Julio Soria

# Direct numerical simulation of a thermal turbulent boundary layer: an
analogy to simulate bushfires and a testbed for artificial intelligence remote
sensing of bushfire propagation

<EMAIL_ADDRESS>Shahram Karami  Callum Atkinson  Minghang Li
Laboratory for Turbulence Research in Aerospace & Combustion (LTRAC),
Department of Mechanical and Aerospace Engineering, Monash University,
(Clayton Campus), Melbourne, 3800, Victoria, Australia

###### Abstract

Direct numerical simulation of a turbulent thermal boundary layer (TTBL) can
perform the role of an analogy to simulate bushfires that can serve as a
testbed for artificial intelligence (AI) enhanced remote sensing of bushfire
propagation. By solving the Navier-Stokes equations for a turbulent flow, DNS
predicts the flow field and allows for a detailed study of the interactions
between the turbulent flow and thermal plumes. In addition to potentially
providing insights into the complex bushfire behaviour, direct numerical
simulation (DNS) can generate synthetic remote sensing data to train AI
algorithms such as convolutional neural networks and recurrent neural
networks, which can process large amounts of remotely sensed data associated
with bushfire. Using the results of DNS as training data can improve the
accuracy of AI remote sensing in predicting fire front propagation of
bushfires. DNS can also test the accuracy of the AI remote sensing algorithms
by generating synthetic remote sensing data that allows their performance
assessment and uncertainty quantification in predicting the evolution of a
bushfire. The combination of DNS and AI can improve our understanding of
bushfire dynamics, develop more accurate prediction models, and aid in
bushfire management and mitigation.

##  1 Introduction

Australia, like many other places in the world with a similar climate,
experiences frequent bushfires or wildfires, which as was recently
experienced, pose a serious threat to the local population, unique Australian
wildlife, and natural resources, as illustrated in Fig. 1 (BlueMountaiFire2019
; Damany-Pearce2022 ). These bushfires also contribute to an increase in
global CO2 emissions.

Despite decades of research on bushfires (nla.cat-vn8555232 ; CSIRO2020 ),
there are no verified theories on how they spread that can serve as a basis
for accurate prediction of bushfire dynamics. However, such understanding is
necessary to develop optimal fire prevention, mitigation, and control
strategies to minimise the negative impact on the population and the
environment. computational fluid dynamics (CFD) or lower resolution numerical
weather prediction models of the atmosphere coupled with empirical (or quasi-
empirical) fire spread models, as used in front-tracking approaches, are
unsuitable for operational fire spread prediction CSIRO2020 .

Figure 1: Blue Mountains bushfire (Gospers Mountain, NSW Australia, December
2019) burned more than 510,000 ha (1.26 million acres) making it the largest
forest fire ever recorded in Australia BlueMountaiFire2019

Presently, one approach for remote monitoring of bushfires involves using
infrared satellite sensing. However, while this approach provides temperature
data, it does not provide information on how and at what rate the fire is
moving and behaving within the complex multi-scale, highly dynamic, turbulent
boundary layer (TBL) of the atmosphere. As a result, this approach cannot
accurately predict how the fire front will spread. To tackle this problem,
there is a requirement to supplement the temperature data obtained from
satellites or other aerial platforms like unmanned aerial vehicles fitted with
infrared cameras with the ability to predict the behaviour and movement of
bushfires, including the spreading rate of the fire front. Such a predictive
ability would represent a significant improvement in all aspects of the
disaster management cycle of bushfires. Therefore, this paper proposes a
domain-specific scientific machine learning (SciML) methodology that utilises
physics-informed machine learning (ML) Baker:2019up ; WilcoxICIAM2019 ;
Fukami:2021ka  based on deep learning (DL) to assimilate remotely sensed
temperature data and yield the augmented information on bushfire heat release
rates and transport properties, such as wind velocity, convective energy
transport, and their spatio-temporal evolution. The real-time generation and
availability of such augmented bushfire dynamics information has the potential
to be a vital new tool in all aspects of the disaster management cycle of
bushfires, including prevention, planning, response, and recovery, by
providing high-fidelity, low-uncertainty predictions of bushfire propagation
that is currently unavailable. In order to develop, test and undertake
uncertainty quantification (UQ) of the proposed SciML methodology that will
provide the predictive capability of bushfire dynamics and fire front
propagation by enhancing remotely sensed data, it is imperative to have high-
quality fully resolved and completely charatcerised TTBL data to serve as the
“ground truth”. This fully resolved and quantified TTBL data of a bushfire is
only available via DNS. However, a realistic bushfire DNS with real world
topographies of which there are a large multitude, with all its multi-physics
including combustion is computationally infeasible at the moment, even with
the most powerful Exascale supercomputers. Furthermore, the actual parameter
space is incredibly large, making DNSs of all possible cases to establish the
necessary statistical data for all possible scenarios unfeasible. Therefore,
in this paper an analogy to a bushfire is proposed to serve as the “ground
truth” and to be the testbed for AI enhanced remote sensing of bushfire
propagation. This paper briefly describes the proposed SciML methodology that
utilises physics-informed ML based on DL to assimilate remotely sensed
temperature data and the approach to its UQ. This is followed with a
description of the TTBL DNS methodology, which permits distributed and quite
arbitrary energy sources to be defined and which includes a temperature-
dependent heat-release model as a source term in the energy equation Li2022 .
The proposed implementation of the energy source distribution allows biomass
fuels, i.e. grass, scrubs, trees, etc., to be modelled as localised energy
source with temperature dependent energy release rate depreciating at the same
rate as the source term in the energy equation. Finally the results of one
TTBL DNS, which serves as the “ground truth” to develop, test and UQ any AI
enhanced remotely sensed data of a bushfire are illustrated.

##  2 SciML Based on Physics-informed Deep Learning for Bushfire Predictions

Currently, there is significant effort into remote sensing for detection and
prediction of bushfires/wildfires, such as the Fire Urgency Estimator in
Geosynchronous Orbit (FUEGO) Pennypacker2013 . However, there is currently no
operational nor proposed system which employs AI in the form of discipline
specific SciML to enhance this type of data and provide bushfire dynamics and
reliable fire front propagation rate predictions. The proposed discipline
specific SciML presented in this paper is planned to employ remote sensing by
Satellites, and aerial platforms like UAV, etc. fitted with infrared sensors
to acquire 3D temperature field information of bushfires as outlined
Pennypacker2013 . Furthermore the idea here is to couple this 3D temperature
field information with data assimilation (DA)/SciML to provide information on
the heat release rate distribution, turbulence, transport and fire front
spreading rate. This will enable the development of an improved AI enhanced
predictive model to forecast bushfire spreading rates.

Figure 2 shows the proposed SciML based on physics-informed deep learning
(PiDL) for bushfire predictions. The inputs to the PiDL is the 4-dimensional
vector space of three-dimensional (3D) space and time, $(x,y,z,t)$, which can
be defined on an arbitrary three-dimensional unstructured grid, and the
sampled 3D temperature data, $T_{m}(x_{m},y_{m},z_{m},t_{m})$, which can come
from a range of sources fitted with infrared sensors ranging from low orbit
satellites to fixed wing aircraft to UAVs or drones and serves as the training
data set for the PiDL. The PiDL uses this data to both post-dict (via
training) and predict the TTBL turbulent velocity vector field, the turbulent
pressure and temperature fields, as well as the source term, which represents
the heat release rate due to burning of the biomass during the bushfire, i.e.
$\left(u(x,y,z,t),v(x,y,z,t),w(x,y,z,t)\right),p(x,y,z,t),T(x,y,z,t)\mbox{ and
}\dot{S}_{\theta}(x,y,z,t)$.

