Thermal and rainfall sensitivity with stage wise optimum temperature of rice in Ranchi, Jharkhand

Introduction

Rice (Oryza sativa L.) is the world's most critical staple food crop, sustaining more than half of the global population and supplying over 21% of daily caloric intake worldwide [1] . Global rice demand is projected to rise by approximately 35% by 2035, driven by population growth and shifting dietary preferences [2] . Yet the capacity to meet this demand is increasingly threatened by climate change. Between 2022 and 2023, global rice production declined by an estimated 300, 000 tonnes compared to the preceding year, with major producing countries recording significant yield losses attributable to climatic disruptions [3] . Global mean surface temperatures have already risen by approximately 1.1 °C above pre-industrial levels and projections suggest a further increase of 1.5-4.8 °C by 2100, with the frequency and intensity of heat extremes increasing disproportionately in major rice-growing regions of South and Southeast Asia [4] . Temperature is one of the most dominant abiotic factors governing rice growth, development and yield formation. Each 1 °C increase in global mean temperature is projected to reduce rice yield by approximately 3.2% globally and by up to 5.2% per °C as measured in field warming experiments [5] . In India alone, the world's second-largest rice producer, climatedriven yield losses prompted a nationwide rice export ban in 2023, causing international prices to rise by ~20% and amplifying food security concerns across import-dependent nations [4,6] . Temperature sensitivity of rice is not uniform across its life cycle.

The vegetative stage benefits from moderate warmth (optimal temperature ~28-30 °C) for canopy development and dry matter accumulation, while reproductive stagespanicle initiation, flowering and grain filling -are far more vulnerable to temperature extremes [7] . At the flowering stage, exposure to temperatures above 33-35 °C for even one to two hours during anthesis triggers irreversible spikelet sterility through pollen desiccation, impaired anther dehiscence and disrupted fertilisation [8] . During grain filling, temperatures exceeding 26-27 °C shorten the grainfilling duration, reduce starch biosynthesis rates and lower 1, 000-grain weight, collectively compressing final yield [9,10] . (10) (10) demonstrated that growing-season temperature is a key statistical predictor of inter-annual yield variability in major cereals, explaining 30% or more of year-to-year fluctuations in global average yields. Subsequent work has refined this understanding by showing that crop yield responses to temperature are highly stage-specific: the same degree of warming can be neutral or even beneficial during early vegetative growth but catastrophic during the reproductive window [4,8] . This body of literature largely emerged from temperate, irrigated, or controlledenvironment systems and their direct applicability to rainfed humid subtropical ecosystems of South Asia, where erratic monsoon timing superimposes moisture stress on already challenging thermal regimes, remains poorly characterised. Adjusting sowing dates is widely recognised as one of the most accessible and low-cost agronomic strategies to synchronise crop phenology with favourable thermal and moisture windows, thereby buffering the impact of climate variability on yield [11] . In the Eastern Indo-Gangetic Plain (EIGP) of India, a region encompassing the humid subtropical states of Jharkhand, Bihar and Odisha, sowing date decisions are closely intertwined with the onset and cessation of the south-west monsoon, which delivers ~85% of the annual rainfall in the June-September window. Early sowings risk exposing the crop to pre-monsoon heat buildup during establishment, while late sowings may push grain filling into cooler, drier post-monsoon conditions that limit productivity [12] . Despite the agronomic importance of this region, long-term empirical evidence quantifying how sowing date modulates phenophase-specific temperature sensitivity across multiple rice varieties under field conditions remains limited. Most crop-weather studies from India have either been conducted at a single location and season [7] , relied on simulation modelling without multi-year field validation [11] , or focused on temperature thresholds for spikelet sterility without resolving the continuous sensitivity coefficient across the full crop cycle [4] . Similarly, the role of phenophase-specific rainfall beyond total seasonal accumulation in shaping yield outcomes has received scant attention at the variety × sowing date level in humid subtropical settings [6,13] .

