Combining randomized field experiments with observational satellite data to assess the benefits of crop rotations on yields

Our study region was the Corn Belt of the United States, which is characterized by high-yielding commercial agriculture for corn and soybeans and contributes nearly 30% of the global production for these crops [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib30" id="fnref-erlac6083bib30"="">30</a>]. We focus on a nine-state region within the Corn Belt (figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f1"="">1</a>) spanning the 19 year period from 2000 to 2018 due to availability of yield data.

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Our observational satellite-dataset consisted of 180 000 randomly sampled 30 <b="">×</b> 30 m agricultural pixels from the nine-state study region. For each pixel and for each year in the study span, the dataset contained information on yield, crop rotation, as well as weather and soil covariates. Our yield data was taken from previously published yield maps for corn [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib31" id="fnref-erlac6083bib31"="">31</a>] and soybean [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib32" id="fnref-erlac6083bib32"="">32</a>] that were produced using the Scalable Crop Yield Mapper [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib31" id="fnref-erlac6083bib31"="">31</a>–<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib34" id="fnref-erlac6083bib34"="">34</a>], a method that estimates yields using a combination of satellite data and crop modelling simulations. For each year and pixel in our dataset, crop type was determined using satellite-based crop maps [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib35" id="fnref-erlac6083bib35"="">35</a>, <a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib36" id="fnref-erlac6083bib36"="">36</a>]. Crop rotation within each 2 year window was inferred from this data and was categorized into five types of observed rotations: corn planted before corn (CC), soybean planted before corn (SC), soybean planted before soybean (SS), corn planted before soybean (CS), and rotations involving other crops. Our analysis ignores rotations involving other crops, because the specific crop type among the other crops could not be determined with accuracy that was close to that of the corn and soybean classifications and because yield maps were not available for the other crops. Weather and soil covariates were extracted from a combination of sources [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib37" id="fnref-erlac6083bib37"="">37</a>–<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib40" id="fnref-erlac6083bib40"="">40</a>], and the pre-selected covariates are summarized in table <a xmlns:xlink="http://www.w3.org/1999/xlink" class="tabref" href="#erlac6083t1"="">1</a>.

Our experimental dataset came from two open-source datasets [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib5" id="fnref-erlac6083bib5"="">5</a>, <a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib6" id="fnref-erlac6083bib6"="">6</a>], each containing the yield data from multiple different randomized field experiments in North America. For assessing the benefit of rotation on corn yields we selected experiments that contained instances of both SC and CC, and for assessing the benefit of rotation on soybean yields we selected experiments that contained instances of both CS and SS (see section M.2.2 for our other inclusion criteria). Our final dataset consisted of 11 experiments, each lasting at least three years, and combined they included 89 site-years of yield data and spanned the years 2000–2016. All experiments in our final dataset were completely randomized block designs with 2–5 replications per site [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib42" id="fnref-erlac6083bib42"="">42</a>–<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib46" id="fnref-erlac6083bib46"="">46</a>]. In figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f1"="">1</a>, we see that the 11 experiments in our final dataset were spread out throughout the Corn Belt and were conducted in a variety of climatic conditions. Despite this variety, our dataset contained no experiments from certain states, only one experiment in a climate with low early season precipitation, and only one experiment in a climate with a large number of extreme degree days.

Throughout the text, we will use the term 'rotation benefit' to denote the causal effect of crop rotation on yield (or equivalently, the term denotes the treatment effect for a setting where the treatment variable is crop rotation and the outcome variable is yield). In this subsection, we describe three approaches for estimating the rotation benefits. One uses only the satellite-based dataset, the second uses only the experimental dataset, and the third is our proposed hybrid approach which uses both the experimental and satellite-based dataset.

