Temperature, photoperiod, and the timing of leaf emergence and senescence
2026-02-26
Since 1736, volunteers have recorded the date each year when cherry trees bloom along the shores of Suwa Lake in Japan. The record is the longest continuous phenological dataset in the world, and it shows something remarkable: peak bloom now occurs roughly three to four weeks earlier than it did three centuries ago, with the rate of advance accelerating sharply since the 1950s. The cherry blossoms are a biological thermometer, integrating winter and spring temperatures in a way that instruments alone cannot replicate.
Phenology — the science of seasonal timing in living organisms — is one of the most sensitive indicators of climate change available. Spring leaf-out, first flower, bird migration, insect emergence, fish spawning: all of these are triggered by environmental cues, primarily temperature accumulation and day length, that have shifted measurably as the climate warms. The agricultural implications are immediate: growing seasons are lengthening, frost-free periods expanding, and the thermal calendar that farmers use for crop scheduling is drifting year by year. The ecological implications are subtler but potentially more serious: when the timing of insect emergence decouples from the timing of migrating birds that feed on them, entire food webs can become mismatched. This model derives the thermal time framework — growing degree days — that underlies most phenological prediction, introduces the photoperiod constraint that prevents premature flowering, and shows how the two interact to set the length and productivity of the growing season.
Why do trees in Minnesota leaf out in May, while trees in Florida leaf out in February?
Phenology is the study of seasonal timing in organisms: - Bud break: When buds open and leaves emerge - Flowering: When plants produce flowers - Senescence: When leaves die and fall - Migration: When animals move (birds, butterflies)
These events are triggered by environmental cues: - Temperature: Accumulated warmth (thermal time) - Photoperiod: Day length - Chilling: Cold exposure needed for dormancy break
The mathematical question: How do we model phenological timing from weather data, and how does phenology affect ecosystem productivity?
Thermal time: Plants accumulate heat above a base temperature.
\text{GDD} = \sum_{t=1}^{n} \max(0, T_{\text{avg}}(t) - T_{\text{base}})
Where: - T_{\text{avg}} = daily average temperature (°C) - T_{\text{base}} = base temperature (typically 5–10°C) - Sum over days
Example: Day with T_{\text{avg}} = 15°C, T_{\text{base}} = 5°C:
\text{GDD} = 15 - 5 = 10 \text{ degree-days}
Threshold for bud break: Typically 100–300 GDD accumulated since spring.
Day length varies with latitude and day of year.
Approximation:
D = 12 + 2 \arcsin(\tan \phi \tan \delta) \times \frac{24}{2\pi}
Where: - D = day length (hours) - \phi = latitude (radians) - \delta = solar declination (function of day of year)
Solar declination:
\delta = 23.45° \sin\left(\frac{360}{365}(d - 81)\right)
Where d is day of year (1 = Jan 1).
Critical photoperiod: Some plants require day length > threshold to flower. - Long-day plants: Flower when days exceed ~14 hours (wheat, spinach) - Short-day plants: Flower when days fall below ~12 hours (soybeans, rice) - Day-neutral plants: Flower independent of photoperiod (tomatoes, corn)
Dormancy: Many temperate plants require cold exposure before they can respond to spring warmth.
Chilling units: Days with temperature 0–7°C.
Example: Apple trees need ~1000 chilling hours (42 days at 0–7°C) before bud break.
Problem in warming climate: Insufficient winter chilling can delay spring phenology.
Bud break timing:
GDD threshold varies by species: - Early species (willow): 100 GDD - Mid-season (oak): 200 GDD - Late species (ash): 300 GDD
Spring green-up:
\frac{d\text{LAI}}{dt} = r_g \times (T - T_{\text{base}}) \times (LAI_{\text{max}} - \text{LAI})
Where: - r_g = growth rate parameter - LAI asymptotes to LAI_{\text{max}} (maximum leaf area)
Autumn senescence:
Triggered by: - Decreasing photoperiod (day length < threshold) - Frost events (temperature < 0°C) - Age (days since leaf emergence > 150)
\frac{d\text{LAI}}{dt} = -r_s \times \text{LAI}
Where r_s is senescence rate (day⁻¹).
Start of season (SOS): When LAI > 0.5 or NDVI > 0.3
End of season (EOS): When LAI < 0.5 or NDVI < 0.3
Growing season length:
\text{GSL} = \text{EOS} - \text{SOS}
Typical values: - Tropics: GSL = 365 days (year-round) - Temperate: GSL = 150–200 days - Boreal: GSL = 90–120 days - Tundra: GSL = 60–90 days
Last spring frost: Latest date with T_{\min} < 0°C
First fall frost: Earliest date with T_{\min} < 0°C
Frost-free period: Time between last spring and first fall frost.
Agricultural importance: Crops must mature within frost-free period.
Example: Corn needs 120–140 GDD from planting to maturity. In short-season climates, must plant as soon as last frost passes.
Problem: A deciduous tree at 45°N has: - Base temperature: T_{\text{base}} = 5°C - GDD requirement for bud break: 200 degree-days - Chilling requirement met by April 1
Temperature record (daily average): - April 1–10: 10°C - April 11–20: 12°C - April 21–30: 15°C
When does bud break occur?
