Veloz et al. [12] applied machine learning methods to map soil carbon pools for all California rangelands at a 270 m pixel size. Boosted regression as a machine learning algorithm was used in a classification tree model that iteratively adds new trees to the set, and at each step focuses on explaining the remaining unexplained variation from the set of previous trees. The final parameters for the algorithm were selected by balancing the ability of the model to explain the variation in the input data set (training values) while also being able to accurately predict the data set withheld from the training values (i.e., the testing values).

Soil carbon concentrations were first measured from both 0 - 10 cm and 10 - 40 cm depths at 282 grassland sites across California from 2015 to 2021. Samples were collected in a standardized way and analyzed at the University of Idaho Analytical Lab via dry combustion. Bulk density measurements were also taken at each site and used to convert carbon concentrations to stocks on a fixed mass basis (Mg C ha⁻¹).

Input data sets to the Machine Learning model included:

•Elevation from the Shuttle Radar Topography Mission Digital Elevation Dataset, 30 m resolution.

•Climate data, including monthly average winter minimum temperature (Dec-Feb) and average summer maximum temperature (Jun-Aug), as well as annual precipitation, runoff, recharge, storage, and climactic water deficit, averaged over the years 2016 to 2021 from California’s Basin Characterization Model v8, 270 m resolution [13] .

•Nine measures of annual vegetative productivity derived from the NASA Moderate Resolution Imaging Spectroradiometer (MODIS) satellite Normalized Difference Vegetation Index (NDVI) data; averaged over the years 2016 to 2021, 250 m resolution [14] .

• Fractional landcover of bare ground, litter, annual, annual herbaceous, shrub, and sagebrush as well as sagebrush and shrub height in 2016 from the National land Cover Dataset (NLCD) Rangeland Components dataset, 30 m resolution [14] .

•Soil class, suborder, order, and drainage class; and the weighted average by horizon of pH, sand, silt, and clay; bulk density from the Soil Survey Geographic Database (SSURGO) Soil Survey Staff from 2022.

The best boosted regression model results for the 0 - 10 cm soil depth had a correlation coefficient (R²) between the observed average soil carbon stocks and predicted soil carbon stocks of 0.72 (SE ± 0.022), whereas the best model results for the combined 0 - 40 cm soil depth had a correlation coefficient R² of 0.85 (SE ± 0.015).

Bi-weekly Landsat 8 Collection 2 images from the years 2022 to 2024 at 30-m pixel size, were used to calculate the normalized difference vegetation index (NDVI) of the near-infrared (NIR) and red spectral bands. NDVI provides consistent spatial and temporal profiles of herbaceous vegetation biomass according to the equation:

$NDVI=\left(NIR-Red\right)/\left(NIR+Red\right)$

Which resulted in values between −1.0 and +1.0 NDVI units. Negative NDVI values are indicative of water bodies, low values of NDVI (near 0.1) indicate barren land cover, and high values of NDVI (above 0.8) indicate dense green plant cover. NDVI has been shown to be an accurate index of herbaceous green cover in grasslands of California and can be converted with high accuracy into seasonal herbaceous biomass (g C m⁻²) each year [15] .

This study used a Soil Fertility Index (FI) map previously generated for the lower 48 United States by the U. S. Department of Agriculture (USDA) [16] . The FI uses family-level Soil Taxonomy information to rank soils from 0 (least fertile) to 19 (most fertile). To calculate the FI, the following variables were used to guide expert assessments of fertility among 12 main soil orders: 1) organic matter content, 2) cation exchange capacity—CEC, and 3) clay mineralogy, as well as USDA knowledge of general land uses in each of the soil orders.

This study used the 30-year normal maps previously generated from the PRISM project which were used to quantify average annual climate conditions across California over the most recent three full decades (1991 to 2020) at 4-km pixel resolution. Long-term average datasets are modeled from weather station records in PRISM using a digital elevation model (DEM) as the predictor grid [17] .

The CASA (Carnegie-Ames-Stanford Approach) carbon cycle model [18] [19] predicts the monthly net primary production (NPP) flux of atmospheric CO₂ between plants and soils on a global scale using satellite image inputs from MODIS. CASA is the only global carbon model that has consistently used MODIS and Landsat products for land cover classes and green vegetation indices as monthly inputs to drive the prediction of NPP and soil CO₂ emissions in the terrestrial biosphere. It is the most well-integrated model of the global carbon and water cycles with high-level products from NASA satellite remote sensing missions. Moreover, the nominal 8-km grid cell resolution of the CASA model enables localized studies of ecosystem carbon and water fluxes of interest to public sector stakeholders working at nearly every organizational level. CASA NPP model calibration has been validated repeatedly, first globally by comparing predicted annual NPP to more than 1900 field measurements of NPP by Potter et al. [18] . More recently, Jay et al. [14] validated CASA NPP estimates using 17 Ameriflux tower flux sites located across North America.