To estimate the benefit of crop rotation on yield using only satellite-based observations, we fit causal forests [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib47" id="fnref-erlac6083bib47"="">47</a>, <a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib48" id="fnref-erlac6083bib48"="">48</a>] using the grf R package [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib49" id="fnref-erlac6083bib49"="">49</a>]. The causal forest method is a recent adaptation of the classical random forest algorithm [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib50" id="fnref-erlac6083bib50"="">50</a>] designed for estimation and inference of causal effects in settings where it is of interest either to understand how the causal effects vary as a function of the covariates in the model or to predict the causal effect for specific samples. For example, in our setting, a causal forest can be used to investigate how the causal effect of crop rotation on yield varies as a function of the weather and soil covariates, and it can also be used to predict the effect of crop rotation on yield for a field with known weather and soil covariates. The causal forest method has previously been used to study the effect of tillage on crop yields [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib16" id="fnref-erlac6083bib16"="">16</a>], the impact of weather on agricultural productivity [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib51" id="fnref-erlac6083bib51"="">51</a>], and the effectiveness of forest management policies [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib52" id="fnref-erlac6083bib52"="">52</a>], fishery policies [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib53" id="fnref-erlac6083bib53"="">53</a>], and growth mindset interventions [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib54" id="fnref-erlac6083bib54"="">54</a>].

Letting <em="">x</em> denote the vector of our covariates (see table <a xmlns:xlink="http://www.w3.org/1999/xlink" class="tabref" href="#erlac6083t1"="">1</a>), our first causal forest learned a function which we call ECRB<sub="">Sat</sub>(<em="">x</em>), denoting the satellite-based estimated corn rotation benefit. In particular, ECRB<sub="">Sat</sub>(<em="">x</em>) is an estimate of the average second-year corn yield in a soybean-corn rotation minus that in a corn-corn rotation, stratified by the specific year, geolocation, soil covariates and weather covariates encoded in <em="">x</em>. Analogously, we fit a separate causal forest to learn a function ESRB<sub="">Sat</sub>(<em="">x</em>), the satellite-based estimated soybean rotation benefit. It should be emphasized that ECRB<sub="">Sat</sub>(<em="">x</em>) and ESRB<sub="">Sat</sub>(<em="">x</em>) may not give reliable estimates of the causal effect of rotation on corn and soy, because they can be biased due to unmeasured confounders (such as fertilizer) and because of errors in the treatment and outcome variables (the rotation and yield variables in this observational dataset were estimated using satellite imagery). See section M.3.1 for more details and discussion about the quantities ECRB<sub="">Sat</sub>(<em="">x</em>) and ESRB<sub="">Sat</sub>(<em="">x</em>).

In the second approach, rotation benefits were estimated using only the experiments. In each site $s$, for each year $t$, we estimated the effect of rotation on corn yield by taking the difference of means between SC subplots and CC subplots:

$$\begin{align}{\text{ECR}}{{\text{B}}_{{\text{Exp}}}}\left( {s,t} \right) & = {\text{average yield across SC subplots }} \nonumber\\ & \quad - {\text{ average yields across CC subplots}}.\end{align}$$

Similarly, for each site <em="">s</em> and year <em="">t</em>, we estimated the experimental benefit of rotation on soybean yields with

$$\begin{align}{\text{ESR}}{{\text{B}}_{{\text{Exp}}}}\left( {s,t} \right) & = {\text{average yield across CS subplots }} \nonumber\\ & \quad - \,{\text{average yield across SS subplots}}{\text{. }}\end{align}$$

Because most sites did not have yield data for a continuous soybean rotation, we were only able to calculate ${\text{ESR}}{{\text{B}}_{{\text{Exp}}}}\left( {s,t} \right)$ at three out of the 11 experimental sites in our study. For details on inclusion criterion for the subplots, see section M.3.2.