A key knowledge gap exists across three dimensions: how temperature and rainfall effects vary by individual growth stage rather than the whole season; how the direction and strength of sensitivity shifts with sowing date; and whether commercially grown varieties differ in their thermal and moisture responses. No multi-year, multi-variety field study has addressed all three together under humid subtropical conditions of eastern India. Therefore, this study quantifies phenophase-specific temperature and rainfall sensitivity of rice grain yield across varieties and sowing dates, with three specific objectives: (i) to estimate stage-wise optimum temperatures (Topt) using quadratic regression; (ii) to identify the most temperaturesensitive phenophase and quantify the sensitivity coefficient (S, kg ha⁻¹ °C⁻¹); and (iii) to assess phenophase-specific rainfall-yield relationships to identify moisture-critical growth windows. The study makes four novel contributions: it provides the first multi-year, field-based characterisation of stageresolved thermal sensitivity across three varieties in the humid subtropical eastern Indo-Gangetic Plain; it documents a sowing-date-driven directional shift in sensitivity from negative under early sowing to positive under mid-to-late sowing, not previously reported at this resolution in India; it identifies flowering-milking as the most rainfall-critical stage, offering actionable targets for irrigation management; and it generates robust, biologically consistent estimates to support climate-smart cultivar recommendations, sowing calendar optimisation and crop model parameterisation under projected warming.

Materials and Methods

Experimental Site, Design and Crop Management

Field experiments were conducted at Birsa Agricultural University, Ranchi, Jharkhand, India (23.17°N, 85.19°E; 625 m msl) under humid subtropical climatic conditions across eight consecutive cropping seasons from 2017 to 2024. A factorial randomised block design (FRBD) with three replications was adopted to evaluate three rice (Oryza sativa L.) varieties viz. Sahbhagi Dhan, Naveen and MTU1010 sown under three sowing dates: D1 (05 June), D2 (15 June) and D3 (25 June). Daily meteorological data comprising maximum temperature (Tmax), minimum temperature (Tmin) and rainfall (mm) were systematically recorded across five key phenological stages: panicle initiation, 50% flowering, milking, grain filling and physiological maturity.

Computation of Mean Temperature

For each phenological stage, the mean temperature (Tmean; °C) was computed as the arithmetic mean of daily maximum (Tmax; °C) and minimum (Tmin; °C) temperatures, following the standard procedure widely adopted in cropweather analysis [14,15] :

where Tmean is the phenophase-specific mean temperature (°C), Tmax is the daily maximum temperature (°C) and Tmin is the daily minimum temperature (°C). This widely used metric effectively characterises the thermal environment experienced by the crop during each developmental stage.

Estimation of Optimum Temperature

The optimum temperature (Topt; °C) for grain yield at each phenological stage was estimated by fitting a quadratic polynomial regression of grain yield (Y; kg ha⁻¹) on phenophase mean temperature (T; °C) for each variety × sowing date combination [10,14,15] :

where Y is the grain yield (kg ha⁻¹); T is the phenophase mean temperature (°C); β₀ is the intercept; β₁ and β₂ are the linear and quadratic regression coefficients, respectively; and ε is the random error term. The Topt was derived analytically by differentiating Equation [2] with respect to T and equating the first derivative to zero:

To be biologically valid, a Topt estimate must meet two conditions: (i) β₂ < 0, confirming a concave-downward parabola indicating a genuine yield maximum and (ii) Topt fell within the observed range of Tmean for that specific phenophase-sowing date combination, preventing extrapolation beyond the measured thermal domain. When these parameters were not met because of limited interannual thermal variation across the eight-year observational record, the empirical Topt was reported as the observed Tmean that corresponded to the maximum grain production in that combination [10] .

Phenophase-Specific Temperature Sensitivity of Grain Yield

The sensitivity of grain yield to phenophase-specific temperature was quantified by estimating the slope coefficient from a simple ordinary least-squares (OLS) linear regression of grain yield (Y; kg ha⁻¹) on phenophase mean temperature (T; °C) for each variety × sowing date combination [10,16] :

where Y is the grain yield (kg ha⁻¹); T is the phenophase mean temperature (°C); α is the regression intercept (kg ha⁻¹); S is the temperature sensitivity coefficient (kg ha⁻¹ °C⁻¹), representing the change in grain yield per unit increase of 1 °C in mean temperature; and ε is the residual error term. A negative S indicates a yield penalty (heat stress) per unit warming, while a positive S shows a yield advantage as temperature rises. Regression slopes were classified as Very High = |S| > 200; High = |S| 100-200; Moderate = |S| 50-100 kg ha⁻¹ °C⁻¹ [17] . The phenophase exhibiting the maximum absolute sensitivity value (|S|max) was identified as the most temperature-sensitive developmental stage for each variety × sowing date combination.

Relative sensitivity (Srel) was calculated as:

where S = temperature sensitivity coefficient (kg ha⁻¹ °C⁻¹).

