Introduction

Animal production using grazed pastures depends on the rate of accumulation of forage mass (FM), as well as on the timely allocation of an adequate stocking rate to take advantage of the FM; other important aspects are nutritional quality and seasonality in the rate of accumulation of FM. Cost-effective management of a pasture through direct grazing involves, among other things, implementing grazing management without compromising vegetation cover regrowth, as well as accurately knowing the FM in the pasture before and after grazing¹. Traditionally, FM is measured directly with forage cuts in quadrants of known area, distributed in a spatially representative manner and in a sufficient number that represents the variability of the vegetation cover in the pasture^2,3. The cutting of quadrants is laborious and therefore methods and devices have been developed for the indirect estimation of FM^4-6. Pasture canopy height, measured with a sward stick, is useful to represent the FM, although the relationship may be different depending on the botanical composition, density of the pasture canopy and season of the year^7-9. The height of the compressed forage measured with a rising plate meter estimates the FM considering the density of the canopy and is a very common practice at the farm level in countries such as New Zealand². The relationship between canopy height and FM in ryegrass and white clover pastures is well known and routinely applied in New Zealand¹⁰; for pastures with other forage species such as alfalfa, more research is needed to determine the relationship between canopy height and FM⁸.

Remote sensing (RS) by orbital satellites measures spectral reflectance, the proportion of incident energy reflected by the Earth’s surface at different wavelengths; these measurements have been associated with vegetation activity processes¹¹. With RS information, it is also possible to estimate environmental variables such as temperature, rainfall, and others¹². The wide availability and free access of RS products is an opportunity to explore crop dynamics and establish relationships with productive parameters, such as FM. The time series available for different RS products allow retrospective studies to be made, which is valuable for evaluating pasture management practices and regional grassland studies. However, the spatial scale of measurement is coarse in some RS sensors and is an important disadvantage in studies such as the one described in this research.

Recently, a variety of machine learning (ML) algorithms have been incorporated into regression analysis and they are an alternative to ordinary least squares (OLS) regression. Photosynthesis in ecosystems, named gross primary productivity and net primary productivity (when discounting losses by respiration), has been modeled with empirical or mechanistic approaches, from OLS models to those that simulate ecophysiological processes at the global level based on RS¹³. Net primary productivity includes photosynthetic partitioning into aerial and root biomass and therefore does not reflect the FM available for grazing. Lang et al¹⁴ estimated arid grassland production using measurements from rainfall RS sensors, spectral reflectance obtained from the Landsat 7 satellite and random forest; a ML algorithm. Using Neural Networks, another ML-type algorithm, Chen et al¹⁵ related the spectral reflectance measured by the Sentinel-2 satellite and FM on dairy farms of Tasmania in Australia. In these studies, the coefficient of determination (r²) in different models was between 0.6 and 0.7. Conceptually, it is important to incorporate humidity conditions, in the short or medium term, to explain the carrying capacity of the grassland¹⁶, since water is the main limiting resource of plants in arid and semi-arid environments. The conditions of water availability for plants can be represented by the precipitation (P) that occurred, water available in the soil or vapor deficit in the atmosphere. However, to explain the FM, not only the P occurred in the period of accumulation of the FM (month in which the FM was measured) is important, but also the humidity conditions that occurred in previous months.

In the present work, the relationship between FM and pasture height was examined as a baseline to compare other models that used meteorological variables obtained by RS or in conjunction with variables representative of pasture management (PM) conditions; such as the grazing and rest periods of the grazed area or the pasture height itself. In particular, the usefulness of models to predict FM based on previous rainfall and temperature conditions in different time windows was explored; for example, the P accumulated in the previous month, in two months or three months before the measurement of the FM. The objective was to obtain a predictive model of FM that could be incorporated into grazing planning. For this purpose, three years of measurements on a mixed of alfalfa-grass pasture grazed by beef cattle, were used.

Material and methods

Results and discussion

The average of FM of the pasture was 2,134 kg DM ha^-1 with a seasonal pattern of lower production in winter and higher production in summer (Figure 1a). FM was different among the three years 2,121, 1,770 and 2,392 kg ha^-1 for 2008 to 2010 (P<0.05). The rainfall was 636, 382 and 552 mm, respectively. The greatest amount of rainfall was from July to September; for 2010, February was atypical with 151 mm (Figure 1b) and possibly positively impacting the FM from March in that year. The rainfall recorded by the IMERG product in 2008 and 2010 was higher than that recorded by the climatological station closest to the study site; this rainfall estimate was considered accurate because this product has shown good agreement with terrestrial precipitation records³⁰. The seasonal behavior of the FM suggested an important effect of rainfall, even in the case of this irrigated pasture. April and May were the months with the highest average LST_d (Figure 1c). The difference between LST_d and LST_n was greater from April to May (28.5 and 27.3 °C) and lower in July to September (17.3, 16.4 and 15.6 °C); which indicates the site’s extreme characteristic of the climate during the spring. These environmental conditions were also reflected in seasonal changes in pasture management on rest days, forage height, and PAR (Figure 2).

