A framework to assess the dynamics of climate extremes on irrigation water requirement using machine learning techniques

Abstract

A methodological framework has been proposed that consists of six different modules to compute and analyze the dynamics of climate-related extremes on irrigation water requirement (IWR) using machine learning techniques. These modules interactively supply information to compute irrigation water requirement, extreme indices, selection of appropriate indices, clustering of stations, and machine learning models to demonstrate the impact of rain and temperature-based extreme indices on water requirement for crops in a region. The proposed framework was implemented for the kharif paddy crop at 206 grids in the Mahanadi basin (Catchment area: 1.41 lakh km²) of India. The seasonal rainfall, daily temperature range (DT), maximum one-day rainfall (RX1D), simple daily intensity index (SDII), and mean daily minimum temperature (TxM) were found to be the most significant indices, and the whole region was categorized into three clusters. The extra tree regressor with different parameters was found to be the most suited regressor technique among all 17 models used in the analysis and able to predict IWR with more than 75% accuracy in testing and training. The proposed theoretical framework is capable of quantifying the impact of climate extremes on IWR for any crop and automation may be useful to field practitioners and policymakers to plan available water resources optimally.

Appendix

1.1 A1. Rainfall extreme indices

1.1.1 A1.1 Annual total wet-day precipitation (PRCPTOT)

The annual total wet-day precipitation (PRCPTOT) may be defined as the total rainfall at any station during wet days and can be represented by the following expression:

$${PRCPTOT}_{j}=\sum\limits_{i=1}^{n}{R}_{ij}$$

(A1)

where PRCPTOT_j is the total precipitation for the jth year and R_ij is the daily precipitation greater than or equal to 2 mm for the ith day in the jth year.

1.1.2 A1.2 Number of rainy days (RD)

The number of rainy days, which is a significant index for water resource planning, is described as days with rainfall above a threshold limit, which in this case is 2 mm. If R_ij is the amount of regular rainfall on the ith day of the jth period/year, then the number of rainy days (RD_j) for the ith season/year is:

$${RD}_{j}=\text{Count}\left[{R}_{ij}>2\,\text{mm}\right].$$

(A2)

1.1.3 A1.3 Maximum one-day rainfall (RX1D)

The one-day maximum rainfall is significant for drainage design and flood studies. The maximum one-day rainfall (RX1D) can be expressed as the highest one-day rainfall. Let R_ij be the daily rainfall on the ith day of jth period/year, the maximum one-day rainfall for the jth period (RX1D_j) will be:

$${RX\textit{1}D}_{j}=\mathrm{Max}\left[\textit{R}_{\textit{ij}}\right].$$

(A3)

1.1.4 A1.4 Maximum 5-day rainfall (RX5D)

The maximum 5-day rainfall may be defined as the highest accumulated rainfall during the consecutive 5-day period. Let R5_ij be the total rainfall of the ith interval for the 5 days in the jth period/year. Here, i is the last day of the 5-day interval. The RX5D_j can be defined as:

$${RX\textit{5}D}_{j}=\mathrm{Max}\left[\textit{R5}_{\textit{ij}}\right].$$

(A4)

1.1.5 A1.5 Very wet days (R95P)

The number of days with rainfall exceeding the 95th percentile of the long term is known as very wet days (R95P). Let R_ij be the precipitation series of the wet days (R_ij > 2 mm) in j = 1, 2, 3, …, n period/year. The probability analysis of R_Wj is used to compute the 95 percentile (R₉₅). Now, the moderate wet days will be the count of the days where rainfall is greater than R₉₅ in the R_ij series.

$${R\textit{95}P}_{j}=\sum_{i=1}^{n}\mathrm{Count}\left[\textit{R}_{\textit{ij}}>\textit{R}_{95}\right].$$

(A5)

1.1.6 A1.6 Contribution from very wet days (R95PTOT)

It is usually expressed in percentage or friction as the ratio of total rainfall in a cycle that comes from very wet days to total rainfall during the period.

