# Improving leaf wetness duration modeling with simple physics: applications to apple scab

## Alexandre Leca

### ► To cite this version:

Alexandre Leca. Improving leaf wetness duration modeling with simple physics: applications to apple scab. 75. New England, NY, Canada Fruit Pest Management Workshop, 2013, Burlington, VT, United States. hal-01594312

HAL Id: hal-01594312

https://hal.science/hal-01594312v1

Submitted on 6 Jun 2020

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# Improving leaf wetness duration modeling with simple physics

## Application to apple scab

Alexandre Leca

alexandre.leca@irda.qc.ca

<figure><img src="image_2.png" /></figure>
# Who are you really, Leaf Wetness Duration ?

$$LWD = \text{Time during which a leaf is wet}$$

<figure><img src="image_3.png" /></figure>

Two phenomena

$$WD = \text{Liquid Water Deposition} + \text{Liquid Water Evaporation}$$

<figure><img src="image_4.png" /></figure>

How much water on which leaves?

How fast does it dry?
# How do we measure WD?

Many techniques used<fnref n="1" />

<figure><img src="image_5.png" /></figure>

Mostly used one : **Impedance grid**

BUT

The sensors "dried when 15-30% of the foliage was still wet"<fnref n="2" />: still, we don't know **how susceptible to fungal pathogens** this foliage was

Which inclination?<fnref n="3" /> Latex painted or not?<fnref n="2" />,<fnref n="3" />
Covered or under clear sky?<fnref n="4" /> At which height?<fnref n="3" />,<fnref n="5" />,<fnref n="6" />

**How can we be accurate and progress when there is no standard in WD sensing?**
**Are drying times really that different from sensors to susceptible apple leaves?**

<footnote n="1">¹ Huber, 1992</footnote>

<footnote n="2">² Gillespie & Kidd, 1978</footnote>

<footnote n="3">³ Lau et al., 2000</footnote>

<footnote n="4">⁴ Leca, 2011</footnote>

<footnote n="5">⁵ Batzer et al., 2008</footnote>

<footnote n="6">⁶ Sentelhas et al., 2005</footnote>
# A simple WD measurement

Objective: to estimate ΔWD between susceptible leaves and sensors

Same volume of water evaporated under controlled conditions
(temperature, relative humidity, radiation)

<figure><img src="image_6.png" /><figcaption>Controlled Environment Chamber</figcaption></figure>

<caption>Timelapse
video camera</caption>

$$WD = \text{Time dry} - \text{Time drop deposition}$$

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>Still shot from the timecoded video</figcaption></figure>
# A simple WD measurement

<figure><img src="image_9.png" /></figure>

cv McIntosh, apple scab susceptible leaves

- Temperature: 0 – 26 °C

- Relative Humidity: 15 – 91 %

- PAR Radiation: 0 – 510 µMol.m⁻².s⁻¹

$$DH_{leaf} = 1,54 * DH_{sensor} + 66,99; R^{2} = 0,79$$

Water drying on leaves is 1.5 times slower than on sensors!

No standard, large discrepancies between leaves and sensors...

**What about a physics based modeling approach?**
# How we model LWD

## Water production

<figure><img src="image_10.png" /></figure>
# How we model LWD

## Spatial distribution of water

<figure><img src="image_11.png" /></figure>

### Water interception

Assuming the "Leaf Area Index proxy" (Magarey, 2005)

Tree's LAI or better : LAI of different layers in the tree

$V_p$ = precipitation water volume

$V_0$ = intercepted water volume

$$V_0 = (1 - \exp(-0,5LAI))*V_p$$

### Water storage capacity

<figure><img src="image_12.png" /></figure>

$V_1$ = critical water volume before overflowing

$V_2$ = overflown water volume

$V_3$ = remaining water volume

$$\text{If } V_0 \ge V_1 : V_3 = V_1 - V_2$$

$$\text{If } V_0 < V_1 : V_3 = V_0$$
# How we model LWD

## Evaporation

Energy budget at the water – air interface

<figure><img src="image_13.png" /></figure>

$$ \lambda E + C = R_n $$

<table><tr><td>- T<sub>air</sub></td></tr><tr><td>- RH</td></tr><tr><td>- U</td></tr><tr><td>- R<sub>g</sub></td></tr><tr><td>- V<sub>water</sub> = V<sub>3</sub></td></tr><tr><td>- Exchange surface</td></tr></table>
# How we model LWD

## Exchange surface and wettability

$$ \text{Exchange surface at air-liquid interface} = f(\text{drop shape}) $$

$$ \text{Drop shape} = f(\text{surface tensions coexistence at triple point}) $$

Quantified by the contact angle θ

<figure><img src="image_14.png" /></figure>
# How we model LWD

## Variables involved

<figure><img src="image_15.png" /></figure>
# What has been done so far

## Data acquisition to define model parameters :

* ☑ Meteorological data collection throughout the season

* ☑ Wettability Measurements on cv McIntosh susceptible leaves

* ☑ Water storage capacity of cv McIntosh susceptible leaves

* ☑ McIntosh trees LAI measurement in our experimental orchard

## Model programming and development :

* ☑ Evaporation module
# Why measure wettability?

