. By omitting multiple input data points simultaneously, it is possible to see whether combinations input data points, rather than individual data points standing alone, contributed to crop yields/predictions. 
       FIG.  17    illustrates a flowchart of an example method  1700  for practicing selected aspects of the present disclosure. The steps of  FIG.  17    can be performed by one or more processors, such as one or more processors of the various computing devices/systems described herein. For convenience, operations of method  1700  will be described as being performed by a system configured with selected aspects of the present disclosure. Other implementations may include additional steps than those illustrated in  FIG.  17   , may perform step(s) of  FIG.  17    in a different order and/or in parallel, and/or may omit one or more of the steps of  FIG.  17   . 
     At block  1702 , the system may obtain a first temporal sequence of high-elevation digital images (e.g.,  1572  in  FIG.  15   ). In various implementations, the first temporal sequence of high elevation digital images may capture a first geographic area under consideration over a given time interval through a crop cycle of a first type of crop growing in the first geographic area. As with previous implementations, one or more high-elevation digital images of the first temporal sequence may or may not include one or more transient-obstruction-free, synthetic high-elevation digital images generated using various techniques described herein. This operation may be similar in some ways to the operations of block  1302  in  FIG.  13   . 
     At block  1704 , the system may obtain ground truth operational data generated through the given time interval that influence a final crop yield of the first geographic area after the crop cycle. In various implementations, the ground truth operational data may be grouped into temporal chunks, with each temporal chunk of the ground truth operational data corresponding temporally with a respective high-elevation digital image of the first temporal sequence of high-elevation digital images. This operation may be similar in some ways to the operations of block  1304  in  FIG.  13   . 
     At block  1706 , the system may generate a ground truth-based crop yield prediction of the first geographic area at the end of the crop cycle by applying the high-elevation digital images of the first temporal sequence and the temporal chunks of the operational as input across a machine learning model. The machine learning model may take various forms, such as a neural network, a memory-based neural network (e.g., LSTM, GRU, recurrent, etc.), and so forth. In implementations in which the machine learning model is a memory-based network, the applying performed at block  1706  may be performed iteratively, with each iteration corresponding to a single high-elevation digital image of the first temporal sequence and temporally corresponding ground truth operational data, similar to block  1306  in  FIG.  13   . 
     At block  1708 , the system may identify one or more recommended operational changes, which may include generating one or more hypothetical crop yield predictions. This is demonstrated in  FIG.  17    as a loop that includes blocks  1710 - 1714 . At block  1710 , it may be determined whether an exit condition has been satisfied. In some implementations, the exit condition may be whether a desired number N (positive integer) of hypothetical crop yield predictions has been generated. Additionally or alternatively, in some implementations, the exit condition may be whether the latest hypothetical crop yield prediction exceeds some predetermined threshold (at which point that hypothetical crop yield prediction may be used to generate recommended operational changes). Such a predetermined threshold may be, for instance, whether the hypothetical crop yield prediction is sufficiently greater than the ground-truth-based crop yield prediction generated at block  1706 . Additionally or alternatively, in some implementations, other exit conditions may be used, such as whether a sufficient number of hypothetical crop yield predictions that exceed the ground-truth based crop yield prediction have been generated (e.g., to ultimately provide more recommended operational changes to choose from). 
     If the answer at block  1710  is no, then at block  1712 , the system may alter one or more data points of the ground truth operational data to generate an instance of hypothetical operational data. For example, an amount of nitrogen, fertilizer, water, etc., may be altered from the ground truth data that was actually applied to a different amount, which may be greater than or less than the ground truth. Additionally or alternatively, a frequency of application of one or more chemicals or water, or other parameter of operational data, may be altered. Additionally or alternatively, in some implementations, observational data may be altered to determine the impact of its constituent factors on predicted crop yield. For example, rather than predicting a hypothetical crop yield that would have occurred with more irrigation, a hypothetical crop yield might be predicted for a greater amount of natural precipitation. 
     At block  1714 , the system may generate a distinct hypothetical crop yield prediction based on the hypothetical operational data generated at block  1712 . The hypothetical crop yield prediction may be distinct insofar as it is generated using hypothetical operational that is different in some respect from hypothetical operational data to generate other hypothetical crop yield predictions. In some implementations, each distinct hypothetical crop yield prediction may be generated at block  1714  by applying the high-elevation digital images of the first temporal sequence and temporal chunks of hypothetical operational data as input across the machine learning model. Control of method  1700  may then pass back to block  1710 . Blocks  1710 - 1714  may repeat for as long as necessary or desired, which may be set by choosing a particular exit condition. 