The PiDL is contained entirely within the black rectangular box in Fig. 2 with
only the independent 4-dimensional vector space of (3D) space and time, the
sampled 3D temperature data and the turbulent velocity vector, pressure and
temperature fields as well as source term field crossing its boundaries.
Within the PiDL is the DL sub-system, which can be a fully connected neural
network (NN), CNN or a recurrent neural network (RNN), etc., the disciple
specific physics-information in the form of the incompressible Navier-Stokes
equations, the temperature energy equation, which are both liked via a
Boussinesq approximation and written in terms of residual
$e_{i},i\in[1,2,3,4,5]$, for the 5 governing equations. The temperature output
from the DL sub-system, $T(x,y,z,t)$, is spatially and temporally sampled to
be spatially and temporally coincident with the sampled 3D temperature data
$T_{m}(x_{m},y_{m},z_{m},t_{m})$ resulting from the application of the
sampling operator $F_{sampling}(T)$ resulting in
$T_{s}(x_{m},y_{m},z_{m},t_{m})$, which is compared to
$T_{m}(x_{m},y_{m},z_{m},t_{m})$ and yields a residual $e_{data}$.

Figure 2: Proposed SciML for bushfire predictions based on PiDL. The
components of the system within the black rectangular box represent the PiDL.
The inputs to the PiDL is the independent 4-dimensional vector space of space
and time $(x,y,z,t)$ and the sampled 3D temperature data $T_{m}$, which is
here pictorially represented from data that is obtainable from the FUEGO
vertical envelope Pennypacker2013 . The AI learned output of the PiDL is the
TTBL turbulent velocity vector field, the 3D turbulent temperature field and
the source term which represents the heat release due to burning of the
biomass during the bushfire. All outputs are provided by the PiDL as functions
of 4-dimensional vector space of space and time $(x,y,z,t)$.

As shown in Fig. 2 the $e_{i}\textquoteright s$ are combined and integrated
over space and time to yield an error norm pertaining to the physics
information $L_{phy}$, while the $e_{data}$ is also integrated over its space
and time to yield an error norm $L_{data}$. These two error norms are combined
into a cost function $J_{Loss}$ using complementary weights given by the PiDL
parameter $\alpha\in[0,1]$ , which is minimised to train the DL sub-system.

Note that $\alpha=1$ corresponds to a PiDL that is purely a partial
differential equation (PDE) DL solver. Although highly inefficient compared to
traditional numerical methods and it would have to be augmented with
additional physics information in the form of boundary and initial conditions,
otherwise it would produce nonsensical results.

An $\alpha=0$ corresponds to purely machine learning using the DL system, but
no physics information. This could yield temperature interpolation, but no
sensible turbulent fluid velocity and pressure field and heat source
information and since there is no physical constraints on this version of the
PiDL it could also produce nonsensical temperature interpolation results.
Hence, away from these two limits of $\alpha$, both physics information and
measured temperature data contribute to the training and predictions of the
PiDL with its performance therefore dependant on $\alpha$.

###  2.1 “Ground Truth” Data and Uncertainty Quantification of PiDL

In order to develop the details of the PiDL, i.e. the specific DL sub-system,
and test it, i.e. determine the sensitivity of the PiDL output with respect to
$\alpha$ and/or find its optimal value and UQ of the PiDL, “ground truth” data
of every aspect is invaluable. However, this type of data is impossible to
acquire from real bushfires and even limited experimental laboratory “bush”
fires due to the current complete absence of full field 3D simultaneous
velocity vector and temperature field measurement techniques to provide any
reliable measurements in the highly challenging environment of a bushfire.
Nevertheless, DNS of a TTBL with distributed and quite arbitrary energy
sources with a well-defined temperature-dependent heat-release rate model as a
source term in the energy equation Li2022 , serving as an analog to a bushfire
provides the full highly resolved turbulent velocity vector field, the
pressure and temperature field and the heat release source term as the
necessary “ground truth” data as shown in Fig. 3.

Figure 3: Development, testing and UQ of proposed SciML based on PiDL for
bushfire predictions using “ground truth” TTBL DNS temperature data. The
approach to UQ of the PiDL is illustrated in Fig. 4. The TTBL DNS fully
resolved temperature data $T_{e}(\mathbf{x},t)$ is downsampled at random
locations and a given sparsity with measurement noise introduced to simulate
measurement uncertainty, which yield the sampled 3D temperature data
$T_{m}(\mathbf{x}_{m},t_{m})$.

The output from the PiDL at the same spatial resolution as the TTBL DNS:
$\mathbf{u}(\mathbf{x},t)$, $p(\mathbf{x},t)$, $T(\mathbf{x},t)$ and
$\dot{S}_{\theta}(\mathbf{x},t)$ is then used with the “ground truth” TTBL DNS
data: $\mathbf{u}_{e}(\mathbf{x},t)$, $p_{e}(\mathbf{x},t)$,
$T_{e}(\mathbf{x},t)$ and $\dot{S}_{\theta_{e}}(\mathbf{x},t)$ to UQ the PiDL
with respect to bias error, uncertainty, time horizon predictability, etc. as
a function of sampling spacial resolution, sparsity and measurement
uncertainty introduced via noise in $T_{m}(\mathbf{x}_{m},t_{m})$.

Figure 4: System diagram for UQ of the proposed SciML based on PiDL for
bushfire predictions using “ground truth” TTBL DNS data. Variables with the
subscript "$e$" indicates TTBL DNS data, variables with the subscript "$m$"
indicates simulated measured temperature data, while variables without any
subscript indicate output variables from the PiDL.

##  3 Direct Numerical Simulation of a Thermal Turbulent Boundary Layer - An
Analogy to Simulate Bushfires

Given the enormous parameter space necessary to represent all bushfire
scenarios and fuel load characteristics, it is clearly not possible to develop
a universal mathematical model of bushfire and fire propagation that provides
pertinent information in real-time and with high confidence, which is
essential for bushfire management. This will in fact be the work of the fully
implemented, tested and UQ PiDL, which it is hypothesised, will learn from the
field data all these necessary details.

Instead, DNS is used to accurately simulate a canonical TTBL case, which is an
analogy to a bushfire as a first step by including a fully resolved zero-
pressure-gradient (ZPG)-TBL with the bushfire modelled as a distribution of
localised heat sources with a temperature dependent energy release rate Li2022
.

###  3.1 Theoretical Framework of the TTBL DNS

The governing equations for the TTBL are the incompressible Navier-Stokes
equations with the temperature-energy equation, which includes an energy
source term to model the heat release rate due to the burning of the biomass
representing the bush, etc. The Navier-Stokes equations are coupled to the
temperature-energy equation via a Boussinesq approximation Tritton1977  and
are given by:

$\displaystyle\frac{\partial u_{i}}{\partial x_{i}}$ $\displaystyle=$
$\displaystyle 0$ (1) $\displaystyle\frac{\partial u_{i}}{\partial
t}+\frac{\partial u_{i}u_{j}}{\partial x_{j}}$ $\displaystyle=$
$\displaystyle-\frac{\partial p}{\partial
x_{i}}+\frac{1}{\mathrm{Re}}\frac{\partial^{2}u_{k}}{\partial
x^{2}_{k}}+\frac{\kappa_{i}}{\mathrm{Fr_{o}}^{2}}\theta$ (2)
$\displaystyle\frac{\partial\theta}{\partial t}+\frac{\partial
u_{j}\theta}{\partial x_{j}}$ $\displaystyle=$
$\displaystyle\frac{1}{Re\,Pr}\frac{\partial^{2}\theta}{\partial
x^{2}_{i}}+\dot{S}_{\theta},$ (3)

where Eq. 1 represents the continuity equation, a statement of conservation of
mass, Eq. 2 represents the 3 momentum equations, which are a statement of
conservation of linear momentum and Eq. 3 is the temperature-energy equation,
which is a statement of conservation of energy. The last term on the right
hand side of Eq. 2 is the Boussinesq approximation with $\kappa_{i}$ a vector
indicating the direction of the gravitational field which in this case is
$[0,-1,0]$, while the last term on the right-hand side of Eq. 3,
$\dot{S}_{\theta}$, represents the source term, which provides the heat
release rate from the burning of biomass sources. This term needs to be
modelled.