For our hybrid approach, we leverage both the experimental dataset and the satellite-based observational dataset by fitting a linear calibration of the ECRB_Sat values at the experimental sites towards the ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}$ values. In particular, at each experimental site s and year t, we used the precise latitudes and longitudes of the experimental site to determine the covariate vector $x\left( {s,t} \right)$ and compute ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}\left( {x\left( {s,t} \right)} \right)$ using the previously fitted causal forest. Using all the site and year combinations that had both ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}\left( {x\left( {s,t} \right)} \right)$ and ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}\left( {s,t} \right)$ estimates, we fit the following mixed effects regression model

$$\begin{align*}{\text{ECR}}{{\text{B}}_{{\text{Exp}}}}\left( {s,t} \right) & = a + b \times {\text{ECR}}{{\text{B}}_{{\text{Sat}}}}\left( {x\left( {s,t} \right)} \right) + {\alpha _s} + {\beta _t} \nonumber\\ & \quad + {\varepsilon _{s,t}},\end{align*}$$

where ${\alpha _s}$ is a random effect for site, ${\beta _t}$ is a random effect for year, and ${\varepsilon _{s,t}}$ is mean zero, independent Gaussian noise with variance that depends on the number of SC and CC subplots at each site. After fitting the mixed effects model, we used the estimated intercept $\hat a$ and slope $\hat b$ to construct a calibrated estimate of the effect of crop rotation on corn yield for any choice of covariate vector x:

$$\begin{equation*}{\text{ECR}}{{\text{B}}_{{\text{Calib}}}}\left( x \right) = \hat a + \hat b \times {\text{ECR}}{{\text{B}}_{{\text{Sat}}}}\left( x \right).\end{equation*}$$

Because we only had three distinct experimental sites with continuous soybean yield data, to calculate calibrated estimates of the soybean rotation benefit, ${\text{ESR}}{{\text{B}}_{{\text{Calib}}}}\left( x \right),$ we fit a more parsimonious calibration model, producing calibrations of the form ${\text{ESR}}{{\text{B}}_{{\text{Calib}}}}\left( x \right) = \hat c + {\text{ESR}}{{\text{B}}_{{\text{Sat}}}}\left( x \right)$. See section M.3.3 for more details on the calibration and discussion about the modelling choices. Variants of the above approaches for estimating the rotation benefit that were attempted but not ultimately included in this manuscript are acknowledged in section M.5.

To estimate the errors associated with our calibration approach in predicting the experimental rotation effect on corn yield at an unobserved experimental site, we used a variant of leave-one-out cross validation (see section M.4 for a description of the leave-one-out cross validation approach used and the alternative prediction approaches that were used for a comparison). The leave-one-out cross validation was only performed for corn rotation benefits and not for soybean rotation benefits because only three experimental sites had available yield data from both CS and SS subplots.

The satellite-based and experimental estimates for the benefit of crop rotation are visualized in Figures S2 and S3 for corn and soy, respectively. As expected, we generally see a positive effect of rotation on both corn and soybean yield, although the observational corn rotation benefit, ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$, is negative in some regions. We suspect that in many of the regions where ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$ is negative, rotation still has a positive effect on corn yields, and the apparent harm of rotation is due to bias in the uncalibrated satellite-based estimates (although, there could be some cases where the causal effect of rotation on corn yield is truly negative).

To directly visualize how correlated the satellite-based estimates are with the experiment-based estimates, we create a scatterplot of ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}\left( {x\left( {s,t} \right)} \right)$ versus ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}\left( {s,t} \right)$ (figure 2, top) and ${\text{ESR}}{{\text{B}}_{{\text{Sat}}}}\left( {x\left( {s,t} \right)} \right)$ versus ${\text{ESR}}{{\text{B}}_{{\text{Exp}}}}\left( {s,t} \right)$ (figure 2, bottom). Each point in the scatter plot corresponds to one year of data at one site.

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We observe a significant positive correlation between ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}$ and ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$, but with clear differences between the two estimates. In particular, the satellite-based estimates exhibit a much smaller range than the experimental estimates, which is not surprising for two reasons. First, due to inaccurate classifications of the rotation in the satellite-based dataset, we expect the satellite-based estimates to be biased towards zero by a multiplicative factor smaller than 1 (this well-established phenomena [55-57] is known as attenuation bias, and a mathematical justification for this phenomena in the setting of a causal forest is presented in appendix B). Second, satellite-based estimates are estimated using a large sample and therefore are not very noisy, whereas each experimental estimate is based on yields from only a few subplots. The experimental estimates are therefore much noisier (see 95% confidence intervals on figure 2), and hence the extreme positive and negative experimental benefits can be partially explained by noise. The noise in the experimental estimates can also partially explain some unexpected observations where ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}$ is negative and ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$ is positive. Despite the inconsistencies between satellite-based estimates and experimental estimates, the differing ranges of the two types of estimates and the apparent positive association between ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}$ and ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$, suggest the benefits of using our linear calibration approach over a satellite-only approach.