The CASA soil model design is based closely on the DAYCENT model [10] and includes three-layer (M1 - M3) heat and moisture content computations: surface organic matter (SOM), topsoil (0.3 m), and subsoil to grassland rooting depth (1 m). These layers can differ in soil texture, moisture holding capacity, and carbon–nitrogen dynamics. Water balance in the soil is modeled as the difference between precipitation or volumetric percolation inputs, monthly estimates of evaporation, and the drainage output for each layer. First-order equations simulate exchanges of decomposing plant residue (metabolic and structural fractions) at the soil surface. CASA also simulates surface soil organic matter fractions that vary in age and chemical composition. Active (microbial biomass and labile substrates), Slow (chemically protected), and Passive (physically protected) fractions of the soil organic matter are represented in the model. Along with moisture availability and organic residue quality, estimated soil temperature in the M1 - 3 layers controls soil organic matter decomposition rates at the monthly time step.

Following the DAYCENT modeling approach reported by Ryals et al. [9] for the present study, compost amendments to rangelands across California were simulated starting with a single amendment of 14 Mg C ha⁻¹ added to the CASA soil organic pools. Compost is a source of stabilized organic matter, more prone to be incorporated for years into soil than are additions of fresh manure, which rapidly mineralize [20] . Hence, for these CASA model runs, it was assumed that compost was nearly identical in protected chemical properties and stabilized microbial products to the CASA-Century model’s Slow C pool, with residence times in a temperate zone soil profile typically ranging from 20 to 60 years [18] . Using monthly PRISM climate inputs, CASA was then run to simulate the lifetime decay function of a one-time compost application with C:N ratio of 20 - 30 (for close-to-zero N₂O emission risk) [9] .

The linear trend (positive or negative) in bi-weekly NDVI values at every 30-m Landsat pixel location across all of California was calculated in Google Earth Engine from the wet seasons (October to May water year) of 2021 to 2024 as a greening regression slope coefficient, following the approach described by Potter and Alexander [21] . According to NOAA’s National Centers for Environmental Information, 2021-22 was the driest water year ever recorded in the state (dating back to 1895), whereas 2022-23 recorded one of the four wettest seasons in the modern history of the state. This historic and abrupt trend upward in seasonal precipitation totals and available soil water in grasslands for annual growth provided a surrogate to test the central hypotheses outlined in this study: Future compost applications to grassland ecosystems will increase available soil water to herbaceous plants in the same manner that years of high annual precipitation makes added soil water available for elevated plant growth.

Zonal statistics for simulated compost lifetime and NDVI trends were computed within the boundaries of California counties ( Figure 1 , with name labels), and eventually for selected river and creek drainage basins, using the geographic information systems application QGIS. The population mean, standard deviation, and maximum values were computed for the set of raster pixels that intersected each polygon-delineated layer.

The counties estimated by the CASA model with the highest average Slow C pool sizes (in excess of 70 Mg C ha⁻¹) were all located in northern California ( Figure 1 ), from the Del Norte to Sonoma county lines ( Table 1 ). Other counties located further south and with relatively high average Slow C pool sizes (in excess of 50 Mg C ha⁻¹) included Santa Cruz, Tuolumne, Tulare, and Santa Barbara. Counties with the highest geographic variability in Slow C pool sizes included Humboldt, Mendocino, Siskiyou, Tuolumne, Tulare, and Santa Barbara. Counties with the lowest Slow C pool sizes included Solano, Yolo, Contra Costa, San Diego, San Mateo, Stanislaus, San Joaquin, Merced, and Alameda. This ranking of counties with the highest average Slow C pool sizes represents the CASA model’s synthesis of the combined effects of climate conditions that favor relatively high annual NPP and the soil types that favor high levels of long-term carbon sequestration in a chemically protected form.

Statewide map results ( Figure 2 ) from the CASA model show the number of years for practically 100% of the 14 Mg C ha⁻¹ of applied compost tonnage to decompose (i.e., its full lifetime in the soil), with the light green shades showing time periods in the 20 - 50 years range and the dark green shades in the 80 - 90 years range. For most Marin County grazed rangelands, CASA estimates of the compost lifetime were between 40 - 60 years, consistent with the Ryals et al. [9] DAYCENT model results for these coastal rangeland sites near Nicasio (at 38.06˚ N, 122.71˚ W). In comparison, grassland sites measured for soil carbon at the Sierra Foothill Research and Extension Center (SFREC) by Ryals et al. [9] in Yuba County (at 39.24˚ N, 121.30˚ W) were predicted by the CASA model to have a compost lifetime in the soil of over 100 years. This longer compost lifetime resulted mainly from a shorter growing season with lower annual mean temperatures and higher summer evapotranspiration in Yuba County, compared to Marin County.