Equations 1 \- 3 are written in non-dimensional form with respect to the non-
dimensional spatial vector $x_{j}$, velocity vector $u_{i}$, pressure $p$ and
temperature $\theta$, defined with respect to its dimensional starred
independent and dependent variables, fluid properties and parameters as:

$\begin{array}[]{l}x_{j}=\frac{x_{j}^{*}}{L}\mathchar
24635\relax\;\;\;t=\frac{t^{*}\,U_{\infty}^{*}}{L}\mathchar
24635\relax\\\\[5.69054pt] u_{j}=\frac{u_{j}^{*}}{U_{\infty}^{*}}\mathchar
24635\relax\;\;\;p=\frac{p^{*}}{\rho_{\infty}^{*}\,U_{\infty}^{*2}}\mathchar
24635\relax\;\;\;\theta=\frac{T^{*}-T_{\infty}^{*}}{T_{ad}^{*}-T_{\infty}^{*}}\mathchar
24635\relax\;\;\;\zeta_{0}=\frac{T^{*}}{T_{ad}^{*}-T_{\infty}^{*}}\mathchar
24635\relax\\\\[5.69054pt] \rho=\frac{\rho^{*}}{\rho_{\infty}^{*}}\mathchar
24635\relax\;\;\;\mu=\frac{\mu^{*}}{\mu_{\infty}^{*}}\mathchar
24635\relax\;\;\;Re=\frac{\rho_{\infty}^{*}\,U_{\infty}^{*}\,L}{\mu_{\infty}^{*}}\mathchar
24635\relax\;\;\;Pr=\frac{\nu_{\infty}^{*}}{\alpha_{\infty}^{*}}\mathchar
24635\relax\;\;\;Fr=\frac{U_{\infty}^{*}}{\sqrt{g\,L}}\mathchar
24635\relax\;\;\;\;Fr_{0}=\zeta_{0}^{1/2}\,Fr\end{array}$ (4)

where the characteristic quantities: $L$ = characteristic length,
$U_{\infty}^{*}$ = characteristic free-stream velocity, $\rho_{\infty}^{*}$ =
characteristic density, $T_{\infty}^{*}$ = characteristic free-stream
temperature, $\mu_{\infty}^{*}$ = characteristic dynamic viscosity,
$\nu_{\infty}^{*}=\frac{\mu_{\infty}^{*}}{\rho_{\infty}^{*}}$ = characteristic
kinematic viscosity, $\alpha_{\infty}^{*}$ = characteristic thermal
diffusivity, $g$ = acceleration due to gravity and $T_{ad}^{*}$ =
characteristic adiabatic flame temperature. The non-dimensional parameters
$Re$ = Reynolds number, $Pr$ = Prandtl number and $Fr$ = Froude number.

###  3.2 Model for the Heat Release Rate of the Burning of Biomass

The source term in Eq. 3 which accounts for the heat release rate of the
burning of biomass in bushfires needs to be modelled. For simplicity, an
exothermic reaction of the type $F\longrightarrow P$, where $F$ is the
unburned biomass and $P$ is the product, is assumed. Furthermore, it is
assumed that the biomass and product have the same constant heat capacity,
molecular weight and molecular diffusion coefficient,. The fuel mass fraction
and temperature transport equation can then be written as:

$\frac{\partial Y^{*}_{F}}{\partial t^{*}}+\frac{\partial
u^{*}_{j}Y^{*}_{F}}{\partial x^{*}_{j}}=\frac{\partial}{\partial
x^{*}_{j}}\left(D^{*}\frac{\partial Y^{*}_{F}}{\partial
x^{*}_{j}}\right)-\dot{\omega}^{*}_{F}$ (5)

and

$\frac{\partial T^{*}}{\partial t^{*}}+\frac{\partial u^{*}_{j}T^{*}}{\partial
x^{*}_{j}}=\frac{\partial}{\partial
x^{*}_{j}}\left(\frac{\lambda^{*}}{c^{*}_{p}}\frac{\partial T^{*}}{\partial
x^{*}_{j}}\right)+\frac{Q^{*}}{c^{*}_{p}}\dot{\omega}^{*}_{F}$ (6)

respectively, where $D^{*}$ = molecular diffusion coefficient, $\lambda^{*}$ =
heat diffusion coefficient, $Q^{*}$ = heat released per unit mass of fuel and
$\dot{\omega}_{F}$ = fuel reaction rate. The fuel reaction rate depends on
temperature with the relationship

$\dot{\omega}^{*}_{F}=BY^{*}_{F}T^{*^{\beta_{1}}}\exp[\frac{-T_{a}}{T^{*}}]$
(7)

where $B$ is a constant, $\beta_{1}$ is temperature exponent and $T_{a}$
denotes the constant activation temperature for the Arrhenius reaction, i.e.
the ratio of the activation energy to the universal gas constant. It should be
noted that the density of the gas mixture has been assumed to be constant.

The non-dimensional form of these equations using $\theta$ as the non-
dimensionalised temperature and $Y=Y^{*}_{F}/Y_{F,0}$ as the non-
dimensionalised mass fraction, where $Y_{F,0}$ = mass fraction of the fuel in
the mixture and using
$c^{*}_{p}T_{\infty}^{*}+Q^{*}Y_{F,0}=c^{*}_{p}T^{*}_{ad}$ , leads to the non-
dimensional form of Eqs. 5 and 6:

$\frac{\partial Y}{\partial t}+\frac{\partial u_{j}Y}{\partial
x_{j}}=\frac{1}{Re\,Pr}\frac{\partial^{2}Y}{\partial
x^{2}_{i}}-\frac{\dot{\omega}_{F}}{Y_{F,0}}$ (8)

and

$\frac{\partial\theta}{\partial t}+\frac{\partial u_{j}\theta}{\partial
x_{j}}=\frac{1}{Re\,Sc}\frac{\partial^{2}\theta}{\partial
x^{2}_{i}}+\frac{\dot{\omega}_{F}}{Y_{F,0}},$ (9)

respectively. Here $Sc=\frac{\nu^{*}}{D^{*}}$ = Schmidt number. If the Lewis
number, which is defined as $Le=\frac{Sc}{Pr}=1$, then adding these two
equations leads to a transport equation for $\theta+Y$ with no source term.
Considering $Y$ and $\theta$ has a value of 1 and 0, respectively in the
unburned mixture and 0 and 1, respectively in the burned mixture, the solution
this resulting equation is $\theta+Y=1$. Hence, the temperature-energy
transport equation, Eq. 3 is the only equation that needs to be solved in
addition to the mass and momentum equations Eq. 1 \- 2. If the non-
dimensionalised temperature defined in Eq. 4 is used for non-
dimensionalisation, then the non-dimensionalised temperature-energy equation
is given by Eq. 3 with the source term, $\dot{S}_{\theta}$ appearing in this
equation given by

$\dot{S}_{\theta}=C(\zeta_{o}+\theta)^{\beta_{1}}(1-\theta)\exp[\frac{-\beta(1-\theta)}{1-\alpha(1-\theta)}],$
(10)

where $\alpha=(T^{*}_{ad}-T^{*}_{\infty})/T^{*}_{ad}$, $\beta=\alpha
T_{a}/T^{*}_{ad}$ and $C$ depends on $c^{*}_{p}$ = heat capacity at constant
pressure, $B$, $Q$ and $Y_{F,0}$. It is not an unreasonable assumption to
consider that $Y_{F,0}$ is a constant where any $c^{*}_{p}$ variation with
temperature can be modelled by adjusting ${\beta_{1}}$. Hence, the source term
can be simplified to read

$\dot{S}_{\theta}=A\,(1-\theta)\,\exp\left[\frac{-\beta\,(1-\theta)}{1-\alpha\,(1-\theta)}\right],$
(11)

where $A$ is a constant.

This approach is the centre of many early development in theoretical
combustion (Clavin:1979 ; Bychkov:2000 ). Despite its restrictive assumptions,
especially at the chemistry level, this source term model preserves many
features, including non-linear heat release and variable temperature.