GDD accumulation:
April 1–10 (10 days at 10°C):
\text{GDD} = 10 \times (10 - 5) = 10 \times 5 = 50 \text{ degree-days}
Cumulative: 50
April 11–20 (10 days at 12°C):
\text{GDD} = 10 \times (12 - 5) = 10 \times 7 = 70 \text{ degree-days}
Cumulative: 50 + 70 = 120
April 21–30 (10 days at 15°C):
\text{GDD} = 10 \times (15 - 5) = 10 \times 10 = 100 \text{ degree-days}
Cumulative: 120 + 100 = 220
Bud break occurs when cumulative GDD reaches 200.
Within April 21–30:
Need 200 - 120 = 80 more degree-days.
At 10 degree-days per day: 80 / 10 = 8 days.
Bud break date: April 21 + 8 = April 29
Below is an interactive phenology simulator.
<label>
Latitude:
<input type="range" id="latitude-slider" min="30" max="60" step="5" value="45">
<span id="latitude-value">45</span>°N
</label>
<label>
Species type:
<select id="species-type">
<option value="early">Early (willow, 100 GDD)</option>
<option value="mid" selected>Mid-season (oak, 200 GDD)</option>
<option value="late">Late (ash, 300 GDD)</option>
</select>
</label>
<label>
Climate scenario:
<select id="climate-scenario">
<option value="current">Current Climate</option>
<option value="warm2c" selected>+2°C Warming</option>
<option value="warm4c">+4°C Warming</option>
</select>
</label>
<div class="button-group">
<button id="run-phenology-sim">Run Year</button>
</div><p><strong>Bud break (SOS):</strong> <span id="bud-break-date"></span></p>
<p><strong>Peak LAI date:</strong> <span id="peak-lai-date"></span></p>
<p><strong>Senescence start (EOS):</strong> <span id="senescence-date"></span></p>
<p><strong>Growing season length:</strong> <span id="gsl-result"></span> days</p>
<p><strong>Annual GPP:</strong> <span id="annual-gpp"></span> kg C/m²</p>Try this: - Higher latitude: Later bud break (cooler spring), shorter growing season - Warming scenarios: Earlier bud break, longer growing season, higher annual GPP - Early species: Lower GDD requirement → earlier green-up - Late species: Higher GDD requirement → later green-up but avoid late frosts - Notice: Photoperiod (blue dotted) triggers senescence in autumn (falls below 12 hours)
Key insight: Climate warming extends growing season by triggering earlier spring phenology and delaying autumn senescence.
Observations: - Earlier spring: Bud break 2–3 weeks earlier than 50 years ago - Later autumn: Leaf fall 1–2 weeks later - Longer growing season: +10 to +20 days in temperate zones
Consequences: - Increased NPP: Longer photosynthesis season - Water demand: Earlier spring → earlier drought stress - Frost risk: Early bud break → vulnerable to late frosts - Phenological mismatch: Plants and pollinators/herbivores out of sync
Crop maturity:
\text{Days to maturity} = \frac{\text{GDD}_{\text{required}}}{\text{Daily GDD average}}
Example: Corn requiring 1400 GDD in climate with 12 GDD/day average:
\text{Days} = \frac{1400}{12} = 117 \text{ days}
Planting date optimization: - Too early → frost risk - Too late → insufficient GDD before first fall frost
Variety selection: - Short-season varieties for high latitudes - Long-season varieties for warm climates
NDVI time series (from Model 25) tracks phenology: - Green-up date: When NDVI increases rapidly - Peak NDVI: Maximum LAI - Brown-down date: When NDVI decreases
Applications: - Crop monitoring (planting, harvest dates) - Forest health - Climate change detection
Photoperiod matters for: - Senescence timing (day length < 12 hours) - Flowering in long/short-day plants - Prevents false spring (warm January day doesn’t trigger growth)
Better models: Combine GDD + photoperiod thresholds.
Insufficient winter chill: - Delays or prevents bud break - Problem in warming climates (California cherries, wine grapes) - May require “chill hours” below 7°C, not just cumulative cold
Real plants have dynamic thresholds: - Varies with chilling received - Varies with water stress - Genetics (cultivar differences)
Actual phenology: - Bud break takes days to weeks - LAI increases gradually (not step function) - Senescence is progressive, not sudden
Better models: Use sigmoid curves for smooth transitions.
Freeze tolerance varies with season:
Autumn: Plants acclimate as temperatures drop - Harden tissues - Accumulate sugars (antifreeze) - Tolerate −20 to −40°C
Spring: De-acclimate as warmth returns - Tissues more vulnerable - Tolerate only −2 to −5°C
Critical period: Early spring after de-acclimation.
Frost damage function:
D = \begin{cases} 0 & \text{if } T > T_{\text{kill}} \\ 1 - \frac{T}{T_{\text{kill}}} & \text{if } T < T_{\text{kill}} \end{cases}
Where T_{\text{kill}} is killing temperature (depends on acclimation state).
Continuous form:
\text{GDD}(t) = \int_0^t \max(0, T(\tau) - T_{\text{base}}) \, d\tau
Discrete (daily) approximation:
\text{GDD}(n) = \sum_{i=1}^n \max(0, T_i - T_{\text{base}})
Event occurs when cumulative variable crosses threshold:
t^* = \min\{t : \text{GDD}(t) > \text{GDD}_{\text{crit}}\}
Example: Find day when cumulative GDD exceeds 200:
Check daily until condition met.
Gradual transition instead of step function:
\text{Response} = \frac{1}{1 + e^{-k(x - x_0)}}
Where: - x_0 = threshold - k = steepness parameter
For LAI: Smooth green-up instead of instant jump.