SubDailyInterpolation

A function that interpolates daily minimum and maximum values to sub-daily time steps, applies a response function to each interpolated value, and aggregates the results to produce a daily average or sum.

Overview

SubDailyInterpolation is a temporal interpolation function that enhances the accuracy of daily calculations by accounting for sub-daily variation in environmental variables, most commonly air temperature. In agricultural systems, using only daily maximum and minimum values to represent diurnal patterns can introduce significant errors, particularly for non-linear responses such as thermal time accumulation near temperature thresholds.

This function operates in three sequential steps:

Interpolation: A child InterpolationMethod generates sub-daily values from daily minimum and maximum inputs (e.g., from weather data).
Response Transformation: Each interpolated value is passed through a child Response function, which can apply non-linear transformations such as temperature response curves with base and optimal thresholds.
Aggregation: The transformed sub-daily values are either averaged or summed to produce the final daily value, depending on the specified aggregation method.

SubDailyInterpolation is particularly critical for thermal time calculations, where temperature effects on crop development are highly non-linear. Using sub-daily temperature resolution prevents underestimation or overestimation that occurs when applying response functions to daily mean temperatures.

Model Structure

This section describes how this model is positioned within the APSIM framework. It outlines the broader structural and computational components that define its role and interactions in the simulation system.

This model inherits structural and functional behaviour from the following core APSIM components:

Connections to Other Components

This section describes how the model interacts with other components in the APSIM Next Generation framework.
These connections allow the model to exchange information—such as environmental conditions, developmental stage, or physiological responses—with other parts of the simulation system. For a general overview of how model components are connected in APSIM, see the Connections Overview.

Component	Model	Connection Type	Description
InterpolationMethod	IInterpolationMethod	Child, ByName	Generates sub-daily values from daily minimum and maximum inputs. Common implementations include ThreeHourAirTemperature and other temporal interpolation methods.
Response	IIndexedFunction	Child, ByName	Applies a transformation to each sub-daily interpolated value. Typically an XYPairs function defining temperature response curves with base, optimum, and maximum thresholds.
MetData	IWeather	First Available	Provides daily weather data including minimum and maximum values for the variable being interpolated (usually air temperature).

Model Variables

This section lists the key variables that describe or control the behaviour of this component. Some variables can be adjusted by the user to modify how the model behaves (configurable), while others are calculated internally and can be viewed as model outputs (reportable). For a general explanation of variable types and how they are used within the APSIM Next Generation framework, see the Model Variables Overview.

Configurable and Reportable Properties

Property	Type	Description
agregationMethod	AgregationMethod (enum)	Method used to aggregate sub-daily response values. Options are: Average (returns mean of sub-daily values) or Sum (returns total of sub-daily values). Default is typically Average for thermal time calculations.

Read-Only Reportable Properties

Property	Type	Description
Value	double	The final aggregated daily value after interpolation, response transformation, and aggregation. This is the primary output used by parent models.
SubDailyInput	List<double>	The raw sub-daily interpolated values before response transformation. Useful for diagnostics and validation.
SubDailyResponse	List<double>	The transformed sub-daily values after applying the Response function. Useful for understanding the contribution of each time step to the final aggregated value.

Events

This section describes the events associated with this component. Events are signals or notifications that indicate when a particular process occurs within the simulation, or when a component needs to respond to a change in another part of the system. Some events are listened for by this component to trigger its processes, while others are raised to inform other components about changes. For a general overview of how APSIM Next Generation uses events to coordinate processes between components, see the Events Overview.

Events Listened For

Event	Purpose
DoDailyInitialisation	Triggers the sub-daily interpolation and response calculation at the start of each simulation day. This ensures sub-daily values are ready before other daily processes execute.

Events Raised

No events are raised by this function.

Processes and Algorithms

This section describes the scientific processes and algorithms represented by this component. Each process corresponds to a biological, physical, or chemical mechanism simulated during a model time step. Where appropriate, equations or conceptual summaries are provided to explain how the process operates within the APSIM Next Generation framework.

Sub-Daily Interpolation and Aggregation

At the start of each simulation day (triggered by the DoDailyInitialisation event), SubDailyInterpolation performs the following sequence:

1. Interpolation

The child InterpolationMethod (e.g., ThreeHourAirTemperature) generates a series of sub-daily values from the daily minimum and maximum inputs:

\[ T_{i} = f_{\text{interpolate}}(T_{\min}, T_{\max}, t_i) \]

where: - \(T_i\) = interpolated value at sub-daily time step \(i\) - \(T_{\min}\) = daily minimum value (from weather data) - \(T_{\max}\) = daily maximum value (from weather data) - \(t_i\) = time of day for sub-daily step \(i\) - \(f_{\text{interpolate}}\) = interpolation function (e.g., sinusoidal curve fitting diurnal temperature pattern)

For ThreeHourAirTemperature, this produces 8 values at 3-hour intervals (0:00, 3:00, 6:00, …, 21:00).

