Forestry GIS Python · Forestry · Ecology

Deriving Bioclimatic Variables from Monthly Climate Rasters in Python

Standard bioclimatic layers are published for the present and for a handful of future scenarios, which covers most needs — until you have a downscaled regional climate product, a station-interpolated surface for your own catchment, or a scenario nobody has published. Then the derivation has to be done locally, and the definitions turn out to be more particular than they look: “warmest quarter” means a specific rolling window, and getting it wrong changes several variables at once. This guide derives them, inside Environmental Predictor Stacking, part of Species Distribution Modeling with MaxEnt.

What you need, and what comes out

The inputs are three monthly stacks of twelve layers each: minimum temperature, maximum temperature, and precipitation. From them come nineteen indices in three families.

Family Variables What they capture
Temperature level bio1, bio5, bio6, bio8, bio9, bio10, bio11 Means and extremes, annual and by quarter
Temperature variability bio2, bio3, bio4, bio7 Diurnal range, isothermality, seasonality, annual range
Precipitation bio12–bio19 Total, seasonality, and wettest/driest/warmest/coldest quarters

The quarter variables are where implementations diverge. A “quarter” is any three consecutive months, evaluated as a rolling window that wraps around the year end — so December-January-February is a valid quarter. An implementation that treats quarters as fixed calendar blocks gets different answers everywhere and identical answers nowhere obvious enough to notice.

Rolling quarters wrap around the year end A strip of twelve month cells from January to December is drawn twice. The upper strip shows fixed calendar quarters as four separate blocks. The lower strip shows the rolling definition: a three month window slid across every starting month, including one that begins in November and wraps around to January, giving twelve candidate quarters rather than four. Fixed calendar quarters — wrong JFMA MJJA SOND Rolling quarters — correct JFMA MJJA SOND F–A J–A N–J wraps the year end Twelve candidate quarters, not four — and the wrapping one matters most in the southern hemisphere.

Minimal reproducible example

import numpy as np


def rolling_quarters(monthly: np.ndarray) -> np.ndarray:
    """Sum of each of the 12 wrapping three-month windows. monthly is (12, y, x)."""
    doubled = np.concatenate([monthly, monthly[:2]], axis=0)      # wrap the year
    return np.stack([doubled[i:i + 3].sum(axis=0) for i in range(12)])


def bioclim(tmin: np.ndarray, tmax: np.ndarray, prec: np.ndarray) -> dict:
    """The 19 standard bioclimatic indices from monthly stacks of shape (12, y, x)."""
    tavg = (tmin + tmax) / 2.0
    q_t = rolling_quarters(tavg) / 3.0        # quarter MEAN temperature
    q_p = rolling_quarters(prec)              # quarter TOTAL precipitation

    bio1 = tavg.mean(axis=0)
    bio2 = (tmax - tmin).mean(axis=0)
    bio4 = tavg.std(axis=0, ddof=0) * 100.0
    bio5 = tmax.max(axis=0)
    bio6 = tmin.min(axis=0)
    bio7 = bio5 - bio6
    bio3 = 100.0 * bio2 / np.where(bio7 == 0, np.nan, bio7)

    wettest_q = np.argmax(q_p, axis=0)
    driest_q = np.argmin(q_p, axis=0)
    warmest_q = np.argmax(q_t, axis=0)
    coldest_q = np.argmin(q_t, axis=0)

    def pick(stack, idx):
        return np.take_along_axis(stack, idx[None, ...], axis=0)[0]

    bio12 = prec.sum(axis=0)
    mean_p = prec.mean(axis=0)
    return {
        "bio1": bio1, "bio2": bio2, "bio3": bio3, "bio4": bio4,
        "bio5": bio5, "bio6": bio6, "bio7": bio7,
        "bio8": pick(q_t, wettest_q),      # mean temperature of the wettest quarter
        "bio9": pick(q_t, driest_q),
        "bio10": pick(q_t, warmest_q),
        "bio11": pick(q_t, coldest_q),
        "bio12": bio12,
        "bio13": prec.max(axis=0),
        "bio14": prec.min(axis=0),
        "bio15": 100.0 * prec.std(axis=0, ddof=0) / np.where(mean_p == 0, np.nan, mean_p),
        "bio16": pick(q_p, wettest_q),
        "bio17": pick(q_p, driest_q),
        "bio18": pick(q_p, warmest_q),     # precipitation of the WARMEST quarter
        "bio19": pick(q_p, coldest_q),
    }

Three details carry most of the correctness. Quarter temperature is a mean while quarter precipitation is a total, which is why q_t is divided by three and q_p is not. Variables 8, 9, 18 and 19 are cross-indexed: bio18 is precipitation during the quarter selected by temperature, not the wettest quarter, and swapping the index is a common and invisible error. And bio4 is the standard deviation of monthly temperature ×100, a scaling convention that exists so the layer can ship as an integer.

Parameter reference

Variable Definition Units Notes
bio1 Annual mean temperature °C Mean of monthly means
bio2 Mean diurnal range °C Mean of monthly (tmax − tmin)
bio3 Isothermality % 100 × bio2 / bio7
bio4 Temperature seasonality °C × 100 Standard deviation, population (ddof = 0)
bio5 / bio6 Max of warmest / min of coldest month °C From tmax and tmin, not from tavg
bio7 Annual temperature range °C bio5 − bio6
bio8 / bio9 Mean temp of wettest / driest quarter °C Quarter chosen by precipitation
bio10 / bio11 Mean temp of warmest / coldest quarter °C Quarter chosen by temperature
bio12 Annual precipitation mm Sum of months
bio13 / bio14 Precipitation of wettest / driest month mm —
bio15 Precipitation seasonality % Coefficient of variation, ddof = 0
bio16 / bio17 Precipitation of wettest / driest quarter mm Quarter chosen by precipitation
bio18 / bio19 Precipitation of warmest / coldest quarter mm Quarter chosen by temperature

