The Newhall Simulation Model

Introduction

This paper describes the rationale of two software programs that use the Newhall model for the determination of soil moisture regimes: one is written in Basic, the other one is written in and compiled in Fortran 77.

This text is an excerpt of a mimeographed article by Frank Newhall (1972) It explained the rationale of his soil moisture regime model that he developed in the Soil Conservation Service of USDA as a climatologist working with Guy D. Smith. The sections which follow are only a part of Newhall’s paper and are limited to the description of the mechanisms that his model uses to follow soil moisture changes and identify soil moisture regimes on the basis of monthly rainfall and temperature data..

The Basic software works with monthly input data of only one year (either one indiviual year, monthly averages of a number of years, or normal years), longitude and latitude information, and computes potential evapotranspiration according to Thornthwaite (1948). It calculates the criteria that Soil Taxonomy (1999) uses to define soil moisture and soil temperature regimes and classifies the regimes according to these criteria. The original Newhall model that he wrote in Cobol used inputs of several years, calculated the criteria of each year, and computed the frequency of occurrence of each of them durimg the years that data were available. It identified the soil regimes on the basis of these frequencies. The Basic software discussed in this paper therefore differs in its approach from the original Newhall model by using average years. Newhall actually was opposed to the use of average input data. The Basic model however strictly follows the mechanisms that Newhall used for moisture changes in the soil profile, as well as the Soil Taxonomy definitions of the moisture and temperature regimes.

Other additions were introduced in the Basic model. The subdivisions of the soil moisture regimes were set up by A. Van Wambeke in 1976 in a research perspective and not modified since. They do not correspond to certain subdivisions that Soil Taxonomy uses in some taxa. The Basic model also allows changes in the water holding capacity of the soil moisture profile that can be increased to 400 mm. water. Finally, a year in the Basic software is only 360 days long and all months last 30 days.

The Fortran model follows Newhall’s rationale entirely and works with input data of several years that are processed separately. It allows changes in the water holding capacity of the moisture profile, and changes in the factors that relate air temperatures with soil temperatures.

1. Preliminary Assumptions of the Newhall Model

1.1 The Soil Moisture Profile

The soil moisture profile considered by the model extends from the surface down to the depth of an available water holding capacity (AWC) of 200 mm (8 inches).

The profile is divided into 8 layers each of which retains 25 mm of available water; the second and the third layer form the moisture control section (fig.1). It is defined as the layer having an upper boundary at the depth to which a dry (tension of more than 1500 kPa) but not air dry soil will be moistened by 25 mm of water moving downward from the surface within 24 hours. The lower boundary is the depth to which a dry soil will be moistened by 75 mm of water moving downward from the surface within 48 hours.

Figure 1 represents Newhall’s soil moisture profile. The vertical axis indicates the depth of the eight layers, and the horizontal axis scales the amounts of available water present in each of them. The tension at which water is held in the profile decreases from left (permanent wilting point, PWP) to right (field capacity, FC). Each layer is divided into eight slots to form an eight by eight square matrix of 64 slots, which is designated as the soil moisture diagram shown in table1. Each slot can be filled with a value corresponding to an amount of water which can vary between 0 and 1/64th part of the total available water holding capacity, or 3.125 mm in the case of water holding capacity of 200 mm.

Figure 1. Newhall’s Soil Moisture Profile

1.2 Water Uptake and Water Removal

The model simulates the downward movement of moisture into the soil as the progression of a wetting front; it is further referred to as accretion. The distance that the wetting front moves downward depends on the amount of water needed to bring all the soil above it to field capacity.

When the wetting front reaches the bottom of the profile and the complete soil moisture profile is at field capacity, the excess water is lost either by percolation or by runoff.

The rate of removal of water out of the soil, or depletion depends on the energy available for moisture extraction, expressed in terms of potential evapotranspiration (PE) which acts on the soil and the plants growing in the soil. The energy required to remove moisture from the soil depends on the amount of water (AW) present and the forces exerted by the soil to retain it. Water is removed more readily when the soil water is at low tensions than when the water content in the profile is at a minimum.