The counties with large areas of rangeland (in excess of 90,000 ha) that were mapped using the CASA model with the shortest average lifetime of 14 Mg C ha⁻¹ applied compost in the soil were ranked as Mendocino, Lake, Napa, Sonoma, and Santa Barbara ( Table 2 ). Counties with notable rangeland acreage and with the longest average lifetime (greater than 85 years) of 14 Mg C ha⁻¹ applied compost to the soil were San Benito, Stanislaus, Mariposa, Modoc, Alameda, San Joaquin, and Merced. This ranking of counties by compost lifetime in the soil represents the CASA model’s estimation of the combined effects of climate conditions and soil types that favor the most rapid (to the slowest) decomposition rates of organic matter added as compost to rangeland soils. Areas of counties with the longest average lifetime represent those where compost applied to rangeland soil surfaces will persist for the longest period of time, largely as a result of climate conditions (drier annually and hotter in the summer) that are relatively unfavorable to rapid litter/soil carbon decay.

Statewide map results ( Figure 3 ) from Landsat NDVI time series analysis show the strongest response of rangelands to the transition from an historically extreme dry year (2021-2022) to two wet years (2023 and 2024) occurred in the northern Sacramento Valley and the eastern side of the Central Valley south to around Fresno. Other regions that showed a strong greening trend with increasing rainfall were in the grasslands north and east of San Francico Bay, the southern Santa Clara Valley, and on the central coastal prairies from San Simeon to Morro Bay.

The counties with the strongest positive response and among the lowest geographic variability in rangeland NDVI from extreme dry to wet years were ranked in Table 3 as Calaveras, Tuolumne, Marin, Sacramento, Amador, and Yuba. Counties with the highest geographic variability in response of rangeland NDVI from extreme dry to wet years (2022 to 2024) included San Joaquin, Sonoma, Plumas, Stanislaus, and Santa Cruz. Counties with the lowest response of rangeland NDVI from extreme dry to wet years included Monterey, Tulare, Santa Barbara, Glenn, Napa, and San Luis Obispo. This ranking of counties by rangeland NDVI response to varying yearly precipitation (most positive to most negative) reflects the soil types and potential grassland productivity that should also favor a positive of response of soil carbon sequestration following compost applications in rangelands across California.

The coastal rangeland sites near Nicasio in Marin County studied by Ryals et al. [9] for soil carbon dynamics had a strong NDVI response to varying yearly precipitation, with a regression slope between +1.5 and +2.6 from 2022 and 2024, whereas grassland sites at the SFREC in Yuba County showed a very strong NDVI response with a regression slope of +2.9 from 2022 and 2024.

The counties with large areas of rangeland (in excess of 90,000 ha) that were mapped using Machine Learning methods by Veloz et al. [12] with high soil carbon content (percent by volume to 10 cm depth) were ranked as Siskiyou, Mendocino, Sonoma, Alameda, Shasta, Lassen, and Santa Clara ( Table 4 ). Counties with notable rangeland acreage and low geographic variability in soil carbon content included Marin, Santa Cruz, Contra Costa, and Santa Clara. Counties with notable rangeland acreage and among the lowest soil carbon content included Stanislaus, San Joaquin, Glenn, San Luis Obispo, San Benito, and Merced, all at lower than 0.8 percent on average and commonly with a maximum surface soil carbon content no higher than 1.6 percent.

Statewide mapping of the USDA Soil Fertility Index ( Figure 4 ) relatively high values in the Modoc National Forest region, the northern Sacramento Valley, the southern Santa Clara Valley, and on the Central Coast prairies from Marin to Morro Bay. The counties with the highest Soil Fertility Index on average in California were ranked as San Benito, Kings, Ventura, Marin, Santa Cruz, and Monterey ( Table 5 ). Counties with notable rangeland acreage and averaged among the lowest Soil Fertility Index included Merced, Sonoma, Siskiyou, Santa Barbara, Humboldt, and Santa Clara. Both the coastal rangeland sites in Marin County and in Yuba County studied by Ryals et al. [9] for soil carbon dynamics had high Soil Fertility Index values that ranged between 13 - 14 in the grasslands of these locations.