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Overview

Intensity Analysis is a quantitative method to analyze land use and cover (LUC) maps at multiple time steps. It evaluates how the size and rate of change varies across three hierarchical levels.

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What is Intensity Analysis?

Intensity Analysis examines LUC transitions using cross-tabulation matrices, comparing observed change intensity against a uniform (expected) change intensity.

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Three Analysis Levels

Level 1 - Interval Level
How does the size and speed of change vary across time intervals? Level 2 - Category Level
How do gross gains and losses vary across categories within each interval? Level 3 - Transition Level
How do specific category transitions vary from uniform expectations?
Each level provides increasingly detailed information about land use change patterns. The method tests for stationarity - whether change patterns are consistent across time intervals.

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Complete Workflow

1
Load data and create contingency table
2
First, extract LUC transitions from your raster time series:
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library(OpenLand)

# Load sample dataset (or use your own rasters)
url <- "https://zenodo.org/record/3685230/files/SaoLourencoBasin.rda?download=1"
temp <- tempfile()
download.file(url, temp, mode = "wb")
load(temp)

# Extract contingency tables
SL_2002_2014 <- contingencyTable(input_raster = SaoLourencoBasin, 
                                 pixelresolution = 30)
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The contingencyTable() function returns 5 objects:
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  • lulc_Multistep: Transitions for all consecutive time steps
  • lulc_Onestep: Transitions from first to last year only
  • tb_legend: Category values, names, and colors
  • totalArea: Study area in km² and pixels
  • totalInterval: Total years in the time series
    • 6
    Edit the legend table
    7
    The tb_legend table is created with random category names and colors. You must edit these before analysis.
    8
    # View the legend structure
SL_2002_2014$tb_legend

# A tibble:
#   categoryValue categoryName color   
#           <dbl> <fct>        <chr>   
# 1             2 ABC          #002F70
# 2             3 XYZ          #0A468D
# ...
    9
    Edit category names (as factor with levels in desired plot order):
    10
    SL_2002_2014$tb_legend$categoryName <- factor(
  c("Ap", "FF", "SA", "SG", "aa", "SF", "Agua", "Iu", "Ac", "R", "Im"),
  levels = c("FF", "SF", "SA", "SG", "aa", "Ap", "Ac", "Im", "Iu", "Agua", "R")
)
    11
    Category names:
    • Ap = Pasture
    • FF = Forest
    • SA = Park Savannah
    • SG = Gramineous Savannah
    • aa = Anthropized Vegetation
    • SF = Wooded Savannah
    • Agua = Water
    • Iu = Urban
    • Ac = Crop farming
    • R = Reforestation
    • Im = Mining
    12
    Edit colors (in same order as categoryValue column):
    13
    SL_2002_2014$tb_legend$color <- c(
  "#FFE4B5",  # Ap - Pasture
  "#228B22",  # FF - Forest
  "#00FF00",  # SA - Park Savannah
  "#CAFF70",  # SG - Gramineous Savannah
  "#EE6363",  # aa - Anthropized Vegetation
  "#00CD00",  # SF - Wooded Savannah
  "#436EEE",  # Agua - Water
  "#FFAEB9",  # Iu - Urban
  "#FFA54F",  # Ac - Crop farming
  "#68228B",  # R - Reforestation
  "#636363"   # Im - Mining
)
    14
    Run intensity analysis
    15
    Run the three-level intensity analysis by specifying:
    16
  • category_n: A category with important gains (target category)
  • category_m: A category with important losses (source category)
    • 17
    my_intensity <- intensityAnalysis(
  dataset = SL_2002_2014,
  category_n = "Ap",  # Pasture (gaining category)
  category_m = "SG",  # Gramineous Savannah (losing category)
  area_km2 = TRUE     # Use km² instead of pixel counts
)

# View the output structure
names(my_intensity)
# [1] "lulc_table"           "interval_lvl"         
# [3] "category_lvlGain"     "category_lvlLoss"     
# [5] "transition_lvlGain_n" "transition_lvlLoss_m"
    18
    Understand the 6 output objects
    19
    1. lulc_table
    Contingency table with category names (instead of codes):
    20
    my_intensity$lulc_table

# A tibble:
#   Period    From To      km2 QtPixel Interval
#   <fct>     <fct> <fct> <dbl>   <int>    <dbl>
# 1 2012-2014 Ap    Ap    1234.    1234        2
# 2 2012-2014 FF    FF    5678.    5678        2
# ...
    21
    2. interval_lvl (Interval object)
    Interval-level analysis showing change rate (St) vs. uniform rate (U):
    22
    my_intensity$interval_lvl

# Slot "intervalData":
#   Period    PercentChange    St     U
#   <fct>            <dbl> <dbl> <dbl>
# 1 2012-2014         3.92  1.96  1.66
# 2 2010-2012         4.24  2.12  1.66
# ...
    23
  • St: Annual change intensity for the interval
  • U: Uniform intensity across entire period
  • St > U: Fast interval (more active than average)
  • St < U: Slow interval (less active than average)
    • 24
    3. category_lvlGain (Category object)
    Gain intensity (Gtj) for each category:
    25
    my_intensity$category_lvlGain

# Slot "categoryData":
#   Period    To    Interval GG_km2  Gtj    St
#   <fct>     <fct>    <int>  <dbl> <dbl> <dbl>
# 1 2012-2014 Ap           2  612.   3.92  1.66
# 2 2012-2014 Ac           2  110.   1.14  1.66
# ...
    26
  • Gtj: Annual gain intensity for category j
  • Gtj > St: Active gain (gaining faster than average)
  • Gtj < St: Dormant gain (gaining slower than average)
    • 27
    4. category_lvlLoss (Category object)
    Loss intensity (Lti) for each category:
    28
    my_intensity$category_lvlLoss