We fit the model described in section M.3.3 and estimated $\hat a = 0.58$ (95% CI = [0.00, 1.15]) and $\hat b = 1.75$ (95% CI = [0.37, 3.12]). These confidence intervals are based on the estimated standard errors in the mixed effects model, and the positive confidence interval for $b$ gives evidence that there is a positive association between ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$ and ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}.$ To confirm the statistical significance of the positive association between ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$ and ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}$ we also ran 10 000 iterations of the cluster bootstrap, where the experiments were sampled with replacement, but the data within each experiment was not (see for example, 'Strategy 1' in section 3.8 of [58]). The 95% bootstrap confidence interval for the Pearson correlation between ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$ and ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}$ was [0.03, 0.36] and the 95% bootstrap confidence interval for the linear regression slope of ${\text{ECR}}{{\text{B}}_{{\text{Exp}}}}$ on ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$ was [0.33, 4.11].

For soybean calibration, the additive bias correction term $\hat c$ was equal to 0.003 t ha⁻¹ (95% CI = [−0.10, 0.11]). Therefore, our calibrated estimates, ${\text{ESR}}{{\text{B}}_{{\text{Calib}}}}$, and our satellite-based estimates, ${\text{ESR}}{{\text{B}}_{{\text{Sat}}}}$, are nearly identical, and some readers may prefer to interpret our plots of ${\text{ESR}}{{\text{B}}_{{\text{Calib}}}}$ as simply plots of ${\text{ESR}}{{\text{B}}_{{\text{Sat}}}}$ values.

The results for the leave-one-out cross validation indicate that the hybrid calibration approach is better at predicting the rotation benefits in an unobserved experimental site than various reasonable approaches to using only the experimental data (table <a xmlns:xlink="http://www.w3.org/1999/xlink" class="tabref" href="#erlac6083t2"="">2</a>). We also found that the hybrid calibration is better at predicting the treatment in an unobserved experimental site than using only the observational data. Overall, the hybrid approach resulted in errors that were 13% lower than using experimental data alone, and 26% lower than using the satellite data alone. The second and third rows of table <a xmlns:xlink="http://www.w3.org/1999/xlink" class="tabref" href="#erlac6083t2"="">2</a> indicate that these findings are not sensitive to our calibration model choices of including a random effect for site and year and our choice of not including tillage in the model. In table S2, we consider an additional sensitivity check to see if our conclusions would still hold had we taken a weighted average rather than a standard average of the squared prediction errors when performing leave-one-out cross validation.

Table 2. Comparison of errors associated with various methods of predicting the average experimental effects. Each entry is reported in terms of root mean squared error (t ha⁻¹) when using leave-one-out cross validation. In columns 3–8, values were calculated by fitting the model in section M.3.3 when the ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}\left( {x\left( {s,t} \right)} \right)$ term is dropped and is either not replaced (column 3), or replaced by one weather covariate (columns 4–7), or replaced by all four weather covariates in a multivariate regression (column 8). In the first row, the preferred mixed effects model is used. The second row includes a sensitivity check where we drop the random effects for site and year from the calibration model and fit a linear model instead. The third row includes another sensitivity check where we add an indicator of whether each experimental subplot had tillage as a variable in the mixed effects calibration model. The entries with the lowest root mean square error in each row are in bold.