Figure 1 Environmental variables and production of a mixed alfalfa-grass mixed pasture grazed by beef cattle: a) forage mass (FM), b) rainfall (P) and c) diurnal (●) and nocturnal (○) surface temperature (LST) 

Figure 2 Management of a mixed alfalfa-grass mixed pasture grazed by beef cattle during 2008 (●), 2009 (○) and 2010 (■): a) Rest days before grazing, b) rate of accumulation of forage (PAR) of the period, c) pasture height 

In MA regression, the intercept was numerically close to 0 in the ML_RS_PM scenario and its slope was equal to 1, a model with slope equal to 1 and intercept equal to 0 indicates good fit. The lower value of the RMSE, AIC, BIC and deviance suggested a better representation of the FM with the ML_RS_PM scenario (Table 1). Regarding deviance analysis, the comparison between two or more models will be valid if they fit the same data set, this requirement was not met because the predicted values of FM were inherently different for each model generated. The difference of deviances is distributed approximately as X² with degrees of freedom equal to the difference in the number of parameters between the models¹⁴, with this difference being 0 for the case of simple linear regression models used to represent the relationship between estimated and predicted values in each modeling scenario. For these two reasons, deviance analysis was not possible; therefore, the selection of the best model was based solely on the numerical value of the goodness-of-fit measures. The worst model was the simple regression between FM and H_pasture, not only according to the goodness-of-fit means but also in the graphical representation of the estimated vs. observed values (Figure 3).

a) OLS, predictor variable forage height; b) OLS_RS scenario; c) OLS_RS_PM scenario; d) ML_RS scenario; e) ML_RS_PM scenario. Coefficient of determination (r²), root mean square error (RMSE), bias and its 95 % confidence interval (CI=IC).

Figure 3 Evaluation between observed and estimated values of FM using algorithms of ordinary least squares (OLS) or machine learning (ML) 

The PAR and H_pasture variables of PM were the most important (Table 2), both in the ML and OLS models; the variable R_time was much less important (Table 2). The most important RS variables were: LST_n, P, P_lag_3 or P_lag_5, LST_d_avg_3 or LST_n_avg_3; indicating the relevance of the environmental conditions of precipitation and temperature not only of the current month, but of the conditions preceding the measurement of the FM. Reflectance (b1 - b7) and vegetation indices were incorporated into ML models, but the stepwise procedure did not choose them for OLS. Compared with PAR and H_pasture, reflectance variables were of low importance in the RS_PM scenarios of ML. Spectral reflectance bands were more important than EVI and NDVI; this finding coincides with the FM study for mixed pastures of temperate climate¹⁵. Although the prediction of fresh biomass in Brachiaria pastures based on the NDVI with r²= 0.73³¹ was considered adequate.

The partial dependence that existed between the prediction of FM and the value of some of the most important variables in some ML models is shown in Figure 4, in the ML_RS scenario and in Figure 5 for the ML_RS_PM scenario. The ensembles of ML models had lower deviance compared to some ML algorithms in the two scenarios and were therefore considered better representations of the FM. The partial dependence figures indicate how the explanatory variable influences the predictions of one of the models or ensembles, after standardizing the effect of other variables. For linear regression models (such as the GLM model obtained by ML), the figure is a straight line with slope equal to the parameter of the model³². FM depended directly and proportionally on the variables PAR, H_pasture and R_time in different models even for a GLM model (pink line), but for variables P_lag_3 and LST_d, the dependence differed between the GLM model and ML models, particularly the DL-type model (dark green line) which was the best individual ML model (Figure 5). The interpretation of the figures is improved with the frequency histogram of the observations, depending on the value of the variable. Where there was less frequency of data, it was interpreted that dependence was not supported by sufficient evidence. An example of this situation was the dependence of LST_n in Figure 4, where the DL-type model has an abrupt ascent, but the last two class intervals of the histogram have few observations.

The gray bars are the data frequency according to class intervals of the variable. Only models of lower deviance (value in parentheses) obtained by machine learning in the scenario using only variables measured with remote sensors (ML_RS) are shown.