2. Response Transformation

Each interpolated value is passed through the child Response function, which applies a transformation (typically a temperature response curve):

\[ R_i = f_{\text{response}}(T_i) \]

where: - \(R_i\) = response value at sub-daily time step \(i\) - \(f_{\text{response}}\) = response function (e.g., XYPairs defining piecewise linear or non-linear response)

For thermal time calculations, the response function typically implements a piecewise curve:

\[ f_{\text{response}}(T) = \begin{cases} 0 & \text{if } T < T_{\text{base}} \\ T - T_{\text{base}} & \text{if } T_{\text{base}} \le T \le T_{\text{opt}} \\ T_{\text{opt}} - T_{\text{base}} - \frac{(T - T_{\text{opt}})(T_{\text{opt}} - T_{\text{base}})}{T_{\text{max}} - T_{\text{opt}}} & \text{if } T_{\text{opt}} < T \le T_{\text{max}} \\ 0 & \text{if } T > T_{\text{max}} \end{cases} \]

where \(T_{\text{base}}\), \(T_{\text{opt}}\), and \(T_{\text{max}}\) are cardinal temperatures defining the crop’s temperature response.

3. Aggregation

The transformed sub-daily values are aggregated according to the specified agregationMethod:

Average Method (typical for thermal time): \[ V_{\text{daily}} = \frac{1}{n} \sum_{i=1}^{n} R_i \]

Sum Method (used when accumulating total effects): \[ V_{\text{daily}} = \sum_{i=1}^{n} R_i \]

where: - \(V_{\text{daily}}\) = final daily aggregated value - \(n\) = number of sub-daily time steps - \(R_i\) = response value at time step \(i\)

Biological Significance

The sub-daily approach is essential for accurate thermal time calculation because:

Non-linear Response: Temperature effects on development are non-linear with distinct base, optimum, and maximum thresholds. Applying these thresholds to daily mean temperature produces different results than averaging the responses to sub-daily temperatures.
Threshold Effects: When daily mean temperature falls within the optimal range but sub-daily temperatures exceed or fall below cardinal thresholds, using only the mean temperature misses important inhibitory effects.
Diurnal Asymmetry: The timing and duration of exposure to different temperature ranges during the day affects developmental responses. Sub-daily resolution captures these temporal patterns.
Accuracy at Temperature Extremes: When daily temperature ranges span multiple thermal response zones (base to optimal to supra-optimal), sub-daily interpolation provides substantially more accurate thermal time estimates than using daily averages.

For example, with a daily minimum of 5°C and maximum of 35°C (mean 20°C), and cardinal temperatures of base=0°C, optimum=30°C, maximum=40°C, applying the response to the mean temperature produces a different thermal time value than averaging the responses to the actual diurnal temperature curve.

User Interface

SubDailyInterpolation can be added as a child node under components that require daily aggregated values from sub-daily calculations (commonly under ThermalTime or other phenology-related functions). Right-click the parent node, select “Add Model…”, and search for “SubDailyInterpolation” in the Filter Box.

Required Child Components:

InterpolationMethod: Must add an interpolation method (e.g., ThreeHourAirTemperature) with the name “InterpolationMethod” as the function expects a child with this specific name.
Response: Must add a response function (typically XYPairs) with the name “Response” to define the transformation applied to each interpolated value.

Configuration:

Set the agregationMethod property to either “Average” or “Sum” depending on whether you want the mean or total of sub-daily responses.

Practical Example

Example: Thermal Time Calculation for Oats

In oat phenology, thermal time drives developmental progress through growth stages. Using SubDailyInterpolation with three-hour temperature intervals and a piecewise thermal response provides accurate thermal time accumulation:

Configuration: - agregationMethod: Average - InterpolationMethod: ThreeHourAirTemperature - Response: XYPairs with coordinates (0,0), (30,30), (40,0) - Base temperature: 0°C - Optimum temperature: 30°C
- Maximum temperature: 40°C

Calculation on a Day with Tmin=5°C, Tmax=35°C:

ThreeHourAirTemperature interpolates to 8 values: [5.0, 7.2, 15.8, 26.4, 32.8, 34.2, 28.6, 14.2]°C
Response function applied to each:
- \(R(5.0) = 5.0\)°C
- \(R(7.2) = 7.2\)°C
- \(R(15.8) = 15.8\)°C
- \(R(26.4) = 26.4\)°C
- \(R(32.8) = 30.0 - \frac{(32.8-30)(30)}{10} = 21.6\)°C
- \(R(34.2) = 30.0 - \frac{(34.2-30)(30)}{10} = 17.4\)°C
- \(R(28.6) = 28.6\)°C
- \(R(14.2) = 14.2\)°C
Average = \((5.0 + 7.2 + 15.8 + 26.4 + 21.6 + 17.4 + 28.6 + 14.2) / 8 = 17.0\)°C·d

Compare this to the naive approach using daily mean temperature (20°C), which would yield 20.0°C·d—a 17.6% overestimation of thermal time for this particular day.

Over the course of a growing season, these daily differences accumulate, potentially shifting predicted phenological events (flowering, maturity) by several days or more, which can have significant implications for crop management decisions.