Expected output and verification

The decisive test is a comparison against a published layer over the same extent. If the derivation is correct the two agree to within interpolation noise; if a quarter definition is wrong, four or five variables disagree in a structured way.

import numpy as np
import rasterio


def compare_to_published(derived: dict, published_paths: dict) -> list[dict]:
    """Correlate each derived layer against its published counterpart."""
    rows = []
    for name, path in published_paths.items():
        with rasterio.open(path) as src:
            ref = src.read(1, masked=True).astype("float64").filled(np.nan)
        got = derived[name].astype("float64")
        ok = np.isfinite(ref) & np.isfinite(got)
        if ok.sum() < 100:
            rows.append({"var": name, "status": "insufficient_overlap"})
            continue
        r = float(np.corrcoef(ref[ok], got[ok])[0, 1])
        bias = float((got[ok] - ref[ok]).mean())
        rows.append({"var": name, "r": round(r, 4), "bias": round(bias, 3),
                     "rmse": round(float(np.sqrt(((got[ok] - ref[ok]) ** 2).mean())), 3)})
    return rows


for row in compare_to_published(derived, published):
    if "r" in row:
        assert row["r"] > 0.98, f"derived {row['var']} disagrees with published: {row}"

Read the failures as a group rather than one at a time. If bio8, bio9, bio18 and bio19 all fail while everything else passes, the cross-indexing is swapped. If every quarter variable fails but the annual ones pass, the quarters are not wrapping. If bio4 is off by exactly a factor of 100, it is the scaling convention.

The self-consistency checks catch errors even with no published layer to compare against:

import numpy as np


def bioclim_consistency(b: dict) -> dict:
    """Relations that must hold between the indices by construction."""
    checks = {
        "bio5_ge_bio1": bool(np.nanmin(b["bio5"] - b["bio1"]) >= -0.01),
        "bio6_le_bio1": bool(np.nanmax(b["bio6"] - b["bio1"]) <= 0.01),
        "bio7_positive": bool(np.nanmin(b["bio7"]) >= 0.0),
        "bio10_ge_bio11": bool(np.nanmin(b["bio10"] - b["bio11"]) >= -0.01),
        "bio13_ge_bio14": bool(np.nanmin(b["bio13"] - b["bio14"]) >= -0.01),
        "bio16_ge_bio17": bool(np.nanmin(b["bio16"] - b["bio17"]) >= -0.01),
        "bio12_ge_bio16": bool(np.nanmin(b["bio12"] - b["bio16"]) >= -0.01),
        "bio3_bounded": bool(np.nanmax(b["bio3"]) <= 100.0),
    }
    return checks


chk = bioclim_consistency(derived)
assert all(chk.values()), f"bioclim internal consistency failed: {chk}"

Every one of those is true by construction — the warmest quarter cannot be colder than the coldest, annual precipitation cannot be less than any quarter’s — so a failure localises the bug immediately. Feeding the function a deliberately corrupted stack, with two variables swapped, should make it fail; if it does not, the checks are not doing their job.

Correlation with published layers isolates the definition error A bar chart of correlation between derived and published bioclimatic layers for variables one to nineteen. Fifteen bars sit at or above 0.99. Four bars, corresponding to variables 8, 9, 18 and 19, drop to around 0.7. Those four are exactly the cross-indexed quarter variables, so the pattern of failure identifies a swapped selection index rather than a general problem. 0.6 0.8 0.9 1.0 correlation 123 456 789 101112 131415 161718 19 bioclimatic variable Exactly the four cross-indexed variables fail — which names the bug without further debugging. The four quarters on one pixel's climate Monthly mean temperature and monthly precipitation are plotted for one pixel across a year. The warmest quarter runs June to August and the coldest December to February. The wettest quarter runs October to December and the driest June to August. Because the wettest and warmest quarters do not coincide, the cross-indexed variables — temperature of the wettest quarter and precipitation of the warmest quarter — describe genuinely different windows. JFMA MJJA SOND temperature precipitation warmest & driest quarter wettest quarter coldest quarter wraps Dec–Feb Different windows, so bio18 and bio16 are different numbers — swapping the index is invisible.

Common pitfalls

  • Quarters that do not wrap. December-January-February is a real quarter and the coldest one across most of the northern hemisphere.
  • Cross-indexed variables swapped. bio18 uses the warmest quarter, chosen by temperature, not the wettest.
  • Sample standard deviation for bio4 and bio15. The convention is the population standard deviation; ddof=1 gives a consistent 4% offset.
  • bio5 computed from monthly means. It is the maximum of tmax, not the maximum of tavg, and the difference is several degrees.
  • Unscaled inputs. Many climate products ship temperature ×10 as integers. Convert before deriving or every temperature index is out by an order of magnitude.

Frequently Asked Questions

Do I need all nineteen variables?

No, and using all of them is usually harmful. They are heavily collinear by construction — bio1, bio10 and bio11 are near-duplicates in most regions — and a model fitted on all nineteen transfers poorly. Select four to eight that are both ecologically motivated and mutually uncorrelated, as covered in Reducing Predictor Collinearity with VIF in Python.

Can I derive these from daily data instead of monthly?

Aggregate to monthly first. The definitions are written in monthly terms, and deriving from daily values produces indices that are not comparable with any published layer — a difference that will be attributed to your study area rather than to your method.

What about a species whose limits are set by growing degree days?

Then add it as a separate predictor rather than hoping a bioclim variable proxies it. Degree-day sums, frost-free period and water balance are all more mechanistic than the standard nineteen, and for temperate forest trees they frequently outperform them.

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