	Satellite only	Experiment only		Experiment plus weather covariates					Hybrid
	Just predict with${\text{ ECR}}{{\text{B}}_{{\text{Sat}}}}$	Nearest experiment	All other experiments	Early season precipitation	Growing season precipitation	GDD	EDD	All four weather covariates	Calibration approach (section M.3.3)
Preferred model	0.99	0.97	0.84	0.77	0.83	0.88	0.83	0.83	0.73
Linear model	0.99	0.97	0.84	0.75	0.84	0.92	0.87	0.82	0.73
Tillage model	0.99	1.24	0.92	0.88	0.92	0.96	0.92	0.93	0.84

These tables suggest that the hybrid calibration approach of section M.3.3 performs the best overall in predicting the experimental rotation benefit at a held-out site (see section M.4, for explanation of the term 'held-out site'), but it does not perform substantially better than fitting a model that uses just the experimental data and the early season precipitation weather covariate. However, whereas the hybrid calibration approach was a principled choice in the absence of <em="">a priori</em> knowledge about which weather covariates are associated with the actual rotation benefits, the model with early season precipitation was merely found to perform well empirically, among four possible choices of weather covariates, on a dataset with a small number of different experiments.

Having established that the calibration leads to improved estimates of the effect of rotation on corn yields, we visualize a map of these calibrated effects in figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f3"="">3</a> (top). We also visualize ESRB<sub="">Calib</sub> in figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f3"="">3</a> (bottom), but we emphasize that because we have only three experiments with continuous soybean data, our calibration merely accounted for additive bias rather than both additive bias and multiplicative bias, and the approach was not validated on held-out data. The causal effects of rotation on yield were found to be geographically heterogenous, with corn yields benefitting most from rotation in the northwest parts of the Corn Belt and soybean yields benefitting most from rotation in the southern and central parts.

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We can also see from figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f3"="">3</a> that the calibrated rotation benefits for corn yield are generally positive. While only 91.5% of ECRB<sub="">Sat</sub> values are positive, 99.8% of ECRB<sub="">Calib</sub> values are positive (one sided 95% CI = [91%, 100%], using the same cluster bootstrap as in section <a xmlns:xlink="http://www.w3.org/1999/xlink" class="secref" href="#erlac6083s3-1"="">3.1</a>), implying that the causal effect of rotation on corn yields is negative less often than observational data alone would suggest.

A key benefit of using observational data in addition to experimental data is the ability to study the rotation benefits under weather conditions that were not observed in the experimental data. In figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f4"="">4</a>, we plot a heatmap of our calibrated estimates of the rotation benefit for soybean and corn yields as a function of temperature and precipitation, with points indicating the weather covariates observed at experimental sites.

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We observe that the corn rotation benefit is smaller at high temperatures and low growing season precipitation values, but this likely could not be inferred from experimental data alone as only one site-year was observed to have temperature greater than 2400 growing degree days and growing season precipitation less than 500 mm. The lower absolute effects of rotation on corn yield in the high temperature and low precipitation regime are perhaps partly explained by these conditions leading to lower corn yields in general [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib59" id="fnref-erlac6083bib59"="">59</a>–<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib61" id="fnref-erlac6083bib61"="">61</a>]. Heatmaps of ECRB<sub="">Calib</sub> as a function of other temperature and precipitation variables are presented in figure S4. While it appears that the benefit of rotation on corn yield is particularly high when at the lowest observed early season precipitation values, this phenomenon only occurs in a narrow window of temperature values and is potentially an artifact of most of such points being in South Dakota, where the rotation benefit is seen to be particularly high. This phenomenon may also be explained by the greater uncertainty and inaccuracy of our estimates near the boundary of covariate space, which we discuss below.

We caution readers that near the boundaries of the heatmaps (e.g. outside 1st–99th percentile range for the covariates) in figures 4, S4 and S5, the estimated rotation benefits have higher uncertainty and are likely less accurate than those well within the interior of the heatmaps for two reasons. First, at each point near the boundary of covariate space, there are fewer samples within a neighborhood of that point, so the causal forest model will return ${\text{ECR}}{{\text{B}}_{{\text{Sat}}}}$ oder ${\text{ESR}}{{\text{B}}_{{\text{Sat}}}}$ values that have higher variance. Second, the points near the boundary of covariate space are further away from the experimental sites, so if the true relationship between the satellite-based rotation benefits and the experimental-based rotation benefits is not the linear model described in section M.3.3, the extrapolation errors of using this calibration model will be largest near the boundary.