The heat release parameter $\alpha$ in Eq. 11 depends on the maximum flame
temperature. A recent systematic experimental measurement of the flame
temperature of fires in dry eucalyptus forest by Wotton:2012  reported the
maximum temperature from approximately 700${}^{\circ}C$ to 1200${}^{\circ}C$.
This maximum flame temperature leads to $\alpha$ values between 0.69 and 0.8,
which can be considered a hyper-parameter.

Another parameter is the Zeldovich number $\beta$ in Eq. 11, which is
difficult to obtain for the proposed simple heat release model. However, it is
typically below 10 and no more than about 15 in hydrocarbon flames at
atmospheric pressure (Peters:1997 ; Dold:2002 ). Considering a heterogeneous
reaction that occurs, for instance, at the gas-to-solid interface with the
main source of fuel being solid carbon, the Zeldovich number can be considered
as approximately 8.0. Variations of the normalised heat source term
$\dot{S}_{\theta}/(\dot{S}_{\theta})_{max}$ for $\alpha=0.75$ and various
values of $\beta$ are presented in Fig. 5.

Figure 5: Variations of the normalised heat release rate source term
$\dot{S}_{\theta}/(\dot{S}_{\theta})_{max}$ for $\alpha=0.75$ and various
values of $\beta$ as a function of the non-dimensionalised temperature
$\theta$.

###  3.3 Numerical Method

The high-fidelity simulation of TTBL is conducted using a modified version of
a hybrid parallel MPI/OpenMP TBL DNS code Simens:2009mz ; Borrell:2012ks ;
Kitsios-etal-IJHFF:2016 ; Kitsios:2017eu . The code solves the three-
dimensional incompressible Navier-Stokes equations in a three-dimensional
rectangular volume. The three flow directions are streamwise, (flow
direction), wall-normal, and spanwise (cross-flow). The numerical simulation
code uses the fractional-step method of Harlow:1965  to solve the governing
equations for the velocity, temperature and pressure fields. Fourier
decomposition is used in the periodic spanwise direction with 2/3-dealising,
with compact finite difference Lele:1992  used in the streamwise and wall-
normal directions. The equations are stepped forward in time using a modified
three sub-step Runge-Kutta scheme Simens:2009mz . The bottom surface is a flat
plate with a no-slip boundary condition. The thermal boundary condition can be
specified as a constant temperature or a constant heat flux. The former is
used in the TTBL DNS results presented here.

###  3.4 Results

A high-fidelity simulation was undertaken with a dualTBL DNS as shown in Fig.
6 the computational domain characteristics for TBL1 and TTBL2 are given in
Table 1 and 2, respectively.

Figure 6: A dual TBL DNS configuration. TTBL2 yields the TTBL DNS, which is an analogy of a bushfire. TBL1 provides a proper inflow boundary condition to TTBL2. The thin green layer in TTBL2 is the biomass energy source. Computational Domain | Computational Grid
---|---
$L_{x}$ |  $L_{y}$ |  $L_{z}$ |  $N_{x}$ |  $N_{y}$ |  $N_{z}$
$100\,\pi$ |  $30$ |  $33.4\,\pi$ |  $4,096$ |  $315$ |  $1,024$
Table 1: Computational Domain for TBL1 in Fig. 6.

The uniform biomass energy source is only located within TTBL2 and ranges in
the streamwise direction starting at $\frac{L_{x}}{4}$ and ending at
$\frac{L_{x}}{2}$, while spanning the entire width of the TTBL2 domain
$L_{z}$. The uniform biomass height was set at $y^{+}=50$ referenced at
$x=\frac{L_{x}}{4}$. The values used for the source term given by Eq. 11,
which characterises the biomass heat release rate in Eq. 3 are: $A=50$,
$\alpha=0.8$ and $\beta=8$. The fire is started by instantaneously raising the
temperature of the fluid above $\theta=0.5$ over a small streamwise domain at
$x=\frac{L_{x}}{4}$ spanning $0.8L_{z}$ along the spanwise domain as shown in
Fig. 7 and 8.

Computational Domain | Computational Grid
---|---
$L_{x}$ |  $L_{y}$ |  $L_{z}$ |  $N_{x}$ |  $N_{y}$ |  $N_{z}$
$50\,\pi$ |  $40$ |  $33.4\,\pi$ |  $6,554$ |  $536$ |  $2,048$
Computational domain normalised by boundary layer thickness at $L_{x}/4$
$L_{x}/\delta$ | $L_{y}/\delta$ | $L_{z}/\delta$
$27.7$ | $7.1$ | $18.5$
Table 2: Computational Domain for TTBL2 in Fig. 6, $\delta$ is the TBL
thickness at the beginning of this computational domain.

Figure 7 shows the full computational domain of TTBL2 and a zoomed in version
of the biomass domain. The yellow structures in the full computational domain
represent coherent vortical structures visualised using the second invariant
of the velocity gradient tensor Ooi99 , while the blue streaks in the zoomed
in view representing low velocity streaks. The red colour in both indicates
the bushfire front at the start of the bushfire.

Figure 7: Visualisation of the TTBL DNS with the green region indicating the
biomass fuel, the yellow structures in the full computational domain being
coherent vortical structures visualised using the second invariant of the
velocity gradient tensor, while the blue streaks in the zoomed in view
representing low velocity streak. The red colour in both indicates the
bushfire front at the beginning of the bushfire. A full animation can be
viewed at Li2022 .

Figure 8, shows three snapshot along the bushfire simulation, beginning from
the fire starting, evolving as a bushfire without too much of a smoke bloom
and subsequently evolving into a bushfire with significant smoke reaching the
upper parts of the TTBL. A full animation of the bushfire analogy provided by
this TTBL DNS can be viewed at Li2022 . It is worth noting the qualitative
similarities in the latter stages of the TTBL DNS and the photograph of the
Blue Mountain bushfire given in Fig. 1.

##  4 Conclusion

This paper has proposes a SciML methodology that utilises physics-informed ML
based on DL \- PiDL to assimilate remotely sensed temperature data and the
approach to its UQ. The development, testing and UQ is entirely reliant on the
TTBL DNS, which is a canonical analogy of a bushfire, to provide training data
and the “ground truth” for UQ. Ultimately in the field the PiDL will learn
from remotely sensed 3D temperature data gathered from a variety of sources
ranging from low orbit satellites to fixed wing aircraft and UAVs or drones
fitted with infrared sensors and be able to predict the thermal turbulent
boundary layer associated with a bushfire, as well as predict its dynamics and
fire front spreading rate. A realistic heat source rate model has been
developed based on approaches which have their roots in the classical
developments of theoretical combustion. This model has been employed to
undertake an initial canonical bushfire analogy employing a uniform biomass
distribution. The resulting TTBL DNS has shown close qualitative aspects with
images of the recent Blue Mountains Bushfire in Australia.

Figure 8: Some snapshots of the biomass burning evolution zoomed in from Fig.
7 (a) indicates the staring of the bushfire, (b) is a time after the bushfire
has started, but with little smoke at this stage, (c) indicates the progress
of the bushfire with the grey colour indicating fluid temperatures which are
typical of smoke rather than fire.

## Acknowledgements

This research was supported by a NCI Australasian Leadership Computing Grant
and a Monash Data Futures Institute Seed Grant. The authors also gratefully
acknowledge the NCMAS HPC allocation of NCI supported by the Australian
Federal Government and of Pawsey also supported by the Australian Federal
Government and the State Government of Western Australia.