# Similar structure to gains, showing losses
    29
    5. transition_lvlGain_n (Transition object)
    Transitions targeting category n (“Ap” in our example):
    30
    my_intensity$transition_lvlGain_n

# Which categories transition TO Ap?
# Slot "transitionData":
#   Period    From To   Interval T_i2n_km2  Rtin   Wtn
#   <fct>     <fct> <fct>   <int>     <dbl> <dbl> <dbl>
# 1 2012-2014 SG    Ap          2     123.4  2.45  1.82
# ...
    31
  • Rtin: Transition intensity from i to n
  • Wtn: Uniform transition intensity to n
  • Rtin > Wtn: Category i is “targeted by” n
  • Rtin < Wtn: Category i “avoids” transition to n
    • 32
    6. transition_lvlLoss_m (Transition object)
    Transitions from category m (“SG” in our example):
    33
    my_intensity$transition_lvlLoss_m

# Which categories does SG transition TO?
# Similar structure showing losses from m
    34
    Plot interval level results
    35
    plot(my_intensity$interval_lvl,
     labels = c(leftlabel = "Interval Change Area (%)",
                rightlabel = "Annual Change Area (%)"),
     marginplot = c(-8, 0), 
     labs = c("Changes", "Uniform Rate"), 
     leg_curv = c(x = 2/10, y = 3/10))
    36
    The plot shows:
    37
  • Left bars: Total change in each interval (%)
  • Right bars: Annual change intensity (St) vs uniform line (U)
  • Bars above uniform line = fast intervals
  • Bars below uniform line = slow intervals
    • 38
    Plot category level results
    39
    Gain intensity:
    40
    plot(my_intensity$category_lvlGain,
     labels = c(leftlabel = bquote("Gain Area (" ~ km^2 ~ ")"),
                rightlabel = "Intensity Gain (%)"),
     marginplot = c(.3, .3), 
     labs = c("Categories", "Uniform Rate"), 
     leg_curv = c(x = 5/10, y = 5/10))
    41
    Loss intensity:
    42
    plot(my_intensity$category_lvlLoss,
     labels = c(leftlabel = bquote("Loss Area (" ~ km^2 ~ ")"),
                rightlabel = "Loss Intensity (%)"),
     marginplot = c(.3, .3),
     labs = c("Categories", "Uniform Rate"),
     leg_curv = c(x = 5/10, y = 5/10))
    43
    These plots show:
    44
  • Left side: Area gained/lost (km²) by each category
  • Right side: Gain/loss intensity relative to uniform rate
  • Color-coded by time interval
    • 45
    Plot transition level results
    46
    Gains to category n:
    47
    plot(my_intensity$transition_lvlGain_n,
     labels = c(leftlabel = bquote("Gain of Ap (" ~ km^2 ~ ")"),
                rightlabel = "Intensity Gain of Ap (%)"),
     marginplot = c(.3, .3),
     labs = c("Categories", "Uniform Rate"),
     leg_curv = c(x = 5/10, y = 5/10))
    48
    Losses from category m:
    49
    plot(my_intensity$transition_lvlLoss_m,
     labels = c(leftlabel = bquote("Loss of SG (" ~ km^2 ~ ")"),
                rightlabel = "Intensity Loss of SG (%)"),
     marginplot = c(.3, .3),
     labs = c("Categories", "Uniform Rate"),
     leg_curv = c(x = 1/10, y = 5/10))
    50
    These plots reveal:
    51
  • Which categories are particularly active/dormant in transitions
  • Whether specific transitions are targeted or avoided
  • Consistency of patterns across time intervals

    • ​
    Interpreting Results

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    Stationarity Testing

    At each level, OpenLand tests whether patterns are stationary (consistent) across time intervals. Stationary pattern: All intervals show the same relationship to uniform intensity
    • All above uniform → Consistently active
    • All below uniform → Consistently dormant
    Non-stationary pattern: Intervals show mixed relationships
    • Some above, some below → Changing behavior over time
    View stationarity results: 
    # Category level
my_intensity$category_lvlGain@categoryStationarity

# Transition level  
my_intensity$transition_lvlGain_n@transitionStationarity

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    Key Metrics Summary

    LevelMetricComparisonInterpretation
    IntervalSt vs USt > UFast interval (active period)
    St < USlow interval (dormant period)
    CategoryGtj vs StGtj > StActive gain (targeting this category)
    Gtj < StDormant gain
    Lti vs StLti > StActive loss (avoiding this category)
    Lti < StDormant loss
    TransitionRtin vs WtnRtin > WtnCategory i targeted by n
    Rtin < WtnCategory i avoids n
    Qtmj vs VtmQtmj > VtmCategory j targets m
    Qtmj < VtmCategory j avoids m

    ​
    Using Pixel Counts Instead of Area

    To use pixel counts instead of km²: 
    my_intensity <- intensityAnalysis(
  dataset = SL_2002_2014,
  category_n = "Ap",
  category_m = "SG",
  area_km2 = FALSE  # Use pixel counts
)
    This changes column names from km2 to QtPixel in output tables.

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    Next Steps

    After completing intensity analysis:
    1. Create visualizations with Sankey diagrams, chord diagrams, and bar plots
    2. Perform spatial analysis to map accumulated changes
    3. Export results for publication or reporting

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    References

    Aldwaik, S. Z. and Pontius, R. G. (2012). Intensity analysis to unify measurements of size and stationarity of land changes by interval, category, and transition. Landscape and Urban Planning, 106(1), 103-114.

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