EcoPro Tree Mortality Drought Indexes

BCMv8_indexes.nc4 holds annual (water-year) climate and water-balance variables and multi-year drought indexes for California on the 270 m grid of the USGS Basin Characterization Model version 8 (BCMv8), for water years 2006–2024. The drought indexes are the standardized precipitation index (SPI), the standardized precipitation–evapotranspiration index (SPEI) and the cumulative precipitation and water balance they are computed from, each accumulated over 1 to 6 water years. All standardized indexes use the water years 1980–2005 as the reference period. Source data and provenance All variables come from the monthly BCMv8 grids: Flint, L.E., Flint, A.L., Stern, M.A., Seymour, W.A., and Zamora-Reyes, D., 2021, The Basin Characterization Model – A monthly regional water balance software package (BCMv8) data release and model archive for hydrologic California: U.S. Geological Survey data release, https://doi.org/10.5066/P9PT36UI. (CC0 1.0.) The model itself is described in Flint, L.E., Flint, A.L., and Stern, M.A., 2021, The basin characterization model – A regional water balance software package: U.S. Geological Survey Techniques and Methods 6–H1, 85 p., https://doi.org/10.3133/tm6H1. We downloaded the monthly grids for water years 1980–2020 from the child item “BCMv8 climate inputs for water years 1896–2020” and the parent item (September 2023), and those for water years 2021–2024 from the child items “BCMv8 climate inputs and outputs for water year 2021” through “…2024”. We used ten variables: aet, cwd, pck, pet, ppt, rch, run, str, tmn and tmx (October 1979 – September 2024). We did not change the values in the source grids. Our processing did the following: Read the monthly ASCII grids and stacked them into one monthly data cube (convert_bcm_v8.py, merge_bcm.py). Aggregated each grid cell to water years (aggregate_bcm_v8.py; see below). Computed the cumulative and standardized indexes (append_climate_indexes.py). Wrote the result to NetCDF-4 with zlib compression, level 9 (zarr_to_nc4.py). Grid, time and file format Projection: NAD83 / California Albers (EPSG:3310), stored in the spatial_ref variable. Grid: 3486 (easting) × 4477 (northing) cells of 270 m × 270 m, identical to BCMv8. Coordinates are cell centres in metres: easting runs from −374,360.8 to 566,589.2, northing from 592,501.7 to −616,018.3. Time: year = water year, 2006–2024 (19 values). Water year \(t\) runs from 1 October of calendar year \(t-1\) to 30 September of calendar year \(t\) (e.g. water year 2015 = Oct 2014 – Sep 2015). Dimensions: every data variable is (year, northing, easting). Cells outside the BCMv8 domain, and windows with any missing month or year, are NaN. Types: the base variables, PR and PRET are float32; SPI and SPEI are float64. Notation For grid cell \(s\) and water year \(t\), let \(m \in t\) denote the twelve months of water year \(t\), and let \(\mathrm{ppt}_m\), \(\mathrm{pet}_m\), … denote the monthly BCMv8 values. \(\Phi^{-1}\) is the quantile function of the standard normal distribution. Base variables (single water year) Water-year aggregates of the monthly BCMv8 grids. Fluxes and storages are summed over the twelve months, \(X(t)=\sum_{m\in t} X_m\); temperatures take the monthly extreme. A water year with any missing month is NaN. Variable Definition (BCMv8 long name) Annual aggregation Units aet Actual evapotranspiration sum of monthly values mm cwd Climatic water deficit (PET − AET) sum of monthly values mm pck Snowpack (snow water equivalent) sum of monthly values mm pet Potential evapotranspiration sum of monthly values mm ppt Precipitation sum of monthly values mm rch Recharge sum of monthly values mm run Runoff sum of monthly values mm str Soil water storage sum of monthly values mm tmn Minimum air temperature minimum of the monthly mean minimum temperatures °C tmx Maximum air temperature maximum of the monthly mean maximum temperatures °C Because pck and str are storages, their annual sums are twelve times the water-year mean rather than a physical amount. Accumulation numbering The trailing number \(n\) in PRn, PRETn, SPIn and SPEIn (\(n = 1,\dots,6\)) is the accumulation period in water years. The value stored at year \(t\) covers the \(n\) water years ending with \(t\), i.e. water years \(t-n+1,\dots,t\) (1 October of calendar year \(t-n\) to 30 September of calendar year \(t\)). For example, SPEI4 at year = 2015 covers water years 2012–2015. These windows use