## References

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  *[TTBL]: turbulent thermal boundary layer
  *[AI]: artificial intelligence
  *[DNS]: direct numerical simulation
  *[CFD]: computational fluid dynamics
  *[TBL]: turbulent boundary layer
  *[SciML]: scientific machine learning
  *[ML]: machine learning
  *[DL]: deep learning
  *[UQ]: uncertainty quantification
  *[DNSs]: direct numerical simulation
  *[DA]: data assimilation
  *[PiDL]: physics-informed deep learning
  *[NN]: neural network
  *[CNN]: convolutional neural network
  *[RNN]: recurrent neural network
  *[PDE]: partial differential equation
  *[ZPG]: zero-pressure-gradient


# Navigating Cultural Diversity: Barriers and Potentials in Multicultural
Agile Software Development Teams

Daniel Welsch  0009-0007-7439-4750 University of Applied Sciences and Arts
HannoverDpt. of Business Information SystemsHannoverGermany
<EMAIL_ADDRESS>,  Luisa Burk  0009-0006-6784-3346
University of Applied Sciences and Arts HannoverDpt. of Business Information
SystemsHannoverGermany<EMAIL_ADDRESS>,  David Mötefindt
0009-0008-7526-7654 Agile MoveHannoverGermany<EMAIL_ADDRESS>and  Michael
Neumann  0000-0002-4220-9641 0000-0002-4220-9641 University of Applied
Sciences and Arts HannoverDpt. of Business Information SystemsHannoverGermany
<EMAIL_ADDRESS>
###### Abstract.

Context: Social aspects are of high importance for being successful using
agile methods in software development. People are influenced by their cultural
imprint, as the underlying cultural values are guiding us in how we think and
act. Thus, one may assume that in multicultural agile software development
teams, cultural characteristics influence the result in terms of quality of
the team work and consequently, the product to be delivered. Objective: We aim
to identify barriers and potentials that may arise in multicultural agile
software development teams to provide valuable strategies for both researchers
and practitioners faced with barriers or unrealized potentials of cultural
diversity. Method: The study is designed as a single-case study with two units
of analysis using a mixed-method design consisting quantitative and
qualitative methods. Results: First, our results suggest that the cultural
characteristics at the team level need to be analyzed individually in
intercultural teams, Second, we identified key potentials regarding cultural
characteristics providing key potentials such as a individual team subculture
that fits agile values like open communication. Third, we derived strategies
supporting the potentials of cultural diversity in agile software development
teams. Conclusion: Our findings show, that a deeper understanding of cultural
influences in multicultural agile software development teams is needed. Based
on the results, we already prepare future work to validate the results in
other industries.

Agile methods, culture, diversity, multicultural teams, influence, challenges,
barriers, potentials

††doi: xx.xxx/xxx_x††isbn: 978-x-xxxx-xxxx-x/YY/MM. . . ††conference:
Conference’17, July 2017, Washington, DC, USA; 2017††journalyear: ;††article:
4††price: 15.00††ccs: Software and its engineering Agile software development

##  1\. Introduction

Today, many companies are using agile methods and approaches in their software
development teams to address the dynamics of the markets (VersionOne and
Collabnet, 2022). This high level of dynamism is manifested in the potential
for changing requirements, new technologies, or increasingly shorter product
life cycles. To meet these challenges, social skills and cultural aspects such
as values and principles are of great importance in agile methods (Neumann et
al., 2023). While fundamental values and principles are formulated in the
Agile Manifesto (Beck et al., 2021), we know that the guidelines of widely
used agile methods such as Scrum (Schwaber and Sutherland, 2020), XP (Beck,
2000) or even Lean approaches like Kanban (Anderson, 2010) define further
specific values for the application. We also know that social skills, such as
communication (Ram et al., 2019), are critical success factors. Other success
factors include organizational culture (Claps et al., 2015), stakeholder
integration (Hoda et al., 2011), customer collaboration (Altaf et al., 2019),
and both intra- and inter-team cooperation.

In recent decades, globalization in the area of software development has
increased. We know, that global software development is the term used when
cooperation between companies, divisions, or even teams crosses national or
continental borders, or even time zones (Šmite et al., 2014). Also, we know
that teams operating in a global software development setting are challenged
by various aspects like cultural influences (Paasivaara, 2017) or language
barriers (Ebert and de Neve, 2001). There are still various motivations and
reasons for the globalization in the software development: Purposeful cost
reduction, high availability of the teams (e.g., follow the sun principle), or
also lack of specialists in the industry nations. We know from various
studies, that the effects of global collaboration in software development have
been studied in recent years ((Casado-Lumbreras and Colomo-Palacios, 2015;
Lous et al., 2017; Šmite et al., 2021) to name a few).

However, cultural diversity in agile software development teams operating in a
non-global distributed setting is an increasing phenomenon (Gröschke, 2021).
Furthermore, we argue the need for investigation due to the forced recruitment
of specialists abroad (from the perspective of the respective company), the
cost pressure, and the increasing digitization (Abadir et al., 2020). For
instance, the Covid-19 pandemic and the comprehensive shift to remote work in
many companies have had a further influence on the increased recruitment of
experts from other cities and countries as they do not move to the company’s
site (Neumann, 2022). Thus, one may assume that cultural diversity will
increase in software development teams because the shortage of potential
employees with the required skill sets will increase. Especially in the
western industrialized nations due to the age situation of the societies. We
know from several studies that cultural diversity may be challenging in
software development teams (Hoffmann et al., 2023).

In the context of agile software development, these challenges are highly
relevant. For the successful use of agile methods, social skills such as
communication, collaboration, or integration of stakeholders are of great
importance (Schön et al., 2015). As mentioned above, these social aspects are
critical success factors, which is why we need an in-depth understanding of
how cultural diversity influences agile software development teams, and what
strategies we need to use to address impediments and foster potential. In
contrast to global software development, this topic has been underrepresented
in literature.

The above motivates the objective of our study, which is refined by the
following research questions:

RQ 1::

Which cultural profiles exist in the teams?

RQ 2::

What cultural barriers or potentials exist in multicultural teams?

RQ 3::

What strategies help to mitigate barriers or to promote potentials?

Table 1. Overview of the related work Publication | Research design |  Findings wrt. cultural diversity
---|---|---
Abadir et al. (2019) (Abadir et al., 2020) | Integrative literature review |  The authors found that the intercultural skills for integrating employees with different cultural backgrounds in existing teams is gaining more importance. Covering a wide range of literature dealing with leadership of multicultural in agile organizations the authors identified a research gap. The authors point to the need for further research focusing on the leadership impact on the effectiveness of multicultural teams in agile organizations.
Granow and Asbrock (2021) (Granow and Asbrock, 2021) | Qualitative study |  Based on their results, the authors present a framework indicating that the behaviour of agile teams influencing the performance of multicultural teams. The authors call for future research to get a better understanding how cultural diversity impacts agility on a team level.
Kohl Silveira and Prikladnicki (2019) (Kohl Silveira and Prikladnicki, 2019) | Systematic mapping study |  The presented systematic maps covers an overview focussing on agile software development. They identified 67 papers dealing with cultural diversity in this area. However, how cultural diversity impacts specific aspects like the software process or the effectiveness of a team was not in scope of the study. Finally, the authors call for research activities combining the several aspects of diversity like age or gender, and cultural background.
(Preprint) Verwijs and Russo (2023) (Verwijs and Russo, 2023) | Quantitative survey |  The authors analyzed how diversity influences the performance of agile software development teams. Their study results show that the cultural background do not contribute to the effectiveness of the teams performance. The authors point to the interesting findings comparing their results with the categorization-elaboration model (CEM). Focussing on the cultural background, the results are not in line with the CEM. They assume that the task interdependence, which may differ significantly among the agile software development teams.

This paper is structured as follows: We give a brief background of the
fundamentals of culture and outline the related work in Section 2. In Section
3, we explain our mixed-method research design. The results are presented and
discussed in Section 4, including the answers of our research questions. The
limitations of our study are described in Section 5, before the paper closes
with a conclusion and future work in Section 6.

##  2\. Background & Related Work

###  2.1. Background

According to Hofstede’s definition in (Hofstede, 1981)111Hofstede defined
culture as “The collective programming of the mind that distinguishes the
members of one group or category of people from others.”, we understand
culture as the ground for shared values, beliefs, and behaviours of a group or
society. Thus, culture guides us in terms of “what is an expected behaviour”
or “what is implicitly allowed” and “what is forbidden”. Several authors
presented descriptive and comparative models to characterize culture in some
ways (e.g., (House et al., 2002; Hofstede and Minkov, 2013; Karahanna et al.,
2006; Trompenaars and Hampden-Turner, 2012)). In this study, we focus on the
well-known model by Hofstede (Hofstede, 2001) as it is used extensively in the
area of empirical software engineering (e.g., (Alsanoosy et al., 2019; Ayed et
al., 2017; Ghinea et al., 2011)).