$${R\textit{95}PTOT}_{j}=\frac{\sum_{i=1}^{n}{R}_{ij}>{R\textit{95}P}_{j}}{W}$$

(A6)

1.1.7 A1.7 Simple daily intensity index (SDII)

The simple daily intensity index (SDII) is the mean precipitation that occurred during wet days. Let, R_Wj be the daily precipitation on a rainy day where precipitation ≥ 2 mm in any and rainfall days is W in any jth period. The simple daily intensity index (SDII_j) for the jth period/year can be computed using the following equation:

$${SDII}_{j}=\frac{\sum {R}_{Wj}}{W}.$$

(A7)

1.1.8 A1.8 Consecutive dry days (CDD)

The consecutive dry days (CDD_j) for any jth period can be described as the maximum number of days with rainfall <1 mm.

1.1.9 A1.9 Consecutive wet days (CWD)

Consecutive wet days (CWD_j) for any jth period is the longest wet spell that may be defined as the maximum number of days where rainfall is equal to or more than 1 mm.

1.2 A2. Temperature extreme indices

1.2.1 A2.1 Mean daily maximum temperature (TxX)

The average of maximum temperatures for any jth period/cycle is the mean daily maximum temperature (TxX), which can be described as:

$${TxX}_{j}=\frac{\sum_{i=1}^{n}{TX}_{ij}}{n}$$

(A8)

where TxX_j is the mean daily maximum temperature at the jth period, TX_ij is the maximum daily temperature on the ith day of the jth period and n is the total number of days in a period.

1.2.2 A2.2 Mean daily minimum temperature (TxM)

The mean daily minimum temperature may be defined as the average minimum temperature for any jth period and can be defined as:

$${TxM}_{j}=\frac{\sum_{i=1}^{n}{TM}_{ij}}{n}$$

(A9)

where TxM_j is the mean daily maximum temperature at the jth period, TM_ij is the minimum daily temperature on the ith day of the jth period and n is the total number of days in a period.

1.2.3 A2.3 Hot days (TX90P)

Hot days (TX90P_j) may be defined as the fraction or percentage when the maximum temperature is higher than the 90th percentile value of the maximum temperature.

$${TX\textit{90}P}_{j}=\frac{\sum_{i=1}^{n}{\mathrm{Count}}\left[{TX}_{ij}>{\textit{TX}}_{\textit{90}}\right]}{n}*100$$

(A10)

where TX_ij is the maximum temperature on the ith day of the jth period and TX₉₀ is the 90th percentile maximum temperature of the long-term period.

1.2.4 A2.4 Warm nights (TN90P)

Warm nights (TN90P_j) may be defined as the fraction or percentage when the minimum temperature is higher than the 90th percentile value of minimum temperature.

$${TN\textit{90}P}_{j}=\frac{\sum_{i=1}^{n}{\text{Count}}\left[{TM}_{ij}>{TM}_{\textit{90}}\right]}{n}*100$$

(A11)

where TM_ij is the minimum temperature on the ith day of the jth period and TM₉₀ is the 90th percentile maximum temperature of the long-term period.

1.2.5 A2.5 Daily temperature range (DT)

The daily temperature range (DT_j) may be defined as the mean difference between the maximum and minimum temperature.

$${DT}_{j}=\frac{\sum_{i=1}^{n}\left[{TX}_{\textit{ij}}-{TM}_{ij}\right]}{n}.$$

(A12)

1.2.6 A2.6 Warm spell duration indicator (WSDI)

The warm spell duration indicator (WSDI) implies a long-term warm period and is characterized as the number of days with a maximum temperature greater than the 90th percentile value for six or more consecutive days.

1.2.7 A2.7 Cold spell duration indicator (CSDI)

The cold spell duration indicator (CSDI) shows a long-term cold period and is characterized as the number of days with a minimum temperature below the 10th percentile value for six or more consecutive days.