Modeling with the right wettability is **crucial**

<figure><img src="image_16.png" /></figure>

$$WD_{\theta110} \approx 2*WD_{\theta55}$$

<figure><img src="image_17.png" /></figure>

Seems to be cultivar dependent (2 cv studied so far) <fnref n="1" />: requires measures for each cv ?

Are there average values on susceptible apple leaves? Reps would tell!

Once the device is set, measurements are quite fast !

<figure><img src="image_18.png" /></figure>

First step : **McIntosh** (64% of apples produced in Quebec)

<footnote n="1">¹ Leca, 2011</footnote>
# McIntosh wettability

Contact angle value depends on initial conditions :

* leaf's initial wetting (wet or dry?)

* dew water forming on the leaf or dripping?

* raindrops falling at which speed?

<figure><img src="image_19.png" /></figure>

In laboratory conditions : different falling speeds reproduced by varying falling height

Contact angle correlated with falling height
→ Correlated with drop speed at the impact

What about the initial wetting of leaf ?
# McIntosh wettability

Wettability in function of falling speed for different wetting initial conditions

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>
# McIntosh wettability

**Weber number** links impact velocity to spreading of the drop (further utility as a splashing descriptor<fnref n="1" />)

$$W_e = \frac{m v^2}{\sigma} \qquad \begin{array}{l} m : \text{mass of raindrop} \\ v : \text{raindrop terminal velocity} \\ \sigma : \text{water surface tension} \end{array}$$

Using Weber number to model contact angle of falling droplets :

**In the case of falling droplets :**

$$\theta_{dry}(^{\circ}) = -1,59 * \alpha + 73,02; R^2 = 0,74$$

$$\theta_{wet}(^{\circ}) = -0,69 * \alpha + 33,92; R^2 = 0,84$$

$$\alpha = \frac{W_e \sigma}{2 m g} \qquad \text{g : earth gravity constant}$$

**In the case of formed dew**
**(no falling speed) :**

$$\theta_{dry} = (110,2 \pm 3,2)^{\circ}$$

$$\theta_{wet} = (56,4 \pm 5,8)^{\circ}$$

<footnote n="1">¹ Saint-Jean et al., 2006</footnote>
# Evaporation module

## Evaporation module fully coded

Accuracy evaluated by using controled conditions drying durations <fnref n="1" />,<fnref n="2" />,<fnref n="3" />

### Evaporation module accuracy test

<figure><img src="image_22.png" /></figure>

Variations range :

$T_{air}$ : 10 – 35 °C

$RH$ : 14 – 90 %

$U$ : 0,025 – 5 m.s-1

$R_g$ : 0 – 875 W.m-2

$V$ : 1 – 50 µL

$$D_{sim} = 0,96 * D_{obs} + 4,17$$

$$R^2 = 0,93$$

<footnote n="1">¹ Leclerc et al., 1985</footnote>

<footnote n="2">² Magarey et al., 2005</footnote>

<footnote n="3">³ Leca, 2011 *unpublished work*</footnote>
# What is left to do

* Develop the water input module to finish LWD model

* Use the measured data (Tair, RH, U, Rg, LWD) to validate and adjust model

* Spread out model in decision aid tools

<figure><img src="image_23.png" /></figure>

Are forecasts accurate ?

<figure><img src="image_24.png" /></figure>

If Yes : **Mission Accomplished!**

If Not : **What have we done wrong?**
# Leads for the future ?

<figure><img src="image_25.png" /></figure>

## LWD for other species

- not much to change (wettability, boundary layer)

- might be of interest for several pathosystems

<figure><img src="image_26.png" /></figure>

## FWD : Fruit Wetness Duration?

- Great fruits temperature model exists <fnref n="1" />

- Useful to estimate sooty blotch flyspeck

- water dynamics (wettability, droplets sliding, etc.) are a nice and realistic challenge

<figure><img src="image_27.png" /></figure>

## Any other idea ?

<footnote n="1">¹ Saudreau et al., 2011</footnote>
Thank you for your attention !!

<figure><img src="image_28.png" /></figure>

Contributed to this work : M. Boissières, J.Tardif, V. Joubert, V.Philion

<figure><img src="image_29.png" /></figure>

Funding for this project has been provided in part through the Canadian Agricultural Adaptation Program (CAAP) on behalf of Agriculture and Agri-Food Canada. In Quebec, the portion intended for the agricultural-production sector is being managed by the Conseil pour le développement de l'agriculture du Québec (CDAQ).

<figure><img src="image_30.png" /></figure>

Agriculture and
Agri-Food Canada

Agriculture et
Agroalimentaire Canada