Power Distance Index (PDI): This represents the extent to which individuals
with less power accept or expect unequal distribution of power. An example of
this is the way people behave toward their superiors in a company. Societies
with a high PDI value believe in hierarchy and take orders without question.
Societies with a low PDI strive for equality in the distribution of power.

Uncertainty Avoidance (UAI): This dimension describes whether members of a
culture feel comfortable or uncomfortable in new or unknown situations. If
there is a high level of uncertainty avoidance, the national culture is
characterized by clear rules (such as laws or security measures). It tries to
create structures that are as clear as possible. There is tolerance for
different opinions in national cultures with a low level of uncertainty
avoidance. Also, regulations are less precise and strict.

Individualism vs. Collectivism (IDV): According to Hofstede, national cultures
are either individualistic or collectivistic. Low scores are interpreted as
collectivist, high scores as individualistic. Members of individualistic
societies are interested in their own resources. They tend to care for
themselves and their families first and foremost. Collectivist societies share
resources and a common understanding of moral standards.

Masculinity vs. Femininity (MAS): This dimension describes cultural values in
line with traditional gender stereotypes. Societies that score high on the MAS
scale prioritize values typically associated with masculinity, such as
achieving success, power, and achievement. Cultures with low MAS scores place
greater emphasis on relational dynamics and cooperative efforts, which
correlate with the IDV dimension.

Long Term Orientation (LTO): This dimension is a measure of the extent to
which a society values long-term gains over immediate gratification. Long-term
oriented cultures often exhibit traits such as thrift and perseverance. Short-
term cultures, on the other hand, as exemplified by organizational control
mechanisms and executive performance evaluations that focus on short-term
results, emphasize immediate results, sometimes at the expense of long-term
implications.

Indulgence vs. Restraint (IVR): This dimension assesses the extent to which a
culture permits or restricts the free expression of innate human desires,
particularly in the pursuit of life’s pleasures. Enjoyment-oriented societies
place a high value on leisure time and are less focused on material
acquisitions such as rewards.

The model of cultural dimensions by Hofstede has been discussed and criticized
in the past decades (e.g., (Baskerville, 2003; Schmitz and Weber, 2014)).
Major critic arguments relate to the limitations of few dimensions and that
the national level of culture may not be the best unit for cultural
characterization (McSweeney, 2002) and pose the risk of stereotyping (Carmel
and Agarwal, 2001). Also, the chosen research design is criticized as surveys
may not be an appropriate approach for cultural studies and the
representativeness of the population (Alsanoosy et al., 2020). Nevertheless,
the model is based on a strong empirical basis including a large data set and
it has been validated by other researchers. Furthermore, the model applies to
several different contexts and has been adopted by various studies (e.g,
(Baskerville, 2003)).

###  2.2. Related Work

To provide an overview of the literature related to the effects of cultural
diversity in agile software development teams, we searched for both primary
and secondary studies. The results of our focused literature search show that
the topic has been underrepresented in the recent literature and thus, we
identified only three peer-reviewed studies. Thus, we decided to integrate
preprints as well and found one more study. To ensure the quality of the
preprint, we reviewed the preprint by Verwijs and Russo(Verwijs and Russo,
2023) considering the Empirical Standards by SIGSOFT (SIGSOFT, 2023). The
search was performed using Google Scholar because the search engine indexes
multiple publishers (e.g., ACM, IEEE). In addition, Google Scholar results
show a high degree of consistency with digital libraries such as Scopus (Yasin
et al., 2020). Table 1 gives a brief overview of the identified literature.

The research landscape in the field of multicultural agile teams lacks on
detail. This is shown by the secondary studies we identified and the calls
from other researchers to fill the gap (see Table1 for details). However, we
could identify some interesting findings from other studies. Most of the
studies both from the included studies in the literature reviews as well as
the primary study by Verwijs and Russo (Verwijs and Russo, 2023) focusing
strongly on teams performance indicators aiming to understand how diversity
impacts the effectiveness using well-known and validated approaches like CEM.
Granow and Asbrock present a framework aiming to describe the impact of
diversity on teams performance. Interestingly, the findings from both primary
studies are contrasting one another in some ways. Verwijs and Russo state that
the cultural background does not have a significant influence on the
effectiveness of agile teams. However, they also argue that their results may
be biased by the task interdependence of agile teams. In contrast, Granow and
Asbrock’s results indicate such an influence of the individual cultural
background. These insights were very valuable for us in designing our research
design as we decided to try to create a cultural profile of the teams under
study before we analyze the potential impact of the cultural background.

Although we have searched for related work that deals with challenges and
opportunities in culturally diverse agile software development teams, we could
not find literature that closely addresses the objective of our study. Hence,
to the best of our knowledge, this is the first paper that identifies barriers
and potentials in multicultural agile software development teams.

##  3\. Research Design

Figure 1. Research approach

In this section, we explain the mixed-method approach, followed by a brief
overview of our research design. We then introduce the case company.
Afterwards, we provide a detailed presentation of the research methods used,
beginning with the survey by Hofstede.

The study is designed as a single case study based on the guidelines by
Runeson and Hoest (Runeson and Höst, 2009) using a mixed-method research
approach (see Figure 1). Based on a focused literature review to find studies
dealing with topics closely related to our study and the identified research
gap, we used the validated survey by Hofstede to be able to analyze and
describe the cultural profiles of the teams under study (RQ 1). As we want to
identify specific barriers, potentials (RQ 2) and analyze them to provide
strategies (RQ 3) to manage and handle them, we decided to collect data using
qualitative research methods.

###  3.1. Research Context

We conducted the study at the case company. The research took place at a firm
we refer to as Daily Bugle (anonymized), a global enterprise specializing in
online marketing with around 1,000 employees.

Our investigation centered on the agile software development divisions within
Daily Bugle. The organization operates software development locations across
Germany, Poland, the United Kingdom, and the United States. For the purpose of
this study, we focused on one of the development sites in Germany. At this
site, two agile software development teams are operating, which we refer to as
Peter and Ororo for anonymity.

The Peter team consists of seven developers, while the Ororo team has five
members. Each team is overseen by a Lead Engineer and adopts Scrum, utilizing
two-week sprints. A single Scrum Master assists both teams, and they also
receive guidance and coaching on software quality from a dedicated Quality
Specialist.

Table 2. Profiles of the interviewees ID | Current Role | Team |  Years working for Daily Bugle
---|---|---|---
I1 | Agile Coach | Both teams |  15 years
I2 | Software Engineer | Peter |  3 years
I3 | Lead Engineer | Peter |  7 years
I4 | Software Engineer | Peter |  1 year 9 months
I5 | Product Owner | Ororo |  2 years 4 months
I6 | Lead Engineer | Ororo |  2 years 6 months
I7 | Software Engineer | Ororo |  7 months
I8 | Software Engineer | Peter |  9 months

###  3.2. VSM by Hofstede

To ascertain the cultural dimensions of the participants, we decided to use
the validated Value Survey Module (VSM) from Hofstede (Hofstede, 2013). The
VSM was administered to the participants through a LimeSurvey questionnaire.
This approach was utilized to establish the diverse cultural profiles within
the teams Peter and Ororo. To determine the manifestations of cultural
dimensions, indices were calculated based on the mean scores of four distinct
questions (Details can be found in our research protocol; see Appendix A.1).

The survey was conducted over a three-week period in April 2023. We used a
dedicated questionnaire in LimeSurvey per team. The respondents rate in team
Ororo was 100% (n=3) and for team Peter 96.5% (n=6).