Figure 4 Partial dependence of FM and: A) monthly average of nocturnal surface temperature (LST_n), B) precipitation accumulated in the previous three months (P_lag_3), C) reflectance band b7 of the MODIS MCD43A4 product, D) monthly average of the diurnal surface temperature in the previous three months (LST_d_avg_3) 

The gray bars are the data frequency according to class intervals of the variable. Only models of lower deviance (value in parentheses) obtained by machine learning in the scenario using variables measured with remote sensors and of pasture management (ML_RS_PM) are shown.

Figure 5 Partial dependence of FM and: A) rate of accumulation of forage (PAR), B) forage height (H_pasture), C) pasture rest days (R_time), D) monthly average of the diurnal surface temperature (LST_d) 

The ML_RS_PM scenario included the PAR variable, and this could be a limitation for the practical application of the model. To clarify this aspect, an ML model was built without this variable and using the same training data, resulting in an r² of 0.76, RMSE of 232.2 and bias of -35.6 (CI -94.4 to 23.1), being better than that obtained in the ML_RS scenario (data not shown). This result has two aspects of importance: other variables available for modeling can replace a variable identified as the most important and second, it is possible to incur into a local optimal solution, even when the ML algorithm explored a solution space with different optimization parameters. A possible alternative would be to increase the number of times the h2o.automl function is run and increase the value of the max_runtime_secs constant.

Despite the coarse spatial resolution of the MODIS and GPM remote sensors (250 m² and 10 km²), the FM was adequately estimated in the ML_RS scenario (Figure 3d), the r²= 0.70 of this model was within the range recently reported in the literature for ML models that estimate biomass with RS data^14,15 or gross primary productivity³³. A model based on RS data is only attractive for the management of large grasslands. When RS variables were used in combination with pasture management variables that are easy to measure (H_pasture) or record (R_time and Month_beg_grow), the estimate was very good (Figure 3e); the r²= 0.97 was similar to the r²= 0.96 of biomass estimated from 30 m spatial resolution RS data⁵. The prediction of the forage mass obtained with forage height measurements improved when pasture management variables and local meteorological data were incorporated into an ML algorithm of random forest (r²= 0.82), this approach was judged practical for producers, albeit the cost of meteorological instruments².

Despite being an irrigated pasture, the previous short-term rain was important information for OLS and ML models. In a recent study, it was identified that the spatial-temporal variation of gross primary productivity was not only explained by reflectance bands of the MODIS MCD43A4 but was also related to the vapor pressure deficit³³. Similar to the result of these authors, here it was useful to include other reflectance bands besides b1, b2 and vegetation indices such as NDVI and EVI. From a practical point of view, the model of the ML_RS_PM scenario was considered very feasible to implement as it used routine measurements of the management of the pasture and NASA’s remote sensor data which are publicly accessible.

Animal production under grazing is sustainable when feed consumption that meets nutrient needs is ensured. In grazing management, this depends on adjusting the stoking rate according to the phenological stage of the plant, to the FM before and after grazing and to the forage that is decided to leave as residual pasture mass. For beef cattle, adequate FM before grazing can be set at 2,500 kg ha^-1 and FM after grazing around 1,200 kg ha^-110; although these thresholds will depend on the reproductive and physiological stage of the animal, the season of year and different pasture management strategies for feed rationing, phenological control or balance in botanical composition³⁴. For these reasons, it is important that the predictive model of FM fits well at the extremes of its range and with the exception of the ML_RS_PM scenario, there was an overestimation of the FM when it was less than approximately 1,500 kg ha^-1 (Figure 3).

Pasture mass is spatially variable given by differences in soil moisture and fertility, dung deposition, alterations in the plant community by selective grazing and other factors. Forage quadrant cuttings are limited to represent and capture this spatial variability in pastures and therefore the statistical method of sampling is important. Sensors on board unmanned aerial vehicles or drones are an alternative to capture variability in vegetation reflectance on the spatial scale of centimeters, but the cost of multispectral equipment, data processing and operational limitation to cover the territory ³⁵, in addition to the need for a calibration function for forage mass, must be considered.

Conclusions and implications

The prediction of FM had lower bias with ML models than with OLS models, especially when remote sensors and pasture management variables were incorporated in the models. ML ensembles had lower deviance compared to some of the individual ML models. The use of RS variables predicted FM similarly to the relationship between H_pasture and FM, although the ML model had lower bias. The models explored would have to be tested in other pasture conditions in order to have a spatial application, be able to represent ecosystems and to value the environmental service of carbon capture. At the local farm scale, these models could be applicable for everyday use in farm feed budgeting or retrospective evaluation of farm pasture management. In these cases, the results presented here are promising.