Model fit was assessed using the coefficient of determination (R²), calculated as [18] :

where 𝑆𝑆𝑟𝑒𝑠 = 𝛴(𝑌𝑖 -Ŷ𝑖)² is the residual sum of squares and SStot = Σ(Yi -Ÿ)² is the total sum of squares. The student's t-test was used to determine statistical significance at p< 0.05, p< 0.01 and p< 0.001. Given the eight-year observational record (n = 8 per sowing group; degrees of freedom = 6), statistical power was naturally limited. As a result, temperature sensitivity was predominantly evaluated using the magnitude (|S|) and direction of regression slopes, as well as their biological consistency across varieties and sowing dates, as recommended by (10) (10) and Rezaei et al. (2015) [16] .

Effect of Rainfall on Grain Yield

The relationship between cumulative seasonal rainfall and grain yield was quantified for each variety × sowing date combination using the Pearson correlation coefficient (r) and OLS linear regression. Total seasonal rainfall (Rain Total ; mm) was computed as the cumulative sum of rainfall recorded across all five phenological stages:

Rain Total = Rain S-Veg + Rain Veg-Flow + Rain Flow-Milk + Rain MilkGFill + Rain GFill-Mat (7) where Rain S-Veg , Rain Veg-Flow , Rain Flow-Milk , Rain Milk-GFill and Rain GFill-Mat represent cumulative rainfall (mm) during the sowing-vegetative, vegetative-flowering, flowering-milking, milking-grain filling and grain filling-maturity stages, respectively. Phenophase-wise rainfall sensitivity was assessed by computing the standardised OLS regression coefficient (β; dimensionless) of grain yield on phenophase-specific rainfall for each variety × sowing date combination, following the elasticity-based sensitivity framework of Lobell and Burke (2010) [19] as adapted by Deb et al. (2023) [20] :

where dY and dR are the changes in yield and rainfall, respectively and SDY and SDR are their standard deviations. Both variables were standardised to zero mean and unit variance prior to regression, enabling direct comparison of sensitivity magnitude across phenophases with differing rainfall scales. A positive β indicates a yield benefit from phase rainfall, while a negative β denotes a yield penalty. Model fit was assessed using R² and statistical significance was tested at p< 0.05, p< 0.01 and p< 0.001 using the student's t-test. Given the eight-year record (n = 8; df = 6), biological consistency of the direction and magnitude of β across varieties and sowing dates was prioritised over formal significance thresholds, as recommended by (10) (10) and Rezaei et al. (2015) [16] . All analyses were performed in R (version 4.5.1) using the lm() function and visualisations were produced with ggplot2.

Results

Optimum Temperature and Grain Yield under Optimal Sowing Dates

The stage-wise optimum temperatures (Topt) and corresponding mean grain yields for each variety under their respective optimum sowing dates are listed in

Phenophase-Specific Temperature Sensitivity of Grain Yield

The most temperature-sensitive phenological intervals and their corresponding absolute (S, kg ha⁻¹ °C⁻¹) and relative (Srel,% °C⁻¹) sensitivity coefficients are summarised in

Effect of Seasonal Rainfall on Grain Yield

Seasonal rainfall ranged from 781 mm to 1797 mm across years and sowing dates, yet total accumulation did not linearly govern yield outcomes, rainfall timing across phenophases proved far more decisive. The standardised sensitivity index (β) heatmap (Fig. 2) and phenophase-wise summary (Table 3) consistently show that reproductive stages were the most rainfall-sensitive across all varieties and sowing windows. Under D1 (05 June), milking-grain filling was the most sensitive phenophase for all three varieties, with Naveen recording the strongest negative response (β = -0.65), followed by Sahbhagi Dhan (β = -0.49) and MTU1010 (β = -0.43). Flowering-milking showed similarly strong negative sensitivity (β = -0.59, -0.46 and -0.40 for Naveen, Sahbhagi Dhan and MTU1010, respectively). It is indicating that excess rainfall across consecutive reproductive stages consistently depressed yield, likely through lodging, poor pollination and disease pressure. Early-season rainfall showed a slight positive association (β = +0.10 to +0.18), while vegetative-flowering remained negligible. D2 (15 June) showed the most dampened sensitivity profile.

Reproductive stage penalties persisted but were considerably weaker. Flowering-milking β ranged from -0.22 to -0.32 and milking-grain filling from -0.08 to -0.24, making D2 the most stable sowing window against rainfalldriven yield variability. Under D3 (25 June), a clear sign reversal emerged at grain filling-maturity, where all varieties recorded positive β values (Naveen: +0.57; Sahbhagi Dhan and MTU1010: +0.53), reflecting supplementary benefit of residual postmonsoon rainfall during terminal grain development. Despite this, mid-season stages remained strongly negative.