The rate of removal of water out of the soil, or depletion depends on the energy available for moisture extraction, expressed in terms of potential evapotranspiration (PE), which acts on the soil and the plants growing in the soil. The energy required to remove moisture from the soil depends on the amount of water (AW) present and the forces exerted by the soil to retain it. Water is removed more readily when the soil water is at low tensions than when the water content in the profile is at a minimum.

Less energy is used by the model to remove water from the upper layers of a soil than from the lower layers. The time needed to extract water from the soil depends on the depth at which it is located; this is in line with the fact that roots are more abundant near the surface than in deeper layers.

Depletion continues until the soil is at wilting point, e.g. when the soil moisture tension is 1500 kPa. The amount of water held in the soil is assumed not to be reduced below the amount held at 1500 kPa.

1.3 The Climatic Factors

The distribution of rainfall

The monthly precipitation (MP) is distributed in each month according to the following sequence:

1. One half of the monthly precipitation (HP for heavy precipitation) falls during one storm in the middle of the month; this moisture enters the soil immediately without losses, except when the available water capacity of the soil moisture profiles is exceeded.
2. One half of the monthly precipitation (LP for light precipitation) occurs in several light falls, and is partly lost by evapotranspiration before it enters the soil; it can only infiltrate into the soil when LP exceeds the potential evapotranspiration.

Potential evapotranspiration

The potential evapotranspiration (PE) is assumed to be uniformly distributed during each month. Not all its energy is used to extract water from the soil. A part is used to dissipate as much light precipitation as possible before it reaches the soil. If there is surplus energy, it is used for water extraction from the profile. PE is calculated according to Thorntwaite.

2. The Time-Step Progression of the Model

Each month, all of which have 30 days, is divided into three parts. The first is a 15-day period of light precipitation (LP), the second is the heavy rainfall (HP) which occurs at midnight between the 15th and 16th of the month, and the third corresponds to another fortnight of light precipitation.

For each of these events water is either added to the soil or extracted from it. At the completion of each step, the moisture condition of the soil is determined, and if it changed, the model computes the number of days that each condition prevailed in the moisture control section.

The starting soil moisture condition of the profile is determined by running the simulation program for a number of consecutive iterations using each time the same yearly input until the moisture content of December 30th does not differ by more than one hundredth of the content found at the same date in the immediately preceding iteration. The program then starts the diagnostic processing of monthly data with an initial amount of water in each slot equal to the one found on December 30th.

When all months are processed the soil moisture conditions for each day are combined in the moisture condition calendar which forms the data base for the determination of the soil moisture regime criteria according to the definitions of Soil Taxonomy.

2.1 Processing sequence during one month

Each half-month interval is processed using the following inputs: monthly precipitation (MP) and monthly potential evapotranspiration (PE). The steps are as follows:

if NPE > 0 accretion will take place during the period under consideration; if NPE is smaller than zero, water will be extracted from the profile.

All heavy precipitations in the middle of each month are processed by computing the heavy precipitations HP = MP/2 and entering this amount in the profile as accretion.

2.2 Changes in Water Content during each Period

2.2.1 Accretion

To simulate the additions of moisture to the profile, water is entered in the soil in,each non-full slot following a specific order shown in the soil moisture diagram of table 1.

The sequence starts with the left slot in the top row. Water is added to each successive slot in a row until the row is filled, or until the water supply is exhausted. When a row is completely full the program proceeds with the immediately underlying row, starting again on the left side of the moisture diagram. The accretion procedures in this way simulate the downward movement of a wetting front.

2.2.2. Depletion.

The sequence for the extraction of water from the profile starts with the top right-hand slot and scans the slots in successive right-downward diagonals (table 2).

29 22 16 11 07 04 02 01

37 30 23 17 12 08 05 03

44 38 31 24 18 13 09 06

50 45 39 32 25 19 14 10

55 51 46 40 33 26 20 15

59 56 52 47 41 34 27 21

64 63 61 58 54 49 43 36

Table 2. Sequence of Slots during Depletion

Table 3. Depletion requirement diagram

The processing continues until the entire evapotranspiration potential has been used, or until all slots have been set to zero. In the latter case any remaining depletion amount is not carried forward but is discarded.

2.2.3 Definitions of Soil Moisture Conditions.