For soybean we observe a different and clearer pattern (figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f4"="">4</a>, bottom). When the number of growing degree days is high, the rotation benefit for soybean yields is high and the opposite is true when the number of growing degree days is low. Intriguingly, this pattern is not observed when we measure temperature with extreme degree days rather than growing degree days, and in fact, for a fixed value of growing degree days, the benefit of rotation on soybean yields does not increase with extreme degree days (figure S5).

As a complimentary analysis to the heatmaps in figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f4"="">4</a>, we compute the average calibrated rotation benefits in the top and bottom quintile for temperature (GDD). The average calibrated corn rotation benefit was 0.85 versus 1.19 t ha<sup="">−1</sup> across observations in the top and bottom quintile of GDD values, respectively. For soybean yields, we observe the opposite pattern where the rotation benefit is larger with higher temperatures. In particular, the average calibrated soybean rotation benefit was 0.24 versus 0.16 t ha<sup="">−1</sup> across observations in the top and bottom quintile of GDD values, respectively. For reference, across the whole dataset, the average calibrated corn rotation benefit across the Corn Belt was 1.03 t ha<sup="">−1</sup> and the average calibrated soybean rotation benefit was 0.21 t ha<sup="">−1</sup>.

We also check whether there is a clear temporal trend in rotation benefits during the 19 year study period. In figure S6, we see that there is no clear or substantial temporal trend in the rotation benefits for either corn or soybean. It appears that ECRB<sub="">Calib</sub> has a slight positive trend while the ESRB<sub="">Calib</sub> values may have a slightly negative trend throughout the duration of the study period, a phenomenon which would be explainable by decreasing temperatures in the Corn Belt between 2000 and 2019.

We recognize several limitations of this study. First, there were only three experimental sites for assessing soybean rotation benefit in our dataset. These three sites were not representative of the entire Corn Belt, as they were geographically clustered (figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f3"="">3</a>, bottom) and did not contain any observations at lower temperatures (figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f4"="">4</a>, bottom). Therefore, the calibration fitted to the three experiments may not extrapolate as well to western, northern, and eastern parts of the Corn Belt and to settings with lower temperatures, and future studies on soybean rotation benefit should collate a larger and more diverse set of experiments if possible. While calibration suffers in such settings with a limited collection of experimental sites, our example highlights that in such settings, observational data is especially critical for addressing external validity issues.

Second, our analysis implicitly assumed that the experimental data gave unbiased estimates of the rotation benefits, as our proposed approach involved transforming the satellite-based estimates to better match the experimental estimates. In reality, the experimental estimates could be based on a biased sample, as experimental sites that observed an unexpected negative rotation benefit may have been more likely to be excluded from the two experimental databases we used [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib5" id="fnref-erlac6083bib5"="">5</a>, <a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib6" id="fnref-erlac6083bib6"="">6</a>] (e.g. [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib6" id="fnref-erlac6083bib6"="">6</a>], identified experimental sites to include in their database via a literature search, so their collection of sites could be subject to publication bias).

Third, by only looking at the crop type in 2 year windows, our analysis does not directly address the relevant question of quantifying the long-term rotation benefits in the corn-soybean rotation. Further complicating the matter, a sizable percentage of both the experimental dataset and the satellite-based dataset that we used involved farms with a corn-soybean rotation over a long period of time, meaning that our approach is likely estimating some weighted average of the short-term and long-term rotation benefits. Future work can analyze crop rotations using more sophisticated and longer-term rotational diversity scores such as the one proposed in [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib62" id="fnref-erlac6083bib62"="">62</a>].