     Back at block  1710 , if the stop condition is satisfied, then method  1700  may proceed to block  1716 . At block  1716 , the system may identify the one or more recommended operational changes based on one or more of the altered data points that were used to generate one or more of the hypothetical crop yield predictions. In some implementations, only hypothetical crop yield predictions that are greater than the ground truth-based crop yield prediction may be considered, because intuitively, the goal is usually to increase crop yield. For example, if increasing a particular pesticide generated a hypothetical crop yield prediction that is considerably greater than the ground truth-based crop yield prediction, a recommended operational change may be to increase the amount of pesticide moving forward (this may suggest a previously undetected or under-detected pest infestation). However, this is not required. 
     At block  1718 , the system may cause one or more output components of one or more computing devices, such as client device  106   N  in  FIG.  1    or the display of a computing device installed in a tractor, to audibly or visually convey one or more of the recommended operational changes, e.g., as part of crop prediction client  109 . Additionally or alternatively, in some implementations, at block  1720 , the system may generate one or more commands and transmit those commands to autonomous and/or semi-autonomous farm machinery, such as autonomous tractors, irrigation systems, etc., to cause those farm machinery to implement the recommended operational changes automatically. 
       FIG.  18    is a block diagram of an example computer system  1810 . Computer system  1810  typically includes at least one processor  1814  which communicates with a number of peripheral devices via bus subsystem  1812 . These peripheral devices may include a storage subsystem  1824 , including, for example, a memory subsystem  1825  and a file storage subsystem  1826 , user interface output devices  1820 , user interface input devices  1822 , and a network interface subsystem  1816 . The input and output devices allow user interaction with computer system  1810 . Network interface subsystem  1816  provides an interface to outside networks and is coupled to corresponding interface devices in other computer systems. 
     User interface input devices  1822  may include a keyboard, pointing devices such as a mouse, trackball, touchpad, or graphics tablet, a scanner, a touchscreen incorporated into the display, audio input devices such as voice recognition systems, microphones, and/or other types of input devices. In general, use of the term “input device” is intended to include all possible types of devices and ways to input information into computer system  1810  or onto a communication network. 
     User interface output devices  1820  may include a display subsystem, a printer, a fax machine, or non-visual displays such as audio output devices. The display subsystem may include a cathode ray tube (CRT), a flat-panel device such as a liquid crystal display (LCD), a projection device, or some other mechanism for creating a visible image. The display subsystem may also provide non-visual display such as via audio output devices. In general, use of the term “output device” is intended to include all possible types of devices and ways to output information from computer system  1810  to the user or to another machine or computer system. 
     Storage subsystem  1824  stores programming and data constructs that provide the functionality of some or all of the modules described herein. For example, the storage subsystem  1824  may include the logic to perform selected aspects of the methods described herein, and/or to implement one or more components depicted in prior figures. 
     These software modules are generally executed by processor  1814  alone or in combination with other processors. Memory  1825  used in the storage subsystem  1824  can include a number of memories including a main random access memory (RAM)  1830  for storage of instructions and data during program execution and a read only memory (ROM)  1832  in which fixed instructions are stored. A file storage subsystem  1826  can provide persistent storage for program and data files, and may include a hard disk drive, a floppy disk drive along with associated removable media, a CD-ROM drive, an optical drive, or removable media cartridges. The modules implementing the functionality of certain implementations may be stored by file storage subsystem  1826  in the storage subsystem  1824 , or in other machines accessible by the processor(s)  1814 . 
     Bus subsystem  1812  provides a mechanism for letting the various components and subsystems of computer system  1810  communicate with each other as intended. Although bus subsystem  1812  is shown schematically as a single bus, alternative implementations of the bus subsystem may use multiple busses. 
     Computer system  1810  can be of varying types including a workstation, server, computing cluster, blade server, server farm, or any other data processing system or computing device. Due to the ever-changing nature of computers and networks, the description of computer system  1810  depicted in  FIG.  18    is intended only as a specific example for purposes of illustrating some implementations. Many other configurations of computer system  1810  are possible having more or fewer components than the computer system depicted in  FIG.  18   . 
     While several implementations have been described and illustrated herein, a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein may be utilized, and each of such variations and/or modifications is deemed to be within the scope of the implementations described herein. More generally, all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific implementations described herein. It is, therefore, to be understood that the foregoing implementations are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, implementations may be practiced otherwise than as specifically described and claimed. Implementations of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the scope of the present disclosure.