BCMv8 data from before 2006, so every variable is defined for all of 2006–2024. Cumulative precipitation, PRn (mm) Long name: “n-Year Cumulative Precipitation”. \[ \mathrm{PR}_n(t) = \sum_{i=0}^{n-1} \mathrm{ppt}(t-i) \] Cumulative water balance, PRETn (mm) Long name: “n-Year Cumulative Water Balance”. This is the climatic water balance (precipitation minus potential evapotranspiration) on which the SPEI is based. \[ \mathrm{PRET}_n(t) = \sum_{i=0}^{n-1} \left[\mathrm{ppt}(t-i) - \mathrm{pet}(t-i)\right] \] Reference period SPI and SPEI are fitted separately for each grid cell and each accumulation \(n\), using the values of \(\mathrm{PR}_n\) or \(\mathrm{PRET}_n\) for the reference water years 1980–2005. A reference-year window must lie entirely within the BCMv8 record that we used (from water year 1980), so the effective reference years are \(1979+n,\dots,2005\), giving \(27-n\) values (26 for \(n=1\), 21 for \(n=6\)). All years from 2006 to 2024 are then standardized against this fixed fit, which is not refitted. Standardized Precipitation Index, SPIn (standard deviations) Long name: “n-Year Standard Precipitation Index”. Following McKee et al. (1993), a two-parameter gamma distribution \(G(x;\,\alpha,\beta)\) (location fixed at 0) is fitted by maximum likelihood to the non-zero reference values of \(\mathrm{PR}_n\). Zeros are handled with a mixed distribution, where \(p_0\) is the fraction of reference years with \(\mathrm{PR}_n = 0\): \[ H(x) = p_0 + (1-p_0)\,G(x;\,\hat\alpha,\hat\beta), \qquad H(0) = p_0 \] \[ \mathrm{SPI}_n(t) = \Phi^{-1}\!\left[H\left(\mathrm{PR}_n(t)\right)\right] \] Standardized Precipitation–Evapotranspiration Index, SPEIn (standard deviations) Long name: “n-Year Standardized Water Balance Index”. Following Vicente-Serrano et al. (2010), the water balance is standardized. Here a three-parameter gamma distribution with shape \(a\), location \(\mu\) and scale \(\sigma\) (the location allows the negative values that \(P-\mathrm{PET}\) can take) is fitted by maximum likelihood (SciPy scipy.stats.gamma.fit) to the reference values of \(\mathrm{PRET}_n\): \[ F(x) = \frac{1}{\Gamma(a)}\,\gamma\!\left(a,\ \frac{x-\mu}{\sigma}\right), \qquad x \gt \mu \] \[ \mathrm{SPEI}_n(t) = \Phi^{-1}\!\left[F\left(\mathrm{PRET}_n(t);\,\hat a,\hat\mu,\hat\sigma\right)\right] \] \(\gamma(\cdot,\cdot)\) is the lower incomplete gamma function. Negative SPI or SPEI means drier than the 1980–2005 climatology, and positive means wetter. Lag numbering (derived features) The file stores each index at the water year in which its accumulation window ends. In the accompanying analyses, lagged predictors are named {INDEX}{n}-{k}, where \(n\) is the accumulation in water years (above) and \(k = 1,\dots,6\) is the lag. Lag 1 is the current water year \(t\), lag 2 is the previous water year, and so on: \[ \texttt{INDEX}n\text{-}k\ (t) = \texttt{INDEX}n\,\left(t-k+1\right) \] Lag \(k\) therefore covers water years \(t-k-n+2,\dots,t-k+1\). For example, for water year \(t = 2015\): SPEI1-1 = SPEI1 at year = 2015 (water year 2015 alone); SPEI1-2 = SPEI1 at year = 2014 (1-year accumulation, the previous water year); SPEI4-1 = SPEI4 at year = 2015 (water years 2012–2015); SPEI4-3 = SPEI4 at year = 2013 (water years 2010–2013). To get any lagged value, select year = t - (k - 1) from this file. Variable list Base (10): aet, cwd, pck, pet, ppt, rch, run, str, tmn, tmx Cumulative precipitation (6): PR1–PR6 Cumulative water balance (6): PRET1–PRET6 SPI (6): SPI1–SPI6 SPEI (6): SPEI1–SPEI6 References Flint, L.E., Flint, A.L., and Stern, M.A., 2021, The basin characterization model – A regional water balance software package: U.S. Geological Survey Techniques and Methods 6–H1, 85 p., https://doi.org/10.3133/tm6H1. Flint, L.E., Flint, A.L., Stern, M.A., Seymour, W.A., and Zamora-Reyes, D., 2021, The Basin Characterization Model – A monthly regional water balance software package (BCMv8) data release and model archive for hydrologic California: U.S. Geological Survey data release, https://doi.org/10.5066/P9PT36UI. McKee, T.B., Doesken, N.J., and Kleist, J., 1993, The relationship of drought frequency and duration to time scales: Proceedings of the 8th Conference on Applied Climatology, American Meteorological Society, p. 179–184. Vicente-Serrano, S.M., Beguería, S., and López-Moreno, J.I., 2010, A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index: Journal of Climate, v. 23, p. 1696–1718, https://doi.org/10.1175/2009JCLI2909.1.