###  3.3. Qualitative Research Design

In the case study, eight interviewees, each with distinct roles and varying
years of experience in agile software development (ASD), were interviewed
(Table 2)

To get an insight into the experience, perception and challenges of
participants in the context of cultural variety and collaboration a semi-
structured interview (Runeson and Höst, 2009) was chosen as a methodological
approach. This qualitative approach was selected to adjust the discussion
sequence of the interview depending on the participants responses.

With this approach, the case study could be divided into questions about
barriers and potentials. To have a systematic method to answer the research
questions RQ 2 and RQ 3 we used the Goal-Question-Metric (GQM) (Basili et al.,
2014). Based on the GQM an interview guide (App.D) was created. The guide
consists of three parts:

#### Part 1:

An initial sequence delineating the interview sequences, introducing the
interview facilitators, and elucidating the particulars of the case study.

#### Part 2:

A primary sequence pertaining participants teams. The participant is asked if
he would describe his team as international and intercultural. The
differentiation serves as an indicator whether a well-established team culture
exists within the team. Furthermore the participant is tasked with assessing
if their team adhere to the definition of an agile culture (Kuchel et al.,
2023).

#### Part 3:

A concluding section categorizes the interview into inquiries concerning
barriers or potentials of multicultural collaboration, alongside neutral
queries related to multicultural collaboration. If the participants team
adheres to an agile culture (Kuchel et al., 2023) they are subjected to
targeted inquiries regarding the potentials of intercultural collaboration. If
the team does not adhere to it, he is specifically inquired about barriers of
multicultural collaboration.

To mitigate potential bias in research outcomes, each interview was conducted
by two researchers. One researcher held the interview, the other was observing
and taking notes. Moreover, all interviews were recorded and subsequently
transcribed to enhance analytical comprehensibility. The interviews and
observations were held in May 2023. The interviews were conducted during
working hours, not during off-peak hours (at the beginning of the workday,
just before the end of the workday). Each interview was conducted using MS
Teams and was scheduled to last for 60 minutes. On average, an interview took
18:41 minutes, the shortest interview duration was 14:31 minutes, and the
longest interview 23:11 minutes.

We collectively analyzed the transcripts to minimize possible research bias.
Each of the transcripts underwent a thorough examination, with an emphasis on
identifying barriers, potentials and the strategies already in use to mitigate
barriers or to promote potentials. Afterwards, we transferred these findings
onto a Miro online-whiteboard (see Appendix A.1), where we analyzed our data
using axial coding. Each researcher did the coding by himself to mitigate
bias. The results of the coding process were compared afterwards and the
differences were discussed in the group. Finally, with an in-depth evaluation
of the clustered data, we developed additional strategies to answer RQ 3.

##  4\. Results

This section presents the results of our mixed-method study. Initially, we
present the cultural profiles derived from Hofstede’s VSM to answer RQ 1.
Next, we discuss the results derived from the qualitative part of the study to
present barriers and potentials of multicultural agile teams and answer RQ 2.
Finally, we use the barriers and opportunities we have identified to introduce
the strategies developed in response to RQ 3.

###  4.1. Cultural Profiles

As our study focuses on multicultural characteristics and their influences on
agile software development teams, we need to examine the cultural profiles of
the team members, because the teams do not consist solely of members with the
same cultural background. Thus, in this section, we answer RQ 1: Which
cultural profiles exist in the teams?

Besides our own data collection using the VSM by Hofstede, we asked for the
nationality of the team members. As we were aware of the risk of stereotyping
by using cultural characteristics, it is necessary to be able to compare our
determined values with them from Hofstede (Insights, 2022). The members of
Team Peter are from Germany, Italy and Azerbaijan. The team members working in
team Ororo are from India, Pakistan and Turkey. For both teams, the Hofstede
data shows different cultural characteristics for the various national
cultures. Below, we discuss the determined cultural characteristics at team
level comparing them with the values provided by Hofstede. The results are
presented for each cultural dimension (see Section 2.1 for a detailed
description). We present the specific values per dimension for each team in
brackets. However, a figure illustrating this can be found in our research
protocol (see Appendix A.1).

Power Distance: Interestingly, team Ororo (2) has a lower PDI than team Peter
(40), although the nationalities of the team members suggest a higher value
according to Hofstede (Insights, 2022)). Again, according to the Hofstede
values, the nationalities in team Peter have very different Power Distance
values. However, due to the German team members, a lower value would be
expected. This could be a possible barrier for team Peter as one may assume
that the team members would not communicate open about their mistakes and
failures.

Answer RQ 1: First and foremost, the cultural profiles of both teams show
differences in half of the cultural dimensions to the values provided by
Hofstede (Insights, 2022): Power Distance, Uncertainty Avoidance, and
Individualism vs. Collectivism. Team Peters cultural profile is collaborative,
emphasizes feminin aspects and focus on long term success. The culture also
consists of an existing but low Power Distance. The team do not put much
importance to uncertainty avoidance. There is a relaxed, casual interaction
between team members and their managers. It is important for this team to have
fun and enjoyment at work in order to be able to keep their own lives in
balance. Team Ororo also values collectivism, but not as much pronounced as
team Peter. Otherwise, the power distance do not exist. The team is focusing
more on short term success by keeping uncertainty avoidance in mind. In
contrast to team Peter, team Ororo values a regulated interaction with each
other that focuses on professionalism. Excessive joy, such as laughter, is not
welcome and is perceived as unprofessional and disruptive. The results show,
that the teams do have a specific team subculture, which is represented by the
cultural profile using the Hofstede dimensions.

Uncertainty Avoidance: It is noticeable that team Ororo has a higher level of
uncertainty avoidance (35), although three nationalities are represented in
team Peter (6), which according to Hofstede have a high value. This could be a
potential barrier in team Ororo, as uncertainty and unstructured situations
are avoided.

Individualism vs. Collectivism: Here, team Ororo (35) shows a higher value
than team Peter (18). This is interesting, as the national values by Hofstede
of the specific teams indicate an opposite distribution of the indices. The
low value in team Peter can be seen as a potential for close cooperation and
good interaction in groups.

Masculinity vs. Femininity: Upon comparison, it can be seen that the value is
higher for team Peter (19) than for team Ororo (1). This is consistent with
the values provided by Hofstede (Insights, 2022). According to Hofstede,
Germany and Italy in particular showed a high MAS index, which is reflected in
the results of our survey.

Long Term Orientation: According to Hofstede, the nationalities in team Ororo
tend to have lower LTO, while the nationalities in team Peter tend to have
higher one. This can be confirmed in our determined values (Ororo = 33; Peter
= 60). The future-oriented actions and willingness of team Peter to adapt
represent an important potential. Additionally, the results the dimensions
Long Term Orientation and Uncertainty Avoidance confirm each other. Team Peter
acts more future-oriented, is willing to adapt and does not avoid
uncertainties. Team Ororo is more conservative and avoids uncertainty.

Indulgence vs. Restraint: The nationalities of both teams have rather low
indices (Insights, 2022). In the results, it is noticeable that team Peter has
a higher value (52) than team Ororo (15). This could be due to the fact that
half of the members of team Peter live and work in their home country. The
members of team Ororo come from countries where there are large cultural
differences, so they may feel more subject to societal values and norms.

###  4.2. Barriers and Potentials in Multicultural Teams

In this section, we discuss our results to answer RQ 2: What cultural barriers
or potentials exist in multicultural teams?

Openness emerged as a great potential in both teams. Different cultures were
found to bring new viewpoints and perspectives to the team. Consequently,
fostering an environment of respect and tolerance became imperative for
effective collaboration among team members from different countries. By
cultivating an open minded team culture and promoting transparent
communication, the prospects for successful teamwork were enhanced. This is
exemplified by one Junior Software Engineer’s perspective from team Peter: “It
requires people to be open for everything and to be willing to meet people and
connect with people. And that is what makes this so easy, because all of my
colleagues that are from other countries […] have no issues with talking to
you, trying to understand different opinions[…]”. Similar opinions were also
expressed in the interviews of the team Ororo.

