.. include:: ../temp_lag_and_period.rst

Amplitude and Phase Characteristics of Diurnal Soil-Temperature Waves
=====================================================================

.. contents::
   :depth: 2
   :local:

Amplitude Differences with Depth
--------------------------------

Daily temperature-wave *amplitude* (half the peak-to-peak swing) normally
**decreases sharply as depth increases**.  This attenuation reveals key
thermal properties:

* **Shallow layers (≈ 5–10 cm)**
  
  * Exposed directly to surface heating and cooling.
  * Exhibit the **largest amplitude**, warming rapidly by day and
    cooling quickly at night.

* **Deep layers (≈ 70–90 cm)**
  
  * Receive energy only after it travels through the overlying soil.
  * Show a **much smaller amplitude** because the soil mass dampens the
    heat wave.

Interpretation
~~~~~~~~~~~~~~

* **Rapid amplitude decay** ⇒ high heat-storage capacity
  (large *C\ :sub:`v`*) and/or low–moderate thermal diffusivity.

* **Amplitude that persists deeply** ⇒ higher thermal diffusivity,
  often due to higher thermal conductivity (*k*) or lower heat capacity
  (dry or sandy soils).

Phase (Lag) Between Diurnal Peaks
---------------------------------

The daily **time lag** (phase shift) between temperature peaks at two
depths reflects how quickly heat moves downward.

* **Short lag**

  * Indicates **high thermal diffusivity** and high *k*.
  * Typical of sandy or dry soils where heat propagates efficiently.

* **Long lag**

  * Reflects **low thermal diffusivity** and low *k*.
  * Common in moist, clay-rich, or organic soils that transmit
    heat slowly.

Summary of Indicators
---------------------

.. list-table:: Relation between field observations and inferred
                 heat-transfer properties
   :header-rows: 1
   :widths: 35 65

   * - **Observation**
     - **Likely interpretation**
   * - Rapid decrease in amplitude with depth
     - High volumetric heat capacity; moderate–low thermal diffusivity
   * - Gradual amplitude decrease persists to depth
     - Higher thermal conductivity; lower heat capacity
   * - Short lag time between successive peaks
     - Higher thermal diffusivity; efficient downward heat transfer
       (sandy, dry soils)
   * - Long lag time between successive peaks
     - Lower thermal diffusivity; sluggish transfer
       (moist clay or organic-rich soils)