Fourth, we merely provide point estimates and do not provide standard errors for our calibrated estimates. The standard errors for the calibrated estimates might be quite large due to the small number of experiments, large noise in the experimental estimates, and propagation of the noise in the satellite-based estimates.

Despite these limitations, our findings about the relationship between temperature corn rotation benefits are consistent with recent results in the literature (see appendix D for a more detailed comparison with results from [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib46" id="fnref-erlac6083bib46"="">46</a>], a study which uses 11 long-term experimental sites). In addition, as we discuss next, our findings about the corn and soybean rotation benefits are consistent with current understanding of why rotation is beneficial for each crop.

Pest pressure could largely explain our findings that the benefit of crop rotation on soybean yields is larger in observations with higher temperatures (in GDD, but not in EDD). It is well established that the benefits of crop rotation for soybean yields result largely because of reductions in pest pressure. For example, [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib63" id="fnref-erlac6083bib63"="">63</a>] found that the benefit of rotation on soybean yields in two Louisiana experiments was largely explained by a reduction in soybean cyst nematode and [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib64" id="fnref-erlac6083bib64"="">64</a>] found crop rotation to be effective in reducing soybean cyst nematode. Meanwhile, using pesticide application rate as a proxy for pest pressure, [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib65" id="fnref-erlac6083bib65"="">65</a>] showed that increased yearly minimum temperatures are associated with increased pest pressure, as many agricultural pests are not able to survive low winter temperatures. Therefore, in warmer conditions, we would expect there to be higher pest pressure on soy, rendering crop rotation a more beneficial management practice in increasing soybean yields because of its effectiveness in reducing pest pressure.

To explore the hypothesis that ESRB is larger in warmer conditions due to increased pest pressure, we plot pesticide use per acre versus ESRB values in figure <a xmlns:xlink="http://www.w3.org/1999/xlink" href="#erlac6083f5"="">5</a>. Because pesticide use on soybean crops is thought to be a proxy for pest pressure on soybeans (pesticides tend to be applied after pests are reported in the region), the figure indicates that soybean rotation benefit tends to be higher under conditions with greater pest pressure.

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The mechanisms driving the rotation benefit for corn are different than those for soybean. While crop rotation also alleviates pest pressure on corn, pest pressure reduction is unlikely to be the main reason that corn benefits from crop rotation because of the prevalence of effective pest-resistant corn hybrids (for example, in 2020 Bt corn represented 82% of US corn acreage, while Bt soybeans were not yet commercially available [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib68" id="fnref-erlac6083bib68"="">68</a>]). Instead, the rotation benefit for corn is largely driven by effects on soil nitrogen. Fixation of atmospheric nitrogen in soybean benefits the subsequent corn yields, whereas corn residues can compete for nitrogen with the subsequent crop. Soybean nitrogen fixation is less efficient at higher temperatures [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib69" id="fnref-erlac6083bib69"="">69</a>], while mineralization of nitrogen from corn residues occurs at a faster rate at higher temperatures [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib70" id="fnref-erlac6083bib70"="">70</a>, <a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib71" id="fnref-erlac6083bib71"="">71</a>], which would tend to reduce nutrient limitations. These mechanisms would both serve to reduce the benefit of rotation for subsequent corn crops at higher temperatures.

Beyond nutrient dynamics, crop residues can also affect corn by lowering early season soil temperatures, which can inhibit early season corn growth when temperatures are low [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib72" id="fnref-erlac6083bib72"="">72</a>]. This effect is diminished in rotation because soybean produces less residues than corn. Thus, the penalty from growing two consecutive corn crops (i.e. the benefit of rotating) would be smaller at higher temperatures. We investigated the influence of crop residues on rotation benefits using previous year county-level crop yields [<a xmlns:xlink="http://www.w3.org/1999/xlink" class="cite" href="#erlac6083bib66" id="fnref-erlac6083bib66"="">66</a>] as a proxy for residues; however, the results of this additional analysis suggested that either the impacts of crop residues on rotation benefits are relatively minor compared to the impacts of temperature or that previous year county-level yields are a poor proxy for crop residues (see appendix D).