During our observations of team Ororo, we noticed that a lack of open
communication disrupted teamwork, and extended pauses between conversations
could be identified. This phenomenon may lead to unaddressed issues within the
team, potentially causing team members to experience heightened levels of
stress and pressure.

Team Peter characterized their communication within the team as very open and
direct. This fosters a culture of mutual assistance, constructive feedback and
agile practices such as pair programming.

The openness influences the personal relationship between the team members.
The participants of both teams expressed a positive relationship with their
colleagues and an interest in meetings outside of work. Teams which meet
outside of work tend to have a better team performance.

After a team has been working together for a while, a team culture
(subculture) can grow. The more established this subculture is, the better the
team’s internal cooperation works . This subculture can mean that a
collaborative team customizes the agile approach. A Software Engineer of Peter
said: “We just tailor Agile to our needs, which is in the end what I believe
is being Agile, because everyone has different requirements as a team”.

The phenomenon of a distinct team could be noticed in the observations at
agile events. Direct and respectful communication within the team with a
subculture was observed, with criticism being expressed openly.

The team with the less distinctive subcultures showed restraint when questions
or ambiguities arose. It was noticeable that all opinions were accepted and
there was no discussion. The stand-up did not follow the agile practice,
instead the focus was on the backlog.

A discrepancy was found in Team Ororo between the portrayal of direct and open
communication in the interviews and the observations. The results of the
questionnaire show a high UAI in the Team Ororo. Reticence among the team
members in the agile practices could be observed. The reason for this may be
the team composition, which has only existed for a few months. Team Ororo has
not existed long enough for a subculture to develop and establish itself. The
prevailing impression suggests that team members are prioritizing completing
individual tasks, often at the expense of teamwork.

Teams with a history of collaboration exhibit a pronounced team dynamic. This
was particularly evident during the observations. They cultivate a distinctive
subculture, which can lead to new potentials. A pronounced collaboration can
be confirmed by the interviews and the questionnaire. The Individualism Index
is low in teams with a subculture because the team members are adaptable.

Answer RQ 2: A team culture that emphasize openness represents a key potential
of cultural diversity in multicultural teams. It provides the opportunity for
new viewpoints and perspectives. Furthermore it supports Kaizen and thus, is
eminent for the success to create an agile culture. In turn, teams which do
not put focus on creating its own subculture are impeded by hindered feedback,
criticism and thus, identifying optimization potential.

Another potential is the individualization of the Agile Manifesto to the needs
and demands of the individual multicultural team.

###  4.3. Strategies to manage Barriers and Potentials

The following section outlines strategies for addressing RQ 3: What strategies
help to mitigate barriers or to promote potentials?

A strategy arises from team members’ personal meetings outside of work. This
fosters the development of a distinct subculture in the team. Therefore,
successful teams should continue these personal meetings to preserve and
reinforce the potential. In addition to leisure-time gatherings, team-building
measures within the teams can bolster trust and alleviate uncertainties.

Furthermore, we found reinforcing a feedback-culture and integrating into the
daily schedule can faciliate a shared understanding of feedback and account
for cultural differences. In this regard, a guideline or regulatory framework
can be supportive in its formulation.

The high workload suggests that team members lack the time for team-building
activities, as a result, a team culture cannot develop. One of the
interviewees mentioned that not even a 15-minute coffee break, scheduled every
two weeks, could be adhered to. One strategy is to give new teams or team
members a lighter workload initially to help them integrate into the
multicultural team. To support this integration, scheduled coffee breaks for
personal interaction should be implemented more frequently.

Another hypothesis is that as the age of a team increases, its performance
capabilities also increase. This is attributed to the well-established
subculture within a team. Therefore, organizations should prioritize long-term
employee retention as a means to sustain the team in the long run. Special
emphasis should be placed on multicultural backgrounds.

Our identified potentials and barriers (see Section 4.2) by creating such a
subculture is confirmed by the team members understanding of what an agile
culture should be. The team members from both teams agree with the definition
by Kuchel et al. (Kuchel et al., 2023): “An Agile Culture reflects to the
behaviour of people working in an organization using agile practices based on
the underlying values and principles defined in the agile manifesto and the
guidelines of agile methods.”

Thus, we finally recommend to be aware of the importance of value-based work
emphasizing the specific cultural characteristics, which supporting important
aspects like open communication or feedback. However, as mentioned above, such
a development of a teams subculture that fit with the attributes of an agile
culture needs time and patience.

##  5\. Threats to Validity

Despite adhering to established guidelines for designing our single case study
and for the data collection and analysis process, it’s important to take some
inherent limitations into account.

Construct validity: Designing the interview guideline, we applied the Goal-
Question-Metric (GQM) methodology, a well-validated and widely-recognized
approach. To ensure quality, the document was initially formulated by a
research team of five members and subsequently reviewed by an agile software
development expert and one senior researcher. Our interview guide consists of
both, closed and open-ended questions to obtain targeted insights.
Additionally, the questions were designed to be non-leading to minimize
influence on the respondents from the agile software development teams. We
also provided an option for respondents to add their own answers when the
preset choices were not applicable.

However, the quantitative nature of the survey limits the depth of
understanding we can achieve, especially when presented with intriguing or
diverse responses. There’s also the potential for bias among respondents due
to their past experiences. For example, the teams in the study have been
working remotely for over two years, which could lead to a focus on the
positive aspects of their experience.

Internal validity: Although we performed a thorough analysis of existing
literature, some internal validity threats are worth to mention. It is a
significant challenge to ensure that we identified the relevant literature.
Based on a systematic approach, we tried to find and analyze as much relevant
work related to our study as possible. Thus, we decided to search in two
digital libraries (Google Scholar and Scopus). As the survey by Hofstede is
validated several times, we add another layer of robustness to our research
approach.

External validity: The study’s external validity is constrained due to its
focus on a single case study. To enhance the generalizability of the findings,
future research could include additional cases from not only other software
development departments within Daily Bugle but also from companies in diverse
industries and countries. Nevertheless, we aimed to minimize other variables
that could affect the outcomes, such as the development stage of the agile
teams being studied or the unique circumstances surrounding product
development. It’s worth noting that the response rate for our single-case
study was high and encompassed both agile development teams as well as the
Scrum Master. As a result, we are confident that the data collected provides a
meaningful representation of the situation in this specific case.

##  6\. Conclusion and Future Work

This paper presents the findings of our mixed method study dealing with the
potentials and barriers of intercultural agile software development teams.
Additionally, we present strategies to promote the potential and mitigate the
barriers of cultural diversity based on a discussion of our results.

We identified that a team subculture, which emphasized agile values is a great
potential for intercultural teams, as it provides the opportunity for open
communication, easier integration of new colleagues and it fosters new
viewpoints on specific problems or challenges. These aspects are eminent for
the success of agile software development teams.

However, creating a subculture needs time and patience from both the team
members as well as their stakeholders and organization around them. Thus, we
analyzed our results to create specific strategies promoting the potential and
mitigating the barriers of intercultural agile software development teams. We
recommend to focus on social activities to encourage the team members for
taking their time to integrate new colleagues, discuss problems and find
solutions together. Furthermore, team events may be a good idea to foster a
team’s subculture. These team events could be coffee breaks, team breakfast
sessions, or even team building events outside the remote or onsite office.
Also, it is important that such a subculture relies on the team’s composition.
Thus, we recommend to focusing on the employee’s well-being and foster long
term employee loyalty and create a strategy to decrease the turnover of the
team members.

Our findings support both practitioners and researchers agile community as one
may assume that cultural diversity will increase in future. However, as we
designed the study as a single case study, we call other researchers to
investigate this phenomenon in other industries or contexts (like regions).

##  Appendix A Appendices

###  A.1. Research Protocol

As recommended by Runeson and Hoest (Runeson and Höst, 2009), we created a
research protocol for documenting our research activities. The research
protocol is available at FigShare.

###### Acknowledgements.

The authors want to express their deep gratitude to the participants to the
study and the support from our case company Daily Bugle.

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