Milking-grain filling reached β = -0.51, -0.46 and -0.38 and flowering-milking β = -0.38, -0.35 and -0.30 for Sahbhagi Dhan, MTU1010 and Naveen, respectively, confirming that the reproductive stage rainfall penalty is a cross-variety phenomenon independent of sowing date. Among all combinations, Naveen under D1 returned the highest R² for milking-grain filling (R² = 0.424), indicating rainfall variability in this phase alone explained ~42% of interannual yield variation, which is the strongest single-phase moisture control in the dataset (Table 3). Although none of the β values attained formal significance (all p> 0.05), the directional consistency across varieties and sowing dates provides strong biological evidence that phenophasespecific rainfall timing, not seasonal totals, drives yield variability in this system.

Discussion

Topt was phenophase-specific and variety-dependent, peaking at 28.40 °C during flowering-milking in Naveen/D2 and declining toward maturity (24.65-25.35 °C) across all varieties. This is consistent with known thermal sensitivity of carbohydrate accumulation during grain filling [9] and reproductive impairment above 33 °C [8] . The most prominent finding was the sowing-date-driven directional reversal of temperature sensitivity. Under D1, Sahbhagi Dhan and Naveen showed very high negative sensitivity at sowing-vegetative (Srel = -8.60% to -11.32% °C⁻¹), which is 2.7 to 3.5-fold larger than the global rice warming penalty of -3.2% °C⁻¹ [5] . It is reflecting premonsoon heat stress suppressing early establishment. MTU1010 diverged markedly, showing peak positive sensitivity at milking-grain filling (S = +431.94 kg ha⁻¹ °C⁻¹; Srel = +11.60% °C⁻¹), suggesting this variety may possess relatively greater early-season heat tolerance, possibly through deeper root architecture or stronger osmotic adjustment, while remaining thermally responsive during later grain development. Though physiological characterisation studies would be needed to confirm this mechanism. This variety-level divergence under the same sowing window cautions against applying uniform thermal response assumptions across varieties in climate adaptation planning. Under D2 and D3, sensitivity shifted to strongly positive at vegetative-flowering and flowering-milking (Srel = +4.17% to +9.92% °C⁻¹), suggesting moderate warming during reproductive development remains within beneficial thresholds below the critical spikelet sterility temperature of 35 °C [21] . This directional shift is largely absent from global meta-analyses that report uniformly negative warming responses [4,23] and the wide Srel range (-11.32% to +9.92% °C⁻¹) confirms that a single global sensitivity estimate cannot capture stage-and sowing-specific variability.

Modest R² values (0.043-0.210) further indicate that temperature explains only a fraction of inter-annual yield variability, with other factors such as rainfall distribution and solar radiation contributing substantially. Rainfall timing governed yield outcomes more decisively than total seasonal accumulation, consistent with findings from Indian monsoon rice systems [6,13] . Under D1, milkinggrain filling exerted the strongest negative rainfall influence across all varieties (β = -0.49 to -0.65), with Naveen showing the highest explained variance (R² = 0.424) moisture variability in this single phase accounted for over 40% of inter-annual yield fluctuation. Excess rainfall during consecutive reproductive stages likely intensified disease pressure, caused physical lodging and impaired pollination [22] . D2 showed the most checked and balanced rainfall sensitivity profile across all phenophases, reinforcing its status as the most climate-stable sowing option with direct implications for irrigation scheduling. Under D3, a positive reversal at grain filling-maturity (β = +0.53 to +0.57) reflects supplementary benefit of residual post-monsoon rainfall during terminal grain development when monsoon withdrawal otherwise limits moisture availability. That midseason reproductive stages remained strongly negative even under D3 confirms the rainfall penalty during these phases is a cross-variety phenomenon independent of sowing date. Overall, Naveen/D2 emerged as the most productive combination, with higher reproductive-stage Topt indicating greater heat buffering capacity. The convergence of both thermal and rainfall sensitivity analyses on D2 dampened negative thermal sensitivity, moderate and balanced rainfall penalties and avoidance of both pre-monsoon heat stress and mid-season waterlogging risk. It makes mid-June sowing the most robust adaptation recommendation under current and near-future climate conditions in this region, consistent with broader Indo-Gangetic Plain policy guidance [11,24] .

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